[{"data":1,"prerenderedAt":112989},["ShallowReactive",2],{"total-stats":3,"sidebar-tag-counts":9,"recent-list":43},{"courses":4,"topics":5,"summaries":6,"outputs":7,"zapisku":8},3,31,53,2,86,[10,13,16,19,22,25,28,31,33,36,38,41],{"tag":11,"count":12},"imork",42,{"tag":14,"count":15},"ipmrk",25,{"tag":17,"count":18},"imek",22,{"tag":20,"count":21},"isms",13,{"tag":23,"count":24},"neuronove-site",8,{"tag":26,"count":27},"optimalizace",7,{"tag":29,"count":30},"fuzzy",6,{"tag":32,"count":30},"nist",{"tag":34,"count":35},"makroekonomie",5,{"tag":37,"count":35},"geneticke-algoritmy",{"tag":39,"count":40},"mikroekonomie",4,{"tag":42,"count":40},"lagrange",[44,180,300,810,2020,3945,9656,10696,12259,12507,12852,13728,18015,18557,19018,20624,30506,30791,39789,41051,55123,59416,59588,78933,91043,91392,91641,91971,92325,101286,101573,105858,106009,106493,107028,107355,108333,108552,108879,109487,109656,109879,110463,110957,111142,111321,111566,111824,112250,112752],{"id":45,"title":46,"body":47,"course":163,"courses":164,"created":165,"description":156,"extension":166,"meta":167,"navigation":168,"path":169,"seo":170,"sources":171,"stem":173,"tags":174,"type":177,"updated":178,"__hash__":179},"topics\u002Ftopics\u002Fanfis.md","ANFIS — Adaptive Neuro-Fuzzy Inference System",{"type":48,"value":49,"toc":155},"minimark",[50,54,65,83,88,112,116,127,137,140,144],[51,52,46],"h1",{"id":53},"anfis-adaptive-neuro-fuzzy-inference-system",[55,56,57],"p",{},[58,59],"img",{"alt":60,"className":61,"src":64},"anfis-architektura",[62,63],"wikilink","wikilink-broken","\u002Fwiki-assets\u002Fanfis-architektura.jpeg",[55,66,67,68,75,76,82],{},"Hybridní přístup propojující ",[69,70,74],"a",{"className":71,"dataFsResolvedFilePath":72,"href":73},[62],"topics\u002Ffuzzy-logika.md","\u002Fwiki\u002Ffuzzy-logika","fuzzy logiku"," a ",[69,77,81],{"className":78,"dataFsResolvedFilePath":79,"href":80},[62],"topics\u002Fumele-neuronove-site.md","\u002Fwiki\u002Fumele-neuronove-site","umělé neuronové sítě",". Spojuje výhody obou světů.",[84,85,87],"h2",{"id":86},"princip","Princip",[89,90,91,103],"ul",{},[92,93,94,98,99,102],"li",{},[95,96,97],"strong",{},"Od fuzzy logiky"," přebírá: pravidla KDYŽ–POTOM, jazykové proměnné, funkce členství → ",[95,100,101],{},"interpretovatelnost"," (model dává lidský smysl)",[92,104,105,108,109],{},[95,106,107],{},"Od neuronových sítí"," přebírá: schopnost učit se z dat, automatická úprava parametrů → ",[95,110,111],{},"adaptivnost",[84,113,115],{"id":114},"kdy-je-anfis-vhodný","Kdy je ANFIS vhodný",[89,117,118,121,124],{},[92,119,120],{},"Chceme model srozumitelný člověku (na rozdíl od čisté neuronové sítě)",[92,122,123],{},"Nechceme vše nastavovat ručně (na rozdíl od čistého fuzzy systému)",[92,125,126],{},"Máme data i expertní znalost",[84,128,130,131],{"id":129},"význam-v-kurzu-ipmrk","Význam v kurzu ",[69,132,136],{"className":133,"dataFsResolvedFilePath":134,"href":135},[62],"courses\u002Fipmrk.md","\u002Fwiki\u002Fipmrk","IpmrK",[55,138,139],{},"ANFIS je klíčový styčný bod kurzu — propojuje dva hlavní bloky (fuzzy logika a neuronové sítě) do jednoho systému. Zkouškově důležité.",[84,141,143],{"id":142},"zdroje","Zdroje",[89,145,146],{},[92,147,148,154],{},[69,149,153],{"className":150,"dataFsResolvedFilePath":151,"href":152},[62],"summaries\u002Fipmrk-nn-aplikace.md","\u002Fwiki\u002Fipmrk-nn-aplikace","Neuronové sítě — aplikace"," — ANFIS je zde představen",{"title":156,"searchDepth":7,"depth":7,"links":157},"",[158,159,160,162],{"id":86,"depth":7,"text":87},{"id":114,"depth":7,"text":115},{"id":129,"depth":7,"text":161},"Význam v kurzu IpmrK",{"id":142,"depth":7,"text":143},null,[14],"2026-04-10","md",{},true,"\u002Ftopics\u002Fanfis",{"title":46,"description":156},[172],"raw\u002Fipmrk\u002Fnn-aplikace.md","topics\u002Fanfis",[14,175,29,23,176],"anfis","hybridni-system","topic","2026-04-25","w3x8TjfldoFMelvK-RKRrgErKY5CwNSfUH40UpDM_M4",{"id":181,"title":182,"body":183,"course":163,"courses":287,"created":165,"description":288,"extension":166,"meta":289,"navigation":168,"path":290,"seo":291,"sources":292,"stem":295,"tags":296,"type":177,"updated":178,"__hash__":299},"topics\u002Ftopics\u002Fbackpropagation.md","Backpropagation (zpětné šíření chyby)",{"type":48,"value":184,"toc":282},[185,188,196,200,233,237,251,255],[51,186,182],{"id":187},"backpropagation-zpětné-šíření-chyby",[55,189,190,191,195],{},"Základní a nejdůležitější algoritmus učení vícevrstvých ",[69,192,194],{"className":193,"dataFsResolvedFilePath":79,"href":80},[62],"neuronových sítí",".",[84,197,199],{"id":198},"postup","Postup",[201,202,203,209,215,221,227],"ol",{},[92,204,205,208],{},[95,206,207],{},"Dopředný průchod"," — síť spočítá výstup z aktuálních vah",[92,210,211,214],{},[95,212,213],{},"Výpočet chyby"," — porovnání skutečného výstupu s cílem (e = y − m)",[92,216,217,220],{},[95,218,219],{},"Zpětné šíření"," — chyba se šíří zpět přes vrstvy, určuje příspěvek každé váhy k chybě",[92,222,223,226],{},[95,224,225],{},"Úprava vah"," — w_new = w_old + η · e · x (η = učicí koeficient)",[92,228,229,232],{},[95,230,231],{},"Opakování"," — celý cyklus se opakuje přes trénovací data, dokud chyba neklesne pod mez",[84,234,236],{"id":235},"klíčové-vlastnosti","Klíčové vlastnosti",[89,238,239,242,245,248],{},[92,240,241],{},"Iterativní proces — jedna iterace nestačí",[92,243,244],{},"Učicí koeficient (learning rate) řídí velikost kroků",[92,246,247],{},"Příliš velký → nestabilita, příliš malý → pomalé učení",[92,249,250],{},"Může uváznout v lokálním minimu",[84,252,254],{"id":253},"souvislosti","Souvislosti",[89,256,257,264,273],{},[92,258,259,263],{},[69,260,262],{"className":261,"dataFsResolvedFilePath":79,"href":80},[62],"Umělé neuronové sítě"," — backpropagation je jejich hlavní učicí mechanismus",[92,265,266,272],{},[69,267,271],{"className":268,"dataFsResolvedFilePath":269,"href":270},[62],"summaries\u002Fipmrk-nn-teorie.md","\u002Fwiki\u002Fipmrk-nn-teorie","Neuronové sítě — teorie"," — zde je backpropagation zaveden",[92,274,275,281],{},[69,276,280],{"className":277,"dataFsResolvedFilePath":278,"href":279},[62],"summaries\u002Fipmrk-nn-vypocet.md","\u002Fwiki\u002Fipmrk-nn-vypocet","Neuronové sítě — výpočet"," — ruční demonstrace principu",{"title":156,"searchDepth":7,"depth":7,"links":283},[284,285,286],{"id":198,"depth":7,"text":199},{"id":235,"depth":7,"text":236},{"id":253,"depth":7,"text":254},[14],"Základní a nejdůležitější algoritmus učení vícevrstvých neuronových sítí.",{},"\u002Ftopics\u002Fbackpropagation",{"title":182,"description":288},[293,294],"raw\u002Fipmrk\u002Fnn-teorie.md","raw\u002Fipmrk\u002Fnn-vypocet.md","topics\u002Fbackpropagation",[14,297,23,298],"backpropagation","uceni","p2r9NLMc5uEQNYcZ19-gTHFKa1wYriITtRQEGsTyZmE",{"id":301,"title":302,"body":303,"course":163,"courses":794,"created":795,"description":156,"extension":166,"meta":796,"navigation":168,"path":797,"seo":798,"sources":799,"stem":802,"tags":803,"type":177,"updated":178,"__hash__":809},"topics\u002Ftopics\u002Fbcm.md","BCM — Řízení kontinuity činnosti",{"type":48,"value":304,"toc":781},[305,308,315,318,322,423,427,481,485,508,512,601,605,608,613,690,694,720,724,753,763],[51,306,302],{"id":307},"bcm-řízení-kontinuity-činnosti",[55,309,310],{},[58,311],{"alt":312,"className":313,"src":314},"bcm-rpo-rto",[62,63],"\u002Fwiki-assets\u002Fbcm-rpo-rto.jpeg",[55,316,317],{},"Identifikuje potenciální dopady incidentů a zajišťuje kontinuitu a obnovu klíčových procesů organizace na předem stanovenou minimální úroveň.",[84,319,321],{"id":320},"klíčové-pojmy","Klíčové pojmy",[323,324,325,341],"table",{},[326,327,328],"thead",{},[329,330,331,335,338],"tr",{},[332,333,334],"th",{},"Pojem",[332,336,337],{},"Anglicky",[332,339,340],{},"Popis",[342,343,344,358,371,384,397,410],"tbody",{},[329,345,346,352,355],{},[347,348,349],"td",{},[95,350,351],{},"BCMS",[347,353,354],{},"Business Continuity Management System",[347,356,357],{},"Plánovaný, kontinuální a dokumentovaný systém",[329,359,360,365,368],{},[347,361,362],{},[95,363,364],{},"BCM",[347,366,367],{},"Business Continuity Management",[347,369,370],{},"Činnost identifikující dopady a zajišťující kontinuitu",[329,372,373,378,381],{},[347,374,375],{},[95,376,377],{},"BIA",[347,379,380],{},"Business Impact Analysis",[347,382,383],{},"Identifikace kritických činností (orientace na dopad, ne příčinu)",[329,385,386,391,394],{},[347,387,388],{},[95,389,390],{},"MBCO",[347,392,393],{},"Minimum Business Continuity Objective",[347,395,396],{},"Minimální přijatelná úroveň služeb",[329,398,399,404,407],{},[347,400,401],{},[95,402,403],{},"RPO",[347,405,406],{},"Recovery Point Objective",[347,408,409],{},"Do jakého bodu v minulosti lze obnovit data",[329,411,412,417,420],{},[347,413,414],{},[95,415,416],{},"RTO",[347,418,419],{},"Recovery Time Objective",[347,421,422],{},"Čas potřebný pro obnovu provozu",[84,424,426],{"id":425},"pdca-cyklus-pro-bcms","PDCA cyklus pro BCMS",[323,428,429,439],{},[326,430,431],{},[329,432,433,436],{},[332,434,435],{},"Fáze",[332,437,438],{},"Obsah",[342,440,441,451,461,471],{},[329,442,443,448],{},[347,444,445],{},[95,446,447],{},"Plan",[347,449,450],{},"Kontext, požadavky, rozsah, politika, BIA, posouzení rizik",[329,452,453,458],{},[347,454,455],{},[95,456,457],{},"Do",[347,459,460],{},"Strategie kontinuity, implementace plánů, cvičení",[329,462,463,468],{},[347,464,465],{},[95,466,467],{},"Check",[347,469,470],{},"Monitoring, audit, přezkoumání managementem",[329,472,473,478],{},[347,474,475],{},[95,476,477],{},"Act",[347,479,480],{},"Nápravná opatření, neustálé zlepšování",[84,482,484],{"id":483},"iso-223012019-struktura","ISO 22301:2019 — struktura",[89,486,487,490,493,496,499,502,505],{},[92,488,489],{},"Kap. 4 — kontext organizace",[92,491,492],{},"Kap. 5 — vedení (leadership)",[92,494,495],{},"Kap. 6 — plánování (BIA, rizika)",[92,497,498],{},"Kap. 7 — podpora (kompetence, dokumentace, komunikace)",[92,500,501],{},"Kap. 8 — provoz (strategie, plány, cvičení)",[92,503,504],{},"Kap. 9 — hodnocení výkonnosti (monitoring, audit)",[92,506,507],{},"Kap. 10 — zlepšování (neshody, nápravná opatření)",[84,509,511],{"id":510},"analýza-steeple","Analýza STEEPLE",[323,513,514,524],{},[326,515,516],{},[329,517,518,521],{},[332,519,520],{},"Faktor",[332,522,523],{},"Oblast",[342,525,526,537,548,559,569,580,591],{},[329,527,528,534],{},[347,529,530,533],{},[95,531,532],{},"S","ociální",[347,535,536],{},"Zaměstnanost, bezpečnost, komunity",[329,538,539,545],{},[347,540,541,544],{},[95,542,543],{},"T","echnologický",[347,546,547],{},"Závislost na technologiích",[329,549,550,556],{},[347,551,552,555],{},[95,553,554],{},"E","konomický",[347,557,558],{},"Ekonomická situace, finanční instituce",[329,560,561,566],{},[347,562,563,565],{},[95,564,554],{},"tický",[347,567,568],{},"Podnikatelská etika, média, veřejnost",[329,570,571,577],{},[347,572,573,576],{},[95,574,575],{},"P","olitický",[347,578,579],{},"Politický systém, hrozba nepokojů",[329,581,582,588],{},[347,583,584,587],{},[95,585,586],{},"L","egislativní",[347,589,590],{},"Předpisy, zákony",[329,592,593,598],{},[347,594,595,597],{},[95,596,554],{},"nvironmentální",[347,599,600],{},"Životní prostředí, přírodní hrozby",[84,602,604],{"id":603},"disaster-recovery-dr","Disaster Recovery (DR)",[55,606,607],{},"Předem stanovený scénář obnovy provozu po havárii — součást BCM.",[609,610,612],"h3",{"id":611},"_7-úrovní-dr-tiers","7 úrovní DR (Tiers)",[323,614,615,624],{},[326,616,617],{},[329,618,619,622],{},[332,620,621],{},"Tier",[332,623,340],{},[342,625,626,634,642,650,658,666,674,682],{},[329,627,628,631],{},[347,629,630],{},"0",[347,632,633],{},"Žádná off-site data",[329,635,636,639],{},[347,637,638],{},"1",[347,640,641],{},"Fyzická záloha + cold site",[329,643,644,647],{},[347,645,646],{},"2",[347,648,649],{},"Fyzická záloha + hot site",[329,651,652,655],{},[347,653,654],{},"3",[347,656,657],{},"Elektronický trezor (electronic vaulting)",[329,659,660,663],{},[347,661,662],{},"4",[347,664,665],{},"Point-in-time recovery",[329,667,668,671],{},[347,669,670],{},"5",[347,672,673],{},"Two-site commit (kontinuální přenos)",[329,675,676,679],{},[347,677,678],{},"6",[347,680,681],{},"Minimální až nulová ztráta dat (zrcadlení)",[329,683,684,687],{},[347,685,686],{},"7",[347,688,689],{},"Automatizovaná obnova (AI monitoring)",[609,691,693],{"id":692},"cloud-dr","Cloud DR",[89,695,696,702,708,714],{},[92,697,698,701],{},[95,699,700],{},"Cold DR"," — nejlevnější, nejdelší odstávka",[92,703,704,707],{},[95,705,706],{},"Warm DR"," — aktualizované zálohy u poskytovatele",[92,709,710,713],{},[95,711,712],{},"Hot DR"," — paralelní řešení v tandemu",[92,715,716,719],{},[95,717,718],{},"DRaaS"," — Disaster Recovery as a Service (řízené\u002Fasistované\u002Fvlastní)",[84,721,723],{"id":722},"propojení-s-dalšími-tématy","Propojení s dalšími tématy",[89,725,726,735,744],{},[92,727,728,734],{},[69,729,733],{"className":730,"dataFsResolvedFilePath":731,"href":732},[62],"topics\u002Fisms.md","\u002Fwiki\u002Fisms","ISMS"," — BCM jako součást bezpečnostního systému",[92,736,737,743],{},[69,738,742],{"className":739,"dataFsResolvedFilePath":740,"href":741},[62],"topics\u002Frizeni-rizik.md","\u002Fwiki\u002Frizeni-rizik","Řízení rizik"," — krizové plány pro zbytková rizika",[92,745,746,752],{},[69,747,751],{"className":748,"dataFsResolvedFilePath":749,"href":750},[62],"topics\u002Fkyberneticka-bezpecnost.md","\u002Fwiki\u002Fkyberneticka-bezpecnost","Kybernetická bezpečnost"," — reakce na incidenty",[84,754,756,757],{"id":755},"zdroje-v-kurzu-imork","Zdroje v kurzu ",[69,758,762],{"className":759,"dataFsResolvedFilePath":760,"href":761},[62],"courses\u002Fimork.md","\u002Fwiki\u002Fimork","ImorK",[89,764,765,773],{},[92,766,767],{},[69,768,772],{"className":769,"dataFsResolvedFilePath":770,"href":771},[62],"summaries\u002Fimork-bcm.md","\u002Fwiki\u002Fimork-bcm","BCM — shrnutí přednášky",[92,774,775],{},[69,776,780],{"className":777,"dataFsResolvedFilePath":778,"href":779},[62],"summaries\u002Fimork-dr.md","\u002Fwiki\u002Fimork-dr","Disaster Recovery — shrnutí přednášky",{"title":156,"searchDepth":7,"depth":7,"links":782},[783,784,785,786,787,791,792],{"id":320,"depth":7,"text":321},{"id":425,"depth":7,"text":426},{"id":483,"depth":7,"text":484},{"id":510,"depth":7,"text":511},{"id":603,"depth":7,"text":604,"children":788},[789,790],{"id":611,"depth":4,"text":612},{"id":692,"depth":4,"text":693},{"id":722,"depth":7,"text":723},{"id":755,"depth":7,"text":793},"Zdroje v kurzu ImorK",[11],"2026-04-12",{},"\u002Ftopics\u002Fbcm",{"title":302,"description":156},[800,801],"raw\u002Fimork\u002F2014 VUT_Bezp BCM-2021.pdf","raw\u002Fimork\u002F2013 VUT_Bezp DR-2021.pdf","topics\u002Fbcm",[11,804,805,806,807,808],"bcm","kontinuita-cinnosti","iso-22301","bia","disaster-recovery","ZJwDCcNpVg_0RD-SpeyBFhimC2w94ZwCp5TdUgQNLTI",{"id":811,"title":812,"body":813,"course":14,"courses":163,"created":2004,"description":820,"extension":166,"meta":2005,"navigation":168,"path":2006,"seo":2007,"sources":2008,"stem":2011,"tags":2012,"type":177,"updated":178,"__hash__":2019},"topics\u002Ftopics\u002Fdatamining.md","Datamining",{"type":48,"value":814,"toc":1980},[815,818,821,828,851,855,878,882,908,911,915,921,931,1022,1032,1034,1038,1042,1049,1059,1064,1078,1083,1115,1120,1131,1133,1137,1143,1148,1154,1159,1184,1189,1194,1224,1228,1235,1240,1254,1259,1279,1285,1287,1291,1296,1300,1305,1311,1319,1324,1330,1337,1342,1348,1356,1361,1365,1421,1427,1429,1433,1440,1450,1454,1459,1465,1470,1476,1481,1487,1498,1502,1508,1513,1530,1532,1536,1542,1548,1559,1569,1574,1600,1606,1615,1617,1621,1627,1631,1639,1689,1700,1720,1724,1732,1752,1760,1780,1785,1800,1802,1806,1910,1914,1943,1947,1950,1956,1976],[51,816,812],{"id":817},"datamining",[55,819,820],{},"Datamining (dolování z dat) je sada automatizovaných postupů pro nalézání dosud neznámých vzorů a vztahů ve velkých databázích. Zastřešuje širokou škálu technik používaných v řadě odvětví. Rozvoj začal počátkem 90. let 20. století u bank specializovaných na kreditní karty, rozšířil se do pojišťovnictví, veřejných služeb, zásilkových služeb, energetiky, maloobchodu a dalších.",[55,822,823,824,827],{},"Datamining je analytický krok procesu ",[95,825,826],{},"KDD (Knowledge Discovery in Databases)",". Stojí na průsečíku tří disciplín: strojové učení + statistika + správa databází.",[55,829,830,831,835,836,835,840,835,846,195],{},"Souvisí s: ",[69,832,834],{"className":833,"dataFsResolvedFilePath":72,"href":73},[62],"fuzzy-logika",", ",[69,837,839],{"className":838,"dataFsResolvedFilePath":79,"href":80},[62],"neuronové sítě",[69,841,845],{"className":842,"dataFsResolvedFilePath":843,"href":844},[62],"topics\u002Fevolucni-algoritmy.md","\u002Fwiki\u002Fevolucni-algoritmy","evoluční algoritmy",[69,847,26],{"className":848,"dataFsResolvedFilePath":849,"href":850},[62],"topics\u002Foptimalizace.md","\u002Fwiki\u002Foptimalizace",[84,852,854],{"id":853},"cíle-dataminingu","Cíle dataminingu",[89,856,857,863,869,875],{},[92,858,859,862],{},[95,860,861],{},"Zvýšení zisku"," — identifikace nových zákazníků a příležitostí",[92,864,865,868],{},[95,866,867],{},"Snížení nákladů"," — efektivnější cílení a alokace zdrojů",[92,870,871,874],{},[95,872,873],{},"Snížení rizika ztrát"," — odhalení rizikových zákazníků, predikce odchodu",[92,876,877],{},"Správný výrobek → správný zákazník → správné místo → správný čas",[84,879,881],{"id":880},"praktické-aplikace","Praktické aplikace",[89,883,884,890,896,902],{},[92,885,886,889],{},[95,887,888],{},"Bankovnictví",": Fraud detection, credit scoring, churn prediction, segmentace zákazníků",[92,891,892,895],{},[95,893,894],{},"Pojišťovnictví",": Detekce podvodných pojistných událostí, optimalizace pojistných sazeb",[92,897,898,901],{},[95,899,900],{},"Retail",": Market basket analysis (Amazon), doporučovací systémy, rozmístění zboží",[92,903,904,907],{},[95,905,906],{},"Energetika\u002Fprůmysl",": Prediktivní údržba, optimalizace spotřeby",[909,910],"hr",{},[84,912,914],{"id":913},"proces-práce-s-daty-crisp-dm","Proces práce s daty — CRISP-DM",[55,916,917,920],{},[95,918,919],{},"CRISP-DM"," (Cross-Industry Standard Process for Data Mining) je nejrozšířenější metodika — průzkumy ukazovaly 3–4× vyšší využití než konkurence.",[922,923,928],"pre",{"className":924,"code":926,"language":927},[925],"language-text","Business Understanding → Data Understanding → Data Preparation\n        ↑                                             ↓\n   Deployment ← Evaluation ← Modeling ← (iterativně zpět)\n","text",[929,930,926],"code",{"__ignoreMap":156},[323,932,933,944],{},[326,934,935],{},[329,936,937,939,941],{},[332,938,435],{},[332,940,438],{},[332,942,943],{},"Poznámka",[342,945,946,958,970,985,998,1010],{},[329,947,948,953,956],{},[347,949,950],{},[95,951,952],{},"1. Business Understanding",[347,954,955],{},"Definice cílů, obchodní otázka, kritéria úspěchu",[347,957],{},[329,959,960,965,968],{},[347,961,962],{},[95,963,964],{},"2. Data Understanding",[347,966,967],{},"Sběr dat, průzkum, kvalita, vhodnost pro analýzu",[347,969],{},[329,971,972,977,980],{},[347,973,974],{},[95,975,976],{},"3. Data Preparation",[347,978,979],{},"Čištění, klasifikace, vzorkování, sumarizace, transformace",[347,981,982],{},[95,983,984],{},"50–80 % celkového úsilí",[329,986,987,992,995],{},[347,988,989],{},[95,990,991],{},"4. Modeling",[347,993,994],{},"Výběr a aplikace technik, kalibrace parametrů",[347,996,997],{},"Nejkratší, ale nejviditelnější",[329,999,1000,1005,1008],{},[347,1001,1002],{},[95,1003,1004],{},"5. Evaluation",[347,1006,1007],{},"Ověření vůči obchodním cílům, metriky přesnosti",[347,1009],{},[329,1011,1012,1017,1020],{},[347,1013,1014],{},[95,1015,1016],{},"6. Deployment",[347,1018,1019],{},"Nasazení do produkce, monitoring, finální zpráva",[347,1021],{},[1023,1024,1025],"blockquote",{},[55,1026,1027,1028,1031],{},"Proces je ",[95,1029,1030],{},"iterativní"," — z každé fáze se lze vracet zpět.",[909,1033],{},[84,1035,1037],{"id":1036},"klíčové-techniky-dataminingu","Klíčové techniky dataminingu",[609,1039,1041],{"id":1040},"link-analýza-analýza-vazeb","Link analýza (Analýza vazeb)",[55,1043,1044,1045,1048],{},"Technika zaměřená na vyhodnocování ",[95,1046,1047],{},"vztahů (vazeb)"," mezi entitami v síti, místo studia vlastností jednotlivých entit.",[55,1050,1051,1054,1055,1058],{},[95,1052,1053],{},"Princip:"," Data jako ",[95,1056,1057],{},"graf"," — uzly = entity (osoby, účty, produkty), hrany = vztahy nebo interakce.",[55,1060,1061],{},[95,1062,1063],{},"Typy přístupů:",[89,1065,1066,1069,1072,1075],{},[92,1067,1068],{},"Heuristické — rozhodovací pravidla z odborných znalostí",[92,1070,1071],{},"Šablonové — zpracování nestrukturovaných dat",[92,1073,1074],{},"Podobnostní — vážené skórování atributů",[92,1076,1077],{},"Statistické — lexikální statistika",[55,1079,1080],{},[95,1081,1082],{},"Příklady použití:",[89,1084,1085,1091,1097,1103,1109],{},[92,1086,1087,1090],{},[95,1088,1089],{},"Fraud detection"," — odhalování fraud rings (překrývající se adresy, telefony u různých žadatelů)",[92,1092,1093,1096],{},[95,1094,1095],{},"AML"," (Anti-Money Laundering) — praní peněz",[92,1098,1099,1102],{},[95,1100,1101],{},"FBI ViCAP"," — propojování trestných činů",[92,1104,1105,1108],{},[95,1106,1107],{},"Google PageRank"," — hodnocení stránek podle příchozích odkazů",[92,1110,1111,1114],{},[95,1112,1113],{},"Sociální sítě"," — detekce komunit, šíření vlivu, doporučení přátel",[55,1116,1117],{},[95,1118,1119],{},"Historický vývoj:",[201,1121,1122,1125,1128],{},[92,1123,1124],{},"Generace (1975): Ruční maticové grafy",[92,1126,1127],{},"Generace: Automatizované nástroje (IBM i2 Analyst's Notebook)",[92,1129,1130],{},"Generace: Automatická vizualizace napojená na datové zdroje",[909,1132],{},[609,1134,1136],{"id":1135},"klastrování-clustering","Klastrování (Clustering)",[55,1138,1139,1142],{},[95,1140,1141],{},"Definice:"," Unsupervised learning — rozdělení dat do skupin (clusterů\u002Fshluků) tak, aby objekty uvnitř skupiny byly si co nejpodobnější a objekty z různých skupin co nejodlišnější. Kategorie předem neznáme — algoritmus je hledá sám.",[1144,1145,1147],"h4",{"id":1146},"k-means-algoritmus","K-means algoritmus",[55,1149,1150,1153],{},[95,1151,1152],{},"Minimalizuje:"," WCSS (Within-Cluster Sum of Squares) — vnitřní varianci clusterů.",[55,1155,1156],{},[95,1157,1158],{},"Kroky:",[201,1160,1161,1167,1173,1179],{},[92,1162,1163,1166],{},[95,1164,1165],{},"Inicializace"," — náhodně zvolit k centroidů (moderní: k-means++)",[92,1168,1169,1172],{},[95,1170,1171],{},"Přiřazení"," — každý bod přiřadit do nejbližšího centroidu (Euklidovská vzdálenost)",[92,1174,1175,1178],{},[95,1176,1177],{},"Aktualizace"," — přepočítat centroidy jako průměr přiřazených bodů",[92,1180,1181,1183],{},[95,1182,231],{}," — dokud se přiřazení stabilizuje nebo max. iterace",[1023,1185,1186],{},[55,1187,1188],{},"Při různých spuštěních může dávat různé výsledky → doporučuje se spustit vícekrát.",[55,1190,1191],{},[95,1192,1193],{},"Výběr počtu clusterů k:",[89,1195,1196,1202,1208,1214],{},[92,1197,1198,1201],{},[95,1199,1200],{},"Elbow method"," — vynést WCSS vs. k, hledat „loket\"",[92,1203,1204,1207],{},[95,1205,1206],{},"Silhouette analysis"," — jak dobře bod pasuje do svého vs. sousedního clusteru (hodnoty 0–1)",[92,1209,1210,1213],{},[95,1211,1212],{},"Gap statistic"," — porovnání se vzdáleností náhodných dat",[92,1215,1216,1219,1220,1223],{},[95,1217,1218],{},"Davies-Bouldin Index"," — nižší = lepší; ",[95,1221,1222],{},"Calinski-Harabasz Index"," — vyšší = lepší",[1144,1225,1227],{"id":1226},"hierarchické-klastrování","Hierarchické klastrování",[55,1229,1230,1231,1234],{},"Vytváří ",[95,1232,1233],{},"dendrogram"," — stromovou strukturu zobrazující postupné slučování clusterů.",[55,1236,1237],{},[95,1238,1239],{},"Přístupy:",[89,1241,1242,1248],{},[92,1243,1244,1247],{},[95,1245,1246],{},"Agglomerativní (zdola nahoru)"," — každý bod = vlastní cluster, postupně slučovat",[92,1249,1250,1253],{},[95,1251,1252],{},"Divisivní (shora dolů)"," — jeden velký cluster, postupně dělit",[55,1255,1256],{},[95,1257,1258],{},"Metody výpočtu vzdálenosti (linkage):",[89,1260,1261,1267,1273],{},[92,1262,1263,1266],{},[95,1264,1265],{},"Ward"," — minimalizuje nárůst SSE; clustery ≈ stejné velikosti; nejčastěji doporučovaná",[92,1268,1269,1272],{},[95,1270,1271],{},"Complete"," — vzdálenost = maximum mezi body",[92,1274,1275,1278],{},[95,1276,1277],{},"Average"," — vzdálenost = průměr",[55,1280,1281,1284],{},[95,1282,1283],{},"Čtení dendrogramu:"," Hledat nejdelší vertikální úsečku nepřerušenou horizontálou — tam nakrájíme strom. Počet clusterů = počet průsečíků řezné linie s dendrogramem.",[909,1286],{},[609,1288,1290],{"id":1289},"rozhodovací-stromy-decision-trees","Rozhodovací stromy (Decision Trees)",[55,1292,1293,1295],{},[95,1294,1141],{}," Model klasifikující data pomocí hierarchického větvení. Každý vnitřní uzel = test atributu; každá větev = výsledek testu; každý list = výsledná třída nebo hodnota.",[1144,1297,1299],{"id":1298},"míry-nečistoty-uzlu","Míry nečistoty uzlu",[55,1301,1302],{},[95,1303,1304],{},"Entropie:",[922,1306,1309],{"className":1307,"code":1308,"language":927},[925],"H(S) = −Σ pᵢ × log₂(pᵢ)\n",[929,1310,1308],{"__ignoreMap":156},[89,1312,1313,1316],{},[92,1314,1315],{},"H = 0 → čistý uzel (vše jedné třídy)",[92,1317,1318],{},"H = 1 → maximální smíšenost (binární, 50\u002F50)",[55,1320,1321],{},[95,1322,1323],{},"Informační zisk (Information Gain):",[922,1325,1328],{"className":1326,"code":1327,"language":927},[925],"Gain(S, A) = H(S) − Σ (|Sᵥ| \u002F |S|) × H(Sᵥ)\n",[929,1329,1327],{"__ignoreMap":156},[55,1331,1332,1333,1336],{},"Vybíráme atribut A s ",[95,1334,1335],{},"nejvyšším"," informačním ziskem.",[55,1338,1339],{},[95,1340,1341],{},"Giniho index (Gini Impurity):",[922,1343,1346],{"className":1344,"code":1345,"language":927},[925],"Gini(S) = 1 − Σ pᵢ²\n",[929,1347,1345],{"__ignoreMap":156},[89,1349,1350,1353],{},[92,1351,1352],{},"Gini = 0 → čistý uzel",[92,1354,1355],{},"Gini = 0,5 → maximální nečistota (binární)",[1023,1357,1358],{},[55,1359,1360],{},"Gini je výpočetně jednodušší (bez logaritmů) — prakticky dávají podobné výsledky.",[1144,1362,1364],{"id":1363},"algoritmy-rozhodovacích-stromů","Algoritmy rozhodovacích stromů",[323,1366,1367,1380],{},[326,1368,1369],{},[329,1370,1371,1374,1377],{},[332,1372,1373],{},"Algoritmus",[332,1375,1376],{},"Metrika",[332,1378,1379],{},"Vlastnosti",[342,1381,1382,1395,1408],{},[329,1383,1384,1389,1392],{},[347,1385,1386],{},[95,1387,1388],{},"ID3",[347,1390,1391],{},"Informační zisk (entropie)",[347,1393,1394],{},"Pouze kategorická data, bez prořezávání",[329,1396,1397,1402,1405],{},[347,1398,1399],{},[95,1400,1401],{},"C4.5",[347,1403,1404],{},"Gain ratio (normalizovaný)",[347,1406,1407],{},"Spojité proměnné, chybějící hodnoty, prořezávání",[329,1409,1410,1415,1418],{},[347,1411,1412],{},[95,1413,1414],{},"CART",[347,1416,1417],{},"Giniho index",[347,1419,1420],{},"Binární stromy, klasifikace i regrese, prořezávání",[55,1422,1423,1426],{},[95,1424,1425],{},"Prořezávání (pruning):"," Stromy mají tendenci přetrénovat se (overfitting). Pruning odstraňuje statisticky nevýznamné větve.",[909,1428],{},[84,1430,1432],{"id":1431},"asociační-pravidla-apriori-algoritmus","Asociační pravidla — Apriori algoritmus",[55,1434,1435,1436,1439],{},"Hledá vzory souvýskytu v databázích transakcí. Typicky: ",[95,1437,1438],{},"market basket analysis"," — které produkty se kupují společně.",[55,1441,1442,1445,1446,1449],{},[95,1443,1444],{},"Formát pravidla:"," ",[929,1447,1448],{},"{A} → {B}"," — „kdo koupí A, koupí i B\"",[609,1451,1453],{"id":1452},"klíčové-metriky","Klíčové metriky",[55,1455,1456],{},[95,1457,1458],{},"Support (podpora):",[922,1460,1463],{"className":1461,"code":1462,"language":927},[925],"Support(A) = počet transakcí s A \u002F celkový počet transakcí\n",[929,1464,1462],{"__ignoreMap":156},[55,1466,1467],{},[95,1468,1469],{},"Confidence (důvěra):",[922,1471,1474],{"className":1472,"code":1473,"language":927},[925],"Confidence(A → B) = Support(A ∪ B) \u002F Support(A)\n",[929,1475,1473],{"__ignoreMap":156},[55,1477,1478],{},[95,1479,1480],{},"Lift:",[922,1482,1485],{"className":1483,"code":1484,"language":927},[925],"Lift(A → B) = Confidence(A → B) \u002F Support(B)\n",[929,1486,1484],{"__ignoreMap":156},[89,1488,1489,1492,1495],{},[92,1490,1491],{},"Lift = 1 → A a B jsou nezávislé",[92,1493,1494],{},"Lift > 1 → pozitivní asociace (A zvyšuje pravděpodobnost B)",[92,1496,1497],{},"Lift \u003C 1 → negativní asociace",[609,1499,1501],{"id":1500},"princip-apriori","Princip Apriori",[55,1503,1504,1507],{},[95,1505,1506],{},"Anti-monotone property:"," Pokud množina A nesplňuje min. support, žádná její nadmnožina nemůže být frekventovaná → efektivní prořezávání prostoru hledání.",[55,1509,1510],{},[95,1511,1512],{},"Postup:",[201,1514,1515,1518,1521,1524,1527],{},[92,1516,1517],{},"Nastavit min_sup a min_conf",[92,1519,1520],{},"Najít frekventované 1-itemsety",[92,1522,1523],{},"Generovat kandidáty (k+1)-itemsetů z frekventovaných k-itemsetů",[92,1525,1526],{},"Prořezat nesplňující min_sup",[92,1528,1529],{},"Opakovat; pak generovat pravidla splňující min_conf",[909,1531],{},[84,1533,1535],{"id":1534},"witness-miner-lanner-group","Witness Miner \u002F Lanner Group",[55,1537,1538,1541],{},[95,1539,1540],{},"Lanner Group Ltd"," — softwarová společnost, Birmingham (UK), 1996. Specializace na simulační software.",[55,1543,1544,1547],{},[95,1545,1546],{},"WITNESS"," — diskrétní simulační software od 1986. Integrován v produktech Oracle, SAP, IBM. Umožňuje:",[89,1549,1550,1553,1556],{},[92,1551,1552],{},"Modelování podnikových procesů a výrobních operací",[92,1554,1555],{},"3D modelování, diskrétní a stochastická simulace",[92,1557,1558],{},"Integraci s MS Excel, MS Access, ODBC, CAD",[55,1560,1561,1564,1565,1568],{},[95,1562,1563],{},"Witness Miner"," — označení pro integraci ",[95,1566,1567],{},"process mining"," technik (Disco\u002FFluxicon) se simulačním nástrojem WITNESS.",[55,1570,1571],{},[95,1572,1573],{},"Funkce analýzy ze simulačních dat:",[89,1575,1576,1582,1588,1594],{},[92,1577,1578,1581],{},[95,1579,1580],{},"Závislosti vstupů a výstupů"," — jaké kombinace vstupních parametrů vedou k jakým výstupům",[92,1583,1584,1587],{},[95,1585,1586],{},"Pravidla"," — extrakce rozhodovacích pravidel z chování simulovaného systému",[92,1589,1590,1593],{},[95,1591,1592],{},"Shluky (clustery)"," — seskupení podobných scénářů výsledků simulace",[92,1595,1596,1599],{},[95,1597,1598],{},"Statistiky\u002FKPI"," — exportovatelné do Excel",[55,1601,1602,1605],{},[95,1603,1604],{},"WITNESS Optimizer"," — využívá Simulated Annealing a Tabu Search pro optimalizaci parametrů.",[1023,1607,1608],{},[55,1609,1610,1611,1614],{},"Poznámka: Specifický modul \"Witness Miner\" není podrobně zdokumentován veřejně — pravděpodobně proprietární terminologie nebo starší funkce. Viz ",[69,1612,845],{"className":1613,"dataFsResolvedFilePath":843,"href":844},[62]," pro principy SA a Tabu Search.",[909,1616],{},[84,1618,1620],{"id":1619},"matlab-pro-datamining","MATLAB pro datamining",[55,1622,1623,1624,195],{},"MATLAB nabízí funkce v rámci ",[95,1625,1626],{},"Statistics and Machine Learning Toolbox",[609,1628,1630],{"id":1629},"klastrování","Klastrování",[55,1632,1633],{},[95,1634,1635,1638],{},[929,1636,1637],{},"kmeans"," — k-means:",[922,1640,1644],{"className":1641,"code":1642,"language":1643,"meta":156,"style":156},"language-matlab shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","[idx, C] = kmeans(data, k);\n% idx = přiřazení bodů; C = centroidy (k×p matice)\n\n% S vizualizací:\n[idx, C] = kmeans(data, 2);\ngscatter(data(:,1), data(:,2), idx);\nhold on;\nplot(C(:,1), C(:,2), 'kx', 'MarkerSize', 15, 'LineWidth', 3);\n","matlab",[929,1645,1646,1654,1659,1664,1669,1674,1679,1684],{"__ignoreMap":156},[1647,1648,1651],"span",{"class":1649,"line":1650},"line",1,[1647,1652,1653],{},"[idx, C] = kmeans(data, k);\n",[1647,1655,1656],{"class":1649,"line":7},[1647,1657,1658],{},"% idx = přiřazení bodů; C = centroidy (k×p matice)\n",[1647,1660,1661],{"class":1649,"line":4},[1647,1662,1663],{"emptyLinePlaceholder":168},"\n",[1647,1665,1666],{"class":1649,"line":40},[1647,1667,1668],{},"% S vizualizací:\n",[1647,1670,1671],{"class":1649,"line":35},[1647,1672,1673],{},"[idx, C] = kmeans(data, 2);\n",[1647,1675,1676],{"class":1649,"line":30},[1647,1677,1678],{},"gscatter(data(:,1), data(:,2), idx);\n",[1647,1680,1681],{"class":1649,"line":27},[1647,1682,1683],{},"hold on;\n",[1647,1685,1686],{"class":1649,"line":24},[1647,1687,1688],{},"plot(C(:,1), C(:,2), 'kx', 'MarkerSize', 15, 'LineWidth', 3);\n",[55,1690,1691],{},[95,1692,1693,1696,1697,1699],{},[929,1694,1695],{},"linkage"," + ",[929,1698,1233],{}," — hierarchické klastrování:",[922,1701,1703],{"className":1641,"code":1702,"language":1643,"meta":156,"style":156},"Z = linkage(data, 'ward');      % vytvoří hierarchickou strukturu\ndendrogram(Z);                  % vizualizace\nclusters = cluster(Z, 'maxclust', 4);   % řez na 4 clustery\n",[929,1704,1705,1710,1715],{"__ignoreMap":156},[1647,1706,1707],{"class":1649,"line":1650},[1647,1708,1709],{},"Z = linkage(data, 'ward');      % vytvoří hierarchickou strukturu\n",[1647,1711,1712],{"class":1649,"line":7},[1647,1713,1714],{},"dendrogram(Z);                  % vizualizace\n",[1647,1716,1717],{"class":1649,"line":4},[1647,1718,1719],{},"clusters = cluster(Z, 'maxclust', 4);   % řez na 4 clustery\n",[609,1721,1723],{"id":1722},"rozhodovací-stromy","Rozhodovací stromy",[55,1725,1726],{},[95,1727,1728,1731],{},[929,1729,1730],{},"fitctree"," — trénování:",[922,1733,1735],{"className":1641,"code":1734,"language":1643,"meta":156,"style":156},"Mdl = fitctree(X_train, Y_train);\nview(Mdl, 'Mode', 'graph');     % vizualizace stromu\nresubLoss(Mdl)                  % přesnost na trénovacích datech\n",[929,1736,1737,1742,1747],{"__ignoreMap":156},[1647,1738,1739],{"class":1649,"line":1650},[1647,1740,1741],{},"Mdl = fitctree(X_train, Y_train);\n",[1647,1743,1744],{"class":1649,"line":7},[1647,1745,1746],{},"view(Mdl, 'Mode', 'graph');     % vizualizace stromu\n",[1647,1748,1749],{"class":1649,"line":4},[1647,1750,1751],{},"resubLoss(Mdl)                  % přesnost na trénovacích datech\n",[55,1753,1754],{},[95,1755,1756,1759],{},[929,1757,1758],{},"predict"," — predikce:",[922,1761,1763],{"className":1641,"code":1762,"language":1643,"meta":156,"style":156},"YPred = predict(Mdl, X_test);\naccuracy = sum(YPred == Y_test) \u002F numel(Y_test);\nfprintf('Přesnost: %.2f%%\\n', accuracy * 100);\n",[929,1764,1765,1770,1775],{"__ignoreMap":156},[1647,1766,1767],{"class":1649,"line":1650},[1647,1768,1769],{},"YPred = predict(Mdl, X_test);\n",[1647,1771,1772],{"class":1649,"line":7},[1647,1773,1774],{},"accuracy = sum(YPred == Y_test) \u002F numel(Y_test);\n",[1647,1776,1777],{"class":1649,"line":4},[1647,1778,1779],{},"fprintf('Přesnost: %.2f%%\\n', accuracy * 100);\n",[55,1781,1782],{},[95,1783,1784],{},"Prevence overfittingu:",[922,1786,1788],{"className":1641,"code":1787,"language":1643,"meta":156,"style":156},"Mdl = fitctree(X, Y, 'MaxNumSplits', 10);   % omezení hloubky\nMdl = fitctree(X, Y, 'MinLeafSize', 5);     % min. vzorků v listu\n",[929,1789,1790,1795],{"__ignoreMap":156},[1647,1791,1792],{"class":1649,"line":1650},[1647,1793,1794],{},"Mdl = fitctree(X, Y, 'MaxNumSplits', 10);   % omezení hloubky\n",[1647,1796,1797],{"class":1649,"line":7},[1647,1798,1799],{},"Mdl = fitctree(X, Y, 'MinLeafSize', 5);     % min. vzorků v listu\n",[909,1801],{},[84,1803,1805],{"id":1804},"přehled-technik-pro-zkoušku","Přehled technik pro zkoušku",[323,1807,1808,1820],{},[326,1809,1810],{},[329,1811,1812,1815,1818],{},[332,1813,1814],{},"Technika",[332,1816,1817],{},"Co dělá",[332,1819,321],{},[342,1821,1822,1835,1848,1860,1872,1885,1897],{},[329,1823,1824,1829,1832],{},[347,1825,1826],{},[95,1827,1828],{},"Link analýza",[347,1830,1831],{},"Hledá vazby v síti entit",[347,1833,1834],{},"Graf, uzly, hrany, fraud detection",[329,1836,1837,1842,1845],{},[347,1838,1839],{},[95,1840,1841],{},"K-means",[347,1843,1844],{},"Seskupuje podobné objekty",[347,1846,1847],{},"Centroid, WCSS, Elbow method, k",[329,1849,1850,1854,1857],{},[347,1851,1852],{},[95,1853,1227],{},[347,1855,1856],{},"Stromová struktura podobnosti",[347,1858,1859],{},"Dendrogram, Ward, linkage",[329,1861,1862,1866,1869],{},[347,1863,1864],{},[95,1865,1723],{},[347,1867,1868],{},"Klasifikace větvícím se stromem",[347,1870,1871],{},"Entropie, informační zisk, Gini, ID3\u002FC4.5\u002FCART",[329,1873,1874,1879,1882],{},[347,1875,1876],{},[95,1877,1878],{},"Asociační pravidla",[347,1880,1881],{},"Vzory souvýskytu",[347,1883,1884],{},"Support, Confidence, Lift, Apriori",[329,1886,1887,1891,1894],{},[347,1888,1889],{},[95,1890,919],{},[347,1892,1893],{},"Standardní proces projektu",[347,1895,1896],{},"6 fází, iterativní",[329,1898,1899,1904,1907],{},[347,1900,1901],{},[95,1902,1903],{},"WITNESS\u002FLanner",[347,1905,1906],{},"Simulace + process mining",[347,1908,1909],{},"Diskrétní simulace, KPIs, Optimizer",[84,1911,1913],{"id":1912},"kontrolní-otázky-ke-zkoušce","Kontrolní otázky ke zkoušce",[201,1915,1916,1919,1922,1925,1928,1931,1934,1937,1940],{},[92,1917,1918],{},"Čím se zabývá datamining?",[92,1920,1921],{},"Jak jsou data získávána?",[92,1923,1924],{},"Jak jsou data zpracovávána?",[92,1926,1927],{},"K čemu nám slouží datamining?",[92,1929,1930],{},"Co znamená Link analýza?",[92,1932,1933],{},"K čemu slouží klastrování?",[92,1935,1936],{},"K čemu slouží a co je to rozhodovací strom?",[92,1938,1939],{},"Jak lze využít programu MATLAB v dataminingu?",[92,1941,1942],{},"K čemu slouží program Witness Miner?",[84,1944,1946],{"id":1945},"pojmy-k-zapamatování","Pojmy k zapamatování",[55,1948,1949],{},"Datamining, zpracování dat, MATLAB, Witness Miner, závislosti vstupů a výstupů, volba pravidel, shluky, statistické charakteristiky.",[84,1951,756,1953],{"id":1952},"zdroje-v-kurzu-ipmrk",[69,1954,136],{"className":1955,"dataFsResolvedFilePath":134,"href":135},[62],[89,1957,1958,1967],{},[92,1959,1960,1966],{},[69,1961,1965],{"className":1962,"dataFsResolvedFilePath":1963,"href":1964},[62],"summaries\u002Fipmrk-kniha.md","\u002Fwiki\u002Fipmrk-kniha","Kniha"," — definice, shrnutí, kontrolní otázky, pojmy",[92,1968,1969,1975],{},[69,1970,1974],{"className":1971,"dataFsResolvedFilePath":1972,"href":1973},[62],"summaries\u002Fipmrk-datamining.md","\u002Fwiki\u002Fipmrk-datamining","Techniky a nástroje"," — CRISP-DM, Link analýza, k-means, rozhodovací stromy, Apriori, Witness Miner, MATLAB kód (Wikipedia, GeeksforGeeks, IBM, Lanner)",[1977,1978,1979],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":156,"searchDepth":7,"depth":7,"links":1981},[1982,1983,1984,1985,1990,1994,1995,1999,2000,2001,2002],{"id":853,"depth":7,"text":854},{"id":880,"depth":7,"text":881},{"id":913,"depth":7,"text":914},{"id":1036,"depth":7,"text":1037,"children":1986},[1987,1988,1989],{"id":1040,"depth":4,"text":1041},{"id":1135,"depth":4,"text":1136},{"id":1289,"depth":4,"text":1290},{"id":1431,"depth":7,"text":1432,"children":1991},[1992,1993],{"id":1452,"depth":4,"text":1453},{"id":1500,"depth":4,"text":1501},{"id":1534,"depth":7,"text":1535},{"id":1619,"depth":7,"text":1620,"children":1996},[1997,1998],{"id":1629,"depth":4,"text":1630},{"id":1722,"depth":4,"text":1723},{"id":1804,"depth":7,"text":1805},{"id":1912,"depth":7,"text":1913},{"id":1945,"depth":7,"text":1946},{"id":1952,"depth":7,"text":2003},"Zdroje v kurzu IpmrK","2026-04-16",{},"\u002Ftopics\u002Fdatamining",{"title":812,"description":820},[2009,2010],"raw\u002Fipmrk\u002Fkniha.md","raw\u002Fipmrk\u002Fdatamining-online.md","topics\u002Fdatamining",[14,817,2013,2014,2015,2016,2017,2018],"crisp-dm","link-analyza","klastrovani","rozhodovaci-stromy","apriori","witness-miner","PUkq0tAb0hdh4jBddhFDQLtfyJlrKVogvd_v45wMY5w",{"id":2021,"title":2022,"body":2023,"course":17,"courses":163,"created":3932,"description":3933,"extension":166,"meta":3934,"navigation":168,"path":3935,"seo":3936,"sources":3937,"stem":3939,"tags":3940,"type":177,"updated":178,"__hash__":3944},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":48,"value":2024,"toc":3915},[2025,2028,2049,2053,2145,2148,2277,2428,2432,2516,2520,2581,2631,2638,2642,2778,2829,2833,2876,2945,3016,3026,3030,3069,3141,3145,3226,3275,3319,3323,3327,3397,3401,3451,3530,3537,3540,3593,3863,3867],[51,2026,2022],{"id":2027},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[55,2029,2030,2031,2037,2038,2041,2042,2045,2046,195],{},"Matematický aparát kurzu ",[69,2032,2036],{"className":2033,"dataFsResolvedFilePath":2034,"href":2035},[62],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","ImeK",". Bez derivace se neobejdou ",[95,2039,2040],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[95,2043,2044],{},"maximalizace zisku"," ani ",[95,2047,2048],{},"minimalizace nákladů",[84,2050,2052],{"id":2051},"funkce-a-polynomy","Funkce a polynomy",[55,2054,2055,2056,2096,2097,2110,2111,2124,2125,195],{},"Funkce jedné proměnné ",[1647,2057,2060],{"className":2058},[2059],"katex",[2061,2062,2064],"math",{"xmlns":2063},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[2065,2066,2067,2091],"semantics",{},[2068,2069,2070,2074,2078,2081,2085,2088],"mrow",{},[2071,2072,2073],"mi",{},"y",[2075,2076,2077],"mo",{},"=",[2071,2079,2080],{},"f",[2075,2082,2084],{"stretchy":2083},"false","(",[2071,2086,2087],{},"x",[2075,2089,2090],{"stretchy":2083},")",[2092,2093,2095],"annotation",{"encoding":2094},"application\u002Fx-tex","y = f(x)"," — předpis závislosti ",[1647,2098,2100],{"className":2099},[2059],[2061,2101,2102],{"xmlns":2063},[2065,2103,2104,2108],{},[2068,2105,2106],{},[2071,2107,2087],{},[2092,2109,2087],{"encoding":2094}," (nezávislá) → ",[1647,2112,2114],{"className":2113},[2059],[2061,2115,2116],{"xmlns":2063},[2065,2117,2118,2122],{},[2068,2119,2120],{},[2071,2121,2073],{},[2092,2123,2073],{"encoding":2094}," (závislá). Hodnota v bodě: ",[1647,2126,2128],{"className":2127},[2059],[2061,2129,2130],{"xmlns":2063},[2065,2131,2132,2142],{},[2068,2133,2134,2136,2138,2140],{},[2071,2135,2080],{},[2075,2137,2084],{"stretchy":2083},[2071,2139,69],{},[2075,2141,2090],{"stretchy":2083},[2092,2143,2144],{"encoding":2094},"f(a)",[55,2146,2147],{},"Polynomy:",[89,2149,2150,2183,2226],{},[92,2151,2152],{},[201,2153,2154],{},[92,2155,2156,2157],{},"stupně: ",[1647,2158,2160],{"className":2159},[2059],[2061,2161,2162],{"xmlns":2063},[2065,2163,2164,2180],{},[2068,2165,2166,2168,2170,2172,2174,2177],{},[2071,2167,2073],{},[2075,2169,2077],{},[2071,2171,69],{},[2071,2173,2087],{},[2075,2175,2176],{},"+",[2071,2178,2179],{},"b",[2092,2181,2182],{"encoding":2094},"y = ax + b",[92,2184,2185],{},[201,2186,2187],{"start":7},[92,2188,2156,2189],{},[1647,2190,2192],{"className":2191},[2059],[2061,2193,2194],{"xmlns":2063},[2065,2195,2196,2223],{},[2068,2197,2198,2200,2202,2204,2212,2214,2216,2218,2220],{},[2071,2199,2073],{},[2075,2201,2077],{},[2071,2203,69],{},[2205,2206,2207,2209],"msup",{},[2071,2208,2087],{},[2210,2211,646],"mn",{},[2075,2213,2176],{},[2071,2215,2179],{},[2071,2217,2087],{},[2075,2219,2176],{},[2071,2221,2222],{},"c",[2092,2224,2225],{"encoding":2094},"y = ax^2 + bx + c",[92,2227,2228],{},[201,2229,2230],{"start":4},[92,2231,2156,2232],{},[1647,2233,2235],{"className":2234},[2059],[2061,2236,2237],{"xmlns":2063},[2065,2238,2239,2274],{},[2068,2240,2241,2243,2245,2247,2253,2255,2257,2263,2265,2267,2269,2271],{},[2071,2242,2073],{},[2075,2244,2077],{},[2071,2246,69],{},[2205,2248,2249,2251],{},[2071,2250,2087],{},[2210,2252,654],{},[2075,2254,2176],{},[2071,2256,2179],{},[2205,2258,2259,2261],{},[2071,2260,2087],{},[2210,2262,646],{},[2075,2264,2176],{},[2071,2266,2222],{},[2071,2268,2087],{},[2075,2270,2176],{},[2071,2272,2273],{},"d",[2092,2275,2276],{"encoding":2094},"y = ax^3 + bx^2 + cx + d",[55,2278,2279,1445,2282,2337,2338,2379,2380,195],{},[95,2280,2281],{},"Příklad rozkladu:",[1647,2283,2285],{"className":2284},[2059],[2061,2286,2287],{"xmlns":2063},[2065,2288,2289,2334],{},[2068,2290,2291,2293,2295,2301,2304,2306,2308,2310,2312,2314,2316,2318,2320,2322,2324,2326,2328,2330,2332],{},[2071,2292,2073],{},[2075,2294,2077],{},[2205,2296,2297,2299],{},[2071,2298,2087],{},[2210,2300,646],{},[2075,2302,2303],{},"−",[2210,2305,670],{},[2071,2307,2087],{},[2075,2309,2176],{},[2210,2311,678],{},[2075,2313,2077],{},[2075,2315,2084],{"stretchy":2083},[2071,2317,2087],{},[2075,2319,2303],{},[2210,2321,646],{},[2075,2323,2090],{"stretchy":2083},[2075,2325,2084],{"stretchy":2083},[2071,2327,2087],{},[2075,2329,2303],{},[2210,2331,654],{},[2075,2333,2090],{"stretchy":2083},[2092,2335,2336],{"encoding":2094},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[1647,2339,2341],{"className":2340},[2059],[2061,2342,2343],{"xmlns":2063},[2065,2344,2345,2376],{},[2068,2346,2347,2354,2356,2358,2362,2366,2372,2374],{},[2348,2349,2350,2352],"msub",{},[2071,2351,2087],{},[2210,2353,638],{},[2075,2355,2077],{},[2210,2357,646],{},[2075,2359,2361],{"separator":2360},"true",",",[2363,2364,2365],"mtext",{}," ",[2348,2367,2368,2370],{},[2071,2369,2087],{},[2210,2371,646],{},[2075,2373,2077],{},[2210,2375,654],{},[2092,2377,2378],{"encoding":2094},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[1647,2381,2383],{"className":2382},[2059],[2061,2384,2385],{"xmlns":2063},[2065,2386,2387,2425],{},[2068,2388,2389,2391,2393,2395,2397,2399,2409,2415,2417],{},[2071,2390,2073],{},[2075,2392,2077],{},[2075,2394,2084],{"stretchy":2083},[2071,2396,2087],{},[2075,2398,2303],{},[2400,2401,2402],"mstyle",{"scriptlevel":630,"displaystyle":2083},[2403,2404,2405,2407],"mfrac",{},[2210,2406,670],{},[2210,2408,646],{},[2205,2410,2411,2413],{},[2075,2412,2090],{"stretchy":2083},[2210,2414,646],{},[2075,2416,2303],{},[2400,2418,2419],{"scriptlevel":630,"displaystyle":2083},[2403,2420,2421,2423],{},[2210,2422,638],{},[2210,2424,662],{},[2092,2426,2427],{"encoding":2094},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[84,2429,2431],{"id":2430},"derivace","Derivace",[55,2433,2434,2435,2462,2463,2491,2492,195],{},"Označení ",[1647,2436,2438],{"className":2437},[2059],[2061,2439,2440],{"xmlns":2063},[2065,2441,2442,2459],{},[2068,2443,2444,2453,2455,2457],{},[2205,2445,2446,2448],{},[2071,2447,2080],{},[2075,2449,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},"normal","0em","′",[2075,2454,2084],{"stretchy":2083},[2071,2456,2087],{},[2075,2458,2090],{"stretchy":2083},[2092,2460,2461],{"encoding":2094},"f'(x)"," nebo ",[1647,2464,2466],{"className":2465},[2059],[2061,2467,2468],{"xmlns":2063},[2065,2469,2470,2488],{},[2068,2471,2472],{},[2400,2473,2474],{"scriptlevel":630,"displaystyle":2360},[2403,2475,2476,2482],{},[2068,2477,2478,2480],{},[2071,2479,2273],{},[2071,2481,2073],{},[2068,2483,2484,2486],{},[2071,2485,2273],{},[2071,2487,2087],{},[2092,2489,2490],{"encoding":2094},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[1647,2493,2495],{"className":2494},[2059],[2061,2496,2497],{"xmlns":2063},[2065,2498,2499,2513],{},[2068,2500,2501,2507,2509,2511],{},[2205,2502,2503,2505],{},[2071,2504,2080],{},[2075,2506,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,2508,2084],{"stretchy":2083},[2071,2510,69],{},[2075,2512,2090],{"stretchy":2083},[2092,2514,2515],{"encoding":2094},"f'(a)",[609,2517,2519],{"id":2518},"geometrická-interpretace","Geometrická interpretace",[55,2521,2522,2545,2546,2549,2550,2580],{},[1647,2523,2525],{"className":2524},[2059],[2061,2526,2527],{"xmlns":2063},[2065,2528,2529,2543],{},[2068,2530,2531,2537,2539,2541],{},[2205,2532,2533,2535],{},[2071,2534,2080],{},[2075,2536,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,2538,2084],{"stretchy":2083},[2071,2540,69],{},[2075,2542,2090],{"stretchy":2083},[2092,2544,2515],{"encoding":2094}," = ",[95,2547,2548],{},"sklon tečny"," ke grafu funkce v bodě ",[1647,2551,2553],{"className":2552},[2059],[2061,2554,2555],{"xmlns":2063},[2065,2556,2557,2577],{},[2068,2558,2559,2562,2564,2566,2568,2570,2572,2574],{},[2075,2560,2561],{"stretchy":2083},"[",[2071,2563,69],{},[2075,2565,2361],{"separator":2360},[2071,2567,2080],{},[2075,2569,2084],{"stretchy":2083},[2071,2571,69],{},[2075,2573,2090],{"stretchy":2083},[2075,2575,2576],{"stretchy":2083},"]",[2092,2578,2579],{"encoding":2094},"[a, f(a)]",". Rovnice tečny:",[55,2582,2583],{},[1647,2584,2586],{"className":2585},[2059],[2061,2587,2588],{"xmlns":2063},[2065,2589,2590,2628],{},[2068,2591,2592,2594,2596,2598,2600,2602,2604,2606,2612,2614,2616,2618,2620,2622,2624,2626],{},[2071,2593,2073],{},[2075,2595,2303],{},[2071,2597,2080],{},[2075,2599,2084],{"stretchy":2083},[2071,2601,69],{},[2075,2603,2090],{"stretchy":2083},[2075,2605,2077],{},[2205,2607,2608,2610],{},[2071,2609,2080],{},[2075,2611,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,2613,2084],{"stretchy":2083},[2071,2615,69],{},[2075,2617,2090],{"stretchy":2083},[2075,2619,2084],{"stretchy":2083},[2071,2621,2087],{},[2075,2623,2303],{},[2071,2625,69],{},[2075,2627,2090],{"stretchy":2083},[2092,2629,2630],{"encoding":2094},"y - f(a) = f'(a)(x - a)",[55,2632,2633],{},[58,2634],{"alt":2635,"className":2636,"src":2637},"imek-derivace-tecna",[62,63],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[609,2639,2641],{"id":2640},"inženýrská-interpretace","Inženýrská interpretace",[55,2643,2644,2545,2667,1445,2670,2683,2684,2697,2698,2716,2717,2730,2731,2744,2745,2758,2759,2777],{},[1647,2645,2647],{"className":2646},[2059],[2061,2648,2649],{"xmlns":2063},[2065,2650,2651,2665],{},[2068,2652,2653,2659,2661,2663],{},[2205,2654,2655,2657],{},[2071,2656,2080],{},[2075,2658,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,2660,2084],{"stretchy":2083},[2071,2662,69],{},[2075,2664,2090],{"stretchy":2083},[2092,2666,2515],{"encoding":2094},[95,2668,2669],{},"rychlost změny",[1647,2671,2673],{"className":2672},[2059],[2061,2674,2675],{"xmlns":2063},[2065,2676,2677,2681],{},[2068,2678,2679],{},[2071,2680,2073],{},[2092,2682,2073],{"encoding":2094}," vzhledem k ",[1647,2685,2687],{"className":2686},[2059],[2061,2688,2689],{"xmlns":2063},[2065,2690,2691,2695],{},[2068,2692,2693],{},[2071,2694,2087],{},[2092,2696,2087],{"encoding":2094}," v bodě ",[1647,2699,2701],{"className":2700},[2059],[2061,2702,2703],{"xmlns":2063},[2065,2704,2705,2713],{},[2068,2706,2707,2709,2711],{},[2071,2708,2087],{},[2075,2710,2077],{},[2071,2712,69],{},[2092,2714,2715],{"encoding":2094},"x = a","; přibližná změna ",[1647,2718,2720],{"className":2719},[2059],[2061,2721,2722],{"xmlns":2063},[2065,2723,2724,2728],{},[2068,2725,2726],{},[2071,2727,2073],{},[2092,2729,2073],{"encoding":2094}," při změně ",[1647,2732,2734],{"className":2733},[2059],[2061,2735,2736],{"xmlns":2063},[2065,2737,2738,2742],{},[2068,2739,2740],{},[2071,2741,2087],{},[2092,2743,2087],{"encoding":2094}," z ",[1647,2746,2748],{"className":2747},[2059],[2061,2749,2750],{"xmlns":2063},[2065,2751,2752,2756],{},[2068,2753,2754],{},[2071,2755,69],{},[2092,2757,69],{"encoding":2094}," na ",[1647,2760,2762],{"className":2761},[2059],[2061,2763,2764],{"xmlns":2063},[2065,2765,2766,2774],{},[2068,2767,2768,2770,2772],{},[2071,2769,69],{},[2075,2771,2176],{},[2210,2773,638],{},[2092,2775,2776],{"encoding":2094},"a+1",":",[55,2779,2780],{},[1647,2781,2783],{"className":2782},[2059],[2061,2784,2785],{"xmlns":2063},[2065,2786,2787,2826],{},[2068,2788,2789,2791,2793,2795,2797,2799,2801,2804,2806,2808,2810,2812,2814,2820,2822,2824],{},[2071,2790,2080],{},[2075,2792,2084],{"stretchy":2083},[2071,2794,69],{},[2075,2796,2176],{},[2210,2798,638],{},[2075,2800,2090],{"stretchy":2083},[2075,2802,2803],{},"≈",[2071,2805,2080],{},[2075,2807,2084],{"stretchy":2083},[2071,2809,69],{},[2075,2811,2090],{"stretchy":2083},[2075,2813,2176],{},[2205,2815,2816,2818],{},[2071,2817,2080],{},[2075,2819,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,2821,2084],{"stretchy":2083},[2071,2823,69],{},[2075,2825,2090],{"stretchy":2083},[2092,2827,2828],{"encoding":2094},"f(a+1) \\approx f(a) + f'(a)",[609,2830,2832],{"id":2831},"příklad-mezní-náklady","Příklad — mezní náklady",[55,2834,2835,2836,195],{},"Celkové náklady ",[1647,2837,2839],{"className":2838},[2059],[2061,2840,2841],{"xmlns":2063},[2065,2842,2843,2873],{},[2068,2844,2845,2847,2850,2852,2855,2857,2859,2862,2864,2867],{},[2071,2846,543],{},[2071,2848,2849],{},"C",[2075,2851,2077],{},[2210,2853,2854],{},"1000",[2075,2856,2176],{},[2210,2858,646],{},[2071,2860,2861],{},"Q",[2075,2863,2176],{},[2210,2865,2866],{},"0,1",[2205,2868,2869,2871],{},[2071,2870,2861],{},[2210,2872,646],{},[2092,2874,2875],{"encoding":2094},"TC = 1000 + 2Q + 0{,}1 Q^2",[55,2877,2878,2879,2917,2918,195],{},"Mezní náklady: ",[1647,2880,2882],{"className":2881},[2059],[2061,2883,2884],{"xmlns":2063},[2065,2885,2886,2914],{},[2068,2887,2888,2891,2893,2895,2897,2903,2905,2907,2909,2912],{},[2071,2889,2890],{},"M",[2071,2892,2849],{},[2075,2894,2077],{},[2071,2896,543],{},[2205,2898,2899,2901],{},[2071,2900,2849],{},[2075,2902,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,2904,2077],{},[2210,2906,646],{},[2075,2908,2176],{},[2210,2910,2911],{},"0,2",[2071,2913,2861],{},[2092,2915,2916],{"encoding":2094},"MC = TC' = 2 + 0{,}2 Q",", takže ",[1647,2919,2921],{"className":2920},[2059],[2061,2922,2923],{"xmlns":2063},[2065,2924,2925,2942],{},[2068,2926,2927,2929,2931,2933,2936,2938,2940],{},[2071,2928,2890],{},[2071,2930,2849],{},[2075,2932,2084],{"stretchy":2083},[2210,2934,2935],{},"10",[2075,2937,2090],{"stretchy":2083},[2075,2939,2077],{},[2210,2941,662],{},[2092,2943,2944],{"encoding":2094},"MC(10) = 4",[55,2946,2947,1445,2950,2999,3000,1445,3003,195],{},[95,2948,2949],{},"Skutečný přírůstek:",[1647,2951,2953],{"className":2952},[2059],[2061,2954,2955],{"xmlns":2063},[2065,2956,2957,2996],{},[2068,2958,2959,2962,2964,2966,2968,2970,2972,2974,2977,2979,2981,2983,2985,2987,2989,2991,2993],{},[2071,2960,2961],{"mathvariant":2450},"Δ",[2071,2963,543],{},[2071,2965,2849],{},[2075,2967,2077],{},[2071,2969,543],{},[2071,2971,2849],{},[2075,2973,2084],{"stretchy":2083},[2210,2975,2976],{},"11",[2075,2978,2090],{"stretchy":2083},[2075,2980,2303],{},[2071,2982,543],{},[2071,2984,2849],{},[2075,2986,2084],{"stretchy":2083},[2210,2988,2935],{},[2075,2990,2090],{"stretchy":2083},[2075,2992,2077],{},[2210,2994,2995],{},"4,2",[2092,2997,2998],{"encoding":2094},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[95,3001,3002],{},"Přibližný (lineární):",[1647,3004,3006],{"className":3005},[2059],[2061,3007,3008],{"xmlns":2063},[2065,3009,3010,3014],{},[2068,3011,3012],{},[2210,3013,662],{},[2092,3015,662],{"encoding":2094},[55,3017,3018,3019,3025],{},"(Viz aplikace v ",[69,3020,3024],{"className":3021,"dataFsResolvedFilePath":3022,"href":3023},[62],"topics\u002Fprijem-naklady-zisk.md","\u002Fwiki\u002Fprijem-naklady-zisk","prijem-naklady-zisk",".)",[84,3027,3029],{"id":3028},"diferenciál","Diferenciál",[55,3031,3032],{},[1647,3033,3035],{"className":3034},[2059],[2061,3036,3037],{"xmlns":2063},[2065,3038,3039,3066],{},[2068,3040,3041,3043,3045,3047,3053,3055,3057,3059,3062,3064],{},[2071,3042,2273],{},[2071,3044,2080],{},[2075,3046,2077],{},[2205,3048,3049,3051],{},[2071,3050,2080],{},[2075,3052,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,3054,2084],{"stretchy":2083},[2071,3056,2087],{},[2075,3058,2090],{"stretchy":2083},[2363,3060,3061],{}," ",[2071,3063,2273],{},[2071,3065,2087],{},[2092,3067,3068],{"encoding":2094},"df = f'(x)\\, dx",[55,3070,3071,3072,3088,3089,3137,3138,195],{},"Pro malá ",[1647,3073,3075],{"className":3074},[2059],[2061,3076,3077],{"xmlns":2063},[2065,3078,3079,3085],{},[2068,3080,3081,3083],{},[2071,3082,2273],{},[2071,3084,2087],{},[2092,3086,3087],{"encoding":2094},"dx"," platí: ",[1647,3090,3092],{"className":3091},[2059],[2061,3093,3094],{"xmlns":2063},[2065,3095,3096,3134],{},[2068,3097,3098,3100,3102,3104,3106,3108,3110,3112,3114,3116,3118,3120,3122,3124,3126,3128,3130,3132],{},[2071,3099,2961],{"mathvariant":2450},[2071,3101,2080],{},[2075,3103,2077],{},[2071,3105,2080],{},[2075,3107,2084],{"stretchy":2083},[2071,3109,2087],{},[2075,3111,2176],{},[2071,3113,2273],{},[2071,3115,2087],{},[2075,3117,2090],{"stretchy":2083},[2075,3119,2303],{},[2071,3121,2080],{},[2075,3123,2084],{"stretchy":2083},[2071,3125,2087],{},[2075,3127,2090],{"stretchy":2083},[2075,3129,2803],{},[2071,3131,2273],{},[2071,3133,2080],{},[2092,3135,3136],{"encoding":2094},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[95,3139,3140],{},"lineární odhad přírůstku",[609,3142,3144],{"id":3143},"příklad","Příklad",[55,3146,3147,3178,3179,3204,3205,3225],{},[1647,3148,3150],{"className":3149},[2059],[2061,3151,3152],{"xmlns":2063},[2065,3153,3154,3175],{},[2068,3155,3156,3158,3160,3162,3165,3167,3169],{},[2071,3157,543],{},[2071,3159,2849],{},[2075,3161,2077],{},[2210,3163,3164],{},"100",[2075,3166,2176],{},[2210,3168,2866],{},[2205,3170,3171,3173],{},[2071,3172,2861],{},[2210,3174,646],{},[2092,3176,3177],{"encoding":2094},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[1647,3180,3182],{"className":3181},[2059],[2061,3183,3184],{"xmlns":2063},[2065,3185,3186,3201],{},[2068,3187,3188,3190,3192,3195,3198],{},[2071,3189,2861],{},[2075,3191,2777],{},[2210,3193,3194],{},"50",[2075,3196,3197],{},"→",[2210,3199,3200],{},"60",[2092,3202,3203],{"encoding":2094},"Q: 50 \\to 60"," (tj. ",[1647,3206,3208],{"className":3207},[2059],[2061,3209,3210],{"xmlns":2063},[2065,3211,3212,3222],{},[2068,3213,3214,3216,3218,3220],{},[2071,3215,2273],{},[2071,3217,2861],{},[2075,3219,2077],{},[2210,3221,2935],{},[2092,3223,3224],{"encoding":2094},"dQ = 10","):",[55,3227,3228],{},[1647,3229,3231],{"className":3230},[2059],[2061,3232,3233],{"xmlns":2063},[2065,3234,3235,3272],{},[2068,3236,3237,3239,3241,3243,3245,3247,3249,3252,3254,3256,3258,3260,3262,3264,3266,3268,3270],{},[2071,3238,2273],{},[2071,3240,543],{},[2071,3242,2849],{},[2075,3244,2077],{},[2210,3246,2911],{},[2071,3248,2861],{},[2075,3250,3251],{},"⋅",[2071,3253,2273],{},[2071,3255,2861],{},[2075,3257,2077],{},[2210,3259,2911],{},[2075,3261,3251],{},[2210,3263,3194],{},[2075,3265,3251],{},[2210,3267,2935],{},[2075,3269,2077],{},[2210,3271,3164],{},[2092,3273,3274],{"encoding":2094},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[55,3276,3277,3278,3301,3302,3318],{},"Přesná změna: ",[1647,3279,3281],{"className":3280},[2059],[2061,3282,3283],{"xmlns":2063},[2065,3284,3285,3298],{},[2068,3286,3287,3289,3291,3293,3295],{},[2071,3288,2961],{"mathvariant":2450},[2071,3290,543],{},[2071,3292,2849],{},[2075,3294,2077],{},[2210,3296,3297],{},"110",[2092,3299,3300],{"encoding":2094},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[1647,3303,3305],{"className":3304},[2059],[2061,3306,3307],{"xmlns":2063},[2065,3308,3309,3315],{},[2068,3310,3311,3313],{},[2071,3312,543],{},[2071,3314,2849],{},[2092,3316,3317],{"encoding":2094},"TC"," je konvexní.",[84,3320,3322],{"id":3321},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[609,3324,3326],{"id":3325},"nutná-podmínka","Nutná podmínka",[55,3328,3329,3330,2697,3350,3363,3364,3392,3393,3396],{},"Má-li ",[1647,3331,3333],{"className":3332},[2059],[2061,3334,3335],{"xmlns":2063},[2065,3336,3337,3347],{},[2068,3338,3339,3341,3343,3345],{},[2071,3340,2080],{},[2075,3342,2084],{"stretchy":2083},[2071,3344,2087],{},[2075,3346,2090],{"stretchy":2083},[2092,3348,3349],{"encoding":2094},"f(x)",[1647,3351,3353],{"className":3352},[2059],[2061,3354,3355],{"xmlns":2063},[2065,3356,3357,3361],{},[2068,3358,3359],{},[2071,3360,69],{},[2092,3362,69],{"encoding":2094}," extrém, pak ",[1647,3365,3367],{"className":3366},[2059],[2061,3368,3369],{"xmlns":2063},[2065,3370,3371,3389],{},[2068,3372,3373,3379,3381,3383,3385,3387],{},[2205,3374,3375,3377],{},[2071,3376,2080],{},[2075,3378,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,3380,2084],{"stretchy":2083},[2071,3382,69],{},[2075,3384,2090],{"stretchy":2083},[2075,3386,2077],{},[2210,3388,630],{},[2092,3390,3391],{"encoding":2094},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[95,3394,3395],{},"stacionární"," (podezřelé) body.",[609,3398,3400],{"id":3399},"postačující-podmínka","Postačující podmínka",[55,3402,3403,3404,3417,3418,2777],{},"Pro stacionární bod ",[1647,3405,3407],{"className":3406},[2059],[2061,3408,3409],{"xmlns":2063},[2065,3410,3411,3415],{},[2068,3412,3413],{},[2071,3414,69],{},[2092,3416,69],{"encoding":2094},", je-li ",[1647,3419,3421],{"className":3420},[2059],[2061,3422,3423],{"xmlns":2063},[2065,3424,3425,3448],{},[2068,3426,3427,3437,3439,3441,3443,3446],{},[2205,3428,3429,3431],{},[2071,3430,2080],{},[2068,3432,3433,3435],{},[2075,3434,2452],{"mathvariant":2450},[2075,3436,2452],{"mathvariant":2450},[2075,3438,2084],{"stretchy":2083},[2071,3440,69],{},[2075,3442,2090],{"stretchy":2083},[2075,3444,3445],{"mathvariant":2450},"≠",[2210,3447,630],{},[2092,3449,3450],{"encoding":2094},"f''(a) \\neq 0",[89,3452,3453,3492],{},[92,3454,3455,3488,3489],{},[1647,3456,3458],{"className":3457},[2059],[2061,3459,3460],{"xmlns":2063},[2065,3461,3462,3485],{},[2068,3463,3464,3474,3476,3478,3480,3483],{},[2205,3465,3466,3468],{},[2071,3467,2080],{},[2068,3469,3470,3472],{},[2075,3471,2452],{"mathvariant":2450},[2075,3473,2452],{"mathvariant":2450},[2075,3475,2084],{"stretchy":2083},[2071,3477,69],{},[2075,3479,2090],{"stretchy":2083},[2075,3481,3482],{},">",[2210,3484,630],{},[2092,3486,3487],{"encoding":2094},"f''(a) > 0"," ⇒ ",[95,3490,3491],{},"lokální minimum",[92,3493,3494,3488,3527],{},[1647,3495,3497],{"className":3496},[2059],[2061,3498,3499],{"xmlns":2063},[2065,3500,3501,3524],{},[2068,3502,3503,3513,3515,3517,3519,3522],{},[2205,3504,3505,3507],{},[2071,3506,2080],{},[2068,3508,3509,3511],{},[2075,3510,2452],{"mathvariant":2450},[2075,3512,2452],{"mathvariant":2450},[2075,3514,2084],{"stretchy":2083},[2071,3516,69],{},[2075,3518,2090],{"stretchy":2083},[2075,3520,3521],{},"\u003C",[2210,3523,630],{},[2092,3525,3526],{"encoding":2094},"f''(a) \u003C 0",[95,3528,3529],{},"lokální maximum",[55,3531,3532],{},[58,3533],{"alt":3534,"className":3535,"src":3536},"imek-extremy-1d",[62,63],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[609,3538,3144],{"id":3539},"příklad-1",[55,3541,3542],{},[1647,3543,3545],{"className":3544},[2059],[2061,3546,3547],{"xmlns":2063},[2065,3548,3549,3590],{},[2068,3550,3551,3553,3555,3557,3559,3561,3563,3569,3571,3573,3579,3581,3584,3586,3588],{},[2071,3552,2080],{},[2075,3554,2084],{"stretchy":2083},[2071,3556,2087],{},[2075,3558,2090],{"stretchy":2083},[2075,3560,2077],{},[2210,3562,646],{},[2205,3564,3565,3567],{},[2071,3566,2087],{},[2210,3568,654],{},[2075,3570,2303],{},[2210,3572,654],{},[2205,3574,3575,3577],{},[2071,3576,2087],{},[2210,3578,646],{},[2075,3580,2303],{},[2210,3582,3583],{},"12",[2071,3585,2087],{},[2075,3587,2176],{},[2210,3589,654],{},[2092,3591,3592],{"encoding":2094},"f(x) = 2x^3 - 3x^2 - 12x + 3",[89,3594,3595,3706,3746,3809],{},[92,3596,3597,3669,3670],{},[1647,3598,3600],{"className":3599},[2059],[2061,3601,3602],{"xmlns":2063},[2065,3603,3604,3666],{},[2068,3605,3606,3612,3614,3616,3618,3620,3622,3628,3630,3632,3634,3636,3638,3640,3642,3644,3646,3648,3650,3652,3654,3656,3658,3660,3662,3664],{},[2205,3607,3608,3610],{},[2071,3609,2080],{},[2075,3611,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,3613,2084],{"stretchy":2083},[2071,3615,2087],{},[2075,3617,2090],{"stretchy":2083},[2075,3619,2077],{},[2210,3621,678],{},[2205,3623,3624,3626],{},[2071,3625,2087],{},[2210,3627,646],{},[2075,3629,2303],{},[2210,3631,678],{},[2071,3633,2087],{},[2075,3635,2303],{},[2210,3637,3583],{},[2075,3639,2077],{},[2210,3641,678],{},[2075,3643,2084],{"stretchy":2083},[2071,3645,2087],{},[2075,3647,2176],{},[2210,3649,638],{},[2075,3651,2090],{"stretchy":2083},[2075,3653,2084],{"stretchy":2083},[2071,3655,2087],{},[2075,3657,2303],{},[2210,3659,646],{},[2075,3661,2090],{"stretchy":2083},[2075,3663,2077],{},[2210,3665,630],{},[2092,3667,3668],{"encoding":2094},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[1647,3671,3673],{"className":3672},[2059],[2061,3674,3675],{"xmlns":2063},[2065,3676,3677,3703],{},[2068,3678,3679,3685,3687,3689,3691,3693,3699,3701],{},[2348,3680,3681,3683],{},[2071,3682,2087],{},[2210,3684,638],{},[2075,3686,2077],{},[2075,3688,2303],{},[2210,3690,638],{},[2075,3692,2361],{"separator":2360},[2348,3694,3695,3697],{},[2071,3696,2087],{},[2210,3698,646],{},[2075,3700,2077],{},[2210,3702,646],{},[2092,3704,3705],{"encoding":2094},"x_1 = -1, x_2 = 2",[92,3707,3708],{},[1647,3709,3711],{"className":3710},[2059],[2061,3712,3713],{"xmlns":2063},[2065,3714,3715,3743],{},[2068,3716,3717,3727,3729,3731,3733,3735,3737,3739,3741],{},[2205,3718,3719,3721],{},[2071,3720,2080],{},[2068,3722,3723,3725],{},[2075,3724,2452],{"mathvariant":2450},[2075,3726,2452],{"mathvariant":2450},[2075,3728,2084],{"stretchy":2083},[2071,3730,2087],{},[2075,3732,2090],{"stretchy":2083},[2075,3734,2077],{},[2210,3736,3583],{},[2071,3738,2087],{},[2075,3740,2303],{},[2210,3742,678],{},[2092,3744,3745],{"encoding":2094},"f''(x) = 12x - 6",[92,3747,3748,3488,3789,3792,3793],{},[1647,3749,3751],{"className":3750},[2059],[2061,3752,3753],{"xmlns":2063},[2065,3754,3755,3786],{},[2068,3756,3757,3767,3769,3771,3773,3775,3777,3779,3782,3784],{},[2205,3758,3759,3761],{},[2071,3760,2080],{},[2068,3762,3763,3765],{},[2075,3764,2452],{"mathvariant":2450},[2075,3766,2452],{"mathvariant":2450},[2075,3768,2084],{"stretchy":2083},[2075,3770,2303],{},[2210,3772,638],{},[2075,3774,2090],{"stretchy":2083},[2075,3776,2077],{},[2075,3778,2303],{},[2210,3780,3781],{},"18",[2075,3783,3521],{},[2210,3785,630],{},[2092,3787,3788],{"encoding":2094},"f''(-1) = -18 \u003C 0",[95,3790,3791],{},"maximum"," v ",[1647,3794,3796],{"className":3795},[2059],[2061,3797,3798],{"xmlns":2063},[2065,3799,3800,3806],{},[2068,3801,3802,3804],{},[2075,3803,2303],{},[2210,3805,638],{},[2092,3807,3808],{"encoding":2094},"-1",[92,3810,3811,3488,3847,3792,3850],{},[1647,3812,3814],{"className":3813},[2059],[2061,3815,3816],{"xmlns":2063},[2065,3817,3818,3844],{},[2068,3819,3820,3830,3832,3834,3836,3838,3840,3842],{},[2205,3821,3822,3824],{},[2071,3823,2080],{},[2068,3825,3826,3828],{},[2075,3827,2452],{"mathvariant":2450},[2075,3829,2452],{"mathvariant":2450},[2075,3831,2084],{"stretchy":2083},[2210,3833,646],{},[2075,3835,2090],{"stretchy":2083},[2075,3837,2077],{},[2210,3839,3781],{},[2075,3841,3482],{},[2210,3843,630],{},[2092,3845,3846],{"encoding":2094},"f''(2) = 18 > 0",[95,3848,3849],{},"minimum",[1647,3851,3853],{"className":3852},[2059],[2061,3854,3855],{"xmlns":2063},[2065,3856,3857,3861],{},[2068,3858,3859],{},[2210,3860,646],{},[2092,3862,646],{"encoding":2094},[84,3864,3866],{"id":3865},"navigace","Navigace",[89,3868,3869,3880,3891],{},[92,3870,3871,1445,3874],{},[95,3872,3873],{},"Předchozí:",[69,3875,3879],{"className":3876,"dataFsResolvedFilePath":3877,"href":3878},[62],"topics\u002Fzaklady-matematicke-ekonomie.md","\u002Fwiki\u002Fzaklady-matematicke-ekonomie","Základy matematické ekonomie",[92,3881,3882,1445,3885],{},[95,3883,3884],{},"Navazující:",[69,3886,3890],{"className":3887,"dataFsResolvedFilePath":3888,"href":3889},[62],"topics\u002Fintegral.md","\u002Fwiki\u002Fintegral","Integrál",[92,3892,3893,1445,3896,3902,3903,3907,3908,3914],{},[95,3894,3895],{},"Souvislosti:",[69,3897,3901],{"className":3898,"dataFsResolvedFilePath":3899,"href":3900},[62],"topics\u002Ffunkce-vice-promennych.md","\u002Fwiki\u002Ffunkce-vice-promennych","Funkce více proměnných"," (rozšíření na 2D), ",[69,3904,3906],{"className":3905,"dataFsResolvedFilePath":3022,"href":3023},[62],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[69,3909,3913],{"className":3910,"dataFsResolvedFilePath":3911,"href":3912},[62],"topics\u002Felasticita.md","\u002Fwiki\u002Felasticita","Elasticita"," (procentní citlivost přes derivaci)",{"title":156,"searchDepth":7,"depth":7,"links":3916},[3917,3918,3923,3926,3931],{"id":2051,"depth":7,"text":2052},{"id":2430,"depth":7,"text":2431,"children":3919},[3920,3921,3922],{"id":2518,"depth":4,"text":2519},{"id":2640,"depth":4,"text":2641},{"id":2831,"depth":4,"text":2832},{"id":3028,"depth":7,"text":3029,"children":3924},[3925],{"id":3143,"depth":4,"text":3144},{"id":3321,"depth":7,"text":3322,"children":3927},[3928,3929,3930],{"id":3325,"depth":4,"text":3326},{"id":3399,"depth":4,"text":3400},{"id":3539,"depth":4,"text":3144},{"id":3865,"depth":7,"text":3866},"2026-04-20","Matematický aparát kurzu ImeK. Bez derivace se neobejdou mezní veličiny (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde maximalizace zisku ani minimalizace nákladů.",{},"\u002Ftopics\u002Fderivace",{"title":2022,"description":3933},[3938],"raw\u002Fimek\u002FKS_prvni_blok.pdf","topics\u002Fderivace",[17,2430,3941,3942,3943],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":3946,"title":3947,"body":3948,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":9643,"navigation":168,"path":9644,"seo":9645,"sources":9646,"stem":9649,"tags":9650,"type":177,"updated":178,"__hash__":9655},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":48,"value":3949,"toc":9615},[3950,3953,3974,3978,4008,4012,4053,4144,4188,4192,4216,4223,4227,4237,4249,4253,4282,4291,4347,4353,4356,4362,4389,4395,4493,4653,4944,4948,5028,5034,5038,5136,5202,5370,5374,5452,5483,5510,5516,5548,5626,5713,5717,5780,5786,5789,5795,5909,5994,6038,6042,6088,6095,6412,6417,6441,6470,6537,6634,6638,6645,6652,6723,6843,6927,6930,6936,7263,7267,7430,7438,7574,7582,7820,7828,7831,7836,8092,8096,8270,8404,8441,8485,8488,8618,8708,8726,8730,8737,8743,8803,8806,8830,8833,8839,8842,8848,8851,8855,8893,8951,9140,9144,9217,9223,9230,9234,9240,9382,9386,9392,9428,9433,9610],[51,3951,3947],{"id":3952},"elasticita-poptávky-a-nabídky",[1023,3954,3955],{},[55,3956,3957,3960,3961,3963,3964,3967,3968,75,3971,195],{},[1647,3958,3959],{},"!abstract"," TL;DR\n",[95,3962,3913],{}," je bezrozměrná míra toho, o kolik procent přibližně zareaguje jedna veličina na jednoprocentní změnu veličiny jiné. Studujeme ji proto, abychom mohli kvantitativně rozhodovat o cenové politice (kdy cenu snížit, kdy zvýšit) a charakterizovat povahu zboží. V kapitole rozlišujeme tři typy: ",[95,3965,3966],{},"cenovou elasticitu poptávky"," (a nabídky), ",[95,3969,3970],{},"křížově-cenovou elasticitu",[95,3972,3973],{},"důchodovou elasticitu",[84,3975,3977],{"id":3976},"úvod-motivace","Úvod — motivace",[55,3979,3980,3981,3985,3986,3989,3990,3993,3994,3997,3998,4001,4002,4007],{},"Termín ",[3982,3983,3984],"em",{},"elasticita"," (alternativně ",[3982,3987,3988],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[95,3991,3992],{},"kvantifikaci citlivosti (míry) odezvy"," jisté veličiny na změnu veličiny jiné. Bezprostředně nás zajímá citlivost množství (poptávaného či nabízeného) na změnu ceny zboží, což vede k pojmům ",[3982,3995,3996],{},"cenové elasticity poptávky"," (resp. ",[3982,3999,4000],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[69,4003,2431],{"className":4004,"dataFsResolvedFilePath":4005,"href":4006},[62],"topics\u002Fderivace.md","\u002Fwiki\u002Fderivace",").",[609,4009,4011],{"id":4010},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[55,4013,4014,4015,4033,4034,4052],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[1647,4016,4018],{"className":4017},[2059],[2061,4019,4020],{"xmlns":2063},[2065,4021,4022,4030],{},[2068,4023,4024,4026,4028],{},[2071,4025,575],{},[2075,4027,2077],{},[2210,4029,2935],{},[2092,4031,4032],{"encoding":2094},"P=10"," a při této ceně se prodá ",[1647,4035,4037],{"className":4036},[2059],[2061,4038,4039],{"xmlns":2063},[2065,4040,4041,4049],{},[2068,4042,4043,4045,4047],{},[2071,4044,2861],{},[2075,4046,2077],{},[2210,4048,3164],{},[2092,4050,4051],{"encoding":2094},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[89,4054,4055,4101],{},[92,4056,4057,4060,4061,4100],{},[95,4058,4059],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[1647,4062,4064],{"className":4063},[2059],[2061,4065,4066],{"xmlns":2063},[2065,4067,4068,4097],{},[2068,4069,4070,4073,4076,4078,4080,4083,4085,4088,4090,4092,4094],{},[2363,4071,4072],{},"  ",[2075,4074,4075],{},"⇒",[2363,4077,4072],{},[2071,4079,543],{},[2071,4081,4082],{},"R",[2075,4084,2077],{},[2210,4086,4087],{},"9",[2075,4089,3251],{},[2210,4091,3297],{},[2075,4093,2077],{},[2210,4095,4096],{},"990",[2092,4098,4099],{"encoding":2094},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[92,4102,4103,4106,4107,4143],{},[95,4104,4105],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[1647,4108,4110],{"className":4109},[2059],[2061,4111,4112],{"xmlns":2063},[2065,4113,4114,4140],{},[2068,4115,4116,4118,4120,4122,4124,4126,4128,4130,4132,4135,4137],{},[2363,4117,4072],{},[2075,4119,4075],{},[2363,4121,4072],{},[2071,4123,543],{},[2071,4125,4082],{},[2075,4127,2077],{},[2210,4129,4087],{},[2075,4131,3251],{},[2210,4133,4134],{},"120",[2075,4136,2077],{},[2210,4138,4139],{},"1080",[2092,4141,4142],{"encoding":2094},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[55,4145,4146,4147,4150,4151,4154,4155,4158,4159,4162,4163,4166,4167,4183,4184,4187],{},"Závěr: snížení ceny bylo na Trhu 1 ",[95,4148,4149],{},"nerozumné",", na Trhu 2 ",[95,4152,4153],{},"rozumné",". Trh 2 je ",[95,4156,4157],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[3982,4160,4161],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[3982,4164,4165],{},"neelastická"," a vyššího ",[1647,4168,4170],{"className":4169},[2059],[2061,4171,4172],{"xmlns":2063},[2065,4173,4174,4180],{},[2068,4175,4176,4178],{},[2071,4177,543],{},[2071,4179,4082],{},[2092,4181,4182],{"encoding":2094},"TR"," lze naopak dosáhnout ",[3982,4185,4186],{},"zvýšením"," ceny.",[609,4189,4191],{"id":4190},"hypotéza-41","Hypotéza 4.1",[1023,4193,4194],{},[55,4195,4196,4197],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[1647,4198,4200],{"className":4199},[2059],[2061,4201,4202],{"xmlns":2063},[2065,4203,4204,4213],{},[2068,4205,4206,4208,4211],{},[2075,4207,2084],{"stretchy":2083},[2210,4209,4210],{},"4.1",[2075,4212,2090],{"stretchy":2083},[2092,4214,4215],{"encoding":2094},"(4.1)",[55,4217,4218,4219,4222],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[95,4220,4221],{},"procentní změny"," obou faktorů.",[84,4224,4226],{"id":4225},"pojem-elasticity","Pojem elasticity",[55,4228,4229,4230,4232,4233,4236],{},"Obecně ",[95,4231,3984],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[95,4234,4235],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1023,4238,4239],{},[55,4240,4241,4244,4245,4248],{},[1647,4242,4243],{},"!info"," Intuice\nElasticitu lze číst jako ",[95,4246,4247],{},"procentní odpověď na procentní podnět",". Místo „o kolik kusů se změní prodej, když zlevním o korunu\" (což závisí na jednotkách) se ptáme „o kolik procent se změní prodej, když zlevním o 1 %\". Tato procentní citlivost je univerzální a umožňuje srovnávat zboží různých řádů i měn.",[84,4250,4252],{"id":4251},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[55,4254,4255,4256,4281],{},"Nechť ",[1647,4257,4259],{"className":4258},[2059],[2061,4260,4261],{"xmlns":2063},[2065,4262,4263,4278],{},[2068,4264,4265,4267,4269,4272,4274,4276],{},[2071,4266,2861],{},[2075,4268,2077],{},[2071,4270,4271],{},"D",[2075,4273,2084],{"stretchy":2083},[2071,4275,575],{},[2075,4277,2090],{"stretchy":2083},[2092,4279,4280],{"encoding":2094},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[55,4283,4284],{},[1647,4285,4290],{"className":4286,"title":4288,"style":4289},[4287],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[55,4292,4293,4294,75,4310,4326,4327,4346],{},"Znaménko minus je korekce: změny ",[1647,4295,4297],{"className":4296},[2059],[2061,4298,4299],{"xmlns":2063},[2065,4300,4301,4307],{},[2068,4302,4303,4305],{},[2071,4304,2961],{"mathvariant":2450},[2071,4306,2861],{},[2092,4308,4309],{"encoding":2094},"\\Delta Q",[1647,4311,4313],{"className":4312},[2059],[2061,4314,4315],{"xmlns":2063},[2065,4316,4317,4323],{},[2068,4318,4319,4321],{},[2071,4320,2961],{"mathvariant":2450},[2071,4322,575],{},[2092,4324,4325],{"encoding":2094},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[1647,4328,4330],{"className":4329},[2059],[2061,4331,4332],{"xmlns":2063},[2065,4333,4334,4343],{},[2068,4335,4336],{},[2205,4337,4338,4340],{},[2071,4339,554],{},[2071,4341,4342],{},"A",[2092,4344,4345],{"encoding":2094},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[55,4348,4349],{},[1647,4350,4352],{"className":4351,"title":4288,"style":4289},[4287],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[55,4354,4355],{},"Po dosazení:",[55,4357,4358],{},[1647,4359,4361],{"className":4360,"title":4288,"style":4289},[4287],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[55,4363,4364,4365,4385,4386,4388],{},"Limitním přechodem ",[1647,4366,4368],{"className":4367},[2059],[2061,4369,4370],{"xmlns":2063},[2065,4371,4372,4382],{},[2068,4373,4374,4376,4378,4380],{},[2071,4375,2961],{"mathvariant":2450},[2071,4377,575],{},[2075,4379,3197],{},[2210,4381,630],{},[2092,4383,4384],{"encoding":2094},"\\Delta P \\to 0"," získáme definici ",[95,4387,3996],{}," (price elasticity of demand):",[55,4390,4391],{},[1647,4392,4394],{"className":4393,"title":4288,"style":4289},[4287],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[55,4396,4397,4398,4421,4422,4445,4446,4470,4471,4492],{},"kde ",[1647,4399,4401],{"className":4400},[2059],[2061,4402,4403],{"xmlns":2063},[2065,4404,4405,4419],{},[2068,4406,4407,4409,4411,4413,4415,4417],{},[2071,4408,2861],{},[2075,4410,2077],{},[2071,4412,4271],{},[2075,4414,2084],{"stretchy":2083},[2071,4416,575],{},[2075,4418,2090],{"stretchy":2083},[2092,4420,4280],{"encoding":2094},". Pro pevnou cenu ",[1647,4423,4425],{"className":4424},[2059],[2061,4426,4427],{"xmlns":2063},[2065,4428,4429,4442],{},[2068,4430,4431,4433,4435],{},[2071,4432,575],{},[2075,4434,2077],{},[2205,4436,4437,4439],{},[2071,4438,575],{},[2075,4440,4441],{},"∗",[2092,4443,4444],{"encoding":2094},"P = P^*"," se ",[1647,4447,4449],{"className":4448},[2059],[2061,4450,4451],{"xmlns":2063},[2065,4452,4453,4467],{},[2068,4454,4455,4457,4459,4465],{},[2071,4456,554],{},[2075,4458,2084],{"stretchy":2083},[2205,4460,4461,4463],{},[2071,4462,575],{},[2075,4464,4441],{},[2075,4466,2090],{"stretchy":2083},[2092,4468,4469],{"encoding":2094},"E(P^*)"," nazývá ",[3982,4472,4473,4474],{},"elasticita poptávky při ceně ",[1647,4475,4477],{"className":4476},[2059],[2061,4478,4479],{"xmlns":2063},[2065,4480,4481,4489],{},[2068,4482,4483],{},[2205,4484,4485,4487],{},[2071,4486,575],{},[2075,4488,4441],{},[2092,4490,4491],{"encoding":2094},"P^*"," a je to vždy nezáporné číslo.",[1023,4494,4495],{},[55,4496,4497,4500,4501,4519,4520,4548,4549,4578,4579,835,4597,835,4615,4633,4634,4649,4650,195],{},[1647,4498,4499],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[95,4502,4503,4504],{},"explicitní ",[1647,4505,4507],{"className":4506},[2059],[2061,4508,4509],{"xmlns":2063},[2065,4510,4511,4517],{},[2068,4512,4513,4515],{},[2075,4514,2303],{},[2210,4516,638],{},[2092,4518,3808],{"encoding":2094}," právě proto, že ",[1647,4521,4523],{"className":4522},[2059],[2061,4524,4525],{"xmlns":2063},[2065,4526,4527,4545],{},[2068,4528,4529,4535,4537,4539,4541,4543],{},[2205,4530,4531,4533],{},[2071,4532,2861],{},[2075,4534,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,4536,2084],{"stretchy":2083},[2071,4538,575],{},[2075,4540,2090],{"stretchy":2083},[2075,4542,3521],{},[2210,4544,630],{},[2092,4546,4547],{"encoding":2094},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[1647,4550,4552],{"className":4551},[2059],[2061,4553,4554],{"xmlns":2063},[2065,4555,4556,4575],{},[2068,4557,4558,4560,4562,4568,4570,4573],{},[2071,4559,554],{},[2075,4561,2084],{"stretchy":2083},[2205,4563,4564,4566],{},[2071,4565,575],{},[2075,4567,4441],{},[2075,4569,2090],{"stretchy":2083},[2075,4571,4572],{},"≥",[2210,4574,630],{},[2092,4576,4577],{"encoding":2094},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[1647,4580,4582],{"className":4581},[2059],[2061,4583,4584],{"xmlns":2063},[2065,4585,4586,4594],{},[2068,4587,4588,4590,4592],{},[2071,4589,554],{},[2075,4591,3482],{},[2210,4593,638],{},[2092,4595,4596],{"encoding":2094},"E > 1",[1647,4598,4600],{"className":4599},[2059],[2061,4601,4602],{"xmlns":2063},[2065,4603,4604,4612],{},[2068,4605,4606,4608,4610],{},[2071,4607,554],{},[2075,4609,3521],{},[2210,4611,638],{},[2092,4613,4614],{"encoding":2094},"E \u003C 1",[1647,4616,4618],{"className":4617},[2059],[2061,4619,4620],{"xmlns":2063},[2065,4621,4622,4630],{},[2068,4623,4624,4626,4628],{},[2071,4625,554],{},[2075,4627,2077],{},[2210,4629,638],{},[2092,4631,4632],{"encoding":2094},"E = 1",". V některých starších pramenech se ",[1647,4635,4637],{"className":4636},[2059],[2061,4638,4639],{"xmlns":2063},[2065,4640,4641,4647],{},[2068,4642,4643,4645],{},[2075,4644,2303],{},[2210,4646,638],{},[2092,4648,3808],{"encoding":2094}," vynechává a uvádějí se záporné hodnoty; obsah pojmu se tím nemění, ale srovnávat hodnoty napříč zdroji je třeba opatrně. Pokud narazíte na zápornou hodnotu, pracujte s ",[95,4651,4652],{},"absolutní hodnotou",[1023,4654,4655,4675],{},[55,4656,4657,4660,4661,4674],{},[1647,4658,4659],{},"!tip"," Postup: jak spočítat ",[1647,4662,4664],{"className":4663},[2059],[2061,4665,4666],{"xmlns":2063},[2065,4667,4668,4672],{},[2068,4669,4670],{},[2071,4671,554],{},[2092,4673,554],{"encoding":2094}," v bodě",[201,4676,4677,4729,4769,4822,4887],{},[92,4678,4679,4680,4703,4704,4728],{},"Zapište ",[1647,4681,4683],{"className":4682},[2059],[2061,4684,4685],{"xmlns":2063},[2065,4686,4687,4701],{},[2068,4688,4689,4691,4693,4695,4697,4699],{},[2071,4690,2861],{},[2075,4692,2077],{},[2071,4694,4271],{},[2075,4696,2084],{"stretchy":2083},[2071,4698,575],{},[2075,4700,2090],{"stretchy":2083},[2092,4702,4280],{"encoding":2094},". Pokud je poptávka zadaná jako ",[1647,4705,4707],{"className":4706},[2059],[2061,4708,4709],{"xmlns":2063},[2065,4710,4711,4725],{},[2068,4712,4713,4715,4717,4719,4721,4723],{},[2071,4714,575],{},[2075,4716,2077],{},[2071,4718,4271],{},[2075,4720,2084],{"stretchy":2083},[2071,4722,2861],{},[2075,4724,2090],{"stretchy":2083},[2092,4726,4727],{"encoding":2094},"P = D(Q)",", použijte vztah (4.9).",[92,4730,4731,4732,195],{},"Spočítejte derivaci ",[1647,4733,4735],{"className":4734},[2059],[2061,4736,4737],{"xmlns":2063},[2065,4738,4739,4766],{},[2068,4740,4741,4747,4749,4751,4753,4755,4757,4759,4762,4764],{},[2205,4742,4743,4745],{},[2071,4744,2861],{},[2075,4746,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,4748,2084],{"stretchy":2083},[2071,4750,575],{},[2075,4752,2090],{"stretchy":2083},[2075,4754,2077],{},[2071,4756,2273],{"mathvariant":2450},[2071,4758,2861],{},[2071,4760,4761],{"mathvariant":2450},"\u002F",[2071,4763,2273],{"mathvariant":2450},[2071,4765,575],{},[2092,4767,4768],{"encoding":2094},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[92,4770,4771,4772,4789,4790,195],{},"Dosaďte zadanou cenu ",[1647,4773,4775],{"className":4774},[2059],[2061,4776,4777],{"xmlns":2063},[2065,4778,4779,4787],{},[2068,4780,4781],{},[2205,4782,4783,4785],{},[2071,4784,575],{},[2075,4786,4441],{},[2092,4788,4491],{"encoding":2094}," a dopočítejte odpovídající ",[1647,4791,4793],{"className":4792},[2059],[2061,4794,4795],{"xmlns":2063},[2065,4796,4797,4819],{},[2068,4798,4799,4805,4807,4809,4811,4817],{},[2205,4800,4801,4803],{},[2071,4802,2861],{},[2075,4804,4441],{},[2075,4806,2077],{},[2071,4808,4271],{},[2075,4810,2084],{"stretchy":2083},[2205,4812,4813,4815],{},[2071,4814,575],{},[2075,4816,4441],{},[2075,4818,2090],{"stretchy":2083},[2092,4820,4821],{"encoding":2094},"Q^* = D(P^*)",[92,4823,4824,4825,195],{},"Dosaďte do (4.5): ",[1647,4826,4828],{"className":4827},[2059],[2061,4829,4830],{"xmlns":2063},[2065,4831,4832,4884],{},[2068,4833,4834,4836,4838,4844,4846,4848,4850,4866,4868,4874,4876,4882],{},[2071,4835,554],{},[2075,4837,2084],{"stretchy":2083},[2205,4839,4840,4842],{},[2071,4841,575],{},[2075,4843,4441],{},[2075,4845,2090],{"stretchy":2083},[2075,4847,2077],{},[2075,4849,2303],{},[2400,4851,4852],{"scriptlevel":630,"displaystyle":2360},[2403,4853,4854,4860],{},[2205,4855,4856,4858],{},[2071,4857,575],{},[2075,4859,4441],{},[2205,4861,4862,4864],{},[2071,4863,2861],{},[2075,4865,4441],{},[2363,4867,3061],{},[2205,4869,4870,4872],{},[2071,4871,2861],{},[2075,4873,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,4875,2084],{"stretchy":2083},[2205,4877,4878,4880],{},[2071,4879,575],{},[2075,4881,4441],{},[2075,4883,2090],{"stretchy":2083},[2092,4885,4886],{"encoding":2094},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[92,4888,4889,4890,4907,4908,4925,4926,4943],{},"Klasifikujte: ",[1647,4891,4893],{"className":4892},[2059],[2061,4894,4895],{"xmlns":2063},[2065,4896,4897,4905],{},[2068,4898,4899,4901,4903],{},[2071,4900,554],{},[2075,4902,3482],{},[2210,4904,638],{},[2092,4906,4596],{"encoding":2094}," elastická, ",[1647,4909,4911],{"className":4910},[2059],[2061,4912,4913],{"xmlns":2063},[2065,4914,4915,4923],{},[2068,4916,4917,4919,4921],{},[2071,4918,554],{},[2075,4920,2077],{},[2210,4922,638],{},[2092,4924,4632],{"encoding":2094}," jednotková, ",[1647,4927,4929],{"className":4928},[2059],[2061,4930,4931],{"xmlns":2063},[2065,4932,4933,4941],{},[2068,4934,4935,4937,4939],{},[2071,4936,554],{},[2075,4938,3521],{},[2210,4940,638],{},[2092,4942,4614],{"encoding":2094}," neelastická.",[609,4945,4947],{"id":4946},"interpretace-46","Interpretace (4.6)",[1023,4949,4950],{},[55,4951,4952,4953,4976,4977,4990,4991,5008,5009],{},"Číslo ",[1647,4954,4956],{"className":4955},[2059],[2061,4957,4958],{"xmlns":2063},[2065,4959,4960,4974],{},[2068,4961,4962,4964,4966,4972],{},[2071,4963,554],{},[2075,4965,2084],{"stretchy":2083},[2205,4967,4968,4970],{},[2071,4969,575],{},[2075,4971,4441],{},[2075,4973,2090],{"stretchy":2083},[2092,4975,4469],{"encoding":2094}," udává, o kolik % se přibližně změní poptávané množství ",[1647,4978,4980],{"className":4979},[2059],[2061,4981,4982],{"xmlns":2063},[2065,4983,4984,4988],{},[2068,4985,4986],{},[2071,4987,2861],{},[2092,4989,2861],{"encoding":2094},", jestliže se cena ",[1647,4992,4994],{"className":4993},[2059],[2061,4995,4996],{"xmlns":2063},[2065,4997,4998,5006],{},[2068,4999,5000],{},[2205,5001,5002,5004],{},[2071,5003,575],{},[2075,5005,4441],{},[2092,5007,4491],{"encoding":2094}," změní o 1 %. ",[1647,5010,5012],{"className":5011},[2059],[2061,5013,5014],{"xmlns":2063},[2065,5015,5016,5025],{},[2068,5017,5018,5020,5023],{},[2075,5019,2084],{"stretchy":2083},[2210,5021,5022],{},"4.6",[2075,5024,2090],{"stretchy":2083},[2092,5026,5027],{"encoding":2094},"(4.6)",[55,5029,5030,5033],{},[95,5031,5032],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[609,5035,5037],{"id":5036},"příklad-41","Příklad 4.1",[55,5039,5040,5041,5075,5076,835,5102,2777],{},"Poptávka ",[1647,5042,5044],{"className":5043},[2059],[2061,5045,5046],{"xmlns":2063},[2065,5047,5048,5072],{},[2068,5049,5050,5052,5054,5056,5058,5060,5062,5064,5066,5068,5070],{},[2071,5051,575],{},[2075,5053,2077],{},[2071,5055,4271],{},[2075,5057,2084],{"stretchy":2083},[2071,5059,2861],{},[2075,5061,2090],{"stretchy":2083},[2075,5063,2077],{},[2210,5065,3194],{},[2075,5067,2303],{},[2210,5069,646],{},[2071,5071,2861],{},[2092,5073,5074],{"encoding":2094},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[1647,5077,5079],{"className":5078},[2059],[2061,5080,5081],{"xmlns":2063},[2065,5082,5083,5099],{},[2068,5084,5085,5087,5089,5092,5094,5097],{},[2071,5086,2861],{},[2075,5088,2077],{},[2210,5090,5091],{},"25",[2075,5093,2303],{},[2210,5095,5096],{},"0,5",[2071,5098,575],{},[2092,5100,5101],{"encoding":2094},"Q = 25 - 0{,}5P",[1647,5103,5105],{"className":5104},[2059],[2061,5106,5107],{"xmlns":2063},[2065,5108,5109,5133],{},[2068,5110,5111,5127,5129,5131],{},[2400,5112,5113],{"scriptlevel":630,"displaystyle":2360},[2403,5114,5115,5121],{},[2068,5116,5117,5119],{},[2071,5118,2273],{"mathvariant":2450},[2071,5120,2861],{},[2068,5122,5123,5125],{},[2071,5124,2273],{"mathvariant":2450},[2071,5126,575],{},[2075,5128,2077],{},[2075,5130,2303],{},[2210,5132,5096],{},[2092,5134,5135],{"encoding":2094},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[55,5137,5138],{},[1647,5139,5141],{"className":5140},[2059],[2061,5142,5143],{"xmlns":2063},[2065,5144,5145,5199],{},[2068,5146,5147,5149,5151,5153,5167,5169,5171,5173,5175,5177,5179,5197],{},[2071,5148,554],{},[2075,5150,2077],{},[2075,5152,2303],{},[2403,5154,5155,5157],{},[2071,5156,575],{},[2068,5158,5159,5161,5163,5165],{},[2210,5160,5091],{},[2075,5162,2303],{},[2210,5164,5096],{},[2071,5166,575],{},[2075,5168,3251],{},[2075,5170,2084],{"stretchy":2083},[2075,5172,2303],{},[2210,5174,5096],{},[2075,5176,2090],{"stretchy":2083},[2075,5178,2077],{},[2403,5180,5181,5187],{},[2068,5182,5183,5185],{},[2210,5184,5096],{},[2071,5186,575],{},[2068,5188,5189,5191,5193,5195],{},[2210,5190,5091],{},[2075,5192,2303],{},[2210,5194,5096],{},[2071,5196,575],{},[2071,5198,195],{"mathvariant":2450},[2092,5200,5201],{"encoding":2094},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[55,5203,5204,5205,835,5229,835,5259,835,5283,5308,5309,5332,5333,2758,5351,4007],{},"Potom ",[1647,5206,5208],{"className":5207},[2059],[2061,5209,5210],{"xmlns":2063},[2065,5211,5212,5226],{},[2068,5213,5214,5216,5218,5220,5222,5224],{},[2071,5215,554],{},[2075,5217,2084],{"stretchy":2083},[2210,5219,630],{},[2075,5221,2090],{"stretchy":2083},[2075,5223,2077],{},[2210,5225,630],{},[2092,5227,5228],{"encoding":2094},"E(0)=0",[1647,5230,5232],{"className":5231},[2059],[2061,5233,5234],{"xmlns":2063},[2065,5235,5236,5256],{},[2068,5237,5238,5240,5242,5244,5246,5248],{},[2071,5239,554],{},[2075,5241,2084],{"stretchy":2083},[2210,5243,2935],{},[2075,5245,2090],{"stretchy":2083},[2075,5247,2077],{},[2400,5249,5250],{"scriptlevel":630,"displaystyle":2083},[2403,5251,5252,5254],{},[2210,5253,638],{},[2210,5255,662],{},[2092,5257,5258],{"encoding":2094},"E(10)=\\tfrac{1}{4}",[1647,5260,5262],{"className":5261},[2059],[2061,5263,5264],{"xmlns":2063},[2065,5265,5266,5280],{},[2068,5267,5268,5270,5272,5274,5276,5278],{},[2071,5269,554],{},[2075,5271,2084],{"stretchy":2083},[2210,5273,5091],{},[2075,5275,2090],{"stretchy":2083},[2075,5277,2077],{},[2210,5279,638],{},[2092,5281,5282],{"encoding":2094},"E(25)=1",[1647,5284,5286],{"className":5285},[2059],[2061,5287,5288],{"xmlns":2063},[2065,5289,5290,5305],{},[2068,5291,5292,5294,5296,5299,5301,5303],{},[2071,5293,554],{},[2075,5295,2084],{"stretchy":2083},[2210,5297,5298],{},"40",[2075,5300,2090],{"stretchy":2083},[2075,5302,2077],{},[2210,5304,662],{},[2092,5306,5307],{"encoding":2094},"E(40)=4",". Např. ",[1647,5310,5312],{"className":5311},[2059],[2061,5313,5314],{"xmlns":2063},[2065,5315,5316,5330],{},[2068,5317,5318,5320,5322,5324,5326,5328],{},[2071,5319,554],{},[2075,5321,2084],{"stretchy":2083},[2210,5323,5298],{},[2075,5325,2090],{"stretchy":2083},[2075,5327,2077],{},[2210,5329,662],{},[2092,5331,5307],{"encoding":2094}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[1647,5334,5336],{"className":5335},[2059],[2061,5337,5338],{"xmlns":2063},[2065,5339,5340,5348],{},[2068,5341,5342,5344,5346],{},[2071,5343,2861],{},[2075,5345,2077],{},[2210,5347,670],{},[2092,5349,5350],{"encoding":2094},"Q=5",[1647,5352,5354],{"className":5353},[2059],[2061,5355,5356],{"xmlns":2063},[2065,5357,5358,5367],{},[2068,5359,5360,5362,5364],{},[2071,5361,2861],{},[2075,5363,2077],{},[2210,5365,5366],{},"4,8",[2092,5368,5369],{"encoding":2094},"Q=4{,}8",[609,5371,5373],{"id":5372},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[89,5375,5376,5432],{},[92,5377,5378,5381,5382,5399,5400,195],{},[95,5379,5380],{},"Oblouková"," (průměrná) elasticita: výraz ",[1647,5383,5385],{"className":5384},[2059],[2061,5386,5387],{"xmlns":2063},[2065,5388,5389,5397],{},[2068,5390,5391],{},[2205,5392,5393,5395],{},[2071,5394,554],{},[2071,5396,4342],{},[2092,5398,4345],{"encoding":2094}," ze (4.4) vztažený k intervalu ",[1647,5401,5403],{"className":5402},[2059],[2061,5404,5405],{"xmlns":2063},[2065,5406,5407,5429],{},[2068,5408,5409,5412,5414,5416,5418,5420,5422,5424,5426],{},[2075,5410,5411],{"stretchy":2083},"⟨",[2071,5413,575],{},[2075,5415,2361],{"separator":2360},[2363,5417,3061],{},[2071,5419,575],{},[2075,5421,2176],{},[2071,5423,2961],{"mathvariant":2450},[2071,5425,575],{},[2075,5427,5428],{"stretchy":2083},"⟩",[2092,5430,5431],{"encoding":2094},"\\langle P,\\, P+\\Delta P\\rangle",[92,5433,5434,5437,5438,5451],{},[95,5435,5436],{},"Bodová"," (okamžitá) elasticita: ",[1647,5439,5441],{"className":5440},[2059],[2061,5442,5443],{"xmlns":2063},[2065,5444,5445,5449],{},[2068,5446,5447],{},[2071,5448,554],{},[2092,5450,554],{"encoding":2094}," dle (4.5) — výchozí pojem dále v textu.",[609,5453,5455,5456,5469,5470],{"id":5454},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[1647,5457,5459],{"className":5458},[2059],[2061,5460,5461],{"xmlns":2063},[2065,5462,5463,5467],{},[2068,5464,5465],{},[2071,5466,575],{},[2092,5468,575],{"encoding":2094}," jako funkce ",[1647,5471,5473],{"className":5472},[2059],[2061,5474,5475],{"xmlns":2063},[2065,5476,5477,5481],{},[2068,5478,5479],{},[2071,5480,2861],{},[2092,5482,2861],{"encoding":2094},[55,5484,5485,5486,5509],{},"Pokud je poptávka zadaná ve tvaru ",[1647,5487,5489],{"className":5488},[2059],[2061,5490,5491],{"xmlns":2063},[2065,5492,5493,5507],{},[2068,5494,5495,5497,5499,5501,5503,5505],{},[2071,5496,575],{},[2075,5498,2077],{},[2071,5500,4271],{},[2075,5502,2084],{"stretchy":2083},[2071,5504,2861],{},[2075,5506,2090],{"stretchy":2083},[2092,5508,4727],{"encoding":2094},", využijeme vztah pro derivaci inverzní funkce",[55,5511,5512],{},[1647,5513,5515],{"className":5514,"title":4288,"style":4289},[4287],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[55,5517,5518,1445,5521,5547],{},[95,5519,5520],{},"Příklad 4.3.",[1647,5522,5524],{"className":5523},[2059],[2061,5525,5526],{"xmlns":2063},[2065,5527,5528,5544],{},[2068,5529,5530,5532,5534,5536,5538],{},[2071,5531,575],{},[2075,5533,2077],{},[2210,5535,3164],{},[2075,5537,2303],{},[2205,5539,5540,5542],{},[2071,5541,2861],{},[2210,5543,646],{},[2092,5545,5546],{"encoding":2094},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[55,5549,5550],{},[1647,5551,5553],{"className":5552},[2059],[2061,5554,5555],{"xmlns":2063},[2065,5556,5557,5623],{},[2068,5558,5559,5561,5563,5565,5581,5583,5595,5597,5621],{},[2071,5560,554],{},[2075,5562,2077],{},[2075,5564,2303],{},[2403,5566,5567,5579],{},[2068,5568,5569,5571,5573],{},[2210,5570,3164],{},[2075,5572,2303],{},[2205,5574,5575,5577],{},[2071,5576,2861],{},[2210,5578,646],{},[2071,5580,2861],{},[2075,5582,3251],{},[2403,5584,5585,5587],{},[2210,5586,638],{},[2068,5588,5589,5591,5593],{},[2075,5590,2303],{},[2210,5592,646],{},[2071,5594,2861],{},[2075,5596,2077],{},[2403,5598,5599,5611],{},[2068,5600,5601,5603,5605],{},[2210,5602,3164],{},[2075,5604,2303],{},[2205,5606,5607,5609],{},[2071,5608,2861],{},[2210,5610,646],{},[2068,5612,5613,5615],{},[2210,5614,646],{},[2205,5616,5617,5619],{},[2071,5618,2861],{},[2210,5620,646],{},[2071,5622,195],{"mathvariant":2450},[2092,5624,5625],{"encoding":2094},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[55,5627,5628,5629,5656,5657,5676,5677,195],{},"Z rovnice ",[1647,5630,5632],{"className":5631},[2059],[2061,5633,5634],{"xmlns":2063},[2065,5635,5636,5653],{},[2068,5637,5638,5640,5642,5648,5650],{},[2210,5639,3164],{},[2075,5641,2303],{},[2205,5643,5644,5646],{},[2071,5645,2861],{},[2210,5647,646],{},[2075,5649,2077],{},[2210,5651,5652],{},"36",[2092,5654,5655],{"encoding":2094},"100 - Q^2 = 36"," plyne ",[1647,5658,5660],{"className":5659},[2059],[2061,5661,5662],{"xmlns":2063},[2065,5663,5664,5673],{},[2068,5665,5666,5668,5670],{},[2071,5667,2861],{},[2075,5669,2077],{},[2210,5671,5672],{},"8",[2092,5674,5675],{"encoding":2094},"Q = 8",", tedy ",[1647,5678,5680],{"className":5679},[2059],[2061,5681,5682],{"xmlns":2063},[2065,5683,5684,5710],{},[2068,5685,5686,5688,5690,5692,5694,5696,5705,5707],{},[2071,5687,554],{},[2075,5689,2084],{"stretchy":2083},[2210,5691,5672],{},[2075,5693,2090],{"stretchy":2083},[2075,5695,2077],{},[2400,5697,5698],{"scriptlevel":630,"displaystyle":2083},[2403,5699,5700,5702],{},[2210,5701,5652],{},[2210,5703,5704],{},"128",[2075,5706,2077],{},[2210,5708,5709],{},"0,281",[2092,5711,5712],{"encoding":2094},"E(8) = \\tfrac{36}{128} = 0{,}281",[609,5714,5716],{"id":5715},"přibližné-změny","Přibližné změny",[55,5718,5719,5720,5756,5757,5779],{},"Diferenciál ",[1647,5721,5723],{"className":5722},[2059],[2061,5724,5725],{"xmlns":2063},[2065,5726,5727,5753],{},[2068,5728,5729,5731,5733,5735,5741,5743,5745,5747,5749,5751],{},[2071,5730,2273],{"mathvariant":2450},[2071,5732,2861],{},[2075,5734,2077],{},[2205,5736,5737,5739],{},[2071,5738,2861],{},[2075,5740,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,5742,2084],{"stretchy":2083},[2071,5744,575],{},[2075,5746,2090],{"stretchy":2083},[2363,5748,3061],{},[2071,5750,2273],{"mathvariant":2450},[2071,5752,575],{},[2092,5754,5755],{"encoding":2094},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[1647,5758,5760],{"className":5759},[2059],[2061,5761,5762],{"xmlns":2063},[2065,5763,5764,5776],{},[2068,5765,5766,5768,5770,5772,5774],{},[2071,5767,2273],{"mathvariant":2450},[2071,5769,575],{},[2075,5771,2077],{},[2071,5773,2961],{"mathvariant":2450},[2071,5775,575],{},[2092,5777,5778],{"encoding":2094},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[55,5781,5782],{},[1647,5783,5785],{"className":5784,"title":4288,"style":4289},[4287],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[55,5787,5788],{},"Po přechodu na procentní změny (vztah (4.3)):",[55,5790,5791],{},[1647,5792,5794],{"className":5793,"title":4288,"style":4289},[4287],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[55,5796,5797,1445,5800,5835,5836,5855,5856,5890,5891,5908],{},[95,5798,5799],{},"Příklad 4.5.",[1647,5801,5803],{"className":5802},[2059],[2061,5804,5805],{"xmlns":2063},[2065,5806,5807,5832],{},[2068,5808,5809,5811,5813,5815,5821,5823,5825,5827,5829],{},[2071,5810,575],{},[2075,5812,2077],{},[2075,5814,2303],{},[2205,5816,5817,5819],{},[2071,5818,2861],{},[2210,5820,646],{},[2075,5822,2303],{},[2210,5824,662],{},[2071,5826,2861],{},[2075,5828,2176],{},[2210,5830,5831],{},"96",[2092,5833,5834],{"encoding":2094},"P = -Q^2 - 4Q + 96",", cena ",[1647,5837,5839],{"className":5838},[2059],[2061,5840,5841],{"xmlns":2063},[2065,5842,5843,5852],{},[2068,5844,5845,5847,5849],{},[2071,5846,575],{},[2075,5848,2077],{},[2210,5850,5851],{},"51",[2092,5853,5854],{"encoding":2094},"P=51",". Z rovnice ",[1647,5857,5859],{"className":5858},[2059],[2061,5860,5861],{"xmlns":2063},[2065,5862,5863,5887],{},[2068,5864,5865,5867,5869,5871,5877,5879,5881,5883,5885],{},[2210,5866,5851],{},[2075,5868,2077],{},[2075,5870,2303],{},[2205,5872,5873,5875],{},[2071,5874,2861],{},[2210,5876,646],{},[2075,5878,2303],{},[2210,5880,662],{},[2071,5882,2861],{},[2075,5884,2176],{},[2210,5886,5831],{},[2092,5888,5889],{"encoding":2094},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[1647,5892,5894],{"className":5893},[2059],[2061,5895,5896],{"xmlns":2063},[2065,5897,5898,5906],{},[2068,5899,5900,5902,5904],{},[2071,5901,2861],{},[2075,5903,2077],{},[2210,5905,670],{},[2092,5907,5350],{"encoding":2094},". Elasticita:",[55,5910,5911],{},[1647,5912,5914],{"className":5913},[2059],[2061,5915,5916],{"xmlns":2063},[2065,5917,5918,5991],{},[2068,5919,5920,5922,5924,5962,5964,5968,5970,5972,5974,5976,5978,5985,5988],{},[2071,5921,554],{},[2075,5923,2077],{},[2403,5925,5926,5946],{},[2068,5927,5928,5930,5936,5938,5940,5942,5944],{},[2075,5929,2303],{},[2205,5931,5932,5934],{},[2071,5933,2861],{},[2210,5935,646],{},[2075,5937,2303],{},[2210,5939,662],{},[2071,5941,2861],{},[2075,5943,2176],{},[2210,5945,5831],{},[2068,5947,5948,5950,5952,5954,5956,5958,5960],{},[2071,5949,2861],{},[2075,5951,2084],{"stretchy":2083},[2210,5953,646],{},[2071,5955,2861],{},[2075,5957,2176],{},[2210,5959,662],{},[2075,5961,2090],{"stretchy":2083},[2075,5963,2361],{"separator":2360},[5965,5966],"mspace",{"width":5967},"2em",[2071,5969,554],{},[2075,5971,2084],{"stretchy":2083},[2210,5973,670],{},[2075,5975,2090],{"stretchy":2083},[2075,5977,2077],{},[2403,5979,5980,5982],{},[2210,5981,5851],{},[2210,5983,5984],{},"70",[2075,5986,5987],{},"≐",[2210,5989,5990],{},"0,728.",[2092,5992,5993],{"encoding":2094},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[55,5995,5996,5997,195],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[1647,5998,6000],{"className":5999},[2059],[2061,6001,6002],{"xmlns":2063},[2065,6003,6004,6035],{},[2068,6005,6006,6008,6010,6013,6015,6017,6020,6022,6024,6026,6028,6031,6033],{},[2071,6007,2961],{"mathvariant":2450},[2071,6009,2861],{},[2071,6011,6012],{"mathvariant":2450},"%",[2075,6014,2803],{},[2075,6016,2303],{},[2210,6018,6019],{},"0,728",[2075,6021,3251],{},[2210,6023,646],{},[2075,6025,2077],{},[2075,6027,2303],{},[2210,6029,6030],{},"1,456",[2363,6032,3061],{},[2071,6034,6012],{"mathvariant":2450},[2092,6036,6037],{"encoding":2094},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[84,6039,6041],{"id":6040},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[55,6043,6044,6045,6068,6069,2777],{},"V závislosti na hodnotě ",[1647,6046,6048],{"className":6047},[2059],[2061,6049,6050],{"xmlns":2063},[2065,6051,6052,6066],{},[2068,6053,6054,6056,6058,6064],{},[2071,6055,554],{},[2075,6057,2084],{"stretchy":2083},[2205,6059,6060,6062],{},[2071,6061,575],{},[2075,6063,4441],{},[2075,6065,2090],{"stretchy":2083},[2092,6067,4469],{"encoding":2094}," mluvíme o poptávce podle následující tabulky ",[1647,6070,6072],{"className":6071},[2059],[2061,6073,6074],{"xmlns":2063},[2065,6075,6076,6085],{},[2068,6077,6078,6080,6083],{},[2075,6079,2084],{"stretchy":2083},[2210,6081,6082],{},"4.7",[2075,6084,2090],{"stretchy":2083},[2092,6086,6087],{"encoding":2094},"(4.7)",[55,6089,6090],{},[58,6091],{"alt":6092,"className":6093,"src":6094},"imek-typy-elasticity-5panelu",[62,63],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[323,6096,6097,6136],{},[326,6098,6099],{},[329,6100,6101,6127,6130,6133],{},[332,6102,6103,6104],{},"Hodnota ",[1647,6105,6107],{"className":6106},[2059],[2061,6108,6109],{"xmlns":2063},[2065,6110,6111,6125],{},[2068,6112,6113,6115,6117,6123],{},[2071,6114,554],{},[2075,6116,2084],{"stretchy":2083},[2205,6118,6119,6121],{},[2071,6120,575],{},[2075,6122,4441],{},[2075,6124,2090],{"stretchy":2083},[2092,6126,4469],{"encoding":2094},[332,6128,6129],{},"Typ poptávky",[332,6131,6132],{},"Termín",[332,6134,6135],{},"Význam",[342,6137,6138,6171,6233,6308,6365],{},[329,6139,6140,6160,6165,6168],{},[347,6141,6142],{},[1647,6143,6145],{"className":6144},[2059],[2061,6146,6147],{"xmlns":2063},[2065,6148,6149,6157],{},[2068,6150,6151,6153,6155],{},[2071,6152,554],{},[2075,6154,2077],{},[2210,6156,630],{},[2092,6158,6159],{"encoding":2094},"E = 0",[347,6161,6162],{},[95,6163,6164],{},"dokonale neelastická",[347,6166,6167],{},"perfectly inelastic",[347,6169,6170],{},"množství se nemění bez ohledu na cenu",[329,6172,6173,6197,6201,6204],{},[347,6174,6175],{},[1647,6176,6178],{"className":6177},[2059],[2061,6179,6180],{"xmlns":2063},[2065,6181,6182,6194],{},[2068,6183,6184,6186,6188,6190,6192],{},[2210,6185,630],{},[2075,6187,3521],{},[2071,6189,554],{},[2075,6191,3521],{},[2210,6193,638],{},[2092,6195,6196],{"encoding":2094},"0 \u003C E \u003C 1",[347,6198,6199],{},[95,6200,4165],{},[347,6202,6203],{},"inelastic",[347,6205,6206,6219,6220],{},[1647,6207,6209],{"className":6208},[2059],[2061,6210,6211],{"xmlns":2063},[2065,6212,6213,6217],{},[2068,6214,6215],{},[2071,6216,2861],{},[2092,6218,2861],{"encoding":2094}," se mění pomaleji než ",[1647,6221,6223],{"className":6222},[2059],[2061,6224,6225],{"xmlns":2063},[2065,6226,6227,6231],{},[2068,6228,6229],{},[2071,6230,575],{},[2092,6232,575],{"encoding":2094},[329,6234,6235,6254,6259,6262],{},[347,6236,6237],{},[1647,6238,6240],{"className":6239},[2059],[2061,6241,6242],{"xmlns":2063},[2065,6243,6244,6252],{},[2068,6245,6246,6248,6250],{},[2071,6247,554],{},[2075,6249,2077],{},[2210,6251,638],{},[2092,6253,4632],{"encoding":2094},[347,6255,6256],{},[95,6257,6258],{},"jednotkově elastická",[347,6260,6261],{},"unit elastic",[347,6263,6264,6277,6278,6291,6292,6307],{},[1647,6265,6267],{"className":6266},[2059],[2061,6268,6269],{"xmlns":2063},[2065,6270,6271,6275],{},[2068,6272,6273],{},[2071,6274,2861],{},[2092,6276,2861],{"encoding":2094}," i ",[1647,6279,6281],{"className":6280},[2059],[2061,6282,6283],{"xmlns":2063},[2065,6284,6285,6289],{},[2068,6286,6287],{},[2071,6288,575],{},[2092,6290,575],{"encoding":2094}," se mění stejně rychle; ",[1647,6293,6295],{"className":6294},[2059],[2061,6296,6297],{"xmlns":2063},[2065,6298,6299,6305],{},[2068,6300,6301,6303],{},[2071,6302,543],{},[2071,6304,4082],{},[2092,6306,4182],{"encoding":2094}," má maximum",[329,6309,6310,6329,6333,6336],{},[347,6311,6312],{},[1647,6313,6315],{"className":6314},[2059],[2061,6316,6317],{"xmlns":2063},[2065,6318,6319,6327],{},[2068,6320,6321,6323,6325],{},[2071,6322,554],{},[2075,6324,3482],{},[2210,6326,638],{},[2092,6328,4596],{"encoding":2094},[347,6330,6331],{},[95,6332,4161],{},[347,6334,6335],{},"elastic",[347,6337,6338,6351,6352],{},[1647,6339,6341],{"className":6340},[2059],[2061,6342,6343],{"xmlns":2063},[2065,6344,6345,6349],{},[2068,6346,6347],{},[2071,6348,2861],{},[2092,6350,2861],{"encoding":2094}," se mění rychleji než ",[1647,6353,6355],{"className":6354},[2059],[2061,6356,6357],{"xmlns":2063},[2065,6358,6359,6363],{},[2068,6360,6361],{},[2071,6362,575],{},[2092,6364,575],{"encoding":2094},[329,6366,6367,6388,6393,6396],{},[347,6368,6369],{},[1647,6370,6372],{"className":6371},[2059],[2061,6373,6374],{"xmlns":2063},[2065,6375,6376,6385],{},[2068,6377,6378,6380,6382],{},[2071,6379,554],{},[2075,6381,3197],{},[2071,6383,6384],{"mathvariant":2450},"∞",[2092,6386,6387],{"encoding":2094},"E \\to \\infty",[347,6389,6390],{},[95,6391,6392],{},"dokonale elastická",[347,6394,6395],{},"perfectly elastic",[347,6397,6398,6399],{},"sebemenší změna ceny úplně mění ",[1647,6400,6402],{"className":6401},[2059],[2061,6403,6404],{"xmlns":2063},[2065,6405,6406,6410],{},[2068,6407,6408],{},[2071,6409,2861],{},[2092,6411,2861],{"encoding":2094},[55,6413,6414],{},[95,6415,6416],{},"Pravidlo růstu elasticity s cenou:",[1023,6418,6419],{},[55,6420,6421,6422],{},"S rostoucí cenou elasticita poptávky roste. ",[1647,6423,6425],{"className":6424},[2059],[2061,6426,6427],{"xmlns":2063},[2065,6428,6429,6438],{},[2068,6430,6431,6433,6436],{},[2075,6432,2084],{"stretchy":2083},[2210,6434,6435],{},"4.8",[2075,6437,2090],{"stretchy":2083},[2092,6439,6440],{"encoding":2094},"(4.8)",[55,6442,6443,6444,6447,6448,6451,6452,6469],{},"Z toho plyne, že při ",[3982,6445,6446],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[3982,6449,6450],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[1647,6453,6455],{"className":6454},[2059],[2061,6456,6457],{"xmlns":2063},[2065,6458,6459,6467],{},[2068,6460,6461],{},[2205,6462,6463,6465],{},[2071,6464,575],{},[2075,6466,4441],{},[2092,6468,4491],{"encoding":2094},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1023,6471,6472,6477],{},[55,6473,6474,6476],{},[1647,6475,4659],{}," Postup: jak klasifikovat poptávku",[201,6478,6479,6506,6509],{},[92,6480,6481,6482,6505],{},"Spočítejte ",[1647,6483,6485],{"className":6484},[2059],[2061,6486,6487],{"xmlns":2063},[2065,6488,6489,6503],{},[2068,6490,6491,6493,6495,6501],{},[2071,6492,554],{},[2075,6494,2084],{"stretchy":2083},[2205,6496,6497,6499],{},[2071,6498,575],{},[2075,6500,4441],{},[2075,6502,2090],{"stretchy":2083},[2092,6504,4469],{"encoding":2094}," dle (4.5).",[92,6507,6508],{},"Porovnejte s jedničkou (viz tabulka výše).",[92,6510,6511,6512,6536],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[1647,6513,6515],{"className":6514},[2059],[2061,6516,6517],{"xmlns":2063},[2065,6518,6519,6533],{},[2068,6520,6521,6523,6525,6527,6529,6531],{},[2071,6522,554],{},[2075,6524,2084],{"stretchy":2083},[2071,6526,575],{},[2075,6528,2090],{"stretchy":2083},[2075,6530,2077],{},[2210,6532,638],{},[2092,6534,6535],{"encoding":2094},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[55,6538,6539,6542,6543,6560,6561,6579,6580,6607,6608,195],{},[95,6540,6541],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[1647,6544,6546],{"className":6545},[2059],[2061,6547,6548],{"xmlns":2063},[2065,6549,6550,6558],{},[2068,6551,6552,6554,6556],{},[2071,6553,554],{},[2075,6555,2077],{},[2210,6557,638],{},[2092,6559,4632],{"encoding":2094}," pro ",[1647,6562,6564],{"className":6563},[2059],[2061,6565,6566],{"xmlns":2063},[2065,6567,6568,6576],{},[2068,6569,6570,6572,6574],{},[2071,6571,575],{},[2075,6573,2077],{},[2210,6575,5091],{},[2092,6577,6578],{"encoding":2094},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[1647,6581,6583],{"className":6582},[2059],[2061,6584,6585],{"xmlns":2063},[2065,6586,6587,6604],{},[2068,6588,6589,6591,6594,6596,6598,6600,6602],{},[2071,6590,575],{},[2075,6592,6593],{},"∈",[2075,6595,5411],{"stretchy":2083},[2210,6597,630],{},[2075,6599,2361],{"separator":2360},[2210,6601,5091],{},[2075,6603,2090],{"stretchy":2083},[2092,6605,6606],{"encoding":2094},"P \\in \\langle 0, 25)"," a elastická pro ",[1647,6609,6611],{"className":6610},[2059],[2061,6612,6613],{"xmlns":2063},[2065,6614,6615,6631],{},[2068,6616,6617,6619,6621,6623,6625,6627,6629],{},[2071,6618,575],{},[2075,6620,6593],{},[2075,6622,2084],{"stretchy":2083},[2210,6624,5091],{},[2075,6626,2361],{"separator":2360},[2210,6628,3194],{},[2075,6630,5428],{"stretchy":2083},[2092,6632,6633],{"encoding":2094},"P \\in (25, 50\\rangle",[84,6635,6637],{"id":6636},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[55,6639,6640],{},[58,6641],{"alt":6642,"className":6643,"src":6644},"imek-elasticita-tr",[62,63],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[55,6646,6647],{},[58,6648],{"alt":6649,"className":6650,"src":6651},"imek-elasticita-podel-linearni-poptavky",[62,63],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[55,6653,6654,6655,6705,6706,6722],{},"Pro celkový příjem platí ",[1647,6656,6658],{"className":6657},[2059],[2061,6659,6660],{"xmlns":2063},[2065,6661,6662,6702],{},[2068,6663,6664,6666,6668,6670,6672,6674,6676,6678,6680,6682,6684,6686,6688,6690,6692,6694,6696,6698,6700],{},[2071,6665,543],{},[2071,6667,4082],{},[2075,6669,2077],{},[2071,6671,543],{},[2071,6673,4082],{},[2075,6675,2084],{"stretchy":2083},[2071,6677,2861],{},[2075,6679,2090],{"stretchy":2083},[2075,6681,2077],{},[2071,6683,575],{},[2075,6685,3251],{},[2071,6687,2861],{},[2075,6689,2077],{},[2071,6691,2861],{},[2075,6693,3251],{},[2071,6695,4271],{},[2075,6697,2084],{"stretchy":2083},[2071,6699,2861],{},[2075,6701,2090],{"stretchy":2083},[2092,6703,6704],{"encoding":2094},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[1647,6707,6709],{"className":6708},[2059],[2061,6710,6711],{"xmlns":2063},[2065,6712,6713,6719],{},[2068,6714,6715,6717],{},[2071,6716,2890],{},[2071,6718,4082],{},[2092,6720,6721],{"encoding":2094},"MR"," odvodíme:",[55,6724,6725],{},[1647,6726,6728],{"className":6727},[2059],[2061,6729,6730],{"xmlns":2063},[2065,6731,6732,6840],{},[2068,6733,6734,6736,6738,6740,6742,6748,6750,6752,6754,6756,6758,6760,6762,6764,6766,6768,6770,6776,6778,6780,6782,6784,6786,6788,6790,6804,6806,6808],{},[2071,6735,2890],{},[2071,6737,4082],{},[2075,6739,2077],{},[2071,6741,543],{},[2205,6743,6744,6746],{},[2071,6745,4082],{},[2075,6747,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,6749,2084],{"stretchy":2083},[2071,6751,2861],{},[2075,6753,2090],{"stretchy":2083},[2075,6755,2077],{},[2071,6757,4271],{},[2075,6759,2084],{"stretchy":2083},[2071,6761,2861],{},[2075,6763,2090],{"stretchy":2083},[2075,6765,2176],{},[2071,6767,2861],{},[2363,6769,3061],{},[2205,6771,6772,6774],{},[2071,6773,4271],{},[2075,6775,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,6777,2084],{"stretchy":2083},[2071,6779,2861],{},[2075,6781,2090],{"stretchy":2083},[2075,6783,2077],{},[2071,6785,575],{},[2075,6787,2176],{},[2071,6789,2861],{},[2403,6791,6792,6798],{},[2068,6793,6794,6796],{},[2071,6795,2273],{"mathvariant":2450},[2071,6797,575],{},[2068,6799,6800,6802],{},[2071,6801,2273],{"mathvariant":2450},[2071,6803,2861],{},[2075,6805,2077],{},[2071,6807,575],{},[2068,6809,6810,6812,6814,6816,6822,6824,6838],{},[2075,6811,2084],{"fence":2360},[2210,6813,638],{},[2075,6815,2176],{},[2403,6817,6818,6820],{},[2071,6819,2861],{},[2071,6821,575],{},[2075,6823,3251],{},[2403,6825,6826,6832],{},[2068,6827,6828,6830],{},[2071,6829,2273],{"mathvariant":2450},[2071,6831,575],{},[2068,6833,6834,6836],{},[2071,6835,2273],{"mathvariant":2450},[2071,6837,2861],{},[2075,6839,2090],{"fence":2360},[2092,6841,6842],{"encoding":2094},"MR = TR'(Q) = D(Q) + Q\\,D'(Q) = P + Q\\frac{\\mathrm{d}P}{\\mathrm{d}Q} = P\\left(1 + \\frac{Q}{P}\\cdot\\frac{\\mathrm{d}P}{\\mathrm{d}Q}\\right)",[55,6844,6845],{},[1647,6846,6848],{"className":6847},[2059],[2061,6849,6850],{"xmlns":2063},[2065,6851,6852,6924],{},[2068,6853,6854,6856,6858,6900,6902,6904],{},[2075,6855,2077],{},[2071,6857,575],{},[2068,6859,6860,6862,6864,6866,6898],{},[2075,6861,2084],{"fence":2360},[2210,6863,638],{},[2075,6865,2176],{},[2403,6867,6868,6870],{},[2210,6869,638],{},[2068,6871,6872,6880,6882],{},[2400,6873,6874],{"scriptlevel":630,"displaystyle":2083},[2403,6875,6876,6878],{},[2071,6877,575],{},[2071,6879,2861],{},[2075,6881,3251],{},[2400,6883,6884],{"scriptlevel":630,"displaystyle":2083},[2403,6885,6886,6892],{},[2068,6887,6888,6890],{},[2071,6889,2273],{"mathvariant":2450},[2071,6891,2861],{},[2068,6893,6894,6896],{},[2071,6895,2273],{"mathvariant":2450},[2071,6897,575],{},[2075,6899,2090],{"fence":2360},[2075,6901,2077],{},[2071,6903,575],{},[2068,6905,6906,6908,6910,6912,6922],{},[2075,6907,2084],{"fence":2360},[2210,6909,638],{},[2075,6911,2176],{},[2403,6913,6914,6916],{},[2210,6915,638],{},[2068,6917,6918,6920],{},[2075,6919,2303],{},[2071,6921,554],{},[2075,6923,2090],{"fence":2360},[2092,6925,6926],{"encoding":2094},"= P\\left(1 + \\frac{1}{\\tfrac{P}{Q}\\cdot\\tfrac{\\mathrm{d}Q}{\\mathrm{d}P}}\\right) = P\\left(1 + \\frac{1}{-E}\\right)",[55,6928,6929],{},"a tedy",[55,6931,6932],{},[1647,6933,6935],{"className":6934,"title":4288,"style":4289},[4287],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1023,6937,6938,7007,7257],{},[55,6939,6940,6942,6943,6977,6978,6993,6994,2777],{},[1647,6941,4243],{}," Intuice: vztah ",[1647,6944,6946],{"className":6945},[2059],[2061,6947,6948],{"xmlns":2063},[2065,6949,6950,6974],{},[2068,6951,6952,6954,6956,6958,6960,6962,6964,6966,6968,6970,6972],{},[2071,6953,2890],{},[2071,6955,4082],{},[2075,6957,2077],{},[2071,6959,575],{},[2075,6961,2084],{"stretchy":2083},[2210,6963,638],{},[2075,6965,2303],{},[2210,6967,638],{},[2071,6969,4761],{"mathvariant":2450},[2071,6971,554],{},[2075,6973,2090],{"stretchy":2083},[2092,6975,6976],{"encoding":2094},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[1647,6979,6981],{"className":6980},[2059],[2061,6982,6983],{"xmlns":2063},[2065,6984,6985,6991],{},[2068,6986,6987,6989],{},[2071,6988,2890],{},[2071,6990,4082],{},[2092,6992,6721],{"encoding":2094}," jednoznačně určuje hodnota ",[1647,6995,6997],{"className":6996},[2059],[2061,6998,6999],{"xmlns":2063},[2065,7000,7001,7005],{},[2068,7002,7003],{},[2071,7004,554],{},[2092,7006,554],{"encoding":2094},[89,7008,7009,7119,7188],{},[92,7010,7011,7028,7029,1445,7043,1445,7069,1445,7082,7102,7103,7118],{},[1647,7012,7014],{"className":7013},[2059],[2061,7015,7016],{"xmlns":2063},[2065,7017,7018,7026],{},[2068,7019,7020,7022,7024],{},[2071,7021,554],{},[2075,7023,3482],{},[2210,7025,638],{},[2092,7027,4596],{"encoding":2094}," (elastická) ",[1647,7030,7032],{"className":7031},[2059],[2061,7033,7034],{"xmlns":2063},[2065,7035,7036,7040],{},[2068,7037,7038],{},[2075,7039,4075],{},[2092,7041,7042],{"encoding":2094},"\\Rightarrow",[1647,7044,7046],{"className":7045},[2059],[2061,7047,7048],{"xmlns":2063},[2065,7049,7050,7066],{},[2068,7051,7052,7054,7056,7058,7060,7062,7064],{},[2210,7053,638],{},[2075,7055,2303],{},[2210,7057,638],{},[2071,7059,4761],{"mathvariant":2450},[2071,7061,554],{},[2075,7063,3482],{},[2210,7065,630],{},[2092,7067,7068],{"encoding":2094},"1 - 1\u002FE > 0",[1647,7070,7072],{"className":7071},[2059],[2061,7073,7074],{"xmlns":2063},[2065,7075,7076,7080],{},[2068,7077,7078],{},[2075,7079,4075],{},[2092,7081,7042],{"encoding":2094},[1647,7083,7085],{"className":7084},[2059],[2061,7086,7087],{"xmlns":2063},[2065,7088,7089,7099],{},[2068,7090,7091,7093,7095,7097],{},[2071,7092,2890],{},[2071,7094,4082],{},[2075,7096,3482],{},[2210,7098,630],{},[2092,7100,7101],{"encoding":2094},"MR > 0"," — ",[1647,7104,7106],{"className":7105},[2059],[2061,7107,7108],{"xmlns":2063},[2065,7109,7110,7116],{},[2068,7111,7112,7114],{},[2071,7113,543],{},[2071,7115,4082],{},[2092,7117,4182],{"encoding":2094}," roste s množstvím, tj. klesá s cenou.",[92,7120,7121,7138,7139,1445,7152,7102,7172,7187],{},[1647,7122,7124],{"className":7123},[2059],[2061,7125,7126],{"xmlns":2063},[2065,7127,7128,7136],{},[2068,7129,7130,7132,7134],{},[2071,7131,554],{},[2075,7133,2077],{},[2210,7135,638],{},[2092,7137,4632],{"encoding":2094}," (jednotková) ",[1647,7140,7142],{"className":7141},[2059],[2061,7143,7144],{"xmlns":2063},[2065,7145,7146,7150],{},[2068,7147,7148],{},[2075,7149,4075],{},[2092,7151,7042],{"encoding":2094},[1647,7153,7155],{"className":7154},[2059],[2061,7156,7157],{"xmlns":2063},[2065,7158,7159,7169],{},[2068,7160,7161,7163,7165,7167],{},[2071,7162,2890],{},[2071,7164,4082],{},[2075,7166,2077],{},[2210,7168,630],{},[2092,7170,7171],{"encoding":2094},"MR = 0",[1647,7173,7175],{"className":7174},[2059],[2061,7176,7177],{"xmlns":2063},[2065,7178,7179,7185],{},[2068,7180,7181,7183],{},[2071,7182,543],{},[2071,7184,4082],{},[2092,7186,4182],{"encoding":2094}," je extrém (maximum).",[92,7189,7190,7207,7208,1445,7221,7102,7241,7256],{},[1647,7191,7193],{"className":7192},[2059],[2061,7194,7195],{"xmlns":2063},[2065,7196,7197,7205],{},[2068,7198,7199,7201,7203],{},[2071,7200,554],{},[2075,7202,3521],{},[2210,7204,638],{},[2092,7206,4614],{"encoding":2094}," (neelastická) ",[1647,7209,7211],{"className":7210},[2059],[2061,7212,7213],{"xmlns":2063},[2065,7214,7215,7219],{},[2068,7216,7217],{},[2075,7218,4075],{},[2092,7220,7042],{"encoding":2094},[1647,7222,7224],{"className":7223},[2059],[2061,7225,7226],{"xmlns":2063},[2065,7227,7228,7238],{},[2068,7229,7230,7232,7234,7236],{},[2071,7231,2890],{},[2071,7233,4082],{},[2075,7235,3521],{},[2210,7237,630],{},[2092,7239,7240],{"encoding":2094},"MR \u003C 0",[1647,7242,7244],{"className":7243},[2059],[2061,7245,7246],{"xmlns":2063},[2065,7247,7248,7254],{},[2068,7249,7250,7252],{},[2071,7251,543],{},[2071,7253,4082],{},[2092,7255,4182],{"encoding":2094}," klesá s množstvím, tj. roste s cenou.",[55,7258,7259,7260,195],{},"Viz také ",[69,7261,3906],{"className":7262,"dataFsResolvedFilePath":3022,"href":3023},[62],[609,7264,7266],{"id":7265},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[55,7268,7269,7289,7290,7316,7317,7332,7333,7346,7347,7360,7361,7374,7375,7391,7392,1445,7407,7410,7411,7391,7427,195],{},[95,7270,7271,7272,4007],{},"(a) Poptávka elastická (",[1647,7273,7275],{"className":7274},[2059],[2061,7276,7277],{"xmlns":2063},[2065,7278,7279,7287],{},[2068,7280,7281,7283,7285],{},[2071,7282,554],{},[2075,7284,3482],{},[2210,7286,638],{},[2092,7288,4596],{"encoding":2094}," Z (4.12) plyne ",[1647,7291,7293],{"className":7292},[2059],[2061,7294,7295],{"xmlns":2063},[2065,7296,7297,7313],{},[2068,7298,7299,7301,7303,7305,7307,7309,7311],{},[2071,7300,2890],{},[2071,7302,4082],{},[2075,7304,2084],{"stretchy":2083},[2071,7306,2861],{},[2075,7308,2090],{"stretchy":2083},[2075,7310,3482],{},[2210,7312,630],{},[2092,7314,7315],{"encoding":2094},"MR(Q) > 0",", a tedy celkový příjem ",[1647,7318,7320],{"className":7319},[2059],[2061,7321,7322],{"xmlns":2063},[2065,7323,7324,7330],{},[2068,7325,7326,7328],{},[2071,7327,543],{},[2071,7329,4082],{},[2092,7331,4182],{"encoding":2094}," je rostoucí funkcí ",[1647,7334,7336],{"className":7335},[2059],[2061,7337,7338],{"xmlns":2063},[2065,7339,7340,7344],{},[2068,7341,7342],{},[2071,7343,2861],{},[2092,7345,2861],{"encoding":2094},". Avšak růst ",[1647,7348,7350],{"className":7349},[2059],[2061,7351,7352],{"xmlns":2063},[2065,7353,7354,7358],{},[2068,7355,7356],{},[2071,7357,2861],{},[2092,7359,2861],{"encoding":2094}," je odezvou na pokles ceny ",[1647,7362,7364],{"className":7363},[2059],[2061,7365,7366],{"xmlns":2063},[2065,7367,7368,7372],{},[2068,7369,7370],{},[2071,7371,575],{},[2092,7373,575],{"encoding":2094},". Tudíž s ",[3982,7376,7377,7378],{},"poklesem ceny ",[1647,7379,7381],{"className":7380},[2059],[2061,7382,7383],{"xmlns":2063},[2065,7384,7385,7389],{},[2068,7386,7387],{},[2071,7388,575],{},[2092,7390,575],{"encoding":2094}," celkový příjem ",[1647,7393,7395],{"className":7394},[2059],[2061,7396,7397],{"xmlns":2063},[2065,7398,7399,7405],{},[2068,7400,7401,7403],{},[2071,7402,543],{},[2071,7404,4082],{},[2092,7406,4182],{"encoding":2094},[3982,7408,7409],{},"roste"," a s ",[3982,7412,7413,7414],{},"růstem ceny ",[1647,7415,7417],{"className":7416},[2059],[2061,7418,7419],{"xmlns":2063},[2065,7420,7421,7425],{},[2068,7422,7423],{},[2071,7424,575],{},[2092,7426,575],{"encoding":2094},[3982,7428,7429],{},"klesá",[1023,7431,7432],{},[55,7433,7434,7437],{},[95,7435,7436],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[55,7439,7440,7289,7460,835,7486,7501,7502,7515,7516,7529,7530,7543,7544,7391,7557,1445,7572,195],{},[95,7441,7442,7443,4007],{},"(b) Poptávka neelastická (",[1647,7444,7446],{"className":7445},[2059],[2061,7447,7448],{"xmlns":2063},[2065,7449,7450,7458],{},[2068,7451,7452,7454,7456],{},[2071,7453,554],{},[2075,7455,3521],{},[2210,7457,638],{},[2092,7459,4614],{"encoding":2094},[1647,7461,7463],{"className":7462},[2059],[2061,7464,7465],{"xmlns":2063},[2065,7466,7467,7483],{},[2068,7468,7469,7471,7473,7475,7477,7479,7481],{},[2071,7470,2890],{},[2071,7472,4082],{},[2075,7474,2084],{"stretchy":2083},[2071,7476,2861],{},[2075,7478,2090],{"stretchy":2083},[2075,7480,3521],{},[2210,7482,630],{},[2092,7484,7485],{"encoding":2094},"MR(Q) \u003C 0",[1647,7487,7489],{"className":7488},[2059],[2061,7490,7491],{"xmlns":2063},[2065,7492,7493,7499],{},[2068,7494,7495,7497],{},[2071,7496,543],{},[2071,7498,4082],{},[2092,7500,4182],{"encoding":2094}," je klesající funkce ",[1647,7503,7505],{"className":7504},[2059],[2061,7506,7507],{"xmlns":2063},[2065,7508,7509,7513],{},[2068,7510,7511],{},[2071,7512,2861],{},[2092,7514,2861],{"encoding":2094},", tj. s růstem ",[1647,7517,7519],{"className":7518},[2059],[2061,7520,7521],{"xmlns":2063},[2065,7522,7523,7527],{},[2068,7524,7525],{},[2071,7526,2861],{},[2092,7528,2861],{"encoding":2094}," (s poklesem ceny ",[1647,7531,7533],{"className":7532},[2059],[2061,7534,7535],{"xmlns":2063},[2065,7536,7537,7541],{},[2068,7538,7539],{},[2071,7540,575],{},[2092,7542,575],{"encoding":2094},") celkový příjem klesá. S růstem ceny ",[1647,7545,7547],{"className":7546},[2059],[2061,7548,7549],{"xmlns":2063},[2065,7550,7551,7555],{},[2068,7552,7553],{},[2071,7554,575],{},[2092,7556,575],{"encoding":2094},[1647,7558,7560],{"className":7559},[2059],[2061,7561,7562],{"xmlns":2063},[2065,7563,7564,7570],{},[2068,7565,7566,7568],{},[2071,7567,543],{},[2071,7569,4082],{},[2092,7571,4182],{"encoding":2094},[3982,7573,7409],{},[1023,7575,7576],{},[55,7577,7578,7581],{},[95,7579,7580],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[55,7583,7584,7289,7604,7623,7624,7639,7640,7710,7711,75,7739,7772,7773,5676,7801,7816,7817,195],{},[95,7585,7586,7587,4007],{},"(c) Jednotková elasticita (",[1647,7588,7590],{"className":7589},[2059],[2061,7591,7592],{"xmlns":2063},[2065,7593,7594,7602],{},[2068,7595,7596,7598,7600],{},[2071,7597,554],{},[2075,7599,2077],{},[2210,7601,638],{},[2092,7603,4632],{"encoding":2094},[1647,7605,7607],{"className":7606},[2059],[2061,7608,7609],{"xmlns":2063},[2065,7610,7611,7621],{},[2068,7612,7613,7615,7617,7619],{},[2071,7614,2890],{},[2071,7616,4082],{},[2075,7618,2077],{},[2210,7620,630],{},[2092,7622,7171],{"encoding":2094}," — nutná podmínka extrému ",[1647,7625,7627],{"className":7626},[2059],[2061,7628,7629],{"xmlns":2063},[2065,7630,7631,7637],{},[2068,7632,7633,7635],{},[2071,7634,543],{},[2071,7636,4082],{},[2092,7638,4182],{"encoding":2094},". Dále ",[1647,7641,7643],{"className":7642},[2059],[2061,7644,7645],{"xmlns":2063},[2065,7646,7647,7707],{},[2068,7648,7649,7651,7661,7663,7665,7671,7673,7679,7681,7683,7685,7687,7689,7691,7701,7703,7705],{},[2071,7650,543],{},[2205,7652,7653,7655],{},[2071,7654,4082],{},[2068,7656,7657,7659],{},[2075,7658,2452],{"mathvariant":2450},[2075,7660,2452],{"mathvariant":2450},[2075,7662,2077],{},[2071,7664,2890],{},[2205,7666,7667,7669],{},[2071,7668,4082],{},[2075,7670,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,7672,2077],{},[2205,7674,7675,7677],{},[2071,7676,4271],{},[2075,7678,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,7680,2084],{"stretchy":2083},[2071,7682,2861],{},[2075,7684,2090],{"stretchy":2083},[2075,7686,2176],{},[2071,7688,2861],{},[2363,7690,3061],{},[2205,7692,7693,7695],{},[2071,7694,4271],{},[2068,7696,7697,7699],{},[2075,7698,2452],{"mathvariant":2450},[2075,7700,2452],{"mathvariant":2450},[2075,7702,2084],{"stretchy":2083},[2071,7704,2861],{},[2075,7706,2090],{"stretchy":2083},[2092,7708,7709],{"encoding":2094},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[1647,7712,7714],{"className":7713},[2059],[2061,7715,7716],{"xmlns":2063},[2065,7717,7718,7736],{},[2068,7719,7720,7726,7728,7730,7732,7734],{},[2205,7721,7722,7724],{},[2071,7723,4271],{},[2075,7725,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,7727,2084],{"stretchy":2083},[2071,7729,2861],{},[2075,7731,2090],{"stretchy":2083},[2075,7733,3521],{},[2210,7735,630],{},[2092,7737,7738],{"encoding":2094},"D'(Q) \u003C 0",[1647,7740,7742],{"className":7741},[2059],[2061,7743,7744],{"xmlns":2063},[2065,7745,7746,7769],{},[2068,7747,7748,7758,7760,7762,7764,7767],{},[2205,7749,7750,7752],{},[2071,7751,4271],{},[2068,7753,7754,7756],{},[2075,7755,2452],{"mathvariant":2450},[2075,7757,2452],{"mathvariant":2450},[2075,7759,2084],{"stretchy":2083},[2071,7761,2861],{},[2075,7763,2090],{"stretchy":2083},[2075,7765,7766],{},"≤",[2210,7768,630],{},[2092,7770,7771],{"encoding":2094},"D''(Q) \\le 0",", odkud ",[1647,7774,7776],{"className":7775},[2059],[2061,7777,7778],{"xmlns":2063},[2065,7779,7780,7798],{},[2068,7781,7782,7784,7794,7796],{},[2071,7783,543],{},[2205,7785,7786,7788],{},[2071,7787,4082],{},[2068,7789,7790,7792],{},[2075,7791,2452],{"mathvariant":2450},[2075,7793,2452],{"mathvariant":2450},[2075,7795,3521],{},[2210,7797,630],{},[2092,7799,7800],{"encoding":2094},"TR'' \u003C 0",[1647,7802,7804],{"className":7803},[2059],[2061,7805,7806],{"xmlns":2063},[2065,7807,7808,7814],{},[2068,7809,7810,7812],{},[2071,7811,543],{},[2071,7813,4082],{},[2092,7815,4182],{"encoding":2094}," nabývá ",[95,7818,7819],{},"maxima",[1023,7821,7822],{},[55,7823,7824,7827],{},[95,7825,7826],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[55,7829,7830],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[55,7832,7833],{},[95,7834,7835],{},"Souhrnná tabulka Pravidel 1–3:",[323,7837,7838,7942],{},[326,7839,7840],{},[329,7841,7842,7845,7860,7877,7908,7939],{},[332,7843,7844],{},"Charakter poptávky",[332,7846,7847],{},[1647,7848,7850],{"className":7849},[2059],[2061,7851,7852],{"xmlns":2063},[2065,7853,7854,7858],{},[2068,7855,7856],{},[2071,7857,554],{},[2092,7859,554],{"encoding":2094},[332,7861,7862],{},[1647,7863,7865],{"className":7864},[2059],[2061,7866,7867],{"xmlns":2063},[2065,7868,7869,7875],{},[2068,7870,7871,7873],{},[2071,7872,2890],{},[2071,7874,4082],{},[2092,7876,6721],{"encoding":2094},[332,7878,7879,7880,1445,7893],{},"Pokles ceny ",[1647,7881,7883],{"className":7882},[2059],[2061,7884,7885],{"xmlns":2063},[2065,7886,7887,7891],{},[2068,7888,7889],{},[2075,7890,4075],{},[2092,7892,7042],{"encoding":2094},[1647,7894,7896],{"className":7895},[2059],[2061,7897,7898],{"xmlns":2063},[2065,7899,7900,7906],{},[2068,7901,7902,7904],{},[2071,7903,543],{},[2071,7905,4082],{},[2092,7907,4182],{"encoding":2094},[332,7909,7910,7911,1445,7924],{},"Růst ceny ",[1647,7912,7914],{"className":7913},[2059],[2061,7915,7916],{"xmlns":2063},[2065,7917,7918,7922],{},[2068,7919,7920],{},[2075,7921,4075],{},[2092,7923,7042],{"encoding":2094},[1647,7925,7927],{"className":7926},[2059],[2061,7928,7929],{"xmlns":2063},[2065,7930,7931,7937],{},[2068,7932,7933,7935],{},[2071,7934,543],{},[2071,7936,4082],{},[2092,7938,4182],{"encoding":2094},[332,7940,7941],{},"Doporučení",[342,7943,7944,7993,8043],{},[329,7945,7946,7948,7966,7984,7986,7988],{},[347,7947,4161],{},[347,7949,7950],{},[1647,7951,7953],{"className":7952},[2059],[2061,7954,7955],{"xmlns":2063},[2065,7956,7957,7963],{},[2068,7958,7959,7961],{},[2075,7960,3482],{},[2210,7962,638],{},[2092,7964,7965],{"encoding":2094},"> 1",[347,7967,7968],{},[1647,7969,7971],{"className":7970},[2059],[2061,7972,7973],{"xmlns":2063},[2065,7974,7975,7981],{},[2068,7976,7977,7979],{},[2075,7978,3482],{},[2210,7980,630],{},[2092,7982,7983],{"encoding":2094},"> 0",[347,7985,7409],{},[347,7987,7429],{},[347,7989,7990],{},[95,7991,7992],{},"snížit cenu",[329,7994,7995,7998,8016,8034,8036,8038],{},[347,7996,7997],{},"jednotková",[347,7999,8000],{},[1647,8001,8003],{"className":8002},[2059],[2061,8004,8005],{"xmlns":2063},[2065,8006,8007,8013],{},[2068,8008,8009,8011],{},[2075,8010,2077],{},[2210,8012,638],{},[2092,8014,8015],{"encoding":2094},"= 1",[347,8017,8018],{},[1647,8019,8021],{"className":8020},[2059],[2061,8022,8023],{"xmlns":2063},[2065,8024,8025,8031],{},[2068,8026,8027,8029],{},[2075,8028,2077],{},[2210,8030,630],{},[2092,8032,8033],{"encoding":2094},"= 0",[347,8035,3791],{},[347,8037,3791],{},[347,8039,8040],{},[95,8041,8042],{},"držet cenu",[329,8044,8045,8047,8065,8083,8085,8087],{},[347,8046,4165],{},[347,8048,8049],{},[1647,8050,8052],{"className":8051},[2059],[2061,8053,8054],{"xmlns":2063},[2065,8055,8056,8062],{},[2068,8057,8058,8060],{},[2075,8059,3521],{},[2210,8061,638],{},[2092,8063,8064],{"encoding":2094},"\u003C 1",[347,8066,8067],{},[1647,8068,8070],{"className":8069},[2059],[2061,8071,8072],{"xmlns":2063},[2065,8073,8074,8080],{},[2068,8075,8076,8078],{},[2075,8077,3521],{},[2210,8079,630],{},[2092,8081,8082],{"encoding":2094},"\u003C 0",[347,8084,7429],{},[347,8086,7409],{},[347,8088,8089],{},[95,8090,8091],{},"zvýšit cenu",[609,8093,8095],{"id":8094},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[55,8097,8098,8099,8124,8125,8147,8148,8161,8162,8175,8176,8189,8190,5676,8217,8269],{},"Aplikujme pravidla 1–3 pro poptávku ",[1647,8100,8102],{"className":8101},[2059],[2061,8103,8104],{"xmlns":2063},[2065,8105,8106,8122],{},[2068,8107,8108,8110,8112,8114,8116],{},[2071,8109,575],{},[2075,8111,2077],{},[2210,8113,3164],{},[2075,8115,2303],{},[2205,8117,8118,8120],{},[2071,8119,2861],{},[2210,8121,646],{},[2092,8123,5546],{"encoding":2094},". Reálné cenové rozpětí je ",[1647,8126,8128],{"className":8127},[2059],[2061,8129,8130],{"xmlns":2063},[2065,8131,8132,8144],{},[2068,8133,8134,8136,8138,8140,8142],{},[2075,8135,5411],{"stretchy":2083},[2210,8137,638],{},[2075,8139,2361],{"separator":2360},[2210,8141,3164],{},[2075,8143,5428],{"stretchy":2083},[2092,8145,8146],{"encoding":2094},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[1647,8149,8151],{"className":8150},[2059],[2061,8152,8153],{"xmlns":2063},[2065,8154,8155,8159],{},[2068,8156,8157],{},[2071,8158,2861],{},[2092,8160,2861],{"encoding":2094}," jako funkci ",[1647,8163,8165],{"className":8164},[2059],[2061,8166,8167],{"xmlns":2063},[2065,8168,8169,8173],{},[2068,8170,8171],{},[2071,8172,575],{},[2092,8174,575],{"encoding":2094},"; pro nezáporné ",[1647,8177,8179],{"className":8178},[2059],[2061,8180,8181],{"xmlns":2063},[2065,8182,8183,8187],{},[2068,8184,8185],{},[2071,8186,2861],{},[2092,8188,2861],{"encoding":2094}," je ",[1647,8191,8193],{"className":8192},[2059],[2061,8194,8195],{"xmlns":2063},[2065,8196,8197,8214],{},[2068,8198,8199,8201,8203],{},[2071,8200,2861],{},[2075,8202,2077],{},[8204,8205,8206],"msqrt",{},[2068,8207,8208,8210,8212],{},[2210,8209,3164],{},[2075,8211,2303],{},[2071,8213,575],{},[2092,8215,8216],{"encoding":2094},"Q = \\sqrt{100 - P}",[1647,8218,8220],{"className":8219},[2059],[2061,8221,8222],{"xmlns":2063},[2065,8223,8224,8266],{},[2068,8225,8226,8242,8244,8246],{},[2400,8227,8228],{"scriptlevel":630,"displaystyle":2360},[2403,8229,8230,8236],{},[2068,8231,8232,8234],{},[2071,8233,2273],{"mathvariant":2450},[2071,8235,2861],{},[2068,8237,8238,8240],{},[2071,8239,2273],{"mathvariant":2450},[2071,8241,575],{},[2075,8243,2077],{},[2075,8245,2303],{},[2400,8247,8248],{"scriptlevel":630,"displaystyle":2360},[2403,8249,8250,8252],{},[2210,8251,638],{},[2068,8253,8254,8256],{},[2210,8255,646],{},[8204,8257,8258],{},[2068,8259,8260,8262,8264],{},[2210,8261,3164],{},[2075,8263,2303],{},[2071,8265,575],{},[2092,8267,8268],{"encoding":2094},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[55,8271,8272],{},[1647,8273,8275],{"className":8274},[2059],[2061,8276,8277],{"xmlns":2063},[2065,8278,8279,8401],{},[2068,8280,8281,8283,8285,8287,8289,8291,8293,8299,8301,8315,8317,8319,8333,8335,8361,8363,8381,8383,8399],{},[2071,8282,554],{},[2075,8284,2084],{"stretchy":2083},[2071,8286,575],{},[2075,8288,2090],{"stretchy":2083},[2075,8290,2077],{},[2075,8292,2303],{},[2403,8294,8295,8297],{},[2071,8296,575],{},[2071,8298,2861],{},[2075,8300,3251],{},[2403,8302,8303,8309],{},[2068,8304,8305,8307],{},[2071,8306,2273],{"mathvariant":2450},[2071,8308,2861],{},[2068,8310,8311,8313],{},[2071,8312,2273],{"mathvariant":2450},[2071,8314,575],{},[2075,8316,2077],{},[2075,8318,2303],{},[2403,8320,8321,8323],{},[2071,8322,575],{},[8204,8324,8325],{},[2068,8326,8327,8329,8331],{},[2210,8328,3164],{},[2075,8330,2303],{},[2071,8332,575],{},[2075,8334,3251],{},[2068,8336,8337,8339,8341,8359],{},[2075,8338,2084],{"fence":2360},[2075,8340,2303],{},[2403,8342,8343,8345],{},[2210,8344,638],{},[2068,8346,8347,8349],{},[2210,8348,646],{},[8204,8350,8351],{},[2068,8352,8353,8355,8357],{},[2210,8354,3164],{},[2075,8356,2303],{},[2071,8358,575],{},[2075,8360,2090],{"fence":2360},[2075,8362,2077],{},[2403,8364,8365,8367],{},[2071,8366,575],{},[2068,8368,8369,8371,8373,8375,8377,8379],{},[2210,8370,646],{},[2075,8372,2084],{"stretchy":2083},[2210,8374,3164],{},[2075,8376,2303],{},[2071,8378,575],{},[2075,8380,2090],{"stretchy":2083},[2075,8382,2077],{},[2403,8384,8385,8391],{},[2068,8386,8387,8389],{},[2210,8388,5096],{},[2071,8390,575],{},[2068,8392,8393,8395,8397],{},[2210,8394,3164],{},[2075,8396,2303],{},[2071,8398,575],{},[2071,8400,195],{"mathvariant":2450},[2092,8402,8403],{"encoding":2094},"E(P) = -\\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{\\sqrt{100-P}}\\cdot\\left(-\\frac{1}{2\\sqrt{100-P}}\\right) = \\frac{P}{2(100-P)} = \\frac{0{,}5P}{100-P}.",[55,8405,8406,8407,2777],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[1647,8408,8410],{"className":8409},[2059],[2061,8411,8412],{"xmlns":2063},[2065,8413,8414,8438],{},[2068,8415,8416,8434,8436],{},[2400,8417,8418],{"scriptlevel":630,"displaystyle":2360},[2403,8419,8420,8426],{},[2068,8421,8422,8424],{},[2210,8423,5096],{},[2071,8425,575],{},[2068,8427,8428,8430,8432],{},[2210,8429,3164],{},[2075,8431,2303],{},[2071,8433,575],{},[2075,8435,2077],{},[2210,8437,638],{},[2092,8439,8440],{"encoding":2094},"\\dfrac{0{,}5P}{100-P} = 1",[55,8442,8443],{},[1647,8444,8446],{"className":8445},[2059],[2061,8447,8448],{"xmlns":2063},[2065,8449,8450,8482],{},[2068,8451,8452,8458,8460,8467,8469,8472,8480],{},[2205,8453,8454,8456],{},[2071,8455,575],{},[2075,8457,4441],{},[2075,8459,2077],{},[2403,8461,8462,8465],{},[2210,8463,8464],{},"200",[2210,8466,654],{},[2075,8468,5987],{},[2210,8470,8471],{},"66,",[8473,8474,8475,8477],"mover",{"accent":2360},[2210,8476,678],{},[2075,8478,8479],{"stretchy":2360},"‾",[2071,8481,195],{"mathvariant":2450},[2092,8483,8484],{"encoding":2094},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[55,8486,8487],{},"S využitím vlastnosti (4.8):",[89,8489,8490,8536,8578],{},[92,8491,8492,8493,8528,8529,8531,8532,8535],{},"Při cenách ",[1647,8494,8496],{"className":8495},[2059],[2061,8497,8498],{"xmlns":2063},[2065,8499,8500,8525],{},[2068,8501,8502,8504,8506,8508,8510,8513,8515,8517,8523],{},[2071,8503,575],{},[2075,8505,6593],{},[2075,8507,5411],{"stretchy":2083},[2210,8509,638],{},[2075,8511,8512],{"separator":2360},";",[2363,8514,3061],{},[2210,8516,8471],{},[8473,8518,8519,8521],{"accent":2360},[2210,8520,678],{},[2075,8522,8479],{"stretchy":2360},[2075,8524,2090],{"stretchy":2083},[2092,8526,8527],{"encoding":2094},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[95,8530,4165],{}," — dle ",[3982,8533,8534],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[92,8537,8492,8538,8528,8572,8531,8574,8577],{},[1647,8539,8541],{"className":8540},[2059],[2061,8542,8543],{"xmlns":2063},[2065,8544,8545,8569],{},[2068,8546,8547,8549,8551,8553,8555,8561,8563,8565,8567],{},[2071,8548,575],{},[2075,8550,6593],{},[2075,8552,2084],{"stretchy":2083},[2210,8554,8471],{},[8473,8556,8557,8559],{"accent":2360},[2210,8558,678],{},[2075,8560,8479],{"stretchy":2360},[2075,8562,8512],{"separator":2360},[2363,8564,3061],{},[2210,8566,3164],{},[2075,8568,5428],{"stretchy":2083},[2092,8570,8571],{"encoding":2094},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[95,8573,4161],{},[3982,8575,8576],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[92,8579,8580,8581,8584,8585,8613,8614,8617],{},"Dle ",[3982,8582,8583],{},"Pravidla 3"," je při ceně ",[1647,8586,8588],{"className":8587},[2059],[2061,8589,8590],{"xmlns":2063},[2065,8591,8592,8610],{},[2068,8593,8594,8600,8602,8604],{},[2205,8595,8596,8598],{},[2071,8597,575],{},[2075,8599,4441],{},[2075,8601,2077],{},[2210,8603,8471],{},[8473,8605,8606,8608],{"accent":2360},[2210,8607,678],{},[2075,8609,8479],{"stretchy":2360},[2092,8611,8612],{"encoding":2094},"P^* = 66{,}\\overline{6}"," dosaženo ",[95,8615,8616],{},"maxima celkového příjmu"," ve výši",[55,8619,8620],{},[1647,8621,8623],{"className":8622},[2059],[2061,8624,8625],{"xmlns":2063},[2065,8626,8627,8705],{},[2068,8628,8629,8631,8633,8635,8641,8643,8645,8651,8653,8667,8669,8675,8677,8685,8687,8700,8702],{},[2071,8630,543],{},[2071,8632,4082],{},[2075,8634,2084],{"stretchy":2083},[2205,8636,8637,8639],{},[2071,8638,575],{},[2075,8640,4441],{},[2075,8642,2090],{"stretchy":2083},[2075,8644,2077],{},[2205,8646,8647,8649],{},[2071,8648,575],{},[2075,8650,4441],{},[2075,8652,3251],{},[8204,8654,8655],{},[2068,8656,8657,8659,8661],{},[2210,8658,3164],{},[2075,8660,2303],{},[2205,8662,8663,8665],{},[2071,8664,575],{},[2075,8666,4441],{},[2075,8668,2077],{},[2403,8670,8671,8673],{},[2210,8672,8464],{},[2210,8674,654],{},[2075,8676,3251],{},[8204,8678,8679],{},[2403,8680,8681,8683],{},[2210,8682,3164],{},[2210,8684,654],{},[2075,8686,2077],{},[2403,8688,8689,8692],{},[2210,8690,8691],{},"2000",[2068,8693,8694,8696],{},[2210,8695,654],{},[8204,8697,8698],{},[2210,8699,654],{},[2075,8701,5987],{},[2210,8703,8704],{},"384,9.",[2092,8706,8707],{"encoding":2094},"TR(P^*) = P^*\\cdot\\sqrt{100 - P^*} = \\frac{200}{3}\\cdot\\sqrt{\\frac{100}{3}} = \\frac{2000}{3\\sqrt{3}} \\doteq 384{,}9.",[55,8709,8710,8711,195],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[1647,8712,8714],{"className":8713},[2059],[2061,8715,8716],{"xmlns":2063},[2065,8717,8718,8724],{},[2068,8719,8720,8722],{},[2071,8721,543],{},[2071,8723,4082],{},[2092,8725,4182],{"encoding":2094},[84,8727,8729],{"id":8728},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[55,8731,8732,8733,8736],{},"Analogicky se definuje ",[95,8734,8735],{},"cenová elasticita nabídky"," (price elasticity of supply):",[55,8738,8739],{},[1647,8740,8742],{"className":8741,"title":4288,"style":4289},[4287],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[55,8744,4397,8745,8769,8770,8802],{},[1647,8746,8748],{"className":8747},[2059],[2061,8749,8750],{"xmlns":2063},[2065,8751,8752,8766],{},[2068,8753,8754,8756,8758,8760,8762,8764],{},[2071,8755,2861],{},[2075,8757,2077],{},[2071,8759,532],{},[2075,8761,2084],{"stretchy":2083},[2071,8763,575],{},[2075,8765,2090],{"stretchy":2083},[2092,8767,8768],{"encoding":2094},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[1647,8771,8773],{"className":8772},[2059],[2061,8774,8775],{"xmlns":2063},[2065,8776,8777,8799],{},[2068,8778,8779,8795,8797],{},[2400,8780,8781],{"scriptlevel":630,"displaystyle":2360},[2403,8782,8783,8789],{},[2068,8784,8785,8787],{},[2071,8786,2273],{"mathvariant":2450},[2071,8788,2861],{},[2068,8790,8791,8793],{},[2071,8792,2273],{"mathvariant":2450},[2071,8794,575],{},[2075,8796,3482],{},[2210,8798,630],{},[2092,8800,8801],{"encoding":2094},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[55,8804,8805],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1023,8807,8808],{},[55,8809,8810,8811],{},"S rostoucí cenou elasticita nabídky roste. ",[1647,8812,8814],{"className":8813},[2059],[2061,8815,8816],{"xmlns":2063},[2065,8817,8818,8827],{},[2068,8819,8820,8822,8825],{},[2075,8821,2084],{"stretchy":2083},[2210,8823,8824],{},"4.14",[2075,8826,2090],{"stretchy":2083},[2092,8828,8829],{"encoding":2094},"(4.14)",[55,8831,8832],{},"Pro nominální změny platí",[55,8834,8835],{},[1647,8836,8838],{"className":8837,"title":4288,"style":4289},[4287],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[55,8840,8841],{},"a pro procentní změny",[55,8843,8844],{},[1647,8845,8847],{"className":8846,"title":4288,"style":4289},[4287],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[55,8849,8850],{},"(bez znaménka minus).",[609,8852,8854],{"id":8853},"příklad-47","Příklad 4.7",[55,8856,8857,8858,2777],{},"Nabídka ",[1647,8859,8861],{"className":8860},[2059],[2061,8862,8863],{"xmlns":2063},[2065,8864,8865,8890],{},[2068,8866,8867,8869,8871,8873,8879,8881,8883,8885,8887],{},[2071,8868,2861],{},[2075,8870,2077],{},[2210,8872,2866],{},[2205,8874,8875,8877],{},[2071,8876,575],{},[2210,8878,646],{},[2075,8880,2176],{},[2210,8882,670],{},[2071,8884,575],{},[2075,8886,2176],{},[2210,8888,8889],{},"150",[2092,8891,8892],{"encoding":2094},"Q = 0{,}1P^2 + 5P + 150",[55,8894,8895],{},[1647,8896,8898],{"className":8897},[2059],[2061,8899,8900],{"xmlns":2063},[2065,8901,8902,8948],{},[2068,8903,8904,8906,8908,8932,8934,8936,8938,8940,8942,8944,8946],{},[2071,8905,554],{},[2075,8907,2077],{},[2403,8909,8910,8912],{},[2071,8911,575],{},[2068,8913,8914,8916,8922,8924,8926,8928,8930],{},[2210,8915,2866],{},[2205,8917,8918,8920],{},[2071,8919,575],{},[2210,8921,646],{},[2075,8923,2176],{},[2210,8925,670],{},[2071,8927,575],{},[2075,8929,2176],{},[2210,8931,8889],{},[2363,8933,3061],{},[2075,8935,2084],{"stretchy":2083},[2210,8937,2911],{},[2071,8939,575],{},[2075,8941,2176],{},[2210,8943,670],{},[2075,8945,2090],{"stretchy":2083},[2071,8947,195],{"mathvariant":2450},[2092,8949,8950],{"encoding":2094},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[55,8952,5204,8953,835,8983,835,9010,9046,9047,9072,9073,9091,9092,195],{},[1647,8954,8956],{"className":8955},[2059],[2061,8957,8958],{"xmlns":2063},[2065,8959,8960,8980],{},[2068,8961,8962,8964,8966,8968,8970,8972],{},[2071,8963,554],{},[2075,8965,2084],{"stretchy":2083},[2210,8967,2935],{},[2075,8969,2090],{"stretchy":2083},[2075,8971,2077],{},[2400,8973,8974],{"scriptlevel":630,"displaystyle":2083},[2403,8975,8976,8978],{},[2210,8977,638],{},[2210,8979,654],{},[2092,8981,8982],{"encoding":2094},"E(10) = \\tfrac{1}{3}",[1647,8984,8986],{"className":8985},[2059],[2061,8987,8988],{"xmlns":2063},[2065,8989,8990,9007],{},[2068,8991,8992,8994,8996,9001,9003,9005],{},[2071,8993,554],{},[2075,8995,2084],{"stretchy":2083},[8204,8997,8998],{},[2210,8999,9000],{},"1500",[2075,9002,2090],{"stretchy":2083},[2075,9004,2077],{},[2210,9006,638],{},[2092,9008,9009],{"encoding":2094},"E(\\sqrt{1500}) = 1",[1647,9011,9013],{"className":9012},[2059],[2061,9014,9015],{"xmlns":2063},[2065,9016,9017,9043],{},[2068,9018,9019,9021,9023,9025,9027,9029,9038,9040],{},[2071,9020,554],{},[2075,9022,2084],{"stretchy":2083},[2210,9024,3164],{},[2075,9026,2090],{"stretchy":2083},[2075,9028,2077],{},[2400,9030,9031],{"scriptlevel":630,"displaystyle":2083},[2403,9032,9033,9035],{},[2210,9034,3194],{},[2210,9036,9037],{},"33",[2075,9039,5987],{},[2210,9041,9042],{},"1,515",[2092,9044,9045],{"encoding":2094},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[1647,9048,9050],{"className":9049},[2059],[2061,9051,9052],{"xmlns":2063},[2065,9053,9054,9069],{},[2068,9055,9056,9058,9060,9064,9066],{},[2071,9057,575],{},[2075,9059,3482],{},[8204,9061,9062],{},[2210,9063,9000],{},[2075,9065,2803],{},[2210,9067,9068],{},"38,7",[2092,9070,9071],{"encoding":2094},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[1647,9074,9076],{"className":9075},[2059],[2061,9077,9078],{"xmlns":2063},[2065,9079,9080,9088],{},[2068,9081,9082,9084,9086],{},[2071,9083,575],{},[2075,9085,3521],{},[2210,9087,9068],{},[2092,9089,9090],{"encoding":2094},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[1647,9093,9095],{"className":9094},[2059],[2061,9096,9097],{"xmlns":2063},[2065,9098,9099,9137],{},[2068,9100,9101,9103,9105,9107,9109,9117,9119,9122,9124,9127,9133,9135],{},[2071,9102,2961],{"mathvariant":2450},[2071,9104,2861],{},[2071,9106,6012],{"mathvariant":2450},[2075,9108,2803],{},[2400,9110,9111],{"scriptlevel":630,"displaystyle":2083},[2403,9112,9113,9115],{},[2210,9114,638],{},[2210,9116,654],{},[2075,9118,3251],{},[2210,9120,9121],{},"20",[2075,9123,2077],{},[2210,9125,9126],{},"6,",[8473,9128,9129,9131],{"accent":2360},[2210,9130,678],{},[2075,9132,8479],{"stretchy":2360},[2363,9134,3061],{},[2071,9136,6012],{"mathvariant":2450},[2092,9138,9139],{"encoding":2094},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[84,9141,9143],{"id":9142},"vícefaktorový-model","Vícefaktorový model",[55,9145,9146,9147,9160,9161,1445,9164,9177,9178,1445,9181,9199,9200,1445,9203,2777],{},"Předpokládejme, že poptávané množství ",[1647,9148,9150],{"className":9149},[2059],[2061,9151,9152],{"xmlns":2063},[2065,9153,9154,9158],{},[2068,9155,9156],{},[2071,9157,2861],{},[2092,9159,2861],{"encoding":2094}," závisí na ",[95,9162,9163],{},"ceně základního zboží",[1647,9165,9167],{"className":9166},[2059],[2061,9168,9169],{"xmlns":2063},[2065,9170,9171,9175],{},[2068,9172,9173],{},[2071,9174,575],{},[2092,9176,575],{"encoding":2094},", na ",[95,9179,9180],{},"ceně alternativního zboží",[1647,9182,9184],{"className":9183},[2059],[2061,9185,9186],{"xmlns":2063},[2065,9187,9188,9196],{},[2068,9189,9190],{},[2348,9191,9192,9194],{},[2071,9193,575],{},[2071,9195,4342],{},[2092,9197,9198],{"encoding":2094},"P_A"," a na ",[95,9201,9202],{},"důchodu",[1647,9204,9206],{"className":9205},[2059],[2061,9207,9208],{"xmlns":2063},[2065,9209,9210,9215],{},[2068,9211,9212],{},[2071,9213,9214],{},"Y",[2092,9216,9214],{"encoding":2094},[55,9218,9219],{},[1647,9220,9222],{"className":9221,"title":4288,"style":4289},[4287],"Q = D(P, P_A, Y). \\tag{4.17}",[55,9224,9225,9226,9229],{},"V analogii jednofaktorového modelu pracujeme s ",[95,9227,9228],{},"parciálními derivacemi"," funkce poptávky.",[609,9231,9233],{"id":9232},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[55,9235,9236],{},[1647,9237,9239],{"className":9238,"title":4288,"style":4289},[4287],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[55,9241,4397,9242,9263,9264,9277,9278,2999,9300,1445,9303,9349,9350,9363,9364,9381],{},[1647,9243,9245],{"className":9244},[2059],[2061,9246,9247],{"xmlns":2063},[2065,9248,9249,9260],{},[2068,9250,9251],{},[9252,9253,9254,9256,9258],"msubsup",{},[2071,9255,2861],{},[2071,9257,575],{},[2075,9259,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,9261,9262],{"encoding":2094},"Q'_P"," je parciální derivace (4.17) podle ",[1647,9265,9267],{"className":9266},[2059],[2061,9268,9269],{"xmlns":2063},[2065,9270,9271,9275],{},[2068,9272,9273],{},[2071,9274,575],{},[2092,9276,575],{"encoding":2094},". Vždy ",[1647,9279,9281],{"className":9280},[2059],[2061,9282,9283],{"xmlns":2063},[2065,9284,9285,9297],{},[2068,9286,9287,9293,9295],{},[2348,9288,9289,9291],{},[2071,9290,554],{},[2071,9292,575],{},[2075,9294,4572],{},[2210,9296,630],{},[2092,9298,9299],{"encoding":2094},"E_P \\ge 0",[3982,9301,9302],{},"Interpretace:",[1647,9304,9306],{"className":9305},[2059],[2061,9307,9308],{"xmlns":2063},[2065,9309,9310,9346],{},[2068,9311,9312,9318,9320,9326,9328,9336,9338,9344],{},[2348,9313,9314,9316],{},[2071,9315,554],{},[2071,9317,575],{},[2075,9319,2084],{"stretchy":2083},[2205,9321,9322,9324],{},[2071,9323,575],{},[2075,9325,4441],{},[2075,9327,2361],{"separator":2360},[9252,9329,9330,9332,9334],{},[2071,9331,575],{},[2071,9333,4342],{},[2075,9335,4441],{},[2075,9337,2361],{"separator":2360},[2205,9339,9340,9342],{},[2071,9341,9214],{},[2075,9343,4441],{},[2075,9345,2090],{"stretchy":2083},[2092,9347,9348],{"encoding":2094},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[1647,9351,9353],{"className":9352},[2059],[2061,9354,9355],{"xmlns":2063},[2065,9356,9357,9361],{},[2068,9358,9359],{},[2071,9360,2861],{},[2092,9362,2861],{"encoding":2094}," při 1% změně ",[1647,9365,9367],{"className":9366},[2059],[2061,9368,9369],{"xmlns":2063},[2065,9370,9371,9379],{},[2068,9372,9373],{},[2205,9374,9375,9377],{},[2071,9376,575],{},[2075,9378,4441],{},[2092,9380,4491],{"encoding":2094},", ceteris paribus.",[609,9383,9385],{"id":9384},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[55,9387,9388],{},[1647,9389,9391],{"className":9390,"title":4288,"style":4289},[4287],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[55,9393,9394,9349,9396,9409,9410,9427],{},[3982,9395,9302],{},[1647,9397,9399],{"className":9398},[2059],[2061,9400,9401],{"xmlns":2063},[2065,9402,9403,9407],{},[2068,9404,9405],{},[2071,9406,2861],{},[2092,9408,2861],{"encoding":2094}," základního zboží při 1% změně ceny ",[1647,9411,9413],{"className":9412},[2059],[2061,9414,9415],{"xmlns":2063},[2065,9416,9417,9425],{},[2068,9418,9419],{},[2348,9420,9421,9423],{},[2071,9422,575],{},[2071,9424,4342],{},[2092,9426,9198],{"encoding":2094}," alternativního zboží (ceteris paribus).",[55,9429,9430],{},[95,9431,9432],{},"Znaménko závisí na povaze alternativního zboží:",[89,9434,9435,9523],{},[92,9436,9437,9438,9441,9442,9459,9460,1445,9473,195],{},"Je-li alternativní zboží ",[95,9439,9440],{},"komplement",", růst ",[1647,9443,9445],{"className":9444},[2059],[2061,9446,9447],{"xmlns":2063},[2065,9448,9449,9457],{},[2068,9450,9451],{},[2348,9452,9453,9455],{},[2071,9454,575],{},[2071,9456,4342],{},[2092,9458,9198],{"encoding":2094}," způsobí zdražení dvojice, pokles ",[1647,9461,9463],{"className":9462},[2059],[2061,9464,9465],{"xmlns":2063},[2065,9466,9467,9471],{},[2068,9468,9469],{},[2071,9470,2861],{},[2092,9472,2861],{"encoding":2094},[1647,9474,9476],{"className":9475},[2059],[2061,9477,9478],{"xmlns":2063},[2065,9479,9480,9520],{},[2068,9481,9482,9484,9486,9498,9500,9502,9504,9506,9516,9518],{},[2075,9483,4075],{},[2363,9485,4072],{},[9252,9487,9488,9490,9496],{},[2071,9489,2861],{},[2348,9491,9492,9494],{},[2071,9493,575],{},[2071,9495,4342],{},[2075,9497,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,9499,3521],{},[2210,9501,630],{},[2075,9503,2361],{"separator":2360},[2363,9505,4072],{},[2348,9507,9508,9510],{},[2071,9509,554],{},[2348,9511,9512,9514],{},[2071,9513,575],{},[2071,9515,4342],{},[2075,9517,3521],{},[2210,9519,630],{},[2092,9521,9522],{"encoding":2094},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[92,9524,9437,9525,9441,9528,9545,9546,9559,9560,195],{},[95,9526,9527],{},"substitut",[1647,9529,9531],{"className":9530},[2059],[2061,9532,9533],{"xmlns":2063},[2065,9534,9535,9543],{},[2068,9536,9537],{},[2348,9538,9539,9541],{},[2071,9540,575],{},[2071,9542,4342],{},[2092,9544,9198],{"encoding":2094}," učiní základní zboží relativně levnější, zájem se přesune, ",[1647,9547,9549],{"className":9548},[2059],[2061,9550,9551],{"xmlns":2063},[2065,9552,9553,9557],{},[2068,9554,9555],{},[2071,9556,2861],{},[2092,9558,2861],{"encoding":2094}," roste ",[1647,9561,9563],{"className":9562},[2059],[2061,9564,9565],{"xmlns":2063},[2065,9566,9567,9607],{},[2068,9568,9569,9571,9573,9585,9587,9589,9591,9593,9603,9605],{},[2075,9570,4075],{},[2363,9572,4072],{},[9252,9574,9575,9577,9583],{},[2071,9576,2861],{},[2348,9578,9579,9581],{},[2071,9580,575],{},[2071,9582,4342],{},[2075,9584,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,9586,3482],{},[2210,9588,630],{},[2075,9590,2361],{"separator":2360},[2363,9592,4072],{},[2348,9594,9595,9597],{},[2071,9596,554],{},[2348,9598,9599,9601],{},[2071,9600,575],{},[2071,9602,4342],{},[2075,9604,3482],{},[2210,9606,630],{},[2092,9608,9609],{"encoding":2094},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[1647,9611,9614],{"className":9612,"title":9613,"style":4289},[4287],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":156,"searchDepth":7,"depth":7,"links":9616},[9617,9621,9622,9630,9631,9635,9638],{"id":3976,"depth":7,"text":3977,"children":9618},[9619,9620],{"id":4010,"depth":4,"text":4011},{"id":4190,"depth":4,"text":4191},{"id":4225,"depth":7,"text":4226},{"id":4251,"depth":7,"text":4252,"children":9623},[9624,9625,9626,9627,9629],{"id":4946,"depth":4,"text":4947},{"id":5036,"depth":4,"text":5037},{"id":5372,"depth":4,"text":5373},{"id":5454,"depth":4,"text":9628},"Výpočet, je-li dáno PP jako funkce QQ",{"id":5715,"depth":4,"text":5716},{"id":6040,"depth":7,"text":6041},{"id":6636,"depth":7,"text":6637,"children":9632},[9633,9634],{"id":7265,"depth":4,"text":7266},{"id":8094,"depth":4,"text":8095},{"id":8728,"depth":7,"text":8729,"children":9636},[9637],{"id":8853,"depth":4,"text":8854},{"id":9142,"depth":7,"text":9143,"children":9639},[9640,9641],{"id":9232,"depth":4,"text":9233},{"id":9384,"depth":4,"text":9385},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":3947,"description":156},[9647,9648],"raw\u002Fimek\u002Fkniha_scanned\u002F","raw\u002Fimek\u002FKS_druhy_blok.pdf","topics\u002Felasticita",[17,3984,9651,9652,9653,9654],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":9657,"title":9658,"body":9659,"course":14,"courses":163,"created":2004,"description":9666,"extension":166,"meta":10681,"navigation":168,"path":10682,"seo":10683,"sources":10684,"stem":10686,"tags":10687,"type":177,"updated":178,"__hash__":10695},"topics\u002Ftopics\u002Fevolucni-algoritmy.md","Evoluční algoritmy",{"type":48,"value":9660,"toc":10655},[9661,9664,9667,9684,9688,9706,9710,9716,9746,9752,9754,9758,9762,9765,9770,9796,9802,9804,9808,9811,9816,9840,9846,9851,9857,9862,9864,9868,9871,9875,9895,9899,9905,9910,9912,9916,9920,9923,9927,9954,9959,9965,9968,9973,9975,9979,9982,9986,10018,10023,10029,10035,10044,10046,10050,10053,10057,10083,10088,10094,10096,10100,10103,10108,10128,10130,10134,10137,10145,10153,10155,10159,10163,10166,10171,10190,10195,10201,10204,10209,10215,10217,10221,10224,10228,10266,10271,10277,10279,10283,10377,10379,10383,10585,10587,10615,10617,10628,10630,10633,10638],[51,9662,9658],{"id":9663},"evoluční-algoritmy",[55,9665,9666],{},"Evoluční algoritmy jsou rodina optimalizačních metod inspirovaných přírodními procesy — evolucí, chováním rojů, imunitním systémem aj. Umožňují řešit složité optimalizační úlohy, kde klasické gradientní metody selhávají. Každý algoritmus má své klady a zápory — je nutné prozkoumat, který bude aplikaci nejlépe vyhovovat.",[55,9668,830,9669,9675,9676,835,9679,195],{},[69,9670,9674],{"className":9671,"dataFsResolvedFilePath":9672,"href":9673},[62],"topics\u002Fgeneticke-algoritmy.md","\u002Fwiki\u002Fgeneticke-algoritmy","genetické algoritmy"," (podmnožina EA), ",[69,9677,26],{"className":9678,"dataFsResolvedFilePath":849,"href":850},[62],[69,9680,817],{"className":9681,"dataFsResolvedFilePath":9682,"href":9683},[62],"topics\u002Fdatamining.md","\u002Fwiki\u002Fdatamining",[84,9685,9687],{"id":9686},"základní-princip","Základní princip",[89,9689,9690,9700,9703],{},[92,9691,9692,9693,9696,9697],{},"Hledáme optimum ",[95,9694,9695],{},"účelové funkce"," za daných ",[95,9698,9699],{},"omezujících podmínek",[92,9701,9702],{},"Algoritmy pracují iterativně s kandidátními řešeními",[92,9704,9705],{},"Parametry výpočtu: velikost populace, počet iterací, specifické parametry algoritmu",[84,9707,9709],{"id":9708},"ga-vs-ea-hierarchie","GA vs. EA — hierarchie",[55,9711,9712,9715],{},[95,9713,9714],{},"Evoluční algoritmy (EA)"," jsou zastřešující pojem. Zahrnují:",[89,9717,9718,9728,9734,9740],{},[92,9719,9720,9723,9724,2090],{},[95,9721,9722],{},"Genetické algoritmy (GA)"," — binární kódování, selekce, crossover, mutace (",[69,9725,9727],{"className":9726,"dataFsResolvedFilePath":9672,"href":9673},[62],"viz téma",[92,9729,9730,9733],{},[95,9731,9732],{},"Evoluční strategie (ES)"," — reálné vektory, důraz na mutaci",[92,9735,9736,9739],{},[95,9737,9738],{},"Diferenciální evoluce (DE)"," — mutace jako rozdíl vektorů",[92,9741,9742,9745],{},[95,9743,9744],{},"Genetické programování (GP)"," — jedinci jsou programy\u002Fstromy",[55,9747,9748,9751],{},[95,9749,9750],{},"Klíčový rozdíl:"," GA je podmnožinou EA. GA je definován specifickými operátory (zejména crossover) a typicky binárním kódováním.",[909,9753],{},[84,9755,9757],{"id":9756},"trajektoriové-metaheuristiky","Trajektoriové metaheuristiky",[609,9759,9761],{"id":9760},"hill-climbing-výstup-na-kopec","Hill Climbing (Výstup na kopec)",[55,9763,9764],{},"Jednoduché lokální prohledávání — iterativně přechází do lepšího sousedního řešení.",[55,9766,9767],{},[95,9768,9769],{},"Varianty:",[89,9771,9772,9778,9784,9790],{},[92,9773,9774,9777],{},[95,9775,9776],{},"Steepest Ascent"," — vyhodnotí všechny sousedy, vybere nejlepšího",[92,9779,9780,9783],{},[95,9781,9782],{},"First-Choice"," — přijme prvního lepšího souseda (rychlejší)",[92,9785,9786,9789],{},[95,9787,9788],{},"Stochastic"," — náhodně vybírá z lepších sousedů",[92,9791,9792,9795],{},[95,9793,9794],{},"Random Restart"," — opakovaně spouští HC z náhodných startů → překonává lokální optima",[55,9797,9798,9801],{},[95,9799,9800],{},"Problém:"," Uvízne v lokálním optimu — nemá mechanismus pro přijetí horšího řešení.",[909,9803],{},[609,9805,9807],{"id":9806},"simulated-annealing-simulované-žíhání","Simulated Annealing (Simulované žíhání)",[55,9809,9810],{},"Pravděpodobnostní metaheuristika inspirovaná metalurgickým žíháním kovů.",[55,9812,9813],{},[95,9814,9815],{},"Klíčové pojmy:",[89,9817,9818,9824,9834],{},[92,9819,9820,9823],{},[95,9821,9822],{},"Teplota T"," — řídí míru ochoty přijmout horší řešení. Vysoká T ≈ velká pravděpodobnost; T → 0 ≈ přijímáme jen lepší.",[92,9825,9826,9829,9830,9833],{},[95,9827,9828],{},"Cooling schedule"," — geometrické chlazení: ",[929,9831,9832],{},"T := α · T",", kde α ∈ (0,8; 0,995). Příliš rychlé → lokální optimum; příliš pomalé → algoritmus běží velmi dlouho.",[92,9835,9836,9839],{},[95,9837,9838],{},"Metropolisovo kritérium"," — horší řešení (ΔE > 0) přijmeme s pravděpodobností:",[922,9841,9844],{"className":9842,"code":9843,"language":927},[925],"P = exp(-ΔE \u002F T)\n",[929,9845,9843],{"__ignoreMap":156},[55,9847,9848],{},[95,9849,9850],{},"Pseudokód:",[922,9852,9855],{"className":9853,"code":9854,"language":927},[925],"s ← náhodné počáteční řešení\nT ← T_max\n\nopakuj dokud T > T_min:\n    s_new ← náhodný soused(s)\n    ΔE ← E(s_new) - E(s)\n\n    pokud ΔE \u003C 0:\n        s ← s_new               \u002F\u002F lepší řešení vždy přijmeme\n    jinak:\n        pokud random(0,1) \u003C exp(-ΔE \u002F T):\n            s ← s_new           \u002F\u002F horší řešení přijmeme s pravděp. P\n\n    T ← α · T                   \u002F\u002F geometrické ochlazování\n\nvrať s\n",[929,9856,9854],{"__ignoreMap":156},[55,9858,9859,9861],{},[95,9860,1082],{}," PCB optimalizace, TSP, rozvrhování.",[909,9863],{},[609,9865,9867],{"id":9866},"tabu-search-prohledávání-se-zákazem","Tabu Search (Prohledávání se zákazem)",[55,9869,9870],{},"Metaheuristika pro kombinatorickou optimalizaci (Fred Glover, 1986\u002F1989). Používá paměť pro systematický průzkum stavového prostoru.",[55,9872,9873],{},[95,9874,9815],{},[89,9876,9877,9883,9889],{},[92,9878,9879,9882],{},[95,9880,9881],{},"Tabu list"," — seznam nedávno provedených tahů. Tahy na seznamu jsou zakázány → brání cyklení. Pevná velikost, nejstarší záznamy se odstraňují.",[92,9884,9885,9888],{},[95,9886,9887],{},"Aspirační kritérium"," — výjimka ze zákazu: pokud tabu tah vede k řešení lepšímu než dosud nejlepší, zákaz se ignoruje.",[92,9890,9891,9894],{},[95,9892,9893],{},"Dlouhodobá paměť"," — sleduje frekventovaně navštívené oblasti; přesměruje prohledávání do neprozkoumaných oblastí (diverzifikace).",[55,9896,9897],{},[95,9898,9850],{},[922,9900,9903],{"className":9901,"code":9902,"language":927},[925],"s ← počáteční řešení\ns_best ← s\ntabu_list ← prázdný\n\nopakuj dokud podmínka ukončení:\n    N ← vygeneruj sousední řešení\n    admissible ← { s' ∈ N | s' není tabu NEBO splňuje aspirační kritérium }\n    s ← nejlepší z admissible\n\n    pokud E(s) \u003C E(s_best):\n        s_best ← s\n\n    aktualizuj tabu_list\n\nvrať s_best\n",[929,9904,9902],{"__ignoreMap":156},[55,9906,9907,9909],{},[95,9908,1082],{}," Rozvrhování (job scheduling), TSP, optimalizace sítí.",[909,9911],{},[84,9913,9915],{"id":9914},"rojové-metody-swarm-intelligence","Rojové metody (Swarm Intelligence)",[609,9917,9919],{"id":9918},"ant-colony-optimization-aco","Ant Colony Optimization (ACO)",[55,9921,9922],{},"Inspirováno mravenci hledajícími cestu k potravě. Kratší cesty jsou více frekventovány → více feromonu → pozitivní zpětná vazba.",[55,9924,9925],{},[95,9926,9815],{},[89,9928,9929,9935,9944],{},[92,9930,9931,9934],{},[95,9932,9933],{},"Feromonová stopa τ_xy"," — míra atraktivity hrany. Vyšší = větší pravděpodobnost výběru.",[92,9936,9937,7102,9940,9943],{},[95,9938,9939],{},"Evaporace",[929,9941,9942],{},"τ_xy := (1 − ρ) · τ_xy + Σ Δτ_xy^k",". Bez evaporace by algoritmus rychle konvergoval k první nalezené (suboptimální) cestě.",[92,9945,9946,9949,9950,9953],{},[95,9947,9948],{},"Heuristická informace η_xy"," — typicky ",[929,9951,9952],{},"η = 1\u002Fd_xy"," (inverze vzdálenosti).",[55,9955,9956],{},[95,9957,9958],{},"Pravděpodobnostní vzorec výběru uzlu:",[922,9960,9963],{"className":9961,"code":9962,"language":927},[925],"p_xy^k = (τ_xy^α · η_xy^β) \u002F Σ_z (τ_xz^α · η_xz^β)\n",[929,9964,9962],{"__ignoreMap":156},[55,9966,9967],{},"kde α = váha feromonu, β = váha heuristiky.",[55,9969,9970,9972],{},[95,9971,1082],{}," TSP, optimalizace sítí, logistika.",[909,9974],{},[609,9976,9978],{"id":9977},"particle-swarm-optimization-pso","Particle Swarm Optimization (PSO)",[55,9980,9981],{},"Simuluje chování ptačího hejna nebo rybí líhně (Kennedy a Eberhart, 1995).",[55,9983,9984],{},[95,9985,9815],{},[89,9987,9988,9994,10000,10006,10012],{},[92,9989,9990,9993],{},[95,9991,9992],{},"pbest"," — nejlepší pozice, kterou daná částice dosud navštívila",[92,9995,9996,9999],{},[95,9997,9998],{},"gbest"," — nejlepší pozice celého hejna",[92,10001,10002,10005],{},[95,10003,10004],{},"w"," (inertia weight) — setrvačnost: vysoké w = explorace, nízké w = exploatace",[92,10007,10008,10011],{},[95,10009,10010],{},"c1"," (kognitivní koeficient) — přitažlivost k vlastnímu pbest",[92,10013,10014,10017],{},[95,10015,10016],{},"c2"," (sociální koeficient) — přitažlivost ke gbest",[55,10019,10020],{},[95,10021,10022],{},"Vzorec pro aktualizaci rychlosti a polohy:",[922,10024,10027],{"className":10025,"code":10026,"language":927},[925],"v_i,d ← w · v_i,d + c1 · r1 · (pbest_i,d - x_i,d) + c2 · r2 · (gbest_d - x_i,d)\nx_i,d ← x_i,d + v_i,d\n",[929,10028,10026],{"__ignoreMap":156},[55,10030,10031,10032,195],{},"kde r1, r2 jsou náhodná čísla z ",[1647,10033,10034],{},"0, 1",[55,10036,10037,10039,10040,10043],{},[95,10038,1082],{}," Spojitá optimalizace, trénování ",[69,10041,194],{"className":10042,"dataFsResolvedFilePath":79,"href":80},[62],", optimalizace parametrů.",[909,10045],{},[609,10047,10049],{"id":10048},"soma-self-organizing-migrating-algorithm","SOMA — Self-Organizing Migrating Algorithm",[55,10051,10052],{},"Česká metaheuristika (Ivan Zelinka, VŠB Ostrava). Jedinci migrují k nejlepšímu jedinci (Leaderovi), místo reprodukce.",[55,10054,10055],{},[95,10056,9815],{},[89,10058,10059,10065,10071,10077],{},[92,10060,10061,10064],{},[95,10062,10063],{},"Leader"," — jedinec s nejlepší hodnotou účelové funkce v populaci (přehodnocuje se každou migraci)",[92,10066,10067,10070],{},[95,10068,10069],{},"PathLength"," — jak daleko za Leadera jedinec „přestřelí\" (typicky 3,0)",[92,10072,10073,10076],{},[95,10074,10075],{},"Step"," — velikost kroku; menší = jemnější prohledávání trasy, více vyhodnocení funkce",[92,10078,10079,10082],{},[95,10080,10081],{},"PRT vektor"," — perturbační vektor: každá dimenze pohybu je s pravděpodobností (1−PRT) „zmrazena\" → diverzita",[55,10084,10085],{},[95,10086,10087],{},"Strategie AllToOne — pseudokód:",[922,10089,10092],{"className":10090,"code":10091,"language":927},[925],"urči Leader ← nejlepší f(x) v populaci\n\npro každého jedince x_i ≠ Leader:\n    t ← 0\n    x_i_best ← x_i\n\n    opakuj dokud t \u003C PathLength:\n        vygeneruj PRT vektor (dim = 1 s pravděp. PRT, jinak 0)\n        x_trial = x_i + t · (Leader - x_i) · PRT_vektor\n\n        pokud f(x_trial) \u003C f(x_i_best):\n            x_i_best ← x_trial\n\n        t ← t + Step\n\n    x_i ← x_i_best    \u002F\u002F přesuň jedince na nejlepší pozici na trase\n\naktualizuj Leader pro příští migraci\n",[929,10093,10091],{"__ignoreMap":156},[909,10095],{},[609,10097,10099],{"id":10098},"artificial-bee-colony-abc","Artificial Bee Colony (ABC)",[55,10101,10102],{},"Inspirováno chováním včelího roje (Derviş Karaboğa, 2005).",[55,10104,10105],{},[95,10106,10107],{},"Tři typy včel:",[89,10109,10110,10116,10122],{},[92,10111,10112,10115],{},[95,10113,10114],{},"Employed bees"," (zaměstnané) — přiřazeny ke zdroji, prohledávají okolí, sdílejí informace",[92,10117,10118,10121],{},[95,10119,10120],{},"Onlooker bees"," (čekající) — vybírají zdroj pravděpodobnostně podle kvality (waggle dance), ruletová selekce",[92,10123,10124,10127],{},[95,10125,10126],{},"Scout bees"," (průzkumné) — po vyčerpání zdroje hledají náhodně nový → udržují diverzitu",[909,10129],{},[609,10131,10133],{"id":10132},"glowworm-swarm-optimization-gso","Glowworm Swarm Optimization (GSO)",[55,10135,10136],{},"Inspirováno světluškami (Krishnanand a Ghose, 2005).",[55,10138,10139,10141,10142,195],{},[95,10140,1053],{}," Luciferin odpovídá kvalitě řešení. Světluška se pohybuje k jasnějšímu (lepšímu) sousedovi. Přirozeně nachází více optim naráz — vhodné pro ",[95,10143,10144],{},"multimodální optimalizaci",[55,10146,10147,1445,10150],{},[95,10148,10149],{},"Aktualizace luceferinu:",[929,10151,10152],{},"l_i ← (1 − ρ) · l_i + γ · J(x_i)",[909,10154],{},[84,10156,10158],{"id":10157},"evoluční-algoritmy-detailní","Evoluční algoritmy (detailní)",[609,10160,10162],{"id":10161},"differential-evolution-de","Differential Evolution (DE)",[55,10164,10165],{},"Evoluční algoritmus pro spojitou optimalizaci (Storn a Price, 1997). Mutace jako rozdíl vektorů — nevyžaduje gradient.",[55,10167,10168],{},[95,10169,10170],{},"Klíčové parametry:",[89,10172,10173,10182],{},[92,10174,10175,10178,10179],{},[95,10176,10177],{},"F"," (scaling factor) — váha diferenčního vektoru, typicky F ≈ 0,8; F ∈ ",[1647,10180,10181],{},"0, 2",[92,10183,10184,10187,10188],{},[95,10185,10186],{},"CR"," (crossover rate) — pravděpodobnost přijetí hodnoty z mutantu, typicky CR ≈ 0,9; CR ∈ ",[1647,10189,10034],{},[55,10191,10192],{},[95,10193,10194],{},"Vzorec mutace (strategie DE\u002Frand\u002F1):",[922,10196,10199],{"className":10197,"code":10198,"language":927},[925],"y_i = x_a + F · (x_b - x_c)\n",[929,10200,10198],{"__ignoreMap":156},[55,10202,10203],{},"kde a, b, c jsou tři náhodně vybraní jedinci (a ≠ b ≠ c ≠ i).",[55,10205,10206],{},[95,10207,10208],{},"Jedna generace (pseudokód):",[922,10210,10213],{"className":10211,"code":10212,"language":927},[925],"pro každého jedince x_i:\n    \u002F\u002F Mutace\n    y_i = x_a + F · (x_b - x_c)\n\n    \u002F\u002F Křížení (binomiální)\n    pro každou dimenzi d:\n        pokud random(0,1) \u003C CR nebo d = d_rand:\n            trial_i,d = y_i,d      \u002F\u002F z mutantu\n        jinak:\n            trial_i,d = x_i,d     \u002F\u002F z originálu\n\n    \u002F\u002F Selekce (greedy)\n    pokud f(trial_i) ≤ f(x_i):\n        x_i ← trial_i\n",[929,10214,10212],{"__ignoreMap":156},[909,10216],{},[609,10218,10220],{"id":10219},"artificial-immune-system-ais-clonalg","Artificial Immune System (AIS) — CLONALG",[55,10222,10223],{},"Inspirováno biologickým imunitním systémem (De Castro a Von Zuben, 2000).",[55,10225,10226],{},[95,10227,9815],{},[89,10229,10230,10236,10242,10248,10254,10260],{},[92,10231,10232,10235],{},[95,10233,10234],{},"Antigen"," — optimalizační problém",[92,10237,10238,10241],{},[95,10239,10240],{},"Protilátka"," — kandidátní řešení",[92,10243,10244,10247],{},[95,10245,10246],{},"Afinita"," — míra kvality řešení",[92,10249,10250,10253],{},[95,10251,10252],{},"Klonální selekce"," — jedinci s vyšší afinitou vytvářejí více klonů",[92,10255,10256,10259],{},[95,10257,10258],{},"Hypermutace"," — intenzita mutace ∝ 1\u002Fafinita (slabší jedinci mutují silněji)",[92,10261,10262,10265],{},[95,10263,10264],{},"Paměťové buňky"," — uchovávají nejlepší nalezená řešení",[55,10267,10268],{},[95,10269,10270],{},"Pseudokód (CLONALG):",[922,10272,10275],{"className":10273,"code":10274,"language":927},[925],"inicializuj populaci P náhodně; inicializuj paměť M\n\nopakuj dokud podmínka ukončení:\n    vypočti afinitu f(p_i) pro každého jedince\n    vyber n nejlepších protilátek\n    klonuj je (počet klonů ∝ afinita)\n    aplikuj hypermutaci (intenzita ∝ 1\u002Fafinita)\n    vyber nejlepší klony → aktualizuj M\n    nahraď nejhorší jedince náhodnými novými\n\nvrať nejlepší z M\n",[929,10276,10274],{"__ignoreMap":156},[909,10278],{},[84,10280,10282],{"id":10281},"základní-prohledávací-metody","Základní prohledávací metody",[323,10284,10285,10297],{},[326,10286,10287],{},[329,10288,10289,10292,10294],{},[332,10290,10291],{},"Metoda",[332,10293,87],{},[332,10295,10296],{},"Kdy použít",[342,10298,10299,10312,10325,10338,10351,10364],{},[329,10300,10301,10306,10309],{},[347,10302,10303],{},[95,10304,10305],{},"Exhaustive Search",[347,10307,10308],{},"Prohledá úplně všechna řešení; garantuje optimum",[347,10310,10311],{},"Malé prostory (do ~10⁶ kombinací)",[329,10313,10314,10319,10322],{},[347,10315,10316],{},[95,10317,10318],{},"Random Search",[347,10320,10321],{},"Náhodné vzorkování; vrací nejlepší nalezené",[347,10323,10324],{},"Baseline, extrémně nespojité prostory",[329,10326,10327,10332,10335],{},[347,10328,10329],{},[95,10330,10331],{},"Blind Search",[347,10333,10334],{},"Bez heuristické informace (BFS, DFS, random)",[347,10336,10337],{},"Neinformované prohledávání",[329,10339,10340,10345,10348],{},[347,10341,10342],{},[95,10343,10344],{},"Scatter Search",[347,10346,10347],{},"Kombinace referenčních řešení z různých oblastí",[347,10349,10350],{},"Kombinatorická optimalizace",[329,10352,10353,10358,10361],{},[347,10354,10355],{},[95,10356,10357],{},"Backtracking",[347,10359,10360],{},"Zpětné vracení při neúspěchu",[347,10362,10363],{},"Constraint satisfaction problémy",[329,10365,10366,10371,10374],{},[347,10367,10368],{},[95,10369,10370],{},"Greedy",[347,10372,10373],{},"V každém kroku lokálně nejlepší volba",[347,10375,10376],{},"Funguje pro MST (Kruskal, Prim); selhává pro knapsack, mince",[909,10378],{},[84,10380,10382],{"id":10381},"přehledová-tabulka-všech-algoritmů","Přehledová tabulka všech algoritmů",[323,10384,10385,10403],{},[326,10386,10387],{},[329,10388,10389,10391,10394,10397,10400],{},[332,10390,1373],{},[332,10392,10393],{},"Typ",[332,10395,10396],{},"Inspirace",[332,10398,10399],{},"Klíčový mechanismus",[332,10401,10402],{},"Vhodné pro",[342,10404,10405,10422,10439,10455,10472,10488,10504,10520,10536,10553,10569],{},[329,10406,10407,10410,10413,10416,10419],{},[347,10408,10409],{},"Hill Climbing",[347,10411,10412],{},"Lokální",[347,10414,10415],{},"—",[347,10417,10418],{},"Iterativní zlepšování",[347,10420,10421],{},"Jednoduché problémy",[329,10423,10424,10427,10430,10433,10436],{},[347,10425,10426],{},"Simulated Annealing",[347,10428,10429],{},"Trajektoriová",[347,10431,10432],{},"Metalurgie",[347,10434,10435],{},"Metropolisovo kritérium, chlazení",[347,10437,10438],{},"Kombinatorická i spojitá",[329,10440,10441,10444,10446,10449,10452],{},[347,10442,10443],{},"Tabu Search",[347,10445,10429],{},[347,10447,10448],{},"Lidská paměť",[347,10450,10451],{},"Tabu list, aspirace",[347,10453,10454],{},"Kombinatorická",[329,10456,10457,10460,10463,10466,10469],{},[347,10458,10459],{},"Genetic Algorithm",[347,10461,10462],{},"Evoluční",[347,10464,10465],{},"Biologie",[347,10467,10468],{},"Selekce, crossover, mutace",[347,10470,10471],{},"Diskrétní i spojité",[329,10473,10474,10477,10479,10482,10485],{},[347,10475,10476],{},"Differential Evolution",[347,10478,10462],{},[347,10480,10481],{},"Evoluce",[347,10483,10484],{},"Mutace rozdílem vektorů",[347,10486,10487],{},"Spojitá optimalizace",[329,10489,10490,10493,10496,10499,10502],{},[347,10491,10492],{},"PSO",[347,10494,10495],{},"Swarm",[347,10497,10498],{},"Ptačí hejna",[347,10500,10501],{},"pbest + gbest + inertia",[347,10503,10487],{},[329,10505,10506,10509,10511,10514,10517],{},[347,10507,10508],{},"ACO",[347,10510,10495],{},[347,10512,10513],{},"Mravenci",[347,10515,10516],{},"Feromony, evaporace",[347,10518,10519],{},"Kombinatorická (grafy)",[329,10521,10522,10525,10527,10530,10533],{},[347,10523,10524],{},"SOMA",[347,10526,10495],{},[347,10528,10529],{},"Sociální chování",[347,10531,10532],{},"Migrace k Leaderovi, PRT",[347,10534,10535],{},"Spojitá i diskrétní",[329,10537,10538,10541,10544,10547,10550],{},[347,10539,10540],{},"AIS (CLONALG)",[347,10542,10543],{},"Imuno",[347,10545,10546],{},"Imunitní systém",[347,10548,10549],{},"Klonální selekce, hypermutace",[347,10551,10552],{},"Optimalizace, pattern rec.",[329,10554,10555,10558,10560,10563,10566],{},[347,10556,10557],{},"Artificial Bee Colony",[347,10559,10495],{},[347,10561,10562],{},"Včely",[347,10564,10565],{},"Employed\u002FOnlooker\u002FScout",[347,10567,10568],{},"Spojitá i kombinatorická",[329,10570,10571,10574,10576,10579,10582],{},[347,10572,10573],{},"Glowworm Swarm",[347,10575,10495],{},[347,10577,10578],{},"Světlušky",[347,10580,10581],{},"Luciferin, pohyb k jasnějšímu",[347,10583,10584],{},"Multimodální optimalizace",[84,10586,881],{"id":880},[89,10588,10589,10592,10599,10602,10609],{},[92,10590,10591],{},"Rozvrhování výroby a výuky",[92,10593,10594,10598],{},[69,10595,10597],{"className":10596,"dataFsResolvedFilePath":849,"href":850},[62],"Optimalizace"," ekonomických problémů (min. nákladů, min. rizik)",[92,10600,10601],{},"Optimalizace technických systémů",[92,10603,10604,10605,10608],{},"Trénování ",[69,10606,194],{"className":10607,"dataFsResolvedFilePath":79,"href":80},[62]," a ladění parametrů modelů",[92,10610,10611,10614],{},[69,10612,812],{"className":10613,"dataFsResolvedFilePath":9682,"href":9683},[62]," — klastrování dat (PSO, ABC)",[84,10616,1913],{"id":1912},[201,10618,10619,10622,10625],{},[92,10620,10621],{},"Popište metodu a vysvětlete princip evolučních algoritmů.",[92,10623,10624],{},"Popište realizaci a výpočet evolučních algoritmů na počítači.",[92,10626,10627],{},"Jak lze využít evolučních algoritmů v praxi?",[84,10629,1946],{"id":1945},[55,10631,10632],{},"Evoluční algoritmy, optimalizace, účelová funkce, omezující podmínky, parametry výpočtu, Exhaustive Search, Random Search, Blind Search, Scatter Search, Backtracking, Greedy, Hill Climbing, Tabu Search, Simulated Annealing, Ant Colony, Particle Swarms, Artificial Bee Colony, Glowworm Swarm, Genetic Search, DNA Based Genetic Algorithm, Parallel Genetic Search, Diploid and Haploid Genetic Search, Differential Evolution, Artificial Immune System, SOMA Evolution Strategy, Psychoclonal Search.",[84,10634,756,10635],{"id":1952},[69,10636,136],{"className":10637,"dataFsResolvedFilePath":134,"href":135},[62],[89,10639,10640,10646],{},[92,10641,10642,10645],{},[69,10643,1965],{"className":10644,"dataFsResolvedFilePath":1963,"href":1964},[62]," — přehled algoritmů, kontrolní otázky, pojmy k zapamatování",[92,10647,10648,10654],{},[69,10649,10653],{"className":10650,"dataFsResolvedFilePath":10651,"href":10652},[62],"summaries\u002Fipmrk-evolucni-algoritmy.md","\u002Fwiki\u002Fipmrk-evolucni-algoritmy","Principy a přehled"," — pseudokódy, vzorce, detailní principy (Wikipedia, Cornell, Springer)",{"title":156,"searchDepth":7,"depth":7,"links":10656},[10657,10658,10659,10664,10671,10675,10676,10677,10678,10679,10680],{"id":9686,"depth":7,"text":9687},{"id":9708,"depth":7,"text":9709},{"id":9756,"depth":7,"text":9757,"children":10660},[10661,10662,10663],{"id":9760,"depth":4,"text":9761},{"id":9806,"depth":4,"text":9807},{"id":9866,"depth":4,"text":9867},{"id":9914,"depth":7,"text":9915,"children":10665},[10666,10667,10668,10669,10670],{"id":9918,"depth":4,"text":9919},{"id":9977,"depth":4,"text":9978},{"id":10048,"depth":4,"text":10049},{"id":10098,"depth":4,"text":10099},{"id":10132,"depth":4,"text":10133},{"id":10157,"depth":7,"text":10158,"children":10672},[10673,10674],{"id":10161,"depth":4,"text":10162},{"id":10219,"depth":4,"text":10220},{"id":10281,"depth":7,"text":10282},{"id":10381,"depth":7,"text":10382},{"id":880,"depth":7,"text":881},{"id":1912,"depth":7,"text":1913},{"id":1945,"depth":7,"text":1946},{"id":1952,"depth":7,"text":2003},{},"\u002Ftopics\u002Fevolucni-algoritmy",{"title":9658,"description":9666},[2009,10685],"raw\u002Fipmrk\u002Fevolucni-algoritmy-online.md","topics\u002Fevolucni-algoritmy",[14,10688,10689,10690,10691,10692,10693,10694],"evolucni-algoritmy","metaheuristiky","simulated-annealing","tabu-search","aco","pso","soma","2iZO9GpjkAfcGdCCz6z2lyz5UKhCMs6jY6tqmgvxlhQ",{"id":10697,"title":10698,"body":10699,"course":17,"courses":163,"created":3932,"description":12247,"extension":166,"meta":12248,"navigation":168,"path":12249,"seo":12250,"sources":12251,"stem":12252,"tags":12253,"type":177,"updated":178,"__hash__":12258},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":48,"value":10700,"toc":12232},[10701,10704,10777,10784,10788,10852,10945,10949,10976,11043,11098,11102,11129,11222,11224,11256,11427,11431,11501,11549,11553,11613,11719,11734,11738,11740,11768,11833,11835,11842,11930,11955,12153,12157,12196,12198],[51,10702,10698],{"id":10703},"kalkul-funkcí-více-proměnných",[55,10705,10706,10707,10710,10711,835,10740,195],{},"Většina ekonomických veličin závisí na ",[95,10708,10709],{},"více faktorech"," — produkce na práci a kapitálu, užitečnost na množství různých statků, poptávka na cenách více zboží i důchodu. Kalkul jedné proměnné se proto rozšiřuje na ",[1647,10712,10714],{"className":10713},[2059],[2061,10715,10716],{"xmlns":2063},[2065,10717,10718,10737],{},[2068,10719,10720,10723,10725,10727,10729,10731,10733,10735],{},[2071,10721,10722],{},"z",[2075,10724,2077],{},[2071,10726,2080],{},[2075,10728,2084],{"stretchy":2083},[2071,10730,2087],{},[2075,10732,2361],{"separator":2360},[2071,10734,2073],{},[2075,10736,2090],{"stretchy":2083},[2092,10738,10739],{"encoding":2094},"z = f(x, y)",[1647,10741,10743],{"className":10742},[2059],[2061,10744,10745],{"xmlns":2063},[2065,10746,10747,10774],{},[2068,10748,10749,10751,10753,10755,10757,10759,10761,10763,10765,10767,10769,10771],{},[2071,10750,10004],{},[2075,10752,2077],{},[2071,10754,2080],{},[2075,10756,2084],{"stretchy":2083},[2071,10758,2087],{},[2075,10760,2361],{"separator":2360},[2071,10762,2073],{},[2075,10764,2361],{"separator":2360},[2071,10766,10722],{},[2075,10768,2090],{"stretchy":2083},[2075,10770,2361],{"separator":2360},[2075,10772,10773],{},"…",[2092,10775,10776],{"encoding":2094},"w = f(x, y, z), \\ldots",[55,10778,10779],{},[58,10780],{"alt":10781,"className":10782,"src":10783},"imek-funkce-2d-vrstevnice",[62,63],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[84,10785,10787],{"id":10786},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[55,10789,10790,10791,10818,10819,10847,10848,10851],{},"Pro ",[1647,10792,10794],{"className":10793},[2059],[2061,10795,10796],{"xmlns":2063},[2065,10797,10798,10816],{},[2068,10799,10800,10802,10804,10806,10808,10810,10812,10814],{},[2071,10801,10722],{},[2075,10803,2077],{},[2071,10805,2080],{},[2075,10807,2084],{"stretchy":2083},[2071,10809,2087],{},[2075,10811,2361],{"separator":2360},[2071,10813,2073],{},[2075,10815,2090],{"stretchy":2083},[2092,10817,10739],{"encoding":2094}," se křivkou s předpisem ",[1647,10820,10822],{"className":10821},[2059],[2061,10823,10824],{"xmlns":2063},[2065,10825,10826,10844],{},[2068,10827,10828,10830,10832,10834,10836,10838,10840,10842],{},[2071,10829,2080],{},[2075,10831,2084],{"stretchy":2083},[2071,10833,2087],{},[2075,10835,2361],{"separator":2360},[2071,10837,2073],{},[2075,10839,2090],{"stretchy":2083},[2075,10841,2077],{},[2071,10843,2222],{},[2092,10845,10846],{"encoding":2094},"f(x, y) = c"," (konstanta) rozumí ",[95,10849,10850],{},"vrstevnice"," funkce. V ekonomii:",[89,10853,10854,10904],{},[92,10855,10856,10859,10860,10897,10898,195],{},[95,10857,10858],{},"Indiferenční křivky"," užitečnosti ",[1647,10861,10863],{"className":10862},[2059],[2061,10864,10865],{"xmlns":2063},[2065,10866,10867,10894],{},[2068,10868,10869,10872,10874,10880,10882,10888,10890,10892],{},[2071,10870,10871],{},"U",[2075,10873,2084],{"stretchy":2083},[2348,10875,10876,10878],{},[2071,10877,2861],{},[2210,10879,638],{},[2075,10881,2361],{"separator":2360},[2348,10883,10884,10886],{},[2071,10885,2861],{},[2210,10887,646],{},[2075,10889,2090],{"stretchy":2083},[2075,10891,2077],{},[2071,10893,2222],{},[2092,10895,10896],{"encoding":2094},"U(Q_1, Q_2) = c"," — viz ",[69,10899,10903],{"className":10900,"dataFsResolvedFilePath":10901,"href":10902},[62],"topics\u002Fuzitecnost.md","\u002Fwiki\u002Fuzitecnost","uzitecnost",[92,10905,10906,10909,10910,10897,10939,195],{},[95,10907,10908],{},"Izokvanty"," produkce ",[1647,10911,10913],{"className":10912},[2059],[2061,10914,10915],{"xmlns":2063},[2065,10916,10917,10936],{},[2068,10918,10919,10921,10923,10925,10927,10930,10932,10934],{},[2071,10920,2861],{},[2075,10922,2084],{"stretchy":2083},[2071,10924,586],{},[2075,10926,2361],{"separator":2360},[2071,10928,10929],{},"K",[2075,10931,2090],{"stretchy":2083},[2075,10933,2077],{},[2071,10935,2222],{},[2092,10937,10938],{"encoding":2094},"Q(L, K) = c",[69,10940,10944],{"className":10941,"dataFsResolvedFilePath":10942,"href":10943},[62],"topics\u002Fprodukce.md","\u002Fwiki\u002Fprodukce","produkce",[84,10946,10948],{"id":10947},"parciální-derivace","Parciální derivace",[55,10950,10790,10951,10975],{},[1647,10952,10954],{"className":10953},[2059],[2061,10955,10956],{"xmlns":2063},[2065,10957,10958,10972],{},[2068,10959,10960,10962,10964,10966,10968,10970],{},[2071,10961,2080],{},[2075,10963,2084],{"stretchy":2083},[2071,10965,2087],{},[2075,10967,2361],{"separator":2360},[2071,10969,2073],{},[2075,10971,2090],{"stretchy":2083},[2092,10973,10974],{"encoding":2094},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[55,10977,10978],{},[1647,10979,10981],{"className":10980},[2059],[2061,10982,10983],{"xmlns":2063},[2065,10984,10985,11040],{},[2068,10986,10987,10995,10997,11012,11014,11016,11024,11026],{},[9252,10988,10989,10991,10993],{},[2071,10990,2080],{},[2071,10992,2087],{},[2075,10994,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,10996,2077],{},[2403,10998,10999,11006],{},[2068,11000,11001,11004],{},[2071,11002,11003],{"mathvariant":2450},"∂",[2071,11005,2080],{},[2068,11007,11008,11010],{},[2071,11009,11003],{"mathvariant":2450},[2071,11011,2087],{},[2075,11013,2361],{"separator":2360},[5965,11015],{"width":5967},[9252,11017,11018,11020,11022],{},[2071,11019,2080],{},[2071,11021,2073],{},[2075,11023,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11025,2077],{},[2403,11027,11028,11034],{},[2068,11029,11030,11032],{},[2071,11031,11003],{"mathvariant":2450},[2071,11033,2080],{},[2068,11035,11036,11038],{},[2071,11037,11003],{"mathvariant":2450},[2071,11039,2073],{},[2092,11041,11042],{"encoding":2094},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[55,11044,11045,11046,195],{},"Hodnoty v bodě: ",[1647,11047,11049],{"className":11048},[2059],[2061,11050,11051],{"xmlns":2063},[2065,11052,11053,11095],{},[2068,11054,11055,11063,11065,11067,11069,11071,11073,11075,11077,11085,11087,11089,11091,11093],{},[9252,11056,11057,11059,11061],{},[2071,11058,2080],{},[2071,11060,2087],{},[2075,11062,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11064,2084],{"stretchy":2083},[2071,11066,69],{},[2075,11068,2361],{"separator":2360},[2071,11070,2179],{},[2075,11072,2090],{"stretchy":2083},[2075,11074,2361],{"separator":2360},[2363,11076,2365],{},[9252,11078,11079,11081,11083],{},[2071,11080,2080],{},[2071,11082,2073],{},[2075,11084,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11086,2084],{"stretchy":2083},[2071,11088,69],{},[2075,11090,2361],{"separator":2360},[2071,11092,2179],{},[2075,11094,2090],{"stretchy":2083},[2092,11096,11097],{"encoding":2094},"f'_x(a, b),\\ f'_y(a, b)",[609,11099,11101],{"id":11100},"ekonomické-značení","Ekonomické značení",[55,11103,11104,11105,2777],{},"Pro produkční funkci ",[1647,11106,11108],{"className":11107},[2059],[2061,11109,11110],{"xmlns":2063},[2065,11111,11112,11126],{},[2068,11113,11114,11116,11118,11120,11122,11124],{},[2071,11115,2861],{},[2075,11117,2084],{"stretchy":2083},[2071,11119,586],{},[2075,11121,2361],{"separator":2360},[2071,11123,10929],{},[2075,11125,2090],{"stretchy":2083},[2092,11127,11128],{"encoding":2094},"Q(L, K)",[89,11130,11131,11177],{},[92,11132,11133,2545,11153,11156,11157,2090],{},[1647,11134,11136],{"className":11135},[2059],[2061,11137,11138],{"xmlns":2063},[2065,11139,11140,11150],{},[2068,11141,11142],{},[9252,11143,11144,11146,11148],{},[2071,11145,2861],{},[2071,11147,586],{},[2075,11149,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,11151,11152],{"encoding":2094},"Q'_L",[95,11154,11155],{},"mezní produkt práce"," (",[1647,11158,11160],{"className":11159},[2059],[2061,11161,11162],{"xmlns":2063},[2065,11163,11164,11174],{},[2068,11165,11166,11168],{},[2071,11167,2890],{},[2348,11169,11170,11172],{},[2071,11171,575],{},[2071,11173,586],{},[2092,11175,11176],{"encoding":2094},"MP_L",[92,11178,11179,2545,11199,11156,11202,2090],{},[1647,11180,11182],{"className":11181},[2059],[2061,11183,11184],{"xmlns":2063},[2065,11185,11186,11196],{},[2068,11187,11188],{},[9252,11189,11190,11192,11194],{},[2071,11191,2861],{},[2071,11193,10929],{},[2075,11195,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,11197,11198],{"encoding":2094},"Q'_K",[95,11200,11201],{},"mezní produkt kapitálu",[1647,11203,11205],{"className":11204},[2059],[2061,11206,11207],{"xmlns":2063},[2065,11208,11209,11219],{},[2068,11210,11211,11213],{},[2071,11212,2890],{},[2348,11214,11215,11217],{},[2071,11216,575],{},[2071,11218,10929],{},[2092,11220,11221],{"encoding":2094},"MP_K",[609,11223,2641],{"id":2640},[55,11225,11226,2777],{},[1647,11227,11229],{"className":11228},[2059],[2061,11230,11231],{"xmlns":2063},[2065,11232,11233,11253],{},[2068,11234,11235,11243,11245,11247,11249,11251],{},[9252,11236,11237,11239,11241],{},[2071,11238,2080],{},[2071,11240,2087],{},[2075,11242,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11244,2084],{"stretchy":2083},[2071,11246,69],{},[2075,11248,2361],{"separator":2360},[2071,11250,2179],{},[2075,11252,2090],{"stretchy":2083},[2092,11254,11255],{"encoding":2094},"f'_x(a, b)",[89,11257,11258,11316],{},[92,11259,11260,11261,11274,11275,11288,11289,11315],{},"rychlost změny ",[1647,11262,11264],{"className":11263},[2059],[2061,11265,11266],{"xmlns":2063},[2065,11267,11268,11272],{},[2068,11269,11270],{},[2071,11271,2080],{},[2092,11273,2080],{"encoding":2094}," vůči ",[1647,11276,11278],{"className":11277},[2059],[2061,11279,11280],{"xmlns":2063},[2065,11281,11282,11286],{},[2068,11283,11284],{},[2071,11285,2087],{},[2092,11287,2087],{"encoding":2094}," při ",[1647,11290,11292],{"className":11291},[2059],[2061,11293,11294],{"xmlns":2063},[2065,11295,11296,11312],{},[2068,11297,11298,11300,11302,11304,11306,11308,11310],{},[2071,11299,2087],{},[2075,11301,2077],{},[2071,11303,69],{},[2075,11305,2361],{"separator":2360},[2071,11307,2073],{},[2075,11309,2077],{},[2071,11311,2179],{},[2092,11313,11314],{"encoding":2094},"x = a, y = b"," (kapitál fixní),",[92,11317,11318,11319,2730,11332,11345,11346,11364,11365,195],{},"přibližná změna ",[1647,11320,11322],{"className":11321},[2059],[2061,11323,11324],{"xmlns":2063},[2065,11325,11326,11330],{},[2068,11327,11328],{},[2071,11329,2080],{},[2092,11331,2080],{"encoding":2094},[1647,11333,11335],{"className":11334},[2059],[2061,11336,11337],{"xmlns":2063},[2065,11338,11339,11343],{},[2068,11340,11341],{},[2071,11342,2087],{},[2092,11344,2087],{"encoding":2094}," o 1 (a pevném ",[1647,11347,11349],{"className":11348},[2059],[2061,11350,11351],{"xmlns":2063},[2065,11352,11353,11361],{},[2068,11354,11355,11357,11359],{},[2071,11356,2073],{},[2075,11358,2077],{},[2071,11360,2179],{},[2092,11362,11363],{"encoding":2094},"y = b","): ",[1647,11366,11368],{"className":11367},[2059],[2061,11369,11370],{"xmlns":2063},[2065,11371,11372,11424],{},[2068,11373,11374,11376,11378,11380,11382,11384,11386,11388,11390,11392,11394,11396,11398,11400,11402,11404,11406,11414,11416,11418,11420,11422],{},[2071,11375,2080],{},[2075,11377,2084],{"stretchy":2083},[2071,11379,69],{},[2075,11381,2176],{},[2210,11383,638],{},[2075,11385,2361],{"separator":2360},[2071,11387,2179],{},[2075,11389,2090],{"stretchy":2083},[2075,11391,2803],{},[2071,11393,2080],{},[2075,11395,2084],{"stretchy":2083},[2071,11397,69],{},[2075,11399,2361],{"separator":2360},[2071,11401,2179],{},[2075,11403,2090],{"stretchy":2083},[2075,11405,2176],{},[9252,11407,11408,11410,11412],{},[2071,11409,2080],{},[2071,11411,2087],{},[2075,11413,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11415,2084],{"stretchy":2083},[2071,11417,69],{},[2075,11419,2361],{"separator":2360},[2071,11421,2179],{},[2075,11423,2090],{"stretchy":2083},[2092,11425,11426],{"encoding":2094},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[84,11428,11430],{"id":11429},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[55,11432,11433],{},[1647,11434,11436],{"className":11435},[2059],[2061,11437,11438],{"xmlns":2063},[2065,11439,11440,11498],{},[2068,11441,11442,11444,11446,11448,11456,11458,11460,11462,11464,11466,11468,11470,11472,11474,11482,11484,11486,11488,11490,11492,11494,11496],{},[2071,11443,2273],{},[2071,11445,2080],{},[2075,11447,2077],{},[9252,11449,11450,11452,11454],{},[2071,11451,2080],{},[2071,11453,2087],{},[2075,11455,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11457,2084],{"stretchy":2083},[2071,11459,2087],{},[2075,11461,2361],{"separator":2360},[2071,11463,2073],{},[2075,11465,2090],{"stretchy":2083},[2363,11467,3061],{},[2071,11469,2273],{},[2071,11471,2087],{},[2075,11473,2176],{},[9252,11475,11476,11478,11480],{},[2071,11477,2080],{},[2071,11479,2073],{},[2075,11481,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11483,2084],{"stretchy":2083},[2071,11485,2087],{},[2075,11487,2361],{"separator":2360},[2071,11489,2073],{},[2075,11491,2090],{"stretchy":2083},[2363,11493,3061],{},[2071,11495,2273],{},[2071,11497,2073],{},[2092,11499,11500],{"encoding":2094},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[55,11502,3071,11503,11525,11526,11548],{},[1647,11504,11506],{"className":11505},[2059],[2061,11507,11508],{"xmlns":2063},[2065,11509,11510,11522],{},[2068,11511,11512,11514,11516,11518,11520],{},[2071,11513,2273],{},[2071,11515,2087],{},[2075,11517,2361],{"separator":2360},[2071,11519,2273],{},[2071,11521,2073],{},[2092,11523,11524],{"encoding":2094},"dx, dy"," platí ",[1647,11527,11529],{"className":11528},[2059],[2061,11530,11531],{"xmlns":2063},[2065,11532,11533,11545],{},[2068,11534,11535,11537,11539,11541,11543],{},[2071,11536,2961],{"mathvariant":2450},[2071,11538,2080],{},[2075,11540,2803],{},[2071,11542,2273],{},[2071,11544,2080],{},[2092,11546,11547],{"encoding":2094},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[84,11550,11552],{"id":11551},"implicitní-funkce","Implicitní funkce",[55,11554,11555,11556,11584,11585,11598,11599,11612],{},"Je-li vztah dán rovnicí ",[1647,11557,11559],{"className":11558},[2059],[2061,11560,11561],{"xmlns":2063},[2065,11562,11563,11581],{},[2068,11564,11565,11567,11569,11571,11573,11575,11577,11579],{},[2071,11566,10177],{},[2075,11568,2084],{"stretchy":2083},[2071,11570,2087],{},[2075,11572,2361],{"separator":2360},[2071,11574,2073],{},[2075,11576,2090],{"stretchy":2083},[2075,11578,2077],{},[2210,11580,630],{},[2092,11582,11583],{"encoding":2094},"F(x, y) = 0"," a chceme derivaci ",[1647,11586,11588],{"className":11587},[2059],[2061,11589,11590],{"xmlns":2063},[2065,11591,11592,11596],{},[2068,11593,11594],{},[2071,11595,2073],{},[2092,11597,2073],{"encoding":2094}," podle ",[1647,11600,11602],{"className":11601},[2059],[2061,11603,11604],{"xmlns":2063},[2065,11605,11606,11610],{},[2068,11607,11608],{},[2071,11609,2087],{},[2092,11611,2087],{"encoding":2094}," (nebo naopak):",[55,11614,11615],{},[1647,11616,11618],{"className":11617},[2059],[2061,11619,11620],{"xmlns":2063},[2065,11621,11622,11716],{},[2068,11623,11624,11630,11632,11646,11648,11650,11668,11670,11672,11678,11680,11694,11696,11698],{},[2205,11625,11626,11628],{},[2071,11627,2073],{},[2075,11629,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11631,2077],{},[2403,11633,11634,11640],{},[2068,11635,11636,11638],{},[2071,11637,2273],{},[2071,11639,2073],{},[2068,11641,11642,11644],{},[2071,11643,2273],{},[2071,11645,2087],{},[2075,11647,2077],{},[2075,11649,2303],{},[2403,11651,11652,11660],{},[9252,11653,11654,11656,11658],{},[2071,11655,10177],{},[2071,11657,2087],{},[2075,11659,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,11661,11662,11664,11666],{},[2071,11663,10177],{},[2071,11665,2073],{},[2075,11667,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11669,2361],{"separator":2360},[5965,11671],{"width":5967},[2205,11673,11674,11676],{},[2071,11675,2087],{},[2075,11677,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11679,2077],{},[2403,11681,11682,11688],{},[2068,11683,11684,11686],{},[2071,11685,2273],{},[2071,11687,2087],{},[2068,11689,11690,11692],{},[2071,11691,2273],{},[2071,11693,2073],{},[2075,11695,2077],{},[2075,11697,2303],{},[2403,11699,11700,11708],{},[9252,11701,11702,11704,11706],{},[2071,11703,10177],{},[2071,11705,2073],{},[2075,11707,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,11709,11710,11712,11714],{},[2071,11711,10177],{},[2071,11713,2087],{},[2075,11715,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,11717,11718],{"encoding":2094},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[55,11720,11721,11722,11725,11726,75,11730,195],{},"Tato vzorec dává ",[95,11723,11724],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[69,11727,11729],{"className":11728,"dataFsResolvedFilePath":10942,"href":10943},[62],"MRTS",[69,11731,11733],{"className":11732,"dataFsResolvedFilePath":10901,"href":10902},[62],"MRCS",[84,11735,11737],{"id":11736},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[609,11739,3326],{"id":3325},[55,11741,11742,11743,11767],{},"V bodě extrému ",[1647,11744,11746],{"className":11745},[2059],[2061,11747,11748],{"xmlns":2063},[2065,11749,11750,11764],{},[2068,11751,11752,11754,11756,11758,11760,11762],{},[2071,11753,4342],{},[2075,11755,2561],{"stretchy":2083},[2071,11757,69],{},[2075,11759,2361],{"separator":2360},[2071,11761,2179],{},[2075,11763,2576],{"stretchy":2083},[2092,11765,11766],{"encoding":2094},"A[a, b]"," musí platit současně:",[55,11769,11770],{},[1647,11771,11773],{"className":11772},[2059],[2061,11774,11775],{"xmlns":2063},[2065,11776,11777,11830],{},[2068,11778,11779,11787,11789,11791,11793,11795,11797,11799,11801,11803,11806,11808,11816,11818,11820,11822,11824,11826,11828],{},[9252,11780,11781,11783,11785],{},[2071,11782,2080],{},[2071,11784,2087],{},[2075,11786,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11788,2084],{"stretchy":2083},[2071,11790,69],{},[2075,11792,2361],{"separator":2360},[2071,11794,2179],{},[2075,11796,2090],{"stretchy":2083},[2075,11798,2077],{},[2210,11800,630],{},[2363,11802,4072],{},[2075,11804,11805],{},"∧",[2363,11807,4072],{},[9252,11809,11810,11812,11814],{},[2071,11811,2080],{},[2071,11813,2073],{},[2075,11815,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,11817,2084],{"stretchy":2083},[2071,11819,69],{},[2075,11821,2361],{"separator":2360},[2071,11823,2179],{},[2075,11825,2090],{"stretchy":2083},[2075,11827,2077],{},[2210,11829,630],{},[2092,11831,11832],{"encoding":2094},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[609,11834,3400],{"id":3399},[55,11836,11837,11838,11841],{},"Definujeme ",[95,11839,11840],{},"diskriminant"," (Hessián zjednodušeně):",[55,11843,11844],{},[1647,11845,11847],{"className":11846},[2059],[2061,11848,11849],{"xmlns":2063},[2065,11850,11851,11927],{},[2068,11852,11853,11855,11857,11859,11861,11863,11865,11867,11883,11885,11901,11903,11905,11921],{},[2071,11854,4271],{},[2075,11856,2084],{"stretchy":2083},[2071,11858,2087],{},[2075,11860,2361],{"separator":2360},[2071,11862,2073],{},[2075,11864,2090],{"stretchy":2083},[2075,11866,2077],{},[9252,11868,11869,11871,11877],{},[2071,11870,2080],{},[2068,11872,11873,11875],{},[2071,11874,2087],{},[2071,11876,2087],{},[2068,11878,11879,11881],{},[2075,11880,2452],{"mathvariant":2450},[2075,11882,2452],{"mathvariant":2450},[2075,11884,3251],{},[9252,11886,11887,11889,11895],{},[2071,11888,2080],{},[2068,11890,11891,11893],{},[2071,11892,2073],{},[2071,11894,2073],{},[2068,11896,11897,11899],{},[2075,11898,2452],{"mathvariant":2450},[2075,11900,2452],{"mathvariant":2450},[2075,11902,2303],{},[2075,11904,2084],{"stretchy":2083},[9252,11906,11907,11909,11915],{},[2071,11908,2080],{},[2068,11910,11911,11913],{},[2071,11912,2087],{},[2071,11914,2073],{},[2068,11916,11917,11919],{},[2075,11918,2452],{"mathvariant":2450},[2075,11920,2452],{"mathvariant":2450},[2205,11922,11923,11925],{},[2075,11924,2090],{"stretchy":2083},[2210,11926,646],{},[2092,11928,11929],{"encoding":2094},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[55,11931,11932,11933,2777],{},"V podezřelém bodě ",[1647,11934,11936],{"className":11935},[2059],[2061,11937,11938],{"xmlns":2063},[2065,11939,11940,11952],{},[2068,11941,11942,11944,11946,11948,11950],{},[2075,11943,2561],{"stretchy":2083},[2071,11945,69],{},[2075,11947,2361],{"separator":2360},[2071,11949,2179],{},[2075,11951,2576],{"stretchy":2083},[2092,11953,11954],{"encoding":2094},"[a, b]",[201,11956,11957,12084,12120],{},[92,11958,11959,11989,11990],{},[95,11960,11961,2777],{},[1647,11962,11964],{"className":11963},[2059],[2061,11965,11966],{"xmlns":2063},[2065,11967,11968,11986],{},[2068,11969,11970,11972,11974,11976,11978,11980,11982,11984],{},[2071,11971,4271],{},[2075,11973,2084],{"stretchy":2083},[2071,11975,69],{},[2075,11977,2361],{"separator":2360},[2071,11979,2179],{},[2075,11981,2090],{"stretchy":2083},[2075,11983,3482],{},[2210,11985,630],{},[2092,11987,11988],{"encoding":2094},"D(a, b) > 0"," je to extrém.\n",[89,11991,11992,12038],{},[92,11993,11994,3488,12036],{},[1647,11995,11997],{"className":11996},[2059],[2061,11998,11999],{"xmlns":2063},[2065,12000,12001,12033],{},[2068,12002,12003,12019,12021,12023,12025,12027,12029,12031],{},[9252,12004,12005,12007,12013],{},[2071,12006,2080],{},[2068,12008,12009,12011],{},[2071,12010,2087],{},[2071,12012,2087],{},[2068,12014,12015,12017],{},[2075,12016,2452],{"mathvariant":2450},[2075,12018,2452],{"mathvariant":2450},[2075,12020,2084],{"stretchy":2083},[2071,12022,69],{},[2075,12024,2361],{"separator":2360},[2071,12026,2179],{},[2075,12028,2090],{"stretchy":2083},[2075,12030,3482],{},[2210,12032,630],{},[2092,12034,12035],{"encoding":2094},"f''_{xx}(a, b) > 0",[95,12037,3849],{},[92,12039,12040,3488,12082],{},[1647,12041,12043],{"className":12042},[2059],[2061,12044,12045],{"xmlns":2063},[2065,12046,12047,12079],{},[2068,12048,12049,12065,12067,12069,12071,12073,12075,12077],{},[9252,12050,12051,12053,12059],{},[2071,12052,2080],{},[2068,12054,12055,12057],{},[2071,12056,2087],{},[2071,12058,2087],{},[2068,12060,12061,12063],{},[2075,12062,2452],{"mathvariant":2450},[2075,12064,2452],{"mathvariant":2450},[2075,12066,2084],{"stretchy":2083},[2071,12068,69],{},[2075,12070,2361],{"separator":2360},[2071,12072,2179],{},[2075,12074,2090],{"stretchy":2083},[2075,12076,3521],{},[2210,12078,630],{},[2092,12080,12081],{"encoding":2094},"f''_{xx}(a, b) \u003C 0",[95,12083,3791],{},[92,12085,12086,1445,12116,12119],{},[95,12087,12088,2777],{},[1647,12089,12091],{"className":12090},[2059],[2061,12092,12093],{"xmlns":2063},[2065,12094,12095,12113],{},[2068,12096,12097,12099,12101,12103,12105,12107,12109,12111],{},[2071,12098,4271],{},[2075,12100,2084],{"stretchy":2083},[2071,12102,69],{},[2075,12104,2361],{"separator":2360},[2071,12106,2179],{},[2075,12108,2090],{"stretchy":2083},[2075,12110,3521],{},[2210,12112,630],{},[2092,12114,12115],{"encoding":2094},"D(a, b) \u003C 0",[95,12117,12118],{},"sedlo"," (v daném bodě extrém není).",[92,12121,12122,12152],{},[95,12123,12124,2777],{},[1647,12125,12127],{"className":12126},[2059],[2061,12128,12129],{"xmlns":2063},[2065,12130,12131,12149],{},[2068,12132,12133,12135,12137,12139,12141,12143,12145,12147],{},[2071,12134,4271],{},[2075,12136,2084],{"stretchy":2083},[2071,12138,69],{},[2075,12140,2361],{"separator":2360},[2071,12142,2179],{},[2075,12144,2090],{"stretchy":2083},[2075,12146,2077],{},[2210,12148,630],{},[2092,12150,12151],{"encoding":2094},"D(a, b) = 0"," podmínka nerozhoduje.",[84,12154,12156],{"id":12155},"vázané-extrémy","Vázané extrémy",[55,12158,12159,12160,12189,12190,195],{},"Pro extrémy s omezující podmínkou ",[1647,12161,12163],{"className":12162},[2059],[2061,12164,12165],{"xmlns":2063},[2065,12166,12167,12186],{},[2068,12168,12169,12172,12174,12176,12178,12180,12182,12184],{},[2071,12170,12171],{},"g",[2075,12173,2084],{"stretchy":2083},[2071,12175,2087],{},[2075,12177,2361],{"separator":2360},[2071,12179,2073],{},[2075,12181,2090],{"stretchy":2083},[2075,12183,2077],{},[2210,12185,630],{},[2092,12187,12188],{"encoding":2094},"g(x, y) = 0"," se používá ",[69,12191,12195],{"className":12192,"dataFsResolvedFilePath":12193,"href":12194},[62],"topics\u002Flagrangeova-metoda.md","\u002Fwiki\u002Flagrangeova-metoda","Lagrangeova metoda",[84,12197,3866],{"id":3865},[89,12199,12200,12207,12214],{},[92,12201,12202,1445,12204],{},[95,12203,3873],{},[69,12205,3890],{"className":12206,"dataFsResolvedFilePath":3888,"href":3889},[62],[92,12208,12209,1445,12211],{},[95,12210,3884],{},[69,12212,12195],{"className":12213,"dataFsResolvedFilePath":12193,"href":12194},[62],[92,12215,12216,1445,12218,12222,12223,12227,12228,12231],{},[95,12217,3895],{},[69,12219,12221],{"className":12220,"dataFsResolvedFilePath":10942,"href":10943},[62],"Produkce"," (parciální derivace = mezní produkty), ",[69,12224,12226],{"className":12225,"dataFsResolvedFilePath":10901,"href":10902},[62],"Užitečnost"," (parciální derivace = mezní užitečnost), ",[69,12229,3913],{"className":12230,"dataFsResolvedFilePath":3911,"href":3912},[62]," (vícefaktorový model)",{"title":156,"searchDepth":7,"depth":7,"links":12233},[12234,12235,12239,12240,12241,12245,12246],{"id":10786,"depth":7,"text":10787},{"id":10947,"depth":7,"text":10948,"children":12236},[12237,12238],{"id":11100,"depth":4,"text":11101},{"id":2640,"depth":4,"text":2641},{"id":11429,"depth":7,"text":11430},{"id":11551,"depth":7,"text":11552},{"id":11736,"depth":7,"text":11737,"children":12242},[12243,12244],{"id":3325,"depth":4,"text":3326},{"id":3399,"depth":4,"text":3400},{"id":12155,"depth":7,"text":12156},{"id":3865,"depth":7,"text":3866},"Většina ekonomických veličin závisí na více faktorech — produkce na práci a kapitálu, užitečnost na množství různých statků, poptávka na cenách více zboží i důchodu. Kalkul jedné proměnné se proto rozšiřuje na z=f(x,y)z = f(x, y), w=f(x,y,z),…w = f(x, y, z), \\ldots.",{},"\u002Ftopics\u002Ffunkce-vice-promennych",{"title":10698,"description":12247},[3938],"topics\u002Ffunkce-vice-promennych",[17,12254,3941,12255,12256,12257],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":12260,"title":12261,"body":12262,"course":163,"courses":12493,"created":165,"description":156,"extension":166,"meta":12494,"navigation":168,"path":12495,"seo":12496,"sources":12497,"stem":12500,"tags":12501,"type":177,"updated":178,"__hash__":12506},"topics\u002Ftopics\u002Ffuzzy-logika.md","Fuzzy logika",{"type":48,"value":12263,"toc":12483},[12264,12266,12272,12279,12283,12309,12313,12345,12348,12352,12366,12370,12387,12389,12422,12424,12447,12449,12452,12457],[51,12265,12261],{"id":834},[55,12267,12268],{},[58,12269],{"alt":834,"className":12270,"src":12271},[62,63],"\u002Fwiki-assets\u002Ffuzzy-logika.jpeg",[55,12273,12274,12275,12278],{},"Metoda modelování rozhodování s vágními (neostrými) pojmy. Na rozdíl od klasické binární logiky (0\u002F1) pracuje fuzzy logika s ",[95,12276,12277],{},"mírou členství"," μ ∈ ⟨0, 1⟩ — prvek může patřit do více množin současně s různou intenzitou.",[84,12280,12282],{"id":12281},"základní-principy","Základní principy",[89,12284,12285,12291,12297,12303],{},[92,12286,12287,12290],{},[95,12288,12289],{},"Funkce členství"," — přiřazuje každému prvku stupeň příslušnosti k fuzzy množině. Základní tvary: L-funkce, trojúhelníková (Λ), trapezoidní (Π), S-funkce, Z-funkce.",[92,12292,12293,12296],{},[95,12294,12295],{},"Jazykové proměnné"," — vágní pojmy (nízké riziko, vysoký plat) formalizované jako termy. Např. riziko: {velmi nízké, nízké, střední, vysoké, velmi vysoké}.",[92,12298,12299,12302],{},[95,12300,12301],{},"Pravidla KDYŽ–POTOM"," — jádro fuzzy inferenčního systému. Modelují expertní znalost. AND = minimum\u002Fsoučin, OR = maximum.",[92,12304,12305,12308],{},[95,12306,12307],{},"Defuzzifikace"," — převod fuzzy výsledku na konečné rozhodnutí (např. normalizace na 0–100 % a rozdělení do kategorií).",[84,12310,12312],{"id":12311},"architektura-fuzzy-systému","Architektura fuzzy systému",[201,12314,12315,12321,12327,12333,12339],{},[92,12316,12317,12320],{},[95,12318,12319],{},"Vstupy"," — číselné veličiny",[92,12322,12323,12326],{},[95,12324,12325],{},"Fuzzifikace"," — převod na stupně členství",[92,12328,12329,12332],{},[95,12330,12331],{},"Blok pravidel"," — KDYŽ–POTOM pravidla",[92,12334,12335,12338],{},[95,12336,12337],{},"Inference"," — vyhodnocení pravidel",[92,12340,12341,12344],{},[95,12342,12343],{},"Výstup"," — fuzzy nebo defuzzifikovaný výsledek",[55,12346,12347],{},"Systém může mít více vstupů i více výstupů (např. celkové riziko + typ investora).",[84,12349,12351],{"id":12350},"nástroje","Nástroje",[89,12353,12354,12360],{},[92,12355,12356,12359],{},[95,12357,12358],{},"Excel"," — jednoduché modely, matice příslušnosti, funkce KDYŽ pro defuzzifikaci",[92,12361,12362,12365],{},[95,12363,12364],{},"MATLAB Fuzzy Logic Toolbox"," — pokročilejší modely, vizualizace, ladění pravidel",[84,12367,12369],{"id":12368},"typické-aplikace","Typické aplikace",[89,12371,12372,12375,12378,12381,12384],{},[92,12373,12374],{},"Hodnocení investičního rizika",[92,12376,12377],{},"Úvěrové skórování",[92,12379,12380],{},"Výběr projektu, hodnocení dodavatele",[92,12382,12383],{},"Rozhodování o výrobě",[92,12385,12386],{},"Profilace investora (averze vs. vyhledávání rizika)",[84,12388,723],{"id":722},[89,12390,12391,12404,12413],{},[92,12392,12393,12399,12400],{},[69,12394,12398],{"className":12395,"dataFsResolvedFilePath":12396,"href":12397},[62],"topics\u002Fanfis.md","\u002Fwiki\u002Fanfis","ANFIS"," — hybridní systém propojující fuzzy logiku s ",[69,12401,12403],{"className":12402,"dataFsResolvedFilePath":79,"href":80},[62],"neuronovými sítěmi",[92,12405,12406,12412],{},[69,12407,12411],{"className":12408,"dataFsResolvedFilePath":12409,"href":12410},[62],"topics\u002Fteorie-chaosu.md","\u002Fwiki\u002Fteorie-chaosu","Teorie chaosu"," — oba přístupy řeší nejistotu, ale jiným způsobem",[92,12414,12415,12421],{},[69,12416,12420],{"className":12417,"dataFsResolvedFilePath":12418,"href":12419},[62],"topics\u002Fpredikce.md","\u002Fwiki\u002Fpredikce","Predikce"," — fuzzy systémy mohou sloužit jako základ predikčních modelů",[84,12423,1913],{"id":1912},[201,12425,12426,12429,12432,12435,12438,12441,12444],{},[92,12427,12428],{},"Popište metodu a vysvětlete princip fuzzy logiky.",[92,12430,12431],{},"Popište realizaci a výpočet fuzzy logiky na počítači.",[92,12433,12434],{},"Jak lze využít fuzzy logiky v praxi?",[92,12436,12437],{},"Kdo byl zakladatelem fuzzy logiky?",[92,12439,12440],{},"Jaká je posloupnost kroků při zpracování případů fuzzy logikou?",[92,12442,12443],{},"Co znamená proces fuzzifikace?",[92,12445,12446],{},"Co je to defuzzifikace?",[84,12448,1946],{"id":1945},[55,12450,12451],{},"Fuzzy logika, fuzzifikace, fuzzy inference, defuzzifikace, transformační a retransformační matice, vstup, rozhodovací blok, výstup.",[84,12453,756,12454],{"id":1952},[69,12455,136],{"className":12456,"dataFsResolvedFilePath":134,"href":135},[62],[89,12458,12459,12468,12477],{},[92,12460,12461,12467],{},[69,12462,12466],{"className":12463,"dataFsResolvedFilePath":12464,"href":12465},[62],"summaries\u002Fipmrk-fuzzy-excel.md","\u002Fwiki\u002Fipmrk-fuzzy-excel","Fuzzy logika — Excel"," — základní princip, funkce členství, implementace",[92,12469,12470,12476],{},[69,12471,12475],{"className":12472,"dataFsResolvedFilePath":12473,"href":12474},[62],"summaries\u002Fipmrk-fuzzy-matlab.md","\u002Fwiki\u002Fipmrk-fuzzy-matlab","Fuzzy logika — MATLAB"," — architektura systému, návrh modelu",[92,12478,12479,12482],{},[69,12480,1965],{"className":12481,"dataFsResolvedFilePath":1963,"href":1964},[62]," — shrnutí kapitoly, kontrolní otázky, pojmy",{"title":156,"searchDepth":7,"depth":7,"links":12484},[12485,12486,12487,12488,12489,12490,12491,12492],{"id":12281,"depth":7,"text":12282},{"id":12311,"depth":7,"text":12312},{"id":12350,"depth":7,"text":12351},{"id":12368,"depth":7,"text":12369},{"id":722,"depth":7,"text":723},{"id":1912,"depth":7,"text":1913},{"id":1945,"depth":7,"text":1946},{"id":1952,"depth":7,"text":2003},[14],{},"\u002Ftopics\u002Ffuzzy-logika",{"title":12261,"description":156},[12498,12499,2009],"raw\u002Fipmrk\u002Ffuzzy-excel.md","raw\u002Fipmrk\u002Ffuzzy-matlab.md","topics\u002Ffuzzy-logika",[14,29,12502,12503,12504,12505],"funkce-clenstvi","pravidla","inference","defuzzifikace","2QGb9et6Ck5AGYFKMs7BnN3IeorbBz8DsZp0aSyXVZk",{"id":12508,"title":12509,"body":12510,"course":163,"courses":12839,"created":165,"description":156,"extension":166,"meta":12840,"navigation":168,"path":12841,"seo":12842,"sources":12843,"stem":12846,"tags":12847,"type":177,"updated":178,"__hash__":12851},"topics\u002Ftopics\u002Fgeneticke-algoritmy.md","Genetické algoritmy",{"type":48,"value":12511,"toc":12826},[12512,12515,12522,12529,12533,12559,12563,12570,12607,12611,12625,12629,12632,12639,12643,12657,12661,12729,12733,12739,12745,12747,12768,12770,12793,12795,12798,12803],[51,12513,12509],{"id":12514},"genetické-algoritmy",[55,12516,12517],{},[58,12518],{"alt":12519,"className":12520,"src":12521},"ga-cyklus",[62,63],"\u002Fwiki-assets\u002Fga-cyklus.jpeg",[55,12523,12524,12525,12528],{},"Evoluční optimalizační metoda inspirovaná biologickou dědičností a přirozeným výběrem (Mendel, Darwin). Místo přímého hledání řešení pracuje s ",[95,12526,12527],{},"populací kandidátních řešení",", která se postupně zlepšuje.",[84,12530,12532],{"id":12531},"základní-pojmy","Základní pojmy",[89,12534,12535,12541,12547,12553],{},[92,12536,12537,12540],{},[95,12538,12539],{},"Chromozom"," — kódované řešení (často binární řetězec, např. 1100)",[92,12542,12543,12546],{},[95,12544,12545],{},"Gen"," — jednotlivý bit chromozomu",[92,12548,12549,12552],{},[95,12550,12551],{},"Fitness funkce"," — účelová funkce hodnotící kvalitu řešení",[92,12554,12555,12558],{},[95,12556,12557],{},"Populace"," — soubor chromozomů v jedné generaci",[84,12560,12562],{"id":12561},"cyklus-algoritmu","Cyklus algoritmu",[55,12564,12565],{},[58,12566],{"alt":12567,"className":12568,"src":12569},"ga-krizeni-mutace",[62,63],"\u002Fwiki-assets\u002Fga-krizeni-mutace.jpeg",[201,12571,12572,12577,12583,12589,12595,12601],{},[92,12573,12574,12576],{},[95,12575,1165],{}," — vytvoření počáteční (náhodné) populace",[92,12578,12579,12582],{},[95,12580,12581],{},"Hodnocení"," — ohodnocení každého chromozomu fitness funkcí",[92,12584,12585,12588],{},[95,12586,12587],{},"Selekce"," — výběr lepších jedinců (lepší = větší šance přežít, ale i horší mohou zůstat pro diverzitu)",[92,12590,12591,12594],{},[95,12592,12593],{},"Křížení"," — kombinace dvou rodičů → potomci s vlastnostmi obou (pravděpodobnost ~0,9)",[92,12596,12597,12600],{},[95,12598,12599],{},"Mutace"," — náhodná změna bitu (0↔1), vzácná (~0,1), zabraňuje zamrznutí populace",[92,12602,12603,12606],{},[95,12604,12605],{},"Ukončení?"," — pokud ne, zpět na krok 2 (nová generace)",[84,12608,12610],{"id":12609},"parametry","Parametry",[89,12612,12613,12616,12619,12622],{},[92,12614,12615],{},"Velikost populace (~1000)",[92,12617,12618],{},"Pravděpodobnost křížení (~0,9)",[92,12620,12621],{},"Pravděpodobnost mutace (~0,1 nebo méně)",[92,12623,12624],{},"Kritéria ukončení: max generací, max čas, populace se nemění",[84,12626,12628],{"id":12627},"binární-kódování","Binární kódování",[55,12630,12631],{},"Chromozom jako binární řetězec → převod na reálnou hodnotu:\nH_D = a₃·2³ + a₂·2² + a₁·2¹ + a₀·2⁰",[55,12633,12634,12635,12638],{},"Mapování na interval ",[1647,12636,12637],{},"x_min, x_max"," umožňuje optimalizovat reálné parametry.",[84,12640,12642],{"id":12641},"dva-typy-úloh","Dva typy úloh",[89,12644,12645,12651],{},[92,12646,12647,12650],{},[95,12648,12649],{},"Přímá optimalizace"," — min nákladů, max zisku, min času, min odpadu",[92,12652,12653,12656],{},[95,12654,12655],{},"Parametrická optimalizace modelu"," — nejlepší parametry funkce, nejlepší nastavení predikčního systému",[84,12658,12660],{"id":12659},"aplikace","Aplikace",[323,12662,12663,12671],{},[326,12664,12665],{},[329,12666,12667,12669],{},[332,12668,523],{},[332,12670,3144],{},[342,12672,12673,12681,12689,12697,12705,12713,12721],{},[329,12674,12675,12678],{},[347,12676,12677],{},"Ekonomika",[347,12679,12680],{},"Minimalizace nákladů, maximalizace zisku",[329,12682,12683,12686],{},[347,12684,12685],{},"Výroba",[347,12687,12688],{},"Minimalizace výrobního času, rozvrhování strojů",[329,12690,12691,12694],{},[347,12692,12693],{},"Logistika",[347,12695,12696],{},"Obchodní cestující (TSP), nejkratší trasa",[329,12698,12699,12702],{},[347,12700,12701],{},"Materiál",[347,12703,12704],{},"Cutting plan — řezání s minimálním odpadem",[329,12706,12707,12710],{},[347,12708,12709],{},"Investice",[347,12711,12712],{},"Knapsack — výběr projektů při omezeném rozpočtu",[329,12714,12715,12718],{},[347,12716,12717],{},"Data",[347,12719,12720],{},"Aproximace měřených dat, klastrování, segmentace",[329,12722,12723,12726],{},[347,12724,12725],{},"Finance",[347,12727,12728],{},"[[predikce",[84,12730,12732],{"id":12731},"výhody-a-nevýhody","Výhody a nevýhody",[55,12734,12735,12738],{},[95,12736,12737],{},"Výhody",": nepotřebují derivace, pracují s diskrétními i spojitými problémy, zvládají mnoho lokálních extrémů, univerzálně použitelné.",[55,12740,12741,12744],{},[95,12742,12743],{},"Nevýhody",": negarantují globální optimum, výpočetně náročné, výsledek závisí na nastavení parametrů.",[84,12746,723],{"id":722},[89,12748,12749,12756,12762],{},[92,12750,12751,12755],{},[69,12752,12754],{"className":12753,"dataFsResolvedFilePath":79,"href":80},[62],"Neuronové sítě"," — GA mohou optimalizovat architekturu sítě",[92,12757,12758,12761],{},[69,12759,12420],{"className":12760,"dataFsResolvedFilePath":12418,"href":12419},[62]," — optimalizace predikčních modelů",[92,12763,12764,12767],{},[69,12765,12261],{"className":12766,"dataFsResolvedFilePath":72,"href":73},[62]," — GA mohou ladit parametry fuzzy systému",[84,12769,1913],{"id":1912},[201,12771,12772,12775,12778,12781,12784,12787,12790],{},[92,12773,12774],{},"Popište metodu a vysvětlete princip genetických algoritmů.",[92,12776,12777],{},"Popište realizaci a výpočet genetických algoritmů na počítači.",[92,12779,12780],{},"Jak lze využít genetických algoritmů v praxi?",[92,12782,12783],{},"Jaké jsou prvky reprodukce?",[92,12785,12786],{},"Co znamená proces selekce?",[92,12788,12789],{},"Co znamená proces mutace?",[92,12791,12792],{},"Jaká se volí velikost populace?",[84,12794,1946],{"id":1945},[55,12796,12797],{},"Genetické algoritmy, optimalizace, reprodukce, selekce, křížení, mutace, účelová funkce, omezující podmínky, parametry výpočtu.",[84,12799,756,12800],{"id":1952},[69,12801,136],{"className":12802,"dataFsResolvedFilePath":134,"href":135},[62],[89,12804,12805,12813,12821],{},[92,12806,12807],{},[69,12808,12812],{"className":12809,"dataFsResolvedFilePath":12810,"href":12811},[62],"summaries\u002Fipmrk-ga-teorie.md","\u002Fwiki\u002Fipmrk-ga-teorie","Genetické algoritmy — teorie",[92,12814,12815],{},[69,12816,12820],{"className":12817,"dataFsResolvedFilePath":12818,"href":12819},[62],"summaries\u002Fipmrk-ga-vyuziti.md","\u002Fwiki\u002Fipmrk-ga-vyuziti","Genetické algoritmy — využití",[92,12822,12823,12482],{},[69,12824,1965],{"className":12825,"dataFsResolvedFilePath":1963,"href":1964},[62],{"title":156,"searchDepth":7,"depth":7,"links":12827},[12828,12829,12830,12831,12832,12833,12834,12835,12836,12837,12838],{"id":12531,"depth":7,"text":12532},{"id":12561,"depth":7,"text":12562},{"id":12609,"depth":7,"text":12610},{"id":12627,"depth":7,"text":12628},{"id":12641,"depth":7,"text":12642},{"id":12659,"depth":7,"text":12660},{"id":12731,"depth":7,"text":12732},{"id":722,"depth":7,"text":723},{"id":1912,"depth":7,"text":1913},{"id":1945,"depth":7,"text":1946},{"id":1952,"depth":7,"text":2003},[14],{},"\u002Ftopics\u002Fgeneticke-algoritmy",{"title":12509,"description":156},[12844,12845,2009],"raw\u002Fipmrk\u002Fga-teorie.md","raw\u002Fipmrk\u002Fga-vyuziti.md","topics\u002Fgeneticke-algoritmy",[14,37,26,12848,12849,12850],"selekce","krizeni","mutace","EOZsCFN6Xx3jsNFX_SunmlY9UI9b8VubGTEwPCfPmQ8",{"id":12853,"title":3890,"body":12854,"course":17,"courses":163,"created":3932,"description":13714,"extension":166,"meta":13715,"navigation":168,"path":13716,"seo":13717,"sources":13718,"stem":13719,"tags":13720,"type":177,"updated":178,"__hash__":13727},"topics\u002Ftopics\u002Fintegral.md",{"type":48,"value":12855,"toc":13704},[12856,12859,12870,12874,12919,12999,13003,13079,13121,13128,13132,13136,13165,13223,13270,13308,13312,13362,13414,13466,13510,13514,13517,13589,13592,13664,13673,13675],[51,12857,3890],{"id":12858},"integrál",[55,12860,12861,12862,12865,12866,12869],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[95,12863,12864],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[95,12867,12868],{},"přebytků"," (consumer\u002Fproducer surplus).",[84,12871,12873],{"id":12872},"neurčitý-integrál","Neurčitý integrál",[55,12875,12876],{},[1647,12877,12879],{"className":12878},[2059],[2061,12880,12881],{"xmlns":2063},[2065,12882,12883,12916],{},[2068,12884,12885,12887,12889,12891,12893,12895,12898,12900,12902,12904,12906,12908,12910,12912,12914],{},[2071,12886,10177],{},[2075,12888,2084],{"stretchy":2083},[2071,12890,2087],{},[2075,12892,2090],{"stretchy":2083},[2075,12894,2077],{},[2075,12896,12897],{},"∫",[2071,12899,2080],{},[2075,12901,2084],{"stretchy":2083},[2071,12903,2087],{},[2075,12905,2090],{"stretchy":2083},[2363,12907,3061],{},[2071,12909,2273],{},[2071,12911,2087],{},[2075,12913,2176],{},[2071,12915,2849],{},[2092,12917,12918],{"encoding":2094},"F(x) = \\int f(x)\\, dx + C",[55,12920,4397,12921,2999,12955,8189,12968,12971,12972,835,12985,12998],{},[1647,12922,12924],{"className":12923},[2059],[2061,12925,12926],{"xmlns":2063},[2065,12927,12928,12952],{},[2068,12929,12930,12936,12938,12940,12942,12944,12946,12948,12950],{},[2205,12931,12932,12934],{},[2071,12933,10177],{},[2075,12935,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,12937,2084],{"stretchy":2083},[2071,12939,2087],{},[2075,12941,2090],{"stretchy":2083},[2075,12943,2077],{},[2071,12945,2080],{},[2075,12947,2084],{"stretchy":2083},[2071,12949,2087],{},[2075,12951,2090],{"stretchy":2083},[2092,12953,12954],{"encoding":2094},"F'(x) = f(x)",[1647,12956,12958],{"className":12957},[2059],[2061,12959,12960],{"xmlns":2063},[2065,12961,12962,12966],{},[2068,12963,12964],{},[2071,12965,10177],{},[2092,12967,10177],{"encoding":2094},[95,12969,12970],{},"primitivní funkce"," k ",[1647,12973,12975],{"className":12974},[2059],[2061,12976,12977],{"xmlns":2063},[2065,12978,12979,12983],{},[2068,12980,12981],{},[2071,12982,2080],{},[2092,12984,2080],{"encoding":2094},[1647,12986,12988],{"className":12987},[2059],[2061,12989,12990],{"xmlns":2063},[2065,12991,12992,12996],{},[2068,12993,12994],{},[2071,12995,2849],{},[2092,12997,2849],{"encoding":2094}," konstanta.",[84,13000,13002],{"id":13001},"určitý-integrál","Určitý integrál",[55,13004,13005],{},[1647,13006,13008],{"className":13007},[2059],[2061,13009,13010],{"xmlns":2063},[2065,13011,13012,13076],{},[2068,13013,13014,13022,13024,13026,13028,13030,13032,13034,13036,13038,13040,13042,13044,13046,13048,13056,13058,13060,13062,13064,13066,13068,13070,13072,13074],{},[9252,13015,13016,13018,13020],{},[2075,13017,12897],{},[2071,13019,69],{},[2071,13021,2179],{},[2071,13023,2080],{},[2075,13025,2084],{"stretchy":2083},[2071,13027,2087],{},[2075,13029,2090],{"stretchy":2083},[2363,13031,3061],{},[2071,13033,2273],{},[2071,13035,2087],{},[2075,13037,2077],{},[2075,13039,2561],{"stretchy":2083},[2071,13041,10177],{},[2075,13043,2084],{"stretchy":2083},[2071,13045,2087],{},[2075,13047,2090],{"stretchy":2083},[9252,13049,13050,13052,13054],{},[2075,13051,2576],{"stretchy":2083},[2071,13053,69],{},[2071,13055,2179],{},[2075,13057,2077],{},[2071,13059,10177],{},[2075,13061,2084],{"stretchy":2083},[2071,13063,2179],{},[2075,13065,2090],{"stretchy":2083},[2075,13067,2303],{},[2071,13069,10177],{},[2075,13071,2084],{"stretchy":2083},[2071,13073,69],{},[2075,13075,2090],{"stretchy":2083},[2092,13077,13078],{"encoding":2094},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[55,13080,13081,13082,1445,13085,13098,13099,13120],{},"Geometricky ",[95,13083,13084],{},"plocha pod grafem",[1647,13086,13088],{"className":13087},[2059],[2061,13089,13090],{"xmlns":2063},[2065,13091,13092,13096],{},[2068,13093,13094],{},[2071,13095,2080],{},[2092,13097,2080],{"encoding":2094}," na intervalu ",[1647,13100,13102],{"className":13101},[2059],[2061,13103,13104],{"xmlns":2063},[2065,13105,13106,13118],{},[2068,13107,13108,13110,13112,13114,13116],{},[2075,13109,2561],{"stretchy":2083},[2071,13111,69],{},[2075,13113,2361],{"separator":2360},[2071,13115,2179],{},[2075,13117,2576],{"stretchy":2083},[2092,13119,11954],{"encoding":2094}," (orientovaná).",[55,13122,13123],{},[58,13124],{"alt":13125,"className":13126,"src":13127},"imek-integral-plocha",[62,63],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[84,13129,13131],{"id":13130},"aplikace-v-ekonomii","Aplikace v ekonomii",[609,13133,13135],{"id":13134},"příklad-tr-z-mr","Příklad — TR z MR",[55,13137,13138,13139,195],{},"Mezní příjem ",[1647,13140,13142],{"className":13141},[2059],[2061,13143,13144],{"xmlns":2063},[2065,13145,13146,13162],{},[2068,13147,13148,13150,13152,13154,13156,13158,13160],{},[2071,13149,2890],{},[2071,13151,4082],{},[2075,13153,2077],{},[2210,13155,3164],{},[2075,13157,2303],{},[2210,13159,646],{},[2071,13161,2861],{},[2092,13163,13164],{"encoding":2094},"MR = 100 - 2Q",[55,13166,13167],{},[1647,13168,13170],{"className":13169},[2059],[2061,13171,13172],{"xmlns":2063},[2065,13173,13174,13220],{},[2068,13175,13176,13178,13180,13182,13184,13186,13188,13190,13192,13194,13196,13198,13200,13202,13204,13206,13208,13210,13216,13218],{},[2071,13177,543],{},[2071,13179,4082],{},[2075,13181,2077],{},[2075,13183,12897],{},[2075,13185,2084],{"stretchy":2083},[2210,13187,3164],{},[2075,13189,2303],{},[2210,13191,646],{},[2071,13193,2861],{},[2075,13195,2090],{"stretchy":2083},[2363,13197,3061],{},[2071,13199,2273],{},[2071,13201,2861],{},[2075,13203,2077],{},[2210,13205,3164],{},[2071,13207,2861],{},[2075,13209,2303],{},[2205,13211,13212,13214],{},[2071,13213,2861],{},[2210,13215,646],{},[2075,13217,2176],{},[2071,13219,2222],{},[2092,13221,13222],{"encoding":2094},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[55,13224,13225,13226,3488,13252,2777],{},"Okrajová podmínka ",[1647,13227,13229],{"className":13228},[2059],[2061,13230,13231],{"xmlns":2063},[2065,13232,13233,13249],{},[2068,13234,13235,13237,13239,13241,13243,13245,13247],{},[2071,13236,543],{},[2071,13238,4082],{},[2075,13240,2084],{"stretchy":2083},[2210,13242,630],{},[2075,13244,2090],{"stretchy":2083},[2075,13246,2077],{},[2210,13248,630],{},[2092,13250,13251],{"encoding":2094},"TR(0) = 0",[1647,13253,13255],{"className":13254},[2059],[2061,13256,13257],{"xmlns":2063},[2065,13258,13259,13267],{},[2068,13260,13261,13263,13265],{},[2071,13262,2222],{},[2075,13264,2077],{},[2210,13266,630],{},[2092,13268,13269],{"encoding":2094},"c = 0",[55,13271,13272],{},[1647,13273,13275],{"className":13274},[2059],[2061,13276,13277],{"xmlns":2063},[2065,13278,13279,13305],{},[2068,13280,13281,13283,13285,13287,13289,13291,13293,13295,13297,13299],{},[2071,13282,543],{},[2071,13284,4082],{},[2075,13286,2084],{"stretchy":2083},[2071,13288,2861],{},[2075,13290,2090],{"stretchy":2083},[2075,13292,2077],{},[2210,13294,3164],{},[2071,13296,2861],{},[2075,13298,2303],{},[2205,13300,13301,13303],{},[2071,13302,2861],{},[2210,13304,646],{},[2092,13306,13307],{"encoding":2094},"TR(Q) = 100Q - Q^2",[609,13309,13311],{"id":13310},"příklad-tc-z-mc","Příklad — TC z MC",[55,13313,13314,13315,13341,13342,195],{},"Mezní náklady ",[1647,13316,13318],{"className":13317},[2059],[2061,13319,13320],{"xmlns":2063},[2065,13321,13322,13338],{},[2068,13323,13324,13326,13328,13330,13332,13334,13336],{},[2071,13325,2890],{},[2071,13327,2849],{},[2075,13329,2077],{},[2210,13331,646],{},[2075,13333,2176],{},[2210,13335,2911],{},[2071,13337,2861],{},[2092,13339,13340],{"encoding":2094},"MC = 2 + 0{,}2 Q",", fixní náklady ",[1647,13343,13345],{"className":13344},[2059],[2061,13346,13347],{"xmlns":2063},[2065,13348,13349,13359],{},[2068,13350,13351,13353,13355,13357],{},[2071,13352,10177],{},[2071,13354,2849],{},[2075,13356,2077],{},[2210,13358,3164],{},[2092,13360,13361],{"encoding":2094},"FC = 100",[55,13363,13364],{},[1647,13365,13367],{"className":13366},[2059],[2061,13368,13369],{"xmlns":2063},[2065,13370,13371,13411],{},[2068,13372,13373,13375,13377,13379,13381,13383,13385,13387,13389,13391,13393,13395,13397,13399,13401,13407,13409],{},[2071,13374,543],{},[2071,13376,2849],{},[2075,13378,2077],{},[2075,13380,12897],{},[2071,13382,2890],{},[2071,13384,2849],{},[2363,13386,3061],{},[2071,13388,2273],{},[2071,13390,2861],{},[2075,13392,2077],{},[2210,13394,646],{},[2071,13396,2861],{},[2075,13398,2176],{},[2210,13400,2866],{},[2205,13402,13403,13405],{},[2071,13404,2861],{},[2210,13406,646],{},[2075,13408,2176],{},[2071,13410,2222],{},[2092,13412,13413],{"encoding":2094},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[55,13415,13225,13416,3488,13448,2777],{},[1647,13417,13419],{"className":13418},[2059],[2061,13420,13421],{"xmlns":2063},[2065,13422,13423,13445],{},[2068,13424,13425,13427,13429,13431,13433,13435,13437,13439,13441,13443],{},[2071,13426,543],{},[2071,13428,2849],{},[2075,13430,2084],{"stretchy":2083},[2210,13432,630],{},[2075,13434,2090],{"stretchy":2083},[2075,13436,2077],{},[2071,13438,10177],{},[2071,13440,2849],{},[2075,13442,2077],{},[2210,13444,3164],{},[2092,13446,13447],{"encoding":2094},"TC(0) = FC = 100",[1647,13449,13451],{"className":13450},[2059],[2061,13452,13453],{"xmlns":2063},[2065,13454,13455,13463],{},[2068,13456,13457,13459,13461],{},[2071,13458,2222],{},[2075,13460,2077],{},[2210,13462,3164],{},[2092,13464,13465],{"encoding":2094},"c = 100",[55,13467,13468],{},[1647,13469,13471],{"className":13470},[2059],[2061,13472,13473],{"xmlns":2063},[2065,13474,13475,13507],{},[2068,13476,13477,13479,13481,13483,13485,13487,13489,13491,13493,13495,13497,13499,13501],{},[2071,13478,543],{},[2071,13480,2849],{},[2075,13482,2084],{"stretchy":2083},[2071,13484,2861],{},[2075,13486,2090],{"stretchy":2083},[2075,13488,2077],{},[2210,13490,3164],{},[2075,13492,2176],{},[2210,13494,646],{},[2071,13496,2861],{},[2075,13498,2176],{},[2210,13500,2866],{},[2205,13502,13503,13505],{},[2071,13504,2861],{},[2210,13506,646],{},[2092,13508,13509],{"encoding":2094},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[609,13511,13513],{"id":13512},"přebytek-spotřebitele-a-výrobce","Přebytek spotřebitele a výrobce",[55,13515,13516],{},"Přebytek spotřebitele:",[55,13518,13519],{},[1647,13520,13522],{"className":13521},[2059],[2061,13523,13524],{"xmlns":2063},[2065,13525,13526,13586],{},[2068,13527,13528,13530,13532,13534,13540,13542,13544,13556,13558,13560,13562,13564,13566,13568,13570,13572,13578,13580],{},[2071,13529,2849],{},[2071,13531,532],{},[2075,13533,2084],{"stretchy":2083},[2348,13535,13536,13538],{},[2071,13537,2861],{},[2210,13539,630],{},[2075,13541,2090],{"stretchy":2083},[2075,13543,2077],{},[9252,13545,13546,13548,13550],{},[2075,13547,12897],{},[2210,13549,630],{},[2348,13551,13552,13554],{},[2071,13553,2861],{},[2210,13555,630],{},[2071,13557,4271],{},[2075,13559,2084],{"stretchy":2083},[2071,13561,2861],{},[2075,13563,2090],{"stretchy":2083},[2363,13565,3061],{},[2071,13567,2273],{},[2071,13569,2861],{},[2075,13571,2303],{},[2348,13573,13574,13576],{},[2071,13575,575],{},[2210,13577,630],{},[2363,13579,3061],{},[2348,13581,13582,13584],{},[2071,13583,2861],{},[2210,13585,630],{},[2092,13587,13588],{"encoding":2094},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[55,13590,13591],{},"Přebytek výrobce:",[55,13593,13594],{},[1647,13595,13597],{"className":13596},[2059],[2061,13598,13599],{"xmlns":2063},[2065,13600,13601,13661],{},[2068,13602,13603,13605,13607,13609,13615,13617,13619,13625,13627,13633,13635,13647,13649,13651,13653,13655,13657,13659],{},[2071,13604,575],{},[2071,13606,532],{},[2075,13608,2084],{"stretchy":2083},[2348,13610,13611,13613],{},[2071,13612,2861],{},[2210,13614,630],{},[2075,13616,2090],{"stretchy":2083},[2075,13618,2077],{},[2348,13620,13621,13623],{},[2071,13622,575],{},[2210,13624,630],{},[2363,13626,3061],{},[2348,13628,13629,13631],{},[2071,13630,2861],{},[2210,13632,630],{},[2075,13634,2303],{},[9252,13636,13637,13639,13641],{},[2075,13638,12897],{},[2210,13640,630],{},[2348,13642,13643,13645],{},[2071,13644,2861],{},[2210,13646,630],{},[2071,13648,532],{},[2075,13650,2084],{"stretchy":2083},[2071,13652,2861],{},[2075,13654,2090],{"stretchy":2083},[2363,13656,3061],{},[2071,13658,2273],{},[2071,13660,2861],{},[2092,13662,13663],{"encoding":2094},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[55,13665,13666,13667,195],{},"Detailně viz ",[69,13668,13672],{"className":13669,"dataFsResolvedFilePath":13670,"href":13671},[62],"topics\u002Fpoptavka-nabidka.md","\u002Fwiki\u002Fpoptavka-nabidka","Poptávka a nabídka",[84,13674,3866],{"id":3865},[89,13676,13677,13685,13692],{},[92,13678,13679,1445,13681],{},[95,13680,3873],{},[69,13682,13684],{"className":13683,"dataFsResolvedFilePath":4005,"href":4006},[62],"Derivace, diferenciál a extrémy 1D",[92,13686,13687,1445,13689],{},[95,13688,3884],{},[69,13690,3901],{"className":13691,"dataFsResolvedFilePath":3899,"href":3900},[62],[92,13693,13694,1445,13696,13699,13700,13703],{},[95,13695,3895],{},[69,13697,3906],{"className":13698,"dataFsResolvedFilePath":3022,"href":3023},[62]," (TR\u002FTC), ",[69,13701,13672],{"className":13702,"dataFsResolvedFilePath":13670,"href":13671},[62]," (přebytky CS\u002FPS)",{"title":156,"searchDepth":7,"depth":7,"links":13705},[13706,13707,13708,13713],{"id":12872,"depth":7,"text":12873},{"id":13001,"depth":7,"text":13002},{"id":13130,"depth":7,"text":13131,"children":13709},[13710,13711,13712],{"id":13134,"depth":4,"text":13135},{"id":13310,"depth":4,"text":13311},{"id":13512,"depth":4,"text":13513},{"id":3865,"depth":7,"text":3866},"Druhá polovina kalkulu jedné proměnné. Slouží k rekonstrukci totální veličiny z mezní (TR z MR, TC z MC) a k výpočtu přebytků (consumer\u002Fproducer surplus).",{},"\u002Ftopics\u002Fintegral",{"title":3890,"description":13714},[3938],"topics\u002Fintegral",[17,13721,13722,13723,13724,13725,13726],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":13729,"title":13730,"body":13731,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":18002,"navigation":168,"path":18003,"seo":18004,"sources":18005,"stem":18007,"tags":18008,"type":177,"updated":178,"__hash__":18014},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":48,"value":13732,"toc":17990},[13733,13736,13740,13884,13891,13895,13967,14005,14108,14112,14142,14208,14255,14258,14327,14330,14365,14401,14405,14453,14460,14506,14552,14555,14634,14731,14814,14818,14862,14892,14898,14927,14949,14999,15052,15118,15121,15187,15216,15275,15291,15378,15476,15607,15611,15768,15917,16297,16301,16304,16363,16366,16452,16480,16518,16521,16558,16598,16632,16634,16671,16703,16801,16806,16930,16982,17064,17203,17207,17327,17334,17445,17452,17454,17929,17931],[51,13734,13730],{"id":13735},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[84,13737,13739],{"id":13738},"tldr","TL;DR",[55,13741,13742,13745,13746,11156,13749,13762,13763,13777,13778,13781,13782,835,13785,13788,13789,835,13792,13795,13796,1445,13799,13829,13830,13833,13834,835,13848,13861,13862,13865,13866,4007],{},[95,13743,13744],{},"IS-LM"," je makroekonomický model se ",[95,13747,13748],{},"dvěma neznámými",[1647,13750,13752],{"className":13751},[2059],[2061,13753,13754],{"xmlns":2063},[2065,13755,13756,13760],{},[2068,13757,13758],{},[2071,13759,9214],{},[2092,13761,9214],{"encoding":2094}," — národní důchod a ",[1647,13764,13766],{"className":13765},[2059],[2061,13767,13768],{"xmlns":2063},[2065,13769,13770,13775],{},[2068,13771,13772],{},[2071,13773,13774],{},"r",[2092,13776,13774],{"encoding":2094}," — úroková míra) a ",[95,13779,13780],{},"dvěma trhy",": trhem zboží (křivka ",[95,13783,13784],{},"IS",[3982,13786,13787],{},"Investment = Savings",") a trhem peněz (křivka ",[95,13790,13791],{},"LM",[3982,13793,13794],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[95,13797,13798],{},"simultánní rovnováhu",[1647,13800,13802],{"className":13801},[2059],[2061,13803,13804],{"xmlns":2063},[2065,13805,13806,13826],{},[2068,13807,13808,13810,13816,13818,13824],{},[2075,13809,2084],{"stretchy":2083},[2205,13811,13812,13814],{},[2071,13813,9214],{},[2071,13815,554],{},[2075,13817,2361],{"separator":2360},[2205,13819,13820,13822],{},[2071,13821,13774],{},[2071,13823,554],{},[2075,13825,2090],{"stretchy":2083},[2092,13827,13828],{"encoding":2094},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[95,13831,13832],{},"fiskální politiky"," (posun IS změnou ",[1647,13835,13837],{"className":13836},[2059],[2061,13838,13839],{"xmlns":2063},[2065,13840,13841,13846],{},[2068,13842,13843],{},[2071,13844,13845],{},"G",[2092,13847,13845],{"encoding":2094},[1647,13849,13851],{"className":13850},[2059],[2061,13852,13853],{"xmlns":2063},[2065,13854,13855,13859],{},[2068,13856,13857],{},[2071,13858,543],{},[2092,13860,543],{"encoding":2094},") a ",[95,13863,13864],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[1647,13867,13869],{"className":13868},[2059],[2061,13870,13871],{"xmlns":2063},[2065,13872,13873,13881],{},[2068,13874,13875],{},[2205,13876,13877,13879],{},[2071,13878,2890],{},[2075,13880,4441],{},[2092,13882,13883],{"encoding":2094},"M^*",[55,13885,13886],{},[58,13887],{"alt":13888,"className":13889,"src":13890},"imek-is-lm-model",[62,63],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[84,13892,13894],{"id":13893},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[55,13896,13897,13898,13904,13905,11156,13908,13931,13932,13935,13936,13952,13953,13966],{},"V modelech ",[69,13899,13903],{"className":13900,"dataFsResolvedFilePath":13901,"href":13902},[62],"topics\u002Fnarodni-duchod.md","\u002Fwiki\u002Fnarodni-duchod","C-I, C-I-G a C-I-G-X"," byly ",[95,13906,13907],{},"investice pokládány za konstantní",[1647,13909,13911],{"className":13910},[2059],[2061,13912,13913],{"xmlns":2063},[2065,13914,13915,13928],{},[2068,13916,13917,13920,13922],{},[2071,13918,13919],{},"I",[2075,13921,2077],{},[2205,13923,13924,13926],{},[2071,13925,13919],{},[2075,13927,4441],{},[2092,13929,13930],{"encoding":2094},"I = I^*","). To není realistické — investice firem závisejí na ",[95,13933,13934],{},"ceně peněz",", tedy na ",[95,13937,13938,13939],{},"úrokové míře ",[1647,13940,13942],{"className":13941},[2059],[2061,13943,13944],{"xmlns":2063},[2065,13945,13946,13950],{},[2068,13947,13948],{},[2071,13949,13774],{},[2092,13951,13774],{"encoding":2094},": čím vyšší ",[1647,13954,13956],{"className":13955},[2059],[2061,13957,13958],{"xmlns":2063},[2065,13959,13960,13964],{},[2068,13961,13962],{},[2071,13963,13774],{},[2092,13965,13774],{"encoding":2094},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[89,13968,13969,13999],{},[92,13970,13971,1445,13974,13998],{},[95,13972,13973],{},"funkci investic",[1647,13975,13977],{"className":13976},[2059],[2061,13978,13979],{"xmlns":2063},[2065,13980,13981,13995],{},[2068,13982,13983,13985,13987,13989,13991,13993],{},[2071,13984,13919],{},[2075,13986,2077],{},[2071,13988,13919],{},[2075,13990,2084],{"stretchy":2083},[2071,13992,13774],{},[2075,13994,2090],{"stretchy":2083},[2092,13996,13997],{"encoding":2094},"I = I(r)"," jako klesající funkci úrokové míry,",[92,14000,14001,14004],{},[95,14002,14003],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1023,14006,14007],{},[55,14008,14009,14011,14012,14031,14032,14059,14060,14073,14074,14103,14104,14107],{},[1647,14010,4499],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[1647,14013,14015],{"className":14014},[2059],[2061,14016,14017],{"xmlns":2063},[2065,14018,14019,14028],{},[2068,14020,14021,14023,14026],{},[2071,14022,2849],{},[2363,14024,14025],{},"-",[2071,14027,13919],{},[2092,14029,14030],{"encoding":2094},"C\\text{-}I"," až ",[1647,14033,14035],{"className":14034},[2059],[2061,14036,14037],{"xmlns":2063},[2065,14038,14039,14056],{},[2068,14040,14041,14043,14045,14047,14049,14051,14053],{},[2071,14042,2849],{},[2363,14044,14025],{},[2071,14046,13919],{},[2363,14048,14025],{},[2071,14050,13845],{},[2363,14052,14025],{},[2071,14054,14055],{},"X",[2092,14057,14058],{"encoding":2094},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[1647,14061,14063],{"className":14062},[2059],[2061,14064,14065],{"xmlns":2063},[2065,14066,14067,14071],{},[2068,14068,14069],{},[2071,14070,9214],{},[2092,14072,9214],{"encoding":2094},". V IS-LM jsou ",[95,14075,14076,14077,75,14090],{},"dvě neznámé ",[1647,14078,14080],{"className":14079},[2059],[2061,14081,14082],{"xmlns":2063},[2065,14083,14084,14088],{},[2068,14085,14086],{},[2071,14087,9214],{},[2092,14089,9214],{"encoding":2094},[1647,14091,14093],{"className":14092},[2059],[2061,14094,14095],{"xmlns":2063},[2065,14096,14097,14101],{},[2068,14098,14099],{},[2071,14100,13774],{},[2092,14102,13774],{"encoding":2094},", a proto potřebujeme ",[95,14105,14106],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[84,14109,14111],{"id":14110},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[55,14113,14114,14115,14128,14129,2777],{},"Lineární závislost investic ",[1647,14116,14118],{"className":14117},[2059],[2061,14119,14120],{"xmlns":2063},[2065,14121,14122,14126],{},[2068,14123,14124],{},[2071,14125,13919],{},[2092,14127,13919],{"encoding":2094}," na úrokové míře ",[1647,14130,14132],{"className":14131},[2059],[2061,14133,14134],{"xmlns":2063},[2065,14135,14136,14140],{},[2068,14137,14138],{},[2071,14139,13774],{},[2092,14141,13774],{"encoding":2094},[55,14143,14144],{},[1647,14145,14147],{"className":14146},[2059],[2061,14148,14149],{"xmlns":2063},[2065,14150,14151,14205],{},[2068,14152,14153,14155,14157,14159,14161,14163,14165,14167,14169,14171,14173,14175,14177,14179,14181,14183,14185,14187,14189,14191,14193,14196,14198,14200,14203],{},[2071,14154,13919],{},[2075,14156,2077],{},[2071,14158,13919],{},[2075,14160,2084],{"stretchy":2083},[2071,14162,13774],{},[2075,14164,2090],{"stretchy":2083},[2075,14166,2077],{},[2071,14168,2222],{},[2071,14170,13774],{},[2075,14172,2176],{},[2071,14174,2273],{},[2075,14176,2361],{"separator":2360},[5965,14178],{"width":5967},[2071,14180,2222],{},[2075,14182,3521],{},[2210,14184,630],{},[2075,14186,2361],{"separator":2360},[2363,14188,2365],{},[2071,14190,2273],{},[2075,14192,3482],{},[2210,14194,14195],{},"0.",[5965,14197],{"width":5967},[2075,14199,2084],{"stretchy":2083},[2210,14201,14202],{},"7.11",[2075,14204,2090],{"stretchy":2083},[2092,14206,14207],{"encoding":2094},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[89,14209,14210,14231],{},[92,14211,14212,14230],{},[1647,14213,14215],{"className":14214},[2059],[2061,14216,14217],{"xmlns":2063},[2065,14218,14219,14227],{},[2068,14220,14221,14223,14225],{},[2071,14222,2273],{},[2075,14224,3482],{},[2210,14226,630],{},[2092,14228,14229],{"encoding":2094},"d > 0"," zřejmé,",[92,14232,14233,14251,14252,195],{},[1647,14234,14236],{"className":14235},[2059],[2061,14237,14238],{"xmlns":2063},[2065,14239,14240,14248],{},[2068,14241,14242,14244,14246],{},[2071,14243,2222],{},[2075,14245,3521],{},[2210,14247,630],{},[2092,14249,14250],{"encoding":2094},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[95,14253,14254],{},"klesající",[55,14256,14257],{},"Spotřeba zůstává lineární funkcí důchodu:",[55,14259,14260],{},[1647,14261,14263],{"className":14262},[2059],[2061,14264,14265],{"xmlns":2063},[2065,14266,14267,14324],{},[2068,14268,14269,14271,14273,14275,14277,14279,14281,14283,14285,14287,14289,14291,14293,14295,14297,14299,14301,14303,14305,14307,14309,14311,14313,14315,14317,14319,14322],{},[2071,14270,2849],{},[2075,14272,2077],{},[2071,14274,2849],{},[2075,14276,2084],{"stretchy":2083},[2071,14278,9214],{},[2075,14280,2090],{"stretchy":2083},[2075,14282,2077],{},[2071,14284,69],{},[2071,14286,9214],{},[2075,14288,2176],{},[2071,14290,2179],{},[2075,14292,2361],{"separator":2360},[5965,14294],{"width":5967},[2210,14296,630],{},[2075,14298,3521],{},[2071,14300,69],{},[2075,14302,3521],{},[2210,14304,638],{},[2075,14306,2361],{"separator":2360},[2363,14308,2365],{},[2071,14310,2179],{},[2075,14312,3482],{},[2210,14314,14195],{},[5965,14316],{"width":5967},[2075,14318,2084],{"stretchy":2083},[2210,14320,14321],{},"7.12",[2075,14323,2090],{"stretchy":2083},[2092,14325,14326],{"encoding":2094},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[55,14328,14329],{},"Podmínka rovnováhy na trhu zboží:",[55,14331,14332],{},[1647,14333,14335],{"className":14334},[2059],[2061,14336,14337],{"xmlns":2063},[2065,14338,14339,14362],{},[2068,14340,14341,14343,14345,14347,14349,14351,14353,14355,14357,14360],{},[2071,14342,9214],{},[2075,14344,2077],{},[2071,14346,2849],{},[2075,14348,2176],{},[2071,14350,13919],{},[2071,14352,195],{"mathvariant":2450},[5965,14354],{"width":5967},[2075,14356,2084],{"stretchy":2083},[2210,14358,14359],{},"7.13",[2075,14361,2090],{"stretchy":2083},[2092,14363,14364],{"encoding":2094},"Y = C + I. \\qquad (7.13)",[55,14366,14367,14368,1445,14371,14397,14398,195],{},"To dává ",[95,14369,14370],{},"tři rovnice o čtyřech neznámých",[1647,14372,14374],{"className":14373},[2059],[2061,14375,14376],{"xmlns":2063},[2065,14377,14378,14394],{},[2068,14379,14380,14382,14384,14386,14388,14390,14392],{},[2071,14381,9214],{},[2075,14383,2361],{"separator":2360},[2071,14385,2849],{},[2075,14387,2361],{"separator":2360},[2071,14389,13919],{},[2075,14391,2361],{"separator":2360},[2071,14393,13774],{},[2092,14395,14396],{"encoding":2094},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[95,14399,14400],{},"rovnováhy na trhu peněz",[84,14402,14404],{"id":14403},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[55,14406,14407,14408,5656,14430,14448,14449,14452],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[1647,14409,14411],{"className":14410},[2059],[2061,14412,14413],{"xmlns":2063},[2065,14414,14415,14427],{},[2068,14416,14417,14419,14421,14423,14425],{},[2071,14418,9214],{},[2075,14420,2077],{},[2071,14422,2849],{},[2075,14424,2176],{},[2071,14426,532],{},[2092,14428,14429],{"encoding":2094},"Y = C + S",[1647,14431,14433],{"className":14432},[2059],[2061,14434,14435],{"xmlns":2063},[2065,14436,14437,14445],{},[2068,14438,14439,14441,14443],{},[2071,14440,13919],{},[2075,14442,2077],{},[2071,14444,532],{},[2092,14446,14447],{"encoding":2094},"I = S"," (plánované ",[95,14450,14451],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[55,14454,14455],{},[58,14456],{"alt":14457,"className":14458,"src":14459},"imek-odvozeni-is-4panelu",[62,63],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[55,14461,14462],{},[1647,14463,14465],{"className":14464},[2059],[2061,14466,14467],{"xmlns":2063},[2065,14468,14469,14503],{},[2068,14470,14471,14473,14475,14477,14479,14481,14483,14485,14487,14489,14491,14493,14495,14497,14499,14501],{},[2071,14472,9214],{},[2075,14474,2077],{},[2075,14476,2084],{"stretchy":2083},[2071,14478,69],{},[2071,14480,9214],{},[2075,14482,2176],{},[2071,14484,2179],{},[2075,14486,2090],{"stretchy":2083},[2075,14488,2176],{},[2075,14490,2084],{"stretchy":2083},[2071,14492,2222],{},[2071,14494,13774],{},[2075,14496,2176],{},[2071,14498,2273],{},[2075,14500,2090],{"stretchy":2083},[2075,14502,2361],{"separator":2360},[2092,14504,14505],{"encoding":2094},"Y = (aY + b) + (cr + d),",[55,14507,14508],{},[1647,14509,14511],{"className":14510},[2059],[2061,14512,14513],{"xmlns":2063},[2065,14514,14515,14549],{},[2068,14516,14517,14519,14521,14523,14525,14527,14529,14531,14533,14535,14537,14539,14541,14543,14545,14547],{},[2075,14518,2084],{"stretchy":2083},[2210,14520,638],{},[2075,14522,2303],{},[2071,14524,69],{},[2075,14526,2090],{"stretchy":2083},[2071,14528,9214],{},[2075,14530,2303],{},[2071,14532,2222],{},[2071,14534,13774],{},[2075,14536,2303],{},[2071,14538,2179],{},[2075,14540,2303],{},[2071,14542,2273],{},[2075,14544,2077],{},[2210,14546,630],{},[2075,14548,2361],{"separator":2360},[2092,14550,14551],{"encoding":2094},"(1 - a)Y - cr - b - d = 0,",[55,14553,14554],{},"odkud",[55,14556,14557],{},[1647,14558,14560],{"className":14559},[2059],[2061,14561,14562],{"xmlns":2063},[2065,14563,14564,14631],{},[2068,14565,14566,14622,14624,14626,14629],{},[14567,14568,14570],"menclose",{"notation":14569},"box",[2400,14571,14572],{"scriptlevel":630,"displaystyle":2083},[2400,14573,14574],{"scriptlevel":630,"displaystyle":2083},[2400,14575,14576],{"scriptlevel":630,"displaystyle":2360},[2068,14577,14578,14580,14582,14584,14596,14598,14600,14602,14620],{},[2363,14579,3061],{},[2071,14581,9214],{},[2075,14583,2077],{},[2403,14585,14586,14588],{},[2071,14587,2222],{},[2068,14589,14590,14592,14594],{},[2210,14591,638],{},[2075,14593,2303],{},[2071,14595,69],{},[2363,14597,3061],{},[2071,14599,13774],{},[2075,14601,2176],{},[2403,14603,14604,14612],{},[2068,14605,14606,14608,14610],{},[2071,14607,2179],{},[2075,14609,2176],{},[2071,14611,2273],{},[2068,14613,14614,14616,14618],{},[2210,14615,638],{},[2075,14617,2303],{},[2071,14619,69],{},[2363,14621,3061],{},[5965,14623],{"width":5967},[2075,14625,2084],{"stretchy":2083},[2210,14627,14628],{},"7.14",[2075,14630,2090],{"stretchy":2083},[2092,14632,14633],{"encoding":2094},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[55,14635,14636,14637,11156,14640,14643,14644,14647,14648,14650,14651,14673,14674,14702,14703,14724,14725,14727,14728,14730],{},"Tento vztah se nazývá ",[95,14638,14639],{},"funkce IS",[3982,14641,14642],{},"IS schedule",") a její graf ",[95,14645,14646],{},"křivka IS",". Křivka je ",[95,14649,14254],{}," přímka v rovině ",[1647,14652,14654],{"className":14653},[2059],[2061,14655,14656],{"xmlns":2063},[2065,14657,14658,14670],{},[2068,14659,14660,14662,14664,14666,14668],{},[2075,14661,2084],{"stretchy":2083},[2071,14663,13774],{},[2075,14665,2361],{"separator":2360},[2071,14667,9214],{},[2075,14669,2090],{"stretchy":2083},[2092,14671,14672],{"encoding":2094},"(r, Y)",", neboť ",[1647,14675,14677],{"className":14676},[2059],[2061,14678,14679],{"xmlns":2063},[2065,14680,14681,14699],{},[2068,14682,14683,14695,14697],{},[2403,14684,14685,14687],{},[2071,14686,2222],{},[2068,14688,14689,14691,14693],{},[2210,14690,638],{},[2075,14692,2303],{},[2071,14694,69],{},[2075,14696,3521],{},[2210,14698,630],{},[2092,14700,14701],{"encoding":2094},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[1647,14704,14706],{"className":14705},[2059],[2061,14707,14708],{"xmlns":2063},[2065,14709,14710,14722],{},[2068,14711,14712,14714,14716,14718,14720],{},[2075,14713,2084],{"stretchy":2083},[2071,14715,13774],{},[2075,14717,2361],{"separator":2360},[2071,14719,9214],{},[2075,14721,2090],{"stretchy":2083},[2092,14723,14672],{"encoding":2094},", pro které plánované ",[95,14726,13919],{},"nvestment = ",[95,14729,532],{},"avings.",[1023,14732,14733],{},[55,14734,14735,14737,14738,14751,14752,1445,14755,14768,14769,14782,14783,75,14796,14809,14810,14813],{},[1647,14736,4243],{}," Intuice — proč IS klesá\nNižší úroková míra ",[1647,14739,14741],{"className":14740},[2059],[2061,14742,14743],{"xmlns":2063},[2065,14744,14745,14749],{},[2068,14746,14747],{},[2071,14748,13774],{},[2092,14750,13774],{"encoding":2094}," → levnější úvěr → ",[95,14753,14754],{},"více investic",[1647,14756,14758],{"className":14757},[2059],[2061,14759,14760],{"xmlns":2063},[2065,14761,14762,14766],{},[2068,14763,14764],{},[2071,14765,13919],{},[2092,14767,13919],{"encoding":2094}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[1647,14770,14772],{"className":14771},[2059],[2061,14773,14774],{"xmlns":2063},[2065,14775,14776,14780],{},[2068,14777,14778],{},[2071,14779,9214],{},[2092,14781,9214],{"encoding":2094},". Vztah mezi ",[1647,14784,14786],{"className":14785},[2059],[2061,14787,14788],{"xmlns":2063},[2065,14789,14790,14794],{},[2068,14791,14792],{},[2071,14793,13774],{},[2092,14795,13774],{"encoding":2094},[1647,14797,14799],{"className":14798},[2059],[2061,14800,14801],{"xmlns":2063},[2065,14802,14803,14807],{},[2068,14804,14805],{},[2071,14806,9214],{},[2092,14808,9214],{"encoding":2094}," na trhu zboží je proto ",[95,14811,14812],{},"nepřímý"," (klesající křivka).",[84,14815,14817],{"id":14816},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[55,14819,14820,14821,14839,14840,2999,14858,14861],{},"Rovnováha na trhu peněz: poptávka po penězích ",[1647,14822,14824],{"className":14823},[2059],[2061,14825,14826],{"xmlns":2063},[2065,14827,14828,14836],{},[2068,14829,14830],{},[2205,14831,14832,14834],{},[2071,14833,2890],{},[2071,14835,4271],{},[2092,14837,14838],{"encoding":2094},"M^D"," se rovná nabídce peněz ",[1647,14841,14843],{"className":14842},[2059],[2061,14844,14845],{"xmlns":2063},[2065,14846,14847,14855],{},[2068,14848,14849],{},[2205,14850,14851,14853],{},[2071,14852,2890],{},[2071,14854,532],{},[2092,14856,14857],{"encoding":2094},"M^S",[95,14859,14860],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[55,14863,14864],{},[1647,14865,14867],{"className":14866},[2059],[2061,14868,14869],{"xmlns":2063},[2065,14870,14871,14889],{},[2068,14872,14873,14879,14881,14887],{},[2205,14874,14875,14877],{},[2071,14876,2890],{},[2071,14878,532],{},[2075,14880,2077],{},[2205,14882,14883,14885],{},[2071,14884,2890],{},[2075,14886,4441],{},[2071,14888,195],{"mathvariant":2450},[2092,14890,14891],{"encoding":2094},"M^S = M^*.",[55,14893,14894,14897],{},[95,14895,14896],{},"Poptávka"," po penězích má tři zdroje:",[89,14899,14900,14909,14918],{},[92,14901,14902,11156,14905,14908],{},[95,14903,14904],{},"transakční poptávka",[3982,14906,14907],{},"transactions demand",") — peníze pro nákup zboží,",[92,14910,14911,11156,14914,14917],{},[95,14912,14913],{},"opatrnostní poptávka",[3982,14915,14916],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[92,14919,14920,11156,14923,14926],{},[95,14921,14922],{},"spekulační poptávka",[3982,14924,14925],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[55,14928,14929,14930,14948],{},"Součet transakční a opatrnostní poptávky ",[1647,14931,14933],{"className":14932},[2059],[2061,14934,14935],{"xmlns":2063},[2065,14936,14937,14945],{},[2068,14938,14939],{},[2348,14940,14941,14943],{},[2071,14942,586],{},[2210,14944,638],{},[2092,14946,14947],{"encoding":2094},"L_1"," je úměrný důchodu:",[55,14950,14951],{},[1647,14952,14954],{"className":14953},[2059],[2061,14955,14956],{"xmlns":2063},[2065,14957,14958,14996],{},[2068,14959,14960,14966,14968,14975,14977,14979,14981,14983,14985,14991,14993],{},[2348,14961,14962,14964],{},[2071,14963,586],{},[2210,14965,638],{},[2075,14967,2077],{},[2348,14969,14970,14973],{},[2071,14971,14972],{},"k",[2210,14974,638],{},[2071,14976,9214],{},[2075,14978,2361],{"separator":2360},[5965,14980],{"width":5967},[2210,14982,630],{},[2075,14984,3521],{},[2348,14986,14987,14989],{},[2071,14988,14972],{},[2210,14990,638],{},[2075,14992,3521],{},[2210,14994,14995],{},"1.",[2092,14997,14998],{"encoding":2094},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[55,15000,15001,15002,15020,15021,835,15034,15051],{},"Spekulační poptávka ",[1647,15003,15005],{"className":15004},[2059],[2061,15006,15007],{"xmlns":2063},[2065,15008,15009,15017],{},[2068,15010,15011],{},[2348,15012,15013,15015],{},[2071,15014,586],{},[2210,15016,646],{},[2092,15018,15019],{"encoding":2094},"L_2"," závisí na úrokové míře (roste-li ",[1647,15022,15024],{"className":15023},[2059],[2061,15025,15026],{"xmlns":2063},[2065,15027,15028,15032],{},[2068,15029,15030],{},[2071,15031,13774],{},[2092,15033,13774],{"encoding":2094},[1647,15035,15037],{"className":15036},[2059],[2061,15038,15039],{"xmlns":2063},[2065,15040,15041,15049],{},[2068,15042,15043],{},[2348,15044,15045,15047],{},[2071,15046,586],{},[2210,15048,646],{},[2092,15050,15019],{"encoding":2094}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[55,15053,15054],{},[1647,15055,15057],{"className":15056},[2059],[2061,15058,15059],{"xmlns":2063},[2065,15060,15061,15115],{},[2068,15062,15063,15069,15071,15077,15079,15081,15087,15089,15091,15097,15099,15101,15103,15105,15111,15113],{},[2348,15064,15065,15067],{},[2071,15066,586],{},[2210,15068,646],{},[2075,15070,2077],{},[2348,15072,15073,15075],{},[2071,15074,14972],{},[2210,15076,646],{},[2071,15078,13774],{},[2075,15080,2176],{},[2348,15082,15083,15085],{},[2071,15084,14972],{},[2210,15086,654],{},[2075,15088,2361],{"separator":2360},[5965,15090],{"width":5967},[2348,15092,15093,15095],{},[2071,15094,14972],{},[2210,15096,646],{},[2075,15098,3521],{},[2210,15100,630],{},[2075,15102,2361],{"separator":2360},[2363,15104,2365],{},[2348,15106,15107,15109],{},[2071,15108,14972],{},[2210,15110,654],{},[2075,15112,3482],{},[2210,15114,14195],{},[2092,15116,15117],{"encoding":2094},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[55,15119,15120],{},"Celková poptávka po penězích:",[55,15122,15123],{},[1647,15124,15126],{"className":15125},[2059],[2061,15127,15128],{"xmlns":2063},[2065,15129,15130,15184],{},[2068,15131,15132,15138,15140,15146,15148,15154,15156,15162,15164,15166,15172,15174,15176,15182],{},[2205,15133,15134,15136],{},[2071,15135,2890],{},[2071,15137,4271],{},[2075,15139,2077],{},[2348,15141,15142,15144],{},[2071,15143,586],{},[2210,15145,638],{},[2075,15147,2176],{},[2348,15149,15150,15152],{},[2071,15151,586],{},[2210,15153,646],{},[2075,15155,2077],{},[2348,15157,15158,15160],{},[2071,15159,14972],{},[2210,15161,638],{},[2071,15163,9214],{},[2075,15165,2176],{},[2348,15167,15168,15170],{},[2071,15169,14972],{},[2210,15171,646],{},[2071,15173,13774],{},[2075,15175,2176],{},[2348,15177,15178,15180],{},[2071,15179,14972],{},[2210,15181,654],{},[2071,15183,195],{"mathvariant":2450},[2092,15185,15186],{"encoding":2094},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[55,15188,15189,15190,2777],{},"Podmínka rovnováhy na trhu peněz ",[1647,15191,15193],{"className":15192},[2059],[2061,15194,15195],{"xmlns":2063},[2065,15196,15197,15213],{},[2068,15198,15199,15205,15207],{},[2205,15200,15201,15203],{},[2071,15202,2890],{},[2071,15204,4271],{},[2075,15206,2077],{},[2205,15208,15209,15211],{},[2071,15210,2890],{},[2075,15212,4441],{},[2092,15214,15215],{"encoding":2094},"M^D = M^*",[55,15217,15218],{},[1647,15219,15221],{"className":15220},[2059],[2061,15222,15223],{"xmlns":2063},[2065,15224,15225,15272],{},[2068,15226,15227,15233,15235,15241,15243,15245,15251,15253,15255,15261,15263,15265,15267,15270],{},[2205,15228,15229,15231],{},[2071,15230,2890],{},[2075,15232,4441],{},[2075,15234,2077],{},[2348,15236,15237,15239],{},[2071,15238,14972],{},[2210,15240,638],{},[2071,15242,9214],{},[2075,15244,2176],{},[2348,15246,15247,15249],{},[2071,15248,14972],{},[2210,15250,646],{},[2071,15252,13774],{},[2075,15254,2176],{},[2348,15256,15257,15259],{},[2071,15258,14972],{},[2210,15260,654],{},[2075,15262,2361],{"separator":2360},[5965,15264],{"width":5967},[2075,15266,2084],{"stretchy":2083},[2210,15268,15269],{},"7.15",[2075,15271,2090],{"stretchy":2083},[2092,15273,15274],{"encoding":2094},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[55,15276,15277,15278,3225],{},"po úpravě (vyjádření ",[1647,15279,15281],{"className":15280},[2059],[2061,15282,15283],{"xmlns":2063},[2065,15284,15285,15289],{},[2068,15286,15287],{},[2071,15288,9214],{},[2092,15290,9214],{"encoding":2094},[55,15292,15293],{},[1647,15294,15296],{"className":15295},[2059],[2061,15297,15298],{"xmlns":2063},[2065,15299,15300,15375],{},[2068,15301,15302,15366,15368,15370,15373],{},[14567,15303,15304],{"notation":14569},[2400,15305,15306],{"scriptlevel":630,"displaystyle":2083},[2400,15307,15308],{"scriptlevel":630,"displaystyle":2083},[2400,15309,15310],{"scriptlevel":630,"displaystyle":2360},[2068,15311,15312,15314,15316,15318,15320,15334,15336,15338,15340,15364],{},[2363,15313,3061],{},[2071,15315,9214],{},[2075,15317,2077],{},[2075,15319,2303],{},[2403,15321,15322,15328],{},[2348,15323,15324,15326],{},[2071,15325,14972],{},[2210,15327,646],{},[2348,15329,15330,15332],{},[2071,15331,14972],{},[2210,15333,638],{},[2363,15335,3061],{},[2071,15337,13774],{},[2075,15339,2176],{},[2403,15341,15342,15358],{},[2068,15343,15344,15350,15352],{},[2205,15345,15346,15348],{},[2071,15347,2890],{},[2075,15349,4441],{},[2075,15351,2303],{},[2348,15353,15354,15356],{},[2071,15355,14972],{},[2210,15357,654],{},[2348,15359,15360,15362],{},[2071,15361,14972],{},[2210,15363,638],{},[2363,15365,3061],{},[5965,15367],{"width":5967},[2075,15369,2084],{"stretchy":2083},[2210,15371,15372],{},"7.16",[2075,15374,2090],{"stretchy":2083},[2092,15376,15377],{"encoding":2094},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[55,15379,14636,15380,11156,15383,15386,15387,14647,15390,14650,15393,14673,15414,15446,15447,15469,15470,15472,15473,15475],{},[95,15381,15382],{},"funkce LM",[3982,15384,15385],{},"LM schedule","), její graf ",[95,15388,15389],{},"křivka LM",[95,15391,15392],{},"rostoucí",[1647,15394,15396],{"className":15395},[2059],[2061,15397,15398],{"xmlns":2063},[2065,15399,15400,15412],{},[2068,15401,15402,15404,15406,15408,15410],{},[2075,15403,2084],{"stretchy":2083},[2071,15405,13774],{},[2075,15407,2361],{"separator":2360},[2071,15409,9214],{},[2075,15411,2090],{"stretchy":2083},[2092,15413,14672],{"encoding":2094},[1647,15415,15417],{"className":15416},[2059],[2061,15418,15419],{"xmlns":2063},[2065,15420,15421,15443],{},[2068,15422,15423,15425,15439,15441],{},[2075,15424,2303],{},[2403,15426,15427,15433],{},[2348,15428,15429,15431],{},[2071,15430,14972],{},[2210,15432,646],{},[2348,15434,15435,15437],{},[2071,15436,14972],{},[2210,15438,638],{},[2075,15440,3482],{},[2210,15442,630],{},[2092,15444,15445],{"encoding":2094},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[1647,15448,15450],{"className":15449},[2059],[2061,15451,15452],{"xmlns":2063},[2065,15453,15454,15466],{},[2068,15455,15456,15462,15464],{},[2348,15457,15458,15460],{},[2071,15459,14972],{},[2210,15461,646],{},[2075,15463,3521],{},[2210,15465,630],{},[2092,15467,15468],{"encoding":2094},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[95,15471,586],{},"iquidity of ",[95,15474,2890],{},"oney.",[1023,15477,15478],{},[55,15479,15480,15482,15483,15496,15497,15525,15526,15543,15544,15557,15558,15575,15576,75,15589,15602,15603,15606],{},[1647,15481,4243],{}," Intuice — proč LM roste\nVyšší důchod ",[1647,15484,15486],{"className":15485},[2059],[2061,15487,15488],{"xmlns":2063},[2065,15489,15490,15494],{},[2068,15491,15492],{},[2071,15493,9214],{},[2092,15495,9214],{"encoding":2094}," → větší transakční poptávka po penězích ",[1647,15498,15500],{"className":15499},[2059],[2061,15501,15502],{"xmlns":2063},[2065,15503,15504,15522],{},[2068,15505,15506,15512,15514,15520],{},[2348,15507,15508,15510],{},[2071,15509,586],{},[2210,15511,638],{},[2075,15513,2077],{},[2348,15515,15516,15518],{},[2071,15517,14972],{},[2210,15519,638],{},[2071,15521,9214],{},[2092,15523,15524],{"encoding":2094},"L_1 = k_1 Y"," → při pevné nabídce ",[1647,15527,15529],{"className":15528},[2059],[2061,15530,15531],{"xmlns":2063},[2065,15532,15533,15541],{},[2068,15534,15535],{},[2205,15536,15537,15539],{},[2071,15538,2890],{},[2075,15540,4441],{},[2092,15542,13883],{"encoding":2094}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[1647,15545,15547],{"className":15546},[2059],[2061,15548,15549],{"xmlns":2063},[2065,15550,15551,15555],{},[2068,15552,15553],{},[2071,15554,13774],{},[2092,15556,13774],{"encoding":2094}," musí vzrůst, aby se spekulační poptávka ",[1647,15559,15561],{"className":15560},[2059],[2061,15562,15563],{"xmlns":2063},[2065,15564,15565,15573],{},[2068,15566,15567],{},[2348,15568,15569,15571],{},[2071,15570,586],{},[2210,15572,646],{},[2092,15574,15019],{"encoding":2094}," stlačila a trh se vyrovnal. Vztah mezi ",[1647,15577,15579],{"className":15578},[2059],[2061,15580,15581],{"xmlns":2063},[2065,15582,15583,15587],{},[2068,15584,15585],{},[2071,15586,9214],{},[2092,15588,9214],{"encoding":2094},[1647,15590,15592],{"className":15591},[2059],[2061,15593,15594],{"xmlns":2063},[2065,15595,15596,15600],{},[2068,15597,15598],{},[2071,15599,13774],{},[2092,15601,13774],{"encoding":2094}," na trhu peněz je proto ",[95,15604,15605],{},"přímý"," (rostoucí křivka).",[84,15608,15610],{"id":15609},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[55,15612,15613,15614,15617,15618,1445,15621,75,15639,1445,15642,15660,15661,15679,15680,15698,15699,15715,15716,75,15731,15746,15747,195],{},"Řešením ",[95,15615,15616],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[95,15619,15620],{},"rovnovážný důchod",[1647,15622,15624],{"className":15623},[2059],[2061,15625,15626],{"xmlns":2063},[2065,15627,15628,15636],{},[2068,15629,15630],{},[2205,15631,15632,15634],{},[2071,15633,9214],{},[2071,15635,554],{},[2092,15637,15638],{"encoding":2094},"Y^E",[95,15640,15641],{},"rovnovážnou úrokovou míru",[1647,15643,15645],{"className":15644},[2059],[2061,15646,15647],{"xmlns":2063},[2065,15648,15649,15657],{},[2068,15650,15651],{},[2205,15652,15653,15655],{},[2071,15654,13774],{},[2071,15656,554],{},[2092,15658,15659],{"encoding":2094},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[1647,15662,15664],{"className":15663},[2059],[2061,15665,15666],{"xmlns":2063},[2065,15667,15668,15676],{},[2068,15669,15670],{},[2205,15671,15672,15674],{},[2071,15673,13919],{},[2071,15675,554],{},[2092,15677,15678],{"encoding":2094},"I^E"," a rovnovážnou spotřebu ",[1647,15681,15683],{"className":15682},[2059],[2061,15684,15685],{"xmlns":2063},[2065,15686,15687,15695],{},[2068,15688,15689],{},[2205,15690,15691,15693],{},[2071,15692,2849],{},[2071,15694,554],{},[2092,15696,15697],{"encoding":2094},"C^E",". Graficky jde o ",[95,15700,15701,15702],{},"průsečík ",[1647,15703,15705],{"className":15704},[2059],[2061,15706,15707],{"xmlns":2063},[2065,15708,15709,15713],{},[2068,15710,15711],{},[2071,15712,554],{},[2092,15714,554],{"encoding":2094}," křivek ",[1647,15717,15719],{"className":15718},[2059],[2061,15720,15721],{"xmlns":2063},[2065,15722,15723,15729],{},[2068,15724,15725,15727],{},[2071,15726,13919],{},[2071,15728,532],{},[2092,15730,13784],{"encoding":2094},[1647,15732,15734],{"className":15733},[2059],[2061,15735,15736],{"xmlns":2063},[2065,15737,15738,15744],{},[2068,15739,15740,15742],{},[2071,15741,586],{},[2071,15743,2890],{},[2092,15745,13791],{"encoding":2094}," v rovině ",[1647,15748,15750],{"className":15749},[2059],[2061,15751,15752],{"xmlns":2063},[2065,15753,15754,15766],{},[2068,15755,15756,15758,15760,15762,15764],{},[2075,15757,2084],{"stretchy":2083},[2071,15759,13774],{},[2075,15761,2361],{"separator":2360},[2071,15763,9214],{},[2075,15765,2090],{"stretchy":2083},[2092,15767,14672],{"encoding":2094},[55,15769,15770],{},[3982,15771,15772,15773,15794,15795,15810,15811,15826,15827,15840,15841,15858,15859,13861,15872,15858,15889,15902,15903,15916],{},"Obrázek 7.6 — Schematický graf v rovině ",[1647,15774,15776],{"className":15775},[2059],[2061,15777,15778],{"xmlns":2063},[2065,15779,15780,15792],{},[2068,15781,15782,15784,15786,15788,15790],{},[2075,15783,2084],{"stretchy":2083},[2071,15785,13774],{},[2075,15787,2361],{"separator":2360},[2071,15789,9214],{},[2075,15791,2090],{"stretchy":2083},[2092,15793,14672],{"encoding":2094},". Rostoucí přímka ",[1647,15796,15798],{"className":15797},[2059],[2061,15799,15800],{"xmlns":2063},[2065,15801,15802,15808],{},[2068,15803,15804,15806],{},[2071,15805,586],{},[2071,15807,2890],{},[2092,15809,13791],{"encoding":2094}," a klesající přímka ",[1647,15812,15814],{"className":15813},[2059],[2061,15815,15816],{"xmlns":2063},[2065,15817,15818,15824],{},[2068,15819,15820,15822],{},[2071,15821,13919],{},[2071,15823,532],{},[2092,15825,13784],{"encoding":2094}," se protínají v bodě ",[1647,15828,15830],{"className":15829},[2059],[2061,15831,15832],{"xmlns":2063},[2065,15833,15834,15838],{},[2068,15835,15836],{},[2071,15837,554],{},[2092,15839,554],{"encoding":2094}," se souřadnicemi ",[1647,15842,15844],{"className":15843},[2059],[2061,15845,15846],{"xmlns":2063},[2065,15847,15848,15856],{},[2068,15849,15850],{},[2205,15851,15852,15854],{},[2071,15853,13774],{},[2071,15855,554],{},[2092,15857,15659],{"encoding":2094}," (na ose ",[1647,15860,15862],{"className":15861},[2059],[2061,15863,15864],{"xmlns":2063},[2065,15865,15866,15870],{},[2068,15867,15868],{},[2071,15869,13774],{},[2092,15871,13774],{"encoding":2094},[1647,15873,15875],{"className":15874},[2059],[2061,15876,15877],{"xmlns":2063},[2065,15878,15879,15887],{},[2068,15880,15881],{},[2205,15882,15883,15885],{},[2071,15884,9214],{},[2071,15886,554],{},[2092,15888,15638],{"encoding":2094},[1647,15890,15892],{"className":15891},[2059],[2061,15893,15894],{"xmlns":2063},[2065,15895,15896,15900],{},[2068,15897,15898],{},[2071,15899,9214],{},[2092,15901,9214],{"encoding":2094},"); tečkované čáry z ",[1647,15904,15906],{"className":15905},[2059],[2061,15907,15908],{"xmlns":2063},[2065,15909,15910,15914],{},[2068,15911,15912],{},[2071,15913,554],{},[2092,15915,554],{"encoding":2094}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1023,15918,15919,15924],{},[55,15920,15921,15923],{},[1647,15922,4659],{}," Postup — jak najít IS-LM rovnováhu",[201,15925,15926,16002,16070,16128,16201],{},[92,15927,15928,15931,15932,75,15952,15972,15973,75,15986,15999,16000,195],{},[95,15929,15930],{},"Z trhu zboží (7.13)"," dosaď funkce ",[1647,15933,15935],{"className":15934},[2059],[2061,15936,15937],{"xmlns":2063},[2065,15938,15939,15949],{},[2068,15940,15941,15943,15945,15947],{},[2071,15942,2849],{},[2075,15944,2084],{"stretchy":2083},[2071,15946,9214],{},[2075,15948,2090],{"stretchy":2083},[2092,15950,15951],{"encoding":2094},"C(Y)",[1647,15953,15955],{"className":15954},[2059],[2061,15956,15957],{"xmlns":2063},[2065,15958,15959,15969],{},[2068,15960,15961,15963,15965,15967],{},[2071,15962,13919],{},[2075,15964,2084],{"stretchy":2083},[2071,15966,13774],{},[2075,15968,2090],{"stretchy":2083},[2092,15970,15971],{"encoding":2094},"I(r)"," a vyjádři vztah mezi ",[1647,15974,15976],{"className":15975},[2059],[2061,15977,15978],{"xmlns":2063},[2065,15979,15980,15984],{},[2068,15981,15982],{},[2071,15983,9214],{},[2092,15985,9214],{"encoding":2094},[1647,15987,15989],{"className":15988},[2059],[2061,15990,15991],{"xmlns":2063},[2065,15992,15993,15997],{},[2068,15994,15995],{},[2071,15996,13774],{},[2092,15998,13774],{"encoding":2094}," — dostaneš rovnici ",[95,16001,13784],{},[92,16003,16004,16007,16008,75,16025,16042,16043,15999,16068,195],{},[95,16005,16006],{},"Z trhu peněz (7.15)"," dosaď ",[1647,16009,16011],{"className":16010},[2059],[2061,16012,16013],{"xmlns":2063},[2065,16014,16015,16023],{},[2068,16016,16017],{},[2348,16018,16019,16021],{},[2071,16020,586],{},[2210,16022,638],{},[2092,16024,14947],{"encoding":2094},[1647,16026,16028],{"className":16027},[2059],[2061,16029,16030],{"xmlns":2063},[2065,16031,16032,16040],{},[2068,16033,16034],{},[2348,16035,16036,16038],{},[2071,16037,586],{},[2210,16039,646],{},[2092,16041,15019],{"encoding":2094}," a vztah ",[1647,16044,16046],{"className":16045},[2059],[2061,16047,16048],{"xmlns":2063},[2065,16049,16050,16066],{},[2068,16051,16052,16058,16060],{},[2205,16053,16054,16056],{},[2071,16055,2890],{},[2071,16057,4271],{},[2075,16059,2077],{},[2205,16061,16062,16064],{},[2071,16063,2890],{},[2075,16065,4441],{},[2092,16067,15215],{"encoding":2094},[95,16069,13791],{},[92,16071,16072,16075,16076,75,16089,16102,16103,16127],{},[95,16073,16074],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[1647,16077,16079],{"className":16078},[2059],[2061,16080,16081],{"xmlns":2063},[2065,16082,16083,16087],{},[2068,16084,16085],{},[2071,16086,9214],{},[2092,16088,9214],{"encoding":2094},[1647,16090,16092],{"className":16091},[2059],[2061,16093,16094],{"xmlns":2063},[2065,16095,16096,16100],{},[2068,16097,16098],{},[2071,16099,13774],{},[2092,16101,13774],{"encoding":2094}," — nejsnáze substituční metodou (vyjádři z IS ",[1647,16104,16106],{"className":16105},[2059],[2061,16107,16108],{"xmlns":2063},[2065,16109,16110,16124],{},[2068,16111,16112,16114,16116,16118,16120,16122],{},[2071,16113,9214],{},[2075,16115,2077],{},[2071,16117,2080],{},[2075,16119,2084],{"stretchy":2083},[2071,16121,13774],{},[2075,16123,2090],{"stretchy":2083},[2092,16125,16126],{"encoding":2094},"Y = f(r)"," a dosaď do LM).",[92,16129,16130,1445,16133,75,16167,195],{},[95,16131,16132],{},"Zpětně dopočítej",[1647,16134,16136],{"className":16135},[2059],[2061,16137,16138],{"xmlns":2063},[2065,16139,16140,16164],{},[2068,16141,16142,16148,16150,16152,16154,16160,16162],{},[2205,16143,16144,16146],{},[2071,16145,2849],{},[2071,16147,554],{},[2075,16149,2077],{},[2071,16151,69],{},[2363,16153,3061],{},[2205,16155,16156,16158],{},[2071,16157,9214],{},[2071,16159,554],{},[2075,16161,2176],{},[2071,16163,2179],{},[2092,16165,16166],{"encoding":2094},"C^E = a\\,Y^E + b",[1647,16168,16170],{"className":16169},[2059],[2061,16171,16172],{"xmlns":2063},[2065,16173,16174,16198],{},[2068,16175,16176,16182,16184,16186,16188,16194,16196],{},[2205,16177,16178,16180],{},[2071,16179,13919],{},[2071,16181,554],{},[2075,16183,2077],{},[2071,16185,2222],{},[2363,16187,3061],{},[2205,16189,16190,16192],{},[2071,16191,13774],{},[2071,16193,554],{},[2075,16195,2176],{},[2071,16197,2273],{},[2092,16199,16200],{"encoding":2094},"I^E = c\\,r^E + d",[92,16202,16203,16206,16207,16241,16242,16296],{},[95,16204,16205],{},"Ověř:"," musí platit ",[1647,16208,16210],{"className":16209},[2059],[2061,16211,16212],{"xmlns":2063},[2065,16213,16214,16238],{},[2068,16215,16216,16222,16224,16230,16232],{},[2205,16217,16218,16220],{},[2071,16219,9214],{},[2071,16221,554],{},[2075,16223,2077],{},[2205,16225,16226,16228],{},[2071,16227,2849],{},[2071,16229,554],{},[2075,16231,2176],{},[2205,16233,16234,16236],{},[2071,16235,13919],{},[2071,16237,554],{},[2092,16239,16240],{"encoding":2094},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[1647,16243,16245],{"className":16244},[2059],[2061,16246,16247],{"xmlns":2063},[2065,16248,16249,16293],{},[2068,16250,16251,16257,16259,16265,16271,16273,16279,16285,16287],{},[2205,16252,16253,16255],{},[2071,16254,2890],{},[2075,16256,4441],{},[2075,16258,2077],{},[2348,16260,16261,16263],{},[2071,16262,14972],{},[2210,16264,638],{},[2205,16266,16267,16269],{},[2071,16268,9214],{},[2071,16270,554],{},[2075,16272,2176],{},[2348,16274,16275,16277],{},[2071,16276,14972],{},[2210,16278,646],{},[2205,16280,16281,16283],{},[2071,16282,13774],{},[2071,16284,554],{},[2075,16286,2176],{},[2348,16288,16289,16291],{},[2071,16290,14972],{},[2210,16292,654],{},[2092,16294,16295],{"encoding":2094},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[84,16298,16300],{"id":16299},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[55,16302,16303],{},"Pro trh zboží jsou dány:",[89,16305,16306,16334],{},[92,16307,16308,16309,2361],{},"spotřeba ",[1647,16310,16312],{"className":16311},[2059],[2061,16313,16314],{"xmlns":2063},[2065,16315,16316,16331],{},[2068,16317,16318,16320,16322,16325,16327,16329],{},[2071,16319,2849],{},[2075,16321,2077],{},[2210,16323,16324],{},"0,8",[2071,16326,9214],{},[2075,16328,2176],{},[2210,16330,3164],{},[2092,16332,16333],{"encoding":2094},"C = 0{,}8Y + 100",[92,16335,16336,16337,195],{},"investice ",[1647,16338,16340],{"className":16339},[2059],[2061,16341,16342],{"xmlns":2063},[2065,16343,16344,16360],{},[2068,16345,16346,16348,16350,16352,16354,16356,16358],{},[2071,16347,13919],{},[2075,16349,2077],{},[2075,16351,2303],{},[2210,16353,9121],{},[2071,16355,13774],{},[2075,16357,2176],{},[2210,16359,2854],{},[2092,16361,16362],{"encoding":2094},"I = -20r + 1000",[55,16364,16365],{},"Pro trh peněz:",[89,16367,16368,16394,16426],{},[92,16369,16370,2361],{},[1647,16371,16373],{"className":16372},[2059],[2061,16374,16375],{"xmlns":2063},[2065,16376,16377,16391],{},[2068,16378,16379,16385,16387,16389],{},[2348,16380,16381,16383],{},[2071,16382,586],{},[2210,16384,638],{},[2075,16386,2077],{},[2210,16388,2866],{},[2071,16390,9214],{},[2092,16392,16393],{"encoding":2094},"L_1 = 0{,}1Y",[92,16395,16396,2361],{},[1647,16397,16399],{"className":16398},[2059],[2061,16400,16401],{"xmlns":2063},[2065,16402,16403,16423],{},[2068,16404,16405,16411,16413,16415,16417,16419,16421],{},[2348,16406,16407,16409],{},[2071,16408,586],{},[2210,16410,646],{},[2075,16412,2077],{},[2075,16414,2303],{},[2210,16416,5091],{},[2071,16418,13774],{},[2075,16420,2176],{},[2210,16422,8691],{},[2092,16424,16425],{"encoding":2094},"L_2 = -25r + 2000",[92,16427,16428,16429,195],{},"nabídka peněz ",[1647,16430,16432],{"className":16431},[2059],[2061,16433,16434],{"xmlns":2063},[2065,16435,16436,16449],{},[2068,16437,16438,16444,16446],{},[2205,16439,16440,16442],{},[2071,16441,2890],{},[2075,16443,4441],{},[2075,16445,2077],{},[2210,16447,16448],{},"2375",[2092,16450,16451],{"encoding":2094},"M^* = 2375",[55,16453,16454,16457,16458,2777],{},[95,16455,16456],{},"Funkce IS"," — dosazením do (7.13) ",[1647,16459,16461],{"className":16460},[2059],[2061,16462,16463],{"xmlns":2063},[2065,16464,16465,16477],{},[2068,16466,16467,16469,16471,16473,16475],{},[2071,16468,9214],{},[2075,16470,2077],{},[2071,16472,2849],{},[2075,16474,2176],{},[2071,16476,13919],{},[2092,16478,16479],{"encoding":2094},"Y = C + I",[55,16481,16482],{},[1647,16483,16485],{"className":16484},[2059],[2061,16486,16487],{"xmlns":2063},[2065,16488,16489,16515],{},[2068,16490,16491,16493,16495,16497,16499,16501,16503,16505,16507,16509,16511,16513],{},[2071,16492,9214],{},[2075,16494,2077],{},[2210,16496,16324],{},[2071,16498,9214],{},[2075,16500,2176],{},[2210,16502,3164],{},[2075,16504,2303],{},[2210,16506,9121],{},[2071,16508,13774],{},[2075,16510,2176],{},[2210,16512,2854],{},[2075,16514,2361],{"separator":2360},[2092,16516,16517],{"encoding":2094},"Y = 0{,}8Y + 100 - 20r + 1000,",[55,16519,16520],{},"tj.",[55,16522,16523],{},[1647,16524,16526],{"className":16525},[2059],[2061,16527,16528],{"xmlns":2063},[2065,16529,16530,16555],{},[2068,16531,16532,16534,16536,16538,16540,16542,16544,16547,16549,16551,16553],{},[2210,16533,2911],{},[2071,16535,9214],{},[2075,16537,2176],{},[2210,16539,9121],{},[2071,16541,13774],{},[2075,16543,2077],{},[2210,16545,16546],{},"1100.",[5965,16548],{"width":5967},[2075,16550,2084],{"stretchy":2083},[2363,16552,13784],{},[2075,16554,2090],{"stretchy":2083},[2092,16556,16557],{"encoding":2094},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[55,16559,16560,16563,16564,2777],{},[95,16561,16562],{},"Funkce LM"," — dosazením do (7.15) ",[1647,16565,16567],{"className":16566},[2059],[2061,16568,16569],{"xmlns":2063},[2065,16570,16571,16595],{},[2068,16572,16573,16579,16581,16587,16589],{},[2205,16574,16575,16577],{},[2071,16576,2890],{},[2075,16578,4441],{},[2075,16580,2077],{},[2348,16582,16583,16585],{},[2071,16584,586],{},[2210,16586,638],{},[2075,16588,2176],{},[2348,16590,16591,16593],{},[2071,16592,586],{},[2210,16594,646],{},[2092,16596,16597],{"encoding":2094},"M^* = L_1 + L_2",[55,16599,16600],{},[1647,16601,16603],{"className":16602},[2059],[2061,16604,16605],{"xmlns":2063},[2065,16606,16607,16629],{},[2068,16608,16609,16611,16613,16615,16617,16619,16621,16623,16625,16627],{},[2210,16610,16448],{},[2075,16612,2077],{},[2210,16614,2866],{},[2071,16616,9214],{},[2075,16618,2303],{},[2210,16620,5091],{},[2071,16622,13774],{},[2075,16624,2176],{},[2210,16626,8691],{},[2075,16628,2361],{"separator":2360},[2092,16630,16631],{"encoding":2094},"2375 = 0{,}1Y - 25r + 2000,",[55,16633,16520],{},[55,16635,16636],{},[1647,16637,16639],{"className":16638},[2059],[2061,16640,16641],{"xmlns":2063},[2065,16642,16643,16668],{},[2068,16644,16645,16647,16649,16651,16653,16655,16657,16660,16662,16664,16666],{},[2210,16646,2866],{},[2071,16648,9214],{},[2075,16650,2303],{},[2210,16652,5091],{},[2071,16654,13774],{},[2075,16656,2077],{},[2210,16658,16659],{},"375.",[5965,16661],{"width":5967},[2075,16663,2084],{"stretchy":2083},[2363,16665,13791],{},[2075,16667,2090],{"stretchy":2083},[2092,16669,16670],{"encoding":2094},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[55,16672,16673,16676,16677,16702],{},[95,16674,16675],{},"Řešení soustavy."," Z (IS) vyjádříme ",[1647,16678,16680],{"className":16679},[2059],[2061,16681,16682],{"xmlns":2063},[2065,16683,16684,16699],{},[2068,16685,16686,16688,16690,16693,16695,16697],{},[2071,16687,9214],{},[2075,16689,2077],{},[2210,16691,16692],{},"5500",[2075,16694,2303],{},[2210,16696,3164],{},[2071,16698,13774],{},[2092,16700,16701],{"encoding":2094},"Y = 5500 - 100r"," a dosadíme do (LM):",[55,16704,16705],{},[1647,16706,16708],{"className":16707},[2059],[2061,16709,16710],{"xmlns":2063},[2065,16711,16712,16798],{},[2068,16713,16714,16716,16718,16720,16722,16724,16726,16728,16730,16732,16734,16736,16739,16741,16744,16746,16749,16751,16753,16755,16757,16759,16761,16763,16765,16767,16769,16771,16774,16776,16778,16781,16783,16785,16787,16793,16795],{},[2210,16715,2866],{},[2075,16717,2084],{"stretchy":2083},[2210,16719,16692],{},[2075,16721,2303],{},[2210,16723,3164],{},[2071,16725,13774],{},[2075,16727,2090],{"stretchy":2083},[2075,16729,2303],{},[2210,16731,5091],{},[2071,16733,13774],{},[2075,16735,2077],{},[2210,16737,16738],{},"375",[2363,16740,4072],{},[2075,16742,16743],{},"⟹",[2363,16745,4072],{},[2210,16747,16748],{},"550",[2075,16750,2303],{},[2210,16752,2935],{},[2071,16754,13774],{},[2075,16756,2303],{},[2210,16758,5091],{},[2071,16760,13774],{},[2075,16762,2077],{},[2210,16764,16738],{},[2363,16766,4072],{},[2075,16768,16743],{},[2363,16770,4072],{},[2210,16772,16773],{},"35",[2071,16775,13774],{},[2075,16777,2077],{},[2210,16779,16780],{},"175",[2363,16782,4072],{},[2075,16784,16743],{},[2363,16786,4072],{},[2205,16788,16789,16791],{},[2071,16790,13774],{},[2071,16792,554],{},[2075,16794,2077],{},[2210,16796,16797],{},"5.",[2092,16799,16800],{"encoding":2094},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[55,16802,16803],{},[95,16804,16805],{},"Zpětné dosazení:",[89,16807,16808,16854,16891],{},[92,16809,16810,2361],{},[1647,16811,16813],{"className":16812},[2059],[2061,16814,16815],{"xmlns":2063},[2065,16816,16817,16851],{},[2068,16818,16819,16825,16827,16829,16831,16833,16835,16837,16839,16841,16843,16846,16848],{},[2205,16820,16821,16823],{},[2071,16822,9214],{},[2071,16824,554],{},[2075,16826,2077],{},[2210,16828,16692],{},[2075,16830,2303],{},[2210,16832,3164],{},[2075,16834,3251],{},[2210,16836,670],{},[2075,16838,2077],{},[2210,16840,16692],{},[2075,16842,2303],{},[2210,16844,16845],{},"500",[2075,16847,2077],{},[2210,16849,16850],{},"5000",[2092,16852,16853],{"encoding":2094},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[92,16855,16856,2361],{},[1647,16857,16859],{"className":16858},[2059],[2061,16860,16861],{"xmlns":2063},[2065,16862,16863,16888],{},[2068,16864,16865,16871,16873,16875,16877,16879,16881,16883,16885],{},[2205,16866,16867,16869],{},[2071,16868,2849],{},[2071,16870,554],{},[2075,16872,2077],{},[2210,16874,16324],{},[2075,16876,3251],{},[2210,16878,16850],{},[2075,16880,2176],{},[2210,16882,3164],{},[2075,16884,2077],{},[2210,16886,16887],{},"4100",[2092,16889,16890],{"encoding":2094},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[92,16892,16893,195],{},[1647,16894,16896],{"className":16895},[2059],[2061,16897,16898],{"xmlns":2063},[2065,16899,16900,16927],{},[2068,16901,16902,16908,16910,16912,16914,16916,16918,16920,16922,16924],{},[2205,16903,16904,16906],{},[2071,16905,13919],{},[2071,16907,554],{},[2075,16909,2077],{},[2075,16911,2303],{},[2210,16913,9121],{},[2075,16915,3251],{},[2210,16917,670],{},[2075,16919,2176],{},[2210,16921,2854],{},[2075,16923,2077],{},[2210,16925,16926],{},"900",[2092,16928,16929],{"encoding":2094},"I^E = -20 \\cdot 5 + 1000 = 900",[55,16931,16932,1445,16935,16981],{},[95,16933,16934],{},"Ověření:",[1647,16936,16938],{"className":16937},[2059],[2061,16939,16940],{"xmlns":2063},[2065,16941,16942,16978],{},[2068,16943,16944,16950,16952,16958,16960,16962,16964,16966,16968,16970,16972],{},[2205,16945,16946,16948],{},[2071,16947,2849],{},[2071,16949,554],{},[2075,16951,2176],{},[2205,16953,16954,16956],{},[2071,16955,13919],{},[2071,16957,554],{},[2075,16959,2077],{},[2210,16961,16887],{},[2075,16963,2176],{},[2210,16965,16926],{},[2075,16967,2077],{},[2210,16969,16850],{},[2075,16971,2077],{},[2205,16973,16974,16976],{},[2071,16975,9214],{},[2071,16977,554],{},[2092,16979,16980],{"encoding":2094},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[55,16983,16984],{},[1647,16985,16987],{"className":16986},[2059],[2061,16988,16989],{"xmlns":2063},[2065,16990,16991,17061],{},[2068,16992,16993],{},[14567,16994,16995],{"notation":14569},[2400,16996,16997],{"scriptlevel":630,"displaystyle":2083},[2400,16998,16999],{"scriptlevel":630,"displaystyle":2083},[2400,17000,17001],{"scriptlevel":630,"displaystyle":2360},[2068,17002,17003,17005,17011,17013,17015,17017,17020,17026,17028,17030,17032,17034,17040,17042,17044,17046,17048,17054,17056,17059],{},[2363,17004,3061],{},[2205,17006,17007,17009],{},[2071,17008,9214],{},[2071,17010,554],{},[2075,17012,2077],{},[2210,17014,16850],{},[2075,17016,2361],{"separator":2360},[5965,17018],{"width":17019},"1em",[2205,17021,17022,17024],{},[2071,17023,13774],{},[2071,17025,554],{},[2075,17027,2077],{},[2210,17029,670],{},[2075,17031,2361],{"separator":2360},[5965,17033],{"width":17019},[2205,17035,17036,17038],{},[2071,17037,2849],{},[2071,17039,554],{},[2075,17041,2077],{},[2210,17043,16887],{},[2075,17045,2361],{"separator":2360},[5965,17047],{"width":17019},[2205,17049,17050,17052],{},[2071,17051,13919],{},[2071,17053,554],{},[2075,17055,2077],{},[2210,17057,17058],{},"900.",[2363,17060,3061],{},[2092,17062,17063],{"encoding":2094},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[55,17065,17066],{},[3982,17067,17068,17069,17082,17083,17096,17097,17112,17113,17126,17127,17142,17143,17156,17157,17170,17171,195],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[1647,17070,17072],{"className":17071},[2059],[2061,17073,17074],{"xmlns":2063},[2065,17075,17076,17080],{},[2068,17077,17078],{},[2071,17079,9214],{},[2092,17081,9214],{"encoding":2094}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[1647,17084,17086],{"className":17085},[2059],[2061,17087,17088],{"xmlns":2063},[2065,17089,17090,17094],{},[2068,17091,17092],{},[2071,17093,13774],{},[2092,17095,13774],{"encoding":2094}," hodnoty 5 a 55. Přímka ",[1647,17098,17100],{"className":17099},[2059],[2061,17101,17102],{"xmlns":2063},[2065,17103,17104,17110],{},[2068,17105,17106,17108],{},[2071,17107,586],{},[2071,17109,2890],{},[2092,17111,13791],{"encoding":2094}," stoupá z oblasti nízkých ",[1647,17114,17116],{"className":17115},[2059],[2061,17117,17118],{"xmlns":2063},[2065,17119,17120,17124],{},[2068,17121,17122],{},[2071,17123,13774],{},[2092,17125,13774],{"encoding":2094},", přímka ",[1647,17128,17130],{"className":17129},[2059],[2061,17131,17132],{"xmlns":2063},[2065,17133,17134,17140],{},[2068,17135,17136,17138],{},[2071,17137,13919],{},[2071,17139,532],{},[2092,17141,13784],{"encoding":2094}," klesá a protíná osu ",[1647,17144,17146],{"className":17145},[2059],[2061,17147,17148],{"xmlns":2063},[2065,17149,17150,17154],{},[2068,17151,17152],{},[2071,17153,13774],{},[2092,17155,13774],{"encoding":2094}," kolem hodnoty 55. Průsečík ",[1647,17158,17160],{"className":17159},[2059],[2061,17161,17162],{"xmlns":2063},[2065,17163,17164,17168],{},[2068,17165,17166],{},[2071,17167,554],{},[2092,17169,554],{"encoding":2094}," leží v bodě ",[1647,17172,17174],{"className":17173},[2059],[2061,17175,17176],{"xmlns":2063},[2065,17177,17178,17200],{},[2068,17179,17180,17182,17184,17186,17188,17190,17192,17194,17196,17198],{},[2075,17181,2561],{"stretchy":2083},[2071,17183,13774],{},[2075,17185,2077],{},[2210,17187,670],{},[2075,17189,2361],{"separator":2360},[2363,17191,2365],{},[2071,17193,9214],{},[2075,17195,2077],{},[2210,17197,16850],{},[2075,17199,2576],{"stretchy":2083},[2092,17201,17202],{"encoding":2094},"[r = 5,\\ Y = 5000]",[84,17204,17206],{"id":17205},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[55,17208,17209,17212,17213,17226,17227,7102,17240,17243,17244,17262,17263,17280,17281,17298,17299,17312,17313,17326],{},[95,17210,17211],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[1647,17214,17216],{"className":17215},[2059],[2061,17217,17218],{"xmlns":2063},[2065,17219,17220,17224],{},[2068,17221,17222],{},[2071,17223,13845],{},[2092,17225,13845],{"encoding":2094}," nebo snížení daní ",[1647,17228,17230],{"className":17229},[2059],[2061,17231,17232],{"xmlns":2063},[2065,17233,17234,17238],{},[2068,17235,17236],{},[2071,17237,543],{},[2092,17239,543],{"encoding":2094},[95,17241,17242],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[1647,17245,17247],{"className":17246},[2059],[2061,17248,17249],{"xmlns":2063},[2065,17250,17251,17259],{},[2068,17252,17253],{},[2205,17254,17255,17257],{},[2071,17256,554],{},[2075,17258,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,17260,17261],{"encoding":2094},"E'"," má vyšší ",[1647,17264,17266],{"className":17265},[2059],[2061,17267,17268],{"xmlns":2063},[2065,17269,17270,17278],{},[2068,17271,17272],{},[2205,17273,17274,17276],{},[2071,17275,9214],{},[2071,17277,554],{},[2092,17279,15638],{"encoding":2094}," i vyšší ",[1647,17282,17284],{"className":17283},[2059],[2061,17285,17286],{"xmlns":2063},[2065,17287,17288,17296],{},[2068,17289,17290],{},[2205,17291,17292,17294],{},[2071,17293,13774],{},[2071,17295,554],{},[2092,17297,15659],{"encoding":2094}," (vyšší ",[1647,17300,17302],{"className":17301},[2059],[2061,17303,17304],{"xmlns":2063},[2065,17305,17306,17310],{},[2068,17307,17308],{},[2071,17309,9214],{},[2092,17311,9214],{"encoding":2094}," zvedá poptávku po penězích, což tlačí ",[1647,17314,17316],{"className":17315},[2059],[2061,17317,17318],{"xmlns":2063},[2065,17319,17320,17324],{},[2068,17321,17322],{},[2071,17323,13774],{},[2092,17325,13774],{"encoding":2094}," nahoru).",[55,17328,17329],{},[58,17330],{"alt":17331,"className":17332,"src":17333},"imek-posun-is-lm-politiky",[62,63],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[55,17335,17336,17339,17340,17357,17358,17361,17362,17379,17380,17397,17398,17411,17412,17431,17432,4007],{},[95,17337,17338],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[1647,17341,17343],{"className":17342},[2059],[2061,17344,17345],{"xmlns":2063},[2065,17346,17347,17355],{},[2068,17348,17349],{},[2205,17350,17351,17353],{},[2071,17352,2890],{},[2075,17354,4441],{},[2092,17356,13883],{"encoding":2094}," národní bankou — ",[95,17359,17360],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[1647,17363,17365],{"className":17364},[2059],[2061,17366,17367],{"xmlns":2063},[2065,17368,17369,17377],{},[2068,17370,17371],{},[2205,17372,17373,17375],{},[2071,17374,13774],{},[2071,17376,554],{},[2092,17378,15659],{"encoding":2094}," a vyšší ",[1647,17381,17383],{"className":17382},[2059],[2061,17384,17385],{"xmlns":2063},[2065,17386,17387,17395],{},[2068,17388,17389],{},[2205,17390,17391,17393],{},[2071,17392,9214],{},[2071,17394,554],{},[2092,17396,15638],{"encoding":2094}," (nižší ",[1647,17399,17401],{"className":17400},[2059],[2061,17402,17403],{"xmlns":2063},[2065,17404,17405,17409],{},[2068,17406,17407],{},[2071,17408,13774],{},[2092,17410,13774],{"encoding":2094}," povzbuzuje investice ",[1647,17413,17415],{"className":17414},[2059],[2061,17416,17417],{"xmlns":2063},[2065,17418,17419,17429],{},[2068,17420,17421,17423,17425,17427],{},[2071,17422,13919],{},[2075,17424,2084],{"stretchy":2083},[2071,17426,13774],{},[2075,17428,2090],{"stretchy":2083},[2092,17430,15971],{"encoding":2094},", ty zvedají ",[1647,17433,17435],{"className":17434},[2059],[2061,17436,17437],{"xmlns":2063},[2065,17438,17439,17443],{},[2068,17440,17441],{},[2071,17442,9214],{},[2092,17444,9214],{"encoding":2094},[55,17446,17447,17448,17451],{},"IS-LM tak dává jednotný rámec pro diskusi ",[95,17449,17450],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[84,17453,321],{"id":320},[89,17455,17456,17529,17575,17657,17707,17774,17831,17872,17905],{},[92,17457,17458,7102,17491,835,17508,17525,17526,17528],{},[95,17459,17460,17461],{},"Funkce investic ",[1647,17462,17464],{"className":17463},[2059],[2061,17465,17466],{"xmlns":2063},[2065,17467,17468,17488],{},[2068,17469,17470,17472,17474,17476,17478,17480,17482,17484,17486],{},[2071,17471,13919],{},[2075,17473,2084],{"stretchy":2083},[2071,17475,13774],{},[2075,17477,2090],{"stretchy":2083},[2075,17479,2077],{},[2071,17481,2222],{},[2071,17483,13774],{},[2075,17485,2176],{},[2071,17487,2273],{},[2092,17489,17490],{"encoding":2094},"I(r) = cr + d",[1647,17492,17494],{"className":17493},[2059],[2061,17495,17496],{"xmlns":2063},[2065,17497,17498,17506],{},[2068,17499,17500,17502,17504],{},[2071,17501,2222],{},[2075,17503,3521],{},[2210,17505,630],{},[2092,17507,14250],{"encoding":2094},[1647,17509,17511],{"className":17510},[2059],[2061,17512,17513],{"xmlns":2063},[2065,17514,17515,17523],{},[2068,17516,17517,17519,17521],{},[2071,17518,2273],{},[2075,17520,3482],{},[2210,17522,630],{},[2092,17524,14229],{"encoding":2094},"; ",[95,17527,14254],{}," funkce úrokové míry.",[92,17530,17531,17534,17535,17556,17557,17574],{},[95,17532,17533],{},"Trh zboží"," — rovnováha ",[1647,17536,17538],{"className":17537},[2059],[2061,17539,17540],{"xmlns":2063},[2065,17541,17542,17554],{},[2068,17543,17544,17546,17548,17550,17552],{},[2071,17545,9214],{},[2075,17547,2077],{},[2071,17549,2849],{},[2075,17551,2176],{},[2071,17553,13919],{},[2092,17555,16479],{"encoding":2094},", ekvivalentně ",[1647,17558,17560],{"className":17559},[2059],[2061,17561,17562],{"xmlns":2063},[2065,17563,17564,17572],{},[2068,17565,17566,17568,17570],{},[2071,17567,13919],{},[2075,17569,2077],{},[2071,17571,532],{},[2092,17573,14447],{"encoding":2094}," (investice = úspory).",[92,17576,17577,11156,17580,17582,17583,17633,17634,14650,17636,195],{},[95,17578,17579],{},"Křivka IS",[3982,17581,13787],{},") — ",[1647,17584,17586],{"className":17585},[2059],[2061,17587,17588],{"xmlns":2063},[2065,17589,17590,17630],{},[2068,17591,17592,17594,17596,17608,17610,17612],{},[2071,17593,9214],{},[2075,17595,2077],{},[2403,17597,17598,17600],{},[2071,17599,2222],{},[2068,17601,17602,17604,17606],{},[2210,17603,638],{},[2075,17605,2303],{},[2071,17607,69],{},[2071,17609,13774],{},[2075,17611,2176],{},[2403,17613,17614,17622],{},[2068,17615,17616,17618,17620],{},[2071,17617,2179],{},[2075,17619,2176],{},[2071,17621,2273],{},[2068,17623,17624,17626,17628],{},[2210,17625,638],{},[2075,17627,2303],{},[2071,17629,69],{},[2092,17631,17632],{"encoding":2094},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[95,17635,14254],{},[1647,17637,17639],{"className":17638},[2059],[2061,17640,17641],{"xmlns":2063},[2065,17642,17643,17655],{},[2068,17644,17645,17647,17649,17651,17653],{},[2075,17646,2084],{"stretchy":2083},[2071,17648,13774],{},[2075,17650,2361],{"separator":2360},[2071,17652,9214],{},[2075,17654,2090],{"stretchy":2083},[2092,17656,14672],{"encoding":2094},[92,17658,17659,17534,17662,17688,17689,195],{},[95,17660,17661],{},"Trh peněz",[1647,17663,17665],{"className":17664},[2059],[2061,17666,17667],{"xmlns":2063},[2065,17668,17669,17685],{},[2068,17670,17671,17677,17679],{},[2205,17672,17673,17675],{},[2071,17674,2890],{},[2071,17676,4271],{},[2075,17678,2077],{},[2205,17680,17681,17683],{},[2071,17682,2890],{},[2071,17684,532],{},[2092,17686,17687],{"encoding":2094},"M^D = M^S"," při pevné nabídce ",[1647,17690,17692],{"className":17691},[2059],[2061,17693,17694],{"xmlns":2063},[2065,17695,17696,17704],{},[2068,17697,17698],{},[2205,17699,17700,17702],{},[2071,17701,2890],{},[2075,17703,4441],{},[2092,17705,17706],{"encoding":2094},"M^* ",[92,17708,17709,7102,17712,195],{},[95,17710,17711],{},"Transakční, opatrnostní, spekulační poptávka",[1647,17713,17715],{"className":17714},[2059],[2061,17716,17717],{"xmlns":2063},[2065,17718,17719,17771],{},[2068,17720,17721,17727,17729,17735,17737,17743,17745,17751,17753,17755,17761,17763,17765],{},[2205,17722,17723,17725],{},[2071,17724,2890],{},[2071,17726,4271],{},[2075,17728,2077],{},[2348,17730,17731,17733],{},[2071,17732,586],{},[2210,17734,638],{},[2075,17736,2176],{},[2348,17738,17739,17741],{},[2071,17740,586],{},[2210,17742,646],{},[2075,17744,2077],{},[2348,17746,17747,17749],{},[2071,17748,14972],{},[2210,17750,638],{},[2071,17752,9214],{},[2075,17754,2176],{},[2348,17756,17757,17759],{},[2071,17758,14972],{},[2210,17760,646],{},[2071,17762,13774],{},[2075,17764,2176],{},[2348,17766,17767,17769],{},[2071,17768,14972],{},[2210,17770,654],{},[2092,17772,17773],{"encoding":2094},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[92,17775,17776,11156,17779,17582,17781,17827,17828,17830],{},[95,17777,17778],{},"Křivka LM",[3982,17780,13794],{},[1647,17782,17784],{"className":17783},[2059],[2061,17785,17786],{"xmlns":2063},[2065,17787,17788,17824],{},[2068,17789,17790,17796,17798,17804,17806,17808,17814,17816,17818],{},[2205,17791,17792,17794],{},[2071,17793,2890],{},[2075,17795,4441],{},[2075,17797,2077],{},[2348,17799,17800,17802],{},[2071,17801,14972],{},[2210,17803,638],{},[2071,17805,9214],{},[2075,17807,2176],{},[2348,17809,17810,17812],{},[2071,17811,14972],{},[2210,17813,646],{},[2071,17815,13774],{},[2075,17817,2176],{},[2348,17819,17820,17822],{},[2071,17821,14972],{},[2210,17823,654],{},[2092,17825,17826],{"encoding":2094},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[95,17829,15392],{}," přímka.",[92,17832,17833,17836,17837,17871],{},[95,17834,17835],{},"Simultánní rovnováha"," — průsečík ",[1647,17838,17840],{"className":17839},[2059],[2061,17841,17842],{"xmlns":2063},[2065,17843,17844,17868],{},[2068,17845,17846,17848,17850,17852,17858,17860,17866],{},[2071,17847,554],{},[2075,17849,2077],{},[2075,17851,2084],{"stretchy":2083},[2205,17853,17854,17856],{},[2071,17855,13774],{},[2071,17857,554],{},[2075,17859,2361],{"separator":2360},[2205,17861,17862,17864],{},[2071,17863,9214],{},[2071,17865,554],{},[2075,17867,2090],{"stretchy":2083},[2092,17869,17870],{"encoding":2094},"E = (r^E, Y^E)"," křivek IS a LM.",[92,17873,17874,17877,17878,835,17891,17904],{},[95,17875,17876],{},"Fiskální politika"," — nástroje ",[1647,17879,17881],{"className":17880},[2059],[2061,17882,17883],{"xmlns":2063},[2065,17884,17885,17889],{},[2068,17886,17887],{},[2071,17888,13845],{},[2092,17890,13845],{"encoding":2094},[1647,17892,17894],{"className":17893},[2059],[2061,17895,17896],{"xmlns":2063},[2065,17897,17898,17902],{},[2068,17899,17900],{},[2071,17901,543],{},[2092,17903,543],{"encoding":2094}," posouvající křivku IS.",[92,17906,17907,17910,17911,17928],{},[95,17908,17909],{},"Monetární politika"," — nástroj ",[1647,17912,17914],{"className":17913},[2059],[2061,17915,17916],{"xmlns":2063},[2065,17917,17918,17926],{},[2068,17919,17920],{},[2205,17921,17922,17924],{},[2071,17923,2890],{},[2075,17925,4441],{},[2092,17927,13883],{"encoding":2094}," posouvající křivku LM.",[84,17930,3866],{"id":3865},[89,17932,17933,17942,17953,17963],{},[92,17934,17935,1445,17938],{},[95,17936,17937],{},"Kurz:",[69,17939,17941],{"className":17940,"dataFsResolvedFilePath":2034,"href":2035},[62],"Matematická ekonomie",[92,17943,17944,1445,17947],{},[95,17945,17946],{},"Přednáška:",[69,17948,17952],{"className":17949,"dataFsResolvedFilePath":17950,"href":17951},[62],"summaries\u002Fimek-blok-03.md","\u002Fwiki\u002Fimek-blok-03","imek-blok-03",[92,17954,17955,1445,17958,17962],{},[95,17956,17957],{},"Nadřazené téma:",[69,17959,17961],{"className":17960,"dataFsResolvedFilePath":13901,"href":13902},[62],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[92,17964,17965,17968],{},[95,17966,17967],{},"Související:",[89,17969,17970,17977,17983],{},[92,17971,17972,17976],{},[69,17973,17975],{"className":17974,"dataFsResolvedFilePath":13670,"href":13671},[62],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[92,17978,17979,17982],{},[69,17980,2430],{"className":17981,"dataFsResolvedFilePath":4005,"href":4006},[62]," — matematický základ pro směrnice IS a LM",[92,17984,17985,17989],{},[69,17986,17988],{"className":17987,"dataFsResolvedFilePath":3899,"href":3900},[62],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":156,"searchDepth":7,"depth":7,"links":17991},[17992,17993,17994,17995,17996,17997,17998,17999,18000,18001],{"id":13738,"depth":7,"text":13739},{"id":13893,"depth":7,"text":13894},{"id":14110,"depth":7,"text":14111},{"id":14403,"depth":7,"text":14404},{"id":14816,"depth":7,"text":14817},{"id":15609,"depth":7,"text":15610},{"id":16299,"depth":7,"text":16300},{"id":17205,"depth":7,"text":17206},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fis-lm",{"title":13730,"description":156},[9647,18006],"raw\u002Fimek\u002FKS_treti_blok.pdf","topics\u002Fis-lm",[17,18009,34,18010,18011,18012,18013,17961],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":18016,"title":18017,"body":18018,"course":163,"courses":18542,"created":795,"description":156,"extension":166,"meta":18543,"navigation":168,"path":18544,"seo":18545,"sources":18546,"stem":18550,"tags":18551,"type":177,"updated":178,"__hash__":18556},"topics\u002Ftopics\u002Fisms.md","ISMS — Systém řízení bezpečnosti informací",{"type":48,"value":18019,"toc":18527},[18020,18023,18030,18037,18040,18044,18111,18115,18119,18183,18187,18207,18211,18215,18316,18320,18346,18350,18372,18376,18383,18457,18459,18496,18501],[51,18021,18017],{"id":18022},"isms-systém-řízení-bezpečnosti-informací",[55,18024,18025],{},[58,18026],{"alt":18027,"className":18028,"src":18029},"isms-pdca-cyklus",[62,63],"\u002Fwiki-assets\u002Fisms-pdca-cyklus.jpeg",[55,18031,18032],{},[58,18033],{"alt":18034,"className":18035,"src":18036},"isms-oborova-mapa",[62,63],"\u002Fwiki-assets\u002Fisms-oborova-mapa.jpeg",[55,18038,18039],{},"Information Security Management System (ISMS) je systematický přístup k řízení citlivých informací organizace tak, aby zůstaly bezpečné. Zahrnuje lidi, procesy a IT systémy.",[84,18041,18043],{"id":18042},"základní-pilíře","Základní pilíře",[323,18045,18046,18057],{},[326,18047,18048],{},[329,18049,18050,18053,18055],{},[332,18051,18052],{},"Pilíř",[332,18054,337],{},[332,18056,340],{},[342,18058,18059,18072,18085,18098],{},[329,18060,18061,18066,18069],{},[347,18062,18063],{},[95,18064,18065],{},"Důvěrnost",[347,18067,18068],{},"Confidentiality",[347,18070,18071],{},"Přístup pouze oprávněným osobám",[329,18073,18074,18079,18082],{},[347,18075,18076],{},[95,18077,18078],{},"Integrita",[347,18080,18081],{},"Integrity",[347,18083,18084],{},"Ochrana před neoprávněnou změnou",[329,18086,18087,18092,18095],{},[347,18088,18089],{},[95,18090,18091],{},"Dostupnost",[347,18093,18094],{},"Availability",[347,18096,18097],{},"Systémy a data dostupné v potřebný čas",[329,18099,18100,18105,18108],{},[347,18101,18102],{},[95,18103,18104],{},"Nepopiratelnost",[347,18106,18107],{},"Non-repudiation",[347,18109,18110],{},"Prokázání autorství akce",[84,18112,18114],{"id":18113},"normativní-rámec","Normativní rámec",[609,18116,18118],{"id":18117},"isoiec-27000-rodina","ISO\u002FIEC 27000 rodina",[89,18120,18121,18127,18133,18143,18149,18161,18172],{},[92,18122,18123,18126],{},[95,18124,18125],{},"ISO\u002FIEC 27001"," — požadavky na ISMS (certifikační norma)",[92,18128,18129,18132],{},[95,18130,18131],{},"ISO\u002FIEC 27002"," — soubor bezpečnostních opatření (best practices)",[92,18134,18135,7102,18138,18142],{},[95,18136,18137],{},"ISO\u002FIEC 27005",[69,18139,18141],{"className":18140,"dataFsResolvedFilePath":740,"href":741},[62],"řízení rizik"," bezpečnosti informací",[92,18144,18145,18148],{},[95,18146,18147],{},"ISO\u002FIEC 27014"," — governance bezpečnosti informací",[92,18150,18151,18154,18155],{},[95,18152,18153],{},"ISO\u002FIEC 27011"," — ISMS pro ",[69,18156,18160],{"className":18157,"dataFsResolvedFilePath":18158,"href":18159},[62],"summaries\u002Fimork-isp.md","\u002Fwiki\u002Fimork-isp","telekomunikace",[92,18162,18163,18154,18166],{},[95,18164,18165],{},"ISO\u002FIEC 27019",[69,18167,18171],{"className":18168,"dataFsResolvedFilePath":18169,"href":18170},[62],"summaries\u002Fimork-energetika.md","\u002Fwiki\u002Fimork-energetika","energetiku",[92,18173,18174,18154,18177],{},[95,18175,18176],{},"ISO\u002FIEC 27799",[69,18178,18182],{"className":18179,"dataFsResolvedFilePath":18180,"href":18181},[62],"summaries\u002Fimork-zdravotnictvi.md","\u002Fwiki\u002Fimork-zdravotnictvi","zdravotnictví",[609,18184,18186],{"id":18185},"další-rámce","Další rámce",[89,18188,18189,18195,18201],{},[92,18190,18191,18194],{},[95,18192,18193],{},"NIST"," — americké standardy (SP 800 řada)",[92,18196,18197,18200],{},[95,18198,18199],{},"ISACA"," — profesní certifikace (CISM, CISA)",[92,18202,18203,18206],{},[95,18204,18205],{},"ENISA"," — evropská agentura pro kybernetickou bezpečnost",[84,18208,18210],{"id":18209},"governance-řízení","Governance (řízení)",[609,18212,18214],{"id":18213},"bezpečnostní-role","Bezpečnostní role",[323,18216,18217,18230],{},[326,18218,18219],{},[329,18220,18221,18224,18227],{},[332,18222,18223],{},"Role",[332,18225,18226],{},"Zkratka",[332,18228,18229],{},"Odpovědnost",[342,18231,18232,18243,18254,18265,18276,18286,18296,18306],{},[329,18233,18234,18237,18240],{},[347,18235,18236],{},"Chief Information Officer",[347,18238,18239],{},"CIO",[347,18241,18242],{},"Celkové řízení ICT",[329,18244,18245,18248,18251],{},[347,18246,18247],{},"Chief Information Security Officer",[347,18249,18250],{},"CISO",[347,18252,18253],{},"Řízení informační bezpečnosti",[329,18255,18256,18259,18262],{},[347,18257,18258],{},"Chief Technology Officer",[347,18260,18261],{},"CTO",[347,18263,18264],{},"Technologická strategie",[329,18266,18267,18270,18273],{},[347,18268,18269],{},"IS Security Officer",[347,18271,18272],{},"ISSO",[347,18274,18275],{},"Bezpečnost IS",[329,18277,18278,18281,18283],{},[347,18279,18280],{},"Manažer KB",[347,18282,10415],{},[347,18284,18285],{},"Odpovědný za ISMS",[329,18287,18288,18291,18293],{},[347,18289,18290],{},"Architekt KB",[347,18292,10415],{},[347,18294,18295],{},"Návrh a implementace opatření",[329,18297,18298,18301,18303],{},[347,18299,18300],{},"Auditor KB",[347,18302,10415],{},[347,18304,18305],{},"Provádění auditů",[329,18307,18308,18311,18313],{},[347,18309,18310],{},"Garant aktiva",[347,18312,10415],{},[347,18314,18315],{},"Rozvoj, použití a bezpečnost aktiva",[609,18317,18319],{"id":18318},"tři-třídy-informační-bezpečnosti","Tři třídy informační bezpečnosti",[201,18321,18322,18328,18340],{},[92,18323,18324,18327],{},[95,18325,18326],{},"Management"," — hodnocení rizik, plánování, akvizice, certifikace",[92,18329,18330,18333,18334],{},[95,18331,18332],{},"Provoz"," — kontinuita, personální bezpečnost, fyzická ochrana, incidenty, ",[69,18335,18339],{"className":18336,"dataFsResolvedFilePath":18337,"href":18338},[62],"topics\u002Fsae.md","\u002Fwiki\u002Fsae","SAE",[92,18341,18342,18345],{},[95,18343,18344],{},"Technická"," — identifikace\u002Fautentizace, řízení přístupu, audit, ochrana komunikace",[84,18347,18349],{"id":18348},"isms-cyklus-pdca","ISMS cyklus (PDCA)",[201,18351,18352,18357,18362,18367],{},[92,18353,18354,18356],{},[95,18355,447],{}," — stanovení kontextu, politiky, rozsahu ISMS",[92,18358,18359,18361],{},[95,18360,457],{}," — implementace opatření, řízení rizik",[92,18363,18364,18366],{},[95,18365,467],{}," — monitorování, audit, přezkoumání",[92,18368,18369,18371],{},[95,18370,477],{}," — nápravná opatření, neustálé zlepšování",[84,18373,18375],{"id":18374},"oborová-řešení-isms","Oborová řešení ISMS",[55,18377,18378,18379,18382],{},"Kurz ",[69,18380,762],{"className":18381,"dataFsResolvedFilePath":760,"href":761},[62]," pokrývá ISMS specifika pro:",[89,18384,18385,18393,18400,18407,18416,18425,18434,18441,18449],{},[92,18386,18387],{},[69,18388,18392],{"className":18389,"dataFsResolvedFilePath":18390,"href":18391},[62],"summaries\u002Fimork-akademicke-prostredi.md","\u002Fwiki\u002Fimork-akademicke-prostredi","Akademické\u002Funiverzitní prostředí",[92,18394,18395,18399],{},[69,18396,18398],{"className":18397,"dataFsResolvedFilePath":18180,"href":18181},[62],"Zdravotnictví"," (HIPAA, ISO 27799)",[92,18401,18402,18406],{},[69,18403,18405],{"className":18404,"dataFsResolvedFilePath":18169,"href":18170},[62],"Energetiku"," (ISO 27019, IEC 61850)",[92,18408,18409,18415],{},[69,18410,18414],{"className":18411,"dataFsResolvedFilePath":18412,"href":18413},[62],"summaries\u002Fimork-smart-grid.md","\u002Fwiki\u002Fimork-smart-grid","Smart Grid"," (NISTIR 7628)",[92,18417,18418,18424],{},[69,18419,18423],{"className":18420,"dataFsResolvedFilePath":18421,"href":18422},[62],"summaries\u002Fimork-doprava.md","\u002Fwiki\u002Fimork-doprava","Dopravu\u002Fželeznici"," (CLC\u002FTS 50701)",[92,18426,18427,18433],{},[69,18428,18432],{"className":18429,"dataFsResolvedFilePath":18430,"href":18431},[62],"summaries\u002Fimork-automotive.md","\u002Fwiki\u002Fimork-automotive","Automotive"," (TISAX)",[92,18435,18436,18440],{},[69,18437,18439],{"className":18438,"dataFsResolvedFilePath":18158,"href":18159},[62],"ISP\u002Ftelekomunikace"," (ISO 27011)",[92,18442,18443],{},[69,18444,18448],{"className":18445,"dataFsResolvedFilePath":18446,"href":18447},[62],"summaries\u002Fimork-mcn.md","\u002Fwiki\u002Fimork-mcn","Mission Critical Networks",[92,18450,18451],{},[69,18452,18456],{"className":18453,"dataFsResolvedFilePath":18454,"href":18455},[62],"summaries\u002Fimork-financni-sektor.md","\u002Fwiki\u002Fimork-financni-sektor","Finanční sektor",[84,18458,723],{"id":722},[89,18460,18461,18467,18473,18481,18487],{},[92,18462,18463,18466],{},[69,18464,742],{"className":18465,"dataFsResolvedFilePath":740,"href":741},[62]," — jádro ISMS procesu",[92,18468,18469,18472],{},[69,18470,18339],{"className":18471,"dataFsResolvedFilePath":18337,"href":18338},[62]," — budování bezpečnostního povědomí",[92,18474,18475,18480],{},[69,18476,364],{"className":18477,"dataFsResolvedFilePath":18478,"href":18479},[62],"topics\u002Fbcm.md","\u002Fwiki\u002Fbcm"," — kontinuita činnosti",[92,18482,18483,18486],{},[69,18484,751],{"className":18485,"dataFsResolvedFilePath":749,"href":750},[62]," — širší kontext",[92,18488,18489,18495],{},[69,18490,18494],{"className":18491,"dataFsResolvedFilePath":18492,"href":18493},[62],"topics\u002Fochrana-dat.md","\u002Fwiki\u002Fochrana-dat","Ochrana dat"," — technologická opatření",[84,18497,756,18498],{"id":755},[69,18499,762],{"className":18500,"dataFsResolvedFilePath":760,"href":761},[62],[89,18502,18503,18511,18519],{},[92,18504,18505],{},[69,18506,18510],{"className":18507,"dataFsResolvedFilePath":18508,"href":18509},[62],"summaries\u002Fimork-manazerska-bezpecnost.md","\u002Fwiki\u002Fimork-manazerska-bezpecnost","Manažerská bezpečnost",[92,18512,18513],{},[69,18514,18518],{"className":18515,"dataFsResolvedFilePath":18516,"href":18517},[62],"summaries\u002Fimork-risk-management.md","\u002Fwiki\u002Fimork-risk-management","Risk Management",[92,18520,18521],{},[69,18522,18526],{"className":18523,"dataFsResolvedFilePath":18524,"href":18525},[62],"summaries\u002Fimork-bezpecnostni-strategie.md","\u002Fwiki\u002Fimork-bezpecnostni-strategie","Bezpečnostní strategie",{"title":156,"searchDepth":7,"depth":7,"links":18528},[18529,18530,18534,18538,18539,18540,18541],{"id":18042,"depth":7,"text":18043},{"id":18113,"depth":7,"text":18114,"children":18531},[18532,18533],{"id":18117,"depth":4,"text":18118},{"id":18185,"depth":4,"text":18186},{"id":18209,"depth":7,"text":18210,"children":18535},[18536,18537],{"id":18213,"depth":4,"text":18214},{"id":18318,"depth":4,"text":18319},{"id":18348,"depth":7,"text":18349},{"id":18374,"depth":7,"text":18375},{"id":722,"depth":7,"text":723},{"id":755,"depth":7,"text":793},[11],{},"\u002Ftopics\u002Fisms",{"title":18017,"description":156},[18547,18548,18549],"raw\u002Fimork\u002F2001 VUT_Bezp Managerská 2022.pdf","raw\u002Fimork\u002F2003 VUT_Bezp Risk Mngmt-2021.pdf","raw\u002Fimork\u002FDetail předmětu.md","topics\u002Fisms",[11,20,18552,18553,18554,18555],"iso-27001","iso-27002","informacni-bezpecnost","governance","Itz64OPbMNGx3-X4N8-TmPXcCQeAMc2WpvRFQxHLSUs",{"id":18558,"title":751,"body":18559,"course":163,"courses":19002,"created":795,"description":156,"extension":166,"meta":19003,"navigation":168,"path":19004,"seo":19005,"sources":19006,"stem":19009,"tags":19010,"type":177,"updated":178,"__hash__":19017},"topics\u002Ftopics\u002Fkyberneticka-bezpecnost.md",{"type":48,"value":18560,"toc":18988},[18561,18564,18571,18578,18580,18618,18622,18626,18667,18671,18678,18681,18707,18711,18728,18732,18764,18768,18836,18840,18843,18860,18864,18902,18904,18941,18946],[51,18562,751],{"id":18563},"kybernetická-bezpečnost",[55,18565,18566],{},[58,18567],{"alt":18568,"className":18569,"src":18570},"kb-defense-in-depth",[62,63],"\u002Fwiki-assets\u002Fkb-defense-in-depth.jpeg",[55,18572,18573,18574,18577],{},"Ochrana informačních systémů, sítí a dat před kybernetickými hrozbami. V kontextu ",[69,18575,733],{"className":18576,"dataFsResolvedFilePath":731,"href":732},[62]," zahrnuje jak manažerské, tak technické aspekty bezpečnosti.",[84,18579,12532],{"id":12531},[89,18581,18582,18588,18594,18600,18606,18612],{},[92,18583,18584,18587],{},[95,18585,18586],{},"Útočná plocha"," (Attack Surface) — celkový počet vstupních bodů pro neoprávněný přístup (digitální + fyzická)",[92,18589,18590,18593],{},[95,18591,18592],{},"Vektor útoku"," (Attack Vector) — způsob zneužití zranitelnosti",[92,18595,18596,18599],{},[95,18597,18598],{},"Zranitelnost"," (Vulnerability) — slabé místo v aktivu nebo procesu",[92,18601,18602,18605],{},[95,18603,18604],{},"Exploit"," — kód zneužívající konkrétní zranitelnost",[92,18607,18608,18611],{},[95,18609,18610],{},"Payload"," — kód spuštěný po úspěšném exploitu",[92,18613,18614,18617],{},[95,18615,18616],{},"Shellcode"," — kód spouštěný v shellu napadeného systému",[84,18619,18621],{"id":18620},"typy-útoků","Typy útoků",[609,18623,18625],{"id":18624},"podle-cílení","Podle cílení",[323,18627,18628,18639],{},[326,18629,18630],{},[329,18631,18632,18634,18636],{},[332,18633,10393],{},[332,18635,340],{},[332,18637,18638],{},"Cíl",[342,18640,18641,18654],{},[329,18642,18643,18648,18651],{},[347,18644,18645],{},[95,18646,18647],{},"Plošný",[347,18649,18650],{},"Útočníkovi je jedno, kdo je obětí",[347,18652,18653],{},"Botnety, spam, ransomware",[329,18655,18656,18661,18664],{},[347,18657,18658],{},[95,18659,18660],{},"Cílený (APT)",[347,18662,18663],{},"Soustředěná pozornost na konkrétní cíl",[347,18665,18666],{},"Špionáž, sabotáž, krádež dat",[609,18668,18670],{"id":18669},"apt-advanced-persistent-threat","APT — Advanced Persistent Threat",[55,18672,18673],{},[58,18674],{"alt":18675,"className":18676,"src":18677},"apt-faze-utoku",[62,63],"\u002Fwiki-assets\u002Fapt-faze-utoku.jpeg",[55,18679,18680],{},"4 fáze:",[201,18682,18683,18689,18695,18701],{},[92,18684,18685,18688],{},[95,18686,18687],{},"Příprava"," — sběr informací, skenování zranitelností, sociální inženýrství",[92,18690,18691,18694],{},[95,18692,18693],{},"Průnik"," — spear phishing, watering hole, malvertising",[92,18696,18697,18700],{},[95,18698,18699],{},"Kompromitace"," — laterální pohyb, eskalace oprávnění, trvalý přístup",[92,18702,18703,18706],{},[95,18704,18705],{},"Dokončení"," — exfiltrace dat, vydírání, sabotáž",[609,18708,18710],{"id":18709},"základní-vektory-útoku","Základní vektory útoku",[89,18712,18713,18716,18719,18722,18725],{},[92,18714,18715],{},"Email s přílohou (spear phishing)",[92,18717,18718],{},"Trojanizované aplikace",[92,18720,18721],{},"Drive-by download (webové exploity)",[92,18723,18724],{},"Výměnná média (BadUSB)",[92,18726,18727],{},"Watering hole (kompromitace důvěryhodného webu)",[609,18729,18731],{"id":18730},"software-útoky","Software útoky",[89,18733,18734,18740,18746,18752,18758],{},[92,18735,18736,18739],{},[95,18737,18738],{},"Adware\u002FSpyware"," — sběr dat, odposlech",[92,18741,18742,18745],{},[95,18743,18744],{},"Viry"," — poškození HW\u002FSW",[92,18747,18748,18751],{},[95,18749,18750],{},"Trojské koně"," — skrytá funkčnost",[92,18753,18754,18757],{},[95,18755,18756],{},"Ransomware"," — šifrování dat za výkupné (single\u002Fdouble\u002Ftriple)",[92,18759,18760,18763],{},[95,18761,18762],{},"WormGPT"," — AI nástroj pro automatizaci kybernetické kriminality",[84,18765,18767],{"id":18766},"webové-útoky-owasp","Webové útoky (OWASP)",[323,18769,18770,18782],{},[326,18771,18772],{},[329,18773,18774,18777,18779],{},[332,18775,18776],{},"Útok",[332,18778,18638],{},[332,18780,18781],{},"Efekt",[342,18783,18784,18795,18805,18816,18826],{},[329,18785,18786,18789,18792],{},[347,18787,18788],{},"Content Spoofing",[347,18790,18791],{},"Klient",[347,18793,18794],{},"Ztráta přihlašovacích údajů",[329,18796,18797,18800,18802],{},[347,18798,18799],{},"XSS",[347,18801,18791],{},[347,18803,18804],{},"Přístup k cookies",[329,18806,18807,18810,18813],{},[347,18808,18809],{},"SQL Injection",[347,18811,18812],{},"Server",[347,18814,18815],{},"Neoprávněný přístup do DB",[329,18817,18818,18821,18823],{},[347,18819,18820],{},"DoS\u002FDDoS",[347,18822,18812],{},[347,18824,18825],{},"Nedostupnost služby",[329,18827,18828,18831,18833],{},[347,18829,18830],{},"Path Traversal",[347,18832,18812],{},[347,18834,18835],{},"Přístup k souborům",[84,18837,18839],{"id":18838},"bec-business-email-compromise","BEC — Business Email Compromise",[55,18841,18842],{},"Zneužití firemního emailu k podvodným platbám. 5 typů dle FBI:",[201,18844,18845,18848,18851,18854,18857],{},[92,18846,18847],{},"Vydávání se za právníka",[92,18849,18850],{},"Podvod na CEO",[92,18852,18853],{},"Krádež dat (personální oddělení)",[92,18855,18856],{},"Kompromitace účtu",[92,18858,18859],{},"Falešné faktury",[84,18861,18863],{"id":18862},"obranné-technologie","Obranné technologie",[89,18865,18866,18872,18878,18884,18890,18896],{},[92,18867,18868,18871],{},[95,18869,18870],{},"NAC"," — řízení přístupu k síti",[92,18873,18874,18877],{},[95,18875,18876],{},"IDS"," — detekce průniku (pasivní)",[92,18879,18880,18883],{},[95,18881,18882],{},"IPS"," — prevence průniku (aktivní, in-line)",[92,18885,18886,18889],{},[95,18887,18888],{},"SIEM"," — centralizovaná správa bezpečnostních událostí",[92,18891,18892,18895],{},[95,18893,18894],{},"DLP"," — prevence úniku dat",[92,18897,18898,18901],{},[95,18899,18900],{},"FW\u002FVPN"," — perimetrová ochrana",[84,18903,723],{"id":722},[89,18905,18906,18912,18918,18924,18935],{},[92,18907,18908,18911],{},[69,18909,733],{"className":18910,"dataFsResolvedFilePath":731,"href":732},[62]," — manažerský rámec bezpečnosti",[92,18913,18914,18917],{},[69,18915,742],{"className":18916,"dataFsResolvedFilePath":740,"href":741},[62]," — hodnocení hrozeb a zranitelností",[92,18919,18920,18923],{},[69,18921,18339],{"className":18922,"dataFsResolvedFilePath":18337,"href":18338},[62]," — budování povědomí jako obrana č. 1",[92,18925,18926,18929,18930,18934],{},[69,18927,364],{"className":18928,"dataFsResolvedFilePath":18478,"href":18479},[62]," \u002F ",[69,18931,18933],{"className":18932,"dataFsResolvedFilePath":778,"href":779},[62],"DR"," — reakce na incidenty a obnova",[92,18936,18937,18940],{},[69,18938,18494],{"className":18939,"dataFsResolvedFilePath":18492,"href":18493},[62]," — technologická ochrana",[84,18942,756,18943],{"id":755},[69,18944,762],{"className":18945,"dataFsResolvedFilePath":760,"href":761},[62],[89,18947,18948,18956,18964,18972,18980],{},[92,18949,18950],{},[69,18951,18955],{"className":18952,"dataFsResolvedFilePath":18953,"href":18954},[62],"summaries\u002Fimork-anatomie-utoku.md","\u002Fwiki\u002Fimork-anatomie-utoku","Anatomie kybernetického útoku",[92,18957,18958],{},[69,18959,18963],{"className":18960,"dataFsResolvedFilePath":18961,"href":18962},[62],"summaries\u002Fimork-ai-utoky.md","\u002Fwiki\u002Fimork-ai-utoky","AI útoky",[92,18965,18966],{},[69,18967,18971],{"className":18968,"dataFsResolvedFilePath":18969,"href":18970},[62],"summaries\u002Fimork-www.md","\u002Fwiki\u002Fimork-www","Bezpečnost webu",[92,18973,18974],{},[69,18975,18979],{"className":18976,"dataFsResolvedFilePath":18977,"href":18978},[62],"summaries\u002Fimork-sitove-utoky.md","\u002Fwiki\u002Fimork-sitove-utoky","Síťové útoky",[92,18981,18982],{},[69,18983,18987],{"className":18984,"dataFsResolvedFilePath":18985,"href":18986},[62],"summaries\u002Fimork-pripadovky.md","\u002Fwiki\u002Fimork-pripadovky","Případové studie",{"title":156,"searchDepth":7,"depth":7,"links":18989},[18990,18991,18997,18998,18999,19000,19001],{"id":12531,"depth":7,"text":12532},{"id":18620,"depth":7,"text":18621,"children":18992},[18993,18994,18995,18996],{"id":18624,"depth":4,"text":18625},{"id":18669,"depth":4,"text":18670},{"id":18709,"depth":4,"text":18710},{"id":18730,"depth":4,"text":18731},{"id":18766,"depth":7,"text":18767},{"id":18838,"depth":7,"text":18839},{"id":18862,"depth":7,"text":18863},{"id":722,"depth":7,"text":723},{"id":755,"depth":7,"text":793},[11],{},"\u002Ftopics\u002Fkyberneticka-bezpecnost",{"title":751,"description":156},[19007,19008,18547],"raw\u002Fimork\u002FCV 02 VUT_Anatomie útoku-2022.pdf","raw\u002Fimork\u002FCV 05 VUT_ AI útoky-2023 (1).pdf","topics\u002Fkyberneticka-bezpecnost",[11,19011,19012,19013,19014,19015,19016],"kyberneticka-bezpecnost","utoky","apt","ransomware","phishing","owasp","YTY7yZ-dcytzBVML0ABbKkLBPI4HcQkkY-i_yZbQNy8",{"id":19019,"title":19020,"body":19021,"course":163,"courses":20613,"created":3932,"description":20614,"extension":166,"meta":20615,"navigation":168,"path":20616,"seo":20617,"sources":20618,"stem":20619,"tags":20620,"type":177,"updated":178,"__hash__":20623},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":48,"value":19022,"toc":20601},[19023,19026,19122,19129,19149,19151,19156,19219,19238,19240,19243,19379,19381,19591,19625,19762,19766,19830,19846,19874,19878,19976,19980,19984,20037,20143,20357,20361,20404,20510,20562,20564],[51,19024,19020],{"id":19025},"lagrangeova-metoda-vázané-extrémy",[55,19027,19028,19029,3997,19052,19084,19085,19088,19089,19116,19117,19121],{},"Hledáme extrém funkce ",[1647,19030,19032],{"className":19031},[2059],[2061,19033,19034],{"xmlns":2063},[2065,19035,19036,19050],{},[2068,19037,19038,19040,19042,19044,19046,19048],{},[2071,19039,2080],{},[2075,19041,2084],{"stretchy":2083},[2071,19043,2087],{},[2075,19045,2361],{"separator":2360},[2071,19047,2073],{},[2075,19049,2090],{"stretchy":2083},[2092,19051,10974],{"encoding":2094},[1647,19053,19055],{"className":19054},[2059],[2061,19056,19057],{"xmlns":2063},[2065,19058,19059,19081],{},[2068,19060,19061,19063,19065,19071,19073,19079],{},[2071,19062,10871],{},[2075,19064,2084],{"stretchy":2083},[2348,19066,19067,19069],{},[2071,19068,2861],{},[2210,19070,638],{},[2075,19072,2361],{"separator":2360},[2348,19074,19075,19077],{},[2071,19076,2861],{},[2210,19078,646],{},[2075,19080,2090],{"stretchy":2083},[2092,19082,19083],{"encoding":2094},"U(Q_1, Q_2)"," apod.) ",[95,19086,19087],{},"podmíněný"," rovnicí ",[1647,19090,19092],{"className":19091},[2059],[2061,19093,19094],{"xmlns":2063},[2065,19095,19096,19114],{},[2068,19097,19098,19100,19102,19104,19106,19108,19110,19112],{},[2071,19099,12171],{},[2075,19101,2084],{"stretchy":2083},[2071,19103,2087],{},[2075,19105,2361],{"separator":2360},[2071,19107,2073],{},[2075,19109,2090],{"stretchy":2083},[2075,19111,2077],{},[2210,19113,630],{},[2092,19115,12188],{"encoding":2094},". V ",[69,19118,19120],{"className":19119,"dataFsResolvedFilePath":2034,"href":2035},[62],"matematické ekonomii"," se používá pro:",[55,19123,19124],{},[58,19125],{"alt":19126,"className":19127,"src":19128},"imek-lagrange-tecnost",[62,63],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[89,19130,19131,19140,19146],{},[92,19132,19133,19136,19137,2090],{},[95,19134,19135],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[69,19138,10903],{"className":19139,"dataFsResolvedFilePath":10901,"href":10902},[62],[92,19141,19142,19145],{},[95,19143,19144],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[92,19147,19148],{},"Optimalizaci produkce \u002F nákladů za omezení",[84,19150,87],{"id":86},[55,19152,11837,19153,2777],{},[95,19154,19155],{},"Lagrangeovu funkci",[55,19157,19158],{},[1647,19159,19161],{"className":19160},[2059],[2061,19162,19163],{"xmlns":2063},[2065,19164,19165,19216],{},[2068,19166,19167,19169,19171,19173,19175,19177,19179,19182,19184,19186,19188,19190,19192,19194,19196,19198,19200,19202,19204,19206,19208,19210,19212,19214],{},[2071,19168,586],{},[2075,19170,2084],{"stretchy":2083},[2071,19172,2087],{},[2075,19174,2361],{"separator":2360},[2071,19176,2073],{},[2075,19178,2361],{"separator":2360},[2071,19180,19181],{},"λ",[2075,19183,2090],{"stretchy":2083},[2075,19185,2077],{},[2071,19187,2080],{},[2075,19189,2084],{"stretchy":2083},[2071,19191,2087],{},[2075,19193,2361],{"separator":2360},[2071,19195,2073],{},[2075,19197,2090],{"stretchy":2083},[2075,19199,2176],{},[2071,19201,19181],{},[2363,19203,3061],{},[2071,19205,12171],{},[2075,19207,2084],{"stretchy":2083},[2071,19209,2087],{},[2075,19211,2361],{"separator":2360},[2071,19213,2073],{},[2075,19215,2090],{"stretchy":2083},[2092,19217,19218],{"encoding":2094},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[55,19220,4397,19221,8189,19235,195],{},[1647,19222,19224],{"className":19223},[2059],[2061,19225,19226],{"xmlns":2063},[2065,19227,19228,19232],{},[2068,19229,19230],{},[2071,19231,19181],{},[2092,19233,19234],{"encoding":2094},"\\lambda",[95,19236,19237],{},"Lagrangeův multiplikátor",[84,19239,3326],{"id":3325},[55,19241,19242],{},"Řešíme soustavu:",[55,19244,19245,19293,19341],{},[1647,19246,19248],{"className":19247},[2059],[2061,19249,19250],{"xmlns":2063},[2065,19251,19252,19290],{},[2068,19253,19254,19262,19264,19272,19274,19276,19278,19286,19288],{},[9252,19255,19256,19258,19260],{},[2071,19257,586],{},[2071,19259,2087],{},[2075,19261,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19263,2077],{},[9252,19265,19266,19268,19270],{},[2071,19267,2080],{},[2071,19269,2087],{},[2075,19271,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19273,2176],{},[2071,19275,19181],{},[2363,19277,3061],{},[9252,19279,19280,19282,19284],{},[2071,19281,12171],{},[2071,19283,2087],{},[2075,19285,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19287,2077],{},[2210,19289,630],{},[2092,19291,19292],{"encoding":2094},"L'_x = f'_x + \\lambda\\, g'_x = 0",[1647,19294,19296],{"className":19295},[2059],[2061,19297,19298],{"xmlns":2063},[2065,19299,19300,19338],{},[2068,19301,19302,19310,19312,19320,19322,19324,19326,19334,19336],{},[9252,19303,19304,19306,19308],{},[2071,19305,586],{},[2071,19307,2073],{},[2075,19309,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19311,2077],{},[9252,19313,19314,19316,19318],{},[2071,19315,2080],{},[2071,19317,2073],{},[2075,19319,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19321,2176],{},[2071,19323,19181],{},[2363,19325,3061],{},[9252,19327,19328,19330,19332],{},[2071,19329,12171],{},[2071,19331,2073],{},[2075,19333,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19335,2077],{},[2210,19337,630],{},[2092,19339,19340],{"encoding":2094},"L'_y = f'_y + \\lambda\\, g'_y = 0",[1647,19342,19344],{"className":19343},[2059],[2061,19345,19346],{"xmlns":2063},[2065,19347,19348,19376],{},[2068,19349,19350,19358,19360,19362,19364,19366,19368,19370,19372,19374],{},[9252,19351,19352,19354,19356],{},[2071,19353,586],{},[2071,19355,19181],{},[2075,19357,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19359,2077],{},[2071,19361,12171],{},[2075,19363,2084],{"stretchy":2083},[2071,19365,2087],{},[2075,19367,2361],{"separator":2360},[2071,19369,2073],{},[2075,19371,2090],{"stretchy":2083},[2075,19373,2077],{},[2210,19375,630],{},[2092,19377,19378],{"encoding":2094},"L'_\\lambda = g(x, y) = 0",[84,19380,3400],{"id":3399},[55,19382,19383],{},[1647,19384,19386],{"className":19385},[2059],[2061,19387,19388],{"xmlns":2063},[2065,19389,19390,19588],{},[2068,19391,19392,19394,19396,19398,19400,19402,19404,19406,19408,19410,19412,19428,19430,19432,19448,19450,19452,19460,19466,19468,19470,19486,19488,19490,19506,19508,19510,19518,19524,19526,19528,19530,19546,19548,19550,19566,19568,19570,19578,19580],{},[2071,19393,4271],{},[2075,19395,2084],{"stretchy":2083},[2071,19397,2087],{},[2075,19399,2361],{"separator":2360},[2071,19401,2073],{},[2075,19403,2361],{"separator":2360},[2071,19405,19181],{},[2075,19407,2090],{"stretchy":2083},[2075,19409,2077],{},[2075,19411,2084],{"stretchy":2083},[9252,19413,19414,19416,19422],{},[2071,19415,2080],{},[2068,19417,19418,19420],{},[2071,19419,2087],{},[2071,19421,2087],{},[2068,19423,19424,19426],{},[2075,19425,2452],{"mathvariant":2450},[2075,19427,2452],{"mathvariant":2450},[2075,19429,2176],{},[2071,19431,19181],{},[9252,19433,19434,19436,19442],{},[2071,19435,12171],{},[2068,19437,19438,19440],{},[2071,19439,2087],{},[2071,19441,2087],{},[2068,19443,19444,19446],{},[2075,19445,2452],{"mathvariant":2450},[2075,19447,2452],{"mathvariant":2450},[2075,19449,2090],{"stretchy":2083},[2075,19451,2084],{"stretchy":2083},[9252,19453,19454,19456,19458],{},[2071,19455,12171],{},[2071,19457,2073],{},[2075,19459,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2205,19461,19462,19464],{},[2075,19463,2090],{"stretchy":2083},[2210,19465,646],{},[2075,19467,2176],{},[2075,19469,2084],{"stretchy":2083},[9252,19471,19472,19474,19480],{},[2071,19473,2080],{},[2068,19475,19476,19478],{},[2071,19477,2073],{},[2071,19479,2073],{},[2068,19481,19482,19484],{},[2075,19483,2452],{"mathvariant":2450},[2075,19485,2452],{"mathvariant":2450},[2075,19487,2176],{},[2071,19489,19181],{},[9252,19491,19492,19494,19500],{},[2071,19493,12171],{},[2068,19495,19496,19498],{},[2071,19497,2073],{},[2071,19499,2073],{},[2068,19501,19502,19504],{},[2075,19503,2452],{"mathvariant":2450},[2075,19505,2452],{"mathvariant":2450},[2075,19507,2090],{"stretchy":2083},[2075,19509,2084],{"stretchy":2083},[9252,19511,19512,19514,19516],{},[2071,19513,12171],{},[2071,19515,2087],{},[2075,19517,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2205,19519,19520,19522],{},[2075,19521,2090],{"stretchy":2083},[2210,19523,646],{},[2075,19525,2303],{},[2210,19527,646],{},[2075,19529,2084],{"stretchy":2083},[9252,19531,19532,19534,19540],{},[2071,19533,2080],{},[2068,19535,19536,19538],{},[2071,19537,2087],{},[2071,19539,2073],{},[2068,19541,19542,19544],{},[2075,19543,2452],{"mathvariant":2450},[2075,19545,2452],{"mathvariant":2450},[2075,19547,2176],{},[2071,19549,19181],{},[9252,19551,19552,19554,19560],{},[2071,19553,12171],{},[2068,19555,19556,19558],{},[2071,19557,2087],{},[2071,19559,2073],{},[2068,19561,19562,19564],{},[2075,19563,2452],{"mathvariant":2450},[2075,19565,2452],{"mathvariant":2450},[2075,19567,2090],{"stretchy":2083},[2363,19569,3061],{},[9252,19571,19572,19574,19576],{},[2071,19573,12171],{},[2071,19575,2087],{},[2075,19577,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,19579,3061],{},[9252,19581,19582,19584,19586],{},[2071,19583,12171],{},[2071,19585,2073],{},[2075,19587,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,19589,19590],{"encoding":2094},"D(x, y, \\lambda) = (f''_{xx} + \\lambda g''_{xx})(g'_y)^2 + (f''_{yy} + \\lambda g''_{yy})(g'_x)^2 - 2(f''_{xy} + \\lambda g''_{xy})\\, g'_x\\, g'_y",[55,19592,19593,19594,19624],{},"Je-li ",[1647,19595,19597],{"className":19596},[2059],[2061,19598,19599],{"xmlns":2063},[2065,19600,19601,19621],{},[2068,19602,19603,19605,19607,19609,19611,19613,19619],{},[2075,19604,2561],{"stretchy":2083},[2071,19606,69],{},[2075,19608,2361],{"separator":2360},[2071,19610,2179],{},[2075,19612,2361],{"separator":2360},[2348,19614,19615,19617],{},[2071,19616,19181],{},[2210,19618,630],{},[2075,19620,2576],{"stretchy":2083},[2092,19622,19623],{"encoding":2094},"[a, b, \\lambda_0]"," podezřelý bod:",[89,19626,19627,19695],{},[92,19628,19629,3488,19665,19667,19668],{},[1647,19630,19632],{"className":19631},[2059],[2061,19633,19634],{"xmlns":2063},[2065,19635,19636,19662],{},[2068,19637,19638,19640,19642,19644,19646,19648,19650,19656,19658,19660],{},[2071,19639,4271],{},[2075,19641,2084],{"stretchy":2083},[2071,19643,69],{},[2075,19645,2361],{"separator":2360},[2071,19647,2179],{},[2075,19649,2361],{"separator":2360},[2348,19651,19652,19654],{},[2071,19653,19181],{},[2210,19655,630],{},[2075,19657,2090],{"stretchy":2083},[2075,19659,3521],{},[2210,19661,630],{},[2092,19663,19664],{"encoding":2094},"D(a, b, \\lambda_0) \u003C 0",[95,19666,3791],{}," vázané podmínkou ",[1647,19669,19671],{"className":19670},[2059],[2061,19672,19673],{"xmlns":2063},[2065,19674,19675,19693],{},[2068,19676,19677,19679,19681,19683,19685,19687,19689,19691],{},[2071,19678,12171],{},[2075,19680,2084],{"stretchy":2083},[2071,19682,2087],{},[2075,19684,2361],{"separator":2360},[2071,19686,2073],{},[2075,19688,2090],{"stretchy":2083},[2075,19690,2077],{},[2210,19692,630],{},[2092,19694,12188],{"encoding":2094},[92,19696,19697,3488,19733,19667,19735],{},[1647,19698,19700],{"className":19699},[2059],[2061,19701,19702],{"xmlns":2063},[2065,19703,19704,19730],{},[2068,19705,19706,19708,19710,19712,19714,19716,19718,19724,19726,19728],{},[2071,19707,4271],{},[2075,19709,2084],{"stretchy":2083},[2071,19711,69],{},[2075,19713,2361],{"separator":2360},[2071,19715,2179],{},[2075,19717,2361],{"separator":2360},[2348,19719,19720,19722],{},[2071,19721,19181],{},[2210,19723,630],{},[2075,19725,2090],{"stretchy":2083},[2075,19727,3482],{},[2210,19729,630],{},[2092,19731,19732],{"encoding":2094},"D(a, b, \\lambda_0) > 0",[95,19734,3849],{},[1647,19736,19738],{"className":19737},[2059],[2061,19739,19740],{"xmlns":2063},[2065,19741,19742,19760],{},[2068,19743,19744,19746,19748,19750,19752,19754,19756,19758],{},[2071,19745,12171],{},[2075,19747,2084],{"stretchy":2083},[2071,19749,2087],{},[2075,19751,2361],{"separator":2360},[2071,19753,2073],{},[2075,19755,2090],{"stretchy":2083},[2075,19757,2077],{},[2210,19759,630],{},[2092,19761,12188],{"encoding":2094},[84,19763,19765],{"id":19764},"význam-multiplikátoru","Význam multiplikátoru",[55,19767,19768],{},[1647,19769,19771],{"className":19770},[2059],[2061,19772,19773],{"xmlns":2063},[2065,19774,19775,19827],{},[2068,19776,19777,19779,19781,19803,19805],{},[2071,19778,19181],{},[2075,19780,2077],{},[2403,19782,19783,19791],{},[9252,19784,19785,19787,19789],{},[2071,19786,2080],{},[2071,19788,2087],{},[2075,19790,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2068,19792,19793,19795],{},[2075,19794,2303],{},[9252,19796,19797,19799,19801],{},[2071,19798,12171],{},[2071,19800,2087],{},[2075,19802,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,19804,2077],{},[2403,19806,19807,19815],{},[9252,19808,19809,19811,19813],{},[2071,19810,2080],{},[2071,19812,2073],{},[2075,19814,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2068,19816,19817,19819],{},[2075,19818,2303],{},[9252,19820,19821,19823,19825],{},[2071,19822,12171],{},[2071,19824,2073],{},[2075,19826,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,19828,19829],{"encoding":2094},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[55,19831,19832,19845],{},[1647,19833,19835],{"className":19834},[2059],[2061,19836,19837],{"xmlns":2063},[2065,19838,19839,19843],{},[2068,19840,19841],{},[2071,19842,19181],{},[2092,19844,19234],{"encoding":2094}," udává:",[89,19847,19848,19854],{},[92,19849,19850,19851],{},"konstantní ",[95,19852,19853],{},"poměr mezi mezním prospěchem a mezním nákladem",[92,19855,19856,19859,19860,19873],{},[95,19857,19858],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[1647,19861,19863],{"className":19862},[2059],[2061,19864,19865],{"xmlns":2063},[2065,19866,19867,19871],{},[2068,19868,19869],{},[2071,19870,2080],{},[2092,19872,2080],{"encoding":2094},", uvolní-li se omezení o jednotku",[84,19875,19877],{"id":19876},"alternativní-postup","Alternativní postup",[55,19879,19880,19881,19908,19909,19933,19934,19958,19959,19972,19973,195],{},"Lze-li z ",[1647,19882,19884],{"className":19883},[2059],[2061,19885,19886],{"xmlns":2063},[2065,19887,19888,19906],{},[2068,19889,19890,19892,19894,19896,19898,19900,19902,19904],{},[2071,19891,12171],{},[2075,19893,2084],{"stretchy":2083},[2071,19895,2087],{},[2075,19897,2361],{"separator":2360},[2071,19899,2073],{},[2075,19901,2090],{"stretchy":2083},[2075,19903,2077],{},[2210,19905,630],{},[2092,19907,12188],{"encoding":2094}," vyjádřit ",[1647,19910,19912],{"className":19911},[2059],[2061,19913,19914],{"xmlns":2063},[2065,19915,19916,19930],{},[2068,19917,19918,19920,19922,19924,19926,19928],{},[2071,19919,2073],{},[2075,19921,2077],{},[2071,19923,2073],{},[2075,19925,2084],{"stretchy":2083},[2071,19927,2087],{},[2075,19929,2090],{"stretchy":2083},[2092,19931,19932],{"encoding":2094},"y = y(x)"," (nebo ",[1647,19935,19937],{"className":19936},[2059],[2061,19938,19939],{"xmlns":2063},[2065,19940,19941,19955],{},[2068,19942,19943,19945,19947,19949,19951,19953],{},[2071,19944,2087],{},[2075,19946,2077],{},[2071,19948,2087],{},[2075,19950,2084],{"stretchy":2083},[2071,19952,2073],{},[2075,19954,2090],{"stretchy":2083},[2092,19956,19957],{"encoding":2094},"x = x(y)","), dosadíme do ",[1647,19960,19962],{"className":19961},[2059],[2061,19963,19964],{"xmlns":2063},[2065,19965,19966,19970],{},[2068,19967,19968],{},[2071,19969,2080],{},[2092,19971,2080],{"encoding":2094}," a převedeme na ",[95,19974,19975],{},"extrém funkce jedné proměnné",[84,19977,19979],{"id":19978},"použití-v-imek","Použití v ImeK",[609,19981,19983],{"id":19982},"maximalizace-užitečnosti","Maximalizace užitečnosti",[55,19985,19986,19987,195],{},"Rozpočtové omezení: ",[1647,19988,19990],{"className":19989},[2059],[2061,19991,19992],{"xmlns":2063},[2065,19993,19994,20034],{},[2068,19995,19996,20002,20004,20012,20018,20020,20028],{},[2205,19997,19998,20000],{},[2071,19999,9214],{},[2075,20001,4441],{},[2075,20003,2077],{},[9252,20005,20006,20008,20010],{},[2071,20007,575],{},[2210,20009,638],{},[2075,20011,4441],{},[2348,20013,20014,20016],{},[2071,20015,2861],{},[2210,20017,638],{},[2075,20019,2176],{},[9252,20021,20022,20024,20026],{},[2071,20023,575],{},[2210,20025,646],{},[2075,20027,4441],{},[2348,20029,20030,20032],{},[2071,20031,2861],{},[2210,20033,646],{},[2092,20035,20036],{"encoding":2094},"Y^* = P_1^* Q_1 + P_2^* Q_2",[55,20038,20039],{},[1647,20040,20042],{"className":20041},[2059],[2061,20043,20044],{"xmlns":2063},[2065,20045,20046,20140],{},[2068,20047,20048,20050,20052,20058,20060,20066,20068,20070,20072,20074,20076,20078,20084,20086,20092,20094,20096,20098,20100,20106,20108,20116,20122,20124,20132,20138],{},[2071,20049,586],{},[2075,20051,2084],{"stretchy":2083},[2348,20053,20054,20056],{},[2071,20055,2861],{},[2210,20057,638],{},[2075,20059,2361],{"separator":2360},[2348,20061,20062,20064],{},[2071,20063,2861],{},[2210,20065,646],{},[2075,20067,2361],{"separator":2360},[2071,20069,19181],{},[2075,20071,2090],{"stretchy":2083},[2075,20073,2077],{},[2071,20075,10871],{},[2075,20077,2084],{"stretchy":2083},[2348,20079,20080,20082],{},[2071,20081,2861],{},[2210,20083,638],{},[2075,20085,2361],{"separator":2360},[2348,20087,20088,20090],{},[2071,20089,2861],{},[2210,20091,646],{},[2075,20093,2090],{"stretchy":2083},[2075,20095,2176],{},[2071,20097,19181],{},[2075,20099,2084],{"stretchy":2083},[2205,20101,20102,20104],{},[2071,20103,9214],{},[2075,20105,4441],{},[2075,20107,2303],{},[9252,20109,20110,20112,20114],{},[2071,20111,575],{},[2210,20113,638],{},[2075,20115,4441],{},[2348,20117,20118,20120],{},[2071,20119,2861],{},[2210,20121,638],{},[2075,20123,2303],{},[9252,20125,20126,20128,20130],{},[2071,20127,575],{},[2210,20129,646],{},[2075,20131,4441],{},[2348,20133,20134,20136],{},[2071,20135,2861],{},[2210,20137,646],{},[2075,20139,2090],{"stretchy":2083},[2092,20141,20142],{"encoding":2094},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[55,20144,20145,20146,835,20178,835,20210,20259,20260,20314,20315,195],{},"Soustava: ",[1647,20147,20149],{"className":20148},[2059],[2061,20150,20151],{"xmlns":2063},[2065,20152,20153,20175],{},[2068,20154,20155,20163,20165,20167],{},[9252,20156,20157,20159,20161],{},[2071,20158,10871],{},[2210,20160,638],{},[2075,20162,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,20164,2077],{},[2071,20166,19181],{},[9252,20168,20169,20171,20173],{},[2071,20170,575],{},[2210,20172,638],{},[2075,20174,4441],{},[2092,20176,20177],{"encoding":2094},"U'_1 = \\lambda P_1^*",[1647,20179,20181],{"className":20180},[2059],[2061,20182,20183],{"xmlns":2063},[2065,20184,20185,20207],{},[2068,20186,20187,20195,20197,20199],{},[9252,20188,20189,20191,20193],{},[2071,20190,10871],{},[2210,20192,646],{},[2075,20194,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,20196,2077],{},[2071,20198,19181],{},[9252,20200,20201,20203,20205],{},[2071,20202,575],{},[2210,20204,646],{},[2075,20206,4441],{},[2092,20208,20209],{"encoding":2094},"U'_2 = \\lambda P_2^*",[1647,20211,20213],{"className":20212},[2059],[2061,20214,20215],{"xmlns":2063},[2065,20216,20217,20257],{},[2068,20218,20219,20225,20227,20235,20241,20243,20251],{},[2205,20220,20221,20223],{},[2071,20222,9214],{},[2075,20224,4441],{},[2075,20226,2077],{},[9252,20228,20229,20231,20233],{},[2071,20230,575],{},[2210,20232,638],{},[2075,20234,4441],{},[2348,20236,20237,20239],{},[2071,20238,2861],{},[2210,20240,638],{},[2075,20242,2176],{},[9252,20244,20245,20247,20249],{},[2071,20246,575],{},[2210,20248,646],{},[2075,20250,4441],{},[2348,20252,20253,20255],{},[2071,20254,2861],{},[2210,20256,646],{},[2092,20258,20036],{"encoding":2094},". Z prvních dvou: ",[1647,20261,20263],{"className":20262},[2059],[2061,20264,20265],{"xmlns":2063},[2065,20266,20267,20311],{},[2068,20268,20269,20289,20291],{},[2400,20270,20271],{"scriptlevel":630,"displaystyle":2083},[2403,20272,20273,20281],{},[9252,20274,20275,20277,20279],{},[2071,20276,10871],{},[2210,20278,638],{},[2075,20280,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,20282,20283,20285,20287],{},[2071,20284,10871],{},[2210,20286,646],{},[2075,20288,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,20290,2077],{},[2400,20292,20293],{"scriptlevel":630,"displaystyle":2083},[2403,20294,20295,20303],{},[9252,20296,20297,20299,20301],{},[2071,20298,575],{},[2210,20300,638],{},[2075,20302,4441],{},[9252,20304,20305,20307,20309],{},[2071,20306,575],{},[2210,20308,646],{},[2075,20310,4441],{},[2092,20312,20313],{"encoding":2094},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[1647,20316,20318],{"className":20317},[2059],[2061,20319,20320],{"xmlns":2063},[2065,20321,20322,20354],{},[2068,20323,20324,20326,20328,20330,20332,20334],{},[2071,20325,2890],{},[2071,20327,4082],{},[2071,20329,2849],{},[2071,20331,532],{},[2075,20333,2077],{},[2400,20335,20336],{"scriptlevel":630,"displaystyle":2083},[2403,20337,20338,20346],{},[9252,20339,20340,20342,20344],{},[2071,20341,575],{},[2210,20343,638],{},[2075,20345,4441],{},[9252,20347,20348,20350,20352],{},[2071,20349,575],{},[2210,20351,646],{},[2075,20353,4441],{},[2092,20355,20356],{"encoding":2094},"MRCS = \\tfrac{P_1^*}{P_2^*}",[609,20358,20360],{"id":20359},"minimalizace-výdajů","Minimalizace výdajů",[55,20362,20363,20364,195],{},"Podmínka dané užitečnosti ",[1647,20365,20367],{"className":20366},[2059],[2061,20368,20369],{"xmlns":2063},[2065,20370,20371,20401],{},[2068,20372,20373,20379,20381,20383,20385,20391,20393,20399],{},[2205,20374,20375,20377],{},[2071,20376,10871],{},[2075,20378,4441],{},[2075,20380,2077],{},[2071,20382,10871],{},[2075,20384,2084],{"stretchy":2083},[2348,20386,20387,20389],{},[2071,20388,2861],{},[2210,20390,638],{},[2075,20392,2361],{"separator":2360},[2348,20394,20395,20397],{},[2071,20396,2861],{},[2210,20398,646],{},[2075,20400,2090],{"stretchy":2083},[2092,20402,20403],{"encoding":2094},"U^* = U(Q_1, Q_2)",[55,20405,20406],{},[1647,20407,20409],{"className":20408},[2059],[2061,20410,20411],{"xmlns":2063},[2065,20412,20413,20507],{},[2068,20414,20415,20417,20419,20425,20427,20433,20435,20437,20439,20441,20449,20455,20457,20465,20471,20473,20475,20477,20483,20485,20487,20489,20495,20497,20503,20505],{},[2071,20416,586],{},[2075,20418,2084],{"stretchy":2083},[2348,20420,20421,20423],{},[2071,20422,2861],{},[2210,20424,638],{},[2075,20426,2361],{"separator":2360},[2348,20428,20429,20431],{},[2071,20430,2861],{},[2210,20432,646],{},[2075,20434,2361],{"separator":2360},[2071,20436,19181],{},[2075,20438,2090],{"stretchy":2083},[2075,20440,2077],{},[9252,20442,20443,20445,20447],{},[2071,20444,575],{},[2210,20446,638],{},[2075,20448,4441],{},[2348,20450,20451,20453],{},[2071,20452,2861],{},[2210,20454,638],{},[2075,20456,2176],{},[9252,20458,20459,20461,20463],{},[2071,20460,575],{},[2210,20462,646],{},[2075,20464,4441],{},[2348,20466,20467,20469],{},[2071,20468,2861],{},[2210,20470,646],{},[2075,20472,2176],{},[2071,20474,19181],{},[2075,20476,2084],{"stretchy":2083},[2205,20478,20479,20481],{},[2071,20480,10871],{},[2075,20482,4441],{},[2075,20484,2303],{},[2071,20486,10871],{},[2075,20488,2084],{"stretchy":2083},[2348,20490,20491,20493],{},[2071,20492,2861],{},[2210,20494,638],{},[2075,20496,2361],{"separator":2360},[2348,20498,20499,20501],{},[2071,20500,2861],{},[2210,20502,646],{},[2075,20504,2090],{"stretchy":2083},[2075,20506,2090],{"stretchy":2083},[2092,20508,20509],{"encoding":2094},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[55,20511,20512,20513,195],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[1647,20514,20516],{"className":20515},[2059],[2061,20517,20518],{"xmlns":2063},[2065,20519,20520,20559],{},[2068,20521,20522,20529,20531,20537,20539,20545,20547,20553,20555,20557],{},[2348,20523,20524,20526],{},[2071,20525,2861],{},[2071,20527,20528],{},"i",[2075,20530,2077],{},[2348,20532,20533,20535],{},[2071,20534,4271],{},[2071,20536,20528],{},[2075,20538,2084],{"stretchy":2083},[2348,20540,20541,20543],{},[2071,20542,575],{},[2210,20544,638],{},[2075,20546,2361],{"separator":2360},[2348,20548,20549,20551],{},[2071,20550,575],{},[2210,20552,646],{},[2075,20554,2361],{"separator":2360},[2071,20556,10871],{},[2075,20558,2090],{"stretchy":2083},[2092,20560,20561],{"encoding":2094},"Q_i = D_i(P_1, P_2, U)",[84,20563,3866],{"id":3865},[89,20565,20566,20573,20580,20589],{},[92,20567,20568,1445,20570],{},[95,20569,3873],{},[69,20571,3901],{"className":20572,"dataFsResolvedFilePath":3899,"href":3900},[62],[92,20574,20575,1445,20577],{},[95,20576,3884],{},[69,20578,13672],{"className":20579,"dataFsResolvedFilePath":13670,"href":13671},[62],[92,20581,20582,1445,20585,20588],{},[95,20583,20584],{},"Aplikace v kurzu:",[69,20586,12226],{"className":20587,"dataFsResolvedFilePath":10901,"href":10902},[62]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[92,20590,20591,1445,20593,835,20597,20600],{},[95,20592,3895],{},[69,20594,20596],{"className":20595,"dataFsResolvedFilePath":13901,"href":13902},[62],"Národní důchod",[69,20598,10597],{"className":20599,"dataFsResolvedFilePath":849,"href":850},[62]," (IpmrK)",{"title":156,"searchDepth":7,"depth":7,"links":20602},[20603,20604,20605,20606,20607,20608,20612],{"id":86,"depth":7,"text":87},{"id":3325,"depth":7,"text":3326},{"id":3399,"depth":7,"text":3400},{"id":19764,"depth":7,"text":19765},{"id":19876,"depth":7,"text":19877},{"id":19978,"depth":7,"text":19979,"children":20609},[20610,20611],{"id":19982,"depth":4,"text":19983},{"id":20359,"depth":4,"text":20360},{"id":3865,"depth":7,"text":3866},[17,14],"Hledáme extrém funkce f(x,y)f(x, y) (resp. U(Q1,Q2)U(Q_1, Q_2) apod.) podmíněný rovnicí g(x,y)=0g(x, y) = 0. V matematické ekonomii se používá pro:",{},"\u002Ftopics\u002Flagrangeova-metoda",{"title":19020,"description":20614},[3938,18006],"topics\u002Flagrangeova-metoda",[17,26,20621,20622],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":20625,"title":20596,"body":20626,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":30496,"navigation":168,"path":30497,"seo":30498,"sources":30499,"stem":30500,"tags":30501,"type":177,"updated":178,"__hash__":30505},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":48,"value":20627,"toc":30458},[20628,20631,20633,20756,20891,20895,20898,21011,21015,21043,21090,21093,21159,21204,21207,21233,21264,21268,21272,21316,21360,21422,21477,21480,21484,21487,21534,21631,21737,21743,21820,21849,21988,21992,22021,22071,22218,22308,22312,22338,22376,22403,22441,22503,22578,22656,22714,22780,22824,22828,22886,22935,22980,23193,23313,23319,23323,23346,23350,23357,23361,23392,23427,23431,23481,23569,23611,23632,23694,23754,23758,23829,23897,23969,24084,24132,24136,24139,24180,24219,24242,24356,24520,24528,24555,24585,24588,24665,24818,24902,25241,25245,25369,25505,25641,25694,25697,25947,26028,26032,26035,26093,26125,26128,26177,26180,26251,26447,26451,26602,26832,26870,26923,26968,26971,27027,27076,27280,27370,27374,27390,27397,27566,27570,27641,27722,27803,27882,28028,28116,28120,28303,28434,28479,28579,28583,29322,29324,30375,30377],[51,20629,20596],{"id":20630},"národní-důchod",[84,20632,13739],{"id":13738},[55,20634,20635,20636,1445,20640,20643,20644,1445,20647,20660,20661,20664,20665,20668,20669,20672,20673,20675,20676,1445,20678,20695,20696,20713,20714,20717,20718,4007],{},"Kapitola 7 ",[69,20637,20639],{"className":20638,"dataFsResolvedFilePath":2034,"href":2035},[62],"Matematické ekonomie",[95,20641,20642],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[95,20645,20646],{},"národním důchodem",[1647,20648,20650],{"className":20649},[2059],[2061,20651,20652],{"xmlns":2063},[2065,20653,20654,20658],{},[2068,20655,20656],{},[2071,20657,9214],{},[2092,20659,9214],{"encoding":2094},". Budují se postupně bohatší modely — ",[95,20662,20663],{},"C-I"," (jen spotřeba a investice) → ",[95,20666,20667],{},"C-I-G"," (přidá vládu a zdanění) → ",[95,20670,20671],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[95,20674,13744],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[95,20677,15620],{},[1647,20679,20681],{"className":20680},[2059],[2061,20682,20683],{"xmlns":2063},[2065,20684,20685,20693],{},[2068,20686,20687],{},[2205,20688,20689,20691],{},[2071,20690,9214],{},[2071,20692,554],{},[2092,20694,15638],{"encoding":2094}," jako řešení soustavy lineárních rovnic; citlivost ",[1647,20697,20699],{"className":20698},[2059],[2061,20700,20701],{"xmlns":2063},[2065,20702,20703,20711],{},[2068,20704,20705],{},[2205,20706,20707,20709],{},[2071,20708,9214],{},[2071,20710,554],{},[2092,20712,15638],{"encoding":2094}," na exogenní veličiny popisují ",[95,20715,20716],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[1647,20719,20721],{"className":20720},[2059],[2061,20722,20723],{"xmlns":2063},[2065,20724,20725,20753],{},[2068,20726,20727,20729,20731,20733,20735,20737,20739,20741,20743,20745,20747,20749,20751],{},[2210,20728,638],{},[2071,20730,4761],{"mathvariant":2450},[2075,20732,2084],{"stretchy":2083},[2210,20734,638],{},[2075,20736,2303],{},[2071,20738,69],{},[2075,20740,2090],{"stretchy":2083},[2075,20742,2077],{},[2210,20744,638],{},[2071,20746,4761],{"mathvariant":2450},[2071,20748,2890],{},[2071,20750,575],{},[2071,20752,532],{},[2092,20754,20755],{"encoding":2094},"1\u002F(1-a) = 1\u002FMPS",[1023,20757,20758],{},[55,20759,20760,20762,20763,20766,20767,20785,20786,20816,20817,20864,20865,20867,20868,20890],{},[1647,20761,4243],{}," Intuice\n",[95,20764,20765],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[1647,20768,20770],{"className":20769},[2059],[2061,20771,20772],{"xmlns":2063},[2065,20773,20774,20782],{},[2068,20775,20776,20778,20780],{},[2071,20777,2890],{},[2071,20779,575],{},[2071,20781,2849],{},[2092,20783,20784],{"encoding":2094},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[1647,20787,20789],{"className":20788},[2059],[2061,20790,20791],{"xmlns":2063},[2065,20792,20793,20813],{},[2068,20794,20795,20797,20799,20801,20803,20805,20807,20809,20811],{},[2071,20796,2890],{},[2071,20798,575],{},[2071,20800,532],{},[2075,20802,2077],{},[2210,20804,638],{},[2075,20806,2303],{},[2071,20808,2890],{},[2071,20810,575],{},[2071,20812,2849],{},[2092,20814,20815],{"encoding":2094},"MPS = 1 - MPC"," jde na úspory. Keynesův multiplikátor vyjadřuje, že jedna koruna navíc v investicích zvedne důchod o víc než korunu — utracená koruna se stane něčím důchodem, ten z ní část utratí, atd. (geometrická řada ",[1647,20818,20820],{"className":20819},[2059],[2061,20821,20822],{"xmlns":2063},[2065,20823,20824,20861],{},[2068,20825,20826,20828,20830,20832,20834,20840,20842,20845,20847,20849,20851,20853,20855,20857,20859],{},[2210,20827,638],{},[2075,20829,2176],{},[2071,20831,69],{},[2075,20833,2176],{},[2205,20835,20836,20838],{},[2071,20837,69],{},[2210,20839,646],{},[2075,20841,2176],{},[2075,20843,20844],{},"⋯",[2075,20846,2077],{},[2210,20848,638],{},[2071,20850,4761],{"mathvariant":2450},[2075,20852,2084],{"stretchy":2083},[2210,20854,638],{},[2075,20856,2303],{},[2071,20858,69],{},[2075,20860,2090],{"stretchy":2083},[2092,20862,20863],{"encoding":2094},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[95,20866,13744],{}," popisuje dva trhy zároveň: IS je rovnováha na trhu zboží (investice = úspory), LM je rovnováha na trhu peněz (poptávka = nabídka); společný bod určuje, při jakém páru ",[1647,20869,20871],{"className":20870},[2059],[2061,20872,20873],{"xmlns":2063},[2065,20874,20875,20887],{},[2068,20876,20877,20879,20881,20883,20885],{},[2075,20878,2084],{"stretchy":2083},[2071,20880,9214],{},[2075,20882,2361],{"separator":2360},[2071,20884,13774],{},[2075,20886,2090],{"stretchy":2083},[2092,20888,20889],{"encoding":2094},"(Y, r)"," jsou oba trhy v rovnováze současně.",[84,20892,20894],{"id":20893},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[55,20896,20897],{},"Po prostudování kapitoly by čtenář měl umět:",[89,20899,20900,20903,20906,20909,20912,20915,20918,21008],{},[92,20901,20902],{},"popsat zjednodušený model národní ekonomiky,",[92,20904,20905],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[92,20907,20908],{},"popsat lineární model spotřeby a úspor,",[92,20910,20911],{},"stanovit mezní sklony ke spotřebě a úsporám,",[92,20913,20914],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[92,20916,20917],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[92,20919,20920,20921,835,20938,835,20960,75,20985,21007],{},"popsat modely ",[1647,20922,20924],{"className":20923},[2059],[2061,20925,20926],{"xmlns":2063},[2065,20927,20928,20936],{},[2068,20929,20930,20932,20934],{},[2071,20931,2849],{},[2363,20933,14025],{},[2071,20935,13919],{},[2092,20937,14030],{"encoding":2094},[1647,20939,20941],{"className":20940},[2059],[2061,20942,20943],{"xmlns":2063},[2065,20944,20945,20957],{},[2068,20946,20947,20949,20951,20953,20955],{},[2071,20948,2849],{},[2363,20950,14025],{},[2071,20952,13919],{},[2363,20954,14025],{},[2071,20956,13845],{},[2092,20958,20959],{"encoding":2094},"C\\text{-}I\\text{-}G",[1647,20961,20963],{"className":20962},[2059],[2061,20964,20965],{"xmlns":2063},[2065,20966,20967,20983],{},[2068,20968,20969,20971,20973,20975,20977,20979,20981],{},[2071,20970,2849],{},[2363,20972,14025],{},[2071,20974,13919],{},[2363,20976,14025],{},[2071,20978,13845],{},[2363,20980,14025],{},[2071,20982,14055],{},[2092,20984,14058],{"encoding":2094},[1647,20986,20988],{"className":20987},[2059],[2061,20989,20990],{"xmlns":2063},[2065,20991,20992,21004],{},[2068,20993,20994,20996,20998,21000,21002],{},[2071,20995,13919],{},[2071,20997,532],{},[2363,20999,14025],{},[2071,21001,586],{},[2071,21003,2890],{},[2092,21005,21006],{"encoding":2094},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[92,21009,21010],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[84,21012,21014],{"id":21013},"gnp-a-národní-důchod","GNP a národní důchod",[55,21016,21017,1445,21020,11156,21039,21042],{},[95,21018,21019],{},"Hrubý národní produkt",[1647,21021,21023],{"className":21022},[2059],[2061,21024,21025],{"xmlns":2063},[2065,21026,21027,21036],{},[2068,21028,21029,21031,21034],{},[2071,21030,13845],{},[2071,21032,21033],{},"N",[2071,21035,575],{},[2092,21037,21038],{"encoding":2094},"GNP",[3982,21040,21041],{},"gross national product",") vyjadřuje hodnotu (v peněžních jednotkách) finálních statků a služeb vytvořených ekonomikou během daného období (obvykle jednoho roku). Je základním ukazatelem výkonnosti národní ekonomiky:",[55,21044,21045],{},[1647,21046,21048],{"className":21047},[2059],[2061,21049,21050],{"xmlns":2063},[2065,21051,21052,21087],{},[2068,21053,21054,21056,21058,21060,21062,21064,21066,21068,21070,21072,21074,21076,21078,21080,21082,21085],{},[2071,21055,13845],{},[2071,21057,21033],{},[2071,21059,575],{},[2075,21061,2077],{},[2071,21063,2849],{},[2075,21065,2176],{},[2071,21067,13919],{},[2075,21069,2176],{},[2071,21071,13845],{},[2075,21073,2176],{},[2071,21075,14055],{},[2075,21077,2361],{"separator":2360},[5965,21079],{"width":5967},[2075,21081,2084],{"stretchy":2083},[2210,21083,21084],{},"7.1",[2075,21086,2090],{"stretchy":2083},[2092,21088,21089],{"encoding":2094},"GNP = C + I + G + X, \\qquad (7.1)",[55,21091,21092],{},"kde",[89,21094,21095,21111,21127,21143],{},[92,21096,21097,21110],{},[1647,21098,21100],{"className":21099},[2059],[2061,21101,21102],{"xmlns":2063},[2065,21103,21104,21108],{},[2068,21105,21106],{},[2071,21107,2849],{},[2092,21109,2849],{"encoding":2094}," — výdaje domácností na spotřebu,",[92,21112,21113,21126],{},[1647,21114,21116],{"className":21115},[2059],[2061,21117,21118],{"xmlns":2063},[2065,21119,21120,21124],{},[2068,21121,21122],{},[2071,21123,13919],{},[2092,21125,13919],{"encoding":2094}," — hrubé domácí investice,",[92,21128,21129,21142],{},[1647,21130,21132],{"className":21131},[2059],[2061,21133,21134],{"xmlns":2063},[2065,21135,21136,21140],{},[2068,21137,21138],{},[2071,21139,13845],{},[2092,21141,13845],{"encoding":2094}," — vládní výdaje,",[92,21144,21145,21158],{},[1647,21146,21148],{"className":21147},[2059],[2061,21149,21150],{"xmlns":2063},[2065,21151,21152,21156],{},[2068,21153,21154],{},[2071,21155,14055],{},[2092,21157,14055],{"encoding":2094}," — čistý export.",[55,21160,21161,21162,21179,21180,21183,21184,1445,21187,11156,21200,21203],{},"K měření ",[1647,21163,21165],{"className":21164},[2059],[2061,21166,21167],{"xmlns":2063},[2065,21168,21169,21177],{},[2068,21170,21171,21173,21175],{},[2071,21172,13845],{},[2071,21174,21033],{},[2071,21176,575],{},[2092,21178,21038],{"encoding":2094}," se užívá ",[95,21181,21182],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[95,21185,21186],{},"národní důchod",[1647,21188,21190],{"className":21189},[2059],[2061,21191,21192],{"xmlns":2063},[2065,21193,21194,21198],{},[2068,21195,21196],{},[2071,21197,9214],{},[2092,21199,9214],{"encoding":2094},[3982,21201,21202],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[55,21205,21206],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[55,21208,21209],{},[1647,21210,21212],{"className":21211},[2059],[2061,21213,21214],{"xmlns":2063},[2065,21215,21216,21230],{},[2068,21217,21218,21220,21222,21224,21226,21228],{},[2071,21219,13845],{},[2071,21221,21033],{},[2071,21223,575],{},[2075,21225,2803],{},[2071,21227,9214],{},[2075,21229,2361],{"separator":2360},[2092,21231,21232],{"encoding":2094},"GNP \\approx Y,",[55,21234,21235,21236,11156,21239,21242,21243,21256,21257,21260,21261,195],{},"a užívá se společného názvu ",[95,21237,21238],{},"důchod",[3982,21240,21241],{},"income",") s označením ",[1647,21244,21246],{"className":21245},[2059],[2061,21247,21248],{"xmlns":2063},[2065,21249,21250,21254],{},[2068,21251,21252],{},[2071,21253,9214],{},[2092,21255,9214],{"encoding":2094},". Domácnosti důchod použijí ke ",[95,21258,21259],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[95,21262,21263],{},"úspor",[84,21265,21267],{"id":21266},"spotřeba-a-úspory","Spotřeba a úspory",[609,21269,21271],{"id":21270},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[55,21273,21274,21275,21288,21289,21302,21303,2777],{},"Jak spotřeba ",[1647,21276,21278],{"className":21277},[2059],[2061,21279,21280],{"xmlns":2063},[2065,21281,21282,21286],{},[2068,21283,21284],{},[2071,21285,2849],{},[2092,21287,2849],{"encoding":2094},", tak úspory ",[1647,21290,21292],{"className":21291},[2059],[2061,21293,21294],{"xmlns":2063},[2065,21295,21296,21300],{},[2068,21297,21298],{},[2071,21299,532],{},[2092,21301,532],{"encoding":2094}," závisejí na důchodu ",[1647,21304,21306],{"className":21305},[2059],[2061,21307,21308],{"xmlns":2063},[2065,21309,21310,21314],{},[2068,21311,21312],{},[2071,21313,9214],{},[2092,21315,9214],{"encoding":2094},[55,21317,21318],{},[1647,21319,21321],{"className":21320},[2059],[2061,21322,21323],{"xmlns":2063},[2065,21324,21325,21357],{},[2068,21326,21327,21329,21331,21333,21335,21337,21339,21341,21343,21345,21347,21349,21351,21353,21355],{},[2071,21328,2849],{},[2075,21330,2077],{},[2071,21332,2849],{},[2075,21334,2084],{"stretchy":2083},[2071,21336,9214],{},[2075,21338,2090],{"stretchy":2083},[2075,21340,2361],{"separator":2360},[5965,21342],{"width":5967},[2071,21344,532],{},[2075,21346,2077],{},[2071,21348,532],{},[2075,21350,2084],{"stretchy":2083},[2071,21352,9214],{},[2075,21354,2090],{"stretchy":2083},[2071,21356,195],{"mathvariant":2450},[2092,21358,21359],{"encoding":2094},"C = C(Y), \\qquad S = S(Y).",[55,21361,21362,8189,21381,11156,21384,21387,21388,8189,21408,11156,21411,21414,21415,75,21418,21421],{},[1647,21363,21365],{"className":21364},[2059],[2061,21366,21367],{"xmlns":2063},[2065,21368,21369,21379],{},[2068,21370,21371,21373,21375,21377],{},[2071,21372,2849],{},[2075,21374,2084],{"stretchy":2083},[2071,21376,9214],{},[2075,21378,2090],{"stretchy":2083},[2092,21380,15951],{"encoding":2094},[95,21382,21383],{},"funkce spotřeby",[3982,21385,21386],{},"consumption function","), ",[1647,21389,21391],{"className":21390},[2059],[2061,21392,21393],{"xmlns":2063},[2065,21394,21395,21405],{},[2068,21396,21397,21399,21401,21403],{},[2071,21398,532],{},[2075,21400,2084],{"stretchy":2083},[2071,21402,9214],{},[2075,21404,2090],{"stretchy":2083},[2092,21406,21407],{"encoding":2094},"S(Y)",[95,21409,21410],{},"funkce úspor",[3982,21412,21413],{},"savings function","); jejich grafy se nazývají ",[95,21416,21417],{},"křivka spotřeby",[95,21419,21420],{},"křivka úspor",". Platí základní identita",[55,21423,21424],{},[1647,21425,21427],{"className":21426},[2059],[2061,21428,21429],{"xmlns":2063},[2065,21430,21431,21474],{},[2068,21432,21433,21435,21437,21439,21441,21443,21445,21447,21449,21451,21453,21455,21457,21459,21461,21463,21465,21467,21469,21472],{},[2071,21434,9214],{},[2075,21436,2077],{},[2071,21438,2849],{},[2075,21440,2176],{},[2071,21442,532],{},[2075,21444,2077],{},[2071,21446,2849],{},[2075,21448,2084],{"stretchy":2083},[2071,21450,9214],{},[2075,21452,2090],{"stretchy":2083},[2075,21454,2176],{},[2071,21456,532],{},[2075,21458,2084],{"stretchy":2083},[2071,21460,9214],{},[2075,21462,2090],{"stretchy":2083},[2071,21464,195],{"mathvariant":2450},[5965,21466],{"width":5967},[2075,21468,2084],{"stretchy":2083},[2210,21470,21471],{},"7.2",[2075,21473,2090],{"stretchy":2083},[2092,21475,21476],{"encoding":2094},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[55,21478,21479],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[609,21481,21483],{"id":21482},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[55,21485,21486],{},"Nejjednodušší model předpokládá lineární tvar",[55,21488,21489],{},[1647,21490,21492],{"className":21491},[2059],[2061,21493,21494],{"xmlns":2063},[2065,21495,21496,21531],{},[2068,21497,21498,21500,21502,21504,21506,21508,21510,21512,21514,21516,21518,21520,21522,21524,21526,21529],{},[2071,21499,2849],{},[2075,21501,2077],{},[2071,21503,2849],{},[2075,21505,2084],{"stretchy":2083},[2071,21507,9214],{},[2075,21509,2090],{"stretchy":2083},[2075,21511,2077],{},[2071,21513,69],{},[2071,21515,9214],{},[2075,21517,2176],{},[2071,21519,2179],{},[2075,21521,2361],{"separator":2360},[5965,21523],{"width":5967},[2075,21525,2084],{"stretchy":2083},[2210,21527,21528],{},"7.3",[2075,21530,2090],{"stretchy":2083},[2092,21532,21533],{"encoding":2094},"C = C(Y) = aY + b, \\qquad (7.3)",[55,21535,4397,21536,75,21554,21576,21577,21617,21618,195],{},[1647,21537,21539],{"className":21538},[2059],[2061,21540,21541],{"xmlns":2063},[2065,21542,21543,21551],{},[2068,21544,21545,21547,21549],{},[2071,21546,2179],{},[2075,21548,3482],{},[2210,21550,630],{},[2092,21552,21553],{"encoding":2094},"b > 0",[1647,21555,21557],{"className":21556},[2059],[2061,21558,21559],{"xmlns":2063},[2065,21560,21561,21573],{},[2068,21562,21563,21565,21567,21569,21571],{},[2210,21564,630],{},[2075,21566,3521],{},[2071,21568,69],{},[2075,21570,3521],{},[2210,21572,638],{},[2092,21574,21575],{"encoding":2094},"0 \u003C a \u003C 1",". Směrnice ",[1647,21578,21580],{"className":21579},[2059],[2061,21581,21582],{"xmlns":2063},[2065,21583,21584,21614],{},[2068,21585,21586,21588,21590,21597,21599,21602,21604,21606,21608,21610,21612],{},[2071,21587,69],{},[2075,21589,2077],{},[2068,21591,21592,21595],{},[2071,21593,21594],{"mathvariant":2450},"t",[2071,21596,12171],{"mathvariant":2450},[2363,21598,3061],{},[2071,21600,21601],{},"α",[2075,21603,2077],{},[2071,21605,2961],{"mathvariant":2450},[2071,21607,2849],{},[2071,21609,4761],{"mathvariant":2450},[2071,21611,2961],{"mathvariant":2450},[2071,21613,9214],{},[2092,21615,21616],{"encoding":2094},"a = \\mathrm{tg}\\,\\alpha = \\Delta C \u002F \\Delta Y",": vzroste-li důchod o jednotku, spotřeba vzroste o méně než 1 (část „dodatečné jednotky“ jde na úspory). Domácnost v tomto modelu nevydává na spotřebu víc, než kolik dostala navíc — pokud by čerpala víc, musela by sáhnout do úspor; toto je reálné zejména pro malé ",[1647,21619,21621],{"className":21620},[2059],[2061,21622,21623],{"xmlns":2063},[2065,21624,21625,21629],{},[2068,21626,21627],{},[2071,21628,9214],{},[2092,21630,9214],{"encoding":2094},[55,21632,21633],{},[3982,21634,21635,21636,21660,21661,21699,21700,21716,21717,195],{},"Obrázek 7.1 — Přímka spotřeby ",[1647,21637,21639],{"className":21638},[2059],[2061,21640,21641],{"xmlns":2063},[2065,21642,21643,21657],{},[2068,21644,21645,21647,21649,21651,21653,21655],{},[2071,21646,2849],{},[2075,21648,2077],{},[2071,21650,69],{},[2071,21652,9214],{},[2075,21654,2176],{},[2071,21656,2179],{},[2092,21658,21659],{"encoding":2094},"C = aY + b"," se směrnicí ",[1647,21662,21664],{"className":21663},[2059],[2061,21665,21666],{"xmlns":2063},[2065,21667,21668,21696],{},[2068,21669,21670,21672,21674,21680,21682,21684,21686,21688,21690,21692,21694],{},[2071,21671,69],{},[2075,21673,2077],{},[2068,21675,21676,21678],{},[2071,21677,21594],{"mathvariant":2450},[2071,21679,12171],{"mathvariant":2450},[2363,21681,3061],{},[2071,21683,21601],{},[2075,21685,2077],{},[2071,21687,2961],{"mathvariant":2450},[2071,21689,2849],{},[2071,21691,4761],{"mathvariant":2450},[2071,21693,2961],{"mathvariant":2450},[2071,21695,9214],{},[2092,21697,21698],{"encoding":2094},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[1647,21701,21703],{"className":21702},[2059],[2061,21704,21705],{"xmlns":2063},[2065,21706,21707,21713],{},[2068,21708,21709,21711],{},[2071,21710,2961],{"mathvariant":2450},[2071,21712,2849],{},[2092,21714,21715],{"encoding":2094},"\\Delta C"," při jednotkovém přírůstku ",[1647,21718,21720],{"className":21719},[2059],[2061,21721,21722],{"xmlns":2063},[2065,21723,21724,21734],{},[2068,21725,21726,21728,21730,21732],{},[2071,21727,2961],{"mathvariant":2450},[2071,21729,9214],{},[2075,21731,2077],{},[2210,21733,638],{},[2092,21735,21736],{"encoding":2094},"\\Delta Y = 1",[55,21738,21739,21740,2777],{},"Dosazením do (7.2) plyne ",[95,21741,21742],{},"lineární model úspor",[55,21744,21745],{},[1647,21746,21748],{"className":21747},[2059],[2061,21749,21750],{"xmlns":2063},[2065,21751,21752,21817],{},[2068,21753,21754,21756,21758,21760,21762,21764,21766,21768,21770,21772,21774,21776,21778,21780,21782,21784,21786,21788,21790,21792,21794,21796,21798,21800,21802,21804,21806,21808,21810,21812,21815],{},[2071,21755,532],{},[2075,21757,2077],{},[2071,21759,9214],{},[2075,21761,2303],{},[2071,21763,2849],{},[2075,21765,2084],{"stretchy":2083},[2071,21767,9214],{},[2075,21769,2090],{"stretchy":2083},[2075,21771,2077],{},[2071,21773,9214],{},[2075,21775,2303],{},[2075,21777,2084],{"stretchy":2083},[2071,21779,69],{},[2071,21781,9214],{},[2075,21783,2176],{},[2071,21785,2179],{},[2075,21787,2090],{"stretchy":2083},[2075,21789,2077],{},[2075,21791,2084],{"stretchy":2083},[2210,21793,638],{},[2075,21795,2303],{},[2071,21797,69],{},[2075,21799,2090],{"stretchy":2083},[2071,21801,9214],{},[2075,21803,2303],{},[2071,21805,2179],{},[2071,21807,195],{"mathvariant":2450},[5965,21809],{"width":5967},[2075,21811,2084],{"stretchy":2083},[2210,21813,21814],{},"7.4",[2075,21816,2090],{"stretchy":2083},[2092,21818,21819],{"encoding":2094},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[55,21821,21822,21823,4007],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[1647,21824,21826],{"className":21825},[2059],[2061,21827,21828],{"xmlns":2063},[2065,21829,21830,21846],{},[2068,21831,21832,21834,21836,21838,21840,21842,21844],{},[2210,21833,630],{},[2075,21835,3521],{},[2210,21837,638],{},[2075,21839,2303],{},[2071,21841,69],{},[2075,21843,3521],{},[2210,21845,638],{},[2092,21847,21848],{"encoding":2094},"0 \u003C 1 - a \u003C 1",[55,21850,21851],{},[3982,21852,21853,21854,75,21877,21909,21910,2697,21923,21953,21954,2697,21972,195],{},"Obrázek 7.2 — Přímky ",[1647,21855,21857],{"className":21856},[2059],[2061,21858,21859],{"xmlns":2063},[2065,21860,21861,21875],{},[2068,21862,21863,21865,21867,21869,21871,21873],{},[2071,21864,2849],{},[2075,21866,2077],{},[2071,21868,69],{},[2071,21870,9214],{},[2075,21872,2176],{},[2071,21874,2179],{},[2092,21876,21659],{"encoding":2094},[1647,21878,21880],{"className":21879},[2059],[2061,21881,21882],{"xmlns":2063},[2065,21883,21884,21906],{},[2068,21885,21886,21888,21890,21892,21894,21896,21898,21900,21902,21904],{},[2071,21887,532],{},[2075,21889,2077],{},[2075,21891,2084],{"stretchy":2083},[2210,21893,638],{},[2075,21895,2303],{},[2071,21897,69],{},[2075,21899,2090],{"stretchy":2083},[2071,21901,9214],{},[2075,21903,2303],{},[2071,21905,2179],{},[2092,21907,21908],{"encoding":2094},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[1647,21911,21913],{"className":21912},[2059],[2061,21914,21915],{"xmlns":2063},[2065,21916,21917,21921],{},[2068,21918,21919],{},[2071,21920,9214],{},[2092,21922,9214],{"encoding":2094},[1647,21924,21926],{"className":21925},[2059],[2061,21927,21928],{"xmlns":2063},[2065,21929,21930,21950],{},[2068,21931,21932,21934,21936,21938,21940,21942,21944,21946,21948],{},[2071,21933,9214],{},[2075,21935,2077],{},[2071,21937,2179],{},[2071,21939,4761],{"mathvariant":2450},[2075,21941,2084],{"stretchy":2083},[2210,21943,638],{},[2075,21945,2303],{},[2071,21947,69],{},[2075,21949,2090],{"stretchy":2083},[2092,21951,21952],{"encoding":2094},"Y = b\u002F(1-a)"," a osu ",[1647,21955,21957],{"className":21956},[2059],[2061,21958,21959],{"xmlns":2063},[2065,21960,21961,21969],{},[2068,21962,21963,21965,21967],{},[2071,21964,2849],{},[2075,21966,2361],{"separator":2360},[2071,21968,532],{},[2092,21970,21971],{"encoding":2094},"C, S",[1647,21973,21975],{"className":21974},[2059],[2061,21976,21977],{"xmlns":2063},[2065,21978,21979,21985],{},[2068,21980,21981,21983],{},[2075,21982,2303],{},[2071,21984,2179],{},[2092,21986,21987],{"encoding":2094},"-b",[609,21989,21991],{"id":21990},"příklad-71","Příklad 7.1",[55,21993,21994,21995,22020],{},"Pro spotřebu ",[1647,21996,21998],{"className":21997},[2059],[2061,21999,22000],{"xmlns":2063},[2065,22001,22002,22017],{},[2068,22003,22004,22006,22008,22011,22013,22015],{},[2071,22005,2849],{},[2075,22007,2077],{},[2210,22009,22010],{},"0,4",[2071,22012,9214],{},[2075,22014,2176],{},[2210,22016,2935],{},[2092,22018,22019],{"encoding":2094},"C = 0{,}4Y + 10"," jsou úspory",[55,22022,22023],{},[1647,22024,22026],{"className":22025},[2059],[2061,22027,22028],{"xmlns":2063},[2065,22029,22030,22068],{},[2068,22031,22032,22034,22036,22038,22040,22042,22044,22046,22048,22050,22052,22054,22056,22058,22061,22063,22065],{},[2071,22033,532],{},[2075,22035,2077],{},[2071,22037,9214],{},[2075,22039,2303],{},[2071,22041,2849],{},[2075,22043,2077],{},[2071,22045,9214],{},[2075,22047,2303],{},[2210,22049,22010],{},[2071,22051,9214],{},[2075,22053,2303],{},[2210,22055,2935],{},[2075,22057,2077],{},[2210,22059,22060],{},"0,6",[2071,22062,9214],{},[2075,22064,2303],{},[2210,22066,22067],{},"10.",[2092,22069,22070],{"encoding":2094},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[55,22072,22073],{},[3982,22074,22075,22076,75,22099,22123,22124,8189,22137,22161,22162,8189,22179,22195,22196,195],{},"Obrázek 7.3 — Přímky ",[1647,22077,22079],{"className":22078},[2059],[2061,22080,22081],{"xmlns":2063},[2065,22082,22083,22097],{},[2068,22084,22085,22087,22089,22091,22093,22095],{},[2071,22086,2849],{},[2075,22088,2077],{},[2210,22090,22010],{},[2071,22092,9214],{},[2075,22094,2176],{},[2210,22096,2935],{},[2092,22098,22019],{"encoding":2094},[1647,22100,22102],{"className":22101},[2059],[2061,22103,22104],{"xmlns":2063},[2065,22105,22106,22120],{},[2068,22107,22108,22110,22112,22114,22116,22118],{},[2071,22109,532],{},[2075,22111,2077],{},[2210,22113,22060],{},[2071,22115,9214],{},[2075,22117,2303],{},[2210,22119,2935],{},[2092,22121,22122],{"encoding":2094},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[1647,22125,22127],{"className":22126},[2059],[2061,22128,22129],{"xmlns":2063},[2065,22130,22131,22135],{},[2068,22132,22133],{},[2071,22134,9214],{},[2092,22136,9214],{"encoding":2094},[1647,22138,22140],{"className":22139},[2059],[2061,22141,22142],{"xmlns":2063},[2065,22143,22144,22158],{},[2068,22145,22146,22148,22151],{},[2075,22147,2803],{},[2210,22149,22150],{},"16,",[8473,22152,22153,22155],{"accent":2360},[2210,22154,678],{},[2075,22156,22157],{},"ˉ",[2092,22159,22160],{"encoding":2094},"\\approx 16{,}\\bar{6}",", s osou ",[1647,22163,22165],{"className":22164},[2059],[2061,22166,22167],{"xmlns":2063},[2065,22168,22169,22177],{},[2068,22170,22171,22173,22175],{},[2071,22172,2849],{},[2075,22174,2361],{"separator":2360},[2071,22176,532],{},[2092,22178,21971],{"encoding":2094},[1647,22180,22182],{"className":22181},[2059],[2061,22183,22184],{"xmlns":2063},[2065,22185,22186,22192],{},[2068,22187,22188,22190],{},[2075,22189,2303],{},[2210,22191,2935],{},[2092,22193,22194],{"encoding":2094},"-10","; přímka spotřeby prochází bodem ",[1647,22197,22199],{"className":22198},[2059],[2061,22200,22201],{"xmlns":2063},[2065,22202,22203,22215],{},[2068,22204,22205,22207,22209,22211,22213],{},[2075,22206,2084],{"stretchy":2083},[2210,22208,630],{},[2075,22210,2361],{"separator":2360},[2210,22212,2935],{},[2075,22214,2090],{"stretchy":2083},[2092,22216,22217],{"encoding":2094},"(0, 10)",[55,22219,22220,22221,8189,22239,22269,22270,11156,22273,22276,22277,8189,22301,11156,22304,22307],{},"Funkce úspor může nabývat záporných hodnot — pro ",[1647,22222,22224],{"className":22223},[2059],[2061,22225,22226],{"xmlns":2063},[2065,22227,22228,22236],{},[2068,22229,22230,22232,22234],{},[2071,22231,9214],{},[2075,22233,2077],{},[2210,22235,630],{},[2092,22237,22238],{"encoding":2094},"Y = 0",[1647,22240,22242],{"className":22241},[2059],[2061,22243,22244],{"xmlns":2063},[2065,22245,22246,22266],{},[2068,22247,22248,22250,22252,22254,22256,22258,22260,22262,22264],{},[2071,22249,532],{},[2075,22251,2084],{"stretchy":2083},[2210,22253,630],{},[2075,22255,2090],{"stretchy":2083},[2075,22257,2077],{},[2075,22259,2303],{},[2071,22261,2179],{},[2075,22263,3521],{},[2210,22265,630],{},[2092,22267,22268],{"encoding":2094},"S(0) = -b \u003C 0","; hovoří se o ",[95,22271,22272],{},"autonomních úsporách",[3982,22274,22275],{},"autonomous savings","). Analogicky ",[1647,22278,22280],{"className":22279},[2059],[2061,22281,22282],{"xmlns":2063},[2065,22283,22284,22298],{},[2068,22285,22286,22288,22290,22292,22294,22296],{},[2071,22287,2849],{},[2075,22289,2084],{"stretchy":2083},[2210,22291,630],{},[2075,22293,2090],{"stretchy":2083},[2075,22295,2077],{},[2071,22297,2179],{},[2092,22299,22300],{"encoding":2094},"C(0) = b",[95,22302,22303],{},"autonomní spotřeba",[3982,22305,22306],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[84,22309,22311],{"id":22310},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[55,22313,22314,1445,22317,11156,22334,22337],{},[95,22315,22316],{},"Mezní sklon ke spotřebě",[1647,22318,22320],{"className":22319},[2059],[2061,22321,22322],{"xmlns":2063},[2065,22323,22324,22332],{},[2068,22325,22326,22328,22330],{},[2071,22327,2890],{},[2071,22329,575],{},[2071,22331,2849],{},[2092,22333,20784],{"encoding":2094},[3982,22335,22336],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[55,22339,22340],{},[1647,22341,22343],{"className":22342},[2059],[2061,22344,22345],{"xmlns":2063},[2065,22346,22347,22373],{},[2068,22348,22349,22351,22353,22355,22357,22371],{},[2071,22350,2890],{},[2071,22352,575],{},[2071,22354,2849],{},[2075,22356,2077],{},[2403,22358,22359,22365],{},[2068,22360,22361,22363],{},[2071,22362,2273],{"mathvariant":2450},[2071,22364,2849],{},[2068,22366,22367,22369],{},[2071,22368,2273],{"mathvariant":2450},[2071,22370,9214],{},[2071,22372,195],{"mathvariant":2450},[2092,22374,22375],{"encoding":2094},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[55,22377,22378,1445,22381,11156,22399,22402],{},[95,22379,22380],{},"Mezní sklon k úsporám",[1647,22382,22384],{"className":22383},[2059],[2061,22385,22386],{"xmlns":2063},[2065,22387,22388,22396],{},[2068,22389,22390,22392,22394],{},[2071,22391,2890],{},[2071,22393,575],{},[2071,22395,532],{},[2092,22397,22398],{"encoding":2094},"MPS",[3982,22400,22401],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[55,22404,22405],{},[1647,22406,22408],{"className":22407},[2059],[2061,22409,22410],{"xmlns":2063},[2065,22411,22412,22438],{},[2068,22413,22414,22416,22418,22420,22422,22436],{},[2071,22415,2890],{},[2071,22417,575],{},[2071,22419,532],{},[2075,22421,2077],{},[2403,22423,22424,22430],{},[2068,22425,22426,22428],{},[2071,22427,2273],{"mathvariant":2450},[2071,22429,532],{},[2068,22431,22432,22434],{},[2071,22433,2273],{"mathvariant":2450},[2071,22435,9214],{},[2071,22437,195],{"mathvariant":2450},[2092,22439,22440],{"encoding":2094},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[55,22442,22443,22444,22502],{},"Z (7.2) plyne ",[1647,22445,22447],{"className":22446},[2059],[2061,22448,22449],{"xmlns":2063},[2065,22450,22451,22499],{},[2068,22452,22453,22467,22469,22483,22485],{},[2403,22454,22455,22461],{},[2068,22456,22457,22459],{},[2071,22458,2273],{"mathvariant":2450},[2071,22460,9214],{},[2068,22462,22463,22465],{},[2071,22464,2273],{"mathvariant":2450},[2071,22466,9214],{},[2075,22468,2077],{},[2403,22470,22471,22477],{},[2068,22472,22473,22475],{},[2071,22474,2273],{"mathvariant":2450},[2071,22476,2849],{},[2068,22478,22479,22481],{},[2071,22480,2273],{"mathvariant":2450},[2071,22482,9214],{},[2075,22484,2176],{},[2403,22486,22487,22493],{},[2068,22488,22489,22491],{},[2071,22490,2273],{"mathvariant":2450},[2071,22492,532],{},[2068,22494,22495,22497],{},[2071,22496,2273],{"mathvariant":2450},[2071,22498,9214],{},[2092,22500,22501],{"encoding":2094},"\\frac{\\mathrm{d}Y}{\\mathrm{d}Y} = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} + \\frac{\\mathrm{d}S}{\\mathrm{d}Y}",", a tedy",[55,22504,22505],{},[1647,22506,22508],{"className":22507},[2059],[2061,22509,22510],{"xmlns":2063},[2065,22511,22512,22575],{},[2068,22513,22514,22566,22568,22570,22573],{},[14567,22515,22516],{"notation":14569},[2400,22517,22518],{"scriptlevel":630,"displaystyle":2083},[2400,22519,22520],{"scriptlevel":630,"displaystyle":2083},[2400,22521,22522],{"scriptlevel":630,"displaystyle":2360},[2068,22523,22524,22526,22528,22530,22532,22534,22536,22538,22540,22542,22544,22546,22548,22550,22552,22554,22556,22558,22560,22562,22564],{},[2071,22525,2890],{},[2071,22527,575],{},[2071,22529,2849],{},[2075,22531,2176],{},[2071,22533,2890],{},[2071,22535,575],{},[2071,22537,532],{},[2075,22539,2077],{},[2210,22541,638],{},[2075,22543,2361],{"separator":2360},[5965,22545],{"width":5967},[2071,22547,2890],{},[2071,22549,575],{},[2071,22551,532],{},[2075,22553,2077],{},[2210,22555,638],{},[2075,22557,2303],{},[2071,22559,2890],{},[2071,22561,575],{},[2071,22563,2849],{},[2071,22565,195],{"mathvariant":2450},[5965,22567],{"width":5967},[2075,22569,2084],{"stretchy":2083},[2210,22571,22572],{},"7.5",[2075,22574,2090],{"stretchy":2083},[2092,22576,22577],{"encoding":2094},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[55,22579,22580,1445,22583,22606,22607,75,22629,22655],{},[95,22581,22582],{},"Pro lineární model",[1647,22584,22586],{"className":22585},[2059],[2061,22587,22588],{"xmlns":2063},[2065,22589,22590,22604],{},[2068,22591,22592,22594,22596,22598,22600,22602],{},[2071,22593,2849],{},[2075,22595,2077],{},[2071,22597,69],{},[2071,22599,9214],{},[2075,22601,2176],{},[2071,22603,2179],{},[2092,22605,21659],{"encoding":2094}," vychází ",[1647,22608,22610],{"className":22609},[2059],[2061,22611,22612],{"xmlns":2063},[2065,22613,22614,22626],{},[2068,22615,22616,22618,22620,22622,22624],{},[2071,22617,2890],{},[2071,22619,575],{},[2071,22621,2849],{},[2075,22623,2077],{},[2071,22625,69],{},[2092,22627,22628],{"encoding":2094},"MPC = a",[1647,22630,22632],{"className":22631},[2059],[2061,22633,22634],{"xmlns":2063},[2065,22635,22636,22652],{},[2068,22637,22638,22640,22642,22644,22646,22648,22650],{},[2071,22639,2890],{},[2071,22641,575],{},[2071,22643,532],{},[2075,22645,2077],{},[2210,22647,638],{},[2075,22649,2303],{},[2071,22651,69],{},[2092,22653,22654],{"encoding":2094},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[55,22657,22658,22661,22662,22684,22685,22713],{},[95,22659,22660],{},"Interpretace diferenciálem."," Pro pevné ",[1647,22663,22665],{"className":22664},[2059],[2061,22666,22667],{"xmlns":2063},[2065,22668,22669,22681],{},[2068,22670,22671,22673,22675],{},[2071,22672,9214],{},[2075,22674,2077],{},[2205,22676,22677,22679],{},[2071,22678,9214],{},[2075,22680,4441],{},[2092,22682,22683],{"encoding":2094},"Y = Y^*"," udává ",[1647,22686,22688],{"className":22687},[2059],[2061,22689,22690],{"xmlns":2063},[2065,22691,22692,22710],{},[2068,22693,22694,22696,22698,22700,22702,22708],{},[2071,22695,2890],{},[2071,22697,575],{},[2071,22699,2849],{},[2075,22701,2084],{"stretchy":2083},[2205,22703,22704,22706],{},[2071,22705,9214],{},[2075,22707,4441],{},[2075,22709,2090],{"stretchy":2083},[2092,22711,22712],{"encoding":2094},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[55,22715,22716],{},[1647,22717,22719],{"className":22718},[2059],[2061,22720,22721],{"xmlns":2063},[2065,22722,22723,22777],{},[2068,22724,22725,22727,22729,22731,22733,22735,22737,22743,22745,22747,22749,22751,22753,22755,22757,22759,22761,22763,22765,22767,22769,22771,22773,22775],{},[2071,22726,2961],{"mathvariant":2450},[2071,22728,2849],{},[2075,22730,2803],{},[2071,22732,2273],{"mathvariant":2450},[2071,22734,2849],{},[2075,22736,2077],{},[2205,22738,22739,22741],{},[2071,22740,2849],{},[2075,22742,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,22744,2084],{"stretchy":2083},[2071,22746,9214],{},[2075,22748,2090],{"stretchy":2083},[2363,22750,3061],{},[2071,22752,2273],{"mathvariant":2450},[2071,22754,9214],{},[2075,22756,2077],{},[2071,22758,2890],{},[2071,22760,575],{},[2071,22762,2849],{},[2075,22764,2084],{"stretchy":2083},[2071,22766,9214],{},[2075,22768,2090],{"stretchy":2083},[2363,22770,3061],{},[2071,22772,2273],{"mathvariant":2450},[2071,22774,9214],{},[2071,22776,195],{"mathvariant":2450},[2092,22778,22779],{"encoding":2094},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[55,22781,22782,22783,22819,22820,22823],{},"Analogicky ",[1647,22784,22786],{"className":22785},[2059],[2061,22787,22788],{"xmlns":2063},[2065,22789,22790,22816],{},[2068,22791,22792,22794,22796,22798,22800,22802,22804,22806,22808,22810,22812,22814],{},[2071,22793,2961],{"mathvariant":2450},[2071,22795,532],{},[2075,22797,2803],{},[2071,22799,2890],{},[2071,22801,575],{},[2071,22803,532],{},[2075,22805,2084],{"stretchy":2083},[2071,22807,9214],{},[2075,22809,2090],{"stretchy":2083},[2363,22811,3061],{},[2071,22813,2273],{"mathvariant":2450},[2071,22815,9214],{},[2092,22817,22818],{"encoding":2094},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[69,22821,2430],{"className":22822,"dataFsResolvedFilePath":4005,"href":4006},[62]," a její ekonomická interpretace.",[609,22825,22827],{"id":22826},"příklad-72","Příklad 7.2",[55,22829,21994,22830,22865,22866,22885],{},[1647,22831,22833],{"className":22832},[2059],[2061,22834,22835],{"xmlns":2063},[2065,22836,22837,22862],{},[2068,22838,22839,22841,22843,22846,22852,22854,22856,22858,22860],{},[2071,22840,2849],{},[2075,22842,2077],{},[2210,22844,22845],{},"0,001",[2205,22847,22848,22850],{},[2071,22849,9214],{},[2210,22851,646],{},[2075,22853,2176],{},[2210,22855,2911],{},[2071,22857,9214],{},[2075,22859,2176],{},[2210,22861,3194],{},[2092,22863,22864],{"encoding":2094},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[1647,22867,22869],{"className":22868},[2059],[2061,22870,22871],{"xmlns":2063},[2065,22872,22873,22882],{},[2068,22874,22875,22877,22879],{},[2071,22876,9214],{},[2075,22878,3521],{},[2210,22880,22881],{},"400",[2092,22883,22884],{"encoding":2094},"Y \u003C 400",") platí",[55,22887,22888],{},[1647,22889,22891],{"className":22890},[2059],[2061,22892,22893],{"xmlns":2063},[2065,22894,22895,22932],{},[2068,22896,22897,22899,22901,22903,22905,22919,22921,22924,22926,22928,22930],{},[2071,22898,2890],{},[2071,22900,575],{},[2071,22902,2849],{},[2075,22904,2077],{},[2403,22906,22907,22913],{},[2068,22908,22909,22911],{},[2071,22910,2273],{"mathvariant":2450},[2071,22912,2849],{},[2068,22914,22915,22917],{},[2071,22916,2273],{"mathvariant":2450},[2071,22918,9214],{},[2075,22920,2077],{},[2210,22922,22923],{},"0,002",[2071,22925,9214],{},[2075,22927,2176],{},[2210,22929,2911],{},[2075,22931,2361],{"separator":2360},[2092,22933,22934],{"encoding":2094},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[55,22936,22937],{},[1647,22938,22940],{"className":22939},[2059],[2061,22941,22942],{"xmlns":2063},[2065,22943,22944,22977],{},[2068,22945,22946,22948,22950,22952,22954,22956,22958,22960,22962,22964,22966,22968,22970,22972,22974],{},[2071,22947,2890],{},[2071,22949,575],{},[2071,22951,532],{},[2075,22953,2077],{},[2210,22955,638],{},[2075,22957,2303],{},[2071,22959,2890],{},[2071,22961,575],{},[2071,22963,2849],{},[2075,22965,2077],{},[2075,22967,2303],{},[2210,22969,22923],{},[2071,22971,9214],{},[2075,22973,2176],{},[2210,22975,22976],{},"0,8.",[2092,22978,22979],{"encoding":2094},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[89,22981,22982,23062,23141],{},[92,22983,22984,835,23012,23040,23041,8189,23059,195],{},[1647,22985,22987],{"className":22986},[2059],[2061,22988,22989],{"xmlns":2063},[2065,22990,22991,23009],{},[2068,22992,22993,22995,22997,22999,23001,23003,23005,23007],{},[2071,22994,2890],{},[2071,22996,575],{},[2071,22998,2849],{},[2075,23000,2084],{"stretchy":2083},[2210,23002,3164],{},[2075,23004,2090],{"stretchy":2083},[2075,23006,2077],{},[2210,23008,22010],{},[2092,23010,23011],{"encoding":2094},"MPC(100) = 0{,}4",[1647,23013,23015],{"className":23014},[2059],[2061,23016,23017],{"xmlns":2063},[2065,23018,23019,23037],{},[2068,23020,23021,23023,23025,23027,23029,23031,23033,23035],{},[2071,23022,2890],{},[2071,23024,575],{},[2071,23026,532],{},[2075,23028,2084],{"stretchy":2083},[2210,23030,3164],{},[2075,23032,2090],{"stretchy":2083},[2075,23034,2077],{},[2210,23036,22060],{},[2092,23038,23039],{"encoding":2094},"MPS(100) = 0{,}6"," — při ",[1647,23042,23044],{"className":23043},[2059],[2061,23045,23046],{"xmlns":2063},[2065,23047,23048,23056],{},[2068,23049,23050,23052,23054],{},[2071,23051,9214],{},[2075,23053,2077],{},[2210,23055,3164],{},[2092,23057,23058],{"encoding":2094},"Y = 100",[95,23060,23061],{},"větší sklon k úsporám",[92,23063,23064,835,23092,23040,23120,8189,23138,195],{},[1647,23065,23067],{"className":23066},[2059],[2061,23068,23069],{"xmlns":2063},[2065,23070,23071,23089],{},[2068,23072,23073,23075,23077,23079,23081,23083,23085,23087],{},[2071,23074,2890],{},[2071,23076,575],{},[2071,23078,2849],{},[2075,23080,2084],{"stretchy":2083},[2210,23082,8464],{},[2075,23084,2090],{"stretchy":2083},[2075,23086,2077],{},[2210,23088,22060],{},[2092,23090,23091],{"encoding":2094},"MPC(200) = 0{,}6",[1647,23093,23095],{"className":23094},[2059],[2061,23096,23097],{"xmlns":2063},[2065,23098,23099,23117],{},[2068,23100,23101,23103,23105,23107,23109,23111,23113,23115],{},[2071,23102,2890],{},[2071,23104,575],{},[2071,23106,532],{},[2075,23108,2084],{"stretchy":2083},[2210,23110,8464],{},[2075,23112,2090],{"stretchy":2083},[2075,23114,2077],{},[2210,23116,22010],{},[2092,23118,23119],{"encoding":2094},"MPS(200) = 0{,}4",[1647,23121,23123],{"className":23122},[2059],[2061,23124,23125],{"xmlns":2063},[2065,23126,23127,23135],{},[2068,23128,23129,23131,23133],{},[2071,23130,9214],{},[2075,23132,2077],{},[2210,23134,8464],{},[2092,23136,23137],{"encoding":2094},"Y = 200",[95,23139,23140],{},"větší sklon ke spotřebě",[92,23142,23143,23144,23162,23163,4007],{},"Přesně při ",[1647,23145,23147],{"className":23146},[2059],[2061,23148,23149],{"xmlns":2063},[2065,23150,23151,23159],{},[2068,23152,23153,23155,23157],{},[2071,23154,9214],{},[2075,23156,2077],{},[2210,23158,8889],{},[2092,23160,23161],{"encoding":2094},"Y = 150"," se oba sklony rovnají (",[1647,23164,23166],{"className":23165},[2059],[2061,23167,23168],{"xmlns":2063},[2065,23169,23170,23190],{},[2068,23171,23172,23174,23176,23178,23180,23182,23184,23186,23188],{},[2071,23173,2890],{},[2071,23175,575],{},[2071,23177,2849],{},[2075,23179,2077],{},[2071,23181,2890],{},[2071,23183,575],{},[2071,23185,532],{},[2075,23187,2077],{},[2210,23189,5096],{},[2092,23191,23192],{"encoding":2094},"MPC = MPS = 0{,}5",[55,23194,23195,23196,23213,23214,23228,23229,2758,23242,23256,23257,23270,23271,23312],{},"Interpretace: při ",[1647,23197,23199],{"className":23198},[2059],[2061,23200,23201],{"xmlns":2063},[2065,23202,23203,23211],{},[2068,23204,23205,23207,23209],{},[2071,23206,9214],{},[2075,23208,2077],{},[2210,23210,3164],{},[2092,23212,23058],{"encoding":2094}," se spotřeba mění ",[1647,23215,23217],{"className":23216},[2059],[2061,23218,23219],{"xmlns":2063},[2065,23220,23221,23225],{},[2068,23222,23223],{},[2210,23224,22010],{},[2092,23226,23227],{"encoding":2094},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[1647,23230,23232],{"className":23231},[2059],[2061,23233,23234],{"xmlns":2063},[2065,23235,23236,23240],{},[2068,23237,23238],{},[2210,23239,3164],{},[2092,23241,3164],{"encoding":2094},[1647,23243,23245],{"className":23244},[2059],[2061,23246,23247],{"xmlns":2063},[2065,23248,23249,23254],{},[2068,23250,23251],{},[2210,23252,23253],{},"101",[2092,23255,23253],{"encoding":2094},", změní se spotřeba přibližně o ",[1647,23258,23260],{"className":23259},[2059],[2061,23261,23262],{"xmlns":2063},[2065,23263,23264,23268],{},[2068,23265,23266],{},[2210,23267,22010],{},[2092,23269,23227],{"encoding":2094},". Skutečná změna ",[1647,23272,23274],{"className":23273},[2059],[2061,23275,23276],{"xmlns":2063},[2065,23277,23278,23309],{},[2068,23279,23280,23282,23284,23286,23288,23290,23292,23294,23296,23298,23300,23302,23304,23306],{},[2071,23281,2961],{"mathvariant":2450},[2071,23283,2849],{},[2075,23285,2077],{},[2071,23287,2849],{},[2075,23289,2084],{"stretchy":2083},[2210,23291,23253],{},[2075,23293,2090],{"stretchy":2083},[2075,23295,2303],{},[2071,23297,2849],{},[2075,23299,2084],{"stretchy":2083},[2210,23301,3164],{},[2075,23303,2090],{"stretchy":2083},[2075,23305,2077],{},[2210,23307,23308],{},"0,401",[2092,23310,23311],{"encoding":2094},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[55,23314,23315,23316],{},"Obecný trend: ",[95,23317,23318],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[84,23320,23322],{"id":23321},"makroekonomická-rovnováha","Makroekonomická rovnováha",[55,23324,23325,23326,11156,23329,23332,23333,11156,23336,13861,23339,11156,23342,23345],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[95,23327,23328],{},"makroekonomická rovnováha",[3982,23330,23331],{},"macroeconomic equilibrium",") — stav, kdy se všechny trhy nacházejí v rovnováze: trh zboží a služeb, trh práce a ostatních výrobních faktorů, trh kapitálu a peněz. Významnou součástí je rovnost ",[95,23334,23335],{},"agregátní poptávky",[3982,23337,23338],{},"aggregate demand",[95,23340,23341],{},"agregátní nabídky",[3982,23343,23344],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[84,23347,23349],{"id":23348},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[55,23351,23352],{},[58,23353],{"alt":23354,"className":23355,"src":23356},"imek-keynesian-kriz",[62,63],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[609,23358,23360],{"id":23359},"zadání-modelu","Zadání modelu",[55,23362,23363,23364,23377,23378,23391],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[1647,23365,23367],{"className":23366},[2059],[2061,23368,23369],{"xmlns":2063},[2065,23370,23371,23375],{},[2068,23372,23373],{},[2071,23374,2849],{},[2092,23376,2849],{"encoding":2094}," a investice ",[1647,23379,23381],{"className":23380},[2059],[2061,23382,23383],{"xmlns":2063},[2065,23384,23385,23389],{},[2068,23386,23387],{},[2071,23388,13919],{},[2092,23390,13919],{"encoding":2094},". Podmínka rovnováhy:",[55,23393,23394],{},[1647,23395,23397],{"className":23396},[2059],[2061,23398,23399],{"xmlns":2063},[2065,23400,23401,23424],{},[2068,23402,23403,23405,23407,23409,23411,23413,23415,23417,23419,23422],{},[2071,23404,9214],{},[2075,23406,2077],{},[2071,23408,2849],{},[2075,23410,2176],{},[2071,23412,13919],{},[2071,23414,195],{"mathvariant":2450},[5965,23416],{"width":5967},[2075,23418,2084],{"stretchy":2083},[2210,23420,23421],{},"7.6",[2075,23423,2090],{"stretchy":2083},[2092,23425,23426],{"encoding":2094},"Y = C + I. \\qquad (7.6)",[609,23428,23430],{"id":23429},"soustava-rovnic","Soustava rovnic",[55,23432,23433,23434,23455,23456,23480],{},"Pro pevně zadané (plánované) investice ",[1647,23435,23437],{"className":23436},[2059],[2061,23438,23439],{"xmlns":2063},[2065,23440,23441,23453],{},[2068,23442,23443,23445,23447],{},[2071,23444,13919],{},[2075,23446,2077],{},[2205,23448,23449,23451],{},[2071,23450,13919],{},[2075,23452,4441],{},[2092,23454,13930],{"encoding":2094}," a funkci spotřeby ",[1647,23457,23459],{"className":23458},[2059],[2061,23460,23461],{"xmlns":2063},[2065,23462,23463,23477],{},[2068,23464,23465,23467,23469,23471,23473,23475],{},[2071,23466,2849],{},[2075,23468,2077],{},[2071,23470,2849],{},[2075,23472,2084],{"stretchy":2083},[2071,23474,9214],{},[2075,23476,2090],{"stretchy":2083},[2092,23478,23479],{"encoding":2094},"C = C(Y)"," dostáváme soustavu",[55,23482,23483],{},[1647,23484,23486],{"className":23485},[2059],[2061,23487,23488],{"xmlns":2063},[2065,23489,23490,23566],{},[2068,23491,23492,23557,23559,23561,23564],{},[23493,23494,23497,23529],"mtable",{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},"0.25em","right left",[23498,23499,23500,23507],"mtr",{},[23501,23502,23503],"mtd",{},[2400,23504,23505],{"scriptlevel":630,"displaystyle":2360},[2071,23506,9214],{},[23501,23508,23509],{},[2400,23510,23511],{"scriptlevel":630,"displaystyle":2360},[2068,23512,23513,23515,23517,23519,23521,23527],{},[2068,23514],{},[2075,23516,2077],{},[2071,23518,2849],{},[2075,23520,2176],{},[2205,23522,23523,23525],{},[2071,23524,13919],{},[2075,23526,4441],{},[2075,23528,2361],{"separator":2360},[23498,23530,23531,23537],{},[23501,23532,23533],{},[2400,23534,23535],{"scriptlevel":630,"displaystyle":2360},[2071,23536,2849],{},[23501,23538,23539],{},[2400,23540,23541],{"scriptlevel":630,"displaystyle":2360},[2068,23542,23543,23545,23547,23549,23551,23553,23555],{},[2068,23544],{},[2075,23546,2077],{},[2071,23548,2849],{},[2075,23550,2084],{"stretchy":2083},[2071,23552,9214],{},[2075,23554,2090],{"stretchy":2083},[2075,23556,2361],{"separator":2360},[5965,23558],{"width":5967},[2075,23560,2084],{"stretchy":2083},[2210,23562,23563],{},"7.7",[2075,23565,2090],{"stretchy":2083},[2092,23567,23568],{"encoding":2094},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[55,23570,23571,23572,1445,23574,75,23591,1445,23594,195],{},"jejímž řešením jsou ",[95,23573,15620],{},[1647,23575,23577],{"className":23576},[2059],[2061,23578,23579],{"xmlns":2063},[2065,23580,23581,23589],{},[2068,23582,23583],{},[2205,23584,23585,23587],{},[2071,23586,9214],{},[2071,23588,554],{},[2092,23590,15638],{"encoding":2094},[95,23592,23593],{},"rovnovážná spotřeba",[1647,23595,23597],{"className":23596},[2059],[2061,23598,23599],{"xmlns":2063},[2065,23600,23601,23609],{},[2068,23602,23603],{},[2205,23604,23605,23607],{},[2071,23606,2849],{},[2071,23608,554],{},[2092,23610,15697],{"encoding":2094},[609,23612,23614,23615],{"id":23613},"výpočet-yeye","Výpočet ",[1647,23616,23618],{"className":23617},[2059],[2061,23619,23620],{"xmlns":2063},[2065,23621,23622,23630],{},[2068,23623,23624],{},[2205,23625,23626,23628],{},[2071,23627,9214],{},[2071,23629,554],{},[2092,23631,15638],{"encoding":2094},[55,23633,23634,23635,23658,23659,7772,23691],{},"Pro lineární spotřebu ",[1647,23636,23638],{"className":23637},[2059],[2061,23639,23640],{"xmlns":2063},[2065,23641,23642,23656],{},[2068,23643,23644,23646,23648,23650,23652,23654],{},[2071,23645,2849],{},[2075,23647,2077],{},[2071,23649,69],{},[2071,23651,9214],{},[2075,23653,2176],{},[2071,23655,2179],{},[2092,23657,21659],{"encoding":2094}," plyne z (7.7) rovnice ",[1647,23660,23662],{"className":23661},[2059],[2061,23663,23664],{"xmlns":2063},[2065,23665,23666,23688],{},[2068,23667,23668,23670,23672,23674,23676,23678,23680,23682],{},[2071,23669,9214],{},[2075,23671,2077],{},[2071,23673,69],{},[2071,23675,9214],{},[2075,23677,2176],{},[2071,23679,2179],{},[2075,23681,2176],{},[2205,23683,23684,23686],{},[2071,23685,13919],{},[2075,23687,4441],{},[2092,23689,23690],{"encoding":2094},"Y = aY + b + I^*",[95,23692,23693],{},"redukovaný tvar",[55,23695,23696],{},[1647,23697,23699],{"className":23698},[2059],[2061,23700,23701],{"xmlns":2063},[2065,23702,23703,23751],{},[2068,23704,23705],{},[14567,23706,23707],{"notation":14569},[2400,23708,23709],{"scriptlevel":630,"displaystyle":2083},[2400,23710,23711],{"scriptlevel":630,"displaystyle":2083},[2400,23712,23713],{"scriptlevel":630,"displaystyle":2360},[2068,23714,23715,23717,23723,23725,23747,23749],{},[2363,23716,3061],{},[2205,23718,23719,23721],{},[2071,23720,9214],{},[2071,23722,554],{},[2075,23724,2077],{},[2403,23726,23727,23739],{},[2068,23728,23729,23731,23733],{},[2071,23730,2179],{},[2075,23732,2176],{},[2205,23734,23735,23737],{},[2071,23736,13919],{},[2075,23738,4441],{},[2068,23740,23741,23743,23745],{},[2210,23742,638],{},[2075,23744,2303],{},[2071,23746,69],{},[2071,23748,195],{"mathvariant":2450},[2363,23750,3061],{},[2092,23752,23753],{"encoding":2094},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[609,23755,23757],{"id":23756},"příklad-73","Příklad 7.3",[55,23759,23760,23761,8189,23778,75,23802,23828],{},"V modelu ",[1647,23762,23764],{"className":23763},[2059],[2061,23765,23766],{"xmlns":2063},[2065,23767,23768,23776],{},[2068,23769,23770,23772,23774],{},[2071,23771,2849],{},[2363,23773,14025],{},[2071,23775,13919],{},[2092,23777,14030],{"encoding":2094},[1647,23779,23781],{"className":23780},[2059],[2061,23782,23783],{"xmlns":2063},[2065,23784,23785,23799],{},[2068,23786,23787,23789,23791,23793,23795,23797],{},[2071,23788,2849],{},[2075,23790,2077],{},[2210,23792,22060],{},[2071,23794,9214],{},[2075,23796,2176],{},[2210,23798,2935],{},[2092,23800,23801],{"encoding":2094},"C = 0{,}6Y + 10",[1647,23803,23805],{"className":23804},[2059],[2061,23806,23807],{"xmlns":2063},[2065,23808,23809,23825],{},[2068,23810,23811,23813,23815,23817,23819],{},[2071,23812,13919],{},[2075,23814,2077],{},[2210,23816,3583],{},[2075,23818,2077],{},[2205,23820,23821,23823],{},[2071,23822,13919],{},[2075,23824,4441],{},[2092,23826,23827],{"encoding":2094},"I = 12 = I^*",". Soustava",[55,23830,23831],{},[1647,23832,23834],{"className":23833},[2059],[2061,23835,23836],{"xmlns":2063},[2065,23837,23838,23894],{},[23493,23839,23840,23866],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,23841,23842,23848],{},[23501,23843,23844],{},[2400,23845,23846],{"scriptlevel":630,"displaystyle":2360},[2071,23847,9214],{},[23501,23849,23850],{},[2400,23851,23852],{"scriptlevel":630,"displaystyle":2360},[2068,23853,23854,23856,23858,23860,23862,23864],{},[2068,23855],{},[2075,23857,2077],{},[2071,23859,2849],{},[2075,23861,2176],{},[2210,23863,3583],{},[2075,23865,2361],{"separator":2360},[23498,23867,23868,23874],{},[23501,23869,23870],{},[2400,23871,23872],{"scriptlevel":630,"displaystyle":2360},[2071,23873,2849],{},[23501,23875,23876],{},[2400,23877,23878],{"scriptlevel":630,"displaystyle":2360},[2068,23879,23880,23882,23884,23886,23888,23890,23892],{},[2068,23881],{},[2075,23883,2077],{},[2210,23885,22060],{},[2071,23887,9214],{},[2075,23889,2176],{},[2210,23891,2935],{},[2075,23893,2361],{"separator":2360},[2092,23895,23896],{"encoding":2094},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[55,23898,23899,23900,835,23923,23946,23947,4007],{},"má řešení ",[1647,23901,23903],{"className":23902},[2059],[2061,23904,23905],{"xmlns":2063},[2065,23906,23907,23920],{},[2068,23908,23909,23915,23917],{},[2205,23910,23911,23913],{},[2071,23912,9214],{},[2071,23914,554],{},[2075,23916,2077],{},[2210,23918,23919],{},"55",[2092,23921,23922],{"encoding":2094},"Y^E = 55",[1647,23924,23926],{"className":23925},[2059],[2061,23927,23928],{"xmlns":2063},[2065,23929,23930,23943],{},[2068,23931,23932,23938,23940],{},[2205,23933,23934,23936],{},[2071,23935,2849],{},[2071,23937,554],{},[2075,23939,2077],{},[2210,23941,23942],{},"43",[2092,23944,23945],{"encoding":2094},"C^E = 43"," (a ",[1647,23948,23950],{"className":23949},[2059],[2061,23951,23952],{"xmlns":2063},[2065,23953,23954,23966],{},[2068,23955,23956,23962,23964],{},[2205,23957,23958,23960],{},[2071,23959,532],{},[2071,23961,554],{},[2075,23963,2077],{},[2210,23965,3583],{},[2092,23967,23968],{"encoding":2094},"S^E = 12",[55,23970,23971],{},[3982,23972,23973,23974,23996,23997,13861,24018,24041,24042,195],{},"Obrázek 7.5 — Přímky ",[1647,23975,23977],{"className":23976},[2059],[2061,23978,23979],{"xmlns":2063},[2065,23980,23981,23993],{},[2068,23982,23983,23985,23987,23989,23991],{},[2071,23984,2849],{},[2075,23986,2077],{},[2071,23988,9214],{},[2075,23990,2303],{},[2210,23992,3583],{},[2092,23994,23995],{"encoding":2094},"C = Y - 12"," (rovnováha ",[1647,23998,24000],{"className":23999},[2059],[2061,24001,24002],{"xmlns":2063},[2065,24003,24004,24016],{},[2068,24005,24006,24008,24010,24012,24014],{},[2071,24007,9214],{},[2075,24009,2077],{},[2071,24011,2849],{},[2075,24013,2176],{},[2071,24015,13919],{},[2092,24017,16479],{"encoding":2094},[1647,24019,24021],{"className":24020},[2059],[2061,24022,24023],{"xmlns":2063},[2065,24024,24025,24039],{},[2068,24026,24027,24029,24031,24033,24035,24037],{},[2071,24028,2849],{},[2075,24030,2077],{},[2210,24032,22060],{},[2071,24034,9214],{},[2075,24036,2176],{},[2210,24038,2935],{},[2092,24040,23801],{"encoding":2094}," (funkce spotřeby) se protínají v bodě ",[1647,24043,24045],{"className":24044},[2059],[2061,24046,24047],{"xmlns":2063},[2065,24048,24049,24081],{},[2068,24050,24051,24053,24059,24061,24067,24069,24071,24073,24075,24077,24079],{},[2075,24052,2561],{"stretchy":2083},[2205,24054,24055,24057],{},[2071,24056,9214],{},[2071,24058,554],{},[2075,24060,2361],{"separator":2360},[2205,24062,24063,24065],{},[2071,24064,2849],{},[2071,24066,554],{},[2075,24068,2576],{"stretchy":2083},[2075,24070,2077],{},[2075,24072,2561],{"stretchy":2083},[2210,24074,23919],{},[2075,24076,2361],{"separator":2360},[2210,24078,23942],{},[2075,24080,2576],{"stretchy":2083},[2092,24082,24083],{"encoding":2094},"[Y^E, C^E] = [55, 43]",[55,24085,24086,24089,24090,24107,24108,195],{},[95,24087,24088],{},"Komentář k přechodu."," Model ",[1647,24091,24093],{"className":24092},[2059],[2061,24094,24095],{"xmlns":2063},[2065,24096,24097,24105],{},[2068,24098,24099,24101,24103],{},[2071,24100,2849],{},[2363,24102,14025],{},[2071,24104,13919],{},[2092,24106,14030],{"encoding":2094}," ignoruje stát. V praxi však stát vybírá daně a provádí vlastní výdaje, což ovlivňuje jak disponibilní důchod domácností, tak celkovou poptávku — přidáním vládního sektoru dostaneme ",[95,24109,24110,24111],{},"model ",[1647,24112,24114],{"className":24113},[2059],[2061,24115,24116],{"xmlns":2063},[2065,24117,24118,24130],{},[2068,24119,24120,24122,24124,24126,24128],{},[2071,24121,2849],{},[2363,24123,14025],{},[2071,24125,13919],{},[2363,24127,14025],{},[2071,24129,13845],{},[2092,24131,20959],{"encoding":2094},[84,24133,24135],{"id":24134},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[609,24137,23360],{"id":24138},"zadání-modelu-1",[55,24140,24141,24142,24159,24160,1445,24163,11156,24176,24179],{},"Rozšíření modelu ",[1647,24143,24145],{"className":24144},[2059],[2061,24146,24147],{"xmlns":2063},[2065,24148,24149,24157],{},[2068,24150,24151,24153,24155],{},[2071,24152,2849],{},[2363,24154,14025],{},[2071,24156,13919],{},[2092,24158,14030],{"encoding":2094}," o ",[95,24161,24162],{},"vládní výdaje",[1647,24164,24166],{"className":24165},[2059],[2061,24167,24168],{"xmlns":2063},[2065,24169,24170,24174],{},[2068,24171,24172],{},[2071,24173,13845],{},[2092,24175,13845],{"encoding":2094},[3982,24177,24178],{},"government expenditure","). Podmínka rovnováhy:",[55,24181,24182],{},[1647,24183,24185],{"className":24184},[2059],[2061,24186,24187],{"xmlns":2063},[2065,24188,24189,24216],{},[2068,24190,24191,24193,24195,24197,24199,24201,24203,24205,24207,24209,24211,24214],{},[2071,24192,9214],{},[2075,24194,2077],{},[2071,24196,2849],{},[2075,24198,2176],{},[2071,24200,13919],{},[2075,24202,2176],{},[2071,24204,13845],{},[2071,24206,195],{"mathvariant":2450},[5965,24208],{"width":5967},[2075,24210,2084],{"stretchy":2083},[2210,24212,24213],{},"7.8",[2075,24215,2090],{"stretchy":2083},[2092,24217,24218],{"encoding":2094},"Y = C + I + G. \\qquad (7.8)",[55,24220,24221,24222,1445,24225,11156,24238,24241],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[95,24223,24224],{},"zdaněním domácností",[1647,24226,24228],{"className":24227},[2059],[2061,24229,24230],{"xmlns":2063},[2065,24231,24232,24236],{},[2068,24233,24234],{},[2071,24235,543],{},[2092,24237,543],{"encoding":2094},[3982,24239,24240],{},"taxation","). Zdanění bývá:",[89,24243,24244,24277,24302],{},[92,24245,24246,24247,2361],{},"úměrné důchodu: ",[1647,24248,24250],{"className":24249},[2059],[2061,24251,24252],{"xmlns":2063},[2065,24253,24254,24274],{},[2068,24255,24256,24258,24260,24262,24264,24266,24268,24270,24272],{},[2071,24257,543],{},[2075,24259,2077],{},[2071,24261,543],{},[2075,24263,2084],{"stretchy":2083},[2071,24265,9214],{},[2075,24267,2090],{"stretchy":2083},[2075,24269,2077],{},[2071,24271,21594],{},[2071,24273,9214],{},[2092,24275,24276],{"encoding":2094},"T = T(Y) = tY",[92,24278,24279,24280,2361],{},"fixní: ",[1647,24281,24283],{"className":24282},[2059],[2061,24284,24285],{"xmlns":2063},[2065,24286,24287,24299],{},[2068,24288,24289,24291,24293],{},[2071,24290,543],{},[2075,24292,2077],{},[2205,24294,24295,24297],{},[2071,24296,543],{},[2075,24298,4441],{},[2092,24300,24301],{"encoding":2094},"T = T^*",[92,24303,24304,24305,24333,24334,195],{},"kombinované: ",[1647,24306,24308],{"className":24307},[2059],[2061,24309,24310],{"xmlns":2063},[2065,24311,24312,24330],{},[2068,24313,24314,24316,24318,24324,24326,24328],{},[2071,24315,543],{},[2075,24317,2077],{},[2205,24319,24320,24322],{},[2071,24321,543],{},[2075,24323,4441],{},[2075,24325,2176],{},[2071,24327,21594],{},[2071,24329,9214],{},[2092,24331,24332],{"encoding":2094},"T = T^* + tY",", kde ",[1647,24335,24337],{"className":24336},[2059],[2061,24338,24339],{"xmlns":2063},[2065,24340,24341,24353],{},[2068,24342,24343,24345,24347,24349,24351],{},[2210,24344,630],{},[2075,24346,7766],{},[2071,24348,21594],{},[2075,24350,3521],{},[2210,24352,638],{},[2092,24354,24355],{"encoding":2094},"0 \\le t \u003C 1",[1023,24357,24358],{},[55,24359,24360,24362,24363,24384,24385,24388,24389,24402,24403,13861,24429,1445,24432,24458,24459,24487,24488,75,24501,24519],{},[1647,24361,4499],{}," Pozor na disponibilní důchod\nV modelu ",[1647,24364,24366],{"className":24365},[2059],[2061,24367,24368],{"xmlns":2063},[2065,24369,24370,24382],{},[2068,24371,24372,24374,24376,24378,24380],{},[2071,24373,2849],{},[2363,24375,14025],{},[2071,24377,13919],{},[2363,24379,14025],{},[2071,24381,13845],{},[2092,24383,20959],{"encoding":2094}," je nutné ",[95,24386,24387],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[1647,24390,24392],{"className":24391},[2059],[2061,24393,24394],{"xmlns":2063},[2065,24395,24396,24400],{},[2068,24397,24398],{},[2071,24399,9214],{},[2092,24401,9214],{"encoding":2094}," (vstupuje do podmínky rovnováhy ",[1647,24404,24406],{"className":24405},[2059],[2061,24407,24408],{"xmlns":2063},[2065,24409,24410,24426],{},[2068,24411,24412,24414,24416,24418,24420,24422,24424],{},[2071,24413,9214],{},[2075,24415,2077],{},[2071,24417,2849],{},[2075,24419,2176],{},[2071,24421,13919],{},[2075,24423,2176],{},[2071,24425,13845],{},[2092,24427,24428],{"encoding":2094},"Y = C + I + G",[95,24430,24431],{},"disponibilní důchod",[1647,24433,24435],{"className":24434},[2059],[2061,24436,24437],{"xmlns":2063},[2065,24438,24439,24455],{},[2068,24440,24441,24447,24449,24451,24453],{},[2348,24442,24443,24445],{},[2071,24444,9214],{},[2071,24446,4271],{},[2075,24448,2077],{},[2071,24450,9214],{},[2075,24452,2303],{},[2071,24454,543],{},[2092,24456,24457],{"encoding":2094},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[1647,24460,24462],{"className":24461},[2059],[2061,24463,24464],{"xmlns":2063},[2065,24465,24466,24484],{},[2068,24467,24468,24470,24472,24474,24476,24482],{},[2071,24469,2849],{},[2075,24471,2077],{},[2071,24473,2849],{},[2075,24475,2084],{"stretchy":2083},[2348,24477,24478,24480],{},[2071,24479,9214],{},[2071,24481,4271],{},[2075,24483,2090],{"stretchy":2083},[2092,24485,24486],{"encoding":2094},"C = C(Y_D)","). Záměna ",[1647,24489,24491],{"className":24490},[2059],[2061,24492,24493],{"xmlns":2063},[2065,24494,24495,24499],{},[2068,24496,24497],{},[2071,24498,9214],{},[2092,24500,9214],{"encoding":2094},[1647,24502,24504],{"className":24503},[2059],[2061,24505,24506],{"xmlns":2063},[2065,24507,24508,24516],{},[2068,24509,24510],{},[2348,24511,24512,24514],{},[2071,24513,9214],{},[2071,24515,4271],{},[2092,24517,24518],{"encoding":2094},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[55,24521,24522,11156,24525,2090],{},[95,24523,24524],{},"Disponibilní důchod",[3982,24526,24527],{},"disposable income",[55,24529,24530],{},[1647,24531,24533],{"className":24532},[2059],[2061,24534,24535],{"xmlns":2063},[2065,24536,24537,24553],{},[2068,24538,24539,24545,24547,24549,24551],{},[2348,24540,24541,24543],{},[2071,24542,9214],{},[2071,24544,4271],{},[2075,24546,2077],{},[2071,24548,9214],{},[2075,24550,2303],{},[2071,24552,543],{},[2092,24554,24457],{"encoding":2094},[55,24556,24557,24558,195],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[1647,24559,24561],{"className":24560},[2059],[2061,24562,24563],{"xmlns":2063},[2065,24564,24565,24583],{},[2068,24566,24567,24569,24571,24573,24575,24581],{},[2071,24568,2849],{},[2075,24570,2077],{},[2071,24572,2849],{},[2075,24574,2084],{"stretchy":2083},[2348,24576,24577,24579],{},[2071,24578,9214],{},[2071,24580,4271],{},[2075,24582,2090],{"stretchy":2083},[2092,24584,24486],{"encoding":2094},[609,24586,23430],{"id":24587},"soustava-rovnic-1",[55,24589,24590,24591,835,24612,24634,24635,2777],{},"Pro pevně zadané ",[1647,24592,24594],{"className":24593},[2059],[2061,24595,24596],{"xmlns":2063},[2065,24597,24598,24610],{},[2068,24599,24600,24602,24604],{},[2071,24601,13919],{},[2075,24603,2077],{},[2205,24605,24606,24608],{},[2071,24607,13919],{},[2075,24609,4441],{},[2092,24611,13930],{"encoding":2094},[1647,24613,24615],{"className":24614},[2059],[2061,24616,24617],{"xmlns":2063},[2065,24618,24619,24631],{},[2068,24620,24621,24623,24625],{},[2071,24622,13845],{},[2075,24624,2077],{},[2205,24626,24627,24629],{},[2071,24628,13845],{},[2075,24630,4441],{},[2092,24632,24633],{"encoding":2094},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[1647,24636,24638],{"className":24637},[2059],[2061,24639,24640],{"xmlns":2063},[2065,24641,24642,24662],{},[2068,24643,24644,24646,24648,24650,24652,24658,24660],{},[2071,24645,9214],{},[2075,24647,2361],{"separator":2360},[2071,24649,2849],{},[2075,24651,2361],{"separator":2360},[2348,24653,24654,24656],{},[2071,24655,9214],{},[2071,24657,4271],{},[2075,24659,2361],{"separator":2360},[2071,24661,543],{},[2092,24663,24664],{"encoding":2094},"Y, C, Y_D, T",[55,24666,24667],{},[1647,24668,24670],{"className":24669},[2059],[2061,24671,24672],{"xmlns":2063},[2065,24673,24674,24815],{},[2068,24675,24676,24806,24808,24810,24813],{},[23493,24677,24678,24716,24744,24776],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,24679,24680,24686],{},[23501,24681,24682],{},[2400,24683,24684],{"scriptlevel":630,"displaystyle":2360},[2071,24685,9214],{},[23501,24687,24688],{},[2400,24689,24690],{"scriptlevel":630,"displaystyle":2360},[2068,24691,24692,24694,24696,24698,24700,24706,24708,24714],{},[2068,24693],{},[2075,24695,2077],{},[2071,24697,2849],{},[2075,24699,2176],{},[2205,24701,24702,24704],{},[2071,24703,13919],{},[2075,24705,4441],{},[2075,24707,2176],{},[2205,24709,24710,24712],{},[2071,24711,13845],{},[2075,24713,4441],{},[2075,24715,2361],{"separator":2360},[23498,24717,24718,24724],{},[23501,24719,24720],{},[2400,24721,24722],{"scriptlevel":630,"displaystyle":2360},[2071,24723,543],{},[23501,24725,24726],{},[2400,24727,24728],{"scriptlevel":630,"displaystyle":2360},[2068,24729,24730,24732,24734,24736,24738,24740,24742],{},[2068,24731],{},[2075,24733,2077],{},[2071,24735,543],{},[2075,24737,2084],{"stretchy":2083},[2071,24739,9214],{},[2075,24741,2090],{"stretchy":2083},[2075,24743,2361],{"separator":2360},[23498,24745,24746,24752],{},[23501,24747,24748],{},[2400,24749,24750],{"scriptlevel":630,"displaystyle":2360},[2071,24751,2849],{},[23501,24753,24754],{},[2400,24755,24756],{"scriptlevel":630,"displaystyle":2360},[2068,24757,24758,24760,24762,24764,24766,24772,24774],{},[2068,24759],{},[2075,24761,2077],{},[2071,24763,2849],{},[2075,24765,2084],{"stretchy":2083},[2348,24767,24768,24770],{},[2071,24769,9214],{},[2071,24771,4271],{},[2075,24773,2090],{"stretchy":2083},[2075,24775,2361],{"separator":2360},[23498,24777,24778,24788],{},[23501,24779,24780],{},[2400,24781,24782],{"scriptlevel":630,"displaystyle":2360},[2348,24783,24784,24786],{},[2071,24785,9214],{},[2071,24787,4271],{},[23501,24789,24790],{},[2400,24791,24792],{"scriptlevel":630,"displaystyle":2360},[2068,24793,24794,24796,24798,24800,24802,24804],{},[2068,24795],{},[2075,24797,2077],{},[2071,24799,9214],{},[2075,24801,2303],{},[2071,24803,543],{},[2075,24805,2361],{"separator":2360},[5965,24807],{"width":5967},[2075,24809,2084],{"stretchy":2083},[2210,24811,24812],{},"7.9",[2075,24814,2090],{"stretchy":2083},[2092,24816,24817],{"encoding":2094},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[55,24819,24820,24821,24865,24866,195],{},"s řešeními ",[1647,24822,24824],{"className":24823},[2059],[2061,24825,24826],{"xmlns":2063},[2065,24827,24828,24862],{},[2068,24829,24830,24836,24838,24844,24846,24852,24854],{},[2205,24831,24832,24834],{},[2071,24833,9214],{},[2071,24835,554],{},[2075,24837,2361],{"separator":2360},[2205,24839,24840,24842],{},[2071,24841,2849],{},[2071,24843,554],{},[2075,24845,2361],{"separator":2360},[2205,24847,24848,24850],{},[2071,24849,543],{},[2071,24851,554],{},[2075,24853,2361],{"separator":2360},[9252,24855,24856,24858,24860],{},[2071,24857,9214],{},[2071,24859,4271],{},[2071,24861,554],{},[2092,24863,24864],{"encoding":2094},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[1647,24867,24869],{"className":24868},[2059],[2061,24870,24871],{"xmlns":2063},[2065,24872,24873,24899],{},[2068,24874,24875,24881,24883,24891,24893],{},[2205,24876,24877,24879],{},[2071,24878,532],{},[2071,24880,554],{},[2075,24882,2077],{},[9252,24884,24885,24887,24889],{},[2071,24886,9214],{},[2071,24888,4271],{},[2071,24890,554],{},[2075,24892,2303],{},[2205,24894,24895,24897],{},[2071,24896,2849],{},[2071,24898,554],{},[2092,24900,24901],{"encoding":2094},"S^E = Y_D^E - C^E",[1023,24903,24904,24909],{},[55,24905,24906,24908],{},[1647,24907,4659],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[201,24910,24911,24934,25017,25072,25162],{},[92,24912,24913,24916,24917,195],{},[95,24914,24915],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[1647,24918,24920],{"className":24919},[2059],[2061,24921,24922],{"xmlns":2063},[2065,24923,24924,24932],{},[2068,24925,24926],{},[2348,24927,24928,24930],{},[2071,24929,9214],{},[2071,24931,4271],{},[2092,24933,24518],{"encoding":2094},[92,24935,24936,24985,24986,25003,25004,195],{},[95,24937,24938,24939,24959,24960],{},"Dosaď ",[1647,24940,24942],{"className":24941},[2059],[2061,24943,24944],{"xmlns":2063},[2065,24945,24946,24956],{},[2068,24947,24948,24950,24952,24954],{},[2071,24949,543],{},[2075,24951,2084],{"stretchy":2083},[2071,24953,9214],{},[2075,24955,2090],{"stretchy":2083},[2092,24957,24958],{"encoding":2094},"T(Y)"," do ",[1647,24961,24963],{"className":24962},[2059],[2061,24964,24965],{"xmlns":2063},[2065,24966,24967,24983],{},[2068,24968,24969,24975,24977,24979,24981],{},[2348,24970,24971,24973],{},[2071,24972,9214],{},[2071,24974,4271],{},[2075,24976,2077],{},[2071,24978,9214],{},[2075,24980,2303],{},[2071,24982,543],{},[2092,24984,24457],{"encoding":2094}," — dostaneš ",[1647,24987,24989],{"className":24988},[2059],[2061,24990,24991],{"xmlns":2063},[2065,24992,24993,25001],{},[2068,24994,24995],{},[2348,24996,24997,24999],{},[2071,24998,9214],{},[2071,25000,4271],{},[2092,25002,24518],{"encoding":2094}," jako lineární funkci ",[1647,25005,25007],{"className":25006},[2059],[2061,25008,25009],{"xmlns":2063},[2065,25010,25011,25015],{},[2068,25012,25013],{},[2071,25014,9214],{},[2092,25016,9214],{"encoding":2094},[92,25018,25019,24985,25046,25003,25059,195],{},[95,25020,24938,25021,25045],{},[1647,25022,25024],{"className":25023},[2059],[2061,25025,25026],{"xmlns":2063},[2065,25027,25028,25042],{},[2068,25029,25030,25036,25038,25040],{},[2348,25031,25032,25034],{},[2071,25033,9214],{},[2071,25035,4271],{},[2075,25037,2084],{"stretchy":2083},[2071,25039,9214],{},[2075,25041,2090],{"stretchy":2083},[2092,25043,25044],{"encoding":2094},"Y_D(Y)"," do funkce spotřeby",[1647,25047,25049],{"className":25048},[2059],[2061,25050,25051],{"xmlns":2063},[2065,25052,25053,25057],{},[2068,25054,25055],{},[2071,25056,2849],{},[2092,25058,2849],{"encoding":2094},[1647,25060,25062],{"className":25061},[2059],[2061,25063,25064],{"xmlns":2063},[2065,25065,25066,25070],{},[2068,25067,25068],{},[2071,25069,9214],{},[2092,25071,9214],{"encoding":2094},[92,25073,25074,1445,25096,25130,25131,25144,25145,195],{},[95,25075,24938,25076,25095],{},[1647,25077,25079],{"className":25078},[2059],[2061,25080,25081],{"xmlns":2063},[2065,25082,25083,25093],{},[2068,25084,25085,25087,25089,25091],{},[2071,25086,2849],{},[2075,25088,2084],{"stretchy":2083},[2071,25090,9214],{},[2075,25092,2090],{"stretchy":2083},[2092,25094,15951],{"encoding":2094}," do podmínky rovnováhy",[1647,25097,25099],{"className":25098},[2059],[2061,25100,25101],{"xmlns":2063},[2065,25102,25103,25127],{},[2068,25104,25105,25107,25109,25111,25113,25119,25121],{},[2071,25106,9214],{},[2075,25108,2077],{},[2071,25110,2849],{},[2075,25112,2176],{},[2205,25114,25115,25117],{},[2071,25116,13919],{},[2075,25118,4441],{},[2075,25120,2176],{},[2205,25122,25123,25125],{},[2071,25124,13845],{},[2075,25126,4441],{},[2092,25128,25129],{"encoding":2094},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[1647,25132,25134],{"className":25133},[2059],[2061,25135,25136],{"xmlns":2063},[2065,25137,25138,25142],{},[2068,25139,25140],{},[2071,25141,9214],{},[2092,25143,9214],{"encoding":2094},", odtud ",[1647,25146,25148],{"className":25147},[2059],[2061,25149,25150],{"xmlns":2063},[2065,25151,25152,25160],{},[2068,25153,25154],{},[2205,25155,25156,25158],{},[2071,25157,9214],{},[2071,25159,554],{},[2092,25161,15638],{"encoding":2094},[92,25163,25164,25167,25168,835,25186,835,25206,835,25223,195],{},[95,25165,25166],{},"Zpětným dosazením"," dopočítej ",[1647,25169,25171],{"className":25170},[2059],[2061,25172,25173],{"xmlns":2063},[2065,25174,25175,25183],{},[2068,25176,25177],{},[2205,25178,25179,25181],{},[2071,25180,543],{},[2071,25182,554],{},[2092,25184,25185],{"encoding":2094},"T^E",[1647,25187,25189],{"className":25188},[2059],[2061,25190,25191],{"xmlns":2063},[2065,25192,25193,25203],{},[2068,25194,25195],{},[9252,25196,25197,25199,25201],{},[2071,25198,9214],{},[2071,25200,4271],{},[2071,25202,554],{},[2092,25204,25205],{"encoding":2094},"Y_D^E",[1647,25207,25209],{"className":25208},[2059],[2061,25210,25211],{"xmlns":2063},[2065,25212,25213,25221],{},[2068,25214,25215],{},[2205,25216,25217,25219],{},[2071,25218,2849],{},[2071,25220,554],{},[2092,25222,15697],{"encoding":2094},[1647,25224,25226],{"className":25225},[2059],[2061,25227,25228],{"xmlns":2063},[2065,25229,25230,25238],{},[2068,25231,25232],{},[2205,25233,25234,25236],{},[2071,25235,532],{},[2071,25237,554],{},[2092,25239,25240],{"encoding":2094},"S^E",[609,25242,25244],{"id":25243},"příklad-74","Příklad 7.4",[55,25246,23760,25247,25268,25269,835,25300,835,25324,835,25346,25368],{},[1647,25248,25250],{"className":25249},[2059],[2061,25251,25252],{"xmlns":2063},[2065,25253,25254,25266],{},[2068,25255,25256,25258,25260,25262,25264],{},[2071,25257,2849],{},[2363,25259,14025],{},[2071,25261,13919],{},[2363,25263,14025],{},[2071,25265,13845],{},[2092,25267,20959],{"encoding":2094}," jsou dány ",[1647,25270,25272],{"className":25271},[2059],[2061,25273,25274],{"xmlns":2063},[2065,25275,25276,25297],{},[2068,25277,25278,25280,25282,25285,25287,25293,25295],{},[2071,25279,2849],{},[2075,25281,2077],{},[2210,25283,25284],{},"0,9",[2363,25286,3061],{},[2348,25288,25289,25291],{},[2071,25290,9214],{},[2071,25292,4271],{},[2075,25294,2176],{},[2210,25296,5984],{},[2092,25298,25299],{"encoding":2094},"C = 0{,}9\\,Y_D + 70",[1647,25301,25303],{"className":25302},[2059],[2061,25304,25305],{"xmlns":2063},[2065,25306,25307,25321],{},[2068,25308,25309,25311,25313,25315,25317,25319],{},[2071,25310,543],{},[2075,25312,2077],{},[2210,25314,2911],{},[2071,25316,9214],{},[2075,25318,2176],{},[2210,25320,5091],{},[2092,25322,25323],{"encoding":2094},"T = 0{,}2Y + 25",[1647,25325,25327],{"className":25326},[2059],[2061,25328,25329],{"xmlns":2063},[2065,25330,25331,25343],{},[2068,25332,25333,25339,25341],{},[2205,25334,25335,25337],{},[2071,25336,13919],{},[2075,25338,4441],{},[2075,25340,2077],{},[2210,25342,16773],{},[2092,25344,25345],{"encoding":2094},"I^* = 35",[1647,25347,25349],{"className":25348},[2059],[2061,25350,25351],{"xmlns":2063},[2065,25352,25353,25365],{},[2068,25354,25355,25361,25363],{},[2205,25356,25357,25359],{},[2071,25358,13845],{},[2075,25360,4441],{},[2075,25362,2077],{},[2210,25364,9121],{},[2092,25366,25367],{"encoding":2094},"G^* = 20",". Soustava (7.9):",[55,25370,25371],{},[1647,25372,25374],{"className":25373},[2059],[2061,25375,25376],{"xmlns":2063},[2065,25377,25378,25502],{},[23493,25379,25380,25410,25438,25472],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,25381,25382,25388],{},[23501,25383,25384],{},[2400,25385,25386],{"scriptlevel":630,"displaystyle":2360},[2071,25387,9214],{},[23501,25389,25390],{},[2400,25391,25392],{"scriptlevel":630,"displaystyle":2360},[2068,25393,25394,25396,25398,25400,25402,25404,25406,25408],{},[2068,25395],{},[2075,25397,2077],{},[2071,25399,2849],{},[2075,25401,2176],{},[2210,25403,16773],{},[2075,25405,2176],{},[2210,25407,9121],{},[2075,25409,2361],{"separator":2360},[23498,25411,25412,25418],{},[23501,25413,25414],{},[2400,25415,25416],{"scriptlevel":630,"displaystyle":2360},[2071,25417,543],{},[23501,25419,25420],{},[2400,25421,25422],{"scriptlevel":630,"displaystyle":2360},[2068,25423,25424,25426,25428,25430,25432,25434,25436],{},[2068,25425],{},[2075,25427,2077],{},[2210,25429,2911],{},[2071,25431,9214],{},[2075,25433,2176],{},[2210,25435,5091],{},[2075,25437,2361],{"separator":2360},[23498,25439,25440,25446],{},[23501,25441,25442],{},[2400,25443,25444],{"scriptlevel":630,"displaystyle":2360},[2071,25445,2849],{},[23501,25447,25448],{},[2400,25449,25450],{"scriptlevel":630,"displaystyle":2360},[2068,25451,25452,25454,25456,25458,25460,25466,25468,25470],{},[2068,25453],{},[2075,25455,2077],{},[2210,25457,25284],{},[2363,25459,3061],{},[2348,25461,25462,25464],{},[2071,25463,9214],{},[2071,25465,4271],{},[2075,25467,2176],{},[2210,25469,5984],{},[2075,25471,2361],{"separator":2360},[23498,25473,25474,25484],{},[23501,25475,25476],{},[2400,25477,25478],{"scriptlevel":630,"displaystyle":2360},[2348,25479,25480,25482],{},[2071,25481,9214],{},[2071,25483,4271],{},[23501,25485,25486],{},[2400,25487,25488],{"scriptlevel":630,"displaystyle":2360},[2068,25489,25490,25492,25494,25496,25498,25500],{},[2068,25491],{},[2075,25493,2077],{},[2071,25495,9214],{},[2075,25497,2303],{},[2071,25499,543],{},[2071,25501,195],{"mathvariant":2450},[2092,25503,25504],{"encoding":2094},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[55,25506,25507,25510,25511,25565,25566,25612,25613,2777],{},[95,25508,25509],{},"Řešení."," Z definice ",[1647,25512,25514],{"className":25513},[2059],[2061,25515,25516],{"xmlns":2063},[2065,25517,25518,25562],{},[2068,25519,25520,25526,25528,25530,25532,25534,25536,25538,25540,25542,25544,25546,25548,25550,25552,25554,25556,25558,25560],{},[2348,25521,25522,25524],{},[2071,25523,9214],{},[2071,25525,4271],{},[2075,25527,2077],{},[2071,25529,9214],{},[2075,25531,2303],{},[2071,25533,543],{},[2075,25535,2077],{},[2071,25537,9214],{},[2075,25539,2303],{},[2075,25541,2084],{"stretchy":2083},[2210,25543,2911],{},[2071,25545,9214],{},[2075,25547,2176],{},[2210,25549,5091],{},[2075,25551,2090],{"stretchy":2083},[2075,25553,2077],{},[2210,25555,16324],{},[2071,25557,9214],{},[2075,25559,2303],{},[2210,25561,5091],{},[2092,25563,25564],{"encoding":2094},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[1647,25567,25569],{"className":25568},[2059],[2061,25570,25571],{"xmlns":2063},[2065,25572,25573,25609],{},[2068,25574,25575,25577,25579,25581,25583,25585,25587,25589,25591,25593,25595,25597,25599,25602,25604,25606],{},[2071,25576,2849],{},[2075,25578,2077],{},[2210,25580,25284],{},[2075,25582,2084],{"stretchy":2083},[2210,25584,16324],{},[2071,25586,9214],{},[2075,25588,2303],{},[2210,25590,5091],{},[2075,25592,2090],{"stretchy":2083},[2075,25594,2176],{},[2210,25596,5984],{},[2075,25598,2077],{},[2210,25600,25601],{},"0,72",[2071,25603,9214],{},[2075,25605,2176],{},[2210,25607,25608],{},"47,5",[2092,25610,25611],{"encoding":2094},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[1647,25614,25616],{"className":25615},[2059],[2061,25617,25618],{"xmlns":2063},[2065,25619,25620,25638],{},[2068,25621,25622,25624,25626,25628,25630,25632,25634,25636],{},[2071,25623,9214],{},[2075,25625,2077],{},[2210,25627,25601],{},[2071,25629,9214],{},[2075,25631,2176],{},[2210,25633,25608],{},[2075,25635,2176],{},[2210,25637,23919],{},[2092,25639,25640],{"encoding":2094},"Y = 0{,}72Y + 47{,}5 + 55",[55,25642,25643],{},[1647,25644,25646],{"className":25645},[2059],[2061,25647,25648],{"xmlns":2063},[2065,25649,25650,25691],{},[2068,25651,25652,25655,25657,25659,25662,25664,25666,25668,25674,25676,25686,25688],{},[2210,25653,25654],{},"0,28",[2071,25656,9214],{},[2075,25658,2077],{},[2210,25660,25661],{},"102,5",[2363,25663,4072],{},[2075,25665,16743],{},[2363,25667,4072],{},[2205,25669,25670,25672],{},[2071,25671,9214],{},[2071,25673,554],{},[2075,25675,2077],{},[2400,25677,25678],{"scriptlevel":630,"displaystyle":2083},[2403,25679,25680,25683],{},[2210,25681,25682],{},"5125",[2210,25684,25685],{},"14",[2075,25687,5987],{},[2210,25689,25690],{},"366,071.",[2092,25692,25693],{"encoding":2094},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[55,25695,25696],{},"Rovnovážné veličiny:",[89,25698,25699,25734,25786,25840,25888],{},[92,25700,25701,2361],{},[1647,25702,25704],{"className":25703},[2059],[2061,25705,25706],{"xmlns":2063},[2065,25707,25708,25731],{},[2068,25709,25710,25716,25718,25726,25728],{},[2205,25711,25712,25714],{},[2071,25713,9214],{},[2071,25715,554],{},[2075,25717,2077],{},[2400,25719,25720],{"scriptlevel":630,"displaystyle":2083},[2403,25721,25722,25724],{},[2210,25723,25682],{},[2210,25725,25685],{},[2075,25727,5987],{},[2210,25729,25730],{},"366,071",[2092,25732,25733],{"encoding":2094},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[92,25735,25736,2361],{},[1647,25737,25739],{"className":25738},[2059],[2061,25740,25741],{"xmlns":2063},[2065,25742,25743,25783],{},[2068,25744,25745,25751,25753,25755,25757,25763,25765,25767,25769,25778,25780],{},[2205,25746,25747,25749],{},[2071,25748,543],{},[2071,25750,554],{},[2075,25752,2077],{},[2210,25754,2911],{},[2363,25756,3061],{},[2205,25758,25759,25761],{},[2071,25760,9214],{},[2071,25762,554],{},[2075,25764,2176],{},[2210,25766,5091],{},[2075,25768,2077],{},[2400,25770,25771],{"scriptlevel":630,"displaystyle":2083},[2403,25772,25773,25776],{},[2210,25774,25775],{},"1375",[2210,25777,25685],{},[2075,25779,5987],{},[2210,25781,25782],{},"98,214",[2092,25784,25785],{"encoding":2094},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[92,25787,25788,2361],{},[1647,25789,25791],{"className":25790},[2059],[2061,25792,25793],{"xmlns":2063},[2065,25794,25795,25837],{},[2068,25796,25797,25805,25807,25813,25815,25821,25823,25832,25834],{},[9252,25798,25799,25801,25803],{},[2071,25800,9214],{},[2071,25802,4271],{},[2071,25804,554],{},[2075,25806,2077],{},[2205,25808,25809,25811],{},[2071,25810,9214],{},[2071,25812,554],{},[2075,25814,2303],{},[2205,25816,25817,25819],{},[2071,25818,543],{},[2071,25820,554],{},[2075,25822,2077],{},[2400,25824,25825],{"scriptlevel":630,"displaystyle":2083},[2403,25826,25827,25830],{},[2210,25828,25829],{},"3750",[2210,25831,25685],{},[2075,25833,5987],{},[2210,25835,25836],{},"267,857",[2092,25838,25839],{"encoding":2094},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[92,25841,25842,2361],{},[1647,25843,25845],{"className":25844},[2059],[2061,25846,25847],{"xmlns":2063},[2065,25848,25849,25885],{},[2068,25850,25851,25857,25859,25865,25867,25869,25871,25880,25882],{},[2205,25852,25853,25855],{},[2071,25854,2849],{},[2071,25856,554],{},[2075,25858,2077],{},[2205,25860,25861,25863],{},[2071,25862,9214],{},[2071,25864,554],{},[2075,25866,2303],{},[2210,25868,23919],{},[2075,25870,2077],{},[2400,25872,25873],{"scriptlevel":630,"displaystyle":2083},[2403,25874,25875,25878],{},[2210,25876,25877],{},"4355",[2210,25879,25685],{},[2075,25881,5987],{},[2210,25883,25884],{},"311,071",[2092,25886,25887],{"encoding":2094},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[92,25889,25890,25946],{},[1647,25891,25893],{"className":25892},[2059],[2061,25894,25895],{"xmlns":2063},[2065,25896,25897,25943],{},[2068,25898,25899,25905,25907,25915,25917,25923,25925,25927,25936,25938,25940],{},[2205,25900,25901,25903],{},[2071,25902,532],{},[2071,25904,554],{},[2075,25906,2077],{},[9252,25908,25909,25911,25913],{},[2071,25910,9214],{},[2071,25912,4271],{},[2071,25914,554],{},[2075,25916,2303],{},[2205,25918,25919,25921],{},[2071,25920,2849],{},[2071,25922,554],{},[2075,25924,2077],{},[2075,25926,2303],{},[2400,25928,25929],{"scriptlevel":630,"displaystyle":2083},[2403,25930,25931,25934],{},[2210,25932,25933],{},"605",[2210,25935,25685],{},[2075,25937,5987],{},[2075,25939,2303],{},[2210,25941,25942],{},"43,214",[2092,25944,25945],{"encoding":2094},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[55,25948,25949,24089,25951,25972,25973,25976,25977,26000,26001,195],{},[95,25950,24088],{},[1647,25952,25954],{"className":25953},[2059],[2061,25955,25956],{"xmlns":2063},[2065,25957,25958,25970],{},[2068,25959,25960,25962,25964,25966,25968],{},[2071,25961,2849],{},[2363,25963,14025],{},[2071,25965,13919],{},[2363,25967,14025],{},[2071,25969,13845],{},[2092,25971,20959],{"encoding":2094}," stále uvažuje ",[95,25974,25975],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[1647,25978,25980],{"className":25979},[2059],[2061,25981,25982],{"xmlns":2063},[2065,25983,25984,25997],{},[2068,25985,25986,25988,25990,25993,25995],{},[2071,25987,14055],{},[2075,25989,2077],{},[2071,25991,25992],{},"B",[2075,25994,2303],{},[2071,25996,2890],{},[2092,25998,25999],{"encoding":2094},"X = B - M"," dává ",[95,26002,24110,26003],{},[1647,26004,26006],{"className":26005},[2059],[2061,26007,26008],{"xmlns":2063},[2065,26009,26010,26026],{},[2068,26011,26012,26014,26016,26018,26020,26022,26024],{},[2071,26013,2849],{},[2363,26015,14025],{},[2071,26017,13919],{},[2363,26019,14025],{},[2071,26021,13845],{},[2363,26023,14025],{},[2071,26025,14055],{},[2092,26027,14058],{"encoding":2094},[84,26029,26031],{"id":26030},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[609,26033,23360],{"id":26034},"zadání-modelu-2",[55,26036,26037,26038,1445,26041,24333,26062,26075,26076,13861,26079,26092],{},"Rozšíření o ",[95,26039,26040],{},"čistý export",[1647,26042,26044],{"className":26043},[2059],[2061,26045,26046],{"xmlns":2063},[2065,26047,26048,26060],{},[2068,26049,26050,26052,26054,26056,26058],{},[2071,26051,14055],{},[2075,26053,2077],{},[2071,26055,25992],{},[2075,26057,2303],{},[2071,26059,2890],{},[2092,26061,25999],{"encoding":2094},[1647,26063,26065],{"className":26064},[2059],[2061,26066,26067],{"xmlns":2063},[2065,26068,26069,26073],{},[2068,26070,26071],{},[2071,26072,25992],{},[2092,26074,25992],{"encoding":2094}," je hrubý export (",[3982,26077,26078],{},"brutto export",[1647,26080,26082],{"className":26081},[2059],[2061,26083,26084],{"xmlns":2063},[2065,26085,26086,26090],{},[2068,26087,26088],{},[2071,26089,2890],{},[2092,26091,2890],{"encoding":2094}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[55,26094,26095],{},[1647,26096,26098],{"className":26097},[2059],[2061,26099,26100],{"xmlns":2063},[2065,26101,26102,26122],{},[2068,26103,26104,26106,26108,26110,26112,26118,26120],{},[2071,26105,2890],{},[2075,26107,2077],{},[2071,26109,2890],{},[2075,26111,2084],{"stretchy":2083},[2348,26113,26114,26116],{},[2071,26115,9214],{},[2071,26117,4271],{},[2075,26119,2090],{"stretchy":2083},[2071,26121,195],{"mathvariant":2450},[2092,26123,26124],{"encoding":2094},"M = M(Y_D).",[55,26126,26127],{},"Podmínka rovnováhy:",[55,26129,26130],{},[1647,26131,26133],{"className":26132},[2059],[2061,26134,26135],{"xmlns":2063},[2065,26136,26137,26174],{},[2068,26138,26139,26141,26143,26145,26147,26149,26151,26153,26155,26157,26159,26161,26163,26165,26167,26170,26172],{},[2071,26140,9214],{},[2075,26142,2077],{},[2071,26144,2849],{},[2075,26146,2176],{},[2071,26148,13919],{},[2075,26150,2176],{},[2071,26152,13845],{},[2075,26154,2176],{},[2071,26156,25992],{},[2075,26158,2303],{},[2071,26160,2890],{},[2071,26162,195],{"mathvariant":2450},[5965,26164],{"width":5967},[2075,26166,2084],{"stretchy":2083},[2210,26168,26169],{},"7.10",[2363,26171,69],{},[2075,26173,2090],{"stretchy":2083},[2092,26175,26176],{"encoding":2094},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[609,26178,23430],{"id":26179},"soustava-rovnic-2",[55,26181,24590,26182,26216,26217,2777],{},[1647,26183,26185],{"className":26184},[2059],[2061,26186,26187],{"xmlns":2063},[2065,26188,26189,26213],{},[2068,26190,26191,26197,26199,26205,26207],{},[2205,26192,26193,26195],{},[2071,26194,13919],{},[2075,26196,4441],{},[2075,26198,2361],{"separator":2360},[2205,26200,26201,26203],{},[2071,26202,13845],{},[2075,26204,4441],{},[2075,26206,2361],{"separator":2360},[2205,26208,26209,26211],{},[2071,26210,25992],{},[2075,26212,4441],{},[2092,26214,26215],{"encoding":2094},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[1647,26218,26220],{"className":26219},[2059],[2061,26221,26222],{"xmlns":2063},[2065,26223,26224,26248],{},[2068,26225,26226,26228,26230,26232,26234,26236,26238,26244,26246],{},[2071,26227,9214],{},[2075,26229,2361],{"separator":2360},[2071,26231,2849],{},[2075,26233,2361],{"separator":2360},[2071,26235,543],{},[2075,26237,2361],{"separator":2360},[2348,26239,26240,26242],{},[2071,26241,9214],{},[2071,26243,4271],{},[2075,26245,2361],{"separator":2360},[2071,26247,2890],{},[2092,26249,26250],{"encoding":2094},"Y, C, T, Y_D, M",[55,26252,26253],{},[1647,26254,26256],{"className":26255},[2059],[2061,26257,26258],{"xmlns":2063},[2065,26259,26260,26444],{},[2068,26261,26262,26436,26438,26440,26442],{},[23493,26263,26264,26296,26326,26354,26386],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,26265,26266,26272],{},[23501,26267,26268],{},[2400,26269,26270],{"scriptlevel":630,"displaystyle":2360},[2071,26271,2849],{},[23501,26273,26274],{},[2400,26275,26276],{"scriptlevel":630,"displaystyle":2360},[2068,26277,26278,26280,26282,26284,26286,26292,26294],{},[2068,26279],{},[2075,26281,2077],{},[2071,26283,2849],{},[2075,26285,2084],{"stretchy":2083},[2348,26287,26288,26290],{},[2071,26289,9214],{},[2071,26291,4271],{},[2075,26293,2090],{"stretchy":2083},[2075,26295,2361],{"separator":2360},[23498,26297,26298,26308],{},[23501,26299,26300],{},[2400,26301,26302],{"scriptlevel":630,"displaystyle":2360},[2348,26303,26304,26306],{},[2071,26305,9214],{},[2071,26307,4271],{},[23501,26309,26310],{},[2400,26311,26312],{"scriptlevel":630,"displaystyle":2360},[2068,26313,26314,26316,26318,26320,26322,26324],{},[2068,26315],{},[2075,26317,2077],{},[2071,26319,9214],{},[2075,26321,2303],{},[2071,26323,543],{},[2075,26325,2361],{"separator":2360},[23498,26327,26328,26334],{},[23501,26329,26330],{},[2400,26331,26332],{"scriptlevel":630,"displaystyle":2360},[2071,26333,543],{},[23501,26335,26336],{},[2400,26337,26338],{"scriptlevel":630,"displaystyle":2360},[2068,26339,26340,26342,26344,26346,26348,26350,26352],{},[2068,26341],{},[2075,26343,2077],{},[2071,26345,543],{},[2075,26347,2084],{"stretchy":2083},[2071,26349,9214],{},[2075,26351,2090],{"stretchy":2083},[2075,26353,2361],{"separator":2360},[23498,26355,26356,26362],{},[23501,26357,26358],{},[2400,26359,26360],{"scriptlevel":630,"displaystyle":2360},[2071,26361,2890],{},[23501,26363,26364],{},[2400,26365,26366],{"scriptlevel":630,"displaystyle":2360},[2068,26367,26368,26370,26372,26374,26376,26382,26384],{},[2068,26369],{},[2075,26371,2077],{},[2071,26373,2890],{},[2075,26375,2084],{"stretchy":2083},[2348,26377,26378,26380],{},[2071,26379,9214],{},[2071,26381,4271],{},[2075,26383,2090],{"stretchy":2083},[2075,26385,2361],{"separator":2360},[23498,26387,26388,26394],{},[23501,26389,26390],{},[2400,26391,26392],{"scriptlevel":630,"displaystyle":2360},[2071,26393,9214],{},[23501,26395,26396],{},[2400,26397,26398],{"scriptlevel":630,"displaystyle":2360},[2068,26399,26400,26402,26404,26406,26408,26414,26416,26422,26424,26430,26432,26434],{},[2068,26401],{},[2075,26403,2077],{},[2071,26405,2849],{},[2075,26407,2176],{},[2205,26409,26410,26412],{},[2071,26411,13919],{},[2075,26413,4441],{},[2075,26415,2176],{},[2205,26417,26418,26420],{},[2071,26419,13845],{},[2075,26421,4441],{},[2075,26423,2176],{},[2205,26425,26426,26428],{},[2071,26427,25992],{},[2075,26429,4441],{},[2075,26431,2303],{},[2071,26433,2890],{},[2071,26435,195],{"mathvariant":2450},[5965,26437],{"width":5967},[2075,26439,2084],{"stretchy":2083},[2210,26441,26169],{},[2075,26443,2090],{"stretchy":2083},[2092,26445,26446],{"encoding":2094},"\\begin{aligned} C &= C(Y_D), \\\\ Y_D &= Y - T, \\\\ T &= T(Y), \\\\ M &= M(Y_D), \\\\ Y &= C + I^* + G^* + B^* - M. \\end{aligned} \\qquad (7.10)",[609,26448,26450],{"id":26449},"příklad-75","Příklad 7.5",[55,26452,26453,26454,835,26486,835,26513,835,26534,835,26556,835,26578,26601],{},"Dáno: ",[1647,26455,26457],{"className":26456},[2059],[2061,26458,26459],{"xmlns":2063},[2065,26460,26461,26483],{},[2068,26462,26463,26465,26467,26470,26472,26478,26480],{},[2071,26464,2849],{},[2075,26466,2077],{},[2210,26468,26469],{},"0,75",[2363,26471,3061],{},[2348,26473,26474,26476],{},[2071,26475,9214],{},[2071,26477,4271],{},[2075,26479,2176],{},[2210,26481,26482],{},"750",[2092,26484,26485],{"encoding":2094},"C = 0{,}75\\,Y_D + 750",[1647,26487,26489],{"className":26488},[2059],[2061,26490,26491],{"xmlns":2063},[2065,26492,26493,26510],{},[2068,26494,26495,26497,26499,26502,26504],{},[2071,26496,2890],{},[2075,26498,2077],{},[2210,26500,26501],{},"0,15",[2363,26503,3061],{},[2348,26505,26506,26508],{},[2071,26507,9214],{},[2071,26509,4271],{},[2092,26511,26512],{"encoding":2094},"M = 0{,}15\\,Y_D",[1647,26514,26516],{"className":26515},[2059],[2061,26517,26518],{"xmlns":2063},[2065,26519,26520,26531],{},[2068,26521,26522,26524,26526,26529],{},[2071,26523,543],{},[2075,26525,2077],{},[2210,26527,26528],{},"0,25",[2071,26530,9214],{},[2092,26532,26533],{"encoding":2094},"T = 0{,}25Y",[1647,26535,26537],{"className":26536},[2059],[2061,26538,26539],{"xmlns":2063},[2065,26540,26541,26553],{},[2068,26542,26543,26549,26551],{},[2205,26544,26545,26547],{},[2071,26546,13919],{},[2075,26548,4441],{},[2075,26550,2077],{},[2210,26552,16845],{},[2092,26554,26555],{"encoding":2094},"I^* = 500",[1647,26557,26559],{"className":26558},[2059],[2061,26560,26561],{"xmlns":2063},[2065,26562,26563,26575],{},[2068,26564,26565,26571,26573],{},[2205,26566,26567,26569],{},[2071,26568,13845],{},[2075,26570,4441],{},[2075,26572,2077],{},[2210,26574,8889],{},[2092,26576,26577],{"encoding":2094},"G^* = 150",[1647,26579,26581],{"className":26580},[2059],[2061,26582,26583],{"xmlns":2063},[2065,26584,26585,26598],{},[2068,26586,26587,26593,26595],{},[2205,26588,26589,26591],{},[2071,26590,25992],{},[2075,26592,4441],{},[2075,26594,2077],{},[2210,26596,26597],{},"800",[2092,26599,26600],{"encoding":2094},"B^* = 800",". Soustava:",[55,26603,26604],{},[1647,26605,26607],{"className":26606},[2059],[2061,26608,26609],{"xmlns":2063},[2065,26610,26611,26829],{},[23493,26612,26613,26659,26701,26737,26779],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,26614,26615,26631],{},[23501,26616,26617],{},[2400,26618,26619],{"scriptlevel":630,"displaystyle":2360},[2068,26620,26621,26623,26625,26627,26629],{},[2075,26622,2084],{"stretchy":2083},[2071,26624,13774],{},[2210,26626,638],{},[2075,26628,2090],{"stretchy":2083},[2363,26630,2365],{},[23501,26632,26633],{},[2400,26634,26635],{"scriptlevel":630,"displaystyle":2360},[2068,26636,26637,26639,26641,26643,26645,26647,26653,26655,26657],{},[2068,26638],{},[2071,26640,2849],{},[2075,26642,2077],{},[2210,26644,26469],{},[2363,26646,3061],{},[2348,26648,26649,26651],{},[2071,26650,9214],{},[2071,26652,4271],{},[2075,26654,2176],{},[2210,26656,26482],{},[2075,26658,2361],{"separator":2360},[23498,26660,26661,26677],{},[23501,26662,26663],{},[2400,26664,26665],{"scriptlevel":630,"displaystyle":2360},[2068,26666,26667,26669,26671,26673,26675],{},[2075,26668,2084],{"stretchy":2083},[2071,26670,13774],{},[2210,26672,646],{},[2075,26674,2090],{"stretchy":2083},[2363,26676,2365],{},[23501,26678,26679],{},[2400,26680,26681],{"scriptlevel":630,"displaystyle":2360},[2068,26682,26683,26685,26691,26693,26695,26697,26699],{},[2068,26684],{},[2348,26686,26687,26689],{},[2071,26688,9214],{},[2071,26690,4271],{},[2075,26692,2077],{},[2071,26694,9214],{},[2075,26696,2303],{},[2071,26698,543],{},[2075,26700,2361],{"separator":2360},[23498,26702,26703,26719],{},[23501,26704,26705],{},[2400,26706,26707],{"scriptlevel":630,"displaystyle":2360},[2068,26708,26709,26711,26713,26715,26717],{},[2075,26710,2084],{"stretchy":2083},[2071,26712,13774],{},[2210,26714,654],{},[2075,26716,2090],{"stretchy":2083},[2363,26718,2365],{},[23501,26720,26721],{},[2400,26722,26723],{"scriptlevel":630,"displaystyle":2360},[2068,26724,26725,26727,26729,26731,26733,26735],{},[2068,26726],{},[2071,26728,543],{},[2075,26730,2077],{},[2210,26732,26528],{},[2071,26734,9214],{},[2075,26736,2361],{"separator":2360},[23498,26738,26739,26755],{},[23501,26740,26741],{},[2400,26742,26743],{"scriptlevel":630,"displaystyle":2360},[2068,26744,26745,26747,26749,26751,26753],{},[2075,26746,2084],{"stretchy":2083},[2071,26748,13774],{},[2210,26750,662],{},[2075,26752,2090],{"stretchy":2083},[2363,26754,2365],{},[23501,26756,26757],{},[2400,26758,26759],{"scriptlevel":630,"displaystyle":2360},[2068,26760,26761,26763,26765,26767,26769,26771,26777],{},[2068,26762],{},[2071,26764,2890],{},[2075,26766,2077],{},[2210,26768,26501],{},[2363,26770,3061],{},[2348,26772,26773,26775],{},[2071,26774,9214],{},[2071,26776,4271],{},[2075,26778,2361],{"separator":2360},[23498,26780,26781,26797],{},[23501,26782,26783],{},[2400,26784,26785],{"scriptlevel":630,"displaystyle":2360},[2068,26786,26787,26789,26791,26793,26795],{},[2075,26788,2084],{"stretchy":2083},[2071,26790,13774],{},[2210,26792,670],{},[2075,26794,2090],{"stretchy":2083},[2363,26796,2365],{},[23501,26798,26799],{},[2400,26800,26801],{"scriptlevel":630,"displaystyle":2360},[2068,26802,26803,26805,26807,26809,26811,26813,26815,26817,26819,26821,26823,26825,26827],{},[2068,26804],{},[2071,26806,9214],{},[2075,26808,2077],{},[2071,26810,2849],{},[2075,26812,2176],{},[2210,26814,16845],{},[2075,26816,2176],{},[2210,26818,8889],{},[2075,26820,2176],{},[2210,26822,26597],{},[2075,26824,2303],{},[2071,26826,2890],{},[2071,26828,195],{"mathvariant":2450},[2092,26830,26831],{"encoding":2094},"\\begin{aligned} (r1)\\ & C = 0{,}75\\,Y_D + 750, \\\\ (r2)\\ & Y_D = Y - T, \\\\ (r3)\\ & T = 0{,}25Y, \\\\ (r4)\\ & M = 0{,}15\\,Y_D, \\\\ (r5)\\ & Y = C + 500 + 150 + 800 - M. \\end{aligned}",[55,26833,26834,26835,26869],{},"Postupná substituce — z (r3) do (r2): ",[1647,26836,26838],{"className":26837},[2059],[2061,26839,26840],{"xmlns":2063},[2065,26841,26842,26866],{},[2068,26843,26844,26850,26852,26854,26856,26858,26860,26862,26864],{},[2348,26845,26846,26848],{},[2071,26847,9214],{},[2071,26849,4271],{},[2075,26851,2077],{},[2071,26853,9214],{},[2075,26855,2303],{},[2210,26857,26528],{},[2071,26859,9214],{},[2075,26861,2077],{},[2210,26863,26469],{},[2071,26865,9214],{},[2092,26867,26868],{"encoding":2094},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[55,26871,26872],{},[1647,26873,26875],{"className":26874},[2059],[2061,26876,26877],{"xmlns":2063},[2065,26878,26879,26920],{},[2068,26880,26881,26883,26885,26887,26889,26891,26893,26895,26897,26899,26901,26903,26905,26907,26909,26912,26914,26916,26918],{},[2075,26882,2084],{"stretchy":2083},[2071,26884,13774],{},[2210,26886,678],{},[2075,26888,2090],{"stretchy":2083},[2363,26890,2365],{},[2071,26892,2849],{},[2075,26894,2077],{},[2210,26896,26469],{},[2075,26898,3251],{},[2210,26900,26469],{},[2071,26902,9214],{},[2075,26904,2176],{},[2210,26906,26482],{},[2075,26908,2077],{},[2210,26910,26911],{},"0,5625",[2071,26913,9214],{},[2075,26915,2176],{},[2210,26917,26482],{},[2075,26919,2361],{"separator":2360},[2092,26921,26922],{"encoding":2094},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[55,26924,26925],{},[1647,26926,26928],{"className":26927},[2059],[2061,26929,26930],{"xmlns":2063},[2065,26931,26932,26965],{},[2068,26933,26934,26936,26938,26940,26942,26944,26946,26948,26950,26952,26954,26956,26958,26961,26963],{},[2075,26935,2084],{"stretchy":2083},[2071,26937,13774],{},[2210,26939,686],{},[2075,26941,2090],{"stretchy":2083},[2363,26943,2365],{},[2071,26945,2890],{},[2075,26947,2077],{},[2210,26949,26501],{},[2075,26951,3251],{},[2210,26953,26469],{},[2071,26955,9214],{},[2075,26957,2077],{},[2210,26959,26960],{},"0,1125",[2071,26962,9214],{},[2071,26964,195],{"mathvariant":2450},[2092,26966,26967],{"encoding":2094},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[55,26969,26970],{},"Dosazením do (r5):",[55,26972,26973],{},[1647,26974,26976],{"className":26975},[2059],[2061,26977,26978],{"xmlns":2063},[2065,26979,26980,27024],{},[2068,26981,26982,26984,26986,26988,26990,26992,26994,26996,26998,27000,27002,27004,27006,27008,27010,27012,27014,27017,27019,27021],{},[2071,26983,9214],{},[2075,26985,2077],{},[2210,26987,26911],{},[2071,26989,9214],{},[2075,26991,2176],{},[2210,26993,26482],{},[2075,26995,2176],{},[2210,26997,16845],{},[2075,26999,2176],{},[2210,27001,8889],{},[2075,27003,2176],{},[2210,27005,26597],{},[2075,27007,2303],{},[2210,27009,26960],{},[2071,27011,9214],{},[2075,27013,2077],{},[2210,27015,27016],{},"0,45",[2071,27018,9214],{},[2075,27020,2176],{},[2210,27022,27023],{},"2200.",[2092,27025,27026],{"encoding":2094},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[55,27028,27029,27030,5676,27052,27075],{},"Odtud ",[1647,27031,27033],{"className":27032},[2059],[2061,27034,27035],{"xmlns":2063},[2065,27036,27037,27049],{},[2068,27038,27039,27042,27044,27046],{},[2210,27040,27041],{},"0,55",[2071,27043,9214],{},[2075,27045,2077],{},[2210,27047,27048],{},"2200",[2092,27050,27051],{"encoding":2094},"0{,}55Y = 2200",[1647,27053,27055],{"className":27054},[2059],[2061,27056,27057],{"xmlns":2063},[2065,27058,27059,27072],{},[2068,27060,27061,27067,27069],{},[2205,27062,27063,27065],{},[2071,27064,9214],{},[2071,27066,554],{},[2075,27068,2077],{},[2210,27070,27071],{},"4000",[2092,27073,27074],{"encoding":2094},"Y^E = 4000",". Rovnovážné veličiny:",[89,27077,27078,27101,27133,27168,27201,27237],{},[92,27079,27080,2361],{},[1647,27081,27083],{"className":27082},[2059],[2061,27084,27085],{"xmlns":2063},[2065,27086,27087,27099],{},[2068,27088,27089,27095,27097],{},[2205,27090,27091,27093],{},[2071,27092,9214],{},[2071,27094,554],{},[2075,27096,2077],{},[2210,27098,27071],{},[2092,27100,27074],{"encoding":2094},[92,27102,27103,2361],{},[1647,27104,27106],{"className":27105},[2059],[2061,27107,27108],{"xmlns":2063},[2065,27109,27110,27130],{},[2068,27111,27112,27118,27120,27122,27124,27126,27128],{},[2205,27113,27114,27116],{},[2071,27115,543],{},[2071,27117,554],{},[2075,27119,2077],{},[2210,27121,26528],{},[2075,27123,3251],{},[2210,27125,27071],{},[2075,27127,2077],{},[2210,27129,2854],{},[2092,27131,27132],{"encoding":2094},"T^E = 0{,}25 \\cdot 4000 = 1000",[92,27134,27135,2361],{},[1647,27136,27138],{"className":27137},[2059],[2061,27139,27140],{"xmlns":2063},[2065,27141,27142,27165],{},[2068,27143,27144,27152,27154,27156,27158,27160,27162],{},[9252,27145,27146,27148,27150],{},[2071,27147,9214],{},[2071,27149,4271],{},[2071,27151,554],{},[2075,27153,2077],{},[2210,27155,26469],{},[2075,27157,3251],{},[2210,27159,27071],{},[2075,27161,2077],{},[2210,27163,27164],{},"3000",[2092,27166,27167],{"encoding":2094},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[92,27169,27170,2361],{},[1647,27171,27173],{"className":27172},[2059],[2061,27174,27175],{"xmlns":2063},[2065,27176,27177,27198],{},[2068,27178,27179,27185,27187,27189,27191,27193,27195],{},[2205,27180,27181,27183],{},[2071,27182,2890],{},[2071,27184,554],{},[2075,27186,2077],{},[2210,27188,26501],{},[2075,27190,3251],{},[2210,27192,27164],{},[2075,27194,2077],{},[2210,27196,27197],{},"450",[2092,27199,27200],{"encoding":2094},"M^E = 0{,}15 \\cdot 3000 = 450",[92,27202,27203,2361],{},[1647,27204,27206],{"className":27205},[2059],[2061,27207,27208],{"xmlns":2063},[2065,27209,27210,27234],{},[2068,27211,27212,27218,27220,27222,27224,27226,27228,27230,27232],{},[2205,27213,27214,27216],{},[2071,27215,2849],{},[2071,27217,554],{},[2075,27219,2077],{},[2210,27221,26469],{},[2075,27223,3251],{},[2210,27225,27164],{},[2075,27227,2176],{},[2210,27229,26482],{},[2075,27231,2077],{},[2210,27233,27164],{},[2092,27235,27236],{"encoding":2094},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[92,27238,27239,27279],{},[1647,27240,27242],{"className":27241},[2059],[2061,27243,27244],{"xmlns":2063},[2065,27245,27246,27276],{},[2068,27247,27248,27254,27256,27264,27266,27272,27274],{},[2205,27249,27250,27252],{},[2071,27251,532],{},[2071,27253,554],{},[2075,27255,2077],{},[9252,27257,27258,27260,27262],{},[2071,27259,9214],{},[2071,27261,4271],{},[2071,27263,554],{},[2075,27265,2303],{},[2205,27267,27268,27270],{},[2071,27269,2849],{},[2071,27271,554],{},[2075,27273,2077],{},[2210,27275,630],{},[2092,27277,27278],{"encoding":2094},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[55,27281,27282,27284,27285,835,27302,75,27323,27348,27349,27352,27353,27366,27367,195],{},[95,27283,24088],{}," Modely ",[1647,27286,27288],{"className":27287},[2059],[2061,27289,27290],{"xmlns":2063},[2065,27291,27292,27300],{},[2068,27293,27294,27296,27298],{},[2071,27295,2849],{},[2363,27297,14025],{},[2071,27299,13919],{},[2092,27301,14030],{"encoding":2094},[1647,27303,27305],{"className":27304},[2059],[2061,27306,27307],{"xmlns":2063},[2065,27308,27309,27321],{},[2068,27310,27311,27313,27315,27317,27319],{},[2071,27312,2849],{},[2363,27314,14025],{},[2071,27316,13919],{},[2363,27318,14025],{},[2071,27320,13845],{},[2092,27322,20959],{"encoding":2094},[1647,27324,27326],{"className":27325},[2059],[2061,27327,27328],{"xmlns":2063},[2065,27329,27330,27346],{},[2068,27331,27332,27334,27336,27338,27340,27342,27344],{},[2071,27333,2849],{},[2363,27335,14025],{},[2071,27337,13919],{},[2363,27339,14025],{},[2071,27341,13845],{},[2363,27343,14025],{},[2071,27345,14055],{},[2092,27347,14058],{"encoding":2094}," pokládají investice za ",[95,27350,27351],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[1647,27354,27356],{"className":27355},[2059],[2061,27357,27358],{"xmlns":2063},[2065,27359,27360,27364],{},[2068,27361,27362],{},[2071,27363,13774],{},[2092,27365,13774],{"encoding":2094},". Přidáním trhu peněz a úrokové míry vzniká ",[95,27368,27369],{},"model IS-LM",[84,27371,27373],{"id":27372},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[55,27375,27376,27377,27381,27382,27385,27386,27389],{},"V článku ",[69,27378,27380],{"className":27379,"dataFsResolvedFilePath":3022,"href":3023},[62],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[95,27383,27384],{},"Analogické úvahy dovedou k multiplikátorům pro modely makroekonomického typu","; role multiplikátorů jako nástrojů pro postižení kvalitativních a kvantitativních charakteristik chování modelů je v makroekonomických analýzách ještě ",[95,27387,27388],{},"výraznější"," než v mikroekonomických modelech.",[55,27391,27392],{},[58,27393],{"alt":27394,"className":27395,"src":27396},"imek-multiplikatorovy-efekt-chain",[62,63],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[55,27398,13897,27399,835,27416,835,27437,27462,27463,27466,27467,27485,27486,27504,27505,27523,27524,27527,27528,835,27545,27562,27563,27565],{},[1647,27400,27402],{"className":27401},[2059],[2061,27403,27404],{"xmlns":2063},[2065,27405,27406,27414],{},[2068,27407,27408,27410,27412],{},[2071,27409,2849],{},[2363,27411,14025],{},[2071,27413,13919],{},[2092,27415,14030],{"encoding":2094},[1647,27417,27419],{"className":27418},[2059],[2061,27420,27421],{"xmlns":2063},[2065,27422,27423,27435],{},[2068,27424,27425,27427,27429,27431,27433],{},[2071,27426,2849],{},[2363,27428,14025],{},[2071,27430,13919],{},[2363,27432,14025],{},[2071,27434,13845],{},[2092,27436,20959],{"encoding":2094},[1647,27438,27440],{"className":27439},[2059],[2061,27441,27442],{"xmlns":2063},[2065,27443,27444,27460],{},[2068,27445,27446,27448,27450,27452,27454,27456,27458],{},[2071,27447,2849],{},[2363,27449,14025],{},[2071,27451,13919],{},[2363,27453,14025],{},[2071,27455,13845],{},[2363,27457,14025],{},[2071,27459,14055],{},[2092,27461,14058],{"encoding":2094}," se vyšetřuje vliv změn ",[95,27464,27465],{},"exogenních"," veličin (plánovaných investic ",[1647,27468,27470],{"className":27469},[2059],[2061,27471,27472],{"xmlns":2063},[2065,27473,27474,27482],{},[2068,27475,27476],{},[2205,27477,27478,27480],{},[2071,27479,13919],{},[2075,27481,4441],{},[2092,27483,27484],{"encoding":2094},"I^*",", vládních výdajů ",[1647,27487,27489],{"className":27488},[2059],[2061,27490,27491],{"xmlns":2063},[2065,27492,27493,27501],{},[2068,27494,27495],{},[2205,27496,27497,27499],{},[2071,27498,13845],{},[2075,27500,4441],{},[2092,27502,27503],{"encoding":2094},"G^*",", exportu ",[1647,27506,27508],{"className":27507},[2059],[2061,27509,27510],{"xmlns":2063},[2065,27511,27512,27520],{},[2068,27513,27514],{},[2205,27515,27516,27518],{},[2071,27517,25992],{},[2075,27519,4441],{},[2092,27521,27522],{"encoding":2094},"B^*",") na změny ",[95,27525,27526],{},"endogenních"," rovnovážných veličin (",[1647,27529,27531],{"className":27530},[2059],[2061,27532,27533],{"xmlns":2063},[2065,27534,27535,27543],{},[2068,27536,27537],{},[2205,27538,27539,27541],{},[2071,27540,9214],{},[2071,27542,554],{},[2092,27544,15638],{"encoding":2094},[1647,27546,27548],{"className":27547},[2059],[2061,27549,27550],{"xmlns":2063},[2065,27551,27552,27560],{},[2068,27553,27554],{},[2205,27555,27556,27558],{},[2071,27557,2849],{},[2071,27559,554],{},[2092,27561,15697],{"encoding":2094}," atd.). Tyto citlivosti se vyjadřují ",[95,27564,20716],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[609,27567,27569],{"id":27568},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[55,27571,23634,27572,27595,27596,27640],{},[1647,27573,27575],{"className":27574},[2059],[2061,27576,27577],{"xmlns":2063},[2065,27578,27579,27593],{},[2068,27580,27581,27583,27585,27587,27589,27591],{},[2071,27582,2849],{},[2075,27584,2077],{},[2071,27586,69],{},[2071,27588,9214],{},[2075,27590,2176],{},[2071,27592,2179],{},[2092,27594,21659],{"encoding":2094}," dává (7.7) redukovaný tvar ",[1647,27597,27599],{"className":27598},[2059],[2061,27600,27601],{"xmlns":2063},[2065,27602,27603,27637],{},[2068,27604,27605,27611,27613],{},[2205,27606,27607,27609],{},[2071,27608,9214],{},[2071,27610,554],{},[2075,27612,2077],{},[2400,27614,27615],{"scriptlevel":630,"displaystyle":2360},[2403,27616,27617,27629],{},[2068,27618,27619,27621,27623],{},[2071,27620,2179],{},[2075,27622,2176],{},[2205,27624,27625,27627],{},[2071,27626,13919],{},[2075,27628,4441],{},[2068,27630,27631,27633,27635],{},[2210,27632,638],{},[2075,27634,2303],{},[2071,27636,69],{},[2092,27638,27639],{"encoding":2094},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[55,27642,27643],{},[1647,27644,27646],{"className":27645},[2059],[2061,27647,27648],{"xmlns":2063},[2065,27649,27650,27719],{},[2068,27651,27652,27670,27672,27702,27704],{},[2403,27653,27654,27664],{},[2068,27655,27656,27658],{},[2071,27657,11003],{"mathvariant":2450},[2205,27659,27660,27662],{},[2071,27661,9214],{},[2071,27663,554],{},[2068,27665,27666,27668],{},[2071,27667,11003],{"mathvariant":2450},[2071,27669,69],{},[2075,27671,2077],{},[2403,27673,27674,27686],{},[2068,27675,27676,27678,27680],{},[2071,27677,2179],{},[2075,27679,2176],{},[2205,27681,27682,27684],{},[2071,27683,13919],{},[2075,27685,4441],{},[2068,27687,27688,27690,27692,27694,27696],{},[2075,27689,2084],{"stretchy":2083},[2210,27691,638],{},[2075,27693,2303],{},[2071,27695,69],{},[2205,27697,27698,27700],{},[2075,27699,2090],{"stretchy":2083},[2210,27701,646],{},[5965,27703],{"width":5967},[2068,27705,27706,27709,27716],{},[2363,27707,27708],{},"(multiplik",[8473,27710,27711,27713],{"accent":2360},[2363,27712,69],{},[2075,27714,27715],{},"ˊ",[2363,27717,27718],{},"tor MPC)",[2092,27720,27721],{"encoding":2094},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[55,27723,27724],{},[1647,27725,27727],{"className":27726},[2059],[2061,27728,27729],{"xmlns":2063},[2065,27730,27731,27800],{},[2068,27732,27733,27751,27753,27765,27767],{},[2403,27734,27735,27745],{},[2068,27736,27737,27739],{},[2071,27738,11003],{"mathvariant":2450},[2205,27740,27741,27743],{},[2071,27742,9214],{},[2071,27744,554],{},[2068,27746,27747,27749],{},[2071,27748,11003],{"mathvariant":2450},[2071,27750,2179],{},[2075,27752,2077],{},[2403,27754,27755,27757],{},[2210,27756,638],{},[2068,27758,27759,27761,27763],{},[2210,27760,638],{},[2075,27762,2303],{},[2071,27764,69],{},[5965,27766],{"width":5967},[2068,27768,27769,27771,27777,27780,27787,27790,27797],{},[2363,27770,27708],{},[8473,27772,27773,27775],{"accent":2360},[2363,27774,69],{},[2075,27776,27715],{},[2363,27778,27779],{},"tor autonomn",[8473,27781,27782,27785],{"accent":2360},[2363,27783,27784],{},"ı",[2075,27786,27715],{},[2363,27788,27789],{}," spot",[8473,27791,27792,27794],{"accent":2360},[2363,27793,13774],{},[2075,27795,27796],{},"ˇ",[2363,27798,27799],{},"eby)",[2092,27801,27802],{"encoding":2094},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[55,27804,27805],{},[1647,27806,27808],{"className":27807},[2059],[2061,27809,27810],{"xmlns":2063},[2065,27811,27812,27879],{},[2068,27813,27814,27836,27838,27850,27852,27864,27866],{},[2403,27815,27816,27826],{},[2068,27817,27818,27820],{},[2071,27819,11003],{"mathvariant":2450},[2205,27821,27822,27824],{},[2071,27823,9214],{},[2071,27825,554],{},[2068,27827,27828,27830],{},[2071,27829,11003],{"mathvariant":2450},[2205,27831,27832,27834],{},[2071,27833,13919],{},[2075,27835,4441],{},[2075,27837,2077],{},[2403,27839,27840,27842],{},[2210,27841,638],{},[2068,27843,27844,27846,27848],{},[2210,27845,638],{},[2075,27847,2303],{},[2071,27849,69],{},[2075,27851,2077],{},[2403,27853,27854,27856],{},[2210,27855,638],{},[2068,27857,27858,27860,27862],{},[2071,27859,2890],{},[2071,27861,575],{},[2071,27863,532],{},[5965,27865],{"width":5967},[2068,27867,27868,27870,27876],{},[2363,27869,27708],{},[8473,27871,27872,27874],{"accent":2360},[2363,27873,69],{},[2075,27875,27715],{},[2363,27877,27878],{},"tor investic)",[2092,27880,27881],{"encoding":2094},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1023,27883,27884],{},[55,27885,27886,27888,27889,27892,27893,27906,27907,27924,27925,27943,27944,27988,27989,24159,28006,28009,28010,28027],{},[1647,27887,4243],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[95,27890,27891],{},"důchodem","; z něj se utratí ",[1647,27894,27896],{"className":27895},[2059],[2061,27897,27898],{"xmlns":2063},[2065,27899,27900,27904],{},[2068,27901,27902],{},[2071,27903,69],{},[2092,27905,69],{"encoding":2094}," Kč (= ",[1647,27908,27910],{"className":27909},[2059],[2061,27911,27912],{"xmlns":2063},[2065,27913,27914,27922],{},[2068,27915,27916,27918,27920],{},[2071,27917,2890],{},[2071,27919,575],{},[2071,27921,2849],{},[2092,27923,20784],{"encoding":2094},"), to je zase něčí důchod, z něj ",[1647,27926,27928],{"className":27927},[2059],[2061,27929,27930],{"xmlns":2063},[2065,27931,27932,27940],{},[2068,27933,27934],{},[2205,27935,27936,27938],{},[2071,27937,69],{},[2210,27939,646],{},[2092,27941,27942],{"encoding":2094},"a^2"," Kč… Součet geometrické řady ",[1647,27945,27947],{"className":27946},[2059],[2061,27948,27949],{"xmlns":2063},[2065,27950,27951,27985],{},[2068,27952,27953,27955,27957,27959,27961,27967,27969,27971,27973],{},[2210,27954,638],{},[2075,27956,2176],{},[2071,27958,69],{},[2075,27960,2176],{},[2205,27962,27963,27965],{},[2071,27964,69],{},[2210,27966,646],{},[2075,27968,2176],{},[2075,27970,20844],{},[2075,27972,2077],{},[2403,27974,27975,27977],{},[2210,27976,638],{},[2068,27978,27979,27981,27983],{},[2210,27980,638],{},[2075,27982,2303],{},[2071,27984,69],{},[2092,27986,27987],{"encoding":2094},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[1647,27990,27992],{"className":27991},[2059],[2061,27993,27994],{"xmlns":2063},[2065,27995,27996,28004],{},[2068,27997,27998],{},[2205,27999,28000,28002],{},[2071,28001,9214],{},[2071,28003,554],{},[2092,28005,15638],{"encoding":2094},[95,28007,28008],{},"více"," než korunu — čím vyšší ",[1647,28011,28013],{"className":28012},[2059],[2061,28014,28015],{"xmlns":2063},[2065,28016,28017,28025],{},[2068,28018,28019,28021,28023],{},[2071,28020,2890],{},[2071,28022,575],{},[2071,28024,2849],{},[2092,28026,20784],{"encoding":2094},", tím silnější multiplikační efekt.",[55,28029,28030,28033,28034,28060,28061,28064,28065,75,28086,28111,28112,195],{},[95,28031,28032],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[1647,28035,28037],{"className":28036},[2059],[2061,28038,28039],{"xmlns":2063},[2065,28040,28041,28057],{},[2068,28042,28043],{},[2400,28044,28045],{"scriptlevel":630,"displaystyle":2083},[2403,28046,28047,28049],{},[2210,28048,638],{},[2068,28050,28051,28053,28055],{},[2210,28052,638],{},[2075,28054,2303],{},[2071,28056,69],{},[2092,28058,28059],{"encoding":2094},"\\tfrac{1}{1-a}",", což je standardní ",[95,28062,28063],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[1647,28066,28068],{"className":28067},[2059],[2061,28069,28070],{"xmlns":2063},[2065,28071,28072,28084],{},[2068,28073,28074,28076,28078,28080,28082],{},[2071,28075,2849],{},[2363,28077,14025],{},[2071,28079,13919],{},[2363,28081,14025],{},[2071,28083,13845],{},[2092,28085,20959],{"encoding":2094},[1647,28087,28089],{"className":28088},[2059],[2061,28090,28091],{"xmlns":2063},[2065,28092,28093,28109],{},[2068,28094,28095,28097,28099,28101,28103,28105,28107],{},[2071,28096,2849],{},[2363,28098,14025],{},[2071,28100,13919],{},[2363,28102,14025],{},[2071,28104,13845],{},[2363,28106,14025],{},[2071,28108,14055],{},[2092,28110,14058],{"encoding":2094}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[69,28113,28115],{"className":28114,"dataFsResolvedFilePath":13670,"href":13671},[62],"poptávka a nabídka",[84,28117,28119],{"id":28118},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[55,28121,13897,28122,835,28139,75,28160,13904,28185,11156,28188,28209,28210,1445,28213,28226,28227,5756,28256,28273,28274,28277,28278,28280,28281,28302],{},[1647,28123,28125],{"className":28124},[2059],[2061,28126,28127],{"xmlns":2063},[2065,28128,28129,28137],{},[2068,28130,28131,28133,28135],{},[2071,28132,2849],{},[2363,28134,14025],{},[2071,28136,13919],{},[2092,28138,14030],{"encoding":2094},[1647,28140,28142],{"className":28141},[2059],[2061,28143,28144],{"xmlns":2063},[2065,28145,28146,28158],{},[2068,28147,28148,28150,28152,28154,28156],{},[2071,28149,2849],{},[2363,28151,14025],{},[2071,28153,13919],{},[2363,28155,14025],{},[2071,28157,13845],{},[2092,28159,20959],{"encoding":2094},[1647,28161,28163],{"className":28162},[2059],[2061,28164,28165],{"xmlns":2063},[2065,28166,28167,28183],{},[2068,28168,28169,28171,28173,28175,28177,28179,28181],{},[2071,28170,2849],{},[2363,28172,14025],{},[2071,28174,13919],{},[2363,28176,14025],{},[2071,28178,13845],{},[2363,28180,14025],{},[2071,28182,14055],{},[2092,28184,14058],{"encoding":2094},[95,28186,28187],{},"investice konstantní",[1647,28189,28191],{"className":28190},[2059],[2061,28192,28193],{"xmlns":2063},[2065,28194,28195,28207],{},[2068,28196,28197,28199,28201],{},[2071,28198,13919],{},[2075,28200,2077],{},[2205,28202,28203,28205],{},[2071,28204,13919],{},[2075,28206,4441],{},[2092,28208,13930],{"encoding":2094},"). Reálnější je předpoklad, že ",[95,28211,28212],{},"investice závisejí na úrokové míře",[1647,28214,28216],{"className":28215},[2059],[2061,28217,28218],{"xmlns":2063},[2065,28219,28220,28224],{},[2068,28221,28222],{},[2071,28223,13774],{},[2092,28225,13774],{"encoding":2094}," — klesající funkce ",[1647,28228,28230],{"className":28229},[2059],[2061,28231,28232],{"xmlns":2063},[2065,28233,28234,28254],{},[2068,28235,28236,28238,28240,28242,28244,28246,28248,28250,28252],{},[2071,28237,13919],{},[2075,28239,2084],{"stretchy":2083},[2071,28241,13774],{},[2075,28243,2090],{"stretchy":2083},[2075,28245,2077],{},[2071,28247,2222],{},[2071,28249,13774],{},[2075,28251,2176],{},[2071,28253,2273],{},[2092,28255,17490],{"encoding":2094},[1647,28257,28259],{"className":28258},[2059],[2061,28260,28261],{"xmlns":2063},[2065,28262,28263,28271],{},[2068,28264,28265,28267,28269],{},[2071,28266,2222],{},[2075,28268,3521],{},[2210,28270,630],{},[2092,28272,14250],{"encoding":2094},". Přidáním ",[95,28275,28276],{},"trhu peněz"," k trhu zboží vzniká model ",[95,28279,13744],{}," se dvěma neznámými ",[1647,28282,28284],{"className":28283},[2059],[2061,28285,28286],{"xmlns":2063},[2065,28287,28288,28300],{},[2068,28289,28290,28292,28294,28296,28298],{},[2075,28291,2084],{"stretchy":2083},[2071,28293,9214],{},[2075,28295,2361],{"separator":2360},[2071,28297,13774],{},[2075,28299,2090],{"stretchy":2083},[2092,28301,20889],{"encoding":2094}," a dvěma rovnicemi:",[89,28304,28305,28355],{},[92,28306,28307,11156,28309,28311,28312,28333,28334,195],{},[95,28308,17579],{},[3982,28310,13787],{},") — klesající přímka v rovině ",[1647,28313,28315],{"className":28314},[2059],[2061,28316,28317],{"xmlns":2063},[2065,28318,28319,28331],{},[2068,28320,28321,28323,28325,28327,28329],{},[2075,28322,2084],{"stretchy":2083},[2071,28324,13774],{},[2075,28326,2361],{"separator":2360},[2071,28328,9214],{},[2075,28330,2090],{"stretchy":2083},[2092,28332,14672],{"encoding":2094},", odvozená z rovnováhy trhu zboží ",[1647,28335,28337],{"className":28336},[2059],[2061,28338,28339],{"xmlns":2063},[2065,28340,28341,28353],{},[2068,28342,28343,28345,28347,28349,28351],{},[2071,28344,9214],{},[2075,28346,2077],{},[2071,28348,2849],{},[2075,28350,2176],{},[2071,28352,13919],{},[2092,28354,16479],{"encoding":2094},[92,28356,28357,11156,28359,28361,28362,24333,28387,28433],{},[95,28358,17778],{},[3982,28360,13794],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[1647,28363,28365],{"className":28364},[2059],[2061,28366,28367],{"xmlns":2063},[2065,28368,28369,28385],{},[2068,28370,28371,28377,28379],{},[2205,28372,28373,28375],{},[2071,28374,2890],{},[2071,28376,4271],{},[2075,28378,2077],{},[2205,28380,28381,28383],{},[2071,28382,2890],{},[2075,28384,4441],{},[2092,28386,15215],{"encoding":2094},[1647,28388,28390],{"className":28389},[2059],[2061,28391,28392],{"xmlns":2063},[2065,28393,28394,28430],{},[2068,28395,28396,28402,28404,28410,28412,28414,28420,28422,28424],{},[2205,28397,28398,28400],{},[2071,28399,2890],{},[2071,28401,4271],{},[2075,28403,2077],{},[2348,28405,28406,28408],{},[2071,28407,14972],{},[2210,28409,638],{},[2071,28411,9214],{},[2075,28413,2176],{},[2348,28415,28416,28418],{},[2071,28417,14972],{},[2210,28419,646],{},[2071,28421,13774],{},[2075,28423,2176],{},[2348,28425,28426,28428],{},[2071,28427,14972],{},[2210,28429,654],{},[2092,28431,28432],{"encoding":2094},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[55,28435,28436,1445,28439,28472,28473,28475,28476,28478],{},[95,28437,28438],{},"Simultánní rovnovážný bod",[1647,28440,28442],{"className":28441},[2059],[2061,28443,28444],{"xmlns":2063},[2065,28445,28446,28470],{},[2068,28447,28448,28450,28452,28454,28460,28462,28468],{},[2071,28449,554],{},[2075,28451,2077],{},[2075,28453,2084],{"stretchy":2083},[2205,28455,28456,28458],{},[2071,28457,13774],{},[2071,28459,554],{},[2075,28461,2361],{"separator":2360},[2205,28463,28464,28466],{},[2071,28465,9214],{},[2071,28467,554],{},[2075,28469,2090],{"stretchy":2083},[2092,28471,17870],{"encoding":2094}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[95,28474,13832],{}," (posun IS) a ",[95,28477,13864],{}," (posun LM).",[55,28480,28481],{},[95,28482,28483,28484,835,28506,835,28528,835,28550,28572,28573,195],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[1647,28485,28487],{"className":28486},[2059],[2061,28488,28489],{"xmlns":2063},[2065,28490,28491,28503],{},[2068,28492,28493,28499,28501],{},[2205,28494,28495,28497],{},[2071,28496,9214],{},[2071,28498,554],{},[2075,28500,2077],{},[2210,28502,16850],{},[2092,28504,28505],{"encoding":2094},"Y^E = 5000",[1647,28507,28509],{"className":28508},[2059],[2061,28510,28511],{"xmlns":2063},[2065,28512,28513,28525],{},[2068,28514,28515,28521,28523],{},[2205,28516,28517,28519],{},[2071,28518,13774],{},[2071,28520,554],{},[2075,28522,2077],{},[2210,28524,670],{},[2092,28526,28527],{"encoding":2094},"r^E = 5",[1647,28529,28531],{"className":28530},[2059],[2061,28532,28533],{"xmlns":2063},[2065,28534,28535,28547],{},[2068,28536,28537,28543,28545],{},[2205,28538,28539,28541],{},[2071,28540,2849],{},[2071,28542,554],{},[2075,28544,2077],{},[2210,28546,16887],{},[2092,28548,28549],{"encoding":2094},"C^E = 4100",[1647,28551,28553],{"className":28552},[2059],[2061,28554,28555],{"xmlns":2063},[2065,28556,28557,28569],{},[2068,28558,28559,28565,28567],{},[2205,28560,28561,28563],{},[2071,28562,13919],{},[2071,28564,554],{},[2075,28566,2077],{},[2210,28568,16926],{},[2092,28570,28571],{"encoding":2094},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[69,28574,28578],{"className":28575,"dataFsResolvedFilePath":28576,"href":28577},[62],"topics\u002Fis-lm.md","\u002Fwiki\u002Fis-lm","IS-LM analýza",[84,28580,28582],{"id":28581},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[201,28584,28585,28649,28760,28903,29145,29213],{},[92,28586,28587,28590,28591,28613,28614,28648],{},[95,28588,28589],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[1647,28592,28594],{"className":28593},[2059],[2061,28595,28596],{"xmlns":2063},[2065,28597,28598,28610],{},[2068,28599,28600,28602,28604,28606,28608],{},[2071,28601,13845],{},[2071,28603,21033],{},[2071,28605,575],{},[2075,28607,2803],{},[2071,28609,9214],{},[2092,28611,28612],{"encoding":2094},"GNP \\approx Y"," (národní důchod). Základ: ",[1647,28615,28617],{"className":28616},[2059],[2061,28618,28619],{"xmlns":2063},[2065,28620,28621,28645],{},[2068,28622,28623,28625,28627,28629,28631,28633,28635,28637,28639,28641,28643],{},[2071,28624,13845],{},[2071,28626,21033],{},[2071,28628,575],{},[2075,28630,2077],{},[2071,28632,2849],{},[2075,28634,2176],{},[2071,28636,13919],{},[2075,28638,2176],{},[2071,28640,13845],{},[2075,28642,2176],{},[2071,28644,14055],{},[2092,28646,28647],{"encoding":2094},"GNP = C + I + G + X"," (7.1).",[92,28650,28651,28653,28654,28675,28676,835,28699,28730,28731,28744,28745,195],{},[95,28652,21267],{}," splňují ",[1647,28655,28657],{"className":28656},[2059],[2061,28658,28659],{"xmlns":2063},[2065,28660,28661,28673],{},[2068,28662,28663,28665,28667,28669,28671],{},[2071,28664,9214],{},[2075,28666,2077],{},[2071,28668,2849],{},[2075,28670,2176],{},[2071,28672,532],{},[2092,28674,14429],{"encoding":2094}," (7.2); lineární model ",[1647,28677,28679],{"className":28678},[2059],[2061,28680,28681],{"xmlns":2063},[2065,28682,28683,28697],{},[2068,28684,28685,28687,28689,28691,28693,28695],{},[2071,28686,2849],{},[2075,28688,2077],{},[2071,28690,69],{},[2071,28692,9214],{},[2075,28694,2176],{},[2071,28696,2179],{},[2092,28698,21659],{"encoding":2094},[1647,28700,28702],{"className":28701},[2059],[2061,28703,28704],{"xmlns":2063},[2065,28705,28706,28728],{},[2068,28707,28708,28710,28712,28714,28716,28718,28720,28722,28724,28726],{},[2071,28709,532],{},[2075,28711,2077],{},[2075,28713,2084],{"stretchy":2083},[2210,28715,638],{},[2075,28717,2303],{},[2071,28719,69],{},[2075,28721,2090],{"stretchy":2083},[2071,28723,9214],{},[2075,28725,2303],{},[2071,28727,2179],{},[2092,28729,21908],{"encoding":2094}," s autonomní spotřebou ",[1647,28732,28734],{"className":28733},[2059],[2061,28735,28736],{"xmlns":2063},[2065,28737,28738,28742],{},[2068,28739,28740],{},[2071,28741,2179],{},[2092,28743,2179],{"encoding":2094}," a autonomními úsporami ",[1647,28746,28748],{"className":28747},[2059],[2061,28749,28750],{"xmlns":2063},[2065,28751,28752,28758],{},[2068,28753,28754,28756],{},[2075,28755,2303],{},[2071,28757,2179],{},[2092,28759,21987],{"encoding":2094},[92,28761,28762,1445,28765,835,28795,28825,28826,28856,28857,835,28878,195],{},[95,28763,28764],{},"Mezní sklony",[1647,28766,28768],{"className":28767},[2059],[2061,28769,28770],{"xmlns":2063},[2065,28771,28772,28792],{},[2068,28773,28774,28776,28778,28780,28782,28784,28786,28788,28790],{},[2071,28775,2890],{},[2071,28777,575],{},[2071,28779,2849],{},[2075,28781,2077],{},[2071,28783,2273],{"mathvariant":2450},[2071,28785,2849],{},[2071,28787,4761],{"mathvariant":2450},[2071,28789,2273],{"mathvariant":2450},[2071,28791,9214],{},[2092,28793,28794],{"encoding":2094},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[1647,28796,28798],{"className":28797},[2059],[2061,28799,28800],{"xmlns":2063},[2065,28801,28802,28822],{},[2068,28803,28804,28806,28808,28810,28812,28814,28816,28818,28820],{},[2071,28805,2890],{},[2071,28807,575],{},[2071,28809,532],{},[2075,28811,2077],{},[2071,28813,2273],{"mathvariant":2450},[2071,28815,532],{},[2071,28817,4761],{"mathvariant":2450},[2071,28819,2273],{"mathvariant":2450},[2071,28821,9214],{},[2092,28823,28824],{"encoding":2094},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[1647,28827,28829],{"className":28828},[2059],[2061,28830,28831],{"xmlns":2063},[2065,28832,28833,28853],{},[2068,28834,28835,28837,28839,28841,28843,28845,28847,28849,28851],{},[2071,28836,2890],{},[2071,28838,575],{},[2071,28840,2849],{},[2075,28842,2176],{},[2071,28844,2890],{},[2071,28846,575],{},[2071,28848,532],{},[2075,28850,2077],{},[2210,28852,638],{},[2092,28854,28855],{"encoding":2094},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[1647,28858,28860],{"className":28859},[2059],[2061,28861,28862],{"xmlns":2063},[2065,28863,28864,28876],{},[2068,28865,28866,28868,28870,28872,28874],{},[2071,28867,2890],{},[2071,28869,575],{},[2071,28871,2849],{},[2075,28873,2077],{},[2071,28875,69],{},[2092,28877,22628],{"encoding":2094},[1647,28879,28881],{"className":28880},[2059],[2061,28882,28883],{"xmlns":2063},[2065,28884,28885,28901],{},[2068,28886,28887,28889,28891,28893,28895,28897,28899],{},[2071,28888,2890],{},[2071,28890,575],{},[2071,28892,532],{},[2075,28894,2077],{},[2210,28896,638],{},[2075,28898,2303],{},[2071,28900,69],{},[2092,28902,22654],{"encoding":2094},[92,28904,28905,28908,28909],{},[95,28906,28907],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[89,28910,28911,28999,29068],{},[92,28912,28913,28930,28931,28952,28953,2361],{},[1647,28914,28916],{"className":28915},[2059],[2061,28917,28918],{"xmlns":2063},[2065,28919,28920,28928],{},[2068,28921,28922,28924,28926],{},[2071,28923,2849],{},[2363,28925,14025],{},[2071,28927,13919],{},[2092,28929,14030],{"encoding":2094},": ",[1647,28932,28934],{"className":28933},[2059],[2061,28935,28936],{"xmlns":2063},[2065,28937,28938,28950],{},[2068,28939,28940,28942,28944,28946,28948],{},[2071,28941,9214],{},[2075,28943,2077],{},[2071,28945,2849],{},[2075,28947,2176],{},[2071,28949,13919],{},[2092,28951,16479],{"encoding":2094}," (uzavřená ekonomika bez vlády), ",[1647,28954,28956],{"className":28955},[2059],[2061,28957,28958],{"xmlns":2063},[2065,28959,28960,28996],{},[2068,28961,28962,28968,28970,28972,28974,28976,28982,28984,28986,28988,28990,28992,28994],{},[2205,28963,28964,28966],{},[2071,28965,9214],{},[2071,28967,554],{},[2075,28969,2077],{},[2075,28971,2084],{"stretchy":2083},[2071,28973,2179],{},[2075,28975,2176],{},[2205,28977,28978,28980],{},[2071,28979,13919],{},[2075,28981,4441],{},[2075,28983,2090],{"stretchy":2083},[2071,28985,4761],{"mathvariant":2450},[2075,28987,2084],{"stretchy":2083},[2210,28989,638],{},[2075,28991,2303],{},[2071,28993,69],{},[2075,28995,2090],{"stretchy":2083},[2092,28997,28998],{"encoding":2094},"Y^E = (b + I^*)\u002F(1-a)",[92,29000,29001,29022,29023,29042,29043,2361],{},[1647,29002,29004],{"className":29003},[2059],[2061,29005,29006],{"xmlns":2063},[2065,29007,29008,29020],{},[2068,29009,29010,29012,29014,29016,29018],{},[2071,29011,2849],{},[2363,29013,14025],{},[2071,29015,13919],{},[2363,29017,14025],{},[2071,29019,13845],{},[2092,29021,20959],{"encoding":2094},": přidává vládu, zdanění ",[1647,29024,29026],{"className":29025},[2059],[2061,29027,29028],{"xmlns":2063},[2065,29029,29030,29040],{},[2068,29031,29032,29034,29036,29038],{},[2071,29033,543],{},[2075,29035,2084],{"stretchy":2083},[2071,29037,9214],{},[2075,29039,2090],{"stretchy":2083},[2092,29041,24958],{"encoding":2094}," a disponibilní důchod ",[1647,29044,29046],{"className":29045},[2059],[2061,29047,29048],{"xmlns":2063},[2065,29049,29050,29066],{},[2068,29051,29052,29058,29060,29062,29064],{},[2348,29053,29054,29056],{},[2071,29055,9214],{},[2071,29057,4271],{},[2075,29059,2077],{},[2071,29061,9214],{},[2075,29063,2303],{},[2071,29065,543],{},[2092,29067,24457],{"encoding":2094},[92,29069,29070,29095,29096,24333,29117,195],{},[1647,29071,29073],{"className":29072},[2059],[2061,29074,29075],{"xmlns":2063},[2065,29076,29077,29093],{},[2068,29078,29079,29081,29083,29085,29087,29089,29091],{},[2071,29080,2849],{},[2363,29082,14025],{},[2071,29084,13919],{},[2363,29086,14025],{},[2071,29088,13845],{},[2363,29090,14025],{},[2071,29092,14055],{},[2092,29094,14058],{"encoding":2094},": otevírá ekonomiku čistým exportem ",[1647,29097,29099],{"className":29098},[2059],[2061,29100,29101],{"xmlns":2063},[2065,29102,29103,29115],{},[2068,29104,29105,29107,29109,29111,29113],{},[2071,29106,14055],{},[2075,29108,2077],{},[2071,29110,25992],{},[2075,29112,2303],{},[2071,29114,2890],{},[2092,29116,25999],{"encoding":2094},[1647,29118,29120],{"className":29119},[2059],[2061,29121,29122],{"xmlns":2063},[2065,29123,29124,29142],{},[2068,29125,29126,29128,29130,29132,29134,29140],{},[2071,29127,2890],{},[2075,29129,2077],{},[2071,29131,2890],{},[2075,29133,2084],{"stretchy":2083},[2348,29135,29136,29138],{},[2071,29137,9214],{},[2071,29139,4271],{},[2075,29141,2090],{"stretchy":2083},[2092,29143,29144],{"encoding":2094},"M = M(Y_D)",[92,29146,29147,29150,29151,1445,29154,29212],{},[95,29148,29149],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[95,29152,29153],{},"multiplikátor investic",[1647,29155,29157],{"className":29156},[2059],[2061,29158,29159],{"xmlns":2063},[2065,29160,29161,29209],{},[2068,29162,29163,29165,29171,29173,29175,29181,29183,29185,29187,29189,29191,29193,29195,29197,29199,29201,29203,29205,29207],{},[2071,29164,11003],{"mathvariant":2450},[2205,29166,29167,29169],{},[2071,29168,9214],{},[2071,29170,554],{},[2071,29172,4761],{"mathvariant":2450},[2071,29174,11003],{"mathvariant":2450},[2205,29176,29177,29179],{},[2071,29178,13919],{},[2075,29180,4441],{},[2075,29182,2077],{},[2210,29184,638],{},[2071,29186,4761],{"mathvariant":2450},[2075,29188,2084],{"stretchy":2083},[2210,29190,638],{},[2075,29192,2303],{},[2071,29194,69],{},[2075,29196,2090],{"stretchy":2083},[2075,29198,2077],{},[2210,29200,638],{},[2071,29202,4761],{"mathvariant":2450},[2071,29204,2890],{},[2071,29206,575],{},[2071,29208,532],{},[2092,29210,29211],{"encoding":2094},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[92,29214,29215,29217,29218,29233,29234,21387,29251,29266,29267,29292,29293,195],{},[95,29216,28578],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[1647,29219,29221],{"className":29220},[2059],[2061,29222,29223],{"xmlns":2063},[2065,29224,29225,29231],{},[2068,29226,29227,29229],{},[2071,29228,13919],{},[2071,29230,532],{},[2092,29232,13784],{"encoding":2094}," popisuje rovnováhu trhu zboží (",[1647,29235,29237],{"className":29236},[2059],[2061,29238,29239],{"xmlns":2063},[2065,29240,29241,29249],{},[2068,29242,29243,29245,29247],{},[2071,29244,13919],{},[2075,29246,2077],{},[2071,29248,532],{},[2092,29250,14447],{"encoding":2094},[1647,29252,29254],{"className":29253},[2059],[2061,29255,29256],{"xmlns":2063},[2065,29257,29258,29264],{},[2068,29259,29260,29262],{},[2071,29261,586],{},[2071,29263,2890],{},[2092,29265,13791],{"encoding":2094}," rovnováhu trhu peněz (",[1647,29268,29270],{"className":29269},[2059],[2061,29271,29272],{"xmlns":2063},[2065,29273,29274,29290],{},[2068,29275,29276,29282,29284],{},[2205,29277,29278,29280],{},[2071,29279,2890],{},[2071,29281,4271],{},[2075,29283,2077],{},[2205,29285,29286,29288],{},[2071,29287,2890],{},[2075,29289,4441],{},[2092,29291,15215],{"encoding":2094},"); průsečík dává ",[1647,29294,29296],{"className":29295},[2059],[2061,29297,29298],{"xmlns":2063},[2065,29299,29300,29320],{},[2068,29301,29302,29304,29310,29312,29318],{},[2075,29303,2084],{"stretchy":2083},[2205,29305,29306,29308],{},[2071,29307,9214],{},[2071,29309,554],{},[2075,29311,2361],{"separator":2360},[2205,29313,29314,29316],{},[2071,29315,13774],{},[2071,29317,554],{},[2075,29319,2090],{"stretchy":2083},[2092,29321,13828],{"encoding":2094},[84,29323,321],{"id":320},[89,29325,29326,29364,29404,29494,29576,29630,29686,29745,29780,29785,29857,29932,30018,30080,30148,30206,30259,30298],{},[92,29327,29328,7102,29331,28648],{},[95,29329,29330],{},"Hrubý národní produkt (GNP)",[1647,29332,29334],{"className":29333},[2059],[2061,29335,29336],{"xmlns":2063},[2065,29337,29338,29362],{},[2068,29339,29340,29342,29344,29346,29348,29350,29352,29354,29356,29358,29360],{},[2071,29341,13845],{},[2071,29343,21033],{},[2071,29345,575],{},[2075,29347,2077],{},[2071,29349,2849],{},[2075,29351,2176],{},[2071,29353,13919],{},[2075,29355,2176],{},[2071,29357,13845],{},[2075,29359,2176],{},[2071,29361,14055],{},[2092,29363,28647],{"encoding":2094},[92,29365,29366,29382,29383,195],{},[95,29367,29368,29369],{},"Národní důchod ",[1647,29370,29372],{"className":29371},[2059],[2061,29373,29374],{"xmlns":2063},[2065,29375,29376,29380],{},[2068,29377,29378],{},[2071,29379,9214],{},[2092,29381,9214],{"encoding":2094}," — součet důchodů domácností; v modelech ",[1647,29384,29386],{"className":29385},[2059],[2061,29387,29388],{"xmlns":2063},[2065,29389,29390,29402],{},[2068,29391,29392,29394,29396,29398,29400],{},[2071,29393,13845],{},[2071,29395,21033],{},[2071,29397,575],{},[2075,29399,2803],{},[2071,29401,9214],{},[2092,29403,28612],{"encoding":2094},[92,29405,29406,29432,29433,835,29456,835,29477,195],{},[95,29407,29408,29409],{},"Funkce spotřeby ",[1647,29410,29412],{"className":29411},[2059],[2061,29413,29414],{"xmlns":2063},[2065,29415,29416,29430],{},[2068,29417,29418,29420,29422,29424,29426,29428],{},[2071,29419,2849],{},[2075,29421,2077],{},[2071,29423,2849],{},[2075,29425,2084],{"stretchy":2083},[2071,29427,9214],{},[2075,29429,2090],{"stretchy":2083},[2092,29431,23479],{"encoding":2094}," — lineární model ",[1647,29434,29436],{"className":29435},[2059],[2061,29437,29438],{"xmlns":2063},[2065,29439,29440,29454],{},[2068,29441,29442,29444,29446,29448,29450,29452],{},[2071,29443,2849],{},[2075,29445,2077],{},[2071,29447,69],{},[2071,29449,9214],{},[2075,29451,2176],{},[2071,29453,2179],{},[2092,29455,21659],{"encoding":2094},[1647,29457,29459],{"className":29458},[2059],[2061,29460,29461],{"xmlns":2063},[2065,29462,29463,29475],{},[2068,29464,29465,29467,29469,29471,29473],{},[2210,29466,630],{},[2075,29468,3521],{},[2071,29470,69],{},[2075,29472,3521],{},[2210,29474,638],{},[2092,29476,21575],{"encoding":2094},[1647,29478,29480],{"className":29479},[2059],[2061,29481,29482],{"xmlns":2063},[2065,29483,29484,29492],{},[2068,29485,29486,29488,29490],{},[2071,29487,2179],{},[2075,29489,3482],{},[2210,29491,630],{},[2092,29493,21553],{"encoding":2094},[92,29495,29496,7102,29523,29544,29545,195],{},[95,29497,29498,29499],{},"Funkce úspor ",[1647,29500,29502],{"className":29501},[2059],[2061,29503,29504],{"xmlns":2063},[2065,29505,29506,29520],{},[2068,29507,29508,29510,29512,29514,29516,29518],{},[2071,29509,532],{},[2075,29511,2077],{},[2071,29513,532],{},[2075,29515,2084],{"stretchy":2083},[2071,29517,9214],{},[2075,29519,2090],{"stretchy":2083},[2092,29521,29522],{"encoding":2094},"S = S(Y)",[1647,29524,29526],{"className":29525},[2059],[2061,29527,29528],{"xmlns":2063},[2065,29529,29530,29542],{},[2068,29531,29532,29534,29536,29538,29540],{},[2071,29533,9214],{},[2075,29535,2077],{},[2071,29537,2849],{},[2075,29539,2176],{},[2071,29541,532],{},[2092,29543,14429],{"encoding":2094},"; lineární ",[1647,29546,29548],{"className":29547},[2059],[2061,29549,29550],{"xmlns":2063},[2065,29551,29552,29574],{},[2068,29553,29554,29556,29558,29560,29562,29564,29566,29568,29570,29572],{},[2071,29555,532],{},[2075,29557,2077],{},[2075,29559,2084],{"stretchy":2083},[2210,29561,638],{},[2075,29563,2303],{},[2071,29565,69],{},[2075,29567,2090],{"stretchy":2083},[2071,29569,9214],{},[2075,29571,2303],{},[2071,29573,2179],{},[2092,29575,21908],{"encoding":2094},[92,29577,29578,7102,29581,835,29604,195],{},[95,29579,29580],{},"Autonomní spotřeba\u002Fúspory",[1647,29582,29584],{"className":29583},[2059],[2061,29585,29586],{"xmlns":2063},[2065,29587,29588,29602],{},[2068,29589,29590,29592,29594,29596,29598,29600],{},[2071,29591,2849],{},[2075,29593,2084],{"stretchy":2083},[2210,29595,630],{},[2075,29597,2090],{"stretchy":2083},[2075,29599,2077],{},[2071,29601,2179],{},[2092,29603,22300],{"encoding":2094},[1647,29605,29607],{"className":29606},[2059],[2061,29608,29609],{"xmlns":2063},[2065,29610,29611,29627],{},[2068,29612,29613,29615,29617,29619,29621,29623,29625],{},[2071,29614,532],{},[2075,29616,2084],{"stretchy":2083},[2210,29618,630],{},[2075,29620,2090],{"stretchy":2083},[2075,29622,2077],{},[2075,29624,2303],{},[2071,29626,2179],{},[2092,29628,29629],{"encoding":2094},"S(0) = -b",[92,29631,29632,29664,29665,4007],{},[95,29633,29634,29635],{},"Mezní sklon ke spotřebě ",[1647,29636,29638],{"className":29637},[2059],[2061,29639,29640],{"xmlns":2063},[2065,29641,29642,29662],{},[2068,29643,29644,29646,29648,29650,29652,29654,29656,29658,29660],{},[2071,29645,2890],{},[2071,29647,575],{},[2071,29649,2849],{},[2075,29651,2077],{},[2071,29653,2273],{"mathvariant":2450},[2071,29655,2849],{},[2071,29657,4761],{"mathvariant":2450},[2071,29659,2273],{"mathvariant":2450},[2071,29661,9214],{},[2092,29663,28794],{"encoding":2094}," (v lineárním modelu ",[1647,29666,29668],{"className":29667},[2059],[2061,29669,29670],{"xmlns":2063},[2065,29671,29672,29684],{},[2068,29673,29674,29676,29678,29680,29682],{},[2071,29675,2890],{},[2071,29677,575],{},[2071,29679,2849],{},[2075,29681,2077],{},[2071,29683,69],{},[2092,29685,22628],{"encoding":2094},[92,29687,29688,29664,29720,4007],{},[95,29689,29690,29691],{},"Mezní sklon k úsporám ",[1647,29692,29694],{"className":29693},[2059],[2061,29695,29696],{"xmlns":2063},[2065,29697,29698,29718],{},[2068,29699,29700,29702,29704,29706,29708,29710,29712,29714,29716],{},[2071,29701,2890],{},[2071,29703,575],{},[2071,29705,532],{},[2075,29707,2077],{},[2071,29709,2273],{"mathvariant":2450},[2071,29711,532],{},[2071,29713,4761],{"mathvariant":2450},[2071,29715,2273],{"mathvariant":2450},[2071,29717,9214],{},[2092,29719,28824],{"encoding":2094},[1647,29721,29723],{"className":29722},[2059],[2061,29724,29725],{"xmlns":2063},[2065,29726,29727,29743],{},[2068,29728,29729,29731,29733,29735,29737,29739,29741],{},[2071,29730,2890],{},[2071,29732,575],{},[2071,29734,532],{},[2075,29736,2077],{},[2210,29738,638],{},[2075,29740,2303],{},[2071,29742,69],{},[2092,29744,22654],{"encoding":2094},[92,29746,29747,1445,29750,29779],{},[95,29748,29749],{},"Vztah",[1647,29751,29753],{"className":29752},[2059],[2061,29754,29755],{"xmlns":2063},[2065,29756,29757,29777],{},[2068,29758,29759,29761,29763,29765,29767,29769,29771,29773,29775],{},[2071,29760,2890],{},[2071,29762,575],{},[2071,29764,2849],{},[2075,29766,2176],{},[2071,29768,2890],{},[2071,29770,575],{},[2071,29772,532],{},[2075,29774,2077],{},[2210,29776,638],{},[2092,29778,28855],{"encoding":2094}," (7.5).",[92,29781,29782,29784],{},[95,29783,23322],{}," — rovnováha agregátní poptávky a nabídky.",[92,29786,29787,29790,29791,17525,29812,195],{},[95,29788,29789],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[1647,29792,29794],{"className":29793},[2059],[2061,29795,29796],{"xmlns":2063},[2065,29797,29798,29810],{},[2068,29799,29800,29802,29804,29806,29808],{},[2071,29801,9214],{},[2075,29803,2077],{},[2071,29805,2849],{},[2075,29807,2176],{},[2071,29809,13919],{},[2092,29811,16479],{"encoding":2094},[1647,29813,29815],{"className":29814},[2059],[2061,29816,29817],{"xmlns":2063},[2065,29818,29819,29855],{},[2068,29820,29821,29827,29829,29831,29833,29835,29841,29843,29845,29847,29849,29851,29853],{},[2205,29822,29823,29825],{},[2071,29824,9214],{},[2071,29826,554],{},[2075,29828,2077],{},[2075,29830,2084],{"stretchy":2083},[2071,29832,2179],{},[2075,29834,2176],{},[2205,29836,29837,29839],{},[2071,29838,13919],{},[2075,29840,4441],{},[2075,29842,2090],{"stretchy":2083},[2071,29844,4761],{"mathvariant":2450},[2075,29846,2084],{"stretchy":2083},[2210,29848,638],{},[2075,29850,2303],{},[2071,29852,69],{},[2075,29854,2090],{"stretchy":2083},[2092,29856,28998],{"encoding":2094},[92,29858,29859,29862,29863,835,29882,17525,29907,195],{},[95,29860,29861],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[1647,29864,29866],{"className":29865},[2059],[2061,29867,29868],{"xmlns":2063},[2065,29869,29870,29880],{},[2068,29871,29872,29874,29876,29878],{},[2071,29873,543],{},[2075,29875,2084],{"stretchy":2083},[2071,29877,9214],{},[2075,29879,2090],{"stretchy":2083},[2092,29881,24958],{"encoding":2094},[1647,29883,29885],{"className":29884},[2059],[2061,29886,29887],{"xmlns":2063},[2065,29888,29889,29905],{},[2068,29890,29891,29897,29899,29901,29903],{},[2348,29892,29893,29895],{},[2071,29894,9214],{},[2071,29896,4271],{},[2075,29898,2077],{},[2071,29900,9214],{},[2075,29902,2303],{},[2071,29904,543],{},[2092,29906,24457],{"encoding":2094},[1647,29908,29910],{"className":29909},[2059],[2061,29911,29912],{"xmlns":2063},[2065,29913,29914,29930],{},[2068,29915,29916,29918,29920,29922,29924,29926,29928],{},[2071,29917,9214],{},[2075,29919,2077],{},[2071,29921,2849],{},[2075,29923,2176],{},[2071,29925,13919],{},[2075,29927,2176],{},[2071,29929,13845],{},[2092,29931,24428],{"encoding":2094},[92,29933,29934,29937,29938,29959,29960,17525,29984,195],{},[95,29935,29936],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[1647,29939,29941],{"className":29940},[2059],[2061,29942,29943],{"xmlns":2063},[2065,29944,29945,29957],{},[2068,29946,29947,29949,29951,29953,29955],{},[2071,29948,14055],{},[2075,29950,2077],{},[2071,29952,25992],{},[2075,29954,2303],{},[2071,29956,2890],{},[2092,29958,25999],{"encoding":2094},", importem ",[1647,29961,29963],{"className":29962},[2059],[2061,29964,29965],{"xmlns":2063},[2065,29966,29967,29981],{},[2068,29968,29969,29971,29973,29979],{},[2071,29970,2890],{},[2075,29972,2084],{"stretchy":2083},[2348,29974,29975,29977],{},[2071,29976,9214],{},[2071,29978,4271],{},[2075,29980,2090],{"stretchy":2083},[2092,29982,29983],{"encoding":2094},"M(Y_D)",[1647,29985,29987],{"className":29986},[2059],[2061,29988,29989],{"xmlns":2063},[2065,29990,29991,30015],{},[2068,29992,29993,29995,29997,29999,30001,30003,30005,30007,30009,30011,30013],{},[2071,29994,9214],{},[2075,29996,2077],{},[2071,29998,2849],{},[2075,30000,2176],{},[2071,30002,13919],{},[2075,30004,2176],{},[2071,30006,13845],{},[2075,30008,2176],{},[2071,30010,25992],{},[2075,30012,2303],{},[2071,30014,2890],{},[2092,30016,30017],{"encoding":2094},"Y = C + I + G + B - M",[92,30019,30020,7102,30023,29212],{},[95,30021,30022],{},"Multiplikátor investic",[1647,30024,30026],{"className":30025},[2059],[2061,30027,30028],{"xmlns":2063},[2065,30029,30030,30078],{},[2068,30031,30032,30034,30040,30042,30044,30050,30052,30054,30056,30058,30060,30062,30064,30066,30068,30070,30072,30074,30076],{},[2071,30033,11003],{"mathvariant":2450},[2205,30035,30036,30038],{},[2071,30037,9214],{},[2071,30039,554],{},[2071,30041,4761],{"mathvariant":2450},[2071,30043,11003],{"mathvariant":2450},[2205,30045,30046,30048],{},[2071,30047,13919],{},[2075,30049,4441],{},[2075,30051,2077],{},[2210,30053,638],{},[2071,30055,4761],{"mathvariant":2450},[2075,30057,2084],{"stretchy":2083},[2210,30059,638],{},[2075,30061,2303],{},[2071,30063,69],{},[2075,30065,2090],{"stretchy":2083},[2075,30067,2077],{},[2210,30069,638],{},[2071,30071,4761],{"mathvariant":2450},[2071,30073,2890],{},[2071,30075,575],{},[2071,30077,532],{},[2092,30079,29211],{"encoding":2094},[92,30081,30082,7102,30113,835,30130,30147],{},[95,30083,17460,30084],{},[1647,30085,30087],{"className":30086},[2059],[2061,30088,30089],{"xmlns":2063},[2065,30090,30091,30111],{},[2068,30092,30093,30095,30097,30099,30101,30103,30105,30107,30109],{},[2071,30094,13919],{},[2075,30096,2084],{"stretchy":2083},[2071,30098,13774],{},[2075,30100,2090],{"stretchy":2083},[2075,30102,2077],{},[2071,30104,2222],{},[2071,30106,13774],{},[2075,30108,2176],{},[2071,30110,2273],{},[2092,30112,17490],{"encoding":2094},[1647,30114,30116],{"className":30115},[2059],[2061,30117,30118],{"xmlns":2063},[2065,30119,30120,30128],{},[2068,30121,30122,30124,30126],{},[2071,30123,2222],{},[2075,30125,3521],{},[2210,30127,630],{},[2092,30129,14250],{"encoding":2094},[1647,30131,30133],{"className":30132},[2059],[2061,30134,30135],{"xmlns":2063},[2065,30136,30137,30145],{},[2068,30138,30139,30141,30143],{},[2071,30140,2273],{},[2075,30142,3482],{},[2210,30144,630],{},[2092,30146,14229],{"encoding":2094},"; klesající.",[92,30149,30150,30152,30153,30155,30156,30205],{},[95,30151,17579],{}," — rovnováha na trhu zboží (",[3982,30154,13787],{},"); ",[1647,30157,30159],{"className":30158},[2059],[2061,30160,30161],{"xmlns":2063},[2065,30162,30163,30203],{},[2068,30164,30165,30167,30169,30181,30183,30185],{},[2071,30166,9214],{},[2075,30168,2077],{},[2403,30170,30171,30173],{},[2071,30172,2222],{},[2068,30174,30175,30177,30179],{},[2210,30176,638],{},[2075,30178,2303],{},[2071,30180,69],{},[2071,30182,13774],{},[2075,30184,2176],{},[2403,30186,30187,30195],{},[2068,30188,30189,30191,30193],{},[2071,30190,2179],{},[2075,30192,2176],{},[2071,30194,2273],{},[2068,30196,30197,30199,30201],{},[2210,30198,638],{},[2075,30200,2303],{},[2071,30202,69],{},[2092,30204,17632],{"encoding":2094}," (7.14); klesající.",[92,30207,30208,30210,30211,30155,30213,30258],{},[95,30209,17778],{}," — rovnováha na trhu peněz (",[3982,30212,13794],{},[1647,30214,30216],{"className":30215},[2059],[2061,30217,30218],{"xmlns":2063},[2065,30219,30220,30256],{},[2068,30221,30222,30228,30230,30236,30238,30240,30246,30248,30250],{},[2205,30223,30224,30226],{},[2071,30225,2890],{},[2075,30227,4441],{},[2075,30229,2077],{},[2348,30231,30232,30234],{},[2071,30233,14972],{},[2210,30235,638],{},[2071,30237,9214],{},[2075,30239,2176],{},[2348,30241,30242,30244],{},[2071,30243,14972],{},[2210,30245,646],{},[2071,30247,13774],{},[2075,30249,2176],{},[2348,30251,30252,30254],{},[2071,30253,14972],{},[2210,30255,654],{},[2092,30257,17826],{"encoding":2094}," (7.15); rostoucí.",[92,30260,30261,7102,30264,195],{},[95,30262,30263],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[1647,30265,30267],{"className":30266},[2059],[2061,30268,30269],{"xmlns":2063},[2065,30270,30271,30295],{},[2068,30272,30273,30279,30281,30287,30289],{},[2205,30274,30275,30277],{},[2071,30276,2890],{},[2071,30278,4271],{},[2075,30280,2077],{},[2348,30282,30283,30285],{},[2071,30284,586],{},[2210,30286,638],{},[2075,30288,2176],{},[2348,30290,30291,30293],{},[2071,30292,586],{},[2210,30294,646],{},[2092,30296,30297],{"encoding":2094},"M^D = L_1 + L_2",[92,30299,30300,17836,30302,15715,30315,75,30330,30345,30346,195],{},[95,30301,28578],{},[1647,30303,30305],{"className":30304},[2059],[2061,30306,30307],{"xmlns":2063},[2065,30308,30309,30313],{},[2068,30310,30311],{},[2071,30312,554],{},[2092,30314,554],{"encoding":2094},[1647,30316,30318],{"className":30317},[2059],[2061,30319,30320],{"xmlns":2063},[2065,30321,30322,30328],{},[2068,30323,30324,30326],{},[2071,30325,13919],{},[2071,30327,532],{},[2092,30329,13784],{"encoding":2094},[1647,30331,30333],{"className":30332},[2059],[2061,30334,30335],{"xmlns":2063},[2065,30336,30337,30343],{},[2068,30338,30339,30341],{},[2071,30340,586],{},[2071,30342,2890],{},[2092,30344,13791],{"encoding":2094}," určuje ",[1647,30347,30349],{"className":30348},[2059],[2061,30350,30351],{"xmlns":2063},[2065,30352,30353,30373],{},[2068,30354,30355,30357,30363,30365,30371],{},[2075,30356,2084],{"stretchy":2083},[2205,30358,30359,30361],{},[2071,30360,9214],{},[2071,30362,554],{},[2075,30364,2361],{"separator":2360},[2205,30366,30367,30369],{},[2071,30368,13774],{},[2071,30370,554],{},[2075,30372,2090],{"stretchy":2083},[2092,30374,13828],{"encoding":2094},[84,30376,3866],{"id":3865},[89,30378,30379,30386,30393],{},[92,30380,30381,1445,30383],{},[95,30382,17937],{},[69,30384,17941],{"className":30385,"dataFsResolvedFilePath":2034,"href":2035},[62],[92,30387,30388,1445,30390],{},[95,30389,17946],{},[69,30391,17952],{"className":30392,"dataFsResolvedFilePath":17950,"href":17951},[62],[92,30394,30395,30397],{},[95,30396,17967],{},[89,30398,30399,30405,30411,30417],{},[92,30400,30401,30404],{},[69,30402,18009],{"className":30403,"dataFsResolvedFilePath":28576,"href":28577},[62]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[92,30406,30407,30410],{},[69,30408,17975],{"className":30409,"dataFsResolvedFilePath":13670,"href":13671},[62]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[92,30412,30413,30416],{},[69,30414,3024],{"className":30415,"dataFsResolvedFilePath":3022,"href":3023},[62]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[92,30418,30419,30422,30423,835,30440,30457],{},[69,30420,2430],{"className":30421,"dataFsResolvedFilePath":4005,"href":4006},[62]," — matematický základ pro ",[1647,30424,30426],{"className":30425},[2059],[2061,30427,30428],{"xmlns":2063},[2065,30429,30430,30438],{},[2068,30431,30432,30434,30436],{},[2071,30433,2890],{},[2071,30435,575],{},[2071,30437,2849],{},[2092,30439,20784],{"encoding":2094},[1647,30441,30443],{"className":30442},[2059],[2061,30444,30445],{"xmlns":2063},[2065,30446,30447,30455],{},[2068,30448,30449,30451,30453],{},[2071,30450,2890],{},[2071,30452,575],{},[2071,30454,532],{},[2092,30456,22398],{"encoding":2094}," a interpretaci změn diferenciálem",{"title":156,"searchDepth":7,"depth":7,"links":30459},[30460,30461,30462,30463,30468,30471,30472,30479,30484,30489,30492,30493,30494,30495],{"id":13738,"depth":7,"text":13739},{"id":20893,"depth":7,"text":20894},{"id":21013,"depth":7,"text":21014},{"id":21266,"depth":7,"text":21267,"children":30464},[30465,30466,30467],{"id":21270,"depth":4,"text":21271},{"id":21482,"depth":4,"text":21483},{"id":21990,"depth":4,"text":21991},{"id":22310,"depth":7,"text":22311,"children":30469},[30470],{"id":22826,"depth":4,"text":22827},{"id":23321,"depth":7,"text":23322},{"id":23348,"depth":7,"text":23349,"children":30473},[30474,30475,30476,30478],{"id":23359,"depth":4,"text":23360},{"id":23429,"depth":4,"text":23430},{"id":23613,"depth":4,"text":30477},"Výpočet YEY^E",{"id":23756,"depth":4,"text":23757},{"id":24134,"depth":7,"text":24135,"children":30480},[30481,30482,30483],{"id":24138,"depth":4,"text":23360},{"id":24587,"depth":4,"text":23430},{"id":25243,"depth":4,"text":25244},{"id":26030,"depth":7,"text":26031,"children":30485},[30486,30487,30488],{"id":26034,"depth":4,"text":23360},{"id":26179,"depth":4,"text":23430},{"id":26449,"depth":4,"text":26450},{"id":27372,"depth":7,"text":27373,"children":30490},[30491],{"id":27568,"depth":4,"text":27569},{"id":28118,"depth":7,"text":28119},{"id":28581,"depth":7,"text":28582},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":20596,"description":156},[9647,18006],"topics\u002Fnarodni-duchod",[17,17961,34,30502,30503,30504,18009,20622],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":30507,"title":18494,"body":30508,"course":163,"courses":30774,"created":795,"description":156,"extension":166,"meta":30775,"navigation":168,"path":30776,"seo":30777,"sources":30778,"stem":30782,"tags":30783,"type":177,"updated":178,"__hash__":30790},"topics\u002Ftopics\u002Fochrana-dat.md",{"type":48,"value":30509,"toc":30760},[30510,30513,30520,30523,30527,30587,30591,30595,30606,30610,30621,30625,30633,30637,30648,30652,30657,30661,30672,30676,30696,30698,30733,30738],[51,30511,18494],{"id":30512},"ochrana-dat",[55,30514,30515],{},[58,30516],{"alt":30517,"className":30518,"src":30519},"ochrana-dat-technologie",[62,63],"\u002Fwiki-assets\u002Fochrana-dat-technologie.jpeg",[55,30521,30522],{},"Technologická řešení pro zabezpečení dat v interní infrastruktuře i kyberprostoru. Zahrnuje síťové, aplikační i datové bezpečnostní mechanismy.",[84,30524,30526],{"id":30525},"formy-zneužití-dat","Formy zneužití dat",[323,30528,30529,30538],{},[326,30530,30531],{},[329,30532,30533,30536],{},[332,30534,30535],{},"Forma",[332,30537,340],{},[342,30539,30540,30547,30555,30563,30571,30579],{},[329,30541,30542,30545],{},[347,30543,30544],{},"Zašifrování",[347,30546,18756],{},[329,30548,30549,30552],{},[347,30550,30551],{},"Zveřejnění",[347,30553,30554],{},"Double ransomware",[329,30556,30557,30560],{},[347,30558,30559],{},"Odposlech",[347,30561,30562],{},"Pasivní sběr dat",[329,30564,30565,30568],{},[347,30566,30567],{},"Krádež",[347,30569,30570],{},"Cílená exfiltrace",[329,30572,30573,30576],{},[347,30574,30575],{},"Krádež dodavatelského řetězce",[347,30577,30578],{},"Triple ransomware",[329,30580,30581,30584],{},[347,30582,30583],{},"Prodej",[347,30585,30586],{},"Darknet marketplace",[84,30588,30590],{"id":30589},"bezpečnostní-technologie","Bezpečnostní technologie",[609,30592,30594],{"id":30593},"nac-network-access-control","NAC (Network Access Control)",[89,30596,30597,30600,30603],{},[92,30598,30599],{},"Proaktivní ochrana sítě před neautorizovaným přístupem",[92,30601,30602],{},"4 fáze: detekce → autentizace → vyhodnocení → autorizace",[92,30604,30605],{},"Ekvivalenty: MDM, BYOD",[609,30607,30609],{"id":30608},"ids-intrusion-detection-system","IDS (Intrusion Detection System)",[89,30611,30612,30615,30618],{},[92,30613,30614],{},"Monitoruje síťový provoz, generuje alerty",[92,30616,30617],{},"Pasivní systém — nezasahuje do provozu",[92,30619,30620],{},"Signaturová a anomální detekce",[609,30622,30624],{"id":30623},"ips-intrusion-prevention-system","IPS (Intrusion Prevention System)",[89,30626,30627,30630],{},[92,30628,30629],{},"Aktivní systém — blokuje škodlivý provoz",[92,30631,30632],{},"Zařazen přímo do síťové cesty (in-line)",[609,30634,30636],{"id":30635},"siem-security-information-and-event-management","SIEM (Security Information and Event Management)",[89,30638,30639,30642,30645],{},[92,30640,30641],{},"Centralizovaná správa bezpečnostních logů",[92,30643,30644],{},"Sběr s agentem i bez agenta",[92,30646,30647],{},"Prioritizace: třídy zpráv, zdroje, IP adresy, četnost",[609,30649,30651],{"id":30650},"dlp-data-loss-prevention","DLP (Data Loss Prevention)",[89,30653,30654],{},[92,30655,30656],{},"Klasifikace citlivých dat a vynucení ochrany",[609,30658,30660],{"id":30659},"šifrování","Šifrování",[89,30662,30663,30666,30669],{},[92,30664,30665],{},"AES (128\u002F192\u002F256 bit), 3DES",[92,30667,30668],{},"RSA (2048+ bit), DSS",[92,30670,30671],{},"SHA-256, SHA-1",[84,30673,30675],{"id":30674},"ipv6-bezpečnost","IPv6 bezpečnost",[89,30677,30678,30684,30690,30693],{},[92,30679,30680,30683],{},[95,30681,30682],{},"AH"," (Authentication Header) — ověření odesílatele a integrity",[92,30685,30686,30689],{},[95,30687,30688],{},"ESP"," (Encapsulating Security Payload) — šifrování dat",[92,30691,30692],{},"Transportní a tunelovací režim",[92,30694,30695],{},"SPD (Security Policy Database), bezpečnostní asociace",[84,30697,723],{"id":722},[89,30699,30700,30706,30712,30718,30724],{},[92,30701,30702,30705],{},[69,30703,733],{"className":30704,"dataFsResolvedFilePath":731,"href":732},[62]," — ochrana dat jako technická vrstva ISMS",[92,30707,30708,30711],{},[69,30709,751],{"className":30710,"dataFsResolvedFilePath":749,"href":750},[62]," — kontext hrozeb",[92,30713,30714,30717],{},[69,30715,742],{"className":30716,"dataFsResolvedFilePath":740,"href":741},[62]," — hodnocení aktiv a hrozeb",[92,30719,30720,30723],{},[69,30721,18971],{"className":30722,"dataFsResolvedFilePath":18969,"href":18970},[62]," — webové útoky a obrana",[92,30725,30726,30732],{},[69,30727,30731],{"className":30728,"dataFsResolvedFilePath":30729,"href":30730},[62],"summaries\u002Fimork-email.md","\u002Fwiki\u002Fimork-email","Bezpečnost emailu"," — emailové protokoly",[84,30734,756,30735],{"id":755},[69,30736,762],{"className":30737,"dataFsResolvedFilePath":760,"href":761},[62],[89,30739,30740,30748,30754],{},[92,30741,30742],{},[69,30743,30747],{"className":30744,"dataFsResolvedFilePath":30745,"href":30746},[62],"summaries\u002Fimork-ochrana-dat.md","\u002Fwiki\u002Fimork-ochrana-dat","Ochrana dat — shrnutí přednášky",[92,30749,30750],{},[69,30751,30753],{"className":30752,"dataFsResolvedFilePath":18969,"href":18970},[62],"Bezpečnost webových služeb",[92,30755,30756],{},[69,30757,30759],{"className":30758,"dataFsResolvedFilePath":30729,"href":30730},[62],"Bezpečnost emailových služeb",{"title":156,"searchDepth":7,"depth":7,"links":30761},[30762,30763,30771,30772,30773],{"id":30525,"depth":7,"text":30526},{"id":30589,"depth":7,"text":30590,"children":30764},[30765,30766,30767,30768,30769,30770],{"id":30593,"depth":4,"text":30594},{"id":30608,"depth":4,"text":30609},{"id":30623,"depth":4,"text":30624},{"id":30635,"depth":4,"text":30636},{"id":30650,"depth":4,"text":30651},{"id":30659,"depth":4,"text":30660},{"id":30674,"depth":7,"text":30675},{"id":722,"depth":7,"text":723},{"id":755,"depth":7,"text":793},[11],{},"\u002Ftopics\u002Fochrana-dat",{"title":18494,"description":156},[30779,30780,30781],"raw\u002Fimork\u002F2017 VUT_Ochrana dat-2022.pdf","raw\u002Fimork\u002F2015 VUT_Bezp WWW-2019.pdf","raw\u002Fimork\u002F2016 VUT_Bezp Email-2022.pdf","topics\u002Fochrana-dat",[11,30512,30784,30785,30786,30787,30788,30789],"sifrovani","nac","ids","ips","dlp","gdpr","UMZ1-ocv30-Pg4Vr5J6J041nf2SKNlg1hXH3YgNhcA4",{"id":30792,"title":30793,"body":30794,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":39778,"navigation":168,"path":39779,"seo":39780,"sources":39781,"stem":39782,"tags":39783,"type":177,"updated":178,"__hash__":39788},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":48,"value":30795,"toc":39747},[30796,30799,30801,31031,31035,31088,31158,31270,31429,31433,31549,31553,31556,31678,31681,31874,31898,31966,32130,32148,32214,32592,32596,32603,32847,32903,32907,32972,33090,33222,33254,33374,33456,33459,33581,33774,33995,33999,34038,34143,34200,34300,34477,34607,34660,34663,34750,34754,34930,34934,34937,35022,35025,35082,35187,35191,35312,35315,35498,35501,35609,35818,36138,36186,36259,36333,36335,36559,36794,37062,37066,37069,37174,37231,37265,37312,37345,37429,37431,37663,37796,37873,37995,38150,38154,38295,38302,38526,38537,38541,38545,38650,38792,38902,39001,39005,39164,39274,39276,39669,39671],[51,30797,30793],{"id":30798},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[84,30800,13739],{"id":13738},[55,30802,30803,30806,30807,30841,30842,30845,30846,30877,30878,30924,30925,30928,30929,30971,30972,30990,30991,30995,30996,31026,31027,31030],{},[95,30804,30805],{},"Optimalizace spotřebitele"," řeší, jaký svazek zboží ",[1647,30808,30810],{"className":30809},[2059],[2061,30811,30812],{"xmlns":2063},[2065,30813,30814,30838],{},[2068,30815,30816,30818,30826,30828,30836],{},[2075,30817,2561],{"stretchy":2083},[9252,30819,30820,30822,30824],{},[2071,30821,2861],{},[2210,30823,638],{},[2075,30825,4441],{},[2075,30827,2361],{"separator":2360},[9252,30829,30830,30832,30834],{},[2071,30831,2861],{},[2210,30833,646],{},[2075,30835,4441],{},[2075,30837,2576],{"stretchy":2083},[2092,30839,30840],{"encoding":2094},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[95,30843,30844],{},"primární úloha"," — maximalizace užitečnosti ",[1647,30847,30849],{"className":30848},[2059],[2061,30850,30851],{"xmlns":2063},[2065,30852,30853,30875],{},[2068,30854,30855,30857,30859,30865,30867,30873],{},[2071,30856,10871],{},[2075,30858,2084],{"stretchy":2083},[2348,30860,30861,30863],{},[2071,30862,2861],{},[2210,30864,638],{},[2075,30866,2361],{"separator":2360},[2348,30868,30869,30871],{},[2071,30870,2861],{},[2210,30872,646],{},[2075,30874,2090],{"stretchy":2083},[2092,30876,19083],{"encoding":2094}," při rozpočtovém omezení ",[1647,30879,30881],{"className":30880},[2059],[2061,30882,30883],{"xmlns":2063},[2065,30884,30885,30921],{},[2068,30886,30887,30893,30895,30901,30907,30909,30915],{},[2205,30888,30889,30891],{},[2071,30890,9214],{},[2075,30892,4441],{},[2075,30894,2077],{},[2348,30896,30897,30899],{},[2071,30898,575],{},[2210,30900,638],{},[2348,30902,30903,30905],{},[2071,30904,2861],{},[2210,30906,638],{},[2075,30908,2176],{},[2348,30910,30911,30913],{},[2071,30912,575],{},[2210,30914,646],{},[2348,30916,30917,30919],{},[2071,30918,2861],{},[2210,30920,646],{},[2092,30922,30923],{"encoding":2094},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[95,30926,30927],{},"duální úloha"," — minimalizace výdajů ",[1647,30930,30932],{"className":30931},[2059],[2061,30933,30934],{"xmlns":2063},[2065,30935,30936,30968],{},[2068,30937,30938,30940,30942,30948,30954,30956,30962],{},[2071,30939,554],{},[2075,30941,2077],{},[2348,30943,30944,30946],{},[2071,30945,575],{},[2210,30947,638],{},[2348,30949,30950,30952],{},[2071,30951,2861],{},[2210,30953,638],{},[2075,30955,2176],{},[2348,30957,30958,30960],{},[2071,30959,575],{},[2210,30961,646],{},[2348,30963,30964,30966],{},[2071,30965,2861],{},[2210,30967,646],{},[2092,30969,30970],{"encoding":2094},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[1647,30973,30975],{"className":30974},[2059],[2061,30976,30977],{"xmlns":2063},[2065,30978,30979,30987],{},[2068,30980,30981],{},[2205,30982,30983,30985],{},[2071,30984,10871],{},[2075,30986,4441],{},[2092,30988,30989],{"encoding":2094},"U^*",". Obě úlohy se řeší ",[69,30992,30994],{"className":30993,"dataFsResolvedFilePath":12193,"href":12194},[62],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[1647,30997,30999],{"className":30998},[2059],[2061,31000,31001],{"xmlns":2063},[2065,31002,31003,31023],{},[2068,31004,31005,31007,31009,31015,31017],{},[2363,31006,11733],{},[2075,31008,2077],{},[2348,31010,31011,31013],{},[2071,31012,575],{},[2210,31014,638],{},[2071,31016,4761],{"mathvariant":2450},[2348,31018,31019,31021],{},[2071,31020,575],{},[2210,31022,646],{},[2092,31024,31025],{"encoding":2094},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[95,31028,31029],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[84,31032,31034],{"id":31033},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[55,31036,31037,31038,31056,31057,31087],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[1647,31039,31041],{"className":31040},[2059],[2061,31042,31043],{"xmlns":2063},[2065,31044,31045,31053],{},[2068,31046,31047],{},[2205,31048,31049,31051],{},[2071,31050,9214],{},[2075,31052,4441],{},[2092,31054,31055],{"encoding":2094},"Y^*"," a ceny ",[1647,31058,31060],{"className":31059},[2059],[2061,31061,31062],{"xmlns":2063},[2065,31063,31064,31084],{},[2068,31065,31066,31074,31076],{},[9252,31067,31068,31070,31072],{},[2071,31069,575],{},[2210,31071,638],{},[2075,31073,4441],{},[2075,31075,2361],{"separator":2360},[9252,31077,31078,31080,31082],{},[2071,31079,575],{},[2210,31081,646],{},[2075,31083,4441],{},[2092,31085,31086],{"encoding":2094},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[1647,31089,31091],{"className":31090},[2059],[2061,31092,31094],{"xmlns":2063,"display":31093},"block",[2065,31095,31096,31155],{},[23493,31097,31099],{"width":31098},"100%",[23498,31100,31101,31104,31148,31150],{},[23501,31102],{"width":31103},"50%",[23501,31105,31106],{},[2068,31107,31108,31114,31116,31124,31130,31132,31140,31146],{},[2205,31109,31110,31112],{},[2071,31111,9214],{},[2075,31113,4441],{},[2075,31115,2077],{},[9252,31117,31118,31120,31122],{},[2071,31119,575],{},[2210,31121,638],{},[2075,31123,4441],{},[2348,31125,31126,31128],{},[2071,31127,2861],{},[2210,31129,638],{},[2075,31131,2176],{},[9252,31133,31134,31136,31138],{},[2071,31135,575],{},[2210,31137,646],{},[2075,31139,4441],{},[2348,31141,31142,31144],{},[2071,31143,2861],{},[2210,31145,646],{},[2075,31147,2361],{"separator":2360},[23501,31149],{"width":31103},[23501,31151,31152],{},[2363,31153,31154],{},"(6.12)",[2092,31156,31157],{"encoding":2094},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[55,31159,31160,31161,31164,31165,75,31201,31237,31238,31251,31252,31266,31267,195],{},"geometricky ",[95,31162,31163],{},"rozpočtová přímka (budget line)"," procházející body ",[1647,31166,31168],{"className":31167},[2059],[2061,31169,31170],{"xmlns":2063},[2065,31171,31172,31198],{},[2068,31173,31174,31176,31182,31184,31192,31194,31196],{},[2075,31175,2561],{"stretchy":2083},[2205,31177,31178,31180],{},[2071,31179,9214],{},[2075,31181,4441],{},[2071,31183,4761],{"mathvariant":2450},[9252,31185,31186,31188,31190],{},[2071,31187,575],{},[2210,31189,638],{},[2075,31191,4441],{},[2075,31193,2361],{"separator":2360},[2210,31195,630],{},[2075,31197,2576],{"stretchy":2083},[2092,31199,31200],{"encoding":2094},"[Y^*\u002FP_1^*, 0]",[1647,31202,31204],{"className":31203},[2059],[2061,31205,31206],{"xmlns":2063},[2065,31207,31208,31234],{},[2068,31209,31210,31212,31214,31216,31222,31224,31232],{},[2075,31211,2561],{"stretchy":2083},[2210,31213,630],{},[2075,31215,2361],{"separator":2360},[2205,31217,31218,31220],{},[2071,31219,9214],{},[2075,31221,4441],{},[2071,31223,4761],{"mathvariant":2450},[9252,31225,31226,31228,31230],{},[2071,31227,575],{},[2210,31229,646],{},[2075,31231,4441],{},[2075,31233,2576],{"stretchy":2083},[2092,31235,31236],{"encoding":2094},"[0, Y^*\u002FP_2^*]",". Spotřebitel chce v rámci této přímky (a pod ní) najít svazek s nejvyšší dostupnou užitečností. Teorie před optimalizací — tvar funkce ",[1647,31239,31241],{"className":31240},[2059],[2061,31242,31243],{"xmlns":2063},[2065,31244,31245,31249],{},[2068,31246,31247],{},[2071,31248,10871],{},[2092,31250,10871],{"encoding":2094},", indiferenční křivky a ",[1647,31253,31255],{"className":31254},[2059],[2061,31256,31257],{"xmlns":2063},[2065,31258,31259,31263],{},[2068,31260,31261],{},[2363,31262,11733],{},[2092,31264,31265],{"encoding":2094},"\\text{MRCS}"," — je shrnuta v ",[69,31268,12226],{"className":31269,"dataFsResolvedFilePath":10901,"href":10902},[62],[1023,31271,31272],{},[55,31273,31274,31276,31277,31280,31281,31294,31295,31297,31298,31311,31312,1445,31315,31355,31356,31373,31374,31391,31392,31409,31410,31428],{},[1647,31275,4499],{}," Pozor — dvě úlohy, totéž řešení\n",[95,31278,31279],{},"Primární úloha"," (max ",[1647,31282,31284],{"className":31283},[2059],[2061,31285,31286],{"xmlns":2063},[2065,31287,31288,31292],{},[2068,31289,31290],{},[2071,31291,10871],{},[2092,31293,10871],{"encoding":2094}," při pevném rozpočtu) a ",[95,31296,30927],{}," (min ",[1647,31299,31301],{"className":31300},[2059],[2061,31302,31303],{"xmlns":2063},[2065,31304,31305,31309],{},[2068,31306,31307],{},[2071,31308,554],{},[2092,31310,554],{"encoding":2094}," při pevné užitečnosti) vedou na ",[95,31313,31314],{},"tentýž bod",[1647,31316,31318],{"className":31317},[2059],[2061,31319,31320],{"xmlns":2063},[2065,31321,31322,31352],{},[2068,31323,31324,31330,31332,31340,31342,31350],{},[2205,31325,31326,31328],{},[2071,31327,2861],{},[2075,31329,4441],{},[2075,31331,2561],{"stretchy":2083},[9252,31333,31334,31336,31338],{},[2071,31335,2861],{},[2210,31337,638],{},[2075,31339,4441],{},[2075,31341,2361],{"separator":2360},[9252,31343,31344,31346,31348],{},[2071,31345,2861],{},[2210,31347,646],{},[2075,31349,4441],{},[2075,31351,2576],{"stretchy":2083},[2092,31353,31354],{"encoding":2094},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[1647,31357,31359],{"className":31358},[2059],[2061,31360,31361],{"xmlns":2063},[2065,31362,31363,31371],{},[2068,31364,31365],{},[2205,31366,31367,31369],{},[2071,31368,9214],{},[2075,31370,4441],{},[2092,31372,31055],{"encoding":2094}," a hledáme maximální ",[1647,31375,31377],{"className":31376},[2059],[2061,31378,31379],{"xmlns":2063},[2065,31380,31381,31389],{},[2068,31382,31383],{},[2205,31384,31385,31387],{},[2071,31386,10871],{},[2075,31388,4441],{},[2092,31390,30989],{"encoding":2094},"; u duální úlohy je zadána hladina ",[1647,31393,31395],{"className":31394},[2059],[2061,31396,31397],{"xmlns":2063},[2065,31398,31399,31407],{},[2068,31400,31401],{},[2205,31402,31403,31405],{},[2071,31404,10871],{},[2075,31406,4441],{},[2092,31408,30989],{"encoding":2094}," a hledáme minimální ",[1647,31411,31413],{"className":31412},[2059],[2061,31414,31415],{"xmlns":2063},[2065,31416,31417,31425],{},[2068,31418,31419],{},[2205,31420,31421,31423],{},[2071,31422,554],{},[2075,31424,4441],{},[2092,31426,31427],{"encoding":2094},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[84,31430,31432],{"id":31431},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[55,31434,31435,31436,31467,31468,31544,31545,195],{},"Úlohou je najít maximum ",[1647,31437,31439],{"className":31438},[2059],[2061,31440,31441],{"xmlns":2063},[2065,31442,31443,31465],{},[2068,31444,31445,31447,31449,31455,31457,31463],{},[2071,31446,10871],{},[2075,31448,2084],{"stretchy":2083},[2348,31450,31451,31453],{},[2071,31452,2861],{},[2210,31454,638],{},[2075,31456,2361],{"separator":2360},[2348,31458,31459,31461],{},[2071,31460,2861],{},[2210,31462,646],{},[2075,31464,2090],{"stretchy":2083},[2092,31466,19083],{"encoding":2094}," vázané podmínkou (6.12) ve tvaru ",[1647,31469,31471],{"className":31470},[2059],[2061,31472,31473],{"xmlns":2063},[2065,31474,31475,31541],{},[2068,31476,31477,31479,31481,31487,31489,31495,31497,31499,31505,31507,31515,31521,31523,31531,31537,31539],{},[2071,31478,12171],{},[2075,31480,2084],{"stretchy":2083},[2348,31482,31483,31485],{},[2071,31484,2861],{},[2210,31486,638],{},[2075,31488,2361],{"separator":2360},[2348,31490,31491,31493],{},[2071,31492,2861],{},[2210,31494,646],{},[2075,31496,2090],{"stretchy":2083},[2075,31498,2077],{},[2205,31500,31501,31503],{},[2071,31502,9214],{},[2075,31504,4441],{},[2075,31506,2303],{},[9252,31508,31509,31511,31513],{},[2071,31510,575],{},[2210,31512,638],{},[2075,31514,4441],{},[2348,31516,31517,31519],{},[2071,31518,2861],{},[2210,31520,638],{},[2075,31522,2303],{},[9252,31524,31525,31527,31529],{},[2071,31526,575],{},[2210,31528,646],{},[2075,31530,4441],{},[2348,31532,31533,31535],{},[2071,31534,2861],{},[2210,31536,646],{},[2075,31538,2077],{},[2210,31540,630],{},[2092,31542,31543],{"encoding":2094},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[69,31546,31548],{"className":31547,"dataFsResolvedFilePath":12193,"href":12194},[62],"metodu Lagrangeových multiplikátorů",[609,31550,31552],{"id":31551},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[55,31554,31555],{},"Sestavíme",[1647,31557,31559],{"className":31558},[2059],[2061,31560,31561],{"xmlns":2063,"display":31093},[2065,31562,31563,31675],{},[23493,31564,31565],{"width":31098},[23498,31566,31567,31569,31668,31670],{},[23501,31568],{"width":31103},[23501,31570,31571],{},[2068,31572,31573,31576,31578,31584,31586,31592,31594,31596,31598,31600,31602,31604,31610,31612,31618,31620,31622,31624,31626,31632,31634,31642,31648,31650,31658,31664,31666],{},[2071,31574,586],{"mathvariant":31575},"script",[2075,31577,2084],{"stretchy":2083},[2348,31579,31580,31582],{},[2071,31581,2861],{},[2210,31583,638],{},[2075,31585,2361],{"separator":2360},[2348,31587,31588,31590],{},[2071,31589,2861],{},[2210,31591,646],{},[2075,31593,2361],{"separator":2360},[2071,31595,19181],{},[2075,31597,2090],{"stretchy":2083},[2075,31599,2077],{},[2071,31601,10871],{},[2075,31603,2084],{"stretchy":2083},[2348,31605,31606,31608],{},[2071,31607,2861],{},[2210,31609,638],{},[2075,31611,2361],{"separator":2360},[2348,31613,31614,31616],{},[2071,31615,2861],{},[2210,31617,646],{},[2075,31619,2090],{"stretchy":2083},[2075,31621,2176],{},[2071,31623,19181],{},[2075,31625,2084],{"stretchy":2083},[2205,31627,31628,31630],{},[2071,31629,9214],{},[2075,31631,4441],{},[2075,31633,2303],{},[9252,31635,31636,31638,31640],{},[2071,31637,575],{},[2210,31639,638],{},[2075,31641,4441],{},[2348,31643,31644,31646],{},[2071,31645,2861],{},[2210,31647,638],{},[2075,31649,2303],{},[9252,31651,31652,31654,31656],{},[2071,31653,575],{},[2210,31655,646],{},[2075,31657,4441],{},[2348,31659,31660,31662],{},[2071,31661,2861],{},[2210,31663,646],{},[2075,31665,2090],{"stretchy":2083},[2071,31667,195],{"mathvariant":2450},[23501,31669],{"width":31103},[23501,31671,31672],{},[2363,31673,31674],{},"(6.13)",[2092,31676,31677],{"encoding":2094},"\\mathcal{L}(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2). \\tag{6.13}",[55,31679,31680],{},"Soustava prvního řádu:",[1647,31682,31684],{"className":31683},[2059],[2061,31685,31686],{"xmlns":2063,"display":31093},[2065,31687,31688,31871],{},[23493,31689,31690],{"width":31098},[23498,31691,31692,31694,31864,31866],{},[23501,31693],{"width":31103},[23501,31695,31696],{},[23493,31697,31698,31748,31798],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,31699,31700,31712],{},[23501,31701,31702],{},[2400,31703,31704],{"scriptlevel":630,"displaystyle":2360},[9252,31705,31706,31708,31710],{},[2071,31707,586],{"mathvariant":31575},[2210,31709,638],{},[2075,31711,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,31713,31714],{},[2400,31715,31716],{"scriptlevel":630,"displaystyle":2360},[2068,31717,31718,31720,31722,31730,31732,31734,31742,31744,31746],{},[2068,31719],{},[2075,31721,2077],{},[9252,31723,31724,31726,31728],{},[2071,31725,10871],{},[2210,31727,638],{},[2075,31729,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,31731,2303],{},[2071,31733,19181],{},[9252,31735,31736,31738,31740],{},[2071,31737,575],{},[2210,31739,638],{},[2075,31741,4441],{},[2075,31743,2077],{},[2210,31745,630],{},[2075,31747,2361],{"separator":2360},[23498,31749,31750,31762],{},[23501,31751,31752],{},[2400,31753,31754],{"scriptlevel":630,"displaystyle":2360},[9252,31755,31756,31758,31760],{},[2071,31757,586],{"mathvariant":31575},[2210,31759,646],{},[2075,31761,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,31763,31764],{},[2400,31765,31766],{"scriptlevel":630,"displaystyle":2360},[2068,31767,31768,31770,31772,31780,31782,31784,31792,31794,31796],{},[2068,31769],{},[2075,31771,2077],{},[9252,31773,31774,31776,31778],{},[2071,31775,10871],{},[2210,31777,646],{},[2075,31779,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,31781,2303],{},[2071,31783,19181],{},[9252,31785,31786,31788,31790],{},[2071,31787,575],{},[2210,31789,646],{},[2075,31791,4441],{},[2075,31793,2077],{},[2210,31795,630],{},[2075,31797,2361],{"separator":2360},[23498,31799,31800,31812],{},[23501,31801,31802],{},[2400,31803,31804],{"scriptlevel":630,"displaystyle":2360},[9252,31805,31806,31808,31810],{},[2071,31807,586],{"mathvariant":31575},[2071,31809,19181],{},[2075,31811,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,31813,31814],{},[2400,31815,31816],{"scriptlevel":630,"displaystyle":2360},[2068,31817,31818,31820,31822,31828,31830,31838,31844,31846,31854,31860,31862],{},[2068,31819],{},[2075,31821,2077],{},[2205,31823,31824,31826],{},[2071,31825,9214],{},[2075,31827,4441],{},[2075,31829,2303],{},[9252,31831,31832,31834,31836],{},[2071,31833,575],{},[2210,31835,638],{},[2075,31837,4441],{},[2348,31839,31840,31842],{},[2071,31841,2861],{},[2210,31843,638],{},[2075,31845,2303],{},[9252,31847,31848,31850,31852],{},[2071,31849,575],{},[2210,31851,646],{},[2075,31853,4441],{},[2348,31855,31856,31858],{},[2071,31857,2861],{},[2210,31859,646],{},[2075,31861,2077],{},[2210,31863,14195],{},[23501,31865],{"width":31103},[23501,31867,31868],{},[2363,31869,31870],{},"(6.14)",[2092,31872,31873],{"encoding":2094},"\\begin{aligned}\n\\mathcal{L}'_1 &= U'_1 - \\lambda P_1^* = 0, \\\\\n\\mathcal{L}'_2 &= U'_2 - \\lambda P_2^* = 0, \\\\\n\\mathcal{L}'_\\lambda &= Y^* - P_1^* Q_1 - P_2^* Q_2 = 0.\n\\end{aligned}\n\\tag{6.14}",[55,31875,31876,31877,31880,31881,31894,31895,2777],{},"Díky konvexitě indiferenčních křivek je řešení ",[95,31878,31879],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[1647,31882,31884],{"className":31883},[2059],[2061,31885,31886],{"xmlns":2063},[2065,31887,31888,31892],{},[2068,31889,31890],{},[2071,31891,19181],{},[2092,31893,19234],{"encoding":2094}," dostáváme ",[95,31896,31897],{},"podmínku optimality",[1647,31899,31901],{"className":31900},[2059],[2061,31902,31903],{"xmlns":2063,"display":31093},[2065,31904,31905,31963],{},[2068,31906,31907],{},[14567,31908,31909],{"notation":14569},[2400,31910,31911],{"scriptlevel":630,"displaystyle":2083},[2400,31912,31913],{"scriptlevel":630,"displaystyle":2083},[2400,31914,31915],{"scriptlevel":630,"displaystyle":2360},[2068,31916,31917,31919,31921,31923,31941,31943,31961],{},[2363,31918,4072],{},[2363,31920,11733],{},[2075,31922,2077],{},[2403,31924,31925,31933],{},[9252,31926,31927,31929,31931],{},[2071,31928,10871],{},[2210,31930,638],{},[2075,31932,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,31934,31935,31937,31939],{},[2071,31936,10871],{},[2210,31938,646],{},[2075,31940,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,31942,2077],{},[2403,31944,31945,31953],{},[9252,31946,31947,31949,31951],{},[2071,31948,575],{},[2210,31950,638],{},[2075,31952,4441],{},[9252,31954,31955,31957,31959],{},[2071,31956,575],{},[2210,31958,646],{},[2075,31960,4441],{},[2363,31962,4072],{},[2092,31964,31965],{"encoding":2094},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1023,31967,31968],{},[55,31969,31970,31972,31973,32007,32008,32011,32012,32030,32031,32049,32050,32080,32081,32098,32099,32129],{},[1647,31971,4243],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[1647,31974,31976],{"className":31975},[2059],[2061,31977,31978],{"xmlns":2063},[2065,31979,31980,32004],{},[2068,31981,31982,31984,31986,31994,31996],{},[2363,31983,11733],{},[2075,31985,2077],{},[9252,31987,31988,31990,31992],{},[2071,31989,575],{},[2210,31991,638],{},[2075,31993,4441],{},[2071,31995,4761],{"mathvariant":2450},[9252,31997,31998,32000,32002],{},[2071,31999,575],{},[2210,32001,646],{},[2075,32003,4441],{},[2092,32005,32006],{"encoding":2094},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[95,32009,32010],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[1647,32013,32015],{"className":32014},[2059],[2061,32016,32017],{"xmlns":2063},[2065,32018,32019,32027],{},[2068,32020,32021],{},[2348,32022,32023,32025],{},[2071,32024,2861],{},[2210,32026,638],{},[2092,32028,32029],{"encoding":2094},"Q_1"," za ",[1647,32032,32034],{"className":32033},[2059],[2061,32035,32036],{"xmlns":2063},[2065,32037,32038,32046],{},[2068,32039,32040],{},[2348,32041,32042,32044],{},[2071,32043,2861],{},[2210,32045,646],{},[2092,32047,32048],{"encoding":2094},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[1647,32051,32053],{"className":32052},[2059],[2061,32054,32055],{"xmlns":2063},[2065,32056,32057,32077],{},[2068,32058,32059,32061,32063,32069,32071],{},[2363,32060,11733],{},[2075,32062,3482],{},[2348,32064,32065,32067],{},[2071,32066,575],{},[2210,32068,638],{},[2071,32070,4761],{"mathvariant":2450},[2348,32072,32073,32075],{},[2071,32074,575],{},[2210,32076,646],{},[2092,32078,32079],{"encoding":2094},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[1647,32082,32084],{"className":32083},[2059],[2061,32085,32086],{"xmlns":2063},[2065,32087,32088,32096],{},[2068,32089,32090],{},[2348,32091,32092,32094],{},[2071,32093,2861],{},[2210,32095,638],{},[2092,32097,32029],{"encoding":2094}," (subjektivní ocenění převažuje nad tržním); kdyby ",[1647,32100,32102],{"className":32101},[2059],[2061,32103,32104],{"xmlns":2063},[2065,32105,32106,32126],{},[2068,32107,32108,32110,32112,32118,32120],{},[2363,32109,11733],{},[2075,32111,3521],{},[2348,32113,32114,32116],{},[2071,32115,575],{},[2210,32117,638],{},[2071,32119,4761],{"mathvariant":2450},[2348,32121,32122,32124],{},[2071,32123,575],{},[2210,32125,646],{},[2092,32127,32128],{"encoding":2094},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[609,32131,32133,32134,32147],{"id":32132},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[1647,32135,32137],{"className":32136},[2059],[2061,32138,32139],{"xmlns":2063},[2065,32140,32141,32145],{},[2068,32142,32143],{},[2071,32144,19181],{},[2092,32146,19234],{"encoding":2094}," — mezní užitečnost důchodu",[55,32149,32150,32151,32169,32170,32173,32174,32191,32192,32209,32210,32213],{},"Lagrangeův multiplikátor ",[1647,32152,32154],{"className":32153},[2059],[2061,32155,32156],{"xmlns":2063},[2065,32157,32158,32166],{},[2068,32159,32160],{},[2205,32161,32162,32164],{},[2071,32163,19181],{},[2075,32165,4441],{},[2092,32167,32168],{"encoding":2094},"\\lambda^*"," představuje ",[95,32171,32172],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[1647,32175,32177],{"className":32176},[2059],[2061,32178,32179],{"xmlns":2063},[2065,32180,32181,32189],{},[2068,32182,32183],{},[2205,32184,32185,32187],{},[2071,32186,10871],{},[2075,32188,4441],{},[2092,32190,30989],{"encoding":2094}," při jednotkové změně důchodu ",[1647,32193,32195],{"className":32194},[2059],[2061,32196,32197],{"xmlns":2063},[2065,32198,32199,32207],{},[2068,32200,32201],{},[2205,32202,32203,32205],{},[2071,32204,9214],{},[2075,32206,4441],{},[2092,32208,31055],{"encoding":2094},". Je to ",[95,32211,32212],{},"stínová cena"," rozpočtového omezení.",[1023,32215,32216,32221],{},[55,32217,32218,32220],{},[1647,32219,4659],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[201,32222,32223,32283,32370,32406,32493],{},[92,32224,32225,32228,32229,195],{},[95,32226,32227],{},"Zapiš rozpočtové omezení"," ve tvaru ",[1647,32230,32232],{"className":32231},[2059],[2061,32233,32234],{"xmlns":2063},[2065,32235,32236,32280],{},[2068,32237,32238,32244,32246,32254,32260,32262,32270,32276,32278],{},[2205,32239,32240,32242],{},[2071,32241,9214],{},[2075,32243,4441],{},[2075,32245,2303],{},[9252,32247,32248,32250,32252],{},[2071,32249,575],{},[2210,32251,638],{},[2075,32253,4441],{},[2348,32255,32256,32258],{},[2071,32257,2861],{},[2210,32259,638],{},[2075,32261,2303],{},[9252,32263,32264,32266,32268],{},[2071,32265,575],{},[2210,32267,646],{},[2075,32269,4441],{},[2348,32271,32272,32274],{},[2071,32273,2861],{},[2210,32275,646],{},[2075,32277,2077],{},[2210,32279,630],{},[2092,32281,32282],{"encoding":2094},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[92,32284,32285,1445,32288,195],{},[95,32286,32287],{},"Sestav Lagrangeovu funkci",[1647,32289,32291],{"className":32290},[2059],[2061,32292,32293],{"xmlns":2063},[2065,32294,32295,32367],{},[2068,32296,32297,32299,32301,32303,32305,32311,32313,32319,32321,32323,32325,32327,32333,32335,32343,32349,32351,32359,32365],{},[2071,32298,586],{"mathvariant":31575},[2075,32300,2077],{},[2071,32302,10871],{},[2075,32304,2084],{"stretchy":2083},[2348,32306,32307,32309],{},[2071,32308,2861],{},[2210,32310,638],{},[2075,32312,2361],{"separator":2360},[2348,32314,32315,32317],{},[2071,32316,2861],{},[2210,32318,646],{},[2075,32320,2090],{"stretchy":2083},[2075,32322,2176],{},[2071,32324,19181],{},[2075,32326,2084],{"stretchy":2083},[2205,32328,32329,32331],{},[2071,32330,9214],{},[2075,32332,4441],{},[2075,32334,2303],{},[9252,32336,32337,32339,32341],{},[2071,32338,575],{},[2210,32340,638],{},[2075,32342,4441],{},[2348,32344,32345,32347],{},[2071,32346,2861],{},[2210,32348,638],{},[2075,32350,2303],{},[9252,32352,32353,32355,32357],{},[2071,32354,575],{},[2210,32356,646],{},[2075,32358,4441],{},[2348,32360,32361,32363],{},[2071,32362,2861],{},[2210,32364,646],{},[2075,32366,2090],{"stretchy":2083},[2092,32368,32369],{"encoding":2094},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[92,32371,32372,11598,32375,32405],{},[95,32373,32374],{},"Spočítej parciální derivace",[1647,32376,32378],{"className":32377},[2059],[2061,32379,32380],{"xmlns":2063},[2065,32381,32382,32402],{},[2068,32383,32384,32390,32392,32398,32400],{},[2348,32385,32386,32388],{},[2071,32387,2861],{},[2210,32389,638],{},[2075,32391,2361],{"separator":2360},[2348,32393,32394,32396],{},[2071,32395,2861],{},[2210,32397,646],{},[2075,32399,2361],{"separator":2360},[2071,32401,19181],{},[2092,32403,32404],{"encoding":2094},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[92,32407,32408,32424,32425,32458,32459,75,32476,195],{},[95,32409,32410,32411],{},"Vyluč ",[1647,32412,32414],{"className":32413},[2059],[2061,32415,32416],{"xmlns":2063},[2065,32417,32418,32422],{},[2068,32419,32420],{},[2071,32421,19181],{},[2092,32423,19234],{"encoding":2094}," dělením prvních dvou rovnic — dostaneš podmínku ",[1647,32426,32428],{"className":32427},[2059],[2061,32429,32430],{"xmlns":2063},[2065,32431,32432,32456],{},[2068,32433,32434,32436,32438,32446,32448],{},[2363,32435,11733],{},[2075,32437,2077],{},[9252,32439,32440,32442,32444],{},[2071,32441,575],{},[2210,32443,638],{},[2075,32445,4441],{},[2071,32447,4761],{"mathvariant":2450},[9252,32449,32450,32452,32454],{},[2071,32451,575],{},[2210,32453,646],{},[2075,32455,4441],{},[2092,32457,32006],{"encoding":2094},", která dá vztah mezi ",[1647,32460,32462],{"className":32461},[2059],[2061,32463,32464],{"xmlns":2063},[2065,32465,32466,32474],{},[2068,32467,32468],{},[2348,32469,32470,32472],{},[2071,32471,2861],{},[2210,32473,638],{},[2092,32475,32029],{"encoding":2094},[1647,32477,32479],{"className":32478},[2059],[2061,32480,32481],{"xmlns":2063},[2065,32482,32483,32491],{},[2068,32484,32485],{},[2348,32486,32487,32489],{},[2071,32488,2861],{},[2210,32490,646],{},[2092,32492,32048],{"encoding":2094},[92,32494,32495,32498,32499,32529,32530,32547,32548,195],{},[95,32496,32497],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[1647,32500,32502],{"className":32501},[2059],[2061,32503,32504],{"xmlns":2063},[2065,32505,32506,32526],{},[2068,32507,32508,32516,32518],{},[9252,32509,32510,32512,32514],{},[2071,32511,2861],{},[2210,32513,638],{},[2075,32515,4441],{},[2075,32517,2361],{"separator":2360},[9252,32519,32520,32522,32524],{},[2071,32521,2861],{},[2210,32523,646],{},[2075,32525,4441],{},[2092,32527,32528],{"encoding":2094},"Q_1^*, Q_2^*",", případně ",[1647,32531,32533],{"className":32532},[2059],[2061,32534,32535],{"xmlns":2063},[2065,32536,32537,32545],{},[2068,32538,32539],{},[2205,32540,32541,32543],{},[2071,32542,19181],{},[2075,32544,4441],{},[2092,32546,32168],{"encoding":2094}," a maximální užitečnost ",[1647,32549,32551],{"className":32550},[2059],[2061,32552,32553],{"xmlns":2063},[2065,32554,32555,32589],{},[2068,32556,32557,32563,32565,32567,32569,32577,32579,32587],{},[2205,32558,32559,32561],{},[2071,32560,10871],{},[2075,32562,4441],{},[2075,32564,2077],{},[2071,32566,10871],{},[2075,32568,2084],{"stretchy":2083},[9252,32570,32571,32573,32575],{},[2071,32572,2861],{},[2210,32574,638],{},[2075,32576,4441],{},[2075,32578,2361],{"separator":2360},[9252,32580,32581,32583,32585],{},[2071,32582,2861],{},[2210,32584,646],{},[2075,32586,4441],{},[2075,32588,2090],{"stretchy":2083},[2092,32590,32591],{"encoding":2094},"U^* = U(Q_1^*, Q_2^*)",[84,32593,32595],{"id":32594},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[55,32597,32598],{},[58,32599],{"alt":32600,"className":32601,"src":32602},"imek-uzitecnost-optimum",[62,63],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[55,32604,32605],{},[3982,32606,32607,32608,32657,32658,75,32686,32714,32715,32749,32750,32789,32790,32808,32809,32827,32828,32846],{},"Obrázek 6.7 — Rozpočtová přímka ",[1647,32609,32611],{"className":32610},[2059],[2061,32612,32613],{"xmlns":2063},[2065,32614,32615,32655],{},[2068,32616,32617,32623,32625,32633,32639,32641,32649],{},[2205,32618,32619,32621],{},[2071,32620,9214],{},[2075,32622,4441],{},[2075,32624,2077],{},[9252,32626,32627,32629,32631],{},[2071,32628,575],{},[2210,32630,638],{},[2075,32632,4441],{},[2348,32634,32635,32637],{},[2071,32636,2861],{},[2210,32638,638],{},[2075,32640,2176],{},[9252,32642,32643,32645,32647],{},[2071,32644,575],{},[2210,32646,646],{},[2075,32648,4441],{},[2348,32650,32651,32653],{},[2071,32652,2861],{},[2210,32654,646],{},[2092,32656,20036],{"encoding":2094}," protíná osy v ",[1647,32659,32661],{"className":32660},[2059],[2061,32662,32663],{"xmlns":2063},[2065,32664,32665,32683],{},[2068,32666,32667,32673,32675],{},[2205,32668,32669,32671],{},[2071,32670,9214],{},[2075,32672,4441],{},[2071,32674,4761],{"mathvariant":2450},[9252,32676,32677,32679,32681],{},[2071,32678,575],{},[2210,32680,638],{},[2075,32682,4441],{},[2092,32684,32685],{"encoding":2094},"Y^*\u002FP_1^*",[1647,32687,32689],{"className":32688},[2059],[2061,32690,32691],{"xmlns":2063},[2065,32692,32693,32711],{},[2068,32694,32695,32701,32703],{},[2205,32696,32697,32699],{},[2071,32698,9214],{},[2075,32700,4441],{},[2071,32702,4761],{"mathvariant":2450},[9252,32704,32705,32707,32709],{},[2071,32706,575],{},[2210,32708,646],{},[2075,32710,4441],{},[2092,32712,32713],{"encoding":2094},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[1647,32716,32718],{"className":32717},[2059],[2061,32719,32720],{"xmlns":2063},[2065,32721,32722,32746],{},[2068,32723,32724,32730,32732,32738,32740],{},[2348,32725,32726,32728],{},[2071,32727,2222],{},[2210,32729,638],{},[2075,32731,3521],{},[2205,32733,32734,32736],{},[2071,32735,2222],{},[2075,32737,4441],{},[2075,32739,3521],{},[2348,32741,32742,32744],{},[2071,32743,2222],{},[2210,32745,646],{},[2092,32747,32748],{"encoding":2094},"c_1 \u003C c^* \u003C c_2",". Optimum ",[1647,32751,32753],{"className":32752},[2059],[2061,32754,32755],{"xmlns":2063},[2065,32756,32757,32787],{},[2068,32758,32759,32765,32767,32775,32777,32785],{},[2205,32760,32761,32763],{},[2071,32762,2861],{},[2075,32764,4441],{},[2075,32766,2561],{"stretchy":2083},[9252,32768,32769,32771,32773],{},[2071,32770,2861],{},[2210,32772,638],{},[2075,32774,4441],{},[2075,32776,2361],{"separator":2360},[9252,32778,32779,32781,32783],{},[2071,32780,2861],{},[2210,32782,646],{},[2075,32784,4441],{},[2075,32786,2576],{"stretchy":2083},[2092,32788,31354],{"encoding":2094}," je bod dotyku rozpočtové přímky s křivkou ",[1647,32791,32793],{"className":32792},[2059],[2061,32794,32795],{"xmlns":2063},[2065,32796,32797,32805],{},[2068,32798,32799],{},[2205,32800,32801,32803],{},[2071,32802,2222],{},[2075,32804,4441],{},[2092,32806,32807],{"encoding":2094},"c^*",". Křivka ",[1647,32810,32812],{"className":32811},[2059],[2061,32813,32814],{"xmlns":2063},[2065,32815,32816,32824],{},[2068,32817,32818],{},[2348,32819,32820,32822],{},[2071,32821,2222],{},[2210,32823,638],{},[2092,32825,32826],{"encoding":2094},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[1647,32829,32831],{"className":32830},[2059],[2061,32832,32833],{"xmlns":2063},[2065,32834,32835,32843],{},[2068,32836,32837],{},[2348,32838,32839,32841],{},[2071,32840,2222],{},[2210,32842,646],{},[2092,32844,32845],{"encoding":2094},"c_2"," není při daném důchodu dosažitelná.",[55,32848,32849,32850,32853,32854,32872,32873,32902],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[95,32851,32852],{},"dotýkají",", tj. mají v bodě ",[1647,32855,32857],{"className":32856},[2059],[2061,32858,32859],{"xmlns":2063},[2065,32860,32861,32869],{},[2068,32862,32863],{},[2205,32864,32865,32867],{},[2071,32866,2861],{},[2075,32868,4441],{},[2092,32870,32871],{"encoding":2094},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[1647,32874,32876],{"className":32875},[2059],[2061,32877,32878],{"xmlns":2063},[2065,32879,32880,32900],{},[2068,32881,32882,32884,32886,32892,32894],{},[2363,32883,11733],{},[2075,32885,2077],{},[2348,32887,32888,32890],{},[2071,32889,575],{},[2210,32891,638],{},[2071,32893,4761],{"mathvariant":2450},[2348,32895,32896,32898],{},[2071,32897,575],{},[2210,32899,646],{},[2092,32901,31025],{"encoding":2094}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[84,32904,32906],{"id":32905},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[55,32908,10790,32909,32971],{},[1647,32910,32912],{"className":32911},[2059],[2061,32913,32914],{"xmlns":2063},[2065,32915,32916,32968],{},[2068,32917,32918,32920,32922,32928,32930,32936,32938,32940,32954],{},[2071,32919,10871],{},[2075,32921,2084],{"stretchy":2083},[2348,32923,32924,32926],{},[2071,32925,2861],{},[2210,32927,638],{},[2075,32929,2361],{"separator":2360},[2348,32931,32932,32934],{},[2071,32933,2861],{},[2210,32935,646],{},[2075,32937,2090],{"stretchy":2083},[2075,32939,2077],{},[9252,32941,32942,32944,32946],{},[2071,32943,2861],{},[2210,32945,638],{},[2068,32947,32948,32950,32952],{},[2210,32949,638],{},[2071,32951,4761],{"mathvariant":2450},[2210,32953,646],{},[9252,32955,32956,32958,32960],{},[2071,32957,2861],{},[2210,32959,646],{},[2068,32961,32962,32964,32966],{},[2210,32963,638],{},[2071,32965,4761],{"mathvariant":2450},[2210,32967,646],{},[2092,32969,32970],{"encoding":2094},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[55,32973,32974],{},[1647,32975,32977],{"className":32976},[2059],[2061,32978,32979],{"xmlns":2063},[2065,32980,32981,33087],{},[2068,32982,32983,32985,32987,33069,33071,33085],{},[2363,32984,11733],{},[2075,32986,2077],{},[2403,32988,32989,33029],{},[2068,32990,32991,32999,33015],{},[2400,32992,32993],{"scriptlevel":630,"displaystyle":2083},[2403,32994,32995,32997],{},[2210,32996,638],{},[2210,32998,646],{},[9252,33000,33001,33003,33005],{},[2071,33002,2861],{},[2210,33004,638],{},[2068,33006,33007,33009,33011,33013],{},[2075,33008,2303],{},[2210,33010,638],{},[2071,33012,4761],{"mathvariant":2450},[2210,33014,646],{},[9252,33016,33017,33019,33021],{},[2071,33018,2861],{},[2210,33020,646],{},[2068,33022,33023,33025,33027],{},[2210,33024,638],{},[2071,33026,4761],{"mathvariant":2450},[2210,33028,646],{},[2068,33030,33031,33039,33053],{},[2400,33032,33033],{"scriptlevel":630,"displaystyle":2083},[2403,33034,33035,33037],{},[2210,33036,638],{},[2210,33038,646],{},[9252,33040,33041,33043,33045],{},[2071,33042,2861],{},[2210,33044,638],{},[2068,33046,33047,33049,33051],{},[2210,33048,638],{},[2071,33050,4761],{"mathvariant":2450},[2210,33052,646],{},[9252,33054,33055,33057,33059],{},[2071,33056,2861],{},[2210,33058,646],{},[2068,33060,33061,33063,33065,33067],{},[2075,33062,2303],{},[2210,33064,638],{},[2071,33066,4761],{"mathvariant":2450},[2210,33068,646],{},[2075,33070,2077],{},[2403,33072,33073,33079],{},[2348,33074,33075,33077],{},[2071,33076,2861],{},[2210,33078,646],{},[2348,33080,33081,33083],{},[2071,33082,2861],{},[2210,33084,638],{},[2071,33086,195],{"mathvariant":2450},[2092,33088,33089],{"encoding":2094},"\\text{MRCS} = \\frac{\\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F2}}{\\tfrac{1}{2} Q_1^{1\u002F2} Q_2^{-1\u002F2}} = \\frac{Q_2}{Q_1}.",[55,33091,33092,33093,2999,33138,33140,33141,33161,33162,33192,33193,195],{},"Tedy ",[1647,33094,33096],{"className":33095},[2059],[2061,33097,33098],{"xmlns":2063},[2065,33099,33100,33135],{},[2068,33101,33102,33104,33106,33109,33111,33113,33115,33117,33125,33127],{},[2363,33103,11733],{},[2075,33105,2084],{"stretchy":2083},[2210,33107,33108],{},"300",[2075,33110,2361],{"separator":2360},[2210,33112,16845],{},[2075,33114,2090],{"stretchy":2083},[2075,33116,2077],{},[2400,33118,33119],{"scriptlevel":630,"displaystyle":2083},[2403,33120,33121,33123],{},[2210,33122,16845],{},[2210,33124,33108],{},[2075,33126,2077],{},[2400,33128,33129],{"scriptlevel":630,"displaystyle":2083},[2403,33130,33131,33133],{},[2210,33132,670],{},[2210,33134,654],{},[2092,33136,33137],{"encoding":2094},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[3982,33139,9302],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[1647,33142,33144],{"className":33143},[2059],[2061,33145,33146],{"xmlns":2063},[2065,33147,33148,33158],{},[2068,33149,33150],{},[2400,33151,33152],{"scriptlevel":630,"displaystyle":2083},[2403,33153,33154,33156],{},[2210,33155,670],{},[2210,33157,654],{},[2092,33159,33160],{"encoding":2094},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[1647,33163,33165],{"className":33164},[2059],[2061,33166,33167],{"xmlns":2063},[2065,33168,33169,33189],{},[2068,33170,33171,33173,33175,33181,33183],{},[2363,33172,11733],{},[2075,33174,2077],{},[2348,33176,33177,33179],{},[2071,33178,2861],{},[2210,33180,646],{},[2071,33182,4761],{"mathvariant":2450},[2348,33184,33185,33187],{},[2071,33186,2861],{},[2210,33188,638],{},[2092,33190,33191],{"encoding":2094},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[1647,33194,33196],{"className":33195},[2059],[2061,33197,33198],{"xmlns":2063},[2065,33199,33200,33220],{},[2068,33201,33202,33204,33206,33212,33214],{},[2363,33203,11733],{},[2075,33205,2077],{},[2348,33207,33208,33210],{},[2071,33209,575],{},[2210,33211,638],{},[2071,33213,4761],{"mathvariant":2450},[2348,33215,33216,33218],{},[2071,33217,575],{},[2210,33219,646],{},[2092,33221,31025],{"encoding":2094},[84,33223,33225,33226],{"id":33224},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[1647,33227,33229],{"className":33228},[2059],[2061,33230,33231],{"xmlns":2063},[2065,33232,33233,33251],{},[2068,33234,33235,33237,33239,33245],{},[2071,33236,10871],{},[2075,33238,2077],{},[2348,33240,33241,33243],{},[2071,33242,2861],{},[2210,33244,638],{},[2348,33246,33247,33249],{},[2071,33248,2861],{},[2210,33250,646],{},[2092,33252,33253],{"encoding":2094},"U = Q_1 Q_2",[55,33255,33256,33257,835,33303,835,33327,835,33351,33373],{},"Je dána ",[1647,33258,33260],{"className":33259},[2059],[2061,33261,33262],{"xmlns":2063},[2065,33263,33264,33300],{},[2068,33265,33266,33268,33270,33276,33278,33284,33286,33288,33294],{},[2071,33267,10871],{},[2075,33269,2084],{"stretchy":2083},[2348,33271,33272,33274],{},[2071,33273,2861],{},[2210,33275,638],{},[2075,33277,2361],{"separator":2360},[2348,33279,33280,33282],{},[2071,33281,2861],{},[2210,33283,646],{},[2075,33285,2090],{"stretchy":2083},[2075,33287,2077],{},[2348,33289,33290,33292],{},[2071,33291,2861],{},[2210,33293,638],{},[2348,33295,33296,33298],{},[2071,33297,2861],{},[2210,33299,646],{},[2092,33301,33302],{"encoding":2094},"U(Q_1, Q_2) = Q_1 Q_2",[1647,33304,33306],{"className":33305},[2059],[2061,33307,33308],{"xmlns":2063},[2065,33309,33310,33324],{},[2068,33311,33312,33320,33322],{},[9252,33313,33314,33316,33318],{},[2071,33315,575],{},[2210,33317,638],{},[2075,33319,4441],{},[2075,33321,2077],{},[2210,33323,646],{},[2092,33325,33326],{"encoding":2094},"P_1^* = 2",[1647,33328,33330],{"className":33329},[2059],[2061,33331,33332],{"xmlns":2063},[2065,33333,33334,33348],{},[2068,33335,33336,33344,33346],{},[9252,33337,33338,33340,33342],{},[2071,33339,575],{},[2210,33341,646],{},[2075,33343,4441],{},[2075,33345,2077],{},[2210,33347,670],{},[2092,33349,33350],{"encoding":2094},"P_2^* = 5",[1647,33352,33354],{"className":33353},[2059],[2061,33355,33356],{"xmlns":2063},[2065,33357,33358,33370],{},[2068,33359,33360,33366,33368],{},[2205,33361,33362,33364],{},[2071,33363,9214],{},[2075,33365,4441],{},[2075,33367,2077],{},[2210,33369,3164],{},[2092,33371,33372],{"encoding":2094},"Y^* = 100",". Lagrangeova funkce:",[1647,33375,33377],{"className":33376},[2059],[2061,33378,33379],{"xmlns":2063,"display":31093},[2065,33380,33381,33453],{},[2068,33382,33383,33385,33387,33393,33395,33401,33403,33405,33407,33409,33415,33421,33423,33425,33427,33429,33431,33433,33439,33441,33443,33449,33451],{},[2071,33384,586],{"mathvariant":31575},[2075,33386,2084],{"stretchy":2083},[2348,33388,33389,33391],{},[2071,33390,2861],{},[2210,33392,638],{},[2075,33394,2361],{"separator":2360},[2348,33396,33397,33399],{},[2071,33398,2861],{},[2210,33400,646],{},[2075,33402,2361],{"separator":2360},[2071,33404,19181],{},[2075,33406,2090],{"stretchy":2083},[2075,33408,2077],{},[2348,33410,33411,33413],{},[2071,33412,2861],{},[2210,33414,638],{},[2348,33416,33417,33419],{},[2071,33418,2861],{},[2210,33420,646],{},[2075,33422,2176],{},[2071,33424,19181],{},[2075,33426,2084],{"stretchy":2083},[2210,33428,3164],{},[2075,33430,2303],{},[2210,33432,646],{},[2348,33434,33435,33437],{},[2071,33436,2861],{},[2210,33438,638],{},[2075,33440,2303],{},[2210,33442,670],{},[2348,33444,33445,33447],{},[2071,33446,2861],{},[2210,33448,646],{},[2075,33450,2090],{"stretchy":2083},[2071,33452,195],{"mathvariant":2450},[2092,33454,33455],{"encoding":2094},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[55,33457,33458],{},"Soustava:",[1647,33460,33462],{"className":33461},[2059],[2061,33463,33464],{"xmlns":2063,"display":31093},[2065,33465,33466,33578],{},[23493,33467,33468,33502,33536],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,33469,33470,33488],{},[23501,33471,33472],{},[2400,33473,33474],{"scriptlevel":630,"displaystyle":2360},[2068,33475,33476,33482,33484,33486],{},[2348,33477,33478,33480],{},[2071,33479,2861],{},[2210,33481,646],{},[2075,33483,2303],{},[2210,33485,646],{},[2071,33487,19181],{},[23501,33489,33490],{},[2400,33491,33492],{"scriptlevel":630,"displaystyle":2360},[2068,33493,33494,33496,33498,33500],{},[2068,33495],{},[2075,33497,2077],{},[2210,33499,630],{},[2075,33501,2361],{"separator":2360},[23498,33503,33504,33522],{},[23501,33505,33506],{},[2400,33507,33508],{"scriptlevel":630,"displaystyle":2360},[2068,33509,33510,33516,33518,33520],{},[2348,33511,33512,33514],{},[2071,33513,2861],{},[2210,33515,638],{},[2075,33517,2303],{},[2210,33519,670],{},[2071,33521,19181],{},[23501,33523,33524],{},[2400,33525,33526],{"scriptlevel":630,"displaystyle":2360},[2068,33527,33528,33530,33532,33534],{},[2068,33529],{},[2075,33531,2077],{},[2210,33533,630],{},[2075,33535,2361],{"separator":2360},[23498,33537,33538,33566],{},[23501,33539,33540],{},[2400,33541,33542],{"scriptlevel":630,"displaystyle":2360},[2068,33543,33544,33546,33548,33550,33556,33558,33560],{},[2210,33545,3164],{},[2075,33547,2303],{},[2210,33549,646],{},[2348,33551,33552,33554],{},[2071,33553,2861],{},[2210,33555,638],{},[2075,33557,2303],{},[2210,33559,670],{},[2348,33561,33562,33564],{},[2071,33563,2861],{},[2210,33565,646],{},[23501,33567,33568],{},[2400,33569,33570],{"scriptlevel":630,"displaystyle":2360},[2068,33571,33572,33574,33576],{},[2068,33573],{},[2075,33575,2077],{},[2210,33577,14195],{},[2092,33579,33580],{"encoding":2094},"\\begin{aligned}\nQ_2 - 2 \\lambda &= 0, \\\\\nQ_1 - 5 \\lambda &= 0, \\\\\n100 - 2 Q_1 - 5 Q_2 &= 0.\n\\end{aligned}",[55,33582,33583,33584,835,33608,33632,33633,5676,33673,33691,33692,33742,33743,195],{},"Z prvních dvou rovnic ",[1647,33585,33587],{"className":33586},[2059],[2061,33588,33589],{"xmlns":2063},[2065,33590,33591,33605],{},[2068,33592,33593,33599,33601,33603],{},[2348,33594,33595,33597],{},[2071,33596,2861],{},[2210,33598,646],{},[2075,33600,2077],{},[2210,33602,646],{},[2071,33604,19181],{},[2092,33606,33607],{"encoding":2094},"Q_2 = 2\\lambda",[1647,33609,33611],{"className":33610},[2059],[2061,33612,33613],{"xmlns":2063},[2065,33614,33615,33629],{},[2068,33616,33617,33623,33625,33627],{},[2348,33618,33619,33621],{},[2071,33620,2861],{},[2210,33622,638],{},[2075,33624,2077],{},[2210,33626,670],{},[2071,33628,19181],{},[2092,33630,33631],{"encoding":2094},"Q_1 = 5\\lambda","; dosazením do třetí ",[1647,33634,33636],{"className":33635},[2059],[2061,33637,33638],{"xmlns":2063},[2065,33639,33640,33670],{},[2068,33641,33642,33644,33646,33648,33650,33652,33654,33656,33658,33660,33662,33664,33666,33668],{},[2210,33643,3164],{},[2075,33645,2077],{},[2210,33647,646],{},[2075,33649,3251],{},[2210,33651,670],{},[2071,33653,19181],{},[2075,33655,2176],{},[2210,33657,670],{},[2075,33659,3251],{},[2210,33661,646],{},[2071,33663,19181],{},[2075,33665,2077],{},[2210,33667,9121],{},[2071,33669,19181],{},[2092,33671,33672],{"encoding":2094},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[1647,33674,33676],{"className":33675},[2059],[2061,33677,33678],{"xmlns":2063},[2065,33679,33680,33688],{},[2068,33681,33682,33684,33686],{},[2071,33683,19181],{},[2075,33685,2077],{},[2210,33687,670],{},[2092,33689,33690],{"encoding":2094},"\\lambda = 5",". Odtud ",[95,33693,33694,835,33718],{},[1647,33695,33697],{"className":33696},[2059],[2061,33698,33699],{"xmlns":2063},[2065,33700,33701,33715],{},[2068,33702,33703,33711,33713],{},[9252,33704,33705,33707,33709],{},[2071,33706,2861],{},[2210,33708,638],{},[2075,33710,4441],{},[2075,33712,2077],{},[2210,33714,5091],{},[2092,33716,33717],{"encoding":2094},"Q_1^* = 25",[1647,33719,33721],{"className":33720},[2059],[2061,33722,33723],{"xmlns":2063},[2065,33724,33725,33739],{},[2068,33726,33727,33735,33737],{},[9252,33728,33729,33731,33733],{},[2071,33730,2861],{},[2210,33732,646],{},[2075,33734,4441],{},[2075,33736,2077],{},[2210,33738,2935],{},[2092,33740,33741],{"encoding":2094},"Q_2^* = 10",", maximální užitečnost ",[1647,33744,33746],{"className":33745},[2059],[2061,33747,33748],{"xmlns":2063},[2065,33749,33750,33771],{},[2068,33751,33752,33758,33760,33762,33764,33766,33768],{},[2205,33753,33754,33756],{},[2071,33755,10871],{},[2075,33757,4441],{},[2075,33759,2077],{},[2210,33761,5091],{},[2075,33763,3251],{},[2210,33765,2935],{},[2075,33767,2077],{},[2210,33769,33770],{},"250",[2092,33772,33773],{"encoding":2094},"U^* = 25 \\cdot 10 = 250",[55,33775,33776],{},[3982,33777,33778,33779,31164,33817,75,33841,33865,33866,33896,33897,33921,33922,33944,33945,195],{},"Obrázek 6.8 — Rozpočtová přímka ",[1647,33780,33782],{"className":33781},[2059],[2061,33783,33784],{"xmlns":2063},[2065,33785,33786,33814],{},[2068,33787,33788,33790,33792,33794,33800,33802,33804,33810,33812],{},[2210,33789,3164],{},[2075,33791,2303],{},[2210,33793,646],{},[2348,33795,33796,33798],{},[2071,33797,2861],{},[2210,33799,638],{},[2075,33801,2303],{},[2210,33803,670],{},[2348,33805,33806,33808],{},[2071,33807,2861],{},[2210,33809,646],{},[2075,33811,2077],{},[2210,33813,630],{},[2092,33815,33816],{"encoding":2094},"100 - 2 Q_1 - 5 Q_2 = 0",[1647,33818,33820],{"className":33819},[2059],[2061,33821,33822],{"xmlns":2063},[2065,33823,33824,33838],{},[2068,33825,33826,33828,33830,33832,33834,33836],{},[2071,33827,4342],{},[2075,33829,2561],{"stretchy":2083},[2210,33831,630],{},[2075,33833,2361],{"separator":2360},[2210,33835,9121],{},[2075,33837,2576],{"stretchy":2083},[2092,33839,33840],{"encoding":2094},"A[0, 20]",[1647,33842,33844],{"className":33843},[2059],[2061,33845,33846],{"xmlns":2063},[2065,33847,33848,33862],{},[2068,33849,33850,33852,33854,33856,33858,33860],{},[2071,33851,25992],{},[2075,33853,2561],{"stretchy":2083},[2210,33855,3194],{},[2075,33857,2361],{"separator":2360},[2210,33859,630],{},[2075,33861,2576],{"stretchy":2083},[2092,33863,33864],{"encoding":2094},"B[50, 0]","; hyperbolická indiferenční křivka ",[1647,33867,33869],{"className":33868},[2059],[2061,33870,33871],{"xmlns":2063},[2065,33872,33873,33893],{},[2068,33874,33875,33881,33883,33885,33887],{},[2348,33876,33877,33879],{},[2071,33878,2861],{},[2210,33880,646],{},[2075,33882,2077],{},[2210,33884,33770],{},[2071,33886,4761],{"mathvariant":2450},[2348,33888,33889,33891],{},[2071,33890,2861],{},[2210,33892,638],{},[2092,33894,33895],{"encoding":2094},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[1647,33898,33900],{"className":33899},[2059],[2061,33901,33902],{"xmlns":2063},[2065,33903,33904,33918],{},[2068,33905,33906,33908,33910,33912,33914,33916],{},[2071,33907,554],{},[2075,33909,2561],{"stretchy":2083},[2210,33911,5091],{},[2075,33913,2361],{"separator":2360},[2210,33915,2935],{},[2075,33917,2576],{"stretchy":2083},[2092,33919,33920],{"encoding":2094},"E[25, 10]",". Sklon přímky ",[1647,33923,33925],{"className":33924},[2059],[2061,33926,33927],{"xmlns":2063},[2065,33928,33929,33941],{},[2068,33930,33931,33933],{},[2075,33932,2303],{},[2400,33934,33935],{"scriptlevel":630,"displaystyle":2083},[2403,33936,33937,33939],{},[2210,33938,646],{},[2210,33940,670],{},[2092,33942,33943],{"encoding":2094},"-\\tfrac{2}{5}"," odpovídá ",[1647,33946,33948],{"className":33947},[2059],[2061,33949,33950],{"xmlns":2063},[2065,33951,33952,33992],{},[2068,33953,33954,33956,33958,33960,33962,33964,33966,33968,33970,33972,33980,33982,33984],{},[2075,33955,2303],{},[2363,33957,11733],{},[2075,33959,2084],{"stretchy":2083},[2210,33961,5091],{},[2075,33963,2361],{"separator":2360},[2210,33965,2935],{},[2075,33967,2090],{"stretchy":2083},[2075,33969,2077],{},[2075,33971,2303],{},[2400,33973,33974],{"scriptlevel":630,"displaystyle":2083},[2403,33975,33976,33978],{},[2210,33977,2935],{},[2210,33979,5091],{},[2075,33981,2077],{},[2075,33983,2303],{},[2400,33985,33986],{"scriptlevel":630,"displaystyle":2083},[2403,33987,33988,33990],{},[2210,33989,646],{},[2210,33991,670],{},[2092,33993,33994],{"encoding":2094},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[84,33996,33998],{"id":33997},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[55,34000,34001,34002,32030,34032,34034,34035,2777],{},"Považujeme-li v úloze ",[1647,34003,34005],{"className":34004},[2059],[2061,34006,34007],{"xmlns":2063},[2065,34008,34009,34029],{},[2068,34010,34011,34017,34019,34025,34027],{},[2348,34012,34013,34015],{},[2071,34014,575],{},[2210,34016,638],{},[2075,34018,2361],{"separator":2360},[2348,34020,34021,34023],{},[2071,34022,575],{},[2210,34024,646],{},[2075,34026,2361],{"separator":2360},[2071,34028,9214],{},[2092,34030,34031],{"encoding":2094},"P_1, P_2, Y",[95,34033,12609],{}," (nikoli čísla), dostáváme z první řádové podmínky ",[95,34036,34037],{},"Marshallovy poptávkové funkce",[1647,34039,34041],{"className":34040},[2059],[2061,34042,34043],{"xmlns":2063,"display":31093},[2065,34044,34045,34140],{},[23493,34046,34047],{"width":31098},[23498,34048,34049,34051,34133,34135],{},[23501,34050],{"width":31103},[23501,34052,34053],{},[2068,34054,34055,34061,34063,34069,34071,34077,34079,34085,34087,34089,34091,34093,34095,34101,34103,34109,34111,34117,34119,34125,34127,34129,34131],{},[2348,34056,34057,34059],{},[2071,34058,2861],{},[2210,34060,638],{},[2075,34062,2077],{},[2348,34064,34065,34067],{},[2071,34066,4271],{},[2210,34068,638],{},[2075,34070,2084],{"stretchy":2083},[2348,34072,34073,34075],{},[2071,34074,575],{},[2210,34076,638],{},[2075,34078,2361],{"separator":2360},[2348,34080,34081,34083],{},[2071,34082,575],{},[2210,34084,646],{},[2075,34086,2361],{"separator":2360},[2071,34088,9214],{},[2075,34090,2090],{"stretchy":2083},[2075,34092,2361],{"separator":2360},[5965,34094],{"width":17019},[2348,34096,34097,34099],{},[2071,34098,2861],{},[2210,34100,646],{},[2075,34102,2077],{},[2348,34104,34105,34107],{},[2071,34106,4271],{},[2210,34108,646],{},[2075,34110,2084],{"stretchy":2083},[2348,34112,34113,34115],{},[2071,34114,575],{},[2210,34116,638],{},[2075,34118,2361],{"separator":2360},[2348,34120,34121,34123],{},[2071,34122,575],{},[2210,34124,646],{},[2075,34126,2361],{"separator":2360},[2071,34128,9214],{},[2075,34130,2090],{"stretchy":2083},[2075,34132,2361],{"separator":2360},[23501,34134],{"width":31103},[23501,34136,34137],{},[2363,34138,34139],{},"(6.15)",[2092,34141,34142],{"encoding":2094},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[1647,34144,34146],{"className":34145},[2059],[2061,34147,34148],{"xmlns":2063,"display":31093},[2065,34149,34150,34197],{},[23493,34151,34152],{"width":31098},[23498,34153,34154,34156,34190,34192],{},[23501,34155],{"width":31103},[23501,34157,34158],{},[2068,34159,34160,34162,34164,34166,34168,34174,34176,34182,34184,34186,34188],{},[2071,34161,19181],{},[2075,34163,2077],{},[2071,34165,19181],{},[2075,34167,2084],{"stretchy":2083},[2348,34169,34170,34172],{},[2071,34171,575],{},[2210,34173,638],{},[2075,34175,2361],{"separator":2360},[2348,34177,34178,34180],{},[2071,34179,575],{},[2210,34181,646],{},[2075,34183,2361],{"separator":2360},[2071,34185,9214],{},[2075,34187,2090],{"stretchy":2083},[2071,34189,195],{"mathvariant":2450},[23501,34191],{"width":31103},[23501,34193,34194],{},[2363,34195,34196],{},"(6.16)",[2092,34198,34199],{"encoding":2094},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[55,34201,34202,34232,34233,34299],{},[95,34203,34204,34205,195],{},"Odvození pro ",[1647,34206,34208],{"className":34207},[2059],[2061,34209,34210],{"xmlns":2063},[2065,34211,34212,34230],{},[2068,34213,34214,34216,34218,34224],{},[2071,34215,10871],{},[2075,34217,2077],{},[2348,34219,34220,34222],{},[2071,34221,2861],{},[2210,34223,638],{},[2348,34225,34226,34228],{},[2071,34227,2861],{},[2210,34229,646],{},[2092,34231,33253],{"encoding":2094}," Lagrangeova funkce ",[1647,34234,34236],{"className":34235},[2059],[2061,34237,34238],{"xmlns":2063},[2065,34239,34240,34296],{},[2068,34241,34242,34244,34246,34252,34258,34260,34262,34264,34266,34268,34274,34280,34282,34288,34294],{},[2071,34243,586],{"mathvariant":31575},[2075,34245,2077],{},[2348,34247,34248,34250],{},[2071,34249,2861],{},[2210,34251,638],{},[2348,34253,34254,34256],{},[2071,34255,2861],{},[2210,34257,646],{},[2075,34259,2176],{},[2071,34261,19181],{},[2075,34263,2084],{"stretchy":2083},[2071,34265,9214],{},[2075,34267,2303],{},[2348,34269,34270,34272],{},[2071,34271,575],{},[2210,34273,638],{},[2348,34275,34276,34278],{},[2071,34277,2861],{},[2210,34279,638],{},[2075,34281,2303],{},[2348,34283,34284,34286],{},[2071,34285,575],{},[2210,34287,646],{},[2348,34289,34290,34292],{},[2071,34291,2861],{},[2210,34293,646],{},[2075,34295,2090],{"stretchy":2083},[2092,34297,34298],{"encoding":2094},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[1647,34301,34303],{"className":34302},[2059],[2061,34304,34305],{"xmlns":2063,"display":31093},[2065,34306,34307,34474],{},[23493,34308,34309],{"width":31098},[23498,34310,34311,34313,34467,34469],{},[23501,34312],{"width":31103},[23501,34314,34315],{},[23493,34316,34317,34363,34409],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,34318,34319,34331],{},[23501,34320,34321],{},[2400,34322,34323],{"scriptlevel":630,"displaystyle":2360},[9252,34324,34325,34327,34329],{},[2071,34326,586],{"mathvariant":31575},[2210,34328,638],{},[2075,34330,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,34332,34333],{},[2400,34334,34335],{"scriptlevel":630,"displaystyle":2360},[2068,34336,34337,34339,34341,34347,34349,34351,34357,34359,34361],{},[2068,34338],{},[2075,34340,2077],{},[2348,34342,34343,34345],{},[2071,34344,2861],{},[2210,34346,646],{},[2075,34348,2303],{},[2071,34350,19181],{},[2348,34352,34353,34355],{},[2071,34354,575],{},[2210,34356,638],{},[2075,34358,2077],{},[2210,34360,630],{},[2075,34362,2361],{"separator":2360},[23498,34364,34365,34377],{},[23501,34366,34367],{},[2400,34368,34369],{"scriptlevel":630,"displaystyle":2360},[9252,34370,34371,34373,34375],{},[2071,34372,586],{"mathvariant":31575},[2210,34374,646],{},[2075,34376,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,34378,34379],{},[2400,34380,34381],{"scriptlevel":630,"displaystyle":2360},[2068,34382,34383,34385,34387,34393,34395,34397,34403,34405,34407],{},[2068,34384],{},[2075,34386,2077],{},[2348,34388,34389,34391],{},[2071,34390,2861],{},[2210,34392,638],{},[2075,34394,2303],{},[2071,34396,19181],{},[2348,34398,34399,34401],{},[2071,34400,575],{},[2210,34402,646],{},[2075,34404,2077],{},[2210,34406,630],{},[2075,34408,2361],{"separator":2360},[23498,34410,34411,34423],{},[23501,34412,34413],{},[2400,34414,34415],{"scriptlevel":630,"displaystyle":2360},[9252,34416,34417,34419,34421],{},[2071,34418,586],{"mathvariant":31575},[2071,34420,19181],{},[2075,34422,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,34424,34425],{},[2400,34426,34427],{"scriptlevel":630,"displaystyle":2360},[2068,34428,34429,34431,34433,34435,34437,34443,34449,34451,34457,34463,34465],{},[2068,34430],{},[2075,34432,2077],{},[2071,34434,9214],{},[2075,34436,2303],{},[2348,34438,34439,34441],{},[2071,34440,575],{},[2210,34442,638],{},[2348,34444,34445,34447],{},[2071,34446,2861],{},[2210,34448,638],{},[2075,34450,2303],{},[2348,34452,34453,34455],{},[2071,34454,575],{},[2210,34456,646],{},[2348,34458,34459,34461],{},[2071,34460,2861],{},[2210,34462,646],{},[2075,34464,2077],{},[2210,34466,14195],{},[23501,34468],{"width":31103},[23501,34470,34471],{},[2363,34472,34473],{},"(6.17)",[2092,34475,34476],{"encoding":2094},"\\begin{aligned}\n\\mathcal{L}'_1 &= Q_2 - \\lambda P_1 = 0, \\\\\n\\mathcal{L}'_2 &= Q_1 - \\lambda P_2 = 0, \\\\\n\\mathcal{L}'_\\lambda &= Y - P_1 Q_1 - P_2 Q_2 = 0.\n\\end{aligned}\n\\tag{6.17}",[55,34478,34479,34480,34508,34509,34537,34538,34606],{},"Z prvních dvou: ",[1647,34481,34483],{"className":34482},[2059],[2061,34484,34485],{"xmlns":2063},[2065,34486,34487,34505],{},[2068,34488,34489,34495,34497,34503],{},[2348,34490,34491,34493],{},[2071,34492,2861],{},[2210,34494,646],{},[2075,34496,2077],{},[2348,34498,34499,34501],{},[2071,34500,575],{},[2210,34502,638],{},[2071,34504,19181],{},[2092,34506,34507],{"encoding":2094},"Q_2 = P_1 \\lambda"," (6.18), ",[1647,34510,34512],{"className":34511},[2059],[2061,34513,34514],{"xmlns":2063},[2065,34515,34516,34534],{},[2068,34517,34518,34524,34526,34532],{},[2348,34519,34520,34522],{},[2071,34521,2861],{},[2210,34523,638],{},[2075,34525,2077],{},[2348,34527,34528,34530],{},[2071,34529,575],{},[2210,34531,646],{},[2071,34533,19181],{},[2092,34535,34536],{"encoding":2094},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[1647,34539,34541],{"className":34540},[2059],[2061,34542,34543],{"xmlns":2063},[2065,34544,34545,34603],{},[2068,34546,34547,34549,34551,34557,34559,34565,34567,34569,34575,34577,34583,34585,34587,34589,34595,34601],{},[2071,34548,9214],{},[2075,34550,2077],{},[2348,34552,34553,34555],{},[2071,34554,575],{},[2210,34556,638],{},[2075,34558,3251],{},[2348,34560,34561,34563],{},[2071,34562,575],{},[2210,34564,646],{},[2071,34566,19181],{},[2075,34568,2176],{},[2348,34570,34571,34573],{},[2071,34572,575],{},[2210,34574,646],{},[2075,34576,3251],{},[2348,34578,34579,34581],{},[2071,34580,575],{},[2210,34582,638],{},[2071,34584,19181],{},[2075,34586,2077],{},[2210,34588,646],{},[2348,34590,34591,34593],{},[2071,34592,575],{},[2210,34594,638],{},[2348,34596,34597,34599],{},[2071,34598,575],{},[2210,34600,646],{},[2071,34602,19181],{},[2092,34604,34605],{"encoding":2094},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[1647,34608,34610],{"className":34609},[2059],[2061,34611,34612],{"xmlns":2063,"display":31093},[2065,34613,34614,34657],{},[23493,34615,34616],{"width":31098},[23498,34617,34618,34620,34650,34652],{},[23501,34619],{"width":31103},[23501,34621,34622],{},[2068,34623,34624,34626,34628,34648],{},[2071,34625,19181],{},[2075,34627,2077],{},[2403,34629,34630,34632],{},[2071,34631,9214],{},[2068,34633,34634,34636,34642],{},[2210,34635,646],{},[2348,34637,34638,34640],{},[2071,34639,575],{},[2210,34641,638],{},[2348,34643,34644,34646],{},[2071,34645,575],{},[2210,34647,646],{},[2071,34649,195],{"mathvariant":2450},[23501,34651],{"width":31103},[23501,34653,34654],{},[2363,34655,34656],{},"(6.20)",[2092,34658,34659],{"encoding":2094},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[55,34661,34662],{},"Zpětně:",[1647,34664,34666],{"className":34665},[2059],[2061,34667,34668],{"xmlns":2063,"display":31093},[2065,34669,34670,34747],{},[23493,34671,34672],{"width":31098},[23498,34673,34674,34676,34740,34742],{},[23501,34675],{"width":31103},[23501,34677,34678],{},[14567,34679,34680],{"notation":14569},[2400,34681,34682],{"scriptlevel":630,"displaystyle":2083},[2400,34683,34684],{"scriptlevel":630,"displaystyle":2083},[2400,34685,34686],{"scriptlevel":630,"displaystyle":2360},[2068,34687,34688,34690,34696,34698,34712,34714,34716,34722,34724,34738],{},[2363,34689,4072],{},[2348,34691,34692,34694],{},[2071,34693,2861],{},[2210,34695,638],{},[2075,34697,2077],{},[2403,34699,34700,34702],{},[2071,34701,9214],{},[2068,34703,34704,34706],{},[2210,34705,646],{},[2348,34707,34708,34710],{},[2071,34709,575],{},[2210,34711,638],{},[2075,34713,2361],{"separator":2360},[5965,34715],{"width":17019},[2348,34717,34718,34720],{},[2071,34719,2861],{},[2210,34721,646],{},[2075,34723,2077],{},[2403,34725,34726,34728],{},[2071,34727,9214],{},[2068,34729,34730,34732],{},[2210,34731,646],{},[2348,34733,34734,34736],{},[2071,34735,575],{},[2210,34737,646],{},[2363,34739,4072],{},[23501,34741],{"width":31103},[23501,34743,34744],{},[2363,34745,34746],{},"(6.21)",[2092,34748,34749],{"encoding":2094},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[609,34751,34753],{"id":34752},"engelova-funkce","Engelova funkce",[55,34755,10790,34756,34759,34760,34763,34764,22606,34781,835,34811,34841,34842,34876,34877,835,34903,34929],{},[95,34757,34758],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[95,34761,34762],{},"Engelovou funkcí",": pro ",[1647,34765,34767],{"className":34766},[2059],[2061,34768,34769],{"xmlns":2063},[2065,34770,34771,34779],{},[2068,34772,34773,34775,34777],{},[2071,34774,9214],{},[2075,34776,2077],{},[2210,34778,3164],{},[2092,34780,23058],{"encoding":2094},[1647,34782,34784],{"className":34783},[2059],[2061,34785,34786],{"xmlns":2063},[2065,34787,34788,34808],{},[2068,34789,34790,34796,34798,34800,34802],{},[2348,34791,34792,34794],{},[2071,34793,2861],{},[2210,34795,638],{},[2075,34797,2077],{},[2210,34799,3194],{},[2071,34801,4761],{"mathvariant":2450},[2348,34803,34804,34806],{},[2071,34805,575],{},[2210,34807,638],{},[2092,34809,34810],{"encoding":2094},"Q_1 = 50\u002FP_1",[1647,34812,34814],{"className":34813},[2059],[2061,34815,34816],{"xmlns":2063},[2065,34817,34818,34838],{},[2068,34819,34820,34826,34828,34830,34832],{},[2348,34821,34822,34824],{},[2071,34823,2861],{},[2210,34825,646],{},[2075,34827,2077],{},[2210,34829,3194],{},[2071,34831,4761],{"mathvariant":2450},[2348,34833,34834,34836],{},[2071,34835,575],{},[2210,34837,646],{},[2092,34839,34840],{"encoding":2094},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[1647,34843,34845],{"className":34844},[2059],[2061,34846,34847],{"xmlns":2063},[2065,34848,34849,34873],{},[2068,34850,34851,34857,34859,34861,34863,34869,34871],{},[2348,34852,34853,34855],{},[2071,34854,575],{},[2210,34856,638],{},[2075,34858,2077],{},[2210,34860,2935],{},[2075,34862,2361],{"separator":2360},[2348,34864,34865,34867],{},[2071,34866,575],{},[2210,34868,646],{},[2075,34870,2077],{},[2210,34872,9121],{},[2092,34874,34875],{"encoding":2094},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[1647,34878,34880],{"className":34879},[2059],[2061,34881,34882],{"xmlns":2063},[2065,34883,34884,34900],{},[2068,34885,34886,34892,34894,34896,34898],{},[2348,34887,34888,34890],{},[2071,34889,2861],{},[2210,34891,638],{},[2075,34893,2077],{},[2071,34895,9214],{},[2071,34897,4761],{"mathvariant":2450},[2210,34899,9121],{},[2092,34901,34902],{"encoding":2094},"Q_1 = Y\u002F20",[1647,34904,34906],{"className":34905},[2059],[2061,34907,34908],{"xmlns":2063},[2065,34909,34910,34926],{},[2068,34911,34912,34918,34920,34922,34924],{},[2348,34913,34914,34916],{},[2071,34915,2861],{},[2210,34917,646],{},[2075,34919,2077],{},[2071,34921,9214],{},[2071,34923,4761],{"mathvariant":2450},[2210,34925,5298],{},[2092,34927,34928],{"encoding":2094},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[84,34931,34933],{"id":34932},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[55,34935,34936],{},"Výdaje spotřebitele jsou",[1647,34938,34940],{"className":34939},[2059],[2061,34941,34942],{"xmlns":2063,"display":31093},[2065,34943,34944,35019],{},[23493,34945,34946],{"width":31098},[23498,34947,34948,34950,35012,35014],{},[23501,34949],{"width":31103},[23501,34951,34952],{},[2068,34953,34954,34956,34958,34960,34962,34968,34970,34976,34978,34980,34988,34994,34996,35004,35010],{},[2071,34955,554],{},[2075,34957,2077],{},[2071,34959,554],{},[2075,34961,2084],{"stretchy":2083},[2348,34963,34964,34966],{},[2071,34965,2861],{},[2210,34967,638],{},[2075,34969,2361],{"separator":2360},[2348,34971,34972,34974],{},[2071,34973,2861],{},[2210,34975,646],{},[2075,34977,2090],{"stretchy":2083},[2075,34979,2077],{},[9252,34981,34982,34984,34986],{},[2071,34983,575],{},[2210,34985,638],{},[2075,34987,4441],{},[2348,34989,34990,34992],{},[2071,34991,2861],{},[2210,34993,638],{},[2075,34995,2176],{},[9252,34997,34998,35000,35002],{},[2071,34999,575],{},[2210,35001,646],{},[2075,35003,4441],{},[2348,35005,35006,35008],{},[2071,35007,2861],{},[2210,35009,646],{},[2075,35011,2361],{"separator":2360},[23501,35013],{"width":31103},[23501,35015,35016],{},[2363,35017,35018],{},"(6.22)",[2092,35020,35021],{"encoding":2094},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[55,35023,35024],{},"a je pevně zadána hladina užitečnosti",[1647,35026,35028],{"className":35027},[2059],[2061,35029,35030],{"xmlns":2063,"display":31093},[2065,35031,35032,35079],{},[23493,35033,35034],{"width":31098},[23498,35035,35036,35038,35072,35074],{},[23501,35037],{"width":31103},[23501,35039,35040],{},[2068,35041,35042,35048,35050,35052,35054,35060,35062,35068,35070],{},[2205,35043,35044,35046],{},[2071,35045,10871],{},[2075,35047,4441],{},[2075,35049,2077],{},[2071,35051,10871],{},[2075,35053,2084],{"stretchy":2083},[2348,35055,35056,35058],{},[2071,35057,2861],{},[2210,35059,638],{},[2075,35061,2361],{"separator":2360},[2348,35063,35064,35066],{},[2071,35065,2861],{},[2210,35067,646],{},[2075,35069,2090],{"stretchy":2083},[2071,35071,195],{"mathvariant":2450},[23501,35073],{"width":31103},[23501,35075,35076],{},[2363,35077,35078],{},"(6.23)",[2092,35080,35081],{"encoding":2094},"U^* = U(Q_1, Q_2). \\tag{6.23}",[55,35083,35084,35087,35088,35120,35121,195],{},[95,35085,35086],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[1647,35089,35091],{"className":35090},[2059],[2061,35092,35093],{"xmlns":2063},[2065,35094,35095,35117],{},[2068,35096,35097,35099,35101,35107,35109,35115],{},[2071,35098,554],{},[2075,35100,2084],{"stretchy":2083},[2348,35102,35103,35105],{},[2071,35104,2861],{},[2210,35106,638],{},[2075,35108,2361],{"separator":2360},[2348,35110,35111,35113],{},[2071,35112,2861],{},[2210,35114,646],{},[2075,35116,2090],{"stretchy":2083},[2092,35118,35119],{"encoding":2094},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[1647,35122,35124],{"className":35123},[2059],[2061,35125,35126],{"xmlns":2063},[2065,35127,35128,35184],{},[2068,35129,35130,35132,35134,35140,35142,35148,35150,35152,35158,35160,35162,35164,35170,35172,35178,35180,35182],{},[2071,35131,12171],{},[2075,35133,2084],{"stretchy":2083},[2348,35135,35136,35138],{},[2071,35137,2861],{},[2210,35139,638],{},[2075,35141,2361],{"separator":2360},[2348,35143,35144,35146],{},[2071,35145,2861],{},[2210,35147,646],{},[2075,35149,2090],{"stretchy":2083},[2075,35151,2077],{},[2205,35153,35154,35156],{},[2071,35155,10871],{},[2075,35157,4441],{},[2075,35159,2303],{},[2071,35161,10871],{},[2075,35163,2084],{"stretchy":2083},[2348,35165,35166,35168],{},[2071,35167,2861],{},[2210,35169,638],{},[2075,35171,2361],{"separator":2360},[2348,35173,35174,35176],{},[2071,35175,2861],{},[2210,35177,646],{},[2075,35179,2090],{"stretchy":2083},[2075,35181,2077],{},[2210,35183,630],{},[2092,35185,35186],{"encoding":2094},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[609,35188,35190],{"id":35189},"lagrangeova-funkce","Lagrangeova funkce",[1647,35192,35194],{"className":35193},[2059],[2061,35195,35196],{"xmlns":2063,"display":31093},[2065,35197,35198,35309],{},[23493,35199,35200],{"width":31098},[23498,35201,35202,35204,35302,35304],{},[23501,35203],{"width":31103},[23501,35205,35206],{},[2068,35207,35208,35210,35212,35218,35220,35226,35228,35230,35232,35234,35242,35248,35250,35258,35264,35266,35268,35270,35276,35278,35280,35282,35288,35290,35296,35298,35300],{},[2071,35209,586],{"mathvariant":31575},[2075,35211,2084],{"stretchy":2083},[2348,35213,35214,35216],{},[2071,35215,2861],{},[2210,35217,638],{},[2075,35219,2361],{"separator":2360},[2348,35221,35222,35224],{},[2071,35223,2861],{},[2210,35225,646],{},[2075,35227,2361],{"separator":2360},[2071,35229,19181],{},[2075,35231,2090],{"stretchy":2083},[2075,35233,2077],{},[9252,35235,35236,35238,35240],{},[2071,35237,575],{},[2210,35239,638],{},[2075,35241,4441],{},[2348,35243,35244,35246],{},[2071,35245,2861],{},[2210,35247,638],{},[2075,35249,2176],{},[9252,35251,35252,35254,35256],{},[2071,35253,575],{},[2210,35255,646],{},[2075,35257,4441],{},[2348,35259,35260,35262],{},[2071,35261,2861],{},[2210,35263,646],{},[2075,35265,2176],{},[2071,35267,19181],{},[2075,35269,2084],{"stretchy":2083},[2205,35271,35272,35274],{},[2071,35273,10871],{},[2075,35275,4441],{},[2075,35277,2303],{},[2071,35279,10871],{},[2075,35281,2084],{"stretchy":2083},[2348,35283,35284,35286],{},[2071,35285,2861],{},[2210,35287,638],{},[2075,35289,2361],{"separator":2360},[2348,35291,35292,35294],{},[2071,35293,2861],{},[2210,35295,646],{},[2075,35297,2090],{"stretchy":2083},[2075,35299,2090],{"stretchy":2083},[2071,35301,195],{"mathvariant":2450},[23501,35303],{"width":31103},[23501,35305,35306],{},[2363,35307,35308],{},"(6.24)",[2092,35310,35311],{"encoding":2094},"\\mathcal{L}(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2)). \\tag{6.24}",[55,35313,35314],{},"Soustava podmínek prvního řádu:",[1647,35316,35318],{"className":35317},[2059],[2061,35319,35320],{"xmlns":2063,"display":31093},[2065,35321,35322,35495],{},[23493,35323,35324],{"width":31098},[23498,35325,35326,35328,35488,35490],{},[23501,35327],{"width":31103},[23501,35329,35330],{},[23493,35331,35332,35382,35432],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,35333,35334,35346],{},[23501,35335,35336],{},[2400,35337,35338],{"scriptlevel":630,"displaystyle":2360},[9252,35339,35340,35342,35344],{},[2071,35341,586],{"mathvariant":31575},[2210,35343,638],{},[2075,35345,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,35347,35348],{},[2400,35349,35350],{"scriptlevel":630,"displaystyle":2360},[2068,35351,35352,35354,35356,35364,35366,35368,35376,35378,35380],{},[2068,35353],{},[2075,35355,2077],{},[9252,35357,35358,35360,35362],{},[2071,35359,575],{},[2210,35361,638],{},[2075,35363,4441],{},[2075,35365,2303],{},[2071,35367,19181],{},[9252,35369,35370,35372,35374],{},[2071,35371,10871],{},[2210,35373,638],{},[2075,35375,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,35377,2077],{},[2210,35379,630],{},[2075,35381,2361],{"separator":2360},[23498,35383,35384,35396],{},[23501,35385,35386],{},[2400,35387,35388],{"scriptlevel":630,"displaystyle":2360},[9252,35389,35390,35392,35394],{},[2071,35391,586],{"mathvariant":31575},[2210,35393,646],{},[2075,35395,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,35397,35398],{},[2400,35399,35400],{"scriptlevel":630,"displaystyle":2360},[2068,35401,35402,35404,35406,35414,35416,35418,35426,35428,35430],{},[2068,35403],{},[2075,35405,2077],{},[9252,35407,35408,35410,35412],{},[2071,35409,575],{},[2210,35411,646],{},[2075,35413,4441],{},[2075,35415,2303],{},[2071,35417,19181],{},[9252,35419,35420,35422,35424],{},[2071,35421,10871],{},[2210,35423,646],{},[2075,35425,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,35427,2077],{},[2210,35429,630],{},[2075,35431,2361],{"separator":2360},[23498,35433,35434,35446],{},[23501,35435,35436],{},[2400,35437,35438],{"scriptlevel":630,"displaystyle":2360},[9252,35439,35440,35442,35444],{},[2071,35441,586],{"mathvariant":31575},[2071,35443,19181],{},[2075,35445,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,35447,35448],{},[2400,35449,35450],{"scriptlevel":630,"displaystyle":2360},[2068,35451,35452,35454,35456,35462,35464,35466,35468,35474,35476,35482,35484,35486],{},[2068,35453],{},[2075,35455,2077],{},[2205,35457,35458,35460],{},[2071,35459,10871],{},[2075,35461,4441],{},[2075,35463,2303],{},[2071,35465,10871],{},[2075,35467,2084],{"stretchy":2083},[2348,35469,35470,35472],{},[2071,35471,2861],{},[2210,35473,638],{},[2075,35475,2361],{"separator":2360},[2348,35477,35478,35480],{},[2071,35479,2861],{},[2210,35481,646],{},[2075,35483,2090],{"stretchy":2083},[2075,35485,2077],{},[2210,35487,14195],{},[23501,35489],{"width":31103},[23501,35491,35492],{},[2363,35493,35494],{},"(6.25)",[2092,35496,35497],{"encoding":2094},"\\begin{aligned}\n\\mathcal{L}'_1 &= P_1^* - \\lambda U'_1 = 0, \\\\\n\\mathcal{L}'_2 &= P_2^* - \\lambda U'_2 = 0, \\\\\n\\mathcal{L}'_\\lambda &= U^* - U(Q_1, Q_2) = 0.\n\\end{aligned}\n\\tag{6.25}",[55,35499,35500],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[1647,35502,35504],{"className":35503},[2059],[2061,35505,35506],{"xmlns":2063,"display":31093},[2065,35507,35508,35606],{},[23493,35509,35510],{"width":31098},[23498,35511,35512,35514,35599,35601],{},[23501,35513],{"width":31103},[23501,35515,35516],{},[2068,35517,35518,35520,35522,35528,35530,35536,35538,35540,35542,35544,35546,35548,35597],{},[2071,35519,4271],{},[2075,35521,2084],{"stretchy":2083},[2348,35523,35524,35526],{},[2071,35525,2861],{},[2210,35527,638],{},[2075,35529,2361],{"separator":2360},[2348,35531,35532,35534],{},[2071,35533,2861],{},[2210,35535,646],{},[2075,35537,2361],{"separator":2360},[2071,35539,19181],{},[2075,35541,2090],{"stretchy":2083},[2075,35543,2077],{},[2075,35545,2303],{},[2071,35547,19181],{},[2068,35549,35550,35552,35564,35566,35579,35581,35583,35595],{},[2075,35551,2084],{"fence":2360},[9252,35553,35554,35556,35558],{},[2071,35555,10871],{},[2210,35557,2976],{},[2068,35559,35560,35562],{},[2075,35561,2452],{"mathvariant":2450},[2075,35563,2452],{"mathvariant":2450},[2075,35565,2176],{},[9252,35567,35568,35570,35573],{},[2071,35569,10871],{},[2210,35571,35572],{},"22",[2068,35574,35575,35577],{},[2075,35576,2452],{"mathvariant":2450},[2075,35578,2452],{"mathvariant":2450},[2075,35580,2176],{},[2210,35582,646],{},[9252,35584,35585,35587,35589],{},[2071,35586,10871],{},[2210,35588,3583],{},[2068,35590,35591,35593],{},[2075,35592,2452],{"mathvariant":2450},[2075,35594,2452],{"mathvariant":2450},[2075,35596,2090],{"fence":2360},[2071,35598,195],{"mathvariant":2450},[23501,35600],{"width":31103},[23501,35602,35603],{},[2363,35604,35605],{},"(6.26)",[2092,35607,35608],{"encoding":2094},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[55,35610,35611,35614,35615,35654,35655,35694,35695,35745,35746,35772,35773,35790,35791,35817],{},[95,35612,35613],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[1647,35616,35618],{"className":35617},[2059],[2061,35619,35620],{"xmlns":2063},[2065,35621,35622,35652],{},[2068,35623,35624,35630,35632,35640,35642,35650],{},[2205,35625,35626,35628],{},[2071,35627,2861],{},[2075,35629,4441],{},[2075,35631,2561],{"stretchy":2083},[9252,35633,35634,35636,35638],{},[2071,35635,2861],{},[2210,35637,638],{},[2075,35639,4441],{},[2075,35641,2361],{"separator":2360},[9252,35643,35644,35646,35648],{},[2071,35645,2861],{},[2210,35647,646],{},[2075,35649,4441],{},[2075,35651,2576],{"stretchy":2083},[2092,35653,31354],{"encoding":2094}," dotyku křivky užitečnosti ",[1647,35656,35658],{"className":35657},[2059],[2061,35659,35660],{"xmlns":2063},[2065,35661,35662,35692],{},[2068,35663,35664,35670,35672,35674,35676,35682,35684,35690],{},[2205,35665,35666,35668],{},[2071,35667,10871],{},[2075,35669,4441],{},[2075,35671,2077],{},[2071,35673,10871],{},[2075,35675,2084],{"stretchy":2083},[2348,35677,35678,35680],{},[2071,35679,2861],{},[2210,35681,638],{},[2075,35683,2361],{"separator":2360},[2348,35685,35686,35688],{},[2071,35687,2861],{},[2210,35689,646],{},[2075,35691,2090],{"stretchy":2083},[2092,35693,20403],{"encoding":2094}," s přímkou výdajů ",[1647,35696,35698],{"className":35697},[2059],[2061,35699,35700],{"xmlns":2063},[2065,35701,35702,35742],{},[2068,35703,35704,35710,35712,35720,35726,35728,35736],{},[2205,35705,35706,35708],{},[2071,35707,554],{},[2075,35709,4441],{},[2075,35711,2077],{},[9252,35713,35714,35716,35718],{},[2071,35715,575],{},[2210,35717,638],{},[2075,35719,4441],{},[2348,35721,35722,35724],{},[2071,35723,2861],{},[2210,35725,638],{},[2075,35727,2176],{},[9252,35729,35730,35732,35734],{},[2071,35731,575],{},[2210,35733,646],{},[2075,35735,4441],{},[2348,35737,35738,35740],{},[2071,35739,2861],{},[2210,35741,646],{},[2092,35743,35744],{"encoding":2094},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[1647,35747,35749],{"className":35748},[2059],[2061,35750,35751],{"xmlns":2063},[2065,35752,35753,35769],{},[2068,35754,35755,35761,35763],{},[2348,35756,35757,35759],{},[2071,35758,554],{},[2210,35760,630],{},[2075,35762,3521],{},[2205,35764,35765,35767],{},[2071,35766,554],{},[2075,35768,4441],{},[2092,35770,35771],{"encoding":2094},"E_0 \u003C E^*"," nestačí k dosažení ",[1647,35774,35776],{"className":35775},[2059],[2061,35777,35778],{"xmlns":2063},[2065,35779,35780,35788],{},[2068,35781,35782],{},[2205,35783,35784,35786],{},[2071,35785,10871],{},[2075,35787,4441],{},[2092,35789,30989],{"encoding":2094},", hladina ",[1647,35792,35794],{"className":35793},[2059],[2061,35795,35796],{"xmlns":2063},[2065,35797,35798,35814],{},[2068,35799,35800,35806,35808],{},[2348,35801,35802,35804],{},[2071,35803,554],{},[2210,35805,638],{},[2075,35807,3482],{},[2205,35809,35810,35812],{},[2071,35811,554],{},[2075,35813,4441],{},[2092,35815,35816],{"encoding":2094},"E_1 > E^*"," je nadbytečná.",[1023,35819,35820,35825],{},[55,35821,35822,35824],{},[1647,35823,4659],{}," Postup — duální úloha (minimalizace výdajů)",[201,35826,35827,35877,35963,36003,36078],{},[92,35828,35829,1445,35832,35876],{},[95,35830,35831],{},"Zapiš vazbu",[1647,35833,35835],{"className":35834},[2059],[2061,35836,35837],{"xmlns":2063},[2065,35838,35839,35873],{},[2068,35840,35841,35847,35849,35851,35853,35859,35861,35867,35869,35871],{},[2205,35842,35843,35845],{},[2071,35844,10871],{},[2075,35846,4441],{},[2075,35848,2303],{},[2071,35850,10871],{},[2075,35852,2084],{"stretchy":2083},[2348,35854,35855,35857],{},[2071,35856,2861],{},[2210,35858,638],{},[2075,35860,2361],{"separator":2360},[2348,35862,35863,35865],{},[2071,35864,2861],{},[2210,35866,646],{},[2075,35868,2090],{"stretchy":2083},[2075,35870,2077],{},[2210,35872,630],{},[2092,35874,35875],{"encoding":2094},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[92,35878,35879,1445,35881,195],{},[95,35880,32287],{},[1647,35882,35884],{"className":35883},[2059],[2061,35885,35886],{"xmlns":2063},[2065,35887,35888,35960],{},[2068,35889,35890,35892,35894,35902,35908,35910,35918,35924,35926,35928,35930,35936,35938,35940,35942,35948,35950,35956,35958],{},[2071,35891,586],{"mathvariant":31575},[2075,35893,2077],{},[9252,35895,35896,35898,35900],{},[2071,35897,575],{},[2210,35899,638],{},[2075,35901,4441],{},[2348,35903,35904,35906],{},[2071,35905,2861],{},[2210,35907,638],{},[2075,35909,2176],{},[9252,35911,35912,35914,35916],{},[2071,35913,575],{},[2210,35915,646],{},[2075,35917,4441],{},[2348,35919,35920,35922],{},[2071,35921,2861],{},[2210,35923,646],{},[2075,35925,2176],{},[2071,35927,19181],{},[2075,35929,2084],{"stretchy":2083},[2205,35931,35932,35934],{},[2071,35933,10871],{},[2075,35935,4441],{},[2075,35937,2303],{},[2071,35939,10871],{},[2075,35941,2084],{"stretchy":2083},[2348,35943,35944,35946],{},[2071,35945,2861],{},[2210,35947,638],{},[2075,35949,2361],{"separator":2360},[2348,35951,35952,35954],{},[2071,35953,2861],{},[2210,35955,646],{},[2075,35957,2090],{"stretchy":2083},[2075,35959,2090],{"stretchy":2083},[2092,35961,35962],{"encoding":2094},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[92,35964,35965,35968,35969,36002],{},[95,35966,35967],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[1647,35970,35972],{"className":35971},[2059],[2061,35973,35974],{"xmlns":2063},[2065,35975,35976,36000],{},[2068,35977,35978,35980,35982,35990,35992],{},[2363,35979,11733],{},[2075,35981,2077],{},[9252,35983,35984,35986,35988],{},[2071,35985,575],{},[2210,35987,638],{},[2075,35989,4441],{},[2071,35991,4761],{"mathvariant":2450},[9252,35993,35994,35996,35998],{},[2071,35995,575],{},[2210,35997,646],{},[2075,35999,4441],{},[2092,36001,32006],{"encoding":2094}," (stejná jako u maximalizace!).",[92,36004,36005,1445,36008,36048,36049,195],{},[95,36006,36007],{},"Dosaď do vazby",[1647,36009,36011],{"className":36010},[2059],[2061,36012,36013],{"xmlns":2063},[2065,36014,36015,36045],{},[2068,36016,36017,36019,36021,36027,36029,36035,36037,36039],{},[2071,36018,10871],{},[2075,36020,2084],{"stretchy":2083},[2348,36022,36023,36025],{},[2071,36024,2861],{},[2210,36026,638],{},[2075,36028,2361],{"separator":2360},[2348,36030,36031,36033],{},[2071,36032,2861],{},[2210,36034,646],{},[2075,36036,2090],{"stretchy":2083},[2075,36038,2077],{},[2205,36040,36041,36043],{},[2071,36042,10871],{},[2075,36044,4441],{},[2092,36046,36047],{"encoding":2094},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[1647,36050,36052],{"className":36051},[2059],[2061,36053,36054],{"xmlns":2063},[2065,36055,36056,36076],{},[2068,36057,36058,36066,36068],{},[9252,36059,36060,36062,36064],{},[2071,36061,2861],{},[2210,36063,638],{},[2075,36065,4441],{},[2075,36067,2361],{"separator":2360},[9252,36069,36070,36072,36074],{},[2071,36071,2861],{},[2210,36073,646],{},[2075,36075,4441],{},[2092,36077,32528],{"encoding":2094},[92,36079,36080,1445,36083,36137],{},[95,36081,36082],{},"Vypočítej minimální výdaje",[1647,36084,36086],{"className":36085},[2059],[2061,36087,36088],{"xmlns":2063},[2065,36089,36090,36134],{},[2068,36091,36092,36098,36100,36108,36116,36118,36126],{},[2205,36093,36094,36096],{},[2071,36095,554],{},[2075,36097,4441],{},[2075,36099,2077],{},[9252,36101,36102,36104,36106],{},[2071,36103,575],{},[2210,36105,638],{},[2075,36107,4441],{},[9252,36109,36110,36112,36114],{},[2071,36111,2861],{},[2210,36113,638],{},[2075,36115,4441],{},[2075,36117,2176],{},[9252,36119,36120,36122,36124],{},[2071,36121,575],{},[2210,36123,646],{},[2075,36125,4441],{},[9252,36127,36128,36130,36132],{},[2071,36129,2861],{},[2210,36131,646],{},[2075,36133,4441],{},[2092,36135,36136],{"encoding":2094},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[84,36139,36141,36142],{"id":36140},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[1647,36143,36145],{"className":36144},[2059],[2061,36146,36147],{"xmlns":2063},[2065,36148,36149,36183],{},[2068,36150,36151,36153,36155,36169],{},[2071,36152,10871],{},[2075,36154,2077],{},[9252,36156,36157,36159,36161],{},[2071,36158,2861],{},[2210,36160,638],{},[2068,36162,36163,36165,36167],{},[2210,36164,638],{},[2071,36166,4761],{"mathvariant":2450},[2210,36168,646],{},[9252,36170,36171,36173,36175],{},[2071,36172,2861],{},[2210,36174,646],{},[2068,36176,36177,36179,36181],{},[2210,36178,638],{},[2071,36180,4761],{"mathvariant":2450},[2210,36182,646],{},[2092,36184,36185],{"encoding":2094},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[55,36187,36188,36189,835,36211,835,36235,33373],{},"Dáno ",[1647,36190,36192],{"className":36191},[2059],[2061,36193,36194],{"xmlns":2063},[2065,36195,36196,36208],{},[2068,36197,36198,36204,36206],{},[2205,36199,36200,36202],{},[2071,36201,10871],{},[2075,36203,4441],{},[2075,36205,2077],{},[2210,36207,646],{},[2092,36209,36210],{"encoding":2094},"U^* = 2",[1647,36212,36214],{"className":36213},[2059],[2061,36215,36216],{"xmlns":2063},[2065,36217,36218,36232],{},[2068,36219,36220,36228,36230],{},[9252,36221,36222,36224,36226],{},[2071,36223,575],{},[2210,36225,638],{},[2075,36227,4441],{},[2075,36229,2077],{},[2210,36231,26528],{},[2092,36233,36234],{"encoding":2094},"P_1^* = 0{,}25",[1647,36236,36238],{"className":36237},[2059],[2061,36239,36240],{"xmlns":2063},[2065,36241,36242,36256],{},[2068,36243,36244,36252,36254],{},[9252,36245,36246,36248,36250],{},[2071,36247,575],{},[2210,36249,646],{},[2075,36251,4441],{},[2075,36253,2077],{},[2210,36255,638],{},[2092,36257,36258],{"encoding":2094},"P_2^* = 1",[1647,36260,36262],{"className":36261},[2059],[2061,36263,36264],{"xmlns":2063,"display":31093},[2065,36265,36266,36330],{},[2068,36267,36268,36270,36272,36274,36280,36282,36288,36290,36292,36294,36296,36298,36312,36326,36328],{},[2071,36269,586],{"mathvariant":31575},[2075,36271,2077],{},[2210,36273,26528],{},[2348,36275,36276,36278],{},[2071,36277,2861],{},[2210,36279,638],{},[2075,36281,2176],{},[2348,36283,36284,36286],{},[2071,36285,2861],{},[2210,36287,646],{},[2075,36289,2176],{},[2071,36291,19181],{},[2075,36293,2084],{"stretchy":2083},[2210,36295,646],{},[2075,36297,2303],{},[9252,36299,36300,36302,36304],{},[2071,36301,2861],{},[2210,36303,638],{},[2068,36305,36306,36308,36310],{},[2210,36307,638],{},[2071,36309,4761],{"mathvariant":2450},[2210,36311,646],{},[9252,36313,36314,36316,36318],{},[2071,36315,2861],{},[2210,36317,646],{},[2068,36319,36320,36322,36324],{},[2210,36321,638],{},[2071,36323,4761],{"mathvariant":2450},[2210,36325,646],{},[2075,36327,2090],{"stretchy":2083},[2071,36329,195],{"mathvariant":2450},[2092,36331,36332],{"encoding":2094},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[55,36334,33458],{},[1647,36336,36338],{"className":36337},[2059],[2061,36339,36340],{"xmlns":2063,"display":31093},[2065,36341,36342,36556],{},[23493,36343,36344,36420,36496],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,36345,36346,36358],{},[23501,36347,36348],{},[2400,36349,36350],{"scriptlevel":630,"displaystyle":2360},[9252,36351,36352,36354,36356],{},[2071,36353,586],{"mathvariant":31575},[2210,36355,638],{},[2075,36357,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,36359,36360],{},[2400,36361,36362],{"scriptlevel":630,"displaystyle":2360},[2068,36363,36364,36366,36368,36370,36372,36374,36376,36384,36400,36414,36416,36418],{},[2068,36365],{},[2075,36367,2077],{},[2210,36369,26528],{},[2075,36371,2303],{},[2071,36373,19181],{},[2075,36375,3251],{},[2400,36377,36378],{"scriptlevel":630,"displaystyle":2083},[2403,36379,36380,36382],{},[2210,36381,638],{},[2210,36383,646],{},[9252,36385,36386,36388,36390],{},[2071,36387,2861],{},[2210,36389,638],{},[2068,36391,36392,36394,36396,36398],{},[2075,36393,2303],{},[2210,36395,638],{},[2071,36397,4761],{"mathvariant":2450},[2210,36399,646],{},[9252,36401,36402,36404,36406],{},[2071,36403,2861],{},[2210,36405,646],{},[2068,36407,36408,36410,36412],{},[2210,36409,638],{},[2071,36411,4761],{"mathvariant":2450},[2210,36413,646],{},[2075,36415,2077],{},[2210,36417,630],{},[2075,36419,2361],{"separator":2360},[23498,36421,36422,36434],{},[23501,36423,36424],{},[2400,36425,36426],{"scriptlevel":630,"displaystyle":2360},[9252,36427,36428,36430,36432],{},[2071,36429,586],{"mathvariant":31575},[2210,36431,646],{},[2075,36433,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,36435,36436],{},[2400,36437,36438],{"scriptlevel":630,"displaystyle":2360},[2068,36439,36440,36442,36444,36446,36448,36450,36452,36460,36474,36490,36492,36494],{},[2068,36441],{},[2075,36443,2077],{},[2210,36445,638],{},[2075,36447,2303],{},[2071,36449,19181],{},[2075,36451,3251],{},[2400,36453,36454],{"scriptlevel":630,"displaystyle":2083},[2403,36455,36456,36458],{},[2210,36457,638],{},[2210,36459,646],{},[9252,36461,36462,36464,36466],{},[2071,36463,2861],{},[2210,36465,638],{},[2068,36467,36468,36470,36472],{},[2210,36469,638],{},[2071,36471,4761],{"mathvariant":2450},[2210,36473,646],{},[9252,36475,36476,36478,36480],{},[2071,36477,2861],{},[2210,36479,646],{},[2068,36481,36482,36484,36486,36488],{},[2075,36483,2303],{},[2210,36485,638],{},[2071,36487,4761],{"mathvariant":2450},[2210,36489,646],{},[2075,36491,2077],{},[2210,36493,630],{},[2075,36495,2361],{"separator":2360},[23498,36497,36498,36510],{},[23501,36499,36500],{},[2400,36501,36502],{"scriptlevel":630,"displaystyle":2360},[9252,36503,36504,36506,36508],{},[2071,36505,586],{"mathvariant":31575},[2071,36507,19181],{},[2075,36509,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,36511,36512],{},[2400,36513,36514],{"scriptlevel":630,"displaystyle":2360},[2068,36515,36516,36518,36520,36522,36524,36538,36552,36554],{},[2068,36517],{},[2075,36519,2077],{},[2210,36521,646],{},[2075,36523,2303],{},[9252,36525,36526,36528,36530],{},[2071,36527,2861],{},[2210,36529,638],{},[2068,36531,36532,36534,36536],{},[2210,36533,638],{},[2071,36535,4761],{"mathvariant":2450},[2210,36537,646],{},[9252,36539,36540,36542,36544],{},[2071,36541,2861],{},[2210,36543,646],{},[2068,36545,36546,36548,36550],{},[2210,36547,638],{},[2071,36549,4761],{"mathvariant":2450},[2210,36551,646],{},[2075,36553,2077],{},[2210,36555,14195],{},[2092,36557,36558],{"encoding":2094},"\\begin{aligned}\n\\mathcal{L}'_1 &= 0{,}25 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F2} = 0, \\\\\n\\mathcal{L}'_2 &= 1 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{1\u002F2} Q_2^{-1\u002F2} = 0, \\\\\n\\mathcal{L}'_\\lambda &= 2 - Q_1^{1\u002F2} Q_2^{1\u002F2} = 0.\n\\end{aligned}",[55,36560,36561,36562,20314,36592,36620,36621,5676,36683,835,36733,36755,36756,195],{},"Podílem prvních dvou rovnic: ",[1647,36563,36565],{"className":36564},[2059],[2061,36566,36567],{"xmlns":2063},[2065,36568,36569,36589],{},[2068,36570,36571,36573,36575,36581,36583],{},[2210,36572,26528],{},[2075,36574,2077],{},[2348,36576,36577,36579],{},[2071,36578,2861],{},[2210,36580,646],{},[2071,36582,4761],{"mathvariant":2450},[2348,36584,36585,36587],{},[2071,36586,2861],{},[2210,36588,638],{},[2092,36590,36591],{"encoding":2094},"0{,}25 = Q_2 \u002F Q_1",[1647,36593,36595],{"className":36594},[2059],[2061,36596,36597],{"xmlns":2063},[2065,36598,36599,36617],{},[2068,36600,36601,36607,36609,36611],{},[2348,36602,36603,36605],{},[2071,36604,2861],{},[2210,36606,646],{},[2075,36608,2077],{},[2210,36610,26528],{},[2348,36612,36613,36615],{},[2071,36614,2861],{},[2210,36616,638],{},[2092,36618,36619],{"encoding":2094},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[1647,36622,36624],{"className":36623},[2059],[2061,36625,36626],{"xmlns":2063},[2065,36627,36628,36680],{},[2068,36629,36630,36644,36646,36648,36654,36666,36668,36670,36676,36678],{},[9252,36631,36632,36634,36636],{},[2071,36633,2861],{},[2210,36635,638],{},[2068,36637,36638,36640,36642],{},[2210,36639,638],{},[2071,36641,4761],{"mathvariant":2450},[2210,36643,646],{},[2075,36645,2084],{"stretchy":2083},[2210,36647,26528],{},[2348,36649,36650,36652],{},[2071,36651,2861],{},[2210,36653,638],{},[2205,36655,36656,36658],{},[2075,36657,2090],{"stretchy":2083},[2068,36659,36660,36662,36664],{},[2210,36661,638],{},[2071,36663,4761],{"mathvariant":2450},[2210,36665,646],{},[2075,36667,2077],{},[2210,36669,5096],{},[2348,36671,36672,36674],{},[2071,36673,2861],{},[2210,36675,638],{},[2075,36677,2077],{},[2210,36679,646],{},[2092,36681,36682],{"encoding":2094},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[95,36684,36685,835,36709],{},[1647,36686,36688],{"className":36687},[2059],[2061,36689,36690],{"xmlns":2063},[2065,36691,36692,36706],{},[2068,36693,36694,36702,36704],{},[9252,36695,36696,36698,36700],{},[2071,36697,2861],{},[2210,36699,638],{},[2075,36701,4441],{},[2075,36703,2077],{},[2210,36705,662],{},[2092,36707,36708],{"encoding":2094},"Q_1^* = 4",[1647,36710,36712],{"className":36711},[2059],[2061,36713,36714],{"xmlns":2063},[2065,36715,36716,36730],{},[2068,36717,36718,36726,36728],{},[9252,36719,36720,36722,36724],{},[2071,36721,2861],{},[2210,36723,646],{},[2075,36725,4441],{},[2075,36727,2077],{},[2210,36729,638],{},[2092,36731,36732],{"encoding":2094},"Q_2^* = 1",[1647,36734,36736],{"className":36735},[2059],[2061,36737,36738],{"xmlns":2063},[2065,36739,36740,36752],{},[2068,36741,36742,36748,36750],{},[2205,36743,36744,36746],{},[2071,36745,19181],{},[2075,36747,4441],{},[2075,36749,2077],{},[2210,36751,638],{},[2092,36753,36754],{"encoding":2094},"\\lambda^* = 1",". Minimální výdaje: ",[1647,36757,36759],{"className":36758},[2059],[2061,36760,36761],{"xmlns":2063},[2065,36762,36763,36791],{},[2068,36764,36765,36771,36773,36775,36777,36779,36781,36783,36785,36787,36789],{},[2205,36766,36767,36769],{},[2071,36768,554],{},[2075,36770,4441],{},[2075,36772,2077],{},[2210,36774,26528],{},[2075,36776,3251],{},[2210,36778,662],{},[2075,36780,2176],{},[2210,36782,638],{},[2075,36784,3251],{},[2210,36786,638],{},[2075,36788,2077],{},[2210,36790,646],{},[2092,36792,36793],{"encoding":2094},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[55,36795,36796,36799,36800,835,36866,835,36932,36998,36999,37036,37037,37059,37060,195],{},[3982,36797,36798],{},"Ověření postačující podmínky"," (6.26): ",[1647,36801,36803],{"className":36802},[2059],[2061,36804,36805],{"xmlns":2063},[2065,36806,36807,36863],{},[2068,36808,36809,36821,36823,36825,36833,36849],{},[9252,36810,36811,36813,36815],{},[2071,36812,10871],{},[2210,36814,2976],{},[2068,36816,36817,36819],{},[2075,36818,2452],{"mathvariant":2450},[2075,36820,2452],{"mathvariant":2450},[2075,36822,2077],{},[2075,36824,2303],{},[2400,36826,36827],{"scriptlevel":630,"displaystyle":2083},[2403,36828,36829,36831],{},[2210,36830,638],{},[2210,36832,662],{},[9252,36834,36835,36837,36839],{},[2071,36836,2861],{},[2210,36838,638],{},[2068,36840,36841,36843,36845,36847],{},[2075,36842,2303],{},[2210,36844,654],{},[2071,36846,4761],{"mathvariant":2450},[2210,36848,646],{},[9252,36850,36851,36853,36855],{},[2071,36852,2861],{},[2210,36854,646],{},[2068,36856,36857,36859,36861],{},[2210,36858,638],{},[2071,36860,4761],{"mathvariant":2450},[2210,36862,646],{},[2092,36864,36865],{"encoding":2094},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[1647,36867,36869],{"className":36868},[2059],[2061,36870,36871],{"xmlns":2063},[2065,36872,36873,36929],{},[2068,36874,36875,36887,36889,36891,36899,36913],{},[9252,36876,36877,36879,36881],{},[2071,36878,10871],{},[2210,36880,35572],{},[2068,36882,36883,36885],{},[2075,36884,2452],{"mathvariant":2450},[2075,36886,2452],{"mathvariant":2450},[2075,36888,2077],{},[2075,36890,2303],{},[2400,36892,36893],{"scriptlevel":630,"displaystyle":2083},[2403,36894,36895,36897],{},[2210,36896,638],{},[2210,36898,662],{},[9252,36900,36901,36903,36905],{},[2071,36902,2861],{},[2210,36904,638],{},[2068,36906,36907,36909,36911],{},[2210,36908,638],{},[2071,36910,4761],{"mathvariant":2450},[2210,36912,646],{},[9252,36914,36915,36917,36919],{},[2071,36916,2861],{},[2210,36918,646],{},[2068,36920,36921,36923,36925,36927],{},[2075,36922,2303],{},[2210,36924,654],{},[2071,36926,4761],{"mathvariant":2450},[2210,36928,646],{},[2092,36930,36931],{"encoding":2094},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[1647,36933,36935],{"className":36934},[2059],[2061,36936,36937],{"xmlns":2063},[2065,36938,36939,36995],{},[2068,36940,36941,36953,36955,36963,36979],{},[9252,36942,36943,36945,36947],{},[2071,36944,10871],{},[2210,36946,3583],{},[2068,36948,36949,36951],{},[2075,36950,2452],{"mathvariant":2450},[2075,36952,2452],{"mathvariant":2450},[2075,36954,2077],{},[2400,36956,36957],{"scriptlevel":630,"displaystyle":2083},[2403,36958,36959,36961],{},[2210,36960,638],{},[2210,36962,662],{},[9252,36964,36965,36967,36969],{},[2071,36966,2861],{},[2210,36968,638],{},[2068,36970,36971,36973,36975,36977],{},[2075,36972,2303],{},[2210,36974,638],{},[2071,36976,4761],{"mathvariant":2450},[2210,36978,646],{},[9252,36980,36981,36983,36985],{},[2071,36982,2861],{},[2210,36984,646],{},[2068,36986,36987,36989,36991,36993],{},[2075,36988,2303],{},[2210,36990,638],{},[2071,36992,4761],{"mathvariant":2450},[2210,36994,646],{},[2092,36996,36997],{"encoding":2094},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[1647,37000,37002],{"className":37001},[2059],[2061,37003,37004],{"xmlns":2063},[2065,37005,37006,37033],{},[2068,37007,37008,37010,37012,37014,37016,37018,37020,37022,37024,37026,37029,37031],{},[2071,37009,4271],{},[2075,37011,2084],{"stretchy":2083},[2210,37013,662],{},[2075,37015,2361],{"separator":2360},[2210,37017,638],{},[2075,37019,2361],{"separator":2360},[2210,37021,638],{},[2075,37023,2090],{"stretchy":2083},[2075,37025,2077],{},[2210,37027,37028],{},"0,28125",[2075,37030,3482],{},[2210,37032,630],{},[2092,37034,37035],{"encoding":2094},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[1647,37038,37040],{"className":37039},[2059],[2061,37041,37042],{"xmlns":2063},[2065,37043,37044,37056],{},[2068,37045,37046,37048,37050,37052,37054],{},[2075,37047,2561],{"stretchy":2083},[2210,37049,662],{},[2075,37051,2361],{"separator":2360},[2210,37053,638],{},[2075,37055,2576],{"stretchy":2083},[2092,37057,37058],{"encoding":2094},"[4, 1]"," je vázané ",[95,37061,3849],{},[84,37063,37065],{"id":37064},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[55,37067,37068],{},"Obecně:",[1647,37070,37072],{"className":37071},[2059],[2061,37073,37074],{"xmlns":2063,"display":31093},[2065,37075,37076,37171],{},[23493,37077,37078],{"width":31098},[23498,37079,37080,37082,37164,37166],{},[23501,37081],{"width":31103},[23501,37083,37084],{},[2068,37085,37086,37092,37094,37100,37102,37108,37110,37116,37118,37120,37122,37124,37126,37132,37134,37140,37142,37148,37150,37156,37158,37160,37162],{},[2348,37087,37088,37090],{},[2071,37089,2861],{},[2210,37091,638],{},[2075,37093,2077],{},[2348,37095,37096,37098],{},[2071,37097,4271],{},[2210,37099,638],{},[2075,37101,2084],{"stretchy":2083},[2348,37103,37104,37106],{},[2071,37105,575],{},[2210,37107,638],{},[2075,37109,2361],{"separator":2360},[2348,37111,37112,37114],{},[2071,37113,575],{},[2210,37115,646],{},[2075,37117,2361],{"separator":2360},[2071,37119,10871],{},[2075,37121,2090],{"stretchy":2083},[2075,37123,2361],{"separator":2360},[5965,37125],{"width":17019},[2348,37127,37128,37130],{},[2071,37129,2861],{},[2210,37131,646],{},[2075,37133,2077],{},[2348,37135,37136,37138],{},[2071,37137,4271],{},[2210,37139,646],{},[2075,37141,2084],{"stretchy":2083},[2348,37143,37144,37146],{},[2071,37145,575],{},[2210,37147,638],{},[2075,37149,2361],{"separator":2360},[2348,37151,37152,37154],{},[2071,37153,575],{},[2210,37155,646],{},[2075,37157,2361],{"separator":2360},[2071,37159,10871],{},[2075,37161,2090],{"stretchy":2083},[2075,37163,2361],{"separator":2360},[23501,37165],{"width":31103},[23501,37167,37168],{},[2363,37169,37170],{},"(6.27)",[2092,37172,37173],{"encoding":2094},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[1647,37175,37177],{"className":37176},[2059],[2061,37178,37179],{"xmlns":2063,"display":31093},[2065,37180,37181,37228],{},[23493,37182,37183],{"width":31098},[23498,37184,37185,37187,37221,37223],{},[23501,37186],{"width":31103},[23501,37188,37189],{},[2068,37190,37191,37193,37195,37197,37199,37205,37207,37213,37215,37217,37219],{},[2071,37192,19181],{},[2075,37194,2077],{},[2071,37196,19181],{},[2075,37198,2084],{"stretchy":2083},[2348,37200,37201,37203],{},[2071,37202,575],{},[2210,37204,638],{},[2075,37206,2361],{"separator":2360},[2348,37208,37209,37211],{},[2071,37210,575],{},[2210,37212,646],{},[2075,37214,2361],{"separator":2360},[2071,37216,10871],{},[2075,37218,2090],{"stretchy":2083},[2071,37220,195],{"mathvariant":2450},[23501,37222],{"width":31103},[23501,37224,37225],{},[2363,37226,37227],{},"(6.28)",[2092,37229,37230],{"encoding":2094},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[55,37232,37233,37234,1445,37237,37250,37251,37264],{},"Hicksova poptávka závisí na ",[95,37235,37236],{},"hladině užitečnosti",[1647,37238,37240],{"className":37239},[2059],[2061,37241,37242],{"xmlns":2063},[2065,37243,37244,37248],{},[2068,37245,37246],{},[2071,37247,10871],{},[2092,37249,10871],{"encoding":2094}," (nikoli na důchodu ",[1647,37252,37254],{"className":37253},[2059],[2061,37255,37256],{"xmlns":2063},[2065,37257,37258,37262],{},[2068,37259,37260],{},[2071,37261,9214],{},[2092,37263,9214],{"encoding":2094}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[84,37266,37268,37269],{"id":37267},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[1647,37270,37272],{"className":37271},[2059],[2061,37273,37274],{"xmlns":2063},[2065,37275,37276,37310],{},[2068,37277,37278,37280,37282,37296],{},[2071,37279,10871],{},[2075,37281,2077],{},[9252,37283,37284,37286,37288],{},[2071,37285,2861],{},[2210,37287,638],{},[2068,37289,37290,37292,37294],{},[2210,37291,638],{},[2071,37293,4761],{"mathvariant":2450},[2210,37295,646],{},[9252,37297,37298,37300,37302],{},[2071,37299,2861],{},[2210,37301,646],{},[2068,37303,37304,37306,37308],{},[2210,37305,638],{},[2071,37307,4761],{"mathvariant":2450},[2210,37309,646],{},[2092,37311,36185],{"encoding":2094},[55,37313,37314,37344],{},[1647,37315,37317],{"className":37316},[2059],[2061,37318,37319],{"xmlns":2063},[2065,37320,37321,37341],{},[2068,37322,37323,37329,37331,37337,37339],{},[2348,37324,37325,37327],{},[2071,37326,575],{},[2210,37328,638],{},[2075,37330,2361],{"separator":2360},[2348,37332,37333,37335],{},[2071,37334,575],{},[2210,37336,646],{},[2075,37338,2361],{"separator":2360},[2071,37340,10871],{},[2092,37342,37343],{"encoding":2094},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[1647,37346,37348],{"className":37347},[2059],[2061,37349,37350],{"xmlns":2063,"display":31093},[2065,37351,37352,37426],{},[2068,37353,37354,37356,37358,37364,37370,37372,37378,37384,37386,37388,37390,37392,37394,37408,37422,37424],{},[2071,37355,586],{"mathvariant":31575},[2075,37357,2077],{},[2348,37359,37360,37362],{},[2071,37361,575],{},[2210,37363,638],{},[2348,37365,37366,37368],{},[2071,37367,2861],{},[2210,37369,638],{},[2075,37371,2176],{},[2348,37373,37374,37376],{},[2071,37375,575],{},[2210,37377,646],{},[2348,37379,37380,37382],{},[2071,37381,2861],{},[2210,37383,646],{},[2075,37385,2176],{},[2071,37387,19181],{},[2075,37389,2084],{"stretchy":2083},[2071,37391,10871],{},[2075,37393,2303],{},[9252,37395,37396,37398,37400],{},[2071,37397,2861],{},[2210,37399,638],{},[2068,37401,37402,37404,37406],{},[2210,37403,638],{},[2071,37405,4761],{"mathvariant":2450},[2210,37407,646],{},[9252,37409,37410,37412,37414],{},[2071,37411,2861],{},[2210,37413,646],{},[2068,37415,37416,37418,37420],{},[2210,37417,638],{},[2071,37419,4761],{"mathvariant":2450},[2210,37421,646],{},[2075,37423,2090],{"stretchy":2083},[2071,37425,195],{"mathvariant":2450},[2092,37427,37428],{"encoding":2094},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[55,37430,33458],{},[1647,37432,37434],{"className":37433},[2059],[2061,37435,37436],{"xmlns":2063,"display":31093},[2065,37437,37438,37660],{},[23493,37439,37440,37520,37600],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,37441,37442,37454],{},[23501,37443,37444],{},[2400,37445,37446],{"scriptlevel":630,"displaystyle":2360},[9252,37447,37448,37450,37452],{},[2071,37449,586],{"mathvariant":31575},[2210,37451,638],{},[2075,37453,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,37455,37456],{},[2400,37457,37458],{"scriptlevel":630,"displaystyle":2360},[2068,37459,37460,37462,37464,37470,37472,37474,37476,37484,37500,37514,37516,37518],{},[2068,37461],{},[2075,37463,2077],{},[2348,37465,37466,37468],{},[2071,37467,575],{},[2210,37469,638],{},[2075,37471,2303],{},[2071,37473,19181],{},[2075,37475,3251],{},[2400,37477,37478],{"scriptlevel":630,"displaystyle":2083},[2403,37479,37480,37482],{},[2210,37481,638],{},[2210,37483,646],{},[9252,37485,37486,37488,37490],{},[2071,37487,2861],{},[2210,37489,638],{},[2068,37491,37492,37494,37496,37498],{},[2075,37493,2303],{},[2210,37495,638],{},[2071,37497,4761],{"mathvariant":2450},[2210,37499,646],{},[9252,37501,37502,37504,37506],{},[2071,37503,2861],{},[2210,37505,646],{},[2068,37507,37508,37510,37512],{},[2210,37509,638],{},[2071,37511,4761],{"mathvariant":2450},[2210,37513,646],{},[2075,37515,2077],{},[2210,37517,630],{},[2075,37519,2361],{"separator":2360},[23498,37521,37522,37534],{},[23501,37523,37524],{},[2400,37525,37526],{"scriptlevel":630,"displaystyle":2360},[9252,37527,37528,37530,37532],{},[2071,37529,586],{"mathvariant":31575},[2210,37531,646],{},[2075,37533,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,37535,37536],{},[2400,37537,37538],{"scriptlevel":630,"displaystyle":2360},[2068,37539,37540,37542,37544,37550,37552,37554,37556,37564,37578,37594,37596,37598],{},[2068,37541],{},[2075,37543,2077],{},[2348,37545,37546,37548],{},[2071,37547,575],{},[2210,37549,646],{},[2075,37551,2303],{},[2071,37553,19181],{},[2075,37555,3251],{},[2400,37557,37558],{"scriptlevel":630,"displaystyle":2083},[2403,37559,37560,37562],{},[2210,37561,638],{},[2210,37563,646],{},[9252,37565,37566,37568,37570],{},[2071,37567,2861],{},[2210,37569,638],{},[2068,37571,37572,37574,37576],{},[2210,37573,638],{},[2071,37575,4761],{"mathvariant":2450},[2210,37577,646],{},[9252,37579,37580,37582,37584],{},[2071,37581,2861],{},[2210,37583,646],{},[2068,37585,37586,37588,37590,37592],{},[2075,37587,2303],{},[2210,37589,638],{},[2071,37591,4761],{"mathvariant":2450},[2210,37593,646],{},[2075,37595,2077],{},[2210,37597,630],{},[2075,37599,2361],{"separator":2360},[23498,37601,37602,37614],{},[23501,37603,37604],{},[2400,37605,37606],{"scriptlevel":630,"displaystyle":2360},[9252,37607,37608,37610,37612],{},[2071,37609,586],{"mathvariant":31575},[2071,37611,19181],{},[2075,37613,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[23501,37615,37616],{},[2400,37617,37618],{"scriptlevel":630,"displaystyle":2360},[2068,37619,37620,37622,37624,37626,37628,37642,37656,37658],{},[2068,37621],{},[2075,37623,2077],{},[2071,37625,10871],{},[2075,37627,2303],{},[9252,37629,37630,37632,37634],{},[2071,37631,2861],{},[2210,37633,638],{},[2068,37635,37636,37638,37640],{},[2210,37637,638],{},[2071,37639,4761],{"mathvariant":2450},[2210,37641,646],{},[9252,37643,37644,37646,37648],{},[2071,37645,2861],{},[2210,37647,646],{},[2068,37649,37650,37652,37654],{},[2210,37651,638],{},[2071,37653,4761],{"mathvariant":2450},[2210,37655,646],{},[2075,37657,2077],{},[2210,37659,14195],{},[2092,37661,37662],{"encoding":2094},"\\begin{aligned}\n\\mathcal{L}'_1 &= P_1 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F2} = 0, \\\\\n\\mathcal{L}'_2 &= P_2 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{1\u002F2} Q_2^{-1\u002F2} = 0, \\\\\n\\mathcal{L}'_\\lambda &= U - Q_1^{1\u002F2} Q_2^{1\u002F2} = 0.\n\\end{aligned}",[55,37664,37665,37666,37736,37737,37795],{},"Podílem rovnic: ",[1647,37667,37669],{"className":37668},[2059],[2061,37670,37671],{"xmlns":2063},[2065,37672,37673,37733],{},[2068,37674,37675,37681,37683,37689,37691,37697,37699,37705,37707,37713,37719,37721,37727],{},[2348,37676,37677,37679],{},[2071,37678,575],{},[2210,37680,638],{},[2071,37682,4761],{"mathvariant":2450},[2348,37684,37685,37687],{},[2071,37686,575],{},[2210,37688,646],{},[2075,37690,2077],{},[2348,37692,37693,37695],{},[2071,37694,2861],{},[2210,37696,646],{},[2071,37698,4761],{"mathvariant":2450},[2348,37700,37701,37703],{},[2071,37702,2861],{},[2210,37704,638],{},[2075,37706,4075],{},[2348,37708,37709,37711],{},[2071,37710,575],{},[2210,37712,638],{},[2348,37714,37715,37717],{},[2071,37716,2861],{},[2210,37718,638],{},[2075,37720,2077],{},[2348,37722,37723,37725],{},[2071,37724,575],{},[2210,37726,646],{},[2348,37728,37729,37731],{},[2071,37730,2861],{},[2210,37732,646],{},[2092,37734,37735],{"encoding":2094},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[1647,37738,37740],{"className":37739},[2059],[2061,37741,37742],{"xmlns":2063},[2065,37743,37744,37792],{},[2068,37745,37746,37748,37750,37756,37762,37764,37770,37776,37778,37780,37786],{},[2071,37747,554],{},[2075,37749,2077],{},[2348,37751,37752,37754],{},[2071,37753,575],{},[2210,37755,638],{},[2348,37757,37758,37760],{},[2071,37759,2861],{},[2210,37761,638],{},[2075,37763,2176],{},[2348,37765,37766,37768],{},[2071,37767,575],{},[2210,37769,646],{},[2348,37771,37772,37774],{},[2071,37773,2861],{},[2210,37775,646],{},[2075,37777,2077],{},[2210,37779,646],{},[2348,37781,37782,37784],{},[2071,37783,575],{},[2210,37785,638],{},[2348,37787,37788,37790],{},[2071,37789,2861],{},[2210,37791,638],{},[2092,37793,37794],{"encoding":2094},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[1647,37797,37799],{"className":37798},[2059],[2061,37800,37801],{"xmlns":2063,"display":31093},[2065,37802,37803,37870],{},[23493,37804,37805],{"width":31098},[23498,37806,37807,37809,37863,37865],{},[23501,37808],{"width":31103},[23501,37810,37811],{},[2068,37812,37813,37819,37821,37835,37837,37839,37845,37847,37861],{},[2348,37814,37815,37817],{},[2071,37816,2861],{},[2210,37818,638],{},[2075,37820,2077],{},[2403,37822,37823,37825],{},[2071,37824,554],{},[2068,37826,37827,37829],{},[2210,37828,646],{},[2348,37830,37831,37833],{},[2071,37832,575],{},[2210,37834,638],{},[2075,37836,2361],{"separator":2360},[5965,37838],{"width":17019},[2348,37840,37841,37843],{},[2071,37842,2861],{},[2210,37844,646],{},[2075,37846,2077],{},[2403,37848,37849,37851],{},[2071,37850,554],{},[2068,37852,37853,37855],{},[2210,37854,646],{},[2348,37856,37857,37859],{},[2071,37858,575],{},[2210,37860,646],{},[2071,37862,195],{"mathvariant":2450},[23501,37864],{"width":31103},[23501,37866,37867],{},[2363,37868,37869],{},"(6.29)",[2092,37871,37872],{"encoding":2094},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[55,37874,37875,37876,20314,37958,37994],{},"Ze třetí rovnice ",[1647,37877,37879],{"className":37878},[2059],[2061,37880,37881],{"xmlns":2063},[2065,37882,37883,37955],{},[2068,37884,37885,37887,37889,37927,37929],{},[2071,37886,10871],{},[2075,37888,2077],{},[8204,37890,37891],{},[2068,37892,37893,37909,37911],{},[2400,37894,37895],{"scriptlevel":630,"displaystyle":2083},[2403,37896,37897,37899],{},[2071,37898,554],{},[2068,37900,37901,37903],{},[2210,37902,646],{},[2348,37904,37905,37907],{},[2071,37906,575],{},[2210,37908,638],{},[2075,37910,3251],{},[2400,37912,37913],{"scriptlevel":630,"displaystyle":2083},[2403,37914,37915,37917],{},[2071,37916,554],{},[2068,37918,37919,37921],{},[2210,37920,646],{},[2348,37922,37923,37925],{},[2071,37924,575],{},[2210,37926,646],{},[2075,37928,2077],{},[2400,37930,37931],{"scriptlevel":630,"displaystyle":2083},[2403,37932,37933,37935],{},[2071,37934,554],{},[2068,37936,37937,37939],{},[2210,37938,646],{},[8204,37940,37941],{},[2068,37942,37943,37949],{},[2348,37944,37945,37947],{},[2071,37946,575],{},[2210,37948,638],{},[2348,37950,37951,37953],{},[2071,37952,575],{},[2210,37954,646],{},[2092,37956,37957],{"encoding":2094},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[1647,37959,37961],{"className":37960},[2059],[2061,37962,37963],{"xmlns":2063},[2065,37964,37965,37991],{},[2068,37966,37967,37969,37971,37973,37975],{},[2071,37968,554],{},[2075,37970,2077],{},[2210,37972,646],{},[2071,37974,10871],{},[8204,37976,37977],{},[2068,37978,37979,37985],{},[2348,37980,37981,37983],{},[2071,37982,575],{},[2210,37984,638],{},[2348,37986,37987,37989],{},[2071,37988,575],{},[2210,37990,646],{},[2092,37992,37993],{"encoding":2094},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[1647,37996,37998],{"className":37997},[2059],[2061,37999,38000],{"xmlns":2063,"display":31093},[2065,38001,38002,38147],{},[23493,38003,38004],{"width":31098},[23498,38005,38006,38008,38140,38142],{},[23501,38007],{"width":31103},[23501,38009,38010],{},[14567,38011,38012],{"notation":14569},[2400,38013,38014],{"scriptlevel":630,"displaystyle":2083},[2400,38015,38016],{"scriptlevel":630,"displaystyle":2083},[2400,38017,38018],{"scriptlevel":630,"displaystyle":2360},[2068,38019,38020,38022,38028,38030,38032,38048,38050,38056,38058,38064,38066,38072,38074,38076,38078,38080,38082,38088,38090,38092,38108,38110,38116,38118,38124,38126,38132,38134,38136,38138],{},[2363,38021,4072],{},[2348,38023,38024,38026],{},[2071,38025,2861],{},[2210,38027,638],{},[2075,38029,2077],{},[2071,38031,10871],{},[8204,38033,38034],{},[2403,38035,38036,38042],{},[2348,38037,38038,38040],{},[2071,38039,575],{},[2210,38041,646],{},[2348,38043,38044,38046],{},[2071,38045,575],{},[2210,38047,638],{},[2075,38049,2077],{},[2348,38051,38052,38054],{},[2071,38053,4271],{},[2210,38055,638],{},[2075,38057,2084],{"stretchy":2083},[2348,38059,38060,38062],{},[2071,38061,575],{},[2210,38063,638],{},[2075,38065,2361],{"separator":2360},[2348,38067,38068,38070],{},[2071,38069,575],{},[2210,38071,646],{},[2075,38073,2361],{"separator":2360},[2071,38075,10871],{},[2075,38077,2090],{"stretchy":2083},[2075,38079,2361],{"separator":2360},[5965,38081],{"width":17019},[2348,38083,38084,38086],{},[2071,38085,2861],{},[2210,38087,646],{},[2075,38089,2077],{},[2071,38091,10871],{},[8204,38093,38094],{},[2403,38095,38096,38102],{},[2348,38097,38098,38100],{},[2071,38099,575],{},[2210,38101,638],{},[2348,38103,38104,38106],{},[2071,38105,575],{},[2210,38107,646],{},[2075,38109,2077],{},[2348,38111,38112,38114],{},[2071,38113,4271],{},[2210,38115,646],{},[2075,38117,2084],{"stretchy":2083},[2348,38119,38120,38122],{},[2071,38121,575],{},[2210,38123,638],{},[2075,38125,2361],{"separator":2360},[2348,38127,38128,38130],{},[2071,38129,575],{},[2210,38131,646],{},[2075,38133,2361],{"separator":2360},[2071,38135,10871],{},[2075,38137,2090],{"stretchy":2083},[2363,38139,4072],{},[23501,38141],{"width":31103},[23501,38143,38144],{},[2363,38145,38146],{},"(6.30)",[2092,38148,38149],{"encoding":2094},"\\boxed{\\; Q_1 = U \\sqrt{\\frac{P_2}{P_1}} = D_1(P_1, P_2, U), \\quad Q_2 = U \\sqrt{\\frac{P_1}{P_2}} = D_2(P_1, P_2, U) \\;} \\tag{6.30}",[84,38151,38153],{"id":38152},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[55,38155,38156,38157,38170,38171,38188,38189,38202,38203,38220,38221,38224,38225,38264,38265,38294],{},"Primární (max ",[1647,38158,38160],{"className":38159},[2059],[2061,38161,38162],{"xmlns":2063},[2065,38163,38164,38168],{},[2068,38165,38166],{},[2071,38167,10871],{},[2092,38169,10871],{"encoding":2094}," při rozpočtu ",[1647,38172,38174],{"className":38173},[2059],[2061,38175,38176],{"xmlns":2063},[2065,38177,38178,38186],{},[2068,38179,38180],{},[2205,38181,38182,38184],{},[2071,38183,9214],{},[2075,38185,4441],{},[2092,38187,31055],{"encoding":2094},") a duální (min ",[1647,38190,38192],{"className":38191},[2059],[2061,38193,38194],{"xmlns":2063},[2065,38195,38196,38200],{},[2068,38197,38198],{},[2071,38199,554],{},[2092,38201,554],{"encoding":2094}," při užitečnosti ",[1647,38204,38206],{"className":38205},[2059],[2061,38207,38208],{"xmlns":2063},[2065,38209,38210,38218],{},[2068,38211,38212],{},[2205,38213,38214,38216],{},[2071,38215,10871],{},[2075,38217,4441],{},[2092,38219,30989],{"encoding":2094},") úloha jsou ",[95,38222,38223],{},"ekvivalentní",": mají tentýž bod optima ",[1647,38226,38228],{"className":38227},[2059],[2061,38229,38230],{"xmlns":2063},[2065,38231,38232,38262],{},[2068,38233,38234,38240,38242,38250,38252,38260],{},[2205,38235,38236,38238],{},[2071,38237,2861],{},[2075,38239,4441],{},[2075,38241,2561],{"stretchy":2083},[9252,38243,38244,38246,38248],{},[2071,38245,2861],{},[2210,38247,638],{},[2075,38249,4441],{},[2075,38251,2361],{"separator":2360},[9252,38253,38254,38256,38258],{},[2071,38255,2861],{},[2210,38257,646],{},[2075,38259,4441],{},[2075,38261,2576],{"stretchy":2083},[2092,38263,31354],{"encoding":2094}," a v obou platí ",[1647,38266,38268],{"className":38267},[2059],[2061,38269,38270],{"xmlns":2063},[2065,38271,38272,38292],{},[2068,38273,38274,38276,38278,38284,38286],{},[2363,38275,11733],{},[2075,38277,2077],{},[2348,38279,38280,38282],{},[2071,38281,575],{},[2210,38283,638],{},[2071,38285,4761],{"mathvariant":2450},[2348,38287,38288,38290],{},[2071,38289,575],{},[2210,38291,646],{},[2092,38293,31025],{"encoding":2094},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[55,38296,38297],{},[58,38298],{"alt":38299,"className":38300,"src":38301},"imek-primarni-vs-dualni",[62,63],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[89,38303,38304,38415],{},[92,38305,38306,38309,38310,38323,38324,38364,38365,195],{},[95,38307,38308],{},"Primární"," (Marshall): zadáno ",[1647,38311,38313],{"className":38312},[2059],[2061,38314,38315],{"xmlns":2063},[2065,38316,38317,38321],{},[2068,38318,38319],{},[2071,38320,9214],{},[2092,38322,9214],{"encoding":2094},", hledáme maximální ",[1647,38325,38327],{"className":38326},[2059],[2061,38328,38329],{"xmlns":2063},[2065,38330,38331,38361],{},[2068,38332,38333,38339,38341,38347,38349,38355,38357,38359],{},[2205,38334,38335,38337],{},[2071,38336,10871],{},[2075,38338,4441],{},[2075,38340,2084],{"stretchy":2083},[2348,38342,38343,38345],{},[2071,38344,575],{},[2210,38346,638],{},[2075,38348,2361],{"separator":2360},[2348,38350,38351,38353],{},[2071,38352,575],{},[2210,38354,646],{},[2075,38356,2361],{"separator":2360},[2071,38358,9214],{},[2075,38360,2090],{"stretchy":2083},[2092,38362,38363],{"encoding":2094},"U^*(P_1, P_2, Y)"," a poptávku ",[1647,38366,38368],{"className":38367},[2059],[2061,38369,38370],{"xmlns":2063},[2065,38371,38372,38412],{},[2068,38373,38374,38380,38382,38390,38392,38398,38400,38406,38408,38410],{},[2348,38375,38376,38378],{},[2071,38377,2861],{},[2071,38379,20528],{},[2075,38381,2077],{},[9252,38383,38384,38386,38388],{},[2071,38385,4271],{},[2071,38387,20528],{},[2071,38389,2890],{},[2075,38391,2084],{"stretchy":2083},[2348,38393,38394,38396],{},[2071,38395,575],{},[2210,38397,638],{},[2075,38399,2361],{"separator":2360},[2348,38401,38402,38404],{},[2071,38403,575],{},[2210,38405,646],{},[2075,38407,2361],{"separator":2360},[2071,38409,9214],{},[2075,38411,2090],{"stretchy":2083},[2092,38413,38414],{"encoding":2094},"Q_i = D_i^M(P_1, P_2, Y)",[92,38416,38417,38420,38421,38434,38435,38364,38475,195],{},[95,38418,38419],{},"Duální"," (Hicks): zadáno ",[1647,38422,38424],{"className":38423},[2059],[2061,38425,38426],{"xmlns":2063},[2065,38427,38428,38432],{},[2068,38429,38430],{},[2071,38431,10871],{},[2092,38433,10871],{"encoding":2094},", hledáme minimální ",[1647,38436,38438],{"className":38437},[2059],[2061,38439,38440],{"xmlns":2063},[2065,38441,38442,38472],{},[2068,38443,38444,38450,38452,38458,38460,38466,38468,38470],{},[2205,38445,38446,38448],{},[2071,38447,554],{},[2075,38449,4441],{},[2075,38451,2084],{"stretchy":2083},[2348,38453,38454,38456],{},[2071,38455,575],{},[2210,38457,638],{},[2075,38459,2361],{"separator":2360},[2348,38461,38462,38464],{},[2071,38463,575],{},[2210,38465,646],{},[2075,38467,2361],{"separator":2360},[2071,38469,10871],{},[2075,38471,2090],{"stretchy":2083},[2092,38473,38474],{"encoding":2094},"E^*(P_1, P_2, U)",[1647,38476,38478],{"className":38477},[2059],[2061,38479,38480],{"xmlns":2063},[2065,38481,38482,38523],{},[2068,38483,38484,38490,38492,38501,38503,38509,38511,38517,38519,38521],{},[2348,38485,38486,38488],{},[2071,38487,2861],{},[2071,38489,20528],{},[2075,38491,2077],{},[9252,38493,38494,38496,38498],{},[2071,38495,4271],{},[2071,38497,20528],{},[2071,38499,38500],{},"H",[2075,38502,2084],{"stretchy":2083},[2348,38504,38505,38507],{},[2071,38506,575],{},[2210,38508,638],{},[2075,38510,2361],{"separator":2360},[2348,38512,38513,38515],{},[2071,38514,575],{},[2210,38516,646],{},[2075,38518,2361],{"separator":2360},[2071,38520,10871],{},[2075,38522,2090],{"stretchy":2083},[2092,38524,38525],{"encoding":2094},"Q_i = D_i^H(P_1, P_2, U)",[55,38527,38528,38529,38532,38533,38536],{},"Proč se studují obě? Marshallova poptávka je ",[95,38530,38531],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[95,38534,38535],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[84,38538,38540],{"id":38539},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[609,38542,38544],{"id":38543},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[55,38546,38547,38550,38551,38583,38584,38622,38623,38649],{},[95,38548,38549],{},"6.8"," Jsou dány užitečnost ",[1647,38552,38554],{"className":38553},[2059],[2061,38555,38556],{"xmlns":2063},[2065,38557,38558,38580],{},[2068,38559,38560,38562,38564,38572],{},[2071,38561,10871],{},[2075,38563,2077],{},[9252,38565,38566,38568,38570],{},[2071,38567,2861],{},[2210,38569,638],{},[2210,38571,5096],{},[9252,38573,38574,38576,38578],{},[2071,38575,2861],{},[2210,38577,646],{},[2210,38579,5096],{},[2092,38581,38582],{"encoding":2094},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[1647,38585,38587],{"className":38586},[2059],[2061,38588,38589],{"xmlns":2063},[2065,38590,38591,38619],{},[2068,38592,38593,38601,38603,38605,38607,38615,38617],{},[9252,38594,38595,38597,38599],{},[2071,38596,575],{},[2210,38598,638],{},[2075,38600,4441],{},[2075,38602,2077],{},[2210,38604,662],{},[2075,38606,2361],{"separator":2360},[9252,38608,38609,38611,38613],{},[2071,38610,575],{},[2210,38612,646],{},[2075,38614,4441],{},[2075,38616,2077],{},[2210,38618,2935],{},[2092,38620,38621],{"encoding":2094},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[1647,38624,38626],{"className":38625},[2059],[2061,38627,38628],{"xmlns":2063},[2065,38629,38630,38646],{},[2068,38631,38632,38638,38640],{},[2348,38633,38634,38636],{},[2071,38635,2861],{},[2210,38637,638],{},[2075,38639,2361],{"separator":2360},[2348,38641,38642,38644],{},[2071,38643,2861],{},[2210,38645,646],{},[2092,38647,38648],{"encoding":2094},"Q_1, Q_2"," maximalizující užitečnost.",[55,38651,38652,38655,38656,38698,38699,38730,38731,38753,38754,195],{},[95,38653,38654],{},"6.9"," Jsou dány rozpočtové omezení ",[1647,38657,38659],{"className":38658},[2059],[2061,38660,38661],{"xmlns":2063},[2065,38662,38663,38695],{},[2068,38664,38665,38667,38669,38675,38681,38683,38689],{},[2071,38666,9214],{},[2075,38668,2077],{},[2348,38670,38671,38673],{},[2071,38672,575],{},[2210,38674,638],{},[2348,38676,38677,38679],{},[2071,38678,2861],{},[2210,38680,638],{},[2075,38682,2176],{},[2348,38684,38685,38687],{},[2071,38686,575],{},[2210,38688,646],{},[2348,38690,38691,38693],{},[2071,38692,2861],{},[2210,38694,646],{},[2092,38696,38697],{"encoding":2094},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[1647,38700,38702],{"className":38701},[2059],[2061,38703,38704],{"xmlns":2063},[2065,38705,38706,38728],{},[2068,38707,38708,38710,38712,38720],{},[2071,38709,10871],{},[2075,38711,2077],{},[9252,38713,38714,38716,38718],{},[2071,38715,2861],{},[2210,38717,638],{},[2210,38719,5096],{},[9252,38721,38722,38724,38726],{},[2071,38723,2861],{},[2210,38725,646],{},[2210,38727,5096],{},[2092,38729,38582],{"encoding":2094},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[1647,38732,38734],{"className":38733},[2059],[2061,38735,38736],{"xmlns":2063},[2065,38737,38738,38750],{},[2068,38739,38740,38746,38748],{},[2205,38741,38742,38744],{},[2071,38743,9214],{},[2075,38745,4441],{},[2075,38747,2077],{},[2210,38749,16845],{},[2092,38751,38752],{"encoding":2094},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[1647,38755,38757],{"className":38756},[2059],[2061,38758,38759],{"xmlns":2063},[2065,38760,38761,38789],{},[2068,38762,38763,38771,38773,38775,38777,38785,38787],{},[9252,38764,38765,38767,38769],{},[2071,38766,575],{},[2210,38768,638],{},[2075,38770,4441],{},[2075,38772,2077],{},[2210,38774,670],{},[2075,38776,2361],{"separator":2360},[9252,38778,38779,38781,38783],{},[2071,38780,575],{},[2210,38782,646],{},[2075,38784,4441],{},[2075,38786,2077],{},[2210,38788,2935],{},[2092,38790,38791],{"encoding":2094},"P_1^* = 5, P_2^* = 10",[55,38793,38794,38797,38798,24333,38830,38860,38861,195],{},[95,38795,38796],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[1647,38799,38801],{"className":38800},[2059],[2061,38802,38803],{"xmlns":2063},[2065,38804,38805,38827],{},[2068,38806,38807,38809,38811,38819],{},[2071,38808,10871],{},[2075,38810,2077],{},[9252,38812,38813,38815,38817],{},[2071,38814,2861],{},[2210,38816,638],{},[2071,38818,69],{},[9252,38820,38821,38823,38825],{},[2071,38822,2861],{},[2210,38824,646],{},[2071,38826,2179],{},[2092,38828,38829],{"encoding":2094},"U = Q_1^a Q_2^b",[1647,38831,38833],{"className":38832},[2059],[2061,38834,38835],{"xmlns":2063},[2065,38836,38837,38857],{},[2068,38838,38839,38841,38843,38845,38847,38849,38851,38853,38855],{},[2071,38840,69],{},[2075,38842,2361],{"separator":2360},[2071,38844,2179],{},[2075,38846,6593],{},[2075,38848,5411],{"stretchy":2083},[2210,38850,630],{},[2075,38852,2361],{"separator":2360},[2210,38854,638],{},[2075,38856,5428],{"stretchy":2083},[2092,38858,38859],{"encoding":2094},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[1647,38862,38864],{"className":38863},[2059],[2061,38865,38866],{"xmlns":2063},[2065,38867,38868,38900],{},[2068,38869,38870,38872,38874,38880,38886,38888,38894],{},[2071,38871,9214],{},[2075,38873,2077],{},[2348,38875,38876,38878],{},[2071,38877,575],{},[2210,38879,638],{},[2348,38881,38882,38884],{},[2071,38883,2861],{},[2210,38885,638],{},[2075,38887,2176],{},[2348,38889,38890,38892],{},[2071,38891,575],{},[2210,38893,646],{},[2348,38895,38896,38898],{},[2071,38897,2861],{},[2210,38899,646],{},[2092,38901,38697],{"encoding":2094},[55,38903,38904,38907,38908,24333,38942,38860,38960,195],{},[95,38905,38906],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[1647,38909,38911],{"className":38910},[2059],[2061,38912,38913],{"xmlns":2063},[2065,38914,38915,38939],{},[2068,38916,38917,38919,38921,38929,38931],{},[2071,38918,10871],{},[2075,38920,2077],{},[9252,38922,38923,38925,38927],{},[2071,38924,2861],{},[2210,38926,638],{},[2071,38928,69],{},[2075,38930,2176],{},[9252,38932,38933,38935,38937],{},[2071,38934,2861],{},[2210,38936,646],{},[2071,38938,69],{},[2092,38940,38941],{"encoding":2094},"U = Q_1^a + Q_2^a",[1647,38943,38945],{"className":38944},[2059],[2061,38946,38947],{"xmlns":2063},[2065,38948,38949,38957],{},[2068,38950,38951,38953,38955],{},[2071,38952,69],{},[2075,38954,3445],{"mathvariant":2450},[2210,38956,630],{},[2092,38958,38959],{"encoding":2094},"a \\neq 0",[1647,38961,38963],{"className":38962},[2059],[2061,38964,38965],{"xmlns":2063},[2065,38966,38967,38999],{},[2068,38968,38969,38971,38973,38979,38985,38987,38993],{},[2071,38970,9214],{},[2075,38972,2077],{},[2348,38974,38975,38977],{},[2071,38976,575],{},[2210,38978,638],{},[2348,38980,38981,38983],{},[2071,38982,2861],{},[2210,38984,638],{},[2075,38986,2176],{},[2348,38988,38989,38991],{},[2071,38990,575],{},[2210,38992,646],{},[2348,38994,38995,38997],{},[2071,38996,2861],{},[2210,38998,646],{},[2092,39000,38697],{"encoding":2094},[609,39002,39004],{"id":39003},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[55,39006,39007,38550,39010,835,39037,39059,39060,835,39083,39107,39108,39133,39134,195],{},[95,39008,39009],{},"6.12",[1647,39011,39013],{"className":39012},[2059],[2061,39014,39015],{"xmlns":2063},[2065,39016,39017,39035],{},[2068,39018,39019,39021,39023,39029],{},[2071,39020,10871],{},[2075,39022,2077],{},[2348,39024,39025,39027],{},[2071,39026,2861],{},[2210,39028,638],{},[2348,39030,39031,39033],{},[2071,39032,2861],{},[2210,39034,646],{},[2092,39036,33253],{"encoding":2094},[1647,39038,39040],{"className":39039},[2059],[2061,39041,39042],{"xmlns":2063},[2065,39043,39044,39056],{},[2068,39045,39046,39052,39054],{},[2205,39047,39048,39050],{},[2071,39049,10871],{},[2075,39051,4441],{},[2075,39053,2077],{},[2210,39055,2935],{},[2092,39057,39058],{"encoding":2094},"U^* = 10"," hladina užitečnosti a ceny ",[1647,39061,39063],{"className":39062},[2059],[2061,39064,39065],{"xmlns":2063},[2065,39066,39067,39081],{},[2068,39068,39069,39077,39079],{},[9252,39070,39071,39073,39075],{},[2071,39072,575],{},[2210,39074,638],{},[2075,39076,4441],{},[2075,39078,2077],{},[2210,39080,646],{},[2092,39082,33326],{"encoding":2094},[1647,39084,39086],{"className":39085},[2059],[2061,39087,39088],{"xmlns":2063},[2065,39089,39090,39104],{},[2068,39091,39092,39100,39102],{},[9252,39093,39094,39096,39098],{},[2071,39095,575],{},[2210,39097,646],{},[2075,39099,4441],{},[2075,39101,2077],{},[2210,39103,662],{},[2092,39105,39106],{"encoding":2094},"P_2^* = 4",". Určete množství ",[1647,39109,39111],{"className":39110},[2059],[2061,39112,39113],{"xmlns":2063},[2065,39114,39115,39131],{},[2068,39116,39117,39123,39125],{},[2348,39118,39119,39121],{},[2071,39120,2861],{},[2210,39122,638],{},[2075,39124,2361],{"separator":2360},[2348,39126,39127,39129],{},[2071,39128,2861],{},[2210,39130,646],{},[2092,39132,38648],{"encoding":2094}," minimalizující výdaje spotřebitele ",[1647,39135,39137],{"className":39136},[2059],[2061,39138,39139],{"xmlns":2063},[2065,39140,39141,39161],{},[2068,39142,39143,39145,39147,39153,39155],{},[2071,39144,10871],{},[2075,39146,2077],{},[2348,39148,39149,39151],{},[2071,39150,2861],{},[2210,39152,638],{},[2075,39154,3251],{},[2348,39156,39157,39159],{},[2071,39158,2861],{},[2210,39160,646],{},[2092,39162,39163],{"encoding":2094},"U = Q_1 \\cdot Q_2",[55,39165,39166,39169,39170,39211,39212,39234,39235,195],{},[95,39167,39168],{},"6.13"," Jsou dány výdaje spotřebitele ",[1647,39171,39173],{"className":39172},[2059],[2061,39174,39175],{"xmlns":2063},[2065,39176,39177,39209],{},[2068,39178,39179,39181,39183,39189,39195,39197,39203],{},[2071,39180,554],{},[2075,39182,2077],{},[2348,39184,39185,39187],{},[2071,39186,575],{},[2210,39188,638],{},[2348,39190,39191,39193],{},[2071,39192,2861],{},[2210,39194,638],{},[2075,39196,2176],{},[2348,39198,39199,39201],{},[2071,39200,575],{},[2210,39202,646],{},[2348,39204,39205,39207],{},[2071,39206,2861],{},[2210,39208,646],{},[2092,39210,30970],{"encoding":2094}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[1647,39213,39215],{"className":39214},[2059],[2061,39216,39217],{"xmlns":2063},[2065,39218,39219,39231],{},[2068,39220,39221,39227,39229],{},[2205,39222,39223,39225],{},[2071,39224,10871],{},[2075,39226,4441],{},[2075,39228,2077],{},[2210,39230,5091],{},[2092,39232,39233],{"encoding":2094},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[1647,39236,39238],{"className":39237},[2059],[2061,39239,39240],{"xmlns":2063},[2065,39241,39242,39271],{},[2068,39243,39244,39252,39254,39256,39258,39266,39268],{},[9252,39245,39246,39248,39250],{},[2071,39247,575],{},[2210,39249,638],{},[2075,39251,4441],{},[2075,39253,2077],{},[2210,39255,9121],{},[2075,39257,2361],{"separator":2360},[9252,39259,39260,39262,39264],{},[2071,39261,575],{},[2210,39263,646],{},[2075,39265,4441],{},[2075,39267,2077],{},[2210,39269,39270],{},"15",[2092,39272,39273],{"encoding":2094},"P_1^* = 20, P_2^* = 15",[84,39275,321],{"id":320},[89,39277,39278,39335,39374,39394,39429,39483,39488,39494,39590,39635],{},[92,39279,39280,1445,39283,39332,39333,195],{},[95,39281,39282],{},"Rozpočtové omezení (budget constraint)",[1647,39284,39286],{"className":39285},[2059],[2061,39287,39288],{"xmlns":2063},[2065,39289,39290,39330],{},[2068,39291,39292,39298,39300,39308,39314,39316,39324],{},[2205,39293,39294,39296],{},[2071,39295,9214],{},[2075,39297,4441],{},[2075,39299,2077],{},[9252,39301,39302,39304,39306],{},[2071,39303,575],{},[2210,39305,638],{},[2075,39307,4441],{},[2348,39309,39310,39312],{},[2071,39311,2861],{},[2210,39313,638],{},[2075,39315,2176],{},[9252,39317,39318,39320,39322],{},[2071,39319,575],{},[2210,39321,646],{},[2075,39323,4441],{},[2348,39325,39326,39328],{},[2071,39327,2861],{},[2210,39329,646],{},[2092,39331,20036],{"encoding":2094}," — (6.12); ",[95,39334,31163],{},[92,39336,39337,39340,39341,195],{},[95,39338,39339],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[1647,39342,39344],{"className":39343},[2059],[2061,39345,39346],{"xmlns":2063},[2065,39347,39348,39372],{},[2068,39349,39350,39352,39354,39362,39364],{},[2363,39351,11733],{},[2075,39353,2077],{},[9252,39355,39356,39358,39360],{},[2071,39357,575],{},[2210,39359,638],{},[2075,39361,4441],{},[2071,39363,4761],{"mathvariant":2450},[9252,39365,39366,39368,39370],{},[2071,39367,575],{},[2210,39369,646],{},[2075,39371,4441],{},[2092,39373,32006],{"encoding":2094},[92,39375,39376,39391,39392,195],{},[95,39377,32150,39378],{},[1647,39379,39381],{"className":39380},[2059],[2061,39382,39383],{"xmlns":2063},[2065,39384,39385,39389],{},[2068,39386,39387],{},[2071,39388,19181],{},[2092,39390,19234],{"encoding":2094}," — stínová cena uvolnění omezení; u maximalizace ",[95,39393,32172],{},[92,39395,39396,39399,39400,195],{},[95,39397,39398],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[1647,39401,39403],{"className":39402},[2059],[2061,39404,39405],{"xmlns":2063},[2065,39406,39407,39427],{},[2068,39408,39409,39411,39413,39419,39421],{},[2363,39410,11733],{},[2075,39412,2077],{},[2348,39414,39415,39417],{},[2071,39416,575],{},[2210,39418,638],{},[2071,39420,4761],{"mathvariant":2450},[2348,39422,39423,39425],{},[2071,39424,575],{},[2210,39426,646],{},[2092,39428,31025],{"encoding":2094},[92,39430,39431,7102,39434,39482],{},[95,39432,39433],{},"Poptávka maximalizující užitečnost (Marshallova)",[1647,39435,39437],{"className":39436},[2059],[2061,39438,39439],{"xmlns":2063},[2065,39440,39441,39479],{},[2068,39442,39443,39449,39451,39457,39459,39465,39467,39473,39475,39477],{},[2348,39444,39445,39447],{},[2071,39446,2861],{},[2071,39448,20528],{},[2075,39450,2077],{},[2348,39452,39453,39455],{},[2071,39454,4271],{},[2071,39456,20528],{},[2075,39458,2084],{"stretchy":2083},[2348,39460,39461,39463],{},[2071,39462,575],{},[2210,39464,638],{},[2075,39466,2361],{"separator":2360},[2348,39468,39469,39471],{},[2071,39470,575],{},[2210,39472,646],{},[2075,39474,2361],{"separator":2360},[2071,39476,9214],{},[2075,39478,2090],{"stretchy":2083},[2092,39480,39481],{"encoding":2094},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[92,39484,39485,39487],{},[95,39486,34753],{}," — poptávka jako funkce důchodu při pevných cenách.",[92,39489,39490,39493],{},[95,39491,39492],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[92,39495,39496,7102,39498,39545,39546,39589],{},[95,39497,37065],{},[1647,39499,39501],{"className":39500},[2059],[2061,39502,39503],{"xmlns":2063},[2065,39504,39505,39543],{},[2068,39506,39507,39513,39515,39521,39523,39529,39531,39537,39539,39541],{},[2348,39508,39509,39511],{},[2071,39510,2861],{},[2071,39512,20528],{},[2075,39514,2077],{},[2348,39516,39517,39519],{},[2071,39518,4271],{},[2071,39520,20528],{},[2075,39522,2084],{"stretchy":2083},[2348,39524,39525,39527],{},[2071,39526,575],{},[2210,39528,638],{},[2075,39530,2361],{"separator":2360},[2348,39532,39533,39535],{},[2071,39534,575],{},[2210,39536,646],{},[2075,39538,2361],{"separator":2360},[2071,39540,10871],{},[2075,39542,2090],{"stretchy":2083},[2092,39544,20561],{"encoding":2094}," — (6.27); obecný výsledek pro ",[1647,39547,39549],{"className":39548},[2059],[2061,39550,39551],{"xmlns":2063},[2065,39552,39553,39587],{},[2068,39554,39555,39557,39559,39573],{},[2071,39556,10871],{},[2075,39558,2077],{},[9252,39560,39561,39563,39565],{},[2071,39562,2861],{},[2210,39564,638],{},[2068,39566,39567,39569,39571],{},[2210,39568,638],{},[2071,39570,4761],{"mathvariant":2450},[2210,39572,646],{},[9252,39574,39575,39577,39579],{},[2071,39576,2861],{},[2210,39578,646],{},[2068,39580,39581,39583,39585],{},[2210,39582,638],{},[2071,39584,4761],{"mathvariant":2450},[2210,39586,646],{},[2092,39588,36185],{"encoding":2094},": (6.30).",[92,39591,39592,39634],{},[95,39593,39594,39595],{},"Bod dotyku ",[1647,39596,39598],{"className":39597},[2059],[2061,39599,39600],{"xmlns":2063},[2065,39601,39602,39632],{},[2068,39603,39604,39610,39612,39620,39622,39630],{},[2205,39605,39606,39608],{},[2071,39607,2861],{},[2075,39609,4441],{},[2075,39611,2561],{"stretchy":2083},[9252,39613,39614,39616,39618],{},[2071,39615,2861],{},[2210,39617,638],{},[2075,39619,4441],{},[2075,39621,2361],{"separator":2360},[9252,39623,39624,39626,39628],{},[2071,39625,2861],{},[2210,39627,646],{},[2075,39629,4441],{},[2075,39631,2576],{"stretchy":2083},[2092,39633,31354],{"encoding":2094}," — řešení obou úloh; totožný pro primární i duální formulaci.",[92,39636,39637,39640,39641,39654,39655,39668],{},[95,39638,39639],{},"Dualita"," — ekvivalence max ",[1647,39642,39644],{"className":39643},[2059],[2061,39645,39646],{"xmlns":2063},[2065,39647,39648,39652],{},[2068,39649,39650],{},[2071,39651,10871],{},[2092,39653,10871],{"encoding":2094}," a min ",[1647,39656,39658],{"className":39657},[2059],[2061,39659,39660],{"xmlns":2063},[2065,39661,39662,39666],{},[2068,39663,39664],{},[2071,39665,554],{},[2092,39667,554],{"encoding":2094},"; Marshallova a Hicksova poptávka.",[84,39670,3866],{"id":3865},[89,39672,39673,39696,39712,39725,39740],{},[92,39674,39675,1445,39678,39681,39682,39695],{},[95,39676,39677],{},"Teorie před optimalizací:",[69,39679,12226],{"className":39680,"dataFsResolvedFilePath":10901,"href":10902},[62]," (funkce ",[1647,39683,39685],{"className":39684},[2059],[2061,39686,39687],{"xmlns":2063},[2065,39688,39689,39693],{},[2068,39690,39691],{},[2071,39692,10871],{},[2092,39694,10871],{"encoding":2094},", indiferenční křivky, MRCS).",[92,39697,39698,1445,39701,39704,39705,39708,39709,195],{},[95,39699,39700],{},"Matematický aparát:",[69,39702,12195],{"className":39703,"dataFsResolvedFilePath":12193,"href":12194},[62]," (vázaná optimalizace), ",[69,39706,3901],{"className":39707,"dataFsResolvedFilePath":3899,"href":3900},[62]," (parciální derivace), ",[69,39710,2431],{"className":39711,"dataFsResolvedFilePath":4005,"href":4006},[62],[92,39713,39714,1445,39717,39720,39721,39724],{},[95,39715,39716],{},"Paralely:",[69,39718,12221],{"className":39719,"dataFsResolvedFilePath":10942,"href":10943},[62]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[69,39722,13672],{"className":39723,"dataFsResolvedFilePath":13670,"href":13671},[62]," (Marshallova poptávka jako vstup tržního modelu).",[92,39726,39727,1445,39730,835,39736],{},[95,39728,39729],{},"Přednášky:",[69,39731,39735],{"className":39732,"dataFsResolvedFilePath":39733,"href":39734},[62],"summaries\u002Fimek-blok-02.md","\u002Fwiki\u002Fimek-blok-02","KS 2. blok",[69,39737,39739],{"className":39738,"dataFsResolvedFilePath":17950,"href":17951},[62],"KS 3. blok",[92,39741,39742,1445,39744],{},[95,39743,17937],{},[69,39745,17941],{"className":39746,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":39748},[39749,39750,39751,39756,39757,39758,39760,39763,39766,39768,39769,39771,39772,39776,39777],{"id":13738,"depth":7,"text":13739},{"id":31033,"depth":7,"text":31034},{"id":31431,"depth":7,"text":31432,"children":39752},[39753,39754],{"id":31551,"depth":4,"text":31552},{"id":32132,"depth":4,"text":39755},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":32594,"depth":7,"text":32595},{"id":32905,"depth":7,"text":32906},{"id":33224,"depth":7,"text":39759},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":33997,"depth":7,"text":33998,"children":39761},[39762],{"id":34752,"depth":4,"text":34753},{"id":34932,"depth":7,"text":34933,"children":39764},[39765],{"id":35189,"depth":4,"text":35190},{"id":36140,"depth":7,"text":39767},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":37064,"depth":7,"text":37065},{"id":37267,"depth":7,"text":39770},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":38152,"depth":7,"text":38153},{"id":38539,"depth":7,"text":38540,"children":39773},[39774,39775],{"id":38543,"depth":4,"text":38544},{"id":39003,"depth":4,"text":39004},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":30793,"description":156},[9647,18006],"topics\u002Foptimalizace-spotrebitele",[17,39784,42,10903,39785,39786,39787],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":39790,"title":10597,"body":39791,"course":14,"courses":163,"created":2004,"description":41040,"extension":166,"meta":41041,"navigation":168,"path":41042,"seo":41043,"sources":41044,"stem":41046,"tags":41047,"type":177,"updated":178,"__hash__":41050},"topics\u002Ftopics\u002Foptimalizace.md",{"type":48,"value":39792,"toc":41016},[39793,39795,39806,39817,39819,39822,39842,39847,39853,39865,39869,39950,39956,39960,40029,40033,40072,40074,40078,40084,40087,40092,40101,40106,40205,40210,40251,40258,40310,40315,40382,40387,40402,40404,40410,40413,40418,40427,40436,40445,40450,40489,40491,40497,40501,40510,40518,40523,40548,40553,40578,40580,40586,40590,40599,40609,40614,40639,40641,40647,40650,40654,40663,40671,40716,40721,40741,40743,40749,40753,40762,40767,40869,40874,40914,40916,40920,40971,40973,40987,40989,40992,40997,41014],[51,39794,10597],{"id":26},[55,39796,39797,39798,39801,39802,39805],{},"Optimalizace je matematická disciplína, ve které hledáme minimum (resp. maximum) dané funkce f(x) na dané množině M. Tato funkce se nazývá ",[95,39799,39800],{},"účelová"," či ",[95,39803,39804],{},"cílová",". Množina přípustných řešení bývá typicky popsána omezeními — soustavou rovnic nebo nerovnic.",[55,39807,830,39808,835,39811,835,39814,195],{},[69,39809,9674],{"className":39810,"dataFsResolvedFilePath":9672,"href":9673},[62],[69,39812,845],{"className":39813,"dataFsResolvedFilePath":843,"href":844},[62],[69,39815,817],{"className":39816,"dataFsResolvedFilePath":9682,"href":9683},[62],[84,39818,12532],{"id":12531},[55,39820,39821],{},"Každá optimalizační úloha obsahuje tři složky:",[89,39823,39824,39830,39836],{},[92,39825,39826,39829],{},[95,39827,39828],{},"Stavové (rozhodovací) proměnné"," (x₁, x₂, ..., xₙ) — hodnoty, které měníme",[92,39831,39832,39835],{},[95,39833,39834],{},"Účelová (cílová) funkce"," f(x) — výraz, který minimalizujeme nebo maximalizujeme",[92,39837,39838,39841],{},[95,39839,39840],{},"Omezující podmínky"," — definují přípustnou množinu M",[55,39843,39844],{},[95,39845,39846],{},"Obecná formulace minimalizační úlohy:",[922,39848,39851],{"className":39849,"code":39850,"language":927},[925],"minimalizovat f(x)\nza podmínek:\n  g(x) ≤ 0      (nerovnostní omezení)\n  h(x) = 0      (rovnostní omezení)\n  lb ≤ x ≤ ub   (meze proměnných)\n",[929,39852,39850],{"__ignoreMap":156},[55,39854,39855,1445,39858,39861,39862,195],{},[95,39856,39857],{},"Maximalizace = negace:",[929,39859,39860],{},"max f(x)"," je ekvivalentní ",[929,39863,39864],{},"min(−f(x))",[84,39866,39868],{"id":39867},"typy-omezujících-podmínek-v-matlabu","Typy omezujících podmínek (v MATLABu)",[323,39870,39871,39883],{},[326,39872,39873],{},[329,39874,39875,39878,39881],{},[332,39876,39877],{},"Typ omezení",[332,39879,39880],{},"Zápis v MATLABu",[332,39882,340],{},[342,39884,39885,39898,39911,39924,39937],{},[329,39886,39887,39890,39895],{},[347,39888,39889],{},"Lineární nerovnostní",[347,39891,39892],{},[929,39893,39894],{},"A·x ≤ b",[347,39896,39897],{},"Matice A, vektor b",[329,39899,39900,39903,39908],{},[347,39901,39902],{},"Lineární rovnostní",[347,39904,39905],{},[929,39906,39907],{},"Aeq·x = beq",[347,39909,39910],{},"Matice Aeq, vektor beq",[329,39912,39913,39916,39921],{},[347,39914,39915],{},"Nelineární nerovnostní",[347,39917,39918],{},[929,39919,39920],{},"c(x) ≤ 0",[347,39922,39923],{},"Funkce vracející vektor c",[329,39925,39926,39929,39934],{},[347,39927,39928],{},"Nelineární rovnostní",[347,39930,39931],{},[929,39932,39933],{},"ceq(x) = 0",[347,39935,39936],{},"Funkce vracející vektor ceq",[329,39938,39939,39942,39947],{},[347,39940,39941],{},"Meze proměnných",[347,39943,39944],{},[929,39945,39946],{},"lb ≤ x ≤ ub",[347,39948,39949],{},"Dolní a horní meze",[55,39951,39952,39953,195],{},"Nepotřebná omezení zadáváme jako ",[929,39954,39955],{},"[]",[84,39957,39959],{"id":39958},"typy-optimalizačních-úloh","Typy optimalizačních úloh",[323,39961,39962,39973],{},[326,39963,39964],{},[329,39965,39966,39968,39970],{},[332,39967,10393],{},[332,39969,340],{},[332,39971,39972],{},"MATLAB solver",[342,39974,39975,39988,40004,40017],{},[329,39976,39977,39980,39983],{},[347,39978,39979],{},"Lineární programování (LP)",[347,39981,39982],{},"f(x) i omezení jsou lineární",[347,39984,39985],{},[929,39986,39987],{},"linprog",[329,39989,39990,39993,39996],{},[347,39991,39992],{},"Nelineární programování (NLP)",[347,39994,39995],{},"f(x) nebo omezení jsou nelineární",[347,39997,39998,835,40001],{},[929,39999,40000],{},"fmincon",[929,40002,40003],{},"fminsearch",[329,40005,40006,40009,40012],{},[347,40007,40008],{},"Celočíselné lineární (MILP)",[347,40010,40011],{},"LP, kde proměnné jsou celá čísla",[347,40013,40014],{},[929,40015,40016],{},"intlinprog",[329,40018,40019,40021,40024],{},[347,40020,10454],{},[347,40022,40023],{},"Diskrétní množina řešení",[347,40025,40026],{},[929,40027,40028],{},"ga",[84,40030,40032],{"id":40031},"lokální-vs-globální-optimum","Lokální vs. globální optimum",[89,40034,40035,40041,40047,40058],{},[92,40036,40037,40040],{},[95,40038,40039],{},"Globální minimum"," — absolutně nejnižší hodnota f(x) v celém definičním oboru",[92,40042,40043,40046],{},[95,40044,40045],{},"Lokální minimum"," — nejnižší hodnota v okolí, ale ne nutně nejnižší ze všech",[92,40048,40049,835,40051,40053,40054,40057],{},[929,40050,40000],{},[929,40052,40003],{}," nacházejí ",[95,40055,40056],{},"lokální"," minima — výsledek závisí na počátečním bodu x0",[92,40059,10790,40060,40063,40064,835,40066,835,40069],{},[95,40061,40062],{},"globální"," optimalizaci: ",[929,40065,40028],{},[929,40067,40068],{},"GlobalSearch",[929,40070,40071],{},"MultiStart",[909,40073],{},[84,40075,40077],{"id":40076},"matlab-optimization-toolbox-příkazy","MATLAB Optimization Toolbox — příkazy",[609,40079,40081,40083],{"id":40080},"fmincon-nelineární-optimalizace-s-omezeními",[929,40082,40000],{}," — nelineární optimalizace s omezeními",[55,40085,40086],{},"Nejuniverzálnější solver. Hledá minimum nelineární funkce s lineárními i nelineárními omezeními a mezemi.",[55,40088,40089],{},[95,40090,40091],{},"Plná syntaxe:",[922,40093,40095],{"className":1641,"code":40094,"language":1643,"meta":156,"style":156},"[x, fval, exitflag, output] = fmincon(fun, x0, A, b, Aeq, beq, lb, ub, nonlcon, options)\n",[929,40096,40097],{"__ignoreMap":156},[1647,40098,40099],{"class":1649,"line":1650},[1647,40100,40094],{},[55,40102,40103],{},[95,40104,40105],{},"Parametry:",[323,40107,40108,40117],{},[326,40109,40110],{},[329,40111,40112,40115],{},[332,40113,40114],{},"Parametr",[332,40116,340],{},[342,40118,40119,40132,40142,40153,40166,40179,40192],{},[329,40120,40121,40126],{},[347,40122,40123],{},[929,40124,40125],{},"fun",[347,40127,40128,40129,2090],{},"Účelová funkce (function handle ",[929,40130,40131],{},"@",[329,40133,40134,40139],{},[347,40135,40136],{},[929,40137,40138],{},"x0",[347,40140,40141],{},"Počáteční bod (vektor)",[329,40143,40144,40150],{},[347,40145,40146,835,40148],{},[929,40147,4342],{},[929,40149,2179],{},[347,40151,40152],{},"Lineární nerovnostní omezení: A·x ≤ b",[329,40154,40155,40163],{},[347,40156,40157,835,40160],{},[929,40158,40159],{},"Aeq",[929,40161,40162],{},"beq",[347,40164,40165],{},"Lineární rovnostní omezení: Aeq·x = beq",[329,40167,40168,40176],{},[347,40169,40170,835,40173],{},[929,40171,40172],{},"lb",[929,40174,40175],{},"ub",[347,40177,40178],{},"Dolní a horní meze proměnných",[329,40180,40181,40186],{},[347,40182,40183],{},[929,40184,40185],{},"nonlcon",[347,40187,40188,40189],{},"Nelineární omezení — function handle vracející ",[1647,40190,40191],{},"c, ceq",[329,40193,40194,40199],{},[347,40195,40196],{},[929,40197,40198],{},"options",[347,40200,40201,40202],{},"Nastavení z ",[929,40203,40204],{},"optimoptions",[55,40206,40207],{},[95,40208,40209],{},"Výstupy:",[323,40211,40212,40220],{},[326,40213,40214],{},[329,40215,40216,40218],{},[332,40217,12343],{},[332,40219,340],{},[342,40221,40222,40231,40241],{},[329,40223,40224,40228],{},[347,40225,40226],{},[929,40227,2087],{},[347,40229,40230],{},"Optimální řešení",[329,40232,40233,40238],{},[347,40234,40235],{},[929,40236,40237],{},"fval",[347,40239,40240],{},"Hodnota f(x) v optimu",[329,40242,40243,40248],{},[347,40244,40245],{},[929,40246,40247],{},"exitflag",[347,40249,40250],{},"Důvod ukončení (1 = konvergence, záporné = selhání)",[55,40252,40253],{},[95,40254,40255,40256,2777],{},"Algoritmy ",[929,40257,40000],{},[323,40259,40260,40268],{},[326,40261,40262],{},[329,40263,40264,40266],{},[332,40265,1373],{},[332,40267,10296],{},[342,40269,40270,40280,40290,40300],{},[329,40271,40272,40277],{},[347,40273,40274],{},[929,40275,40276],{},"'interior-point'",[347,40278,40279],{},"Výchozí; velké problémy s mnoha proměnnými",[329,40281,40282,40287],{},[347,40283,40284],{},[929,40285,40286],{},"'sqp'",[347,40288,40289],{},"Dobrá volba pro většinu problémů",[329,40291,40292,40297],{},[347,40293,40294],{},[929,40295,40296],{},"'active-set'",[347,40298,40299],{},"Nehladká omezení",[329,40301,40302,40307],{},[347,40303,40304],{},[929,40305,40306],{},"'trust-region-reflective'",[347,40308,40309],{},"Pouze meze nebo lineární rovnosti",[55,40311,40312],{},[95,40313,40314],{},"Příklad — minimalizace výrobních nákladů:",[922,40316,40318],{"className":1641,"code":40317,"language":1643,"meta":156,"style":156},"% f(x) = 3*x1 + 5*x2\nfun = @(x) 3*x(1) + 5*x(2);\nx0 = [5, 5];\n\n% Omezení: x1 + x2 \u003C= 20, x1 >= 4, x2 >= 3\nA = [1, 1; -1, 0; 0, -1];\nb = [20; -4; -3];\nlb = [0, 0];\nub = [20, 20];\n\noptions = optimoptions('fmincon', 'Display', 'final', 'Algorithm', 'sqp');\n[x, fval] = fmincon(fun, x0, A, b, [], [], lb, ub, [], options);\n",[929,40319,40320,40325,40330,40335,40339,40344,40349,40354,40359,40365,40370,40376],{"__ignoreMap":156},[1647,40321,40322],{"class":1649,"line":1650},[1647,40323,40324],{},"% f(x) = 3*x1 + 5*x2\n",[1647,40326,40327],{"class":1649,"line":7},[1647,40328,40329],{},"fun = @(x) 3*x(1) + 5*x(2);\n",[1647,40331,40332],{"class":1649,"line":4},[1647,40333,40334],{},"x0 = [5, 5];\n",[1647,40336,40337],{"class":1649,"line":40},[1647,40338,1663],{"emptyLinePlaceholder":168},[1647,40340,40341],{"class":1649,"line":35},[1647,40342,40343],{},"% Omezení: x1 + x2 \u003C= 20, x1 >= 4, x2 >= 3\n",[1647,40345,40346],{"class":1649,"line":30},[1647,40347,40348],{},"A = [1, 1; -1, 0; 0, -1];\n",[1647,40350,40351],{"class":1649,"line":27},[1647,40352,40353],{},"b = [20; -4; -3];\n",[1647,40355,40356],{"class":1649,"line":24},[1647,40357,40358],{},"lb = [0, 0];\n",[1647,40360,40362],{"class":1649,"line":40361},9,[1647,40363,40364],{},"ub = [20, 20];\n",[1647,40366,40368],{"class":1649,"line":40367},10,[1647,40369,1663],{"emptyLinePlaceholder":168},[1647,40371,40373],{"class":1649,"line":40372},11,[1647,40374,40375],{},"options = optimoptions('fmincon', 'Display', 'final', 'Algorithm', 'sqp');\n",[1647,40377,40379],{"class":1649,"line":40378},12,[1647,40380,40381],{},"[x, fval] = fmincon(fun, x0, A, b, [], [], lb, ub, [], options);\n",[55,40383,40384],{},[95,40385,40386],{},"Nelineární omezení (syntax nonlcon):",[922,40388,40390],{"className":1641,"code":40389,"language":1643,"meta":156,"style":156},"% Musí vracet [c, ceq] — c(x)\u003C=0 a ceq(x)=0\nnonlcon = @(x) deal(25 - x(1)*x(2)*x(3)*x(4), sum(x.^2) - 40);\n",[929,40391,40392,40397],{"__ignoreMap":156},[1647,40393,40394],{"class":1649,"line":1650},[1647,40395,40396],{},"% Musí vracet [c, ceq] — c(x)\u003C=0 a ceq(x)=0\n",[1647,40398,40399],{"class":1649,"line":7},[1647,40400,40401],{},"nonlcon = @(x) deal(25 - x(1)*x(2)*x(3)*x(4), sum(x.^2) - 40);\n",[909,40403],{},[609,40405,40407,40409],{"id":40406},"fminsearch-optimalizace-bez-omezení-nelder-mead",[929,40408,40003],{}," — optimalizace bez omezení (Nelder-Mead)",[55,40411,40412],{},"Nepotřebuje gradient (derivative-free). Vhodné pro funkce s obtížně spočitatelným gradientem. Pracuje se simplexem n+1 bodů.",[55,40414,40415],{},[95,40416,40417],{},"Syntaxe:",[922,40419,40421],{"className":1641,"code":40420,"language":1643,"meta":156,"style":156},"[x, fval] = fminsearch(fun, x0, options)\n",[929,40422,40423],{"__ignoreMap":156},[1647,40424,40425],{"class":1649,"line":1650},[1647,40426,40420],{},[55,40428,40429,40430,40433,40434,3225],{},"Používá ",[929,40431,40432],{},"optimset"," (ne ",[929,40435,40204],{},[922,40437,40439],{"className":1641,"code":40438,"language":1643,"meta":156,"style":156},"options = optimset('MaxIter', 1000, 'TolFun', 1e-8, 'TolX', 1e-8, 'Display', 'iter');\n",[929,40440,40441],{"__ignoreMap":156},[1647,40442,40443],{"class":1649,"line":1650},[1647,40444,40438],{},[55,40446,40447],{},[95,40448,40449],{},"Příklady:",[922,40451,40453],{"className":1641,"code":40452,"language":1643,"meta":156,"style":156},"% Kvadratická funkce\nfun = @(x) (x - 3)^2 + 2;\n[x, fval] = fminsearch(fun, 0)     % → x≈3, fval≈2\n\n% Rosenbrock (2 proměnné)\nrosenbrock = @(x) (1-x(1))^2 + 100*(x(2)-x(1)^2)^2;\n[x, fval] = fminsearch(rosenbrock, [-1, -1])    % → x≈[1,1]\n",[929,40454,40455,40460,40465,40470,40474,40479,40484],{"__ignoreMap":156},[1647,40456,40457],{"class":1649,"line":1650},[1647,40458,40459],{},"% Kvadratická funkce\n",[1647,40461,40462],{"class":1649,"line":7},[1647,40463,40464],{},"fun = @(x) (x - 3)^2 + 2;\n",[1647,40466,40467],{"class":1649,"line":4},[1647,40468,40469],{},"[x, fval] = fminsearch(fun, 0)     % → x≈3, fval≈2\n",[1647,40471,40472],{"class":1649,"line":40},[1647,40473,1663],{"emptyLinePlaceholder":168},[1647,40475,40476],{"class":1649,"line":35},[1647,40477,40478],{},"% Rosenbrock (2 proměnné)\n",[1647,40480,40481],{"class":1649,"line":30},[1647,40482,40483],{},"rosenbrock = @(x) (1-x(1))^2 + 100*(x(2)-x(1)^2)^2;\n",[1647,40485,40486],{"class":1649,"line":27},[1647,40487,40488],{},"[x, fval] = fminsearch(rosenbrock, [-1, -1])    % → x≈[1,1]\n",[909,40490],{},[609,40492,40494,40496],{"id":40493},"linprog-lineární-programování",[929,40495,39987],{}," — lineární programování",[55,40498,40499],{},[95,40500,40417],{},[922,40502,40504],{"className":1641,"code":40503,"language":1643,"meta":156,"style":156},"[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)\n",[929,40505,40506],{"__ignoreMap":156},[1647,40507,40508],{"class":1649,"line":1650},[1647,40509,40503],{},[55,40511,40512,40514,40515,195],{},[929,40513,2080],{}," je vektor koeficientů účelové funkce — minimalizuje ",[929,40516,40517],{},"f' · x",[55,40519,40520],{},[95,40521,40522],{},"Minimalizace nákladů:",[922,40524,40526],{"className":1641,"code":40525,"language":1643,"meta":156,"style":156},"f = [2; 3];                  % minimalizuje 2*x1 + 3*x2\nA = [1, 1; 2, 1]; b = [10; 14];\nlb = [0; 0];\n[x, fval] = linprog(f, A, b, [], [], lb)\n",[929,40527,40528,40533,40538,40543],{"__ignoreMap":156},[1647,40529,40530],{"class":1649,"line":1650},[1647,40531,40532],{},"f = [2; 3];                  % minimalizuje 2*x1 + 3*x2\n",[1647,40534,40535],{"class":1649,"line":7},[1647,40536,40537],{},"A = [1, 1; 2, 1]; b = [10; 14];\n",[1647,40539,40540],{"class":1649,"line":4},[1647,40541,40542],{},"lb = [0; 0];\n",[1647,40544,40545],{"class":1649,"line":40},[1647,40546,40547],{},"[x, fval] = linprog(f, A, b, [], [], lb)\n",[55,40549,40550],{},[95,40551,40552],{},"Maximalizace zisku (negace f):",[922,40554,40556],{"className":1641,"code":40555,"language":1643,"meta":156,"style":156},"% max z(x) = 12*x1 + 7*x2 → min -z(x)\nf = [-12; -7];\n[x, neg_zisk] = linprog(f, A, b, [], [], lb);\nmax_zisk = -neg_zisk;\n",[929,40557,40558,40563,40568,40573],{"__ignoreMap":156},[1647,40559,40560],{"class":1649,"line":1650},[1647,40561,40562],{},"% max z(x) = 12*x1 + 7*x2 → min -z(x)\n",[1647,40564,40565],{"class":1649,"line":7},[1647,40566,40567],{},"f = [-12; -7];\n",[1647,40569,40570],{"class":1649,"line":4},[1647,40571,40572],{},"[x, neg_zisk] = linprog(f, A, b, [], [], lb);\n",[1647,40574,40575],{"class":1649,"line":40},[1647,40576,40577],{},"max_zisk = -neg_zisk;\n",[909,40579],{},[609,40581,40583,40585],{"id":40582},"intlinprog-celočíselné-lineární-programování-milp",[929,40584,40016],{}," — celočíselné lineární programování (MILP)",[55,40587,40588],{},[95,40589,40417],{},[922,40591,40593],{"className":1641,"code":40592,"language":1643,"meta":156,"style":156},"[x, fval] = intlinprog(f, intcon, A, b, Aeq, beq, lb, ub)\n",[929,40594,40595],{"__ignoreMap":156},[1647,40596,40597],{"class":1649,"line":1650},[1647,40598,40592],{},[55,40600,40601,40604,40605,40608],{},[929,40602,40603],{},"intcon"," = vektor indexů celočíselných proměnných (např. ",[929,40606,40607],{},"[1, 3]"," = x1 a x3 jsou celá čísla).",[55,40610,40611],{},[95,40612,40613],{},"Binární proměnné (lb=0, ub=1):",[922,40615,40617],{"className":1641,"code":40616,"language":1643,"meta":156,"style":156},"f = [5; 8; 3; 6];\nintcon = [1, 2, 3, 4];    % všechny proměnné binární\nlb = zeros(4,1); ub = ones(4,1);\n[x, fval] = intlinprog(f, intcon, A, b, [], [], lb, ub)\n",[929,40618,40619,40624,40629,40634],{"__ignoreMap":156},[1647,40620,40621],{"class":1649,"line":1650},[1647,40622,40623],{},"f = [5; 8; 3; 6];\n",[1647,40625,40626],{"class":1649,"line":7},[1647,40627,40628],{},"intcon = [1, 2, 3, 4];    % všechny proměnné binární\n",[1647,40630,40631],{"class":1649,"line":4},[1647,40632,40633],{},"lb = zeros(4,1); ub = ones(4,1);\n",[1647,40635,40636],{"class":1649,"line":40},[1647,40637,40638],{},"[x, fval] = intlinprog(f, intcon, A, b, [], [], lb, ub)\n",[909,40640],{},[609,40642,40644,40646],{"id":40643},"ga-genetický-algoritmus-global-optimization-toolbox",[929,40645,40028],{}," — genetický algoritmus (Global Optimization Toolbox)",[55,40648,40649],{},"Hledá globální minimum. Vhodný pro nekonvexní, nehladké nebo diskrétní problémy.",[55,40651,40652],{},[95,40653,40417],{},[922,40655,40657],{"className":1641,"code":40656,"language":1643,"meta":156,"style":156},"[x, fval] = ga(fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, intcon, options)\n",[929,40658,40659],{"__ignoreMap":156},[1647,40660,40661],{"class":1649,"line":1650},[1647,40662,40656],{},[55,40664,40665],{},[95,40666,40667,40668,2777],{},"Klíčové parametry ",[929,40669,40670],{},"optimoptions('ga', ...)",[922,40672,40674],{"className":1641,"code":40673,"language":1643,"meta":156,"style":156},"options = optimoptions('ga', ...\n    'PopulationSize',      100, ...    % velikost populace\n    'MaxGenerations',      300, ...    % max počet generací\n    'CrossoverFraction',   0.8, ...    % podíl křížení\n    'EliteCount',          5, ...      % elitní jedinci (přecházejí přímo)\n    'MaxStallGenerations', 50, ...     % zastavení po N generacích bez zlepšení\n    'Display',             'iter', ...\n    'PlotFcn',             @gaplotbestfun);\n",[929,40675,40676,40681,40686,40691,40696,40701,40706,40711],{"__ignoreMap":156},[1647,40677,40678],{"class":1649,"line":1650},[1647,40679,40680],{},"options = optimoptions('ga', ...\n",[1647,40682,40683],{"class":1649,"line":7},[1647,40684,40685],{},"    'PopulationSize',      100, ...    % velikost populace\n",[1647,40687,40688],{"class":1649,"line":4},[1647,40689,40690],{},"    'MaxGenerations',      300, ...    % max počet generací\n",[1647,40692,40693],{"class":1649,"line":40},[1647,40694,40695],{},"    'CrossoverFraction',   0.8, ...    % podíl křížení\n",[1647,40697,40698],{"class":1649,"line":35},[1647,40699,40700],{},"    'EliteCount',          5, ...      % elitní jedinci (přecházejí přímo)\n",[1647,40702,40703],{"class":1649,"line":30},[1647,40704,40705],{},"    'MaxStallGenerations', 50, ...     % zastavení po N generacích bez zlepšení\n",[1647,40707,40708],{"class":1649,"line":27},[1647,40709,40710],{},"    'Display',             'iter', ...\n",[1647,40712,40713],{"class":1649,"line":24},[1647,40714,40715],{},"    'PlotFcn',             @gaplotbestfun);\n",[55,40717,40718],{},[95,40719,40720],{},"Příklad — globální optimum multimodální funkce:",[922,40722,40724],{"className":1641,"code":40723,"language":1643,"meta":156,"style":156},"% Rastriginova funkce má mnoho lokálních minim\nrastrigin = @(x) 10*numel(x) + sum(x.^2 - 10*cos(2*pi*x));\n[x, fval] = ga(rastrigin, 2)    % ga najde globální minimum\n",[929,40725,40726,40731,40736],{"__ignoreMap":156},[1647,40727,40728],{"class":1649,"line":1650},[1647,40729,40730],{},"% Rastriginova funkce má mnoho lokálních minim\n",[1647,40732,40733],{"class":1649,"line":7},[1647,40734,40735],{},"rastrigin = @(x) 10*numel(x) + sum(x.^2 - 10*cos(2*pi*x));\n",[1647,40737,40738],{"class":1649,"line":4},[1647,40739,40740],{},"[x, fval] = ga(rastrigin, 2)    % ga najde globální minimum\n",[909,40742],{},[609,40744,40746,40748],{"id":40745},"optimoptions-nastavení-parametrů-solverů",[929,40747,40204],{}," — nastavení parametrů solverů",[55,40750,40751],{},[95,40752,40417],{},[922,40754,40756],{"className":1641,"code":40755,"language":1643,"meta":156,"style":156},"options = optimoptions('SolverName', 'ParamName', value, ...)\n",[929,40757,40758],{"__ignoreMap":156},[1647,40759,40760],{"class":1649,"line":1650},[1647,40761,40755],{},[55,40763,40764],{},[95,40765,40766],{},"Klíčové parametry zastavení:",[323,40768,40769,40780],{},[326,40770,40771],{},[329,40772,40773,40775,40778],{},[332,40774,40114],{},[332,40776,40777],{},"API",[332,40779,340],{},[342,40781,40782,40796,40810,40824,40838,40852],{},[329,40783,40784,40789,40793],{},[347,40785,40786],{},[929,40787,40788],{},"MaxIterations",[347,40790,40791],{},[929,40792,40204],{},[347,40794,40795],{},"Max počet iterací",[329,40797,40798,40803,40807],{},[347,40799,40800],{},[929,40801,40802],{},"MaxFunctionEvaluations",[347,40804,40805],{},[929,40806,40204],{},[347,40808,40809],{},"Max počet vyhodnocení funkce",[329,40811,40812,40817,40821],{},[347,40813,40814],{},[929,40815,40816],{},"OptimalityTolerance",[347,40818,40819],{},[929,40820,40204],{},[347,40822,40823],{},"Tolerance normy gradientu (dříve TolFun)",[329,40825,40826,40831,40835],{},[347,40827,40828],{},[929,40829,40830],{},"StepTolerance",[347,40832,40833],{},[929,40834,40204],{},[347,40836,40837],{},"Tolerance kroku\u002Fzměny x (dříve TolX)",[329,40839,40840,40845,40849],{},[347,40841,40842],{},[929,40843,40844],{},"ConstraintTolerance",[347,40846,40847],{},[929,40848,40204],{},[347,40850,40851],{},"Max přípustné porušení omezení",[329,40853,40854,40862,40866],{},[347,40855,40856,835,40859],{},[929,40857,40858],{},"TolFun",[929,40860,40861],{},"TolX",[347,40863,40864],{},[929,40865,40432],{},[347,40867,40868],{},"Starší API pro fminsearch\u002Ffminbnd",[55,40870,40871],{},[95,40872,40873],{},"Typické nastavení:",[922,40875,40877],{"className":1641,"code":40876,"language":1643,"meta":156,"style":156},"options = optimoptions('fmincon', ...\n    'Algorithm',              'sqp', ...\n    'Display',                'iter', ...\n    'MaxIterations',          1000, ...\n    'MaxFunctionEvaluations', 3000, ...\n    'OptimalityTolerance',    1e-8, ...\n    'StepTolerance',          1e-8);\n",[929,40878,40879,40884,40889,40894,40899,40904,40909],{"__ignoreMap":156},[1647,40880,40881],{"class":1649,"line":1650},[1647,40882,40883],{},"options = optimoptions('fmincon', ...\n",[1647,40885,40886],{"class":1649,"line":7},[1647,40887,40888],{},"    'Algorithm',              'sqp', ...\n",[1647,40890,40891],{"class":1649,"line":4},[1647,40892,40893],{},"    'Display',                'iter', ...\n",[1647,40895,40896],{"class":1649,"line":40},[1647,40897,40898],{},"    'MaxIterations',          1000, ...\n",[1647,40900,40901],{"class":1649,"line":35},[1647,40902,40903],{},"    'MaxFunctionEvaluations', 3000, ...\n",[1647,40905,40906],{"class":1649,"line":30},[1647,40907,40908],{},"    'OptimalityTolerance',    1e-8, ...\n",[1647,40910,40911],{"class":1649,"line":27},[1647,40912,40913],{},"    'StepTolerance',          1e-8);\n",[909,40915],{},[84,40917,40919],{"id":40918},"klíčové-principy-pro-zkoušku","Klíčové principy pro zkoušku",[201,40921,40922,40933,40941,40947,40954,40961],{},[92,40923,40924,7102,40927,40929,40930],{},[95,40925,40926],{},"Maximalizace = negace",[929,40928,39860],{}," → ",[929,40931,40932],{},"min −f(x)",[92,40934,40935,40938,40939],{},[95,40936,40937],{},"Nepotřebná omezení"," → zadat jako ",[929,40940,39955],{},[92,40942,40943,40946],{},[95,40944,40945],{},"x0 ovlivňuje"," které lokální minimum fmincon\u002Ffminsearch najde",[92,40948,40949,40953],{},[95,40950,40951],{},[929,40952,40204],{}," slouží pro fine-tuning (tolerance, iterace, algoritmus)",[92,40955,40956,40960],{},[95,40957,40958],{},[929,40959,40028],{}," je pomalejší, ale nepotřebuje gradient a hledá globální optimum",[92,40962,40963,40966,40967,40970],{},[95,40964,40965],{},"Nelineární omezení"," musí vracet ",[929,40968,40969],{},"[c, ceq]"," — nerovnosti (c≤0) a rovnosti (ceq=0)",[84,40972,1913],{"id":1912},[201,40974,40975,40978,40981,40984],{},[92,40976,40977],{},"Čím se zabývá optimalizace?",[92,40979,40980],{},"K čemu nám slouží optimalizace?",[92,40982,40983],{},"Jaké jsou příkazy MATLABu pro optimalizaci?",[92,40985,40986],{},"Jaká jsou možná nastavení parametrů optimalizace?",[84,40988,1946],{"id":1945},[55,40990,40991],{},"Optimalizace, hledání minima, hledání maxima, příkazy optimalizace, parametry optimalizace.",[84,40993,756,40994],{"id":1952},[69,40995,136],{"className":40996,"dataFsResolvedFilePath":134,"href":135},[62],[89,40998,40999,41005],{},[92,41000,41001,41004],{},[69,41002,1965],{"className":41003,"dataFsResolvedFilePath":1963,"href":1964},[62]," — definice, kontrolní otázky, pojmy",[92,41006,41007,41013],{},[69,41008,41012],{"className":41009,"dataFsResolvedFilePath":41010,"href":41011},[62],"summaries\u002Fipmrk-optimalizace.md","\u002Fwiki\u002Fipmrk-optimalizace","MATLAB Optimization Toolbox"," — kompletní MATLAB syntaxe, příklady (MathWorks docs, VUT FEEC)",[1977,41015,1979],{},{"title":156,"searchDepth":7,"depth":7,"links":41017},[41018,41019,41020,41021,41022,41036,41037,41038,41039],{"id":12531,"depth":7,"text":12532},{"id":39867,"depth":7,"text":39868},{"id":39958,"depth":7,"text":39959},{"id":40031,"depth":7,"text":40032},{"id":40076,"depth":7,"text":40077,"children":41023},[41024,41026,41028,41030,41032,41034],{"id":40080,"depth":4,"text":41025},"fmincon — nelineární optimalizace s omezeními",{"id":40406,"depth":4,"text":41027},"fminsearch — optimalizace bez omezení (Nelder-Mead)",{"id":40493,"depth":4,"text":41029},"linprog — lineární programování",{"id":40582,"depth":4,"text":41031},"intlinprog — celočíselné lineární programování (MILP)",{"id":40643,"depth":4,"text":41033},"ga — genetický algoritmus (Global Optimization Toolbox)",{"id":40745,"depth":4,"text":41035},"optimoptions — nastavení parametrů solverů",{"id":40918,"depth":7,"text":40919},{"id":1912,"depth":7,"text":1913},{"id":1945,"depth":7,"text":1946},{"id":1952,"depth":7,"text":2003},"Optimalizace je matematická disciplína, ve které hledáme minimum (resp. maximum) dané funkce f(x) na dané množině M. Tato funkce se nazývá účelová či cílová. Množina přípustných řešení bývá typicky popsána omezeními — soustavou rovnic nebo nerovnic.",{},"\u002Ftopics\u002Foptimalizace",{"title":10597,"description":41040},[2009,41045],"raw\u002Fipmrk\u002Foptimalizace-online.md","topics\u002Foptimalizace",[14,26,41048,1643,40000,39987,40028,41049],"ucelova-funkce","omezeni","AHvM3E5ql_eSnU2VAo8AAtzyssDT5aeJHSNTCu1_lN8",{"id":41052,"title":41053,"body":41054,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":55111,"navigation":168,"path":55112,"seo":55113,"sources":55114,"stem":55115,"tags":55116,"type":177,"updated":178,"__hash__":55122},"topics\u002Ftopics\u002Fpoptavka-nabidka.md","Poptávka, nabídka a tržní rovnováha",{"type":48,"value":41055,"toc":55067},[41056,41059,41085,41089,41096,41248,41262,41264,41266,41353,41357,41393,41466,41487,41612,41622,41635,41639,41643,41673,41735,41744,41748,41810,41817,41838,41956,42034,42038,42041,42100,42215,42220,42252,42314,42362,42417,42421,42442,42466,42514,42518,42530,42534,42644,42648,42664,42705,42716,42875,42885,42890,42894,43016,43026,43033,43037,43115,43126,43206,43212,43219,43358,43365,43368,43425,43429,43507,43553,43597,43603,43716,43720,43723,43918,43922,44159,44162,44316,44469,44471,44473,44553,44556,44661,44730,44739,44743,44746,44807,44816,44820,44853,44931,44970,44974,45023,45077,45081,45110,45139,45191,45198,45252,45330,45334,45377,45444,45488,45592,45611,45613,45617,45725,45729,45797,45846,45853,45938,45942,46014,46019,46067,46256,46260,46265,46441,46446,46505,46610,46614,46641,46645,46652,46816,46903,46908,46910,46914,47016,47166,47238,47312,47314,47318,47332,47336,47469,47524,47636,47713,47717,47774,47877,47936,48097,48101,48176,48248,48346,48404,48498,48551,48572,48626,48631,48709,48757,48844,48882,48970,49123,49159,49213,49216,49218,49220,49271,49278,49286,49373,49382,49469,49476,49478,49482,49707,49709,49713,49717,49786,49837,50040,50046,50057,50125,50131,50553,50557,50621,50645,50841,50847,50861,50929,50932,50972,51196,51264,51566,51975,52052,52218,52224,52227,52302,52755,52806,53212,53317,53980,53983,54060,54068,54142,54173,54175,54179,54223,54225,54227,54231,54461,54465,54556,54561,54655,54660,54833,54837,54954,54959,55008,55010,55012],[51,41057,41053],{"id":41058},"poptávka-nabídka-a-tržní-rovnováha",[1023,41060,41061],{},[55,41062,41063,41065,41066,41069,41070,41073,41074,41077,41078,41080,41081,41084],{},[1647,41064,4243],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[95,41067,41068],{},"poptávka",") a výrobce (",[95,41071,41072],{},"nabídka","), jejich interakci v ",[95,41075,41076],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[95,41079,20716],{},"). Uzavírá ji pojem ",[95,41082,41083],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[84,41086,41088],{"id":41087},"úvod-model-a-proměnné","Úvod — model a proměnné",[55,41090,41091,41092,41095],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[3982,41093,41094],{},"homo economicus","). Mezi hlavní proměnné patří:",[89,41097,41098,41115,41157,41173],{},[92,41099,41100,41101,41114],{},"cena ",[1647,41102,41104],{"className":41103},[2059],[2061,41105,41106],{"xmlns":2063},[2065,41107,41108,41112],{},[2068,41109,41110],{},[2071,41111,575],{},[2092,41113,575],{"encoding":2094}," zkoumaného zboží,",[92,41116,41117,41118,2361],{},"ceny alternativních zboží ",[1647,41119,41121],{"className":41120},[2059],[2061,41122,41123],{"xmlns":2063},[2065,41124,41125,41154],{},[2068,41126,41127,41133,41135,41141,41143,41145,41147],{},[2348,41128,41129,41131],{},[2071,41130,575],{},[2210,41132,638],{},[2075,41134,2361],{"separator":2360},[2348,41136,41137,41139],{},[2071,41138,575],{},[2210,41140,646],{},[2075,41142,2361],{"separator":2360},[2075,41144,10773],{},[2075,41146,2361],{"separator":2360},[2348,41148,41149,41151],{},[2071,41150,575],{},[2071,41152,41153],{},"n",[2092,41155,41156],{"encoding":2094},"P_1, P_2, \\dots, P_n",[92,41158,41159,41160,2361],{},"důchod ",[1647,41161,41163],{"className":41162},[2059],[2061,41164,41165],{"xmlns":2063},[2065,41166,41167,41171],{},[2068,41168,41169],{},[2071,41170,9214],{},[2092,41172,9214],{"encoding":2094},[92,41174,41175,41176,41189,41190,41203,41204,41217,41218,41232,41233,41247],{},"preference, očekávání, populace, výrobní faktory (práce ",[1647,41177,41179],{"className":41178},[2059],[2061,41180,41181],{"xmlns":2063},[2065,41182,41183,41187],{},[2068,41184,41185],{},[2071,41186,586],{},[2092,41188,586],{"encoding":2094},", kapitál ",[1647,41191,41193],{"className":41192},[2059],[2061,41194,41195],{"xmlns":2063},[2065,41196,41197,41201],{},[2068,41198,41199],{},[2071,41200,10929],{},[2092,41202,10929],{"encoding":2094},", půda ",[1647,41205,41207],{"className":41206},[2059],[2061,41208,41209],{"xmlns":2063},[2065,41210,41211,41215],{},[2068,41212,41213],{},[2071,41214,554],{},[2092,41216,554],{"encoding":2094},"), technologie, počet výrobců ",[1647,41219,41221],{"className":41220},[2059],[2061,41222,41223],{"xmlns":2063},[2065,41224,41225,41230],{},[2068,41226,41227],{},[2071,41228,41229],{},"O",[2092,41231,41229],{"encoding":2094},", počasí ",[1647,41234,41236],{"className":41235},[2059],[2061,41237,41238],{"xmlns":2063},[2065,41239,41240,41245],{},[2068,41241,41242],{},[2071,41243,41244],{},"W",[2092,41246,41244],{"encoding":2094}," atd.",[55,41249,41250,41251,41254,41255,41258,41259,195],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[3982,41252,41253],{},"ceteris paribus","), hovoříme o ",[95,41256,41257],{},"jednofaktorovém modelu","; jinak jde o model ",[95,41260,41261],{},"vícefaktorový",[909,41263],{},[84,41265,14896],{"id":41068},[1023,41267,41268],{},[55,41269,41270,41272,41273,41286,41287,41300,41301,41304,41305,41328,41329,195],{},[1647,41271,4243],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[1647,41274,41276],{"className":41275},[2059],[2061,41277,41278],{"xmlns":2063},[2065,41279,41280,41284],{},[2068,41281,41282],{},[2071,41283,2861],{},[2092,41285,2861],{"encoding":2094}," na ceně ",[1647,41288,41290],{"className":41289},[2059],[2061,41291,41292],{"xmlns":2063},[2065,41293,41294,41298],{},[2068,41295,41296],{},[2071,41297,575],{},[2092,41299,575],{"encoding":2094}," (případně dalších proměnných). Základní vlastností je ",[95,41302,41303],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[1647,41306,41308],{"className":41307},[2059],[2061,41309,41310],{"xmlns":2063},[2065,41311,41312,41326],{},[2068,41313,41314,41316,41318,41320,41322,41324],{},[2071,41315,2861],{},[2075,41317,2077],{},[2071,41319,4271],{},[2075,41321,2084],{"stretchy":2083},[2071,41323,575],{},[2075,41325,2090],{"stretchy":2083},[2092,41327,4280],{"encoding":2094}," a jeho lineární verzí ",[1647,41330,41332],{"className":41331},[2059],[2061,41333,41334],{"xmlns":2063},[2065,41335,41336,41350],{},[2068,41337,41338,41340,41342,41344,41346,41348],{},[2071,41339,575],{},[2075,41341,2077],{},[2071,41343,69],{},[2071,41345,2861],{},[2075,41347,2176],{},[2071,41349,2179],{},[2092,41351,41352],{"encoding":2094},"P = aQ + b",[609,41354,41356],{"id":41355},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[55,41358,41359,41360,41373,41374,41387,41388,11156,41390,3225],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[1647,41361,41363],{"className":41362},[2059],[2061,41364,41365],{"xmlns":2063},[2065,41366,41367,41371],{},[2068,41368,41369],{},[2071,41370,2861],{},[2092,41372,2861],{"encoding":2094}," závisí na ceně ",[1647,41375,41377],{"className":41376},[2059],[2061,41378,41379],{"xmlns":2063},[2065,41380,41381,41385],{},[2068,41382,41383],{},[2071,41384,575],{},[2092,41386,575],{"encoding":2094},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[95,41389,31029],{},[3982,41391,41392],{},"demand function",[1647,41394,41396],{"className":41395},[2059],[2061,41397,41398],{"xmlns":2063,"display":31093},[2065,41399,41400,41463],{},[23493,41401,41402],{"width":31098},[23498,41403,41404,41406,41456,41458],{},[23501,41405],{"width":31103},[23501,41407,41408],{},[2068,41409,41410,41412,41414,41416,41418,41420,41422,41428,41430,41436,41438,41440,41442,41448,41450,41452,41454],{},[2071,41411,2861],{},[2075,41413,2077],{},[2071,41415,4271],{},[2075,41417,2084],{"stretchy":2083},[2071,41419,575],{},[2075,41421,2361],{"separator":2360},[2348,41423,41424,41426],{},[2071,41425,575],{},[2210,41427,638],{},[2075,41429,2361],{"separator":2360},[2348,41431,41432,41434],{},[2071,41433,575],{},[2210,41435,646],{},[2075,41437,2361],{"separator":2360},[2075,41439,10773],{},[2075,41441,2361],{"separator":2360},[2348,41443,41444,41446],{},[2071,41445,575],{},[2071,41447,41153],{},[2075,41449,2361],{"separator":2360},[2071,41451,9214],{},[2075,41453,2090],{"stretchy":2083},[2071,41455,195],{"mathvariant":2450},[23501,41457],{"width":31103},[23501,41459,41460],{},[2363,41461,41462],{},"(2.1)",[2092,41464,41465],{"encoding":2094},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[55,41467,41468,41469,41472,41473,41486],{},"Důležitou vlastností je ",[95,41470,41471],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[1647,41474,41476],{"className":41475},[2059],[2061,41477,41478],{"xmlns":2063},[2065,41479,41480,41484],{},[2068,41481,41482],{},[2071,41483,13774],{},[2092,41485,13774],{"encoding":2094},"-krát, poptávané množství se nezmění,",[1647,41488,41490],{"className":41489},[2059],[2061,41491,41492],{"xmlns":2063,"display":31093},[2065,41493,41494,41609],{},[23493,41495,41496],{"width":31098},[23498,41497,41498,41500,41602,41604],{},[23501,41499],{"width":31103},[23501,41501,41502],{},[2068,41503,41504,41506,41508,41510,41512,41514,41516,41518,41520,41526,41528,41530,41536,41538,41540,41542,41544,41550,41552,41554,41556,41558,41560,41562,41564,41566,41568,41574,41576,41582,41584,41586,41588,41594,41596,41598,41600],{},[2071,41505,2861],{},[2075,41507,2077],{},[2071,41509,4271],{},[2075,41511,2084],{"stretchy":2083},[2071,41513,13774],{},[2071,41515,575],{},[2075,41517,2361],{"separator":2360},[2071,41519,13774],{},[2348,41521,41522,41524],{},[2071,41523,575],{},[2210,41525,638],{},[2075,41527,2361],{"separator":2360},[2071,41529,13774],{},[2348,41531,41532,41534],{},[2071,41533,575],{},[2210,41535,646],{},[2075,41537,2361],{"separator":2360},[2075,41539,10773],{},[2075,41541,2361],{"separator":2360},[2071,41543,13774],{},[2348,41545,41546,41548],{},[2071,41547,575],{},[2071,41549,41153],{},[2075,41551,2361],{"separator":2360},[2071,41553,13774],{},[2071,41555,9214],{},[2075,41557,2090],{"stretchy":2083},[2075,41559,2077],{},[2071,41561,4271],{},[2075,41563,2084],{"stretchy":2083},[2071,41565,575],{},[2075,41567,2361],{"separator":2360},[2348,41569,41570,41572],{},[2071,41571,575],{},[2210,41573,638],{},[2075,41575,2361],{"separator":2360},[2348,41577,41578,41580],{},[2071,41579,575],{},[2210,41581,646],{},[2075,41583,2361],{"separator":2360},[2075,41585,10773],{},[2075,41587,2361],{"separator":2360},[2348,41589,41590,41592],{},[2071,41591,575],{},[2071,41593,41153],{},[2075,41595,2361],{"separator":2360},[2071,41597,9214],{},[2075,41599,2090],{"stretchy":2083},[2071,41601,195],{"mathvariant":2450},[23501,41603],{"width":31103},[23501,41605,41606],{},[2363,41607,41608],{},"(2.2)",[2092,41610,41611],{"encoding":2094},"Q = D(rP, rP_1, rP_2, \\dots, rP_n, rY) = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.2}",[1023,41613,41614],{},[55,41615,41616,41618,41619,195],{},[1647,41617,4499],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[95,41620,41621],{},"v jednofaktorových modelech neplatí",[55,41623,41624,41625,835,41628,75,41631,41634],{},"Rozlišuje se poptávka ",[95,41626,41627],{},"individuální",[95,41629,41630],{},"tržní",[95,41632,41633],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[609,41636,41638],{"id":41637},"jednofaktorové-modely","Jednofaktorové modely",[1144,41640,41642],{"id":41641},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[55,41644,41645,41646,41659,41660,2777],{},"Poptávané množství ",[1647,41647,41649],{"className":41648},[2059],[2061,41650,41651],{"xmlns":2063},[2065,41652,41653,41657],{},[2068,41654,41655],{},[2071,41656,2861],{},[2092,41658,2861],{"encoding":2094}," závisí pouze na ceně ",[1647,41661,41663],{"className":41662},[2059],[2061,41664,41665],{"xmlns":2063},[2065,41666,41667,41671],{},[2068,41668,41669],{},[2071,41670,575],{},[2092,41672,575],{"encoding":2094},[1647,41674,41676],{"className":41675},[2059],[2061,41677,41678],{"xmlns":2063,"display":31093},[2065,41679,41680,41732],{},[23493,41681,41682],{"width":31098},[23498,41683,41684,41686,41725,41727],{},[23501,41685],{"width":31103},[23501,41687,41688],{},[2068,41689,41690,41692,41694,41696,41698,41700,41702,41704,41706,41709,41711,41713,41715,41717,41719,41721,41723],{},[2071,41691,2861],{},[2075,41693,2077],{},[2071,41695,4271],{},[2075,41697,2084],{"stretchy":2083},[2071,41699,575],{},[2075,41701,2090],{"stretchy":2083},[2075,41703,2361],{"separator":2360},[5965,41705],{"width":5967},[2363,41707,41708],{},"resp.",[5965,41710],{"width":5967},[2071,41712,575],{},[2075,41714,2077],{},[2071,41716,4271],{},[2075,41718,2084],{"stretchy":2083},[2071,41720,2861],{},[2075,41722,2090],{"stretchy":2083},[2071,41724,195],{"mathvariant":2450},[23501,41726],{"width":31103},[23501,41728,41729],{},[2363,41730,41731],{},"(2.3)",[2092,41733,41734],{"encoding":2094},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[55,41736,41737,41738,11156,41741,4007],{},"Graf této funkce se nazývá ",[95,41739,41740],{},"křivka poptávky",[3982,41742,41743],{},"demand curve",[1144,41745,41747],{"id":41746},"zákon-klesající-poptávky","Zákon klesající poptávky",[1023,41749,41750],{},[55,41751,41752],{},[95,41753,41754,41755,41768,41769,41782,41783,41768,41796,41809],{},"Roste-li cena ",[1647,41756,41758],{"className":41757},[2059],[2061,41759,41760],{"xmlns":2063},[2065,41761,41762,41766],{},[2068,41763,41764],{},[2071,41765,575],{},[2092,41767,575],{"encoding":2094},", pak množství ",[1647,41770,41772],{"className":41771},[2059],[2061,41773,41774],{"xmlns":2063},[2065,41775,41776,41780],{},[2068,41777,41778],{},[2071,41779,2861],{},[2092,41781,2861],{"encoding":2094}," klesá; klesá-li cena ",[1647,41784,41786],{"className":41785},[2059],[2061,41787,41788],{"xmlns":2063},[2065,41789,41790,41794],{},[2068,41791,41792],{},[2071,41793,575],{},[2092,41795,575],{"encoding":2094},[1647,41797,41799],{"className":41798},[2059],[2061,41800,41801],{"xmlns":2063},[2065,41802,41803,41807],{},[2068,41804,41805],{},[2071,41806,2861],{},[2092,41808,2861],{"encoding":2094}," roste.",[55,41811,41812,41813,41816],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[95,41814,41815],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1023,41818,41819,41824],{},[55,41820,41821,41823],{},[1647,41822,4243],{}," Intuice — proč zákon platí",[89,41825,41826,41832],{},[92,41827,41828,41831],{},[95,41829,41830],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[92,41833,41834,41837],{},[95,41835,41836],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[55,41839,41840,41841,41854,41855,41868,41869,41895,41896,41922,41923,8189,41949,41952,41953,195],{},"Každá funkce poptávky je tedy klesající. Cena ",[1647,41842,41844],{"className":41843},[2059],[2061,41845,41846],{"xmlns":2063},[2065,41847,41848,41852],{},[2068,41849,41850],{},[2071,41851,575],{},[2092,41853,575],{"encoding":2094}," se vynáší na svislou osu, množství ",[1647,41856,41858],{"className":41857},[2059],[2061,41859,41860],{"xmlns":2063},[2065,41861,41862,41866],{},[2068,41863,41864],{},[2071,41865,2861],{},[2092,41867,2861],{"encoding":2094}," na vodorovnou. Hypotetická křivka prochází body ",[1647,41870,41872],{"className":41871},[2059],[2061,41873,41874],{"xmlns":2063},[2065,41875,41876,41892],{},[2068,41877,41878,41880,41882,41884,41890],{},[2075,41879,2561],{"stretchy":2083},[2210,41881,630],{},[2075,41883,2361],{"separator":2360},[2348,41885,41886,41888],{},[2071,41887,575],{},[2210,41889,630],{},[2075,41891,2576],{"stretchy":2083},[2092,41893,41894],{"encoding":2094},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[1647,41897,41899],{"className":41898},[2059],[2061,41900,41901],{"xmlns":2063},[2065,41902,41903,41919],{},[2068,41904,41905,41907,41913,41915,41917],{},[2075,41906,2561],{"stretchy":2083},[2348,41908,41909,41911],{},[2071,41910,2861],{},[2210,41912,630],{},[2075,41914,2361],{"separator":2360},[2210,41916,630],{},[2075,41918,2576],{"stretchy":2083},[2092,41920,41921],{"encoding":2094},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[1647,41924,41926],{"className":41925},[2059],[2061,41927,41928],{"xmlns":2063},[2065,41929,41930,41946],{},[2068,41931,41932,41934,41936,41938,41944],{},[2075,41933,2084],{"stretchy":2083},[2210,41935,630],{},[2075,41937,2361],{"separator":2360},[2348,41939,41940,41942],{},[2071,41941,575],{},[2210,41943,630],{},[2075,41945,2090],{"stretchy":2083},[2092,41947,41948],{"encoding":2094},"(0, P_0)",[95,41950,41951],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[95,41954,41955],{},"konvexní",[55,41957,41958],{},[3982,41959,41960,41961,41983,41984,75,42009,195],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[1647,41962,41964],{"className":41963},[2059],[2061,41965,41966],{"xmlns":2063},[2065,41967,41968,41980],{},[2068,41969,41970,41972,41974,41976,41978],{},[2075,41971,2084],{"stretchy":2083},[2071,41973,2861],{},[2075,41975,2361],{"separator":2360},[2071,41977,575],{},[2075,41979,2090],{"stretchy":2083},[2092,41981,41982],{"encoding":2094},"(Q, P)"," — klesající, konvexní, procházející body ",[1647,41985,41987],{"className":41986},[2059],[2061,41988,41989],{"xmlns":2063},[2065,41990,41991,42007],{},[2068,41992,41993,41995,41997,41999,42005],{},[2075,41994,2561],{"stretchy":2083},[2210,41996,630],{},[2075,41998,2361],{"separator":2360},[2348,42000,42001,42003],{},[2071,42002,575],{},[2210,42004,630],{},[2075,42006,2576],{"stretchy":2083},[2092,42008,41894],{"encoding":2094},[1647,42010,42012],{"className":42011},[2059],[2061,42013,42014],{"xmlns":2063},[2065,42015,42016,42032],{},[2068,42017,42018,42020,42026,42028,42030],{},[2075,42019,2561],{"stretchy":2083},[2348,42021,42022,42024],{},[2071,42023,2861],{},[2210,42025,630],{},[2075,42027,2361],{"separator":2360},[2210,42029,630],{},[2075,42031,2576],{"stretchy":2083},[2092,42033,41921],{"encoding":2094},[1144,42035,42037],{"id":42036},"lineární-model-poptávky","Lineární model poptávky",[55,42039,42040],{},"Nejjednodušší závislostí je",[1647,42042,42044],{"className":42043},[2059],[2061,42045,42046],{"xmlns":2063,"display":31093},[2065,42047,42048,42097],{},[23493,42049,42050],{"width":31098},[23498,42051,42052,42054,42090,42092],{},[23501,42053],{"width":31103},[23501,42055,42056],{},[2068,42057,42058,42060,42062,42064,42066,42068,42070,42072,42074,42076,42078,42080,42082,42084,42086,42088],{},[2071,42059,575],{},[2075,42061,2077],{},[2071,42063,69],{},[2071,42065,2861],{},[2075,42067,2176],{},[2071,42069,2179],{},[2075,42071,2361],{"separator":2360},[5965,42073],{"width":5967},[2071,42075,69],{},[2075,42077,3521],{},[2210,42079,630],{},[2075,42081,2361],{"separator":2360},[2363,42083,2365],{},[2071,42085,2179],{},[2075,42087,3482],{},[2210,42089,14195],{},[23501,42091],{"width":31103},[23501,42093,42094],{},[2363,42095,42096],{},"(2.4)",[2092,42098,42099],{"encoding":2094},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[55,42101,42102,42103,24333,42139,75,42163,8124,42189,42211,42212,195],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[1647,42104,42106],{"className":42105},[2059],[2061,42107,42108],{"xmlns":2063},[2065,42109,42110,42136],{},[2068,42111,42112,42114,42116,42124,42126,42128],{},[2071,42113,2861],{},[2075,42115,2077],{},[2400,42117,42118],{"scriptlevel":630,"displaystyle":2083},[2403,42119,42120,42122],{},[2210,42121,638],{},[2071,42123,69],{},[2071,42125,575],{},[2075,42127,2303],{},[2400,42129,42130],{"scriptlevel":630,"displaystyle":2083},[2403,42131,42132,42134],{},[2071,42133,2179],{},[2071,42135,69],{},[2092,42137,42138],{"encoding":2094},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[1647,42140,42142],{"className":42141},[2059],[2061,42143,42144],{"xmlns":2063},[2065,42145,42146,42160],{},[2068,42147,42148,42156,42158],{},[2400,42149,42150],{"scriptlevel":630,"displaystyle":2083},[2403,42151,42152,42154],{},[2210,42153,638],{},[2071,42155,69],{},[2075,42157,3521],{},[2210,42159,630],{},[2092,42161,42162],{"encoding":2094},"\\tfrac{1}{a} \u003C 0",[1647,42164,42166],{"className":42165},[2059],[2061,42167,42168],{"xmlns":2063},[2065,42169,42170,42186],{},[2068,42171,42172,42174,42182,42184],{},[2075,42173,2303],{},[2400,42175,42176],{"scriptlevel":630,"displaystyle":2083},[2403,42177,42178,42180],{},[2071,42179,2179],{},[2071,42181,69],{},[2075,42183,3482],{},[2210,42185,630],{},[2092,42187,42188],{"encoding":2094},"-\\tfrac{b}{a} > 0",[1647,42190,42192],{"className":42191},[2059],[2061,42193,42194],{"xmlns":2063},[2065,42195,42196,42208],{},[2068,42197,42198,42200,42202,42204,42206],{},[2075,42199,2084],{"stretchy":2083},[2210,42201,630],{},[2075,42203,2361],{"separator":2360},[2071,42205,2179],{},[2075,42207,2090],{"stretchy":2083},[2092,42209,42210],{"encoding":2094},"(0, b)",". Tento model odpovídá ",[95,42213,42214],{},"nedokonalé konkurenci",[42216,42217,42219],"h5",{"id":42218},"příklad-21","Příklad 2.1",[55,42221,42222,42225,42226,195],{},[95,42223,42224],{},"Zadání:"," Lineární poptávka ",[1647,42227,42229],{"className":42228},[2059],[2061,42230,42231],{"xmlns":2063},[2065,42232,42233,42249],{},[2068,42234,42235,42237,42239,42241,42243,42245,42247],{},[2071,42236,575],{},[2075,42238,2077],{},[2075,42240,2303],{},[2210,42242,646],{},[2071,42244,2861],{},[2075,42246,2176],{},[2210,42248,3200],{},[2092,42250,42251],{"encoding":2094},"P = -2Q + 60",[55,42253,42254,42257,42258,42280,42281,195],{},[95,42255,42256],{},"Řešení:"," Reálné cenové rozpětí je ",[1647,42259,42261],{"className":42260},[2059],[2061,42262,42263],{"xmlns":2063},[2065,42264,42265,42277],{},[2068,42266,42267,42269,42271,42273,42275],{},[2075,42268,2084],{"stretchy":2083},[2210,42270,630],{},[2075,42272,2361],{"separator":2360},[2210,42274,3200],{},[2075,42276,2090],{"stretchy":2083},[2092,42278,42279],{"encoding":2094},"(0, 60)","; alternativní tvar je ",[1647,42282,42284],{"className":42283},[2059],[2061,42285,42286],{"xmlns":2063},[2065,42287,42288,42311],{},[2068,42289,42290,42292,42294,42296,42304,42306,42308],{},[2071,42291,2861],{},[2075,42293,2077],{},[2075,42295,2303],{},[2400,42297,42298],{"scriptlevel":630,"displaystyle":2083},[2403,42299,42300,42302],{},[2210,42301,638],{},[2210,42303,646],{},[2071,42305,575],{},[2075,42307,2176],{},[2210,42309,42310],{},"30",[2092,42312,42313],{"encoding":2094},"Q = -\\tfrac{1}{2}P + 30",[323,42315,42316,42339],{},[326,42317,42318],{},[329,42319,42320,42335,42337],{},[332,42321,42322],{},[1647,42323,42325],{"className":42324},[2059],[2061,42326,42327],{"xmlns":2063},[2065,42328,42329,42333],{},[2068,42330,42331],{},[2071,42332,575],{},[2092,42334,575],{"encoding":2094},[332,42336,5298],{},[332,42338,9121],{},[342,42340,42341],{},[329,42342,42343,42358,42360],{},[347,42344,42345],{},[1647,42346,42348],{"className":42347},[2059],[2061,42349,42350],{"xmlns":2063},[2065,42351,42352,42356],{},[2068,42353,42354],{},[2071,42355,2861],{},[2092,42357,2861],{"encoding":2094},[347,42359,2935],{},[347,42361,9121],{},[55,42363,42364],{},[3982,42365,42366,42367,75,42389,195],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[1647,42368,42370],{"className":42369},[2059],[2061,42371,42372],{"xmlns":2063},[2065,42373,42374,42386],{},[2068,42375,42376,42378,42380,42382,42384],{},[2075,42377,2561],{"stretchy":2083},[2210,42379,630],{},[2075,42381,2361],{"separator":2360},[2071,42383,2179],{},[2075,42385,2576],{"stretchy":2083},[2092,42387,42388],{"encoding":2094},"[0, b]",[1647,42390,42392],{"className":42391},[2059],[2061,42393,42394],{"xmlns":2063},[2065,42395,42396,42414],{},[2068,42397,42398,42400,42402,42404,42406,42408,42410,42412],{},[2075,42399,2561],{"stretchy":2083},[2075,42401,2303],{},[2071,42403,2179],{},[2071,42405,4761],{"mathvariant":2450},[2071,42407,69],{},[2075,42409,2361],{"separator":2360},[2210,42411,630],{},[2075,42413,2576],{"stretchy":2083},[2092,42415,42416],{"encoding":2094},"[-b\u002Fa, 0]",[1144,42418,42420],{"id":42419},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[55,42422,42423,42424,42441],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[1647,42425,42427],{"className":42426},[2059],[2061,42428,42429],{"xmlns":2063},[2065,42430,42431,42439],{},[2068,42432,42433],{},[2205,42434,42435,42437],{},[2071,42436,575],{},[2075,42438,4441],{},[2092,42440,4491],{"encoding":2094},", je funkce poptávky konstantní:",[1647,42443,42445],{"className":42444},[2059],[2061,42446,42447],{"xmlns":2063,"display":31093},[2065,42448,42449,42463],{},[2068,42450,42451,42453,42455,42461],{},[2071,42452,575],{},[2075,42454,2077],{},[2205,42456,42457,42459],{},[2071,42458,575],{},[2075,42460,4441],{},[2071,42462,195],{"mathvariant":2450},[2092,42464,42465],{"encoding":2094},"P = P^*.",[55,42467,42468],{},[3982,42469,42470,42471,42492,42493,195],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[1647,42472,42474],{"className":42473},[2059],[2061,42475,42476],{"xmlns":2063},[2065,42477,42478,42490],{},[2068,42479,42480,42482,42484,42486,42488],{},[2075,42481,2084],{"stretchy":2083},[2071,42483,2861],{},[2075,42485,2361],{"separator":2360},[2071,42487,575],{},[2075,42489,2090],{"stretchy":2083},[2092,42491,41982],{"encoding":2094}," na úrovni ",[1647,42494,42496],{"className":42495},[2059],[2061,42497,42498],{"xmlns":2063},[2065,42499,42500,42512],{},[2068,42501,42502,42504,42506],{},[2071,42503,575],{},[2075,42505,2077],{},[2205,42507,42508,42510],{},[2071,42509,575],{},[2075,42511,4441],{},[2092,42513,4444],{"encoding":2094},[1144,42515,42517],{"id":42516},"giffenův-statek","Giffenův statek",[55,42519,42520,42521,42523,42524,42526,42527,195],{},"Existují zboží, u nichž je křivka poptávky ",[95,42522,15392],{}," — tzv. ",[95,42525,42517],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[95,42528,42529],{},"podřadnému zboží",[42216,42531,42533],{"id":42532},"příklad-22","Příklad 2.2",[55,42535,42536,42539,42540,42558,42559,42581,42582,42600,42601,42619,42620,42643],{},[95,42537,42538],{},"Zadání a popis:"," Křivka ",[1647,42541,42543],{"className":42542},[2059],[2061,42544,42545],{"xmlns":2063},[2065,42546,42547,42555],{},[2068,42548,42549],{},[2348,42550,42551,42553],{},[2071,42552,4271],{},[2210,42554,638],{},[2092,42556,42557],{"encoding":2094},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[1647,42560,42562],{"className":42561},[2059],[2061,42563,42564],{"xmlns":2063},[2065,42565,42566,42578],{},[2068,42567,42568,42570,42572,42574,42576],{},[2075,42569,2084],{"stretchy":2083},[2210,42571,630],{},[2075,42573,2361],{"separator":2360},[2210,42575,39270],{},[2075,42577,2090],{"stretchy":2083},[2092,42579,42580],{"encoding":2094},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[1647,42583,42585],{"className":42584},[2059],[2061,42586,42587],{"xmlns":2063},[2065,42588,42589,42597],{},[2068,42590,42591],{},[2348,42592,42593,42595],{},[2071,42594,2861],{},[2210,42596,630],{},[2092,42598,42599],{"encoding":2094},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[1647,42602,42604],{"className":42603},[2059],[2061,42605,42606],{"xmlns":2063},[2065,42607,42608,42616],{},[2068,42609,42610],{},[2348,42611,42612,42614],{},[2071,42613,4271],{},[2210,42615,646],{},[2092,42617,42618],{"encoding":2094},"D_2"," na širším trhu je konvexní klesající z bodu ",[1647,42621,42623],{"className":42622},[2059],[2061,42624,42625],{"xmlns":2063},[2065,42626,42627,42640],{},[2068,42628,42629,42631,42633,42635,42638],{},[2075,42630,2561],{"stretchy":2083},[2210,42632,630],{},[2075,42634,2361],{"separator":2360},[2210,42636,42637],{},"21",[2075,42639,2576],{"stretchy":2083},[2092,42641,42642],{"encoding":2094},"[0, 21]"," centů.",[609,42645,42647],{"id":42646},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[55,42649,42650,42651,2777],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[1647,42652,42654],{"className":42653},[2059],[2061,42655,42656],{"xmlns":2063},[2065,42657,42658,42662],{},[2068,42659,42660],{},[2071,42661,9214],{},[2092,42663,9214],{"encoding":2094},[1647,42665,42667],{"className":42666},[2059],[2061,42668,42669],{"xmlns":2063,"display":31093},[2065,42670,42671,42702],{},[23493,42672,42673],{"width":31098},[23498,42674,42675,42677,42695,42697],{},[23501,42676],{"width":31103},[23501,42678,42679],{},[2068,42680,42681,42683,42685,42687,42689,42691,42693],{},[2071,42682,2861],{},[2075,42684,2077],{},[2071,42686,554],{},[2075,42688,2084],{"stretchy":2083},[2071,42690,9214],{},[2075,42692,2090],{"stretchy":2083},[2071,42694,195],{"mathvariant":2450},[23501,42696],{"width":31103},[23501,42698,42699],{},[2363,42700,42701],{},"(2.5)",[2092,42703,42704],{"encoding":2094},"Q = E(Y). \\tag{2.5}",[55,42706,42707,42708,42711,42712,42715],{},"Funkce se nazývá ",[95,42709,42710],{},"Engelova",", její graf ",[95,42713,42714],{},"Engelova křivka",". Tvar závisí na typu zboží:",[89,42717,42718,42850],{},[92,42719,42720,7102,42723,42736,42737,42750,42751,42768,42769],{},[95,42721,42722],{},"Normální (superior) zboží",[1647,42724,42726],{"className":42725},[2059],[2061,42727,42728],{"xmlns":2063},[2065,42729,42730,42734],{},[2068,42731,42732],{},[2071,42733,2861],{},[2092,42735,2861],{"encoding":2094}," roste s ",[1647,42738,42740],{"className":42739},[2059],[2061,42741,42742],{"xmlns":2063},[2065,42743,42744,42748],{},[2068,42745,42746],{},[2071,42747,9214],{},[2092,42749,9214],{"encoding":2094},", nepřesáhne hodnotu ",[1647,42752,42754],{"className":42753},[2059],[2061,42755,42756],{"xmlns":2063},[2065,42757,42758,42766],{},[2068,42759,42760],{},[2348,42761,42762,42764],{},[2071,42763,2861],{},[2210,42765,630],{},[2092,42767,42599],{"encoding":2094},":\n",[89,42770,42771,42803],{},[92,42772,42773,42776,42777,42780,42781,195],{},[95,42774,42775],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[95,42778,42779],{},"konkávní"," křivka, autonomní spotřeba ",[1647,42782,42784],{"className":42783},[2059],[2061,42785,42786],{"xmlns":2063},[2065,42787,42788,42800],{},[2068,42789,42790,42796,42798],{},[2348,42791,42792,42794],{},[2071,42793,2861],{},[2210,42795,638],{},[2075,42797,3482],{},[2210,42799,630],{},[2092,42801,42802],{"encoding":2094},"Q_1 > 0",[92,42804,42805,42808,42809,42827,42828,42830,42831,1445,42848,195],{},[95,42806,42807],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[1647,42810,42812],{"className":42811},[2059],[2061,42813,42814],{"xmlns":2063},[2065,42815,42816,42824],{},[2068,42817,42818],{},[2348,42819,42820,42822],{},[2071,42821,9214],{},[2210,42823,638],{},[2092,42825,42826],{"encoding":2094},"Y_1",", křivka je nejprve ",[95,42829,41955],{}," a od ",[1647,42832,42834],{"className":42833},[2059],[2061,42835,42836],{"xmlns":2063},[2065,42837,42838,42846],{},[2068,42839,42840],{},[2348,42841,42842,42844],{},[2071,42843,9214],{},[2210,42845,638],{},[2092,42847,42826],{"encoding":2094},[95,42849,42779],{},[92,42851,42852,42855,42856,42874],{},[95,42853,42854],{},"Podřadné (inferior) zboží"," — od hladiny ",[1647,42857,42859],{"className":42858},[2059],[2061,42860,42861],{"xmlns":2063},[2065,42862,42863,42871],{},[2068,42864,42865],{},[2348,42866,42867,42869],{},[2071,42868,9214],{},[2210,42870,630],{},[2092,42872,42873],{"encoding":2094},"Y_0"," množství s růstem důchodu klesá.",[55,42876,42877,42878,42881,42882,4007],{},"Mírou citlivosti je ",[3982,42879,42880],{},"důchodová elasticita"," (viz ",[69,42883,3984],{"className":42884,"dataFsResolvedFilePath":3911,"href":3912},[62],[55,42886,42887],{},[3982,42888,42889],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[1144,42891,42893],{"id":42892},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1023,42895,42896,42967,43010],{},[55,42897,42898,42900,42901,1445,42904,1445,42917,5756,42919,42932,42933,42936,42937,195],{},[1647,42899,4499],{}," Pozor — nezbytné ≠ podřadné\n",[95,42902,42903],{},"Nezbytné zboží:",[1647,42905,42907],{"className":42906},[2059],[2061,42908,42909],{"xmlns":2063},[2065,42910,42911,42915],{},[2068,42912,42913],{},[2071,42914,2861],{},[2092,42916,2861],{"encoding":2094},[95,42918,7409],{},[1647,42920,42922],{"className":42921},[2059],[2061,42923,42924],{"xmlns":2063},[2065,42925,42926,42930],{},[2068,42927,42928],{},[2071,42929,9214],{},[2092,42931,9214],{"encoding":2094},", ale ",[95,42934,42935],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[1647,42938,42940],{"className":42939},[2059],[2061,42941,42942],{"xmlns":2063},[2065,42943,42944,42964],{},[2068,42945,42946,42952,42954,42956,42958,42960,42962],{},[2348,42947,42948,42950],{},[2071,42949,554],{},[2071,42951,9214],{},[2075,42953,6593],{},[2075,42955,2084],{"stretchy":2083},[2210,42957,630],{},[2075,42959,2361],{"separator":2360},[2210,42961,638],{},[2075,42963,2090],{"stretchy":2083},[2092,42965,42966],{"encoding":2094},"E_Y \\in (0, 1)",[55,42968,42969,1445,42972,1445,42985,42987,42988,195],{},[95,42970,42971],{},"Podřadné zboží:",[1647,42973,42975],{"className":42974},[2059],[2061,42976,42977],{"xmlns":2063},[2065,42978,42979,42983],{},[2068,42980,42981],{},[2071,42982,2861],{},[2092,42984,2861],{"encoding":2094},[95,42986,7429],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[1647,42989,42991],{"className":42990},[2059],[2061,42992,42993],{"xmlns":2063},[2065,42994,42995,43007],{},[2068,42996,42997,43003,43005],{},[2348,42998,42999,43001],{},[2071,43000,554],{},[2071,43002,9214],{},[2075,43004,3521],{},[2210,43006,630],{},[2092,43008,43009],{"encoding":2094},"E_Y \u003C 0",[55,43011,43012,43013,195],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[95,43014,43015],{},"méně kusů, ne jen proporčně méně",[55,43017,43018,43021,43022,43025],{},[95,43019,43020],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[95,43023,43024],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[55,43027,43028],{},[58,43029],{"alt":43030,"className":43031,"src":43032},"imek-engelovy-krivky-3typy",[62,63],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[42216,43034,43036],{"id":43035},"české-příklady","České příklady",[323,43038,43039,43049],{},[326,43040,43041],{},[329,43042,43043,43046],{},[332,43044,43045],{},"Podřadné",[332,43047,43048],{},"Nahradí se za",[342,43050,43051,43059,43067,43075,43083,43091,43099,43107],{},[329,43052,43053,43056],{},[347,43054,43055],{},"Instantní polévky, ramen",[347,43057,43058],{},"Čerstvé jídlo, restaurace",[329,43060,43061,43064],{},[347,43062,43063],{},"MHD (autobus, tramvaj)",[347,43065,43066],{},"Vlastní auto, Uber, taxi",[329,43068,43069,43072],{},[347,43070,43071],{},"Mražené polotovary, pizza z mrazáku",[347,43073,43074],{},"Čerstvé suroviny, hotovky",[329,43076,43077,43080],{},[347,43078,43079],{},"Privátní značky supermarketů (K-Classic, Clever)",[347,43081,43082],{},"Značkové produkty",[329,43084,43085,43088],{},[347,43086,43087],{},"Paštika Májka, obyčejný měkký salám",[347,43089,43090],{},"Kvalitní uzeniny, šunka od kosti",[329,43092,43093,43096],{},[347,43094,43095],{},"Second hand oblečení",[347,43097,43098],{},"Nové oblečení, značky",[329,43100,43101,43104],{},[347,43102,43103],{},"Krabicové víno, nejlevnější pivo",[347,43105,43106],{},"Lahvové víno, řemeslná piva",[329,43108,43109,43112],{},[347,43110,43111],{},"Ojetá auta nižších tříd",[347,43113,43114],{},"Nová auta, prémiové značky",[1023,43116,43117],{},[55,43118,43119,43121,43122,43125],{},[1647,43120,4659],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[95,43123,43124],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[55,43127,43128,43131,43132,11156,43135,43157,43158,11156,43161,43182,43183,43201,43202,43205],{},[95,43129,43130],{},"Pozor — podřadné je relativní k osobě."," Stejný produkt může být pro různé lidi v různých kategoriích. McDonald's je pro studenta s 15k platem možná ",[95,43133,43134],{},"luxus",[1647,43136,43138],{"className":43137},[2059],[2061,43139,43140],{"xmlns":2063},[2065,43141,43142,43154],{},[2068,43143,43144,43150,43152],{},[2348,43145,43146,43148],{},[2071,43147,554],{},[2071,43149,9214],{},[2075,43151,3482],{},[2210,43153,638],{},[2092,43155,43156],{"encoding":2094},"E_Y > 1","), pro manažera s 200k platem ",[95,43159,43160],{},"podřadné",[1647,43162,43164],{"className":43163},[2059],[2061,43165,43166],{"xmlns":2063},[2065,43167,43168,43180],{},[2068,43169,43170,43176,43178],{},[2348,43171,43172,43174],{},[2071,43173,554],{},[2071,43175,9214],{},[2075,43177,3521],{},[2210,43179,630],{},[2092,43181,43009],{"encoding":2094},"). Proto je ",[1647,43184,43186],{"className":43185},[2059],[2061,43187,43188],{"xmlns":2063},[2065,43189,43190,43198],{},[2068,43191,43192],{},[2348,43193,43194,43196],{},[2071,43195,554],{},[2071,43197,9214],{},[2092,43199,43200],{"encoding":2094},"E_Y"," vždy ",[95,43203,43204],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[55,43207,43208,43209,43211],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[95,43210,42517],{}," (viz níže) — tam poptávková křivka dokonce roste.",[609,43213,43215,43216,2090],{"id":43214},"posun-poptávky-shift-of-demand","Posun poptávky (",[3982,43217,43218],{},"shift of demand",[55,43220,43221,43222,43240,43241,43258,43259,43272,43273,2758,43286,43308,43309,43326,43327,43353,43354,43357],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[1647,43223,43225],{"className":43224},[2059],[2061,43226,43227],{"xmlns":2063},[2065,43228,43229,43237],{},[2068,43230,43231],{},[2348,43232,43233,43235],{},[2071,43234,575],{},[2210,43236,630],{},[2092,43238,43239],{"encoding":2094},"P_0"," odpovídá množství ",[1647,43242,43244],{"className":43243},[2059],[2061,43245,43246],{"xmlns":2063},[2065,43247,43248,43256],{},[2068,43249,43250],{},[2348,43251,43252,43254],{},[2071,43253,2861],{},[2210,43255,630],{},[2092,43257,42599],{"encoding":2094}," na křivce ",[1647,43260,43262],{"className":43261},[2059],[2061,43263,43264],{"xmlns":2063},[2065,43265,43266,43270],{},[2068,43267,43268],{},[2071,43269,4271],{},[2092,43271,4271],{"encoding":2094},"; vzroste-li důchod z ",[1647,43274,43276],{"className":43275},[2059],[2061,43277,43278],{"xmlns":2063},[2065,43279,43280,43284],{},[2068,43281,43282],{},[2071,43283,9214],{},[2092,43285,9214],{"encoding":2094},[1647,43287,43289],{"className":43288},[2059],[2061,43290,43291],{"xmlns":2063},[2065,43292,43293,43305],{},[2068,43294,43295,43301,43303],{},[2348,43296,43297,43299],{},[2071,43298,9214],{},[2210,43300,638],{},[2075,43302,3482],{},[2071,43304,9214],{},[2092,43306,43307],{"encoding":2094},"Y_1 > Y",", pak stejné ceně ",[1647,43310,43312],{"className":43311},[2059],[2061,43313,43314],{"xmlns":2063},[2065,43315,43316,43324],{},[2068,43317,43318],{},[2348,43319,43320,43322],{},[2071,43321,575],{},[2210,43323,630],{},[2092,43325,43239],{"encoding":2094}," odpovídá vyšší ",[1647,43328,43330],{"className":43329},[2059],[2061,43331,43332],{"xmlns":2063},[2065,43333,43334,43350],{},[2068,43335,43336,43342,43344],{},[2348,43337,43338,43340],{},[2071,43339,2861],{},[2210,43341,638],{},[2075,43343,3482],{},[2348,43345,43346,43348],{},[2071,43347,2861],{},[2210,43349,630],{},[2092,43351,43352],{"encoding":2094},"Q_1 > Q_0"," — křivka se ",[95,43355,43356],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[55,43359,43360],{},[58,43361],{"alt":43362,"className":43363,"src":43364},"imek-posun-vs-pohyb-po-krivce",[62,63],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[55,43366,43367],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[55,43369,43370],{},[3982,43371,43372,43373,15746,43403,43424],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[1647,43374,43376],{"className":43375},[2059],[2061,43377,43378],{"xmlns":2063},[2065,43379,43380,43400],{},[2068,43381,43382,43388,43390,43392,43394],{},[2348,43383,43384,43386],{},[2071,43385,4271],{},[2210,43387,646],{},[2075,43389,2361],{"separator":2360},[2071,43391,4271],{},[2075,43393,2361],{"separator":2360},[2348,43395,43396,43398],{},[2071,43397,4271],{},[2210,43399,638],{},[2092,43401,43402],{"encoding":2094},"D_2, D, D_1",[1647,43404,43406],{"className":43405},[2059],[2061,43407,43408],{"xmlns":2063},[2065,43409,43410,43422],{},[2068,43411,43412,43414,43416,43418,43420],{},[2075,43413,2084],{"stretchy":2083},[2071,43415,2861],{},[2075,43417,2361],{"separator":2360},[2071,43419,575],{},[2075,43421,2090],{"stretchy":2083},[2092,43423,41982],{"encoding":2094},", šipky naznačují posuny.",[42216,43426,43428],{"id":43427},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[55,43430,43431,43433,43434,43457,43458,43475,43476,43493,43494,195],{},[95,43432,42224],{}," Poptávce ",[1647,43435,43437],{"className":43436},[2059],[2061,43438,43439],{"xmlns":2063},[2065,43440,43441,43455],{},[2068,43442,43443,43445,43447,43449,43451,43453],{},[2071,43444,575],{},[2075,43446,2077],{},[2071,43448,4271],{},[2075,43450,2084],{"stretchy":2083},[2071,43452,2861],{},[2075,43454,2090],{"stretchy":2083},[2092,43456,4727],{"encoding":2094}," odpovídá ceně ",[1647,43459,43461],{"className":43460},[2059],[2061,43462,43463],{"xmlns":2063},[2065,43464,43465,43473],{},[2068,43466,43467],{},[2348,43468,43469,43471],{},[2071,43470,575],{},[2210,43472,630],{},[2092,43474,43239],{"encoding":2094}," množství ",[1647,43477,43479],{"className":43478},[2059],[2061,43480,43481],{"xmlns":2063},[2065,43482,43483,43491],{},[2068,43484,43485],{},[2348,43486,43487,43489],{},[2071,43488,2861],{},[2210,43490,630],{},[2092,43492,42599],{"encoding":2094},". Na kupujícího je uložena jednotková daň ",[1647,43495,43497],{"className":43496},[2059],[2061,43498,43499],{"xmlns":2063},[2065,43500,43501,43505],{},[2068,43502,43503],{},[2071,43504,543],{},[2092,43506,543],{"encoding":2094},[55,43508,43509,43511,43512,43529,43530,43552],{},[95,43510,42256],{}," Kupující nakupuje množství ",[1647,43513,43515],{"className":43514},[2059],[2061,43516,43517],{"xmlns":2063},[2065,43518,43519,43527],{},[2068,43520,43521],{},[2348,43522,43523,43525],{},[2071,43524,2861],{},[2210,43526,638],{},[2092,43528,32029],{"encoding":2094},", které odpovídá ceně ",[1647,43531,43533],{"className":43532},[2059],[2061,43534,43535],{"xmlns":2063},[2065,43536,43537,43549],{},[2068,43538,43539,43545,43547],{},[2348,43540,43541,43543],{},[2071,43542,575],{},[2210,43544,630],{},[2075,43546,2176],{},[2071,43548,543],{},[2092,43550,43551],{"encoding":2094},"P_0 + T"," na původní křivce. Nová poptávka je",[1647,43554,43556],{"className":43555},[2059],[2061,43557,43558],{"xmlns":2063,"display":31093},[2065,43559,43560,43594],{},[2068,43561,43562,43564,43566,43572,43574,43576,43578,43580,43582,43584,43586,43588,43590,43592],{},[2071,43563,575],{},[2075,43565,2077],{},[2348,43567,43568,43570],{},[2071,43569,4271],{},[2210,43571,638],{},[2075,43573,2084],{"stretchy":2083},[2071,43575,2861],{},[2075,43577,2090],{"stretchy":2083},[2075,43579,2077],{},[2071,43581,4271],{},[2075,43583,2084],{"stretchy":2083},[2071,43585,2861],{},[2075,43587,2090],{"stretchy":2083},[2075,43589,2303],{},[2071,43591,543],{},[2075,43593,2361],{"separator":2360},[2092,43595,43596],{"encoding":2094},"P = D_1(Q) = D(Q) - T,",[55,43598,43599,43600,195],{},"tj. dojde k ",[95,43601,43602],{},"posunu poptávky doleva",[55,43604,43605],{},[3982,43606,43607,43608,43629,43630,835,43647,835,43660,43681,43682,75,43699,195],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[1647,43609,43611],{"className":43610},[2059],[2061,43612,43613],{"xmlns":2063},[2065,43614,43615,43627],{},[2068,43616,43617,43619,43621,43623,43625],{},[2075,43618,2084],{"stretchy":2083},[2071,43620,2861],{},[2075,43622,2361],{"separator":2360},[2071,43624,575],{},[2075,43626,2090],{"stretchy":2083},[2092,43628,41982],{"encoding":2094},"; na svislé ose jsou vyznačeny ",[1647,43631,43633],{"className":43632},[2059],[2061,43634,43635],{"xmlns":2063},[2065,43636,43637,43645],{},[2068,43638,43639],{},[2348,43640,43641,43643],{},[2071,43642,575],{},[2210,43644,630],{},[2092,43646,43239],{"encoding":2094},[1647,43648,43650],{"className":43649},[2059],[2061,43651,43652],{"xmlns":2063},[2065,43653,43654,43658],{},[2068,43655,43656],{},[2071,43657,543],{},[2092,43659,543],{"encoding":2094},[1647,43661,43663],{"className":43662},[2059],[2061,43664,43665],{"xmlns":2063},[2065,43666,43667,43679],{},[2068,43668,43669,43675,43677],{},[2348,43670,43671,43673],{},[2071,43672,575],{},[2210,43674,630],{},[2075,43676,2176],{},[2071,43678,543],{},[2092,43680,43551],{"encoding":2094},"; na vodorovné ",[1647,43683,43685],{"className":43684},[2059],[2061,43686,43687],{"xmlns":2063},[2065,43688,43689,43697],{},[2068,43690,43691],{},[2348,43692,43693,43695],{},[2071,43694,2861],{},[2210,43696,638],{},[2092,43698,32029],{"encoding":2094},[1647,43700,43702],{"className":43701},[2059],[2061,43703,43704],{"xmlns":2063},[2065,43705,43706,43714],{},[2068,43707,43708],{},[2348,43709,43710,43712],{},[2071,43711,2861],{},[2210,43713,630],{},[2092,43715,42599],{"encoding":2094},[609,43717,43719],{"id":43718},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[55,43721,43722],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[1647,43724,43726],{"className":43725},[2059],[2061,43727,43728],{"xmlns":2063,"display":31093},[2065,43729,43730,43915],{},[23493,43731,43732],{"width":31098},[23498,43733,43734,43736,43908,43910],{},[23501,43735],{"width":31103},[23501,43737,43738],{},[23493,43739,43740,43824],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,43741,43742,43752],{},[23501,43743,43744],{},[2400,43745,43746],{"scriptlevel":630,"displaystyle":2360},[2348,43747,43748,43750],{},[2071,43749,2861],{},[2210,43751,638],{},[23501,43753,43754],{},[2400,43755,43756],{"scriptlevel":630,"displaystyle":2360},[2068,43757,43758,43760,43762,43768,43770,43776,43778,43784,43786,43788,43794,43796,43802,43808,43810,43816,43822],{},[2068,43759],{},[2075,43761,2077],{},[2348,43763,43764,43766],{},[2071,43765,4271],{},[2210,43767,638],{},[2075,43769,2084],{"stretchy":2083},[2348,43771,43772,43774],{},[2071,43773,575],{},[2210,43775,638],{},[2075,43777,2361],{"separator":2360},[2348,43779,43780,43782],{},[2071,43781,575],{},[2210,43783,646],{},[2075,43785,2090],{"stretchy":2083},[2075,43787,2077],{},[2348,43789,43790,43792],{},[2071,43791,69],{},[2210,43793,638],{},[2075,43795,2176],{},[2348,43797,43798,43800],{},[2071,43799,2179],{},[2210,43801,638],{},[2348,43803,43804,43806],{},[2071,43805,575],{},[2210,43807,638],{},[2075,43809,2176],{},[2348,43811,43812,43814],{},[2071,43813,2222],{},[2210,43815,638],{},[2348,43817,43818,43820],{},[2071,43819,575],{},[2210,43821,646],{},[2075,43823,2361],{"separator":2360},[23498,43825,43826,43836],{},[23501,43827,43828],{},[2400,43829,43830],{"scriptlevel":630,"displaystyle":2360},[2348,43831,43832,43834],{},[2071,43833,2861],{},[2210,43835,646],{},[23501,43837,43838],{},[2400,43839,43840],{"scriptlevel":630,"displaystyle":2360},[2068,43841,43842,43844,43846,43852,43854,43860,43862,43868,43870,43872,43878,43880,43886,43892,43894,43900,43906],{},[2068,43843],{},[2075,43845,2077],{},[2348,43847,43848,43850],{},[2071,43849,4271],{},[2210,43851,646],{},[2075,43853,2084],{"stretchy":2083},[2348,43855,43856,43858],{},[2071,43857,575],{},[2210,43859,638],{},[2075,43861,2361],{"separator":2360},[2348,43863,43864,43866],{},[2071,43865,575],{},[2210,43867,646],{},[2075,43869,2090],{"stretchy":2083},[2075,43871,2077],{},[2348,43873,43874,43876],{},[2071,43875,69],{},[2210,43877,646],{},[2075,43879,2176],{},[2348,43881,43882,43884],{},[2071,43883,2179],{},[2210,43885,646],{},[2348,43887,43888,43890],{},[2071,43889,575],{},[2210,43891,638],{},[2075,43893,2176],{},[2348,43895,43896,43898],{},[2071,43897,2222],{},[2210,43899,646],{},[2348,43901,43902,43904],{},[2071,43903,575],{},[2210,43905,646],{},[2071,43907,195],{"mathvariant":2450},[23501,43909],{"width":31103},[23501,43911,43912],{},[2363,43913,43914],{},"(2.6)",[2092,43916,43917],{"encoding":2094},"\\begin{aligned}\nQ_1 &= D_1(P_1, P_2) = a_1 + b_1 P_1 + c_1 P_2, \\\\\nQ_2 &= D_2(P_1, P_2) = a_2 + b_2 P_1 + c_2 P_2.\n\\end{aligned}\n\\tag{2.6}",[1144,43919,43921],{"id":43920},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[89,43923,43924,43971,44018],{},[92,43925,43926,835,43948,43970],{},[1647,43927,43929],{"className":43928},[2059],[2061,43930,43931],{"xmlns":2063},[2065,43932,43933,43945],{},[2068,43934,43935,43941,43943],{},[2348,43936,43937,43939],{},[2071,43938,69],{},[2210,43940,638],{},[2075,43942,3482],{},[2210,43944,630],{},[2092,43946,43947],{"encoding":2094},"a_1 > 0",[1647,43949,43951],{"className":43950},[2059],[2061,43952,43953],{"xmlns":2063},[2065,43954,43955,43967],{},[2068,43956,43957,43963,43965],{},[2348,43958,43959,43961],{},[2071,43960,69],{},[2210,43962,646],{},[2075,43964,3482],{},[2210,43966,630],{},[2092,43968,43969],{"encoding":2094},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[92,43972,43973,835,43995,44017],{},[1647,43974,43976],{"className":43975},[2059],[2061,43977,43978],{"xmlns":2063},[2065,43979,43980,43992],{},[2068,43981,43982,43988,43990],{},[2348,43983,43984,43986],{},[2071,43985,2179],{},[2210,43987,638],{},[2075,43989,3521],{},[2210,43991,630],{},[2092,43993,43994],{"encoding":2094},"b_1 \u003C 0",[1647,43996,43998],{"className":43997},[2059],[2061,43999,44000],{"xmlns":2063},[2065,44001,44002,44014],{},[2068,44003,44004,44010,44012],{},[2348,44005,44006,44008],{},[2071,44007,2222],{},[2210,44009,646],{},[2075,44011,3521],{},[2210,44013,630],{},[2092,44015,44016],{"encoding":2094},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[92,44019,44020,44021,835,44038,44056,44057],{},"zkřížené koeficienty ",[1647,44022,44024],{"className":44023},[2059],[2061,44025,44026],{"xmlns":2063},[2065,44027,44028,44036],{},[2068,44029,44030],{},[2348,44031,44032,44034],{},[2071,44033,2222],{},[2210,44035,638],{},[2092,44037,32826],{"encoding":2094},[1647,44039,44041],{"className":44040},[2059],[2061,44042,44043],{"xmlns":2063},[2065,44044,44045,44053],{},[2068,44046,44047],{},[2348,44048,44049,44051],{},[2071,44050,2179],{},[2210,44052,646],{},[2092,44054,44055],{"encoding":2094},"b_2"," určují povahu vztahu:\n",[89,44058,44059,44109],{},[92,44060,44061,44064,44065,835,44087,2361],{},[95,44062,44063],{},"substituty"," (máslo vs. margarín): ",[1647,44066,44068],{"className":44067},[2059],[2061,44069,44070],{"xmlns":2063},[2065,44071,44072,44084],{},[2068,44073,44074,44080,44082],{},[2348,44075,44076,44078],{},[2071,44077,2222],{},[2210,44079,638],{},[2075,44081,3482],{},[2210,44083,630],{},[2092,44085,44086],{"encoding":2094},"c_1 > 0",[1647,44088,44090],{"className":44089},[2059],[2061,44091,44092],{"xmlns":2063},[2065,44093,44094,44106],{},[2068,44095,44096,44102,44104],{},[2348,44097,44098,44100],{},[2071,44099,2179],{},[2210,44101,646],{},[2075,44103,3482],{},[2210,44105,630],{},[2092,44107,44108],{"encoding":2094},"b_2 > 0",[92,44110,44111,44114,44115,835,44137,195],{},[95,44112,44113],{},"komplementy"," (auto vs. benzín): ",[1647,44116,44118],{"className":44117},[2059],[2061,44119,44120],{"xmlns":2063},[2065,44121,44122,44134],{},[2068,44123,44124,44130,44132],{},[2348,44125,44126,44128],{},[2071,44127,2222],{},[2210,44129,638],{},[2075,44131,3521],{},[2210,44133,630],{},[2092,44135,44136],{"encoding":2094},"c_1 \u003C 0",[1647,44138,44140],{"className":44139},[2059],[2061,44141,44142],{"xmlns":2063},[2065,44143,44144,44156],{},[2068,44145,44146,44152,44154],{},[2348,44147,44148,44150],{},[2071,44149,2179],{},[2210,44151,646],{},[2075,44153,3521],{},[2210,44155,630],{},[2092,44157,44158],{"encoding":2094},"b_2 \u003C 0",[55,44160,44161],{},"Schematicky:",[55,44163,44164,44167],{},[95,44165,44166],{},"Substituty",[1647,44168,44170],{"className":44169},[2059],[2061,44171,44172],{"xmlns":2063},[2065,44173,44174,44313],{},[2068,44175,44176,44182,44184,44199,44201,44221,44223,44243,44245,44247,44253,44255,44269,44271,44291,44293],{},[2348,44177,44178,44180],{},[2071,44179,2861],{},[2210,44181,638],{},[2075,44183,2077],{},[2071,44185,44186],{},[44187,44188,44189,44197],"munder",{},[2075,44190,44191],{},[2348,44192,44193,44195],{},[2071,44194,69],{},[2210,44196,638],{},[2075,44198,2176],{"lspace":2451,"rspace":2451},[2075,44200,2176],{},[2071,44202,44203],{},[44187,44204,44205,44219],{},[2075,44206,44207,44213],{},[2348,44208,44209,44211],{},[2071,44210,2179],{},[2210,44212,638],{},[2348,44214,44215,44217],{},[2071,44216,575],{},[2210,44218,638],{},[2075,44220,2303],{"lspace":2451,"rspace":2451},[2075,44222,2176],{},[2071,44224,44225],{},[44187,44226,44227,44241],{},[2075,44228,44229,44235],{},[2348,44230,44231,44233],{},[2071,44232,2222],{},[2210,44234,638],{},[2348,44236,44237,44239],{},[2071,44238,575],{},[2210,44240,646],{},[2075,44242,2176],{"lspace":2451,"rspace":2451},[2075,44244,2361],{"separator":2360},[5965,44246],{"width":5967},[2348,44248,44249,44251],{},[2071,44250,2861],{},[2210,44252,646],{},[2075,44254,2077],{},[2071,44256,44257],{},[44187,44258,44259,44267],{},[2075,44260,44261],{},[2348,44262,44263,44265],{},[2071,44264,69],{},[2210,44266,646],{},[2075,44268,2176],{"lspace":2451,"rspace":2451},[2075,44270,2176],{},[2071,44272,44273],{},[44187,44274,44275,44289],{},[2075,44276,44277,44283],{},[2348,44278,44279,44281],{},[2071,44280,2179],{},[2210,44282,646],{},[2348,44284,44285,44287],{},[2071,44286,575],{},[2210,44288,638],{},[2075,44290,2176],{"lspace":2451,"rspace":2451},[2075,44292,2176],{},[2071,44294,44295],{},[44187,44296,44297,44311],{},[2075,44298,44299,44305],{},[2348,44300,44301,44303],{},[2071,44302,2222],{},[2210,44304,646],{},[2348,44306,44307,44309],{},[2071,44308,575],{},[2210,44310,646],{},[2075,44312,2303],{"lspace":2451,"rspace":2451},[2092,44314,44315],{"encoding":2094},"Q_1 = \\underset{+}{a_1} + \\underset{-}{b_1 P_1} + \\underset{+}{c_1 P_2}, \\qquad Q_2 = \\underset{+}{a_2} + \\underset{+}{b_2 P_1} + \\underset{-}{c_2 P_2}",[55,44317,44318,44321],{},[95,44319,44320],{},"Komplementy",[1647,44322,44324],{"className":44323},[2059],[2061,44325,44326],{"xmlns":2063},[2065,44327,44328,44466],{},[2068,44329,44330,44336,44338,44352,44354,44374,44376,44396,44398,44400,44406,44408,44422,44424,44444,44446],{},[2348,44331,44332,44334],{},[2071,44333,2861],{},[2210,44335,638],{},[2075,44337,2077],{},[2071,44339,44340],{},[44187,44341,44342,44350],{},[2075,44343,44344],{},[2348,44345,44346,44348],{},[2071,44347,69],{},[2210,44349,638],{},[2075,44351,2176],{"lspace":2451,"rspace":2451},[2075,44353,2176],{},[2071,44355,44356],{},[44187,44357,44358,44372],{},[2075,44359,44360,44366],{},[2348,44361,44362,44364],{},[2071,44363,2179],{},[2210,44365,638],{},[2348,44367,44368,44370],{},[2071,44369,575],{},[2210,44371,638],{},[2075,44373,2303],{"lspace":2451,"rspace":2451},[2075,44375,2176],{},[2071,44377,44378],{},[44187,44379,44380,44394],{},[2075,44381,44382,44388],{},[2348,44383,44384,44386],{},[2071,44385,2222],{},[2210,44387,638],{},[2348,44389,44390,44392],{},[2071,44391,575],{},[2210,44393,646],{},[2075,44395,2303],{"lspace":2451,"rspace":2451},[2075,44397,2361],{"separator":2360},[5965,44399],{"width":5967},[2348,44401,44402,44404],{},[2071,44403,2861],{},[2210,44405,646],{},[2075,44407,2077],{},[2071,44409,44410],{},[44187,44411,44412,44420],{},[2075,44413,44414],{},[2348,44415,44416,44418],{},[2071,44417,69],{},[2210,44419,646],{},[2075,44421,2176],{"lspace":2451,"rspace":2451},[2075,44423,2176],{},[2071,44425,44426],{},[44187,44427,44428,44442],{},[2075,44429,44430,44436],{},[2348,44431,44432,44434],{},[2071,44433,2179],{},[2210,44435,646],{},[2348,44437,44438,44440],{},[2071,44439,575],{},[2210,44441,638],{},[2075,44443,2303],{"lspace":2451,"rspace":2451},[2075,44445,2176],{},[2071,44447,44448],{},[44187,44449,44450,44464],{},[2075,44451,44452,44458],{},[2348,44453,44454,44456],{},[2071,44455,2222],{},[2210,44457,646],{},[2348,44459,44460,44462],{},[2071,44461,575],{},[2210,44463,646],{},[2075,44465,2303],{"lspace":2451,"rspace":2451},[2092,44467,44468],{"encoding":2094},"Q_1 = \\underset{+}{a_1} + \\underset{-}{b_1 P_1} + \\underset{-}{c_1 P_2}, \\qquad Q_2 = \\underset{+}{a_2} + \\underset{-}{b_2 P_1} + \\underset{-}{c_2 P_2}",[909,44470],{},[84,44472,14860],{"id":41072},[1023,44474,44475],{},[55,44476,44477,44479,44480,41286,44493,41300,44506,44509,44510,5756,44534,44552],{},[1647,44478,4243],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[1647,44481,44483],{"className":44482},[2059],[2061,44484,44485],{"xmlns":2063},[2065,44486,44487,44491],{},[2068,44488,44489],{},[2071,44490,2861],{},[2092,44492,2861],{"encoding":2094},[1647,44494,44496],{"className":44495},[2059],[2061,44497,44498],{"xmlns":2063},[2065,44499,44500,44504],{},[2068,44501,44502],{},[2071,44503,575],{},[2092,44505,575],{"encoding":2094},[95,44507,44508],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[1647,44511,44513],{"className":44512},[2059],[2061,44514,44515],{"xmlns":2063},[2065,44516,44517,44531],{},[2068,44518,44519,44521,44523,44525,44527,44529],{},[2071,44520,575],{},[2075,44522,2077],{},[2071,44524,2222],{},[2071,44526,2861],{},[2075,44528,2176],{},[2071,44530,2273],{},[2092,44532,44533],{"encoding":2094},"P = cQ + d",[1647,44535,44537],{"className":44536},[2059],[2061,44538,44539],{"xmlns":2063},[2065,44540,44541,44549],{},[2068,44542,44543,44545,44547],{},[2071,44544,2222],{},[2075,44546,3482],{},[2210,44548,630],{},[2092,44550,44551],{"encoding":2094},"c > 0"," je standardní aproximací.",[609,44554,41356],{"id":44555},"obecný-vícefaktorový-model-1",[55,44557,44558,11156,44561,44564,44565,44578,44579,41189,44592,41203,44605,44618,44619,44633,44634,41232,44647,44660],{},[95,44559,44560],{},"Nabízené množství",[3982,44562,44563],{},"quantity supplied",") závisí na ceně ",[1647,44566,44568],{"className":44567},[2059],[2061,44569,44570],{"xmlns":2063},[2065,44571,44572,44576],{},[2068,44573,44574],{},[2071,44575,575],{},[2092,44577,575],{"encoding":2094},", cenách výrobních faktorů (práce ",[1647,44580,44582],{"className":44581},[2059],[2061,44583,44584],{"xmlns":2063},[2065,44585,44586,44590],{},[2068,44587,44588],{},[2071,44589,586],{},[2092,44591,586],{"encoding":2094},[1647,44593,44595],{"className":44594},[2059],[2061,44596,44597],{"xmlns":2063},[2065,44598,44599,44603],{},[2068,44600,44601],{},[2071,44602,10929],{},[2092,44604,10929],{"encoding":2094},[1647,44606,44608],{"className":44607},[2059],[2061,44609,44610],{"xmlns":2063},[2065,44611,44612,44616],{},[2068,44613,44614],{},[2071,44615,554],{},[2092,44617,554],{"encoding":2094},"), očekávání ",[1647,44620,44622],{"className":44621},[2059],[2061,44623,44624],{"xmlns":2063},[2065,44625,44626,44631],{},[2068,44627,44628],{},[2071,44629,44630],{},"V",[2092,44632,44630],{"encoding":2094},", počtu výrobců ",[1647,44635,44637],{"className":44636},[2059],[2061,44638,44639],{"xmlns":2063},[2065,44640,44641,44645],{},[2068,44642,44643],{},[2071,44644,41229],{},[2092,44646,41229],{"encoding":2094},[1647,44648,44650],{"className":44649},[2059],[2061,44651,44652],{"xmlns":2063},[2065,44653,44654,44658],{},[2068,44655,44656],{},[2071,44657,41244],{},[2092,44659,41244],{"encoding":2094}," a dalších:",[1647,44662,44664],{"className":44663},[2059],[2061,44665,44666],{"xmlns":2063,"display":31093},[2065,44667,44668,44727],{},[23493,44669,44670],{"width":31098},[23498,44671,44672,44674,44720,44722],{},[23501,44673],{"width":31103},[23501,44675,44676],{},[2068,44677,44678,44680,44682,44684,44686,44688,44690,44692,44694,44696,44698,44700,44702,44704,44706,44708,44710,44712,44714,44716,44718],{},[2071,44679,2861],{},[2075,44681,2077],{},[2071,44683,532],{},[2075,44685,2084],{"stretchy":2083},[2071,44687,575],{},[2075,44689,2361],{"separator":2360},[2071,44691,586],{},[2075,44693,2361],{"separator":2360},[2071,44695,10929],{},[2075,44697,2361],{"separator":2360},[2071,44699,554],{},[2075,44701,2361],{"separator":2360},[2071,44703,44630],{},[2075,44705,2361],{"separator":2360},[2071,44707,41229],{},[2075,44709,2361],{"separator":2360},[2071,44711,41244],{},[2075,44713,2361],{"separator":2360},[2075,44715,10773],{},[2075,44717,2090],{"stretchy":2083},[2071,44719,195],{"mathvariant":2450},[23501,44721],{"width":31103},[23501,44723,44724],{},[2363,44725,44726],{},"(2.7)",[2092,44728,44729],{"encoding":2094},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[55,44731,42707,44732,11156,44735,44738],{},[95,44733,44734],{},"funkce nabídky",[3982,44736,44737],{},"supply function",") v širším slova smyslu.",[609,44740,44742],{"id":44741},"jednofaktorový-model","Jednofaktorový model",[55,44744,44745],{},"V nejpřirozenějším jednofaktorovém modelu",[1647,44747,44749],{"className":44748},[2059],[2061,44750,44751],{"xmlns":2063,"display":31093},[2065,44752,44753,44804],{},[23493,44754,44755],{"width":31098},[23498,44756,44757,44759,44797,44799],{},[23501,44758],{"width":31103},[23501,44760,44761],{},[2068,44762,44763,44765,44767,44769,44771,44773,44775,44777,44779,44781,44783,44785,44787,44789,44791,44793,44795],{},[2071,44764,2861],{},[2075,44766,2077],{},[2071,44768,532],{},[2075,44770,2084],{"stretchy":2083},[2071,44772,575],{},[2075,44774,2090],{"stretchy":2083},[2075,44776,2361],{"separator":2360},[5965,44778],{"width":5967},[2363,44780,41708],{},[5965,44782],{"width":5967},[2071,44784,575],{},[2075,44786,2077],{},[2071,44788,532],{},[2075,44790,2084],{"stretchy":2083},[2071,44792,2861],{},[2075,44794,2090],{"stretchy":2083},[2071,44796,195],{"mathvariant":2450},[23501,44798],{"width":31103},[23501,44800,44801],{},[2363,44802,44803],{},"(2.8)",[2092,44805,44806],{"encoding":2094},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[55,44808,44809,44810,11156,44813,4007],{},"Graf je ",[95,44811,44812],{},"křivka nabídky",[3982,44814,44815],{},"supply curve",[1144,44817,44819],{"id":44818},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1023,44821,44822],{},[55,44823,44824],{},[95,44825,41754,44826,44839,44840,41809],{},[1647,44827,44829],{"className":44828},[2059],[2061,44830,44831],{"xmlns":2063},[2065,44832,44833,44837],{},[2068,44834,44835],{},[2071,44836,575],{},[2092,44838,575],{"encoding":2094},", pak nabízené množství ",[1647,44841,44843],{"className":44842},[2059],[2061,44844,44845],{"xmlns":2063},[2065,44846,44847,44851],{},[2068,44848,44849],{},[2071,44850,2861],{},[2092,44852,2861],{"encoding":2094},[55,44854,44855,44856,44881,44882,44912,44913,44930],{},"Výrobce je ochoten zvýšit produkci jen za vyšší cenu, neboť rostou mezní náklady (kap. 3). Funkce nabídky je proto rostoucí. Křivka nabídky vychází z bodu ",[1647,44857,44859],{"className":44858},[2059],[2061,44860,44861],{"xmlns":2063},[2065,44862,44863,44879],{},[2068,44864,44865,44867,44869,44871,44877],{},[2075,44866,2561],{"stretchy":2083},[2210,44868,630],{},[2075,44870,2361],{"separator":2360},[2348,44872,44873,44875],{},[2071,44874,575],{},[2210,44876,630],{},[2075,44878,2576],{"stretchy":2083},[2092,44880,41894],{"encoding":2094}," na svislé ose (případně z ",[1647,44883,44885],{"className":44884},[2059],[2061,44886,44887],{"xmlns":2063},[2065,44888,44889,44909],{},[2068,44890,44891,44893,44899,44901,44907],{},[2075,44892,2561],{"stretchy":2083},[2348,44894,44895,44897],{},[2071,44896,2861],{},[2210,44898,638],{},[2075,44900,2361],{"separator":2360},[2348,44902,44903,44905],{},[2071,44904,575],{},[2210,44906,638],{},[2075,44908,2576],{"stretchy":2083},[2092,44910,44911],{"encoding":2094},"[Q_1, P_1]","), kde ",[1647,44914,44916],{"className":44915},[2059],[2061,44917,44918],{"xmlns":2063},[2065,44919,44920,44928],{},[2068,44921,44922],{},[2348,44923,44924,44926],{},[2071,44925,575],{},[2210,44927,630],{},[2092,44929,43239],{"encoding":2094}," je minimální cena, při které je výrobce ochoten vyrábět.",[55,44932,44933],{},[3982,44934,44935,44936,3792,44949,195],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[1647,44937,44939],{"className":44938},[2059],[2061,44940,44941],{"xmlns":2063},[2065,44942,44943,44947],{},[2068,44944,44945],{},[2071,44946,532],{},[2092,44948,532],{"encoding":2094},[1647,44950,44952],{"className":44951},[2059],[2061,44953,44954],{"xmlns":2063},[2065,44955,44956,44968],{},[2068,44957,44958,44960,44962,44964,44966],{},[2075,44959,2084],{"stretchy":2083},[2071,44961,2861],{},[2075,44963,2361],{"separator":2360},[2071,44965,575],{},[2075,44967,2090],{"stretchy":2083},[2092,44969,41982],{"encoding":2094},[1144,44971,44973],{"id":44972},"lineární-model-nabídky","Lineární model nabídky",[1647,44975,44977],{"className":44976},[2059],[2061,44978,44979],{"xmlns":2063,"display":31093},[2065,44980,44981,45020],{},[23493,44982,44983],{"width":31098},[23498,44984,44985,44987,45013,45015],{},[23501,44986],{"width":31103},[23501,44988,44989],{},[2068,44990,44991,44993,44995,44997,44999,45001,45003,45005,45007,45009,45011],{},[2071,44992,575],{},[2075,44994,2077],{},[2071,44996,2222],{},[2071,44998,2861],{},[2075,45000,2176],{},[2071,45002,2273],{},[2075,45004,2361],{"separator":2360},[5965,45006],{"width":5967},[2071,45008,2222],{},[2075,45010,3482],{},[2210,45012,14195],{},[23501,45014],{"width":31103},[23501,45016,45017],{},[2363,45018,45019],{},"(2.9)",[2092,45021,45022],{"encoding":2094},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[55,45024,45025,45026,45062,45063,45076],{},"Alternativně ",[1647,45027,45029],{"className":45028},[2059],[2061,45030,45031],{"xmlns":2063},[2065,45032,45033,45059],{},[2068,45034,45035,45037,45039,45047,45049,45051],{},[2071,45036,2861],{},[2075,45038,2077],{},[2400,45040,45041],{"scriptlevel":630,"displaystyle":2083},[2403,45042,45043,45045],{},[2210,45044,638],{},[2071,45046,2222],{},[2071,45048,575],{},[2075,45050,2303],{},[2400,45052,45053],{"scriptlevel":630,"displaystyle":2083},[2403,45054,45055,45057],{},[2071,45056,2273],{},[2071,45058,2222],{},[2092,45060,45061],{"encoding":2094},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[1647,45064,45066],{"className":45065},[2059],[2061,45067,45068],{"xmlns":2063},[2065,45069,45070,45074],{},[2068,45071,45072],{},[2071,45073,575],{},[2092,45075,575],{"encoding":2094}," zůstává, znaménko absolutního členu se mění.",[42216,45078,45080],{"id":45079},"příklad-25","Příklad 2.5",[55,45082,45083,45085,45086,195],{},[95,45084,42224],{}," Lineární nabídka ",[1647,45087,45089],{"className":45088},[2059],[2061,45090,45091],{"xmlns":2063},[2065,45092,45093,45107],{},[2068,45094,45095,45097,45099,45101,45103,45105],{},[2071,45096,575],{},[2075,45098,2077],{},[2210,45100,5096],{},[2071,45102,2861],{},[2075,45104,2176],{},[2210,45106,5091],{},[2092,45108,45109],{"encoding":2094},"P = 0{,}5Q + 25",[55,45111,45112,45114,45115,195],{},[95,45113,42256],{}," Alternativní tvar ",[1647,45116,45118],{"className":45117},[2059],[2061,45119,45120],{"xmlns":2063},[2065,45121,45122,45136],{},[2068,45123,45124,45126,45128,45130,45132,45134],{},[2071,45125,2861],{},[2075,45127,2077],{},[2210,45129,646],{},[2071,45131,575],{},[2075,45133,2303],{},[2210,45135,3194],{},[2092,45137,45138],{"encoding":2094},"Q = 2P - 50",[323,45140,45141,45166],{},[326,45142,45143],{},[329,45144,45145,45160,45162,45164],{},[332,45146,45147],{},[1647,45148,45150],{"className":45149},[2059],[2061,45151,45152],{"xmlns":2063},[2065,45153,45154,45158],{},[2068,45155,45156],{},[2071,45157,575],{},[2092,45159,575],{"encoding":2094},[332,45161,42310],{},[332,45163,16773],{},[332,45165,5298],{},[342,45167,45168],{},[329,45169,45170,45185,45187,45189],{},[347,45171,45172],{},[1647,45173,45175],{"className":45174},[2059],[2061,45176,45177],{"xmlns":2063},[2065,45178,45179,45183],{},[2068,45180,45181],{},[2071,45182,2861],{},[2092,45184,2861],{"encoding":2094},[347,45186,2935],{},[347,45188,9121],{},[347,45190,42310],{},[609,45192,45194,45195,2090],{"id":45193},"posun-nabídky-shift-of-supply","Posun nabídky (",[3982,45196,45197],{},"shift of supply",[55,45199,45200,45201,45204,45205,45222,45223,45248,45249,195],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[95,45202,45203],{},"doprava",": při stejné ceně ",[1647,45206,45208],{"className":45207},[2059],[2061,45209,45210],{"xmlns":2063},[2065,45211,45212,45220],{},[2068,45213,45214],{},[2348,45215,45216,45218],{},[2071,45217,575],{},[2210,45219,630],{},[2092,45221,43239],{"encoding":2094}," vyrobí výrobce větší ",[1647,45224,45226],{"className":45225},[2059],[2061,45227,45228],{"xmlns":2063},[2065,45229,45230,45246],{},[2068,45231,45232,45238,45240],{},[2348,45233,45234,45236],{},[2071,45235,2861],{},[2210,45237,638],{},[2075,45239,3482],{},[2348,45241,45242,45244],{},[2071,45243,2861],{},[2210,45245,630],{},[2092,45247,43352],{"encoding":2094},"); zdražení vstupů posune křivku ",[95,45250,45251],{},"doleva",[55,45253,45254],{},[3982,45255,45256,45257,45270,45271,45289,45290,45308,45309,195],{},"Obrázek 2.11: Původní ",[1647,45258,45260],{"className":45259},[2059],[2061,45261,45262],{"xmlns":2063},[2065,45263,45264,45268],{},[2068,45265,45266],{},[2071,45267,532],{},[2092,45269,532],{"encoding":2094},", posunuté ",[1647,45272,45274],{"className":45273},[2059],[2061,45275,45276],{"xmlns":2063},[2065,45277,45278,45286],{},[2068,45279,45280],{},[2348,45281,45282,45284],{},[2071,45283,532],{},[2210,45285,638],{},[2092,45287,45288],{"encoding":2094},"S_1"," (doprava) a ",[1647,45291,45293],{"className":45292},[2059],[2061,45294,45295],{"xmlns":2063},[2065,45296,45297,45305],{},[2068,45298,45299],{},[2348,45300,45301,45303],{},[2071,45302,532],{},[2210,45304,646],{},[2092,45306,45307],{"encoding":2094},"S_2"," (doleva) v ",[1647,45310,45312],{"className":45311},[2059],[2061,45313,45314],{"xmlns":2063},[2065,45315,45316,45328],{},[2068,45317,45318,45320,45322,45324,45326],{},[2075,45319,2084],{"stretchy":2083},[2071,45321,2861],{},[2075,45323,2361],{"separator":2360},[2071,45325,575],{},[2075,45327,2090],{"stretchy":2083},[2092,45329,41982],{"encoding":2094},[42216,45331,45333],{"id":45332},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[55,45335,45336,45338,45339,45363,45364,195],{},[95,45337,42224],{}," Nabídka ",[1647,45340,45342],{"className":45341},[2059],[2061,45343,45344],{"xmlns":2063},[2065,45345,45346,45360],{},[2068,45347,45348,45350,45352,45354,45356,45358],{},[2071,45349,575],{},[2075,45351,2077],{},[2071,45353,532],{},[2075,45355,2084],{"stretchy":2083},[2071,45357,2861],{},[2075,45359,2090],{"stretchy":2083},[2092,45361,45362],{"encoding":2094},"P = S(Q)","; na výrobce je uložena jednotková daň ",[1647,45365,45367],{"className":45366},[2059],[2061,45368,45369],{"xmlns":2063},[2065,45370,45371,45375],{},[2068,45372,45373],{},[2071,45374,543],{},[2092,45376,543],{"encoding":2094},[55,45378,45379,45381,45382,45395,45396,45414,45415,45443],{},[95,45380,42256],{}," Spotřebitel zaplatí ",[1647,45383,45385],{"className":45384},[2059],[2061,45386,45387],{"xmlns":2063},[2065,45388,45389,45393],{},[2068,45390,45391],{},[2071,45392,575],{},[2092,45394,575],{"encoding":2094},", výrobce obdrží ",[1647,45397,45399],{"className":45398},[2059],[2061,45400,45401],{"xmlns":2063},[2065,45402,45403,45411],{},[2068,45404,45405,45407,45409],{},[2071,45406,575],{},[2075,45408,2303],{},[2071,45410,543],{},[2092,45412,45413],{"encoding":2094},"P - T",". Z podmínky ",[1647,45416,45418],{"className":45417},[2059],[2061,45419,45420],{"xmlns":2063},[2065,45421,45422,45440],{},[2068,45423,45424,45426,45428,45430,45432,45434,45436,45438],{},[2071,45425,575],{},[2075,45427,2303],{},[2071,45429,543],{},[2075,45431,2077],{},[2071,45433,532],{},[2075,45435,2084],{"stretchy":2083},[2071,45437,2861],{},[2075,45439,2090],{"stretchy":2083},[2092,45441,45442],{"encoding":2094},"P - T = S(Q)"," plyne",[1647,45445,45447],{"className":45446},[2059],[2061,45448,45449],{"xmlns":2063,"display":31093},[2065,45450,45451,45485],{},[2068,45452,45453,45455,45457,45463,45465,45467,45469,45471,45473,45475,45477,45479,45481,45483],{},[2071,45454,575],{},[2075,45456,2077],{},[2348,45458,45459,45461],{},[2071,45460,532],{},[2210,45462,638],{},[2075,45464,2084],{"stretchy":2083},[2071,45466,2861],{},[2075,45468,2090],{"stretchy":2083},[2075,45470,2077],{},[2071,45472,532],{},[2075,45474,2084],{"stretchy":2083},[2071,45476,2861],{},[2075,45478,2090],{"stretchy":2083},[2075,45480,2176],{},[2071,45482,543],{},[2071,45484,195],{"mathvariant":2450},[2092,45486,45487],{"encoding":2094},"P = S_1(Q) = S(Q) + T.",[55,45489,45490,45491,45504,45505,1445,45518,45521,45522,75,45542,8189,45560,195],{},"Křivka ",[1647,45492,45494],{"className":45493},[2059],[2061,45495,45496],{"xmlns":2063},[2065,45497,45498,45502],{},[2068,45499,45500],{},[2071,45501,532],{},[2092,45503,532],{"encoding":2094}," se tedy posune o ",[1647,45506,45508],{"className":45507},[2059],[2061,45509,45510],{"xmlns":2063},[2065,45511,45512,45516],{},[2068,45513,45514],{},[2071,45515,543],{},[2092,45517,543],{"encoding":2094},[95,45519,45520],{},"svisle nahoru"," (tj. doleva). Např. pro ",[1647,45523,45525],{"className":45524},[2059],[2061,45526,45527],{"xmlns":2063},[2065,45528,45529,45539],{},[2068,45530,45531,45533,45535,45537],{},[2071,45532,575],{},[2075,45534,2077],{},[2210,45536,646],{},[2071,45538,2861],{},[2092,45540,45541],{"encoding":2094},"P = 2Q",[1647,45543,45545],{"className":45544},[2059],[2061,45546,45547],{"xmlns":2063},[2065,45548,45549,45557],{},[2068,45550,45551,45553,45555],{},[2071,45552,543],{},[2075,45554,2077],{},[2210,45556,678],{},[2092,45558,45559],{"encoding":2094},"T = 6",[1647,45561,45563],{"className":45562},[2059],[2061,45564,45565],{"xmlns":2063},[2065,45566,45567,45589],{},[2068,45568,45569,45575,45577,45579,45581,45583,45585,45587],{},[2348,45570,45571,45573],{},[2071,45572,532],{},[2210,45574,638],{},[2075,45576,2777],{},[2071,45578,575],{},[2075,45580,2077],{},[2210,45582,646],{},[2071,45584,2861],{},[2075,45586,2176],{},[2210,45588,678],{},[2092,45590,45591],{"encoding":2094},"S_1: P = 2Q + 6",[55,45593,45594],{},[3982,45595,45596,45597,45610],{},"Obrázek 2.12: Posun nabídky o ",[1647,45598,45600],{"className":45599},[2059],[2061,45601,45602],{"xmlns":2063},[2065,45603,45604,45608],{},[2068,45605,45606],{},[2071,45607,543],{},[2092,45609,543],{"encoding":2094}," svisle nahoru.",[909,45612],{},[84,45614,45616],{"id":45615},"tržní-rovnováha","Tržní rovnováha",[1023,45618,45619],{},[55,45620,45621,45623,45624,1445,45627,45659,45660,835,45683,45706,45707,45710,45711,45724],{},[1647,45622,4243],{}," TL;DR\nV ",[95,45625,45626],{},"rovnovážném bodě",[1647,45628,45630],{"className":45629},[2059],[2061,45631,45632],{"xmlns":2063},[2065,45633,45634,45656],{},[2068,45635,45636,45638,45640,45646,45648,45654],{},[2071,45637,554],{},[2075,45639,2561],{"stretchy":2083},[2205,45641,45642,45644],{},[2071,45643,2861],{},[2071,45645,554],{},[2075,45647,2361],{"separator":2360},[2205,45649,45650,45652],{},[2071,45651,575],{},[2071,45653,554],{},[2075,45655,2576],{"stretchy":2083},[2092,45657,45658],{"encoding":2094},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[1647,45661,45663],{"className":45662},[2059],[2061,45664,45665],{"xmlns":2063},[2065,45666,45667,45681],{},[2068,45668,45669,45671,45673,45675,45677,45679],{},[2071,45670,575],{},[2075,45672,2077],{},[2071,45674,4271],{},[2075,45676,2084],{"stretchy":2083},[2071,45678,2861],{},[2075,45680,2090],{"stretchy":2083},[2092,45682,4727],{"encoding":2094},[1647,45684,45686],{"className":45685},[2059],[2061,45687,45688],{"xmlns":2063},[2065,45689,45690,45704],{},[2068,45691,45692,45694,45696,45698,45700,45702],{},[2071,45693,575],{},[2075,45695,2077],{},[2071,45697,532],{},[2075,45699,2084],{"stretchy":2083},[2071,45701,2861],{},[2075,45703,2090],{"stretchy":2083},[2092,45705,45362],{"encoding":2094},". Čtyři ",[95,45708,45709],{},"pravidla komparativní statiky"," popisují, jak se ",[1647,45712,45714],{"className":45713},[2059],[2061,45715,45716],{"xmlns":2063},[2065,45717,45718,45722],{},[2068,45719,45720],{},[2071,45721,554],{},[2092,45723,554],{"encoding":2094}," posune při změně poptávky nebo nabídky.",[609,45726,45728],{"id":45727},"definice","Definice",[55,45730,45731,11156,45733,45736,45737,1445,45740,45758,45759,45790,45791,11156,45794,4007],{},[95,45732,45616],{},[3982,45734,45735],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[95,45738,45739],{},"rovnovážné ceně",[1647,45741,45743],{"className":45742},[2059],[2061,45744,45745],{"xmlns":2063},[2065,45746,45747,45755],{},[2068,45748,45749],{},[2205,45750,45751,45753],{},[2071,45752,575],{},[2071,45754,554],{},[2092,45756,45757],{"encoding":2094},"P^E"," není přebytek ani nedostatek zboží. Bod ",[1647,45760,45762],{"className":45761},[2059],[2061,45763,45764],{"xmlns":2063},[2065,45765,45766,45788],{},[2068,45767,45768,45770,45772,45778,45780,45786],{},[2071,45769,554],{},[2075,45771,2561],{"stretchy":2083},[2205,45773,45774,45776],{},[2071,45775,2861],{},[2071,45777,554],{},[2075,45779,2361],{"separator":2360},[2205,45781,45782,45784],{},[2071,45783,575],{},[2071,45785,554],{},[2075,45787,2576],{"stretchy":2083},[2092,45789,45658],{"encoding":2094}," se nazývá ",[95,45792,45793],{},"rovnovážný bod",[3982,45795,45796],{},"equilibrium point",[55,45798,45799,45800,835,45823,195],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[1647,45801,45803],{"className":45802},[2059],[2061,45804,45805],{"xmlns":2063},[2065,45806,45807,45821],{},[2068,45808,45809,45811,45813,45815,45817,45819],{},[2071,45810,575],{},[2075,45812,2077],{},[2071,45814,4271],{},[2075,45816,2084],{"stretchy":2083},[2071,45818,2861],{},[2075,45820,2090],{"stretchy":2083},[2092,45822,4727],{"encoding":2094},[1647,45824,45826],{"className":45825},[2059],[2061,45827,45828],{"xmlns":2063},[2065,45829,45830,45844],{},[2068,45831,45832,45834,45836,45838,45840,45842],{},[2071,45833,575],{},[2075,45835,2077],{},[2071,45837,532],{},[2075,45839,2084],{"stretchy":2083},[2071,45841,2861],{},[2075,45843,2090],{"stretchy":2083},[2092,45845,45362],{"encoding":2094},[55,45847,45848],{},[58,45849],{"alt":45850,"className":45851,"src":45852},"imek-poptavka-nabidka-rovnovaha",[62,63],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[55,45854,45855],{},[3982,45856,45857,45858,45871,45872,15746,45885,45906,45907,195],{},"Obrázek 2.13: Klesající ",[1647,45859,45861],{"className":45860},[2059],[2061,45862,45863],{"xmlns":2063},[2065,45864,45865,45869],{},[2068,45866,45867],{},[2071,45868,4271],{},[2092,45870,4271],{"encoding":2094}," a rostoucí ",[1647,45873,45875],{"className":45874},[2059],[2061,45876,45877],{"xmlns":2063},[2065,45878,45879,45883],{},[2068,45880,45881],{},[2071,45882,532],{},[2092,45884,532],{"encoding":2094},[1647,45886,45888],{"className":45887},[2059],[2061,45889,45890],{"xmlns":2063},[2065,45891,45892,45904],{},[2068,45893,45894,45896,45898,45900,45902],{},[2075,45895,2084],{"stretchy":2083},[2071,45897,2861],{},[2075,45899,2361],{"separator":2360},[2071,45901,575],{},[2075,45903,2090],{"stretchy":2083},[2092,45905,41982],{"encoding":2094}," protínající se v ",[1647,45908,45910],{"className":45909},[2059],[2061,45911,45912],{"xmlns":2063},[2065,45913,45914,45936],{},[2068,45915,45916,45918,45920,45926,45928,45934],{},[2071,45917,554],{},[2075,45919,2561],{"stretchy":2083},[2205,45921,45922,45924],{},[2071,45923,2861],{},[2071,45925,554],{},[2075,45927,2361],{"separator":2360},[2205,45929,45930,45932],{},[2071,45931,575],{},[2071,45933,554],{},[2075,45935,2576],{"stretchy":2083},[2092,45937,45658],{"encoding":2094},[609,45939,45941],{"id":45940},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[55,45943,45944,45946,45947,45981,45982,195],{},[95,45945,42224],{}," Poptávka ",[1647,45948,45950],{"className":45949},[2059],[2061,45951,45952],{"xmlns":2063},[2065,45953,45954,45978],{},[2068,45955,45956,45958,45960,45962,45968,45970,45972,45974,45976],{},[2071,45957,575],{},[2075,45959,2077],{},[2075,45961,2303],{},[2205,45963,45964,45966],{},[2071,45965,2861],{},[2210,45967,646],{},[2075,45969,2303],{},[2210,45971,2935],{},[2071,45973,2861],{},[2075,45975,2176],{},[2210,45977,8889],{},[2092,45979,45980],{"encoding":2094},"P = -Q^2 - 10Q + 150",", nabídka ",[1647,45983,45985],{"className":45984},[2059],[2061,45986,45987],{"xmlns":2063},[2065,45988,45989,46011],{},[2068,45990,45991,45993,45995,46001,46003,46005,46007,46009],{},[2071,45992,575],{},[2075,45994,2077],{},[2205,45996,45997,45999],{},[2071,45998,2861],{},[2210,46000,646],{},[2075,46002,2176],{},[2210,46004,25685],{},[2071,46006,2861],{},[2075,46008,2176],{},[2210,46010,35572],{},[2092,46012,46013],{"encoding":2094},"P = Q^2 + 14Q + 22",[55,46015,46016,46018],{},[95,46017,42256],{}," Z rovnosti",[1647,46020,46022],{"className":46021},[2059],[2061,46023,46024],{"xmlns":2063,"display":31093},[2065,46025,46026,46064],{},[2068,46027,46028,46030,46036,46038,46040,46042,46044,46046,46048,46054,46056,46058,46060,46062],{},[2075,46029,2303],{},[2205,46031,46032,46034],{},[2071,46033,2861],{},[2210,46035,646],{},[2075,46037,2303],{},[2210,46039,2935],{},[2071,46041,2861],{},[2075,46043,2176],{},[2210,46045,8889],{},[2075,46047,2077],{},[2205,46049,46050,46052],{},[2071,46051,2861],{},[2210,46053,646],{},[2075,46055,2176],{},[2210,46057,25685],{},[2071,46059,2861],{},[2075,46061,2176],{},[2210,46063,35572],{},[2092,46065,46066],{"encoding":2094},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[55,46068,46069,46070,46105,46106,46139,46140,46157,46158,46171,46172,835,46194,46231,46232,195],{},"dostaneme ",[1647,46071,46073],{"className":46072},[2059],[2061,46074,46075],{"xmlns":2063},[2065,46076,46077,46102],{},[2068,46078,46079,46081,46087,46089,46092,46094,46096,46098,46100],{},[2210,46080,646],{},[2205,46082,46083,46085],{},[2071,46084,2861],{},[2210,46086,646],{},[2075,46088,2176],{},[2210,46090,46091],{},"24",[2071,46093,2861],{},[2075,46095,2303],{},[2210,46097,5704],{},[2075,46099,2077],{},[2210,46101,630],{},[2092,46103,46104],{"encoding":2094},"2Q^2 + 24Q - 128 = 0",", resp. ",[1647,46107,46109],{"className":46108},[2059],[2061,46110,46111],{"xmlns":2063},[2065,46112,46113,46136],{},[2068,46114,46115,46121,46123,46125,46127,46129,46132,46134],{},[2205,46116,46117,46119],{},[2071,46118,2861],{},[2210,46120,646],{},[2075,46122,2176],{},[2210,46124,3583],{},[2071,46126,2861],{},[2075,46128,2303],{},[2210,46130,46131],{},"64",[2075,46133,2077],{},[2210,46135,630],{},[2092,46137,46138],{"encoding":2094},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[1647,46141,46143],{"className":46142},[2059],[2061,46144,46145],{"xmlns":2063},[2065,46146,46147,46154],{},[2068,46148,46149,46151],{},[2075,46150,2303],{},[2210,46152,46153],{},"16",[2092,46155,46156],{"encoding":2094},"-16"," (nevyhovuje) a ",[1647,46159,46161],{"className":46160},[2059],[2061,46162,46163],{"xmlns":2063},[2065,46164,46165,46169],{},[2068,46166,46167],{},[2210,46168,662],{},[2092,46170,662],{"encoding":2094},". Tedy ",[1647,46173,46175],{"className":46174},[2059],[2061,46176,46177],{"xmlns":2063},[2065,46178,46179,46191],{},[2068,46180,46181,46187,46189],{},[2205,46182,46183,46185],{},[2071,46184,2861],{},[2071,46186,554],{},[2075,46188,2077],{},[2210,46190,662],{},[2092,46192,46193],{"encoding":2094},"Q^E = 4",[1647,46195,46197],{"className":46196},[2059],[2061,46198,46199],{"xmlns":2063},[2065,46200,46201,46228],{},[2068,46202,46203,46209,46211,46213,46215,46217,46219,46221,46223,46225],{},[2205,46204,46205,46207],{},[2071,46206,575],{},[2071,46208,554],{},[2075,46210,2077],{},[2075,46212,2303],{},[2210,46214,46153],{},[2075,46216,2303],{},[2210,46218,5298],{},[2075,46220,2176],{},[2210,46222,8889],{},[2075,46224,2077],{},[2210,46226,46227],{},"94",[2092,46229,46230],{"encoding":2094},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[1647,46233,46235],{"className":46234},[2059],[2061,46236,46237],{"xmlns":2063},[2065,46238,46239,46253],{},[2068,46240,46241,46243,46245,46247,46249,46251],{},[2071,46242,554],{},[2075,46244,2561],{"stretchy":2083},[2210,46246,662],{},[2075,46248,2361],{"separator":2360},[2210,46250,46227],{},[2075,46252,2576],{"stretchy":2083},[2092,46254,46255],{"encoding":2094},"E[4, 94]",[609,46257,46259],{"id":46258},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[55,46261,46262,46264],{},[95,46263,42224],{}," Poptávky a nabídky dvou zboží",[1647,46266,46268],{"className":46267},[2059],[2061,46269,46270],{"xmlns":2063,"display":31093},[2065,46271,46272,46438],{},[23493,46273,46276,46364],{"rowspacing":23495,"columnalign":46274,"columnspacing":46275},"right left right left","0em 1em 0em",[23498,46277,46278,46288,46320,46330],{},[23501,46279,46280],{},[2400,46281,46282],{"scriptlevel":630,"displaystyle":2360},[2348,46283,46284,46286],{},[2071,46285,2861],{},[2210,46287,638],{},[23501,46289,46290],{},[2400,46291,46292],{"scriptlevel":630,"displaystyle":2360},[2068,46293,46294,46296,46298,46300,46302,46304,46310,46312,46318],{},[2068,46295],{},[2075,46297,2077],{},[2210,46299,5298],{},[2075,46301,2303],{},[2210,46303,670],{},[2348,46305,46306,46308],{},[2071,46307,575],{},[2210,46309,638],{},[2075,46311,2303],{},[2348,46313,46314,46316],{},[2071,46315,575],{},[2210,46317,646],{},[2075,46319,2361],{"separator":2360},[23501,46321,46322],{},[2400,46323,46324],{"scriptlevel":630,"displaystyle":2360},[2348,46325,46326,46328],{},[2071,46327,2861],{},[2210,46329,646],{},[23501,46331,46332],{},[2400,46333,46334],{"scriptlevel":630,"displaystyle":2360},[2068,46335,46336,46338,46340,46342,46344,46346,46352,46354,46356,46362],{},[2068,46337],{},[2075,46339,2077],{},[2210,46341,3194],{},[2075,46343,2303],{},[2210,46345,646],{},[2348,46347,46348,46350],{},[2071,46349,575],{},[2210,46351,638],{},[2075,46353,2303],{},[2210,46355,662],{},[2348,46357,46358,46360],{},[2071,46359,575],{},[2210,46361,646],{},[2075,46363,2361],{"separator":2360},[23498,46365,46366,46376,46402,46412],{},[23501,46367,46368],{},[2400,46369,46370],{"scriptlevel":630,"displaystyle":2360},[2348,46371,46372,46374],{},[2071,46373,2861],{},[2210,46375,638],{},[23501,46377,46378],{},[2400,46379,46380],{"scriptlevel":630,"displaystyle":2360},[2068,46381,46382,46384,46386,46388,46390,46392,46394,46400],{},[2068,46383],{},[2075,46385,2077],{},[2075,46387,2303],{},[2210,46389,654],{},[2075,46391,2176],{},[2210,46393,662],{},[2348,46395,46396,46398],{},[2071,46397,575],{},[2210,46399,638],{},[2075,46401,2361],{"separator":2360},[23501,46403,46404],{},[2400,46405,46406],{"scriptlevel":630,"displaystyle":2360},[2348,46407,46408,46410],{},[2071,46409,2861],{},[2210,46411,646],{},[23501,46413,46414],{},[2400,46415,46416],{"scriptlevel":630,"displaystyle":2360},[2068,46417,46418,46420,46422,46424,46426,46428,46430,46436],{},[2068,46419],{},[2075,46421,2077],{},[2075,46423,2303],{},[2210,46425,686],{},[2075,46427,2176],{},[2210,46429,654],{},[2348,46431,46432,46434],{},[2071,46433,575],{},[2210,46435,646],{},[2071,46437,195],{"mathvariant":2450},[2092,46439,46440],{"encoding":2094},"\\begin{aligned}\nQ_1 &= 40 - 5P_1 - P_2, & Q_2 &= 50 - 2P_1 - 4P_2, \\\\\nQ_1 &= -3 + 4P_1, & Q_2 &= -7 + 3P_2.\n\\end{aligned}",[55,46442,46443,46445],{},[95,46444,42256],{}," Z rovností poptávek a nabídek dostaneme",[1647,46447,46449],{"className":46448},[2059],[2061,46450,46451],{"xmlns":2063,"display":31093},[2065,46452,46453,46502],{},[2068,46454,46455,46457,46463,46465,46471,46473,46475,46477,46479,46481,46487,46489,46491,46497,46499],{},[2210,46456,4087],{},[2348,46458,46459,46461],{},[2071,46460,575],{},[2210,46462,638],{},[2075,46464,2176],{},[2348,46466,46467,46469],{},[2071,46468,575],{},[2210,46470,646],{},[2075,46472,2077],{},[2210,46474,23942],{},[2075,46476,2361],{"separator":2360},[5965,46478],{"width":5967},[2210,46480,646],{},[2348,46482,46483,46485],{},[2071,46484,575],{},[2210,46486,638],{},[2075,46488,2176],{},[2210,46490,686],{},[2348,46492,46493,46495],{},[2071,46494,575],{},[2210,46496,646],{},[2075,46498,2077],{},[2210,46500,46501],{},"57.",[2092,46503,46504],{"encoding":2094},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[55,46506,46507,46508,835,46532,46556,46557,835,46582,46606,46607,46609],{},"Řešením je ",[1647,46509,46511],{"className":46510},[2059],[2061,46512,46513],{"xmlns":2063},[2065,46514,46515,46529],{},[2068,46516,46517,46525,46527],{},[9252,46518,46519,46521,46523],{},[2071,46520,575],{},[2210,46522,638],{},[2071,46524,554],{},[2075,46526,2077],{},[2210,46528,662],{},[2092,46530,46531],{"encoding":2094},"P_1^E = 4",[1647,46533,46535],{"className":46534},[2059],[2061,46536,46537],{"xmlns":2063},[2065,46538,46539,46553],{},[2068,46540,46541,46549,46551],{},[9252,46542,46543,46545,46547],{},[2071,46544,575],{},[2210,46546,646],{},[2071,46548,554],{},[2075,46550,2077],{},[2210,46552,686],{},[2092,46554,46555],{"encoding":2094},"P_2^E = 7","; zpětným dosazením ",[1647,46558,46560],{"className":46559},[2059],[2061,46561,46562],{"xmlns":2063},[2065,46563,46564,46579],{},[2068,46565,46566,46574,46576],{},[9252,46567,46568,46570,46572],{},[2071,46569,2861],{},[2210,46571,638],{},[2071,46573,554],{},[2075,46575,2077],{},[2210,46577,46578],{},"13",[2092,46580,46581],{"encoding":2094},"Q_1^E = 13",[1647,46583,46585],{"className":46584},[2059],[2061,46586,46587],{"xmlns":2063},[2065,46588,46589,46603],{},[2068,46590,46591,46599,46601],{},[9252,46592,46593,46595,46597],{},[2071,46594,2861],{},[2210,46596,646],{},[2071,46598,554],{},[2075,46600,2077],{},[2210,46602,25685],{},[2092,46604,46605],{"encoding":2094},"Q_2^E = 14",". Zboží jsou ",[95,46608,44113],{}," (zkřížené koeficienty v poptávce jsou záporné).",[609,46611,46613],{"id":46612},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[55,46615,46616,46617,46634,46635,11156,46638,4007],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[1647,46618,46620],{"className":46619},[2059],[2061,46621,46622],{"xmlns":2063},[2065,46623,46624,46632],{},[2068,46625,46626],{},[2205,46627,46628,46630],{},[2071,46629,575],{},[2071,46631,554],{},[2092,46633,45757],{"encoding":2094},"; mechanismus popisuje ",[95,46636,46637],{},"teorém pavučiny",[3982,46639,46640],{},"cobweb model",[609,46642,46644],{"id":46643},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[55,46646,46647],{},[58,46648],{"alt":46649,"className":46650,"src":46651},"imek-komparativni-statika-4pripady",[62,63],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1023,46653,46654,46695,46735,46775],{},[55,46655,46656,46659,46660,6277,46677,195],{},[95,46657,46658],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[1647,46661,46663],{"className":46662},[2059],[2061,46664,46665],{"xmlns":2063},[2065,46666,46667,46675],{},[2068,46668,46669],{},[2205,46670,46671,46673],{},[2071,46672,575],{},[2071,46674,554],{},[2092,46676,45757],{"encoding":2094},[1647,46678,46680],{"className":46679},[2059],[2061,46681,46682],{"xmlns":2063},[2065,46683,46684,46692],{},[2068,46685,46686],{},[2205,46687,46688,46690],{},[2071,46689,2861],{},[2071,46691,554],{},[2092,46693,46694],{"encoding":2094},"Q^E",[55,46696,46697,46700,46701,6277,46718,195],{},[95,46698,46699],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[1647,46702,46704],{"className":46703},[2059],[2061,46705,46706],{"xmlns":2063},[2065,46707,46708,46716],{},[2068,46709,46710],{},[2205,46711,46712,46714],{},[2071,46713,575],{},[2071,46715,554],{},[2092,46717,45757],{"encoding":2094},[1647,46719,46721],{"className":46720},[2059],[2061,46722,46723],{"xmlns":2063},[2065,46724,46725,46733],{},[2068,46726,46727],{},[2205,46728,46729,46731],{},[2071,46730,2861],{},[2071,46732,554],{},[2092,46734,46694],{"encoding":2094},[55,46736,46737,46740,46741,9441,46758,195],{},[95,46738,46739],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[1647,46742,46744],{"className":46743},[2059],[2061,46745,46746],{"xmlns":2063},[2065,46747,46748,46756],{},[2068,46749,46750],{},[2205,46751,46752,46754],{},[2071,46753,575],{},[2071,46755,554],{},[2092,46757,45757],{"encoding":2094},[1647,46759,46761],{"className":46760},[2059],[2061,46762,46763],{"xmlns":2063},[2065,46764,46765,46773],{},[2068,46766,46767],{},[2205,46768,46769,46771],{},[2071,46770,2861],{},[2071,46772,554],{},[2092,46774,46694],{"encoding":2094},[55,46776,46777,46780,46781,46798,46799,195],{},[95,46778,46779],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[1647,46782,46784],{"className":46783},[2059],[2061,46785,46786],{"xmlns":2063},[2065,46787,46788,46796],{},[2068,46789,46790],{},[2205,46791,46792,46794],{},[2071,46793,575],{},[2071,46795,554],{},[2092,46797,45757],{"encoding":2094},", pokles ",[1647,46800,46802],{"className":46801},[2059],[2061,46803,46804],{"xmlns":2063},[2065,46805,46806,46814],{},[2068,46807,46808],{},[2205,46809,46810,46812],{},[2071,46811,2861],{},[2071,46813,554],{},[2092,46815,46694],{"encoding":2094},[323,46817,46818,46863],{},[326,46819,46820],{},[329,46821,46822,46825,46844],{},[332,46823,46824],{},"Změna",[332,46826,46827],{},[1647,46828,46830],{"className":46829},[2059],[2061,46831,46832],{"xmlns":2063},[2065,46833,46834,46842],{},[2068,46835,46836],{},[2205,46837,46838,46840],{},[2071,46839,575],{},[2071,46841,554],{},[2092,46843,45757],{"encoding":2094},[332,46845,46846],{},[1647,46847,46849],{"className":46848},[2059],[2061,46850,46851],{"xmlns":2063},[2065,46852,46853,46861],{},[2068,46854,46855],{},[2205,46856,46857,46859],{},[2071,46858,2861],{},[2071,46860,554],{},[2092,46862,46694],{"encoding":2094},[342,46864,46865,46875,46885,46894],{},[329,46866,46867,46870,46873],{},[347,46868,46869],{},"Růst poptávky",[347,46871,46872],{},"↑",[347,46874,46872],{},[329,46876,46877,46880,46883],{},[347,46878,46879],{},"Pokles poptávky",[347,46881,46882],{},"↓",[347,46884,46882],{},[329,46886,46887,46890,46892],{},[347,46888,46889],{},"Růst nabídky",[347,46891,46882],{},[347,46893,46872],{},[329,46895,46896,46899,46901],{},[347,46897,46898],{},"Pokles nabídky",[347,46900,46872],{},[347,46902,46882],{},[55,46904,46905],{},[3982,46906,46907],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[909,46909],{},[84,46911,46913],{"id":46912},"zdanění-trhu","Zdanění trhu",[1023,46915,46916,47005],{},[55,46917,46918,46920,46921,46934,46935,2999,46948,46951,46952,41069,46975,47000,47001,47004],{},[1647,46919,4243],{}," TL;DR\nJednotková daň ",[1647,46922,46924],{"className":46923},[2059],[2061,46925,46926],{"xmlns":2063},[2065,46927,46928,46932],{},[2068,46929,46930],{},[2071,46931,543],{},[2092,46933,543],{"encoding":2094}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[1647,46936,46938],{"className":46937},[2059],[2061,46939,46940],{"xmlns":2063},[2065,46941,46942,46946],{},[2068,46943,46944],{},[2071,46945,543],{},[2092,46947,543],{"encoding":2094},[95,46949,46950],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[1647,46953,46955],{"className":46954},[2059],[2061,46956,46957],{"xmlns":2063},[2065,46958,46959,46972],{},[2068,46960,46961],{},[2348,46962,46963,46965],{},[2071,46964,543],{},[2068,46966,46967,46970],{},[2071,46968,46969],{},"s",[2071,46971,55],{},[2092,46973,46974],{"encoding":2094},"T_{sp}",[1647,46976,46978],{"className":46977},[2059],[2061,46979,46980],{"xmlns":2063},[2065,46981,46982,46997],{},[2068,46983,46984],{},[2348,46985,46986,46988],{},[2071,46987,543],{},[2068,46989,46990,46993,46995],{},[2071,46991,46992],{},"v",[2071,46994,2073],{},[2071,46996,13774],{},[2092,46998,46999],{"encoding":2094},"T_{vyr}","). Klíčová vlastnost — ",[95,47002,47003],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[55,47006,47007],{},[3982,47008,47009,47010,195],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[69,47011,47015],{"className":47012,"dataFsResolvedFilePath":47013,"href":47014},[62],"topics\u002Fzdaneni-trhu.md","\u002Fwiki\u002Fzdaneni-trhu","zdaneni-trhu",[55,47017,47018,47019,47022,47023,47049,47050,47053,47054,47080,47081,47098,47099,47139,47140,75,47153,195],{},"Existují dvě formy zdanění — daň uložená ",[95,47020,47021],{},"výrobci"," (posun nabídky ",[1647,47024,47026],{"className":47025},[2059],[2061,47027,47028],{"xmlns":2063},[2065,47029,47030,47046],{},[2068,47031,47032,47038,47040,47042,47044],{},[2348,47033,47034,47036],{},[2071,47035,532],{},[2210,47037,638],{},[2075,47039,2077],{},[2071,47041,532],{},[2075,47043,2176],{},[2071,47045,543],{},[2092,47047,47048],{"encoding":2094},"S_1 = S + T"," svisle nahoru) a daň uložená ",[95,47051,47052],{},"spotřebiteli"," (posun poptávky ",[1647,47055,47057],{"className":47056},[2059],[2061,47058,47059],{"xmlns":2063},[2065,47060,47061,47077],{},[2068,47062,47063,47069,47071,47073,47075],{},[2348,47064,47065,47067],{},[2071,47066,4271],{},[2210,47068,646],{},[2075,47070,2077],{},[2071,47072,4271],{},[2075,47074,2303],{},[2071,47076,543],{},[2092,47078,47079],{"encoding":2094},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[1647,47082,47084],{"className":47083},[2059],[2061,47085,47086],{"xmlns":2063},[2065,47087,47088,47096],{},[2068,47089,47090],{},[2205,47091,47092,47094],{},[2071,47093,2861],{},[2071,47095,554],{},[2092,47097,46694],{"encoding":2094}," klesá a vzniká rozklad daně ",[1647,47100,47102],{"className":47101},[2059],[2061,47103,47104],{"xmlns":2063},[2065,47105,47106,47136],{},[2068,47107,47108,47110,47112,47122,47124],{},[2071,47109,543],{},[2075,47111,2077],{},[2348,47113,47114,47116],{},[2071,47115,543],{},[2068,47117,47118,47120],{},[2071,47119,46969],{},[2071,47121,55],{},[2075,47123,2176],{},[2348,47125,47126,47128],{},[2071,47127,543],{},[2068,47129,47130,47132,47134],{},[2071,47131,46992],{},[2071,47133,2073],{},[2071,47135,13774],{},[2092,47137,47138],{"encoding":2094},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[1647,47141,47143],{"className":47142},[2059],[2061,47144,47145],{"xmlns":2063},[2065,47146,47147,47151],{},[2068,47148,47149],{},[2071,47150,4271],{},[2092,47152,4271],{"encoding":2094},[1647,47154,47156],{"className":47155},[2059],[2061,47157,47158],{"xmlns":2063},[2065,47159,47160,47164],{},[2068,47161,47162],{},[2071,47163,532],{},[2092,47165,532],{"encoding":2094},[55,47167,47168,47169,47172,47173,75,47203,47237],{},"Zásadním výsledkem kapitoly je ",[95,47170,47171],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[1647,47174,47176],{"className":47175},[2059],[2061,47177,47178],{"xmlns":2063},[2065,47179,47180,47200],{},[2068,47181,47182,47190,47192],{},[9252,47183,47184,47186,47188],{},[2071,47185,2861],{},[2210,47187,638],{},[2071,47189,554],{},[2075,47191,2077],{},[9252,47193,47194,47196,47198],{},[2071,47195,2861],{},[2210,47197,646],{},[2071,47199,554],{},[2092,47201,47202],{"encoding":2094},"Q_1^E = Q_2^E",[1647,47204,47206],{"className":47205},[2059],[2061,47207,47208],{"xmlns":2063},[2065,47209,47210,47234],{},[2068,47211,47212,47220,47222,47224,47226],{},[9252,47213,47214,47216,47218],{},[2071,47215,575],{},[2210,47217,638],{},[2071,47219,554],{},[2075,47221,2303],{},[2071,47223,543],{},[2075,47225,2077],{},[9252,47227,47228,47230,47232],{},[2071,47229,575],{},[2210,47231,646],{},[2071,47233,554],{},[2092,47235,47236],{"encoding":2094},"P_1^E - T = P_2^E",". Otázka, \"kdo má platit daň\", je tedy z hlediska trhu formální; skutečné rozdělení určuje struktura trhu, nikoli znění zákona.",[55,47239,47240,47241,47244,47245,47271,47272,47300,47301,47304,47305,47308,47309,195],{},"Podrobný výklad, Příklady ",[95,47242,47243],{},"2.9"," (daň výrobci, ",[1647,47246,47248],{"className":47247},[2059],[2061,47249,47250],{"xmlns":2063},[2065,47251,47252,47268],{},[2068,47253,47254,47264,47266],{},[2348,47255,47256,47258],{},[2071,47257,543],{},[2068,47259,47260,47262],{},[2071,47261,46969],{},[2071,47263,55],{},[2075,47265,2077],{},[2210,47267,646],{},[2092,47269,47270],{"encoding":2094},"T_{sp} = 2"," Kč, ",[1647,47273,47275],{"className":47274},[2059],[2061,47276,47277],{"xmlns":2063},[2065,47278,47279,47297],{},[2068,47280,47281,47293,47295],{},[2348,47282,47283,47285],{},[2071,47284,543],{},[2068,47286,47287,47289,47291],{},[2071,47288,46992],{},[2071,47290,2073],{},[2071,47292,13774],{},[2075,47294,2077],{},[2210,47296,662],{},[2092,47298,47299],{"encoding":2094},"T_{vyr} = 4"," Kč) a ",[95,47302,47303],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[95,47306,47307],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[69,47310,47015],{"className":47311,"dataFsResolvedFilePath":47013,"href":47014},[62],[909,47313],{},[84,47315,47317],{"id":47316},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1023,47319,47320],{},[55,47321,47322,47324,47325,47328,47329,47331],{},[1647,47323,4243],{}," TL;DR\nMultiplikátory jsou ",[95,47326,47327],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[3982,47330,41253],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[609,47333,47335],{"id":47334},"redukovaný-tvar","Redukovaný tvar",[55,47337,47338,47339,11156,47362,835,47380,13861,47397,11156,47420,47437,47438,47468],{},"Pro lineární model ",[1647,47340,47342],{"className":47341},[2059],[2061,47343,47344],{"xmlns":2063},[2065,47345,47346,47360],{},[2068,47347,47348,47350,47352,47354,47356,47358],{},[2071,47349,575],{},[2075,47351,2077],{},[2071,47353,69],{},[2071,47355,2861],{},[2075,47357,2176],{},[2071,47359,2179],{},[2092,47361,41352],{"encoding":2094},[1647,47363,47365],{"className":47364},[2059],[2061,47366,47367],{"xmlns":2063},[2065,47368,47369,47377],{},[2068,47370,47371,47373,47375],{},[2071,47372,69],{},[2075,47374,3521],{},[2210,47376,630],{},[2092,47378,47379],{"encoding":2094},"a \u003C 0",[1647,47381,47383],{"className":47382},[2059],[2061,47384,47385],{"xmlns":2063},[2065,47386,47387,47395],{},[2068,47388,47389,47391,47393],{},[2071,47390,2179],{},[2075,47392,3482],{},[2210,47394,630],{},[2092,47396,21553],{"encoding":2094},[1647,47398,47400],{"className":47399},[2059],[2061,47401,47402],{"xmlns":2063},[2065,47403,47404,47418],{},[2068,47405,47406,47408,47410,47412,47414,47416],{},[2071,47407,575],{},[2075,47409,2077],{},[2071,47411,2222],{},[2071,47413,2861],{},[2075,47415,2176],{},[2071,47417,2273],{},[2092,47419,44533],{"encoding":2094},[1647,47421,47423],{"className":47422},[2059],[2061,47424,47425],{"xmlns":2063},[2065,47426,47427,47435],{},[2068,47428,47429,47431,47433],{},[2071,47430,2222],{},[2075,47432,3482],{},[2210,47434,630],{},[2092,47436,44551],{"encoding":2094},") dává podmínka rovnováhy ",[1647,47439,47441],{"className":47440},[2059],[2061,47442,47443],{"xmlns":2063},[2065,47444,47445,47465],{},[2068,47446,47447,47449,47451,47453,47455,47457,47459,47461,47463],{},[2071,47448,69],{},[2071,47450,2861],{},[2075,47452,2176],{},[2071,47454,2179],{},[2075,47456,2077],{},[2071,47458,2222],{},[2071,47460,2861],{},[2075,47462,2176],{},[2071,47464,2273],{},[2092,47466,47467],{"encoding":2094},"aQ + b = cQ + d",", odkud",[1647,47470,47472],{"className":47471},[2059],[2061,47473,47474],{"xmlns":2063,"display":31093},[2065,47475,47476,47521],{},[23493,47477,47478],{"width":31098},[23498,47479,47480,47482,47514,47516],{},[23501,47481],{"width":31103},[23501,47483,47484],{},[2068,47485,47486,47492,47494,47512],{},[2205,47487,47488,47490],{},[2071,47489,2861],{},[2071,47491,554],{},[2075,47493,2077],{},[2403,47495,47496,47504],{},[2068,47497,47498,47500,47502],{},[2071,47499,2179],{},[2075,47501,2303],{},[2071,47503,2273],{},[2068,47505,47506,47508,47510],{},[2071,47507,2222],{},[2075,47509,2303],{},[2071,47511,69],{},[2071,47513,195],{"mathvariant":2450},[23501,47515],{"width":31103},[23501,47517,47518],{},[2363,47519,47520],{},"(2.10)",[2092,47522,47523],{"encoding":2094},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[55,47525,47526,47527,11156,47529,47532,47533,47550,47551,1445,47554,47580,47581,47594,47595,47613,47614,4007],{},"Vztah (2.10) je ",[95,47528,23693],{},[3982,47530,47531],{},"reduced form",") pro ",[1647,47534,47536],{"className":47535},[2059],[2061,47537,47538],{"xmlns":2063},[2065,47539,47540,47548],{},[2068,47541,47542],{},[2205,47543,47544,47546],{},[2071,47545,2861],{},[2071,47547,554],{},[2092,47549,46694],{"encoding":2094},": endogenní proměnná je vyjádřena pomocí exogenních ",[95,47552,47553],{},"parametrů",[1647,47555,47557],{"className":47556},[2059],[2061,47558,47559],{"xmlns":2063},[2065,47560,47561,47577],{},[2068,47562,47563,47565,47567,47569,47571,47573,47575],{},[2071,47564,69],{},[2075,47566,2361],{"separator":2360},[2071,47568,2179],{},[2075,47570,2361],{"separator":2360},[2071,47572,2222],{},[2075,47574,2361],{"separator":2360},[2071,47576,2273],{},[2092,47578,47579],{"encoding":2094},"a, b, c, d",". Aby ",[1647,47582,47584],{"className":47583},[2059],[2061,47585,47586],{"xmlns":2063},[2065,47587,47588,47592],{},[2068,47589,47590],{},[2071,47591,554],{},[2092,47593,554],{"encoding":2094}," ležel v 1. kvadrantu, musí platit ",[1647,47596,47598],{"className":47597},[2059],[2061,47599,47600],{"xmlns":2063},[2065,47601,47602,47610],{},[2068,47603,47604,47606,47608],{},[2071,47605,2179],{},[2075,47607,3482],{},[2071,47609,2273],{},[2092,47611,47612],{"encoding":2094},"b > d"," (neboť ",[1647,47615,47617],{"className":47616},[2059],[2061,47618,47619],{"xmlns":2063},[2065,47620,47621,47633],{},[2068,47622,47623,47625,47627,47629,47631],{},[2071,47624,2222],{},[2075,47626,2303],{},[2071,47628,69],{},[2075,47630,3482],{},[2210,47632,630],{},[2092,47634,47635],{"encoding":2094},"c - a > 0",[55,47637,47638],{},[3982,47639,47640,47641,47654,47655,47668,47669,21387,47682,46231,47699,47712],{},"Obrázek 2.22: Lineární poptávka (úsek ",[1647,47642,47644],{"className":47643},[2059],[2061,47645,47646],{"xmlns":2063},[2065,47647,47648,47652],{},[2068,47649,47650],{},[2071,47651,2179],{},[2092,47653,2179],{"encoding":2094}," na ose ",[1647,47656,47658],{"className":47657},[2059],[2061,47659,47660],{"xmlns":2063},[2065,47661,47662,47666],{},[2068,47663,47664],{},[2071,47665,575],{},[2092,47667,575],{"encoding":2094},") a nabídka (úsek ",[1647,47670,47672],{"className":47671},[2059],[2061,47673,47674],{"xmlns":2063},[2065,47675,47676,47680],{},[2068,47677,47678],{},[2071,47679,2273],{},[2092,47681,2273],{"encoding":2094},[1647,47683,47685],{"className":47684},[2059],[2061,47686,47687],{"xmlns":2063},[2065,47688,47689,47697],{},[2068,47690,47691,47693,47695],{},[2071,47692,2179],{},[2075,47694,3482],{},[2071,47696,2273],{},[2092,47698,47612],{"encoding":2094},[1647,47700,47702],{"className":47701},[2059],[2061,47703,47704],{"xmlns":2063},[2065,47705,47706,47710],{},[2068,47707,47708],{},[2071,47709,554],{},[2092,47711,554],{"encoding":2094}," v 1. kvadrantu.",[609,47714,47716],{"id":47715},"definice-multiplikátorů","Definice multiplikátorů",[55,47718,47719,47720,47745,47746,47759,47760,47773],{},"V komparativní statice jsou ",[1647,47721,47723],{"className":47722},[2059],[2061,47724,47725],{"xmlns":2063},[2065,47726,47727,47743],{},[2068,47728,47729,47731,47733,47735,47737,47739,47741],{},[2071,47730,69],{},[2075,47732,2361],{"separator":2360},[2071,47734,2179],{},[2075,47736,2361],{"separator":2360},[2071,47738,2222],{},[2075,47740,2361],{"separator":2360},[2071,47742,2273],{},[2092,47744,47579],{"encoding":2094}," exogenní proměnné a ",[1647,47747,47749],{"className":47748},[2059],[2061,47750,47751],{"xmlns":2063},[2065,47752,47753,47757],{},[2068,47754,47755],{},[2071,47756,2861],{},[2092,47758,2861],{"encoding":2094}," endogenní. Přibližná změna ",[1647,47761,47763],{"className":47762},[2059],[2061,47764,47765],{"xmlns":2063},[2065,47766,47767,47771],{},[2068,47768,47769],{},[2071,47770,2861],{},[2092,47772,2861],{"encoding":2094}," se rovná totálnímu diferenciálu:",[1647,47775,47777],{"className":47776},[2059],[2061,47778,47779],{"xmlns":2063,"display":31093},[2065,47780,47781,47874],{},[23493,47782,47783],{"width":31098},[23498,47784,47785,47787,47867,47869],{},[23501,47786],{"width":31103},[23501,47788,47789],{},[2068,47790,47791,47793,47795,47797,47799,47801,47803,47811,47813,47815,47817,47819,47827,47829,47831,47833,47835,47843,47845,47847,47849,47851,47859,47861,47863,47865],{},[2071,47792,2961],{"mathvariant":2450},[2071,47794,2861],{},[2075,47796,2803],{},[2071,47798,2273],{},[2071,47800,2861],{},[2075,47802,2077],{},[9252,47804,47805,47807,47809],{},[2071,47806,2861],{},[2071,47808,69],{},[2075,47810,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,47812,3061],{},[2071,47814,2273],{},[2071,47816,69],{},[2075,47818,2176],{},[9252,47820,47821,47823,47825],{},[2071,47822,2861],{},[2071,47824,2179],{},[2075,47826,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,47828,3061],{},[2071,47830,2273],{},[2071,47832,2179],{},[2075,47834,2176],{},[9252,47836,47837,47839,47841],{},[2071,47838,2861],{},[2071,47840,2222],{},[2075,47842,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,47844,3061],{},[2071,47846,2273],{},[2071,47848,2222],{},[2075,47850,2176],{},[9252,47852,47853,47855,47857],{},[2071,47854,2861],{},[2071,47856,2273],{},[2075,47858,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,47860,3061],{},[2071,47862,2273],{},[2071,47864,2273],{},[2071,47866,195],{"mathvariant":2450},[23501,47868],{"width":31103},[23501,47870,47871],{},[2363,47872,47873],{},"(2.11)",[2092,47875,47876],{"encoding":2094},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[55,47878,47879,47880,47930,47931,11156,47933,3225],{},"Parciální derivace ",[1647,47881,47883],{"className":47882},[2059],[2061,47884,47885],{"xmlns":2063},[2065,47886,47887,47927],{},[2068,47888,47889,47897,47899,47907,47909,47917,47919],{},[9252,47890,47891,47893,47895],{},[2071,47892,2861],{},[2071,47894,69],{},[2075,47896,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,47898,2361],{"separator":2360},[9252,47900,47901,47903,47905],{},[2071,47902,2861],{},[2071,47904,2179],{},[2075,47906,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,47908,2361],{"separator":2360},[9252,47910,47911,47913,47915],{},[2071,47912,2861],{},[2071,47914,2222],{},[2075,47916,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,47918,2361],{"separator":2360},[9252,47920,47921,47923,47925],{},[2071,47922,2861],{},[2071,47924,2273],{},[2075,47926,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,47928,47929],{"encoding":2094},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[95,47932,20716],{},[3982,47934,47935],{},"multipliers",[1647,47937,47939],{"className":47938},[2059],[2061,47940,47941],{"xmlns":2063,"display":31093},[2065,47942,47943,48094],{},[23493,47944,47945],{"width":31098},[23498,47946,47947,47949,48087,48089],{},[23501,47948],{"width":31103},[23501,47950,47951],{},[2068,47952,47953,47961,47963,47989,47991,47993,48001,48003,48015,48017,48019,48027,48029,48031,48057,48059,48061,48069,48071,48073,48085],{},[9252,47954,47955,47957,47959],{},[2071,47956,2861],{},[2071,47958,69],{},[2075,47960,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,47962,2077],{},[2403,47964,47965,47973],{},[2068,47966,47967,47969,47971],{},[2071,47968,2179],{},[2075,47970,2303],{},[2071,47972,2273],{},[2068,47974,47975,47977,47979,47981,47983],{},[2075,47976,2084],{"stretchy":2083},[2071,47978,2222],{},[2075,47980,2303],{},[2071,47982,69],{},[2205,47984,47985,47987],{},[2075,47986,2090],{"stretchy":2083},[2210,47988,646],{},[2075,47990,2361],{"separator":2360},[5965,47992],{"width":17019},[9252,47994,47995,47997,47999],{},[2071,47996,2861],{},[2071,47998,2179],{},[2075,48000,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48002,2077],{},[2403,48004,48005,48007],{},[2210,48006,638],{},[2068,48008,48009,48011,48013],{},[2071,48010,2222],{},[2075,48012,2303],{},[2071,48014,69],{},[2075,48016,2361],{"separator":2360},[5965,48018],{"width":17019},[9252,48020,48021,48023,48025],{},[2071,48022,2861],{},[2071,48024,2222],{},[2075,48026,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48028,2077],{},[2075,48030,2303],{},[2403,48032,48033,48041],{},[2068,48034,48035,48037,48039],{},[2071,48036,2179],{},[2075,48038,2303],{},[2071,48040,2273],{},[2068,48042,48043,48045,48047,48049,48051],{},[2075,48044,2084],{"stretchy":2083},[2071,48046,2222],{},[2075,48048,2303],{},[2071,48050,69],{},[2205,48052,48053,48055],{},[2075,48054,2090],{"stretchy":2083},[2210,48056,646],{},[2075,48058,2361],{"separator":2360},[5965,48060],{"width":17019},[9252,48062,48063,48065,48067],{},[2071,48064,2861],{},[2071,48066,2273],{},[2075,48068,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48070,2077],{},[2075,48072,2303],{},[2403,48074,48075,48077],{},[2210,48076,638],{},[2068,48078,48079,48081,48083],{},[2071,48080,2222],{},[2075,48082,2303],{},[2071,48084,69],{},[2071,48086,195],{"mathvariant":2450},[23501,48088],{"width":31103},[23501,48090,48091],{},[2363,48092,48093],{},"(2.12)",[2092,48095,48096],{"encoding":2094},"Q'_a = \\frac{b - d}{(c - a)^2}, \\quad Q'_b = \\frac{1}{c - a}, \\quad Q'_c = -\\frac{b - d}{(c - a)^2}, \\quad Q'_d = -\\frac{1}{c - a}. \\tag{2.12}",[609,48098,48100],{"id":48099},"znaménka-a-interpretace","Znaménka a interpretace",[55,48102,48103,48104,835,48121,835,48138,835,48155,48172,48173,3225],{},"Za podmínek ",[1647,48105,48107],{"className":48106},[2059],[2061,48108,48109],{"xmlns":2063},[2065,48110,48111,48119],{},[2068,48112,48113,48115,48117],{},[2071,48114,69],{},[2075,48116,3521],{},[2210,48118,630],{},[2092,48120,47379],{"encoding":2094},[1647,48122,48124],{"className":48123},[2059],[2061,48125,48126],{"xmlns":2063},[2065,48127,48128,48136],{},[2068,48129,48130,48132,48134],{},[2071,48131,2179],{},[2075,48133,3482],{},[2210,48135,630],{},[2092,48137,21553],{"encoding":2094},[1647,48139,48141],{"className":48140},[2059],[2061,48142,48143],{"xmlns":2063},[2065,48144,48145,48153],{},[2068,48146,48147,48149,48151],{},[2071,48148,2222],{},[2075,48150,3482],{},[2210,48152,630],{},[2092,48154,44551],{"encoding":2094},[1647,48156,48158],{"className":48157},[2059],[2061,48159,48160],{"xmlns":2063},[2065,48161,48162,48170],{},[2068,48163,48164,48166,48168],{},[2071,48165,2179],{},[2075,48167,3482],{},[2071,48169,2273],{},[2092,48171,47612],{"encoding":2094}," platí (znaménka se ",[95,48174,48175],{},"nemění",[1647,48177,48179],{"className":48178},[2059],[2061,48180,48181],{"xmlns":2063,"display":31093},[2065,48182,48183,48245],{},[2068,48184,48185,48193,48195,48197,48199,48201,48209,48211,48213,48215,48217,48225,48227,48229,48231,48233,48241,48243],{},[9252,48186,48187,48189,48191],{},[2071,48188,2861],{},[2071,48190,69],{},[2075,48192,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48194,3482],{},[2210,48196,630],{},[2075,48198,2361],{"separator":2360},[5965,48200],{"width":5967},[9252,48202,48203,48205,48207],{},[2071,48204,2861],{},[2071,48206,2179],{},[2075,48208,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48210,3482],{},[2210,48212,630],{},[2075,48214,2361],{"separator":2360},[5965,48216],{"width":5967},[9252,48218,48219,48221,48223],{},[2071,48220,2861],{},[2071,48222,2222],{},[2075,48224,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48226,3521],{},[2210,48228,630],{},[2075,48230,2361],{"separator":2360},[5965,48232],{"width":5967},[9252,48234,48235,48237,48239],{},[2071,48236,2861],{},[2071,48238,2273],{},[2075,48240,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48242,3521],{},[2210,48244,14195],{},[2092,48246,48247],{"encoding":2094},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[89,48249,48250,48309],{},[92,48251,48252,1445,48255,48275,48276,48293,48294,835,48307,195],{},[95,48253,48254],{},"Kvantitativní smysl:",[1647,48256,48258],{"className":48257},[2059],[2061,48259,48260],{"xmlns":2063},[2065,48261,48262,48272],{},[2068,48263,48264],{},[9252,48265,48266,48268,48270],{},[2071,48267,2861],{},[2071,48269,2087],{},[2075,48271,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,48273,48274],{"encoding":2094},"Q'_x"," udává, o kolik přibližně vzroste ",[1647,48277,48279],{"className":48278},[2059],[2061,48280,48281],{"xmlns":2063},[2065,48282,48283,48291],{},[2068,48284,48285],{},[2205,48286,48287,48289],{},[2071,48288,2861],{},[2071,48290,554],{},[2092,48292,46694],{"encoding":2094}," při jednotkové změně parametru ",[1647,48295,48297],{"className":48296},[2059],[2061,48298,48299],{"xmlns":2063},[2065,48300,48301,48305],{},[2068,48302,48303],{},[2071,48304,2087],{},[2092,48306,2087],{"encoding":2094},[3982,48308,41253],{},[92,48310,48311,48314,48315,48332,48333,195],{},[95,48312,48313],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[1647,48316,48318],{"className":48317},[2059],[2061,48319,48320],{"xmlns":2063},[2065,48321,48322,48330],{},[2068,48323,48324],{},[2205,48325,48326,48328],{},[2071,48327,2861],{},[2071,48329,554],{},[2092,48331,46694],{"encoding":2094}," na růst ",[1647,48334,48336],{"className":48335},[2059],[2061,48337,48338],{"xmlns":2063},[2065,48339,48340,48344],{},[2068,48341,48342],{},[2071,48343,2087],{},[2092,48345,2087],{"encoding":2094},[55,48347,48348,48349,48362,48363,47613,48380,4007],{},"Např. růst ",[1647,48350,48352],{"className":48351},[2059],[2061,48353,48354],{"xmlns":2063},[2065,48355,48356,48360],{},[2068,48357,48358],{},[2071,48359,2222],{},[2092,48361,2222],{"encoding":2094}," (strmější nabídka) ⟹ pokles ",[1647,48364,48366],{"className":48365},[2059],[2061,48367,48368],{"xmlns":2063},[2065,48369,48370,48378],{},[2068,48371,48372],{},[2205,48373,48374,48376],{},[2071,48375,2861],{},[2071,48377,554],{},[2092,48379,46694],{"encoding":2094},[1647,48381,48383],{"className":48382},[2059],[2061,48384,48385],{"xmlns":2063},[2065,48386,48387,48401],{},[2068,48388,48389,48397,48399],{},[9252,48390,48391,48393,48395],{},[2071,48392,2861],{},[2071,48394,2222],{},[2075,48396,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,48398,3521],{},[2210,48400,630],{},[2092,48402,48403],{"encoding":2094},"Q'_c \u003C 0",[55,48405,48406],{},[3982,48407,48408,48409,48429,48430,48454,48455,48477,48478,195],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[1647,48410,48412],{"className":48411},[2059],[2061,48413,48414],{"xmlns":2063},[2065,48415,48416,48426],{},[2068,48417,48418,48420,48422,48424],{},[2071,48419,2222],{},[2071,48421,2861],{},[2075,48423,2176],{},[2071,48425,2273],{},[2092,48427,48428],{"encoding":2094},"cQ + d"," na strmější ",[1647,48431,48433],{"className":48432},[2059],[2061,48434,48435],{"xmlns":2063},[2065,48436,48437,48451],{},[2068,48438,48439,48445,48447,48449],{},[2348,48440,48441,48443],{},[2071,48442,2222],{},[2210,48444,638],{},[2071,48446,2861],{},[2075,48448,2176],{},[2071,48450,2273],{},[2092,48452,48453],{"encoding":2094},"c_1 Q + d"," (při ",[1647,48456,48458],{"className":48457},[2059],[2061,48459,48460],{"xmlns":2063},[2065,48461,48462,48474],{},[2068,48463,48464,48470,48472],{},[2348,48465,48466,48468],{},[2071,48467,2222],{},[2210,48469,638],{},[2075,48471,3482],{},[2071,48473,2222],{},[2092,48475,48476],{"encoding":2094},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[1647,48479,48481],{"className":48480},[2059],[2061,48482,48483],{"xmlns":2063},[2065,48484,48485,48495],{},[2068,48486,48487,48493],{},[2205,48488,48489,48491],{},[2071,48490,2861],{},[2071,48492,554],{},[2075,48494,46882],{},[2092,48496,48497],{"encoding":2094},"Q^E \\downarrow",[55,48499,48500,48501,48533,48534,195],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[1647,48502,48504],{"className":48503},[2059],[2061,48505,48506],{"xmlns":2063},[2065,48507,48508,48530],{},[2068,48509,48510,48512,48514,48516,48524,48526,48528],{},[2071,48511,2961],{"mathvariant":2450},[2071,48513,2861],{},[2075,48515,2803],{},[9252,48517,48518,48520,48522],{},[2071,48519,2861],{},[2071,48521,2179],{},[2075,48523,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,48525,3061],{},[2071,48527,2273],{},[2071,48529,2179],{},[2092,48531,48532],{"encoding":2094},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[1647,48535,48537],{"className":48536},[2059],[2061,48538,48539],{"xmlns":2063},[2065,48540,48541,48549],{},[2068,48542,48543],{},[2205,48544,48545,48547],{},[2071,48546,575],{},[2071,48548,554],{},[2092,48550,45757],{"encoding":2094},[609,48552,48554,48555],{"id":48553},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[1647,48556,48558],{"className":48557},[2059],[2061,48559,48560],{"xmlns":2063},[2065,48561,48562,48570],{},[2068,48563,48564],{},[2205,48565,48566,48568],{},[2071,48567,2861],{},[2071,48569,554],{},[2092,48571,46694],{"encoding":2094},[55,48573,48574,45946,48576,45981,48602,195],{},[95,48575,42224],{},[1647,48577,48579],{"className":48578},[2059],[2061,48580,48581],{"xmlns":2063},[2065,48582,48583,48599],{},[2068,48584,48585,48587,48589,48591,48593,48595,48597],{},[2071,48586,575],{},[2075,48588,2077],{},[2075,48590,2303],{},[2210,48592,654],{},[2071,48594,2861],{},[2075,48596,2176],{},[2210,48598,5298],{},[2092,48600,48601],{"encoding":2094},"P = -3Q + 40",[1647,48603,48605],{"className":48604},[2059],[2061,48606,48607],{"xmlns":2063},[2065,48608,48609,48623],{},[2068,48610,48611,48613,48615,48617,48619,48621],{},[2071,48612,575],{},[2075,48614,2077],{},[2210,48616,5096],{},[2071,48618,2861],{},[2075,48620,2176],{},[2210,48622,2935],{},[2092,48624,48625],{"encoding":2094},"P = 0{,}5Q + 10",[55,48627,48628,48630],{},[95,48629,42256],{}," Rovnovážné množství",[1647,48632,48634],{"className":48633},[2059],[2061,48635,48636],{"xmlns":2063,"display":31093},[2065,48637,48638,48706],{},[2068,48639,48640,48646,48648,48666,48668,48692,48694,48701,48703],{},[2205,48641,48642,48644],{},[2071,48643,2861],{},[2071,48645,554],{},[2075,48647,2077],{},[2403,48649,48650,48658],{},[2068,48651,48652,48654,48656],{},[2071,48653,2179],{},[2075,48655,2303],{},[2071,48657,2273],{},[2068,48659,48660,48662,48664],{},[2071,48661,2222],{},[2075,48663,2303],{},[2071,48665,69],{},[2075,48667,2077],{},[2403,48669,48670,48678],{},[2068,48671,48672,48674,48676],{},[2210,48673,5298],{},[2075,48675,2303],{},[2210,48677,2935],{},[2068,48679,48680,48682,48684,48686,48688,48690],{},[2210,48681,5096],{},[2075,48683,2303],{},[2075,48685,2084],{"stretchy":2083},[2075,48687,2303],{},[2210,48689,654],{},[2075,48691,2090],{"stretchy":2083},[2075,48693,2077],{},[2403,48695,48696,48698],{},[2210,48697,42310],{},[2210,48699,48700],{},"3,5",[2075,48702,2803],{},[2210,48704,48705],{},"8,571.",[2092,48707,48708],{"encoding":2094},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[55,48710,48711,48756],{},[95,48712,48713,48714,2744,48727,2758,48741,48755],{},"(a) Změna ",[1647,48715,48717],{"className":48716},[2059],[2061,48718,48719],{"xmlns":2063},[2065,48720,48721,48725],{},[2068,48722,48723],{},[2071,48724,2222],{},[2092,48726,2222],{"encoding":2094},[1647,48728,48730],{"className":48729},[2059],[2061,48731,48732],{"xmlns":2063},[2065,48733,48734,48738],{},[2068,48735,48736],{},[2210,48737,5096],{},[2092,48739,48740],{"encoding":2094},"0{,}5",[1647,48742,48744],{"className":48743},[2059],[2061,48745,48746],{"xmlns":2063},[2065,48747,48748,48752],{},[2068,48749,48750],{},[2210,48751,22060],{},[2092,48753,48754],{"encoding":2094},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[1647,48758,48760],{"className":48759},[2059],[2061,48761,48762],{"xmlns":2063,"display":31093},[2065,48763,48764,48841],{},[2068,48765,48766,48774,48776,48778,48780,48782,48784,48810,48812,48814,48816,48818,48820,48830,48832,48834,48836,48838],{},[9252,48767,48768,48770,48772],{},[2071,48769,2861],{},[2071,48771,2222],{},[2075,48773,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,48775,3061],{},[2071,48777,2273],{},[2071,48779,2222],{},[2075,48781,2077],{},[2075,48783,2303],{},[2403,48785,48786,48794],{},[2068,48787,48788,48790,48792],{},[2071,48789,2179],{},[2075,48791,2303],{},[2071,48793,2273],{},[2068,48795,48796,48798,48800,48802,48804],{},[2075,48797,2084],{"stretchy":2083},[2071,48799,2222],{},[2075,48801,2303],{},[2071,48803,69],{},[2205,48805,48806,48808],{},[2075,48807,2090],{"stretchy":2083},[2210,48809,646],{},[2363,48811,3061],{},[2071,48813,2273],{},[2071,48815,2222],{},[2075,48817,2077],{},[2075,48819,2303],{},[2403,48821,48822,48824],{},[2210,48823,42310],{},[2205,48825,48826,48828],{},[2210,48827,48700],{},[2210,48829,646],{},[2075,48831,3251],{},[2210,48833,2866],{},[2075,48835,2803],{},[2075,48837,2303],{},[2210,48839,48840],{},"0,245.",[2092,48842,48843],{"encoding":2094},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[55,48845,48846,48847,195],{},"Nové rovnovážné množství ",[1647,48848,48850],{"className":48849},[2059],[2061,48851,48852],{"xmlns":2063},[2065,48853,48854,48879],{},[2068,48855,48856,48864,48866,48869,48871,48874,48876],{},[9252,48857,48858,48860,48862],{},[2071,48859,2861],{},[2210,48861,638],{},[2071,48863,554],{},[2075,48865,2803],{},[2210,48867,48868],{},"8,571",[2075,48870,2303],{},[2210,48872,48873],{},"0,245",[2075,48875,2077],{},[2210,48877,48878],{},"8,326",[2092,48880,48881],{"encoding":2094},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[55,48883,48884,48969],{},[95,48885,48886,48887,835,48907,835,48929,835,48949,195],{},"(b) Současné změny ",[1647,48888,48890],{"className":48889},[2059],[2061,48891,48892],{"xmlns":2063},[2065,48893,48894,48904],{},[2068,48895,48896,48898,48900,48902],{},[2071,48897,2273],{},[2071,48899,69],{},[2075,48901,2077],{},[2210,48903,5096],{},[2092,48905,48906],{"encoding":2094},"da = 0{,}5",[1647,48908,48910],{"className":48909},[2059],[2061,48911,48912],{"xmlns":2063},[2065,48913,48914,48926],{},[2068,48915,48916,48918,48920,48922,48924],{},[2071,48917,2273],{},[2071,48919,2179],{},[2075,48921,2077],{},[2075,48923,2303],{},[2210,48925,670],{},[2092,48927,48928],{"encoding":2094},"db = -5",[1647,48930,48932],{"className":48931},[2059],[2061,48933,48934],{"xmlns":2063},[2065,48935,48936,48946],{},[2068,48937,48938,48940,48942,48944],{},[2071,48939,2273],{},[2071,48941,2222],{},[2075,48943,2077],{},[2210,48945,2866],{},[2092,48947,48948],{"encoding":2094},"dc = 0{,}1",[1647,48950,48952],{"className":48951},[2059],[2061,48953,48954],{"xmlns":2063},[2065,48955,48956,48966],{},[2068,48957,48958,48960,48962,48964],{},[2071,48959,2273],{},[2071,48961,2273],{},[2075,48963,2077],{},[2210,48965,638],{},[2092,48967,48968],{"encoding":2094},"dd = 1"," Dosazením do (2.11):",[1647,48971,48973],{"className":48972},[2059],[2061,48974,48975],{"xmlns":2063,"display":31093},[2065,48976,48977,49120],{},[23493,48978,48979,49061,49097],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,48980,48981,48991],{},[23501,48982,48983],{},[2400,48984,48985],{"scriptlevel":630,"displaystyle":2360},[2068,48986,48987,48989],{},[2071,48988,2961],{"mathvariant":2450},[2071,48990,2861],{},[23501,48992,48993],{},[2400,48994,48995],{"scriptlevel":630,"displaystyle":2360},[2068,48996,48997,48999,49001,49011,49013,49015,49017,49023,49025,49027,49029,49031,49033,49035,49045,49047,49049,49051,49057,49059],{},[2068,48998],{},[2075,49000,2803],{},[2403,49002,49003,49005],{},[2210,49004,42310],{},[2205,49006,49007,49009],{},[2210,49008,48700],{},[2210,49010,646],{},[2075,49012,3251],{},[2210,49014,5096],{},[2075,49016,2176],{},[2403,49018,49019,49021],{},[2210,49020,638],{},[2210,49022,48700],{},[2075,49024,3251],{},[2075,49026,2084],{"stretchy":2083},[2075,49028,2303],{},[2210,49030,670],{},[2075,49032,2090],{"stretchy":2083},[2075,49034,2303],{},[2403,49036,49037,49039],{},[2210,49038,42310],{},[2205,49040,49041,49043],{},[2210,49042,48700],{},[2210,49044,646],{},[2075,49046,3251],{},[2210,49048,2866],{},[2075,49050,2303],{},[2403,49052,49053,49055],{},[2210,49054,638],{},[2210,49056,48700],{},[2075,49058,3251],{},[2210,49060,638],{},[23498,49062,49063,49069],{},[23501,49064,49065],{},[2400,49066,49067],{"scriptlevel":630,"displaystyle":2360},[2068,49068],{},[23501,49070,49071],{},[2400,49072,49073],{"scriptlevel":630,"displaystyle":2360},[2068,49074,49075,49077,49079,49082,49084,49087,49089,49092,49094],{},[2068,49076],{},[2075,49078,2077],{},[2210,49080,49081],{},"1,2245",[2075,49083,2303],{},[2210,49085,49086],{},"1,4286",[2075,49088,2303],{},[2210,49090,49091],{},"0,2449",[2075,49093,2303],{},[2210,49095,49096],{},"0,2857",[23498,49098,49099,49105],{},[23501,49100,49101],{},[2400,49102,49103],{"scriptlevel":630,"displaystyle":2360},[2068,49104],{},[23501,49106,49107],{},[2400,49108,49109],{"scriptlevel":630,"displaystyle":2360},[2068,49110,49111,49113,49115,49117],{},[2068,49112],{},[2075,49114,2803],{},[2075,49116,2303],{},[2210,49118,49119],{},"0,735.",[2092,49121,49122],{"encoding":2094},"\\begin{aligned}\n\\Delta Q &\\approx \\frac{30}{3{,}5^2}\\cdot 0{,}5 + \\frac{1}{3{,}5}\\cdot(-5) - \\frac{30}{3{,}5^2}\\cdot 0{,}1 - \\frac{1}{3{,}5}\\cdot 1 \\\\\n&= 1{,}2245 - 1{,}4286 - 0{,}2449 - 0{,}2857 \\\\\n&\\approx -0{,}735.\n\\end{aligned}",[55,49124,33092,49125,195],{},[1647,49126,49128],{"className":49127},[2059],[2061,49129,49130],{"xmlns":2063},[2065,49131,49132,49156],{},[2068,49133,49134,49142,49144,49146,49148,49151,49153],{},[9252,49135,49136,49138,49140],{},[2071,49137,2861],{},[2210,49139,638],{},[2071,49141,554],{},[2075,49143,2803],{},[2210,49145,48868],{},[2075,49147,2303],{},[2210,49149,49150],{},"0,735",[2075,49152,2077],{},[2210,49154,49155],{},"7,836",[2092,49157,49158],{"encoding":2094},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1023,49160,49161],{},[55,49162,49163,49165,49166,49189,49190,49212],{},[1647,49164,4499],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[1647,49167,49169],{"className":49168},[2059],[2061,49170,49171],{"xmlns":2063},[2065,49172,49173,49186],{},[2068,49174,49175,49177,49179,49181,49183],{},[2071,49176,2961],{"mathvariant":2450},[2071,49178,2861],{},[2075,49180,2803],{},[2075,49182,2303],{},[2210,49184,49185],{},"2,69",[2092,49187,49188],{"encoding":2094},"\\Delta Q \\approx -2{,}69",", ta však neodpovídá přepočtu parciálních derivací podle (2.11) a (2.12). Správná hodnota při uvedených změnách je ",[1647,49191,49193],{"className":49192},[2059],[2061,49194,49195],{"xmlns":2063},[2065,49196,49197,49209],{},[2068,49198,49199,49201,49203,49205,49207],{},[2071,49200,2961],{"mathvariant":2450},[2071,49202,2861],{},[2075,49204,2803],{},[2075,49206,2303],{},[2210,49208,49150],{},[2092,49210,49211],{"encoding":2094},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[55,49214,49215],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[909,49217],{},[84,49219,13513],{"id":13512},[1023,49221,49222],{},[55,49223,49224,3960,49226,11156,49229,13861,49245,11156,49248,49264,49265,195],{},[1647,49225,4243],{},[95,49227,49228],{},"Přebytek spotřebitele",[1647,49230,49232],{"className":49231},[2059],[2061,49233,49234],{"xmlns":2063},[2065,49235,49236,49242],{},[2068,49237,49238,49240],{},[2071,49239,2849],{},[2071,49241,532],{},[2092,49243,49244],{"encoding":2094},"CS",[95,49246,49247],{},"přebytek výrobce",[1647,49249,49251],{"className":49250},[2059],[2061,49252,49253],{"xmlns":2063},[2065,49254,49255,49261],{},[2068,49256,49257,49259],{},[2071,49258,575],{},[2071,49260,532],{},[2092,49262,49263],{"encoding":2094},"PS",") jsou míry čistého prospěchu stran trhu, definované pomocí určitého integrálu a geometricky odpovídající plochám mezi rovnovážnou cenou a příslušnou křivkou. Podrobný výklad je na samostatné stránce ",[69,49266,49270],{"className":49267,"dataFsResolvedFilePath":49268,"href":49269},[62],"topics\u002Fprebytek-spotrebitele-vyrobce.md","\u002Fwiki\u002Fprebytek-spotrebitele-vyrobce","prebytek-spotrebitele-vyrobce",[55,49272,49273],{},[58,49274],{"alt":49275,"className":49276,"src":49277},"imek-prebytky-cs-ps",[62,63],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[55,49279,49280,11156,49282,49285],{},[95,49281,49228],{},[3982,49283,49284],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[1647,49287,49289],{"className":49288},[2059],[2061,49290,49291],{"xmlns":2063,"display":31093},[2065,49292,49293,49370],{},[23493,49294,49295],{"width":31098},[23498,49296,49297,49299,49363,49365],{},[23501,49298],{"width":31103},[23501,49300,49301],{},[2068,49302,49303,49305,49307,49309,49315,49317,49319,49331,49333,49335,49337,49339,49341,49343,49345,49347,49353,49355,49361],{},[2071,49304,2849],{},[2071,49306,532],{},[2075,49308,2084],{"stretchy":2083},[2348,49310,49311,49313],{},[2071,49312,2861],{},[2210,49314,630],{},[2075,49316,2090],{"stretchy":2083},[2075,49318,2077],{},[9252,49320,49321,49323,49325],{},[2075,49322,12897],{},[2210,49324,630],{},[2348,49326,49327,49329],{},[2071,49328,2861],{},[2210,49330,630],{},[2071,49332,4271],{},[2075,49334,2084],{"stretchy":2083},[2071,49336,2861],{},[2075,49338,2090],{"stretchy":2083},[2363,49340,3061],{},[2071,49342,2273],{},[2071,49344,2861],{},[2075,49346,2303],{},[2348,49348,49349,49351],{},[2071,49350,575],{},[2210,49352,630],{},[2363,49354,3061],{},[2348,49356,49357,49359],{},[2071,49358,2861],{},[2210,49360,630],{},[2071,49362,195],{"mathvariant":2450},[23501,49364],{"width":31103},[23501,49366,49367],{},[2363,49368,49369],{},"(2.14)",[2092,49371,49372],{"encoding":2094},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[55,49374,49375,11156,49378,49381],{},[95,49376,49377],{},"Přebytek výrobce",[3982,49379,49380],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[1647,49383,49385],{"className":49384},[2059],[2061,49386,49387],{"xmlns":2063,"display":31093},[2065,49388,49389,49466],{},[23493,49390,49391],{"width":31098},[23498,49392,49393,49395,49459,49461],{},[23501,49394],{"width":31103},[23501,49396,49397],{},[2068,49398,49399,49401,49403,49405,49411,49413,49415,49421,49423,49429,49431,49443,49445,49447,49449,49451,49453,49455,49457],{},[2071,49400,575],{},[2071,49402,532],{},[2075,49404,2084],{"stretchy":2083},[2348,49406,49407,49409],{},[2071,49408,2861],{},[2210,49410,630],{},[2075,49412,2090],{"stretchy":2083},[2075,49414,2077],{},[2348,49416,49417,49419],{},[2071,49418,575],{},[2210,49420,630],{},[2363,49422,3061],{},[2348,49424,49425,49427],{},[2071,49426,2861],{},[2210,49428,630],{},[2075,49430,2303],{},[9252,49432,49433,49435,49437],{},[2075,49434,12897],{},[2210,49436,630],{},[2348,49438,49439,49441],{},[2071,49440,2861],{},[2210,49442,630],{},[2071,49444,532],{},[2075,49446,2084],{"stretchy":2083},[2071,49448,2861],{},[2075,49450,2090],{"stretchy":2083},[2363,49452,3061],{},[2071,49454,2273],{},[2071,49456,2861],{},[2071,49458,195],{"mathvariant":2450},[23501,49460],{"width":31103},[23501,49462,49463],{},[2363,49464,49465],{},"(2.15)",[2092,49467,49468],{"encoding":2094},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[55,49470,49471,49472,195],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[69,49473,49475],{"className":49474,"dataFsResolvedFilePath":3888,"href":3889},[62],"určitého integrálu",[909,49477],{},[84,49479,49481],{"id":49480},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[89,49483,49484,49515,49520,49526,49554,49560,49589,49595,49675,49701],{},[92,49485,49486,49488,49489,49514],{},[95,49487,42219],{}," — lineární poptávka ",[1647,49490,49492],{"className":49491},[2059],[2061,49493,49494],{"xmlns":2063},[2065,49495,49496,49512],{},[2068,49497,49498,49500,49502,49504,49506,49508,49510],{},[2071,49499,575],{},[2075,49501,2077],{},[2075,49503,2303],{},[2210,49505,646],{},[2071,49507,2861],{},[2075,49509,2176],{},[2210,49511,3200],{},[2092,49513,42251],{"encoding":2094},", alternativní tvar, cenové rozpětí.",[92,49516,49517,49519],{},[95,49518,42533],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[92,49521,49522,49525],{},[95,49523,49524],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[92,49527,49528,49530,49531,195],{},[95,49529,45080],{}," — lineární nabídka ",[1647,49532,49534],{"className":49533},[2059],[2061,49535,49536],{"xmlns":2063},[2065,49537,49538,49552],{},[2068,49539,49540,49542,49544,49546,49548,49550],{},[2071,49541,575],{},[2075,49543,2077],{},[2210,49545,5096],{},[2071,49547,2861],{},[2075,49549,2176],{},[2210,49551,5091],{},[2092,49553,45109],{"encoding":2094},[92,49555,49556,49559],{},[95,49557,49558],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[92,49561,49562,49565,49566,195],{},[95,49563,49564],{},"Příklad 2.7"," — kvadratická rovnováha, ",[1647,49567,49569],{"className":49568},[2059],[2061,49570,49571],{"xmlns":2063},[2065,49572,49573,49587],{},[2068,49574,49575,49577,49579,49581,49583,49585],{},[2071,49576,554],{},[2075,49578,2561],{"stretchy":2083},[2210,49580,662],{},[2075,49582,2361],{"separator":2360},[2210,49584,46227],{},[2075,49586,2576],{"stretchy":2083},[2092,49588,46255],{"encoding":2094},[92,49590,49591,49594],{},[95,49592,49593],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[92,49596,49597,49600,49601,49618,49619,835,49644,49671,49672,3025],{},[95,49598,49599],{},"Příklad 2.9"," — daň ",[1647,49602,49604],{"className":49603},[2059],[2061,49605,49606],{"xmlns":2063},[2065,49607,49608,49616],{},[2068,49609,49610,49612,49614],{},[2071,49611,543],{},[2075,49613,2077],{},[2210,49615,678],{},[2092,49617,45559],{"encoding":2094}," na výrobce; rozklad ",[1647,49620,49622],{"className":49621},[2059],[2061,49623,49624],{"xmlns":2063},[2065,49625,49626,49642],{},[2068,49627,49628,49638,49640],{},[2348,49629,49630,49632],{},[2071,49631,543],{},[2068,49633,49634,49636],{},[2071,49635,46969],{},[2071,49637,55],{},[2075,49639,2077],{},[2210,49641,646],{},[2092,49643,47270],{"encoding":2094},[1647,49645,49647],{"className":49646},[2059],[2061,49648,49649],{"xmlns":2063},[2065,49650,49651,49669],{},[2068,49652,49653,49665,49667],{},[2348,49654,49655,49657],{},[2071,49656,543],{},[2068,49658,49659,49661,49663],{},[2071,49660,46992],{},[2071,49662,2073],{},[2071,49664,13774],{},[2075,49666,2077],{},[2210,49668,662],{},[2092,49670,47299],{"encoding":2094},". (Viz ",[69,49673,47015],{"className":49674,"dataFsResolvedFilePath":47013,"href":47014},[62],[92,49676,49677,49600,49680,49697,49698,3025],{},[95,49678,49679],{},"Příklad 2.10",[1647,49681,49683],{"className":49682},[2059],[2061,49684,49685],{"xmlns":2063},[2065,49686,49687,49695],{},[2068,49688,49689,49691,49693],{},[2071,49690,543],{},[2075,49692,2077],{},[2210,49694,678],{},[2092,49696,45559],{"encoding":2094}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[69,49699,47015],{"className":49700,"dataFsResolvedFilePath":47013,"href":47014},[62],[92,49702,49703,49706],{},[95,49704,49705],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[909,49708],{},[84,49710,49712],{"id":49711},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[609,49714,49716],{"id":49715},"základní-analýza-poptávky","Základní analýza poptávky",[55,49718,49719,49722,49723,49758,49759,49785],{},[95,49720,49721],{},"2.1"," Je dána poptávka ",[1647,49724,49726],{"className":49725},[2059],[2061,49727,49728],{"xmlns":2063},[2065,49729,49730,49755],{},[2068,49731,49732,49734,49736,49738,49740,49742,49744,49746,49749,49751,49753],{},[2071,49733,2861],{},[2075,49735,2077],{},[2071,49737,4271],{},[2075,49739,2084],{"stretchy":2083},[2071,49741,575],{},[2075,49743,2090],{"stretchy":2083},[2075,49745,2077],{},[2210,49747,49748],{},"75",[2075,49750,2303],{},[2210,49752,670],{},[2071,49754,575],{},[2092,49756,49757],{"encoding":2094},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[1647,49760,49762],{"className":49761},[2059],[2061,49763,49764],{"xmlns":2063},[2065,49765,49766,49782],{},[2068,49767,49768,49770,49772,49774,49776,49778,49780],{},[2210,49769,630],{},[2075,49771,2361],{"separator":2360},[2210,49773,670],{},[2075,49775,2361],{"separator":2360},[2210,49777,2935],{},[2075,49779,2361],{"separator":2360},[2210,49781,39270],{},[2092,49783,49784],{"encoding":2094},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[55,49787,49788,49791,49792,49810,49811,3225],{},[95,49789,49790],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[1647,49793,49795],{"className":49794},[2059],[2061,49796,49797],{"xmlns":2063},[2065,49798,49799,49807],{},[2068,49800,49801,49803,49805],{},[2071,49802,575],{},[2075,49804,2361],{"separator":2360},[2071,49806,2861],{},[2092,49808,49809],{"encoding":2094},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[1647,49812,49814],{"className":49813},[2059],[2061,49815,49816],{"xmlns":2063},[2065,49817,49818,49834],{},[2068,49819,49820,49822,49824,49826,49828,49830,49832],{},[2071,49821,69],{},[2075,49823,2361],{"separator":2360},[2071,49825,2179],{},[2075,49827,2361],{"separator":2360},[2071,49829,2222],{},[2075,49831,3482],{},[2210,49833,630],{},[2092,49835,49836],{"encoding":2094},"a, b, c > 0",[89,49838,49839,49872,49903,49938,49969,50004],{},[92,49840,49841,49842],{},"(a) ",[1647,49843,49845],{"className":49844},[2059],[2061,49846,49847],{"xmlns":2063},[2065,49848,49849,49869],{},[2068,49850,49851,49853,49855],{},[2071,49852,2861],{},[2075,49854,2077],{},[2400,49856,49857],{"scriptlevel":630,"displaystyle":2360},[2403,49858,49859,49861],{},[2071,49860,69],{},[2068,49862,49863,49865,49867],{},[2071,49864,575],{},[2075,49866,2176],{},[2071,49868,2222],{},[2092,49870,49871],{"encoding":2094},"Q = \\dfrac{a}{P + c}",[92,49873,49874,49875],{},"(b) ",[1647,49876,49878],{"className":49877},[2059],[2061,49879,49880],{"xmlns":2063},[2065,49881,49882,49900],{},[2068,49883,49884,49886,49888],{},[2071,49885,2861],{},[2075,49887,2077],{},[8204,49889,49890],{},[2068,49891,49892,49894,49896,49898],{},[2071,49893,69],{},[2075,49895,2303],{},[2071,49897,2179],{},[2071,49899,2861],{},[2092,49901,49902],{"encoding":2094},"Q = \\sqrt{a - bQ}",[92,49904,49905,49906],{},"(c) ",[1647,49907,49909],{"className":49908},[2059],[2061,49910,49911],{"xmlns":2063},[2065,49912,49913,49935],{},[2068,49914,49915,49917,49919],{},[2071,49916,2861],{},[2075,49918,2077],{},[2400,49920,49921],{"scriptlevel":630,"displaystyle":2360},[2403,49922,49923,49933],{},[2068,49924,49925,49927,49929],{},[2071,49926,69],{},[2075,49928,2303],{},[8204,49930,49931],{},[2071,49932,575],{},[2071,49934,2179],{},[2092,49936,49937],{"encoding":2094},"Q = \\dfrac{a - \\sqrt{P}}{b}",[92,49939,49940,49941],{},"(d) ",[1647,49942,49944],{"className":49943},[2059],[2061,49945,49946],{"xmlns":2063},[2065,49947,49948,49966],{},[2068,49949,49950,49952,49954,49956,49958,49960],{},[2071,49951,575],{},[2075,49953,2077],{},[2071,49955,69],{},[2075,49957,2303],{},[2071,49959,2179],{},[2205,49961,49962,49964],{},[2071,49963,2861],{},[2210,49965,646],{},[2092,49967,49968],{"encoding":2094},"P = a - bQ^2",[92,49970,49971,49972],{},"(e) ",[1647,49973,49975],{"className":49974},[2059],[2061,49976,49977],{"xmlns":2063},[2065,49978,49979,50001],{},[2068,49980,49981,49983,49985,49987,49997,49999],{},[2071,49982,2861],{},[2075,49984,2077],{},[2071,49986,2179],{},[2205,49988,49989,49991],{},[2071,49990,575],{},[2068,49992,49993,49995],{},[2075,49994,2303],{},[2071,49996,69],{},[2075,49998,2176],{},[2071,50000,2222],{},[2092,50002,50003],{"encoding":2094},"Q = bP^{-a} + c",[92,50005,50006,50007],{},"(f) ",[1647,50008,50010],{"className":50009},[2059],[2061,50011,50012],{"xmlns":2063},[2065,50013,50014,50037],{},[2068,50015,50016,50018,50020,50022,50024],{},[2071,50017,2861],{},[2075,50019,2077],{},[2071,50021,69],{},[2075,50023,3251],{},[2205,50025,50026,50029],{},[2071,50027,50028],{},"e",[2068,50030,50031,50033,50035],{},[2075,50032,2303],{},[2071,50034,2179],{},[2071,50036,575],{},[2092,50038,50039],{"encoding":2094},"Q = a \\cdot e^{-bP}",[55,50041,50042,50045],{},[95,50043,50044],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[89,50047,50048,50051,50054],{},[92,50049,50050],{},"(a) Cena substitutu.",[92,50052,50053],{},"(b) Cena komplementu.",[92,50055,50056],{},"(c) Výdaje na reklamu.",[55,50058,50059,49722,50061,50095,50096,50124],{},[95,50060,27380],{},[1647,50062,50064],{"className":50063},[2059],[2061,50065,50066],{"xmlns":2063},[2065,50067,50068,50092],{},[2068,50069,50070,50072,50074,50076,50078,50080,50082,50084,50086,50088,50090],{},[2071,50071,575],{},[2075,50073,2077],{},[2071,50075,4271],{},[2075,50077,2084],{"stretchy":2083},[2071,50079,2861],{},[2075,50081,2090],{"stretchy":2083},[2075,50083,2077],{},[2210,50085,3583],{},[2075,50087,2303],{},[2210,50089,646],{},[2071,50091,2861],{},[2092,50093,50094],{"encoding":2094},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[1647,50097,50099],{"className":50098},[2059],[2061,50100,50101],{"xmlns":2063},[2065,50102,50103,50121],{},[2068,50104,50105,50107,50109,50115,50117,50119],{},[2071,50106,575],{},[2075,50108,2077],{},[2205,50110,50111,50113],{},[2071,50112,4271],{},[2075,50114,4441],{},[2075,50116,2084],{"stretchy":2083},[2071,50118,2861],{},[2075,50120,2090],{"stretchy":2083},[2092,50122,50123],{"encoding":2094},"P = D^*(Q)",", na kterou se změní původní poptávka v důsledku uložení daně 6 Kč na kupujícího na každou jednotku zboží. Graficky interpretujte.",[55,50126,50127,50130],{},[95,50128,50129],{},"2.5"," Pro zadané dvojice funkcí rozhodněte, zda vyjadřují funkce poptávky ve dvoukomoditním trhu dvou závislých zboží. V kladném případě určete, zda jde o substituty, resp. komplementy a specifikujte zadané proměnné:",[89,50132,50133,50217,50293,50379,50467],{},[92,50134,49841,50135,835,50175,195],{},[1647,50136,50138],{"className":50137},[2059],[2061,50139,50140],{"xmlns":2063},[2065,50141,50142,50172],{},[2068,50143,50144,50150,50152,50154,50156,50158,50164,50166],{},[2348,50145,50146,50148],{},[2071,50147,25992],{},[2210,50149,638],{},[2075,50151,2077],{},[2210,50153,9121],{},[2075,50155,2303],{},[2210,50157,662],{},[2348,50159,50160,50162],{},[2071,50161,4342],{},[2210,50163,638],{},[2075,50165,2176],{},[2348,50167,50168,50170],{},[2071,50169,4342],{},[2210,50171,646],{},[2092,50173,50174],{"encoding":2094},"B_1 = 20 - 4A_1 + A_2",[1647,50176,50178],{"className":50177},[2059],[2061,50179,50180],{"xmlns":2063},[2065,50181,50182,50214],{},[2068,50183,50184,50190,50192,50194,50196,50198,50204,50206,50208],{},[2348,50185,50186,50188],{},[2071,50187,25992],{},[2210,50189,646],{},[2075,50191,2077],{},[2210,50193,2935],{},[2075,50195,2176],{},[2210,50197,646],{},[2348,50199,50200,50202],{},[2071,50201,4342],{},[2210,50203,638],{},[2075,50205,2303],{},[2210,50207,662],{},[2348,50209,50210,50212],{},[2071,50211,4342],{},[2210,50213,646],{},[2092,50215,50216],{"encoding":2094},"B_2 = 10 + 2A_1 - 4A_2",[92,50218,49874,50219,835,50261,195],{},[1647,50220,50222],{"className":50221},[2059],[2061,50223,50224],{"xmlns":2063},[2065,50225,50226,50258],{},[2068,50227,50228,50234,50236,50238,50240,50242,50248,50250,50252],{},[2348,50229,50230,50232],{},[2071,50231,25992],{},[2210,50233,638],{},[2075,50235,2077],{},[2210,50237,3194],{},[2075,50239,2303],{},[2210,50241,2935],{},[2348,50243,50244,50246],{},[2071,50245,4342],{},[2210,50247,638],{},[2075,50249,2303],{},[2210,50251,678],{},[2348,50253,50254,50256],{},[2071,50255,4342],{},[2210,50257,646],{},[2092,50259,50260],{"encoding":2094},"B_1 = 50 - 10A_1 - 6A_2",[1647,50262,50264],{"className":50263},[2059],[2061,50265,50266],{"xmlns":2063},[2065,50267,50268,50290],{},[2068,50269,50270,50276,50278,50280,50282,50284],{},[2348,50271,50272,50274],{},[2071,50273,25992],{},[2210,50275,646],{},[2075,50277,2077],{},[2210,50279,39270],{},[2075,50281,2303],{},[2210,50283,2935],{},[2348,50285,50286,50288],{},[2071,50287,4342],{},[2210,50289,646],{},[2092,50291,50292],{"encoding":2094},"B_2 = 15 - 10A_2",[92,50294,49905,50295,835,50337,195],{},[1647,50296,50298],{"className":50297},[2059],[2061,50299,50300],{"xmlns":2063},[2065,50301,50302,50334],{},[2068,50303,50304,50310,50312,50314,50316,50318,50324,50326,50328],{},[2348,50305,50306,50308],{},[2071,50307,25992],{},[2210,50309,638],{},[2075,50311,2077],{},[2210,50313,42310],{},[2075,50315,2303],{},[2210,50317,646],{},[2348,50319,50320,50322],{},[2071,50321,4342],{},[2210,50323,638],{},[2075,50325,2303],{},[2210,50327,662],{},[2348,50329,50330,50332],{},[2071,50331,4342],{},[2210,50333,646],{},[2092,50335,50336],{"encoding":2094},"B_1 = 30 - 2A_1 - 4A_2",[1647,50338,50340],{"className":50339},[2059],[2061,50341,50342],{"xmlns":2063},[2065,50343,50344,50376],{},[2068,50345,50346,50352,50354,50356,50358,50360,50366,50368,50370],{},[2348,50347,50348,50350],{},[2071,50349,25992],{},[2210,50351,646],{},[2075,50353,2077],{},[2210,50355,39270],{},[2075,50357,2176],{},[2210,50359,646],{},[2348,50361,50362,50364],{},[2071,50363,4342],{},[2210,50365,638],{},[2075,50367,2303],{},[2210,50369,646],{},[2348,50371,50372,50374],{},[2071,50373,4342],{},[2210,50375,646],{},[2092,50377,50378],{"encoding":2094},"B_2 = 15 + 2A_1 - 2A_2",[92,50380,49940,50381,835,50425,195],{},[1647,50382,50384],{"className":50383},[2059],[2061,50385,50386],{"xmlns":2063},[2065,50387,50388,50422],{},[2068,50389,50390,50396,50398,50400,50402,50404,50406,50412,50414,50416],{},[2348,50391,50392,50394],{},[2071,50393,25992],{},[2210,50395,638],{},[2075,50397,2077],{},[2075,50399,2303],{},[2210,50401,9121],{},[2075,50403,2303],{},[2210,50405,646],{},[2348,50407,50408,50410],{},[2071,50409,4342],{},[2210,50411,638],{},[2075,50413,2176],{},[2210,50415,654],{},[2348,50417,50418,50420],{},[2071,50419,4342],{},[2210,50421,646],{},[2092,50423,50424],{"encoding":2094},"B_1 = -20 - 2A_1 + 3A_2",[1647,50426,50428],{"className":50427},[2059],[2061,50429,50430],{"xmlns":2063},[2065,50431,50432,50464],{},[2068,50433,50434,50440,50442,50444,50446,50448,50454,50456,50458],{},[2348,50435,50436,50438],{},[2071,50437,25992],{},[2210,50439,646],{},[2075,50441,2077],{},[2210,50443,2935],{},[2075,50445,2176],{},[2210,50447,646],{},[2348,50449,50450,50452],{},[2071,50451,4342],{},[2210,50453,638],{},[2075,50455,2303],{},[2210,50457,646],{},[2348,50459,50460,50462],{},[2071,50461,4342],{},[2210,50463,646],{},[2092,50465,50466],{"encoding":2094},"B_2 = 10 + 2A_1 - 2A_2",[92,50468,49971,50469,835,50511,195],{},[1647,50470,50472],{"className":50471},[2059],[2061,50473,50474],{"xmlns":2063},[2065,50475,50476,50508],{},[2068,50477,50478,50484,50486,50488,50490,50492,50498,50500,50502],{},[2348,50479,50480,50482],{},[2071,50481,25992],{},[2210,50483,638],{},[2075,50485,2077],{},[2210,50487,9121],{},[2075,50489,2176],{},[2210,50491,646],{},[2348,50493,50494,50496],{},[2071,50495,4342],{},[2210,50497,638],{},[2075,50499,2176],{},[2210,50501,662],{},[2348,50503,50504,50506],{},[2071,50505,4342],{},[2210,50507,646],{},[2092,50509,50510],{"encoding":2094},"B_1 = 20 + 2A_1 + 4A_2",[1647,50512,50514],{"className":50513},[2059],[2061,50515,50516],{"xmlns":2063},[2065,50517,50518,50550],{},[2068,50519,50520,50526,50528,50530,50532,50534,50540,50542,50544],{},[2348,50521,50522,50524],{},[2071,50523,25992],{},[2210,50525,646],{},[2075,50527,2077],{},[2210,50529,5298],{},[2075,50531,2303],{},[2210,50533,654],{},[2348,50535,50536,50538],{},[2071,50537,4342],{},[2210,50539,638],{},[2075,50541,2176],{},[2210,50543,670],{},[2348,50545,50546,50548],{},[2071,50547,4342],{},[2210,50549,646],{},[2092,50551,50552],{"encoding":2094},"B_2 = 40 - 3A_1 + 5A_2",[609,50554,50556],{"id":50555},"základní-analýza-nabídky","Základní analýza nabídky",[55,50558,50559,50562,50563,50597,50598,50620],{},[95,50560,50561],{},"2.6"," Je dána nabídka ",[1647,50564,50566],{"className":50565},[2059],[2061,50567,50568],{"xmlns":2063},[2065,50569,50570,50594],{},[2068,50571,50572,50574,50576,50578,50580,50582,50584,50586,50588,50590,50592],{},[2071,50573,575],{},[2075,50575,2077],{},[2071,50577,532],{},[2075,50579,2084],{"stretchy":2083},[2071,50581,2861],{},[2075,50583,2090],{"stretchy":2083},[2075,50585,2077],{},[2210,50587,9121],{},[2075,50589,2176],{},[2210,50591,2911],{},[2071,50593,2861],{},[2092,50595,50596],{"encoding":2094},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[1647,50599,50601],{"className":50600},[2059],[2061,50602,50603],{"xmlns":2063},[2065,50604,50605,50617],{},[2068,50606,50607,50609,50611,50613,50615],{},[2210,50608,5091],{},[2075,50610,2361],{"separator":2360},[2210,50612,42310],{},[2075,50614,2361],{"separator":2360},[2210,50616,16773],{},[2092,50618,50619],{"encoding":2094},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[55,50622,50623,50626,50627,50644],{},[95,50624,50625],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[1647,50628,50630],{"className":50629},[2059],[2061,50631,50632],{"xmlns":2063},[2065,50633,50634,50642],{},[2068,50635,50636,50638,50640],{},[2071,50637,575],{},[2075,50639,2361],{"separator":2360},[2071,50641,2861],{},[2092,50643,49809],{"encoding":2094},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[89,50646,50647,50673,50701,50734,50768,50804],{},[92,50648,49841,50649],{},[1647,50650,50652],{"className":50651},[2059],[2061,50653,50654],{"xmlns":2063},[2065,50655,50656,50670],{},[2068,50657,50658,50660,50662,50664,50666,50668],{},[2071,50659,575],{},[2075,50661,2077],{},[2210,50663,42310],{},[2075,50665,2176],{},[2210,50667,646],{},[2071,50669,2861],{},[2092,50671,50672],{"encoding":2094},"P = 30 + 2Q",[92,50674,49874,50675],{},[1647,50676,50678],{"className":50677},[2059],[2061,50679,50680],{"xmlns":2063},[2065,50681,50682,50698],{},[2068,50683,50684,50686,50688,50690,50692,50694,50696],{},[2071,50685,2861],{},[2075,50687,2077],{},[2075,50689,2303],{},[2210,50691,654],{},[2075,50693,2176],{},[2210,50695,3583],{},[2071,50697,575],{},[2092,50699,50700],{"encoding":2094},"Q = -3 + 12P",[92,50702,49905,50703],{},[1647,50704,50706],{"className":50705},[2059],[2061,50707,50708],{"xmlns":2063},[2065,50709,50710,50732],{},[2068,50711,50712,50714,50716,50722,50724,50726,50728,50730],{},[2071,50713,575],{},[2075,50715,2077],{},[2205,50717,50718,50720],{},[2071,50719,2861],{},[2210,50721,646],{},[2075,50723,2176],{},[2210,50725,25685],{},[2071,50727,2861],{},[2075,50729,2176],{},[2210,50731,35572],{},[2092,50733,46013],{"encoding":2094},[92,50735,49940,50736],{},[1647,50737,50739],{"className":50738},[2059],[2061,50740,50741],{"xmlns":2063},[2065,50742,50743,50765],{},[2068,50744,50745,50747,50749,50755,50757,50759,50761,50763],{},[2071,50746,575],{},[2075,50748,2077],{},[2205,50750,50751,50753],{},[2071,50752,2861],{},[2210,50754,646],{},[2075,50756,2176],{},[2210,50758,646],{},[2071,50760,2861],{},[2075,50762,2176],{},[2210,50764,3583],{},[2092,50766,50767],{"encoding":2094},"P = Q^2 + 2Q + 12",[92,50769,49971,50770],{},[1647,50771,50773],{"className":50772},[2059],[2061,50774,50775],{"xmlns":2063},[2065,50776,50777,50801],{},[2068,50778,50779,50781,50783,50785,50787,50789,50791,50793,50795],{},[2071,50780,2861],{},[2075,50782,2077],{},[2210,50784,8889],{},[2075,50786,2176],{},[2210,50788,670],{},[2071,50790,575],{},[2075,50792,2176],{},[2210,50794,2866],{},[2205,50796,50797,50799],{},[2071,50798,575],{},[2210,50800,646],{},[2092,50802,50803],{"encoding":2094},"Q = 150 + 5P + 0{,}1P^2",[92,50805,50006,50806],{},[1647,50807,50809],{"className":50808},[2059],[2061,50810,50811],{"xmlns":2063},[2065,50812,50813,50838],{},[2068,50814,50815,50817,50819,50821,50823,50825,50827,50829,50832],{},[2071,50816,2861],{},[2075,50818,2077],{},[2210,50820,686],{},[2075,50822,2176],{},[2210,50824,2866],{},[2071,50826,575],{},[2075,50828,2176],{},[2210,50830,50831],{},"0,004",[2205,50833,50834,50836],{},[2071,50835,575],{},[2210,50837,646],{},[2092,50839,50840],{"encoding":2094},"Q = 7 + 0{,}1P + 0{,}004P^2",[55,50842,50843,50846],{},[95,50844,50845],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[89,50848,50849,50852,50855,50858],{},[92,50850,50851],{},"(a) Sníží ceny surovin — vstupů.",[92,50853,50854],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[92,50856,50857],{},"(c) Zvýší ceny všech energií.",[92,50859,50860],{},"(d) Sníží daňové odvody státu.",[55,50862,50863,50562,50865,50899,50900,50928],{},[95,50864,47243],{},[1647,50866,50868],{"className":50867},[2059],[2061,50869,50870],{"xmlns":2063},[2065,50871,50872,50896],{},[2068,50873,50874,50876,50878,50880,50882,50884,50886,50888,50890,50892,50894],{},[2071,50875,575],{},[2075,50877,2077],{},[2071,50879,532],{},[2075,50881,2084],{"stretchy":2083},[2071,50883,2861],{},[2075,50885,2090],{"stretchy":2083},[2075,50887,2077],{},[2210,50889,5096],{},[2071,50891,2861],{},[2075,50893,2176],{},[2210,50895,39270],{},[2092,50897,50898],{"encoding":2094},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[1647,50901,50903],{"className":50902},[2059],[2061,50904,50905],{"xmlns":2063},[2065,50906,50907,50925],{},[2068,50908,50909,50911,50913,50919,50921,50923],{},[2071,50910,575],{},[2075,50912,2077],{},[2205,50914,50915,50917],{},[2071,50916,532],{},[2075,50918,4441],{},[2075,50920,2084],{"stretchy":2083},[2071,50922,2861],{},[2075,50924,2090],{"stretchy":2083},[2092,50926,50927],{"encoding":2094},"P = S^*(Q)",", na kterou se změní původní nabídka v důsledku uložení daně 5 Kč na výrobce na každou jednotku zboží. Graficky interpretujte.",[609,50930,45616],{"id":50931},"tržní-rovnováha-1",[55,50933,50934,50936,50937,50954,50955,2777],{},[95,50935,47303],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[1647,50938,50940],{"className":50939},[2059],[2061,50941,50942],{"xmlns":2063},[2065,50943,50944,50952],{},[2068,50945,50946],{},[2205,50947,50948,50950],{},[2071,50949,2861],{},[2071,50951,554],{},[2092,50953,46694],{"encoding":2094}," a rovnovážnou cenu ",[1647,50956,50958],{"className":50957},[2059],[2061,50959,50960],{"xmlns":2063},[2065,50961,50962,50970],{},[2068,50963,50964],{},[2205,50965,50966,50968],{},[2071,50967,575],{},[2071,50969,554],{},[2092,50971,45757],{"encoding":2094},[89,50973,50974,51027,51078,51137],{},[92,50975,49841,50976,835,51003,195],{},[1647,50977,50979],{"className":50978},[2059],[2061,50980,50981],{"xmlns":2063},[2065,50982,50983,51000],{},[2068,50984,50985,50987,50989,50991,50993,50995,50997],{},[2071,50986,575],{},[2075,50988,2077],{},[2075,50990,2303],{},[2210,50992,670],{},[2071,50994,2861],{},[2075,50996,2176],{},[2210,50998,50999],{},"80",[2092,51001,51002],{"encoding":2094},"P = -5Q + 80",[1647,51004,51006],{"className":51005},[2059],[2061,51007,51008],{"xmlns":2063},[2065,51009,51010,51024],{},[2068,51011,51012,51014,51016,51018,51020,51022],{},[2071,51013,575],{},[2075,51015,2077],{},[2210,51017,646],{},[2071,51019,2861],{},[2075,51021,2176],{},[2210,51023,2935],{},[2092,51025,51026],{"encoding":2094},"P = 2Q + 10",[92,51028,49874,51029,835,51055,195],{},[1647,51030,51032],{"className":51031},[2059],[2061,51033,51034],{"xmlns":2063},[2065,51035,51036,51052],{},[2068,51037,51038,51040,51042,51044,51046,51048,51050],{},[2071,51039,2861],{},[2075,51041,2077],{},[2075,51043,2303],{},[2210,51045,5096],{},[2071,51047,575],{},[2075,51049,2176],{},[2210,51051,5091],{},[2092,51053,51054],{"encoding":2094},"Q = -0{,}5P + 25",[1647,51056,51058],{"className":51057},[2059],[2061,51059,51060],{"xmlns":2063},[2065,51061,51062,51076],{},[2068,51063,51064,51066,51068,51070,51072,51074],{},[2071,51065,2861],{},[2075,51067,2077],{},[2210,51069,646],{},[2071,51071,575],{},[2075,51073,2303],{},[2210,51075,3194],{},[2092,51077,45138],{"encoding":2094},[92,51079,49905,51080,835,51106,195],{},[1647,51081,51083],{"className":51082},[2059],[2061,51084,51085],{"xmlns":2063},[2065,51086,51087,51103],{},[2068,51088,51089,51091,51093,51095,51097,51099,51101],{},[2071,51090,575],{},[2075,51092,2077],{},[2075,51094,2303],{},[2210,51096,662],{},[2071,51098,2861],{},[2075,51100,2176],{},[2210,51102,4134],{},[2092,51104,51105],{"encoding":2094},"P = -4Q + 120",[1647,51107,51109],{"className":51108},[2059],[2061,51110,51111],{"xmlns":2063},[2065,51112,51113,51134],{},[2068,51114,51115,51117,51119,51127,51129,51131],{},[2071,51116,575],{},[2075,51118,2077],{},[2400,51120,51121],{"scriptlevel":630,"displaystyle":2083},[2403,51122,51123,51125],{},[2210,51124,638],{},[2210,51126,654],{},[2071,51128,2861],{},[2075,51130,2176],{},[2210,51132,51133],{},"29",[2092,51135,51136],{"encoding":2094},"P = \\tfrac{1}{3}Q + 29",[92,51138,49940,51139,835,51168,195],{},[1647,51140,51142],{"className":51141},[2059],[2061,51143,51144],{"xmlns":2063},[2065,51145,51146,51165],{},[2068,51147,51148,51150,51152,51154,51160,51162],{},[2071,51149,575],{},[2075,51151,2077],{},[2075,51153,2303],{},[2205,51155,51156,51158],{},[2071,51157,2861],{},[2210,51159,646],{},[2075,51161,2176],{},[2210,51163,51164],{},"52",[2092,51166,51167],{"encoding":2094},"P = -Q^2 + 52",[1647,51169,51171],{"className":51170},[2059],[2061,51172,51173],{"xmlns":2063},[2065,51174,51175,51193],{},[2068,51176,51177,51179,51181,51183,51189,51191],{},[2071,51178,575],{},[2075,51180,2077],{},[2210,51182,646],{},[2205,51184,51185,51187],{},[2071,51186,2861],{},[2210,51188,646],{},[2075,51190,2176],{},[2210,51192,2935],{},[2092,51194,51195],{"encoding":2094},"P = 2Q^2 + 10",[55,51197,51198,51201,51202,51232,51233,51263],{},[95,51199,51200],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[1647,51203,51205],{"className":51204},[2059],[2061,51206,51207],{"xmlns":2063},[2065,51208,51209,51229],{},[2068,51210,51211,51219,51221],{},[9252,51212,51213,51215,51217],{},[2071,51214,2861],{},[2210,51216,638],{},[2071,51218,554],{},[2075,51220,2361],{"separator":2360},[9252,51222,51223,51225,51227],{},[2071,51224,2861],{},[2210,51226,646],{},[2071,51228,554],{},[2092,51230,51231],{"encoding":2094},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[1647,51234,51236],{"className":51235},[2059],[2061,51237,51238],{"xmlns":2063},[2065,51239,51240,51260],{},[2068,51241,51242,51250,51252],{},[9252,51243,51244,51246,51248],{},[2071,51245,575],{},[2210,51247,638],{},[2071,51249,554],{},[2075,51251,2361],{"separator":2360},[9252,51253,51254,51256,51258],{},[2071,51255,575],{},[2210,51257,646],{},[2071,51259,554],{},[2092,51261,51262],{"encoding":2094},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[89,51265,51266,51418],{},[92,51267,49841,51268,835,51308,835,51350,835,51384,195],{},[1647,51269,51271],{"className":51270},[2059],[2061,51272,51273],{"xmlns":2063},[2065,51274,51275,51305],{},[2068,51276,51277,51283,51285,51287,51289,51291,51297,51299],{},[2348,51278,51279,51281],{},[2071,51280,2861],{},[2210,51282,638],{},[2075,51284,2077],{},[2210,51286,2935],{},[2075,51288,2303],{},[2210,51290,646],{},[2348,51292,51293,51295],{},[2071,51294,575],{},[2210,51296,638],{},[2075,51298,2176],{},[2348,51300,51301,51303],{},[2071,51302,575],{},[2210,51304,646],{},[2092,51306,51307],{"encoding":2094},"Q_1 = 10 - 2P_1 + P_2",[1647,51309,51311],{"className":51310},[2059],[2061,51312,51313],{"xmlns":2063},[2065,51314,51315,51347],{},[2068,51316,51317,51323,51325,51327,51329,51331,51337,51339,51341],{},[2348,51318,51319,51321],{},[2071,51320,2861],{},[2210,51322,646],{},[2075,51324,2077],{},[2210,51326,670],{},[2075,51328,2176],{},[2210,51330,646],{},[2348,51332,51333,51335],{},[2071,51334,575],{},[2210,51336,638],{},[2075,51338,2303],{},[2210,51340,646],{},[2348,51342,51343,51345],{},[2071,51344,575],{},[2210,51346,646],{},[2092,51348,51349],{"encoding":2094},"Q_2 = 5 + 2P_1 - 2P_2",[1647,51351,51353],{"className":51352},[2059],[2061,51354,51355],{"xmlns":2063},[2065,51356,51357,51381],{},[2068,51358,51359,51365,51367,51369,51371,51373,51375],{},[2348,51360,51361,51363],{},[2071,51362,2861],{},[2210,51364,638],{},[2075,51366,2077],{},[2075,51368,2303],{},[2210,51370,654],{},[2075,51372,2176],{},[2210,51374,646],{},[2348,51376,51377,51379],{},[2071,51378,575],{},[2210,51380,638],{},[2092,51382,51383],{"encoding":2094},"Q_1 = -3 + 2P_1",[1647,51385,51387],{"className":51386},[2059],[2061,51388,51389],{"xmlns":2063},[2065,51390,51391,51415],{},[2068,51392,51393,51399,51401,51403,51405,51407,51409],{},[2348,51394,51395,51397],{},[2071,51396,2861],{},[2210,51398,646],{},[2075,51400,2077],{},[2075,51402,2303],{},[2210,51404,646],{},[2075,51406,2176],{},[2210,51408,654],{},[2348,51410,51411,51413],{},[2071,51412,575],{},[2210,51414,646],{},[2092,51416,51417],{"encoding":2094},"Q_2 = -2 + 3P_2",[92,51419,49874,51420,835,51460,835,51502,835,51534,195],{},[1647,51421,51423],{"className":51422},[2059],[2061,51424,51425],{"xmlns":2063},[2065,51426,51427,51457],{},[2068,51428,51429,51435,51437,51439,51441,51443,51449,51451],{},[2348,51430,51431,51433],{},[2071,51432,2861],{},[2210,51434,638],{},[2075,51436,2077],{},[2210,51438,3164],{},[2075,51440,2303],{},[2210,51442,646],{},[2348,51444,51445,51447],{},[2071,51446,575],{},[2210,51448,638],{},[2075,51450,2176],{},[2348,51452,51453,51455],{},[2071,51454,575],{},[2210,51456,646],{},[2092,51458,51459],{"encoding":2094},"Q_1 = 100 - 2P_1 + P_2",[1647,51461,51463],{"className":51462},[2059],[2061,51464,51465],{"xmlns":2063},[2065,51466,51467,51499],{},[2068,51468,51469,51475,51477,51479,51481,51483,51489,51491,51493],{},[2348,51470,51471,51473],{},[2071,51472,2861],{},[2210,51474,646],{},[2075,51476,2077],{},[2210,51478,670],{},[2075,51480,2176],{},[2210,51482,646],{},[2348,51484,51485,51487],{},[2071,51486,575],{},[2210,51488,638],{},[2075,51490,2303],{},[2210,51492,654],{},[2348,51494,51495,51497],{},[2071,51496,575],{},[2210,51498,646],{},[2092,51500,51501],{"encoding":2094},"Q_2 = 5 + 2P_1 - 3P_2",[1647,51503,51505],{"className":51504},[2059],[2061,51506,51507],{"xmlns":2063},[2065,51508,51509,51531],{},[2068,51510,51511,51517,51519,51521,51523,51525],{},[2348,51512,51513,51515],{},[2071,51514,2861],{},[2210,51516,638],{},[2075,51518,2077],{},[2075,51520,2303],{},[2210,51522,2935],{},[2075,51524,2176],{},[2348,51526,51527,51529],{},[2071,51528,575],{},[2210,51530,638],{},[2092,51532,51533],{"encoding":2094},"Q_1 = -10 + P_1",[1647,51535,51537],{"className":51536},[2059],[2061,51538,51539],{"xmlns":2063},[2065,51540,51541,51563],{},[2068,51542,51543,51549,51551,51553,51555,51557],{},[2348,51544,51545,51547],{},[2071,51546,2861],{},[2210,51548,646],{},[2075,51550,2077],{},[2210,51552,670],{},[2075,51554,2176],{},[2210,51556,678],{},[2348,51558,51559,51561],{},[2071,51560,575],{},[2210,51562,646],{},[2092,51564,51565],{"encoding":2094},"Q_2 = 5 + 6P_2",[55,51567,51568,51571,51572,835,51620,835,51666,51716,51717,835,51749,835,51783,24333,51817,75,51835,51853,51854,51867,51868,51894,51895,51232,51935,195],{},[95,51569,51570],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[1647,51573,51575],{"className":51574},[2059],[2061,51576,51577],{"xmlns":2063},[2065,51578,51579,51617],{},[2068,51580,51581,51587,51589,51591,51593,51599,51601,51603,51609,51611],{},[2348,51582,51583,51585],{},[2071,51584,2861],{},[2210,51586,638],{},[2075,51588,2077],{},[2210,51590,39270],{},[2075,51592,2303],{},[2348,51594,51595,51597],{},[2071,51596,575],{},[2210,51598,638],{},[2075,51600,2176],{},[2210,51602,646],{},[2348,51604,51605,51607],{},[2071,51606,575],{},[2210,51608,646],{},[2075,51610,2176],{},[2348,51612,51613,51615],{},[2071,51614,575],{},[2210,51616,654],{},[2092,51618,51619],{"encoding":2094},"Q_1 = 15 - P_1 + 2P_2 + P_3",[1647,51621,51623],{"className":51622},[2059],[2061,51624,51625],{"xmlns":2063},[2065,51626,51627,51663],{},[2068,51628,51629,51635,51637,51639,51641,51647,51649,51655,51657],{},[2348,51630,51631,51633],{},[2071,51632,2861],{},[2210,51634,646],{},[2075,51636,2077],{},[2210,51638,4087],{},[2075,51640,2176],{},[2348,51642,51643,51645],{},[2071,51644,575],{},[2210,51646,638],{},[2075,51648,2303],{},[2348,51650,51651,51653],{},[2071,51652,575],{},[2210,51654,646],{},[2075,51656,2303],{},[2348,51658,51659,51661],{},[2071,51660,575],{},[2210,51662,654],{},[2092,51664,51665],{"encoding":2094},"Q_2 = 9 + P_1 - P_2 - P_3",[1647,51667,51669],{"className":51668},[2059],[2061,51670,51671],{"xmlns":2063},[2065,51672,51673,51713],{},[2068,51674,51675,51681,51683,51685,51687,51689,51695,51697,51703,51705,51707],{},[2348,51676,51677,51679],{},[2071,51678,2861],{},[2210,51680,654],{},[2075,51682,2077],{},[2210,51684,5672],{},[2075,51686,2176],{},[2210,51688,646],{},[2348,51690,51691,51693],{},[2071,51692,575],{},[2210,51694,638],{},[2075,51696,2303],{},[2348,51698,51699,51701],{},[2071,51700,575],{},[2210,51702,646],{},[2075,51704,2303],{},[2210,51706,662],{},[2348,51708,51709,51711],{},[2071,51710,575],{},[2210,51712,654],{},[2092,51714,51715],{"encoding":2094},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[1647,51718,51720],{"className":51719},[2059],[2061,51721,51722],{"xmlns":2063},[2065,51723,51724,51746],{},[2068,51725,51726,51732,51734,51736,51738,51740],{},[2348,51727,51728,51730],{},[2071,51729,2861],{},[2210,51731,638],{},[2075,51733,2077],{},[2075,51735,2303],{},[2210,51737,686],{},[2075,51739,2176],{},[2348,51741,51742,51744],{},[2071,51743,575],{},[2210,51745,638],{},[2092,51747,51748],{"encoding":2094},"Q_1 = -7 + P_1",[1647,51750,51752],{"className":51751},[2059],[2061,51753,51754],{"xmlns":2063},[2065,51755,51756,51780],{},[2068,51757,51758,51764,51766,51768,51770,51772,51774],{},[2348,51759,51760,51762],{},[2071,51761,2861],{},[2210,51763,646],{},[2075,51765,2077],{},[2075,51767,2303],{},[2210,51769,662],{},[2075,51771,2176],{},[2210,51773,662],{},[2348,51775,51776,51778],{},[2071,51777,575],{},[2210,51779,646],{},[2092,51781,51782],{"encoding":2094},"Q_2 = -4 + 4P_2",[1647,51784,51786],{"className":51785},[2059],[2061,51787,51788],{"xmlns":2063},[2065,51789,51790,51814],{},[2068,51791,51792,51798,51800,51802,51804,51806,51808],{},[2348,51793,51794,51796],{},[2071,51795,2861],{},[2210,51797,654],{},[2075,51799,2077],{},[2075,51801,2303],{},[2210,51803,670],{},[2075,51805,2176],{},[2210,51807,646],{},[2348,51809,51810,51812],{},[2071,51811,575],{},[2210,51813,654],{},[2092,51815,51816],{"encoding":2094},"Q_3 = -5 + 2P_3",[1647,51818,51820],{"className":51819},[2059],[2061,51821,51822],{"xmlns":2063},[2065,51823,51824,51832],{},[2068,51825,51826],{},[2348,51827,51828,51830],{},[2071,51829,2861],{},[2071,51831,20528],{},[2092,51833,51834],{"encoding":2094},"Q_i",[1647,51836,51838],{"className":51837},[2059],[2061,51839,51840],{"xmlns":2063},[2065,51841,51842,51850],{},[2068,51843,51844],{},[2348,51845,51846,51848],{},[2071,51847,575],{},[2071,51849,20528],{},[2092,51851,51852],{"encoding":2094},"P_i"," značí příslušné množství a ceny ",[1647,51855,51857],{"className":51856},[2059],[2061,51858,51859],{"xmlns":2063},[2065,51860,51861,51865],{},[2068,51862,51863],{},[2071,51864,20528],{},[2092,51866,20528],{"encoding":2094},"-tého zboží, ",[1647,51869,51871],{"className":51870},[2059],[2061,51872,51873],{"xmlns":2063},[2065,51874,51875,51891],{},[2068,51876,51877,51879,51881,51883,51885,51887,51889],{},[2071,51878,20528],{},[2075,51880,2077],{},[2210,51882,638],{},[2075,51884,2361],{"separator":2360},[2210,51886,646],{},[2075,51888,2361],{"separator":2360},[2210,51890,654],{},[2092,51892,51893],{"encoding":2094},"i = 1, 2, 3",". Najděte rovnovážná množství ",[1647,51896,51898],{"className":51897},[2059],[2061,51899,51900],{"xmlns":2063},[2065,51901,51902,51932],{},[2068,51903,51904,51912,51914,51922,51924],{},[9252,51905,51906,51908,51910],{},[2071,51907,2861],{},[2210,51909,638],{},[2071,51911,554],{},[2075,51913,2361],{"separator":2360},[9252,51915,51916,51918,51920],{},[2071,51917,2861],{},[2210,51919,646],{},[2071,51921,554],{},[2075,51923,2361],{"separator":2360},[9252,51925,51926,51928,51930],{},[2071,51927,2861],{},[2210,51929,654],{},[2071,51931,554],{},[2092,51933,51934],{"encoding":2094},"Q_1^E, Q_2^E, Q_3^E",[1647,51936,51938],{"className":51937},[2059],[2061,51939,51940],{"xmlns":2063},[2065,51941,51942,51972],{},[2068,51943,51944,51952,51954,51962,51964],{},[9252,51945,51946,51948,51950],{},[2071,51947,575],{},[2210,51949,638],{},[2071,51951,554],{},[2075,51953,2361],{"separator":2360},[9252,51955,51956,51958,51960],{},[2071,51957,575],{},[2210,51959,646],{},[2071,51961,554],{},[2075,51963,2361],{"separator":2360},[9252,51965,51966,51968,51970],{},[2071,51967,575],{},[2210,51969,654],{},[2071,51971,554],{},[2092,51973,51974],{"encoding":2094},"P_1^E, P_2^E, P_3^E",[55,51976,51977,51980,51981,52017,52018,195],{},[95,51978,51979],{},"2.13"," Jsou dány poptávka ",[1647,51982,51984],{"className":51983},[2059],[2061,51985,51986],{"xmlns":2063},[2065,51987,51988,52014],{},[2068,51989,51990,51992,51994,51996,51998,52000,52002,52004,52006,52008,52010,52012],{},[2071,51991,575],{},[2075,51993,2077],{},[2071,51995,4271],{},[2075,51997,2084],{"stretchy":2083},[2071,51999,2861],{},[2075,52001,2090],{"stretchy":2083},[2075,52003,2077],{},[2075,52005,2303],{},[2210,52007,662],{},[2071,52009,2861],{},[2075,52011,2176],{},[2210,52013,50999],{},[2092,52015,52016],{"encoding":2094},"P = D(Q) = -4Q + 80"," a nabídka ",[1647,52019,52021],{"className":52020},[2059],[2061,52022,52023],{"xmlns":2063},[2065,52024,52025,52049],{},[2068,52026,52027,52029,52031,52033,52035,52037,52039,52041,52043,52045,52047],{},[2071,52028,575],{},[2075,52030,2077],{},[2071,52032,532],{},[2075,52034,2084],{"stretchy":2083},[2071,52036,2861],{},[2075,52038,2090],{"stretchy":2083},[2075,52040,2077],{},[2210,52042,654],{},[2071,52044,2861],{},[2075,52046,2176],{},[2210,52048,2935],{},[2092,52050,52051],{"encoding":2094},"P = S(Q) = 3Q + 10",[89,52053,52054,52091,52155,52215],{},[92,52055,52056,52057,50954,52074,195],{},"(a) Určete rovnovážné množství ",[1647,52058,52060],{"className":52059},[2059],[2061,52061,52062],{"xmlns":2063},[2065,52063,52064,52072],{},[2068,52065,52066],{},[2205,52067,52068,52070],{},[2071,52069,2861],{},[2071,52071,554],{},[2092,52073,46694],{"encoding":2094},[1647,52075,52077],{"className":52076},[2059],[2061,52078,52079],{"xmlns":2063},[2065,52080,52081,52089],{},[2068,52082,52083],{},[2205,52084,52085,52087],{},[2071,52086,575],{},[2071,52088,554],{},[2092,52090,45757],{"encoding":2094},[92,52092,52093,52094,52112,52113,52133,52134,52154],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[1647,52095,52097],{"className":52096},[2059],[2061,52098,52099],{"xmlns":2063},[2065,52100,52101,52109],{},[2068,52102,52103,52105,52107],{},[2071,52104,543],{},[2075,52106,2077],{},[2210,52108,686],{},[2092,52110,52111],{"encoding":2094},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[1647,52114,52116],{"className":52115},[2059],[2061,52117,52118],{"xmlns":2063},[2065,52119,52120,52130],{},[2068,52121,52122],{},[9252,52123,52124,52126,52128],{},[2071,52125,2861],{},[2210,52127,638],{},[2071,52129,554],{},[2092,52131,52132],{"encoding":2094},"Q_1^E"," a novou rovnovážnou cenu ",[1647,52135,52137],{"className":52136},[2059],[2061,52138,52139],{"xmlns":2063},[2065,52140,52141,52151],{},[2068,52142,52143],{},[9252,52144,52145,52147,52149],{},[2071,52146,575],{},[2210,52148,638],{},[2071,52150,554],{},[2092,52152,52153],{"encoding":2094},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[92,52156,52157,52158,52112,52175,52133,52195,52154],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[1647,52159,52161],{"className":52160},[2059],[2061,52162,52163],{"xmlns":2063},[2065,52164,52165,52173],{},[2068,52166,52167,52169,52171],{},[2071,52168,543],{},[2075,52170,2077],{},[2210,52172,686],{},[2092,52174,52111],{"encoding":2094},[1647,52176,52178],{"className":52177},[2059],[2061,52179,52180],{"xmlns":2063},[2065,52181,52182,52192],{},[2068,52183,52184],{},[9252,52185,52186,52188,52190],{},[2071,52187,2861],{},[2210,52189,646],{},[2071,52191,554],{},[2092,52193,52194],{"encoding":2094},"Q_2^E",[1647,52196,52198],{"className":52197},[2059],[2061,52199,52200],{"xmlns":2063},[2065,52201,52202,52212],{},[2068,52203,52204],{},[9252,52205,52206,52208,52210],{},[2071,52207,575],{},[2210,52209,646],{},[2071,52211,554],{},[2092,52213,52214],{"encoding":2094},"P_2^E",[92,52216,52217],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[55,52219,52220,52221,195],{},"Viz též ",[69,52222,47015],{"className":52223,"dataFsResolvedFilePath":47013,"href":47014},[62],[609,52225,47317],{"id":52226},"multiplikátory-pro-mikroekonomické-proměnné-1",[55,52228,52229,51980,52232,52017,52268,195],{},[95,52230,52231],{},"2.14",[1647,52233,52235],{"className":52234},[2059],[2061,52236,52237],{"xmlns":2063},[2065,52238,52239,52265],{},[2068,52240,52241,52243,52245,52247,52249,52251,52253,52255,52257,52259,52261,52263],{},[2071,52242,575],{},[2075,52244,2077],{},[2071,52246,69],{},[2071,52248,2861],{},[2075,52250,2176],{},[2071,52252,2179],{},[2075,52254,2077],{},[2075,52256,2303],{},[2210,52258,646],{},[2071,52260,2861],{},[2075,52262,2176],{},[2210,52264,3194],{},[2092,52266,52267],{"encoding":2094},"P = aQ + b = -2Q + 50",[1647,52269,52271],{"className":52270},[2059],[2061,52272,52273],{"xmlns":2063},[2065,52274,52275,52299],{},[2068,52276,52277,52279,52281,52283,52285,52287,52289,52291,52293,52295,52297],{},[2071,52278,575],{},[2075,52280,2077],{},[2071,52282,2222],{},[2071,52284,2861],{},[2075,52286,2176],{},[2071,52288,2273],{},[2075,52290,2077],{},[2210,52292,22060],{},[2071,52294,2861],{},[2075,52296,2176],{},[2210,52298,9121],{},[2092,52300,52301],{"encoding":2094},"P = cQ + d = 0{,}6Q + 20",[89,52303,52304,52340,52343,52429,52482,52562,52616],{},[92,52305,52056,52306,50954,52323,195],{},[1647,52307,52309],{"className":52308},[2059],[2061,52310,52311],{"xmlns":2063},[2065,52312,52313,52321],{},[2068,52314,52315],{},[2205,52316,52317,52319],{},[2071,52318,2861],{},[2071,52320,554],{},[2092,52322,46694],{"encoding":2094},[1647,52324,52326],{"className":52325},[2059],[2061,52327,52328],{"xmlns":2063},[2065,52329,52330,52338],{},[2068,52331,52332],{},[2205,52333,52334,52336],{},[2071,52335,575],{},[2071,52337,554],{},[2092,52339,45757],{"encoding":2094},[92,52341,52342],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[92,52344,52345,52346,52363,52364,2744,52377,2758,52393,52409,52410,195],{},"(c) Určete přibližnou změnu rovnovážného množství ",[1647,52347,52349],{"className":52348},[2059],[2061,52350,52351],{"xmlns":2063},[2065,52352,52353,52361],{},[2068,52354,52355],{},[2205,52356,52357,52359],{},[2071,52358,2861],{},[2071,52360,554],{},[2092,52362,46694],{"encoding":2094}," odpovídající změně ",[1647,52365,52367],{"className":52366},[2059],[2061,52368,52369],{"xmlns":2063},[2065,52370,52371,52375],{},[2068,52372,52373],{},[2071,52374,69],{},[2092,52376,69],{"encoding":2094},[1647,52378,52380],{"className":52379},[2059],[2061,52381,52382],{"xmlns":2063},[2065,52383,52384,52390],{},[2068,52385,52386,52388],{},[2075,52387,2303],{},[2210,52389,646],{},[2092,52391,52392],{"encoding":2094},"-2",[1647,52394,52396],{"className":52395},[2059],[2061,52397,52398],{"xmlns":2063},[2065,52399,52400,52406],{},[2068,52401,52402,52404],{},[2075,52403,2303],{},[2210,52405,654],{},[2092,52407,52408],{"encoding":2094},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[1647,52411,52413],{"className":52412},[2059],[2061,52414,52415],{"xmlns":2063},[2065,52416,52417,52427],{},[2068,52418,52419],{},[9252,52420,52421,52423,52425],{},[2071,52422,2861],{},[2210,52424,638],{},[2071,52426,554],{},[2092,52428,52132],{"encoding":2094},[92,52430,52431,52432,52363,52449,52462,52463,195],{},"(d) Určete přibližnou změnu rovnovážného množství ",[1647,52433,52435],{"className":52434},[2059],[2061,52436,52437],{"xmlns":2063},[2065,52438,52439,52447],{},[2068,52440,52441],{},[2205,52442,52443,52445],{},[2071,52444,2861],{},[2071,52446,554],{},[2092,52448,46694],{"encoding":2094},[1647,52450,52452],{"className":52451},[2059],[2061,52453,52454],{"xmlns":2063},[2065,52455,52456,52460],{},[2068,52457,52458],{},[2071,52459,2179],{},[2092,52461,2179],{"encoding":2094}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[1647,52464,52466],{"className":52465},[2059],[2061,52467,52468],{"xmlns":2063},[2065,52469,52470,52480],{},[2068,52471,52472],{},[9252,52473,52474,52476,52478],{},[2071,52475,2861],{},[2210,52477,646],{},[2071,52479,554],{},[2092,52481,52194],{"encoding":2094},[92,52483,52484,52485,52363,52502,2744,52515,2758,52528,52409,52542,195],{},"(e) Určete přibližnou změnu rovnovážného množství ",[1647,52486,52488],{"className":52487},[2059],[2061,52489,52490],{"xmlns":2063},[2065,52491,52492,52500],{},[2068,52493,52494],{},[2205,52495,52496,52498],{},[2071,52497,2861],{},[2071,52499,554],{},[2092,52501,46694],{"encoding":2094},[1647,52503,52505],{"className":52504},[2059],[2061,52506,52507],{"xmlns":2063},[2065,52508,52509,52513],{},[2068,52510,52511],{},[2071,52512,2222],{},[2092,52514,2222],{"encoding":2094},[1647,52516,52518],{"className":52517},[2059],[2061,52519,52520],{"xmlns":2063},[2065,52521,52522,52526],{},[2068,52523,52524],{},[2210,52525,22060],{},[2092,52527,48754],{"encoding":2094},[1647,52529,52531],{"className":52530},[2059],[2061,52532,52533],{"xmlns":2063},[2065,52534,52535,52539],{},[2068,52536,52537],{},[2210,52538,16324],{},[2092,52540,52541],{"encoding":2094},"0{,}8",[1647,52543,52545],{"className":52544},[2059],[2061,52546,52547],{"xmlns":2063},[2065,52548,52549,52559],{},[2068,52550,52551],{},[9252,52552,52553,52555,52557],{},[2071,52554,2861],{},[2210,52556,654],{},[2071,52558,554],{},[2092,52560,52561],{"encoding":2094},"Q_3^E",[92,52563,52564,52565,52363,52582,52595,52596,195],{},"(f) Určete přibližnou změnu rovnovážného množství ",[1647,52566,52568],{"className":52567},[2059],[2061,52569,52570],{"xmlns":2063},[2065,52571,52572,52580],{},[2068,52573,52574],{},[2205,52575,52576,52578],{},[2071,52577,2861],{},[2071,52579,554],{},[2092,52581,46694],{"encoding":2094},[1647,52583,52585],{"className":52584},[2059],[2061,52586,52587],{"xmlns":2063},[2065,52588,52589,52593],{},[2068,52590,52591],{},[2071,52592,2273],{},[2092,52594,2273],{"encoding":2094}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[1647,52597,52599],{"className":52598},[2059],[2061,52600,52601],{"xmlns":2063},[2065,52602,52603,52613],{},[2068,52604,52605],{},[9252,52606,52607,52609,52611],{},[2071,52608,2861],{},[2210,52610,662],{},[2071,52612,554],{},[2092,52614,52615],{"encoding":2094},"Q_4^E",[92,52617,52618,52619,52636,52637,52650,52651,24159,52664,835,52679,24159,52692,75,52706,24159,52719,52734,52735,195],{},"(g) Určete přibližnou změnu rovnovážného množství ",[1647,52620,52622],{"className":52621},[2059],[2061,52623,52624],{"xmlns":2063},[2065,52625,52626,52634],{},[2068,52627,52628],{},[2205,52629,52630,52632],{},[2071,52631,2861],{},[2071,52633,554],{},[2092,52635,46694],{"encoding":2094}," odpovídající změnám ",[1647,52638,52640],{"className":52639},[2059],[2061,52641,52642],{"xmlns":2063},[2065,52643,52644,52648],{},[2068,52645,52646],{},[2071,52647,69],{},[2092,52649,69],{"encoding":2094}," o 1, ",[1647,52652,52654],{"className":52653},[2059],[2061,52655,52656],{"xmlns":2063},[2065,52657,52658,52662],{},[2068,52659,52660],{},[2071,52661,2179],{},[2092,52663,2179],{"encoding":2094},[1647,52665,52667],{"className":52666},[2059],[2061,52668,52669],{"xmlns":2063},[2065,52670,52671,52677],{},[2068,52672,52673,52675],{},[2075,52674,2303],{},[2210,52676,2935],{},[2092,52678,22194],{"encoding":2094},[1647,52680,52682],{"className":52681},[2059],[2061,52683,52684],{"xmlns":2063},[2065,52685,52686,52690],{},[2068,52687,52688],{},[2071,52689,2222],{},[2092,52691,2222],{"encoding":2094},[1647,52693,52695],{"className":52694},[2059],[2061,52696,52697],{"xmlns":2063},[2065,52698,52699,52703],{},[2068,52700,52701],{},[2210,52702,2866],{},[2092,52704,52705],{"encoding":2094},"0{,}1",[1647,52707,52709],{"className":52708},[2059],[2061,52710,52711],{"xmlns":2063},[2065,52712,52713,52717],{},[2068,52714,52715],{},[2071,52716,2273],{},[2092,52718,2273],{"encoding":2094},[1647,52720,52722],{"className":52721},[2059],[2061,52723,52724],{"xmlns":2063},[2065,52725,52726,52732],{},[2068,52727,52728,52730],{},[2075,52729,2303],{},[2210,52731,2935],{},[2092,52733,22194],{"encoding":2094}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[1647,52736,52738],{"className":52737},[2059],[2061,52739,52740],{"xmlns":2063},[2065,52741,52742,52752],{},[2068,52743,52744],{},[9252,52745,52746,52748,52750],{},[2071,52747,2861],{},[2210,52749,670],{},[2071,52751,554],{},[2092,52753,52754],{"encoding":2094},"Q_5^E",[55,52756,52757,51980,52760,52017,52783,195],{},[95,52758,52759],{},"2.15",[1647,52761,52763],{"className":52762},[2059],[2061,52764,52765],{"xmlns":2063},[2065,52766,52767,52781],{},[2068,52768,52769,52771,52773,52775,52777,52779],{},[2071,52770,575],{},[2075,52772,2077],{},[2071,52774,69],{},[2071,52776,2861],{},[2075,52778,2176],{},[2071,52780,2179],{},[2092,52782,41352],{"encoding":2094},[1647,52784,52786],{"className":52785},[2059],[2061,52787,52788],{"xmlns":2063},[2065,52789,52790,52804],{},[2068,52791,52792,52794,52796,52798,52800,52802],{},[2071,52793,575],{},[2075,52795,2077],{},[2071,52797,2222],{},[2071,52799,2861],{},[2075,52801,2176],{},[2071,52803,2273],{},[2092,52805,44533],{"encoding":2094},[89,52807,52808,52883,52900,53009,53062,53116],{},[92,52809,52810,52811,52824,52825,52850,52851,52882],{},"(a) Odvoďte redukovaný tvar pro ",[1647,52812,52814],{"className":52813},[2059],[2061,52815,52816],{"xmlns":2063},[2065,52817,52818,52822],{},[2068,52819,52820],{},[2071,52821,575],{},[2092,52823,575],{"encoding":2094},". Stanovte podmínky pro ",[1647,52826,52828],{"className":52827},[2059],[2061,52829,52830],{"xmlns":2063},[2065,52831,52832,52848],{},[2068,52833,52834,52836,52838,52840,52842,52844,52846],{},[2071,52835,69],{},[2075,52837,2361],{"separator":2360},[2071,52839,2179],{},[2075,52841,2361],{"separator":2360},[2071,52843,2222],{},[2075,52845,2361],{"separator":2360},[2071,52847,2273],{},[2092,52849,47579],{"encoding":2094}," tak, aby rovnovážný bod ",[1647,52852,52854],{"className":52853},[2059],[2061,52855,52856],{"xmlns":2063},[2065,52857,52858,52880],{},[2068,52859,52860,52862,52864,52870,52872,52878],{},[2071,52861,554],{},[2075,52863,2561],{"stretchy":2083},[2205,52865,52866,52868],{},[2071,52867,2861],{},[2071,52869,554],{},[2075,52871,2361],{"separator":2360},[2205,52873,52874,52876],{},[2071,52875,575],{},[2071,52877,554],{},[2075,52879,2576],{"stretchy":2083},[2092,52881,45658],{"encoding":2094}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[92,52884,52885,52886,52899],{},"(b) Vypočtěte multiplikátory pro ",[1647,52887,52889],{"className":52888},[2059],[2061,52890,52891],{"xmlns":2063},[2065,52892,52893,52897],{},[2068,52894,52895],{},[2071,52896,575],{},[2092,52898,575],{"encoding":2094}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[92,52901,52902,52903,835,52923,835,52941,835,52959,52977,52978,52995,52996,195],{},"(c) Pro hodnoty parametrů ",[1647,52904,52906],{"className":52905},[2059],[2061,52907,52908],{"xmlns":2063},[2065,52909,52910,52920],{},[2068,52911,52912,52914,52916,52918],{},[2071,52913,69],{},[2075,52915,2077],{},[2075,52917,2303],{},[2210,52919,646],{},[2092,52921,52922],{"encoding":2094},"a = -2",[1647,52924,52926],{"className":52925},[2059],[2061,52927,52928],{"xmlns":2063},[2065,52929,52930,52938],{},[2068,52931,52932,52934,52936],{},[2071,52933,2179],{},[2075,52935,2077],{},[2210,52937,5298],{},[2092,52939,52940],{"encoding":2094},"b = 40",[1647,52942,52944],{"className":52943},[2059],[2061,52945,52946],{"xmlns":2063},[2065,52947,52948,52956],{},[2068,52949,52950,52952,52954],{},[2071,52951,2222],{},[2075,52953,2077],{},[2210,52955,5096],{},[2092,52957,52958],{"encoding":2094},"c = 0{,}5",[1647,52960,52962],{"className":52961},[2059],[2061,52963,52964],{"xmlns":2063},[2065,52965,52966,52974],{},[2068,52967,52968,52970,52972],{},[2071,52969,2273],{},[2075,52971,2077],{},[2210,52973,2935],{},[2092,52975,52976],{"encoding":2094},"d = 10"," určete rovnovážnou cenu ",[1647,52979,52981],{"className":52980},[2059],[2061,52982,52983],{"xmlns":2063},[2065,52984,52985,52993],{},[2068,52986,52987],{},[2205,52988,52989,52991],{},[2071,52990,575],{},[2071,52992,554],{},[2092,52994,45757],{"encoding":2094}," a hodnoty multiplikátorů pro ",[1647,52997,52999],{"className":52998},[2059],[2061,53000,53001],{"xmlns":2063},[2065,53002,53003,53007],{},[2068,53004,53005],{},[2071,53006,575],{},[2092,53008,575],{"encoding":2094},[92,53010,53011,53012,52363,53029,53042,53043,195],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[1647,53013,53015],{"className":53014},[2059],[2061,53016,53017],{"xmlns":2063},[2065,53018,53019,53027],{},[2068,53020,53021],{},[2205,53022,53023,53025],{},[2071,53024,575],{},[2071,53026,554],{},[2092,53028,45757],{"encoding":2094},[1647,53030,53032],{"className":53031},[2059],[2061,53033,53034],{"xmlns":2063},[2065,53035,53036,53040],{},[2068,53037,53038],{},[2071,53039,69],{},[2092,53041,69],{"encoding":2094}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[1647,53044,53046],{"className":53045},[2059],[2061,53047,53048],{"xmlns":2063},[2065,53049,53050,53060],{},[2068,53051,53052],{},[9252,53053,53054,53056,53058],{},[2071,53055,575],{},[2210,53057,638],{},[2071,53059,554],{},[2092,53061,52153],{"encoding":2094},[92,53063,53064,53065,53082,53083,53096,53097,195],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[1647,53066,53068],{"className":53067},[2059],[2061,53069,53070],{"xmlns":2063},[2065,53071,53072,53080],{},[2068,53073,53074],{},[2205,53075,53076,53078],{},[2071,53077,575],{},[2071,53079,554],{},[2092,53081,45757],{"encoding":2094}," odpovídající poklesu ",[1647,53084,53086],{"className":53085},[2059],[2061,53087,53088],{"xmlns":2063},[2065,53089,53090,53094],{},[2068,53091,53092],{},[2071,53093,69],{},[2092,53095,69],{"encoding":2094}," o 1 a stanovte novou rovnovážnou cenu ",[1647,53098,53100],{"className":53099},[2059],[2061,53101,53102],{"xmlns":2063},[2065,53103,53104,53114],{},[2068,53105,53106],{},[9252,53107,53108,53110,53112],{},[2071,53109,575],{},[2210,53111,646],{},[2071,53113,554],{},[2092,53115,52214],{"encoding":2094},[92,53117,53118,53119,52636,53136,53149,53150,2758,53163,75,53178,53191,53192,195],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[1647,53120,53122],{"className":53121},[2059],[2061,53123,53124],{"xmlns":2063},[2065,53125,53126,53134],{},[2068,53127,53128],{},[2205,53129,53130,53132],{},[2071,53131,575],{},[2071,53133,554],{},[2092,53135,45757],{"encoding":2094},[1647,53137,53139],{"className":53138},[2059],[2061,53140,53141],{"xmlns":2063},[2065,53142,53143,53147],{},[2068,53144,53145],{},[2071,53146,69],{},[2092,53148,69],{"encoding":2094}," na 35, ",[1647,53151,53153],{"className":53152},[2059],[2061,53154,53155],{"xmlns":2063},[2065,53156,53157,53161],{},[2068,53158,53159],{},[2071,53160,2222],{},[2092,53162,2222],{"encoding":2094},[1647,53164,53166],{"className":53165},[2059],[2061,53167,53168],{"xmlns":2063},[2065,53169,53170,53175],{},[2068,53171,53172],{},[2210,53173,53174],{},"0,7",[2092,53176,53177],{"encoding":2094},"0{,}7",[1647,53179,53181],{"className":53180},[2059],[2061,53182,53183],{"xmlns":2063},[2065,53184,53185,53189],{},[2068,53186,53187],{},[2071,53188,2273],{},[2092,53190,2273],{"encoding":2094}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[1647,53193,53195],{"className":53194},[2059],[2061,53196,53197],{"xmlns":2063},[2065,53198,53199,53209],{},[2068,53200,53201],{},[9252,53202,53203,53205,53207],{},[2071,53204,575],{},[2210,53206,654],{},[2071,53208,554],{},[2092,53210,53211],{"encoding":2094},"P_3^E",[55,53213,53214,51980,53217,52017,53245,24333,53273,75,53299,195],{},[95,53215,53216],{},"2.16",[1647,53218,53220],{"className":53219},[2059],[2061,53221,53222],{"xmlns":2063},[2065,53223,53224,53242],{},[2068,53225,53226,53228,53230,53232,53234,53236],{},[2071,53227,575],{},[2075,53229,2077],{},[2071,53231,69],{},[2075,53233,2176],{},[2071,53235,2179],{},[2205,53237,53238,53240],{},[2071,53239,2861],{},[2210,53241,646],{},[2092,53243,53244],{"encoding":2094},"P = a + bQ^2",[1647,53246,53248],{"className":53247},[2059],[2061,53249,53250],{"xmlns":2063},[2065,53251,53252,53270],{},[2068,53253,53254,53256,53258,53260,53262,53264],{},[2071,53255,575],{},[2075,53257,2077],{},[2071,53259,2222],{},[2075,53261,2176],{},[2071,53263,2273],{},[2205,53265,53266,53268],{},[2071,53267,2861],{},[2210,53269,646],{},[2092,53271,53272],{"encoding":2094},"P = c + dQ^2",[1647,53274,53276],{"className":53275},[2059],[2061,53277,53278],{"xmlns":2063},[2065,53279,53280,53296],{},[2068,53281,53282,53284,53286,53288,53290,53292,53294],{},[2071,53283,69],{},[2075,53285,2361],{"separator":2360},[2071,53287,2222],{},[2075,53289,2361],{"separator":2360},[2071,53291,2273],{},[2075,53293,3482],{},[2210,53295,630],{},[2092,53297,53298],{"encoding":2094},"a, c, d > 0",[1647,53300,53302],{"className":53301},[2059],[2061,53303,53304],{"xmlns":2063},[2065,53305,53306,53314],{},[2068,53307,53308,53310,53312],{},[2071,53309,2179],{},[2075,53311,3521],{},[2210,53313,630],{},[2092,53315,53316],{"encoding":2094},"b \u003C 0",[89,53318,53319,53367,53383,53490,53542,53594,53703,53719,53818,53871],{},[92,53320,52810,53321,53334,53335,53366],{},[1647,53322,53324],{"className":53323},[2059],[2061,53325,53326],{"xmlns":2063},[2065,53327,53328,53332],{},[2068,53329,53330],{},[2071,53331,2861],{},[2092,53333,2861],{"encoding":2094},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[1647,53336,53338],{"className":53337},[2059],[2061,53339,53340],{"xmlns":2063},[2065,53341,53342,53364],{},[2068,53343,53344,53346,53348,53354,53356,53362],{},[2071,53345,554],{},[2075,53347,2561],{"stretchy":2083},[2205,53349,53350,53352],{},[2071,53351,2861],{},[2071,53353,554],{},[2075,53355,2361],{"separator":2360},[2205,53357,53358,53360],{},[2071,53359,575],{},[2071,53361,554],{},[2075,53363,2576],{"stretchy":2083},[2092,53365,45658],{"encoding":2094}," patřil do 1. kvadrantu.",[92,53368,52885,53369,53382],{},[1647,53370,53372],{"className":53371},[2059],[2061,53373,53374],{"xmlns":2063},[2065,53375,53376,53380],{},[2068,53377,53378],{},[2071,53379,2861],{},[2092,53381,2861],{"encoding":2094}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[92,53384,52902,53385,835,53403,835,53423,835,53441,53459,53460,52995,53477,195],{},[1647,53386,53388],{"className":53387},[2059],[2061,53389,53390],{"xmlns":2063},[2065,53391,53392,53400],{},[2068,53393,53394,53396,53398],{},[2071,53395,69],{},[2075,53397,2077],{},[2210,53399,3164],{},[2092,53401,53402],{"encoding":2094},"a = 100",[1647,53404,53406],{"className":53405},[2059],[2061,53407,53408],{"xmlns":2063},[2065,53409,53410,53420],{},[2068,53411,53412,53414,53416,53418],{},[2071,53413,2179],{},[2075,53415,2077],{},[2075,53417,2303],{},[2210,53419,638],{},[2092,53421,53422],{"encoding":2094},"b = -1",[1647,53424,53426],{"className":53425},[2059],[2061,53427,53428],{"xmlns":2063},[2065,53429,53430,53438],{},[2068,53431,53432,53434,53436],{},[2071,53433,2222],{},[2075,53435,2077],{},[2210,53437,9121],{},[2092,53439,53440],{"encoding":2094},"c = 20",[1647,53442,53444],{"className":53443},[2059],[2061,53445,53446],{"xmlns":2063},[2065,53447,53448,53456],{},[2068,53449,53450,53452,53454],{},[2071,53451,2273],{},[2075,53453,2077],{},[2210,53455,638],{},[2092,53457,53458],{"encoding":2094},"d = 1"," určete rovnovážné množství ",[1647,53461,53463],{"className":53462},[2059],[2061,53464,53465],{"xmlns":2063},[2065,53466,53467,53475],{},[2068,53468,53469],{},[2205,53470,53471,53473],{},[2071,53472,2861],{},[2071,53474,554],{},[2092,53476,46694],{"encoding":2094},[1647,53478,53480],{"className":53479},[2059],[2061,53481,53482],{"xmlns":2063},[2065,53483,53484,53488],{},[2068,53485,53486],{},[2071,53487,2861],{},[2092,53489,2861],{"encoding":2094},[92,53491,52431,53492,52363,53509,53522,53523,195],{},[1647,53493,53495],{"className":53494},[2059],[2061,53496,53497],{"xmlns":2063},[2065,53498,53499,53507],{},[2068,53500,53501],{},[2205,53502,53503,53505],{},[2071,53504,2861],{},[2071,53506,554],{},[2092,53508,46694],{"encoding":2094},[1647,53510,53512],{"className":53511},[2059],[2061,53513,53514],{"xmlns":2063},[2065,53515,53516,53520],{},[2068,53517,53518],{},[2071,53519,69],{},[2092,53521,69],{"encoding":2094}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[1647,53524,53526],{"className":53525},[2059],[2061,53527,53528],{"xmlns":2063},[2065,53529,53530,53540],{},[2068,53531,53532],{},[9252,53533,53534,53536,53538],{},[2071,53535,2861],{},[2210,53537,638],{},[2071,53539,554],{},[2092,53541,52132],{"encoding":2094},[92,53543,52484,53544,52363,53561,53574,53575,195],{},[1647,53545,53547],{"className":53546},[2059],[2061,53548,53549],{"xmlns":2063},[2065,53550,53551,53559],{},[2068,53552,53553],{},[2205,53554,53555,53557],{},[2071,53556,2861],{},[2071,53558,554],{},[2092,53560,46694],{"encoding":2094},[1647,53562,53564],{"className":53563},[2059],[2061,53565,53566],{"xmlns":2063},[2065,53567,53568,53572],{},[2068,53569,53570],{},[2071,53571,2222],{},[2092,53573,2222],{"encoding":2094}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[1647,53576,53578],{"className":53577},[2059],[2061,53579,53580],{"xmlns":2063},[2065,53581,53582,53592],{},[2068,53583,53584],{},[9252,53585,53586,53588,53590],{},[2071,53587,2861],{},[2210,53589,646],{},[2071,53591,554],{},[2092,53593,52194],{"encoding":2094},[92,53595,52564,53596,52636,53613,53626,53627,2758,53640,53655,53656,53669,53670,53683,53684,195],{},[1647,53597,53599],{"className":53598},[2059],[2061,53600,53601],{"xmlns":2063},[2065,53602,53603,53611],{},[2068,53604,53605],{},[2205,53606,53607,53609],{},[2071,53608,2861],{},[2071,53610,554],{},[2092,53612,46694],{"encoding":2094},[1647,53614,53616],{"className":53615},[2059],[2061,53617,53618],{"xmlns":2063},[2065,53619,53620,53624],{},[2068,53621,53622],{},[2071,53623,69],{},[2092,53625,69],{"encoding":2094}," na 110, poklesu ",[1647,53628,53630],{"className":53629},[2059],[2061,53631,53632],{"xmlns":2063},[2065,53633,53634,53638],{},[2068,53635,53636],{},[2071,53637,2179],{},[2092,53639,2179],{"encoding":2094},[1647,53641,53643],{"className":53642},[2059],[2061,53644,53645],{"xmlns":2063},[2065,53646,53647,53653],{},[2068,53648,53649,53651],{},[2075,53650,2303],{},[2210,53652,646],{},[2092,53654,52392],{"encoding":2094},", růstu ",[1647,53657,53659],{"className":53658},[2059],[2061,53660,53661],{"xmlns":2063},[2065,53662,53663,53667],{},[2068,53664,53665],{},[2071,53666,2222],{},[2092,53668,2222],{"encoding":2094}," na 25 a růstu ",[1647,53671,53673],{"className":53672},[2059],[2061,53674,53675],{"xmlns":2063},[2065,53676,53677,53681],{},[2068,53678,53679],{},[2071,53680,2273],{},[2092,53682,2273],{"encoding":2094}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[1647,53685,53687],{"className":53686},[2059],[2061,53688,53689],{"xmlns":2063},[2065,53690,53691,53701],{},[2068,53692,53693],{},[9252,53694,53695,53697,53699],{},[2071,53696,2861],{},[2210,53698,654],{},[2071,53700,554],{},[2092,53702,52561],{"encoding":2094},[92,53704,53705,53706,53382],{},"(i) Vypočtěte multiplikátory pro ",[1647,53707,53709],{"className":53708},[2059],[2061,53710,53711],{"xmlns":2063},[2065,53712,53713,53717],{},[2068,53714,53715],{},[2071,53716,575],{},[2092,53718,575],{"encoding":2094},[92,53720,53721,53722,52995,53739,53752,53753,52363,53770,2758,53783,53798,53799,195],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[1647,53723,53725],{"className":53724},[2059],[2061,53726,53727],{"xmlns":2063},[2065,53728,53729,53737],{},[2068,53730,53731],{},[2205,53732,53733,53735],{},[2071,53734,575],{},[2071,53736,554],{},[2092,53738,45757],{"encoding":2094},[1647,53740,53742],{"className":53741},[2059],[2061,53743,53744],{"xmlns":2063},[2065,53745,53746,53750],{},[2068,53747,53748],{},[2071,53749,575],{},[2092,53751,575],{"encoding":2094},", přibližnou změnu rovnovážné ceny ",[1647,53754,53756],{"className":53755},[2059],[2061,53757,53758],{"xmlns":2063},[2065,53759,53760,53768],{},[2068,53761,53762],{},[2205,53763,53764,53766],{},[2071,53765,575],{},[2071,53767,554],{},[2092,53769,45757],{"encoding":2094},[1647,53771,53773],{"className":53772},[2059],[2061,53774,53775],{"xmlns":2063},[2065,53776,53777,53781],{},[2068,53778,53779],{},[2071,53780,69],{},[2092,53782,69],{"encoding":2094},[1647,53784,53786],{"className":53785},[2059],[2061,53787,53788],{"xmlns":2063},[2065,53789,53790,53796],{},[2068,53791,53792,53794],{},[2075,53793,2303],{},[2210,53795,654],{},[2092,53797,52408],{"encoding":2094}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[1647,53800,53802],{"className":53801},[2059],[2061,53803,53804],{"xmlns":2063},[2065,53805,53806,53816],{},[2068,53807,53808],{},[9252,53809,53810,53812,53814],{},[2071,53811,575],{},[2210,53813,638],{},[2071,53815,554],{},[2092,53817,52153],{"encoding":2094},[92,53819,53820,53821,52363,53838,53851,53852,195],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[1647,53822,53824],{"className":53823},[2059],[2061,53825,53826],{"xmlns":2063},[2065,53827,53828,53836],{},[2068,53829,53830],{},[2205,53831,53832,53834],{},[2071,53833,575],{},[2071,53835,554],{},[2092,53837,45757],{"encoding":2094},[1647,53839,53841],{"className":53840},[2059],[2061,53842,53843],{"xmlns":2063},[2065,53844,53845,53849],{},[2068,53846,53847],{},[2071,53848,69],{},[2092,53850,69],{"encoding":2094}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[1647,53853,53855],{"className":53854},[2059],[2061,53856,53857],{"xmlns":2063},[2065,53858,53859,53869],{},[2068,53860,53861],{},[9252,53862,53863,53865,53867],{},[2071,53864,575],{},[2210,53866,646],{},[2071,53868,554],{},[2092,53870,52214],{"encoding":2094},[92,53872,53873,53874,53082,53891,53904,53905,2758,53918,53655,53933,53946,53947,53960,53961,195],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[1647,53875,53877],{"className":53876},[2059],[2061,53878,53879],{"xmlns":2063},[2065,53880,53881,53889],{},[2068,53882,53883],{},[2205,53884,53885,53887],{},[2071,53886,575],{},[2071,53888,554],{},[2092,53890,45757],{"encoding":2094},[1647,53892,53894],{"className":53893},[2059],[2061,53895,53896],{"xmlns":2063},[2065,53897,53898,53902],{},[2068,53899,53900],{},[2071,53901,69],{},[2092,53903,69],{"encoding":2094}," na 90, poklesu ",[1647,53906,53908],{"className":53907},[2059],[2061,53909,53910],{"xmlns":2063},[2065,53911,53912,53916],{},[2068,53913,53914],{},[2071,53915,2179],{},[2092,53917,2179],{"encoding":2094},[1647,53919,53921],{"className":53920},[2059],[2061,53922,53923],{"xmlns":2063},[2065,53924,53925,53931],{},[2068,53926,53927,53929],{},[2075,53928,2303],{},[2210,53930,654],{},[2092,53932,52408],{"encoding":2094},[1647,53934,53936],{"className":53935},[2059],[2061,53937,53938],{"xmlns":2063},[2065,53939,53940,53944],{},[2068,53941,53942],{},[2071,53943,2222],{},[2092,53945,2222],{"encoding":2094}," na 30 a růstu ",[1647,53948,53950],{"className":53949},[2059],[2061,53951,53952],{"xmlns":2063},[2065,53953,53954,53958],{},[2068,53955,53956],{},[2071,53957,2273],{},[2092,53959,2273],{"encoding":2094}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[1647,53962,53964],{"className":53963},[2059],[2061,53965,53966],{"xmlns":2063},[2065,53967,53968,53978],{},[2068,53969,53970],{},[9252,53971,53972,53974,53976],{},[2071,53973,575],{},[2210,53975,654],{},[2071,53977,554],{},[2092,53979,53211],{"encoding":2094},[609,53981,13513],{"id":53982},"přebytek-spotřebitele-a-výrobce-1",[55,53984,53985,51980,53988,52017,54024,195],{},[95,53986,53987],{},"2.17",[1647,53989,53991],{"className":53990},[2059],[2061,53992,53993],{"xmlns":2063},[2065,53994,53995,54021],{},[2068,53996,53997,53999,54001,54003,54005,54007,54009,54011,54013,54015],{},[2071,53998,575],{},[2075,54000,2077],{},[2071,54002,4271],{},[2075,54004,2084],{"stretchy":2083},[2071,54006,2861],{},[2075,54008,2090],{"stretchy":2083},[2075,54010,2077],{},[2210,54012,16773],{},[2075,54014,2303],{},[2205,54016,54017,54019],{},[2071,54018,2861],{},[2210,54020,646],{},[2092,54022,54023],{"encoding":2094},"P = D(Q) = 35 - Q^2",[1647,54025,54027],{"className":54026},[2059],[2061,54028,54029],{"xmlns":2063},[2065,54030,54031,54057],{},[2068,54032,54033,54035,54037,54039,54041,54043,54045,54047,54049,54051],{},[2071,54034,575],{},[2075,54036,2077],{},[2071,54038,532],{},[2075,54040,2084],{"stretchy":2083},[2071,54042,2861],{},[2075,54044,2090],{"stretchy":2083},[2075,54046,2077],{},[2210,54048,654],{},[2075,54050,2176],{},[2205,54052,54053,54055],{},[2071,54054,2861],{},[2210,54056,646],{},[2092,54058,54059],{"encoding":2094},"P = S(Q) = 3 + Q^2",[89,54061,54062,54065],{},[92,54063,54064],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[92,54066,54067],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[55,54069,54070,51980,54073,52017,54107,195],{},[95,54071,54072],{},"2.18",[1647,54074,54076],{"className":54075},[2059],[2061,54077,54078],{"xmlns":2063},[2065,54079,54080,54104],{},[2068,54081,54082,54084,54086,54088,54090,54092,54094,54096,54098,54100,54102],{},[2071,54083,575],{},[2075,54085,2077],{},[2071,54087,4271],{},[2075,54089,2084],{"stretchy":2083},[2071,54091,2861],{},[2075,54093,2090],{"stretchy":2083},[2075,54095,2077],{},[2210,54097,3781],{},[2075,54099,2303],{},[2210,54101,646],{},[2071,54103,2861],{},[2092,54105,54106],{"encoding":2094},"P = D(Q) = 18 - 2Q",[1647,54108,54110],{"className":54109},[2059],[2061,54111,54112],{"xmlns":2063},[2065,54113,54114,54140],{},[2068,54115,54116,54118,54120,54122,54124,54126,54128,54130,54132,54134],{},[2071,54117,575],{},[2075,54119,2077],{},[2071,54121,532],{},[2075,54123,2084],{"stretchy":2083},[2071,54125,2861],{},[2075,54127,2090],{"stretchy":2083},[2075,54129,2077],{},[2210,54131,654],{},[2075,54133,2176],{},[2205,54135,54136,54138],{},[2071,54137,2861],{},[2210,54139,646],{},[2092,54141,54059],{"encoding":2094},[89,54143,54144,54164,54167,54170],{},[92,54145,54146,54147,195],{},"(a) Vypočtěte rovnovážné množství ",[1647,54148,54150],{"className":54149},[2059],[2061,54151,54152],{"xmlns":2063},[2065,54153,54154,54162],{},[2068,54155,54156],{},[2205,54157,54158,54160],{},[2071,54159,2861],{},[2071,54161,554],{},[2092,54163,46694],{"encoding":2094},[92,54165,54166],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[92,54168,54169],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[92,54171,54172],{},"(c) Graficky interpretujte.",[909,54174],{},[84,54176,54178],{"id":54177},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[201,54180,54181,54184,54187,54190,54193,54196,54199,54202,54205,54208,54211,54214,54217,54220],{},[92,54182,54183],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[92,54185,54186],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[92,54188,54189],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[92,54191,54192],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[92,54194,54195],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[92,54197,54198],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[92,54200,54201],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[92,54203,54204],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[92,54206,54207],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[92,54209,54210],{},"K čemu slouží multiplikátory?",[92,54212,54213],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[92,54215,54216],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[92,54218,54219],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[92,54221,54222],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[909,54224],{},[84,54226,321],{"id":320},[55,54228,54229],{},[95,54230,14896],{},[89,54232,54233,54268,54273,54303,54308,54371,54397,54402,54432,54441,54448,54454],{},[92,54234,54235,11156,54238,21387,54241,1445,54243,835,54266],{},[95,54236,54237],{},"Poptávané množství",[3982,54239,54240],{},"quantity demanded",[95,54242,31029],{},[1647,54244,54246],{"className":54245},[2059],[2061,54247,54248],{"xmlns":2063},[2065,54249,54250,54264],{},[2068,54251,54252,54254,54256,54258,54260,54262],{},[2071,54253,2861],{},[2075,54255,2077],{},[2071,54257,4271],{},[2075,54259,2084],{"stretchy":2083},[2071,54261,575],{},[2075,54263,2090],{"stretchy":2083},[2092,54265,4280],{"encoding":2094},[95,54267,41740],{},[92,54269,54270,54272],{},[95,54271,41747],{}," — substituční + důchodový efekt",[92,54274,54275,1445,54278],{},[95,54276,54277],{},"Reálné cenové rozpětí",[1647,54279,54281],{"className":54280},[2059],[2061,54282,54283],{"xmlns":2063},[2065,54284,54285,54301],{},[2068,54286,54287,54289,54291,54293,54299],{},[2075,54288,2084],{"stretchy":2083},[2210,54290,630],{},[2075,54292,2361],{"separator":2360},[2348,54294,54295,54297],{},[2071,54296,575],{},[2210,54298,630],{},[2075,54300,2090],{"stretchy":2083},[2092,54302,41948],{"encoding":2094},[92,54304,54305,12231],{},[95,54306,54307],{},"Homogenita poptávky",[92,54309,54310,1445,54313,835,54336,835,54353,54370],{},[95,54311,54312],{},"Lineární poptávka",[1647,54314,54316],{"className":54315},[2059],[2061,54317,54318],{"xmlns":2063},[2065,54319,54320,54334],{},[2068,54321,54322,54324,54326,54328,54330,54332],{},[2071,54323,575],{},[2075,54325,2077],{},[2071,54327,69],{},[2071,54329,2861],{},[2075,54331,2176],{},[2071,54333,2179],{},[2092,54335,41352],{"encoding":2094},[1647,54337,54339],{"className":54338},[2059],[2061,54340,54341],{"xmlns":2063},[2065,54342,54343,54351],{},[2068,54344,54345,54347,54349],{},[2071,54346,69],{},[2075,54348,3521],{},[2210,54350,630],{},[2092,54352,47379],{"encoding":2094},[1647,54354,54356],{"className":54355},[2059],[2061,54357,54358],{"xmlns":2063},[2065,54359,54360,54368],{},[2068,54361,54362,54364,54366],{},[2071,54363,2179],{},[2075,54365,3482],{},[2210,54367,630],{},[2092,54369,21553],{"encoding":2094}," — nedokonalá konkurence",[92,54372,54373,7102,54376],{},[95,54374,54375],{},"Dokonalá konkurence",[1647,54377,54379],{"className":54378},[2059],[2061,54380,54381],{"xmlns":2063},[2065,54382,54383,54395],{},[2068,54384,54385,54387,54389],{},[2071,54386,575],{},[2075,54388,2077],{},[2205,54390,54391,54393],{},[2071,54392,575],{},[2075,54394,4441],{},[2092,54396,4444],{"encoding":2094},[92,54398,54399,54401],{},[95,54400,42517],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[92,54403,54404,1445,54406,835,54430],{},[95,54405,34753],{},[1647,54407,54409],{"className":54408},[2059],[2061,54410,54411],{"xmlns":2063},[2065,54412,54413,54427],{},[2068,54414,54415,54417,54419,54421,54423,54425],{},[2071,54416,2861],{},[2075,54418,2077],{},[2071,54420,554],{},[2075,54422,2084],{"stretchy":2083},[2071,54424,9214],{},[2075,54426,2090],{"stretchy":2083},[2092,54428,54429],{"encoding":2094},"Q = E(Y)",[95,54431,42714],{},[92,54433,54434,54437,54438,54440],{},[95,54435,54436],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[95,54439,43160],{}," zboží",[92,54442,54443,75,54445,54447],{},[95,54444,44166],{},[95,54446,44113],{}," — znaménka zkřížených koeficientů",[92,54449,54450,54453],{},[95,54451,54452],{},"Dvoukomoditní trh"," (2.6)",[92,54455,54456,11156,54459,2090],{},[95,54457,54458],{},"Posun poptávky",[3982,54460,43218],{},[55,54462,54463],{},[95,54464,14860],{},[89,54466,54467,54500,54504,54549],{},[92,54468,54469,11156,54471,21387,54473,1445,54475,835,54498],{},[95,54470,44560],{},[3982,54472,44563],{},[95,54474,44734],{},[1647,54476,54478],{"className":54477},[2059],[2061,54479,54480],{"xmlns":2063},[2065,54481,54482,54496],{},[2068,54483,54484,54486,54488,54490,54492,54494],{},[2071,54485,2861],{},[2075,54487,2077],{},[2071,54489,532],{},[2075,54491,2084],{"stretchy":2083},[2071,54493,575],{},[2075,54495,2090],{"stretchy":2083},[2092,54497,8768],{"encoding":2094},[95,54499,44812],{},[92,54501,54502],{},[95,54503,44819],{},[92,54505,54506,1445,54509,835,54532],{},[95,54507,54508],{},"Lineární nabídka",[1647,54510,54512],{"className":54511},[2059],[2061,54513,54514],{"xmlns":2063},[2065,54515,54516,54530],{},[2068,54517,54518,54520,54522,54524,54526,54528],{},[2071,54519,575],{},[2075,54521,2077],{},[2071,54523,2222],{},[2071,54525,2861],{},[2075,54527,2176],{},[2071,54529,2273],{},[2092,54531,44533],{"encoding":2094},[1647,54533,54535],{"className":54534},[2059],[2061,54536,54537],{"xmlns":2063},[2065,54538,54539,54547],{},[2068,54540,54541,54543,54545],{},[2071,54542,2222],{},[2075,54544,3482],{},[2210,54546,630],{},[2092,54548,44551],{"encoding":2094},[92,54550,54551,11156,54554,2090],{},[95,54552,54553],{},"Posun nabídky",[3982,54555,45197],{},[55,54557,54558],{},[95,54559,54560],{},"Rovnováha a komparativní statika",[89,54562,54563,54642,54648],{},[92,54564,54565,11156,54567,21387,54569,1445,54572,835,54589,1445,54592,835,54609,1445,54611],{},[95,54566,45616],{},[3982,54568,45735],{},[95,54570,54571],{},"rovnovážná cena",[1647,54573,54575],{"className":54574},[2059],[2061,54576,54577],{"xmlns":2063},[2065,54578,54579,54587],{},[2068,54580,54581],{},[2205,54582,54583,54585],{},[2071,54584,575],{},[2071,54586,554],{},[2092,54588,45757],{"encoding":2094},[95,54590,54591],{},"rovnovážné množství",[1647,54593,54595],{"className":54594},[2059],[2061,54596,54597],{"xmlns":2063},[2065,54598,54599,54607],{},[2068,54600,54601],{},[2205,54602,54603,54605],{},[2071,54604,2861],{},[2071,54606,554],{},[2092,54608,46694],{"encoding":2094},[95,54610,45793],{},[1647,54612,54614],{"className":54613},[2059],[2061,54615,54616],{"xmlns":2063},[2065,54617,54618,54640],{},[2068,54619,54620,54622,54624,54630,54632,54638],{},[2071,54621,554],{},[2075,54623,2561],{"stretchy":2083},[2205,54625,54626,54628],{},[2071,54627,2861],{},[2071,54629,554],{},[2075,54631,2361],{"separator":2360},[2205,54633,54634,54636],{},[2071,54635,575],{},[2071,54637,554],{},[2075,54639,2576],{"stretchy":2083},[2092,54641,45658],{"encoding":2094},[92,54643,54644,54647],{},[95,54645,54646],{},"Pravidla 1–4"," komparativní statiky",[92,54649,54650,11156,54653,2090],{},[95,54651,54652],{},"Teorém pavučiny",[3982,54654,46640],{},[55,54656,54657],{},[95,54658,54659],{},"Zdanění",[89,54661,54662,54718,54766],{},[92,54663,54664,54666,54667,54692,54693,2090],{},[95,54665,54659],{}," — daň výrobci (",[1647,54668,54670],{"className":54669},[2059],[2061,54671,54672],{"xmlns":2063},[2065,54673,54674,54690],{},[2068,54675,54676,54682,54684,54686,54688],{},[2348,54677,54678,54680],{},[2071,54679,532],{},[2210,54681,638],{},[2075,54683,2077],{},[2071,54685,532],{},[2075,54687,2176],{},[2071,54689,543],{},[2092,54691,47048],{"encoding":2094},") vs. daň spotřebiteli (",[1647,54694,54696],{"className":54695},[2059],[2061,54697,54698],{"xmlns":2063},[2065,54699,54700,54716],{},[2068,54701,54702,54708,54710,54712,54714],{},[2348,54703,54704,54706],{},[2071,54705,4271],{},[2210,54707,646],{},[2075,54709,2077],{},[2071,54711,4271],{},[2075,54713,2303],{},[2071,54715,543],{},[2092,54717,47079],{"encoding":2094},[92,54719,54720,1445,54722,835,54743],{},[95,54721,46950],{},[1647,54723,54725],{"className":54724},[2059],[2061,54726,54727],{"xmlns":2063},[2065,54728,54729,54741],{},[2068,54730,54731],{},[2348,54732,54733,54735],{},[2071,54734,543],{},[2068,54736,54737,54739],{},[2071,54738,46969],{},[2071,54740,55],{},[2092,54742,46974],{"encoding":2094},[1647,54744,54746],{"className":54745},[2059],[2061,54747,54748],{"xmlns":2063},[2065,54749,54750,54764],{},[2068,54751,54752],{},[2348,54753,54754,54756],{},[2071,54755,543],{},[2068,54757,54758,54760,54762],{},[2071,54759,46992],{},[2071,54761,2073],{},[2071,54763,13774],{},[2092,54765,46999],{"encoding":2094},[92,54767,54768,1445,54771,835,54800],{},[95,54769,54770],{},"Ekvivalence zdanění",[1647,54772,54774],{"className":54773},[2059],[2061,54775,54776],{"xmlns":2063},[2065,54777,54778,54798],{},[2068,54779,54780,54788,54790],{},[9252,54781,54782,54784,54786],{},[2071,54783,2861],{},[2210,54785,638],{},[2071,54787,554],{},[2075,54789,2077],{},[9252,54791,54792,54794,54796],{},[2071,54793,2861],{},[2210,54795,646],{},[2071,54797,554],{},[2092,54799,47202],{"encoding":2094},[1647,54801,54803],{"className":54802},[2059],[2061,54804,54805],{"xmlns":2063},[2065,54806,54807,54831],{},[2068,54808,54809,54817,54819,54821,54823],{},[9252,54810,54811,54813,54815],{},[2071,54812,575],{},[2210,54814,638],{},[2071,54816,554],{},[2075,54818,2303],{},[2071,54820,543],{},[2075,54822,2077],{},[9252,54824,54825,54827,54829],{},[2071,54826,575],{},[2210,54828,646],{},[2071,54830,554],{},[2092,54832,47236],{"encoding":2094},[55,54834,54835],{},[95,54836,29149],{},[89,54838,54839,54885,54915,54920,54926,54933],{},[92,54840,54841,1445,54843],{},[95,54842,47335],{},[1647,54844,54846],{"className":54845},[2059],[2061,54847,54848],{"xmlns":2063},[2065,54849,54850,54882],{},[2068,54851,54852,54858,54860,54862,54864,54866,54868,54870,54872,54874,54876,54878,54880],{},[2205,54853,54854,54856],{},[2071,54855,2861],{},[2071,54857,554],{},[2075,54859,2077],{},[2075,54861,2084],{"stretchy":2083},[2071,54863,2179],{},[2075,54865,2303],{},[2071,54867,2273],{},[2075,54869,2090],{"stretchy":2083},[2071,54871,4761],{"mathvariant":2450},[2075,54873,2084],{"stretchy":2083},[2071,54875,2222],{},[2075,54877,2303],{},[2071,54879,69],{},[2075,54881,2090],{"stretchy":2083},[2092,54883,54884],{"encoding":2094},"Q^E = (b - d)\u002F(c - a)",[92,54886,54887,1445,54889,54914],{},[95,54888,12610],{},[1647,54890,54892],{"className":54891},[2059],[2061,54893,54894],{"xmlns":2063},[2065,54895,54896,54912],{},[2068,54897,54898,54900,54902,54904,54906,54908,54910],{},[2071,54899,69],{},[2075,54901,2361],{"separator":2360},[2071,54903,2179],{},[2075,54905,2361],{"separator":2360},[2071,54907,2222],{},[2075,54909,2361],{"separator":2360},[2071,54911,2273],{},[2092,54913,47579],{"encoding":2094}," — exogenní proměnné",[92,54916,54917],{},[95,54918,54919],{},"Endogenní \u002F exogenní proměnná",[92,54921,54922,54925],{},[95,54923,54924],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[92,54927,54928,835,54931],{},[95,54929,54930],{},"Komparativní statika",[95,54932,41253],{},[92,54934,54935,1445,54937,54953],{},[95,54936,3029],{},[1647,54938,54940],{"className":54939},[2059],[2061,54941,54942],{"xmlns":2063},[2065,54943,54944,54950],{},[2068,54945,54946,54948],{},[2071,54947,2273],{},[2071,54949,2861],{},[2092,54951,54952],{"encoding":2094},"dQ"," (2.11)",[55,54955,54956],{},[95,54957,54958],{},"Přebytky a ostatní",[89,54960,54961,54999],{},[92,54962,54963,1445,54965,54980,54981,1445,54983,54998],{},[95,54964,49228],{},[1647,54966,54968],{"className":54967},[2059],[2061,54969,54970],{"xmlns":2063},[2065,54971,54972,54978],{},[2068,54973,54974,54976],{},[2071,54975,2849],{},[2071,54977,532],{},[2092,54979,49244],{"encoding":2094}," (2.14), ",[95,54982,49247],{},[1647,54984,54986],{"className":54985},[2059],[2061,54987,54988],{"xmlns":2063},[2065,54989,54990,54996],{},[2068,54991,54992,54994],{},[2071,54993,575],{},[2071,54995,532],{},[2092,54997,49263],{"encoding":2094}," (2.15)",[92,55000,55001,835,55004,55007],{},[95,55002,55003],{},"Homo economicus",[95,55005,55006],{},"Marshallova formulace"," (1890)",[909,55009],{},[84,55011,3866],{"id":3865},[89,55013,55014,55049,55060],{},[92,55015,55016,1445,55019,55022,55023,835,55026,55029,55030,55033,55034,55037,55038,55041,55042,55045,55046],{},[95,55017,55018],{},"Související témata:",[69,55020,46913],{"className":55021,"dataFsResolvedFilePath":47013,"href":47014},[62]," (dopady daně, daňové břemeno, ekvivalence), ",[69,55024,13513],{"className":55025,"dataFsResolvedFilePath":49268,"href":49269},[62],[69,55027,2431],{"className":55028,"dataFsResolvedFilePath":4005,"href":4006},[62]," (zákon klesající\u002Frostoucí, monotonie), ",[69,55031,3890],{"className":55032,"dataFsResolvedFilePath":3888,"href":3889},[62]," (CS a PS), ",[69,55035,3901],{"className":55036,"dataFsResolvedFilePath":3899,"href":3900},[62]," (vícefaktorové modely, multiplikátory), ",[69,55039,12195],{"className":55040,"dataFsResolvedFilePath":12193,"href":12194},[62]," (optimalizace spotřebitele), ",[69,55043,3913],{"className":55044,"dataFsResolvedFilePath":3911,"href":3912},[62]," (důchodová a cenová citlivost), ",[69,55047,3906],{"className":55048,"dataFsResolvedFilePath":3022,"href":3023},[62],[92,55050,55051,1445,55054],{},[95,55052,55053],{},"Shrnutí přednášek:",[69,55055,55059],{"className":55056,"dataFsResolvedFilePath":55057,"href":55058},[62],"summaries\u002Fimek-blok-01.md","\u002Fwiki\u002Fimek-blok-01","KS — 1. blok",[92,55061,55062,1445,55064],{},[95,55063,17937],{},[69,55065,17941],{"className":55066,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":55068},[55069,55070,55078,55084,55091,55092,55099,55100,55101,55108,55109,55110],{"id":41087,"depth":7,"text":41088},{"id":41068,"depth":7,"text":14896,"children":55071},[55072,55073,55074,55075,55077],{"id":41355,"depth":4,"text":41356},{"id":41637,"depth":4,"text":41638},{"id":42646,"depth":4,"text":42647},{"id":43214,"depth":4,"text":55076},"Posun poptávky (shift of demand)",{"id":43718,"depth":4,"text":43719},{"id":41072,"depth":7,"text":14860,"children":55079},[55080,55081,55082],{"id":44555,"depth":4,"text":41356},{"id":44741,"depth":4,"text":44742},{"id":45193,"depth":4,"text":55083},"Posun nabídky (shift of supply)",{"id":45615,"depth":7,"text":45616,"children":55085},[55086,55087,55088,55089,55090],{"id":45727,"depth":4,"text":45728},{"id":45940,"depth":4,"text":45941},{"id":46258,"depth":4,"text":46259},{"id":46612,"depth":4,"text":46613},{"id":46643,"depth":4,"text":46644},{"id":46912,"depth":7,"text":46913},{"id":47316,"depth":7,"text":47317,"children":55093},[55094,55095,55096,55097],{"id":47334,"depth":4,"text":47335},{"id":47715,"depth":4,"text":47716},{"id":48099,"depth":4,"text":48100},{"id":48553,"depth":4,"text":55098},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":13512,"depth":7,"text":13513},{"id":49480,"depth":7,"text":49481},{"id":49711,"depth":7,"text":49712,"children":55102},[55103,55104,55105,55106,55107],{"id":49715,"depth":4,"text":49716},{"id":50555,"depth":4,"text":50556},{"id":50931,"depth":4,"text":45616},{"id":52226,"depth":4,"text":47317},{"id":53982,"depth":4,"text":13513},{"id":54177,"depth":7,"text":54178},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":41053,"description":156},[9647,3938],"topics\u002Fpoptavka-nabidka",[17,55117,55118,55119,20622,55120,55121],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":55124,"title":13513,"body":55125,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":59405,"navigation":168,"path":59406,"seo":59407,"sources":59408,"stem":59409,"tags":59410,"type":177,"updated":178,"__hash__":59415},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":48,"value":55126,"toc":59383},[55127,55129,55197,55247,55249,55253,55511,55587,55592,55594,55613,55617,55693,55778,55780,56094,56187,56189,56208,56212,56286,56371,56374,56550,56555,56557,56977,56979,56983,56987,57223,57267,57367,57433,57436,57469,57645,57707,57837,57915,58026,58060,58258,58277,58296,58361,58365,58368,58413,58416,58534,58580,58582,58586,58934,58936,58938,59216,59218,59222,59257,59264,59337,59339,59341],[51,55128,13513],{"id":13512},[1023,55130,55131],{},[55,55132,55133,3960,55135,11156,55137,55152,55153,11156,55155,55170,55171,55193,55194,195],{},[1647,55134,3959],{},[95,55136,49228],{},[1647,55138,55140],{"className":55139},[2059],[2061,55141,55142],{"xmlns":2063},[2065,55143,55144,55150],{},[2068,55145,55146,55148],{},[2071,55147,2849],{},[2071,55149,532],{},[2092,55151,49244],{"encoding":2094},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[95,55154,49377],{},[1647,55156,55158],{"className":55157},[2059],[2061,55159,55160],{"xmlns":2063},[2065,55161,55162,55168],{},[2068,55163,55164,55166],{},[2071,55165,575],{},[2071,55167,532],{},[2092,55169,49263],{"encoding":2094},") je rozdíl mezi tím, co výrobce dostal, a minimální cenou, za kterou by byl ochoten prodávat. Geometricky jsou to plochy mezi křivkou poptávky \u002F nabídky a rovnovážnou cenou; početně určité integrály. Součet ",[1647,55172,55174],{"className":55173},[2059],[2061,55175,55176],{"xmlns":2063},[2065,55177,55178,55190],{},[2068,55179,55180,55182,55184,55186,55188],{},[2071,55181,2849],{},[2071,55183,532],{},[2075,55185,2176],{},[2071,55187,575],{},[2071,55189,532],{},[2092,55191,55192],{"encoding":2094},"CS + PS"," měří ",[95,55195,55196],{},"celkový blahobyt trhu",[55,55198,55199,11156,55201,835,55203,13861,55218,11156,55220,835,55222,55237,55238,55242,55243,195],{},[95,55200,49228],{},[3982,55202,49284],{},[1647,55204,55206],{"className":55205},[2059],[2061,55207,55208],{"xmlns":2063},[2065,55209,55210,55216],{},[2068,55211,55212,55214],{},[2071,55213,2849],{},[2071,55215,532],{},[2092,55217,49244],{"encoding":2094},[95,55219,49247],{},[3982,55221,49380],{},[1647,55223,55225],{"className":55224},[2059],[2061,55226,55227],{"xmlns":2063},[2065,55228,55229,55235],{},[2068,55230,55231,55233],{},[2071,55232,575],{},[2071,55234,532],{},[2092,55236,49263],{"encoding":2094},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[69,55239,55241],{"className":55240,"dataFsResolvedFilePath":13670,"href":13671},[62],"tržní rovnováhy"," a využívají aparát ",[69,55244,55246],{"className":55245,"dataFsResolvedFilePath":3888,"href":3889},[62],"integrálního počtu",[909,55248],{},[84,55250,55252],{"id":55251},"úvod","Úvod",[55,55254,55255,55256,55279,55280,55303,55304,55321,55322,3997,55354,55386,55387,55413,55414,55417,55418,55421,55422,15746,55456,24333,55477,195],{},"Je dána funkce poptávky ",[1647,55257,55259],{"className":55258},[2059],[2061,55260,55261],{"xmlns":2063},[2065,55262,55263,55277],{},[2068,55264,55265,55267,55269,55271,55273,55275],{},[2071,55266,575],{},[2075,55268,2077],{},[2071,55270,4271],{},[2075,55272,2084],{"stretchy":2083},[2071,55274,2861],{},[2075,55276,2090],{"stretchy":2083},[2092,55278,4727],{"encoding":2094},", resp. funkce nabídky ",[1647,55281,55283],{"className":55282},[2059],[2061,55284,55285],{"xmlns":2063},[2065,55286,55287,55301],{},[2068,55288,55289,55291,55293,55295,55297,55299],{},[2071,55290,575],{},[2075,55292,2077],{},[2071,55294,532],{},[2075,55296,2084],{"stretchy":2083},[2071,55298,2861],{},[2075,55300,2090],{"stretchy":2083},[2092,55302,45362],{"encoding":2094},". Pro pevně zadané množství ",[1647,55305,55307],{"className":55306},[2059],[2061,55308,55309],{"xmlns":2063},[2065,55310,55311,55319],{},[2068,55312,55313],{},[2348,55314,55315,55317],{},[2071,55316,2861],{},[2210,55318,630],{},[2092,55320,42599],{"encoding":2094}," je odpovídající cena ",[1647,55323,55325],{"className":55324},[2059],[2061,55326,55327],{"xmlns":2063},[2065,55328,55329,55351],{},[2068,55330,55331,55337,55339,55341,55343,55349],{},[2348,55332,55333,55335],{},[2071,55334,575],{},[2210,55336,630],{},[2075,55338,2077],{},[2071,55340,4271],{},[2075,55342,2084],{"stretchy":2083},[2348,55344,55345,55347],{},[2071,55346,2861],{},[2210,55348,630],{},[2075,55350,2090],{"stretchy":2083},[2092,55352,55353],{"encoding":2094},"P_0 = D(Q_0)",[1647,55355,55357],{"className":55356},[2059],[2061,55358,55359],{"xmlns":2063},[2065,55360,55361,55383],{},[2068,55362,55363,55369,55371,55373,55375,55381],{},[2348,55364,55365,55367],{},[2071,55366,575],{},[2210,55368,630],{},[2075,55370,2077],{},[2071,55372,532],{},[2075,55374,2084],{"stretchy":2083},[2348,55376,55377,55379],{},[2071,55378,2861],{},[2210,55380,630],{},[2075,55382,2090],{"stretchy":2083},[2092,55384,55385],{"encoding":2094},"P_0 = S(Q_0)","). Součin ",[1647,55388,55390],{"className":55389},[2059],[2061,55391,55392],{"xmlns":2063},[2065,55393,55394,55410],{},[2068,55395,55396,55402,55404],{},[2348,55397,55398,55400],{},[2071,55399,575],{},[2210,55401,630],{},[2363,55403,3061],{},[2348,55405,55406,55408],{},[2071,55407,2861],{},[2210,55409,630],{},[2092,55411,55412],{"encoding":2094},"P_0 \\, Q_0"," reprezentuje buď ",[95,55415,55416],{},"výdaje spotřebitele",", nebo ",[95,55419,55420],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[1647,55423,55425],{"className":55424},[2059],[2061,55426,55427],{"xmlns":2063},[2065,55428,55429,55453],{},[2068,55430,55431,55433,55435,55441,55443,55445,55447],{},[2210,55432,630],{},[2363,55434,3061],{},[2348,55436,55437,55439],{},[2071,55438,2861],{},[2210,55440,630],{},[2363,55442,3061],{},[2071,55444,4342],{},[2363,55446,3061],{},[2348,55448,55449,55451],{},[2071,55450,575],{},[2210,55452,630],{},[2092,55454,55455],{"encoding":2094},"0\\,Q_0\\,A\\,P_0",[1647,55457,55459],{"className":55458},[2059],[2061,55460,55461],{"xmlns":2063},[2065,55462,55463,55475],{},[2068,55464,55465,55467,55469,55471,55473],{},[2075,55466,2084],{"stretchy":2083},[2071,55468,2861],{},[2075,55470,2361],{"separator":2360},[2071,55472,575],{},[2075,55474,2090],{"stretchy":2083},[2092,55476,41982],{"encoding":2094},[1647,55478,55480],{"className":55479},[2059],[2061,55481,55482],{"xmlns":2063},[2065,55483,55484,55508],{},[2068,55485,55486,55488,55490,55492,55498,55500,55506],{},[2071,55487,4342],{},[2075,55489,2077],{},[2075,55491,2561],{"stretchy":2083},[2348,55493,55494,55496],{},[2071,55495,2861],{},[2210,55497,630],{},[2075,55499,2361],{"separator":2360},[2348,55501,55502,55504],{},[2071,55503,575],{},[2210,55505,630],{},[2075,55507,2576],{"stretchy":2083},[2092,55509,55510],{"encoding":2094},"A = [Q_0, P_0]",[1023,55512,55513,55518,55576],{},[55,55514,55515,55517],{},[1647,55516,4243],{}," Intuice",[89,55519,55520,55548],{},[92,55521,55522,55523,55526,55527,55529,55530,55547],{},"Za jednotky zboží nakoupené ",[95,55524,55525],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[3982,55528,28008],{}," než ",[1647,55531,55533],{"className":55532},[2059],[2061,55534,55535],{"xmlns":2063},[2065,55536,55537,55545],{},[2068,55538,55539],{},[2348,55540,55541,55543],{},[2071,55542,575],{},[2210,55544,630],{},[2092,55546,43239],{"encoding":2094}," — rozdíl si „šetří do kapsy\" jako přebytek.",[92,55549,55550,55551,55553,55554,55557,55558,55575],{},"Za jednotky zboží prodané ",[95,55552,55525],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[3982,55555,55556],{},"nižší"," cenu než ",[1647,55559,55561],{"className":55560},[2059],[2061,55562,55563],{"xmlns":2063},[2065,55564,55565,55573],{},[2068,55566,55567],{},[2348,55568,55569,55571],{},[2071,55570,575],{},[2210,55572,630],{},[2092,55574,43239],{"encoding":2094}," — rozdíl je jeho přebytek.",[55,55577,55578,55579,55582,55583,55586],{},"Přebytek je tedy rozdíl mezi ",[3982,55580,55581],{},"ochotou"," (platit \u002F prodávat) a ",[3982,55584,55585],{},"skutečností"," (zaplaceno \u002F obdrženo).",[55,55588,55589],{},[58,55590],{"alt":49275,"className":55591,"src":49277},[62,63],[909,55593],{},[84,55595,55597,55598,2090],{"id":55596},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[1647,55599,55601],{"className":55600},[2059],[2061,55602,55603],{"xmlns":2063},[2065,55604,55605,55611],{},[2068,55606,55607,55609],{},[2071,55608,2849],{},[2071,55610,532],{},[2092,55612,49244],{"encoding":2094},[609,55614,55616],{"id":55615},"definice-vzorec-214","Definice (vzorec 2.14)",[55,55618,55619,55620,55643,55644,55661,55662,2777],{},"Pro poptávku ",[1647,55621,55623],{"className":55622},[2059],[2061,55624,55625],{"xmlns":2063},[2065,55626,55627,55641],{},[2068,55628,55629,55631,55633,55635,55637,55639],{},[2071,55630,575],{},[2075,55632,2077],{},[2071,55634,4271],{},[2075,55636,2084],{"stretchy":2083},[2071,55638,2861],{},[2075,55640,2090],{"stretchy":2083},[2092,55642,4727],{"encoding":2094}," a pevně zadané ",[1647,55645,55647],{"className":55646},[2059],[2061,55648,55649],{"xmlns":2063},[2065,55650,55651,55659],{},[2068,55652,55653],{},[2348,55654,55655,55657],{},[2071,55656,2861],{},[2210,55658,630],{},[2092,55660,42599],{"encoding":2094}," s cenou ",[1647,55663,55665],{"className":55664},[2059],[2061,55666,55667],{"xmlns":2063},[2065,55668,55669,55691],{},[2068,55670,55671,55677,55679,55681,55683,55689],{},[2348,55672,55673,55675],{},[2071,55674,575],{},[2210,55676,630],{},[2075,55678,2077],{},[2071,55680,4271],{},[2075,55682,2084],{"stretchy":2083},[2348,55684,55685,55687],{},[2071,55686,2861],{},[2210,55688,630],{},[2075,55690,2090],{"stretchy":2083},[2092,55692,55353],{"encoding":2094},[1647,55694,55696],{"className":55695},[2059],[2061,55697,55698],{"xmlns":2063,"display":31093},[2065,55699,55700,55776],{},[23493,55701,55702],{"width":31098},[23498,55703,55704,55706,55770,55772],{},[23501,55705],{"width":31103},[23501,55707,55708],{},[2068,55709,55710,55712,55714,55716,55722,55724,55726,55738,55740,55742,55744,55746,55748,55750,55752,55754,55760,55762,55768],{},[2071,55711,2849],{},[2071,55713,532],{},[2075,55715,2084],{"stretchy":2083},[2348,55717,55718,55720],{},[2071,55719,2861],{},[2210,55721,630],{},[2075,55723,2090],{"stretchy":2083},[2075,55725,2077],{},[9252,55727,55728,55730,55732],{},[2075,55729,12897],{},[2210,55731,630],{},[2348,55733,55734,55736],{},[2071,55735,2861],{},[2210,55737,630],{},[2071,55739,4271],{},[2075,55741,2084],{"stretchy":2083},[2071,55743,2861],{},[2075,55745,2090],{"stretchy":2083},[2363,55747,3061],{},[2071,55749,2273],{},[2071,55751,2861],{},[2075,55753,2303],{},[2348,55755,55756,55758],{},[2071,55757,575],{},[2210,55759,630],{},[2363,55761,3061],{},[2348,55763,55764,55766],{},[2071,55765,2861],{},[2210,55767,630],{},[2071,55769,195],{"mathvariant":2450},[23501,55771],{"width":31103},[23501,55773,55774],{},[2363,55775,49369],{},[2092,55777,49372],{"encoding":2094},[609,55779,2519],{"id":2518},[89,55781,55782,55874,55936],{},[92,55783,55784,55824,55825,55851,55852,55855,55856,55873],{},[1647,55785,55787],{"className":55786},[2059],[2061,55788,55789],{"xmlns":2063},[2065,55790,55791,55821],{},[2068,55792,55793],{},[2400,55794,55795,55807,55809,55811,55813,55815,55817,55819],{"scriptlevel":630,"displaystyle":2360},[9252,55796,55797,55799,55801],{},[2075,55798,12897],{},[2210,55800,630],{},[2348,55802,55803,55805],{},[2071,55804,2861],{},[2210,55806,630],{},[2071,55808,4271],{},[2075,55810,2084],{"stretchy":2083},[2071,55812,2861],{},[2075,55814,2090],{"stretchy":2083},[2363,55816,3061],{},[2071,55818,2273],{},[2071,55820,2861],{},[2092,55822,55823],{"encoding":2094},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[1647,55826,55828],{"className":55827},[2059],[2061,55829,55830],{"xmlns":2063},[2065,55831,55832,55848],{},[2068,55833,55834,55836,55838,55840,55846],{},[2075,55835,2561],{"stretchy":2083},[2210,55837,630],{},[2075,55839,2361],{"separator":2360},[2348,55841,55842,55844],{},[2071,55843,2861],{},[2210,55845,630],{},[2075,55847,2576],{"stretchy":2083},[2092,55849,55850],{"encoding":2094},"[0, Q_0]","; představuje celkovou ",[95,55853,55854],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[1647,55857,55859],{"className":55858},[2059],[2061,55860,55861],{"xmlns":2063},[2065,55862,55863,55871],{},[2068,55864,55865],{},[2348,55866,55867,55869],{},[2071,55868,2861],{},[2210,55870,630],{},[2092,55872,42599],{"encoding":2094}," jednotek byl ochoten zaplatit).",[92,55875,55876,55902,55903,4007],{},[1647,55877,55879],{"className":55878},[2059],[2061,55880,55881],{"xmlns":2063},[2065,55882,55883,55899],{},[2068,55884,55885,55891,55893],{},[2348,55886,55887,55889],{},[2071,55888,575],{},[2210,55890,630],{},[2363,55892,3061],{},[2348,55894,55895,55897],{},[2071,55896,2861],{},[2210,55898,630],{},[2092,55900,55901],{"encoding":2094},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[1647,55904,55906],{"className":55905},[2059],[2061,55907,55908],{"xmlns":2063},[2065,55909,55910,55934],{},[2068,55911,55912,55914,55916,55922,55924,55926,55928],{},[2210,55913,630],{},[2363,55915,3061],{},[2348,55917,55918,55920],{},[2071,55919,2861],{},[2210,55921,630],{},[2363,55923,3061],{},[2071,55925,4342],{},[2363,55927,3061],{},[2348,55929,55930,55932],{},[2071,55931,575],{},[2210,55933,630],{},[2092,55935,55455],{"encoding":2094},[92,55937,55938,55953,55954,55976,55977,56002,56003,24333,56029,75,56061,195],{},[1647,55939,55941],{"className":55940},[2059],[2061,55942,55943],{"xmlns":2063},[2065,55944,55945,55951],{},[2068,55946,55947,55949],{},[2071,55948,2849],{},[2071,55950,532],{},[2092,55952,49244],{"encoding":2094}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[1647,55955,55957],{"className":55956},[2059],[2061,55958,55959],{"xmlns":2063},[2065,55960,55961,55973],{},[2068,55962,55963,55965,55967],{},[2071,55964,575],{},[2075,55966,2077],{},[2348,55968,55969,55971],{},[2071,55970,575],{},[2210,55972,630],{},[2092,55974,55975],{"encoding":2094},"P = P_0"," v pásu ",[1647,55978,55980],{"className":55979},[2059],[2061,55981,55982],{"xmlns":2063},[2065,55983,55984,56000],{},[2068,55985,55986,55988,55990,55992,55998],{},[2075,55987,2561],{"stretchy":2083},[2210,55989,630],{},[2075,55991,2361],{"separator":2360},[2348,55993,55994,55996],{},[2071,55995,2861],{},[2210,55997,630],{},[2075,55999,2576],{"stretchy":2083},[2092,56001,55850],{"encoding":2094}," — „křivočarý trojúhelník\" ",[1647,56004,56006],{"className":56005},[2059],[2061,56007,56008],{"xmlns":2063},[2065,56009,56010,56026],{},[2068,56011,56012,56018,56020,56022,56024],{},[2348,56013,56014,56016],{},[2071,56015,575],{},[2210,56017,630],{},[2363,56019,3061],{},[2071,56021,25992],{},[2363,56023,3061],{},[2071,56025,4342],{},[2092,56027,56028],{"encoding":2094},"P_0\\,B\\,A",[1647,56030,56032],{"className":56031},[2059],[2061,56033,56034],{"xmlns":2063},[2065,56035,56036,56058],{},[2068,56037,56038,56040,56042,56044,56046,56048,56050,56052,56054,56056],{},[2071,56039,25992],{},[2075,56041,2077],{},[2075,56043,2561],{"stretchy":2083},[2210,56045,630],{},[2075,56047,2361],{"separator":2360},[2071,56049,4271],{},[2075,56051,2084],{"stretchy":2083},[2210,56053,630],{},[2075,56055,2090],{"stretchy":2083},[2075,56057,2576],{"stretchy":2083},[2092,56059,56060],{"encoding":2094},"B = [0, D(0)]",[1647,56062,56064],{"className":56063},[2059],[2061,56065,56066],{"xmlns":2063},[2065,56067,56068,56092],{},[2068,56069,56070,56072,56074,56076,56082,56084,56090],{},[2071,56071,4342],{},[2075,56073,2077],{},[2075,56075,2561],{"stretchy":2083},[2348,56077,56078,56080],{},[2071,56079,2861],{},[2210,56081,630],{},[2075,56083,2361],{"separator":2360},[2348,56085,56086,56088],{},[2071,56087,575],{},[2210,56089,630],{},[2075,56091,2576],{"stretchy":2083},[2092,56093,55510],{"encoding":2094},[55,56095,56096],{},[3982,56097,56098,56099,56112,56113,56146,56147,32169,56172,195],{},"Obrázek 2.24: Křivka poptávky ",[1647,56100,56102],{"className":56101},[2059],[2061,56103,56104],{"xmlns":2063},[2065,56105,56106,56110],{},[2068,56107,56108],{},[2071,56109,4271],{},[2092,56111,4271],{"encoding":2094},", bod ",[1647,56114,56116],{"className":56115},[2059],[2061,56117,56118],{"xmlns":2063},[2065,56119,56120,56144],{},[2068,56121,56122,56124,56126,56128,56134,56136,56142],{},[2071,56123,4342],{},[2075,56125,2077],{},[2075,56127,2561],{"stretchy":2083},[2348,56129,56130,56132],{},[2071,56131,2861],{},[2210,56133,630],{},[2075,56135,2361],{"separator":2360},[2348,56137,56138,56140],{},[2071,56139,575],{},[2210,56141,630],{},[2075,56143,2576],{"stretchy":2083},[2092,56145,55510],{"encoding":2094},", vyšrafovaná plocha trojúhelníku ",[1647,56148,56150],{"className":56149},[2059],[2061,56151,56152],{"xmlns":2063},[2065,56153,56154,56170],{},[2068,56155,56156,56162,56164,56166,56168],{},[2348,56157,56158,56160],{},[2071,56159,575],{},[2210,56161,630],{},[2363,56163,3061],{},[2071,56165,25992],{},[2363,56167,3061],{},[2071,56169,4342],{},[2092,56171,56028],{"encoding":2094},[1647,56173,56175],{"className":56174},[2059],[2061,56176,56177],{"xmlns":2063},[2065,56178,56179,56185],{},[2068,56180,56181,56183],{},[2071,56182,2849],{},[2071,56184,532],{},[2092,56186,49244],{"encoding":2094},[909,56188],{},[84,56190,56192,56193,2090],{"id":56191},"přebytek-výrobce-psps","Přebytek výrobce (",[1647,56194,56196],{"className":56195},[2059],[2061,56197,56198],{"xmlns":2063},[2065,56199,56200,56206],{},[2068,56201,56202,56204],{},[2071,56203,575],{},[2071,56205,532],{},[2092,56207,49263],{"encoding":2094},[609,56209,56211],{"id":56210},"definice-vzorec-215","Definice (vzorec 2.15)",[55,56213,56214,56215,55643,56238,55661,56255,2777],{},"Analogicky — pro nabídku ",[1647,56216,56218],{"className":56217},[2059],[2061,56219,56220],{"xmlns":2063},[2065,56221,56222,56236],{},[2068,56223,56224,56226,56228,56230,56232,56234],{},[2071,56225,575],{},[2075,56227,2077],{},[2071,56229,532],{},[2075,56231,2084],{"stretchy":2083},[2071,56233,2861],{},[2075,56235,2090],{"stretchy":2083},[2092,56237,45362],{"encoding":2094},[1647,56239,56241],{"className":56240},[2059],[2061,56242,56243],{"xmlns":2063},[2065,56244,56245,56253],{},[2068,56246,56247],{},[2348,56248,56249,56251],{},[2071,56250,2861],{},[2210,56252,630],{},[2092,56254,42599],{"encoding":2094},[1647,56256,56258],{"className":56257},[2059],[2061,56259,56260],{"xmlns":2063},[2065,56261,56262,56284],{},[2068,56263,56264,56270,56272,56274,56276,56282],{},[2348,56265,56266,56268],{},[2071,56267,575],{},[2210,56269,630],{},[2075,56271,2077],{},[2071,56273,532],{},[2075,56275,2084],{"stretchy":2083},[2348,56277,56278,56280],{},[2071,56279,2861],{},[2210,56281,630],{},[2075,56283,2090],{"stretchy":2083},[2092,56285,55385],{"encoding":2094},[1647,56287,56289],{"className":56288},[2059],[2061,56290,56291],{"xmlns":2063,"display":31093},[2065,56292,56293,56369],{},[23493,56294,56295],{"width":31098},[23498,56296,56297,56299,56363,56365],{},[23501,56298],{"width":31103},[23501,56300,56301],{},[2068,56302,56303,56305,56307,56309,56315,56317,56319,56325,56327,56333,56335,56347,56349,56351,56353,56355,56357,56359,56361],{},[2071,56304,575],{},[2071,56306,532],{},[2075,56308,2084],{"stretchy":2083},[2348,56310,56311,56313],{},[2071,56312,2861],{},[2210,56314,630],{},[2075,56316,2090],{"stretchy":2083},[2075,56318,2077],{},[2348,56320,56321,56323],{},[2071,56322,575],{},[2210,56324,630],{},[2363,56326,3061],{},[2348,56328,56329,56331],{},[2071,56330,2861],{},[2210,56332,630],{},[2075,56334,2303],{},[9252,56336,56337,56339,56341],{},[2075,56338,12897],{},[2210,56340,630],{},[2348,56342,56343,56345],{},[2071,56344,2861],{},[2210,56346,630],{},[2071,56348,532],{},[2075,56350,2084],{"stretchy":2083},[2071,56352,2861],{},[2075,56354,2090],{"stretchy":2083},[2363,56356,3061],{},[2071,56358,2273],{},[2071,56360,2861],{},[2071,56362,195],{"mathvariant":2450},[23501,56364],{"width":31103},[23501,56366,56367],{},[2363,56368,49465],{},[2092,56370,49468],{"encoding":2094},[609,56372,2519],{"id":56373},"geometrická-interpretace-1",[89,56375,56376,56424,56485],{},[92,56377,56378,7102,56403,56406,56407,195],{},[1647,56379,56381],{"className":56380},[2059],[2061,56382,56383],{"xmlns":2063},[2065,56384,56385,56401],{},[2068,56386,56387,56393,56395],{},[2348,56388,56389,56391],{},[2071,56390,575],{},[2210,56392,630],{},[2363,56394,3061],{},[2348,56396,56397,56399],{},[2071,56398,2861],{},[2210,56400,630],{},[2092,56402,55901],{"encoding":2094},[95,56404,56405],{},"tržba"," výrobce za prodané množství ",[1647,56408,56410],{"className":56409},[2059],[2061,56411,56412],{"xmlns":2063},[2065,56413,56414,56422],{},[2068,56415,56416],{},[2348,56417,56418,56420],{},[2071,56419,2861],{},[2210,56421,630],{},[2092,56423,42599],{"encoding":2094},[92,56425,56426,56466,56467,56484],{},[1647,56427,56429],{"className":56428},[2059],[2061,56430,56431],{"xmlns":2063},[2065,56432,56433,56463],{},[2068,56434,56435],{},[2400,56436,56437,56449,56451,56453,56455,56457,56459,56461],{"scriptlevel":630,"displaystyle":2360},[9252,56438,56439,56441,56443],{},[2075,56440,12897],{},[2210,56442,630],{},[2348,56444,56445,56447],{},[2071,56446,2861],{},[2210,56448,630],{},[2071,56450,532],{},[2075,56452,2084],{"stretchy":2083},[2071,56454,2861],{},[2075,56456,2090],{"stretchy":2083},[2363,56458,3061],{},[2071,56460,2273],{},[2071,56462,2861],{},[2092,56464,56465],{"encoding":2094},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[1647,56468,56470],{"className":56469},[2059],[2061,56471,56472],{"xmlns":2063},[2065,56473,56474,56482],{},[2068,56475,56476],{},[2348,56477,56478,56480],{},[2071,56479,2861],{},[2210,56481,630],{},[2092,56483,42599],{"encoding":2094}," jednotek dodat (souvisí s mezními náklady).",[92,56486,56487,56502,56503,56524,56525,195],{},[1647,56488,56490],{"className":56489},[2059],[2061,56491,56492],{"xmlns":2063},[2065,56493,56494,56500],{},[2068,56495,56496,56498],{},[2071,56497,575],{},[2071,56499,532],{},[2092,56501,49263],{"encoding":2094}," je plocha mezi vodorovnou přímkou ",[1647,56504,56506],{"className":56505},[2059],[2061,56507,56508],{"xmlns":2063},[2065,56509,56510,56522],{},[2068,56511,56512,56514,56516],{},[2071,56513,575],{},[2075,56515,2077],{},[2348,56517,56518,56520],{},[2071,56519,575],{},[2210,56521,630],{},[2092,56523,55975],{"encoding":2094}," a křivkou nabídky v pásu ",[1647,56526,56528],{"className":56527},[2059],[2061,56529,56530],{"xmlns":2063},[2065,56531,56532,56548],{},[2068,56533,56534,56536,56538,56540,56546],{},[2075,56535,2561],{"stretchy":2083},[2210,56537,630],{},[2075,56539,2361],{"separator":2360},[2348,56541,56542,56544],{},[2071,56543,2861],{},[2210,56545,630],{},[2075,56547,2576],{"stretchy":2083},[2092,56549,55850],{"encoding":2094},[55,56551,56552],{},[3982,56553,56554],{},"Obrázek 2.25: Přebytek výrobce (plocha mezi rovnovážnou cenou a křivkou nabídky) a přebytek spotřebitele (plocha mezi křivkou poptávky a rovnovážnou cenou) v rovnovážném bodě.",[909,56556],{},[1023,56558,56559,56564],{},[55,56560,56561,56563],{},[1647,56562,4659],{}," Postup výpočtu CS a PS",[201,56565,56566,56697,56807,56836,56970],{},[92,56567,56568,56569,56586,56587,56618,56619,56650,56651,195],{},"Zjisti (nebo si zvol) množství ",[1647,56570,56572],{"className":56571},[2059],[2061,56573,56574],{"xmlns":2063},[2065,56575,56576,56584],{},[2068,56577,56578],{},[2348,56579,56580,56582],{},[2071,56581,2861],{},[2210,56583,630],{},[2092,56585,42599],{"encoding":2094}," a odpovídající cenu ",[1647,56588,56590],{"className":56589},[2059],[2061,56591,56592],{"xmlns":2063},[2065,56593,56594,56616],{},[2068,56595,56596,56602,56604,56606,56608,56614],{},[2348,56597,56598,56600],{},[2071,56599,575],{},[2210,56601,630],{},[2075,56603,2077],{},[2071,56605,4271],{},[2075,56607,2084],{"stretchy":2083},[2348,56609,56610,56612],{},[2071,56611,2861],{},[2210,56613,630],{},[2075,56615,2090],{"stretchy":2083},[2092,56617,55353],{"encoding":2094}," resp. ",[1647,56620,56622],{"className":56621},[2059],[2061,56623,56624],{"xmlns":2063},[2065,56625,56626,56648],{},[2068,56627,56628,56634,56636,56638,56640,56646],{},[2348,56629,56630,56632],{},[2071,56631,575],{},[2210,56633,630],{},[2075,56635,2077],{},[2071,56637,532],{},[2075,56639,2084],{"stretchy":2083},[2348,56641,56642,56644],{},[2071,56643,2861],{},[2210,56645,630],{},[2075,56647,2090],{"stretchy":2083},[2092,56649,55385],{"encoding":2094},". V rovnováze platí ",[1647,56652,56654],{"className":56653},[2059],[2061,56655,56656],{"xmlns":2063},[2065,56657,56658,56694],{},[2068,56659,56660,56662,56664,56670,56672,56674,56676,56678,56684,56686,56688],{},[2071,56661,4271],{},[2075,56663,2084],{"stretchy":2083},[2205,56665,56666,56668],{},[2071,56667,2861],{},[2071,56669,554],{},[2075,56671,2090],{"stretchy":2083},[2075,56673,2077],{},[2071,56675,532],{},[2075,56677,2084],{"stretchy":2083},[2205,56679,56680,56682],{},[2071,56681,2861],{},[2071,56683,554],{},[2075,56685,2090],{"stretchy":2083},[2075,56687,2077],{},[2205,56689,56690,56692],{},[2071,56691,575],{},[2071,56693,554],{},[2092,56695,56696],{"encoding":2094},"D(Q^E) = S(Q^E) = P^E",[92,56698,56699,56700,22865,56738,56753,56754,22865,56792,4007],{},"Spočti určitý integrál ",[1647,56701,56703],{"className":56702},[2059],[2061,56704,56705],{"xmlns":2063},[2065,56706,56707,56735],{},[2068,56708,56709,56721,56723,56725,56727,56729,56731,56733],{},[9252,56710,56711,56713,56715],{},[2075,56712,12897],{},[2210,56714,630],{},[2348,56716,56717,56719],{},[2071,56718,2861],{},[2210,56720,630],{},[2071,56722,4271],{},[2075,56724,2084],{"stretchy":2083},[2071,56726,2861],{},[2075,56728,2090],{"stretchy":2083},[2363,56730,3061],{},[2071,56732,2273],{},[2071,56734,2861],{},[2092,56736,56737],{"encoding":2094},"\\int_0^{Q_0} D(Q)\\,dQ",[1647,56739,56741],{"className":56740},[2059],[2061,56742,56743],{"xmlns":2063},[2065,56744,56745,56751],{},[2068,56746,56747,56749],{},[2071,56748,2849],{},[2071,56750,532],{},[2092,56752,49244],{"encoding":2094},") nebo ",[1647,56755,56757],{"className":56756},[2059],[2061,56758,56759],{"xmlns":2063},[2065,56760,56761,56789],{},[2068,56762,56763,56775,56777,56779,56781,56783,56785,56787],{},[9252,56764,56765,56767,56769],{},[2075,56766,12897],{},[2210,56768,630],{},[2348,56770,56771,56773],{},[2071,56772,2861],{},[2210,56774,630],{},[2071,56776,532],{},[2075,56778,2084],{"stretchy":2083},[2071,56780,2861],{},[2075,56782,2090],{"stretchy":2083},[2363,56784,3061],{},[2071,56786,2273],{},[2071,56788,2861],{},[2092,56790,56791],{"encoding":2094},"\\int_0^{Q_0} S(Q)\\,dQ",[1647,56793,56795],{"className":56794},[2059],[2061,56796,56797],{"xmlns":2063},[2065,56798,56799,56805],{},[2068,56800,56801,56803],{},[2071,56802,575],{},[2071,56804,532],{},[2092,56806,49263],{"encoding":2094},[92,56808,56809,56810,195],{},"Sestav obdélník ",[1647,56811,56813],{"className":56812},[2059],[2061,56814,56815],{"xmlns":2063},[2065,56816,56817,56833],{},[2068,56818,56819,56825,56827],{},[2348,56820,56821,56823],{},[2071,56822,575],{},[2210,56824,630],{},[2075,56826,3251],{},[2348,56828,56829,56831],{},[2071,56830,2861],{},[2210,56832,630],{},[2092,56834,56835],{"encoding":2094},"P_0 \\cdot Q_0",[92,56837,56838,56839],{},"Dosaď:\n",[89,56840,56841,56906],{},[92,56842,56843,56901,56902,56905],{},[1647,56844,56846],{"className":56845},[2059],[2061,56847,56848],{"xmlns":2063},[2065,56849,56850,56898],{},[2068,56851,56852,56854,56856,56858,56870,56872,56874,56876,56878,56880,56882,56884,56886,56892],{},[2071,56853,2849],{},[2071,56855,532],{},[2075,56857,2077],{},[9252,56859,56860,56862,56864],{},[2075,56861,12897],{},[2210,56863,630],{},[2348,56865,56866,56868],{},[2071,56867,2861],{},[2210,56869,630],{},[2071,56871,4271],{},[2075,56873,2084],{"stretchy":2083},[2071,56875,2861],{},[2075,56877,2090],{"stretchy":2083},[2363,56879,3061],{},[2071,56881,2273],{},[2071,56883,2861],{},[2075,56885,2303],{},[2348,56887,56888,56890],{},[2071,56889,575],{},[2210,56891,630],{},[2348,56893,56894,56896],{},[2071,56895,2861],{},[2210,56897,630],{},[2092,56899,56900],{"encoding":2094},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[95,56903,56904],{},"mínus"," obdélník)",[92,56907,56908,56966,56967,56969],{},[1647,56909,56911],{"className":56910},[2059],[2061,56912,56913],{"xmlns":2063},[2065,56914,56915,56963],{},[2068,56916,56917,56919,56921,56923,56929,56935,56937,56949,56951,56953,56955,56957,56959,56961],{},[2071,56918,575],{},[2071,56920,532],{},[2075,56922,2077],{},[2348,56924,56925,56927],{},[2071,56926,575],{},[2210,56928,630],{},[2348,56930,56931,56933],{},[2071,56932,2861],{},[2210,56934,630],{},[2075,56936,2303],{},[9252,56938,56939,56941,56943],{},[2075,56940,12897],{},[2210,56942,630],{},[2348,56944,56945,56947],{},[2071,56946,2861],{},[2210,56948,630],{},[2071,56950,532],{},[2075,56952,2084],{"stretchy":2083},[2071,56954,2861],{},[2075,56956,2090],{"stretchy":2083},[2363,56958,3061],{},[2071,56960,2273],{},[2071,56962,2861],{},[2092,56964,56965],{"encoding":2094},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[95,56968,56904],{}," integrál)",[92,56971,56972,56973,56976],{},"Kontrola znaménka: obě hodnoty musí být ",[95,56974,56975],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[909,56978],{},[84,56980,56982],{"id":56981},"příklady","Příklady",[609,56984,56986],{"id":56985},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1023,56988,56989],{},[55,56990,56991,56994,56995,52017,57018,57041,57042,835,57062,835,57079,835,57096,57113,57114,57190,57191,57208,57209,57222],{},[1647,56992,56993],{},"!example"," Zadání\nJsou dány poptávka ",[1647,56996,56998],{"className":56997},[2059],[2061,56999,57000],{"xmlns":2063},[2065,57001,57002,57016],{},[2068,57003,57004,57006,57008,57010,57012,57014],{},[2071,57005,575],{},[2075,57007,2077],{},[2071,57009,69],{},[2071,57011,2861],{},[2075,57013,2176],{},[2071,57015,2179],{},[2092,57017,41352],{"encoding":2094},[1647,57019,57021],{"className":57020},[2059],[2061,57022,57023],{"xmlns":2063},[2065,57024,57025,57039],{},[2068,57026,57027,57029,57031,57033,57035,57037],{},[2071,57028,575],{},[2075,57030,2077],{},[2071,57032,2222],{},[2071,57034,2861],{},[2075,57036,2176],{},[2071,57038,2273],{},[2092,57040,44533],{"encoding":2094}," s hodnotami ",[1647,57043,57045],{"className":57044},[2059],[2061,57046,57047],{"xmlns":2063},[2065,57048,57049,57059],{},[2068,57050,57051,57053,57055,57057],{},[2071,57052,69],{},[2075,57054,2077],{},[2075,57056,2303],{},[2210,57058,654],{},[2092,57060,57061],{"encoding":2094},"a = -3",[1647,57063,57065],{"className":57064},[2059],[2061,57066,57067],{"xmlns":2063},[2065,57068,57069,57077],{},[2068,57070,57071,57073,57075],{},[2071,57072,2179],{},[2075,57074,2077],{},[2210,57076,5298],{},[2092,57078,52940],{"encoding":2094},[1647,57080,57082],{"className":57081},[2059],[2061,57083,57084],{"xmlns":2063},[2065,57085,57086,57094],{},[2068,57087,57088,57090,57092],{},[2071,57089,2222],{},[2075,57091,2077],{},[2210,57093,5096],{},[2092,57095,52958],{"encoding":2094},[1647,57097,57099],{"className":57098},[2059],[2061,57100,57101],{"xmlns":2063},[2065,57102,57103,57111],{},[2068,57104,57105,57107,57109],{},[2071,57106,2273],{},[2075,57108,2077],{},[2210,57110,2935],{},[2092,57112,52976],{"encoding":2094},".\nRovnovážné množství:\n",[1647,57115,57117],{"className":57116},[2059],[2061,57118,57119],{"xmlns":2063},[2065,57120,57121,57187],{},[2068,57122,57123,57129,57131,57149,57151,57175,57177,57183,57185],{},[2205,57124,57125,57127],{},[2071,57126,2861],{},[2071,57128,554],{},[2075,57130,2077],{},[2403,57132,57133,57141],{},[2068,57134,57135,57137,57139],{},[2071,57136,2179],{},[2075,57138,2303],{},[2071,57140,2273],{},[2068,57142,57143,57145,57147],{},[2071,57144,2222],{},[2075,57146,2303],{},[2071,57148,69],{},[2075,57150,2077],{},[2403,57152,57153,57161],{},[2068,57154,57155,57157,57159],{},[2210,57156,5298],{},[2075,57158,2303],{},[2210,57160,2935],{},[2068,57162,57163,57165,57167,57169,57171,57173],{},[2210,57164,5096],{},[2075,57166,2303],{},[2075,57168,2084],{"stretchy":2083},[2075,57170,2303],{},[2210,57172,654],{},[2075,57174,2090],{"stretchy":2083},[2075,57176,2077],{},[2403,57178,57179,57181],{},[2210,57180,42310],{},[2210,57182,48700],{},[2075,57184,5987],{},[2210,57186,48705],{},[2092,57188,57189],{"encoding":2094},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[1647,57192,57194],{"className":57193},[2059],[2061,57195,57196],{"xmlns":2063},[2065,57197,57198,57206],{},[2068,57199,57200],{},[2205,57201,57202,57204],{},[2071,57203,2861],{},[2071,57205,554],{},[2092,57207,46694],{"encoding":2094}," (a) při změně samotného parametru ",[1647,57210,57212],{"className":57211},[2059],[2061,57213,57214],{"xmlns":2063},[2065,57215,57216,57220],{},[2068,57217,57218],{},[2071,57219,2222],{},[2092,57221,2222],{"encoding":2094},", (b) při současné změně všech čtyř parametrů.",[55,57224,57225],{},[95,57226,57227,57228,2744,57241,2758,57254,9381],{},"Řešení (a) — změna ",[1647,57229,57231],{"className":57230},[2059],[2061,57232,57233],{"xmlns":2063},[2065,57234,57235,57239],{},[2068,57236,57237],{},[2071,57238,2222],{},[2092,57240,2222],{"encoding":2094},[1647,57242,57244],{"className":57243},[2059],[2061,57245,57246],{"xmlns":2063},[2065,57247,57248,57252],{},[2068,57249,57250],{},[2210,57251,5096],{},[2092,57253,48740],{"encoding":2094},[1647,57255,57257],{"className":57256},[2059],[2061,57258,57259],{"xmlns":2063},[2065,57260,57261,57265],{},[2068,57262,57263],{},[2210,57264,22060],{},[2092,57266,48754],{"encoding":2094},[55,57268,57269,57270,57334,57335,2777],{},"Pomocí vzorce (2.13) pro ",[1647,57271,57273],{"className":57272},[2059],[2061,57274,57275],{"xmlns":2063},[2065,57276,57277,57331],{},[2068,57278,57279,57299,57301,57303],{},[2400,57280,57281],{"scriptlevel":630,"displaystyle":2360},[2403,57282,57283,57293],{},[2068,57284,57285,57287],{},[2071,57286,11003],{"mathvariant":2450},[2205,57288,57289,57291],{},[2071,57290,2861],{},[2071,57292,554],{},[2068,57294,57295,57297],{},[2071,57296,11003],{"mathvariant":2450},[2071,57298,2222],{},[2075,57300,2077],{},[2075,57302,2303],{},[2400,57304,57305],{"scriptlevel":630,"displaystyle":2360},[2403,57306,57307,57315],{},[2068,57308,57309,57311,57313],{},[2071,57310,2179],{},[2075,57312,2303],{},[2071,57314,2273],{},[2068,57316,57317,57319,57321,57323,57325],{},[2075,57318,2084],{"stretchy":2083},[2071,57320,2222],{},[2075,57322,2303],{},[2071,57324,69],{},[2205,57326,57327,57329],{},[2075,57328,2090],{"stretchy":2083},[2210,57330,646],{},[2092,57332,57333],{"encoding":2094},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[1647,57336,57338],{"className":57337},[2059],[2061,57339,57340],{"xmlns":2063},[2065,57341,57342,57364],{},[2068,57343,57344,57346],{},[2075,57345,2303],{},[2400,57347,57348],{"scriptlevel":630,"displaystyle":2360},[2403,57349,57350,57356],{},[2205,57351,57352,57354],{},[2071,57353,2861],{},[2071,57355,554],{},[2068,57357,57358,57360,57362],{},[2071,57359,2222],{},[2075,57361,2303],{},[2071,57363,69],{},[2092,57365,57366],{"encoding":2094},"-\\dfrac{Q^E}{c-a}",[1647,57368,57370],{"className":57369},[2059],[2061,57371,57372],{"xmlns":2063,"display":31093},[2065,57373,57374,57430],{},[2068,57375,57376,57378,57384,57386,57388,57404,57406,57408,57410,57412,57414,57420,57422,57424,57426,57428],{},[2071,57377,2273],{},[2205,57379,57380,57382],{},[2071,57381,2861],{},[2071,57383,554],{},[2075,57385,2077],{},[2075,57387,2303],{},[2403,57389,57390,57396],{},[2205,57391,57392,57394],{},[2071,57393,2861],{},[2071,57395,554],{},[2068,57397,57398,57400,57402],{},[2071,57399,2222],{},[2075,57401,2303],{},[2071,57403,69],{},[2363,57405,3061],{},[2071,57407,2273],{},[2071,57409,2222],{},[2075,57411,2077],{},[2075,57413,2303],{},[2403,57415,57416,57418],{},[2210,57417,48868],{},[2210,57419,48700],{},[2075,57421,3251],{},[2210,57423,2866],{},[2075,57425,5987],{},[2075,57427,2303],{},[2210,57429,48840],{},[2092,57431,57432],{"encoding":2094},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[55,57434,57435],{},"Nové rovnovážné množství:",[1647,57437,57439],{"className":57438},[2059],[2061,57440,57441],{"xmlns":2063,"display":31093},[2065,57442,57443,57466],{},[2068,57444,57445,57453,57455,57457,57459,57461,57463],{},[9252,57446,57447,57449,57451],{},[2071,57448,2861],{},[2210,57450,638],{},[2071,57452,554],{},[2075,57454,2803],{},[2210,57456,48868],{},[2075,57458,2303],{},[2210,57460,48873],{},[2075,57462,2077],{},[2210,57464,57465],{},"8,326.",[2092,57467,57468],{"encoding":2094},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[55,57470,57471,1445,57474,835,57501,835,57523,835,57545,5676,57567,835,57586,835,57607,835,57626,195],{},[95,57472,57473],{},"Řešení (b) — současná změna všech parametrů:",[1647,57475,57477],{"className":57476},[2059],[2061,57478,57479],{"xmlns":2063},[2065,57480,57481,57498],{},[2068,57482,57483,57485,57487,57489,57491,57493,57495],{},[2071,57484,69],{},[2075,57486,2777],{},[2075,57488,2303],{},[2210,57490,654],{},[2075,57492,3197],{},[2075,57494,2303],{},[2210,57496,57497],{},"2,5",[2092,57499,57500],{"encoding":2094},"a: -3 \\to -2{,}5",[1647,57502,57504],{"className":57503},[2059],[2061,57505,57506],{"xmlns":2063},[2065,57507,57508,57520],{},[2068,57509,57510,57512,57514,57516,57518],{},[2071,57511,2179],{},[2075,57513,2777],{},[2210,57515,5298],{},[2075,57517,3197],{},[2210,57519,16773],{},[2092,57521,57522],{"encoding":2094},"b: 40 \\to 35",[1647,57524,57526],{"className":57525},[2059],[2061,57527,57528],{"xmlns":2063},[2065,57529,57530,57542],{},[2068,57531,57532,57534,57536,57538,57540],{},[2071,57533,2222],{},[2075,57535,2777],{},[2210,57537,5096],{},[2075,57539,3197],{},[2210,57541,22060],{},[2092,57543,57544],{"encoding":2094},"c: 0{,}5 \\to 0{,}6",[1647,57546,57548],{"className":57547},[2059],[2061,57549,57550],{"xmlns":2063},[2065,57551,57552,57564],{},[2068,57553,57554,57556,57558,57560,57562],{},[2071,57555,2273],{},[2075,57557,2777],{},[2210,57559,2935],{},[2075,57561,3197],{},[2210,57563,2976],{},[2092,57565,57566],{"encoding":2094},"d: 10 \\to 11",[1647,57568,57570],{"className":57569},[2059],[2061,57571,57572],{"xmlns":2063},[2065,57573,57574,57584],{},[2068,57575,57576,57578,57580,57582],{},[2071,57577,2273],{},[2071,57579,69],{},[2075,57581,2077],{},[2210,57583,5096],{},[2092,57585,48906],{"encoding":2094},[1647,57587,57589],{"className":57588},[2059],[2061,57590,57591],{"xmlns":2063},[2065,57592,57593,57605],{},[2068,57594,57595,57597,57599,57601,57603],{},[2071,57596,2273],{},[2071,57598,2179],{},[2075,57600,2077],{},[2075,57602,2303],{},[2210,57604,670],{},[2092,57606,48928],{"encoding":2094},[1647,57608,57610],{"className":57609},[2059],[2061,57611,57612],{"xmlns":2063},[2065,57613,57614,57624],{},[2068,57615,57616,57618,57620,57622],{},[2071,57617,2273],{},[2071,57619,2222],{},[2075,57621,2077],{},[2210,57623,2866],{},[2092,57625,48948],{"encoding":2094},[1647,57627,57629],{"className":57628},[2059],[2061,57630,57631],{"xmlns":2063},[2065,57632,57633,57643],{},[2068,57634,57635,57637,57639,57641],{},[2071,57636,2273],{},[2071,57638,2273],{},[2075,57640,2077],{},[2210,57642,638],{},[2092,57644,48968],{"encoding":2094},[55,57646,57647,57648,57706],{},"Totální diferenciál ",[1647,57649,57651],{"className":57650},[2059],[2061,57652,57653],{"xmlns":2063},[2065,57654,57655,57703],{},[2068,57656,57657,57663,57665,57667,57669,57671,57673,57675,57677,57679,57681,57683],{},[2205,57658,57659,57661],{},[2071,57660,2861],{},[2071,57662,554],{},[2075,57664,2084],{"stretchy":2083},[2071,57666,69],{},[2075,57668,2361],{"separator":2360},[2071,57670,2179],{},[2075,57672,2361],{"separator":2360},[2071,57674,2222],{},[2075,57676,2361],{"separator":2360},[2071,57678,2273],{},[2075,57680,2090],{"stretchy":2083},[2075,57682,2077],{},[2400,57684,57685],{"scriptlevel":630,"displaystyle":2360},[2403,57686,57687,57695],{},[2068,57688,57689,57691,57693],{},[2071,57690,2179],{},[2075,57692,2303],{},[2071,57694,2273],{},[2068,57696,57697,57699,57701],{},[2071,57698,2222],{},[2075,57700,2303],{},[2071,57702,69],{},[2092,57704,57705],{"encoding":2094},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[1647,57708,57710],{"className":57709},[2059],[2061,57711,57712],{"xmlns":2063,"display":31093},[2065,57713,57714,57834],{},[2068,57715,57716,57718,57724,57726,57752,57754,57756,57758,57760,57772,57774,57776,57778,57780,57806,57808,57810,57812,57814,57826,57828,57830,57832],{},[2071,57717,2273],{},[2205,57719,57720,57722],{},[2071,57721,2861],{},[2071,57723,554],{},[2075,57725,2077],{},[2403,57727,57728,57736],{},[2068,57729,57730,57732,57734],{},[2071,57731,2179],{},[2075,57733,2303],{},[2071,57735,2273],{},[2068,57737,57738,57740,57742,57744,57746],{},[2075,57739,2084],{"stretchy":2083},[2071,57741,2222],{},[2075,57743,2303],{},[2071,57745,69],{},[2205,57747,57748,57750],{},[2075,57749,2090],{"stretchy":2083},[2210,57751,646],{},[2363,57753,3061],{},[2071,57755,2273],{},[2071,57757,69],{},[2075,57759,2176],{},[2403,57761,57762,57764],{},[2210,57763,638],{},[2068,57765,57766,57768,57770],{},[2071,57767,2222],{},[2075,57769,2303],{},[2071,57771,69],{},[2363,57773,3061],{},[2071,57775,2273],{},[2071,57777,2179],{},[2075,57779,2303],{},[2403,57781,57782,57790],{},[2068,57783,57784,57786,57788],{},[2071,57785,2179],{},[2075,57787,2303],{},[2071,57789,2273],{},[2068,57791,57792,57794,57796,57798,57800],{},[2075,57793,2084],{"stretchy":2083},[2071,57795,2222],{},[2075,57797,2303],{},[2071,57799,69],{},[2205,57801,57802,57804],{},[2075,57803,2090],{"stretchy":2083},[2210,57805,646],{},[2363,57807,3061],{},[2071,57809,2273],{},[2071,57811,2222],{},[2075,57813,2303],{},[2403,57815,57816,57818],{},[2210,57817,638],{},[2068,57819,57820,57822,57824],{},[2071,57821,2222],{},[2075,57823,2303],{},[2071,57825,69],{},[2363,57827,3061],{},[2071,57829,2273],{},[2071,57831,2273],{},[2071,57833,195],{"mathvariant":2450},[2092,57835,57836],{"encoding":2094},"dQ^E = \\frac{b-d}{(c-a)^2}\\,da + \\frac{1}{c-a}\\,db - \\frac{b-d}{(c-a)^2}\\,dc - \\frac{1}{c-a}\\,dd.",[55,57838,57839,57840,835,57862,835,57893,3225],{},"Dosazením číselných hodnot (",[1647,57841,57843],{"className":57842},[2059],[2061,57844,57845],{"xmlns":2063},[2065,57846,57847,57859],{},[2068,57848,57849,57851,57853,57855,57857],{},[2071,57850,2222],{},[2075,57852,2303],{},[2071,57854,69],{},[2075,57856,2077],{},[2210,57858,48700],{},[2092,57860,57861],{"encoding":2094},"c - a = 3{,}5",[1647,57863,57865],{"className":57864},[2059],[2061,57866,57867],{"xmlns":2063},[2065,57868,57869,57890],{},[2068,57870,57871,57873,57875,57877,57879,57885,57887],{},[2075,57872,2084],{"stretchy":2083},[2071,57874,2222],{},[2075,57876,2303],{},[2071,57878,69],{},[2205,57880,57881,57883],{},[2075,57882,2090],{"stretchy":2083},[2210,57884,646],{},[2075,57886,2077],{},[2210,57888,57889],{},"12,25",[2092,57891,57892],{"encoding":2094},"(c-a)^2 = 12{,}25",[1647,57894,57896],{"className":57895},[2059],[2061,57897,57898],{"xmlns":2063},[2065,57899,57900,57912],{},[2068,57901,57902,57904,57906,57908,57910],{},[2071,57903,2179],{},[2075,57905,2303],{},[2071,57907,2273],{},[2075,57909,2077],{},[2210,57911,42310],{},[2092,57913,57914],{"encoding":2094},"b - d = 30",[1647,57916,57918],{"className":57917},[2059],[2061,57919,57920],{"xmlns":2063,"display":31093},[2065,57921,57922,58023],{},[2068,57923,57924,57926,57932,57934,57942,57944,57946,57948,57950,57958,57960,57962,57964,57966,57968,57976,57978,57980,57982,57984,57992,57994,57996,57998,58000,58003,58005,58008,58010,58012,58014,58017,58019,58021],{},[2071,57925,2273],{},[2205,57927,57928,57930],{},[2071,57929,2861],{},[2071,57931,554],{},[2075,57933,2803],{},[2400,57935,57936],{"scriptlevel":630,"displaystyle":2083},[2403,57937,57938,57940],{},[2210,57939,42310],{},[2210,57941,57889],{},[2075,57943,2084],{"stretchy":2083},[2210,57945,5096],{},[2075,57947,2090],{"stretchy":2083},[2075,57949,2176],{},[2400,57951,57952],{"scriptlevel":630,"displaystyle":2083},[2403,57953,57954,57956],{},[2210,57955,638],{},[2210,57957,48700],{},[2075,57959,2084],{"stretchy":2083},[2075,57961,2303],{},[2210,57963,670],{},[2075,57965,2090],{"stretchy":2083},[2075,57967,2303],{},[2400,57969,57970],{"scriptlevel":630,"displaystyle":2083},[2403,57971,57972,57974],{},[2210,57973,42310],{},[2210,57975,57889],{},[2075,57977,2084],{"stretchy":2083},[2210,57979,2866],{},[2075,57981,2090],{"stretchy":2083},[2075,57983,2303],{},[2400,57985,57986],{"scriptlevel":630,"displaystyle":2083},[2403,57987,57988,57990],{},[2210,57989,638],{},[2210,57991,48700],{},[2075,57993,2084],{"stretchy":2083},[2210,57995,638],{},[2075,57997,2090],{"stretchy":2083},[2075,57999,5987],{},[2210,58001,58002],{},"1,224",[2075,58004,2303],{},[2210,58006,58007],{},"1,429",[2075,58009,2303],{},[2210,58011,48873],{},[2075,58013,2303],{},[2210,58015,58016],{},"0,286",[2075,58018,5987],{},[2075,58020,2303],{},[2210,58022,49119],{},[2092,58024,58025],{"encoding":2094},"dQ^E \\approx \\tfrac{30}{12{,}25}(0{,}5) + \\tfrac{1}{3{,}5}(-5) - \\tfrac{30}{12{,}25}(0{,}1) - \\tfrac{1}{3{,}5}(1) \\doteq 1{,}224 - 1{,}429 - 0{,}245 - 0{,}286 \\doteq -0{,}735.",[55,58027,33092,58028,195],{},[1647,58029,58031],{"className":58030},[2059],[2061,58032,58033],{"xmlns":2063},[2065,58034,58035,58057],{},[2068,58036,58037,58045,58047,58049,58051,58053,58055],{},[9252,58038,58039,58041,58043],{},[2071,58040,2861],{},[2210,58042,638],{},[2071,58044,554],{},[2075,58046,2803],{},[2210,58048,48868],{},[2075,58050,2303],{},[2210,58052,49150],{},[2075,58054,5987],{},[2210,58056,49155],{},[2092,58058,58059],{"encoding":2094},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1023,58061,58062],{},[55,58063,58064,58066,58067,58088,58089,58115,58116,58119,58120,58216,58217,58240,58241,58257],{},[1647,58065,4499],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[1647,58068,58070],{"className":58069},[2059],[2061,58071,58072],{"xmlns":2063},[2065,58073,58074,58086],{},[2068,58075,58076,58078,58080,58082,58084],{},[2071,58077,2961],{"mathvariant":2450},[2071,58079,2861],{},[2075,58081,2803],{},[2075,58083,2303],{},[2210,58085,49185],{},[2092,58087,49188],{"encoding":2094},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[1647,58090,58092],{"className":58091},[2059],[2061,58093,58094],{"xmlns":2063},[2065,58095,58096,58112],{},[2068,58097,58098,58100,58106,58108,58110],{},[2071,58099,2273],{},[2205,58101,58102,58104],{},[2071,58103,2861],{},[2071,58105,554],{},[2075,58107,5987],{},[2075,58109,2303],{},[2210,58111,49150],{},[2092,58113,58114],{"encoding":2094},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[95,58117,58118],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[1647,58121,58123],{"className":58122},[2059],[2061,58124,58125],{"xmlns":2063},[2065,58126,58127,58213],{},[2068,58128,58129,58137,58139,58173,58175,58199,58201,58208,58210],{},[9252,58130,58131,58133,58135],{},[2071,58132,2861],{},[2210,58134,638],{},[2071,58136,554],{},[2075,58138,2077],{},[2403,58140,58141,58157],{},[2068,58142,58143,58149,58151],{},[2205,58144,58145,58147],{},[2071,58146,2179],{},[2075,58148,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,58150,2303],{},[2205,58152,58153,58155],{},[2071,58154,2273],{},[2075,58156,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2068,58158,58159,58165,58167],{},[2205,58160,58161,58163],{},[2071,58162,2222],{},[2075,58164,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,58166,2303],{},[2205,58168,58169,58171],{},[2071,58170,69],{},[2075,58172,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,58174,2077],{},[2403,58176,58177,58185],{},[2068,58178,58179,58181,58183],{},[2210,58180,16773],{},[2075,58182,2303],{},[2210,58184,2976],{},[2068,58186,58187,58189,58191,58193,58195,58197],{},[2210,58188,22060],{},[2075,58190,2303],{},[2075,58192,2084],{"stretchy":2083},[2075,58194,2303],{},[2210,58196,57497],{},[2075,58198,2090],{"stretchy":2083},[2075,58200,2077],{},[2403,58202,58203,58205],{},[2210,58204,46091],{},[2210,58206,58207],{},"3,1",[2075,58209,5987],{},[2210,58211,58212],{},"7,742",[2092,58214,58215],{"encoding":2094},"Q_1^E = \\frac{b' - d'}{c' - a'} = \\frac{35 - 11}{0{,}6 - (-2{,}5)} = \\frac{24}{3{,}1} \\doteq 7{,}742","\ndává skutečnou změnu ",[1647,58218,58220],{"className":58219},[2059],[2061,58221,58222],{"xmlns":2063},[2065,58223,58224,58237],{},[2068,58225,58226,58228,58230,58232,58234],{},[2071,58227,2961],{"mathvariant":2450},[2071,58229,2861],{},[2075,58231,5987],{},[2075,58233,2303],{},[2210,58235,58236],{},"0,829",[2092,58238,58239],{"encoding":2094},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[1647,58242,58244],{"className":58243},[2059],[2061,58245,58246],{"xmlns":2063},[2065,58247,58248,58254],{},[2068,58249,58250,58252],{},[2075,58251,2303],{},[2210,58253,49185],{},[2092,58255,58256],{"encoding":2094},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[55,58259,58260],{},[3982,58261,58262,58263,58276],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[1647,58264,58266],{"className":58265},[2059],[2061,58267,58268],{"xmlns":2063},[2065,58269,58270,58274],{},[2068,58271,58272],{},[2071,58273,2861],{},[2092,58275,2861],{"encoding":2094},", ale kniha ho zařazuje před výklad přebytků jako přechod ke komparativní statice před aplikací na CS\u002FPS. Princip redukovaného tvaru lze uplatnit na libovolné ekonomické proměnné — v kap. 7 např. pro makroekonomii.",[609,58278,58280,58281],{"id":58279},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[1647,58282,58284],{"className":58283},[2059],[2061,58285,58286],{"xmlns":2063},[2065,58287,58288,58294],{},[2068,58289,58290,58292],{},[2071,58291,575],{},[2071,58293,532],{},[2092,58295,49263],{"encoding":2094},[1023,58297,58298],{},[55,58299,58300,58302,58303,58337,58338,58360],{},[1647,58301,56993],{}," Zadání\nPro nabídku ",[1647,58304,58306],{"className":58305},[2059],[2061,58307,58308],{"xmlns":2063},[2065,58309,58310,58334],{},[2068,58311,58312,58314,58316,58318,58320,58322,58324,58326,58328,58330,58332],{},[2071,58313,575],{},[2075,58315,2077],{},[2071,58317,532],{},[2075,58319,2084],{"stretchy":2083},[2071,58321,2861],{},[2075,58323,2090],{"stretchy":2083},[2075,58325,2077],{},[2210,58327,2935],{},[2075,58329,2176],{},[2210,58331,646],{},[2071,58333,2861],{},[2092,58335,58336],{"encoding":2094},"P = S(Q) = 10 + 2Q"," a množství ",[1647,58339,58341],{"className":58340},[2059],[2061,58342,58343],{"xmlns":2063},[2065,58344,58345,58357],{},[2068,58346,58347,58353,58355],{},[2348,58348,58349,58351],{},[2071,58350,2861],{},[2210,58352,630],{},[2075,58354,2077],{},[2210,58356,2935],{},[2092,58358,58359],{"encoding":2094},"Q_0 = 10"," vypočítejte přebytek výrobce.",[55,58362,58363],{},[95,58364,25509],{},[55,58366,58367],{},"Odpovídající cena:",[1647,58369,58371],{"className":58370},[2059],[2061,58372,58373],{"xmlns":2063,"display":31093},[2065,58374,58375,58410],{},[2068,58376,58377,58383,58385,58387,58389,58391,58393,58395,58397,58399,58401,58403,58405,58407],{},[2348,58378,58379,58381],{},[2071,58380,575],{},[2210,58382,630],{},[2075,58384,2077],{},[2071,58386,532],{},[2075,58388,2084],{"stretchy":2083},[2210,58390,2935],{},[2075,58392,2090],{"stretchy":2083},[2075,58394,2077],{},[2210,58396,2935],{},[2075,58398,2176],{},[2210,58400,646],{},[2075,58402,3251],{},[2210,58404,2935],{},[2075,58406,2077],{},[2210,58408,58409],{},"30.",[2092,58411,58412],{"encoding":2094},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[55,58414,58415],{},"Dle vzorce (2.15):",[1647,58417,58419],{"className":58418},[2059],[2061,58420,58421],{"xmlns":2063,"display":31093},[2065,58422,58423,58531],{},[2068,58424,58425,58427,58429,58431,58433,58435,58437,58443,58449,58451,58459,58461,58463,58465,58467,58469,58471,58473,58475,58477,58479,58481,58483,58485,58487,58490,58492,58494,58496,58502,58510,58512,58514,58516,58518,58520,58522,58524,58526,58528],{},[2071,58426,575],{},[2071,58428,532],{},[2075,58430,2084],{"stretchy":2083},[2210,58432,2935],{},[2075,58434,2090],{"stretchy":2083},[2075,58436,2077],{},[2348,58438,58439,58441],{},[2071,58440,575],{},[2210,58442,630],{},[2348,58444,58445,58447],{},[2071,58446,2861],{},[2210,58448,630],{},[2075,58450,2303],{},[9252,58452,58453,58455,58457],{},[2075,58454,12897],{},[2210,58456,630],{},[2210,58458,2935],{},[2075,58460,2084],{"stretchy":2083},[2210,58462,2935],{},[2075,58464,2176],{},[2210,58466,646],{},[2071,58468,2861],{},[2075,58470,2090],{"stretchy":2083},[2363,58472,3061],{},[2071,58474,2273],{},[2071,58476,2861],{},[2075,58478,2077],{},[2210,58480,2935],{},[2075,58482,3251],{},[2210,58484,42310],{},[2075,58486,2303],{},[2075,58488,2561],{"fence":2083,"stretchy":2360,"minsize":58489,"maxsize":58489},"1.8em",[2210,58491,2935],{},[2071,58493,2861],{},[2075,58495,2176],{},[2205,58497,58498,58500],{},[2071,58499,2861],{},[2210,58501,646],{},[9252,58503,58504,58506,58508],{},[2075,58505,2576],{"fence":2083,"stretchy":2360,"minsize":58489,"maxsize":58489},[2210,58507,630],{},[2210,58509,2935],{},[2075,58511,2077],{},[2210,58513,33108],{},[2075,58515,2303],{},[2075,58517,2084],{"stretchy":2083},[2210,58519,3164],{},[2075,58521,2176],{},[2210,58523,3164],{},[2075,58525,2090],{"stretchy":2083},[2075,58527,2077],{},[2210,58529,58530],{},"100.",[2092,58532,58533],{"encoding":2094},"PS(10) = P_0 Q_0 - \\int_0^{10}(10 + 2Q)\\,dQ = 10 \\cdot 30 - \\Big[10Q + Q^2\\Big]_0^{10} = 300 - (100 + 100) = 100.",[55,58535,58536,58537,58558,58559,58579],{},"Přebytek výrobce při množství ",[1647,58538,58540],{"className":58539},[2059],[2061,58541,58542],{"xmlns":2063},[2065,58543,58544,58556],{},[2068,58545,58546,58552,58554],{},[2348,58547,58548,58550],{},[2071,58549,2861],{},[2210,58551,630],{},[2075,58553,2077],{},[2210,58555,2935],{},[2092,58557,58359],{"encoding":2094}," je tedy ",[1647,58560,58562],{"className":58561},[2059],[2061,58563,58564],{"xmlns":2063},[2065,58565,58566,58576],{},[2068,58567,58568,58570,58572,58574],{},[2071,58569,575],{},[2071,58571,532],{},[2075,58573,2077],{},[2210,58575,3164],{},[2092,58577,58578],{"encoding":2094},"PS = 100"," (peněžních jednotek).",[909,58581],{},[84,58583,58585],{"id":58584},"cheat-sheet","Cheat sheet",[323,58587,58588,58601],{},[326,58589,58590],{},[329,58591,58592,58595,58598],{},[332,58593,58594],{},"Veličina",[332,58596,58597],{},"Vzorec",[332,58599,58600],{},"Geometrie",[342,58602,58603,58721,58835,58903],{},[329,58604,58605,58633,58689],{},[347,58606,58607],{},[1647,58608,58610],{"className":58609},[2059],[2061,58611,58612],{"xmlns":2063},[2065,58613,58614,58630],{},[2068,58615,58616,58618,58620,58622,58628],{},[2071,58617,2849],{},[2071,58619,532],{},[2075,58621,2084],{"stretchy":2083},[2348,58623,58624,58626],{},[2071,58625,2861],{},[2210,58627,630],{},[2075,58629,2090],{"stretchy":2083},[2092,58631,58632],{"encoding":2094},"CS(Q_0)",[347,58634,58635],{},[1647,58636,58638],{"className":58637},[2059],[2061,58639,58640],{"xmlns":2063},[2065,58641,58642,58686],{},[2068,58643,58644],{},[2400,58645,58646,58658,58660,58662,58664,58666,58668,58670,58672,58674,58680],{"scriptlevel":630,"displaystyle":2360},[9252,58647,58648,58650,58652],{},[2075,58649,12897],{},[2210,58651,630],{},[2348,58653,58654,58656],{},[2071,58655,2861],{},[2210,58657,630],{},[2071,58659,4271],{},[2075,58661,2084],{"stretchy":2083},[2071,58663,2861],{},[2075,58665,2090],{"stretchy":2083},[2363,58667,3061],{},[2071,58669,2273],{},[2071,58671,2861],{},[2075,58673,2303],{},[2348,58675,58676,58678],{},[2071,58677,575],{},[2210,58679,630],{},[2348,58681,58682,58684],{},[2071,58683,2861],{},[2210,58685,630],{},[2092,58687,58688],{"encoding":2094},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[347,58690,58691,58692,58695,58696,58699,58700],{},"plocha ",[95,58693,58694],{},"pod"," křivkou poptávky, ",[95,58697,58698],{},"nad"," čárou ",[1647,58701,58703],{"className":58702},[2059],[2061,58704,58705],{"xmlns":2063},[2065,58706,58707,58719],{},[2068,58708,58709,58711,58713],{},[2071,58710,575],{},[2075,58712,2077],{},[2348,58714,58715,58717],{},[2071,58716,575],{},[2210,58718,630],{},[2092,58720,55975],{"encoding":2094},[329,58722,58723,58751,58807],{},[347,58724,58725],{},[1647,58726,58728],{"className":58727},[2059],[2061,58729,58730],{"xmlns":2063},[2065,58731,58732,58748],{},[2068,58733,58734,58736,58738,58740,58746],{},[2071,58735,575],{},[2071,58737,532],{},[2075,58739,2084],{"stretchy":2083},[2348,58741,58742,58744],{},[2071,58743,2861],{},[2210,58745,630],{},[2075,58747,2090],{"stretchy":2083},[2092,58749,58750],{"encoding":2094},"PS(Q_0)",[347,58752,58753],{},[1647,58754,58756],{"className":58755},[2059],[2061,58757,58758],{"xmlns":2063},[2065,58759,58760,58804],{},[2068,58761,58762],{},[2400,58763,58764,58770,58776,58778,58790,58792,58794,58796,58798,58800,58802],{"scriptlevel":630,"displaystyle":2360},[2348,58765,58766,58768],{},[2071,58767,575],{},[2210,58769,630],{},[2348,58771,58772,58774],{},[2071,58773,2861],{},[2210,58775,630],{},[2075,58777,2303],{},[9252,58779,58780,58782,58784],{},[2075,58781,12897],{},[2210,58783,630],{},[2348,58785,58786,58788],{},[2071,58787,2861],{},[2210,58789,630],{},[2071,58791,532],{},[2075,58793,2084],{"stretchy":2083},[2071,58795,2861],{},[2075,58797,2090],{"stretchy":2083},[2363,58799,3061],{},[2071,58801,2273],{},[2071,58803,2861],{},[2092,58805,58806],{"encoding":2094},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[347,58808,58691,58809,58811,58812,58699,58814],{},[95,58810,58698],{}," křivkou nabídky, ",[95,58813,58694],{},[1647,58815,58817],{"className":58816},[2059],[2061,58818,58819],{"xmlns":2063},[2065,58820,58821,58833],{},[2068,58822,58823,58825,58827],{},[2071,58824,575],{},[2075,58826,2077],{},[2348,58828,58829,58831],{},[2071,58830,575],{},[2210,58832,630],{},[2092,58834,55975],{"encoding":2094},[329,58836,58837,58840,58867],{},[347,58838,58839],{},"Výdaje \u002F tržby",[347,58841,58842],{},[1647,58843,58845],{"className":58844},[2059],[2061,58846,58847],{"xmlns":2063},[2065,58848,58849,58865],{},[2068,58850,58851,58857,58859],{},[2348,58852,58853,58855],{},[2071,58854,575],{},[2210,58856,630],{},[2075,58858,3251],{},[2348,58860,58861,58863],{},[2071,58862,2861],{},[2210,58864,630],{},[2092,58866,56835],{"encoding":2094},[347,58868,58869,58870],{},"obdélník ",[1647,58871,58873],{"className":58872},[2059],[2061,58874,58875],{"xmlns":2063},[2065,58876,58877,58901],{},[2068,58878,58879,58881,58883,58889,58891,58893,58895],{},[2210,58880,630],{},[2363,58882,3061],{},[2348,58884,58885,58887],{},[2071,58886,2861],{},[2210,58888,630],{},[2363,58890,3061],{},[2071,58892,4342],{},[2363,58894,3061],{},[2348,58896,58897,58899],{},[2071,58898,575],{},[2210,58900,630],{},[2092,58902,55455],{"encoding":2094},[329,58904,58905,58908,58931],{},[347,58906,58907],{},"Celkový přebytek",[347,58909,58910],{},[1647,58911,58913],{"className":58912},[2059],[2061,58914,58915],{"xmlns":2063},[2065,58916,58917,58929],{},[2068,58918,58919,58921,58923,58925,58927],{},[2071,58920,2849],{},[2071,58922,532],{},[2075,58924,2176],{},[2071,58926,575],{},[2071,58928,532],{},[2092,58930,55192],{"encoding":2094},[347,58932,58933],{},"součet obou ploch v rovnováze",[909,58935],{},[84,58937,321],{"id":320},[89,58939,58940,58962,58984,59028,59072,59135,59163],{},[92,58941,58942,11156,58944,835,58959,58961],{},[95,58943,49228],{},[1647,58945,58947],{"className":58946},[2059],[2061,58948,58949],{"xmlns":2063},[2065,58950,58951,58957],{},[2068,58952,58953,58955],{},[2071,58954,2849],{},[2071,58956,532],{},[2092,58958,49244],{"encoding":2094},[3982,58960,49284],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[92,58963,58964,11156,58966,835,58981,58983],{},[95,58965,49377],{},[1647,58967,58969],{"className":58968},[2059],[2061,58970,58971],{"xmlns":2063},[2065,58972,58973,58979],{},[2068,58974,58975,58977],{},[2071,58976,575],{},[2071,58978,532],{},[2092,58980,49263],{"encoding":2094},[3982,58982,49380],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[92,58985,58986,7102,58989,195],{},[95,58987,58988],{},"Ochota platit",[1647,58990,58992],{"className":58991},[2059],[2061,58993,58994],{"xmlns":2063},[2065,58995,58996,59026],{},[2068,58997,58998],{},[2400,58999,59000,59012,59014,59016,59018,59020,59022,59024],{"scriptlevel":630,"displaystyle":2360},[9252,59001,59002,59004,59006],{},[2075,59003,12897],{},[2210,59005,630],{},[2348,59007,59008,59010],{},[2071,59009,2861],{},[2210,59011,630],{},[2071,59013,4271],{},[2075,59015,2084],{"stretchy":2083},[2071,59017,2861],{},[2075,59019,2090],{"stretchy":2083},[2363,59021,3061],{},[2071,59023,2273],{},[2071,59025,2861],{},[2092,59027,55823],{"encoding":2094},[92,59029,59030,7102,59033,195],{},[95,59031,59032],{},"Minimální cena výrobce",[1647,59034,59036],{"className":59035},[2059],[2061,59037,59038],{"xmlns":2063},[2065,59039,59040,59070],{},[2068,59041,59042],{},[2400,59043,59044,59056,59058,59060,59062,59064,59066,59068],{"scriptlevel":630,"displaystyle":2360},[9252,59045,59046,59048,59050],{},[2075,59047,12897],{},[2210,59049,630],{},[2348,59051,59052,59054],{},[2071,59053,2861],{},[2210,59055,630],{},[2071,59057,532],{},[2075,59059,2084],{"stretchy":2083},[2071,59061,2861],{},[2075,59063,2090],{"stretchy":2083},[2363,59065,3061],{},[2071,59067,2273],{},[2071,59069,2861],{},[2092,59071,56465],{"encoding":2094},[92,59073,59074,7102,59077,56966,59102,4007],{},[95,59075,59076],{},"Výdaje spotřebitele \u002F tržby výrobce",[1647,59078,59080],{"className":59079},[2059],[2061,59081,59082],{"xmlns":2063},[2065,59083,59084,59100],{},[2068,59085,59086,59092,59094],{},[2348,59087,59088,59090],{},[2071,59089,575],{},[2210,59091,630],{},[2363,59093,3061],{},[2348,59095,59096,59098],{},[2071,59097,2861],{},[2210,59099,630],{},[2092,59101,55901],{"encoding":2094},[1647,59103,59105],{"className":59104},[2059],[2061,59106,59107],{"xmlns":2063},[2065,59108,59109,59133],{},[2068,59110,59111,59113,59115,59121,59123,59125,59127],{},[2210,59112,630],{},[2363,59114,3061],{},[2348,59116,59117,59119],{},[2071,59118,2861],{},[2210,59120,630],{},[2363,59122,3061],{},[2071,59124,4342],{},[2363,59126,3061],{},[2348,59128,59129,59131],{},[2071,59130,575],{},[2210,59132,630],{},[2092,59134,55455],{"encoding":2094},[92,59136,59137,59140,59141,59162],{},[95,59138,59139],{},"Celkový přebytek trhu"," — součet ",[1647,59142,59144],{"className":59143},[2059],[2061,59145,59146],{"xmlns":2063},[2065,59147,59148,59160],{},[2068,59149,59150,59152,59154,59156,59158],{},[2071,59151,2849],{},[2071,59153,532],{},[2075,59155,2176],{},[2071,59157,575],{},[2071,59159,532],{},[2092,59161,55192],{"encoding":2094}," v rovnovážném bodě.",[92,59164,59165,59167,59168,835,59181,59194,59195,195],{},[95,59166,2519],{}," — plochy ohraničené křivkami ",[1647,59169,59171],{"className":59170},[2059],[2061,59172,59173],{"xmlns":2063},[2065,59174,59175,59179],{},[2068,59176,59177],{},[2071,59178,4271],{},[2092,59180,4271],{"encoding":2094},[1647,59182,59184],{"className":59183},[2059],[2061,59185,59186],{"xmlns":2063},[2065,59187,59188,59192],{},[2068,59189,59190],{},[2071,59191,532],{},[2092,59193,532],{"encoding":2094}," a přímkou ",[1647,59196,59198],{"className":59197},[2059],[2061,59199,59200],{"xmlns":2063},[2065,59201,59202,59214],{},[2068,59203,59204,59206,59208],{},[2071,59205,575],{},[2075,59207,2077],{},[2348,59209,59210,59212],{},[2071,59211,575],{},[2210,59213,630],{},[2092,59215,55975],{"encoding":2094},[909,59217],{},[84,59219,59221],{"id":59220},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[55,59223,59224,59225,59238,59239,59256],{},"Uvalení jednotkové daně ",[1647,59226,59228],{"className":59227},[2059],[2061,59229,59230],{"xmlns":2063},[2065,59231,59232,59236],{},[2068,59233,59234],{},[2071,59235,543],{},[2092,59237,543],{"encoding":2094}," na trh posouvá rovnovážné množství pod ",[1647,59240,59242],{"className":59241},[2059],[2061,59243,59244],{"xmlns":2063},[2065,59245,59246,59254],{},[2068,59247,59248],{},[2205,59249,59250,59252],{},[2071,59251,2861],{},[2071,59253,554],{},[2092,59255,46694],{"encoding":2094}," a rozkládá původní plochu přebytků na nové části.",[55,59258,59259],{},[58,59260],{"alt":59261,"className":59262,"src":59263},"imek-prebytky-s-dani-deadweight",[62,63],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[55,59265,59266,59267,59282,59283,59298,59299,56966,59302,59326,59327,11156,59330,59333,59334,195],{},"Přebytek spotřebitele ",[1647,59268,59270],{"className":59269},[2059],[2061,59271,59272],{"xmlns":2063},[2065,59273,59274,59280],{},[2068,59275,59276,59278],{},[2071,59277,2849],{},[2071,59279,532],{},[2092,59281,49244],{"encoding":2094}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[1647,59284,59286],{"className":59285},[2059],[2061,59287,59288],{"xmlns":2063},[2065,59289,59290,59296],{},[2068,59291,59292,59294],{},[2071,59293,575],{},[2071,59295,532],{},[2092,59297,49263],{"encoding":2094}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[95,59300,59301],{},"daňový příjem",[1647,59303,59305],{"className":59304},[2059],[2061,59306,59307],{"xmlns":2063},[2065,59308,59309,59323],{},[2068,59310,59311,59313,59315],{},[2071,59312,543],{},[2075,59314,3251],{},[9252,59316,59317,59319,59321],{},[2071,59318,2861],{},[2210,59320,638],{},[2071,59322,554],{},[2092,59324,59325],{"encoding":2094},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[95,59328,59329],{},"mrtvá ztráta",[3982,59331,59332],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[69,59335,46913],{"className":59336,"dataFsResolvedFilePath":47013,"href":47014},[62],[909,59338],{},[84,59340,3866],{"id":3865},[89,59342,59343,59350,59362,59369,59376],{},[92,59344,59345,1445,59347],{},[95,59346,17957],{},[69,59348,41053],{"className":59349,"dataFsResolvedFilePath":13670,"href":13671},[62],[92,59351,59352,1445,59354,59357,59358,59361],{},[95,59353,39700],{},[69,59355,3890],{"className":59356,"dataFsResolvedFilePath":3888,"href":3889},[62]," (určitý integrál, plocha pod křivkou), ",[69,59359,2431],{"className":59360,"dataFsResolvedFilePath":4005,"href":4006},[62]," (monotonie křivek)",[92,59363,59364,1445,59366],{},[95,59365,17967],{},[69,59367,3906],{"className":59368,"dataFsResolvedFilePath":3022,"href":3023},[62],[92,59370,59371,1445,59373],{},[95,59372,55053],{},[69,59374,55059],{"className":59375,"dataFsResolvedFilePath":55057,"href":55058},[62],[92,59377,59378,1445,59380],{},[95,59379,17937],{},[69,59381,17941],{"className":59382,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":59384},[59385,59386,59391,59396,59401,59402,59403,59404],{"id":55251,"depth":7,"text":55252},{"id":55596,"depth":7,"text":59387,"children":59388},"Přebytek spotřebitele (CSCS)",[59389,59390],{"id":55615,"depth":4,"text":55616},{"id":2518,"depth":4,"text":2519},{"id":56191,"depth":7,"text":59392,"children":59393},"Přebytek výrobce (PSPS)",[59394,59395],{"id":56210,"depth":4,"text":56211},{"id":56373,"depth":4,"text":2519},{"id":56981,"depth":7,"text":56982,"children":59397},[59398,59399],{"id":56985,"depth":4,"text":56986},{"id":58279,"depth":4,"text":59400},"Příklad 2.13 — numerický výpočet PSPS",{"id":58584,"depth":7,"text":58585},{"id":320,"depth":7,"text":321},{"id":59220,"depth":7,"text":59221},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":13513,"description":156},[9647,3938],"topics\u002Fprebytek-spotrebitele-vyrobce",[17,55121,59411,59412,13721,17975,59413,59414],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":59417,"title":59418,"body":59419,"course":163,"courses":59575,"created":165,"description":59576,"extension":166,"meta":59577,"navigation":168,"path":59578,"seo":59579,"sources":59580,"stem":59582,"tags":59583,"type":177,"updated":178,"__hash__":59587},"topics\u002Ftopics\u002Fpredikce.md","Predikce a prognózování",{"type":48,"value":59420,"toc":59568},[59421,59424,59430,59434,59451,59455,59512,59516,59533,59537,59544,59549],[51,59422,59418],{"id":59423},"predikce-a-prognózování",[55,59425,59426,59427,195],{},"Předpovídání budoucích hodnot na základě historických dat. Jedna z nejdůležitějších aplikačních oblastí v kurzu ",[69,59428,136],{"className":59429,"href":135,"dataFsResolvedFilePath":134},[62],[84,59431,59433],{"id":59432},"co-se-predikuje","Co se predikuje",[89,59435,59436,59439,59442,59445,59448],{},[92,59437,59438],{},"Akciové indexy",[92,59440,59441],{},"Měnové kurzy (CZK\u002FUSD, USD\u002FEUR)",[92,59443,59444],{},"Kryptoměny",[92,59446,59447],{},"Ceny komodit (zlato, ropa, obilí)",[92,59449,59450],{},"Poptávka, prodeje, výrobní objem",[84,59452,59454],{"id":59453},"metody-predikce-v-kontextu-kurzu","Metody predikce v kontextu kurzu",[323,59456,59457,59466],{},[326,59458,59459],{},[329,59460,59461,59463],{},[332,59462,10291],{},[332,59464,59465],{},"Role v predikci",[342,59467,59468,59479,59490,59501],{},[329,59469,59470,59476],{},[347,59471,59472],{},[69,59473,12754],{"className":59474,"href":59475},[62,63],"\u002Fwiki\u002Fumele-neuronove-site\\",[347,59477,59478],{},"Přímo se učí vzory z dat a predikují budoucí hodnoty",[329,59480,59481,59487],{},[347,59482,59483],{},[69,59484,12509],{"className":59485,"href":59486},[62,63],"\u002Fwiki\u002Fgeneticke-algoritmy\\",[347,59488,59489],{},"Optimalizují parametry predikčního modelu nebo obchodní strategie",[329,59491,59492,59498],{},[347,59493,59494],{},[69,59495,12261],{"className":59496,"href":59497},[62,63],"\u002Fwiki\u002Ffuzzy-logika\\",[347,59499,59500],{},"Modeluje expertní pravidla pro rozhodování o predikcích",[329,59502,59503,59509],{},[347,59504,59505],{},[69,59506,12398],{"className":59507,"href":59508},[62,63],"\u002Fwiki\u002Fanfis\\",[347,59510,59511],{},"Hybridně kombinuje fuzzy pravidla s učením z dat",[84,59513,59515],{"id":59514},"omezení","Omezení",[89,59517,59518,59527,59530],{},[92,59519,59520,59523,59524],{},[69,59521,12411],{"className":59522,"href":12410,"dataFsResolvedFilePath":12409},[62]," ukazuje, že mnoho systémů je extrémně citlivých na počáteční podmínky → ",[95,59525,59526],{},"dlouhodobá přesná předpověď bývá prakticky nemožná",[92,59528,59529],{},"Model nedává jistotu, ale informovaný odhad",[92,59531,59532],{},"Budoucnost je nejistá — model může pracovat s více scénáři",[84,59534,59536],{"id":59535},"hurstův-exponent","Hurstův exponent",[55,59538,59539,59540,195],{},"Rozlišuje charakter časové řady: náhodná (H = 0,5), trendová (H > 0,5), antipersistentní (H \u003C 0,5). Viz ",[69,59541,59543],{"className":59542,"href":12410,"dataFsResolvedFilePath":12409},[62],"teorie chaosu",[84,59545,756,59546],{"id":1952},[69,59547,136],{"className":59548,"href":135,"dataFsResolvedFilePath":134},[62],[89,59550,59551,59556,59561],{},[92,59552,59553],{},[69,59554,153],{"className":59555,"href":152,"dataFsResolvedFilePath":151},[62],[92,59557,59558],{},[69,59559,12820],{"className":59560,"href":12819,"dataFsResolvedFilePath":12818},[62],[92,59562,59563],{},[69,59564,12411],{"className":59565,"href":59566,"dataFsResolvedFilePath":59567},[62],"\u002Fwiki\u002Fipmrk-chaos","summaries\u002Fipmrk-chaos.md",{"title":156,"searchDepth":7,"depth":7,"links":59569},[59570,59571,59572,59573,59574],{"id":59432,"depth":7,"text":59433},{"id":59453,"depth":7,"text":59454},{"id":59514,"depth":7,"text":59515},{"id":59535,"depth":7,"text":59536},{"id":1952,"depth":7,"text":2003},[14],"Předpovídání budoucích hodnot na základě historických dat. Jedna z nejdůležitějších aplikačních oblastí v kurzu IpmrK.",{},"\u002Ftopics\u002Fpredikce",{"title":59418,"description":59576},[172,12845,59581],"raw\u002Fipmrk\u002Fchaos.md","topics\u002Fpredikce",[14,59584,59585,59586],"predikce","casove-rady","prognozovani","K7tNwF_8iNI4b3iwEgRfq_Y_VKJc5d7In2MjQU6YlLA",{"id":59589,"title":59590,"body":59591,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":78921,"navigation":168,"path":78922,"seo":78923,"sources":78924,"stem":78925,"tags":78926,"type":177,"updated":178,"__hash__":78932},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":48,"value":59592,"toc":78885},[59593,59596,59782,59784,59875,59880,60206,60210,60217,60221,60266,60333,60364,60414,60449,60453,60512,60517,60583,60701,60803,60807,60830,60908,60951,60955,60984,61051,61057,61171,61175,61255,61292,61344,61542,61606,61693,61697,61700,61779,61782,61900,61919,61984,61988,62080,62148,62189,62243,62311,62348,62352,62410,62440,62651,62723,62775,62941,63034,63069,63073,63077,63114,63179,63234,63238,63261,63350,63454,63523,63527,63624,63737,63793,63847,63905,63966,63969,64005,64070,64100,64329,64387,64421,64425,64452,64531,64645,64666,64745,64747,64855,64859,64997,65319,65323,65326,65330,65379,65383,65637,65789,65796,65869,66053,66058,66401,66405,66428,66430,66451,66510,66520,66569,66711,66785,66880,66995,67093,67211,67215,67284,67289,67401,67546,67597,67709,67751,67755,67775,67836,67863,67925,67929,67951,68020,68300,68307,68337,68344,68537,68541,68619,68624,68700,68703,68791,68867,68934,68983,69086,69159,69280,69631,69744,69846,69850,69853,69860,69863,69899,69958,69967,70116,70340,70344,70407,70586,70678,70733,70737,70793,70863,70915,70936,71017,71020,71095,71139,71143,71184,71227,71253,71257,71328,71424,71486,71538,71641,71719,71742,71771,71775,71941,72058,72130,72445,72605,72609,72660,72722,72757,72787,72887,72929,73098,73103,73199,73237,73241,73360,73661,73663,73698,73702,73706,73834,73966,74288,74476,74554,74558,74863,74976,75122,75307,75413,75645,75760,75842,75961,76059,76100,76104,76159,76303,76457,76617,76710,76904,77216,77347,77476,77480,77552,77594,77645,77647,78842,78844],[51,59594,59590],{"id":59595},"příjem-náklady-zisk-a-nabídka-firmy",[1023,59597,59598],{},[55,59599,59600,3960,59602,1445,59605,59620,59621,1445,59624,59639,59640,1445,59643,59671,59672,59694,59695,59719,59720,59742,59743,59746,59747,59763,59764,195],{},[1647,59601,3959],{},[95,59603,59604],{},"Příjem",[1647,59606,59608],{"className":59607},[2059],[2061,59609,59610],{"xmlns":2063},[2065,59611,59612,59618],{},[2068,59613,59614,59616],{},[2071,59615,543],{},[2071,59617,4082],{},[2092,59619,4182],{"encoding":2094}," je to, co firma inkasuje (cena krát množství), ",[95,59622,59623],{},"náklady",[1647,59625,59627],{"className":59626},[2059],[2061,59628,59629],{"xmlns":2063},[2065,59630,59631,59637],{},[2068,59632,59633,59635],{},[2071,59634,543],{},[2071,59636,2849],{},[2092,59638,3317],{"encoding":2094}," to, co vynaloží (fixní plus variabilní), a ",[95,59641,59642],{},"zisk",[1647,59644,59646],{"className":59645},[2059],[2061,59647,59648],{"xmlns":2063},[2065,59649,59650,59668],{},[2068,59651,59652,59654,59656,59658,59660,59662,59664,59666],{},[2071,59653,575],{},[2071,59655,4082],{},[2075,59657,2077],{},[2071,59659,543],{},[2071,59661,4082],{},[2075,59663,2303],{},[2071,59665,543],{},[2071,59667,2849],{},[2092,59669,59670],{"encoding":2094},"PR = TR - TC"," jejich rozdíl. Kapitola pro každou ze tří veličin zavádí celkovou, průměrnou a mezní podobu, ukáže jejich grafický průběh (pro lineární poptávku a kubické náklady) a odvodí tři klíčové optimalizační principy: ",[1647,59673,59675],{"className":59674},[2059],[2061,59676,59677],{"xmlns":2063},[2065,59678,59679,59691],{},[2068,59680,59681,59683,59685,59687,59689],{},[2071,59682,4342],{},[2071,59684,2849],{},[2075,59686,2077],{},[2071,59688,2890],{},[2071,59690,2849],{},[2092,59692,59693],{"encoding":2094},"AC = MC"," v minimu průměrných nákladů, ",[1647,59696,59698],{"className":59697},[2059],[2061,59699,59700],{"xmlns":2063},[2065,59701,59702,59716],{},[2068,59703,59704,59706,59708,59710,59712,59714],{},[2071,59705,4342],{},[2071,59707,44630],{},[2071,59709,2849],{},[2075,59711,2077],{},[2071,59713,2890],{},[2071,59715,2849],{},[2092,59717,59718],{"encoding":2094},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[1647,59721,59723],{"className":59722},[2059],[2061,59724,59725],{"xmlns":2063},[2065,59726,59727,59739],{},[2068,59728,59729,59731,59733,59735,59737],{},[2071,59730,2890],{},[2071,59732,4082],{},[2075,59734,2077],{},[2071,59736,2890],{},[2071,59738,2849],{},[2092,59740,59741],{"encoding":2094},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[95,59744,59745],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[1647,59748,59750],{"className":59749},[2059],[2061,59751,59752],{"xmlns":2063},[2065,59753,59754,59760],{},[2068,59755,59756,59758],{},[2071,59757,2890],{},[2071,59759,2849],{},[2092,59761,59762],{"encoding":2094},"MC"," nad bodem minima ",[1647,59765,59767],{"className":59766},[2059],[2061,59768,59769],{"xmlns":2063},[2065,59770,59771,59779],{},[2068,59772,59773,59775,59777],{},[2071,59774,4342],{},[2071,59776,44630],{},[2071,59778,2849],{},[2092,59780,59781],{"encoding":2094},"AVC",[84,59783,55252],{"id":55251},[55,59785,59786,59787,59790,59791,59793,59794,835,59797,835,59800,59802,59803,59806,59807,59810,59811,59814,59815,2744,59830,2462,59845,2744,59860,4007],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[95,59788,59789],{},"příjmem"," (revenue) a ",[95,59792,59623],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[95,59795,59796],{},"zisku",[95,59798,59799],{},"bodů zvratu",[95,59801,2044],{}," a konstrukcí ",[95,59804,59805],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[69,59808,2430],{"className":59809,"dataFsResolvedFilePath":4005,"href":4006},[62]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[69,59812,12858],{"className":59813,"dataFsResolvedFilePath":3888,"href":3889},[62]," (pro zpětnou rekonstrukci ",[1647,59816,59818],{"className":59817},[2059],[2061,59819,59820],{"xmlns":2063},[2065,59821,59822,59828],{},[2068,59823,59824,59826],{},[2071,59825,543],{},[2071,59827,4082],{},[2092,59829,4182],{"encoding":2094},[1647,59831,59833],{"className":59832},[2059],[2061,59834,59835],{"xmlns":2063},[2065,59836,59837,59843],{},[2068,59838,59839,59841],{},[2071,59840,2890],{},[2071,59842,4082],{},[2092,59844,6721],{"encoding":2094},[1647,59846,59848],{"className":59847},[2059],[2061,59849,59850],{"xmlns":2063},[2065,59851,59852,59858],{},[2068,59853,59854,59856],{},[2071,59855,543],{},[2071,59857,2849],{},[2092,59859,3317],{"encoding":2094},[1647,59861,59863],{"className":59862},[2059],[2061,59864,59865],{"xmlns":2063},[2065,59866,59867,59873],{},[2068,59868,59869,59871],{},[2071,59870,2890],{},[2071,59872,2849],{},[2092,59874,59762],{"encoding":2094},[55,59876,59877],{},[95,59878,59879],{},"Cílové znalosti:",[89,59881,59882,60046,60049,60052,60145,60192,60199],{},[92,59883,59884,59885,835,59900,835,59916,75,59931,835,59946,835,59962,835,59980,835,59998,835,60015,835,60031,8512],{},"odvodit a interpretovat funkce ",[1647,59886,59888],{"className":59887},[2059],[2061,59889,59890],{"xmlns":2063},[2065,59891,59892,59898],{},[2068,59893,59894,59896],{},[2071,59895,543],{},[2071,59897,4082],{},[2092,59899,4182],{"encoding":2094},[1647,59901,59903],{"className":59902},[2059],[2061,59904,59905],{"xmlns":2063},[2065,59906,59907,59913],{},[2068,59908,59909,59911],{},[2071,59910,4342],{},[2071,59912,4082],{},[2092,59914,59915],{"encoding":2094},"AR",[1647,59917,59919],{"className":59918},[2059],[2061,59920,59921],{"xmlns":2063},[2065,59922,59923,59929],{},[2068,59924,59925,59927],{},[2071,59926,2890],{},[2071,59928,4082],{},[2092,59930,6721],{"encoding":2094},[1647,59932,59934],{"className":59933},[2059],[2061,59935,59936],{"xmlns":2063},[2065,59937,59938,59944],{},[2068,59939,59940,59942],{},[2071,59941,543],{},[2071,59943,2849],{},[2092,59945,3317],{"encoding":2094},[1647,59947,59949],{"className":59948},[2059],[2061,59950,59951],{"xmlns":2063},[2065,59952,59953,59959],{},[2068,59954,59955,59957],{},[2071,59956,10177],{},[2071,59958,2849],{},[2092,59960,59961],{"encoding":2094},"FC",[1647,59963,59965],{"className":59964},[2059],[2061,59966,59967],{"xmlns":2063},[2065,59968,59969,59977],{},[2068,59970,59971,59973,59975],{},[2071,59972,543],{},[2071,59974,44630],{},[2071,59976,2849],{},[2092,59978,59979],{"encoding":2094},"TVC",[1647,59981,59983],{"className":59982},[2059],[2061,59984,59985],{"xmlns":2063},[2065,59986,59987,59995],{},[2068,59988,59989,59991,59993],{},[2071,59990,4342],{},[2071,59992,10177],{},[2071,59994,2849],{},[2092,59996,59997],{"encoding":2094},"AFC",[1647,59999,60001],{"className":60000},[2059],[2061,60002,60003],{"xmlns":2063},[2065,60004,60005,60013],{},[2068,60006,60007,60009,60011],{},[2071,60008,4342],{},[2071,60010,44630],{},[2071,60012,2849],{},[2092,60014,59781],{"encoding":2094},[1647,60016,60018],{"className":60017},[2059],[2061,60019,60020],{"xmlns":2063},[2065,60021,60022,60028],{},[2068,60023,60024,60026],{},[2071,60025,4342],{},[2071,60027,2849],{},[2092,60029,60030],{"encoding":2094},"AC",[1647,60032,60034],{"className":60033},[2059],[2061,60035,60036],{"xmlns":2063},[2065,60037,60038,60044],{},[2068,60039,60040,60042],{},[2071,60041,2890],{},[2071,60043,2849],{},[2092,60045,59762],{"encoding":2094},[92,60047,60048],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[92,60050,60051],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[92,60053,60054,60055,60058,60059,46105,60101,8512],{},"osvojit si ",[95,60056,60057],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[1647,60060,60062],{"className":60061},[2059],[2061,60063,60064],{"xmlns":2063},[2065,60065,60066,60098],{},[2068,60067,60068,60070,60072,60074,60080,60082,60084,60086,60088,60090,60096],{},[2071,60069,4342],{},[2071,60071,2849],{},[2075,60073,2084],{"stretchy":2083},[2348,60075,60076,60078],{},[2071,60077,2861],{},[2210,60079,630],{},[2075,60081,2090],{"stretchy":2083},[2075,60083,2077],{},[2071,60085,2890],{},[2071,60087,2849],{},[2075,60089,2084],{"stretchy":2083},[2348,60091,60092,60094],{},[2071,60093,2861],{},[2210,60095,630],{},[2075,60097,2090],{"stretchy":2083},[2092,60099,60100],{"encoding":2094},"AC(Q_0)=MC(Q_0)",[1647,60102,60104],{"className":60103},[2059],[2061,60105,60106],{"xmlns":2063},[2065,60107,60108,60142],{},[2068,60109,60110,60112,60114,60116,60118,60124,60126,60128,60130,60132,60134,60140],{},[2071,60111,4342],{},[2071,60113,44630],{},[2071,60115,2849],{},[2075,60117,2084],{"stretchy":2083},[2348,60119,60120,60122],{},[2071,60121,2861],{},[2210,60123,630],{},[2075,60125,2090],{"stretchy":2083},[2075,60127,2077],{},[2071,60129,2890],{},[2071,60131,2849],{},[2075,60133,2084],{"stretchy":2083},[2348,60135,60136,60138],{},[2071,60137,2861],{},[2210,60139,630],{},[2075,60141,2090],{"stretchy":2083},[2092,60143,60144],{"encoding":2094},"AVC(Q_0)=MC(Q_0)",[92,60146,60054,60147,60058,60150,8512],{},[95,60148,60149],{},"princip maximalizace zisku",[1647,60151,60153],{"className":60152},[2059],[2061,60154,60155],{"xmlns":2063},[2065,60156,60157,60189],{},[2068,60158,60159,60161,60163,60165,60171,60173,60175,60177,60179,60181,60187],{},[2071,60160,2890],{},[2071,60162,4082],{},[2075,60164,2084],{"stretchy":2083},[2348,60166,60167,60169],{},[2071,60168,2861],{},[2210,60170,630],{},[2075,60172,2090],{"stretchy":2083},[2075,60174,2077],{},[2071,60176,2890],{},[2071,60178,2849],{},[2075,60180,2084],{"stretchy":2083},[2348,60182,60183,60185],{},[2071,60184,2861],{},[2210,60186,630],{},[2075,60188,2090],{"stretchy":2083},[2092,60190,60191],{"encoding":2094},"MR(Q_0)=MC(Q_0)",[92,60193,60194,60195,60198],{},"stanovit ",[95,60196,60197],{},"body zvratu"," a interval zisku;",[92,60200,60201,60202,60205],{},"zkonstruovat ",[95,60203,60204],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[84,60207,60209],{"id":60208},"příjem-firmy","Příjem firmy",[55,60211,60212],{},[58,60213],{"alt":60214,"className":60215,"src":60216},"imek-ar-mr-dvojnasobny-sklon",[62,63],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[609,60218,60220],{"id":60219},"celkový-příjem","Celkový příjem",[55,60222,60223,60224,11156,60239,60242,60243,32971],{},"Celkový příjem ",[1647,60225,60227],{"className":60226},[2059],[2061,60228,60229],{"xmlns":2063},[2065,60230,60231,60237],{},[2068,60232,60233,60235],{},[2071,60234,543],{},[2071,60236,4082],{},[2092,60238,4182],{"encoding":2094},[95,60240,60241],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[1647,60244,60246],{"className":60245},[2059],[2061,60247,60248],{"xmlns":2063},[2065,60249,60250,60264],{},[2068,60251,60252,60254,60256,60258,60260,60262],{},[2071,60253,575],{},[2075,60255,2077],{},[2071,60257,4271],{},[2075,60259,2084],{"stretchy":2083},[2071,60261,2861],{},[2075,60263,2090],{"stretchy":2083},[2092,60265,4727],{"encoding":2094},[1647,60267,60269],{"className":60268},[2059],[2061,60270,60271],{"xmlns":2063,"display":31093},[2065,60272,60273,60330],{},[23493,60274,60275],{"width":31098},[23498,60276,60277,60279,60323,60325],{},[23501,60278],{"width":31103},[23501,60280,60281],{},[2068,60282,60283,60285,60287,60289,60291,60293,60295,60297,60299,60301,60303,60305,60307,60309,60311,60313,60315,60317,60319,60321],{},[2071,60284,543],{},[2071,60286,4082],{},[2075,60288,2077],{},[2071,60290,543],{},[2071,60292,4082],{},[2075,60294,2084],{"stretchy":2083},[2071,60296,2861],{},[2075,60298,2090],{"stretchy":2083},[2075,60300,2077],{},[2071,60302,575],{},[2075,60304,3251],{},[2071,60306,2861],{},[2075,60308,2077],{},[2071,60310,4271],{},[2075,60312,2084],{"stretchy":2083},[2071,60314,2861],{},[2075,60316,2090],{"stretchy":2083},[2075,60318,3251],{},[2071,60320,2861],{},[2071,60322,195],{"mathvariant":2450},[23501,60324],{"width":31103},[23501,60326,60327],{},[2363,60328,60329],{},"(3.1)",[2092,60331,60332],{"encoding":2094},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[55,60334,60335,60336,60339,60340,60363],{},"Graf funkce se nazývá ",[95,60337,60338],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[1647,60341,60343],{"className":60342},[2059],[2061,60344,60345],{"xmlns":2063},[2065,60346,60347,60361],{},[2068,60348,60349,60351,60353,60355,60357,60359],{},[2071,60350,575],{},[2075,60352,2077],{},[2071,60354,69],{},[2071,60356,2861],{},[2075,60358,2176],{},[2071,60360,2179],{},[2092,60362,41352],{"encoding":2094},", je celkový příjem kvadratickou funkcí, neboť",[1647,60365,60367],{"className":60366},[2059],[2061,60368,60369],{"xmlns":2063,"display":31093},[2065,60370,60371,60411],{},[2068,60372,60373,60375,60377,60379,60381,60383,60385,60387,60389,60391,60393,60395,60397,60403,60405,60407,60409],{},[2071,60374,543],{},[2071,60376,4082],{},[2075,60378,2077],{},[2071,60380,2861],{},[2075,60382,2084],{"stretchy":2083},[2071,60384,69],{},[2071,60386,2861],{},[2075,60388,2176],{},[2071,60390,2179],{},[2075,60392,2090],{"stretchy":2083},[2075,60394,2077],{},[2071,60396,69],{},[2205,60398,60399,60401],{},[2071,60400,2861],{},[2210,60402,646],{},[2075,60404,2176],{},[2071,60406,2179],{},[2071,60408,2861],{},[2075,60410,2361],{"separator":2360},[2092,60412,60413],{"encoding":2094},"TR = Q(aQ + b) = aQ^2 + bQ,",[55,60415,60416,60417,60430,60431,60448],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[1647,60418,60420],{"className":60419},[2059],[2061,60421,60422],{"xmlns":2063},[2065,60423,60424,60428],{},[2068,60425,60426],{},[2071,60427,10871],{},[2092,60429,10871],{"encoding":2094}," (jelikož ",[1647,60432,60434],{"className":60433},[2059],[2061,60435,60436],{"xmlns":2063},[2065,60437,60438,60446],{},[2068,60439,60440,60442,60444],{},[2071,60441,69],{},[2075,60443,3521],{},[2210,60445,630],{},[2092,60447,47379],{"encoding":2094},") procházející počátkem.",[1144,60450,60452],{"id":60451},"příklad-31","Příklad 3.1",[55,60454,60455,60458,60459,60495,60496,60511],{},[95,60456,60457],{},"Zadání."," Pro poptávku ",[1647,60460,60462],{"className":60461},[2059],[2061,60463,60464],{"xmlns":2063},[2065,60465,60466,60492],{},[2068,60467,60468,60470,60472,60474,60476,60478,60480,60482,60484,60486,60488,60490],{},[2071,60469,575],{},[2075,60471,2077],{},[2071,60473,4271],{},[2075,60475,2084],{"stretchy":2083},[2071,60477,2861],{},[2075,60479,2090],{"stretchy":2083},[2075,60481,2077],{},[2075,60483,2303],{},[2210,60485,646],{},[2071,60487,2861],{},[2075,60489,2176],{},[2210,60491,3164],{},[2092,60493,60494],{"encoding":2094},"P = D(Q) = -2Q + 100"," určete ",[1647,60497,60499],{"className":60498},[2059],[2061,60500,60501],{"xmlns":2063},[2065,60502,60503,60509],{},[2068,60504,60505,60507],{},[2071,60506,543],{},[2071,60508,4082],{},[2092,60510,4182],{"encoding":2094}," a charakterizujte jeho křivku.",[55,60513,60514,60516],{},[95,60515,25509],{}," Celkový příjem je",[1647,60518,60520],{"className":60519},[2059],[2061,60521,60522],{"xmlns":2063,"display":31093},[2065,60523,60524,60580],{},[2068,60525,60526,60528,60530,60532,60534,60536,60538,60540,60542,60544,60546,60548,60550,60552,60554,60556,60558,60560,60562,60564,60566,60572,60574,60576,60578],{},[2071,60527,543],{},[2071,60529,4082],{},[2075,60531,2077],{},[2071,60533,543],{},[2071,60535,4082],{},[2075,60537,2084],{"stretchy":2083},[2071,60539,2861],{},[2075,60541,2090],{"stretchy":2083},[2075,60543,2077],{},[2071,60545,2861],{},[2075,60547,2084],{"stretchy":2083},[2075,60549,2303],{},[2210,60551,646],{},[2071,60553,2861],{},[2075,60555,2176],{},[2210,60557,3164],{},[2075,60559,2090],{"stretchy":2083},[2075,60561,2077],{},[2075,60563,2303],{},[2210,60565,646],{},[2205,60567,60568,60570],{},[2071,60569,2861],{},[2210,60571,646],{},[2075,60573,2176],{},[2210,60575,3164],{},[2071,60577,2861],{},[2071,60579,195],{"mathvariant":2450},[2092,60581,60582],{"encoding":2094},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[55,60584,60585,60586,75,60608,60630,60631,60649,60650,195],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[1647,60587,60589],{"className":60588},[2059],[2061,60590,60591],{"xmlns":2063},[2065,60592,60593,60605],{},[2068,60594,60595,60601,60603],{},[2348,60596,60597,60599],{},[2071,60598,2861],{},[2210,60600,638],{},[2075,60602,2077],{},[2210,60604,630],{},[2092,60606,60607],{"encoding":2094},"Q_1 = 0",[1647,60609,60611],{"className":60610},[2059],[2061,60612,60613],{"xmlns":2063},[2065,60614,60615,60627],{},[2068,60616,60617,60623,60625],{},[2348,60618,60619,60621],{},[2071,60620,2861],{},[2210,60622,646],{},[2075,60624,2077],{},[2210,60626,3194],{},[2092,60628,60629],{"encoding":2094},"Q_2 = 50",". Maxima dosahuje při ",[1647,60632,60634],{"className":60633},[2059],[2061,60635,60636],{"xmlns":2063},[2065,60637,60638,60646],{},[2068,60639,60640,60642,60644],{},[2071,60641,2861],{},[2075,60643,2077],{},[2210,60645,5091],{},[2092,60647,60648],{"encoding":2094},"Q = 25"," ve výši ",[1647,60651,60653],{"className":60652},[2059],[2061,60654,60655],{"xmlns":2063},[2065,60656,60657,60698],{},[2068,60658,60659,60661,60671,60673,60675,60677,60679,60682,60684,60686,60688,60690,60692,60694,60696],{},[2071,60660,543],{},[2348,60662,60663,60665,60668],{},[2071,60664,4082],{},[2071,60666,60667],{},"max",[2075,60669,60670],{},"⁡",[2075,60672,2077],{},[2075,60674,2303],{},[2210,60676,646],{},[2075,60678,3251],{},[2210,60680,60681],{},"625",[2075,60683,2176],{},[2210,60685,3164],{},[2075,60687,3251],{},[2210,60689,5091],{},[2075,60691,2077],{},[2210,60693,638],{},[2363,60695,3061],{},[2210,60697,33770],{},[2092,60699,60700],{"encoding":2094},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[55,60702,60703],{},[3982,60704,60705,60706,60740,60741,75,60754,60767,60768,2697,60786,195],{},"Obrázek 3.1: Parabola ",[1647,60707,60709],{"className":60708},[2059],[2061,60710,60711],{"xmlns":2063},[2065,60712,60713,60737],{},[2068,60714,60715,60717,60719,60721,60723,60725,60731,60733,60735],{},[2071,60716,543],{},[2071,60718,4082],{},[2075,60720,2077],{},[2075,60722,2303],{},[2210,60724,646],{},[2205,60726,60727,60729],{},[2071,60728,2861],{},[2210,60730,646],{},[2075,60732,2176],{},[2210,60734,3164],{},[2071,60736,2861],{},[2092,60738,60739],{"encoding":2094},"TR = -2Q^2 + 100Q"," s nulami v ",[1647,60742,60744],{"className":60743},[2059],[2061,60745,60746],{"xmlns":2063},[2065,60747,60748,60752],{},[2068,60749,60750],{},[2210,60751,630],{},[2092,60753,630],{"encoding":2094},[1647,60755,60757],{"className":60756},[2059],[2061,60758,60759],{"xmlns":2063},[2065,60760,60761,60765],{},[2068,60762,60763],{},[2210,60764,3194],{},[2092,60766,3194],{"encoding":2094}," a maximem ",[1647,60769,60771],{"className":60770},[2059],[2061,60772,60773],{"xmlns":2063},[2065,60774,60775,60783],{},[2068,60776,60777,60779,60781],{},[2210,60778,638],{},[2363,60780,3061],{},[2210,60782,33770],{},[2092,60784,60785],{"encoding":2094},"1\\,250",[1647,60787,60789],{"className":60788},[2059],[2061,60790,60791],{"xmlns":2063},[2065,60792,60793,60801],{},[2068,60794,60795,60797,60799],{},[2071,60796,2861],{},[2075,60798,2077],{},[2210,60800,5091],{},[2092,60802,60648],{"encoding":2094},[609,60804,60806],{"id":60805},"průměrný-příjem","Průměrný příjem",[55,60808,60809,1445,60811,11156,60826,60829],{},[95,60810,60806],{},[1647,60812,60814],{"className":60813},[2059],[2061,60815,60816],{"xmlns":2063},[2065,60817,60818,60824],{},[2068,60819,60820,60822],{},[2071,60821,4342],{},[2071,60823,4082],{},[2092,60825,59915],{"encoding":2094},[95,60827,60828],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[1647,60831,60833],{"className":60832},[2059],[2061,60834,60835],{"xmlns":2063,"display":31093},[2065,60836,60837,60905],{},[2068,60838,60839,60841,60843,60845,60847,60849,60851,60853,60855,60857,60873,60875,60893,60895,60897,60899,60901,60903],{},[2071,60840,4342],{},[2071,60842,4082],{},[2075,60844,2077],{},[2071,60846,4342],{},[2071,60848,4082],{},[2075,60850,2084],{"stretchy":2083},[2071,60852,2861],{},[2075,60854,2090],{"stretchy":2083},[2075,60856,2077],{},[2403,60858,60859,60871],{},[2068,60860,60861,60863,60865,60867,60869],{},[2071,60862,543],{},[2071,60864,4082],{},[2075,60866,2084],{"stretchy":2083},[2071,60868,2861],{},[2075,60870,2090],{"stretchy":2083},[2071,60872,2861],{},[2075,60874,2077],{},[2403,60876,60877,60891],{},[2068,60878,60879,60881,60883,60885,60887,60889],{},[2071,60880,2861],{},[2363,60882,3061],{},[2071,60884,4271],{},[2075,60886,2084],{"stretchy":2083},[2071,60888,2861],{},[2075,60890,2090],{"stretchy":2083},[2071,60892,2861],{},[2075,60894,2077],{},[2071,60896,4271],{},[2075,60898,2084],{"stretchy":2083},[2071,60900,2861],{},[2075,60902,2090],{"stretchy":2083},[2071,60904,195],{"mathvariant":2450},[2092,60906,60907],{"encoding":2094},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1023,60909,60910],{},[55,60911,60912,60915,60916,835,60919,195],{},[1647,60913,60914],{},"!note"," Klíčové pozorování\n",[95,60917,60918],{},"Průměrný příjem se vždy rovná poptávkové funkci",[1647,60920,60922],{"className":60921},[2059],[2061,60923,60924],{"xmlns":2063},[2065,60925,60926,60948],{},[2068,60927,60928,60930,60932,60934,60936,60938,60940,60942,60944,60946],{},[2071,60929,4342],{},[2071,60931,4082],{},[2075,60933,2084],{"stretchy":2083},[2071,60935,2861],{},[2075,60937,2090],{"stretchy":2083},[2075,60939,2077],{},[2071,60941,4271],{},[2075,60943,2084],{"stretchy":2083},[2071,60945,2861],{},[2075,60947,2090],{"stretchy":2083},[2092,60949,60950],{"encoding":2094},"AR(Q) = D(Q)",[609,60952,60954],{"id":60953},"mezní-příjem","Mezní příjem",[55,60956,60957,60958,1445,60961,11156,60976,60979,60980,60983],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[95,60959,60960],{},"mezní příjem",[1647,60962,60964],{"className":60963},[2059],[2061,60965,60966],{"xmlns":2063},[2065,60967,60968,60974],{},[2068,60969,60970,60972],{},[2071,60971,2890],{},[2071,60973,4082],{},[2092,60975,6721],{"encoding":2094},[95,60977,60978],{},"marginal revenue","), definovaný jako ",[69,60981,2430],{"className":60982,"dataFsResolvedFilePath":4005,"href":4006},[62]," celkového příjmu podle množství:",[1647,60985,60987],{"className":60986},[2059],[2061,60988,60989],{"xmlns":2063,"display":31093},[2065,60990,60991,61048],{},[23493,60992,60993],{"width":31098},[23498,60994,60995,60997,61041,61043],{},[23501,60996],{"width":31103},[23501,60998,60999],{},[2068,61000,61001,61003,61005,61007,61023,61025,61027,61033,61035,61037,61039],{},[2071,61002,2890],{},[2071,61004,4082],{},[2075,61006,2077],{},[2403,61008,61009,61017],{},[2068,61010,61011,61013,61015],{},[2071,61012,2273],{"mathvariant":2450},[2071,61014,543],{},[2071,61016,4082],{},[2068,61018,61019,61021],{},[2071,61020,2273],{"mathvariant":2450},[2071,61022,2861],{},[2075,61024,2077],{},[2071,61026,543],{},[2205,61028,61029,61031],{},[2071,61030,4082],{},[2075,61032,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,61034,2084],{"stretchy":2083},[2071,61036,2861],{},[2075,61038,2090],{"stretchy":2083},[2071,61040,195],{"mathvariant":2450},[23501,61042],{"width":31103},[23501,61044,61045],{},[2363,61046,61047],{},"(3.2)",[2092,61049,61050],{"encoding":2094},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[55,61052,61053,61054,61056],{},"Mezní příjem udává ",[95,61055,2669],{}," celkového příjmu vzhledem k množství.",[1023,61058,61059],{},[55,61060,61061,61063,61064,61090,61091,61108,61109,195],{},[1647,61062,4243],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[1647,61065,61067],{"className":61066},[2059],[2061,61068,61069],{"xmlns":2063},[2065,61070,61071,61087],{},[2068,61072,61073,61075,61077,61079,61085],{},[2071,61074,2890],{},[2071,61076,4082],{},[2075,61078,2084],{"stretchy":2083},[2205,61080,61081,61083],{},[2071,61082,2861],{},[2075,61084,4441],{},[2075,61086,2090],{"stretchy":2083},[2092,61088,61089],{"encoding":2094},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[1647,61092,61094],{"className":61093},[2059],[2061,61095,61096],{"xmlns":2063},[2065,61097,61098,61106],{},[2068,61099,61100],{},[2205,61101,61102,61104],{},[2071,61103,2861],{},[2075,61105,4441],{},[2092,61107,32871],{"encoding":2094},". Jinak řečeno: ",[1647,61110,61112],{"className":61111},[2059],[2061,61113,61114],{"xmlns":2063},[2065,61115,61116,61168],{},[2068,61117,61118,61120,61122,61124,61130,61132,61134,61136,61138,61140,61146,61148,61150,61152,61154,61156,61158,61160,61166],{},[2071,61119,2890],{},[2071,61121,4082],{},[2075,61123,2084],{"stretchy":2083},[2205,61125,61126,61128],{},[2071,61127,2861],{},[2075,61129,4441],{},[2075,61131,2090],{"stretchy":2083},[2075,61133,2803],{},[2071,61135,543],{},[2071,61137,4082],{},[2075,61139,2084],{"stretchy":2083},[2205,61141,61142,61144],{},[2071,61143,2861],{},[2075,61145,4441],{},[2075,61147,2176],{},[2210,61149,638],{},[2075,61151,2090],{"stretchy":2083},[2075,61153,2303],{},[2071,61155,543],{},[2071,61157,4082],{},[2075,61159,2084],{"stretchy":2083},[2205,61161,61162,61164],{},[2071,61163,2861],{},[2075,61165,4441],{},[2075,61167,2090],{"stretchy":2083},[2092,61169,61170],{"encoding":2094},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[1144,61172,61174],{"id":61173},"příklad-32","Příklad 3.2",[55,61176,61177,60458,61179,60495,61213,61228,61229,195],{},[95,61178,60457],{},[1647,61180,61182],{"className":61181},[2059],[2061,61183,61184],{"xmlns":2063},[2065,61185,61186,61210],{},[2068,61187,61188,61190,61192,61194,61196,61198,61200,61202,61204,61206,61208],{},[2071,61189,575],{},[2075,61191,2077],{},[2071,61193,4271],{},[2075,61195,2084],{"stretchy":2083},[2071,61197,2861],{},[2075,61199,2090],{"stretchy":2083},[2075,61201,2077],{},[2210,61203,3164],{},[2075,61205,2303],{},[2210,61207,646],{},[2071,61209,2861],{},[2092,61211,61212],{"encoding":2094},"P = D(Q) = 100 - 2Q",[1647,61214,61216],{"className":61215},[2059],[2061,61217,61218],{"xmlns":2063},[2065,61219,61220,61226],{},[2068,61221,61222,61224],{},[2071,61223,2890],{},[2071,61225,4082],{},[2092,61227,6721],{"encoding":2094}," a interpretujte jeho hodnoty pro ",[1647,61230,61232],{"className":61231},[2059],[2061,61233,61234],{"xmlns":2063},[2065,61235,61236,61252],{},[2068,61237,61238,61240,61242,61244,61246,61248,61250],{},[2071,61239,2861],{},[2075,61241,2077],{},[2210,61243,39270],{},[2075,61245,2361],{"separator":2360},[2210,61247,46153],{},[2075,61249,2361],{"separator":2360},[2210,61251,9121],{},[2092,61253,61254],{"encoding":2094},"Q = 15, 16, 20",[55,61256,61257,1445,61259,61291],{},[95,61258,25509],{},[1647,61260,61262],{"className":61261},[2059],[2061,61263,61264],{"xmlns":2063},[2065,61265,61266,61288],{},[2068,61267,61268,61270,61272,61274,61276,61278,61280,61282],{},[2071,61269,543],{},[2071,61271,4082],{},[2075,61273,2077],{},[2210,61275,3164],{},[2071,61277,2861],{},[2075,61279,2303],{},[2210,61281,646],{},[2205,61283,61284,61286],{},[2071,61285,2861],{},[2210,61287,646],{},[2092,61289,61290],{"encoding":2094},"TR = 100Q - 2Q^2",", tedy",[1647,61293,61295],{"className":61294},[2059],[2061,61296,61297],{"xmlns":2063,"display":31093},[2065,61298,61299,61341],{},[2068,61300,61301,61303,61305,61307,61309,61311,61313,61315,61317,61323,61329,61331,61333,61335,61337,61339],{},[2071,61302,2890],{},[2071,61304,4082],{},[2075,61306,2077],{},[2075,61308,2084],{"stretchy":2083},[2210,61310,3164],{},[2071,61312,2861],{},[2075,61314,2303],{},[2210,61316,646],{},[2205,61318,61319,61321],{},[2071,61320,2861],{},[2210,61322,646],{},[2205,61324,61325,61327],{},[2075,61326,2090],{"stretchy":2083},[2075,61328,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,61330,2077],{},[2210,61332,3164],{},[2075,61334,2303],{},[2210,61336,662],{},[2071,61338,2861],{},[2071,61340,195],{"mathvariant":2450},[2092,61342,61343],{"encoding":2094},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[55,61345,10790,61346,8189,61364,61390,61391,4445,61404,61419,61420,61433,61434,24159,61447,4445,61460,61475,61476,61489,61490,61521,61522,61541],{},[1647,61347,61349],{"className":61348},[2059],[2061,61350,61351],{"xmlns":2063},[2065,61352,61353,61361],{},[2068,61354,61355,61357,61359],{},[2071,61356,2861],{},[2075,61358,2077],{},[2210,61360,39270],{},[2092,61362,61363],{"encoding":2094},"Q = 15",[1647,61365,61367],{"className":61366},[2059],[2061,61368,61369],{"xmlns":2063},[2065,61370,61371,61387],{},[2068,61372,61373,61375,61377,61379,61381,61383,61385],{},[2071,61374,2890],{},[2071,61376,4082],{},[2075,61378,2084],{"stretchy":2083},[2210,61380,39270],{},[2075,61382,2090],{"stretchy":2083},[2075,61384,2077],{},[2210,61386,5298],{},[2092,61388,61389],{"encoding":2094},"MR(15) = 40",": při množství ",[1647,61392,61394],{"className":61393},[2059],[2061,61395,61396],{"xmlns":2063},[2065,61397,61398,61402],{},[2068,61399,61400],{},[2210,61401,39270],{},[2092,61403,39270],{"encoding":2094},[1647,61405,61407],{"className":61406},[2059],[2061,61408,61409],{"xmlns":2063},[2065,61410,61411,61417],{},[2068,61412,61413,61415],{},[2071,61414,543],{},[2071,61416,4082],{},[2092,61418,4182],{"encoding":2094}," mění asi ",[1647,61421,61423],{"className":61422},[2059],[2061,61424,61425],{"xmlns":2063},[2065,61426,61427,61431],{},[2068,61428,61429],{},[2210,61430,5298],{},[2092,61432,5298],{"encoding":2094},"-krát rychleji než množství; s růstem ",[1647,61435,61437],{"className":61436},[2059],[2061,61438,61439],{"xmlns":2063},[2065,61440,61441,61445],{},[2068,61442,61443],{},[2071,61444,2861],{},[2092,61446,2861],{"encoding":2094},[1647,61448,61450],{"className":61449},[2059],[2061,61451,61452],{"xmlns":2063},[2065,61453,61454,61458],{},[2068,61455,61456],{},[2210,61457,638],{},[2092,61459,638],{"encoding":2094},[1647,61461,61463],{"className":61462},[2059],[2061,61464,61465],{"xmlns":2063},[2065,61466,61467,61473],{},[2068,61468,61469,61471],{},[2071,61470,543],{},[2071,61472,4082],{},[2092,61474,4182],{"encoding":2094}," zvýší přibližně o ",[1647,61477,61479],{"className":61478},[2059],[2061,61480,61481],{"xmlns":2063},[2065,61482,61483,61487],{},[2068,61484,61485],{},[2210,61486,5298],{},[2092,61488,5298],{"encoding":2094},", tj. ze skutečné hodnoty ",[1647,61491,61493],{"className":61492},[2059],[2061,61494,61495],{"xmlns":2063},[2065,61496,61497,61518],{},[2068,61498,61499,61501,61503,61505,61507,61509,61511,61513,61515],{},[2071,61500,543],{},[2071,61502,4082],{},[2075,61504,2084],{"stretchy":2083},[2210,61506,39270],{},[2075,61508,2090],{"stretchy":2083},[2075,61510,2077],{},[2210,61512,638],{},[2363,61514,3061],{},[2210,61516,61517],{},"050",[2092,61519,61520],{"encoding":2094},"TR(15) = 1\\,050"," na přibližně ",[1647,61523,61525],{"className":61524},[2059],[2061,61526,61527],{"xmlns":2063},[2065,61528,61529,61538],{},[2068,61530,61531,61533,61535],{},[2210,61532,638],{},[2363,61534,3061],{},[2210,61536,61537],{},"090",[2092,61539,61540],{"encoding":2094},"1\\,090",". Skutečná změna je",[1647,61543,61545],{"className":61544},[2059],[2061,61546,61547],{"xmlns":2063,"display":31093},[2065,61548,61549,61603],{},[2068,61550,61551,61553,61555,61557,61559,61561,61563,61565,61567,61569,61571,61573,61575,61577,61579,61581,61583,61585,61587,61590,61592,61594,61596,61598,61600],{},[2071,61552,2961],{"mathvariant":2450},[2071,61554,543],{},[2071,61556,4082],{},[2075,61558,2077],{},[2071,61560,543],{},[2071,61562,4082],{},[2075,61564,2084],{"stretchy":2083},[2210,61566,46153],{},[2075,61568,2090],{"stretchy":2083},[2075,61570,2303],{},[2071,61572,543],{},[2071,61574,4082],{},[2075,61576,2084],{"stretchy":2083},[2210,61578,39270],{},[2075,61580,2090],{"stretchy":2083},[2075,61582,2077],{},[2210,61584,638],{},[2363,61586,3061],{},[2210,61588,61589],{},"088",[2075,61591,2303],{},[2210,61593,638],{},[2363,61595,3061],{},[2210,61597,61517],{},[2075,61599,2077],{},[2210,61601,61602],{},"38.",[2092,61604,61605],{"encoding":2094},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[55,61607,61608,61609,835,61635,2999,61661,61676,61677,61692],{},"Podobně ",[1647,61610,61612],{"className":61611},[2059],[2061,61613,61614],{"xmlns":2063},[2065,61615,61616,61632],{},[2068,61617,61618,61620,61622,61624,61626,61628,61630],{},[2071,61619,2890],{},[2071,61621,4082],{},[2075,61623,2084],{"stretchy":2083},[2210,61625,46153],{},[2075,61627,2090],{"stretchy":2083},[2075,61629,2077],{},[2210,61631,5652],{},[2092,61633,61634],{"encoding":2094},"MR(16) = 36",[1647,61636,61638],{"className":61637},[2059],[2061,61639,61640],{"xmlns":2063},[2065,61641,61642,61658],{},[2068,61643,61644,61646,61648,61650,61652,61654,61656],{},[2071,61645,2890],{},[2071,61647,4082],{},[2075,61649,2084],{"stretchy":2083},[2210,61651,9121],{},[2075,61653,2090],{"stretchy":2083},[2075,61655,2077],{},[2210,61657,9121],{},[2092,61659,61660],{"encoding":2094},"MR(20) = 20",[1647,61662,61664],{"className":61663},[2059],[2061,61665,61666],{"xmlns":2063},[2065,61667,61668,61674],{},[2068,61669,61670,61672],{},[2071,61671,2890],{},[2071,61673,4082],{},[2092,61675,6721],{"encoding":2094}," je klesající funkce — rychlost změny ",[1647,61678,61680],{"className":61679},[2059],[2061,61681,61682],{"xmlns":2063},[2065,61683,61684,61690],{},[2068,61685,61686,61688],{},[2071,61687,543],{},[2071,61689,4082],{},[2092,61691,4182],{"encoding":2094}," s růstem množství klesá.",[609,61694,61696],{"id":61695},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[55,61698,61699],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[1647,61701,61703],{"className":61702},[2059],[2061,61704,61705],{"xmlns":2063,"display":31093},[2065,61706,61707,61776],{},[23493,61708,61709],{"width":31098},[23498,61710,61711,61713,61769,61771],{},[23501,61712],{"width":31103},[23501,61714,61715],{},[2068,61716,61717,61719,61721,61723,61725,61727,61729,61731,61733,61735,61737,61739,61741,61743,61749,61751,61753,61755,61757,61759,61761,61763,61765,61767],{},[2071,61718,2961],{"mathvariant":2450},[2071,61720,543],{},[2071,61722,4082],{},[2363,61724,4072],{},[2075,61726,2803],{},[2363,61728,4072],{},[2071,61730,2273],{"mathvariant":2450},[2071,61732,543],{},[2071,61734,4082],{},[2075,61736,2077],{},[2075,61738,2084],{"stretchy":2083},[2071,61740,543],{},[2071,61742,4082],{},[2205,61744,61745,61747],{},[2075,61746,2090],{"stretchy":2083},[2075,61748,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,61750,3061],{},[2071,61752,2273],{"mathvariant":2450},[2071,61754,2861],{},[2075,61756,2077],{},[2071,61758,2890],{},[2071,61760,4082],{},[2363,61762,3061],{},[2071,61764,2273],{"mathvariant":2450},[2071,61766,2861],{},[2075,61768,2361],{"separator":2360},[23501,61770],{"width":31103},[23501,61772,61773],{},[2363,61774,61775],{},"(3.3)",[2092,61777,61778],{"encoding":2094},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[55,61780,61781],{},"schematicky:",[1647,61783,61785],{"className":61784},[2059],[2061,61786,61787],{"xmlns":2063,"display":31093},[2065,61788,61789,61897],{},[2068,61790,61791,61829,61831,61833,61835,61864,61867,61895],{},[2068,61792,61793,61796,61802,61805,61811,61814,61820,61826],{},[2363,61794,61795],{},"zm",[8473,61797,61798,61800],{"accent":2360},[2363,61799,50028],{},[2075,61801,27796],{},[2363,61803,61804],{},"na celkov",[8473,61806,61807,61809],{"accent":2360},[2363,61808,50028],{},[2075,61810,27715],{},[2363,61812,61813],{},"ho p",[8473,61815,61816,61818],{"accent":2360},[2363,61817,13774],{},[2075,61819,27796],{},[8473,61821,61822,61824],{"accent":2360},[2363,61823,27784],{},[2075,61825,27715],{},[2363,61827,61828],{},"jmu",[2363,61830,4072],{},[2075,61832,2803],{},[2363,61834,4072],{},[2068,61836,61837,61840,61846,61849,61855,61861],{},[2363,61838,61839],{},"mezn",[8473,61841,61842,61844],{"accent":2360},[2363,61843,27784],{},[2075,61845,27715],{},[2363,61847,61848],{}," p",[8473,61850,61851,61853],{"accent":2360},[2363,61852,13774],{},[2075,61854,27796],{},[8473,61856,61857,61859],{"accent":2360},[2363,61858,27784],{},[2075,61860,27715],{},[2363,61862,61863],{},"jem",[2075,61865,61866],{},"×",[2068,61868,61869,61871,61877,61880,61886,61889],{},[2363,61870,61795],{},[8473,61872,61873,61875],{"accent":2360},[2363,61874,50028],{},[2075,61876,27796],{},[2363,61878,61879],{},"na mno",[8473,61881,61882,61884],{"accent":2360},[2363,61883,10722],{},[2075,61885,27796],{},[2363,61887,61888],{},"stv",[8473,61890,61891,61893],{"accent":2360},[2363,61892,27784],{},[2075,61894,27715],{},[2071,61896,195],{"mathvariant":2450},[2092,61898,61899],{"encoding":2094},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[55,61901,61902,61903,61918],{},"Pro porovnání skutečná změna ",[1647,61904,61906],{"className":61905},[2059],[2061,61907,61908],{"xmlns":2063},[2065,61909,61910,61916],{},[2068,61911,61912,61914],{},[2071,61913,543],{},[2071,61915,4082],{},[2092,61917,4182],{"encoding":2094}," je",[1647,61920,61922],{"className":61921},[2059],[2061,61923,61924],{"xmlns":2063,"display":31093},[2065,61925,61926,61981],{},[23493,61927,61928],{"width":31098},[23498,61929,61930,61932,61974,61976],{},[23501,61931],{"width":31103},[23501,61933,61934],{},[2068,61935,61936,61938,61940,61942,61944,61946,61948,61950,61952,61954,61956,61958,61960,61962,61964,61966,61968,61970,61972],{},[2071,61937,2961],{"mathvariant":2450},[2071,61939,543],{},[2071,61941,4082],{},[2075,61943,2077],{},[2071,61945,543],{},[2071,61947,4082],{},[2075,61949,2084],{"stretchy":2083},[2071,61951,2861],{},[2075,61953,2176],{},[2071,61955,2273],{"mathvariant":2450},[2071,61957,2861],{},[2075,61959,2090],{"stretchy":2083},[2075,61961,2303],{},[2071,61963,543],{},[2071,61965,4082],{},[2075,61967,2084],{"stretchy":2083},[2071,61969,2861],{},[2075,61971,2090],{"stretchy":2083},[2071,61973,195],{"mathvariant":2450},[23501,61975],{"width":31103},[23501,61977,61978],{},[2363,61979,61980],{},"(3.4)",[2092,61982,61983],{"encoding":2094},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[1144,61985,61987],{"id":61986},"příklad-33","Příklad 3.3",[55,61989,61990,61992,61993,62023,62024,2730,62039,2744,62052,2758,62065,62079],{},[95,61991,60457],{}," Pro ",[1647,61994,61996],{"className":61995},[2059],[2061,61997,61998],{"xmlns":2063},[2065,61999,62000,62020],{},[2068,62001,62002,62004,62006,62008,62010,62012,62014],{},[2071,62003,543],{},[2071,62005,4082],{},[2075,62007,2077],{},[2210,62009,3164],{},[2071,62011,2861],{},[2075,62013,2303],{},[2205,62015,62016,62018],{},[2071,62017,2861],{},[2210,62019,646],{},[2092,62021,62022],{"encoding":2094},"TR = 100Q - Q^2"," odhadněte změnu ",[1647,62025,62027],{"className":62026},[2059],[2061,62028,62029],{"xmlns":2063},[2065,62030,62031,62037],{},[2068,62032,62033,62035],{},[2071,62034,543],{},[2071,62036,4082],{},[2092,62038,4182],{"encoding":2094},[1647,62040,62042],{"className":62041},[2059],[2061,62043,62044],{"xmlns":2063},[2065,62045,62046,62050],{},[2068,62047,62048],{},[2071,62049,2861],{},[2092,62051,2861],{"encoding":2094},[1647,62053,62055],{"className":62054},[2059],[2061,62056,62057],{"xmlns":2063},[2065,62058,62059,62063],{},[2068,62060,62061],{},[2210,62062,3200],{},[2092,62064,3200],{"encoding":2094},[1647,62066,62068],{"className":62067},[2059],[2061,62069,62070],{"xmlns":2063},[2065,62071,62072,62077],{},[2068,62073,62074],{},[2210,62075,62076],{},"63",[2092,62078,62076],{"encoding":2094}," a porovnejte se skutečnou změnou.",[55,62081,62082,1445,62084,62109,62110,835,62128,2777],{},[95,62083,25509],{},[1647,62085,62087],{"className":62086},[2059],[2061,62088,62089],{"xmlns":2063},[2065,62090,62091,62107],{},[2068,62092,62093,62095,62097,62099,62101,62103,62105],{},[2071,62094,2890],{},[2071,62096,4082],{},[2075,62098,2077],{},[2210,62100,3164],{},[2075,62102,2303],{},[2210,62104,646],{},[2071,62106,2861],{},[2092,62108,13164],{"encoding":2094},", tedy při ",[1647,62111,62113],{"className":62112},[2059],[2061,62114,62115],{"xmlns":2063},[2065,62116,62117,62125],{},[2068,62118,62119,62121,62123],{},[2071,62120,2861],{},[2075,62122,2077],{},[2210,62124,3200],{},[2092,62126,62127],{"encoding":2094},"Q = 60",[1647,62129,62131],{"className":62130},[2059],[2061,62132,62133],{"xmlns":2063},[2065,62134,62135,62145],{},[2068,62136,62137,62139,62141,62143],{},[2071,62138,2273],{"mathvariant":2450},[2071,62140,2861],{},[2075,62142,2077],{},[2210,62144,654],{},[2092,62146,62147],{"encoding":2094},"\\mathrm{d}Q = 3",[1647,62149,62151],{"className":62150},[2059],[2061,62152,62153],{"xmlns":2063,"display":31093},[2065,62154,62155,62186],{},[2068,62156,62157,62159,62161,62163,62165,62167,62169,62171,62173,62175,62177,62179,62181,62183],{},[2071,62158,2273],{"mathvariant":2450},[2071,62160,543],{},[2071,62162,4082],{},[2075,62164,2077],{},[2075,62166,2084],{"stretchy":2083},[2210,62168,3164],{},[2075,62170,2303],{},[2210,62172,4134],{},[2075,62174,2090],{"stretchy":2083},[2075,62176,3251],{},[2210,62178,654],{},[2075,62180,2077],{},[2075,62182,2303],{},[2210,62184,62185],{},"60.",[2092,62187,62188],{"encoding":2094},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[55,62190,62191,62192,62222,62223,62242],{},"Celkový příjem klesne z ",[1647,62193,62195],{"className":62194},[2059],[2061,62196,62197],{"xmlns":2063},[2065,62198,62199,62219],{},[2068,62200,62201,62203,62205,62207,62209,62211,62213,62215,62217],{},[2071,62202,543],{},[2071,62204,4082],{},[2075,62206,2084],{"stretchy":2083},[2210,62208,3200],{},[2075,62210,2090],{"stretchy":2083},[2075,62212,2077],{},[2210,62214,646],{},[2363,62216,3061],{},[2210,62218,22881],{},[2092,62220,62221],{"encoding":2094},"TR(60) = 2\\,400"," přibližně na ",[1647,62224,62226],{"className":62225},[2059],[2061,62227,62228],{"xmlns":2063},[2065,62229,62230,62239],{},[2068,62231,62232,62234,62236],{},[2210,62233,646],{},[2363,62235,3061],{},[2210,62237,62238],{},"340",[2092,62240,62241],{"encoding":2094},"2\\,340",". Skutečná změna dle (3.4):",[1647,62244,62246],{"className":62245},[2059],[2061,62247,62248],{"xmlns":2063,"display":31093},[2065,62249,62250,62308],{},[2068,62251,62252,62254,62256,62258,62260,62262,62264,62266,62268,62270,62272,62274,62276,62278,62280,62282,62284,62286,62288,62291,62293,62295,62297,62299,62301,62303,62306],{},[2071,62253,2961],{"mathvariant":2450},[2071,62255,543],{},[2071,62257,4082],{},[2075,62259,2077],{},[2071,62261,543],{},[2071,62263,4082],{},[2075,62265,2084],{"stretchy":2083},[2210,62267,62076],{},[2075,62269,2090],{"stretchy":2083},[2075,62271,2303],{},[2071,62273,543],{},[2071,62275,4082],{},[2075,62277,2084],{"stretchy":2083},[2210,62279,3200],{},[2075,62281,2090],{"stretchy":2083},[2075,62283,2077],{},[2210,62285,646],{},[2363,62287,3061],{},[2210,62289,62290],{},"331",[2075,62292,2303],{},[2210,62294,646],{},[2363,62296,3061],{},[2210,62298,22881],{},[2075,62300,2077],{},[2075,62302,2303],{},[2210,62304,62305],{},"69",[2075,62307,2361],{"separator":2360},[2092,62309,62310],{"encoding":2094},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[55,62312,62313,62314,62329,62330,195],{},"tj. ",[1647,62315,62317],{"className":62316},[2059],[2061,62318,62319],{"xmlns":2063},[2065,62320,62321,62327],{},[2068,62322,62323,62325],{},[2071,62324,543],{},[2071,62326,4082],{},[2092,62328,4182],{"encoding":2094}," klesne na ",[1647,62331,62333],{"className":62332},[2059],[2061,62334,62335],{"xmlns":2063},[2065,62336,62337,62345],{},[2068,62338,62339,62341,62343],{},[2210,62340,646],{},[2363,62342,3061],{},[2210,62344,62290],{},[2092,62346,62347],{"encoding":2094},"2\\,331",[609,62349,62351],{"id":62350},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[55,62353,62354,62355,11525,62378,34606],{},"Obecně pro lineární poptávku ",[1647,62356,62358],{"className":62357},[2059],[2061,62359,62360],{"xmlns":2063},[2065,62361,62362,62376],{},[2068,62363,62364,62366,62368,62370,62372,62374],{},[2071,62365,575],{},[2075,62367,2077],{},[2071,62369,69],{},[2071,62371,2861],{},[2075,62373,2176],{},[2071,62375,2179],{},[2092,62377,41352],{"encoding":2094},[1647,62379,62381],{"className":62380},[2059],[2061,62382,62383],{"xmlns":2063},[2065,62384,62385,62407],{},[2068,62386,62387,62389,62391,62393,62395,62401,62403,62405],{},[2071,62388,543],{},[2071,62390,4082],{},[2075,62392,2077],{},[2071,62394,69],{},[2205,62396,62397,62399],{},[2071,62398,2861],{},[2210,62400,646],{},[2075,62402,2176],{},[2071,62404,2179],{},[2071,62406,2861],{},[2092,62408,62409],{"encoding":2094},"TR = aQ^2 + bQ",[1647,62411,62413],{"className":62412},[2059],[2061,62414,62415],{"xmlns":2063,"display":31093},[2065,62416,62417,62437],{},[2068,62418,62419,62421,62423,62425,62427,62429,62431,62433,62435],{},[2071,62420,2890],{},[2071,62422,4082],{},[2075,62424,2077],{},[2210,62426,646],{},[2071,62428,69],{},[2071,62430,2861],{},[2075,62432,2176],{},[2071,62434,2179],{},[2071,62436,195],{"mathvariant":2450},[2092,62438,62439],{"encoding":2094},"MR = 2aQ + b.",[55,62441,62442,62443,62458,62459,62474,62475,62488,62489,11156,62492,62508,62509,62522,62523,62538,62539,62554,62555,62570,62571,2697,62584,62614,62615,62634,62635,62650],{},"Křivky ",[1647,62444,62446],{"className":62445},[2059],[2061,62447,62448],{"xmlns":2063},[2065,62449,62450,62456],{},[2068,62451,62452,62454],{},[2071,62453,2890],{},[2071,62455,4082],{},[2092,62457,6721],{"encoding":2094}," a poptávky (resp. ",[1647,62460,62462],{"className":62461},[2059],[2061,62463,62464],{"xmlns":2063},[2065,62465,62466,62472],{},[2068,62467,62468,62470],{},[2071,62469,4342],{},[2071,62471,4082],{},[2092,62473,59915],{"encoding":2094},") jsou přímky protínající svislou osu v témže bodě ",[1647,62476,62478],{"className":62477},[2059],[2061,62479,62480],{"xmlns":2063},[2065,62481,62482,62486],{},[2068,62483,62484],{},[2071,62485,2179],{},[2092,62487,2179],{"encoding":2094},", přičemž ",[95,62490,62491],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[1647,62493,62495],{"className":62494},[2059],[2061,62496,62497],{"xmlns":2063},[2065,62498,62499,62505],{},[2068,62500,62501,62503],{},[2210,62502,646],{},[2071,62504,69],{},[2092,62506,62507],{"encoding":2094},"2a"," vs. ",[1647,62510,62512],{"className":62511},[2059],[2061,62513,62514],{"xmlns":2063},[2065,62515,62516,62520],{},[2068,62517,62518],{},[2071,62519,69],{},[2092,62521,69],{"encoding":2094},", obrázek 3.2). ",[1647,62524,62526],{"className":62525},[2059],[2061,62527,62528],{"xmlns":2063},[2065,62529,62530,62536],{},[2068,62531,62532,62534],{},[2071,62533,2890],{},[2071,62535,4082],{},[2092,62537,6721],{"encoding":2094}," nabývá jak kladných, tak záporných hodnot; křivka ",[1647,62540,62542],{"className":62541},[2059],[2061,62543,62544],{"xmlns":2063},[2065,62545,62546,62552],{},[2068,62547,62548,62550],{},[2071,62549,543],{},[2071,62551,4082],{},[2092,62553,4182],{"encoding":2094}," nejprve roste, v bodě maxima protíná ",[1647,62556,62558],{"className":62557},[2059],[2061,62559,62560],{"xmlns":2063},[2065,62561,62562,62568],{},[2068,62563,62564,62566],{},[2071,62565,2890],{},[2071,62567,4082],{},[2092,62569,6721],{"encoding":2094}," osu ",[1647,62572,62574],{"className":62573},[2059],[2061,62575,62576],{"xmlns":2063},[2065,62577,62578,62582],{},[2068,62579,62580],{},[2071,62581,2861],{},[2092,62583,2861],{"encoding":2094},[1647,62585,62587],{"className":62586},[2059],[2061,62588,62589],{"xmlns":2063},[2065,62590,62591,62611],{},[2068,62592,62593,62595,62597,62599],{},[2071,62594,2861],{},[2075,62596,2077],{},[2075,62598,2303],{},[2400,62600,62601],{"scriptlevel":630,"displaystyle":2083},[2403,62602,62603,62605],{},[2071,62604,2179],{},[2068,62606,62607,62609],{},[2210,62608,646],{},[2071,62610,69],{},[2092,62612,62613],{"encoding":2094},"Q = -\\tfrac{b}{2a}"," hodnotou ",[1647,62616,62618],{"className":62617},[2059],[2061,62619,62620],{"xmlns":2063},[2065,62621,62622,62632],{},[2068,62623,62624,62626,62628,62630],{},[2071,62625,2890],{},[2071,62627,4082],{},[2075,62629,2077],{},[2210,62631,630],{},[2092,62633,7171],{"encoding":2094},", a dále ",[1647,62636,62638],{"className":62637},[2059],[2061,62639,62640],{"xmlns":2063},[2065,62641,62642,62648],{},[2068,62643,62644,62646],{},[2071,62645,543],{},[2071,62647,4082],{},[2092,62649,4182],{"encoding":2094}," klesá.",[55,62652,62653,62654,62660,62661,62693,62694,62722],{},"V případě ",[95,62655,62656],{},[69,62657,62659],{"className":62658,"dataFsResolvedFilePath":13670,"href":13671},[62],"dokonalé konkurence",", kdy poptávka ",[1647,62662,62664],{"className":62663},[2059],[2061,62665,62666],{"xmlns":2063},[2065,62667,62668,62690],{},[2068,62669,62670,62672,62674,62676,62678,62680,62682,62684],{},[2071,62671,575],{},[2075,62673,2077],{},[2071,62675,4271],{},[2075,62677,2084],{"stretchy":2083},[2071,62679,2861],{},[2075,62681,2090],{"stretchy":2083},[2075,62683,2077],{},[2205,62685,62686,62688],{},[2071,62687,575],{},[2075,62689,4441],{},[2092,62691,62692],{"encoding":2094},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[1647,62695,62697],{"className":62696},[2059],[2061,62698,62699],{"xmlns":2063},[2065,62700,62701,62719],{},[2068,62702,62703,62705,62707,62709,62711,62713],{},[2071,62704,543],{},[2071,62706,4082],{},[2075,62708,2077],{},[2071,62710,2861],{},[2075,62712,3251],{},[2205,62714,62715,62717],{},[2071,62716,575],{},[2075,62718,4441],{},[2092,62720,62721],{"encoding":2094},"TR = Q \\cdot P^*"," a tedy",[1647,62724,62726],{"className":62725},[2059],[2061,62727,62728],{"xmlns":2063,"display":31093},[2065,62729,62730,62772],{},[2068,62731,62732,62734,62736,62738,62740,62742,62744,62750,62752,62754,62768,62770],{},[2071,62733,2890],{},[2071,62735,4082],{},[2075,62737,2077],{},[2071,62739,4342],{},[2071,62741,4082],{},[2075,62743,2077],{},[2205,62745,62746,62748],{},[2071,62747,575],{},[2075,62749,4441],{},[5965,62751],{"width":17019},[2075,62753,2084],{"stretchy":2083},[2068,62755,62756,62759,62765],{},[2363,62757,62758],{},"obr",[8473,62760,62761,62763],{"accent":2360},[2363,62762,69],{},[2075,62764,27715],{},[2363,62766,62767],{},"zek 3.4",[2075,62769,2090],{"stretchy":2083},[2071,62771,195],{"mathvariant":2450},[2092,62773,62774],{"encoding":2094},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[55,62776,62777],{},[3982,62778,62779,62780,75,62806,62834,62835,62848,62849,62864,62865,3792,62878,835,62904,3792,62919,195],{},"Obrázek 3.2: Přímky ",[1647,62781,62783],{"className":62782},[2059],[2061,62784,62785],{"xmlns":2063},[2065,62786,62787,62803],{},[2068,62788,62789,62791,62793,62795,62797,62799,62801],{},[2071,62790,4342],{},[2071,62792,4082],{},[2075,62794,2077],{},[2071,62796,69],{},[2071,62798,2861],{},[2075,62800,2176],{},[2071,62802,2179],{},[2092,62804,62805],{"encoding":2094},"AR = aQ + b",[1647,62807,62809],{"className":62808},[2059],[2061,62810,62811],{"xmlns":2063},[2065,62812,62813,62831],{},[2068,62814,62815,62817,62819,62821,62823,62825,62827,62829],{},[2071,62816,2890],{},[2071,62818,4082],{},[2075,62820,2077],{},[2210,62822,646],{},[2071,62824,69],{},[2071,62826,2861],{},[2075,62828,2176],{},[2071,62830,2179],{},[2092,62832,62833],{"encoding":2094},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[1647,62836,62838],{"className":62837},[2059],[2061,62839,62840],{"xmlns":2063},[2065,62841,62842,62846],{},[2068,62843,62844],{},[2071,62845,2179],{},[2092,62847,2179],{"encoding":2094}," se svislou osou, ",[1647,62850,62852],{"className":62851},[2059],[2061,62853,62854],{"xmlns":2063},[2065,62855,62856,62862],{},[2068,62857,62858,62860],{},[2071,62859,2890],{},[2071,62861,4082],{},[2092,62863,6721],{"encoding":2094}," protíná osu ",[1647,62866,62868],{"className":62867},[2059],[2061,62869,62870],{"xmlns":2063},[2065,62871,62872,62876],{},[2068,62873,62874],{},[2071,62875,2861],{},[2092,62877,2861],{"encoding":2094},[1647,62879,62881],{"className":62880},[2059],[2061,62882,62883],{"xmlns":2063},[2065,62884,62885,62901],{},[2068,62886,62887,62889],{},[2075,62888,2303],{},[2400,62890,62891],{"scriptlevel":630,"displaystyle":2083},[2403,62892,62893,62895],{},[2071,62894,2179],{},[2068,62896,62897,62899],{},[2210,62898,646],{},[2071,62900,69],{},[2092,62902,62903],{"encoding":2094},"-\\tfrac{b}{2a}",[1647,62905,62907],{"className":62906},[2059],[2061,62908,62909],{"xmlns":2063},[2065,62910,62911,62917],{},[2068,62912,62913,62915],{},[2071,62914,4342],{},[2071,62916,4082],{},[2092,62918,59915],{"encoding":2094},[1647,62920,62922],{"className":62921},[2059],[2061,62923,62924],{"xmlns":2063},[2065,62925,62926,62938],{},[2068,62927,62928,62930],{},[2075,62929,2303],{},[2400,62931,62932],{"scriptlevel":630,"displaystyle":2083},[2403,62933,62934,62936],{},[2071,62935,2179],{},[2071,62937,69],{},[2092,62939,62940],{"encoding":2094},"-\\tfrac{b}{a}",[55,62942,62943],{},[3982,62944,62945,62946,62977,62978,63007,63008,195],{},"Obrázek 3.3: Parabola ",[1647,62947,62949],{"className":62948},[2059],[2061,62950,62951],{"xmlns":2063},[2065,62952,62953,62975],{},[2068,62954,62955,62957,62959,62961,62963,62969,62971,62973],{},[2071,62956,543],{},[2071,62958,4082],{},[2075,62960,2077],{},[2071,62962,69],{},[2205,62964,62965,62967],{},[2071,62966,2861],{},[2210,62968,646],{},[2075,62970,2176],{},[2071,62972,2179],{},[2071,62974,2861],{},[2092,62976,62409],{"encoding":2094}," s maximem v ",[1647,62979,62981],{"className":62980},[2059],[2061,62982,62983],{"xmlns":2063},[2065,62984,62985,63005],{},[2068,62986,62987,62989,62991,62993],{},[2071,62988,2861],{},[2075,62990,2077],{},[2075,62992,2303],{},[2400,62994,62995],{"scriptlevel":630,"displaystyle":2083},[2403,62996,62997,62999],{},[2071,62998,2179],{},[2068,63000,63001,63003],{},[2210,63002,646],{},[2071,63004,69],{},[2092,63006,62613],{"encoding":2094}," a nulou v ",[1647,63009,63011],{"className":63010},[2059],[2061,63012,63013],{"xmlns":2063},[2065,63014,63015,63031],{},[2068,63016,63017,63019,63021,63023],{},[2071,63018,2861],{},[2075,63020,2077],{},[2075,63022,2303],{},[2400,63024,63025],{"scriptlevel":630,"displaystyle":2083},[2403,63026,63027,63029],{},[2071,63028,2179],{},[2071,63030,69],{},[2092,63032,63033],{"encoding":2094},"Q = -\\tfrac{b}{a}",[55,63035,63036],{},[3982,63037,63038,63039,195],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[1647,63040,63042],{"className":63041},[2059],[2061,63043,63044],{"xmlns":2063},[2065,63045,63046,63066],{},[2068,63047,63048,63050,63052,63054,63056,63058,63060],{},[2071,63049,4342],{},[2071,63051,4082],{},[2075,63053,2077],{},[2071,63055,2890],{},[2071,63057,4082],{},[2075,63059,2077],{},[2205,63061,63062,63064],{},[2071,63063,575],{},[2075,63065,4441],{},[2092,63067,63068],{"encoding":2094},"AR = MR = P^*",[84,63070,63072],{"id":63071},"náklady-firmy","Náklady firmy",[609,63074,63076],{"id":63075},"celkové-náklady","Celkové náklady",[55,63078,63079,1445,63081,11156,63096,63099,63100,63113],{},[95,63080,63076],{},[1647,63082,63084],{"className":63083},[2059],[2061,63085,63086],{"xmlns":2063},[2065,63087,63088,63094],{},[2068,63089,63090,63092],{},[2071,63091,543],{},[2071,63093,2849],{},[2092,63095,3317],{"encoding":2094},[95,63097,63098],{},"total cost",") jsou veškeré náklady na realizaci ",[1647,63101,63103],{"className":63102},[2059],[2061,63104,63105],{"xmlns":2063},[2065,63106,63107,63111],{},[2068,63108,63109],{},[2071,63110,2861],{},[2092,63112,2861],{"encoding":2094}," jednotek produkce:",[1647,63115,63117],{"className":63116},[2059],[2061,63118,63119],{"xmlns":2063,"display":31093},[2065,63120,63121,63176],{},[23493,63122,63123],{"width":31098},[23498,63124,63125,63127,63169,63171],{},[23501,63126],{"width":31103},[23501,63128,63129],{},[2068,63130,63131,63133,63135,63137,63139,63141,63143,63145,63147,63149,63151,63153,63155,63157,63159,63161,63163,63165,63167],{},[2071,63132,543],{},[2071,63134,2849],{},[2075,63136,2077],{},[2071,63138,543],{},[2071,63140,2849],{},[2075,63142,2084],{"stretchy":2083},[2071,63144,2861],{},[2075,63146,2090],{"stretchy":2083},[2075,63148,2077],{},[2071,63150,10177],{},[2071,63152,2849],{},[2075,63154,2176],{},[2071,63156,543],{},[2071,63158,44630],{},[2071,63160,2849],{},[2075,63162,2084],{"stretchy":2083},[2071,63164,2861],{},[2075,63166,2090],{"stretchy":2083},[2075,63168,2361],{"separator":2360},[23501,63170],{"width":31103},[23501,63172,63173],{},[2363,63174,63175],{},"(3.5)",[2092,63177,63178],{"encoding":2094},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[55,63180,4397,63181,63196,63197,11156,63200,13861,63203,63196,63227,11156,63230,63233],{},[1647,63182,63184],{"className":63183},[2059],[2061,63185,63186],{"xmlns":2063},[2065,63187,63188,63194],{},[2068,63189,63190,63192],{},[2071,63191,10177],{},[2071,63193,2849],{},[2092,63195,59961],{"encoding":2094}," jsou ",[95,63198,63199],{},"fixní náklady",[95,63201,63202],{},"fixed cost",[1647,63204,63206],{"className":63205},[2059],[2061,63207,63208],{"xmlns":2063},[2065,63209,63210,63224],{},[2068,63211,63212,63214,63216,63218,63220,63222],{},[2071,63213,543],{},[2071,63215,44630],{},[2071,63217,2849],{},[2075,63219,2084],{"stretchy":2083},[2071,63221,2861],{},[2075,63223,2090],{"stretchy":2083},[2092,63225,63226],{"encoding":2094},"TVC(Q)",[95,63228,63229],{},"celkové variabilní náklady",[95,63231,63232],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[609,63235,63237],{"id":63236},"průměrné-náklady","Průměrné náklady",[55,63239,63240,1445,63242,11156,63257,63260],{},[95,63241,63237],{},[1647,63243,63245],{"className":63244},[2059],[2061,63246,63247],{"xmlns":2063},[2065,63248,63249,63255],{},[2068,63250,63251,63253],{},[2071,63252,4342],{},[2071,63254,2849],{},[2092,63256,60030],{"encoding":2094},[95,63258,63259],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[1647,63262,63264],{"className":63263},[2059],[2061,63265,63266],{"xmlns":2063,"display":31093},[2065,63267,63268,63347],{},[23493,63269,63270],{"width":31098},[23498,63271,63272,63274,63340,63342],{},[23501,63273],{"width":31103},[23501,63275,63276],{},[2068,63277,63278,63280,63282,63284,63286,63288,63290,63292,63294,63296,63306,63308,63318,63320,63338],{},[2071,63279,4342],{},[2071,63281,2849],{},[2075,63283,2077],{},[2071,63285,4342],{},[2071,63287,2849],{},[2075,63289,2084],{"stretchy":2083},[2071,63291,2861],{},[2075,63293,2090],{"stretchy":2083},[2075,63295,2077],{},[2403,63297,63298,63304],{},[2068,63299,63300,63302],{},[2071,63301,543],{},[2071,63303,2849],{},[2071,63305,2861],{},[2075,63307,2077],{},[2403,63309,63310,63316],{},[2068,63311,63312,63314],{},[2071,63313,10177],{},[2071,63315,2849],{},[2071,63317,2861],{},[2075,63319,2176],{},[2403,63321,63322,63336],{},[2068,63323,63324,63326,63328,63330,63332,63334],{},[2071,63325,543],{},[2071,63327,44630],{},[2071,63329,2849],{},[2075,63331,2084],{"stretchy":2083},[2071,63333,2861],{},[2075,63335,2090],{"stretchy":2083},[2071,63337,2861],{},[2075,63339,2361],{"separator":2360},[23501,63341],{"width":31103},[23501,63343,63344],{},[2363,63345,63346],{},"(3.6)",[2092,63348,63349],{"encoding":2094},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[55,63351,4397,63352,63196,63376,1445,63379,11156,63396,13861,63399,63196,63431,1445,63434,11156,63451,3225],{},[1647,63353,63355],{"className":63354},[2059],[2061,63356,63357],{"xmlns":2063},[2065,63358,63359,63373],{},[2068,63360,63361],{},[2400,63362,63363],{"scriptlevel":630,"displaystyle":2083},[2403,63364,63365,63371],{},[2068,63366,63367,63369],{},[2071,63368,10177],{},[2071,63370,2849],{},[2071,63372,2861],{},[2092,63374,63375],{"encoding":2094},"\\tfrac{FC}{Q}",[95,63377,63378],{},"průměrné fixní náklady",[1647,63380,63382],{"className":63381},[2059],[2061,63383,63384],{"xmlns":2063},[2065,63385,63386,63394],{},[2068,63387,63388,63390,63392],{},[2071,63389,4342],{},[2071,63391,10177],{},[2071,63393,2849],{},[2092,63395,59997],{"encoding":2094},[95,63397,63398],{},"average fixed cost",[1647,63400,63402],{"className":63401},[2059],[2061,63403,63404],{"xmlns":2063},[2065,63405,63406,63428],{},[2068,63407,63408],{},[2400,63409,63410],{"scriptlevel":630,"displaystyle":2083},[2403,63411,63412,63426],{},[2068,63413,63414,63416,63418,63420,63422,63424],{},[2071,63415,543],{},[2071,63417,44630],{},[2071,63419,2849],{},[2075,63421,2084],{"stretchy":2083},[2071,63423,2861],{},[2075,63425,2090],{"stretchy":2083},[2071,63427,2861],{},[2092,63429,63430],{"encoding":2094},"\\tfrac{TVC(Q)}{Q}",[95,63432,63433],{},"průměrné variabilní náklady",[1647,63435,63437],{"className":63436},[2059],[2061,63438,63439],{"xmlns":2063},[2065,63440,63441,63449],{},[2068,63442,63443,63445,63447],{},[2071,63444,4342],{},[2071,63446,44630],{},[2071,63448,2849],{},[2092,63450,59781],{"encoding":2094},[95,63452,63453],{},"average variable cost",[1647,63455,63457],{"className":63456},[2059],[2061,63458,63459],{"xmlns":2063,"display":31093},[2065,63460,63461,63520],{},[23493,63462,63463],{"width":31098},[23498,63464,63465,63467,63513,63515],{},[23501,63466],{"width":31103},[23501,63468,63469],{},[2068,63470,63471,63473,63475,63477,63479,63481,63483,63485,63487,63489,63491,63493,63511],{},[2071,63472,4342],{},[2071,63474,44630],{},[2071,63476,2849],{},[2075,63478,2077],{},[2071,63480,4342],{},[2071,63482,44630],{},[2071,63484,2849],{},[2075,63486,2084],{"stretchy":2083},[2071,63488,2861],{},[2075,63490,2090],{"stretchy":2083},[2075,63492,2077],{},[2403,63494,63495,63509],{},[2068,63496,63497,63499,63501,63503,63505,63507],{},[2071,63498,543],{},[2071,63500,44630],{},[2071,63502,2849],{},[2075,63504,2084],{"stretchy":2083},[2071,63506,2861],{},[2075,63508,2090],{"stretchy":2083},[2071,63510,2861],{},[2071,63512,195],{"mathvariant":2450},[23501,63514],{"width":31103},[23501,63516,63517],{},[2363,63518,63519],{},"(3.7)",[2092,63521,63522],{"encoding":2094},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[1144,63524,63526],{"id":63525},"příklad-34","Příklad 3.4",[55,63528,63529,61992,63531,75,63556,60495,63580,75,63595,63610,63611,195],{},[95,63530,60457],{},[1647,63532,63534],{"className":63533},[2059],[2061,63535,63536],{"xmlns":2063},[2065,63537,63538,63553],{},[2068,63539,63540,63542,63544,63546,63548,63550],{},[2071,63541,10177],{},[2071,63543,2849],{},[2075,63545,2077],{},[2210,63547,638],{},[2363,63549,3061],{},[2210,63551,63552],{},"000",[2092,63554,63555],{"encoding":2094},"FC = 1\\,000",[1647,63557,63559],{"className":63558},[2059],[2061,63560,63561],{"xmlns":2063},[2065,63562,63563,63577],{},[2068,63564,63565,63567,63569,63571,63573,63575],{},[2071,63566,543],{},[2071,63568,44630],{},[2071,63570,2849],{},[2075,63572,2077],{},[2210,63574,662],{},[2071,63576,2861],{},[2092,63578,63579],{"encoding":2094},"TVC = 4Q",[1647,63581,63583],{"className":63582},[2059],[2061,63584,63585],{"xmlns":2063},[2065,63586,63587,63593],{},[2068,63588,63589,63591],{},[2071,63590,543],{},[2071,63592,2849],{},[2092,63594,3317],{"encoding":2094},[1647,63596,63598],{"className":63597},[2059],[2061,63599,63600],{"xmlns":2063},[2065,63601,63602,63608],{},[2068,63603,63604,63606],{},[2071,63605,4342],{},[2071,63607,2849],{},[2092,63609,60030],{"encoding":2094}," a jejich chování s rostoucím ",[1647,63612,63614],{"className":63613},[2059],[2061,63615,63616],{"xmlns":2063},[2065,63617,63618,63622],{},[2068,63619,63620],{},[2071,63621,2861],{},[2092,63623,2861],{"encoding":2094},[55,63625,63626,1445,63628,75,63658,63694,63695,4445,63708,63723,63724,2777],{},[95,63627,25509],{},[1647,63629,63631],{"className":63630},[2059],[2061,63632,63633],{"xmlns":2063},[2065,63634,63635,63655],{},[2068,63636,63637,63639,63641,63643,63645,63647,63649,63651,63653],{},[2071,63638,543],{},[2071,63640,2849],{},[2075,63642,2077],{},[2210,63644,638],{},[2363,63646,3061],{},[2210,63648,63552],{},[2075,63650,2176],{},[2210,63652,662],{},[2071,63654,2861],{},[2092,63656,63657],{"encoding":2094},"TC = 1\\,000 + 4Q",[1647,63659,63661],{"className":63660},[2059],[2061,63662,63663],{"xmlns":2063},[2065,63664,63665,63691],{},[2068,63666,63667,63669,63671,63673,63687,63689],{},[2071,63668,4342],{},[2071,63670,2849],{},[2075,63672,2077],{},[2400,63674,63675],{"scriptlevel":630,"displaystyle":2083},[2403,63676,63677,63685],{},[2068,63678,63679,63681,63683],{},[2210,63680,638],{},[2363,63682,3061],{},[2210,63684,63552],{},[2071,63686,2861],{},[2075,63688,2176],{},[2210,63690,662],{},[2092,63692,63693],{"encoding":2094},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[1647,63696,63698],{"className":63697},[2059],[2061,63699,63700],{"xmlns":2063},[2065,63701,63702,63706],{},[2068,63703,63704],{},[2071,63705,2861],{},[2092,63707,2861],{"encoding":2094},[1647,63709,63711],{"className":63710},[2059],[2061,63712,63713],{"xmlns":2063},[2065,63714,63715,63721],{},[2068,63716,63717,63719],{},[2071,63718,4342],{},[2071,63720,2849],{},[2092,63722,60030],{"encoding":2094}," blíží ",[1647,63725,63727],{"className":63726},[2059],[2061,63728,63729],{"xmlns":2063},[2065,63730,63731,63735],{},[2068,63732,63733],{},[2210,63734,662],{},[2092,63736,662],{"encoding":2094},[1647,63738,63740],{"className":63739},[2059],[2061,63741,63742],{"xmlns":2063,"display":31093},[2065,63743,63744,63790],{},[2068,63745,63746,63763,63785,63787],{},[44187,63747,63748,63755],{},[2068,63749,63750,63753],{},[2071,63751,63752],{},"lim",[2075,63754,60670],{},[2068,63756,63757,63759,63761],{},[2071,63758,2861],{},[2075,63760,3197],{},[2071,63762,6384],{"mathvariant":2450},[2068,63764,63765,63767,63779,63781,63783],{},[2075,63766,2084],{"fence":2360},[2403,63768,63769,63777],{},[2068,63770,63771,63773,63775],{},[2210,63772,638],{},[2363,63774,3061],{},[2210,63776,63552],{},[2071,63778,2861],{},[2075,63780,2176],{},[2210,63782,662],{},[2075,63784,2090],{"fence":2360},[2075,63786,2077],{},[2210,63788,63789],{},"4.",[2092,63791,63792],{"encoding":2094},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[55,63794,63795,63833,63834,195],{},[1647,63796,63798],{"className":63797},[2059],[2061,63799,63800],{"xmlns":2063},[2065,63801,63802,63830],{},[2068,63803,63804,63806,63808,63810,63812,63826,63828],{},[2071,63805,4342],{},[2071,63807,10177],{},[2071,63809,2849],{},[2075,63811,2077],{},[2400,63813,63814],{"scriptlevel":630,"displaystyle":2083},[2403,63815,63816,63824],{},[2068,63817,63818,63820,63822],{},[2210,63819,638],{},[2363,63821,3061],{},[2210,63823,63552],{},[2071,63825,2861],{},[2075,63827,3197],{},[2210,63829,630],{},[2092,63831,63832],{"encoding":2094},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[1647,63835,63837],{"className":63836},[2059],[2061,63838,63839],{"xmlns":2063},[2065,63840,63841,63845],{},[2068,63842,63843],{},[2071,63844,2861],{},[2092,63846,2861],{"encoding":2094},[55,63848,63849],{},[3982,63850,63851,63852,63881,63882,195],{},"Obrázek 3.5: Přímka ",[1647,63853,63855],{"className":63854},[2059],[2061,63856,63857],{"xmlns":2063},[2065,63858,63859,63879],{},[2068,63860,63861,63863,63865,63867,63869,63871,63873,63875,63877],{},[2071,63862,543],{},[2071,63864,2849],{},[2075,63866,2077],{},[2210,63868,638],{},[2363,63870,3061],{},[2210,63872,63552],{},[2075,63874,2176],{},[2210,63876,662],{},[2071,63878,2861],{},[2092,63880,63657],{"encoding":2094}," protínající svislou osu ve výši ",[1647,63883,63885],{"className":63884},[2059],[2061,63886,63887],{"xmlns":2063},[2065,63888,63889,63903],{},[2068,63890,63891,63893,63895,63897,63899,63901],{},[2071,63892,10177],{},[2071,63894,2849],{},[2075,63896,2077],{},[2210,63898,638],{},[2363,63900,3061],{},[2210,63902,63552],{},[2092,63904,63555],{"encoding":2094},[55,63906,63907],{},[3982,63908,63909,63910,63945,63946,195],{},"Obrázek 3.6: Hyperbola ",[1647,63911,63913],{"className":63912},[2059],[2061,63914,63915],{"xmlns":2063},[2065,63916,63917,63943],{},[2068,63918,63919,63921,63923,63925,63939,63941],{},[2071,63920,4342],{},[2071,63922,2849],{},[2075,63924,2077],{},[2400,63926,63927],{"scriptlevel":630,"displaystyle":2083},[2403,63928,63929,63937],{},[2068,63930,63931,63933,63935],{},[2210,63932,638],{},[2363,63934,3061],{},[2210,63936,63552],{},[2071,63938,2861],{},[2075,63940,2176],{},[2210,63942,662],{},[2092,63944,63693],{"encoding":2094}," s vodorovnou asymptotou ",[1647,63947,63949],{"className":63948},[2059],[2061,63950,63951],{"xmlns":2063},[2065,63952,63953,63963],{},[2068,63954,63955,63957,63959,63961],{},[2071,63956,4342],{},[2071,63958,2849],{},[2075,63960,2077],{},[2210,63962,662],{},[2092,63964,63965],{"encoding":2094},"AC = 4",[55,63967,63968],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[1647,63970,63972],{"className":63971},[2059],[2061,63973,63974],{"xmlns":2063,"display":31093},[2065,63975,63976,64002],{},[2068,63977,63978,63980,63982,63984,63986,63988,63990,63992,63994,63996,63998,64000],{},[2071,63979,543],{},[2071,63981,44630],{},[2071,63983,2849],{},[2075,63985,2077],{},[2071,63987,2861],{},[2075,63989,3251],{},[2071,63991,44630],{},[2071,63993,2849],{},[2075,63995,2084],{"stretchy":2083},[2071,63997,2861],{},[2075,63999,2090],{"stretchy":2083},[2075,64001,2361],{"separator":2360},[2092,64003,64004],{"encoding":2094},"TVC = Q \\cdot VC(Q),",[55,64006,4397,64007,63196,64035,64038,64039,64069],{},[1647,64008,64010],{"className":64009},[2059],[2061,64011,64012],{"xmlns":2063},[2065,64013,64014,64032],{},[2068,64015,64016,64018,64020,64022,64024,64026,64028,64030],{},[2071,64017,44630],{},[2071,64019,2849],{},[2075,64021,2077],{},[2071,64023,44630],{},[2071,64025,2849],{},[2075,64027,2084],{"stretchy":2083},[2071,64029,2861],{},[2075,64031,2090],{"stretchy":2083},[2092,64033,64034],{"encoding":2094},"VC = VC(Q)",[95,64036,64037],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[1647,64040,64042],{"className":64041},[2059],[2061,64043,64044],{"xmlns":2063},[2065,64045,64046,64066],{},[2068,64047,64048,64050,64052,64054,64056,64058,64060,64062,64064],{},[2071,64049,543],{},[2071,64051,44630],{},[2071,64053,2849],{},[2075,64055,2084],{"stretchy":2083},[2071,64057,2861],{},[2075,64059,2090],{"stretchy":2083},[2075,64061,2077],{},[2071,64063,69],{},[2071,64065,2861],{},[2092,64067,64068],{"encoding":2094},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[1647,64071,64073],{"className":64072},[2059],[2061,64074,64075],{"xmlns":2063,"display":31093},[2065,64076,64077,64097],{},[2068,64078,64079,64081,64083,64085,64087,64089,64091,64093,64095],{},[2071,64080,543],{},[2071,64082,2849],{},[2075,64084,2077],{},[2071,64086,10177],{},[2071,64088,2849],{},[2075,64090,2176],{},[2071,64092,69],{},[2071,64094,2861],{},[2071,64096,195],{"mathvariant":2450},[2092,64098,64099],{"encoding":2094},"TC = FC + aQ.",[55,64101,64102,64103,64118,64119,64134,64135,64158,64159,64193,64194,63945,64207,64220,64221,75,64269,64313,64314,195],{},"Křivkou ",[1647,64104,64106],{"className":64105},[2059],[2061,64107,64108],{"xmlns":2063},[2065,64109,64110,64116],{},[2068,64111,64112,64114],{},[2071,64113,543],{},[2071,64115,2849],{},[2092,64117,3317],{"encoding":2094}," je přímka se svislým průsečíkem ",[1647,64120,64122],{"className":64121},[2059],[2061,64123,64124],{"xmlns":2063},[2065,64125,64126,64132],{},[2068,64127,64128,64130],{},[2071,64129,10177],{},[2071,64131,2849],{},[2092,64133,59961],{"encoding":2094}," a sklonem ",[1647,64136,64138],{"className":64137},[2059],[2061,64139,64140],{"xmlns":2063},[2065,64141,64142,64155],{},[2068,64143,64144,64147,64149,64151,64153],{},[2071,64145,64146],{},"tan",[2075,64148,60670],{},[2071,64150,21601],{},[2075,64152,2077],{},[2071,64154,69],{},[2092,64156,64157],{"encoding":2094},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[1647,64160,64162],{"className":64161},[2059],[2061,64163,64164],{"xmlns":2063},[2065,64165,64166,64190],{},[2068,64167,64168,64170,64172,64174,64186,64188],{},[2071,64169,4342],{},[2071,64171,2849],{},[2075,64173,2077],{},[2400,64175,64176],{"scriptlevel":630,"displaystyle":2083},[2403,64177,64178,64184],{},[2068,64179,64180,64182],{},[2071,64181,10177],{},[2071,64183,2849],{},[2071,64185,2861],{},[2075,64187,2176],{},[2071,64189,69],{},[2092,64191,64192],{"encoding":2094},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[1647,64195,64197],{"className":64196},[2059],[2061,64198,64199],{"xmlns":2063},[2065,64200,64201,64205],{},[2068,64202,64203],{},[2071,64204,586],{},[2092,64206,586],{"encoding":2094},[1647,64208,64210],{"className":64209},[2059],[2061,64211,64212],{"xmlns":2063},[2065,64213,64214,64218],{},[2068,64215,64216],{},[2071,64217,69],{},[2092,64219,69],{"encoding":2094}," (obrázek 3.8). Limity ",[1647,64222,64224],{"className":64223},[2059],[2061,64225,64226],{"xmlns":2063},[2065,64227,64228,64266],{},[2068,64229,64230,64250,64262,64264],{},[2348,64231,64232,64238],{},[2068,64233,64234,64236],{},[2071,64235,63752],{},[2075,64237,60670],{},[2068,64239,64240,64242,64244],{},[2071,64241,2861],{},[2075,64243,3197],{},[2205,64245,64246,64248],{},[2210,64247,630],{},[2075,64249,2176],{},[2400,64251,64252],{"scriptlevel":630,"displaystyle":2083},[2403,64253,64254,64260],{},[2068,64255,64256,64258],{},[2071,64257,10177],{},[2071,64259,2849],{},[2071,64261,2861],{},[2075,64263,2077],{},[2071,64265,6384],{"mathvariant":2450},[2092,64267,64268],{"encoding":2094},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[1647,64270,64272],{"className":64271},[2059],[2061,64273,64274],{"xmlns":2063},[2065,64275,64276,64310],{},[2068,64277,64278,64294,64306,64308],{},[2348,64279,64280,64286],{},[2068,64281,64282,64284],{},[2071,64283,63752],{},[2075,64285,60670],{},[2068,64287,64288,64290,64292],{},[2071,64289,2861],{},[2075,64291,3197],{},[2071,64293,6384],{"mathvariant":2450},[2400,64295,64296],{"scriptlevel":630,"displaystyle":2083},[2403,64297,64298,64304],{},[2068,64299,64300,64302],{},[2071,64301,10177],{},[2071,64303,2849],{},[2071,64305,2861],{},[2075,64307,2077],{},[2210,64309,630],{},[2092,64311,64312],{"encoding":2094},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[1647,64315,64317],{"className":64316},[2059],[2061,64318,64319],{"xmlns":2063},[2065,64320,64321,64327],{},[2068,64322,64323,64325],{},[2071,64324,4342],{},[2071,64326,2849],{},[2092,64328,60030],{"encoding":2094},[55,64330,64331],{},[3982,64332,64333,64334,64349,64350,64365,64366,195],{},"Obrázek 3.7: Přímka ",[1647,64335,64337],{"className":64336},[2059],[2061,64338,64339],{"xmlns":2063},[2065,64340,64341,64347],{},[2068,64342,64343,64345],{},[2071,64344,543],{},[2071,64346,2849],{},[2092,64348,3317],{"encoding":2094}," s osovým průsečíkem ve výši ",[1647,64351,64353],{"className":64352},[2059],[2061,64354,64355],{"xmlns":2063},[2065,64356,64357,64363],{},[2068,64358,64359,64361],{},[2071,64360,10177],{},[2071,64362,2849],{},[2092,64364,59961],{"encoding":2094}," a se sklonem ",[1647,64367,64369],{"className":64368},[2059],[2061,64370,64371],{"xmlns":2063},[2065,64372,64373,64385],{},[2068,64374,64375,64377,64379,64381,64383],{},[2071,64376,64146],{},[2075,64378,60670],{},[2071,64380,21601],{},[2075,64382,2077],{},[2071,64384,69],{},[2092,64386,64157],{"encoding":2094},[55,64388,64389],{},[3982,64390,64391,64392,64407,64408,195],{},"Obrázek 3.8: Klesající hyperbola ",[1647,64393,64395],{"className":64394},[2059],[2061,64396,64397],{"xmlns":2063},[2065,64398,64399,64405],{},[2068,64400,64401,64403],{},[2071,64402,4342],{},[2071,64404,2849],{},[2092,64406,60030],{"encoding":2094}," s vodorovnou asymptotou ve výši ",[1647,64409,64411],{"className":64410},[2059],[2061,64412,64413],{"xmlns":2063},[2065,64414,64415,64419],{},[2068,64416,64417],{},[2071,64418,69],{},[2092,64420,69],{"encoding":2094},[609,64422,64424],{"id":64423},"mezní-náklady","Mezní náklady",[55,64426,64427,1445,64429,11156,64444,64447,64448,64451],{},[95,64428,64424],{},[1647,64430,64432],{"className":64431},[2059],[2061,64433,64434],{"xmlns":2063},[2065,64435,64436,64442],{},[2068,64437,64438,64440],{},[2071,64439,2890],{},[2071,64441,2849],{},[2092,64443,59762],{"encoding":2094},[95,64445,64446],{},"marginal cost",") jsou ",[69,64449,2430],{"className":64450,"dataFsResolvedFilePath":4005,"href":4006},[62]," celkových nákladů podle množství:",[1647,64453,64455],{"className":64454},[2059],[2061,64456,64457],{"xmlns":2063,"display":31093},[2065,64458,64459,64528],{},[23493,64460,64461],{"width":31098},[23498,64462,64463,64465,64521,64523],{},[23501,64464],{"width":31103},[23501,64466,64467],{},[2068,64468,64469,64471,64473,64475,64477,64479,64481,64483,64485,64487,64503,64505,64507,64513,64515,64517,64519],{},[2071,64470,2890],{},[2071,64472,2849],{},[2075,64474,2077],{},[2071,64476,2890],{},[2071,64478,2849],{},[2075,64480,2084],{"stretchy":2083},[2071,64482,2861],{},[2075,64484,2090],{"stretchy":2083},[2075,64486,2077],{},[2403,64488,64489,64497],{},[2068,64490,64491,64493,64495],{},[2071,64492,2273],{"mathvariant":2450},[2071,64494,543],{},[2071,64496,2849],{},[2068,64498,64499,64501],{},[2071,64500,2273],{"mathvariant":2450},[2071,64502,2861],{},[2075,64504,2077],{},[2071,64506,543],{},[2205,64508,64509,64511],{},[2071,64510,2849],{},[2075,64512,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,64514,2084],{"stretchy":2083},[2071,64516,2861],{},[2075,64518,2090],{"stretchy":2083},[2071,64520,195],{"mathvariant":2450},[23501,64522],{"width":31103},[23501,64524,64525],{},[2363,64526,64527],{},"(3.8)",[2092,64529,64530],{"encoding":2094},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1023,64532,64533],{},[55,64534,64535,64537,64538,64564,64565,64582,64583,195],{},[1647,64536,4243],{}," Intuice — „kolik stojí další kus\"\n",[1647,64539,64541],{"className":64540},[2059],[2061,64542,64543],{"xmlns":2063},[2065,64544,64545,64561],{},[2068,64546,64547,64549,64551,64553,64559],{},[2071,64548,2890],{},[2071,64550,2849],{},[2075,64552,2084],{"stretchy":2083},[2205,64554,64555,64557],{},[2071,64556,2861],{},[2075,64558,4441],{},[2075,64560,2090],{"stretchy":2083},[2092,64562,64563],{"encoding":2094},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[1647,64566,64568],{"className":64567},[2059],[2061,64569,64570],{"xmlns":2063},[2065,64571,64572,64580],{},[2068,64573,64574],{},[2205,64575,64576,64578],{},[2071,64577,2861],{},[2075,64579,4441],{},[2092,64581,32871],{"encoding":2094},". Formálně ",[1647,64584,64586],{"className":64585},[2059],[2061,64587,64588],{"xmlns":2063},[2065,64589,64590,64642],{},[2068,64591,64592,64594,64596,64598,64604,64606,64608,64610,64612,64614,64620,64622,64624,64626,64628,64630,64632,64634,64640],{},[2071,64593,2890],{},[2071,64595,2849],{},[2075,64597,2084],{"stretchy":2083},[2205,64599,64600,64602],{},[2071,64601,2861],{},[2075,64603,4441],{},[2075,64605,2090],{"stretchy":2083},[2075,64607,2803],{},[2071,64609,543],{},[2071,64611,2849],{},[2075,64613,2084],{"stretchy":2083},[2205,64615,64616,64618],{},[2071,64617,2861],{},[2075,64619,4441],{},[2075,64621,2176],{},[2210,64623,638],{},[2075,64625,2090],{"stretchy":2083},[2075,64627,2303],{},[2071,64629,543],{},[2071,64631,2849],{},[2075,64633,2084],{"stretchy":2083},[2205,64635,64636,64638],{},[2071,64637,2861],{},[2075,64639,4441],{},[2075,64641,2090],{"stretchy":2083},[2092,64643,64644],{"encoding":2094},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[55,64646,64647,64648,2777],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[1647,64649,64651],{"className":64650},[2059],[2061,64652,64653],{"xmlns":2063},[2065,64654,64655,64663],{},[2068,64656,64657,64659,64661],{},[2071,64658,2961],{"mathvariant":2450},[2071,64660,543],{},[2071,64662,2849],{},[2092,64664,64665],{"encoding":2094},"\\Delta TC",[1647,64667,64669],{"className":64668},[2059],[2061,64670,64671],{"xmlns":2063,"display":31093},[2065,64672,64673,64742],{},[23493,64674,64675],{"width":31098},[23498,64676,64677,64679,64735,64737],{},[23501,64678],{"width":31103},[23501,64680,64681],{},[2068,64682,64683,64685,64687,64689,64691,64693,64695,64697,64699,64701,64703,64705,64707,64709,64715,64717,64719,64721,64723,64725,64727,64729,64731,64733],{},[2071,64684,2961],{"mathvariant":2450},[2071,64686,543],{},[2071,64688,2849],{},[2363,64690,4072],{},[2075,64692,2803],{},[2363,64694,4072],{},[2071,64696,2273],{"mathvariant":2450},[2071,64698,543],{},[2071,64700,2849],{},[2075,64702,2077],{},[2075,64704,2084],{"stretchy":2083},[2071,64706,543],{},[2071,64708,2849],{},[2205,64710,64711,64713],{},[2075,64712,2090],{"stretchy":2083},[2075,64714,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,64716,3061],{},[2071,64718,2273],{"mathvariant":2450},[2071,64720,2861],{},[2075,64722,2077],{},[2071,64724,2890],{},[2071,64726,2849],{},[2363,64728,3061],{},[2071,64730,2273],{"mathvariant":2450},[2071,64732,2861],{},[2075,64734,2361],{"separator":2360},[23501,64736],{"width":31103},[23501,64738,64739],{},[2363,64740,64741],{},"(3.9)",[2092,64743,64744],{"encoding":2094},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[55,64746,61781],{},[1647,64748,64750],{"className":64749},[2059],[2061,64751,64752],{"xmlns":2063,"display":31093},[2065,64753,64754,64852],{},[2068,64755,64756,64794,64796,64798,64800,64822,64824,64850],{},[2068,64757,64758,64760,64766,64768,64774,64777,64783,64786],{},[2363,64759,61795],{},[8473,64761,64762,64764],{"accent":2360},[2363,64763,50028],{},[2075,64765,27796],{},[2363,64767,61804],{},[8473,64769,64770,64772],{"accent":2360},[2363,64771,2073],{},[2075,64773,27715],{},[2363,64775,64776],{},"ch n",[8473,64778,64779,64781],{"accent":2360},[2363,64780,69],{},[2075,64782,27715],{},[2363,64784,64785],{},"klad",[8473,64787,64788,64791],{"accent":2360},[2363,64789,64790],{},"u",[2075,64792,64793],{},"˚",[2363,64795,4072],{},[2075,64797,2803],{},[2363,64799,4072],{},[2068,64801,64802,64804,64810,64813,64819],{},[2363,64803,61839],{},[8473,64805,64806,64808],{"accent":2360},[2363,64807,27784],{},[2075,64809,27715],{},[2363,64811,64812],{}," n",[8473,64814,64815,64817],{"accent":2360},[2363,64816,69],{},[2075,64818,27715],{},[2363,64820,64821],{},"klady",[2075,64823,61866],{},[2068,64825,64826,64828,64834,64836,64842,64844],{},[2363,64827,61795],{},[8473,64829,64830,64832],{"accent":2360},[2363,64831,50028],{},[2075,64833,27796],{},[2363,64835,61879],{},[8473,64837,64838,64840],{"accent":2360},[2363,64839,10722],{},[2075,64841,27796],{},[2363,64843,61888],{},[8473,64845,64846,64848],{"accent":2360},[2363,64847,27784],{},[2075,64849,27715],{},[2071,64851,195],{"mathvariant":2450},[2092,64853,64854],{"encoding":2094},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[1144,64856,64858],{"id":64857},"příklad-35","Příklad 3.5",[55,64860,64861,61992,64863,60495,64899,64914,64915,64930,64931,2744,64944,2758,64957,64970,64971,2758,64984,195],{},[95,64862,60457],{},[1647,64864,64866],{"className":64865},[2059],[2061,64867,64868],{"xmlns":2063},[2065,64869,64870,64896],{},[2068,64871,64872,64874,64876,64878,64880,64882,64884,64886,64888,64890],{},[2071,64873,543],{},[2071,64875,2849],{},[2075,64877,2077],{},[2210,64879,8464],{},[2075,64881,2176],{},[2210,64883,678],{},[2071,64885,2861],{},[2075,64887,2176],{},[2210,64889,646],{},[2205,64891,64892,64894],{},[2071,64893,2861],{},[2210,64895,646],{},[2092,64897,64898],{"encoding":2094},"TC = 200 + 6Q + 2Q^2",[1647,64900,64902],{"className":64901},[2059],[2061,64903,64904],{"xmlns":2063},[2065,64905,64906,64912],{},[2068,64907,64908,64910],{},[2071,64909,2890],{},[2071,64911,2849],{},[2092,64913,59762],{"encoding":2094}," a odhadněte změny ",[1647,64916,64918],{"className":64917},[2059],[2061,64919,64920],{"xmlns":2063},[2065,64921,64922,64928],{},[2068,64923,64924,64926],{},[2071,64925,543],{},[2071,64927,2849],{},[2092,64929,3317],{"encoding":2094}," při změnách ",[1647,64932,64934],{"className":64933},[2059],[2061,64935,64936],{"xmlns":2063},[2065,64937,64938,64942],{},[2068,64939,64940],{},[2071,64941,2861],{},[2092,64943,2861],{"encoding":2094},[1647,64945,64947],{"className":64946},[2059],[2061,64948,64949],{"xmlns":2063},[2065,64950,64951,64955],{},[2068,64952,64953],{},[2210,64954,39270],{},[2092,64956,39270],{"encoding":2094},[1647,64958,64960],{"className":64959},[2059],[2061,64961,64962],{"xmlns":2063},[2065,64963,64964,64968],{},[2068,64965,64966],{},[2210,64967,46153],{},[2092,64969,46153],{"encoding":2094}," a z ",[1647,64972,64974],{"className":64973},[2059],[2061,64975,64976],{"xmlns":2063},[2065,64977,64978,64982],{},[2068,64979,64980],{},[2210,64981,39270],{},[2092,64983,39270],{"encoding":2094},[1647,64985,64987],{"className":64986},[2059],[2061,64988,64989],{"xmlns":2063},[2065,64990,64991,64995],{},[2068,64992,64993],{},[2210,64994,3583],{},[2092,64996,3583],{"encoding":2094},[55,64998,64999,1445,65001,2999,65027,835,65054,65081,65082,65097,65098,65113,65114,65141,65142,65162,65163,23270,65184,65240,65241,2744,65254,2758,65267,8189,65280,195],{},[95,65000,25509],{},[1647,65002,65004],{"className":65003},[2059],[2061,65005,65006],{"xmlns":2063},[2065,65007,65008,65024],{},[2068,65009,65010,65012,65014,65016,65018,65020,65022],{},[2071,65011,2890],{},[2071,65013,2849],{},[2075,65015,2077],{},[2210,65017,678],{},[2075,65019,2176],{},[2210,65021,662],{},[2071,65023,2861],{},[2092,65025,65026],{"encoding":2094},"MC = 6 + 4Q",[1647,65028,65030],{"className":65029},[2059],[2061,65031,65032],{"xmlns":2063},[2065,65033,65034,65051],{},[2068,65035,65036,65038,65040,65042,65044,65046,65048],{},[2071,65037,2890],{},[2071,65039,2849],{},[2075,65041,2084],{"stretchy":2083},[2210,65043,39270],{},[2075,65045,2090],{"stretchy":2083},[2075,65047,2077],{},[2210,65049,65050],{},"66",[2092,65052,65053],{"encoding":2094},"MC(15) = 66",[1647,65055,65057],{"className":65056},[2059],[2061,65058,65059],{"xmlns":2063},[2065,65060,65061,65078],{},[2068,65062,65063,65065,65067,65069,65071,65073,65075],{},[2071,65064,2890],{},[2071,65066,2849],{},[2075,65068,2084],{"stretchy":2083},[2210,65070,9121],{},[2075,65072,2090],{"stretchy":2083},[2075,65074,2077],{},[2210,65076,65077],{},"86",[2092,65079,65080],{"encoding":2094},"MC(20) = 86",": s růstem množství se rychlost změny ",[1647,65083,65085],{"className":65084},[2059],[2061,65086,65087],{"xmlns":2063},[2065,65088,65089,65095],{},[2068,65090,65091,65093],{},[2071,65092,543],{},[2071,65094,2849],{},[2092,65096,3317],{"encoding":2094}," zvyšuje (",[1647,65099,65101],{"className":65100},[2059],[2061,65102,65103],{"xmlns":2063},[2065,65104,65105,65111],{},[2068,65106,65107,65109],{},[2071,65108,2890],{},[2071,65110,2849],{},[2092,65112,59762],{"encoding":2094}," je rostoucí). Z ",[1647,65115,65117],{"className":65116},[2059],[2061,65118,65119],{"xmlns":2063},[2065,65120,65121,65138],{},[2068,65122,65123,65125,65127,65129,65131,65133,65135],{},[2071,65124,543],{},[2071,65126,2849],{},[2075,65128,2084],{"stretchy":2083},[2210,65130,39270],{},[2075,65132,2090],{"stretchy":2083},[2075,65134,2077],{},[2210,65136,65137],{},"740",[2092,65139,65140],{"encoding":2094},"TC(15) = 740"," se po přírůstku ",[1647,65143,65145],{"className":65144},[2059],[2061,65146,65147],{"xmlns":2063},[2065,65148,65149,65159],{},[2068,65150,65151,65153,65155,65157],{},[2071,65152,2273],{"mathvariant":2450},[2071,65154,2861],{},[2075,65156,2077],{},[2210,65158,638],{},[2092,65160,65161],{"encoding":2094},"\\mathrm{d}Q = 1"," předpokládá ",[1647,65164,65166],{"className":65165},[2059],[2061,65167,65168],{"xmlns":2063},[2065,65169,65170,65181],{},[2068,65171,65172,65174,65176,65178],{},[2071,65173,543],{},[2071,65175,2849],{},[2075,65177,2803],{},[2210,65179,65180],{},"806",[2092,65182,65183],{"encoding":2094},"TC \\approx 806",[1647,65185,65187],{"className":65186},[2059],[2061,65188,65189],{"xmlns":2063},[2065,65190,65191,65237],{},[2068,65192,65193,65195,65197,65199,65201,65203,65205,65207,65209,65211,65213,65215,65217,65219,65221,65223,65225,65228,65230,65232,65234],{},[2071,65194,2961],{"mathvariant":2450},[2071,65196,543],{},[2071,65198,2849],{},[2075,65200,2077],{},[2071,65202,543],{},[2071,65204,2849],{},[2075,65206,2084],{"stretchy":2083},[2210,65208,46153],{},[2075,65210,2090],{"stretchy":2083},[2075,65212,2303],{},[2071,65214,543],{},[2071,65216,2849],{},[2075,65218,2084],{"stretchy":2083},[2210,65220,39270],{},[2075,65222,2090],{"stretchy":2083},[2075,65224,2077],{},[2210,65226,65227],{},"808",[2075,65229,2303],{},[2210,65231,65137],{},[2075,65233,2077],{},[2210,65235,65236],{},"68",[2092,65238,65239],{"encoding":2094},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[1647,65242,65244],{"className":65243},[2059],[2061,65245,65246],{"xmlns":2063},[2065,65247,65248,65252],{},[2068,65249,65250],{},[2071,65251,2861],{},[2092,65253,2861],{"encoding":2094},[1647,65255,65257],{"className":65256},[2059],[2061,65258,65259],{"xmlns":2063},[2065,65260,65261,65265],{},[2068,65262,65263],{},[2210,65264,39270],{},[2092,65266,39270],{"encoding":2094},[1647,65268,65270],{"className":65269},[2059],[2061,65271,65272],{"xmlns":2063},[2065,65273,65274,65278],{},[2068,65275,65276],{},[2210,65277,3583],{},[2092,65279,3583],{"encoding":2094},[1647,65281,65283],{"className":65282},[2059],[2061,65284,65285],{"xmlns":2063},[2065,65286,65287,65316],{},[2068,65288,65289,65291,65293,65295,65297,65299,65301,65303,65305,65307,65309,65311,65313],{},[2071,65290,2961],{"mathvariant":2450},[2071,65292,543],{},[2071,65294,2849],{},[2075,65296,2803],{},[2210,65298,65050],{},[2075,65300,3251],{},[2075,65302,2084],{"stretchy":2083},[2075,65304,2303],{},[2210,65306,654],{},[2075,65308,2090],{"stretchy":2083},[2075,65310,2077],{},[2075,65312,2303],{},[2210,65314,65315],{},"198",[2092,65317,65318],{"encoding":2094},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[609,65320,65322],{"id":65321},"kubická-nákladová-funkce","Kubická nákladová funkce",[55,65324,65325],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[1144,65327,65329],{"id":65328},"příklad-36","Příklad 3.6",[55,65331,65332,61992,65334,65378],{},[95,65333,60457],{},[1647,65335,65337],{"className":65336},[2059],[2061,65338,65339],{"xmlns":2063},[2065,65340,65341,65375],{},[2068,65342,65343,65345,65347,65349,65351,65353,65355,65357,65359,65361,65367,65369],{},[2071,65344,543],{},[2071,65346,2849],{},[2075,65348,2077],{},[2210,65350,3164],{},[2075,65352,2176],{},[2210,65354,5091],{},[2071,65356,2861],{},[2075,65358,2303],{},[2210,65360,670],{},[2205,65362,65363,65365],{},[2071,65364,2861],{},[2210,65366,646],{},[2075,65368,2176],{},[2205,65370,65371,65373],{},[2071,65372,2861],{},[2210,65374,654],{},[2092,65376,65377],{"encoding":2094},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[55,65380,65381],{},[95,65382,25509],{},[1647,65384,65386],{"className":65385},[2059],[2061,65387,65388],{"xmlns":2063,"display":31093},[2065,65389,65390,65634],{},[23493,65391,65392,65418,65466,65500,65542,65592],{"rowspacing":23495,"columnalign":23496,"columnspacing":2451},[23498,65393,65394,65404],{},[23501,65395,65396],{},[2400,65397,65398],{"scriptlevel":630,"displaystyle":2360},[2068,65399,65400,65402],{},[2071,65401,10177],{},[2071,65403,2849],{},[23501,65405,65406],{},[2400,65407,65408],{"scriptlevel":630,"displaystyle":2360},[2068,65409,65410,65412,65414,65416],{},[2068,65411],{},[2075,65413,2077],{},[2210,65415,3164],{},[2075,65417,2361],{"separator":2360},[23498,65419,65420,65432],{},[23501,65421,65422],{},[2400,65423,65424],{"scriptlevel":630,"displaystyle":2360},[2068,65425,65426,65428,65430],{},[2071,65427,543],{},[2071,65429,44630],{},[2071,65431,2849],{},[23501,65433,65434],{},[2400,65435,65436],{"scriptlevel":630,"displaystyle":2360},[2068,65437,65438,65440,65442,65444,65446,65448,65450,65456,65458,65464],{},[2068,65439],{},[2075,65441,2077],{},[2210,65443,5091],{},[2071,65445,2861],{},[2075,65447,2303],{},[2210,65449,670],{},[2205,65451,65452,65454],{},[2071,65453,2861],{},[2210,65455,646],{},[2075,65457,2176],{},[2205,65459,65460,65462],{},[2071,65461,2861],{},[2210,65463,654],{},[2075,65465,2361],{"separator":2360},[23498,65467,65468,65480],{},[23501,65469,65470],{},[2400,65471,65472],{"scriptlevel":630,"displaystyle":2360},[2068,65473,65474,65476,65478],{},[2071,65475,4342],{},[2071,65477,10177],{},[2071,65479,2849],{},[23501,65481,65482],{},[2400,65483,65484],{"scriptlevel":630,"displaystyle":2360},[2068,65485,65486,65488,65490,65498],{},[2068,65487],{},[2075,65489,2077],{},[2400,65491,65492],{"scriptlevel":630,"displaystyle":2083},[2403,65493,65494,65496],{},[2210,65495,3164],{},[2071,65497,2861],{},[2075,65499,2361],{"separator":2360},[23498,65501,65502,65514],{},[23501,65503,65504],{},[2400,65505,65506],{"scriptlevel":630,"displaystyle":2360},[2068,65507,65508,65510,65512],{},[2071,65509,4342],{},[2071,65511,44630],{},[2071,65513,2849],{},[23501,65515,65516],{},[2400,65517,65518],{"scriptlevel":630,"displaystyle":2360},[2068,65519,65520,65522,65524,65526,65528,65530,65532,65534,65540],{},[2068,65521],{},[2075,65523,2077],{},[2210,65525,5091],{},[2075,65527,2303],{},[2210,65529,670],{},[2071,65531,2861],{},[2075,65533,2176],{},[2205,65535,65536,65538],{},[2071,65537,2861],{},[2210,65539,646],{},[2075,65541,2361],{"separator":2360},[23498,65543,65544,65554],{},[23501,65545,65546],{},[2400,65547,65548],{"scriptlevel":630,"displaystyle":2360},[2068,65549,65550,65552],{},[2071,65551,4342],{},[2071,65553,2849],{},[23501,65555,65556],{},[2400,65557,65558],{"scriptlevel":630,"displaystyle":2360},[2068,65559,65560,65562,65564,65572,65574,65576,65578,65580,65582,65584,65590],{},[2068,65561],{},[2075,65563,2077],{},[2400,65565,65566],{"scriptlevel":630,"displaystyle":2083},[2403,65567,65568,65570],{},[2210,65569,3164],{},[2071,65571,2861],{},[2075,65573,2176],{},[2210,65575,5091],{},[2075,65577,2303],{},[2210,65579,670],{},[2071,65581,2861],{},[2075,65583,2176],{},[2205,65585,65586,65588],{},[2071,65587,2861],{},[2210,65589,646],{},[2075,65591,2361],{"separator":2360},[23498,65593,65594,65604],{},[23501,65595,65596],{},[2400,65597,65598],{"scriptlevel":630,"displaystyle":2360},[2068,65599,65600,65602],{},[2071,65601,2890],{},[2071,65603,2849],{},[23501,65605,65606],{},[2400,65607,65608],{"scriptlevel":630,"displaystyle":2360},[2068,65609,65610,65612,65614,65616,65618,65620,65622,65624,65626,65632],{},[2068,65611],{},[2075,65613,2077],{},[2210,65615,5091],{},[2075,65617,2303],{},[2210,65619,2935],{},[2071,65621,2861],{},[2075,65623,2176],{},[2210,65625,654],{},[2205,65627,65628,65630],{},[2071,65629,2861],{},[2210,65631,646],{},[2071,65633,195],{"mathvariant":2450},[2092,65635,65636],{"encoding":2094},"\\begin{aligned}\nFC &= 100, \\\\\nTVC &= 25Q - 5Q^2 + Q^3, \\\\\nAFC &= \\tfrac{100}{Q}, \\\\\nAVC &= 25 - 5Q + Q^2, \\\\\nAC  &= \\tfrac{100}{Q} + 25 - 5Q + Q^2, \\\\\nMC  &= 25 - 10Q + 3Q^2.\n\\end{aligned}",[55,65638,65639,65640,17525,65655,17525,65670,65685,65686,65701,65702,835,65720,65701,65737,835,65755,65701,65770,65788],{},"Význačné body ",[1647,65641,65643],{"className":65642},[2059],[2061,65644,65645],{"xmlns":2063},[2065,65646,65647,65652],{},[2068,65648,65649],{},[2210,65650,65651],{},"1,67",[2092,65653,65654],{"encoding":2094},"1{,}67",[1647,65656,65658],{"className":65657},[2059],[2061,65659,65660],{"xmlns":2063},[2065,65661,65662,65667],{},[2068,65663,65664],{},[2210,65665,65666],{},"2,50",[2092,65668,65669],{"encoding":2094},"2{,}50",[1647,65671,65673],{"className":65672},[2059],[2061,65674,65675],{"xmlns":2063},[2065,65676,65677,65682],{},[2068,65678,65679],{},[2210,65680,65681],{},"4,73",[2092,65683,65684],{"encoding":2094},"4{,}73"," odpovídají: ",[1647,65687,65689],{"className":65688},[2059],[2061,65690,65691],{"xmlns":2063},[2065,65692,65693,65699],{},[2068,65694,65695,65697],{},[2071,65696,2890],{},[2071,65698,2849],{},[2092,65700,59762],{"encoding":2094}," minimum v ",[1647,65703,65705],{"className":65704},[2059],[2061,65706,65707],{"xmlns":2063},[2065,65708,65709,65717],{},[2068,65710,65711,65713,65715],{},[2071,65712,2861],{},[2075,65714,5987],{},[2210,65716,65651],{},[2092,65718,65719],{"encoding":2094},"Q \\doteq 1{,}67",[1647,65721,65723],{"className":65722},[2059],[2061,65724,65725],{"xmlns":2063},[2065,65726,65727,65735],{},[2068,65728,65729,65731,65733],{},[2071,65730,4342],{},[2071,65732,44630],{},[2071,65734,2849],{},[2092,65736,59781],{"encoding":2094},[1647,65738,65740],{"className":65739},[2059],[2061,65741,65742],{"xmlns":2063},[2065,65743,65744,65752],{},[2068,65745,65746,65748,65750],{},[2071,65747,2861],{},[2075,65749,2077],{},[2210,65751,65666],{},[2092,65753,65754],{"encoding":2094},"Q = 2{,}50",[1647,65756,65758],{"className":65757},[2059],[2061,65759,65760],{"xmlns":2063},[2065,65761,65762,65768],{},[2068,65763,65764,65766],{},[2071,65765,4342],{},[2071,65767,2849],{},[2092,65769,60030],{"encoding":2094},[1647,65771,65773],{"className":65772},[2059],[2061,65774,65775],{"xmlns":2063},[2065,65776,65777,65785],{},[2068,65778,65779,65781,65783],{},[2071,65780,2861],{},[2075,65782,5987],{},[2210,65784,65681],{},[2092,65786,65787],{"encoding":2094},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[55,65790,65791],{},[58,65792],{"alt":65793,"className":65794,"src":65795},"imek-ac-avc-mc",[62,63],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[55,65797,65798],{},[3982,65799,65800,65801,75,65816,65833,65834,17525,65853,65868],{},"Obrázek 3.9: Kubické křivky ",[1647,65802,65804],{"className":65803},[2059],[2061,65805,65806],{"xmlns":2063},[2065,65807,65808,65814],{},[2068,65809,65810,65812],{},[2071,65811,543],{},[2071,65813,2849],{},[2092,65815,3317],{"encoding":2094},[1647,65817,65819],{"className":65818},[2059],[2061,65820,65821],{"xmlns":2063},[2065,65822,65823,65831],{},[2068,65824,65825,65827,65829],{},[2071,65826,543],{},[2071,65828,44630],{},[2071,65830,2849],{},[2092,65832,59979],{"encoding":2094}," rostoucí od bodu ",[1647,65835,65837],{"className":65836},[2059],[2061,65838,65839],{"xmlns":2063},[2065,65840,65841,65851],{},[2068,65842,65843,65845,65847,65849],{},[2071,65844,10177],{},[2071,65846,2849],{},[2075,65848,2077],{},[2210,65850,3164],{},[2092,65852,13361],{"encoding":2094},[1647,65854,65856],{"className":65855},[2059],[2061,65857,65858],{"xmlns":2063},[2065,65859,65860,65866],{},[2068,65861,65862,65864],{},[2071,65863,10177],{},[2071,65865,2849],{},[2092,65867,59961],{"encoding":2094}," je vodorovná přímka.",[55,65870,65871],{},[3982,65872,65873,65874,835,65889,835,65906,32228,65921,65934,65935,2999,65952,65967,65968,6277,65985,66000,66001,28930,66014,835,66027,835,66040,195],{},"Obrázek 3.10: Křivky ",[1647,65875,65877],{"className":65876},[2059],[2061,65878,65879],{"xmlns":2063},[2065,65880,65881,65887],{},[2068,65882,65883,65885],{},[2071,65884,4342],{},[2071,65886,2849],{},[2092,65888,60030],{"encoding":2094},[1647,65890,65892],{"className":65891},[2059],[2061,65893,65894],{"xmlns":2063},[2065,65895,65896,65904],{},[2068,65897,65898,65900,65902],{},[2071,65899,4342],{},[2071,65901,44630],{},[2071,65903,2849],{},[2092,65905,59781],{"encoding":2094},[1647,65907,65909],{"className":65908},[2059],[2061,65910,65911],{"xmlns":2063},[2065,65912,65913,65919],{},[2068,65914,65915,65917],{},[2071,65916,2890],{},[2071,65918,2849],{},[2092,65920,59762],{"encoding":2094},[1647,65922,65924],{"className":65923},[2059],[2061,65925,65926],{"xmlns":2063},[2065,65927,65928,65932],{},[2068,65929,65930],{},[2071,65931,10871],{},[2092,65933,10871],{"encoding":2094}," a klesající hyperbola ",[1647,65936,65938],{"className":65937},[2059],[2061,65939,65940],{"xmlns":2063},[2065,65941,65942,65950],{},[2068,65943,65944,65946,65948],{},[2071,65945,4342],{},[2071,65947,10177],{},[2071,65949,2849],{},[2092,65951,59997],{"encoding":2094},[1647,65953,65955],{"className":65954},[2059],[2061,65956,65957],{"xmlns":2063},[2065,65958,65959,65965],{},[2068,65960,65961,65963],{},[2071,65962,2890],{},[2071,65964,2849],{},[2092,65966,59762],{"encoding":2094}," protíná ",[1647,65969,65971],{"className":65970},[2059],[2061,65972,65973],{"xmlns":2063},[2065,65974,65975,65983],{},[2068,65976,65977,65979,65981],{},[2071,65978,4342],{},[2071,65980,44630],{},[2071,65982,2849],{},[2092,65984,59781],{"encoding":2094},[1647,65986,65988],{"className":65987},[2059],[2061,65989,65990],{"xmlns":2063},[2065,65991,65992,65998],{},[2068,65993,65994,65996],{},[2071,65995,4342],{},[2071,65997,2849],{},[2092,65999,60030],{"encoding":2094}," zdola v jejich minimech; význačné hodnoty na ose ",[1647,66002,66004],{"className":66003},[2059],[2061,66005,66006],{"xmlns":2063},[2065,66007,66008,66012],{},[2068,66009,66010],{},[2071,66011,2861],{},[2092,66013,2861],{"encoding":2094},[1647,66015,66017],{"className":66016},[2059],[2061,66018,66019],{"xmlns":2063},[2065,66020,66021,66025],{},[2068,66022,66023],{},[2210,66024,65651],{},[2092,66026,65654],{"encoding":2094},[1647,66028,66030],{"className":66029},[2059],[2061,66031,66032],{"xmlns":2063},[2065,66033,66034,66038],{},[2068,66035,66036],{},[2210,66037,65666],{},[2092,66039,65669],{"encoding":2094},[1647,66041,66043],{"className":66042},[2059],[2061,66044,66045],{"xmlns":2063},[2065,66046,66047,66051],{},[2068,66048,66049],{},[2210,66050,65681],{},[2092,66052,65684],{"encoding":2094},[55,66054,66055],{},[95,66056,66057],{},"Standardní vlastnosti:",[89,66059,66060,66095,66159,66227,66277,66297],{},[92,66061,66062,75,66077,66094],{},[1647,66063,66065],{"className":66064},[2059],[2061,66066,66067],{"xmlns":2063},[2065,66068,66069,66075],{},[2068,66070,66071,66073],{},[2071,66072,543],{},[2071,66074,2849],{},[2092,66076,3317],{"encoding":2094},[1647,66078,66080],{"className":66079},[2059],[2061,66081,66082],{"xmlns":2063},[2065,66083,66084,66092],{},[2068,66085,66086,66088,66090],{},[2071,66087,543],{},[2071,66089,44630],{},[2071,66091,2849],{},[2092,66093,59979],{"encoding":2094}," jsou kubické funkce;",[92,66096,66097,835,66112,835,66129,66144,66145,66158],{},[1647,66098,66100],{"className":66099},[2059],[2061,66101,66102],{"xmlns":2063},[2065,66103,66104,66110],{},[2068,66105,66106,66108],{},[2071,66107,4342],{},[2071,66109,2849],{},[2092,66111,60030],{"encoding":2094},[1647,66113,66115],{"className":66114},[2059],[2061,66116,66117],{"xmlns":2063},[2065,66118,66119,66127],{},[2068,66120,66121,66123,66125],{},[2071,66122,4342],{},[2071,66124,44630],{},[2071,66126,2849],{},[2092,66128,59781],{"encoding":2094},[1647,66130,66132],{"className":66131},[2059],[2061,66133,66134],{"xmlns":2063},[2065,66135,66136,66142],{},[2068,66137,66138,66140],{},[2071,66139,2890],{},[2071,66141,2849],{},[2092,66143,59762],{"encoding":2094}," jsou křivky tvaru ",[1647,66146,66148],{"className":66147},[2059],[2061,66149,66150],{"xmlns":2063},[2065,66151,66152,66156],{},[2068,66153,66154],{},[2071,66155,10871],{},[2092,66157,10871],{"encoding":2094}," (nejprve klesají, po minimu rostou);",[92,66160,66161,66176,66177,835,66194,66211,66212,8512],{},[1647,66162,66164],{"className":66163},[2059],[2061,66165,66166],{"xmlns":2063},[2065,66167,66168,66174],{},[2068,66169,66170,66172],{},[2071,66171,2890],{},[2071,66173,2849],{},[2092,66175,59762],{"encoding":2094}," nabývá minima před ",[1647,66178,66180],{"className":66179},[2059],[2061,66181,66182],{"xmlns":2063},[2065,66183,66184,66192],{},[2068,66185,66186,66188,66190],{},[2071,66187,4342],{},[2071,66189,44630],{},[2071,66191,2849],{},[2092,66193,59781],{"encoding":2094},[1647,66195,66197],{"className":66196},[2059],[2061,66198,66199],{"xmlns":2063},[2065,66200,66201,66209],{},[2068,66202,66203,66205,66207],{},[2071,66204,4342],{},[2071,66206,44630],{},[2071,66208,2849],{},[2092,66210,59781],{"encoding":2094}," před ",[1647,66213,66215],{"className":66214},[2059],[2061,66216,66217],{"xmlns":2063},[2065,66218,66219,66225],{},[2068,66220,66221,66223],{},[2071,66222,4342],{},[2071,66224,2849],{},[2092,66226,60030],{"encoding":2094},[92,66228,66229,65967,66244,75,66259,66276],{},[1647,66230,66232],{"className":66231},[2059],[2061,66233,66234],{"xmlns":2063},[2065,66235,66236,66242],{},[2068,66237,66238,66240],{},[2071,66239,2890],{},[2071,66241,2849],{},[2092,66243,59762],{"encoding":2094},[1647,66245,66247],{"className":66246},[2059],[2061,66248,66249],{"xmlns":2063},[2065,66250,66251,66257],{},[2068,66252,66253,66255],{},[2071,66254,4342],{},[2071,66256,2849],{},[2092,66258,60030],{"encoding":2094},[1647,66260,66262],{"className":66261},[2059],[2061,66263,66264],{"xmlns":2063},[2065,66265,66266,66274],{},[2068,66267,66268,66270,66272],{},[2071,66269,4342],{},[2071,66271,44630],{},[2071,66273,2849],{},[2092,66275,59781],{"encoding":2094}," zdola právě v jejich minimech;",[92,66278,66279,66296],{},[1647,66280,66282],{"className":66281},[2059],[2061,66283,66284],{"xmlns":2063},[2065,66285,66286,66294],{},[2068,66287,66288,66290,66292],{},[2071,66289,4342],{},[2071,66291,10177],{},[2071,66293,2849],{},[2092,66295,59997],{"encoding":2094}," je hyperbola, stále klesající;",[92,66298,66299,66331,66332,75,66347,66364,66365,66378,66379,4007],{},[1647,66300,66302],{"className":66301},[2059],[2061,66303,66304],{"xmlns":2063},[2065,66305,66306,66328],{},[2068,66307,66308,66310,66312,66314,66316,66318,66320,66322,66324,66326],{},[2071,66309,4342],{},[2071,66311,2849],{},[2075,66313,2077],{},[2071,66315,4342],{},[2071,66317,10177],{},[2071,66319,2849],{},[2075,66321,2176],{},[2071,66323,4342],{},[2071,66325,44630],{},[2071,66327,2849],{},[2092,66329,66330],{"encoding":2094},"AC = AFC + AVC","; vzdálenost mezi ",[1647,66333,66335],{"className":66334},[2059],[2061,66336,66337],{"xmlns":2063},[2065,66338,66339,66345],{},[2068,66340,66341,66343],{},[2071,66342,4342],{},[2071,66344,2849],{},[2092,66346,60030],{"encoding":2094},[1647,66348,66350],{"className":66349},[2059],[2061,66351,66352],{"xmlns":2063},[2065,66353,66354,66362],{},[2068,66355,66356,66358,66360],{},[2071,66357,4342],{},[2071,66359,44630],{},[2071,66361,2849],{},[2092,66363,59781],{"encoding":2094}," klesá s rostoucím ",[1647,66366,66368],{"className":66367},[2059],[2061,66369,66370],{"xmlns":2063},[2065,66371,66372,66376],{},[2068,66373,66374],{},[2071,66375,2861],{},[2092,66377,2861],{"encoding":2094}," (protože ",[1647,66380,66382],{"className":66381},[2059],[2061,66383,66384],{"xmlns":2063},[2065,66385,66386,66398],{},[2068,66387,66388,66390,66392,66394,66396],{},[2071,66389,4342],{},[2071,66391,10177],{},[2071,66393,2849],{},[2075,66395,3197],{},[2210,66397,630],{},[2092,66399,66400],{"encoding":2094},"AFC \\to 0",[84,66402,66404],{"id":66403},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[55,66406,66407,66408,66411,66412,66427],{},"Častou optimalizační úlohou je ",[95,66409,66410],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[1647,66413,66415],{"className":66414},[2059],[2061,66416,66417],{"xmlns":2063},[2065,66418,66419,66425],{},[2068,66420,66421,66423],{},[2071,66422,4342],{},[2071,66424,2849],{},[2092,66426,60030],{"encoding":2094}," minimální.",[609,66429,87],{"id":86},[55,66431,66432,66433,66450],{},"Mají-li průměrné náklady minimum v bodě ",[1647,66434,66436],{"className":66435},[2059],[2061,66437,66438],{"xmlns":2063},[2065,66439,66440,66448],{},[2068,66441,66442],{},[2348,66443,66444,66446],{},[2071,66445,2861],{},[2210,66447,630],{},[2092,66449,42599],{"encoding":2094},", pak platí",[1647,66452,66454],{"className":66453},[2059],[2061,66455,66456],{"xmlns":2063,"display":31093},[2065,66457,66458,66507],{},[23493,66459,66460],{"width":31098},[23498,66461,66462,66464,66500,66502],{},[23501,66463],{"width":31103},[23501,66465,66466],{},[2068,66467,66468,66470,66472,66474,66480,66482,66484,66486,66488,66490,66496,66498],{},[2071,66469,4342],{},[2071,66471,2849],{},[2075,66473,2084],{"stretchy":2083},[2348,66475,66476,66478],{},[2071,66477,2861],{},[2210,66479,630],{},[2075,66481,2090],{"stretchy":2083},[2075,66483,2077],{},[2071,66485,2890],{},[2071,66487,2849],{},[2075,66489,2084],{"stretchy":2083},[2348,66491,66492,66494],{},[2071,66493,2861],{},[2210,66495,630],{},[2075,66497,2090],{"stretchy":2083},[2071,66499,195],{"mathvariant":2450},[23501,66501],{"width":31103},[23501,66503,66504],{},[2363,66505,66506],{},"(3.10)",[2092,66508,66509],{"encoding":2094},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1023,66511,66512],{},[55,66513,66514,66516,66517],{},[1647,66515,60914],{}," Princip\n",[95,66518,66519],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[55,66521,66522,66525,66526,66568],{},[95,66523,66524],{},"Odvození."," Z ",[1647,66527,66529],{"className":66528},[2059],[2061,66530,66531],{"xmlns":2063},[2065,66532,66533,66565],{},[2068,66534,66535,66537,66539,66541,66543,66545,66547],{},[2071,66536,4342],{},[2071,66538,2849],{},[2075,66540,2084],{"stretchy":2083},[2071,66542,2861],{},[2075,66544,2090],{"stretchy":2083},[2075,66546,2077],{},[2400,66548,66549],{"scriptlevel":630,"displaystyle":2083},[2403,66550,66551,66563],{},[2068,66552,66553,66555,66557,66559,66561],{},[2071,66554,543],{},[2071,66556,2849],{},[2075,66558,2084],{"stretchy":2083},[2071,66560,2861],{},[2075,66562,2090],{"stretchy":2083},[2071,66564,2861],{},[2092,66566,66567],{"encoding":2094},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[1647,66570,66572],{"className":66571},[2059],[2061,66573,66574],{"xmlns":2063,"display":31093},[2065,66575,66576,66708],{},[2068,66577,66578,66580,66586,66588,66590,66592,66594,66634,66636,66676,66678,66706],{},[2071,66579,4342],{},[2205,66581,66582,66584],{},[2071,66583,2849],{},[2075,66585,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,66587,2084],{"stretchy":2083},[2071,66589,2861],{},[2075,66591,2090],{"stretchy":2083},[2075,66593,2077],{},[2403,66595,66596,66628],{},[2068,66597,66598,66600,66606,66608,66610,66612,66614,66616,66618,66620,66622,66624,66626],{},[2071,66599,543],{},[2205,66601,66602,66604],{},[2071,66603,2849],{},[2075,66605,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,66607,2084],{"stretchy":2083},[2071,66609,2861],{},[2075,66611,2090],{"stretchy":2083},[2075,66613,3251],{},[2071,66615,2861],{},[2075,66617,2303],{},[2071,66619,543],{},[2071,66621,2849],{},[2075,66623,2084],{"stretchy":2083},[2071,66625,2861],{},[2075,66627,2090],{"stretchy":2083},[2205,66629,66630,66632],{},[2071,66631,2861],{},[2210,66633,646],{},[2075,66635,2077],{},[2403,66637,66638,66670],{},[2068,66639,66640,66642,66644,66646,66648,66650,66652,66654,66656,66658,66660,66662,66664,66666,66668],{},[2071,66641,2890],{},[2071,66643,2849],{},[2075,66645,2084],{"stretchy":2083},[2071,66647,2861],{},[2075,66649,2090],{"stretchy":2083},[2075,66651,3251],{},[2071,66653,2861],{},[2075,66655,2303],{},[2071,66657,4342],{},[2071,66659,2849],{},[2075,66661,2084],{"stretchy":2083},[2071,66663,2861],{},[2075,66665,2090],{"stretchy":2083},[2075,66667,3251],{},[2071,66669,2861],{},[2205,66671,66672,66674],{},[2071,66673,2861],{},[2210,66675,646],{},[2075,66677,2077],{},[2403,66679,66680,66704],{},[2068,66681,66682,66684,66686,66688,66690,66692,66694,66696,66698,66700,66702],{},[2071,66683,2890],{},[2071,66685,2849],{},[2075,66687,2084],{"stretchy":2083},[2071,66689,2861],{},[2075,66691,2090],{"stretchy":2083},[2075,66693,2303],{},[2071,66695,4342],{},[2071,66697,2849],{},[2075,66699,2084],{"stretchy":2083},[2071,66701,2861],{},[2075,66703,2090],{"stretchy":2083},[2071,66705,2861],{},[2071,66707,195],{"mathvariant":2450},[2092,66709,66710],{"encoding":2094},"AC'(Q) = \\frac{TC'(Q) \\cdot Q - TC(Q)}{Q^2} = \\frac{MC(Q) \\cdot Q - AC(Q) \\cdot Q}{Q^2} = \\frac{MC(Q) - AC(Q)}{Q}.",[55,66712,66713,66714,2697,66729,8189,66751,61291],{},"Nutnou podmínkou minima ",[1647,66715,66717],{"className":66716},[2059],[2061,66718,66719],{"xmlns":2063},[2065,66720,66721,66727],{},[2068,66722,66723,66725],{},[2071,66724,4342],{},[2071,66726,2849],{},[2092,66728,60030],{"encoding":2094},[1647,66730,66732],{"className":66731},[2059],[2061,66733,66734],{"xmlns":2063},[2065,66735,66736,66748],{},[2068,66737,66738,66744,66746],{},[2348,66739,66740,66742],{},[2071,66741,2861],{},[2210,66743,630],{},[2075,66745,3482],{},[2210,66747,630],{},[2092,66749,66750],{"encoding":2094},"Q_0 > 0",[1647,66752,66754],{"className":66753},[2059],[2061,66755,66756],{"xmlns":2063},[2065,66757,66758,66782],{},[2068,66759,66760,66762,66768,66770,66776,66778,66780],{},[2071,66761,4342],{},[2205,66763,66764,66766],{},[2071,66765,2849],{},[2075,66767,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,66769,2084],{"stretchy":2083},[2348,66771,66772,66774],{},[2071,66773,2861],{},[2210,66775,630],{},[2075,66777,2090],{"stretchy":2083},[2075,66779,2077],{},[2210,66781,630],{},[2092,66783,66784],{"encoding":2094},"AC'(Q_0) = 0",[1647,66786,66788],{"className":66787},[2059],[2061,66789,66790],{"xmlns":2063,"display":31093},[2065,66791,66792,66877],{},[2068,66793,66794,66834,66836,66838,66840,66843,66845,66847,66849,66851,66857,66859,66861,66863,66865,66867,66873,66875],{},[2403,66795,66796,66828],{},[2068,66797,66798,66800,66802,66804,66810,66812,66814,66816,66818,66820,66826],{},[2071,66799,2890],{},[2071,66801,2849],{},[2075,66803,2084],{"stretchy":2083},[2348,66805,66806,66808],{},[2071,66807,2861],{},[2210,66809,630],{},[2075,66811,2090],{"stretchy":2083},[2075,66813,2303],{},[2071,66815,4342],{},[2071,66817,2849],{},[2075,66819,2084],{"stretchy":2083},[2348,66821,66822,66824],{},[2071,66823,2861],{},[2210,66825,630],{},[2075,66827,2090],{"stretchy":2083},[2348,66829,66830,66832],{},[2071,66831,2861],{},[2210,66833,630],{},[2075,66835,2077],{},[2210,66837,630],{},[5965,66839],{"width":17019},[2075,66841,66842],{},"⟺",[5965,66844],{"width":17019},[2071,66846,2890],{},[2071,66848,2849],{},[2075,66850,2084],{"stretchy":2083},[2348,66852,66853,66855],{},[2071,66854,2861],{},[2210,66856,630],{},[2075,66858,2090],{"stretchy":2083},[2075,66860,2077],{},[2071,66862,4342],{},[2071,66864,2849],{},[2075,66866,2084],{"stretchy":2083},[2348,66868,66869,66871],{},[2071,66870,2861],{},[2210,66872,630],{},[2075,66874,2090],{"stretchy":2083},[2071,66876,195],{"mathvariant":2450},[2092,66878,66879],{"encoding":2094},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[55,66881,66882,1445,66885,65967,66900,66915,66916,66931,66932,8189,66949,66971,66972,66994],{},[95,66883,66884],{},"Geometrická interpretace.",[1647,66886,66888],{"className":66887},[2059],[2061,66889,66890],{"xmlns":2063},[2065,66891,66892,66898],{},[2068,66893,66894,66896],{},[2071,66895,2890],{},[2071,66897,2849],{},[2092,66899,59762],{"encoding":2094},[1647,66901,66903],{"className":66902},[2059],[2061,66904,66905],{"xmlns":2063},[2065,66906,66907,66913],{},[2068,66908,66909,66911],{},[2071,66910,4342],{},[2071,66912,2849],{},[2092,66914,60030],{"encoding":2094}," právě v bodě minima ",[1647,66917,66919],{"className":66918},[2059],[2061,66920,66921],{"xmlns":2063},[2065,66922,66923,66929],{},[2068,66924,66925,66927],{},[2071,66926,4342],{},[2071,66928,2849],{},[2092,66930,60030],{"encoding":2094}," (obrázek 3.10); nalevo od ",[1647,66933,66935],{"className":66934},[2059],[2061,66936,66937],{"xmlns":2063},[2065,66938,66939,66947],{},[2068,66940,66941],{},[2348,66942,66943,66945],{},[2071,66944,2861],{},[2210,66946,630],{},[2092,66948,42599],{"encoding":2094},[1647,66950,66952],{"className":66951},[2059],[2061,66953,66954],{"xmlns":2063},[2065,66955,66956,66968],{},[2068,66957,66958,66960,66962,66964,66966],{},[2071,66959,2890],{},[2071,66961,2849],{},[2075,66963,3521],{},[2071,66965,4342],{},[2071,66967,2849],{},[2092,66969,66970],{"encoding":2094},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[1647,66973,66975],{"className":66974},[2059],[2061,66976,66977],{"xmlns":2063},[2065,66978,66979,66991],{},[2068,66980,66981,66983,66985,66987,66989],{},[2071,66982,2890],{},[2071,66984,2849],{},[2075,66986,3482],{},[2071,66988,4342],{},[2071,66990,2849],{},[2092,66992,66993],{"encoding":2094},"MC > AC"," (průměrné náklady rostou).",[55,66996,66997,66998,67040,67041,67058,67059,195],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[1647,66999,67001],{"className":67000},[2059],[2061,67002,67003],{"xmlns":2063},[2065,67004,67005,67037],{},[2068,67006,67007,67009,67011,67013,67019,67021,67023,67025,67027,67029,67035],{},[2071,67008,4342],{},[2071,67010,2849],{},[2075,67012,2084],{"stretchy":2083},[2348,67014,67015,67017],{},[2071,67016,2861],{},[2210,67018,630],{},[2075,67020,2090],{"stretchy":2083},[2075,67022,2077],{},[2071,67024,2890],{},[2071,67026,2849],{},[2075,67028,2084],{"stretchy":2083},[2348,67030,67031,67033],{},[2071,67032,2861],{},[2210,67034,630],{},[2075,67036,2090],{"stretchy":2083},[2092,67038,67039],{"encoding":2094},"AC(Q_0) = MC(Q_0)",", pak ",[1647,67042,67044],{"className":67043},[2059],[2061,67045,67046],{"xmlns":2063},[2065,67047,67048,67056],{},[2068,67049,67050],{},[2348,67051,67052,67054],{},[2071,67053,2861],{},[2210,67055,630],{},[2092,67057,42599],{"encoding":2094}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[1647,67060,67062],{"className":67061},[2059],[2061,67063,67064],{"xmlns":2063},[2065,67065,67066,67090],{},[2068,67067,67068,67070,67072,67074,67076,67078,67080,67082,67084,67086,67088],{},[2071,67069,4342],{},[2071,67071,2849],{},[2075,67073,2084],{"stretchy":2083},[2071,67075,2861],{},[2075,67077,2090],{"stretchy":2083},[2075,67079,2077],{},[2071,67081,2890],{},[2071,67083,2849],{},[2075,67085,2084],{"stretchy":2083},[2071,67087,2861],{},[2075,67089,2090],{"stretchy":2083},[2092,67091,67092],{"encoding":2094},"AC(Q) = MC(Q)",[1023,67094,67095],{},[55,67096,67097,67099,67100,11525,67118,67139,67140,11525,67143,67164,67165,67180,67181,62508,67196,4007],{},[1647,67098,4499],{}," Pozor — neplést s principem maxima zisku\nPro ",[95,67101,67102,67103],{},"minimum ",[1647,67104,67106],{"className":67105},[2059],[2061,67107,67108],{"xmlns":2063},[2065,67109,67110,67116],{},[2068,67111,67112,67114],{},[2071,67113,4342],{},[2071,67115,2849],{},[2092,67117,60030],{"encoding":2094},[1647,67119,67121],{"className":67120},[2059],[2061,67122,67123],{"xmlns":2063},[2065,67124,67125,67137],{},[2068,67126,67127,67129,67131,67133,67135],{},[2071,67128,4342],{},[2071,67130,2849],{},[2075,67132,2077],{},[2071,67134,2890],{},[2071,67136,2849],{},[2092,67138,59693],{"encoding":2094},", pro ",[95,67141,67142],{},"maximum zisku",[1647,67144,67146],{"className":67145},[2059],[2061,67147,67148],{"xmlns":2063},[2065,67149,67150,67162],{},[2068,67151,67152,67154,67156,67158,67160],{},[2071,67153,2890],{},[2071,67155,4082],{},[2075,67157,2077],{},[2071,67159,2890],{},[2071,67161,2849],{},[2092,67163,59741],{"encoding":2094},". Obě podmínky využívají ",[1647,67166,67168],{"className":67167},[2059],[2061,67169,67170],{"xmlns":2063},[2065,67171,67172,67178],{},[2068,67173,67174,67176],{},[2071,67175,2890],{},[2071,67177,2849],{},[2092,67179,59762],{"encoding":2094},", ale rovnají ho rozdílným veličinám (",[1647,67182,67184],{"className":67183},[2059],[2061,67185,67186],{"xmlns":2063},[2065,67187,67188,67194],{},[2068,67189,67190,67192],{},[2071,67191,4342],{},[2071,67193,2849],{},[2092,67195,60030],{"encoding":2094},[1647,67197,67199],{"className":67198},[2059],[2061,67200,67201],{"xmlns":2063},[2065,67202,67203,67209],{},[2068,67204,67205,67207],{},[2071,67206,2890],{},[2071,67208,4082],{},[2092,67210,6721],{"encoding":2094},[1144,67212,67214],{"id":67213},"příklad-37","Příklad 3.7",[55,67216,67217,61992,67219,67253,67254,67267,67268,67283],{},[95,67218,60457],{},[1647,67220,67222],{"className":67221},[2059],[2061,67223,67224],{"xmlns":2063},[2065,67225,67226,67250],{},[2068,67227,67228,67230,67232,67234,67240,67242,67244,67246,67248],{},[2071,67229,543],{},[2071,67231,2849],{},[2075,67233,2077],{},[2205,67235,67236,67238],{},[2071,67237,2861],{},[2210,67239,646],{},[2075,67241,2176],{},[2210,67243,654],{},[2071,67245,2861],{},[2075,67247,2176],{},[2210,67249,5652],{},[2092,67251,67252],{"encoding":2094},"TC = Q^2 + 3Q + 36"," najděte ",[1647,67255,67257],{"className":67256},[2059],[2061,67258,67259],{"xmlns":2063},[2065,67260,67261,67265],{},[2068,67262,67263],{},[2071,67264,2861],{},[2092,67266,2861],{"encoding":2094}," minimalizující ",[1647,67269,67271],{"className":67270},[2059],[2061,67272,67273],{"xmlns":2063},[2065,67274,67275,67281],{},[2068,67276,67277,67279],{},[2071,67278,4342],{},[2071,67280,2849],{},[2092,67282,60030],{"encoding":2094}," a ověřte princip (3.10).",[55,67285,67286,67288],{},[95,67287,25509],{}," Přímý výpočet:",[1647,67290,67292],{"className":67291},[2059],[2061,67293,67294],{"xmlns":2063,"display":31093},[2065,67295,67296,67398],{},[2068,67297,67298,67300,67302,67304,67326,67328,67330,67332,67334,67336,67342,67344,67346,67348,67350,67352,67358,67360,67362,67364,67374,67376,67396],{},[2071,67299,4342],{},[2071,67301,2849],{},[2075,67303,2077],{},[2403,67305,67306,67324],{},[2068,67307,67308,67314,67316,67318,67320,67322],{},[2205,67309,67310,67312],{},[2071,67311,2861],{},[2210,67313,646],{},[2075,67315,2176],{},[2210,67317,654],{},[2071,67319,2861],{},[2075,67321,2176],{},[2210,67323,5652],{},[2071,67325,2861],{},[2075,67327,2077],{},[2071,67329,2861],{},[2075,67331,2176],{},[2210,67333,654],{},[2075,67335,2176],{},[2403,67337,67338,67340],{},[2210,67339,5652],{},[2071,67341,2861],{},[2075,67343,2361],{"separator":2360},[5965,67345],{"width":5967},[2075,67347,2084],{"stretchy":2083},[2071,67349,4342],{},[2071,67351,2849],{},[2205,67353,67354,67356],{},[2075,67355,2090],{"stretchy":2083},[2075,67357,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,67359,2077],{},[2210,67361,638],{},[2075,67363,2303],{},[2403,67365,67366,67368],{},[2210,67367,5652],{},[2205,67369,67370,67372],{},[2071,67371,2861],{},[2210,67373,646],{},[2075,67375,2077],{},[2403,67377,67378,67390],{},[2068,67379,67380,67386,67388],{},[2205,67381,67382,67384],{},[2071,67383,2861],{},[2210,67385,646],{},[2075,67387,2303],{},[2210,67389,5652],{},[2205,67391,67392,67394],{},[2071,67393,2861],{},[2210,67395,646],{},[2071,67397,195],{"mathvariant":2450},[2092,67399,67400],{"encoding":2094},"AC = \\frac{Q^2 + 3Q + 36}{Q} = Q + 3 + \\frac{36}{Q}, \\qquad (AC)' = 1 - \\frac{36}{Q^2} = \\frac{Q^2 - 36}{Q^2}.",[55,67402,67403,67443,67444,67468,67469,67519,67520,195],{},[1647,67404,67406],{"className":67405},[2059],[2061,67407,67408],{"xmlns":2063},[2065,67409,67410,67440],{},[2068,67411,67412,67414,67416,67418,67424,67426,67428,67430,67436,67438],{},[2075,67413,2084],{"stretchy":2083},[2071,67415,4342],{},[2071,67417,2849],{},[2205,67419,67420,67422],{},[2075,67421,2090],{"stretchy":2083},[2075,67423,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,67425,2077],{},[2210,67427,630],{},[2075,67429,4075],{},[2348,67431,67432,67434],{},[2071,67433,2861],{},[2210,67435,638],{},[2075,67437,2077],{},[2210,67439,678],{},[2092,67441,67442],{"encoding":2094},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[1647,67445,67447],{"className":67446},[2059],[2061,67448,67449],{"xmlns":2063},[2065,67450,67451,67465],{},[2068,67452,67453,67459,67461,67463],{},[2348,67454,67455,67457],{},[2071,67456,2861],{},[2210,67458,646],{},[2075,67460,2077],{},[2075,67462,2303],{},[2210,67464,678],{},[2092,67466,67467],{"encoding":2094},"Q_2 = -6"," (vyloučeno). ",[1647,67470,67472],{"className":67471},[2059],[2061,67473,67474],{"xmlns":2063},[2065,67475,67476,67516],{},[2068,67477,67478,67480,67482,67484,67494,67496,67498,67500,67502,67510,67512,67514],{},[2075,67479,2084],{"stretchy":2083},[2071,67481,4342],{},[2071,67483,2849],{},[2205,67485,67486,67488],{},[2075,67487,2090],{"stretchy":2083},[2068,67489,67490,67492],{},[2075,67491,2452],{"mathvariant":2450},[2075,67493,2452],{"mathvariant":2450},[2075,67495,2084],{"stretchy":2083},[2210,67497,678],{},[2075,67499,2090],{"stretchy":2083},[2075,67501,2077],{},[2400,67503,67504],{"scriptlevel":630,"displaystyle":2083},[2403,67505,67506,67508],{},[2210,67507,638],{},[2210,67509,654],{},[2075,67511,3482],{},[2210,67513,630],{},[2075,67515,4075],{},[2092,67517,67518],{"encoding":2094},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[1647,67521,67523],{"className":67522},[2059],[2061,67524,67525],{"xmlns":2063},[2065,67526,67527,67543],{},[2068,67528,67529,67531,67533,67535,67537,67539,67541],{},[2071,67530,4342],{},[2071,67532,2849],{},[2075,67534,2084],{"stretchy":2083},[2210,67536,678],{},[2075,67538,2090],{"stretchy":2083},[2075,67540,2077],{},[2210,67542,39270],{},[2092,67544,67545],{"encoding":2094},"AC(6) = 15",[55,67547,67548,67549,67575,67576,2777],{},"Pomocí principu: ",[1647,67550,67552],{"className":67551},[2059],[2061,67553,67554],{"xmlns":2063},[2065,67555,67556,67572],{},[2068,67557,67558,67560,67562,67564,67566,67568,67570],{},[2071,67559,2890],{},[2071,67561,2849],{},[2075,67563,2077],{},[2210,67565,646],{},[2071,67567,2861],{},[2075,67569,2176],{},[2210,67571,654],{},[2092,67573,67574],{"encoding":2094},"MC = 2Q + 3",", rovnice ",[1647,67577,67579],{"className":67578},[2059],[2061,67580,67581],{"xmlns":2063},[2065,67582,67583,67595],{},[2068,67584,67585,67587,67589,67591,67593],{},[2071,67586,4342],{},[2071,67588,2849],{},[2075,67590,2077],{},[2071,67592,2890],{},[2071,67594,2849],{},[2092,67596,59693],{"encoding":2094},[1647,67598,67600],{"className":67599},[2059],[2061,67601,67602],{"xmlns":2063,"display":31093},[2065,67603,67604,67706],{},[2068,67605,67606,67628,67630,67632,67634,67636,67638,67640,67642,67644,67650,67652,67654,67656,67658,67660,67662,67664,67670,67672,67674,67676,67678,67680,67682,67688,67690,67692,67694,67696,67698,67700,67702,67704],{},[2403,67607,67608,67626],{},[2068,67609,67610,67616,67618,67620,67622,67624],{},[2205,67611,67612,67614],{},[2071,67613,2861],{},[2210,67615,646],{},[2075,67617,2176],{},[2210,67619,654],{},[2071,67621,2861],{},[2075,67623,2176],{},[2210,67625,5652],{},[2071,67627,2861],{},[2075,67629,2077],{},[2210,67631,646],{},[2071,67633,2861],{},[2075,67635,2176],{},[2210,67637,654],{},[2363,67639,4072],{},[2075,67641,4075],{},[2363,67643,4072],{},[2205,67645,67646,67648],{},[2071,67647,2861],{},[2210,67649,646],{},[2075,67651,2176],{},[2210,67653,654],{},[2071,67655,2861],{},[2075,67657,2176],{},[2210,67659,5652],{},[2075,67661,2077],{},[2210,67663,646],{},[2205,67665,67666,67668],{},[2071,67667,2861],{},[2210,67669,646],{},[2075,67671,2176],{},[2210,67673,654],{},[2071,67675,2861],{},[2363,67677,4072],{},[2075,67679,4075],{},[2363,67681,4072],{},[2205,67683,67684,67686],{},[2071,67685,2861],{},[2210,67687,646],{},[2075,67689,2077],{},[2210,67691,5652],{},[2363,67693,4072],{},[2075,67695,4075],{},[2363,67697,4072],{},[2071,67699,2861],{},[2075,67701,2077],{},[2210,67703,678],{},[2075,67705,2361],{"separator":2360},[2092,67707,67708],{"encoding":2094},"\\frac{Q^2 + 3Q + 36}{Q} = 2Q + 3 \\;\\Rightarrow\\; Q^2 + 3Q + 36 = 2Q^2 + 3Q \\;\\Rightarrow\\; Q^2 = 36 \\;\\Rightarrow\\; Q = 6,",[55,67710,67711,67712,67750],{},"a ",[1647,67713,67715],{"className":67714},[2059],[2061,67716,67717],{"xmlns":2063},[2065,67718,67719,67747],{},[2068,67720,67721,67723,67725,67727,67729,67731,67733,67735,67737,67739,67741,67743,67745],{},[2071,67722,4342],{},[2071,67724,2849],{},[2075,67726,2084],{"stretchy":2083},[2210,67728,678],{},[2075,67730,2090],{"stretchy":2083},[2075,67732,2077],{},[2071,67734,2890],{},[2071,67736,2849],{},[2075,67738,2084],{"stretchy":2083},[2210,67740,678],{},[2075,67742,2090],{"stretchy":2083},[2075,67744,2077],{},[2210,67746,39270],{},[2092,67748,67749],{"encoding":2094},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[609,67752,67754],{"id":67753},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[55,67756,67757,67758,2777],{},"Analogicky pro ",[1647,67759,67761],{"className":67760},[2059],[2061,67762,67763],{"xmlns":2063},[2065,67764,67765,67773],{},[2068,67766,67767,67769,67771],{},[2071,67768,4342],{},[2071,67770,44630],{},[2071,67772,2849],{},[2092,67774,59781],{"encoding":2094},[1647,67776,67778],{"className":67777},[2059],[2061,67779,67780],{"xmlns":2063,"display":31093},[2065,67781,67782,67833],{},[23493,67783,67784],{"width":31098},[23498,67785,67786,67788,67826,67828],{},[23501,67787],{"width":31103},[23501,67789,67790],{},[2068,67791,67792,67794,67796,67798,67800,67806,67808,67810,67812,67814,67816,67822,67824],{},[2071,67793,4342],{},[2071,67795,44630],{},[2071,67797,2849],{},[2075,67799,2084],{"stretchy":2083},[2348,67801,67802,67804],{},[2071,67803,2861],{},[2210,67805,630],{},[2075,67807,2090],{"stretchy":2083},[2075,67809,2077],{},[2071,67811,2890],{},[2071,67813,2849],{},[2075,67815,2084],{"stretchy":2083},[2348,67817,67818,67820],{},[2071,67819,2861],{},[2210,67821,630],{},[2075,67823,2090],{"stretchy":2083},[2071,67825,195],{"mathvariant":2450},[23501,67827],{"width":31103},[23501,67829,67830],{},[2363,67831,67832],{},"(3.11)",[2092,67834,67835],{"encoding":2094},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1023,67837,67838],{},[55,67839,67840,66516,67842],{},[1647,67841,60914],{},[95,67843,67844,67845,67862],{},"V bodě minima průměrných variabilních nákladů se ",[1647,67846,67848],{"className":67847},[2059],[2061,67849,67850],{"xmlns":2063},[2065,67851,67852,67860],{},[2068,67853,67854,67856,67858],{},[2071,67855,4342],{},[2071,67857,44630],{},[2071,67859,2849],{},[2092,67861,59781],{"encoding":2094}," rovnají mezním nákladům.",[55,67864,67865,67866,67888,67889,195],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[1647,67867,67869],{"className":67868},[2059],[2061,67870,67871],{"xmlns":2063},[2065,67872,67873,67885],{},[2068,67874,67875,67881,67883],{},[2348,67876,67877,67879],{},[2071,67878,2861],{},[2210,67880,630],{},[2075,67882,2077],{},[2210,67884,57497],{},[2092,67886,67887],{"encoding":2094},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[1647,67890,67892],{"className":67891},[2059],[2061,67893,67894],{"xmlns":2063},[2065,67895,67896,67922],{},[2068,67897,67898,67900,67902,67904,67906,67908,67910,67912,67914,67916,67918,67920],{},[2071,67899,4342],{},[2071,67901,44630],{},[2071,67903,2849],{},[2075,67905,2084],{"stretchy":2083},[2071,67907,2861],{},[2075,67909,2090],{"stretchy":2083},[2075,67911,2077],{},[2071,67913,2890],{},[2071,67915,2849],{},[2075,67917,2084],{"stretchy":2083},[2071,67919,2861],{},[2075,67921,2090],{"stretchy":2083},[2092,67923,67924],{"encoding":2094},"AVC(Q) = MC(Q)",[84,67926,67928],{"id":67927},"zisk-a-body-zvratu","Zisk a body zvratu",[55,67930,67931,1445,67934,67950],{},[95,67932,67933],{},"Zisk",[1647,67935,67937],{"className":67936},[2059],[2061,67938,67939],{"xmlns":2063},[2065,67940,67941,67947],{},[2068,67942,67943,67945],{},[2071,67944,575],{},[2071,67946,4082],{},[2092,67948,67949],{"encoding":2094},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[1647,67952,67954],{"className":67953},[2059],[2061,67955,67956],{"xmlns":2063,"display":31093},[2065,67957,67958,68017],{},[23493,67959,67960],{"width":31098},[23498,67961,67962,67964,68010,68012],{},[23501,67963],{"width":31103},[23501,67965,67966],{},[2068,67967,67968,67970,67972,67974,67976,67978,67980,67982,67984,67986,67988,67990,67992,67994,67996,67998,68000,68002,68004,68006,68008],{},[2071,67969,575],{},[2071,67971,4082],{},[2075,67973,2077],{},[2071,67975,575],{},[2071,67977,4082],{},[2075,67979,2084],{"stretchy":2083},[2071,67981,2861],{},[2075,67983,2090],{"stretchy":2083},[2075,67985,2077],{},[2071,67987,543],{},[2071,67989,4082],{},[2075,67991,2084],{"stretchy":2083},[2071,67993,2861],{},[2075,67995,2090],{"stretchy":2083},[2075,67997,2303],{},[2071,67999,543],{},[2071,68001,2849],{},[2075,68003,2084],{"stretchy":2083},[2071,68005,2861],{},[2075,68007,2090],{"stretchy":2083},[2071,68009,195],{"mathvariant":2450},[23501,68011],{"width":31103},[23501,68013,68014],{},[2363,68015,68016],{},"(3.12)",[2092,68018,68019],{"encoding":2094},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[55,68021,68022,68023,75,68038,47930,68053,68055,68056,68059,68060,68076,68077,68092,68093,68108,68109,835,68122,68135,68136,835,68154,68172,68173,11156,68176,68179,68180,2462,68202,8189,68224,68246,68247,8189,68277,68299],{},"Body rovnosti ",[1647,68024,68026],{"className":68025},[2059],[2061,68027,68028],{"xmlns":2063},[2065,68029,68030,68036],{},[2068,68031,68032,68034],{},[2071,68033,543],{},[2071,68035,4082],{},[2092,68037,4182],{"encoding":2094},[1647,68039,68041],{"className":68040},[2059],[2061,68042,68043],{"xmlns":2063},[2065,68044,68045,68051],{},[2068,68046,68047,68049],{},[2071,68048,543],{},[2071,68050,2849],{},[2092,68052,3317],{"encoding":2094},[95,68054,60197],{}," (též vyrovnání, ",[3982,68057,68058],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[1647,68061,68063],{"className":68062},[2059],[2061,68064,68065],{"xmlns":2063},[2065,68066,68067,68073],{},[2068,68068,68069,68071],{},[2071,68070,44630],{},[2071,68072,2849],{},[2092,68074,68075],{"encoding":2094},"VC",") je ",[1647,68078,68080],{"className":68079},[2059],[2061,68081,68082],{"xmlns":2063},[2065,68083,68084,68090],{},[2068,68085,68086,68088],{},[2071,68087,543],{},[2071,68089,4082],{},[2092,68091,4182],{"encoding":2094}," kvadratická a ",[1647,68094,68096],{"className":68095},[2059],[2061,68097,68098],{"xmlns":2063},[2065,68099,68100,68106],{},[2068,68101,68102,68104],{},[2071,68103,543],{},[2071,68105,2849],{},[2092,68107,3317],{"encoding":2094}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[1647,68110,68112],{"className":68111},[2059],[2061,68113,68114],{"xmlns":2063},[2065,68115,68116,68120],{},[2068,68117,68118],{},[2071,68119,4342],{},[2092,68121,4342],{"encoding":2094},[1647,68123,68125],{"className":68124},[2059],[2061,68126,68127],{"xmlns":2063},[2065,68128,68129,68133],{},[2068,68130,68131],{},[2071,68132,25992],{},[2092,68134,25992],{"encoding":2094}," odpovídajících množstvím ",[1647,68137,68139],{"className":68138},[2059],[2061,68140,68141],{"xmlns":2063},[2065,68142,68143,68151],{},[2068,68144,68145],{},[2348,68146,68147,68149],{},[2071,68148,2861],{},[2071,68150,4342],{},[2092,68152,68153],{"encoding":2094},"Q_A",[1647,68155,68157],{"className":68156},[2059],[2061,68158,68159],{"xmlns":2063},[2065,68160,68161,68169],{},[2068,68162,68163],{},[2348,68164,68165,68167],{},[2071,68166,2861],{},[2071,68168,25992],{},[2092,68170,68171],{"encoding":2094},"Q_B"," — firma je na ",[95,68174,68175],{},"prahu rentability",[3982,68177,68178],{},"break even","). Pro ",[1647,68181,68183],{"className":68182},[2059],[2061,68184,68185],{"xmlns":2063},[2065,68186,68187,68199],{},[2068,68188,68189,68191,68193],{},[2071,68190,2861],{},[2075,68192,3521],{},[2348,68194,68195,68197],{},[2071,68196,2861],{},[2071,68198,4342],{},[2092,68200,68201],{"encoding":2094},"Q \u003C Q_A",[1647,68203,68205],{"className":68204},[2059],[2061,68206,68207],{"xmlns":2063},[2065,68208,68209,68221],{},[2068,68210,68211,68213,68215],{},[2071,68212,2861],{},[2075,68214,3482],{},[2348,68216,68217,68219],{},[2071,68218,2861],{},[2071,68220,25992],{},[2092,68222,68223],{"encoding":2094},"Q > Q_B",[1647,68225,68227],{"className":68226},[2059],[2061,68228,68229],{"xmlns":2063},[2065,68230,68231,68243],{},[2068,68232,68233,68235,68237,68239,68241],{},[2071,68234,543],{},[2071,68236,2849],{},[2075,68238,3482],{},[2071,68240,543],{},[2071,68242,4082],{},[2092,68244,68245],{"encoding":2094},"TC > TR"," (ztráta); pro ",[1647,68248,68250],{"className":68249},[2059],[2061,68251,68252],{"xmlns":2063},[2065,68253,68254,68274],{},[2068,68255,68256,68262,68264,68266,68268],{},[2348,68257,68258,68260],{},[2071,68259,2861],{},[2071,68261,4342],{},[2075,68263,3521],{},[2071,68265,2861],{},[2075,68267,3521],{},[2348,68269,68270,68272],{},[2071,68271,2861],{},[2071,68273,25992],{},[2092,68275,68276],{"encoding":2094},"Q_A \u003C Q \u003C Q_B",[1647,68278,68280],{"className":68279},[2059],[2061,68281,68282],{"xmlns":2063},[2065,68283,68284,68296],{},[2068,68285,68286,68288,68290,68292,68294],{},[2071,68287,543],{},[2071,68289,4082],{},[2075,68291,3482],{},[2071,68293,543],{},[2071,68295,2849],{},[2092,68297,68298],{"encoding":2094},"TR > TC"," (zisk).",[1023,68301,68302],{},[55,68303,68304,68306],{},[1647,68305,4243],{}," Intuice — body zvratu\nBody zvratu jsou hranice „prodělečné\" a „ziskové\" zóny. Mezi nimi firma vydělává, za nimi prodělává. Maximum zisku leží uvnitř tohoto intervalu — typicky v jeho středu, je-li zisk kvadratický.",[55,68308,68309,68310,68336],{},"Body zvratu jsou řešení rovnice ",[1647,68311,68313],{"className":68312},[2059],[2061,68314,68315],{"xmlns":2063},[2065,68316,68317,68333],{},[2068,68318,68319,68321,68323,68325,68327,68329,68331],{},[2071,68320,575],{},[2071,68322,4082],{},[2075,68324,2084],{"stretchy":2083},[2071,68326,2861],{},[2075,68328,2090],{"stretchy":2083},[2075,68330,2077],{},[2210,68332,630],{},[2092,68334,68335],{"encoding":2094},"PR(Q) = 0",". Pro vyšší stupně polynomu může být nutné použít software či numerický odhad. Maximum zisku se stanoví jako extrém funkce zisku.",[55,68338,68339],{},[58,68340],{"alt":68341,"className":68342,"src":68343},"imek-tr-tc-body-zvratu",[62,63],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[55,68345,68346],{},[3982,68347,68348,68349,68364,68365,68380,68381,75,68394,47654,68407,68420,68421,75,68438,68455,68456,68476,68477,75,68492,6560,68507,68536],{},"Obrázek 3.11: Body zvratu — křivky ",[1647,68350,68352],{"className":68351},[2059],[2061,68353,68354],{"xmlns":2063},[2065,68355,68356,68362],{},[2068,68357,68358,68360],{},[2071,68359,543],{},[2071,68361,4082],{},[2092,68363,4182],{"encoding":2094}," (obrácená parabola) a ",[1647,68366,68368],{"className":68367},[2059],[2061,68369,68370],{"xmlns":2063},[2065,68371,68372,68378],{},[2068,68373,68374,68376],{},[2071,68375,543],{},[2071,68377,2849],{},[2092,68379,3317],{"encoding":2094}," (přímka) se protínají v bodech ",[1647,68382,68384],{"className":68383},[2059],[2061,68385,68386],{"xmlns":2063},[2065,68387,68388,68392],{},[2068,68389,68390],{},[2071,68391,4342],{},[2092,68393,4342],{"encoding":2094},[1647,68395,68397],{"className":68396},[2059],[2061,68398,68399],{"xmlns":2063},[2065,68400,68401,68405],{},[2068,68402,68403],{},[2071,68404,25992],{},[2092,68406,25992],{"encoding":2094},[1647,68408,68410],{"className":68409},[2059],[2061,68411,68412],{"xmlns":2063},[2065,68413,68414,68418],{},[2068,68415,68416],{},[2071,68417,2861],{},[2092,68419,2861],{"encoding":2094}," v hodnotách ",[1647,68422,68424],{"className":68423},[2059],[2061,68425,68426],{"xmlns":2063},[2065,68427,68428,68436],{},[2068,68429,68430],{},[2348,68431,68432,68434],{},[2071,68433,2861],{},[2071,68435,4342],{},[2092,68437,68153],{"encoding":2094},[1647,68439,68441],{"className":68440},[2059],[2061,68442,68443],{"xmlns":2063},[2065,68444,68445,68453],{},[2068,68446,68447],{},[2348,68448,68449,68451],{},[2071,68450,2861],{},[2071,68452,25992],{},[2092,68454,68171],{"encoding":2094},"; maximum zisku leží mezi nimi v bodě ",[1647,68457,68459],{"className":68458},[2059],[2061,68460,68461],{"xmlns":2063},[2065,68462,68463,68473],{},[2068,68464,68465],{},[2348,68466,68467,68469,68471],{},[2071,68468,2861],{},[2071,68470,60667],{},[2075,68472,60670],{},[2092,68474,68475],{"encoding":2094},"Q_{\\max}","; svislá vzdálenost mezi ",[1647,68478,68480],{"className":68479},[2059],[2061,68481,68482],{"xmlns":2063},[2065,68483,68484,68490],{},[2068,68485,68486,68488],{},[2071,68487,543],{},[2071,68489,4082],{},[2092,68491,4182],{"encoding":2094},[1647,68493,68495],{"className":68494},[2059],[2061,68496,68497],{"xmlns":2063},[2065,68498,68499,68505],{},[2068,68500,68501,68503],{},[2071,68502,543],{},[2071,68504,2849],{},[2092,68506,3317],{"encoding":2094},[1647,68508,68510],{"className":68509},[2059],[2061,68511,68512],{"xmlns":2063},[2065,68513,68514,68534],{},[2068,68515,68516,68522,68524,68526,68528],{},[2348,68517,68518,68520],{},[2071,68519,2861],{},[2071,68521,4342],{},[2075,68523,3521],{},[2071,68525,2861],{},[2075,68527,3521],{},[2348,68529,68530,68532],{},[2071,68531,2861],{},[2071,68533,25992],{},[2092,68535,68276],{"encoding":2094}," vyznačuje zisk.",[1144,68538,68540],{"id":68539},"příklad-38","Příklad 3.8",[55,68542,68543,68545,68546,835,68566,835,68592,68618],{},[95,68544,60457],{}," Dáno ",[1647,68547,68549],{"className":68548},[2059],[2061,68550,68551],{"xmlns":2063},[2065,68552,68553,68563],{},[2068,68554,68555,68557,68559,68561],{},[2071,68556,10177],{},[2071,68558,2849],{},[2075,68560,2077],{},[2210,68562,662],{},[2092,68564,68565],{"encoding":2094},"FC = 4",[1647,68567,68569],{"className":68568},[2059],[2061,68570,68571],{"xmlns":2063},[2065,68572,68573,68589],{},[2068,68574,68575,68577,68579,68581,68583],{},[2071,68576,543],{},[2071,68578,44630],{},[2071,68580,2849],{},[2075,68582,2077],{},[2205,68584,68585,68587],{},[2071,68586,2861],{},[2210,68588,646],{},[2092,68590,68591],{"encoding":2094},"TVC = Q^2",[1647,68593,68595],{"className":68594},[2059],[2061,68596,68597],{"xmlns":2063},[2065,68598,68599,68615],{},[2068,68600,68601,68603,68605,68607,68609,68611,68613],{},[2071,68602,575],{},[2075,68604,2077],{},[2075,68606,2303],{},[2210,68608,646],{},[2071,68610,2861],{},[2075,68612,2176],{},[2210,68614,4087],{},[2092,68616,68617],{"encoding":2094},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[55,68620,68621,68623],{},[95,68622,25509],{}," Celkové náklady a příjem:",[1647,68625,68627],{"className":68626},[2059],[2061,68628,68629],{"xmlns":2063,"display":31093},[2065,68630,68631,68697],{},[2068,68632,68633,68635,68637,68639,68641,68643,68649,68651,68653,68655,68657,68659,68661,68663,68665,68667,68669,68671,68673,68675,68677,68679,68681,68683,68689,68691,68693,68695],{},[2071,68634,543],{},[2071,68636,2849],{},[2075,68638,2077],{},[2210,68640,662],{},[2075,68642,2176],{},[2205,68644,68645,68647],{},[2071,68646,2861],{},[2210,68648,646],{},[2075,68650,2361],{"separator":2360},[5965,68652],{"width":5967},[2071,68654,543],{},[2071,68656,4082],{},[2075,68658,2077],{},[2071,68660,2861],{},[2075,68662,3251],{},[2075,68664,2084],{"stretchy":2083},[2075,68666,2303],{},[2210,68668,646],{},[2071,68670,2861],{},[2075,68672,2176],{},[2210,68674,4087],{},[2075,68676,2090],{"stretchy":2083},[2075,68678,2077],{},[2075,68680,2303],{},[2210,68682,646],{},[2205,68684,68685,68687],{},[2071,68686,2861],{},[2210,68688,646],{},[2075,68690,2176],{},[2210,68692,4087],{},[2071,68694,2861],{},[2071,68696,195],{"mathvariant":2450},[2092,68698,68699],{"encoding":2094},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[55,68701,68702],{},"Zisk dle (3.12):",[1647,68704,68706],{"className":68705},[2059],[2061,68707,68708],{"xmlns":2063,"display":31093},[2065,68709,68710,68788],{},[2068,68711,68712,68714,68716,68718,68720,68722,68724,68726,68728,68730,68732,68734,68736,68742,68744,68746,68748,68750,68752,68754,68756,68758,68764,68766,68768,68770,68772,68778,68780,68782,68784,68786],{},[2071,68713,575],{},[2071,68715,4082],{},[2075,68717,2077],{},[2071,68719,543],{},[2071,68721,4082],{},[2075,68723,2303],{},[2071,68725,543],{},[2071,68727,2849],{},[2075,68729,2077],{},[2075,68731,2084],{"stretchy":2083},[2075,68733,2303],{},[2210,68735,646],{},[2205,68737,68738,68740],{},[2071,68739,2861],{},[2210,68741,646],{},[2075,68743,2176],{},[2210,68745,4087],{},[2071,68747,2861],{},[2075,68749,2090],{"stretchy":2083},[2075,68751,2303],{},[2075,68753,2084],{"stretchy":2083},[2210,68755,662],{},[2075,68757,2176],{},[2205,68759,68760,68762],{},[2071,68761,2861],{},[2210,68763,646],{},[2075,68765,2090],{"stretchy":2083},[2075,68767,2077],{},[2075,68769,2303],{},[2210,68771,654],{},[2205,68773,68774,68776],{},[2071,68775,2861],{},[2210,68777,646],{},[2075,68779,2176],{},[2210,68781,4087],{},[2071,68783,2861],{},[2075,68785,2303],{},[2210,68787,63789],{},[2092,68789,68790],{"encoding":2094},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[55,68792,68793,68796,68797,20314,68833,2777],{},[95,68794,68795],{},"Body zvratu"," jsou kořeny rovnice ",[1647,68798,68800],{"className":68799},[2059],[2061,68801,68802],{"xmlns":2063},[2065,68803,68804,68830],{},[2068,68805,68806,68808,68810,68816,68818,68820,68822,68824,68826,68828],{},[2075,68807,2303],{},[2210,68809,654],{},[2205,68811,68812,68814],{},[2071,68813,2861],{},[2210,68815,646],{},[2075,68817,2176],{},[2210,68819,4087],{},[2071,68821,2861],{},[2075,68823,2303],{},[2210,68825,662],{},[2075,68827,2077],{},[2210,68829,630],{},[2092,68831,68832],{"encoding":2094},"-3Q^2 + 9Q - 4 = 0",[1647,68834,68836],{"className":68835},[2059],[2061,68837,68838],{"xmlns":2063},[2065,68839,68840,68864],{},[2068,68841,68842,68844,68850,68852,68854,68856,68858,68860,68862],{},[2210,68843,654],{},[2205,68845,68846,68848],{},[2071,68847,2861],{},[2210,68849,646],{},[2075,68851,2303],{},[2210,68853,4087],{},[2071,68855,2861],{},[2075,68857,2176],{},[2210,68859,662],{},[2075,68861,2077],{},[2210,68863,630],{},[2092,68865,68866],{"encoding":2094},"3Q^2 - 9Q + 4 = 0",[1647,68868,68870],{"className":68869},[2059],[2061,68871,68872],{"xmlns":2063,"display":31093},[2065,68873,68874,68931],{},[2068,68875,68876,68888,68890,68913,68915,68929],{},[2348,68877,68878,68880],{},[2071,68879,2861],{},[2068,68881,68882,68884,68886],{},[2210,68883,638],{},[2075,68885,2361],{"separator":2360},[2210,68887,646],{},[2075,68889,2077],{},[2403,68891,68892,68911],{},[2068,68893,68894,68896,68899],{},[2210,68895,4087],{},[2075,68897,68898],{},"±",[8204,68900,68901],{},[2068,68902,68903,68906,68908],{},[2210,68904,68905],{},"81",[2075,68907,2303],{},[2210,68909,68910],{},"48",[2210,68912,678],{},[2075,68914,2077],{},[2403,68916,68917,68927],{},[2068,68918,68919,68921,68923],{},[2210,68920,4087],{},[2075,68922,68898],{},[8204,68924,68925],{},[2210,68926,9037],{},[2210,68928,678],{},[2075,68930,2361],{"separator":2360},[2092,68932,68933],{"encoding":2094},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[55,68935,68936,68937,75,68960,195],{},"numericky ",[1647,68938,68940],{"className":68939},[2059],[2061,68941,68942],{"xmlns":2063},[2065,68943,68944,68957],{},[2068,68945,68946,68952,68954],{},[2348,68947,68948,68950],{},[2071,68949,2861],{},[2210,68951,638],{},[2075,68953,5987],{},[2210,68955,68956],{},"0,543",[2092,68958,68959],{"encoding":2094},"Q_1 \\doteq 0{,}543",[1647,68961,68963],{"className":68962},[2059],[2061,68964,68965],{"xmlns":2063},[2065,68966,68967,68980],{},[2068,68968,68969,68975,68977],{},[2348,68970,68971,68973],{},[2071,68972,2861],{},[2210,68974,646],{},[2075,68976,5987],{},[2210,68978,68979],{},"2,457",[2092,68981,68982],{"encoding":2094},"Q_2 \\doteq 2{,}457",[55,68984,68985,1445,68988,7639,69033,20314,69067,69085],{},[95,68986,68987],{},"Maximum zisku.",[1647,68989,68991],{"className":68990},[2059],[2061,68992,68993],{"xmlns":2063},[2065,68994,68995,69030],{},[2068,68996,68997,68999,69005,69007,69009,69011,69013,69015,69017,69019,69021,69023,69025,69027],{},[2071,68998,575],{},[2205,69000,69001,69003],{},[2071,69002,4082],{},[2075,69004,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,69006,2077],{},[2075,69008,2303],{},[2210,69010,678],{},[2071,69012,2861],{},[2075,69014,2176],{},[2210,69016,4087],{},[2075,69018,2077],{},[2210,69020,630],{},[2075,69022,4075],{},[2071,69024,2861],{},[2075,69026,2077],{},[2210,69028,69029],{},"1,5",[2092,69031,69032],{"encoding":2094},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[1647,69034,69036],{"className":69035},[2059],[2061,69037,69038],{"xmlns":2063},[2065,69039,69040,69064],{},[2068,69041,69042,69044,69054,69056,69058,69060,69062],{},[2071,69043,575],{},[2205,69045,69046,69048],{},[2071,69047,4082],{},[2068,69049,69050,69052],{},[2075,69051,2452],{"mathvariant":2450},[2075,69053,2452],{"mathvariant":2450},[2075,69055,2077],{},[2075,69057,2303],{},[2210,69059,678],{},[2075,69061,3521],{},[2210,69063,630],{},[2092,69065,69066],{"encoding":2094},"PR'' = -6 \u003C 0",[1647,69068,69070],{"className":69069},[2059],[2061,69071,69072],{"xmlns":2063},[2065,69073,69074,69082],{},[2068,69075,69076,69078,69080],{},[2071,69077,2861],{},[2075,69079,2077],{},[2210,69081,69029],{},[2092,69083,69084],{"encoding":2094},"Q = 1{,}5"," je bod maxima s hodnotou",[1647,69087,69089],{"className":69088},[2059],[2061,69090,69091],{"xmlns":2063,"display":31093},[2065,69092,69093,69156],{},[2068,69094,69095,69097,69099,69101,69103,69105,69107,69109,69111,69113,69115,69117,69123,69125,69127,69129,69131,69133,69135,69137,69139,69142,69144,69147,69149,69151,69153],{},[2071,69096,575],{},[2071,69098,4082],{},[2075,69100,2084],{"stretchy":2083},[2210,69102,69029],{},[2075,69104,2090],{"stretchy":2083},[2075,69106,2077],{},[2075,69108,2303],{},[2210,69110,654],{},[2075,69112,3251],{},[2075,69114,2084],{"stretchy":2083},[2210,69116,69029],{},[2205,69118,69119,69121],{},[2075,69120,2090],{"stretchy":2083},[2210,69122,646],{},[2075,69124,2176],{},[2210,69126,4087],{},[2075,69128,3251],{},[2210,69130,69029],{},[2075,69132,2303],{},[2210,69134,662],{},[2075,69136,2077],{},[2075,69138,2303],{},[2210,69140,69141],{},"6,75",[2075,69143,2176],{},[2210,69145,69146],{},"13,5",[2075,69148,2303],{},[2210,69150,662],{},[2075,69152,2077],{},[2210,69154,69155],{},"2,75.",[2092,69157,69158],{"encoding":2094},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[55,69160,69161,69162,835,69207,69260,69261,69279],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[1647,69163,69165],{"className":69164},[2059],[2061,69166,69167],{"xmlns":2063},[2065,69168,69169,69204],{},[2068,69170,69171,69173,69179,69181,69183,69185,69187,69189,69191,69193,69195,69197,69199,69201],{},[2071,69172,543],{},[2205,69174,69175,69177],{},[2071,69176,4082],{},[2075,69178,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,69180,2077],{},[2075,69182,2303],{},[2210,69184,662],{},[2071,69186,2861],{},[2075,69188,2176],{},[2210,69190,4087],{},[2075,69192,2077],{},[2210,69194,630],{},[2075,69196,4075],{},[2071,69198,2861],{},[2075,69200,2077],{},[2210,69202,69203],{},"2,25",[2092,69205,69206],{"encoding":2094},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[1647,69208,69210],{"className":69209},[2059],[2061,69211,69212],{"xmlns":2063},[2065,69213,69214,69257],{},[2068,69215,69216,69218,69226,69228,69230,69232,69234,69236,69238,69244,69246,69248,69250,69252,69254],{},[2071,69217,543],{},[2348,69219,69220,69222,69224],{},[2071,69221,4082],{},[2071,69223,60667],{},[2075,69225,60670],{},[2075,69227,2077],{},[2075,69229,2303],{},[2210,69231,646],{},[2075,69233,3251],{},[2075,69235,2084],{"stretchy":2083},[2210,69237,69203],{},[2205,69239,69240,69242],{},[2075,69241,2090],{"stretchy":2083},[2210,69243,646],{},[2075,69245,2176],{},[2210,69247,4087],{},[2075,69249,3251],{},[2210,69251,69203],{},[2075,69253,2077],{},[2210,69255,69256],{},"10,125",[2092,69258,69259],{"encoding":2094},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[1647,69262,69264],{"className":69263},[2059],[2061,69265,69266],{"xmlns":2063},[2065,69267,69268,69276],{},[2068,69269,69270,69272,69274],{},[2071,69271,2861],{},[2075,69273,2077],{},[2210,69275,69203],{},[2092,69277,69278],{"encoding":2094},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1023,69281,69282],{},[55,69283,69284,69286,69287,835,69309,69331,69332,835,69349,69370,69371,69403,69404,69442,69443,2744,69461,69478,69479,75,69507,69541,69542,7772,69580,75,69604,195],{},[1647,69285,4499],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[1647,69288,69290],{"className":69289},[2059],[2061,69291,69292],{"xmlns":2063},[2065,69293,69294,69306],{},[2068,69295,69296,69302,69304],{},[2348,69297,69298,69300],{},[2071,69299,2861],{},[2210,69301,638],{},[2075,69303,2077],{},[2210,69305,5096],{},[2092,69307,69308],{"encoding":2094},"Q_1 = 0{,}5",[1647,69310,69312],{"className":69311},[2059],[2061,69313,69314],{"xmlns":2063},[2065,69315,69316,69328],{},[2068,69317,69318,69324,69326],{},[2348,69319,69320,69322],{},[2071,69321,2861],{},[2210,69323,646],{},[2075,69325,2077],{},[2210,69327,662],{},[2092,69329,69330],{"encoding":2094},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[1647,69333,69335],{"className":69334},[2059],[2061,69336,69337],{"xmlns":2063},[2065,69338,69339,69347],{},[2068,69340,69341,69343,69345],{},[2071,69342,2861],{},[2075,69344,2077],{},[2210,69346,69203],{},[2092,69348,69278],{"encoding":2094},[1647,69350,69352],{"className":69351},[2059],[2061,69353,69354],{"xmlns":2063},[2065,69355,69356,69367],{},[2068,69357,69358,69360,69362,69364],{},[2071,69359,575],{},[2071,69361,4082],{},[2075,69363,2077],{},[2210,69365,69366],{},"6,125",[2092,69368,69369],{"encoding":2094},"PR = 6{,}125"," (odpovídající derivaci ",[1647,69372,69374],{"className":69373},[2059],[2061,69375,69376],{"xmlns":2063},[2065,69377,69378,69400],{},[2068,69379,69380,69382,69388,69390,69392,69394,69396,69398],{},[2071,69381,575],{},[2205,69383,69384,69386],{},[2071,69385,4082],{},[2075,69387,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,69389,2077],{},[2075,69391,2303],{},[2210,69393,662],{},[2071,69395,2861],{},[2075,69397,2176],{},[2210,69399,4087],{},[2092,69401,69402],{"encoding":2094},"PR' = -4Q + 9",", tj. zisku ",[1647,69405,69407],{"className":69406},[2059],[2061,69408,69409],{"xmlns":2063},[2065,69410,69411,69439],{},[2068,69412,69413,69415,69417,69419,69421,69423,69429,69431,69433,69435,69437],{},[2071,69414,575],{},[2071,69416,4082],{},[2075,69418,2077],{},[2075,69420,2303],{},[2210,69422,646],{},[2205,69424,69425,69427],{},[2071,69426,2861],{},[2210,69428,646],{},[2075,69430,2176],{},[2210,69432,4087],{},[2071,69434,2861],{},[2075,69436,2303],{},[2210,69438,662],{},[2092,69440,69441],{"encoding":2094},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[1647,69444,69446],{"className":69445},[2059],[2061,69447,69448],{"xmlns":2063},[2065,69449,69450,69458],{},[2068,69451,69452],{},[2205,69453,69454,69456],{},[2071,69455,2861],{},[2210,69457,646],{},[2092,69459,69460],{"encoding":2094},"Q^2",[1647,69462,69464],{"className":69463},[2059],[2061,69465,69466],{"xmlns":2063},[2065,69467,69468,69476],{},[2068,69469,69470,69472,69474],{},[2071,69471,543],{},[2071,69473,44630],{},[2071,69475,2849],{},[2092,69477,59979],{"encoding":2094},"). Zde je uvedena matematicky konzistentní verze: zadané ",[1647,69480,69482],{"className":69481},[2059],[2061,69483,69484],{"xmlns":2063},[2065,69485,69486,69504],{},[2068,69487,69488,69490,69492,69494,69496,69498],{},[2071,69489,543],{},[2071,69491,2849],{},[2075,69493,2077],{},[2210,69495,662],{},[2075,69497,2176],{},[2205,69499,69500,69502],{},[2071,69501,2861],{},[2210,69503,646],{},[2092,69505,69506],{"encoding":2094},"TC = 4 + Q^2",[1647,69508,69510],{"className":69509},[2059],[2061,69511,69512],{"xmlns":2063},[2065,69513,69514,69538],{},[2068,69515,69516,69518,69520,69522,69524,69526,69532,69534,69536],{},[2071,69517,543],{},[2071,69519,4082],{},[2075,69521,2077],{},[2075,69523,2303],{},[2210,69525,646],{},[2205,69527,69528,69530],{},[2071,69529,2861],{},[2210,69531,646],{},[2075,69533,2176],{},[2210,69535,4087],{},[2071,69537,2861],{},[2092,69539,69540],{"encoding":2094},"TR = -2Q^2 + 9Q"," vedou na ",[1647,69543,69545],{"className":69544},[2059],[2061,69546,69547],{"xmlns":2063},[2065,69548,69549,69577],{},[2068,69550,69551,69553,69555,69557,69559,69561,69567,69569,69571,69573,69575],{},[2071,69552,575],{},[2071,69554,4082],{},[2075,69556,2077],{},[2075,69558,2303],{},[2210,69560,654],{},[2205,69562,69563,69565],{},[2071,69564,2861],{},[2210,69566,646],{},[2075,69568,2176],{},[2210,69570,4087],{},[2071,69572,2861],{},[2075,69574,2303],{},[2210,69576,662],{},[2092,69578,69579],{"encoding":2094},"PR = -3Q^2 + 9Q - 4",[1647,69581,69583],{"className":69582},[2059],[2061,69584,69585],{"xmlns":2063},[2065,69586,69587,69601],{},[2068,69588,69589,69597,69599],{},[2348,69590,69591,69593,69595],{},[2071,69592,2861],{},[2071,69594,60667],{},[2075,69596,60670],{},[2075,69598,2077],{},[2210,69600,69029],{},[2092,69602,69603],{"encoding":2094},"Q_{\\max} = 1{,}5",[1647,69605,69607],{"className":69606},[2059],[2061,69608,69609],{"xmlns":2063},[2065,69610,69611,69628],{},[2068,69612,69613,69615,69623,69625],{},[2071,69614,575],{},[2348,69616,69617,69619,69621],{},[2071,69618,4082],{},[2071,69620,60667],{},[2075,69622,60670],{},[2075,69624,2077],{},[2210,69626,69627],{},"2,75",[2092,69629,69630],{"encoding":2094},"PR_{\\max} = 2{,}75",[55,69632,69633],{},[3982,69634,69635,69636,69663,69664,69697,69698,835,69721,195],{},"Obrázek 3.12: Graf ",[1647,69637,69639],{"className":69638},[2059],[2061,69640,69641],{"xmlns":2063},[2065,69642,69643,69661],{},[2068,69644,69645,69647,69649,69651,69653,69655],{},[2071,69646,543],{},[2071,69648,2849],{},[2075,69650,2077],{},[2210,69652,662],{},[2075,69654,2176],{},[2205,69656,69657,69659],{},[2071,69658,2861],{},[2210,69660,646],{},[2092,69662,69506],{"encoding":2094}," (parabola) a ",[1647,69665,69667],{"className":69666},[2059],[2061,69668,69669],{"xmlns":2063},[2065,69670,69671,69695],{},[2068,69672,69673,69675,69677,69679,69681,69683,69689,69691,69693],{},[2071,69674,543],{},[2071,69676,4082],{},[2075,69678,2077],{},[2075,69680,2303],{},[2210,69682,646],{},[2205,69684,69685,69687],{},[2071,69686,2861],{},[2210,69688,646],{},[2075,69690,2176],{},[2210,69692,4087],{},[2071,69694,2861],{},[2092,69696,69540],{"encoding":2094}," (parabola); průsečíky vyznačují body zvratu ",[1647,69699,69701],{"className":69700},[2059],[2061,69702,69703],{"xmlns":2063},[2065,69704,69705,69718],{},[2068,69706,69707,69713,69715],{},[2348,69708,69709,69711],{},[2071,69710,2861],{},[2210,69712,638],{},[2075,69714,5987],{},[2210,69716,69717],{},"0,54",[2092,69719,69720],{"encoding":2094},"Q_1 \\doteq 0{,}54",[1647,69722,69724],{"className":69723},[2059],[2061,69725,69726],{"xmlns":2063},[2065,69727,69728,69741],{},[2068,69729,69730,69736,69738],{},[2348,69731,69732,69734],{},[2071,69733,2861],{},[2210,69735,646],{},[2075,69737,5987],{},[2210,69739,69740],{},"2,46",[2092,69742,69743],{"encoding":2094},"Q_2 \\doteq 2{,}46",[55,69745,69746],{},[3982,69747,69748,69749,62977,69786,69803,69804,835,69825,195],{},"Obrázek 3.13: Graf zisku ",[1647,69750,69752],{"className":69751},[2059],[2061,69753,69754],{"xmlns":2063},[2065,69755,69756,69784],{},[2068,69757,69758,69760,69762,69764,69766,69768,69774,69776,69778,69780,69782],{},[2071,69759,575],{},[2071,69761,4082],{},[2075,69763,2077],{},[2075,69765,2303],{},[2210,69767,654],{},[2205,69769,69770,69772],{},[2071,69771,2861],{},[2210,69773,646],{},[2075,69775,2176],{},[2210,69777,4087],{},[2071,69779,2861],{},[2075,69781,2303],{},[2210,69783,662],{},[2092,69785,69579],{"encoding":2094},[1647,69787,69789],{"className":69788},[2059],[2061,69790,69791],{"xmlns":2063},[2065,69792,69793,69801],{},[2068,69794,69795,69797,69799],{},[2071,69796,2861],{},[2075,69798,2077],{},[2210,69800,69029],{},[2092,69802,69084],{"encoding":2094}," a nulami ",[1647,69805,69807],{"className":69806},[2059],[2061,69808,69809],{"xmlns":2063},[2065,69810,69811,69823],{},[2068,69812,69813,69819,69821],{},[2348,69814,69815,69817],{},[2071,69816,2861],{},[2210,69818,638],{},[2075,69820,5987],{},[2210,69822,69717],{},[2092,69824,69720],{"encoding":2094},[1647,69826,69828],{"className":69827},[2059],[2061,69829,69830],{"xmlns":2063},[2065,69831,69832,69844],{},[2068,69833,69834,69840,69842],{},[2348,69835,69836,69838],{},[2071,69837,2861],{},[2210,69839,646],{},[2075,69841,5987],{},[2210,69843,69740],{},[2092,69845,69743],{"encoding":2094},[84,69847,69849],{"id":69848},"princip-maximalizace-zisku","Princip maximalizace zisku",[55,69851,69852],{},"Kromě standardního hledání extrému lze využít následující princip.",[55,69854,69855],{},[58,69856],{"alt":69857,"className":69858,"src":69859},"imek-max-zisku-dva-pohledy",[62,63],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[609,69861,87],{"id":69862},"princip-1",[55,69864,69865,69866,2697,69881,69898],{},"Má-li zisk ",[1647,69867,69869],{"className":69868},[2059],[2061,69870,69871],{"xmlns":2063},[2065,69872,69873,69879],{},[2068,69874,69875,69877],{},[2071,69876,575],{},[2071,69878,4082],{},[2092,69880,67949],{"encoding":2094},[1647,69882,69884],{"className":69883},[2059],[2061,69885,69886],{"xmlns":2063},[2065,69887,69888,69896],{},[2068,69889,69890],{},[2348,69891,69892,69894],{},[2071,69893,2861],{},[2210,69895,630],{},[2092,69897,42599],{"encoding":2094}," maximum, pak platí",[1647,69900,69902],{"className":69901},[2059],[2061,69903,69904],{"xmlns":2063,"display":31093},[2065,69905,69906,69955],{},[23493,69907,69908],{"width":31098},[23498,69909,69910,69912,69948,69950],{},[23501,69911],{"width":31103},[23501,69913,69914],{},[2068,69915,69916,69918,69920,69922,69928,69930,69932,69934,69936,69938,69944,69946],{},[2071,69917,2890],{},[2071,69919,4082],{},[2075,69921,2084],{"stretchy":2083},[2348,69923,69924,69926],{},[2071,69925,2861],{},[2210,69927,630],{},[2075,69929,2090],{"stretchy":2083},[2075,69931,2077],{},[2071,69933,2890],{},[2071,69935,2849],{},[2075,69937,2084],{"stretchy":2083},[2348,69939,69940,69942],{},[2071,69941,2861],{},[2210,69943,630],{},[2075,69945,2090],{"stretchy":2083},[2071,69947,195],{"mathvariant":2450},[23501,69949],{"width":31103},[23501,69951,69952],{},[2363,69953,69954],{},"(3.13)",[2092,69956,69957],{"encoding":2094},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1023,69959,69960],{},[55,69961,69962,66516,69964],{},[1647,69963,60914],{},[95,69965,69966],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[55,69968,69969,69972,69973,8189,70000,20314,70074,195],{},[95,69970,69971],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[1647,69974,69976],{"className":69975},[2059],[2061,69977,69978],{"xmlns":2063},[2065,69979,69980,69998],{},[2068,69981,69982,69984,69986,69988,69990,69992,69994,69996],{},[2071,69983,575],{},[2071,69985,4082],{},[2075,69987,2077],{},[2071,69989,543],{},[2071,69991,4082],{},[2075,69993,2303],{},[2071,69995,543],{},[2071,69997,2849],{},[2092,69999,59670],{"encoding":2094},[1647,70001,70003],{"className":70002},[2059],[2061,70004,70005],{"xmlns":2063},[2065,70006,70007,70071],{},[2068,70008,70009,70011,70017,70019,70025,70027,70029,70031,70037,70039,70045,70047,70049,70051,70057,70059,70065,70067,70069],{},[2071,70010,575],{},[2205,70012,70013,70015],{},[2071,70014,4082],{},[2075,70016,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,70018,2084],{"stretchy":2083},[2348,70020,70021,70023],{},[2071,70022,2861],{},[2210,70024,630],{},[2075,70026,2090],{"stretchy":2083},[2075,70028,2077],{},[2071,70030,543],{},[2205,70032,70033,70035],{},[2071,70034,4082],{},[2075,70036,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,70038,2084],{"stretchy":2083},[2348,70040,70041,70043],{},[2071,70042,2861],{},[2210,70044,630],{},[2075,70046,2090],{"stretchy":2083},[2075,70048,2303],{},[2071,70050,543],{},[2205,70052,70053,70055],{},[2071,70054,2849],{},[2075,70056,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,70058,2084],{"stretchy":2083},[2348,70060,70061,70063],{},[2071,70062,2861],{},[2210,70064,630],{},[2075,70066,2090],{"stretchy":2083},[2075,70068,2077],{},[2210,70070,630],{},[2092,70072,70073],{"encoding":2094},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[1647,70075,70077],{"className":70076},[2059],[2061,70078,70079],{"xmlns":2063},[2065,70080,70081,70113],{},[2068,70082,70083,70085,70087,70089,70095,70097,70099,70101,70103,70105,70111],{},[2071,70084,2890],{},[2071,70086,4082],{},[2075,70088,2084],{"stretchy":2083},[2348,70090,70091,70093],{},[2071,70092,2861],{},[2210,70094,630],{},[2075,70096,2090],{"stretchy":2083},[2075,70098,2077],{},[2071,70100,2890],{},[2071,70102,2849],{},[2075,70104,2084],{"stretchy":2083},[2348,70106,70107,70109],{},[2071,70108,2861],{},[2210,70110,630],{},[2075,70112,2090],{"stretchy":2083},[2092,70114,70115],{"encoding":2094},"MR(Q_0) = MC(Q_0)",[1023,70117,70118,70123],{},[55,70119,70120,70122],{},[1647,70121,4659],{}," Postup — jak najít maximum zisku",[201,70124,70125,70189,70244,70281,70309],{},[92,70126,70127,70128,75,70143,70158,70159,4007],{},"Sestavte ",[1647,70129,70131],{"className":70130},[2059],[2061,70132,70133],{"xmlns":2063},[2065,70134,70135,70141],{},[2068,70136,70137,70139],{},[2071,70138,543],{},[2071,70140,4082],{},[2092,70142,4182],{"encoding":2094},[1647,70144,70146],{"className":70145},[2059],[2061,70147,70148],{"xmlns":2063},[2065,70149,70150,70156],{},[2068,70151,70152,70154],{},[2071,70153,543],{},[2071,70155,2849],{},[2092,70157,3317],{"encoding":2094}," ze zadání (typicky ",[1647,70160,70162],{"className":70161},[2059],[2061,70163,70164],{"xmlns":2063},[2065,70165,70166,70186],{},[2068,70167,70168,70170,70172,70174,70176,70178,70180,70182,70184],{},[2071,70169,543],{},[2071,70171,4082],{},[2075,70173,2077],{},[2071,70175,575],{},[2075,70177,2084],{"stretchy":2083},[2071,70179,2861],{},[2075,70181,2090],{"stretchy":2083},[2075,70183,3251],{},[2071,70185,2861],{},[2092,70187,70188],{"encoding":2094},"TR = P(Q) \\cdot Q",[92,70190,70191,70192,75,70218,195],{},"Vypočtěte ",[1647,70193,70195],{"className":70194},[2059],[2061,70196,70197],{"xmlns":2063},[2065,70198,70199,70215],{},[2068,70200,70201,70203,70205,70207,70209],{},[2071,70202,2890],{},[2071,70204,4082],{},[2075,70206,2077],{},[2071,70208,543],{},[2205,70210,70211,70213],{},[2071,70212,4082],{},[2075,70214,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,70216,70217],{"encoding":2094},"MR = TR'",[1647,70219,70221],{"className":70220},[2059],[2061,70222,70223],{"xmlns":2063},[2065,70224,70225,70241],{},[2068,70226,70227,70229,70231,70233,70235],{},[2071,70228,2890],{},[2071,70230,2849],{},[2075,70232,2077],{},[2071,70234,543],{},[2205,70236,70237,70239],{},[2071,70238,2849],{},[2075,70240,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,70242,70243],{"encoding":2094},"MC = TC'",[92,70245,70246,70247,195],{},"Řešte rovnici ",[1647,70248,70250],{"className":70249},[2059],[2061,70251,70252],{"xmlns":2063},[2065,70253,70254,70278],{},[2068,70255,70256,70258,70260,70262,70264,70266,70268,70270,70272,70274,70276],{},[2071,70257,2890],{},[2071,70259,4082],{},[2075,70261,2084],{"stretchy":2083},[2071,70263,2861],{},[2075,70265,2090],{"stretchy":2083},[2075,70267,2077],{},[2071,70269,2890],{},[2071,70271,2849],{},[2075,70273,2084],{"stretchy":2083},[2071,70275,2861],{},[2075,70277,2090],{"stretchy":2083},[2092,70279,70280],{"encoding":2094},"MR(Q) = MC(Q)",[92,70282,70283,70284,70308],{},"Ověřte druhou derivaci ",[1647,70285,70287],{"className":70286},[2059],[2061,70288,70289],{"xmlns":2063},[2065,70290,70291,70305],{},[2068,70292,70293,70295],{},[2071,70294,575],{},[2205,70296,70297,70299],{},[2071,70298,4082],{},[2068,70300,70301,70303],{},[2075,70302,2452],{"mathvariant":2450},[2075,70304,2452],{"mathvariant":2450},[2092,70306,70307],{"encoding":2094},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[92,70310,70311,70312,70339],{},"Dosaďte do ",[1647,70313,70315],{"className":70314},[2059],[2061,70316,70317],{"xmlns":2063},[2065,70318,70319,70337],{},[2068,70320,70321,70323,70325,70327,70329,70331,70333,70335],{},[2071,70322,575],{},[2071,70324,4082],{},[2075,70326,2077],{},[2071,70328,543],{},[2071,70330,4082],{},[2075,70332,2303],{},[2071,70334,543],{},[2071,70336,2849],{},[2092,70338,59670],{"encoding":2094}," pro hodnotu maxima.",[1144,70341,70343],{"id":70342},"příklad-39","Příklad 3.9",[55,70345,70346,60458,70348,75,70370,70406],{},[95,70347,60457],{},[1647,70349,70351],{"className":70350},[2059],[2061,70352,70353],{"xmlns":2063},[2065,70354,70355,70367],{},[2068,70356,70357,70359,70361,70363,70365],{},[2071,70358,575],{},[2075,70360,2077],{},[2210,70362,42310],{},[2075,70364,2303],{},[2071,70366,2861],{},[2092,70368,70369],{"encoding":2094},"P = 30 - Q",[1647,70371,70373],{"className":70372},[2059],[2061,70374,70375],{"xmlns":2063},[2065,70376,70377,70403],{},[2068,70378,70379,70381,70383,70385,70387,70393,70395,70397,70399,70401],{},[2071,70380,543],{},[2071,70382,2849],{},[2075,70384,2077],{},[2210,70386,5096],{},[2205,70388,70389,70391],{},[2071,70390,2861],{},[2210,70392,646],{},[2075,70394,2176],{},[2210,70396,678],{},[2071,70398,2861],{},[2075,70400,2176],{},[2210,70402,686],{},[2092,70404,70405],{"encoding":2094},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[55,70408,70409,1445,70411,835,70441,70479,70480,17525,70524,70558,70559,195],{},[95,70410,25509],{},[1647,70412,70414],{"className":70413},[2059],[2061,70415,70416],{"xmlns":2063},[2065,70417,70418,70438],{},[2068,70419,70420,70422,70424,70426,70428,70430,70432],{},[2071,70421,543],{},[2071,70423,4082],{},[2075,70425,2077],{},[2210,70427,42310],{},[2071,70429,2861],{},[2075,70431,2303],{},[2205,70433,70434,70436],{},[2071,70435,2861],{},[2210,70437,646],{},[2092,70439,70440],{"encoding":2094},"TR = 30Q - Q^2",[1647,70442,70444],{"className":70443},[2059],[2061,70445,70446],{"xmlns":2063},[2065,70447,70448,70476],{},[2068,70449,70450,70452,70454,70456,70458,70460,70466,70468,70470,70472,70474],{},[2071,70451,575],{},[2071,70453,4082],{},[2075,70455,2077],{},[2075,70457,2303],{},[2210,70459,69029],{},[2205,70461,70462,70464],{},[2071,70463,2861],{},[2210,70465,646],{},[2075,70467,2176],{},[2210,70469,46091],{},[2071,70471,2861],{},[2075,70473,2303],{},[2210,70475,686],{},[2092,70477,70478],{"encoding":2094},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[1647,70481,70483],{"className":70482},[2059],[2061,70484,70485],{"xmlns":2063},[2065,70486,70487,70521],{},[2068,70488,70489,70491,70497,70499,70501,70503,70505,70507,70509,70511,70513,70515,70517,70519],{},[2071,70490,575],{},[2205,70492,70493,70495],{},[2071,70494,4082],{},[2075,70496,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,70498,2077],{},[2075,70500,2303],{},[2210,70502,654],{},[2071,70504,2861],{},[2075,70506,2176],{},[2210,70508,46091],{},[2075,70510,2077],{},[2210,70512,630],{},[2075,70514,4075],{},[2071,70516,2861],{},[2075,70518,2077],{},[2210,70520,5672],{},[2092,70522,70523],{"encoding":2094},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[1647,70525,70527],{"className":70526},[2059],[2061,70528,70529],{"xmlns":2063},[2065,70530,70531,70555],{},[2068,70532,70533,70535,70545,70547,70549,70551,70553],{},[2071,70534,575],{},[2205,70536,70537,70539],{},[2071,70538,4082],{},[2068,70540,70541,70543],{},[2075,70542,2452],{"mathvariant":2450},[2075,70544,2452],{"mathvariant":2450},[2075,70546,2077],{},[2075,70548,2303],{},[2210,70550,654],{},[2075,70552,3521],{},[2210,70554,630],{},[2092,70556,70557],{"encoding":2094},"PR'' = -3 \u003C 0"," (maximum); ",[1647,70560,70562],{"className":70561},[2059],[2061,70563,70564],{"xmlns":2063},[2065,70565,70566,70583],{},[2068,70567,70568,70570,70572,70574,70576,70578,70580],{},[2071,70569,575],{},[2071,70571,4082],{},[2075,70573,2084],{"stretchy":2083},[2210,70575,5672],{},[2075,70577,2090],{"stretchy":2083},[2075,70579,2077],{},[2210,70581,70582],{},"89",[2092,70584,70585],{"encoding":2094},"PR(8) = 89",[55,70587,70588,70589,835,70615,17525,70639,70677],{},"Ověření principu: ",[1647,70590,70592],{"className":70591},[2059],[2061,70593,70594],{"xmlns":2063},[2065,70595,70596,70612],{},[2068,70597,70598,70600,70602,70604,70606,70608,70610],{},[2071,70599,2890],{},[2071,70601,4082],{},[2075,70603,2077],{},[2210,70605,42310],{},[2075,70607,2303],{},[2210,70609,646],{},[2071,70611,2861],{},[2092,70613,70614],{"encoding":2094},"MR = 30 - 2Q",[1647,70616,70618],{"className":70617},[2059],[2061,70619,70620],{"xmlns":2063},[2065,70621,70622,70636],{},[2068,70623,70624,70626,70628,70630,70632,70634],{},[2071,70625,2890],{},[2071,70627,2849],{},[2075,70629,2077],{},[2071,70631,2861],{},[2075,70633,2176],{},[2210,70635,678],{},[2092,70637,70638],{"encoding":2094},"MC = Q + 6",[1647,70640,70642],{"className":70641},[2059],[2061,70643,70644],{"xmlns":2063},[2065,70645,70646,70674],{},[2068,70647,70648,70650,70652,70654,70656,70658,70660,70662,70664,70666,70668,70670,70672],{},[2071,70649,2890],{},[2071,70651,4082],{},[2075,70653,2084],{"stretchy":2083},[2210,70655,5672],{},[2075,70657,2090],{"stretchy":2083},[2075,70659,2077],{},[2210,70661,25685],{},[2075,70663,2077],{},[2071,70665,2890],{},[2071,70667,2849],{},[2075,70669,2084],{"stretchy":2083},[2210,70671,5672],{},[2075,70673,2090],{"stretchy":2083},[2092,70675,70676],{"encoding":2094},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[55,70679,70680,70681,70714,70715,70732],{},"V řadě případů — má-li rovnice ",[1647,70682,70684],{"className":70683},[2059],[2061,70685,70686],{"xmlns":2063},[2065,70687,70688,70712],{},[2068,70689,70690,70692,70694,70696,70698,70700,70702,70704,70706,70708,70710],{},[2071,70691,2890],{},[2071,70693,4082],{},[2075,70695,2084],{"stretchy":2083},[2071,70697,2861],{},[2075,70699,2090],{"stretchy":2083},[2075,70701,2077],{},[2071,70703,2890],{},[2071,70705,2849],{},[2075,70707,2084],{"stretchy":2083},[2071,70709,2861],{},[2075,70711,2090],{"stretchy":2083},[2092,70713,70280],{"encoding":2094}," jediné ekonomicky smysluplné řešení ",[1647,70716,70718],{"className":70717},[2059],[2061,70719,70720],{"xmlns":2063},[2065,70721,70722,70730],{},[2068,70723,70724],{},[2348,70725,70726,70728],{},[2071,70727,2861],{},[2210,70729,630],{},[2092,70731,42599],{"encoding":2094}," — není třeba provádět test druhé derivace.",[1144,70734,70736],{"id":70735},"příklad-310","Příklad 3.10",[55,70738,70739,70741,70742,70746,70747,70760,70761,70792],{},[95,70740,60457],{}," Firma vyrábí minipočítače v ",[69,70743,70745],{"className":70744,"dataFsResolvedFilePath":13670,"href":13671},[62],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[1647,70748,70750],{"className":70749},[2059],[2061,70751,70752],{"xmlns":2063},[2065,70753,70754,70758],{},[2068,70755,70756],{},[2210,70757,16926],{},[2092,70759,16926],{"encoding":2094}," EUR\u002Fks. ",[1647,70762,70764],{"className":70763},[2059],[2061,70765,70766],{"xmlns":2063},[2065,70767,70768,70789],{},[2068,70769,70770,70772,70774,70776,70778,70780,70783],{},[2071,70771,543],{},[2071,70773,2849],{},[2075,70775,2077],{},[2210,70777,3194],{},[2075,70779,2176],{},[2210,70781,70782],{},"28",[2205,70784,70785,70787],{},[2071,70786,2861],{},[2210,70788,646],{},[2092,70790,70791],{"encoding":2094},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[55,70794,70795,1445,70797,835,70819,835,70839,70862],{},[95,70796,25509],{},[1647,70798,70800],{"className":70799},[2059],[2061,70801,70802],{"xmlns":2063},[2065,70803,70804,70816],{},[2068,70805,70806,70808,70810,70812,70814],{},[2071,70807,543],{},[2071,70809,4082],{},[2075,70811,2077],{},[2210,70813,16926],{},[2071,70815,2861],{},[2092,70817,70818],{"encoding":2094},"TR = 900Q",[1647,70820,70822],{"className":70821},[2059],[2061,70823,70824],{"xmlns":2063},[2065,70825,70826,70836],{},[2068,70827,70828,70830,70832,70834],{},[2071,70829,2890],{},[2071,70831,4082],{},[2075,70833,2077],{},[2210,70835,16926],{},[2092,70837,70838],{"encoding":2094},"MR = 900",[1647,70840,70842],{"className":70841},[2059],[2061,70843,70844],{"xmlns":2063},[2065,70845,70846,70859],{},[2068,70847,70848,70850,70852,70854,70857],{},[2071,70849,2890],{},[2071,70851,2849],{},[2075,70853,2077],{},[2210,70855,70856],{},"56",[2071,70858,2861],{},[2092,70860,70861],{"encoding":2094},"MC = 56Q",". Z principu:",[1647,70864,70866],{"className":70865},[2059],[2061,70867,70868],{"xmlns":2063,"display":31093},[2065,70869,70870,70912],{},[2068,70871,70872,70874,70876,70878,70880,70882,70884,70886,70888,70890,70898,70900,70903,70905,70907,70909],{},[2210,70873,16926],{},[2075,70875,2077],{},[2210,70877,70856],{},[2071,70879,2861],{},[2363,70881,4072],{},[2075,70883,4075],{},[2363,70885,4072],{},[2071,70887,2861],{},[2075,70889,2077],{},[2400,70891,70892],{"scriptlevel":630,"displaystyle":2083},[2403,70893,70894,70896],{},[2210,70895,16926],{},[2210,70897,70856],{},[2075,70899,5987],{},[2210,70901,70902],{},"16,07",[2363,70904,4072],{},[2075,70906,2803],{},[2363,70908,4072],{},[2210,70910,70911],{},"16.",[2092,70913,70914],{"encoding":2094},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[55,70916,70917,70918,2777],{},"Zisk při ",[1647,70919,70921],{"className":70920},[2059],[2061,70922,70923],{"xmlns":2063},[2065,70924,70925,70933],{},[2068,70926,70927,70929,70931],{},[2071,70928,2861],{},[2075,70930,2077],{},[2210,70932,46153],{},[2092,70934,70935],{"encoding":2094},"Q = 16",[1647,70937,70939],{"className":70938},[2059],[2061,70940,70941],{"xmlns":2063,"display":31093},[2065,70942,70943,71014],{},[2068,70944,70945,70947,70949,70951,70953,70955,70957,70959,70961,70963,70965,70967,70969,70971,70973,70975,70981,70983,70985,70987,70989,70991,70993,70995,70997,71000,71002,71004,71006,71009,71012],{},[2071,70946,575],{},[2071,70948,4082],{},[2075,70950,2084],{"stretchy":2083},[2210,70952,46153],{},[2075,70954,2090],{"stretchy":2083},[2075,70956,2077],{},[2210,70958,16926],{},[2075,70960,3251],{},[2210,70962,46153],{},[2075,70964,2303],{},[2075,70966,2084],{"stretchy":2083},[2210,70968,3194],{},[2075,70970,2176],{},[2210,70972,70782],{},[2075,70974,3251],{},[2205,70976,70977,70979],{},[2210,70978,46153],{},[2210,70980,646],{},[2075,70982,2090],{"stretchy":2083},[2075,70984,2077],{},[2210,70986,25685],{},[2363,70988,3061],{},[2210,70990,22881],{},[2075,70992,2303],{},[2210,70994,686],{},[2363,70996,3061],{},[2210,70998,70999],{},"218",[2075,71001,2077],{},[2210,71003,686],{},[2363,71005,3061],{},[2210,71007,71008],{},"182",[2363,71010,71011],{}," EUR",[2071,71013,195],{"mathvariant":2450},[2092,71015,71016],{"encoding":2094},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[55,71018,71019],{},"Pro srovnání při původních 30 ks:",[1647,71021,71023],{"className":71022},[2059],[2061,71024,71025],{"xmlns":2063,"display":31093},[2065,71026,71027,71092],{},[2068,71028,71029,71031,71033,71035,71037,71039,71041,71043,71045,71047,71049,71051,71053,71055,71057,71059,71061,71063,71065,71068,71070,71072,71074,71076,71078,71080,71082,71084,71086,71088,71090],{},[2071,71030,575],{},[2071,71032,4082],{},[2075,71034,2084],{"stretchy":2083},[2210,71036,42310],{},[2075,71038,2090],{"stretchy":2083},[2075,71040,2077],{},[2210,71042,16926],{},[2075,71044,3251],{},[2210,71046,42310],{},[2075,71048,2303],{},[2075,71050,2084],{"stretchy":2083},[2210,71052,3194],{},[2075,71054,2176],{},[2210,71056,70782],{},[2075,71058,3251],{},[2210,71060,16926],{},[2075,71062,2090],{"stretchy":2083},[2075,71064,2077],{},[2210,71066,71067],{},"27",[2363,71069,3061],{},[2210,71071,63552],{},[2075,71073,2303],{},[2210,71075,5091],{},[2363,71077,3061],{},[2210,71079,33770],{},[2075,71081,2077],{},[2210,71083,638],{},[2363,71085,3061],{},[2210,71087,26482],{},[2363,71089,71011],{},[2071,71091,195],{"mathvariant":2450},[2092,71093,71094],{"encoding":2094},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[55,71096,71097,71100,71101,71119,71120,71138],{},[95,71098,71099],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[1647,71102,71104],{"className":71103},[2059],[2061,71105,71106],{"xmlns":2063},[2065,71107,71108,71116],{},[2068,71109,71110,71112,71114],{},[2210,71111,686],{},[2363,71113,3061],{},[2210,71115,71008],{},[2092,71117,71118],{"encoding":2094},"7\\,182"," EUR namísto původních ",[1647,71121,71123],{"className":71122},[2059],[2061,71124,71125],{"xmlns":2063},[2065,71126,71127,71135],{},[2068,71128,71129,71131,71133],{},[2210,71130,638],{},[2363,71132,3061],{},[2210,71134,26482],{},[2092,71136,71137],{"encoding":2094},"1\\,750"," EUR.",[609,71140,71142],{"id":71141},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[55,71144,71145,71146,67040,71159,71183],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[1647,71147,71149],{"className":71148},[2059],[2061,71150,71151],{"xmlns":2063},[2065,71152,71153,71157],{},[2068,71154,71155],{},[2071,71156,575],{},[2092,71158,575],{"encoding":2094},[1647,71160,71162],{"className":71161},[2059],[2061,71163,71164],{"xmlns":2063},[2065,71165,71166,71180],{},[2068,71167,71168,71170,71172,71174,71176,71178],{},[2071,71169,543],{},[2071,71171,4082],{},[2075,71173,2077],{},[2071,71175,575],{},[2075,71177,3251],{},[2071,71179,2861],{},[2092,71181,71182],{"encoding":2094},"TR = P \\cdot Q"," a z (3.13) speciálně:",[1647,71185,71187],{"className":71186},[2059],[2061,71188,71189],{"xmlns":2063,"display":31093},[2065,71190,71191,71224],{},[23493,71192,71193],{"width":31098},[23498,71194,71195,71197,71217,71219],{},[23501,71196],{"width":31103},[23501,71198,71199],{},[2068,71200,71201,71203,71205,71207,71209,71211,71213,71215],{},[2071,71202,575],{},[2075,71204,2077],{},[2071,71206,2890],{},[2071,71208,2849],{},[2075,71210,2084],{"stretchy":2083},[2071,71212,2861],{},[2075,71214,2090],{"stretchy":2083},[2071,71216,195],{"mathvariant":2450},[23501,71218],{"width":31103},[23501,71220,71221],{},[2363,71222,71223],{},"(3.14)",[2092,71225,71226],{"encoding":2094},"P = MC(Q).\n\\tag{3.14}",[55,71228,71229,71230,195],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[1647,71231,71233],{"className":71232},[2059],[2061,71234,71235],{"xmlns":2063},[2065,71236,71237,71251],{},[2068,71238,71239,71241],{},[2071,71240,575],{},[2205,71242,71243,71245],{},[2071,71244,4082],{},[2068,71246,71247,71249],{},[2075,71248,2452],{"mathvariant":2450},[2075,71250,2452],{"mathvariant":2450},[2092,71252,70307],{"encoding":2094},[1144,71254,71256],{"id":71255},"příklad-311","Příklad 3.11",[55,71258,71259,61992,71261,71308,71309,71327],{},[95,71260,60457],{},[1647,71262,71264],{"className":71263},[2059],[2061,71265,71266],{"xmlns":2063},[2065,71267,71268,71305],{},[2068,71269,71270,71272,71274,71276,71279,71285,71287,71289,71295,71297,71299,71301,71303],{},[2071,71271,543],{},[2071,71273,2849],{},[2075,71275,2077],{},[2210,71277,71278],{},"0,04",[2205,71280,71281,71283],{},[2071,71282,2861],{},[2210,71284,654],{},[2075,71286,2303],{},[2210,71288,25284],{},[2205,71290,71291,71293],{},[2071,71292,2861],{},[2210,71294,646],{},[2075,71296,2176],{},[2210,71298,2935],{},[2071,71300,2861],{},[2075,71302,2176],{},[2210,71304,670],{},[2092,71306,71307],{"encoding":2094},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[1647,71310,71312],{"className":71311},[2059],[2061,71313,71314],{"xmlns":2063},[2065,71315,71316,71324],{},[2068,71317,71318,71320,71322],{},[2071,71319,575],{},[2075,71321,2077],{},[2210,71323,662],{},[2092,71325,71326],{"encoding":2094},"P = 4"," stanovte optimální produkci.",[55,71329,71330,71332,71333,20314,71375,71409,71410,2777],{},[95,71331,25509],{}," Z (3.14): ",[1647,71334,71336],{"className":71335},[2059],[2061,71337,71338],{"xmlns":2063},[2065,71339,71340,71372],{},[2068,71341,71342,71344,71346,71348,71351,71357,71359,71362,71364,71366,71368,71370],{},[2071,71343,2890],{},[2071,71345,2849],{},[2075,71347,2077],{},[2210,71349,71350],{},"0,12",[2205,71352,71353,71355],{},[2071,71354,2861],{},[2210,71356,646],{},[2075,71358,2303],{},[2210,71360,71361],{},"1,8",[2071,71363,2861],{},[2075,71365,2176],{},[2210,71367,2935],{},[2075,71369,2077],{},[2210,71371,662],{},[2092,71373,71374],{"encoding":2094},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[1647,71376,71378],{"className":71377},[2059],[2061,71379,71380],{"xmlns":2063},[2065,71381,71382,71406],{},[2068,71383,71384,71386,71392,71394,71396,71398,71400,71402,71404],{},[2210,71385,71350],{},[2205,71387,71388,71390],{},[2071,71389,2861],{},[2210,71391,646],{},[2075,71393,2303],{},[2210,71395,71361],{},[2071,71397,2861],{},[2075,71399,2176],{},[2210,71401,678],{},[2075,71403,2077],{},[2210,71405,630],{},[2092,71407,71408],{"encoding":2094},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[1647,71411,71413],{"className":71412},[2059],[2061,71414,71415],{"xmlns":2063},[2065,71416,71417,71421],{},[2068,71418,71419],{},[2210,71420,71350],{},[2092,71422,71423],{"encoding":2094},"0{,}12",[1647,71425,71427],{"className":71426},[2059],[2061,71428,71429],{"xmlns":2063,"display":31093},[2065,71430,71431,71483],{},[2068,71432,71433,71439,71441,71443,71445,71447,71449,71451,71453,71455,71457,71459,71465,71467,71469,71471,71473,71479,71481],{},[2205,71434,71435,71437],{},[2071,71436,2861],{},[2210,71438,646],{},[2075,71440,2303],{},[2210,71442,39270],{},[2071,71444,2861],{},[2075,71446,2176],{},[2210,71448,3194],{},[2075,71450,2077],{},[2210,71452,630],{},[2363,71454,4072],{},[2075,71456,4075],{},[2363,71458,4072],{},[2348,71460,71461,71463],{},[2071,71462,2861],{},[2210,71464,638],{},[2075,71466,2077],{},[2210,71468,670],{},[2075,71470,2361],{"separator":2360},[2363,71472,4072],{},[2348,71474,71475,71477],{},[2071,71476,2861],{},[2210,71478,646],{},[2075,71480,2077],{},[2210,71482,22067],{},[2092,71484,71485],{"encoding":2094},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[55,71487,71488,71489,2777],{},"Dále ",[1647,71490,71492],{"className":71491},[2059],[2061,71493,71494],{"xmlns":2063},[2065,71495,71496,71535],{},[2068,71497,71498,71500,71510,71512,71514,71516,71522,71524,71526,71529,71531,71533],{},[2071,71499,575],{},[2205,71501,71502,71504],{},[2071,71503,4082],{},[2068,71505,71506,71508],{},[2075,71507,2452],{"mathvariant":2450},[2075,71509,2452],{"mathvariant":2450},[2075,71511,2077],{},[2075,71513,2303],{},[2071,71515,2890],{},[2205,71517,71518,71520],{},[2071,71519,2849],{},[2075,71521,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,71523,2077],{},[2075,71525,2303],{},[2210,71527,71528],{},"0,24",[2071,71530,2861],{},[2075,71532,2176],{},[2210,71534,71361],{},[2092,71536,71537],{"encoding":2094},"PR'' = -MC' = -0{,}24Q + 1{,}8",[89,71539,71540,71590],{},[92,71541,71542,71586,71587,71589],{},[1647,71543,71545],{"className":71544},[2059],[2061,71546,71547],{"xmlns":2063},[2065,71548,71549,71583],{},[2068,71550,71551,71553,71563,71565,71567,71569,71571,71573,71575,71577,71579,71581],{},[2071,71552,575],{},[2205,71554,71555,71557],{},[2071,71556,4082],{},[2068,71558,71559,71561],{},[2075,71560,2452],{"mathvariant":2450},[2075,71562,2452],{"mathvariant":2450},[2075,71564,2084],{"stretchy":2083},[2210,71566,670],{},[2075,71568,2090],{"stretchy":2083},[2075,71570,2077],{},[2210,71572,22060],{},[2075,71574,3482],{},[2210,71576,630],{},[2363,71578,4072],{},[2075,71580,4075],{},[2363,71582,4072],{},[2092,71584,71585],{"encoding":2094},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[95,71588,3849],{}," zisku (minimalizace ztráty);",[92,71591,71592,71586,71638,71640],{},[1647,71593,71595],{"className":71594},[2059],[2061,71596,71597],{"xmlns":2063},[2065,71598,71599,71635],{},[2068,71600,71601,71603,71613,71615,71617,71619,71621,71623,71625,71627,71629,71631,71633],{},[2071,71602,575],{},[2205,71604,71605,71607],{},[2071,71606,4082],{},[2068,71608,71609,71611],{},[2075,71610,2452],{"mathvariant":2450},[2075,71612,2452],{"mathvariant":2450},[2075,71614,2084],{"stretchy":2083},[2210,71616,2935],{},[2075,71618,2090],{"stretchy":2083},[2075,71620,2077],{},[2075,71622,2303],{},[2210,71624,22060],{},[2075,71626,3521],{},[2210,71628,630],{},[2363,71630,4072],{},[2075,71632,4075],{},[2363,71634,4072],{},[2092,71636,71637],{"encoding":2094},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[95,71639,3791],{}," zisku, avšak",[1647,71642,71644],{"className":71643},[2059],[2061,71645,71646],{"xmlns":2063,"display":31093},[2065,71647,71648,71716],{},[2068,71649,71650,71652,71654,71656,71658,71660,71662,71664,71666,71668,71670,71672,71674,71676,71678,71680,71682,71684,71686,71688,71690,71692,71694,71696,71698,71700,71702,71704,71706,71708,71710,71712,71714],{},[2071,71651,575],{},[2071,71653,4082],{},[2075,71655,2084],{"stretchy":2083},[2210,71657,2935],{},[2075,71659,2090],{"stretchy":2083},[2075,71661,2077],{},[2210,71663,662],{},[2075,71665,3251],{},[2210,71667,2935],{},[2075,71669,2303],{},[2075,71671,2084],{"stretchy":2083},[2210,71673,71278],{},[2075,71675,3251],{},[2210,71677,638],{},[2363,71679,3061],{},[2210,71681,63552],{},[2075,71683,2303],{},[2210,71685,25284],{},[2075,71687,3251],{},[2210,71689,3164],{},[2075,71691,2176],{},[2210,71693,3164],{},[2075,71695,2176],{},[2210,71697,670],{},[2075,71699,2090],{"stretchy":2083},[2075,71701,2077],{},[2210,71703,5298],{},[2075,71705,2303],{},[2210,71707,23919],{},[2075,71709,2077],{},[2075,71711,2303],{},[2210,71713,39270],{},[2075,71715,2361],{"separator":2360},[2092,71717,71718],{"encoding":2094},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[55,71720,71721,71722,195],{},"tj. ztráta větší než ",[1647,71723,71725],{"className":71724},[2059],[2061,71726,71727],{"xmlns":2063},[2065,71728,71729,71739],{},[2068,71730,71731,71733,71735,71737],{},[2071,71732,10177],{},[2071,71734,2849],{},[2075,71736,2077],{},[2210,71738,670],{},[2092,71740,71741],{"encoding":2094},"FC = 5",[55,71743,71744,71747,71748,71751,71752,195],{},[95,71745,71746],{},"Závěr:"," firma by měla ",[95,71749,71750],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[1647,71753,71755],{"className":71754},[2059],[2061,71756,71757],{"xmlns":2063},[2065,71758,71759,71769],{},[2068,71760,71761,71763,71765,71767],{},[2071,71762,10177],{},[2071,71764,2849],{},[2075,71766,2077],{},[2210,71768,670],{},[2092,71770,71741],{"encoding":2094},[84,71772,71774],{"id":71773},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[55,71776,71777,71778,71780,71781,71796,71797,71810,71811,71837,71838,71851,71852,71869,71870,2697,71887,71890,71891,71911,71912,71927,71928,2777],{},"Důležitým završením analýzy je konstrukce ",[95,71779,59745],{},". S nabízeným množstvím rostou mezní náklady ",[1647,71782,71784],{"className":71783},[2059],[2061,71785,71786],{"xmlns":2063},[2065,71787,71788,71794],{},[2068,71789,71790,71792],{},[2071,71791,2890],{},[2071,71793,2849],{},[2092,71795,59762],{"encoding":2094}," a tyto určují cenu ",[1647,71798,71800],{"className":71799},[2059],[2061,71801,71802],{"xmlns":2063},[2065,71803,71804,71808],{},[2068,71805,71806],{},[2071,71807,575],{},[2092,71809,575],{"encoding":2094},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[1647,71812,71814],{"className":71813},[2059],[2061,71815,71816],{"xmlns":2063},[2065,71817,71818,71834],{},[2068,71819,71820,71822,71824,71826,71828,71830,71832],{},[2071,71821,575],{},[2075,71823,2077],{},[2071,71825,2890],{},[2071,71827,2849],{},[2075,71829,2084],{"stretchy":2083},[2071,71831,2861],{},[2075,71833,2090],{"stretchy":2083},[2092,71835,71836],{"encoding":2094},"P = MC(Q)"," (obrázek 3.14). Cena ",[1647,71839,71841],{"className":71840},[2059],[2061,71842,71843],{"xmlns":2063},[2065,71844,71845,71849],{},[2068,71846,71847],{},[2071,71848,575],{},[2092,71850,575],{"encoding":2094}," však nemůže být nižší než ",[1647,71853,71855],{"className":71854},[2059],[2061,71856,71857],{"xmlns":2063},[2065,71858,71859,71867],{},[2068,71860,71861],{},[2205,71862,71863,71865],{},[2071,71864,575],{},[2075,71866,4441],{},[2092,71868,4491],{"encoding":2094}," odpovídající množství ",[1647,71871,71873],{"className":71872},[2059],[2061,71874,71875],{"xmlns":2063},[2065,71876,71877,71885],{},[2068,71878,71879],{},[2205,71880,71881,71883],{},[2071,71882,2861],{},[2075,71884,4441],{},[2092,71886,32871],{"encoding":2094},[95,71888,71889],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[1647,71892,71894],{"className":71893},[2059],[2061,71895,71896],{"xmlns":2063},[2065,71897,71898,71908],{},[2068,71899,71900,71902],{},[2210,71901,630],{},[2205,71903,71904,71906],{},[2071,71905,2861],{},[2075,71907,4441],{},[2092,71909,71910],{"encoding":2094},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[1647,71913,71915],{"className":71914},[2059],[2061,71916,71917],{"xmlns":2063},[2065,71918,71919,71925],{},[2068,71920,71921,71923],{},[2071,71922,2890],{},[2071,71924,2849],{},[2092,71926,59762],{"encoding":2094}," nad bodem ",[1647,71929,71931],{"className":71930},[2059],[2061,71932,71933],{"xmlns":2063},[2065,71934,71935,71939],{},[2068,71936,71937],{},[2071,71938,4342],{},[2092,71940,4342],{"encoding":2094},[1647,71942,71944],{"className":71943},[2059],[2061,71945,71946],{"xmlns":2063,"display":31093},[2065,71947,71948,72055],{},[23493,71949,71950],{"width":31098},[23498,71951,71952,71954,72048,72050],{},[23501,71953],{"width":31103},[23501,71955,71956],{},[2068,71957,71958,71960,71962,71964,71966,71968,71970,71972],{},[2071,71959,575],{},[2075,71961,2077],{},[2071,71963,532],{},[2075,71965,2084],{"stretchy":2083},[2071,71967,2861],{},[2075,71969,2090],{"stretchy":2083},[2075,71971,2077],{},[2068,71973,71974,71977],{},[2075,71975,71976],{"fence":2360},"{",[23493,71978,71981,72020],{"rowspacing":71979,"columnalign":71980,"columnspacing":17019},"0.36em","left left",[23498,71982,71983,71999],{},[23501,71984,71985],{},[2400,71986,71987],{"scriptlevel":630,"displaystyle":2083},[2068,71988,71989,71991,71993,71995,71997],{},[2071,71990,2890],{},[2071,71992,2849],{},[2075,71994,2084],{"stretchy":2083},[2071,71996,2861],{},[2075,71998,2090],{"stretchy":2083},[23501,72000,72001],{},[2400,72002,72003],{"scriptlevel":630,"displaystyle":2083},[2068,72004,72005,72008,72010,72012,72018],{},[2363,72006,72007],{},"pro ",[2071,72009,2861],{},[2075,72011,4572],{},[2205,72013,72014,72016],{},[2071,72015,2861],{},[2075,72017,4441],{},[2075,72019,2361],{"separator":2360},[23498,72021,72022,72028],{},[23501,72023,72024],{},[2400,72025,72026],{"scriptlevel":630,"displaystyle":2083},[2210,72027,630],{},[23501,72029,72030],{},[2400,72031,72032],{"scriptlevel":630,"displaystyle":2083},[2068,72033,72034,72036,72038,72040,72046],{},[2363,72035,72007],{},[2071,72037,2861],{},[2075,72039,3521],{},[2205,72041,72042,72044],{},[2071,72043,2861],{},[2075,72045,4441],{},[2075,72047,2361],{"separator":2360},[23501,72049],{"width":31103},[23501,72051,72052],{},[2363,72053,72054],{},"(3.15)",[2092,72056,72057],{"encoding":2094},"P = S(Q) = \\begin{cases} MC(Q) & \\text{pro } Q \\geq Q^*, \\\\ 0 & \\text{pro } Q \u003C Q^*, \\end{cases}\n\\tag{3.15}",[55,72059,4397,72060,72077,72078,72095,72096,45790,72126,72129],{},[1647,72061,72063],{"className":72062},[2059],[2061,72064,72065],{"xmlns":2063},[2065,72066,72067,72075],{},[2068,72068,72069],{},[2205,72070,72071,72073],{},[2071,72072,2861],{},[2075,72074,4441],{},[2092,72076,32871],{"encoding":2094}," je bod minima ",[1647,72079,72081],{"className":72080},[2059],[2061,72082,72083],{"xmlns":2063},[2065,72084,72085,72093],{},[2068,72086,72087,72089,72091],{},[2071,72088,4342],{},[2071,72090,44630],{},[2071,72092,2849],{},[2092,72094,59781],{"encoding":2094},". Bod ",[1647,72097,72099],{"className":72098},[2059],[2061,72100,72101],{"xmlns":2063},[2065,72102,72103,72123],{},[2068,72104,72105,72107,72113,72115,72121],{},[2075,72106,2084],{"stretchy":2083},[2205,72108,72109,72111],{},[2071,72110,2861],{},[2075,72112,4441],{},[2075,72114,2361],{"separator":2360},[2205,72116,72117,72119],{},[2071,72118,575],{},[2075,72120,4441],{},[2075,72122,2090],{"stretchy":2083},[2092,72124,72125],{"encoding":2094},"(Q^*, P^*)",[95,72127,72128],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1023,72131,72132,72137],{},[55,72133,72134,72136],{},[1647,72135,4659],{}," Postup — jak odvodit nabídku firmy",[201,72138,72139,72188,72283,72338,72409],{},[92,72140,72141,72142,75,72164,195],{},"Ze zadaných nákladů určete ",[1647,72143,72145],{"className":72144},[2059],[2061,72146,72147],{"xmlns":2063},[2065,72148,72149,72161],{},[2068,72150,72151,72153,72155,72157,72159],{},[2071,72152,2890],{},[2071,72154,2849],{},[2075,72156,2084],{"stretchy":2083},[2071,72158,2861],{},[2075,72160,2090],{"stretchy":2083},[2092,72162,72163],{"encoding":2094},"MC(Q)",[1647,72165,72167],{"className":72166},[2059],[2061,72168,72169],{"xmlns":2063},[2065,72170,72171,72185],{},[2068,72172,72173,72175,72177,72179,72181,72183],{},[2071,72174,4342],{},[2071,72176,44630],{},[2071,72178,2849],{},[2075,72180,2084],{"stretchy":2083},[2071,72182,2861],{},[2075,72184,2090],{"stretchy":2083},[2092,72186,72187],{"encoding":2094},"AVC(Q)",[92,72189,72190,72191,72208,72209,72226,72227,72259,72260,4007],{},"Najděte ",[1647,72192,72194],{"className":72193},[2059],[2061,72195,72196],{"xmlns":2063},[2065,72197,72198,72206],{},[2068,72199,72200],{},[2205,72201,72202,72204],{},[2071,72203,2861],{},[2075,72205,4441],{},[2092,72207,32871],{"encoding":2094}," jako bod minima ",[1647,72210,72212],{"className":72211},[2059],[2061,72213,72214],{"xmlns":2063},[2065,72215,72216,72224],{},[2068,72217,72218,72220,72222],{},[2071,72219,4342],{},[2071,72221,44630],{},[2071,72223,2849],{},[2092,72225,59781],{"encoding":2094}," (řešením ",[1647,72228,72230],{"className":72229},[2059],[2061,72231,72232],{"xmlns":2063},[2065,72233,72234,72256],{},[2068,72235,72236,72238,72240,72246,72248,72250,72252,72254],{},[2071,72237,4342],{},[2071,72239,44630],{},[2205,72241,72242,72244],{},[2071,72243,2849],{},[2075,72245,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,72247,2084],{"stretchy":2083},[2071,72249,2861],{},[2075,72251,2090],{"stretchy":2083},[2075,72253,2077],{},[2210,72255,630],{},[2092,72257,72258],{"encoding":2094},"AVC'(Q) = 0",", případně rovnice ",[1647,72261,72263],{"className":72262},[2059],[2061,72264,72265],{"xmlns":2063},[2065,72266,72267,72281],{},[2068,72268,72269,72271,72273,72275,72277,72279],{},[2071,72270,4342],{},[2071,72272,44630],{},[2071,72274,2849],{},[2075,72276,2077],{},[2071,72278,2890],{},[2071,72280,2849],{},[2092,72282,59718],{"encoding":2094},[92,72284,70191,72285,72337],{},[1647,72286,72288],{"className":72287},[2059],[2061,72289,72290],{"xmlns":2063},[2065,72291,72292,72334],{},[2068,72293,72294,72300,72302,72304,72306,72308,72314,72316,72318,72320,72322,72324,72326,72332],{},[2205,72295,72296,72298],{},[2071,72297,575],{},[2075,72299,4441],{},[2075,72301,2077],{},[2071,72303,2890],{},[2071,72305,2849],{},[2075,72307,2084],{"stretchy":2083},[2205,72309,72310,72312],{},[2071,72311,2861],{},[2075,72313,4441],{},[2075,72315,2090],{"stretchy":2083},[2075,72317,2077],{},[2071,72319,4342],{},[2071,72321,44630],{},[2071,72323,2849],{},[2075,72325,2084],{"stretchy":2083},[2205,72327,72328,72330],{},[2071,72329,2861],{},[2075,72331,4441],{},[2075,72333,2090],{"stretchy":2083},[2092,72335,72336],{"encoding":2094},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[92,72339,72340,72341,6560,72373,72395,72396,195],{},"Zapište nabídku: ",[1647,72342,72344],{"className":72343},[2059],[2061,72345,72346],{"xmlns":2063},[2065,72347,72348,72370],{},[2068,72349,72350,72352,72354,72356,72358,72360,72362,72364,72366,72368],{},[2071,72351,532],{},[2075,72353,2084],{"stretchy":2083},[2071,72355,2861],{},[2075,72357,2090],{"stretchy":2083},[2075,72359,2077],{},[2071,72361,2890],{},[2071,72363,2849],{},[2075,72365,2084],{"stretchy":2083},[2071,72367,2861],{},[2075,72369,2090],{"stretchy":2083},[2092,72371,72372],{"encoding":2094},"S(Q) = MC(Q)",[1647,72374,72376],{"className":72375},[2059],[2061,72377,72378],{"xmlns":2063},[2065,72379,72380,72392],{},[2068,72381,72382,72384,72386],{},[2071,72383,2861],{},[2075,72385,4572],{},[2205,72387,72388,72390],{},[2071,72389,2861],{},[2075,72391,4441],{},[2092,72393,72394],{"encoding":2094},"Q \\geq Q^*",", jinak ",[1647,72397,72399],{"className":72398},[2059],[2061,72400,72401],{"xmlns":2063},[2065,72402,72403,72407],{},[2068,72404,72405],{},[2210,72406,630],{},[2092,72408,630],{"encoding":2094},[92,72410,72411,72412,72444],{},"V případě potřeby vyjádřete inverzi ",[1647,72413,72415],{"className":72414},[2059],[2061,72416,72417],{"xmlns":2063},[2065,72418,72419,72441],{},[2068,72420,72421,72423,72425,72435,72437,72439],{},[2071,72422,2861],{},[2075,72424,2077],{},[2205,72426,72427,72429],{},[2071,72428,532],{},[2068,72430,72431,72433],{},[2075,72432,2303],{},[2210,72434,638],{},[2075,72436,2084],{"stretchy":2083},[2071,72438,575],{},[2075,72440,2090],{"stretchy":2083},[2092,72442,72443],{"encoding":2094},"Q = S^{-1}(P)"," doplněním na čtverec.",[55,72446,72447],{},[3982,72448,72449,72450,835,72465,75,72482,32228,72497,72510,72511,72536,72537,72550,72551,72568,72569,72586,72587,72604],{},"Obrázek 3.14: Křivky ",[1647,72451,72453],{"className":72452},[2059],[2061,72454,72455],{"xmlns":2063},[2065,72456,72457,72463],{},[2068,72458,72459,72461],{},[2071,72460,4342],{},[2071,72462,2849],{},[2092,72464,60030],{"encoding":2094},[1647,72466,72468],{"className":72467},[2059],[2061,72469,72470],{"xmlns":2063},[2065,72471,72472,72480],{},[2068,72473,72474,72476,72478],{},[2071,72475,4342],{},[2071,72477,44630],{},[2071,72479,2849],{},[2092,72481,59781],{"encoding":2094},[1647,72483,72485],{"className":72484},[2059],[2061,72486,72487],{"xmlns":2063},[2065,72488,72489,72495],{},[2068,72490,72491,72493],{},[2071,72492,2890],{},[2071,72494,2849],{},[2092,72496,59762],{"encoding":2094},[1647,72498,72500],{"className":72499},[2059],[2061,72501,72502],{"xmlns":2063},[2065,72503,72504,72508],{},[2068,72505,72506],{},[2071,72507,10871],{},[2092,72509,10871],{"encoding":2094},"; křivka nabídky ",[1647,72512,72514],{"className":72513},[2059],[2061,72515,72516],{"xmlns":2063},[2065,72517,72518,72534],{},[2068,72519,72520,72522,72524,72526,72528,72530,72532],{},[2071,72521,575],{},[2075,72523,2077],{},[2071,72525,2890],{},[2071,72527,2849],{},[2075,72529,2084],{"stretchy":2083},[2071,72531,2861],{},[2075,72533,2090],{"stretchy":2083},[2092,72535,71836],{"encoding":2094}," začíná v bodě ",[1647,72538,72540],{"className":72539},[2059],[2061,72541,72542],{"xmlns":2063},[2065,72543,72544,72548],{},[2068,72545,72546],{},[2071,72547,4342],{},[2092,72549,4342],{"encoding":2094}," odpovídajícím minimu ",[1647,72552,72554],{"className":72553},[2059],[2061,72555,72556],{"xmlns":2063},[2065,72557,72558,72566],{},[2068,72559,72560,72562,72564],{},[2071,72561,4342],{},[2071,72563,44630],{},[2071,72565,2849],{},[2092,72567,59781],{"encoding":2094}," při ceně ",[1647,72570,72572],{"className":72571},[2059],[2061,72573,72574],{"xmlns":2063},[2065,72575,72576,72584],{},[2068,72577,72578],{},[2205,72579,72580,72582],{},[2071,72581,575],{},[2075,72583,4441],{},[2092,72585,4491],{"encoding":2094}," (minimální cena nabídky); pod ",[1647,72588,72590],{"className":72589},[2059],[2061,72591,72592],{"xmlns":2063},[2065,72593,72594,72602],{},[2068,72595,72596],{},[2205,72597,72598,72600],{},[2071,72599,2861],{},[2075,72601,4441],{},[2092,72603,32871],{"encoding":2094}," je nabídka nulová.",[1144,72606,72608],{"id":72607},"příklad-312","Příklad 3.12",[55,72610,72611,61992,72613,72659],{},[95,72612,60457],{},[1647,72614,72616],{"className":72615},[2059],[2061,72617,72618],{"xmlns":2063},[2065,72619,72620,72656],{},[2068,72621,72622,72624,72626,72628,72630,72636,72638,72640,72646,72648,72650,72652,72654],{},[2071,72623,543],{},[2071,72625,2849],{},[2075,72627,2077],{},[2210,72629,2866],{},[2205,72631,72632,72634],{},[2071,72633,2861],{},[2210,72635,654],{},[2075,72637,2303],{},[2210,72639,646],{},[2205,72641,72642,72644],{},[2071,72643,2861],{},[2210,72645,646],{},[2075,72647,2176],{},[2210,72649,39270],{},[2071,72651,2861],{},[2075,72653,2176],{},[2210,72655,2935],{},[2092,72657,72658],{"encoding":2094},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[55,72661,72662,1445,72664,72701,72702,2777],{},[95,72663,25509],{},[1647,72665,72667],{"className":72666},[2059],[2061,72668,72669],{"xmlns":2063},[2065,72670,72671,72698],{},[2068,72672,72673,72675,72677,72679,72682,72688,72690,72692,72694,72696],{},[2071,72674,2890],{},[2071,72676,2849],{},[2075,72678,2077],{},[2210,72680,72681],{},"0,3",[2205,72683,72684,72686],{},[2071,72685,2861],{},[2210,72687,646],{},[2075,72689,2303],{},[2210,72691,662],{},[2071,72693,2861],{},[2075,72695,2176],{},[2210,72697,39270],{},[2092,72699,72700],{"encoding":2094},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[1647,72703,72705],{"className":72704},[2059],[2061,72706,72707],{"xmlns":2063},[2065,72708,72709,72719],{},[2068,72710,72711,72713,72715,72717],{},[2071,72712,575],{},[2075,72714,2077],{},[2071,72716,2890],{},[2071,72718,2849],{},[2092,72720,72721],{"encoding":2094},"P = MC",[1647,72723,72725],{"className":72724},[2059],[2061,72726,72727],{"xmlns":2063,"display":31093},[2065,72728,72729,72754],{},[2068,72730,72731,72733,72735,72737,72743,72745,72747,72749,72751],{},[2071,72732,575],{},[2075,72734,2077],{},[2210,72736,72681],{},[2205,72738,72739,72741],{},[2071,72740,2861],{},[2210,72742,646],{},[2075,72744,2303],{},[2210,72746,662],{},[2071,72748,2861],{},[2075,72750,2176],{},[2210,72752,72753],{},"15.",[2092,72755,72756],{"encoding":2094},"P = 0{,}3Q^2 - 4Q + 15.",[55,72758,72759,72760,5469,72773,72786],{},"Vyjádření ",[1647,72761,72763],{"className":72762},[2059],[2061,72764,72765],{"xmlns":2063},[2065,72766,72767,72771],{},[2068,72768,72769],{},[2071,72770,2861],{},[2092,72772,2861],{"encoding":2094},[1647,72774,72776],{"className":72775},[2059],[2061,72777,72778],{"xmlns":2063},[2065,72779,72780,72784],{},[2068,72781,72782],{},[2071,72783,575],{},[2092,72785,575],{"encoding":2094}," doplněním na čtverec:",[1647,72788,72790],{"className":72789},[2059],[2061,72791,72792],{"xmlns":2063,"display":31093},[2065,72793,72794,72884],{},[2068,72795,72796,72798,72800,72802,72840,72842,72844,72866,72868,72882],{},[2071,72797,575],{},[2075,72799,2077],{},[2210,72801,72681],{},[2068,72803,72804,72806,72828,72830,72838],{},[2075,72805,2084],{"fence":2360},[2205,72807,72808,72826],{},[2068,72809,72810,72812,72814,72816,72824],{},[2075,72811,2084],{"fence":2360},[2071,72813,2861],{},[2075,72815,2303],{},[2400,72817,72818],{"scriptlevel":630,"displaystyle":2083},[2403,72819,72820,72822],{},[2210,72821,9121],{},[2210,72823,654],{},[2075,72825,2090],{"fence":2360},[2210,72827,646],{},[2075,72829,2176],{},[2400,72831,72832],{"scriptlevel":630,"displaystyle":2083},[2403,72833,72834,72836],{},[2210,72835,3194],{},[2210,72837,4087],{},[2075,72839,2090],{"fence":2360},[2075,72841,2361],{"separator":2360},[5965,72843],{"width":5967},[2205,72845,72846,72864],{},[2068,72847,72848,72850,72852,72854,72862],{},[2075,72849,2084],{"fence":2360},[2071,72851,2861],{},[2075,72853,2303],{},[2400,72855,72856],{"scriptlevel":630,"displaystyle":2083},[2403,72857,72858,72860],{},[2210,72859,9121],{},[2210,72861,654],{},[2075,72863,2090],{"fence":2360},[2210,72865,646],{},[2075,72867,2077],{},[2403,72869,72870,72880],{},[2068,72871,72872,72874,72876,72878],{},[2210,72873,42310],{},[2071,72875,575],{},[2075,72877,2303],{},[2210,72879,3194],{},[2210,72881,4087],{},[2075,72883,2361],{"separator":2360},[2092,72885,72886],{"encoding":2094},"P = 0{,}3\\left(\\left(Q - \\tfrac{20}{3}\\right)^2 + \\tfrac{50}{9}\\right), \\qquad \\left(Q - \\tfrac{20}{3}\\right)^2 = \\frac{30P - 50}{9},",[1647,72888,72890],{"className":72889},[2059],[2061,72891,72892],{"xmlns":2063,"display":31093},[2065,72893,72894,72926],{},[2068,72895,72896,72898,72900,72906,72908,72924],{},[2071,72897,2861],{},[2075,72899,2077],{},[2403,72901,72902,72904],{},[2210,72903,9121],{},[2210,72905,654],{},[2075,72907,2176],{},[2403,72909,72910,72922],{},[8204,72911,72912],{},[2068,72913,72914,72916,72918,72920],{},[2210,72915,42310],{},[2071,72917,575],{},[2075,72919,2303],{},[2210,72921,3194],{},[2210,72923,654],{},[2071,72925,195],{"mathvariant":2450},[2092,72927,72928],{"encoding":2094},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[55,72930,71488,72931,835,72969,835,73017,73051,73052,195],{},[1647,72932,72934],{"className":72933},[2059],[2061,72935,72936],{"xmlns":2063},[2065,72937,72938,72966],{},[2068,72939,72940,72942,72944,72946,72948,72950,72956,72958,72960,72962,72964],{},[2071,72941,4342],{},[2071,72943,44630],{},[2071,72945,2849],{},[2075,72947,2077],{},[2210,72949,2866],{},[2205,72951,72952,72954],{},[2071,72953,2861],{},[2210,72955,646],{},[2075,72957,2303],{},[2210,72959,646],{},[2071,72961,2861],{},[2075,72963,2176],{},[2210,72965,39270],{},[2092,72967,72968],{"encoding":2094},"AVC = 0{,}1Q^2 - 2Q + 15",[1647,72970,72972],{"className":72971},[2059],[2061,72973,72974],{"xmlns":2063},[2065,72975,72976,73014],{},[2068,72977,72978,72980,72982,72988,72990,72992,72994,72996,72998,73000,73002,73004,73010,73012],{},[2071,72979,4342],{},[2071,72981,44630],{},[2205,72983,72984,72986],{},[2071,72985,2849],{},[2075,72987,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,72989,2077],{},[2210,72991,2911],{},[2071,72993,2861],{},[2075,72995,2303],{},[2210,72997,646],{},[2075,72999,2077],{},[2210,73001,630],{},[2075,73003,4075],{},[2205,73005,73006,73008],{},[2071,73007,2861],{},[2075,73009,4441],{},[2075,73011,2077],{},[2210,73013,2935],{},[2092,73015,73016],{"encoding":2094},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[1647,73018,73020],{"className":73019},[2059],[2061,73021,73022],{"xmlns":2063},[2065,73023,73024,73048],{},[2068,73025,73026,73028,73030,73040,73042,73044,73046],{},[2071,73027,4342],{},[2071,73029,44630],{},[2205,73031,73032,73034],{},[2071,73033,2849],{},[2068,73035,73036,73038],{},[2075,73037,2452],{"mathvariant":2450},[2075,73039,2452],{"mathvariant":2450},[2075,73041,2077],{},[2210,73043,2911],{},[2075,73045,3482],{},[2210,73047,630],{},[2092,73049,73050],{"encoding":2094},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[1647,73053,73055],{"className":73054},[2059],[2061,73056,73057],{"xmlns":2063},[2065,73058,73059,73095],{},[2068,73060,73061,73067,73069,73071,73073,73075,73077,73079,73081,73083,73085,73087,73089,73091,73093],{},[2205,73062,73063,73065],{},[2071,73064,575],{},[2075,73066,4441],{},[2075,73068,2077],{},[2071,73070,2890],{},[2071,73072,2849],{},[2075,73074,2084],{"stretchy":2083},[2210,73076,2935],{},[2075,73078,2090],{"stretchy":2083},[2075,73080,2077],{},[2210,73082,42310],{},[2075,73084,2303],{},[2210,73086,5298],{},[2075,73088,2176],{},[2210,73090,39270],{},[2075,73092,2077],{},[2210,73094,670],{},[2092,73096,73097],{"encoding":2094},"P^* = MC(10) = 30 - 40 + 15 = 5",[55,73099,73100],{},[95,73101,73102],{},"Závěr.",[1647,73104,73106],{"className":73105},[2059],[2061,73107,73108],{"xmlns":2063,"display":31093},[2065,73109,73110,73196],{},[2068,73111,73112,73114,73116,73118,73120,73122,73124,73126],{},[2071,73113,575],{},[2075,73115,2077],{},[2071,73117,532],{},[2075,73119,2084],{"stretchy":2083},[2071,73121,2861],{},[2075,73123,2090],{"stretchy":2083},[2075,73125,2077],{},[2068,73127,73128,73130],{},[2075,73129,71976],{"fence":2360},[23493,73131,73132,73174],{"rowspacing":71979,"columnalign":71980,"columnspacing":17019},[23498,73133,73134,73158],{},[23501,73135,73136],{},[2400,73137,73138],{"scriptlevel":630,"displaystyle":2083},[2068,73139,73140,73142,73148,73150,73152,73154,73156],{},[2210,73141,72681],{},[2205,73143,73144,73146],{},[2071,73145,2861],{},[2210,73147,646],{},[2075,73149,2303],{},[2210,73151,662],{},[2071,73153,2861],{},[2075,73155,2176],{},[2210,73157,39270],{},[23501,73159,73160],{},[2400,73161,73162],{"scriptlevel":630,"displaystyle":2083},[2068,73163,73164,73166,73168,73170,73172],{},[2363,73165,72007],{},[2071,73167,2861],{},[2075,73169,4572],{},[2210,73171,2935],{},[2075,73173,2361],{"separator":2360},[23498,73175,73176,73182],{},[23501,73177,73178],{},[2400,73179,73180],{"scriptlevel":630,"displaystyle":2083},[2210,73181,630],{},[23501,73183,73184],{},[2400,73185,73186],{"scriptlevel":630,"displaystyle":2083},[2068,73187,73188,73190,73192,73194],{},[2363,73189,72007],{},[2071,73191,2861],{},[2075,73193,3521],{},[2210,73195,22067],{},[2092,73197,73198],{"encoding":2094},"P = S(Q) = \\begin{cases} 0{,}3Q^2 - 4Q + 15 & \\text{pro } Q \\geq 10, \\\\ 0 & \\text{pro } Q \u003C 10. \\end{cases}",[55,73200,73201],{},[3982,73202,73203,73204,73219,73220,195],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[1647,73205,73207],{"className":73206},[2059],[2061,73208,73209],{"xmlns":2063},[2065,73210,73211,73217],{},[2068,73212,73213,73215],{},[2071,73214,2890],{},[2071,73216,2849],{},[2092,73218,59762],{"encoding":2094}," ležící nad minimem ",[1647,73221,73223],{"className":73222},[2059],[2061,73224,73225],{"xmlns":2063},[2065,73226,73227,73235],{},[2068,73228,73229,73231,73233],{},[2071,73230,4342],{},[2071,73232,44630],{},[2071,73234,2849],{},[2092,73236,59781],{"encoding":2094},[84,73238,73240],{"id":73239},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[55,73242,73243,73244,73248,73249,73264,73265,73285,73286,75,73289,73292,73293,73295,73296,22684,73318,73320,73321,75,73323,63196,73326,1445,73329,46105,73344,73359],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[69,73245,73247],{"className":73246,"dataFsResolvedFilePath":13670,"href":13671},[62],"poptávky",". Pro lineární poptávku je ",[1647,73250,73252],{"className":73251},[2059],[2061,73253,73254],{"xmlns":2063},[2065,73255,73256,73262],{},[2068,73257,73258,73260],{},[2071,73259,543],{},[2071,73261,4082],{},[2092,73263,4182],{"encoding":2094}," kvadratická. Průměrný příjem je podíl ",[1647,73266,73268],{"className":73267},[2059],[2061,73269,73270],{"xmlns":2063},[2065,73271,73272,73282],{},[2068,73273,73274,73276,73278,73280],{},[2071,73275,543],{},[2071,73277,4082],{},[2071,73279,4761],{"mathvariant":2450},[2071,73281,2861],{},[2092,73283,73284],{"encoding":2094},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[95,73287,73288],{},"fixních",[95,73290,73291],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[95,73294,68795],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[1647,73297,73299],{"className":73298},[2059],[2061,73300,73301],{"xmlns":2063},[2065,73302,73303,73315],{},[2068,73304,73305,73307,73309,73311,73313],{},[2071,73306,543],{},[2071,73308,4082],{},[2075,73310,2303],{},[2071,73312,543],{},[2071,73314,2849],{},[2092,73316,73317],{"encoding":2094},"TR - TC",[95,73319,59642],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[95,73322,60954],{},[95,73324,73325],{},"mezní náklady",[69,73327,2430],{"className":73328,"dataFsResolvedFilePath":4005,"href":4006},[62],[1647,73330,73332],{"className":73331},[2059],[2061,73333,73334],{"xmlns":2063},[2065,73335,73336,73342],{},[2068,73337,73338,73340],{},[2071,73339,543],{},[2071,73341,4082],{},[2092,73343,4182],{"encoding":2094},[1647,73345,73347],{"className":73346},[2059],[2061,73348,73349],{"xmlns":2063},[2065,73350,73351,73357],{},[2068,73352,73353,73355],{},[2071,73354,543],{},[2071,73356,2849],{},[2092,73358,3317],{"encoding":2094}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[89,73361,73362,73424,73490,73552],{},[92,73363,73364,73367,73368,11525,73383,195],{},[95,73365,73366],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[1647,73369,73371],{"className":73370},[2059],[2061,73372,73373],{"xmlns":2063},[2065,73374,73375,73381],{},[2068,73376,73377,73379],{},[2071,73378,4342],{},[2071,73380,2849],{},[2092,73382,60030],{"encoding":2094},[1647,73384,73386],{"className":73385},[2059],[2061,73387,73388],{"xmlns":2063},[2065,73389,73390,73422],{},[2068,73391,73392,73394,73396,73398,73404,73406,73408,73410,73412,73414,73420],{},[2071,73393,4342],{},[2071,73395,2849],{},[2075,73397,2084],{"stretchy":2083},[2348,73399,73400,73402],{},[2071,73401,2861],{},[2210,73403,630],{},[2075,73405,2090],{"stretchy":2083},[2075,73407,2077],{},[2071,73409,2890],{},[2071,73411,2849],{},[2075,73413,2084],{"stretchy":2083},[2348,73415,73416,73418],{},[2071,73417,2861],{},[2210,73419,630],{},[2075,73421,2090],{"stretchy":2083},[2092,73423,67039],{"encoding":2094},[92,73425,73426,73367,73429,11525,73446,195],{},[95,73427,73428],{},"Princip minimalizace průměrných variabilních nákladů:",[1647,73430,73432],{"className":73431},[2059],[2061,73433,73434],{"xmlns":2063},[2065,73435,73436,73444],{},[2068,73437,73438,73440,73442],{},[2071,73439,4342],{},[2071,73441,44630],{},[2071,73443,2849],{},[2092,73445,59781],{"encoding":2094},[1647,73447,73449],{"className":73448},[2059],[2061,73450,73451],{"xmlns":2063},[2065,73452,73453,73487],{},[2068,73454,73455,73457,73459,73461,73463,73469,73471,73473,73475,73477,73479,73485],{},[2071,73456,4342],{},[2071,73458,44630],{},[2071,73460,2849],{},[2075,73462,2084],{"stretchy":2083},[2348,73464,73465,73467],{},[2071,73466,2861],{},[2210,73468,630],{},[2075,73470,2090],{"stretchy":2083},[2075,73472,2077],{},[2071,73474,2890],{},[2071,73476,2849],{},[2075,73478,2084],{"stretchy":2083},[2348,73480,73481,73483],{},[2071,73482,2861],{},[2210,73484,630],{},[2075,73486,2090],{"stretchy":2083},[2092,73488,73489],{"encoding":2094},"AVC(Q_0) = MC(Q_0)",[92,73491,73492,73495,73496,11525,73511,195],{},[95,73493,73494],{},"Princip maximalizace zisku:"," v bodě maxima ",[1647,73497,73499],{"className":73498},[2059],[2061,73500,73501],{"xmlns":2063},[2065,73502,73503,73509],{},[2068,73504,73505,73507],{},[2071,73506,575],{},[2071,73508,4082],{},[2092,73510,67949],{"encoding":2094},[1647,73512,73514],{"className":73513},[2059],[2061,73515,73516],{"xmlns":2063},[2065,73517,73518,73550],{},[2068,73519,73520,73522,73524,73526,73532,73534,73536,73538,73540,73542,73548],{},[2071,73521,2890],{},[2071,73523,4082],{},[2075,73525,2084],{"stretchy":2083},[2348,73527,73528,73530],{},[2071,73529,2861],{},[2210,73531,630],{},[2075,73533,2090],{"stretchy":2083},[2075,73535,2077],{},[2071,73537,2890],{},[2071,73539,2849],{},[2075,73541,2084],{"stretchy":2083},[2348,73543,73544,73546],{},[2071,73545,2861],{},[2210,73547,630],{},[2075,73549,2090],{"stretchy":2083},[2092,73551,70115],{"encoding":2094},[92,73553,73554,1445,73557,6560,73593,72395,73614,24333,73627,72077,73644,195],{},[95,73555,73556],{},"Funkce nabídky firmy:",[1647,73558,73560],{"className":73559},[2059],[2061,73561,73562],{"xmlns":2063},[2065,73563,73564,73590],{},[2068,73565,73566,73568,73570,73572,73574,73576,73578,73580,73582,73584,73586,73588],{},[2071,73567,575],{},[2075,73569,2077],{},[2071,73571,532],{},[2075,73573,2084],{"stretchy":2083},[2071,73575,2861],{},[2075,73577,2090],{"stretchy":2083},[2075,73579,2077],{},[2071,73581,2890],{},[2071,73583,2849],{},[2075,73585,2084],{"stretchy":2083},[2071,73587,2861],{},[2075,73589,2090],{"stretchy":2083},[2092,73591,73592],{"encoding":2094},"P = S(Q) = MC(Q)",[1647,73594,73596],{"className":73595},[2059],[2061,73597,73598],{"xmlns":2063},[2065,73599,73600,73612],{},[2068,73601,73602,73604,73606],{},[2071,73603,2861],{},[2075,73605,4572],{},[2205,73607,73608,73610],{},[2071,73609,2861],{},[2075,73611,4441],{},[2092,73613,72394],{"encoding":2094},[1647,73615,73617],{"className":73616},[2059],[2061,73618,73619],{"xmlns":2063},[2065,73620,73621,73625],{},[2068,73622,73623],{},[2210,73624,630],{},[2092,73626,630],{"encoding":2094},[1647,73628,73630],{"className":73629},[2059],[2061,73631,73632],{"xmlns":2063},[2065,73633,73634,73642],{},[2068,73635,73636],{},[2205,73637,73638,73640],{},[2071,73639,2861],{},[2075,73641,4441],{},[2092,73643,32871],{"encoding":2094},[1647,73645,73647],{"className":73646},[2059],[2061,73648,73649],{"xmlns":2063},[2065,73650,73651,73659],{},[2068,73652,73653,73655,73657],{},[2071,73654,4342],{},[2071,73656,44630],{},[2071,73658,2849],{},[2092,73660,59781],{"encoding":2094},[84,73662,54178],{"id":54177},[201,73664,73665,73668,73671,73674,73677,73680,73683,73686,73689,73692,73695],{},[92,73666,73667],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[92,73669,73670],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[92,73672,73673],{},"Jak se vypočte mezní příjem a co udává?",[92,73675,73676],{},"Z jakých složek se skládají celkové náklady?",[92,73678,73679],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[92,73681,73682],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[92,73684,73685],{},"Jak se stanoví přibližně změna celkových nákladů?",[92,73687,73688],{},"Jak se vypočte zisk?",[92,73690,73691],{},"Jaká vlastnost platí v bodě maxima zisku?",[92,73693,73694],{},"Co jsou body zvratu? Jak se najdou?",[92,73696,73697],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[84,73699,73701],{"id":73700},"úlohy-31328","Úlohy 3.1–3.28",[609,73703,73705],{"id":73704},"příjem-3135","Příjem (3.1–3.5)",[55,73707,73708,49722,73711,73739,73740,73755,73756,73771,73772,73787,73788,835,73803,835,73818,73833],{},[95,73709,73710],{},"3.1",[1647,73712,73714],{"className":73713},[2059],[2061,73715,73716],{"xmlns":2063},[2065,73717,73718,73736],{},[2068,73719,73720,73722,73724,73726,73728,73730,73732,73734],{},[2071,73721,575],{},[2075,73723,2077],{},[2071,73725,4271],{},[2075,73727,2084],{"stretchy":2083},[2071,73729,2861],{},[2075,73731,2090],{"stretchy":2083},[2075,73733,2077],{},[2210,73735,3164],{},[2092,73737,73738],{"encoding":2094},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[1647,73741,73743],{"className":73742},[2059],[2061,73744,73745],{"xmlns":2063},[2065,73746,73747,73753],{},[2068,73748,73749,73751],{},[2071,73750,543],{},[2071,73752,4082],{},[2092,73754,4182],{"encoding":2094},", průměrný příjem ",[1647,73757,73759],{"className":73758},[2059],[2061,73760,73761],{"xmlns":2063},[2065,73762,73763,73769],{},[2068,73764,73765,73767],{},[2071,73766,4342],{},[2071,73768,4082],{},[2092,73770,59915],{"encoding":2094}," a mezní příjem ",[1647,73773,73775],{"className":73774},[2059],[2061,73776,73777],{"xmlns":2063},[2065,73778,73779,73785],{},[2068,73780,73781,73783],{},[2071,73782,2890],{},[2071,73784,4082],{},[2092,73786,6721],{"encoding":2094},". (c) Vypočtěte ",[1647,73789,73791],{"className":73790},[2059],[2061,73792,73793],{"xmlns":2063},[2065,73794,73795,73801],{},[2068,73796,73797,73799],{},[2071,73798,543],{},[2071,73800,4082],{},[2092,73802,4182],{"encoding":2094},[1647,73804,73806],{"className":73805},[2059],[2061,73807,73808],{"xmlns":2063},[2065,73809,73810,73816],{},[2068,73811,73812,73814],{},[2071,73813,4342],{},[2071,73815,4082],{},[2092,73817,59915],{"encoding":2094},[1647,73819,73821],{"className":73820},[2059],[2061,73822,73823],{"xmlns":2063},[2065,73824,73825,73831],{},[2068,73826,73827,73829],{},[2071,73828,2890],{},[2071,73830,4082],{},[2092,73832,6721],{"encoding":2094}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[55,73835,73836,49722,73839,73739,73875,73755,73890,73771,73905,73787,73920,835,73935,835,73950,73965],{},[95,73837,73838],{},"3.2",[1647,73840,73842],{"className":73841},[2059],[2061,73843,73844],{"xmlns":2063},[2065,73845,73846,73872],{},[2068,73847,73848,73850,73852,73854,73856,73858,73860,73862,73864,73866,73868,73870],{},[2071,73849,575],{},[2075,73851,2077],{},[2071,73853,4271],{},[2075,73855,2084],{"stretchy":2083},[2071,73857,2861],{},[2075,73859,2090],{"stretchy":2083},[2075,73861,2077],{},[2075,73863,2303],{},[2210,73865,5096],{},[2071,73867,2861],{},[2075,73869,2176],{},[2210,73871,9121],{},[2092,73873,73874],{"encoding":2094},"P = D(Q) = -0{,}5Q + 20",[1647,73876,73878],{"className":73877},[2059],[2061,73879,73880],{"xmlns":2063},[2065,73881,73882,73888],{},[2068,73883,73884,73886],{},[2071,73885,543],{},[2071,73887,4082],{},[2092,73889,4182],{"encoding":2094},[1647,73891,73893],{"className":73892},[2059],[2061,73894,73895],{"xmlns":2063},[2065,73896,73897,73903],{},[2068,73898,73899,73901],{},[2071,73900,4342],{},[2071,73902,4082],{},[2092,73904,59915],{"encoding":2094},[1647,73906,73908],{"className":73907},[2059],[2061,73909,73910],{"xmlns":2063},[2065,73911,73912,73918],{},[2068,73913,73914,73916],{},[2071,73915,2890],{},[2071,73917,4082],{},[2092,73919,6721],{"encoding":2094},[1647,73921,73923],{"className":73922},[2059],[2061,73924,73925],{"xmlns":2063},[2065,73926,73927,73933],{},[2068,73928,73929,73931],{},[2071,73930,543],{},[2071,73932,4082],{},[2092,73934,4182],{"encoding":2094},[1647,73936,73938],{"className":73937},[2059],[2061,73939,73940],{"xmlns":2063},[2065,73941,73942,73948],{},[2068,73943,73944,73946],{},[2071,73945,4342],{},[2071,73947,4082],{},[2092,73949,59915],{"encoding":2094},[1647,73951,73953],{"className":73952},[2059],[2061,73954,73955],{"xmlns":2063},[2065,73956,73957,73963],{},[2068,73958,73959,73961],{},[2071,73960,2890],{},[2071,73962,4082],{},[2092,73964,6721],{"encoding":2094}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[55,73967,73968,49722,73971,74008,74009,73755,74024,73771,74039,74054,74055,6560,74070,74096,74097,74112,74113,835,74128,6560,74143,74096,74168,74183,74184,74197,74198,74213,74214,74229,74230,835,74243,835,74258,835,74273,195],{},[95,73969,73970],{},"3.3",[1647,73972,73974],{"className":73973},[2059],[2061,73975,73976],{"xmlns":2063},[2065,73977,73978,74005],{},[2068,73979,73980,73982,73984,73986,73988,73990,73992,73994,73997,73999],{},[2071,73981,575],{},[2075,73983,2077],{},[2071,73985,4271],{},[2075,73987,2084],{"stretchy":2083},[2071,73989,2861],{},[2075,73991,2090],{"stretchy":2083},[2075,73993,2077],{},[2210,73995,73996],{},"1200",[2075,73998,2303],{},[2205,74000,74001,74003],{},[2071,74002,2861],{},[2210,74004,646],{},[2092,74006,74007],{"encoding":2094},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[1647,74010,74012],{"className":74011},[2059],[2061,74013,74014],{"xmlns":2063},[2065,74015,74016,74022],{},[2068,74017,74018,74020],{},[2071,74019,543],{},[2071,74021,4082],{},[2092,74023,4182],{"encoding":2094},[1647,74025,74027],{"className":74026},[2059],[2061,74028,74029],{"xmlns":2063},[2065,74030,74031,74037],{},[2068,74032,74033,74035],{},[2071,74034,4342],{},[2071,74036,4082],{},[2092,74038,59915],{"encoding":2094},[1647,74040,74042],{"className":74041},[2059],[2061,74043,74044],{"xmlns":2063},[2065,74045,74046,74052],{},[2068,74047,74048,74050],{},[2071,74049,2890],{},[2071,74051,4082],{},[2092,74053,6721],{"encoding":2094},". (b) Vypočtěte ",[1647,74056,74058],{"className":74057},[2059],[2061,74059,74060],{"xmlns":2063},[2065,74061,74062,74068],{},[2068,74063,74064,74066],{},[2071,74065,543],{},[2071,74067,4082],{},[2092,74069,4182],{"encoding":2094},[1647,74071,74073],{"className":74072},[2059],[2061,74074,74075],{"xmlns":2063},[2065,74076,74077,74093],{},[2068,74078,74079,74081,74083,74085,74087,74089,74091],{},[2071,74080,2861],{},[2075,74082,2077],{},[2210,74084,2935],{},[2075,74086,2361],{"separator":2360},[2210,74088,9121],{},[2075,74090,2361],{"separator":2360},[2210,74092,42310],{},[2092,74094,74095],{"encoding":2094},"Q = 10, 20, 30"," a rozhodněte, kdy ",[1647,74098,74100],{"className":74099},[2059],[2061,74101,74102],{"xmlns":2063},[2065,74103,74104,74110],{},[2068,74105,74106,74108],{},[2071,74107,543],{},[2071,74109,4082],{},[2092,74111,4182],{"encoding":2094}," roste, resp. klesá. (c) Vypočtěte ",[1647,74114,74116],{"className":74115},[2059],[2061,74117,74118],{"xmlns":2063},[2065,74119,74120,74126],{},[2068,74121,74122,74124],{},[2071,74123,4342],{},[2071,74125,4082],{},[2092,74127,59915],{"encoding":2094},[1647,74129,74131],{"className":74130},[2059],[2061,74132,74133],{"xmlns":2063},[2065,74134,74135,74141],{},[2068,74136,74137,74139],{},[2071,74138,2890],{},[2071,74140,4082],{},[2092,74142,6721],{"encoding":2094},[1647,74144,74146],{"className":74145},[2059],[2061,74147,74148],{"xmlns":2063},[2065,74149,74150,74166],{},[2068,74151,74152,74154,74156,74158,74160,74162,74164],{},[2071,74153,2861],{},[2075,74155,2077],{},[2210,74157,2935],{},[2075,74159,2361],{"separator":2360},[2210,74161,9121],{},[2075,74163,2361],{"separator":2360},[2210,74165,42310],{},[2092,74167,74095],{"encoding":2094},[1647,74169,74171],{"className":74170},[2059],[2061,74172,74173],{"xmlns":2063},[2065,74174,74175,74181],{},[2068,74176,74177,74179],{},[2071,74178,2890],{},[2071,74180,4082],{},[2092,74182,6721],{"encoding":2094}," roste, resp. klesá. (d) Vypočtěte ",[1647,74185,74187],{"className":74186},[2059],[2061,74188,74189],{"xmlns":2063},[2065,74190,74191,74195],{},[2068,74192,74193],{},[2071,74194,2861],{},[2092,74196,2861],{"encoding":2094},", které maximalizuje ",[1647,74199,74201],{"className":74200},[2059],[2061,74202,74203],{"xmlns":2063},[2065,74204,74205,74211],{},[2068,74206,74207,74209],{},[2071,74208,543],{},[2071,74210,4082],{},[2092,74212,4182],{"encoding":2094}," a stanovte příslušnou hodnotu maxima ",[1647,74215,74217],{"className":74216},[2059],[2061,74218,74219],{"xmlns":2063},[2065,74220,74221,74227],{},[2068,74222,74223,74225],{},[2071,74224,543],{},[2071,74226,4082],{},[2092,74228,4182],{"encoding":2094},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[1647,74231,74233],{"className":74232},[2059],[2061,74234,74235],{"xmlns":2063},[2065,74236,74237,74241],{},[2068,74238,74239],{},[2071,74240,4271],{},[2092,74242,4271],{"encoding":2094},[1647,74244,74246],{"className":74245},[2059],[2061,74247,74248],{"xmlns":2063},[2065,74249,74250,74256],{},[2068,74251,74252,74254],{},[2071,74253,543],{},[2071,74255,4082],{},[2092,74257,4182],{"encoding":2094},[1647,74259,74261],{"className":74260},[2059],[2061,74262,74263],{"xmlns":2063},[2065,74264,74265,74271],{},[2068,74266,74267,74269],{},[2071,74268,4342],{},[2071,74270,4082],{},[2092,74272,59915],{"encoding":2094},[1647,74274,74276],{"className":74275},[2059],[2061,74277,74278],{"xmlns":2063},[2065,74279,74280,74286],{},[2068,74281,74282,74284],{},[2071,74283,2890],{},[2071,74285,4082],{},[2092,74287,6721],{"encoding":2094},[55,74289,74290,74293,74294,74324,74325,74340,74341,11288,74354,835,74372,835,74389,74407,74408,74430,74431,74446,74447,74460,74461,195],{},[95,74291,74292],{},"3.4"," Je dán celkový příjem ",[1647,74295,74297],{"className":74296},[2059],[2061,74298,74299],{"xmlns":2063},[2065,74300,74301,74321],{},[2068,74302,74303,74305,74307,74309,74311,74313,74315],{},[2071,74304,543],{},[2071,74306,4082],{},[2075,74308,2077],{},[2210,74310,73996],{},[2071,74312,2861],{},[2075,74314,2303],{},[2205,74316,74317,74319],{},[2071,74318,2861],{},[2210,74320,654],{},[2092,74322,74323],{"encoding":2094},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[1647,74326,74328],{"className":74327},[2059],[2061,74329,74330],{"xmlns":2063},[2065,74331,74332,74338],{},[2068,74333,74334,74336],{},[2071,74335,543],{},[2071,74337,4082],{},[2092,74339,4182],{"encoding":2094}," vzhledem ke ",[1647,74342,74344],{"className":74343},[2059],[2061,74345,74346],{"xmlns":2063},[2065,74347,74348,74352],{},[2068,74349,74350],{},[2071,74351,2861],{},[2092,74353,2861],{"encoding":2094},[1647,74355,74357],{"className":74356},[2059],[2061,74358,74359],{"xmlns":2063},[2065,74360,74361,74369],{},[2068,74362,74363,74365,74367],{},[2071,74364,2861],{},[2075,74366,2077],{},[2210,74368,670],{},[2092,74370,74371],{"encoding":2094},"Q = 5",[1647,74373,74375],{"className":74374},[2059],[2061,74376,74377],{"xmlns":2063},[2065,74378,74379,74387],{},[2068,74380,74381,74383,74385],{},[2071,74382,2861],{},[2075,74384,2077],{},[2210,74386,5672],{},[2092,74388,5675],{"encoding":2094},[1647,74390,74392],{"className":74391},[2059],[2061,74393,74394],{"xmlns":2063},[2065,74395,74396,74404],{},[2068,74397,74398,74400,74402],{},[2071,74399,2861],{},[2075,74401,2077],{},[2210,74403,3583],{},[2092,74405,74406],{"encoding":2094},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[1647,74409,74411],{"className":74410},[2059],[2061,74412,74413],{"xmlns":2063},[2065,74414,74415,74427],{},[2068,74416,74417,74419,74421,74423,74425],{},[2071,74418,2890],{},[2071,74420,4082],{},[2075,74422,2084],{"stretchy":2083},[2210,74424,2935],{},[2075,74426,2090],{"stretchy":2083},[2092,74428,74429],{"encoding":2094},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[1647,74432,74434],{"className":74433},[2059],[2061,74435,74436],{"xmlns":2063},[2065,74437,74438,74444],{},[2068,74439,74440,74442],{},[2071,74441,543],{},[2071,74443,4082],{},[2092,74445,4182],{"encoding":2094},", jestliže se ",[1647,74448,74450],{"className":74449},[2059],[2061,74451,74452],{"xmlns":2063},[2065,74453,74454,74458],{},[2068,74455,74456],{},[2071,74457,2861],{},[2092,74459,2861],{"encoding":2094}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[1647,74462,74464],{"className":74463},[2059],[2061,74465,74466],{"xmlns":2063},[2065,74467,74468,74474],{},[2068,74469,74470,74472],{},[2071,74471,543],{},[2071,74473,4082],{},[2092,74475,4182],{"encoding":2094},[55,74477,74478,74481,74482,74508,74509,74524,74525,74446,74540,74553],{},[95,74479,74480],{},"3.5"," Je dán mezní příjem ",[1647,74483,74485],{"className":74484},[2059],[2061,74486,74487],{"xmlns":2063},[2065,74488,74489,74505],{},[2068,74490,74491,74493,74495,74497,74499,74501,74503],{},[2071,74492,2890],{},[2071,74494,4082],{},[2075,74496,2077],{},[2075,74498,2303],{},[2071,74500,2861],{},[2075,74502,2176],{},[2210,74504,9121],{},[2092,74506,74507],{"encoding":2094},"MR = -Q + 20",". (a) Určete celkový příjem ",[1647,74510,74512],{"className":74511},[2059],[2061,74513,74514],{"xmlns":2063},[2065,74515,74516,74522],{},[2068,74517,74518,74520],{},[2071,74519,543],{},[2071,74521,4082],{},[2092,74523,4182],{"encoding":2094},". (b) Vypočtěte změnu ",[1647,74526,74528],{"className":74527},[2059],[2061,74529,74530],{"xmlns":2063},[2065,74531,74532,74538],{},[2068,74533,74534,74536],{},[2071,74535,543],{},[2071,74537,4082],{},[2092,74539,4182],{"encoding":2094},[1647,74541,74543],{"className":74542},[2059],[2061,74544,74545],{"xmlns":2063},[2065,74546,74547,74551],{},[2068,74548,74549],{},[2071,74550,2861],{},[2092,74552,2861],{"encoding":2094}," změní z 8 na 12.",[609,74555,74557],{"id":74556},"náklady-36316","Náklady (3.6–3.16)",[55,74559,74560,74563,74564,74604,74605,74620,74621,74638,74639,74656,74657,74672,74673,74688,74689,74054,74704,835,74719,835,74736,835,74753,835,74768,835,74783,6560,74798,74816,74817,835,74832,835,74847,74862],{},[95,74561,74562],{},"3.6"," Jsou dány celkové náklady ",[1647,74565,74567],{"className":74566},[2059],[2061,74568,74569],{"xmlns":2063},[2065,74570,74571,74601],{},[2068,74572,74573,74575,74577,74579,74581,74583,74585,74587,74589],{},[2071,74574,543],{},[2071,74576,2849],{},[2075,74578,2077],{},[2210,74580,3164],{},[2075,74582,2176],{},[2210,74584,646],{},[2071,74586,2861],{},[2075,74588,2176],{},[2400,74590,74591],{"scriptlevel":630,"displaystyle":2083},[2403,74592,74593,74599],{},[2205,74594,74595,74597],{},[2071,74596,2861],{},[2210,74598,646],{},[2210,74600,2935],{},[2092,74602,74603],{"encoding":2094},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[1647,74606,74608],{"className":74607},[2059],[2061,74609,74610],{"xmlns":2063},[2065,74611,74612,74618],{},[2068,74613,74614,74616],{},[2071,74615,10177],{},[2071,74617,2849],{},[2092,74619,59961],{"encoding":2094},", celkové variabilní náklady ",[1647,74622,74624],{"className":74623},[2059],[2061,74625,74626],{"xmlns":2063},[2065,74627,74628,74636],{},[2068,74629,74630,74632,74634],{},[2071,74631,543],{},[2071,74633,44630],{},[2071,74635,2849],{},[2092,74637,59979],{"encoding":2094},", průměrné variabilní náklady ",[1647,74640,74642],{"className":74641},[2059],[2061,74643,74644],{"xmlns":2063},[2065,74645,74646,74654],{},[2068,74647,74648,74650,74652],{},[2071,74649,4342],{},[2071,74651,44630],{},[2071,74653,2849],{},[2092,74655,59781],{"encoding":2094},", variabilní náklady na jednotku ",[1647,74658,74660],{"className":74659},[2059],[2061,74661,74662],{"xmlns":2063},[2065,74663,74664,74670],{},[2068,74665,74666,74668],{},[2071,74667,44630],{},[2071,74669,2849],{},[2092,74671,68075],{"encoding":2094},", průměrné náklady ",[1647,74674,74676],{"className":74675},[2059],[2061,74677,74678],{"xmlns":2063},[2065,74679,74680,74686],{},[2068,74681,74682,74684],{},[2071,74683,4342],{},[2071,74685,2849],{},[2092,74687,60030],{"encoding":2094}," a mezní náklady ",[1647,74690,74692],{"className":74691},[2059],[2061,74693,74694],{"xmlns":2063},[2065,74695,74696,74702],{},[2068,74697,74698,74700],{},[2071,74699,2890],{},[2071,74701,2849],{},[2092,74703,59762],{"encoding":2094},[1647,74705,74707],{"className":74706},[2059],[2061,74708,74709],{"xmlns":2063},[2065,74710,74711,74717],{},[2068,74712,74713,74715],{},[2071,74714,543],{},[2071,74716,2849],{},[2092,74718,3317],{"encoding":2094},[1647,74720,74722],{"className":74721},[2059],[2061,74723,74724],{"xmlns":2063},[2065,74725,74726,74734],{},[2068,74727,74728,74730,74732],{},[2071,74729,543],{},[2071,74731,44630],{},[2071,74733,2849],{},[2092,74735,59979],{"encoding":2094},[1647,74737,74739],{"className":74738},[2059],[2061,74740,74741],{"xmlns":2063},[2065,74742,74743,74751],{},[2068,74744,74745,74747,74749],{},[2071,74746,4342],{},[2071,74748,44630],{},[2071,74750,2849],{},[2092,74752,59781],{"encoding":2094},[1647,74754,74756],{"className":74755},[2059],[2061,74757,74758],{"xmlns":2063},[2065,74759,74760,74766],{},[2068,74761,74762,74764],{},[2071,74763,44630],{},[2071,74765,2849],{},[2092,74767,68075],{"encoding":2094},[1647,74769,74771],{"className":74770},[2059],[2061,74772,74773],{"xmlns":2063},[2065,74774,74775,74781],{},[2068,74776,74777,74779],{},[2071,74778,4342],{},[2071,74780,2849],{},[2092,74782,60030],{"encoding":2094},[1647,74784,74786],{"className":74785},[2059],[2061,74787,74788],{"xmlns":2063},[2065,74789,74790,74796],{},[2068,74791,74792,74794],{},[2071,74793,2890],{},[2071,74795,2849],{},[2092,74797,59762],{"encoding":2094},[1647,74799,74801],{"className":74800},[2059],[2061,74802,74803],{"xmlns":2063},[2065,74804,74805,74813],{},[2068,74806,74807,74809,74811],{},[2071,74808,2861],{},[2075,74810,2077],{},[2210,74812,3194],{},[2092,74814,74815],{"encoding":2094},"Q = 50",". (c) Rozhodněte, kdy ",[1647,74818,74820],{"className":74819},[2059],[2061,74821,74822],{"xmlns":2063},[2065,74823,74824,74830],{},[2068,74825,74826,74828],{},[2071,74827,543],{},[2071,74829,2849],{},[2092,74831,3317],{"encoding":2094},[1647,74833,74835],{"className":74834},[2059],[2061,74836,74837],{"xmlns":2063},[2065,74838,74839,74845],{},[2068,74840,74841,74843],{},[2071,74842,4342],{},[2071,74844,2849],{},[2092,74846,60030],{"encoding":2094},[1647,74848,74850],{"className":74849},[2059],[2061,74851,74852],{"xmlns":2063},[2065,74853,74854,74860],{},[2068,74855,74856,74858],{},[2071,74857,2890],{},[2071,74859,2849],{},[2092,74861,59762],{"encoding":2094}," rostou, resp. klesají.",[55,74864,74865,74868,74869,74688,74899,74914,74915,74930,74931,835,74946,835,74961,195],{},[95,74866,74867],{},"3.7"," Jsou dány průměrné náklady ",[1647,74870,74872],{"className":74871},[2059],[2061,74873,74874],{"xmlns":2063},[2065,74875,74876,74896],{},[2068,74877,74878,74880,74882,74884,74892,74894],{},[2071,74879,4342],{},[2071,74881,2849],{},[2075,74883,2077],{},[2400,74885,74886],{"scriptlevel":630,"displaystyle":2083},[2403,74887,74888,74890],{},[2210,74889,3164],{},[2071,74891,2861],{},[2075,74893,2176],{},[2210,74895,9121],{},[2092,74897,74898],{"encoding":2094},"AC = \\tfrac{100}{Q} + 20",[1647,74900,74902],{"className":74901},[2059],[2061,74903,74904],{"xmlns":2063},[2065,74905,74906,74912],{},[2068,74907,74908,74910],{},[2071,74909,2890],{},[2071,74911,2849],{},[2092,74913,59762],{"encoding":2094},". (a) Určete celkové náklady ",[1647,74916,74918],{"className":74917},[2059],[2061,74919,74920],{"xmlns":2063},[2065,74921,74922,74928],{},[2068,74923,74924,74926],{},[2071,74925,543],{},[2071,74927,2849],{},[2092,74929,3317],{"encoding":2094},". (b) Načrtněte a geometricky charakterizujte křivky ",[1647,74932,74934],{"className":74933},[2059],[2061,74935,74936],{"xmlns":2063},[2065,74937,74938,74944],{},[2068,74939,74940,74942],{},[2071,74941,4342],{},[2071,74943,2849],{},[2092,74945,60030],{"encoding":2094},[1647,74947,74949],{"className":74948},[2059],[2061,74950,74951],{"xmlns":2063},[2065,74952,74953,74959],{},[2068,74954,74955,74957],{},[2071,74956,543],{},[2071,74958,2849],{},[2092,74960,3317],{"encoding":2094},[1647,74962,74964],{"className":74963},[2059],[2061,74965,74966],{"xmlns":2063},[2065,74967,74968,74974],{},[2068,74969,74970,74972],{},[2071,74971,2890],{},[2071,74973,2849],{},[2092,74975,59762],{"encoding":2094},[55,74977,74978,74563,74981,75025,75026,835,75043,835,75058,835,75075,835,75090,835,75107,195],{},[95,74979,74980],{},"3.8",[1647,74982,74984],{"className":74983},[2059],[2061,74985,74986],{"xmlns":2063},[2065,74987,74988,75022],{},[2068,74989,74990,74992,74994,74996,74998,75000,75002,75004,75006,75008,75014,75016],{},[2071,74991,543],{},[2071,74993,2849],{},[2075,74995,2077],{},[2210,74997,50999],{},[2075,74999,2176],{},[2210,75001,42310],{},[2071,75003,2861],{},[2075,75005,2303],{},[2210,75007,678],{},[2205,75009,75010,75012],{},[2071,75011,2861],{},[2210,75013,646],{},[2075,75015,2176],{},[2205,75017,75018,75020],{},[2071,75019,2861],{},[2210,75021,654],{},[2092,75023,75024],{"encoding":2094},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[1647,75027,75029],{"className":75028},[2059],[2061,75030,75031],{"xmlns":2063},[2065,75032,75033,75041],{},[2068,75034,75035,75037,75039],{},[2071,75036,543],{},[2071,75038,44630],{},[2071,75040,2849],{},[2092,75042,59979],{"encoding":2094},[1647,75044,75046],{"className":75045},[2059],[2061,75047,75048],{"xmlns":2063},[2065,75049,75050,75056],{},[2068,75051,75052,75054],{},[2071,75053,10177],{},[2071,75055,2849],{},[2092,75057,59961],{"encoding":2094},[1647,75059,75061],{"className":75060},[2059],[2061,75062,75063],{"xmlns":2063},[2065,75064,75065,75073],{},[2068,75066,75067,75069,75071],{},[2071,75068,4342],{},[2071,75070,44630],{},[2071,75072,2849],{},[2092,75074,59781],{"encoding":2094},[1647,75076,75078],{"className":75077},[2059],[2061,75079,75080],{"xmlns":2063},[2065,75081,75082,75088],{},[2068,75083,75084,75086],{},[2071,75085,4342],{},[2071,75087,2849],{},[2092,75089,60030],{"encoding":2094},[1647,75091,75093],{"className":75092},[2059],[2061,75094,75095],{"xmlns":2063},[2065,75096,75097,75105],{},[2068,75098,75099,75101,75103],{},[2071,75100,4342],{},[2071,75102,10177],{},[2071,75104,2849],{},[2092,75106,59997],{"encoding":2094},[1647,75108,75110],{"className":75109},[2059],[2061,75111,75112],{"xmlns":2063},[2065,75113,75114,75120],{},[2068,75115,75116,75118],{},[2071,75117,2890],{},[2071,75119,2849],{},[2092,75121,59762],{"encoding":2094},[55,75123,75124,74563,75127,75157,75158,74340,75173,6560,75186,835,75204,835,75222,74407,75240,74430,75262,75277,75278,75291,75292,195],{},[95,75125,75126],{},"3.9",[1647,75128,75130],{"className":75129},[2059],[2061,75131,75132],{"xmlns":2063},[2065,75133,75134,75154],{},[2068,75135,75136,75138,75140,75142,75144,75146,75148],{},[2071,75137,543],{},[2071,75139,2849],{},[2075,75141,2077],{},[2210,75143,16845],{},[2075,75145,2176],{},[2210,75147,22060],{},[2205,75149,75150,75152],{},[2071,75151,2861],{},[2210,75153,646],{},[2092,75155,75156],{"encoding":2094},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[1647,75159,75161],{"className":75160},[2059],[2061,75162,75163],{"xmlns":2063},[2065,75164,75165,75171],{},[2068,75166,75167,75169],{},[2071,75168,543],{},[2071,75170,2849],{},[2092,75172,3317],{"encoding":2094},[1647,75174,75176],{"className":75175},[2059],[2061,75177,75178],{"xmlns":2063},[2065,75179,75180,75184],{},[2068,75181,75182],{},[2071,75183,2861],{},[2092,75185,2861],{"encoding":2094},[1647,75187,75189],{"className":75188},[2059],[2061,75190,75191],{"xmlns":2063},[2065,75192,75193,75201],{},[2068,75194,75195,75197,75199],{},[2071,75196,2861],{},[2075,75198,2077],{},[2210,75200,2935],{},[2092,75202,75203],{"encoding":2094},"Q = 10",[1647,75205,75207],{"className":75206},[2059],[2061,75208,75209],{"xmlns":2063},[2065,75210,75211,75219],{},[2068,75212,75213,75215,75217],{},[2071,75214,2861],{},[2075,75216,2077],{},[2210,75218,9121],{},[2092,75220,75221],{"encoding":2094},"Q = 20",[1647,75223,75225],{"className":75224},[2059],[2061,75226,75227],{"xmlns":2063},[2065,75228,75229,75237],{},[2068,75230,75231,75233,75235],{},[2071,75232,2861],{},[2075,75234,2077],{},[2210,75236,42310],{},[2092,75238,75239],{"encoding":2094},"Q = 30",[1647,75241,75243],{"className":75242},[2059],[2061,75244,75245],{"xmlns":2063},[2065,75246,75247,75259],{},[2068,75248,75249,75251,75253,75255,75257],{},[2071,75250,2890],{},[2071,75252,2849],{},[2075,75254,2084],{"stretchy":2083},[2210,75256,39270],{},[2075,75258,2090],{"stretchy":2083},[2092,75260,75261],{"encoding":2094},"MC(15)",[1647,75263,75265],{"className":75264},[2059],[2061,75266,75267],{"xmlns":2063},[2065,75268,75269,75275],{},[2068,75270,75271,75273],{},[2071,75272,543],{},[2071,75274,2849],{},[2092,75276,3317],{"encoding":2094}," v důsledku změny ",[1647,75279,75281],{"className":75280},[2059],[2061,75282,75283],{"xmlns":2063},[2065,75284,75285,75289],{},[2068,75286,75287],{},[2071,75288,2861],{},[2092,75290,2861],{"encoding":2094}," z 15 na 20 a porovnejte se skutečnou změnou ",[1647,75293,75295],{"className":75294},[2059],[2061,75296,75297],{"xmlns":2063},[2065,75298,75299,75305],{},[2068,75300,75301,75303],{},[2071,75302,543],{},[2071,75304,2849],{},[2092,75306,3317],{"encoding":2094},[55,75308,75309,75312,75313,74914,75349,75364,75365,74524,75384,75277,75399,75412],{},[95,75310,75311],{},"3.10"," Jsou dány mezní náklady ",[1647,75314,75316],{"className":75315},[2059],[2061,75317,75318],{"xmlns":2063},[2065,75319,75320,75346],{},[2068,75321,75322,75324,75326,75328,75330,75332,75334,75336,75338,75340],{},[2071,75323,2890],{},[2071,75325,2849],{},[2075,75327,2077],{},[2210,75329,3200],{},[2075,75331,2303],{},[2210,75333,46153],{},[2071,75335,2861],{},[2075,75337,2176],{},[2210,75339,69029],{},[2205,75341,75342,75344],{},[2071,75343,2861],{},[2210,75345,646],{},[2092,75347,75348],{"encoding":2094},"MC = 60 - 16Q + 1{,}5Q^2",[1647,75350,75352],{"className":75351},[2059],[2061,75353,75354],{"xmlns":2063},[2065,75355,75356,75362],{},[2068,75357,75358,75360],{},[2071,75359,543],{},[2071,75361,2849],{},[2092,75363,3317],{"encoding":2094},", jestliže fixní náklady ",[1647,75366,75368],{"className":75367},[2059],[2061,75369,75370],{"xmlns":2063},[2065,75371,75372,75382],{},[2068,75373,75374,75376,75378,75380],{},[2071,75375,10177],{},[2071,75377,2849],{},[2075,75379,2077],{},[2210,75381,3164],{},[2092,75383,13361],{"encoding":2094},[1647,75385,75387],{"className":75386},[2059],[2061,75388,75389],{"xmlns":2063},[2065,75390,75391,75397],{},[2068,75392,75393,75395],{},[2071,75394,543],{},[2071,75396,2849],{},[2092,75398,3317],{"encoding":2094},[1647,75400,75402],{"className":75401},[2059],[2061,75403,75404],{"xmlns":2063},[2065,75405,75406,75410],{},[2068,75407,75408],{},[2071,75409,2861],{},[2092,75411,2861],{"encoding":2094}," z 15 na 20.",[55,75414,75415,74563,75418,75461,75462,75475,75476,75491,75492,75507,75508,75475,75521,75491,75538,75555,75556,75475,75569,75491,75584,75599,75600,75620,75621,75644],{},[95,75416,75417],{},"3.11",[1647,75419,75421],{"className":75420},[2059],[2061,75422,75423],{"xmlns":2063},[2065,75424,75425,75459],{},[2068,75426,75427,75429,75431,75433,75435,75437,75439,75441,75443,75445,75451,75453],{},[2071,75428,543],{},[2071,75430,2849],{},[2075,75432,2077],{},[2210,75434,3164],{},[2075,75436,2176],{},[2210,75438,5091],{},[2071,75440,2861],{},[2075,75442,2303],{},[2210,75444,670],{},[2205,75446,75447,75449],{},[2071,75448,2861],{},[2210,75450,646],{},[2075,75452,2176],{},[2205,75454,75455,75457],{},[2071,75456,2861],{},[2210,75458,654],{},[2092,75460,65377],{"encoding":2094},". (a) Určete ",[1647,75463,75465],{"className":75464},[2059],[2061,75466,75467],{"xmlns":2063},[2065,75468,75469,75473],{},[2068,75470,75471],{},[2071,75472,2861],{},[2092,75474,2861],{"encoding":2094},", které minimalizuje ",[1647,75477,75479],{"className":75478},[2059],[2061,75480,75481],{"xmlns":2063},[2065,75482,75483,75489],{},[2068,75484,75485,75487],{},[2071,75486,2890],{},[2071,75488,2849],{},[2092,75490,59762],{"encoding":2094}," a stanovte příslušnou hodnotu minima ",[1647,75493,75495],{"className":75494},[2059],[2061,75496,75497],{"xmlns":2063},[2065,75498,75499,75505],{},[2068,75500,75501,75503],{},[2071,75502,2890],{},[2071,75504,2849],{},[2092,75506,59762],{"encoding":2094},". (b) Určete ",[1647,75509,75511],{"className":75510},[2059],[2061,75512,75513],{"xmlns":2063},[2065,75514,75515,75519],{},[2068,75516,75517],{},[2071,75518,2861],{},[2092,75520,2861],{"encoding":2094},[1647,75522,75524],{"className":75523},[2059],[2061,75525,75526],{"xmlns":2063},[2065,75527,75528,75536],{},[2068,75529,75530,75532,75534],{},[2071,75531,4342],{},[2071,75533,44630],{},[2071,75535,2849],{},[2092,75537,59781],{"encoding":2094},[1647,75539,75541],{"className":75540},[2059],[2061,75542,75543],{"xmlns":2063},[2065,75544,75545,75553],{},[2068,75546,75547,75549,75551],{},[2071,75548,4342],{},[2071,75550,44630],{},[2071,75552,2849],{},[2092,75554,59781],{"encoding":2094},". (c) Určete ",[1647,75557,75559],{"className":75558},[2059],[2061,75560,75561],{"xmlns":2063},[2065,75562,75563,75567],{},[2068,75564,75565],{},[2071,75566,2861],{},[2092,75568,2861],{"encoding":2094},[1647,75570,75572],{"className":75571},[2059],[2061,75573,75574],{"xmlns":2063},[2065,75575,75576,75582],{},[2068,75577,75578,75580],{},[2071,75579,4342],{},[2071,75581,2849],{},[2092,75583,60030],{"encoding":2094},[1647,75585,75587],{"className":75586},[2059],[2061,75588,75589],{"xmlns":2063},[2065,75590,75591,75597],{},[2068,75592,75593,75595],{},[2071,75594,4342],{},[2071,75596,2849],{},[2092,75598,60030],{"encoding":2094}," (rada: hledaný kořen ",[1647,75601,75603],{"className":75602},[2059],[2061,75604,75605],{"xmlns":2063},[2065,75606,75607,75617],{},[2068,75608,75609,75611],{},[2071,75610,4342],{},[2205,75612,75613,75615],{},[2071,75614,2849],{},[2075,75616,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,75618,75619],{"encoding":2094},"AC'"," určete přibližně, patří do ",[1647,75622,75624],{"className":75623},[2059],[2061,75625,75626],{"xmlns":2063},[2065,75627,75628,75641],{},[2068,75629,75630,75632,75635,75637,75639],{},[2075,75631,2084],{"stretchy":2083},[2210,75633,75634],{},"4,7",[2075,75636,8512],{"separator":2360},[2210,75638,5366],{},[2075,75640,2090],{"stretchy":2083},[2092,75642,75643],{"encoding":2094},"(4{,}7; 4{,}8)",", zpřesněte).",[55,75646,75647,75650,75651,2697,75679,75696,75697,24333,75738,75759],{},[95,75648,75649],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[1647,75652,75654],{"className":75653},[2059],[2061,75655,75656],{"xmlns":2063},[2065,75657,75658,75676],{},[2068,75659,75660,75662,75664,75666,75668,75670,75672,75674],{},[2071,75661,4342],{},[2071,75663,2849],{},[2075,75665,2077],{},[2071,75667,4342],{},[2071,75669,2849],{},[2075,75671,2084],{"stretchy":2083},[2071,75673,2861],{},[2075,75675,2090],{"stretchy":2083},[2092,75677,75678],{"encoding":2094},"AC = AC(Q)",[1647,75680,75682],{"className":75681},[2059],[2061,75683,75684],{"xmlns":2063},[2065,75685,75686,75694],{},[2068,75687,75688],{},[2348,75689,75690,75692],{},[2071,75691,2861],{},[2210,75693,630],{},[2092,75695,42599],{"encoding":2094}," minimum, pak platí ",[1647,75698,75700],{"className":75699},[2059],[2061,75701,75702],{"xmlns":2063},[2065,75703,75704,75736],{},[2068,75705,75706,75708,75710,75712,75718,75720,75722,75724,75726,75728,75734],{},[2071,75707,4342],{},[2071,75709,2849],{},[2075,75711,2084],{"stretchy":2083},[2348,75713,75714,75716],{},[2071,75715,2861],{},[2210,75717,630],{},[2075,75719,2090],{"stretchy":2083},[2075,75721,2077],{},[2071,75723,2890],{},[2071,75725,2849],{},[2075,75727,2084],{"stretchy":2083},[2348,75729,75730,75732],{},[2071,75731,2861],{},[2210,75733,630],{},[2075,75735,2090],{"stretchy":2083},[2092,75737,67039],{"encoding":2094},[1647,75739,75741],{"className":75740},[2059],[2061,75742,75743],{"xmlns":2063},[2065,75744,75745,75757],{},[2068,75746,75747,75749,75751,75753,75755],{},[2071,75748,2890],{},[2071,75750,2849],{},[2075,75752,2084],{"stretchy":2083},[2071,75754,2861],{},[2075,75756,2090],{"stretchy":2083},[2092,75758,72163],{"encoding":2094}," jsou mezní náklady.",[55,75761,75762,74563,75765,75025,75799,75475,75812,75491,75827,195],{},[95,75763,75764],{},"3.13",[1647,75766,75768],{"className":75767},[2059],[2061,75769,75770],{"xmlns":2063},[2065,75771,75772,75796],{},[2068,75773,75774,75776,75778,75780,75786,75788,75790,75792,75794],{},[2071,75775,543],{},[2071,75777,2849],{},[2075,75779,2077],{},[2205,75781,75782,75784],{},[2071,75783,2861],{},[2210,75785,646],{},[2075,75787,2176],{},[2210,75789,646],{},[2071,75791,2861],{},[2075,75793,2176],{},[2210,75795,5091],{},[2092,75797,75798],{"encoding":2094},"TC = Q^2 + 2Q + 25",[1647,75800,75802],{"className":75801},[2059],[2061,75803,75804],{"xmlns":2063},[2065,75805,75806,75810],{},[2068,75807,75808],{},[2071,75809,2861],{},[2092,75811,2861],{"encoding":2094},[1647,75813,75815],{"className":75814},[2059],[2061,75816,75817],{"xmlns":2063},[2065,75818,75819,75825],{},[2068,75820,75821,75823],{},[2071,75822,4342],{},[2071,75824,2849],{},[2092,75826,60030],{"encoding":2094},[1647,75828,75830],{"className":75829},[2059],[2061,75831,75832],{"xmlns":2063},[2065,75833,75834,75840],{},[2068,75835,75836,75838],{},[2071,75837,4342],{},[2071,75839,2849],{},[2092,75841,60030],{"encoding":2094},[55,75843,75844,75847,75848,2697,75880,75696,75897,24333,75940,75759],{},[95,75845,75846],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[1647,75849,75851],{"className":75850},[2059],[2061,75852,75853],{"xmlns":2063},[2065,75854,75855,75877],{},[2068,75856,75857,75859,75861,75863,75865,75867,75869,75871,75873,75875],{},[2071,75858,4342],{},[2071,75860,44630],{},[2071,75862,2849],{},[2075,75864,2077],{},[2071,75866,4342],{},[2071,75868,44630],{},[2071,75870,2849],{},[2075,75872,2084],{"stretchy":2083},[2071,75874,2861],{},[2075,75876,2090],{"stretchy":2083},[2092,75878,75879],{"encoding":2094},"AVC = AVC(Q)",[1647,75881,75883],{"className":75882},[2059],[2061,75884,75885],{"xmlns":2063},[2065,75886,75887,75895],{},[2068,75888,75889],{},[2348,75890,75891,75893],{},[2071,75892,2861],{},[2210,75894,630],{},[2092,75896,42599],{"encoding":2094},[1647,75898,75900],{"className":75899},[2059],[2061,75901,75902],{"xmlns":2063},[2065,75903,75904,75938],{},[2068,75905,75906,75908,75910,75912,75914,75920,75922,75924,75926,75928,75930,75936],{},[2071,75907,4342],{},[2071,75909,44630],{},[2071,75911,2849],{},[2075,75913,2084],{"stretchy":2083},[2348,75915,75916,75918],{},[2071,75917,2861],{},[2210,75919,630],{},[2075,75921,2090],{"stretchy":2083},[2075,75923,2077],{},[2071,75925,2890],{},[2071,75927,2849],{},[2075,75929,2084],{"stretchy":2083},[2348,75931,75932,75934],{},[2071,75933,2861],{},[2210,75935,630],{},[2075,75937,2090],{"stretchy":2083},[2092,75939,73489],{"encoding":2094},[1647,75941,75943],{"className":75942},[2059],[2061,75944,75945],{"xmlns":2063},[2065,75946,75947,75959],{},[2068,75948,75949,75951,75953,75955,75957],{},[2071,75950,2890],{},[2071,75952,2849],{},[2075,75954,2084],{"stretchy":2083},[2071,75956,2861],{},[2075,75958,2090],{"stretchy":2083},[2092,75960,72163],{"encoding":2094},[55,75962,75963,74563,75966,75025,76012,75475,76025,75491,76042,195],{},[95,75964,75965],{},"3.15",[1647,75967,75969],{"className":75968},[2059],[2061,75970,75971],{"xmlns":2063},[2065,75972,75973,76009],{},[2068,75974,75975,75977,75979,75981,75983,75985,75987,75989,75991,75993,75999,76001,76003],{},[2071,75976,543],{},[2071,75978,2849],{},[2075,75980,2077],{},[2210,75982,3194],{},[2075,75984,2176],{},[2210,75986,39270],{},[2071,75988,2861],{},[2075,75990,2303],{},[2210,75992,646],{},[2205,75994,75995,75997],{},[2071,75996,2861],{},[2210,75998,646],{},[2075,76000,2176],{},[2210,76002,2911],{},[2205,76004,76005,76007],{},[2071,76006,2861],{},[2210,76008,654],{},[2092,76010,76011],{"encoding":2094},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[1647,76013,76015],{"className":76014},[2059],[2061,76016,76017],{"xmlns":2063},[2065,76018,76019,76023],{},[2068,76020,76021],{},[2071,76022,2861],{},[2092,76024,2861],{"encoding":2094},[1647,76026,76028],{"className":76027},[2059],[2061,76029,76030],{"xmlns":2063},[2065,76031,76032,76040],{},[2068,76033,76034,76036,76038],{},[2071,76035,4342],{},[2071,76037,44630],{},[2071,76039,2849],{},[2092,76041,59781],{"encoding":2094},[1647,76043,76045],{"className":76044},[2059],[2061,76046,76047],{"xmlns":2063},[2065,76048,76049,76057],{},[2068,76050,76051,76053,76055],{},[2071,76052,4342],{},[2071,76054,44630],{},[2071,76056,2849],{},[2092,76058,59781],{"encoding":2094},[55,76060,76061,76064,76065,76078,76079,76099],{},[95,76062,76063],{},"3.16"," Celkové náklady na výstavbu domu o ",[1647,76066,76068],{"className":76067},[2059],[2061,76069,76070],{"xmlns":2063},[2065,76071,76072,76076],{},[2068,76073,76074],{},[2071,76075,2087],{},[2092,76077,2087],{"encoding":2094}," podlažích se skládají ze tří komponent (1), (2), (3): (1) 10 milionů Kč za pozemek, (2) 0,25 milionu Kč za každé podlaží, (3) zvláštní náklady ",[1647,76080,76082],{"className":76081},[2059],[2061,76083,76084],{"xmlns":2063},[2065,76085,76086,76096],{},[2068,76087,76088,76090,76092,76094],{},[2210,76089,2935],{},[2363,76091,3061],{},[2210,76093,63552],{},[2071,76095,2087],{},[2092,76097,76098],{"encoding":2094},"10\\,000 x"," Kč za podlaží. Určete počet podlaží, které minimalizuje průměrné náklady na jedno podlaží a stanovte příslušnou hodnotu minima průměrných nákladů.",[609,76101,76103],{"id":76102},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[55,76105,76106,76109,76110,75,76132,76158],{},[95,76107,76108],{},"3.17"," Jsou dány ",[1647,76111,76113],{"className":76112},[2059],[2061,76114,76115],{"xmlns":2063},[2065,76116,76117,76129],{},[2068,76118,76119,76121,76123,76125,76127],{},[2071,76120,543],{},[2071,76122,4082],{},[2075,76124,2077],{},[2210,76126,2935],{},[2071,76128,2861],{},[2092,76130,76131],{"encoding":2094},"TR = 10Q",[1647,76133,76135],{"className":76134},[2059],[2061,76136,76137],{"xmlns":2063},[2065,76138,76139,76155],{},[2068,76140,76141,76143,76145,76147,76149,76151,76153],{},[2071,76142,543],{},[2071,76144,2849],{},[2075,76146,2077],{},[2210,76148,3164],{},[2075,76150,2176],{},[2210,76152,670],{},[2071,76154,2861],{},[2092,76156,76157],{"encoding":2094},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[55,76160,76161,76164,76165,6277,76180,76195,76196,835,76218,24333,76245,76267,76268,76302],{},[95,76162,76163],{},"3.18"," Odvoďte, že jestliže ",[1647,76166,76168],{"className":76167},[2059],[2061,76169,76170],{"xmlns":2063},[2065,76171,76172,76178],{},[2068,76173,76174,76176],{},[2071,76175,543],{},[2071,76177,4082],{},[2092,76179,4182],{"encoding":2094},[1647,76181,76183],{"className":76182},[2059],[2061,76184,76185],{"xmlns":2063},[2065,76186,76187,76193],{},[2068,76188,76189,76191],{},[2071,76190,543],{},[2071,76192,2849],{},[2092,76194,3317],{"encoding":2094}," jsou lineární tvaru ",[1647,76197,76199],{"className":76198},[2059],[2061,76200,76201],{"xmlns":2063},[2065,76202,76203,76215],{},[2068,76204,76205,76207,76209,76211,76213],{},[2071,76206,543],{},[2071,76208,4082],{},[2075,76210,2077],{},[2071,76212,55],{},[2071,76214,2861],{},[2092,76216,76217],{"encoding":2094},"TR = pQ",[1647,76219,76221],{"className":76220},[2059],[2061,76222,76223],{"xmlns":2063},[2065,76224,76225,76242],{},[2068,76226,76227,76229,76231,76233,76236,76238,76240],{},[2071,76228,543],{},[2071,76230,2849],{},[2075,76232,2077],{},[2071,76234,76235],{},"m",[2075,76237,2176],{},[2071,76239,41153],{},[2071,76241,2861],{},[2092,76243,76244],{"encoding":2094},"TC = m + nQ",[1647,76246,76248],{"className":76247},[2059],[2061,76249,76250],{"xmlns":2063},[2065,76251,76252,76264],{},[2068,76253,76254,76256,76258,76260,76262],{},[2071,76255,76235],{},[2075,76257,2361],{"separator":2360},[2071,76259,41153],{},[2075,76261,2361],{"separator":2360},[2071,76263,55],{},[2092,76265,76266],{"encoding":2094},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[1647,76269,76271],{"className":76270},[2059],[2061,76272,76273],{"xmlns":2063},[2065,76274,76275,76299],{},[2068,76276,76277,76283,76285],{},[2205,76278,76279,76281],{},[2071,76280,2861],{},[2075,76282,4441],{},[2075,76284,2077],{},[2400,76286,76287],{"scriptlevel":630,"displaystyle":2083},[2403,76288,76289,76291],{},[2071,76290,76235],{},[2068,76292,76293,76295,76297],{},[2071,76294,55],{},[2075,76296,2303],{},[2071,76298,41153],{},[2092,76300,76301],{"encoding":2094},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[55,76304,76305,76109,76308,75,76342,75461,76368,76381,76382,74213,76397,76412,76413,74197,76426,74213,76441,76456],{},[95,76306,76307],{},"3.19",[1647,76309,76311],{"className":76310},[2059],[2061,76312,76313],{"xmlns":2063},[2065,76314,76315,76339],{},[2068,76316,76317,76319,76321,76323,76325,76327,76333,76335,76337],{},[2071,76318,543],{},[2071,76320,4082],{},[2075,76322,2077],{},[2075,76324,2303],{},[2210,76326,646],{},[2205,76328,76329,76331],{},[2071,76330,2861],{},[2210,76332,646],{},[2075,76334,2176],{},[2210,76336,25685],{},[2071,76338,2861],{},[2092,76340,76341],{"encoding":2094},"TR = -2Q^2 + 14Q",[1647,76343,76345],{"className":76344},[2059],[2061,76346,76347],{"xmlns":2063},[2065,76348,76349,76365],{},[2068,76350,76351,76353,76355,76357,76359,76361,76363],{},[2071,76352,543],{},[2071,76354,2849],{},[2075,76356,2077],{},[2210,76358,646],{},[2071,76360,2861],{},[2075,76362,2176],{},[2210,76364,2935],{},[2092,76366,76367],{"encoding":2094},"TC = 2Q + 10",[1647,76369,76371],{"className":76370},[2059],[2061,76372,76373],{"xmlns":2063},[2065,76374,76375,76379],{},[2068,76376,76377],{},[2071,76378,2861],{},[2092,76380,2861],{"encoding":2094},", které maximalizuje zisk ",[1647,76383,76385],{"className":76384},[2059],[2061,76386,76387],{"xmlns":2063},[2065,76388,76389,76395],{},[2068,76390,76391,76393],{},[2071,76392,575],{},[2071,76394,4082],{},[2092,76396,67949],{"encoding":2094},[1647,76398,76400],{"className":76399},[2059],[2061,76401,76402],{"xmlns":2063},[2065,76403,76404,76410],{},[2068,76405,76406,76408],{},[2071,76407,575],{},[2071,76409,4082],{},[2092,76411,67949],{"encoding":2094},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[1647,76414,76416],{"className":76415},[2059],[2061,76417,76418],{"xmlns":2063},[2065,76419,76420,76424],{},[2068,76421,76422],{},[2071,76423,2861],{},[2092,76425,2861],{"encoding":2094},[1647,76427,76429],{"className":76428},[2059],[2061,76430,76431],{"xmlns":2063},[2065,76432,76433,76439],{},[2068,76434,76435,76437],{},[2071,76436,543],{},[2071,76438,4082],{},[2092,76440,4182],{"encoding":2094},[1647,76442,76444],{"className":76443},[2059],[2061,76445,76446],{"xmlns":2063},[2065,76447,76448,76454],{},[2068,76449,76450,76452],{},[2071,76451,543],{},[2071,76453,4082],{},[2092,76455,4182],{"encoding":2094},". (d) Graficky interpretujte.",[55,76458,76459,51980,76462,835,76488,835,76507,75461,76527,76381,76540,74213,76555,76570,76571,76593,76594,75644],{},[95,76460,76461],{},"3.20",[1647,76463,76465],{"className":76464},[2059],[2061,76466,76467],{"xmlns":2063},[2065,76468,76469,76485],{},[2068,76470,76471,76473,76475,76477,76479],{},[2071,76472,575],{},[2075,76474,2077],{},[2210,76476,22881],{},[2075,76478,2303],{},[2205,76480,76481,76483],{},[2071,76482,2861],{},[2210,76484,646],{},[2092,76486,76487],{"encoding":2094},"P = 400 - Q^2",[1647,76489,76491],{"className":76490},[2059],[2061,76492,76493],{"xmlns":2063},[2065,76494,76495,76505],{},[2068,76496,76497,76499,76501,76503],{},[2071,76498,10177],{},[2071,76500,2849],{},[2075,76502,2077],{},[2210,76504,3164],{},[2092,76506,13361],{"encoding":2094},[1647,76508,76510],{"className":76509},[2059],[2061,76511,76512],{"xmlns":2063},[2065,76513,76514,76524],{},[2068,76515,76516,76518,76520,76522],{},[2071,76517,2890],{},[2071,76519,2849],{},[2075,76521,2077],{},[2210,76523,9121],{},[2092,76525,76526],{"encoding":2094},"MC = 20",[1647,76528,76530],{"className":76529},[2059],[2061,76531,76532],{"xmlns":2063},[2065,76533,76534,76538],{},[2068,76535,76536],{},[2071,76537,2861],{},[2092,76539,2861],{"encoding":2094},[1647,76541,76543],{"className":76542},[2059],[2061,76544,76545],{"xmlns":2063},[2065,76546,76547,76553],{},[2068,76548,76549,76551],{},[2071,76550,575],{},[2071,76552,4082],{},[2092,76554,67949],{"encoding":2094},[1647,76556,76558],{"className":76557},[2059],[2061,76559,76560],{"xmlns":2063},[2065,76561,76562,76568],{},[2068,76563,76564,76566],{},[2071,76565,575],{},[2071,76567,4082],{},[2092,76569,67949],{"encoding":2094},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[1647,76572,76574],{"className":76573},[2059],[2061,76575,76576],{"xmlns":2063},[2065,76577,76578,76590],{},[2068,76579,76580,76582,76584,76586,76588],{},[2075,76581,2084],{"stretchy":2083},[2210,76583,630],{},[2075,76585,2361],{"separator":2360},[2210,76587,638],{},[2075,76589,2090],{"stretchy":2083},[2092,76591,76592],{"encoding":2094},"(0, 1)",", druhý do ",[1647,76595,76597],{"className":76596},[2059],[2061,76598,76599],{"xmlns":2063},[2065,76600,76601,76614],{},[2068,76602,76603,76605,76608,76610,76612],{},[2075,76604,2084],{"stretchy":2083},[2210,76606,76607],{},"19",[2075,76609,2361],{"separator":2360},[2210,76611,9121],{},[2075,76613,2090],{"stretchy":2083},[2092,76615,76616],{"encoding":2094},"(19, 20)",[55,76618,76619,76622,76623,2697,76651,76668,76669,195],{},[95,76620,76621],{},"3.21"," Dokažte, že má-li zisk ",[1647,76624,76626],{"className":76625},[2059],[2061,76627,76628],{"xmlns":2063},[2065,76629,76630,76648],{},[2068,76631,76632,76634,76636,76638,76640,76642,76644,76646],{},[2071,76633,575],{},[2071,76635,4082],{},[2075,76637,2077],{},[2071,76639,575],{},[2071,76641,4082],{},[2075,76643,2084],{"stretchy":2083},[2071,76645,2861],{},[2075,76647,2090],{"stretchy":2083},[2092,76649,76650],{"encoding":2094},"PR = PR(Q)",[1647,76652,76654],{"className":76653},[2059],[2061,76655,76656],{"xmlns":2063},[2065,76657,76658,76666],{},[2068,76659,76660],{},[2348,76661,76662,76664],{},[2071,76663,2861],{},[2210,76665,630],{},[2092,76667,42599],{"encoding":2094}," maximum, pak platí ",[1647,76670,76672],{"className":76671},[2059],[2061,76673,76674],{"xmlns":2063},[2065,76675,76676,76708],{},[2068,76677,76678,76680,76682,76684,76690,76692,76694,76696,76698,76700,76706],{},[2071,76679,2890],{},[2071,76681,4082],{},[2075,76683,2084],{"stretchy":2083},[2348,76685,76686,76688],{},[2071,76687,2861],{},[2210,76689,630],{},[2075,76691,2090],{"stretchy":2083},[2075,76693,2077],{},[2071,76695,2890],{},[2071,76697,2849],{},[2075,76699,2084],{"stretchy":2083},[2348,76701,76702,76704],{},[2071,76703,2861],{},[2210,76705,630],{},[2075,76707,2090],{"stretchy":2083},[2092,76709,70115],{"encoding":2094},[55,76711,76712,76715,76716,75,76731,60495,76746,76381,76759,76774,76775,835,76802,76839,76840,835,76867,195],{},[95,76713,76714],{},"3.22"," Pro zadané ",[1647,76717,76719],{"className":76718},[2059],[2061,76720,76721],{"xmlns":2063},[2065,76722,76723,76729],{},[2068,76724,76725,76727],{},[2071,76726,2890],{},[2071,76728,4082],{},[2092,76730,6721],{"encoding":2094},[1647,76732,76734],{"className":76733},[2059],[2061,76735,76736],{"xmlns":2063},[2065,76737,76738,76744],{},[2068,76739,76740,76742],{},[2071,76741,2890],{},[2071,76743,2849],{},[2092,76745,59762],{"encoding":2094},[1647,76747,76749],{"className":76748},[2059],[2061,76750,76751],{"xmlns":2063},[2065,76752,76753,76757],{},[2068,76754,76755],{},[2071,76756,2861],{},[2092,76758,2861],{"encoding":2094},[1647,76760,76762],{"className":76761},[2059],[2061,76763,76764],{"xmlns":2063},[2065,76765,76766,76772],{},[2068,76767,76768,76770],{},[2071,76769,575],{},[2071,76771,4082],{},[2092,76773,67949],{"encoding":2094},". (a) ",[1647,76776,76778],{"className":76777},[2059],[2061,76779,76780],{"xmlns":2063},[2065,76781,76782,76799],{},[2068,76783,76784,76786,76788,76790,76793,76795,76797],{},[2071,76785,2890],{},[2071,76787,4082],{},[2075,76789,2077],{},[2210,76791,76792],{},"236",[2075,76794,2303],{},[2210,76796,46153],{},[2071,76798,2861],{},[2092,76800,76801],{"encoding":2094},"MR = 236 - 16Q",[1647,76803,76805],{"className":76804},[2059],[2061,76806,76807],{"xmlns":2063},[2065,76808,76809,76836],{},[2068,76810,76811,76813,76815,76817,76819,76825,76827,76830,76832,76834],{},[2071,76812,2890],{},[2071,76814,2849],{},[2075,76816,2077],{},[2210,76818,654],{},[2205,76820,76821,76823],{},[2071,76822,2861],{},[2210,76824,646],{},[2075,76826,2303],{},[2210,76828,76829],{},"32",[2071,76831,2861],{},[2075,76833,2176],{},[2210,76835,5831],{},[2092,76837,76838],{"encoding":2094},"MC = 3Q^2 - 32Q + 96",". (b) ",[1647,76841,76843],{"className":76842},[2059],[2061,76844,76845],{"xmlns":2063},[2065,76846,76847,76864],{},[2068,76848,76849,76851,76853,76855,76858,76860,76862],{},[2071,76850,2890],{},[2071,76852,4082],{},[2075,76854,2077],{},[2210,76856,76857],{},"280",[2075,76859,2303],{},[2210,76861,9121],{},[2071,76863,2861],{},[2092,76865,76866],{"encoding":2094},"MR = 280 - 20Q",[1647,76868,76870],{"className":76869},[2059],[2061,76871,76872],{"xmlns":2063},[2065,76873,76874,76901],{},[2068,76875,76876,76878,76880,76882,76885,76891,76893,76895,76897,76899],{},[2071,76877,2890],{},[2071,76879,2849],{},[2075,76881,2077],{},[2210,76883,76884],{},"1,6",[2205,76886,76887,76889],{},[2071,76888,2861],{},[2210,76890,646],{},[2075,76892,2303],{},[2210,76894,39270],{},[2071,76896,2861],{},[2075,76898,2176],{},[2210,76900,3200],{},[2092,76902,76903],{"encoding":2094},"MC = 1{,}6Q^2 - 15Q + 60",[55,76905,76906,76715,76909,75,76924,60495,76939,74197,76952,74213,76967,76774,76982,835,77013,76839,77049,835,77081,77125,77126,835,77158,195],{},[95,76907,76908],{},"3.23",[1647,76910,76912],{"className":76911},[2059],[2061,76913,76914],{"xmlns":2063},[2065,76915,76916,76922],{},[2068,76917,76918,76920],{},[2071,76919,543],{},[2071,76921,4082],{},[2092,76923,4182],{"encoding":2094},[1647,76925,76927],{"className":76926},[2059],[2061,76928,76929],{"xmlns":2063},[2065,76930,76931,76937],{},[2068,76932,76933,76935],{},[2071,76934,543],{},[2071,76936,2849],{},[2092,76938,3317],{"encoding":2094},[1647,76940,76942],{"className":76941},[2059],[2061,76943,76944],{"xmlns":2063},[2065,76945,76946,76950],{},[2068,76947,76948],{},[2071,76949,2861],{},[2092,76951,2861],{"encoding":2094},[1647,76953,76955],{"className":76954},[2059],[2061,76956,76957],{"xmlns":2063},[2065,76958,76959,76965],{},[2068,76960,76961,76963],{},[2071,76962,575],{},[2071,76964,4082],{},[2092,76966,67949],{"encoding":2094},[1647,76968,76970],{"className":76969},[2059],[2061,76971,76972],{"xmlns":2063},[2065,76973,76974,76980],{},[2068,76975,76976,76978],{},[2071,76977,575],{},[2071,76979,4082],{},[2092,76981,67949],{"encoding":2094},[1647,76983,76985],{"className":76984},[2059],[2061,76986,76987],{"xmlns":2063},[2065,76988,76989,77010],{},[2068,76990,76991,76993,76995,76997,77000,77002,77004],{},[2071,76992,543],{},[2071,76994,4082],{},[2075,76996,2077],{},[2210,76998,76999],{},"125",[2071,77001,2861],{},[2075,77003,2303],{},[2205,77005,77006,77008],{},[2071,77007,2861],{},[2210,77009,646],{},[2092,77011,77012],{"encoding":2094},"TR = 125Q - Q^2",[1647,77014,77016],{"className":77015},[2059],[2061,77017,77018],{"xmlns":2063},[2065,77019,77020,77046],{},[2068,77021,77022,77024,77026,77028,77030,77032,77034,77036,77038,77040],{},[2071,77023,543],{},[2071,77025,2849],{},[2075,77027,2077],{},[2210,77029,16845],{},[2075,77031,2176],{},[2210,77033,670],{},[2071,77035,2861],{},[2075,77037,2176],{},[2210,77039,5096],{},[2205,77041,77042,77044],{},[2071,77043,2861],{},[2210,77045,646],{},[2092,77047,77048],{"encoding":2094},"TC = 500 + 5Q + 0{,}5Q^2",[1647,77050,77052],{"className":77051},[2059],[2061,77053,77054],{"xmlns":2063},[2065,77055,77056,77078],{},[2068,77057,77058,77060,77062,77064,77066,77068,77070,77072],{},[2071,77059,543],{},[2071,77061,4082],{},[2075,77063,2077],{},[2210,77065,9121],{},[2071,77067,2861],{},[2075,77069,2303],{},[2210,77071,646],{},[2205,77073,77074,77076],{},[2071,77075,2861],{},[2210,77077,646],{},[2092,77079,77080],{"encoding":2094},"TR = 20Q - 2Q^2",[1647,77082,77084],{"className":77083},[2059],[2061,77085,77086],{"xmlns":2063},[2065,77087,77088,77122],{},[2068,77089,77090,77092,77094,77096,77098,77100,77102,77104,77106,77108,77114,77116],{},[2071,77091,543],{},[2071,77093,2849],{},[2075,77095,2077],{},[2210,77097,646],{},[2075,77099,2176],{},[2210,77101,9121],{},[2071,77103,2861],{},[2075,77105,2303],{},[2210,77107,5672],{},[2205,77109,77110,77112],{},[2071,77111,2861],{},[2210,77113,646],{},[2075,77115,2176],{},[2205,77117,77118,77120],{},[2071,77119,2861],{},[2210,77121,654],{},[2092,77123,77124],{"encoding":2094},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[1647,77127,77129],{"className":77128},[2059],[2061,77130,77131],{"xmlns":2063},[2065,77132,77133,77155],{},[2068,77134,77135,77137,77139,77141,77143,77145,77147,77149],{},[2071,77136,543],{},[2071,77138,4082],{},[2075,77140,2077],{},[2210,77142,662],{},[2071,77144,2861],{},[2075,77146,2303],{},[2210,77148,26528],{},[2205,77150,77151,77153],{},[2071,77152,2861],{},[2210,77154,646],{},[2092,77156,77157],{"encoding":2094},"TR = 4Q - 0{,}25Q^2",[1647,77159,77161],{"className":77160},[2059],[2061,77162,77163],{"xmlns":2063},[2065,77164,77165,77213],{},[2068,77166,77167,77169,77171,77173,77175,77177,77179,77181,77183,77199,77201],{},[2071,77168,543],{},[2071,77170,2849],{},[2075,77172,2077],{},[2210,77174,662],{},[2075,77176,2176],{},[2210,77178,646],{},[2071,77180,2861],{},[2075,77182,2303],{},[2400,77184,77185],{"scriptlevel":630,"displaystyle":2083},[2403,77186,77187,77197],{},[2068,77188,77189,77191],{},[2210,77190,654],{},[2205,77192,77193,77195],{},[2071,77194,2861],{},[2210,77196,646],{},[2210,77198,2935],{},[2075,77200,2176],{},[2400,77202,77203],{"scriptlevel":630,"displaystyle":2083},[2403,77204,77205,77211],{},[2205,77206,77207,77209],{},[2071,77208,2861],{},[2210,77210,654],{},[2210,77212,9121],{},[2092,77214,77215],{"encoding":2094},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[55,77217,77218,77221,77222,77252,77253,77285,77286,24333,77316,77346],{},[95,77219,77220],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[1647,77223,77225],{"className":77224},[2059],[2061,77226,77227],{"xmlns":2063},[2065,77228,77229,77249],{},[2068,77230,77231,77237,77239,77241,77243],{},[2348,77232,77233,77235],{},[2071,77234,575],{},[2210,77236,638],{},[2075,77238,2077],{},[2210,77240,16845],{},[2075,77242,2303],{},[2348,77244,77245,77247],{},[2071,77246,2861],{},[2210,77248,638],{},[2092,77250,77251],{"encoding":2094},"P_1 = 500 - Q_1",", pro velkoodběratele ",[1647,77254,77256],{"className":77255},[2059],[2061,77257,77258],{"xmlns":2063},[2065,77259,77260,77282],{},[2068,77261,77262,77268,77270,77272,77274,77276],{},[2348,77263,77264,77266],{},[2071,77265,575],{},[2210,77267,646],{},[2075,77269,2077],{},[2210,77271,33108],{},[2075,77273,2303],{},[2210,77275,69029],{},[2348,77277,77278,77280],{},[2071,77279,2861],{},[2210,77281,646],{},[2092,77283,77284],{"encoding":2094},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[1647,77287,77289],{"className":77288},[2059],[2061,77290,77291],{"xmlns":2063},[2065,77292,77293,77313],{},[2068,77294,77295,77297,77299,77301,77303,77305,77307,77309,77311],{},[2071,77296,543],{},[2071,77298,2849],{},[2075,77300,2077],{},[2210,77302,3194],{},[2363,77304,3061],{},[2210,77306,63552],{},[2075,77308,2176],{},[2210,77310,9121],{},[2071,77312,2861],{},[2092,77314,77315],{"encoding":2094},"TC = 50\\,000 + 20Q",[1647,77317,77319],{"className":77318},[2059],[2061,77320,77321],{"xmlns":2063},[2065,77322,77323,77343],{},[2068,77324,77325,77327,77329,77335,77337],{},[2071,77326,2861],{},[2075,77328,2077],{},[2348,77330,77331,77333],{},[2071,77332,2861],{},[2210,77334,638],{},[2075,77336,2176],{},[2348,77338,77339,77341],{},[2071,77340,2861],{},[2210,77342,646],{},[2092,77344,77345],{"encoding":2094},"Q = Q_1 + Q_2",". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk v obou případech.",[55,77348,77349,77352,77353,77383,77384,77285,77416,24333,77446,77475],{},[95,77350,77351],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[1647,77354,77356],{"className":77355},[2059],[2061,77357,77358],{"xmlns":2063},[2065,77359,77360,77380],{},[2068,77361,77362,77368,77370,77372,77374],{},[2348,77363,77364,77366],{},[2071,77365,575],{},[2210,77367,638],{},[2075,77369,2077],{},[2210,77371,33108],{},[2075,77373,2303],{},[2348,77375,77376,77378],{},[2071,77377,2861],{},[2210,77379,638],{},[2092,77381,77382],{"encoding":2094},"P_1 = 300 - Q_1",", pro zahraniční trh ",[1647,77385,77387],{"className":77386},[2059],[2061,77388,77389],{"xmlns":2063},[2065,77390,77391,77413],{},[2068,77392,77393,77399,77401,77403,77405,77407],{},[2348,77394,77395,77397],{},[2071,77396,575],{},[2210,77398,646],{},[2075,77400,2077],{},[2210,77402,8464],{},[2075,77404,2303],{},[2210,77406,5096],{},[2348,77408,77409,77411],{},[2071,77410,2861],{},[2210,77412,646],{},[2092,77414,77415],{"encoding":2094},"P_2 = 200 - 0{,}5Q_2",[1647,77417,77419],{"className":77418},[2059],[2061,77420,77421],{"xmlns":2063},[2065,77422,77423,77443],{},[2068,77424,77425,77427,77429,77431,77433,77435,77437,77439,77441],{},[2071,77426,543],{},[2071,77428,2849],{},[2075,77430,2077],{},[2210,77432,670],{},[2363,77434,3061],{},[2210,77436,63552],{},[2075,77438,2176],{},[2210,77440,3164],{},[2071,77442,2861],{},[2092,77444,77445],{"encoding":2094},"TC = 5\\,000 + 100Q",[1647,77447,77449],{"className":77448},[2059],[2061,77450,77451],{"xmlns":2063},[2065,77452,77453,77473],{},[2068,77454,77455,77457,77459,77465,77467],{},[2071,77456,2861],{},[2075,77458,2077],{},[2348,77460,77461,77463],{},[2071,77462,2861],{},[2210,77464,638],{},[2075,77466,2176],{},[2348,77468,77469,77471],{},[2071,77470,2861],{},[2210,77472,646],{},[2092,77474,77345],{"encoding":2094},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[609,77477,77479],{"id":77478},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[55,77481,77482,77485,77486,77533,77534,77551],{},[95,77483,77484],{},"3.26"," Jsou dány celkové variabilní náklady ",[1647,77487,77489],{"className":77488},[2059],[2061,77490,77491],{"xmlns":2063},[2065,77492,77493,77530],{},[2068,77494,77495,77497,77499,77501,77503,77506,77512,77514,77517,77523,77525,77528],{},[2071,77496,543],{},[2071,77498,44630],{},[2071,77500,2849],{},[2075,77502,2077],{},[2210,77504,77505],{},"0,85",[2205,77507,77508,77510],{},[2071,77509,2861],{},[2210,77511,654],{},[2075,77513,2303],{},[2210,77515,77516],{},"11,9",[2205,77518,77519,77521],{},[2071,77520,2861],{},[2210,77522,646],{},[2075,77524,2176],{},[2210,77526,77527],{},"102",[2071,77529,2861],{},[2092,77531,77532],{"encoding":2094},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[1647,77535,77537],{"className":77536},[2059],[2061,77538,77539],{"xmlns":2063},[2065,77540,77541,77549],{},[2068,77542,77543],{},[2205,77544,77545,77547],{},[2071,77546,575],{},[2075,77548,4441],{},[2092,77550,4491],{"encoding":2094}," nabídky a konstruujte nabídku. Graficky interpretujte.",[55,77553,77554,75312,77557,77593],{},[95,77555,77556],{},"3.27",[1647,77558,77560],{"className":77559},[2059],[2061,77561,77562],{"xmlns":2063},[2065,77563,77564,77590],{},[2068,77565,77566,77568,77570,77572,77574,77580,77582,77584,77586,77588],{},[2071,77567,2890],{},[2071,77569,2849],{},[2075,77571,2077],{},[2210,77573,2995],{},[2205,77575,77576,77578],{},[2071,77577,2861],{},[2210,77579,646],{},[2075,77581,2303],{},[2210,77583,68910],{},[2071,77585,2861],{},[2075,77587,2176],{},[2210,77589,33770],{},[2092,77591,77592],{"encoding":2094},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[55,77595,77596,74563,77599,77593],{},[95,77597,77598],{},"3.28",[1647,77600,77602],{"className":77601},[2059],[2061,77603,77604],{"xmlns":2063},[2065,77605,77606,77642],{},[2068,77607,77608,77610,77612,77614,77616,77622,77624,77626,77632,77634,77636,77638,77640],{},[2071,77609,543],{},[2071,77611,2849],{},[2075,77613,2077],{},[2210,77615,5096],{},[2205,77617,77618,77620],{},[2071,77619,2861],{},[2210,77621,654],{},[2075,77623,2303],{},[2210,77625,686],{},[2205,77627,77628,77630],{},[2071,77629,2861],{},[2210,77631,646],{},[2075,77633,2176],{},[2210,77635,3200],{},[2071,77637,2861],{},[2075,77639,2176],{},[2210,77641,16845],{},[2092,77643,77644],{"encoding":2094},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[84,77646,321],{"id":320},[89,77648,77649,77677,77722,77794,77859,77899,77991,78097,78137,78251,78344,78408,78440,78500,78506,78570,78619,78673,78781,78836],{},[92,77650,77651,1445,77653,77676],{},[95,77652,60220],{},[1647,77654,77656],{"className":77655},[2059],[2061,77657,77658],{"xmlns":2063},[2065,77659,77660,77674],{},[2068,77661,77662,77664,77666,77668,77670,77672],{},[2071,77663,543],{},[2071,77665,4082],{},[2075,77667,2077],{},[2071,77669,575],{},[2075,77671,3251],{},[2071,77673,2861],{},[2092,77675,71182],{"encoding":2094}," — křivka celkového příjmu (total revenue curve).",[92,77678,77679,1445,77681,77721],{},[95,77680,60806],{},[1647,77682,77684],{"className":77683},[2059],[2061,77685,77686],{"xmlns":2063},[2065,77687,77688,77718],{},[2068,77689,77690,77692,77694,77696,77708,77710,77712,77714,77716],{},[2071,77691,4342],{},[2071,77693,4082],{},[2075,77695,2077],{},[2400,77697,77698],{"scriptlevel":630,"displaystyle":2083},[2403,77699,77700,77706],{},[2068,77701,77702,77704],{},[2071,77703,543],{},[2071,77705,4082],{},[2071,77707,2861],{},[2075,77709,2077],{},[2071,77711,4271],{},[2075,77713,2084],{"stretchy":2083},[2071,77715,2861],{},[2075,77717,2090],{"stretchy":2083},[2092,77719,77720],{"encoding":2094},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[92,77723,77724,1445,77726,77762,77763,77778,77779,195],{},[95,77725,60954],{},[1647,77727,77729],{"className":77728},[2059],[2061,77730,77731],{"xmlns":2063},[2065,77732,77733,77759],{},[2068,77734,77735,77737,77739,77741],{},[2071,77736,2890],{},[2071,77738,4082],{},[2075,77740,2077],{},[2400,77742,77743],{"scriptlevel":630,"displaystyle":2083},[2403,77744,77745,77753],{},[2068,77746,77747,77749,77751],{},[2071,77748,2273],{"mathvariant":2450},[2071,77750,543],{},[2071,77752,4082],{},[2068,77754,77755,77757],{},[2071,77756,2273],{"mathvariant":2450},[2071,77758,2861],{},[2092,77760,77761],{"encoding":2094},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[1647,77764,77766],{"className":77765},[2059],[2061,77767,77768],{"xmlns":2063},[2065,77769,77770,77776],{},[2068,77771,77772,77774],{},[2071,77773,543],{},[2071,77775,4082],{},[2092,77777,4182],{"encoding":2094},"; pro lineární poptávku má sklon dvojnásobný vůči ",[1647,77780,77782],{"className":77781},[2059],[2061,77783,77784],{"xmlns":2063},[2065,77785,77786,77792],{},[2068,77787,77788,77790],{},[2071,77789,4342],{},[2071,77791,4082],{},[2092,77793,59915],{"encoding":2094},[92,77795,77796,1445,77799,835,77829,195],{},[95,77797,77798],{},"Diferenciál příjmu\u002Fnákladů",[1647,77800,77802],{"className":77801},[2059],[2061,77803,77804],{"xmlns":2063},[2065,77805,77806,77826],{},[2068,77807,77808,77810,77812,77814,77816,77818,77820,77822,77824],{},[2071,77809,2961],{"mathvariant":2450},[2071,77811,543],{},[2071,77813,4082],{},[2075,77815,2803],{},[2071,77817,2890],{},[2071,77819,4082],{},[2363,77821,3061],{},[2071,77823,2273],{"mathvariant":2450},[2071,77825,2861],{},[2092,77827,77828],{"encoding":2094},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[1647,77830,77832],{"className":77831},[2059],[2061,77833,77834],{"xmlns":2063},[2065,77835,77836,77856],{},[2068,77837,77838,77840,77842,77844,77846,77848,77850,77852,77854],{},[2071,77839,2961],{"mathvariant":2450},[2071,77841,543],{},[2071,77843,2849],{},[2075,77845,2803],{},[2071,77847,2890],{},[2071,77849,2849],{},[2363,77851,3061],{},[2071,77853,2273],{"mathvariant":2450},[2071,77855,2861],{},[2092,77857,77858],{"encoding":2094},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[92,77860,77861,1445,77863,195],{},[95,77862,63076],{},[1647,77864,77866],{"className":77865},[2059],[2061,77867,77868],{"xmlns":2063},[2065,77869,77870,77896],{},[2068,77871,77872,77874,77876,77878,77880,77882,77884,77886,77888,77890,77892,77894],{},[2071,77873,543],{},[2071,77875,2849],{},[2075,77877,2077],{},[2071,77879,10177],{},[2071,77881,2849],{},[2075,77883,2176],{},[2071,77885,543],{},[2071,77887,44630],{},[2071,77889,2849],{},[2075,77891,2084],{"stretchy":2083},[2071,77893,2861],{},[2075,77895,2090],{"stretchy":2083},[2092,77897,77898],{"encoding":2094},"TC = FC + TVC(Q)",[92,77900,77901,1445,77904,835,77919,1445,77921,835,77944,1445,77947,195],{},[95,77902,77903],{},"Fixní náklady",[1647,77905,77907],{"className":77906},[2059],[2061,77908,77909],{"xmlns":2063},[2065,77910,77911,77917],{},[2068,77912,77913,77915],{},[2071,77914,10177],{},[2071,77916,2849],{},[2092,77918,59961],{"encoding":2094},[95,77920,63229],{},[1647,77922,77924],{"className":77923},[2059],[2061,77925,77926],{"xmlns":2063},[2065,77927,77928,77942],{},[2068,77929,77930,77932,77934,77936,77938,77940],{},[2071,77931,543],{},[2071,77933,44630],{},[2071,77935,2849],{},[2075,77937,2084],{"stretchy":2083},[2071,77939,2861],{},[2075,77941,2090],{"stretchy":2083},[2092,77943,63226],{"encoding":2094},[95,77945,77946],{},"variabilní náklady na jednotku",[1647,77948,77950],{"className":77949},[2059],[2061,77951,77952],{"xmlns":2063},[2065,77953,77954,77988],{},[2068,77955,77956,77958,77960,77962,77964,77966,77968],{},[2071,77957,44630],{},[2071,77959,2849],{},[2075,77961,2084],{"stretchy":2083},[2071,77963,2861],{},[2075,77965,2090],{"stretchy":2083},[2075,77967,2077],{},[2400,77969,77970],{"scriptlevel":630,"displaystyle":2083},[2403,77971,77972,77986],{},[2068,77973,77974,77976,77978,77980,77982,77984],{},[2071,77975,543],{},[2071,77977,44630],{},[2071,77979,2849],{},[2075,77981,2084],{"stretchy":2083},[2071,77983,2861],{},[2075,77985,2090],{"stretchy":2083},[2071,77987,2861],{},[2092,77989,77990],{"encoding":2094},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[92,77992,77993,1445,77995,835,78025,1445,78028,835,78060,1445,78063,195],{},[95,77994,63237],{},[1647,77996,77998],{"className":77997},[2059],[2061,77999,78000],{"xmlns":2063},[2065,78001,78002,78022],{},[2068,78003,78004,78006,78008,78010],{},[2071,78005,4342],{},[2071,78007,2849],{},[2075,78009,2077],{},[2400,78011,78012],{"scriptlevel":630,"displaystyle":2083},[2403,78013,78014,78020],{},[2068,78015,78016,78018],{},[2071,78017,543],{},[2071,78019,2849],{},[2071,78021,2861],{},[2092,78023,78024],{"encoding":2094},"AC = \\tfrac{TC}{Q}",[95,78026,78027],{},"průměrné fixní",[1647,78029,78031],{"className":78030},[2059],[2061,78032,78033],{"xmlns":2063},[2065,78034,78035,78057],{},[2068,78036,78037,78039,78041,78043,78045],{},[2071,78038,4342],{},[2071,78040,10177],{},[2071,78042,2849],{},[2075,78044,2077],{},[2400,78046,78047],{"scriptlevel":630,"displaystyle":2083},[2403,78048,78049,78055],{},[2068,78050,78051,78053],{},[2071,78052,10177],{},[2071,78054,2849],{},[2071,78056,2861],{},[2092,78058,78059],{"encoding":2094},"AFC = \\tfrac{FC}{Q}",[95,78061,78062],{},"průměrné variabilní",[1647,78064,78066],{"className":78065},[2059],[2061,78067,78068],{"xmlns":2063},[2065,78069,78070,78094],{},[2068,78071,78072,78074,78076,78078,78080],{},[2071,78073,4342],{},[2071,78075,44630],{},[2071,78077,2849],{},[2075,78079,2077],{},[2400,78081,78082],{"scriptlevel":630,"displaystyle":2083},[2403,78083,78084,78092],{},[2068,78085,78086,78088,78090],{},[2071,78087,543],{},[2071,78089,44630],{},[2071,78091,2849],{},[2071,78093,2861],{},[2092,78095,78096],{"encoding":2094},"AVC = \\tfrac{TVC}{Q}",[92,78098,78099,1445,78101,195],{},[95,78100,64424],{},[1647,78102,78104],{"className":78103},[2059],[2061,78105,78106],{"xmlns":2063},[2065,78107,78108,78134],{},[2068,78109,78110,78112,78114,78116],{},[2071,78111,2890],{},[2071,78113,2849],{},[2075,78115,2077],{},[2400,78117,78118],{"scriptlevel":630,"displaystyle":2083},[2403,78119,78120,78128],{},[2068,78121,78122,78124,78126],{},[2071,78123,2273],{"mathvariant":2450},[2071,78125,543],{},[2071,78127,2849],{},[2068,78129,78130,78132],{},[2071,78131,2273],{"mathvariant":2450},[2071,78133,2861],{},[2092,78135,78136],{"encoding":2094},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[92,78138,78139,1445,78141,78189,78190,78203,78204,835,78219,835,78236,195],{},[95,78140,65322],{},[1647,78142,78144],{"className":78143},[2059],[2061,78145,78146],{"xmlns":2063},[2065,78147,78148,78186],{},[2068,78149,78150,78152,78154,78156,78158,78160,78162,78164,78166,78168,78170,78176,78178,78180],{},[2071,78151,543],{},[2071,78153,2849],{},[2075,78155,2077],{},[2071,78157,10177],{},[2071,78159,2849],{},[2075,78161,2176],{},[2071,78163,69],{},[2071,78165,2861],{},[2075,78167,2176],{},[2071,78169,2179],{},[2205,78171,78172,78174],{},[2071,78173,2861],{},[2210,78175,646],{},[2075,78177,2176],{},[2071,78179,2222],{},[2205,78181,78182,78184],{},[2071,78183,2861],{},[2210,78185,654],{},[2092,78187,78188],{"encoding":2094},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[1647,78191,78193],{"className":78192},[2059],[2061,78194,78195],{"xmlns":2063},[2065,78196,78197,78201],{},[2068,78198,78199],{},[2071,78200,10871],{},[2092,78202,10871],{"encoding":2094},"-průběhem ",[1647,78205,78207],{"className":78206},[2059],[2061,78208,78209],{"xmlns":2063},[2065,78210,78211,78217],{},[2068,78212,78213,78215],{},[2071,78214,4342],{},[2071,78216,2849],{},[2092,78218,60030],{"encoding":2094},[1647,78220,78222],{"className":78221},[2059],[2061,78223,78224],{"xmlns":2063},[2065,78225,78226,78234],{},[2068,78227,78228,78230,78232],{},[2071,78229,4342],{},[2071,78231,44630],{},[2071,78233,2849],{},[2092,78235,59781],{"encoding":2094},[1647,78237,78239],{"className":78238},[2059],[2061,78240,78241],{"xmlns":2063},[2065,78242,78243,78249],{},[2068,78244,78245,78247],{},[2071,78246,2890],{},[2071,78248,2849],{},[2092,78250,59762],{"encoding":2094},[92,78252,78253,78255,78256,11525,78271,78312,78313,65967,78328,78343],{},[95,78254,66404],{},": v bodě minima ",[1647,78257,78259],{"className":78258},[2059],[2061,78260,78261],{"xmlns":2063},[2065,78262,78263,78269],{},[2068,78264,78265,78267],{},[2071,78266,4342],{},[2071,78268,2849],{},[2092,78270,60030],{"encoding":2094},[1647,78272,78274],{"className":78273},[2059],[2061,78275,78276],{"xmlns":2063},[2065,78277,78278,78310],{},[2068,78279,78280,78282,78284,78286,78292,78294,78296,78298,78300,78302,78308],{},[2071,78281,4342],{},[2071,78283,2849],{},[2075,78285,2084],{"stretchy":2083},[2348,78287,78288,78290],{},[2071,78289,2861],{},[2210,78291,630],{},[2075,78293,2090],{"stretchy":2083},[2075,78295,2077],{},[2071,78297,2890],{},[2071,78299,2849],{},[2075,78301,2084],{"stretchy":2083},[2348,78303,78304,78306],{},[2071,78305,2861],{},[2210,78307,630],{},[2075,78309,2090],{"stretchy":2083},[2092,78311,67039],{"encoding":2094},"; geometricky ",[1647,78314,78316],{"className":78315},[2059],[2061,78317,78318],{"xmlns":2063},[2065,78319,78320,78326],{},[2068,78321,78322,78324],{},[2071,78323,2890],{},[2071,78325,2849],{},[2092,78327,59762],{"encoding":2094},[1647,78329,78331],{"className":78330},[2059],[2061,78332,78333],{"xmlns":2063},[2065,78334,78335,78341],{},[2068,78336,78337,78339],{},[2071,78338,4342],{},[2071,78340,2849],{},[2092,78342,60030],{"encoding":2094}," v jejím minimu.",[92,78345,78346,78255,78348,11525,78365,195],{},[95,78347,67754],{},[1647,78349,78351],{"className":78350},[2059],[2061,78352,78353],{"xmlns":2063},[2065,78354,78355,78363],{},[2068,78356,78357,78359,78361],{},[2071,78358,4342],{},[2071,78360,44630],{},[2071,78362,2849],{},[2092,78364,59781],{"encoding":2094},[1647,78366,78368],{"className":78367},[2059],[2061,78369,78370],{"xmlns":2063},[2065,78371,78372,78406],{},[2068,78373,78374,78376,78378,78380,78382,78388,78390,78392,78394,78396,78398,78404],{},[2071,78375,4342],{},[2071,78377,44630],{},[2071,78379,2849],{},[2075,78381,2084],{"stretchy":2083},[2348,78383,78384,78386],{},[2071,78385,2861],{},[2210,78387,630],{},[2075,78389,2090],{"stretchy":2083},[2075,78391,2077],{},[2071,78393,2890],{},[2071,78395,2849],{},[2075,78397,2084],{"stretchy":2083},[2348,78399,78400,78402],{},[2071,78401,2861],{},[2210,78403,630],{},[2075,78405,2090],{"stretchy":2083},[2092,78407,73489],{"encoding":2094},[92,78409,78410,1445,78412,78439],{},[95,78411,67933],{},[1647,78413,78415],{"className":78414},[2059],[2061,78416,78417],{"xmlns":2063},[2065,78418,78419,78437],{},[2068,78420,78421,78423,78425,78427,78429,78431,78433,78435],{},[2071,78422,575],{},[2071,78424,4082],{},[2075,78426,2077],{},[2071,78428,543],{},[2071,78430,4082],{},[2075,78432,2303],{},[2071,78434,543],{},[2071,78436,2849],{},[2092,78438,59670],{"encoding":2094}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[92,78441,78442,11156,78444,78446,78447,78473,78474,78499],{},[95,78443,68795],{},[3982,78445,68058],{},") — hodnoty ",[1647,78448,78450],{"className":78449},[2059],[2061,78451,78452],{"xmlns":2063},[2065,78453,78454,78470],{},[2068,78455,78456,78462,78464],{},[2348,78457,78458,78460],{},[2071,78459,2861],{},[2071,78461,4342],{},[2075,78463,2361],{"separator":2360},[2348,78465,78466,78468],{},[2071,78467,2861],{},[2071,78469,25992],{},[2092,78471,78472],{"encoding":2094},"Q_A, Q_B"," splňující ",[1647,78475,78477],{"className":78476},[2059],[2061,78478,78479],{"xmlns":2063},[2065,78480,78481,78497],{},[2068,78482,78483,78485,78487,78489,78491,78493,78495],{},[2071,78484,575],{},[2071,78486,4082],{},[2075,78488,2084],{"stretchy":2083},[2071,78490,2861],{},[2075,78492,2090],{"stretchy":2083},[2075,78494,2077],{},[2210,78496,630],{},[2092,78498,68335],{"encoding":2094},"; oddělují pásma ztráty a zisku.",[92,78501,78502,78505],{},[95,78503,78504],{},"Práh rentability"," — stav firmy v bodě zvratu.",[92,78507,78508,78510,78511,11525,78528,78569],{},[95,78509,69849],{}," — v bodě maxima zisku ",[1647,78512,78514],{"className":78513},[2059],[2061,78515,78516],{"xmlns":2063},[2065,78517,78518,78526],{},[2068,78519,78520],{},[2348,78521,78522,78524],{},[2071,78523,2861],{},[2210,78525,630],{},[2092,78527,42599],{"encoding":2094},[1647,78529,78531],{"className":78530},[2059],[2061,78532,78533],{"xmlns":2063},[2065,78534,78535,78567],{},[2068,78536,78537,78539,78541,78543,78549,78551,78553,78555,78557,78559,78565],{},[2071,78538,2890],{},[2071,78540,4082],{},[2075,78542,2084],{"stretchy":2083},[2348,78544,78545,78547],{},[2071,78546,2861],{},[2210,78548,630],{},[2075,78550,2090],{"stretchy":2083},[2075,78552,2077],{},[2071,78554,2890],{},[2071,78556,2849],{},[2075,78558,2084],{"stretchy":2083},[2348,78560,78561,78563],{},[2071,78562,2861],{},[2210,78564,630],{},[2075,78566,2090],{"stretchy":2083},[2092,78568,70115],{"encoding":2094}," (3.13).",[92,78571,78572,23040,78574,11525,78593,78618],{},[95,78573,71142],{},[1647,78575,78577],{"className":78576},[2059],[2061,78578,78579],{"xmlns":2063},[2065,78580,78581,78590],{},[2068,78582,78583,78585,78587],{},[2071,78584,575],{},[2075,78586,2077],{},[2363,78588,78589],{},"konst",[2092,78591,78592],{"encoding":2094},"P = \\text{konst}",[1647,78594,78596],{"className":78595},[2059],[2061,78597,78598],{"xmlns":2063},[2065,78599,78600,78616],{},[2068,78601,78602,78604,78606,78608,78610,78612,78614],{},[2071,78603,575],{},[2075,78605,2077],{},[2071,78607,2890],{},[2071,78609,2849],{},[2075,78611,2084],{"stretchy":2083},[2071,78613,2861],{},[2075,78615,2090],{"stretchy":2083},[2092,78617,71836],{"encoding":2094}," (3.14).",[92,78620,78621,78624,78625,78654,78655,78672],{},[95,78622,78623],{},"Shutdown point"," — bod ",[1647,78626,78628],{"className":78627},[2059],[2061,78629,78630],{"xmlns":2063},[2065,78631,78632,78652],{},[2068,78633,78634,78636,78642,78644,78650],{},[2075,78635,2084],{"stretchy":2083},[2205,78637,78638,78640],{},[2071,78639,2861],{},[2075,78641,4441],{},[2075,78643,2361],{"separator":2360},[2205,78645,78646,78648],{},[2071,78647,575],{},[2075,78649,4441],{},[2075,78651,2090],{"stretchy":2083},[2092,78653,72125],{"encoding":2094}," v minimu ",[1647,78656,78658],{"className":78657},[2059],[2061,78659,78660],{"xmlns":2063},[2065,78661,78662,78670],{},[2068,78663,78664,78666,78668],{},[2071,78665,4342],{},[2071,78667,44630],{},[2071,78669,2849],{},[2092,78671,59781],{"encoding":2094},"; pod ním se firmě nevyplatí produkovat.",[92,78674,78675,1445,78678,6560,78713,72395,78734,78747,78748,78763,78764,195],{},[95,78676,78677],{},"Funkce nabídky firmy",[1647,78679,78681],{"className":78680},[2059],[2061,78682,78683],{"xmlns":2063},[2065,78684,78685,78711],{},[2068,78686,78687,78689,78691,78693,78695,78697,78699,78701,78703,78705,78707,78709],{},[2071,78688,575],{},[2075,78690,2077],{},[2071,78692,532],{},[2075,78694,2084],{"stretchy":2083},[2071,78696,2861],{},[2075,78698,2090],{"stretchy":2083},[2075,78700,2077],{},[2071,78702,2890],{},[2071,78704,2849],{},[2075,78706,2084],{"stretchy":2083},[2071,78708,2861],{},[2075,78710,2090],{"stretchy":2083},[2092,78712,73592],{"encoding":2094},[1647,78714,78716],{"className":78715},[2059],[2061,78717,78718],{"xmlns":2063},[2065,78719,78720,78732],{},[2068,78721,78722,78724,78726],{},[2071,78723,2861],{},[2075,78725,4572],{},[2205,78727,78728,78730],{},[2071,78729,2861],{},[2075,78731,4441],{},[2092,78733,72394],{"encoding":2094},[1647,78735,78737],{"className":78736},[2059],[2061,78738,78739],{"xmlns":2063},[2065,78740,78741,78745],{},[2068,78742,78743],{},[2210,78744,630],{},[2092,78746,630],{"encoding":2094}," (3.15); vychází z rostoucí části ",[1647,78749,78751],{"className":78750},[2059],[2061,78752,78753],{"xmlns":2063},[2065,78754,78755,78761],{},[2068,78756,78757,78759],{},[2071,78758,2890],{},[2071,78760,2849],{},[2092,78762,59762],{"encoding":2094}," nad minimem ",[1647,78765,78767],{"className":78766},[2059],[2061,78768,78769],{"xmlns":2063},[2065,78770,78771,78779],{},[2068,78772,78773,78775,78777],{},[2071,78774,4342],{},[2071,78776,44630],{},[2071,78778,2849],{},[2092,78780,59781],{"encoding":2094},[92,78782,78783,7102,78785,78806,78807,195],{},[95,78784,54375],{},[1647,78786,78788],{"className":78787},[2059],[2061,78789,78790],{"xmlns":2063},[2065,78791,78792,78804],{},[2068,78793,78794,78796,78798],{},[2071,78795,575],{},[2075,78797,2077],{},[2205,78799,78800,78802],{},[2071,78801,575],{},[2075,78803,4441],{},[2092,78805,4444],{"encoding":2094}," konstantní ⇒ ",[1647,78808,78810],{"className":78809},[2059],[2061,78811,78812],{"xmlns":2063},[2065,78813,78814,78834],{},[2068,78815,78816,78818,78820,78822,78824,78826,78828],{},[2071,78817,4342],{},[2071,78819,4082],{},[2075,78821,2077],{},[2071,78823,2890],{},[2071,78825,4082],{},[2075,78827,2077],{},[2205,78829,78830,78832],{},[2071,78831,575],{},[2075,78833,4441],{},[2092,78835,63068],{"encoding":2094},[92,78837,78838,78841],{},[95,78839,78840],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[84,78843,3866],{"id":3865},[89,78845,78846,78866,78878],{},[92,78847,78848,1445,78850,835,78853,835,78856,835,78859,835,78862],{},[95,78849,55018],{},[69,78851,13672],{"className":78852,"dataFsResolvedFilePath":13670,"href":13671},[62],[69,78854,3913],{"className":78855,"dataFsResolvedFilePath":3911,"href":3912},[62],[69,78857,2431],{"className":78858,"dataFsResolvedFilePath":4005,"href":4006},[62],[69,78860,3890],{"className":78861,"dataFsResolvedFilePath":3888,"href":3889},[62],[69,78863,78865],{"className":78864,"dataFsResolvedFilePath":10942,"href":10943},[62],"Produkční funkce",[92,78867,78868,1445,78870,835,78874],{},[95,78869,39729],{},[69,78871,78873],{"className":78872,"dataFsResolvedFilePath":55057,"href":55058},[62],"KS 1. blok — souhrn",[69,78875,78877],{"className":78876,"dataFsResolvedFilePath":39733,"href":39734},[62],"KS 2. blok — souhrn",[92,78879,78880,1445,78882],{},[95,78881,17937],{},[69,78883,17941],{"className":78884,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":78886},[78887,78888,78895,78901,78905,78906,78910,78911,78912,78913,78919,78920],{"id":55251,"depth":7,"text":55252},{"id":60208,"depth":7,"text":60209,"children":78889},[78890,78891,78892,78893,78894],{"id":60219,"depth":4,"text":60220},{"id":60805,"depth":4,"text":60806},{"id":60953,"depth":4,"text":60954},{"id":61695,"depth":4,"text":61696},{"id":62350,"depth":4,"text":62351},{"id":63071,"depth":7,"text":63072,"children":78896},[78897,78898,78899,78900],{"id":63075,"depth":4,"text":63076},{"id":63236,"depth":4,"text":63237},{"id":64423,"depth":4,"text":64424},{"id":65321,"depth":4,"text":65322},{"id":66403,"depth":7,"text":66404,"children":78902},[78903,78904],{"id":86,"depth":4,"text":87},{"id":67753,"depth":4,"text":67754},{"id":67927,"depth":7,"text":67928},{"id":69848,"depth":7,"text":69849,"children":78907},[78908,78909],{"id":69862,"depth":4,"text":87},{"id":71141,"depth":4,"text":71142},{"id":71773,"depth":7,"text":71774},{"id":73239,"depth":7,"text":73240},{"id":54177,"depth":7,"text":54178},{"id":73700,"depth":7,"text":73701,"children":78914},[78915,78916,78917,78918],{"id":73704,"depth":4,"text":73705},{"id":74556,"depth":4,"text":74557},{"id":76102,"depth":4,"text":76103},{"id":77478,"depth":4,"text":77479},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":59590,"description":156},[9647,3938],"topics\u002Fprijem-naklady-zisk",[17,78927,78928,59642,78929,78930,78931],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":78934,"title":78935,"body":78936,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":91031,"navigation":168,"path":91032,"seo":91033,"sources":91034,"stem":91035,"tags":91036,"type":177,"updated":178,"__hash__":91042},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":48,"value":78937,"toc":90988},[78938,78941,79297,79301,79304,79372,79424,79434,79438,79472,79513,79537,79560,79589,79656,79763,79806,79863,79938,79983,79987,79995,80003,80006,80271,80322,80402,80472,80495,80523,80568,80590,80594,80601,80649,80675,80826,80829,80866,81029,81137,81141,81178,81253,81322,81441,81563,81644,81650,81691,81764,81857,81861,81897,81985,82099,82204,82289,82429,82433,82481,82526,82532,82536,82539,82590,82640,82647,82713,82846,82891,82895,82916,83294,83389,83406,83460,83464,83546,83630,83800,83803,83846,83913,83987,83991,83996,84065,84073,84082,84160,84226,84231,84326,84369,84374,84422,84427,84475,84593,84676,84714,84817,84876,85017,85021,85064,85137,85161,85215,85222,85224,85269,85314,85325,85330,85366,85428,85451,85460,85561,85628,85701,85708,85799,85861,85897,85954,86013,86198,86294,86298,86302,86381,86386,86510,86596,86602,86712,86749,86840,86938,86941,86945,87011,87048,87170,87222,87226,87254,87306,87380,87485,87509,87568,87572,87590,87733,87881,87883,87918,87922,87924,88014,88144,88270,88362,88437,88441,88557,88661,88851,88887,88981,88987,89100,89403,89409,89527,89626,89702,89704,90866,90868],[51,78939,78935],{"id":78940},"produkce-produkční-funkce-cobb-douglas-mrts",[1023,78942,78943],{},[55,78944,78945,3960,78947,78949,78950,41189,78963,78976,78977,19116,78990,11156,78992,79016,79017,1445,79019,75,79053,1445,79056,79084,79085,11525,79105,79135,79136,11156,79139,79167,79168,79171,79172,79202,79203,79233,79234,1445,79237,79277,79278,79296],{},[1647,78946,3959],{},[95,78948,78865],{}," popisuje vztah mezi vstupy (práce ",[1647,78951,78953],{"className":78952},[2059],[2061,78954,78955],{"xmlns":2063},[2065,78956,78957,78961],{},[2068,78958,78959],{},[2071,78960,586],{},[2092,78962,586],{"encoding":2094},[1647,78964,78966],{"className":78965},[2059],[2061,78967,78968],{"xmlns":2063},[2065,78969,78970,78974],{},[2068,78971,78972],{},[2071,78973,10929],{},[2092,78975,10929],{"encoding":2094},") a výstupem ",[1647,78978,78980],{"className":78979},[2059],[2061,78981,78982],{"xmlns":2063},[2065,78983,78984,78988],{},[2068,78985,78986],{},[2071,78987,2861],{},[2092,78989,2861],{"encoding":2094},[95,78991,41257],{},[1647,78993,78995],{"className":78994},[2059],[2061,78996,78997],{"xmlns":2063},[2065,78998,78999,79013],{},[2068,79000,79001,79003,79005,79007,79009,79011],{},[2071,79002,2861],{},[2075,79004,2077],{},[2071,79006,2861],{},[2075,79008,2084],{"stretchy":2083},[2071,79010,586],{},[2075,79012,2090],{"stretchy":2083},[2092,79014,79015],{"encoding":2094},"Q = Q(L)",") studujeme ",[3982,79018,11155],{},[1647,79020,79022],{"className":79021},[2059],[2061,79023,79024],{"xmlns":2063},[2065,79025,79026,79050],{},[2068,79027,79028,79030,79036,79038,79044,79046,79048],{},[2071,79029,2890],{},[2348,79031,79032,79034],{},[2071,79033,575],{},[2071,79035,586],{},[2075,79037,2077],{},[2205,79039,79040,79042],{},[2071,79041,2861],{},[2075,79043,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,79045,2084],{"stretchy":2083},[2071,79047,586],{},[2075,79049,2090],{"stretchy":2083},[2092,79051,79052],{"encoding":2094},"MP_L = Q'(L)",[3982,79054,79055],{},"průměrný produkt",[1647,79057,79059],{"className":79058},[2059],[2061,79060,79061],{"xmlns":2063},[2065,79062,79063,79081],{},[2068,79064,79065,79067,79073,79075,79077,79079],{},[2071,79066,4342],{},[2348,79068,79069,79071],{},[2071,79070,575],{},[2071,79072,586],{},[2075,79074,2077],{},[2071,79076,2861],{},[2071,79078,4761],{"mathvariant":2450},[2071,79080,586],{},[2092,79082,79083],{"encoding":2094},"AP_L = Q\u002FL","; v maximu ",[1647,79086,79088],{"className":79087},[2059],[2061,79089,79090],{"xmlns":2063},[2065,79091,79092,79102],{},[2068,79093,79094,79096],{},[2071,79095,4342],{},[2348,79097,79098,79100],{},[2071,79099,575],{},[2071,79101,586],{},[2092,79103,79104],{"encoding":2094},"AP_L",[1647,79106,79108],{"className":79107},[2059],[2061,79109,79110],{"xmlns":2063},[2065,79111,79112,79132],{},[2068,79113,79114,79116,79122,79124,79126],{},[2071,79115,2890],{},[2348,79117,79118,79120],{},[2071,79119,575],{},[2071,79121,586],{},[2075,79123,2077],{},[2071,79125,4342],{},[2348,79127,79128,79130],{},[2071,79129,575],{},[2071,79131,586],{},[2092,79133,79134],{"encoding":2094},"MP_L = AP_L",". Ve ",[95,79137,79138],{},"dvoufaktorovém modelu",[1647,79140,79142],{"className":79141},[2059],[2061,79143,79144],{"xmlns":2063},[2065,79145,79146,79164],{},[2068,79147,79148,79150,79152,79154,79156,79158,79160,79162],{},[2071,79149,2861],{},[2075,79151,2077],{},[2071,79153,2861],{},[2075,79155,2084],{"stretchy":2083},[2071,79157,586],{},[2075,79159,2361],{"separator":2360},[2071,79161,10929],{},[2075,79163,2090],{"stretchy":2083},[2092,79165,79166],{"encoding":2094},"Q = Q(L,K)",") dominují ",[95,79169,79170],{},"Cobb-Douglasovy"," funkce ",[1647,79173,79175],{"className":79174},[2059],[2061,79176,79177],{"xmlns":2063},[2065,79178,79179,79199],{},[2068,79180,79181,79183,79185,79187,79193],{},[2071,79182,2861],{},[2075,79184,2077],{},[2071,79186,4342],{},[2205,79188,79189,79191],{},[2071,79190,586],{},[2071,79192,69],{},[2205,79194,79195,79197],{},[2071,79196,10929],{},[2071,79198,2179],{},[2092,79200,79201],{"encoding":2094},"Q = AL^a K^b","; mezní produkty ",[1647,79204,79206],{"className":79205},[2059],[2061,79207,79208],{"xmlns":2063},[2065,79209,79210,79230],{},[2068,79211,79212,79214,79220,79222,79224],{},[2071,79213,2890],{},[2348,79215,79216,79218],{},[2071,79217,575],{},[2071,79219,586],{},[2075,79221,2361],{"separator":2360},[2071,79223,2890],{},[2348,79225,79226,79228],{},[2071,79227,575],{},[2071,79229,10929],{},[2092,79231,79232],{"encoding":2094},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[95,79235,79236],{},"mezní míru technické substituce",[1647,79238,79240],{"className":79239},[2059],[2061,79241,79242],{"xmlns":2063},[2065,79243,79244,79274],{},[2068,79245,79246,79248,79250,79252,79254,79256,79258,79264,79266,79268],{},[2071,79247,2890],{},[2071,79249,4082],{},[2071,79251,543],{},[2071,79253,532],{},[2075,79255,2077],{},[2071,79257,2890],{},[2348,79259,79260,79262],{},[2071,79261,575],{},[2071,79263,586],{},[2071,79265,4761],{"mathvariant":2450},[2071,79267,2890],{},[2348,79269,79270,79272],{},[2071,79271,575],{},[2071,79273,10929],{},[2092,79275,79276],{"encoding":2094},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[1647,79279,79281],{"className":79280},[2059],[2061,79282,79283],{"xmlns":2063},[2065,79284,79285,79293],{},[2068,79286,79287,79289,79291],{},[2071,79288,69],{},[2075,79290,2176],{},[2071,79292,2179],{},[2092,79294,79295],{"encoding":2094},"a+b"," určuje typ výnosů z rozsahu.",[84,79298,79300],{"id":79299},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[55,79302,79303],{},"Po prostudování kapitoly 5 student umí:",[89,79305,79306,79312,79322,79328,79334,79339,79345,79355,79360,79366],{},[92,79307,79308,79309,2361],{},"popsat ",[95,79310,79311],{},"jednofaktorový model produkce",[92,79313,79314,79315,75,79318,79321],{},"vypočítat ",[95,79316,79317],{},"mezní",[95,79319,79320],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[92,79323,79324,79325,2361],{},"charakterizovat průběh ",[95,79326,79327],{},"křivky produkce",[92,79329,79330,79331,2361],{},"formulovat ",[95,79332,79333],{},"princip maximalizace průměrného produktu práce",[92,79335,79308,79336,2361],{},[95,79337,79338],{},"dvoufaktorový model produkce",[92,79340,79341,79342,2361],{},"uvést tvar ",[95,79343,79344],{},"Cobb–Douglasových produkčních funkcí",[92,79346,79347,79348,835,79350,835,79352,2361],{},"vyložit, co jsou ",[95,79349,27351],{},[95,79351,15392],{},[95,79353,79354],{},"klesající výnosy z rozsahu",[92,79356,79314,79357,79321],{},[95,79358,79359],{},"mezní produkty práce a kapitálu",[92,79361,79362,79363,2361],{},"najít ",[95,79364,79365],{},"izokvanty",[92,79367,79314,79368,79371],{},[95,79369,79370],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[55,79373,79374,79375,79378,79379,79382,79383,1445,79386,835,79399,1445,79402,75,79415,79418,79419,79421,79422,195],{},"Každý proces produkce je určován ",[95,79376,79377],{},"faktory"," (též ",[95,79380,79381],{},"vstupy",") produkce. K hlavním patří ",[95,79384,79385],{},"práce",[1647,79387,79389],{"className":79388},[2059],[2061,79390,79391],{"xmlns":2063},[2065,79392,79393,79397],{},[2068,79394,79395],{},[2071,79396,586],{},[2092,79398,586],{"encoding":2094},[95,79400,79401],{},"kapitál",[1647,79403,79405],{"className":79404},[2059],[2061,79406,79407],{"xmlns":2063},[2065,79408,79409,79413],{},[2068,79410,79411],{},[2071,79412,10929],{},[2092,79414,10929],{"encoding":2094},[95,79416,79417],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[95,79420,41257],{}," (produkce závisí jen na práci); v opačném případě o ",[95,79423,79138],{},[55,79425,79426,79427,835,79430,79433],{},"Související matematický aparát: ",[69,79428,2431],{"className":79429,"dataFsResolvedFilePath":4005,"href":4006},[62],[69,79431,3901],{"className":79432,"dataFsResolvedFilePath":3899,"href":3900},[62]," (parciální derivace a totální diferenciál).",[84,79435,79437],{"id":79436},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[55,79439,79440,79441,79454,79455,79468,79469],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[1647,79442,79444],{"className":79443},[2059],[2061,79445,79446],{"xmlns":2063},[2065,79447,79448,79452],{},[2068,79449,79450],{},[2071,79451,2861],{},[2092,79453,2861],{"encoding":2094}," na práci ",[1647,79456,79458],{"className":79457},[2059],[2061,79459,79460],{"xmlns":2063},[2065,79461,79462,79466],{},[2068,79463,79464],{},[2071,79465,586],{},[2092,79467,586],{"encoding":2094}," vyjadřuje ",[95,79470,79471],{},"produkční funkce",[1647,79473,79475],{"className":79474},[2059],[2061,79476,79477],{"xmlns":2063,"display":31093},[2065,79478,79479,79510],{},[23493,79480,79481],{"width":31098},[23498,79482,79483,79485,79503,79505],{},[23501,79484],{"width":31103},[23501,79486,79487],{},[2068,79488,79489,79491,79493,79495,79497,79499,79501],{},[2071,79490,2861],{},[2075,79492,2077],{},[2071,79494,2861],{},[2075,79496,2084],{"stretchy":2083},[2071,79498,586],{},[2075,79500,2090],{"stretchy":2083},[2075,79502,2361],{"separator":2360},[23501,79504],{"width":31103},[23501,79506,79507],{},[2363,79508,79509],{},"(5.1)",[2092,79511,79512],{"encoding":2094},"Q = Q(L), \\tag{5.1}",[55,79514,79515,79516,11156,79519,79522,79523,79536],{},"jejíž graf se nazývá ",[95,79517,79518],{},"křivka produkce",[3982,79520,79521],{},"production curve","). Práce ",[1647,79524,79526],{"className":79525},[2059],[2061,79527,79528],{"xmlns":2063},[2065,79529,79530,79534],{},[2068,79531,79532],{},[2071,79533,586],{},[2092,79535,586],{"encoding":2094}," se měří počtem pracovníků, případně počtem pracovních hodin.",[84,79538,79540,79541,2090],{"id":79539},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[1647,79542,79544],{"className":79543},[2059],[2061,79545,79546],{"xmlns":2063},[2065,79547,79548,79558],{},[2068,79549,79550,79552],{},[2071,79551,2890],{},[2348,79553,79554,79556],{},[2071,79555,575],{},[2071,79557,586],{},[2092,79559,11176],{"encoding":2094},[55,79561,79562,11156,79565,79568,79569,79588],{},[95,79563,79564],{},"Mezní produkt práce",[3982,79566,79567],{},"marginal product of labour",") ",[1647,79570,79572],{"className":79571},[2059],[2061,79573,79574],{"xmlns":2063},[2065,79575,79576,79586],{},[2068,79577,79578,79580],{},[2071,79579,2890],{},[2348,79581,79582,79584],{},[2071,79583,575],{},[2071,79585,586],{},[2092,79587,11176],{"encoding":2094}," je derivace produkce podle práce:",[1647,79590,79592],{"className":79591},[2059],[2061,79593,79594],{"xmlns":2063,"display":31093},[2065,79595,79596,79653],{},[23493,79597,79598],{"width":31098},[23498,79599,79600,79602,79646,79648],{},[23501,79601],{"width":31103},[23501,79603,79604],{},[2068,79605,79606,79608,79614,79616,79630,79632,79638,79640,79642,79644],{},[2071,79607,2890],{},[2348,79609,79610,79612],{},[2071,79611,575],{},[2071,79613,586],{},[2075,79615,2077],{},[2403,79617,79618,79624],{},[2068,79619,79620,79622],{},[2071,79621,2273],{},[2071,79623,2861],{},[2068,79625,79626,79628],{},[2071,79627,2273],{},[2071,79629,586],{},[2075,79631,2077],{},[2205,79633,79634,79636],{},[2071,79635,2861],{},[2075,79637,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,79639,2084],{"stretchy":2083},[2071,79641,586],{},[2075,79643,2090],{"stretchy":2083},[2071,79645,195],{"mathvariant":2450},[23501,79647],{"width":31103},[23501,79649,79650],{},[2363,79651,79652],{},"(5.2)",[2092,79654,79655],{"encoding":2094},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[55,79657,79658,79659,22684,79677,79705,79706,79723,79724,2758,79741,4007],{},"Pro pevnou hodnotu ",[1647,79660,79662],{"className":79661},[2059],[2061,79663,79664],{"xmlns":2063},[2065,79665,79666,79674],{},[2068,79667,79668],{},[2205,79669,79670,79672],{},[2071,79671,586],{},[2075,79673,4441],{},[2092,79675,79676],{"encoding":2094},"L^*",[1647,79678,79680],{"className":79679},[2059],[2061,79681,79682],{"xmlns":2063},[2065,79683,79684,79702],{},[2068,79685,79686,79692,79694,79700],{},[2205,79687,79688,79690],{},[2071,79689,2861],{},[2075,79691,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,79693,2084],{"stretchy":2083},[2205,79695,79696,79698],{},[2071,79697,586],{},[2075,79699,4441],{},[2075,79701,2090],{"stretchy":2083},[2092,79703,79704],{"encoding":2094},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[1647,79707,79709],{"className":79708},[2059],[2061,79710,79711],{"xmlns":2063},[2065,79712,79713,79721],{},[2068,79714,79715],{},[2205,79716,79717,79719],{},[2071,79718,586],{},[2075,79720,4441],{},[2092,79722,79676],{"encoding":2094},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[1647,79725,79727],{"className":79726},[2059],[2061,79728,79729],{"xmlns":2063},[2065,79730,79731,79739],{},[2068,79732,79733],{},[2205,79734,79735,79737],{},[2071,79736,586],{},[2075,79738,4441],{},[2092,79740,79676],{"encoding":2094},[1647,79742,79744],{"className":79743},[2059],[2061,79745,79746],{"xmlns":2063},[2065,79747,79748,79760],{},[2068,79749,79750,79756,79758],{},[2205,79751,79752,79754],{},[2071,79753,586],{},[2075,79755,4441],{},[2075,79757,2176],{},[2210,79759,638],{},[2092,79761,79762],{"encoding":2094},"L^*+1",[1023,79764,79765],{},[55,79766,79767,20762,79769,79788,79789,79792,79793,195],{},[1647,79768,4243],{},[1647,79770,79772],{"className":79771},[2059],[2061,79773,79774],{"xmlns":2063},[2065,79775,79776,79786],{},[2068,79777,79778,79780],{},[2071,79779,2890],{},[2348,79781,79782,79784],{},[2071,79783,575],{},[2071,79785,586],{},[2092,79787,11176],{"encoding":2094}," odpovídá na otázku „",[95,79790,79791],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[1647,79794,79796],{"className":79795},[2059],[2061,79797,79798],{"xmlns":2063},[2065,79799,79800,79804],{},[2068,79801,79802],{},[2071,79803,586],{},[2092,79805,586],{"encoding":2094},[55,79807,79808,79811,79812,79828,79829,2758,79842,79862],{},[95,79809,79810],{},"Přibližná změna produkce"," pro změnu práce o ",[1647,79813,79815],{"className":79814},[2059],[2061,79816,79817],{"xmlns":2063},[2065,79818,79819,79825],{},[2068,79820,79821,79823],{},[2071,79822,2273],{},[2071,79824,586],{},[2092,79826,79827],{"encoding":2094},"dL"," (z ",[1647,79830,79832],{"className":79831},[2059],[2061,79833,79834],{"xmlns":2063},[2065,79835,79836,79840],{},[2068,79837,79838],{},[2071,79839,586],{},[2092,79841,586],{"encoding":2094},[1647,79843,79845],{"className":79844},[2059],[2061,79846,79847],{"xmlns":2063},[2065,79848,79849,79859],{},[2068,79850,79851,79853,79855,79857],{},[2071,79852,586],{},[2075,79854,2176],{},[2071,79856,2273],{},[2071,79858,586],{},[2092,79860,79861],{"encoding":2094},"L+dL",") pomocí diferenciálu:",[1647,79864,79866],{"className":79865},[2059],[2061,79867,79868],{"xmlns":2063,"display":31093},[2065,79869,79870,79935],{},[23493,79871,79872],{"width":31098},[23498,79873,79874,79876,79928,79930],{},[23501,79875],{"width":31103},[23501,79877,79878],{},[2068,79879,79880,79882,79884,79886,79888,79890,79892,79898,79900,79902,79904,79906,79908,79910,79912,79914,79920,79922,79924,79926],{},[2071,79881,2961],{"mathvariant":2450},[2071,79883,2861],{},[2075,79885,2803],{},[2071,79887,2273],{},[2071,79889,2861],{},[2075,79891,2077],{},[2205,79893,79894,79896],{},[2071,79895,2861],{},[2075,79897,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,79899,2084],{"stretchy":2083},[2071,79901,586],{},[2075,79903,2090],{"stretchy":2083},[2363,79905,3061],{},[2071,79907,2273],{},[2071,79909,586],{},[2075,79911,2077],{},[2071,79913,2890],{},[2348,79915,79916,79918],{},[2071,79917,575],{},[2071,79919,586],{},[2363,79921,3061],{},[2071,79923,2273],{},[2071,79925,586],{},[2071,79927,195],{"mathvariant":2450},[23501,79929],{"width":31103},[23501,79931,79932],{},[2363,79933,79934],{},"(5.3)",[2092,79936,79937],{"encoding":2094},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[55,79939,79940,79941,195],{},"Skutečná změna je ",[1647,79942,79944],{"className":79943},[2059],[2061,79945,79946],{"xmlns":2063},[2065,79947,79948,79980],{},[2068,79949,79950,79952,79954,79956,79958,79960,79962,79964,79966,79968,79970,79972,79974,79976,79978],{},[2071,79951,2961],{"mathvariant":2450},[2071,79953,2861],{},[2075,79955,2077],{},[2071,79957,2861],{},[2075,79959,2084],{"stretchy":2083},[2071,79961,586],{},[2075,79963,2176],{},[2071,79965,2273],{},[2071,79967,586],{},[2075,79969,2090],{"stretchy":2083},[2075,79971,2303],{},[2071,79973,2861],{},[2075,79975,2084],{"stretchy":2083},[2071,79977,586],{},[2075,79979,2090],{"stretchy":2083},[2092,79981,79982],{"encoding":2094},"\\Delta Q = Q(L+dL) - Q(L)",[609,79984,79986],{"id":79985},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[55,79988,79989,11156,79992,3225],{},[95,79990,79991],{},"Zákon klesajících výnosů",[3982,79993,79994],{},"law of diminishing marginal productivity",[1023,79996,79997],{},[55,79998,79999,80000,80002],{},"Roste-li postupně některý ze vstupů (",[3982,80001,41253],{},"), budou přírůstky výstupu od jistého bodu klesat.",[55,80004,80005],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[55,80007,80008,80009,1445,80030,80049,80050,80100,80101,80103,80104,1445,80124,80143,80144,80100,80176,2999,80178,80197,80198,24333,80215,80249,80250,8189,80267,80270],{},"1° ",[95,80010,80011,80012,2777],{},"Do bodu ",[1647,80013,80015],{"className":80014},[2059],[2061,80016,80017],{"xmlns":2063},[2065,80018,80019,80027],{},[2068,80020,80021],{},[2348,80022,80023,80025],{},[2071,80024,586],{},[2210,80026,630],{},[2092,80028,80029],{"encoding":2094},"L_0",[1647,80031,80033],{"className":80032},[2059],[2061,80034,80035],{"xmlns":2063},[2065,80036,80037,80047],{},[2068,80038,80039,80041],{},[2071,80040,2890],{},[2348,80042,80043,80045],{},[2071,80044,575],{},[2071,80046,586],{},[2092,80048,11176],{"encoding":2094}," roste, tj. ",[1647,80051,80053],{"className":80052},[2059],[2061,80054,80055],{"xmlns":2063},[2065,80056,80057,80097],{},[2068,80058,80059,80061,80063,80069,80075,80077,80087,80089,80091,80093,80095],{},[2075,80060,2084],{"stretchy":2083},[2071,80062,2890],{},[2348,80064,80065,80067],{},[2071,80066,575],{},[2071,80068,586],{},[2205,80070,80071,80073],{},[2075,80072,2090],{"stretchy":2083},[2075,80074,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,80076,2077],{},[2205,80078,80079,80081],{},[2071,80080,2861],{},[2068,80082,80083,80085],{},[2075,80084,2452],{"mathvariant":2450},[2075,80086,2452],{"mathvariant":2450},[2075,80088,2084],{"stretchy":2083},[2071,80090,586],{},[2075,80092,2090],{"stretchy":2083},[2075,80094,3482],{},[2210,80096,630],{},[2092,80098,80099],{"encoding":2094},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[95,80102,41955],{},".\n2° ",[95,80105,80106,80107,2777],{},"Od bodu ",[1647,80108,80110],{"className":80109},[2059],[2061,80111,80112],{"xmlns":2063},[2065,80113,80114,80122],{},[2068,80115,80116],{},[2348,80117,80118,80120],{},[2071,80119,586],{},[2210,80121,630],{},[2092,80123,80029],{"encoding":2094},[1647,80125,80127],{"className":80126},[2059],[2061,80128,80129],{"xmlns":2063},[2065,80130,80131,80141],{},[2068,80132,80133,80135],{},[2071,80134,2890],{},[2348,80136,80137,80139],{},[2071,80138,575],{},[2071,80140,586],{},[2092,80142,11176],{"encoding":2094}," klesá, ",[1647,80145,80147],{"className":80146},[2059],[2061,80148,80149],{"xmlns":2063},[2065,80150,80151,80173],{},[2068,80152,80153,80163,80165,80167,80169,80171],{},[2205,80154,80155,80157],{},[2071,80156,2861],{},[2068,80158,80159,80161],{},[2075,80160,2452],{"mathvariant":2450},[2075,80162,2452],{"mathvariant":2450},[2075,80164,2084],{"stretchy":2083},[2071,80166,586],{},[2075,80168,2090],{"stretchy":2083},[2075,80170,3521],{},[2210,80172,630],{},[2092,80174,80175],{"encoding":2094},"Q''(L) \u003C 0",[95,80177,42779],{},[1647,80179,80181],{"className":80180},[2059],[2061,80182,80183],{"xmlns":2063},[2065,80184,80185,80195],{},[2068,80186,80187,80189],{},[2071,80188,2890],{},[2348,80190,80191,80193],{},[2071,80192,575],{},[2071,80194,586],{},[2092,80196,11176],{"encoding":2094}," v kladných hodnotách klesá do bodu ",[1647,80199,80201],{"className":80200},[2059],[2061,80202,80203],{"xmlns":2063},[2065,80204,80205,80213],{},[2068,80206,80207],{},[2348,80208,80209,80211],{},[2071,80210,586],{},[2210,80212,638],{},[2092,80214,14947],{"encoding":2094},[1647,80216,80218],{"className":80217},[2059],[2061,80219,80220],{"xmlns":2063},[2065,80221,80222,80246],{},[2068,80223,80224,80226,80232,80234,80240,80242,80244],{},[2071,80225,2890],{},[2348,80227,80228,80230],{},[2071,80229,575],{},[2071,80231,586],{},[2075,80233,2084],{"stretchy":2083},[2348,80235,80236,80238],{},[2071,80237,586],{},[2210,80239,638],{},[2075,80241,2090],{"stretchy":2083},[2075,80243,2077],{},[2210,80245,630],{},[2092,80247,80248],{"encoding":2094},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[1647,80251,80253],{"className":80252},[2059],[2061,80254,80255],{"xmlns":2063},[2065,80256,80257,80265],{},[2068,80258,80259],{},[2348,80260,80261,80263],{},[2071,80262,586],{},[2210,80264,630],{},[2092,80266,80029],{"encoding":2094},[95,80268,80269],{},"inflexním bodem"," produkční funkce.",[55,80272,80273,80274,11525,80291,195],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[1647,80275,80277],{"className":80276},[2059],[2061,80278,80279],{"xmlns":2063},[2065,80280,80281,80289],{},[2068,80282,80283],{},[2348,80284,80285,80287],{},[2071,80286,586],{},[2210,80288,630],{},[2092,80290,80029],{"encoding":2094},[1647,80292,80294],{"className":80293},[2059],[2061,80295,80296],{"xmlns":2063},[2065,80297,80298,80320],{},[2068,80299,80300,80310,80312,80314,80316,80318],{},[2205,80301,80302,80304],{},[2071,80303,2861],{},[2068,80305,80306,80308],{},[2075,80307,2452],{"mathvariant":2450},[2075,80309,2452],{"mathvariant":2450},[2075,80311,2084],{"stretchy":2083},[2071,80313,586],{},[2075,80315,2090],{"stretchy":2083},[2075,80317,3521],{},[2210,80319,630],{},[2092,80321,80175],{"encoding":2094},[55,80323,80324,1445,80327,5756,80367,835,80384,80401],{},[95,80325,80326],{},"Typický polynom třetího stupně:",[1647,80328,80330],{"className":80329},[2059],[2061,80331,80332],{"xmlns":2063},[2065,80333,80334,80364],{},[2068,80335,80336,80338,80340,80342,80344,80346,80348,80354,80356,80358],{},[2071,80337,2861],{},[2075,80339,2084],{"stretchy":2083},[2071,80341,586],{},[2075,80343,2090],{"stretchy":2083},[2075,80345,2077],{},[2071,80347,69],{},[2205,80349,80350,80352],{},[2071,80351,586],{},[2210,80353,654],{},[2075,80355,2176],{},[2071,80357,2179],{},[2205,80359,80360,80362],{},[2071,80361,586],{},[2210,80363,646],{},[2092,80365,80366],{"encoding":2094},"Q(L) = aL^3 + bL^2",[1647,80368,80370],{"className":80369},[2059],[2061,80371,80372],{"xmlns":2063},[2065,80373,80374,80382],{},[2068,80375,80376,80378,80380],{},[2071,80377,69],{},[2075,80379,3521],{},[2210,80381,630],{},[2092,80383,47379],{"encoding":2094},[1647,80385,80387],{"className":80386},[2059],[2061,80388,80389],{"xmlns":2063},[2065,80390,80391,80399],{},[2068,80392,80393,80395,80397],{},[2071,80394,2179],{},[2075,80396,3482],{},[2210,80398,630],{},[2092,80400,21553],{"encoding":2094},". Pak",[1647,80403,80405],{"className":80404},[2059],[2061,80406,80407],{"xmlns":2063,"display":31093},[2065,80408,80409,80469],{},[2068,80410,80411,80417,80419,80421,80429,80437,80439,80441,80447,80449,80451,80459,80467],{},[2348,80412,80413,80415],{},[2071,80414,586],{},[2210,80416,630],{},[2075,80418,2077],{},[2075,80420,2303],{},[2400,80422,80423],{"scriptlevel":630,"displaystyle":2083},[2403,80424,80425,80427],{},[2210,80426,638],{},[2210,80428,654],{},[2400,80430,80431],{"scriptlevel":630,"displaystyle":2083},[2403,80432,80433,80435],{},[2071,80434,2179],{},[2071,80436,69],{},[2075,80438,2361],{"separator":2360},[5965,80440],{"width":5967},[2348,80442,80443,80445],{},[2071,80444,586],{},[2210,80446,638],{},[2075,80448,2077],{},[2075,80450,2303],{},[2400,80452,80453],{"scriptlevel":630,"displaystyle":2083},[2403,80454,80455,80457],{},[2210,80456,646],{},[2210,80458,654],{},[2400,80460,80461],{"scriptlevel":630,"displaystyle":2083},[2403,80462,80463,80465],{},[2071,80464,2179],{},[2071,80466,69],{},[2071,80468,195],{"mathvariant":2450},[2092,80470,80471],{"encoding":2094},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[84,80473,80475,80476,2090],{"id":80474},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[1647,80477,80479],{"className":80478},[2059],[2061,80480,80481],{"xmlns":2063},[2065,80482,80483,80493],{},[2068,80484,80485,80487],{},[2071,80486,4342],{},[2348,80488,80489,80491],{},[2071,80490,575],{},[2071,80492,586],{},[2092,80494,79104],{"encoding":2094},[55,80496,80497,11156,80500,79568,80503,80522],{},[95,80498,80499],{},"Průměrný produkt práce",[3982,80501,80502],{},"average product of labour",[1647,80504,80506],{"className":80505},[2059],[2061,80507,80508],{"xmlns":2063},[2065,80509,80510,80520],{},[2068,80511,80512,80514],{},[2071,80513,4342],{},[2348,80515,80516,80518],{},[2071,80517,575],{},[2071,80519,586],{},[2092,80521,79104],{"encoding":2094}," je podíl produkce a práce:",[1647,80524,80526],{"className":80525},[2059],[2061,80527,80528],{"xmlns":2063,"display":31093},[2065,80529,80530,80565],{},[23493,80531,80532],{"width":31098},[23498,80533,80534,80536,80558,80560],{},[23501,80535],{"width":31103},[23501,80537,80538],{},[2068,80539,80540,80542,80548,80550,80556],{},[2071,80541,4342],{},[2348,80543,80544,80546],{},[2071,80545,575],{},[2071,80547,586],{},[2075,80549,2077],{},[2403,80551,80552,80554],{},[2071,80553,2861],{},[2071,80555,586],{},[2071,80557,195],{"mathvariant":2450},[23501,80559],{"width":31103},[23501,80561,80562],{},[2363,80563,80564],{},"(5.4)",[2092,80566,80567],{"encoding":2094},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[55,80569,80570,80571,195],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[1647,80572,80574],{"className":80573},[2059],[2061,80575,80576],{"xmlns":2063},[2065,80577,80578,80588],{},[2068,80579,80580,80582],{},[2071,80581,4342],{},[2348,80583,80584,80586],{},[2071,80585,575],{},[2071,80587,586],{},[2092,80589,79104],{"encoding":2094},[84,80591,80593],{"id":80592},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[55,80595,80596],{},[58,80597],{"alt":80598,"className":80599,"src":80600},"imek-q-mpl-apl-tripanel",[62,63],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1023,80602,80603],{},[55,80604,80605,80607,80608,2697,80627,80644,80645],{},[95,80606,1053],{}," Má-li ",[1647,80609,80611],{"className":80610},[2059],[2061,80612,80613],{"xmlns":2063},[2065,80614,80615,80625],{},[2068,80616,80617,80619],{},[2071,80618,4342],{},[2348,80620,80621,80623],{},[2071,80622,575],{},[2071,80624,586],{},[2092,80626,79104],{"encoding":2094},[1647,80628,80630],{"className":80629},[2059],[2061,80631,80632],{"xmlns":2063},[2065,80633,80634,80642],{},[2068,80635,80636],{},[2348,80637,80638,80640],{},[2071,80639,586],{},[2210,80641,630],{},[2092,80643,80029],{"encoding":2094}," maximum, pak platí\n",[1647,80646,80648],{"className":80647,"title":4288,"style":4289},[4287],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[55,80650,80651,80652,80655,80656,1445,80660,195],{},"Slovně: ",[95,80653,80654],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[69,80657,80659],{"className":80658,"dataFsResolvedFilePath":3022,"href":3023},[62],"principu minimalizace průměrných nákladů",[1647,80661,80663],{"className":80662},[2059],[2061,80664,80665],{"xmlns":2063},[2065,80666,80667,80673],{},[2068,80668,80669,80671],{},[2071,80670,4342],{},[2071,80672,2849],{},[2092,80674,60030],{"encoding":2094},[1023,80676,80677,80701],{},[55,80678,80679,80681,80682],{},[1647,80680,4659],{}," Postup — jak najít max ",[1647,80683,80685],{"className":80684},[2059],[2061,80686,80687],{"xmlns":2063},[2065,80688,80689,80699],{},[2068,80690,80691,80693],{},[2071,80692,4342],{},[2348,80694,80695,80697],{},[2071,80696,575],{},[2071,80698,586],{},[2092,80700,79104],{"encoding":2094},[201,80702,80703,80741,80823],{},[92,80704,80705,80706,80740],{},"Napište ",[1647,80707,80709],{"className":80708},[2059],[2061,80710,80711],{"xmlns":2063},[2065,80712,80713,80737],{},[2068,80714,80715,80717,80723,80725,80727,80729,80731,80733,80735],{},[2071,80716,4342],{},[2348,80718,80719,80721],{},[2071,80720,575],{},[2071,80722,586],{},[2075,80724,2077],{},[2071,80726,2861],{},[2075,80728,2084],{"stretchy":2083},[2071,80730,586],{},[2075,80732,2090],{"stretchy":2083},[2071,80734,4761],{"mathvariant":2450},[2071,80736,586],{},[2092,80738,80739],{"encoding":2094},"AP_L = Q(L)\u002FL"," a zderivujte.",[92,80742,80743,80744,80776,80777,80780,80781,195],{},"Položte ",[1647,80745,80747],{"className":80746},[2059],[2061,80748,80749],{"xmlns":2063},[2065,80750,80751,80773],{},[2068,80752,80753,80755,80757,80763,80769,80771],{},[2075,80754,2084],{"stretchy":2083},[2071,80756,4342],{},[2348,80758,80759,80761],{},[2071,80760,575],{},[2071,80762,586],{},[2205,80764,80765,80767],{},[2075,80766,2090],{"stretchy":2083},[2075,80768,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,80770,2077],{},[2210,80772,630],{},[2092,80774,80775],{"encoding":2094},"(AP_L)' = 0"," a vyřešte. ",[3982,80778,80779],{},"Zkratka:"," můžete rovnou řešit ",[1647,80782,80784],{"className":80783},[2059],[2061,80785,80786],{"xmlns":2063},[2065,80787,80788,80820],{},[2068,80789,80790,80792,80798,80800,80802,80804,80806,80808,80814,80816,80818],{},[2071,80791,2890],{},[2348,80793,80794,80796],{},[2071,80795,575],{},[2071,80797,586],{},[2075,80799,2084],{"stretchy":2083},[2071,80801,586],{},[2075,80803,2090],{"stretchy":2083},[2075,80805,2077],{},[2071,80807,4342],{},[2348,80809,80810,80812],{},[2071,80811,575],{},[2071,80813,586],{},[2075,80815,2084],{"stretchy":2083},[2071,80817,586],{},[2075,80819,2090],{"stretchy":2083},[2092,80821,80822],{"encoding":2094},"MP_L(L) = AP_L(L)",[92,80824,80825],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[609,80827,69971],{"id":80828},"odvození",[55,80830,80831,80832,80865],{},"Z ",[1647,80833,80835],{"className":80834},[2059],[2061,80836,80837],{"xmlns":2063},[2065,80838,80839,80863],{},[2068,80840,80841,80843,80849,80851,80853,80855,80857,80859,80861],{},[2071,80842,4342],{},[2348,80844,80845,80847],{},[2071,80846,575],{},[2071,80848,586],{},[2075,80850,2077],{},[2071,80852,2861],{},[2075,80854,2084],{"stretchy":2083},[2071,80856,586],{},[2075,80858,2090],{"stretchy":2083},[2071,80860,4761],{"mathvariant":2450},[2071,80862,586],{},[2092,80864,80739],{"encoding":2094}," a derivace podílu:",[1647,80867,80869],{"className":80868},[2059],[2061,80870,80871],{"xmlns":2063,"display":31093},[2065,80872,80873,81026],{},[2068,80874,80875,80877,80879,80885,80891,80893,80895,80897,80899,80939,80941,80947,80981,80983,80989,80992,80994,81000,81002,81004,81006,81008,81010,81016,81018,81020,81022,81024],{},[2075,80876,2084],{"stretchy":2083},[2071,80878,4342],{},[2348,80880,80881,80883],{},[2071,80882,575],{},[2071,80884,586],{},[2205,80886,80887,80889],{},[2075,80888,2090],{"stretchy":2083},[2075,80890,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,80892,2084],{"stretchy":2083},[2071,80894,586],{},[2075,80896,2090],{"stretchy":2083},[2075,80898,2077],{},[2403,80900,80901,80933],{},[2068,80902,80903,80909,80911,80913,80915,80917,80919,80921,80923,80925,80927,80929,80931],{},[2205,80904,80905,80907],{},[2071,80906,2861],{},[2075,80908,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,80910,2084],{"stretchy":2083},[2071,80912,586],{},[2075,80914,2090],{"stretchy":2083},[2075,80916,3251],{},[2071,80918,586],{},[2075,80920,2303],{},[2071,80922,2861],{},[2075,80924,2084],{"stretchy":2083},[2071,80926,586],{},[2075,80928,2090],{"stretchy":2083},[2075,80930,3251],{},[2210,80932,638],{},[2205,80934,80935,80937],{},[2071,80936,586],{},[2210,80938,646],{},[2075,80940,2077],{},[2403,80942,80943,80945],{},[2210,80944,638],{},[2071,80946,586],{},[2068,80948,80949,80951,80957,80959,80961,80963,80965,80979],{},[2075,80950,2084],{"fence":2360},[2205,80952,80953,80955],{},[2071,80954,2861],{},[2075,80956,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,80958,2084],{"stretchy":2083},[2071,80960,586],{},[2075,80962,2090],{"stretchy":2083},[2075,80964,2303],{},[2403,80966,80967,80977],{},[2068,80968,80969,80971,80973,80975],{},[2071,80970,2861],{},[2075,80972,2084],{"stretchy":2083},[2071,80974,586],{},[2075,80976,2090],{"stretchy":2083},[2071,80978,586],{},[2075,80980,2090],{"fence":2360},[2075,80982,2077],{},[2403,80984,80985,80987],{},[2210,80986,638],{},[2071,80988,586],{},[2075,80990,2084],{"fence":2360,"stretchy":2360,"minsize":80991,"maxsize":80991},"1.2em",[2071,80993,2890],{},[2348,80995,80996,80998],{},[2071,80997,575],{},[2071,80999,586],{},[2075,81001,2084],{"stretchy":2083},[2071,81003,586],{},[2075,81005,2090],{"stretchy":2083},[2075,81007,2303],{},[2071,81009,4342],{},[2348,81011,81012,81014],{},[2071,81013,575],{},[2071,81015,586],{},[2075,81017,2084],{"stretchy":2083},[2071,81019,586],{},[2075,81021,2090],{"stretchy":2083},[2075,81023,2090],{"fence":2360,"stretchy":2360,"minsize":80991,"maxsize":80991},[2071,81025,195],{"mathvariant":2450},[2092,81027,81028],{"encoding":2094},"(AP_L)'(L) = \\frac{Q'(L)\\cdot L - Q(L)\\cdot 1}{L^2} = \\frac{1}{L}\\left(Q'(L) - \\frac{Q(L)}{L}\\right) = \\frac{1}{L}\\bigl(MP_L(L) - AP_L(L)\\bigr).",[55,81030,10790,81031,8189,81053,81136],{},[1647,81032,81034],{"className":81033},[2059],[2061,81035,81036],{"xmlns":2063},[2065,81037,81038,81050],{},[2068,81039,81040,81046,81048],{},[2348,81041,81042,81044],{},[2071,81043,586],{},[2210,81045,630],{},[2075,81047,3482],{},[2210,81049,630],{},[2092,81051,81052],{"encoding":2094},"L_0 > 0",[1647,81054,81056],{"className":81055},[2059],[2061,81057,81058],{"xmlns":2063},[2065,81059,81060,81133],{},[2068,81061,81062,81064,81066,81072,81078,81080,81086,81088,81090,81092,81095,81097,81103,81105,81111,81113,81115,81117,81123,81125,81131],{},[2075,81063,2084],{"stretchy":2083},[2071,81065,4342],{},[2348,81067,81068,81070],{},[2071,81069,575],{},[2071,81071,586],{},[2205,81073,81074,81076],{},[2075,81075,2090],{"stretchy":2083},[2075,81077,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,81079,2084],{"stretchy":2083},[2348,81081,81082,81084],{},[2071,81083,586],{},[2210,81085,630],{},[2075,81087,2090],{"stretchy":2083},[2075,81089,2077],{},[2210,81091,630],{},[2075,81093,81094],{},"⇔",[2071,81096,2890],{},[2348,81098,81099,81101],{},[2071,81100,575],{},[2071,81102,586],{},[2075,81104,2084],{"stretchy":2083},[2348,81106,81107,81109],{},[2071,81108,586],{},[2210,81110,630],{},[2075,81112,2090],{"stretchy":2083},[2075,81114,2077],{},[2071,81116,4342],{},[2348,81118,81119,81121],{},[2071,81120,575],{},[2071,81122,586],{},[2075,81124,2084],{"stretchy":2083},[2348,81126,81127,81129],{},[2071,81128,586],{},[2210,81130,630],{},[2075,81132,2090],{"stretchy":2083},[2092,81134,81135],{"encoding":2094},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[609,81138,81140],{"id":81139},"příklad-51","Příklad 5.1",[55,81142,81143,81144,195],{},"Je dána produkce ",[1647,81145,81147],{"className":81146},[2059],[2061,81148,81149],{"xmlns":2063},[2065,81150,81151,81175],{},[2068,81152,81153,81155,81157,81159,81165,81167,81169],{},[2071,81154,2861],{},[2075,81156,2077],{},[2210,81158,678],{},[2205,81160,81161,81163],{},[2071,81162,586],{},[2210,81164,646],{},[2075,81166,2303],{},[2210,81168,2911],{},[2205,81170,81171,81173],{},[2071,81172,586],{},[2210,81174,654],{},[2092,81176,81177],{"encoding":2094},"Q = 6L^2 - 0{,}2L^3",[55,81179,81180,61992,81183,81233,81234,195],{},[95,81181,81182],{},"(a)",[1647,81184,81186],{"className":81185},[2059],[2061,81187,81188],{"xmlns":2063},[2065,81189,81190,81230],{},[2068,81191,81192,81194,81196,81198,81200,81202,81204,81206,81208,81210,81212,81214,81216,81218,81220,81222,81224,81226,81228],{},[2071,81193,586],{},[2075,81195,2077],{},[2210,81197,646],{},[2075,81199,2361],{"separator":2360},[2210,81201,670],{},[2075,81203,2361],{"separator":2360},[2210,81205,5672],{},[2075,81207,2361],{"separator":2360},[2210,81209,2935],{},[2075,81211,2361],{"separator":2360},[2210,81213,25685],{},[2075,81215,2361],{"separator":2360},[2210,81217,3781],{},[2075,81219,2361],{"separator":2360},[2210,81221,9121],{},[2075,81223,2361],{"separator":2360},[2210,81225,42637],{},[2075,81227,2361],{"separator":2360},[2210,81229,5091],{},[2092,81231,81232],{"encoding":2094},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[1647,81235,81237],{"className":81236},[2059],[2061,81238,81239],{"xmlns":2063},[2065,81240,81241,81251],{},[2068,81242,81243,81245],{},[2071,81244,2890],{},[2348,81246,81247,81249],{},[2071,81248,575],{},[2071,81250,586],{},[2092,81252,11176],{"encoding":2094},[55,81254,81255,81256,37994],{},"Podle (5.2): ",[1647,81257,81259],{"className":81258},[2059],[2061,81260,81261],{"xmlns":2063},[2065,81262,81263,81319],{},[2068,81264,81265,81267,81273,81275,81281,81283,81285,81287,81289,81291,81293,81295,81297,81303,81305,81307,81309,81311,81313,81315,81317],{},[2071,81266,2890],{},[2348,81268,81269,81271],{},[2071,81270,575],{},[2071,81272,586],{},[2075,81274,2077],{},[2205,81276,81277,81279],{},[2071,81278,2861],{},[2075,81280,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,81282,2084],{"stretchy":2083},[2071,81284,586],{},[2075,81286,2090],{"stretchy":2083},[2075,81288,2077],{},[2210,81290,3583],{},[2071,81292,586],{},[2075,81294,2303],{},[2210,81296,22060],{},[2205,81298,81299,81301],{},[2071,81300,586],{},[2210,81302,646],{},[2075,81304,2077],{},[2071,81306,586],{},[2075,81308,2084],{"stretchy":2083},[2210,81310,3583],{},[2075,81312,2303],{},[2210,81314,22060],{},[2071,81316,586],{},[2075,81318,2090],{"stretchy":2083},[2092,81320,81321],{"encoding":2094},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[323,81323,81324,81361],{},[326,81325,81326],{},[329,81327,81328,81343,81345,81347,81349,81351,81353,81355,81357,81359],{},[332,81329,81330],{},[1647,81331,81333],{"className":81332},[2059],[2061,81334,81335],{"xmlns":2063},[2065,81336,81337,81341],{},[2068,81338,81339],{},[2071,81340,586],{},[2092,81342,586],{"encoding":2094},[332,81344,646],{},[332,81346,670],{},[332,81348,5672],{},[332,81350,2935],{},[332,81352,25685],{},[332,81354,3781],{},[332,81356,9121],{},[332,81358,42637],{},[332,81360,5091],{},[342,81362,81363],{},[329,81364,81365,81386,81389,81392,81395,81397,81400,81402,81404,81423],{},[347,81366,81367],{},[1647,81368,81370],{"className":81369},[2059],[2061,81371,81372],{"xmlns":2063},[2065,81373,81374,81384],{},[2068,81375,81376,81378],{},[2071,81377,2890],{},[2348,81379,81380,81382],{},[2071,81381,575],{},[2071,81383,586],{},[2092,81385,11176],{"encoding":2094},[347,81387,81388],{},"21,6",[347,81390,81391],{},"45",[347,81393,81394],{},"57,6",[347,81396,3200],{},[347,81398,81399],{},"50,4",[347,81401,81388],{},[347,81403,630],{},[347,81405,81406],{},[1647,81407,81409],{"className":81408},[2059],[2061,81410,81411],{"xmlns":2063},[2065,81412,81413,81420],{},[2068,81414,81415,81417],{},[2075,81416,2303],{},[2210,81418,81419],{},"12,6",[2092,81421,81422],{"encoding":2094},"-12{,}6",[347,81424,81425],{},[1647,81426,81428],{"className":81427},[2059],[2061,81429,81430],{"xmlns":2063},[2065,81431,81432,81438],{},[2068,81433,81434,81436],{},[2075,81435,2303],{},[2210,81437,49748],{},[2092,81439,81440],{"encoding":2094},"-75",[55,81442,81443,81462,81463,81481,81482,81499,81500,81518,81519,81543,81544,81562],{},[1647,81444,81446],{"className":81445},[2059],[2061,81447,81448],{"xmlns":2063},[2065,81449,81450,81460],{},[2068,81451,81452,81454],{},[2071,81453,2890],{},[2348,81455,81456,81458],{},[2071,81457,575],{},[2071,81459,586],{},[2092,81461,11176],{"encoding":2094}," nabývá maxima pro ",[1647,81464,81466],{"className":81465},[2059],[2061,81467,81468],{"xmlns":2063},[2065,81469,81470,81478],{},[2068,81471,81472,81474,81476],{},[2071,81473,586],{},[2075,81475,2077],{},[2210,81477,2935],{},[2092,81479,81480],{"encoding":2094},"L = 10"," (60 jednotek\u002Fprac.). Od ",[1647,81483,81485],{"className":81484},[2059],[2061,81486,81487],{"xmlns":2063},[2065,81488,81489,81497],{},[2068,81490,81491,81493,81495],{},[2071,81492,586],{},[2075,81494,2077],{},[2210,81496,2935],{},[2092,81498,81480],{"encoding":2094}," přírůstky klesají, v ",[1647,81501,81503],{"className":81502},[2059],[2061,81504,81505],{"xmlns":2063},[2065,81506,81507,81515],{},[2068,81508,81509,81511,81513],{},[2071,81510,586],{},[2075,81512,2077],{},[2210,81514,9121],{},[2092,81516,81517],{"encoding":2094},"L = 20"," produkce přestává růst (maximum ",[1647,81520,81522],{"className":81521},[2059],[2061,81523,81524],{"xmlns":2063},[2065,81525,81526,81540],{},[2068,81527,81528,81530,81532,81534,81536,81538],{},[2071,81529,2861],{},[2075,81531,2084],{"stretchy":2083},[2210,81533,9121],{},[2075,81535,2090],{"stretchy":2083},[2075,81537,2077],{},[2210,81539,26597],{},[2092,81541,81542],{"encoding":2094},"Q(20) = 800","), od ",[1647,81545,81547],{"className":81546},[2059],[2061,81548,81549],{"xmlns":2063},[2065,81550,81551,81559],{},[2068,81552,81553,81555,81557],{},[2071,81554,586],{},[2075,81556,3482],{},[2210,81558,9121],{},[2092,81560,81561],{"encoding":2094},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[55,81564,81565],{},[3982,81566,81567,81568,81608,81609,2697,81627,195],{},"Obrázek 5.1 — graf produkce ",[1647,81569,81571],{"className":81570},[2059],[2061,81572,81573],{"xmlns":2063},[2065,81574,81575,81605],{},[2068,81576,81577,81579,81581,81583,81585,81587,81589,81595,81597,81599],{},[2071,81578,2861],{},[2075,81580,2084],{"stretchy":2083},[2071,81582,586],{},[2075,81584,2090],{"stretchy":2083},[2075,81586,2077],{},[2210,81588,678],{},[2205,81590,81591,81593],{},[2071,81592,586],{},[2210,81594,646],{},[2075,81596,2303],{},[2210,81598,2911],{},[2205,81600,81601,81603],{},[2071,81602,586],{},[2210,81604,654],{},[2092,81606,81607],{"encoding":2094},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[1647,81610,81612],{"className":81611},[2059],[2061,81613,81614],{"xmlns":2063},[2065,81615,81616,81624],{},[2068,81617,81618,81620,81622],{},[2071,81619,2861],{},[2075,81621,2077],{},[2210,81623,26597],{},[2092,81625,81626],{"encoding":2094},"Q = 800",[1647,81628,81630],{"className":81629},[2059],[2061,81631,81632],{"xmlns":2063},[2065,81633,81634,81642],{},[2068,81635,81636,81638,81640],{},[2071,81637,586],{},[2075,81639,2077],{},[2210,81641,9121],{},[2092,81643,81517],{"encoding":2094},[55,81645,81646,81649],{},[95,81647,81648],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[55,81651,81652,81653,835,81671,2777],{},"Podle (5.3) s ",[1647,81654,81656],{"className":81655},[2059],[2061,81657,81658],{"xmlns":2063},[2065,81659,81660,81668],{},[2068,81661,81662,81664,81666],{},[2071,81663,586],{},[2075,81665,2077],{},[2210,81667,678],{},[2092,81669,81670],{"encoding":2094},"L = 6",[1647,81672,81674],{"className":81673},[2059],[2061,81675,81676],{"xmlns":2063},[2065,81677,81678,81688],{},[2068,81679,81680,81682,81684,81686],{},[2071,81681,2273],{},[2071,81683,586],{},[2075,81685,2077],{},[2210,81687,654],{},[2092,81689,81690],{"encoding":2094},"dL = 3",[1647,81692,81694],{"className":81693},[2059],[2061,81695,81696],{"xmlns":2063,"display":31093},[2065,81697,81698,81761],{},[2068,81699,81700,81702,81704,81706,81708,81714,81716,81718,81720,81722,81724,81726,81728,81730,81732,81734,81736,81738,81740,81742,81744,81746,81748,81750,81752,81754,81756,81758],{},[2071,81701,2273],{},[2071,81703,2861],{},[2075,81705,2077],{},[2071,81707,2890],{},[2348,81709,81710,81712],{},[2071,81711,575],{},[2071,81713,586],{},[2075,81715,2084],{"stretchy":2083},[2210,81717,678],{},[2075,81719,2090],{"stretchy":2083},[2075,81721,3251],{},[2210,81723,654],{},[2075,81725,2077],{},[2075,81727,2084],{"stretchy":2083},[2210,81729,3583],{},[2075,81731,3251],{},[2210,81733,678],{},[2075,81735,2303],{},[2210,81737,22060],{},[2075,81739,3251],{},[2210,81741,5652],{},[2075,81743,2090],{"stretchy":2083},[2075,81745,3251],{},[2210,81747,654],{},[2075,81749,2077],{},[2210,81751,81399],{},[2075,81753,3251],{},[2210,81755,654],{},[2075,81757,2077],{},[2210,81759,81760],{},"151,2.",[2092,81762,81763],{"encoding":2094},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[55,81765,81766,81767,62222,81792,81806,81807,195],{},"Produkce vzroste z ",[1647,81768,81770],{"className":81769},[2059],[2061,81771,81772],{"xmlns":2063},[2065,81773,81774,81789],{},[2068,81775,81776,81778,81780,81782,81784,81786],{},[2071,81777,2861],{},[2075,81779,2084],{"stretchy":2083},[2210,81781,678],{},[2075,81783,2090],{"stretchy":2083},[2075,81785,2077],{},[2210,81787,81788],{},"172,8",[2092,81790,81791],{"encoding":2094},"Q(6) = 172{,}8",[1647,81793,81795],{"className":81794},[2059],[2061,81796,81797],{"xmlns":2063},[2065,81798,81799,81804],{},[2068,81800,81801],{},[2210,81802,81803],{},"324",[2092,81805,81803],{"encoding":2094},". Skutečná hodnota: ",[1647,81808,81810],{"className":81809},[2059],[2061,81811,81812],{"xmlns":2063},[2065,81813,81814,81854],{},[2068,81815,81816,81818,81820,81822,81824,81826,81828,81830,81832,81834,81836,81838,81840,81842,81845,81847,81849,81851],{},[2071,81817,2961],{"mathvariant":2450},[2071,81819,2861],{},[2075,81821,2077],{},[2071,81823,2861],{},[2075,81825,2084],{"stretchy":2083},[2210,81827,4087],{},[2075,81829,2090],{"stretchy":2083},[2075,81831,2303],{},[2071,81833,2861],{},[2075,81835,2084],{"stretchy":2083},[2210,81837,678],{},[2075,81839,2090],{"stretchy":2083},[2075,81841,2077],{},[2210,81843,81844],{},"340,2",[2075,81846,2303],{},[2210,81848,81788],{},[2075,81850,2077],{},[2210,81852,81853],{},"167,4",[2092,81855,81856],{"encoding":2094},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[609,81858,81860],{"id":81859},"příklad-52","Příklad 5.2",[55,81862,81863,81864,195],{},"Ověříme princip (5.5) pro ",[1647,81865,81867],{"className":81866},[2059],[2061,81868,81869],{"xmlns":2063},[2065,81870,81871,81895],{},[2068,81872,81873,81875,81877,81879,81885,81887,81889],{},[2071,81874,2861],{},[2075,81876,2077],{},[2210,81878,678],{},[2205,81880,81881,81883],{},[2071,81882,586],{},[2210,81884,646],{},[2075,81886,2303],{},[2210,81888,2911],{},[2205,81890,81891,81893],{},[2071,81892,586],{},[2210,81894,654],{},[2092,81896,81177],{"encoding":2094},[1647,81898,81900],{"className":81899},[2059],[2061,81901,81902],{"xmlns":2063,"display":31093},[2065,81903,81904,81982],{},[2068,81905,81906,81908,81914,81916,81922,81924,81926,81928,81930,81932,81938,81940,81942,81944,81952,81954,81956,81958,81960,81962,81964,81966,81968,81970,81972,81978,81980],{},[2071,81907,4342],{},[2348,81909,81910,81912],{},[2071,81911,575],{},[2071,81913,586],{},[2075,81915,2077],{},[2403,81917,81918,81920],{},[2071,81919,2861],{},[2071,81921,586],{},[2075,81923,2077],{},[2210,81925,678],{},[2071,81927,586],{},[2075,81929,2303],{},[2210,81931,2911],{},[2205,81933,81934,81936],{},[2071,81935,586],{},[2210,81937,646],{},[2075,81939,2361],{"separator":2360},[5965,81941],{"width":17019},[2071,81943,4342],{},[9252,81945,81946,81948,81950],{},[2071,81947,575],{},[2071,81949,586],{},[2075,81951,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,81953,2077],{},[2210,81955,678],{},[2075,81957,2303],{},[2210,81959,22010],{},[2071,81961,586],{},[2075,81963,2077],{},[2210,81965,630],{},[2363,81967,4072],{},[2075,81969,4075],{},[2363,81971,4072],{},[2348,81973,81974,81976],{},[2071,81975,586],{},[2210,81977,630],{},[2075,81979,2077],{},[2210,81981,72753],{},[2092,81983,81984],{"encoding":2094},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[55,81986,81987,82023,82024,82042,82043,195],{},[1647,81988,81990],{"className":81989},[2059],[2061,81991,81992],{"xmlns":2063},[2065,81993,81994,82020],{},[2068,81995,81996,81998,82010,82012,82014,82016,82018],{},[2071,81997,4342],{},[9252,81999,82000,82002,82004],{},[2071,82001,575],{},[2071,82003,586],{},[2068,82005,82006,82008],{},[2075,82007,2452],{"mathvariant":2450},[2075,82009,2452],{"mathvariant":2450},[2075,82011,2077],{},[2075,82013,2303],{},[2210,82015,22010],{},[2075,82017,3521],{},[2210,82019,630],{},[2092,82021,82022],{"encoding":2094},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[1647,82025,82027],{"className":82026},[2059],[2061,82028,82029],{"xmlns":2063},[2065,82030,82031,82039],{},[2068,82032,82033,82035,82037],{},[2071,82034,586],{},[2075,82036,2077],{},[2210,82038,39270],{},[2092,82040,82041],{"encoding":2094},"L = 15"," je maximum, ",[1647,82044,82046],{"className":82045},[2059],[2061,82047,82048],{"xmlns":2063},[2065,82049,82050,82096],{},[2068,82051,82052,82054,82060,82062,82064,82066,82068,82070,82072,82074,82076,82078,82080,82083,82085,82088,82090,82092,82094],{},[2071,82053,4342],{},[2348,82055,82056,82058],{},[2071,82057,575],{},[2071,82059,586],{},[2075,82061,2084],{"stretchy":2083},[2210,82063,39270],{},[2075,82065,2090],{"stretchy":2083},[2075,82067,2077],{},[2210,82069,678],{},[2075,82071,3251],{},[2210,82073,39270],{},[2075,82075,2303],{},[2210,82077,2911],{},[2075,82079,3251],{},[2210,82081,82082],{},"225",[2075,82084,2077],{},[2210,82086,82087],{},"90",[2075,82089,2303],{},[2210,82091,81391],{},[2075,82093,2077],{},[2210,82095,81391],{},[2092,82097,82098],{"encoding":2094},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[55,82100,82101,46171,82157,82203],{},[1647,82102,82104],{"className":82103},[2059],[2061,82105,82106],{"xmlns":2063},[2065,82107,82108,82154],{},[2068,82109,82110,82112,82118,82120,82122,82124,82126,82128,82130,82132,82134,82136,82138,82140,82142,82145,82147,82150,82152],{},[2071,82111,2890],{},[2348,82113,82114,82116],{},[2071,82115,575],{},[2071,82117,586],{},[2075,82119,2084],{"stretchy":2083},[2210,82121,39270],{},[2075,82123,2090],{"stretchy":2083},[2075,82125,2077],{},[2210,82127,3583],{},[2075,82129,3251],{},[2210,82131,39270],{},[2075,82133,2303],{},[2210,82135,22060],{},[2075,82137,3251],{},[2210,82139,82082],{},[2075,82141,2077],{},[2210,82143,82144],{},"180",[2075,82146,2303],{},[2210,82148,82149],{},"135",[2075,82151,2077],{},[2210,82153,81391],{},[2092,82155,82156],{"encoding":2094},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[1647,82158,82160],{"className":82159},[2059],[2061,82161,82162],{"xmlns":2063},[2065,82163,82164,82200],{},[2068,82165,82166,82168,82174,82176,82178,82180,82182,82184,82190,82192,82194,82196,82198],{},[2071,82167,2890],{},[2348,82169,82170,82172],{},[2071,82171,575],{},[2071,82173,586],{},[2075,82175,2084],{"stretchy":2083},[2210,82177,39270],{},[2075,82179,2090],{"stretchy":2083},[2075,82181,2077],{},[2071,82183,4342],{},[2348,82185,82186,82188],{},[2071,82187,575],{},[2071,82189,586],{},[2075,82191,2084],{"stretchy":2083},[2210,82193,39270],{},[2075,82195,2090],{"stretchy":2083},[2075,82197,2077],{},[2210,82199,81391],{},[2092,82201,82202],{"encoding":2094},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[55,82205,82206,82209,82210,20314,82239,195],{},[95,82207,82208],{},"Zkratka bez hledání extrému:"," stačí řešit ",[1647,82211,82213],{"className":82212},[2059],[2061,82214,82215],{"xmlns":2063},[2065,82216,82217,82237],{},[2068,82218,82219,82221,82227,82229,82231],{},[2071,82220,2890],{},[2348,82222,82223,82225],{},[2071,82224,575],{},[2071,82226,586],{},[2075,82228,2077],{},[2071,82230,4342],{},[2348,82232,82233,82235],{},[2071,82234,575],{},[2071,82236,586],{},[2092,82238,79134],{"encoding":2094},[1647,82240,82242],{"className":82241},[2059],[2061,82243,82244],{"xmlns":2063},[2065,82245,82246,82286],{},[2068,82247,82248,82250,82252,82254,82256,82262,82264,82266,82268,82270,82272,82278,82280,82282,82284],{},[2210,82249,3583],{},[2071,82251,586],{},[2075,82253,2303],{},[2210,82255,22060],{},[2205,82257,82258,82260],{},[2071,82259,586],{},[2210,82261,646],{},[2075,82263,2077],{},[2210,82265,678],{},[2071,82267,586],{},[2075,82269,2303],{},[2210,82271,2911],{},[2205,82273,82274,82276],{},[2071,82275,586],{},[2210,82277,646],{},[2075,82279,4075],{},[2071,82281,586],{},[2075,82283,2077],{},[2210,82285,39270],{},[2092,82287,82288],{"encoding":2094},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[55,82290,82291],{},[3982,82292,82293,82294,82313,82314,13861,82332,82351,82352,82370,82371,82388,82389,82408,82409,82428],{},"Obrázek 5.3 — křivky ",[1647,82295,82297],{"className":82296},[2059],[2061,82298,82299],{"xmlns":2063},[2065,82300,82301,82311],{},[2068,82302,82303,82305],{},[2071,82304,2890],{},[2348,82306,82307,82309],{},[2071,82308,575],{},[2071,82310,586],{},[2092,82312,11176],{"encoding":2094}," (max 60 při ",[1647,82315,82317],{"className":82316},[2059],[2061,82318,82319],{"xmlns":2063},[2065,82320,82321,82329],{},[2068,82322,82323,82325,82327],{},[2071,82324,586],{},[2075,82326,2077],{},[2210,82328,2935],{},[2092,82330,82331],{"encoding":2094},"L=10",[1647,82333,82335],{"className":82334},[2059],[2061,82336,82337],{"xmlns":2063},[2065,82338,82339,82349],{},[2068,82340,82341,82343],{},[2071,82342,4342],{},[2348,82344,82345,82347],{},[2071,82346,575],{},[2071,82348,586],{},[2092,82350,79104],{"encoding":2094}," (max 45 při ",[1647,82353,82355],{"className":82354},[2059],[2061,82356,82357],{"xmlns":2063},[2065,82358,82359,82367],{},[2068,82360,82361,82363,82365],{},[2071,82362,586],{},[2075,82364,2077],{},[2210,82366,39270],{},[2092,82368,82369],{"encoding":2094},"L=15","), průsečík v ",[1647,82372,82374],{"className":82373},[2059],[2061,82375,82376],{"xmlns":2063},[2065,82377,82378,82386],{},[2068,82379,82380,82382,82384],{},[2071,82381,586],{},[2075,82383,2077],{},[2210,82385,39270],{},[2092,82387,82041],{"encoding":2094},". Nalevo od 15 leží ",[1647,82390,82392],{"className":82391},[2059],[2061,82393,82394],{"xmlns":2063},[2065,82395,82396,82406],{},[2068,82397,82398,82400],{},[2071,82399,2890],{},[2348,82401,82402,82404],{},[2071,82403,575],{},[2071,82405,586],{},[2092,82407,11176],{"encoding":2094}," nad ",[1647,82410,82412],{"className":82411},[2059],[2061,82413,82414],{"xmlns":2063},[2065,82415,82416,82426],{},[2068,82417,82418,82420],{},[2071,82419,4342],{},[2348,82421,82422,82424],{},[2071,82423,575],{},[2071,82425,586],{},[2092,82427,79104],{"encoding":2094},", napravo pod ní.",[84,82430,82432],{"id":82431},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[55,82434,82435,82436,2758,82449,1445,82452,6277,82465,1445,82468,2777],{},"V dvoufaktorovém modelu závisí produkce ",[1647,82437,82439],{"className":82438},[2059],[2061,82440,82441],{"xmlns":2063},[2065,82442,82443,82447],{},[2068,82444,82445],{},[2071,82446,2861],{},[2092,82448,2861],{"encoding":2094},[95,82450,82451],{},"práci",[1647,82453,82455],{"className":82454},[2059],[2061,82456,82457],{"xmlns":2063},[2065,82458,82459,82463],{},[2068,82460,82461],{},[2071,82462,586],{},[2092,82464,586],{"encoding":2094},[95,82466,82467],{},"kapitálu",[1647,82469,82471],{"className":82470},[2059],[2061,82472,82473],{"xmlns":2063},[2065,82474,82475,82479],{},[2068,82476,82477],{},[2071,82478,10929],{},[2092,82480,10929],{"encoding":2094},[1647,82482,82484],{"className":82483},[2059],[2061,82485,82486],{"xmlns":2063,"display":31093},[2065,82487,82488,82523],{},[23493,82489,82490],{"width":31098},[23498,82491,82492,82494,82516,82518],{},[23501,82493],{"width":31103},[23501,82495,82496],{},[2068,82497,82498,82500,82502,82504,82506,82508,82510,82512,82514],{},[2071,82499,2861],{},[2075,82501,2077],{},[2071,82503,2861],{},[2075,82505,2084],{"stretchy":2083},[2071,82507,586],{},[2075,82509,2361],{"separator":2360},[2071,82511,10929],{},[2075,82513,2090],{"stretchy":2083},[2071,82515,195],{"mathvariant":2450},[23501,82517],{"width":31103},[23501,82519,82520],{},[2363,82521,82522],{},"(5.6)",[2092,82524,82525],{"encoding":2094},"Q = Q(L, K). \\tag{5.6}",[55,82527,82528,82529,82531],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[95,82530,79471],{}," (v širším smyslu oproti jednofaktorovému modelu).",[84,82533,82535],{"id":82534},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[55,82537,82538],{},"Široce používané produkční funkce mají tvar",[1647,82540,82542],{"className":82541},[2059],[2061,82543,82544],{"xmlns":2063,"display":31093},[2065,82545,82546,82587],{},[23493,82547,82548],{"width":31098},[23498,82549,82550,82552,82580,82582],{},[23501,82551],{"width":31103},[23501,82553,82554],{},[2068,82555,82556,82558,82560,82562,82564,82570,82572,82578],{},[2071,82557,2861],{},[2075,82559,2077],{},[2071,82561,4342],{},[2363,82563,3061],{},[2205,82565,82566,82568],{},[2071,82567,586],{},[2071,82569,69],{},[2363,82571,3061],{},[2205,82573,82574,82576],{},[2071,82575,10929],{},[2071,82577,2179],{},[2075,82579,2361],{"separator":2360},[23501,82581],{"width":31103},[23501,82583,82584],{},[2363,82585,82586],{},"(5.7)",[2092,82588,82589],{"encoding":2094},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[55,82591,4397,82592,82614,82615,82617,82618,195],{},[1647,82593,82595],{"className":82594},[2059],[2061,82596,82597],{"xmlns":2063},[2065,82598,82599,82611],{},[2068,82600,82601,82603,82605,82607,82609],{},[2071,82602,4342],{},[2075,82604,2361],{"separator":2360},[2071,82606,69],{},[2075,82608,2361],{"separator":2360},[2071,82610,2179],{},[2092,82612,82613],{"encoding":2094},"A, a, b"," jsou kladné konstanty. Nazývají se ",[95,82616,79170],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[1647,82619,82621],{"className":82620},[2059],[2061,82622,82623],{"xmlns":2063},[2065,82624,82625,82637],{},[2068,82626,82627,82629,82631,82633,82635],{},[2071,82628,69],{},[2075,82630,2361],{"separator":2360},[2071,82632,2179],{},[2075,82634,3521],{},[2210,82636,638],{},[2092,82638,82639],{"encoding":2094},"a, b \u003C 1",[55,82641,82642],{},[58,82643],{"alt":82644,"className":82645,"src":82646},"imek-vynosy-z-rozsahu-3typy",[62,63],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[55,82648,82649,82650,82653,82654,2758,82667,82683,82684,2758,82697,2777],{},"Reflektují ekonomickou zákonitost, že ",[95,82651,82652],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[1647,82655,82657],{"className":82656},[2059],[2061,82658,82659],{"xmlns":2063},[2065,82660,82661,82665],{},[2068,82662,82663],{},[2071,82664,586],{},[2092,82666,586],{"encoding":2094},[1647,82668,82670],{"className":82669},[2059],[2061,82671,82672],{"xmlns":2063},[2065,82673,82674,82680],{},[2068,82675,82676,82678],{},[2071,82677,13774],{},[2071,82679,586],{},[2092,82681,82682],{"encoding":2094},"rL"," a kapitál z ",[1647,82685,82687],{"className":82686},[2059],[2061,82688,82689],{"xmlns":2063},[2065,82690,82691,82695],{},[2068,82692,82693],{},[2071,82694,10929],{},[2092,82696,10929],{"encoding":2094},[1647,82698,82700],{"className":82699},[2059],[2061,82701,82702],{"xmlns":2063},[2065,82703,82704,82710],{},[2068,82705,82706,82708],{},[2071,82707,13774],{},[2071,82709,10929],{},[2092,82711,82712],{"encoding":2094},"rK",[1647,82714,82716],{"className":82715},[2059],[2061,82717,82718],{"xmlns":2063,"display":31093},[2065,82719,82720,82843],{},[23493,82721,82722],{"width":31098},[23498,82723,82724,82726,82836,82838],{},[23501,82725],{"width":31103},[23501,82727,82728],{},[2068,82729,82730,82732,82734,82736,82738,82740,82742,82744,82746,82748,82750,82752,82754,82756,82762,82764,82766,82768,82774,82776,82778,82780,82792,82794,82800,82806,82808,82820,82822,82824,82826,82828,82830,82832,82834],{},[2071,82731,2861],{},[2075,82733,2084],{"stretchy":2083},[2071,82735,13774],{},[2071,82737,586],{},[2075,82739,2361],{"separator":2360},[2071,82741,13774],{},[2071,82743,10929],{},[2075,82745,2090],{"stretchy":2083},[2075,82747,2077],{},[2071,82749,4342],{},[2075,82751,2084],{"stretchy":2083},[2071,82753,13774],{},[2071,82755,586],{},[2205,82757,82758,82760],{},[2075,82759,2090],{"stretchy":2083},[2071,82761,69],{},[2075,82763,2084],{"stretchy":2083},[2071,82765,13774],{},[2071,82767,10929],{},[2205,82769,82770,82772],{},[2075,82771,2090],{"stretchy":2083},[2071,82773,2179],{},[2075,82775,2077],{},[2071,82777,4342],{},[2363,82779,3061],{},[2205,82781,82782,82784],{},[2071,82783,13774],{},[2068,82785,82786,82788,82790],{},[2071,82787,69],{},[2075,82789,2176],{},[2071,82791,2179],{},[2363,82793,3061],{},[2205,82795,82796,82798],{},[2071,82797,586],{},[2071,82799,69],{},[2205,82801,82802,82804],{},[2071,82803,10929],{},[2071,82805,2179],{},[2075,82807,2077],{},[2205,82809,82810,82812],{},[2071,82811,13774],{},[2068,82813,82814,82816,82818],{},[2071,82815,69],{},[2075,82817,2176],{},[2071,82819,2179],{},[2363,82821,3061],{},[2071,82823,2861],{},[2075,82825,2084],{"stretchy":2083},[2071,82827,586],{},[2075,82829,2361],{"separator":2360},[2071,82831,10929],{},[2075,82833,2090],{"stretchy":2083},[2071,82835,195],{"mathvariant":2450},[23501,82837],{"width":31103},[23501,82839,82840],{},[2363,82841,82842],{},"(5.8)",[2092,82844,82845],{"encoding":2094},"Q(rL, rK) = A(rL)^a(rK)^b = A\\,r^{a+b}\\,L^a K^b = r^{a+b}\\,Q(L, K). \\tag{5.8}",[55,82847,82848,82849],{},"Volně: ",[95,82850,82851,82852,82865,82866,82890],{},"změní-li se vstupy ",[1647,82853,82855],{"className":82854},[2059],[2061,82856,82857],{"xmlns":2063},[2065,82858,82859,82863],{},[2068,82860,82861],{},[2071,82862,13774],{},[2092,82864,13774],{"encoding":2094},"-krát, změní se výstup ",[1647,82867,82869],{"className":82868},[2059],[2061,82870,82871],{"xmlns":2063},[2065,82872,82873,82887],{},[2068,82874,82875],{},[2205,82876,82877,82879],{},[2071,82878,13774],{},[2068,82880,82881,82883,82885],{},[2071,82882,69],{},[2075,82884,2176],{},[2071,82886,2179],{},[2092,82888,82889],{"encoding":2094},"r^{a+b}","-krát.",[609,82892,82894],{"id":82893},"výnosy-z-rozsahu","Výnosy z rozsahu",[55,82896,82897,82898,82915],{},"Součet exponentů ",[1647,82899,82901],{"className":82900},[2059],[2061,82902,82903],{"xmlns":2063},[2065,82904,82905,82913],{},[2068,82906,82907,82909,82911],{},[2071,82908,69],{},[2075,82910,2176],{},[2071,82912,2179],{},[2092,82914,79295],{"encoding":2094}," určuje typ výnosů z rozsahu:",[323,82917,82918,82946],{},[326,82919,82920],{},[329,82921,82922,82924,82927,82944],{},[332,82923,10393],{},[332,82925,82926],{},"Podmínka",[332,82928,82929,82930,82943],{},"Chování produkce při ",[1647,82931,82933],{"className":82932},[2059],[2061,82934,82935],{"xmlns":2063},[2065,82936,82937,82941],{},[2068,82938,82939],{},[2071,82940,13774],{},[2092,82942,13774],{"encoding":2094},"-násobném zvýšení vstupů",[332,82945,3144],{},[342,82947,82948,83059,83174],{},[329,82949,82950,82958,82982,83015],{},[347,82951,80008,82952,11156,82955,2090],{},[95,82953,82954],{},"Konstantní",[3982,82956,82957],{},"constant returns",[347,82959,82960],{},[1647,82961,82963],{"className":82962},[2059],[2061,82964,82965],{"xmlns":2063},[2065,82966,82967,82979],{},[2068,82968,82969,82971,82973,82975,82977],{},[2071,82970,69],{},[2075,82972,2176],{},[2071,82974,2179],{},[2075,82976,2077],{},[2210,82978,638],{},[2092,82980,82981],{"encoding":2094},"a+b = 1",[347,82983,82984,82997,82998,1445,83001,83014],{},[1647,82985,82987],{"className":82986},[2059],[2061,82988,82989],{"xmlns":2063},[2065,82990,82991,82995],{},[2068,82992,82993],{},[2071,82994,2861],{},[2092,82996,2861],{"encoding":2094}," vzroste ",[95,82999,83000],{},"přesně",[1647,83002,83004],{"className":83003},[2059],[2061,83005,83006],{"xmlns":2063},[2065,83007,83008,83012],{},[2068,83009,83010],{},[2071,83011,13774],{},[2092,83013,13774],{"encoding":2094},"-krát",[347,83016,83017],{},[1647,83018,83020],{"className":83019},[2059],[2061,83021,83022],{"xmlns":2063},[2065,83023,83024,83056],{},[2068,83025,83026,83028,83030,83032,83044],{},[2071,83027,2861],{},[2075,83029,2077],{},[2210,83031,646],{},[2205,83033,83034,83036],{},[2071,83035,586],{},[2068,83037,83038,83040,83042],{},[2210,83039,638],{},[2071,83041,4761],{"mathvariant":2450},[2210,83043,662],{},[2205,83045,83046,83048],{},[2071,83047,10929],{},[2068,83049,83050,83052,83054],{},[2210,83051,654],{},[2071,83053,4761],{"mathvariant":2450},[2210,83055,662],{},[2092,83057,83058],{"encoding":2094},"Q = 2L^{1\u002F4}K^{3\u002F4}",[329,83060,83061,83070,83094,83124],{},[347,83062,83063,83064,11156,83067,2090],{},"2° ",[95,83065,83066],{},"Rostoucí",[3982,83068,83069],{},"increasing returns",[347,83071,83072],{},[1647,83073,83075],{"className":83074},[2059],[2061,83076,83077],{"xmlns":2063},[2065,83078,83079,83091],{},[2068,83080,83081,83083,83085,83087,83089],{},[2071,83082,69],{},[2075,83084,2176],{},[2071,83086,2179],{},[2075,83088,3482],{},[2210,83090,638],{},[2092,83092,83093],{"encoding":2094},"a+b > 1",[347,83095,83096,82997,83109,55529,83111,83014],{},[1647,83097,83099],{"className":83098},[2059],[2061,83100,83101],{"xmlns":2063},[2065,83102,83103,83107],{},[2068,83104,83105],{},[2071,83106,2861],{},[2092,83108,2861],{"encoding":2094},[95,83110,28008],{},[1647,83112,83114],{"className":83113},[2059],[2061,83115,83116],{"xmlns":2063},[2065,83117,83118,83122],{},[2068,83119,83120],{},[2071,83121,13774],{},[2092,83123,13774],{"encoding":2094},[347,83125,83126,11156,83152,2090],{},[1647,83127,83129],{"className":83128},[2059],[2061,83130,83131],{"xmlns":2063},[2065,83132,83133,83149],{},[2068,83134,83135,83137,83139,83141,83143],{},[2071,83136,2861],{},[2075,83138,2077],{},[2210,83140,686],{},[2071,83142,586],{},[2205,83144,83145,83147],{},[2071,83146,10929],{},[2210,83148,646],{},[2092,83150,83151],{"encoding":2094},"Q = 7LK^2",[1647,83153,83155],{"className":83154},[2059],[2061,83156,83157],{"xmlns":2063},[2065,83158,83159,83171],{},[2068,83160,83161,83163,83165,83167,83169],{},[2071,83162,69],{},[2075,83164,2176],{},[2071,83166,2179],{},[2075,83168,2077],{},[2210,83170,654],{},[2092,83172,83173],{"encoding":2094},"a+b = 3",[329,83175,83176,83185,83209,83240],{},[347,83177,83178,83179,11156,83182,2090],{},"3° ",[95,83180,83181],{},"Klesající",[3982,83183,83184],{},"decreasing returns",[347,83186,83187],{},[1647,83188,83190],{"className":83189},[2059],[2061,83191,83192],{"xmlns":2063},[2065,83193,83194,83206],{},[2068,83195,83196,83198,83200,83202,83204],{},[2071,83197,69],{},[2075,83199,2176],{},[2071,83201,2179],{},[2075,83203,3521],{},[2210,83205,638],{},[2092,83207,83208],{"encoding":2094},"a+b \u003C 1",[347,83210,83211,82997,83224,55529,83227,83014],{},[1647,83212,83214],{"className":83213},[2059],[2061,83215,83216],{"xmlns":2063},[2065,83217,83218,83222],{},[2068,83219,83220],{},[2071,83221,2861],{},[2092,83223,2861],{"encoding":2094},[95,83225,83226],{},"méně",[1647,83228,83230],{"className":83229},[2059],[2061,83231,83232],{"xmlns":2063},[2065,83233,83234,83238],{},[2068,83235,83236],{},[2071,83237,13774],{},[2092,83239,13774],{"encoding":2094},[347,83241,83242,11156,83272,2090],{},[1647,83243,83245],{"className":83244},[2059],[2061,83246,83247],{"xmlns":2063},[2065,83248,83249,83269],{},[2068,83250,83251,83253,83255,83257,83263],{},[2071,83252,2861],{},[2075,83254,2077],{},[2210,83256,2935],{},[2205,83258,83259,83261],{},[2071,83260,586],{},[2210,83262,72681],{},[2205,83264,83265,83267],{},[2071,83266,10929],{},[2210,83268,5096],{},[2092,83270,83271],{"encoding":2094},"Q = 10L^{0{,}3}K^{0{,}5}",[1647,83273,83275],{"className":83274},[2059],[2061,83276,83277],{"xmlns":2063},[2065,83278,83279,83291],{},[2068,83280,83281,83283,83285,83287,83289],{},[2071,83282,69],{},[2075,83284,2176],{},[2071,83286,2179],{},[2075,83288,2077],{},[2210,83290,16324],{},[2092,83292,83293],{"encoding":2094},"a+b = 0{,}8",[1023,83295,83296],{},[55,83297,83298,83300,83301,83318,83319,83322,83323,1445,83326,83362,83363,83385,83386,195],{},[1647,83299,4499],{}," Pozor\nSoučet ",[1647,83302,83304],{"className":83303},[2059],[2061,83305,83306],{"xmlns":2063},[2065,83307,83308,83316],{},[2068,83309,83310,83312,83314],{},[2071,83311,69],{},[2075,83313,2176],{},[2071,83315,2179],{},[2092,83317,79295],{"encoding":2094}," neudává velikost produkce, ale ",[95,83320,83321],{},"elasticitu vůči škálování vstupů",". Speciálně ",[95,83324,83325],{},"ryzí Cobb-Douglas",[1647,83327,83329],{"className":83328},[2059],[2061,83330,83331],{"xmlns":2063},[2065,83332,83333,83359],{},[2068,83334,83335,83337,83339,83341,83347],{},[2071,83336,2861],{},[2075,83338,2077],{},[2071,83340,4342],{},[2205,83342,83343,83345],{},[2071,83344,586],{},[2071,83346,69],{},[2205,83348,83349,83351],{},[2071,83350,10929],{},[2068,83352,83353,83355,83357],{},[2210,83354,638],{},[2075,83356,2303],{},[2071,83358,69],{},[2092,83360,83361],{"encoding":2094},"Q = AL^a K^{1-a}"," má ",[1647,83364,83366],{"className":83365},[2059],[2061,83367,83368],{"xmlns":2063},[2065,83369,83370,83382],{},[2068,83371,83372,83374,83376,83378,83380],{},[2071,83373,2179],{},[2075,83375,2077],{},[2210,83377,638],{},[2075,83379,2303],{},[2071,83381,69],{},[2092,83383,83384],{"encoding":2094},"b = 1-a",", tedy vždy ",[95,83387,83388],{},"konstantní výnosy z rozsahu",[609,83390,83392,83393],{"id":83391},"parametr-efektivity-aa","Parametr efektivity ",[1647,83394,83396],{"className":83395},[2059],[2061,83397,83398],{"xmlns":2063},[2065,83399,83400,83404],{},[2068,83401,83402],{},[2071,83403,4342],{},[2092,83405,4342],{"encoding":2094},[55,83407,83408,83409,83422,83423,83436,83437,83455,83456,83459],{},"Konstanta ",[1647,83410,83412],{"className":83411},[2059],[2061,83413,83414],{"xmlns":2063},[2065,83415,83416,83420],{},[2068,83417,83418],{},[2071,83419,4342],{},[2092,83421,4342],{"encoding":2094}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[1647,83424,83426],{"className":83425},[2059],[2061,83427,83428],{"xmlns":2063},[2065,83429,83430,83434],{},[2068,83431,83432],{},[2071,83433,2861],{},[2092,83435,2861],{"encoding":2094}," při pevně zadaných ",[1647,83438,83440],{"className":83439},[2059],[2061,83441,83442],{"xmlns":2063},[2065,83443,83444,83452],{},[2068,83445,83446,83448,83450],{},[2071,83447,586],{},[2075,83449,2361],{"separator":2360},[2071,83451,10929],{},[2092,83453,83454],{"encoding":2094},"L, K",", a lze ji proto chápat jako ",[95,83457,83458],{},"parametr efektivity"," — indikátor stavu technologie.",[609,83461,83463],{"id":83462},"příklad-53","Příklad 5.3",[55,83465,83466,83467,83362,83509,83511,83512,195],{},"Produkční funkce ",[1647,83468,83470],{"className":83469},[2059],[2061,83471,83472],{"xmlns":2063},[2065,83473,83474,83506],{},[2068,83475,83476,83478,83480,83482,83494],{},[2071,83477,2861],{},[2075,83479,2077],{},[2210,83481,646],{},[2205,83483,83484,83486],{},[2071,83485,586],{},[2068,83487,83488,83490,83492],{},[2210,83489,638],{},[2071,83491,4761],{"mathvariant":2450},[2210,83493,662],{},[2205,83495,83496,83498],{},[2071,83497,10929],{},[2068,83499,83500,83502,83504],{},[2210,83501,654],{},[2071,83503,4761],{"mathvariant":2450},[2210,83505,662],{},[2092,83507,83508],{"encoding":2094},"Q = 2L^{1\u002F4} K^{3\u002F4}",[95,83510,27351],{}," výnosy z rozsahu, neboť ",[1647,83513,83515],{"className":83514},[2059],[2061,83516,83517],{"xmlns":2063},[2065,83518,83519,83543],{},[2068,83520,83521,83529,83531,83539,83541],{},[2400,83522,83523],{"scriptlevel":630,"displaystyle":2083},[2403,83524,83525,83527],{},[2210,83526,638],{},[2210,83528,662],{},[2075,83530,2176],{},[2400,83532,83533],{"scriptlevel":630,"displaystyle":2083},[2403,83534,83535,83537],{},[2210,83536,654],{},[2210,83538,662],{},[2075,83540,2077],{},[2210,83542,638],{},[2092,83544,83545],{"encoding":2094},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[55,83547,83548,83549,6277,83562,83575,83576,1445,83589,83629],{},"Změní-li se ",[1647,83550,83552],{"className":83551},[2059],[2061,83553,83554],{"xmlns":2063},[2065,83555,83556,83560],{},[2068,83557,83558],{},[2071,83559,586],{},[2092,83561,586],{"encoding":2094},[1647,83563,83565],{"className":83564},[2059],[2061,83566,83567],{"xmlns":2063},[2065,83568,83569,83573],{},[2068,83570,83571],{},[2071,83572,10929],{},[2092,83574,10929],{"encoding":2094}," čtyřnásobně, změní se ",[1647,83577,83579],{"className":83578},[2059],[2061,83580,83581],{"xmlns":2063},[2065,83582,83583,83587],{},[2068,83584,83585],{},[2071,83586,2861],{},[2092,83588,2861],{"encoding":2094},[1647,83590,83592],{"className":83591},[2059],[2061,83593,83594],{"xmlns":2063},[2065,83595,83596,83626],{},[2068,83597,83598,83618,83620],{},[2205,83599,83600,83602],{},[2210,83601,662],{},[2068,83603,83604,83606,83608,83610,83612,83614,83616],{},[2210,83605,638],{},[2071,83607,4761],{"mathvariant":2450},[2210,83609,662],{},[2075,83611,2176],{},[2210,83613,654],{},[2071,83615,4761],{"mathvariant":2450},[2210,83617,662],{},[2075,83619,2077],{},[2205,83621,83622,83624],{},[2210,83623,662],{},[2210,83625,638],{},[2092,83627,83628],{"encoding":2094},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[1647,83631,83633],{"className":83632},[2059],[2061,83634,83635],{"xmlns":2063,"display":31093},[2065,83636,83637,83797],{},[2068,83638,83639,83641,83643,83645,83647,83649,83651,83653,83655,83657,83659,83661,83663,83665,83677,83679,83681,83683,83695,83697,83699,83701,83721,83733,83745,83747,83749,83751,83753,83765,83777,83779,83781,83783,83785,83787,83789,83791,83793,83795],{},[2071,83640,2861],{},[2075,83642,2084],{"stretchy":2083},[2210,83644,662],{},[2071,83646,586],{},[2075,83648,2361],{"separator":2360},[2210,83650,662],{},[2071,83652,10929],{},[2075,83654,2090],{"stretchy":2083},[2075,83656,2077],{},[2210,83658,646],{},[2075,83660,2084],{"stretchy":2083},[2210,83662,662],{},[2071,83664,586],{},[2205,83666,83667,83669],{},[2075,83668,2090],{"stretchy":2083},[2068,83670,83671,83673,83675],{},[2210,83672,638],{},[2071,83674,4761],{"mathvariant":2450},[2210,83676,662],{},[2075,83678,2084],{"stretchy":2083},[2210,83680,662],{},[2071,83682,10929],{},[2205,83684,83685,83687],{},[2075,83686,2090],{"stretchy":2083},[2068,83688,83689,83691,83693],{},[2210,83690,654],{},[2071,83692,4761],{"mathvariant":2450},[2210,83694,662],{},[2075,83696,2077],{},[2210,83698,646],{},[2075,83700,3251],{},[2205,83702,83703,83705],{},[2210,83704,662],{},[2068,83706,83707,83709,83711,83713,83715,83717,83719],{},[2210,83708,638],{},[2071,83710,4761],{"mathvariant":2450},[2210,83712,662],{},[2075,83714,2176],{},[2210,83716,654],{},[2071,83718,4761],{"mathvariant":2450},[2210,83720,662],{},[2205,83722,83723,83725],{},[2071,83724,586],{},[2068,83726,83727,83729,83731],{},[2210,83728,638],{},[2071,83730,4761],{"mathvariant":2450},[2210,83732,662],{},[2205,83734,83735,83737],{},[2071,83736,10929],{},[2068,83738,83739,83741,83743],{},[2210,83740,654],{},[2071,83742,4761],{"mathvariant":2450},[2210,83744,662],{},[2075,83746,2077],{},[2210,83748,662],{},[2075,83750,3251],{},[2210,83752,646],{},[2205,83754,83755,83757],{},[2071,83756,586],{},[2068,83758,83759,83761,83763],{},[2210,83760,638],{},[2071,83762,4761],{"mathvariant":2450},[2210,83764,662],{},[2205,83766,83767,83769],{},[2071,83768,10929],{},[2068,83770,83771,83773,83775],{},[2210,83772,654],{},[2071,83774,4761],{"mathvariant":2450},[2210,83776,662],{},[2075,83778,2077],{},[2210,83780,662],{},[2363,83782,3061],{},[2071,83784,2861],{},[2075,83786,2084],{"stretchy":2083},[2071,83788,586],{},[2075,83790,2361],{"separator":2360},[2071,83792,10929],{},[2075,83794,2090],{"stretchy":2083},[2071,83796,195],{"mathvariant":2450},[2092,83798,83799],{"encoding":2094},"Q(4L, 4K) = 2(4L)^{1\u002F4}(4K)^{3\u002F4} = 2\\cdot 4^{1\u002F4+3\u002F4} L^{1\u002F4} K^{3\u002F4} = 4\\cdot 2L^{1\u002F4}K^{3\u002F4} = 4\\,Q(L,K).",[609,83801,83802],{"id":41471},"Homogenita",[55,83804,83805,83806,8189,83829,83845],{},"Funkce ",[1647,83807,83809],{"className":83808},[2059],[2061,83810,83811],{"xmlns":2063},[2065,83812,83813,83827],{},[2068,83814,83815,83817,83819,83821,83823,83825],{},[2071,83816,2861],{},[2075,83818,2084],{"stretchy":2083},[2071,83820,586],{},[2075,83822,2361],{"separator":2360},[2071,83824,10929],{},[2075,83826,2090],{"stretchy":2083},[2092,83828,11128],{"encoding":2094},[95,83830,83831,83832],{},"homogenní stupně ",[1647,83833,83835],{"className":83834},[2059],[2061,83836,83837],{"xmlns":2063},[2065,83838,83839,83843],{},[2068,83840,83841],{},[2071,83842,41153],{},[2092,83844,41153],{"encoding":2094},", jestliže",[1647,83847,83849],{"className":83848},[2059],[2061,83850,83851],{"xmlns":2063,"display":31093},[2065,83852,83853,83910],{},[23493,83854,83855],{"width":31098},[23498,83856,83857,83859,83903,83905],{},[23501,83858],{"width":31103},[23501,83860,83861],{},[2068,83862,83863,83865,83867,83869,83871,83873,83875,83877,83879,83881,83887,83889,83891,83893,83895,83897,83899,83901],{},[2071,83864,2861],{},[2075,83866,2084],{"stretchy":2083},[2071,83868,13774],{},[2071,83870,586],{},[2075,83872,2361],{"separator":2360},[2071,83874,13774],{},[2071,83876,10929],{},[2075,83878,2090],{"stretchy":2083},[2075,83880,2077],{},[2205,83882,83883,83885],{},[2071,83884,13774],{},[2071,83886,41153],{},[2363,83888,3061],{},[2071,83890,2861],{},[2075,83892,2084],{"stretchy":2083},[2071,83894,586],{},[2075,83896,2361],{"separator":2360},[2071,83898,10929],{},[2075,83900,2090],{"stretchy":2083},[2075,83902,2361],{"separator":2360},[23501,83904],{"width":31103},[23501,83906,83907],{},[2363,83908,83909],{},"(5.10)",[2092,83911,83912],{"encoding":2094},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[55,83914,4397,83915,83933,83934,83952,83953,47930,83966,83969,83970,195],{},[1647,83916,83918],{"className":83917},[2059],[2061,83919,83920],{"xmlns":2063},[2065,83921,83922,83930],{},[2068,83923,83924,83926,83928],{},[2071,83925,41153],{},[2075,83927,4572],{},[2210,83929,630],{},[2092,83931,83932],{"encoding":2094},"n \\geq 0"," je celé číslo a ",[1647,83935,83937],{"className":83936},[2059],[2061,83938,83939],{"xmlns":2063},[2065,83940,83941,83949],{},[2068,83942,83943,83945,83947],{},[2071,83944,13774],{},[2075,83946,3482],{},[2210,83948,630],{},[2092,83950,83951],{"encoding":2094},"r > 0",". Homogenní funkce stupně ",[1647,83954,83956],{"className":83955},[2059],[2061,83957,83958],{"xmlns":2063},[2065,83959,83960,83964],{},[2068,83961,83962],{},[2210,83963,638],{},[2092,83965,638],{"encoding":2094},[95,83967,83968],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[1647,83971,83973],{"className":83972},[2059],[2061,83974,83975],{"xmlns":2063},[2065,83976,83977,83985],{},[2068,83978,83979,83981,83983],{},[2071,83980,69],{},[2075,83982,2176],{},[2071,83984,2179],{},[2092,83986,79295],{"encoding":2094},[84,83988,83990],{"id":83989},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[55,83992,83993],{},[95,83994,83995],{},"Ryzí Cobb-Douglasovy funkce:",[1647,83997,83999],{"className":83998},[2059],[2061,84000,84001],{"xmlns":2063,"display":31093},[2065,84002,84003,84062],{},[23493,84004,84005],{"width":31098},[23498,84006,84007,84009,84055,84057],{},[23501,84008],{"width":31103},[23501,84010,84011],{},[2068,84012,84013,84015,84017,84019,84021,84027,84029,84041,84043,84045,84047,84049,84051,84053],{},[2071,84014,2861],{},[2075,84016,2077],{},[2071,84018,4342],{},[2363,84020,3061],{},[2205,84022,84023,84025],{},[2071,84024,586],{},[2071,84026,69],{},[2363,84028,3061],{},[2205,84030,84031,84033],{},[2071,84032,10929],{},[2068,84034,84035,84037,84039],{},[2210,84036,638],{},[2075,84038,2303],{},[2071,84040,69],{},[2075,84042,2361],{"separator":2360},[5965,84044],{"width":17019},[2210,84046,630],{},[2075,84048,3521],{},[2071,84050,69],{},[2075,84052,3521],{},[2210,84054,14995],{},[23501,84056],{"width":31103},[23501,84058,84059],{},[2363,84060,84061],{},"(5.9)",[2092,84063,84064],{"encoding":2094},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[55,84066,84067,84068,84070,84071,195],{},"Mají vždy ",[95,84069,83388],{}," a jsou ",[95,84072,83968],{},[55,84074,84075,11156,84078,84081],{},[95,84076,84077],{},"CES produkční funkce",[3982,84079,84080],{},"Constant Elasticity of Substitution",", 1961):",[1647,84083,84085],{"className":84084},[2059],[2061,84086,84087],{"xmlns":2063,"display":31093},[2065,84088,84089,84157],{},[2068,84090,84091,84093,84095,84097,84155],{},[2071,84092,2861],{},[2075,84094,2077],{},[2071,84096,4342],{},[2205,84098,84099,84143],{},[2068,84100,84101,84103,84105,84107,84109,84111,84113,84115,84125,84127,84129,84131,84141],{},[2075,84102,2561],{"fence":2360},[2075,84104,2084],{"stretchy":2083},[2210,84106,638],{},[2075,84108,2303],{},[2071,84110,69],{},[2075,84112,2090],{"stretchy":2083},[2363,84114,3061],{},[2205,84116,84117,84119],{},[2071,84118,586],{},[2068,84120,84121,84123],{},[2075,84122,2303],{},[2071,84124,2179],{},[2075,84126,2176],{},[2071,84128,69],{},[2363,84130,3061],{},[2205,84132,84133,84135],{},[2071,84134,10929],{},[2068,84136,84137,84139],{},[2075,84138,2303],{},[2071,84140,2179],{},[2075,84142,2576],{"fence":2360},[2068,84144,84145,84147],{},[2075,84146,2303],{},[2400,84148,84149],{"scriptlevel":630,"displaystyle":2083},[2403,84150,84151,84153],{},[2210,84152,638],{},[2071,84154,2179],{},[2075,84156,2361],{"separator":2360},[2092,84158,84159],{"encoding":2094},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[55,84161,4397,84162,835,84180,835,84201,84225],{},[1647,84163,84165],{"className":84164},[2059],[2061,84166,84167],{"xmlns":2063},[2065,84168,84169,84177],{},[2068,84170,84171,84173,84175],{},[2071,84172,4342],{},[2075,84174,3482],{},[2210,84176,630],{},[2092,84178,84179],{"encoding":2094},"A > 0",[1647,84181,84183],{"className":84182},[2059],[2061,84184,84185],{"xmlns":2063},[2065,84186,84187,84199],{},[2068,84188,84189,84191,84193,84195,84197],{},[2210,84190,630],{},[2075,84192,3521],{},[2071,84194,69],{},[2075,84196,3521],{},[2210,84198,638],{},[2092,84200,21575],{"encoding":2094},[1647,84202,84204],{"className":84203},[2059],[2061,84205,84206],{"xmlns":2063},[2065,84207,84208,84222],{},[2068,84209,84210,84212,84214,84216,84218,84220],{},[2075,84211,2303],{},[2210,84213,638],{},[2075,84215,3521],{},[2071,84217,2179],{},[2075,84219,3445],{"mathvariant":2450},[2210,84221,630],{},[2092,84223,84224],{"encoding":2094},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[55,84227,84228],{},[95,84229,84230],{},"Další typy:",[89,84232,84233,84275],{},[92,84234,84235,1445,84238,84274],{},[95,84236,84237],{},"Lineární:",[1647,84239,84241],{"className":84240},[2059],[2061,84242,84243],{"xmlns":2063},[2065,84244,84245,84271],{},[2068,84246,84247,84249,84251,84253,84255,84257,84259,84261,84263,84265,84267,84269],{},[2071,84248,2861],{},[2075,84250,2084],{"stretchy":2083},[2071,84252,586],{},[2075,84254,2361],{"separator":2360},[2071,84256,10929],{},[2075,84258,2090],{"stretchy":2083},[2075,84260,2077],{},[2071,84262,69],{},[2071,84264,586],{},[2075,84266,2176],{},[2071,84268,2179],{},[2071,84270,10929],{},[2092,84272,84273],{"encoding":2094},"Q(L, K) = aL + bK"," — dokonalé substituty.",[92,84276,84277,1445,84280,84325],{},[95,84278,84279],{},"Leontiefova:",[1647,84281,84283],{"className":84282},[2059],[2061,84284,84285],{"xmlns":2063},[2065,84286,84287,84322],{},[2068,84288,84289,84291,84293,84295,84297,84299,84301,84303,84306,84308,84310,84312,84314,84316,84318,84320],{},[2071,84290,2861],{},[2075,84292,2084],{"stretchy":2083},[2071,84294,586],{},[2075,84296,2361],{"separator":2360},[2071,84298,10929],{},[2075,84300,2090],{"stretchy":2083},[2075,84302,2077],{},[2071,84304,84305],{},"min",[2075,84307,60670],{},[2075,84309,2084],{"stretchy":2083},[2071,84311,69],{},[2071,84313,586],{},[2075,84315,2361],{"separator":2360},[2071,84317,2179],{},[2071,84319,10929],{},[2075,84321,2090],{"stretchy":2083},[2092,84323,84324],{"encoding":2094},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[84,84327,84329,84330,835,84349,84368],{"id":84328},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[1647,84331,84333],{"className":84332},[2059],[2061,84334,84335],{"xmlns":2063},[2065,84336,84337,84347],{},[2068,84338,84339,84341],{},[2071,84340,2890],{},[2348,84342,84343,84345],{},[2071,84344,575],{},[2071,84346,586],{},[2092,84348,11176],{"encoding":2094},[1647,84350,84352],{"className":84351},[2059],[2061,84353,84354],{"xmlns":2063},[2065,84355,84356,84366],{},[2068,84357,84358,84360],{},[2071,84359,2890],{},[2348,84361,84362,84364],{},[2071,84363,575],{},[2071,84365,10929],{},[2092,84367,11221],{"encoding":2094}," a totální diferenciál",[55,84370,84371],{},[95,84372,84373],{},"Mezní produkt práce:",[1647,84375,84377],{"className":84376},[2059],[2061,84378,84379],{"xmlns":2063,"display":31093},[2065,84380,84381,84419],{},[2068,84382,84383,84385,84391,84393,84401,84403,84417],{},[2071,84384,2890],{},[2348,84386,84387,84389],{},[2071,84388,575],{},[2071,84390,586],{},[2075,84392,2077],{},[9252,84394,84395,84397,84399],{},[2071,84396,2861],{},[2071,84398,586],{},[2075,84400,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,84402,2077],{},[2403,84404,84405,84411],{},[2068,84406,84407,84409],{},[2071,84408,11003],{"mathvariant":2450},[2071,84410,2861],{},[2068,84412,84413,84415],{},[2071,84414,11003],{"mathvariant":2450},[2071,84416,586],{},[2071,84418,195],{"mathvariant":2450},[2092,84420,84421],{"encoding":2094},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[55,84423,84424],{},[95,84425,84426],{},"Mezní produkt kapitálu:",[1647,84428,84430],{"className":84429},[2059],[2061,84431,84432],{"xmlns":2063,"display":31093},[2065,84433,84434,84472],{},[2068,84435,84436,84438,84444,84446,84454,84456,84470],{},[2071,84437,2890],{},[2348,84439,84440,84442],{},[2071,84441,575],{},[2071,84443,10929],{},[2075,84445,2077],{},[9252,84447,84448,84450,84452],{},[2071,84449,2861],{},[2071,84451,10929],{},[2075,84453,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,84455,2077],{},[2403,84457,84458,84464],{},[2068,84459,84460,84462],{},[2071,84461,11003],{"mathvariant":2450},[2071,84463,2861],{},[2068,84465,84466,84468],{},[2071,84467,11003],{"mathvariant":2450},[2071,84469,10929],{},[2071,84471,195],{"mathvariant":2450},[2092,84473,84474],{"encoding":2094},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[55,84476,84477,84507,84508,84529,84530,84548,84549,84562,84563,195],{},[1647,84478,84480],{"className":84479},[2059],[2061,84481,84482],{"xmlns":2063},[2065,84483,84484,84504],{},[2068,84485,84486,84488,84494,84496,84498,84500,84502],{},[2071,84487,2890],{},[2348,84489,84490,84492],{},[2071,84491,575],{},[2071,84493,586],{},[2075,84495,2084],{"stretchy":2083},[2071,84497,69],{},[2075,84499,2361],{"separator":2360},[2071,84501,2179],{},[2075,84503,2090],{"stretchy":2083},[2092,84505,84506],{"encoding":2094},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[1647,84509,84511],{"className":84510},[2059],[2061,84512,84513],{"xmlns":2063},[2065,84514,84515,84527],{},[2068,84516,84517,84519,84521,84523,84525],{},[2075,84518,2561],{"stretchy":2083},[2071,84520,69],{},[2075,84522,2361],{"separator":2360},[2071,84524,2179],{},[2075,84526,2576],{"stretchy":2083},[2092,84528,11954],{"encoding":2094}," (na hladině ",[1647,84531,84533],{"className":84532},[2059],[2061,84534,84535],{"xmlns":2063},[2065,84536,84537,84545],{},[2068,84538,84539,84541,84543],{},[2071,84540,10929],{},[2075,84542,2077],{},[2071,84544,2179],{},[2092,84546,84547],{"encoding":2094},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[1647,84550,84552],{"className":84551},[2059],[2061,84553,84554],{"xmlns":2063},[2065,84555,84556,84560],{},[2068,84557,84558],{},[2071,84559,586],{},[2092,84561,586],{"encoding":2094},". Analogicky ",[1647,84564,84566],{"className":84565},[2059],[2061,84567,84568],{"xmlns":2063},[2065,84569,84570,84590],{},[2068,84571,84572,84574,84580,84582,84584,84586,84588],{},[2071,84573,2890],{},[2348,84575,84576,84578],{},[2071,84577,575],{},[2071,84579,10929],{},[2075,84581,2084],{"stretchy":2083},[2071,84583,69],{},[2075,84585,2361],{"separator":2360},[2071,84587,2179],{},[2075,84589,2090],{"stretchy":2083},[2092,84591,84592],{"encoding":2094},"MP_K(a, b)",[1023,84594,84595,84599],{},[55,84596,84597,55517],{},[1647,84598,4243],{},[89,84600,84601,84639],{},[92,84602,84603,28930,84622],{},[1647,84604,84606],{"className":84605},[2059],[2061,84607,84608],{"xmlns":2063},[2065,84609,84610,84620],{},[2068,84611,84612,84614],{},[2071,84613,2890],{},[2348,84615,84616,84618],{},[2071,84617,575],{},[2071,84619,586],{},[2092,84621,11176],{"encoding":2094},[3982,84623,84624,84625,84638],{},"„o kolik vzroste ",[1647,84626,84628],{"className":84627},[2059],[2061,84629,84630],{"xmlns":2063},[2065,84631,84632,84636],{},[2068,84633,84634],{},[2071,84635,2861],{},[2092,84637,2861],{"encoding":2094},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[92,84640,84641,28930,84660],{},[1647,84642,84644],{"className":84643},[2059],[2061,84645,84646],{"xmlns":2063},[2065,84647,84648,84658],{},[2068,84649,84650,84652],{},[2071,84651,2890],{},[2348,84653,84654,84656],{},[2071,84655,575],{},[2071,84657,10929],{},[2092,84659,11221],{"encoding":2094},[3982,84661,84624,84662,84675],{},[1647,84663,84665],{"className":84664},[2059],[2061,84666,84667],{"xmlns":2063},[2065,84668,84669,84673],{},[2068,84670,84671],{},[2071,84672,2861],{},[2092,84674,2861],{"encoding":2094},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[55,84677,84678,84681,84682,84697,84698,2777],{},[95,84679,84680],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[1647,84683,84685],{"className":84684},[2059],[2061,84686,84687],{"xmlns":2063},[2065,84688,84689,84695],{},[2068,84690,84691,84693],{},[2071,84692,2273],{},[2071,84694,586],{},[2092,84696,79827],{"encoding":2094}," a kapitálu o ",[1647,84699,84701],{"className":84700},[2059],[2061,84702,84703],{"xmlns":2063},[2065,84704,84705,84711],{},[2068,84706,84707,84709],{},[2071,84708,2273],{},[2071,84710,10929],{},[2092,84712,84713],{"encoding":2094},"dK",[1647,84715,84717],{"className":84716},[2059],[2061,84718,84719],{"xmlns":2063,"display":31093},[2065,84720,84721,84814],{},[23493,84722,84723],{"width":31098},[23498,84724,84725,84727,84807,84809],{},[23501,84726],{"width":31103},[23501,84728,84729],{},[2068,84730,84731,84733,84735,84737,84739,84741,84743,84751,84753,84755,84757,84759,84767,84769,84771,84773,84775,84777,84783,84785,84787,84789,84791,84793,84799,84801,84803,84805],{},[2071,84732,2961],{"mathvariant":2450},[2071,84734,2861],{},[2075,84736,2803],{},[2071,84738,2273],{},[2071,84740,2861],{},[2075,84742,2077],{},[9252,84744,84745,84747,84749],{},[2071,84746,2861],{},[2071,84748,586],{},[2075,84750,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,84752,3061],{},[2071,84754,2273],{},[2071,84756,586],{},[2075,84758,2176],{},[9252,84760,84761,84763,84765],{},[2071,84762,2861],{},[2071,84764,10929],{},[2075,84766,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2363,84768,3061],{},[2071,84770,2273],{},[2071,84772,10929],{},[2075,84774,2077],{},[2071,84776,2890],{},[2348,84778,84779,84781],{},[2071,84780,575],{},[2071,84782,586],{},[2363,84784,3061],{},[2071,84786,2273],{},[2071,84788,586],{},[2075,84790,2176],{},[2071,84792,2890],{},[2348,84794,84795,84797],{},[2071,84796,575],{},[2071,84798,10929],{},[2363,84800,3061],{},[2071,84802,2273],{},[2071,84804,10929],{},[2071,84806,195],{"mathvariant":2450},[23501,84808],{"width":31103},[23501,84810,84811],{},[2363,84812,84813],{},"(5.11)",[2092,84815,84816],{"encoding":2094},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[55,84818,84819,84820,195],{},"Skutečná změna: ",[1647,84821,84823],{"className":84822},[2059],[2061,84824,84825],{"xmlns":2063},[2065,84826,84827,84873],{},[2068,84828,84829,84831,84833,84835,84837,84839,84841,84843,84845,84847,84849,84851,84853,84855,84857,84859,84861,84863,84865,84867,84869,84871],{},[2071,84830,2961],{"mathvariant":2450},[2071,84832,2861],{},[2075,84834,2077],{},[2071,84836,2861],{},[2075,84838,2084],{"stretchy":2083},[2071,84840,586],{},[2075,84842,2176],{},[2071,84844,2273],{},[2071,84846,586],{},[2075,84848,2361],{"separator":2360},[2071,84850,10929],{},[2075,84852,2176],{},[2071,84854,2273],{},[2071,84856,10929],{},[2075,84858,2090],{"stretchy":2083},[2075,84860,2303],{},[2071,84862,2861],{},[2075,84864,2084],{"stretchy":2083},[2071,84866,586],{},[2075,84868,2361],{"separator":2360},[2071,84870,10929],{},[2075,84872,2090],{"stretchy":2083},[2092,84874,84875],{"encoding":2094},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[55,84877,84878,84880,84881,84899,84900,84913,84914,84933,84934,84966,84967,84999,85000,195],{},[95,84879,79991],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[1647,84882,84884],{"className":84883},[2059],[2061,84885,84886],{"xmlns":2063},[2065,84887,84888,84896],{},[2068,84889,84890],{},[2348,84891,84892,84894],{},[2071,84893,10929],{},[2210,84895,630],{},[2092,84897,84898],{"encoding":2094},"K_0"," se od jistého ",[1647,84901,84903],{"className":84902},[2059],[2061,84904,84905],{"xmlns":2063},[2065,84906,84907,84911],{},[2068,84908,84909],{},[2071,84910,586],{},[2092,84912,586],{"encoding":2094}," stane ",[1647,84915,84917],{"className":84916},[2059],[2061,84918,84919],{"xmlns":2063},[2065,84920,84921,84931],{},[2068,84922,84923,84925],{},[2071,84924,2890],{},[2348,84926,84927,84929],{},[2071,84928,575],{},[2071,84930,586],{},[2092,84932,11176],{"encoding":2094}," klesající (",[1647,84935,84937],{"className":84936},[2059],[2061,84938,84939],{"xmlns":2063},[2065,84940,84941,84963],{},[2068,84942,84943,84959,84961],{},[9252,84944,84945,84947,84953],{},[2071,84946,2861],{},[2068,84948,84949,84951],{},[2071,84950,586],{},[2071,84952,586],{},[2068,84954,84955,84957],{},[2075,84956,2452],{"mathvariant":2450},[2075,84958,2452],{"mathvariant":2450},[2075,84960,3521],{},[2210,84962,630],{},[2092,84964,84965],{"encoding":2094},"Q''_{LL} \u003C 0","); analogicky ",[1647,84968,84970],{"className":84969},[2059],[2061,84971,84972],{"xmlns":2063},[2065,84973,84974,84996],{},[2068,84975,84976,84992,84994],{},[9252,84977,84978,84980,84986],{},[2071,84979,2861],{},[2068,84981,84982,84984],{},[2071,84983,10929],{},[2071,84985,10929],{},[2068,84987,84988,84990],{},[2075,84989,2452],{"mathvariant":2450},[2075,84991,2452],{"mathvariant":2450},[2075,84993,3521],{},[2210,84995,630],{},[2092,84997,84998],{"encoding":2094},"Q''_{KK} \u003C 0"," pro pevné ",[1647,85001,85003],{"className":85002},[2059],[2061,85004,85005],{"xmlns":2063},[2065,85006,85007,85015],{},[2068,85008,85009],{},[2348,85010,85011,85013],{},[2071,85012,586],{},[2210,85014,630],{},[2092,85016,80029],{"encoding":2094},[84,85018,85020],{"id":85019},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[55,85022,85023,85026,85027,85050,85051,32971],{},[95,85024,85025],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[1647,85028,85030],{"className":85029},[2059],[2061,85031,85032],{"xmlns":2063},[2065,85033,85034,85048],{},[2068,85035,85036,85038,85040,85042,85044,85046],{},[2071,85037,2861],{},[2075,85039,2084],{"stretchy":2083},[2071,85041,586],{},[2075,85043,2361],{"separator":2360},[2071,85045,10929],{},[2075,85047,2090],{"stretchy":2083},[2092,85049,11128],{"encoding":2094}," stupně ",[1647,85052,85054],{"className":85053},[2059],[2061,85055,85056],{"xmlns":2063},[2065,85057,85058,85062],{},[2068,85059,85060],{},[2071,85061,41153],{},[2092,85063,41153],{"encoding":2094},[1647,85065,85067],{"className":85066},[2059],[2061,85068,85069],{"xmlns":2063,"display":31093},[2065,85070,85071,85134],{},[23493,85072,85073],{"width":31098},[23498,85074,85075,85077,85127,85129],{},[23501,85076],{"width":31103},[23501,85078,85079],{},[2068,85080,85081,85083,85085,85093,85095,85097,85099,85107,85109,85111,85113,85115,85117,85119,85121,85123,85125],{},[2071,85082,586],{},[2363,85084,3061],{},[9252,85086,85087,85089,85091],{},[2071,85088,2861],{},[2071,85090,586],{},[2075,85092,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,85094,2176],{},[2071,85096,10929],{},[2363,85098,3061],{},[9252,85100,85101,85103,85105],{},[2071,85102,2861],{},[2071,85104,10929],{},[2075,85106,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,85108,2077],{},[2071,85110,41153],{},[2363,85112,3061],{},[2071,85114,2861],{},[2075,85116,2084],{"stretchy":2083},[2071,85118,586],{},[2075,85120,2361],{"separator":2360},[2071,85122,10929],{},[2075,85124,2090],{"stretchy":2083},[2071,85126,195],{"mathvariant":2450},[23501,85128],{"width":31103},[23501,85130,85131],{},[2363,85132,85133],{},"(5.12)",[2092,85135,85136],{"encoding":2094},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[55,85138,85139,85160],{},[95,85140,85141,85142],{},"Speciální případ ",[1647,85143,85145],{"className":85144},[2059],[2061,85146,85147],{"xmlns":2063},[2065,85148,85149,85157],{},[2068,85150,85151,85153,85155],{},[2071,85152,41153],{},[2075,85154,2077],{},[2210,85156,638],{},[2092,85158,85159],{"encoding":2094},"n = 1"," (konstantní výnosy z rozsahu):",[1647,85162,85164],{"className":85163},[2059],[2061,85165,85166],{"xmlns":2063,"display":31093},[2065,85167,85168,85212],{},[2068,85169,85170,85172,85174,85176,85182,85184,85186,85188,85190,85196,85198,85200,85202,85204,85206,85208,85210],{},[2071,85171,586],{},[2075,85173,3251],{},[2071,85175,2890],{},[2348,85177,85178,85180],{},[2071,85179,575],{},[2071,85181,586],{},[2075,85183,2176],{},[2071,85185,10929],{},[2075,85187,3251],{},[2071,85189,2890],{},[2348,85191,85192,85194],{},[2071,85193,575],{},[2071,85195,10929],{},[2075,85197,2077],{},[2071,85199,2861],{},[2075,85201,2084],{"stretchy":2083},[2071,85203,586],{},[2075,85205,2361],{"separator":2360},[2071,85207,10929],{},[2075,85209,2090],{"stretchy":2083},[2071,85211,195],{"mathvariant":2450},[2092,85213,85214],{"encoding":2094},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[55,85216,85217,85218,85221],{},"Slovně — ",[95,85219,85220],{},"v případě konstantních výnosů z rozsahu se součet součinů počtu jednotek vstupů (práce a kapitálu) a jejich mezních produktů rovná výstupu"," (důchodové pravidlo: celkový produkt je přesně rozdělen mezi vstupy podle jejich mezních produktů).",[84,85223,10908],{"id":79365},[55,85225,85226,11156,85228,85231,85232,85254,85255,2777],{},[95,85227,10908],{},[3982,85229,85230],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[1647,85233,85235],{"className":85234},[2059],[2061,85236,85237],{"xmlns":2063},[2065,85238,85239,85251],{},[2068,85240,85241,85243,85245,85247,85249],{},[2075,85242,2561],{"stretchy":2083},[2071,85244,586],{},[2075,85246,2361],{"separator":2360},[2071,85248,10929],{},[2075,85250,2576],{"stretchy":2083},[2092,85252,85253],{"encoding":2094},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[1647,85256,85258],{"className":85257},[2059],[2061,85259,85260],{"xmlns":2063},[2065,85261,85262,85267],{},[2068,85263,85264],{},[2071,85265,85266],{},"q",[2092,85268,85266],{"encoding":2094},[1647,85270,85272],{"className":85271},[2059],[2061,85273,85274],{"xmlns":2063,"display":31093},[2065,85275,85276,85311],{},[23493,85277,85278],{"width":31098},[23498,85279,85280,85282,85304,85306],{},[23501,85281],{"width":31103},[23501,85283,85284],{},[2068,85285,85286,85288,85290,85292,85294,85296,85298,85300,85302],{},[2071,85287,2861],{},[2075,85289,2084],{"stretchy":2083},[2071,85291,586],{},[2075,85293,2361],{"separator":2360},[2071,85295,10929],{},[2075,85297,2090],{"stretchy":2083},[2075,85299,2077],{},[2071,85301,85266],{},[2071,85303,195],{"mathvariant":2450},[23501,85305],{"width":31103},[23501,85307,85308],{},[2363,85309,85310],{},"(5.13)",[2092,85312,85313],{"encoding":2094},"Q(L, K) = q. \\tag{5.13}",[55,85315,85316,85317,85320,85321,4007],{},"Jsou to ",[95,85318,85319],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[69,85322,85324],{"className":85323,"dataFsResolvedFilePath":10901,"href":10902},[62],"užitečnosti",[55,85326,85327],{},[95,85328,85329],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[89,85331,85332,85337,85342,85347],{},[92,85333,85334,85336],{},[95,85335,14254],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[92,85338,85339,85341],{},[95,85340,41955],{}," (úloha 5.14);",[92,85343,85344,8512],{},[95,85345,85346],{},"neprotínají se",[92,85348,85349,85350,4445,85363,195],{},"s rostoucím ",[1647,85351,85353],{"className":85352},[2059],[2061,85354,85355],{"xmlns":2063},[2065,85356,85357,85361],{},[2068,85358,85359],{},[2071,85360,85266],{},[2092,85362,85266],{"encoding":2094},[95,85364,85365],{},"vzdalují od počátku",[55,85367,85368],{},[3982,85369,85370,85371,85393,85394,195],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[1647,85372,85374],{"className":85373},[2059],[2061,85375,85376],{"xmlns":2063},[2065,85377,85378,85390],{},[2068,85379,85380,85382,85384,85386,85388],{},[2075,85381,2084],{"stretchy":2083},[2071,85383,586],{},[2075,85385,2361],{"separator":2360},[2071,85387,10929],{},[2075,85389,2090],{"stretchy":2083},[2092,85391,85392],{"encoding":2094},"(L, K)",": tři klesající konvexní křivky pro ",[1647,85395,85397],{"className":85396},[2059],[2061,85398,85399],{"xmlns":2063},[2065,85400,85401,85425],{},[2068,85402,85403,85409,85411,85417,85419],{},[2348,85404,85405,85407],{},[2071,85406,85266],{},[2210,85408,638],{},[2075,85410,3521],{},[2348,85412,85413,85415],{},[2071,85414,85266],{},[2210,85416,630],{},[2075,85418,3521],{},[2348,85420,85421,85423],{},[2071,85422,85266],{},[2210,85424,646],{},[2092,85426,85427],{"encoding":2094},"q_1 \u003C q_0 \u003C q_2",[84,85429,85431,85432,2090],{"id":85430},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[1647,85433,85435],{"className":85434},[2059],[2061,85436,85437],{"xmlns":2063},[2065,85438,85439,85449],{},[2068,85440,85441,85443,85445,85447],{},[2071,85442,2890],{},[2071,85444,4082],{},[2071,85446,543],{},[2071,85448,532],{},[2092,85450,11729],{"encoding":2094},[55,85452,85453,11156,85456,85459],{},[95,85454,85455],{},"Mezní míra technické substituce",[3982,85457,85458],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[1647,85461,85463],{"className":85462},[2059],[2061,85464,85465],{"xmlns":2063,"display":31093},[2065,85466,85467,85558],{},[23493,85468,85469],{"width":31098},[23498,85470,85471,85473,85551,85553],{},[23501,85472],{"width":31103},[23501,85474,85475],{},[2068,85476,85477,85479,85481,85483,85485,85487,85489,85491,85493,85495,85497,85499,85501,85503,85505,85507,85529,85531,85549],{},[2071,85478,2890],{},[2071,85480,4082],{},[2071,85482,543],{},[2071,85484,532],{},[2075,85486,2077],{},[2071,85488,2890],{},[2071,85490,4082],{},[2071,85492,543],{},[2071,85494,532],{},[2075,85496,2084],{"stretchy":2083},[2071,85498,586],{},[2075,85500,2361],{"separator":2360},[2071,85502,10929],{},[2075,85504,2090],{"stretchy":2083},[2075,85506,2077],{},[2403,85508,85509,85519],{},[2068,85510,85511,85513],{},[2071,85512,2890],{},[2348,85514,85515,85517],{},[2071,85516,575],{},[2071,85518,586],{},[2068,85520,85521,85523],{},[2071,85522,2890],{},[2348,85524,85525,85527],{},[2071,85526,575],{},[2071,85528,10929],{},[2075,85530,2077],{},[2403,85532,85533,85541],{},[9252,85534,85535,85537,85539],{},[2071,85536,2861],{},[2071,85538,586],{},[2075,85540,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,85542,85543,85545,85547],{},[2071,85544,2861],{},[2071,85546,10929],{},[2075,85548,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2071,85550,195],{"mathvariant":2450},[23501,85552],{"width":31103},[23501,85554,85555],{},[2363,85556,85557],{},"(5.14)",[2092,85559,85560],{"encoding":2094},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[55,85562,85563,1445,85565,85595,85596,85627],{},[95,85564,9302],{},[1647,85566,85568],{"className":85567},[2059],[2061,85569,85570],{"xmlns":2063},[2065,85571,85572,85592],{},[2068,85573,85574,85576,85578,85580,85582,85584,85586,85588,85590],{},[2071,85575,2890],{},[2071,85577,4082],{},[2071,85579,543],{},[2071,85581,532],{},[2075,85583,2084],{"stretchy":2083},[2071,85585,586],{},[2075,85587,2361],{"separator":2360},[2071,85589,10929],{},[2075,85591,2090],{"stretchy":2083},[2092,85593,85594],{"encoding":2094},"MRTS(L, K)"," udává, ",[95,85597,85598,85599,85612,85613,85626],{},"o kolik se musí přibližně změnit kapitál ",[1647,85600,85602],{"className":85601},[2059],[2061,85603,85604],{"xmlns":2063},[2065,85605,85606,85610],{},[2068,85607,85608],{},[2071,85609,10929],{},[2092,85611,10929],{"encoding":2094},", jestliže se práce ",[1647,85614,85616],{"className":85615},[2059],[2061,85617,85618],{"xmlns":2063},[2065,85619,85620,85624],{},[2068,85621,85622],{},[2071,85623,586],{},[2092,85625,586],{"encoding":2094}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1023,85629,85630],{},[55,85631,85632,20762,85634,85653,85654,85691,85692,85695,85696,85700],{},[1647,85633,4243],{},[1647,85635,85637],{"className":85636},[2059],[2061,85638,85639],{"xmlns":2063},[2065,85640,85641,85651],{},[2068,85642,85643,85645,85647,85649],{},[2071,85644,2890],{},[2071,85646,4082],{},[2071,85648,543],{},[2071,85650,532],{},[2092,85652,11729],{"encoding":2094}," říká: ",[3982,85655,85656,85657,85676,85677,85690],{},"„jednu jednotku práce musím nahradit přibližně ",[1647,85658,85660],{"className":85659},[2059],[2061,85661,85662],{"xmlns":2063},[2065,85663,85664,85674],{},[2068,85665,85666,85668,85670,85672],{},[2071,85667,2890],{},[2071,85669,4082],{},[2071,85671,543],{},[2071,85673,532],{},[2092,85675,11729],{"encoding":2094}," jednotkami kapitálu, aby produkce ",[1647,85678,85680],{"className":85679},[2059],[2061,85681,85682],{"xmlns":2063},[2065,85683,85684,85688],{},[2068,85685,85686],{},[2071,85687,2861],{},[2092,85689,2861],{"encoding":2094}," zůstala stejná.\""," Je to ",[95,85693,85694],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[69,85697,85699],{"className":85698,"dataFsResolvedFilePath":10901,"href":10902},[62],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[55,85702,85703],{},[58,85704],{"alt":85705,"className":85706,"src":85707},"imek-izokvanty-mrts",[62,63],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[55,85709,85710,85713,85714,8189,85744,85766,85767,3225],{},[95,85711,85712],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[1647,85715,85717],{"className":85716},[2059],[2061,85718,85719],{"xmlns":2063},[2065,85720,85721,85741],{},[2068,85722,85723,85725,85731,85733,85739],{},[2075,85724,2561],{"stretchy":2083},[2348,85726,85727,85729],{},[2071,85728,586],{},[2210,85730,630],{},[2075,85732,2361],{"separator":2360},[2348,85734,85735,85737],{},[2071,85736,10929],{},[2210,85738,630],{},[2075,85740,2576],{"stretchy":2083},[2092,85742,85743],{"encoding":2094},"[L_0, K_0]",[1647,85745,85747],{"className":85746},[2059],[2061,85748,85749],{"xmlns":2063},[2065,85750,85751,85763],{},[2068,85752,85753,85755,85757,85759,85761],{},[2075,85754,2303],{},[2071,85756,2890],{},[2071,85758,4082],{},[2071,85760,543],{},[2071,85762,532],{},[2092,85764,85765],{"encoding":2094},"-MRTS",". Z derivace implicitní funkce (při ",[1647,85768,85770],{"className":85769},[2059],[2061,85771,85772],{"xmlns":2063},[2065,85773,85774,85796],{},[2068,85775,85776,85778,85780,85782,85784,85786,85788,85790],{},[2071,85777,2861],{},[2075,85779,2084],{"stretchy":2083},[2071,85781,586],{},[2075,85783,2361],{"separator":2360},[2071,85785,10929],{},[2075,85787,2090],{"stretchy":2083},[2075,85789,2077],{},[2348,85791,85792,85794],{},[2071,85793,85266],{},[2210,85795,630],{},[2092,85797,85798],{"encoding":2094},"Q(L,K) = q_0",[1647,85800,85802],{"className":85801},[2059],[2061,85803,85804],{"xmlns":2063,"display":31093},[2065,85805,85806,85858],{},[2068,85807,85808,85822,85824,85826,85844,85846,85848,85850,85852,85854,85856],{},[2403,85809,85810,85816],{},[2068,85811,85812,85814],{},[2071,85813,2273],{},[2071,85815,10929],{},[2068,85817,85818,85820],{},[2071,85819,2273],{},[2071,85821,586],{},[2075,85823,2077],{},[2075,85825,2303],{},[2403,85827,85828,85836],{},[9252,85829,85830,85832,85834],{},[2071,85831,2861],{},[2071,85833,586],{},[2075,85835,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,85837,85838,85840,85842],{},[2071,85839,2861],{},[2071,85841,10929],{},[2075,85843,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,85845,2077],{},[2075,85847,2303],{},[2071,85849,2890],{},[2071,85851,4082],{},[2071,85853,543],{},[2071,85855,532],{},[2071,85857,195],{"mathvariant":2450},[2092,85859,85860],{"encoding":2094},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[55,85862,85863,85864,85879,85880,85896],{},"Změní-li se práce o ",[1647,85865,85867],{"className":85866},[2059],[2061,85868,85869],{"xmlns":2063},[2065,85870,85871,85877],{},[2068,85872,85873,85875],{},[2071,85874,2273],{},[2071,85876,586],{},[2092,85878,79827],{"encoding":2094},", lze pro odhad změny kapitálu ",[1647,85881,85883],{"className":85882},[2059],[2061,85884,85885],{"xmlns":2063},[2065,85886,85887,85893],{},[2068,85888,85889,85891],{},[2071,85890,2961],{"mathvariant":2450},[2071,85892,10929],{},[2092,85894,85895],{"encoding":2094},"\\Delta K"," k udržení produkce použít diferenciál:",[1647,85898,85900],{"className":85899},[2059],[2061,85901,85902],{"xmlns":2063,"display":31093},[2065,85903,85904,85951],{},[23493,85905,85906],{"width":31098},[23498,85907,85908,85910,85944,85946],{},[23501,85909],{"width":31103},[23501,85911,85912],{},[2068,85913,85914,85916,85918,85920,85922,85924,85926,85928,85930,85932,85934,85936,85938,85940,85942],{},[2071,85915,2961],{"mathvariant":2450},[2071,85917,10929],{},[2075,85919,2803],{},[2071,85921,2273],{},[2071,85923,10929],{},[2075,85925,2077],{},[2075,85927,2303],{},[2071,85929,2890],{},[2071,85931,4082],{},[2071,85933,543],{},[2071,85935,532],{},[2363,85937,3061],{},[2071,85939,2273],{},[2071,85941,586],{},[2075,85943,2361],{"separator":2360},[23501,85945],{"width":31103},[23501,85947,85948],{},[2363,85949,85950],{},"(5.15)",[2092,85952,85953],{"encoding":2094},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[1647,85955,85957],{"className":85956},[2059],[2061,85958,85959],{"xmlns":2063,"display":31093},[2065,85960,85961,86010],{},[23493,85962,85963],{"width":31098},[23498,85964,85965,85967,86003,86005],{},[23501,85966],{"width":31103},[23501,85968,85969],{},[2068,85970,85971,85973,85975,85977,85995,85997,85999,86001],{},[2071,85972,2273],{},[2071,85974,586],{},[2075,85976,2077],{},[2403,85978,85979,85985],{},[2068,85980,85981,85983],{},[2075,85982,2303],{},[2210,85984,638],{},[2068,85986,85987,85989,85991,85993],{},[2071,85988,2890],{},[2071,85990,4082],{},[2071,85992,543],{},[2071,85994,532],{},[2363,85996,3061],{},[2071,85998,2273],{},[2071,86000,10929],{},[2071,86002,195],{"mathvariant":2450},[23501,86004],{"width":31103},[23501,86006,86007],{},[2363,86008,86009],{},"(5.16)",[2092,86011,86012],{"encoding":2094},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1023,86014,86015,86039],{},[55,86016,86017,86019,86020],{},[1647,86018,4659],{}," Postup — jak spočítat ",[1647,86021,86023],{"className":86022},[2059],[2061,86024,86025],{"xmlns":2063},[2065,86026,86027,86037],{},[2068,86028,86029,86031,86033,86035],{},[2071,86030,2890],{},[2071,86032,4082],{},[2071,86034,543],{},[2071,86036,532],{},[2092,86038,11729],{"encoding":2094},[201,86040,86041,86082,86125,86157],{},[92,86042,86043,86044,75,86063,195],{},"Vypočtěte parciální derivace ",[1647,86045,86047],{"className":86046},[2059],[2061,86048,86049],{"xmlns":2063},[2065,86050,86051,86061],{},[2068,86052,86053],{},[9252,86054,86055,86057,86059],{},[2071,86056,2861],{},[2071,86058,586],{},[2075,86060,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,86062,11152],{"encoding":2094},[1647,86064,86066],{"className":86065},[2059],[2061,86067,86068],{"xmlns":2063},[2065,86069,86070,86080],{},[2068,86071,86072],{},[9252,86073,86074,86076,86078],{},[2071,86075,2861],{},[2071,86077,10929],{},[2075,86079,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,86081,11198],{"encoding":2094},[92,86083,70311,86084,86124],{},[1647,86085,86087],{"className":86086},[2059],[2061,86088,86089],{"xmlns":2063},[2065,86090,86091,86121],{},[2068,86092,86093,86095,86097,86099,86101,86103,86111,86113],{},[2071,86094,2890],{},[2071,86096,4082],{},[2071,86098,543],{},[2071,86100,532],{},[2075,86102,2077],{},[9252,86104,86105,86107,86109],{},[2071,86106,2861],{},[2071,86108,586],{},[2075,86110,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2071,86112,4761],{"mathvariant":2450},[9252,86114,86115,86117,86119],{},[2071,86116,2861],{},[2071,86118,10929],{},[2075,86120,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,86122,86123],{"encoding":2094},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[92,86126,86127,86128,195],{},"Případně dosaďte konkrétní ",[1647,86129,86131],{"className":86130},[2059],[2061,86132,86133],{"xmlns":2063},[2065,86134,86135,86155],{},[2068,86136,86137,86139,86145,86147,86153],{},[2075,86138,2561],{"stretchy":2083},[2348,86140,86141,86143],{},[2071,86142,586],{},[2210,86144,630],{},[2075,86146,2361],{"separator":2360},[2348,86148,86149,86151],{},[2071,86150,10929],{},[2210,86152,630],{},[2075,86154,2576],{"stretchy":2083},[2092,86156,85743],{"encoding":2094},[92,86158,86159,86160,86194,86195,86197],{},"Pro odhad substituce použijte ",[1647,86161,86163],{"className":86162},[2059],[2061,86164,86165],{"xmlns":2063},[2065,86166,86167,86191],{},[2068,86168,86169,86171,86173,86175,86177,86179,86181,86183,86185,86187,86189],{},[2071,86170,2961],{"mathvariant":2450},[2071,86172,10929],{},[2075,86174,2803],{},[2075,86176,2303],{},[2071,86178,2890],{},[2071,86180,4082],{},[2071,86182,543],{},[2071,86184,532],{},[2075,86186,3251],{},[2071,86188,2961],{"mathvariant":2450},[2071,86190,586],{},[2092,86192,86193],{"encoding":2094},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[95,86196,56904],{}," — substituce, ne doplnění).",[55,86199,86200],{},[3982,86201,86202,86203,86235,86236,2697,86249,17525,86278,86293],{},"Obrázek 5.7 — izokvanta ",[1647,86204,86206],{"className":86205},[2059],[2061,86207,86208],{"xmlns":2063},[2065,86209,86210,86232],{},[2068,86211,86212,86218,86220,86222,86224,86226,86228,86230],{},[2348,86213,86214,86216],{},[2071,86215,85266],{},[2210,86217,630],{},[2075,86219,2077],{},[2071,86221,2861],{},[2075,86223,2084],{"stretchy":2083},[2071,86225,586],{},[2075,86227,2361],{"separator":2360},[2071,86229,10929],{},[2075,86231,2090],{"stretchy":2083},[2092,86233,86234],{"encoding":2094},"q_0 = Q(L,K)"," s tečnou ",[1647,86237,86239],{"className":86238},[2059],[2061,86240,86241],{"xmlns":2063},[2065,86242,86243,86247],{},[2068,86244,86245],{},[2071,86246,21594],{},[2092,86248,21594],{"encoding":2094},[1647,86250,86252],{"className":86251},[2059],[2061,86253,86254],{"xmlns":2063},[2065,86255,86256,86276],{},[2068,86257,86258,86260,86266,86268,86274],{},[2075,86259,2561],{"stretchy":2083},[2348,86261,86262,86264],{},[2071,86263,586],{},[2210,86265,630],{},[2075,86267,2361],{"separator":2360},[2348,86269,86270,86272],{},[2071,86271,10929],{},[2210,86273,630],{},[2075,86275,2576],{"stretchy":2083},[2092,86277,85743],{"encoding":2094},[1647,86279,86281],{"className":86280},[2059],[2061,86282,86283],{"xmlns":2063},[2065,86284,86285,86291],{},[2068,86286,86287,86289],{},[2071,86288,2961],{"mathvariant":2450},[2071,86290,10929],{},[2092,86292,85895],{"encoding":2094}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[84,86295,86297],{"id":86296},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[609,86299,86301],{"id":86300},"příklad-54","Příklad 5.4",[55,86303,81143,86304,835,86346,835,86363,195],{},[1647,86305,86307],{"className":86306},[2059],[2061,86308,86309],{"xmlns":2063},[2065,86310,86311,86343],{},[2068,86312,86313,86315,86317,86319,86331],{},[2071,86314,2861],{},[2075,86316,2077],{},[2210,86318,39270],{},[2205,86320,86321,86323],{},[2071,86322,586],{},[2068,86324,86325,86327,86329],{},[2210,86326,638],{},[2071,86328,4761],{"mathvariant":2450},[2210,86330,646],{},[2205,86332,86333,86335],{},[2071,86334,10929],{},[2068,86336,86337,86339,86341],{},[2210,86338,638],{},[2071,86340,4761],{"mathvariant":2450},[2210,86342,654],{},[2092,86344,86345],{"encoding":2094},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[1647,86347,86349],{"className":86348},[2059],[2061,86350,86351],{"xmlns":2063},[2065,86352,86353,86361],{},[2068,86354,86355,86357,86359],{},[2071,86356,586],{},[2075,86358,2077],{},[2210,86360,9121],{},[2092,86362,81517],{"encoding":2094},[1647,86364,86366],{"className":86365},[2059],[2061,86367,86368],{"xmlns":2063},[2065,86369,86370,86378],{},[2068,86371,86372,86374,86376],{},[2071,86373,10929],{},[2075,86375,2077],{},[2210,86377,3164],{},[2092,86379,86380],{"encoding":2094},"K = 100",[55,86382,86383],{},[95,86384,86385],{},"(a) Rychlost změny produkce vzhledem k práci.",[1647,86387,86389],{"className":86388},[2059],[2061,86390,86391],{"xmlns":2063,"display":31093},[2065,86392,86393,86507],{},[2068,86394,86395,86397,86403,86405,86413,86415,86423,86437,86449,86451,86453,86455,86461,86463,86465,86467,86469,86471,86473,86481,86483,86493,86495,86502,86504],{},[2071,86396,2890],{},[2348,86398,86399,86401],{},[2071,86400,575],{},[2071,86402,586],{},[2075,86404,2077],{},[9252,86406,86407,86409,86411],{},[2071,86408,2861],{},[2071,86410,586],{},[2075,86412,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,86414,2077],{},[2400,86416,86417],{"scriptlevel":630,"displaystyle":2083},[2403,86418,86419,86421],{},[2210,86420,39270],{},[2210,86422,646],{},[2205,86424,86425,86427],{},[2071,86426,586],{},[2068,86428,86429,86431,86433,86435],{},[2075,86430,2303],{},[2210,86432,638],{},[2071,86434,4761],{"mathvariant":2450},[2210,86436,646],{},[2205,86438,86439,86441],{},[2071,86440,10929],{},[2068,86442,86443,86445,86447],{},[2210,86444,638],{},[2071,86446,4761],{"mathvariant":2450},[2210,86448,654],{},[2075,86450,2361],{"separator":2360},[5965,86452],{"width":17019},[2071,86454,2890],{},[2348,86456,86457,86459],{},[2071,86458,575],{},[2071,86460,586],{},[2075,86462,2084],{"stretchy":2083},[2210,86464,9121],{},[2075,86466,2361],{"separator":2360},[2210,86468,3164],{},[2075,86470,2090],{"stretchy":2083},[2075,86472,2077],{},[2400,86474,86475],{"scriptlevel":630,"displaystyle":2083},[2403,86476,86477,86479],{},[2210,86478,39270],{},[2210,86480,646],{},[2075,86482,3251],{},[2400,86484,86485],{"scriptlevel":630,"displaystyle":2083},[2403,86486,86487,86489],{},[2210,86488,638],{},[8204,86490,86491],{},[2210,86492,9121],{},[2075,86494,3251],{},[86496,86497,86498,86500],"mroot",{},[2210,86499,3164],{},[2210,86501,654],{},[2075,86503,2803],{},[2210,86505,86506],{},"7,153.",[2092,86508,86509],{"encoding":2094},"MP_L = Q'_L = \\tfrac{15}{2} L^{-1\u002F2} K^{1\u002F3}, \\quad MP_L(20, 100) = \\tfrac{15}{2}\\cdot \\tfrac{1}{\\sqrt{20}}\\cdot \\sqrt[3]{100} \\approx 7{,}153.",[55,86511,86512,86513,48454,86535,11364,86552,86573,86574,86595],{},"Přibližná změna při ",[1647,86514,86516],{"className":86515},[2059],[2061,86517,86518],{"xmlns":2063},[2065,86519,86520,86532],{},[2068,86521,86522,86524,86526,86528,86530],{},[2071,86523,586],{},[2075,86525,2777],{},[2210,86527,9121],{},[2075,86529,3197],{},[2210,86531,42637],{},[2092,86533,86534],{"encoding":2094},"L: 20 \\to 21",[1647,86536,86538],{"className":86537},[2059],[2061,86539,86540],{"xmlns":2063},[2065,86541,86542,86550],{},[2068,86543,86544,86546,86548],{},[2071,86545,10929],{},[2075,86547,2077],{},[2210,86549,3164],{},[2092,86551,86380],{"encoding":2094},[1647,86553,86555],{"className":86554},[2059],[2061,86556,86557],{"xmlns":2063},[2065,86558,86559,86570],{},[2068,86560,86561,86563,86565,86567],{},[2071,86562,2961],{"mathvariant":2450},[2071,86564,2861],{},[2075,86566,2803],{},[2210,86568,86569],{},"7,153",[2092,86571,86572],{"encoding":2094},"\\Delta Q \\approx 7{,}153",". Skutečně ",[1647,86575,86577],{"className":86576},[2059],[2061,86578,86579],{"xmlns":2063},[2065,86580,86581,86592],{},[2068,86582,86583,86585,86587,86589],{},[2071,86584,2961],{"mathvariant":2450},[2071,86586,2861],{},[2075,86588,2803],{},[2210,86590,86591],{},"26,888",[2092,86593,86594],{"encoding":2094},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[55,86597,86598,86601],{},[95,86599,86600],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[1647,86603,86605],{"className":86604},[2059],[2061,86606,86607],{"xmlns":2063,"display":31093},[2065,86608,86609,86709],{},[2068,86610,86611,86613,86619,86621,86629,86631,86633,86645,86659,86661,86663,86665,86671,86673,86675,86677,86679,86681,86683,86685,86689,86691,86704,86706],{},[2071,86612,2890],{},[2348,86614,86615,86617],{},[2071,86616,575],{},[2071,86618,10929],{},[2075,86620,2077],{},[9252,86622,86623,86625,86627],{},[2071,86624,2861],{},[2071,86626,10929],{},[2075,86628,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,86630,2077],{},[2210,86632,670],{},[2205,86634,86635,86637],{},[2071,86636,586],{},[2068,86638,86639,86641,86643],{},[2210,86640,638],{},[2071,86642,4761],{"mathvariant":2450},[2210,86644,646],{},[2205,86646,86647,86649],{},[2071,86648,10929],{},[2068,86650,86651,86653,86655,86657],{},[2075,86652,2303],{},[2210,86654,646],{},[2071,86656,4761],{"mathvariant":2450},[2210,86658,654],{},[2075,86660,2361],{"separator":2360},[5965,86662],{"width":17019},[2071,86664,2890],{},[2348,86666,86667,86669],{},[2071,86668,575],{},[2071,86670,10929],{},[2075,86672,2084],{"stretchy":2083},[2210,86674,9121],{},[2075,86676,2361],{"separator":2360},[2210,86678,3164],{},[2075,86680,2090],{"stretchy":2083},[2075,86682,2077],{},[2210,86684,670],{},[8204,86686,86687],{},[2210,86688,9121],{},[2075,86690,3251],{},[2400,86692,86693],{"scriptlevel":630,"displaystyle":2083},[2403,86694,86695,86697],{},[2210,86696,638],{},[86496,86698,86699,86702],{},[2210,86700,86701],{},"10000",[2210,86703,654],{},[2075,86705,2803],{},[2210,86707,86708],{},"4,525.",[2092,86710,86711],{"encoding":2094},"MP_K = Q'_K = 5 L^{1\u002F2} K^{-2\u002F3}, \\quad MP_K(20, 100) = 5\\sqrt{20}\\cdot \\tfrac{1}{\\sqrt[3]{10000}} \\approx 4{,}525.",[55,86713,86714,86715,2758,86732,4007],{},"Produkce poklesne přibližně o 4,525 (z ",[1647,86716,86718],{"className":86717},[2059],[2061,86719,86720],{"xmlns":2063},[2065,86721,86722,86729],{},[2068,86723,86724,86726],{},[2075,86725,2803],{},[2210,86727,86728],{},"905,126",[2092,86730,86731],{"encoding":2094},"\\approx 905{,}126",[1647,86733,86735],{"className":86734},[2059],[2061,86736,86737],{"xmlns":2063},[2065,86738,86739,86746],{},[2068,86740,86741,86743],{},[2075,86742,2803],{},[2210,86744,86745],{},"900,601",[2092,86747,86748],{"encoding":2094},"\\approx 900{,}601",[55,86750,86751,3204,86798,835,86820,4007],{},[95,86752,86753,86754,75,86776],{},"(c) Změna ",[1647,86755,86757],{"className":86756},[2059],[2061,86758,86759],{"xmlns":2063},[2065,86760,86761,86773],{},[2068,86762,86763,86765,86767,86769,86771],{},[2071,86764,586],{},[2075,86766,2777],{},[2210,86768,9121],{},[2075,86770,3197],{},[2210,86772,39270],{},[2092,86774,86775],{"encoding":2094},"L: 20 \\to 15",[1647,86777,86779],{"className":86778},[2059],[2061,86780,86781],{"xmlns":2063},[2065,86782,86783,86795],{},[2068,86784,86785,86787,86789,86791,86793],{},[2071,86786,10929],{},[2075,86788,2777],{},[2210,86790,3164],{},[2075,86792,3197],{},[2210,86794,8889],{},[2092,86796,86797],{"encoding":2094},"K: 100 \\to 150",[1647,86799,86801],{"className":86800},[2059],[2061,86802,86803],{"xmlns":2063},[2065,86804,86805,86817],{},[2068,86806,86807,86809,86811,86813,86815],{},[2071,86808,2273],{},[2071,86810,586],{},[2075,86812,2077],{},[2075,86814,2303],{},[2210,86816,670],{},[2092,86818,86819],{"encoding":2094},"dL = -5",[1647,86821,86823],{"className":86822},[2059],[2061,86824,86825],{"xmlns":2063},[2065,86826,86827,86837],{},[2068,86828,86829,86831,86833,86835],{},[2071,86830,2273],{},[2071,86832,10929],{},[2075,86834,2077],{},[2210,86836,3194],{},[2092,86838,86839],{"encoding":2094},"dK = 50",[1647,86841,86843],{"className":86842},[2059],[2061,86844,86845],{"xmlns":2063,"display":31093},[2065,86846,86847,86935],{},[2068,86848,86849,86851,86853,86855,86857,86863,86865,86867,86869,86871,86873,86875,86877,86879,86881,86883,86885,86887,86893,86895,86897,86899,86901,86903,86905,86907,86909,86911,86913,86915,86917,86919,86921,86923,86926,86928,86930,86932],{},[2071,86850,2273],{},[2071,86852,2861],{},[2075,86854,2077],{},[2071,86856,2890],{},[2348,86858,86859,86861],{},[2071,86860,575],{},[2071,86862,586],{},[2075,86864,2084],{"stretchy":2083},[2210,86866,9121],{},[2075,86868,2361],{"separator":2360},[2210,86870,3164],{},[2075,86872,2090],{"stretchy":2083},[2075,86874,3251],{},[2075,86876,2084],{"stretchy":2083},[2075,86878,2303],{},[2210,86880,670],{},[2075,86882,2090],{"stretchy":2083},[2075,86884,2176],{},[2071,86886,2890],{},[2348,86888,86889,86891],{},[2071,86890,575],{},[2071,86892,10929],{},[2075,86894,2084],{"stretchy":2083},[2210,86896,9121],{},[2075,86898,2361],{"separator":2360},[2210,86900,3164],{},[2075,86902,2090],{"stretchy":2083},[2075,86904,3251],{},[2210,86906,3194],{},[2075,86908,2077],{},[2210,86910,86569],{},[2075,86912,3251],{},[2075,86914,2084],{"stretchy":2083},[2075,86916,2303],{},[2210,86918,670],{},[2075,86920,2090],{"stretchy":2083},[2075,86922,2176],{},[2210,86924,86925],{},"4,525",[2075,86927,3251],{},[2210,86929,3194],{},[2075,86931,2803],{},[2210,86933,86934],{},"190,485.",[2092,86936,86937],{"encoding":2094},"dQ = MP_L(20,100)\\cdot(-5) + MP_K(20,100)\\cdot 50 = 7{,}153\\cdot(-5) + 4{,}525\\cdot 50 \\approx 190{,}485.",[55,86939,86940],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[609,86942,86944],{"id":86943},"příklad-55","Příklad 5.5",[55,86946,86947,86948,86984,86985,195],{},"Pro produkci ",[1647,86949,86951],{"className":86950},[2059],[2061,86952,86953],{"xmlns":2063},[2065,86954,86955,86981],{},[2068,86956,86957,86959,86961,86963,86965,86967,86969,86971,86977],{},[2071,86958,2861],{},[2075,86960,2084],{"stretchy":2083},[2071,86962,586],{},[2075,86964,2361],{"separator":2360},[2071,86966,10929],{},[2075,86968,2090],{"stretchy":2083},[2075,86970,2077],{},[86496,86972,86973,86975],{},[2071,86974,586],{},[2210,86976,654],{},[8204,86978,86979],{},[2071,86980,10929],{},[2092,86982,86983],{"encoding":2094},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[1647,86986,86988],{"className":86987},[2059],[2061,86989,86990],{"xmlns":2063},[2065,86991,86992,87008],{},[2068,86993,86994,87000,87004,87006],{},[86496,86995,86996,86998],{},[2071,86997,586],{},[2210,86999,654],{},[8204,87001,87002],{},[2071,87003,10929],{},[2075,87005,2077],{},[2071,87007,85266],{},[2092,87009,87010],{"encoding":2094},"\\sqrt[3]{L}\\sqrt{K} = q",[55,87012,87013,87014,195],{},"Umocněním na druhou: ",[1647,87015,87017],{"className":87016},[2059],[2061,87018,87019],{"xmlns":2063},[2065,87020,87021,87045],{},[2068,87022,87023,87025,87027,87033,87035],{},[2071,87024,10929],{},[2075,87026,2077],{},[2205,87028,87029,87031],{},[2071,87030,85266],{},[2210,87032,646],{},[2071,87034,4761],{"mathvariant":2450},[86496,87036,87037,87043],{},[2205,87038,87039,87041],{},[2071,87040,586],{},[2210,87042,646],{},[2210,87044,654],{},[2092,87046,87047],{"encoding":2094},"K = q^2 \u002F \\sqrt[3]{L^2}",[89,87049,87050,87090,87130],{},[92,87051,87052],{},[1647,87053,87055],{"className":87054},[2059],[2061,87056,87057],{"xmlns":2063},[2065,87058,87059,87087],{},[2068,87060,87061,87063,87065,87067,87069,87071,87073,87075,87077],{},[2071,87062,85266],{},[2075,87064,2077],{},[2210,87066,638],{},[2075,87068,4075],{},[2071,87070,10929],{},[2075,87072,2077],{},[2210,87074,638],{},[2071,87076,4761],{"mathvariant":2450},[86496,87078,87079,87085],{},[2205,87080,87081,87083],{},[2071,87082,586],{},[2210,87084,646],{},[2210,87086,654],{},[2092,87088,87089],{"encoding":2094},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[92,87091,87092],{},[1647,87093,87095],{"className":87094},[2059],[2061,87096,87097],{"xmlns":2063},[2065,87098,87099,87127],{},[2068,87100,87101,87103,87105,87107,87109,87111,87113,87115,87117],{},[2071,87102,85266],{},[2075,87104,2077],{},[2210,87106,646],{},[2075,87108,4075],{},[2071,87110,10929],{},[2075,87112,2077],{},[2210,87114,662],{},[2071,87116,4761],{"mathvariant":2450},[86496,87118,87119,87125],{},[2205,87120,87121,87123],{},[2071,87122,586],{},[2210,87124,646],{},[2210,87126,654],{},[2092,87128,87129],{"encoding":2094},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[92,87131,87132],{},[1647,87133,87135],{"className":87134},[2059],[2061,87136,87137],{"xmlns":2063},[2065,87138,87139,87167],{},[2068,87140,87141,87143,87145,87147,87149,87151,87153,87155,87157],{},[2071,87142,85266],{},[2075,87144,2077],{},[2210,87146,654],{},[2075,87148,4075],{},[2071,87150,10929],{},[2075,87152,2077],{},[2210,87154,4087],{},[2071,87156,4761],{"mathvariant":2450},[86496,87158,87159,87165],{},[2205,87160,87161,87163],{},[2071,87162,586],{},[2210,87164,646],{},[2210,87166,654],{},[2092,87168,87169],{"encoding":2094},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[55,87171,87172],{},[3982,87173,87174,87175,6560,87196,195],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[1647,87176,87178],{"className":87177},[2059],[2061,87179,87180],{"xmlns":2063},[2065,87181,87182,87194],{},[2068,87183,87184,87186,87188,87190,87192],{},[2075,87185,2084],{"stretchy":2083},[2071,87187,586],{},[2075,87189,2361],{"separator":2360},[2071,87191,10929],{},[2075,87193,2090],{"stretchy":2083},[2092,87195,85392],{"encoding":2094},[1647,87197,87199],{"className":87198},[2059],[2061,87200,87201],{"xmlns":2063},[2065,87202,87203,87219],{},[2068,87204,87205,87207,87209,87211,87213,87215,87217],{},[2071,87206,85266],{},[2075,87208,2077],{},[2210,87210,638],{},[2075,87212,2361],{"separator":2360},[2210,87214,646],{},[2075,87216,2361],{"separator":2360},[2210,87218,654],{},[2092,87220,87221],{"encoding":2094},"q = 1, 2, 3",[609,87223,87225],{"id":87224},"příklad-56","Příklad 5.6",[55,87227,81143,87228,195],{},[1647,87229,87231],{"className":87230},[2059],[2061,87232,87233],{"xmlns":2063},[2065,87234,87235,87251],{},[2068,87236,87237,87239,87241,87243,87245,87247],{},[2071,87238,2861],{},[2075,87240,2077],{},[2210,87242,646],{},[2071,87244,586],{},[2075,87246,2176],{},[8204,87248,87249],{},[2071,87250,10929],{},[2092,87252,87253],{"encoding":2094},"Q = 2L + \\sqrt{K}",[1647,87255,87257],{"className":87256},[2059],[2061,87258,87259],{"xmlns":2063,"display":31093},[2065,87260,87261,87303],{},[2068,87262,87263,87265,87271,87273,87275,87277,87279,87281,87287,87289,87301],{},[2071,87264,2890],{},[2348,87266,87267,87269],{},[2071,87268,575],{},[2071,87270,586],{},[2075,87272,2077],{},[2210,87274,646],{},[2075,87276,2361],{"separator":2360},[5965,87278],{"width":5967},[2071,87280,2890],{},[2348,87282,87283,87285],{},[2071,87284,575],{},[2071,87286,10929],{},[2075,87288,2077],{},[2403,87290,87291,87293],{},[2210,87292,638],{},[2068,87294,87295,87297],{},[2210,87296,646],{},[8204,87298,87299],{},[2071,87300,10929],{},[2071,87302,195],{"mathvariant":2450},[2092,87304,87305],{"encoding":2094},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[1647,87307,87309],{"className":87308},[2059],[2061,87310,87311],{"xmlns":2063,"display":31093},[2065,87312,87313,87377],{},[2068,87314,87315,87317,87319,87321,87323,87325,87347,87349,87367,87369,87371,87375],{},[2071,87316,2890],{},[2071,87318,4082],{},[2071,87320,543],{},[2071,87322,532],{},[2075,87324,2077],{},[2403,87326,87327,87337],{},[2068,87328,87329,87331],{},[2071,87330,2890],{},[2348,87332,87333,87335],{},[2071,87334,575],{},[2071,87336,586],{},[2068,87338,87339,87341],{},[2071,87340,2890],{},[2348,87342,87343,87345],{},[2071,87344,575],{},[2071,87346,10929],{},[2075,87348,2077],{},[2403,87350,87351,87353],{},[2210,87352,646],{},[2400,87354,87355],{"scriptlevel":630,"displaystyle":2083},[2403,87356,87357,87359],{},[2210,87358,638],{},[2068,87360,87361,87363],{},[2210,87362,646],{},[8204,87364,87365],{},[2071,87366,10929],{},[2075,87368,2077],{},[2210,87370,662],{},[8204,87372,87373],{},[2071,87374,10929],{},[2071,87376,195],{"mathvariant":2450},[2092,87378,87379],{"encoding":2094},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[55,87381,87382,87383,87426,87427,87466,87467,195],{},"Například ",[1647,87384,87386],{"className":87385},[2059],[2061,87387,87388],{"xmlns":2063},[2065,87389,87390,87423],{},[2068,87391,87392,87394,87396,87398,87400,87402,87404,87406,87408,87410,87412,87414,87418,87420],{},[2071,87393,2890],{},[2071,87395,4082],{},[2071,87397,543],{},[2071,87399,532],{},[2075,87401,2084],{"stretchy":2083},[2210,87403,662],{},[2075,87405,2361],{"separator":2360},[2210,87407,686],{},[2075,87409,2090],{"stretchy":2083},[2075,87411,2077],{},[2210,87413,662],{},[8204,87415,87416],{},[2210,87417,686],{},[2075,87419,2803],{},[2210,87421,87422],{},"10,58",[2092,87424,87425],{"encoding":2094},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[1647,87428,87430],{"className":87429},[2059],[2061,87431,87432],{"xmlns":2063},[2065,87433,87434,87463],{},[2068,87435,87436,87438,87440,87442,87444,87446,87448,87450,87452,87454,87458,87460],{},[2071,87437,2861],{},[2075,87439,2084],{"stretchy":2083},[2210,87441,662],{},[2075,87443,2361],{"separator":2360},[2210,87445,686],{},[2075,87447,2090],{"stretchy":2083},[2075,87449,2077],{},[2210,87451,5672],{},[2075,87453,2176],{},[8204,87455,87456],{},[2210,87457,686],{},[2075,87459,2803],{},[2210,87461,87462],{},"10,646",[2092,87464,87465],{"encoding":2094},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[1647,87468,87470],{"className":87469},[2059],[2061,87471,87472],{"xmlns":2063},[2065,87473,87474,87482],{},[2068,87475,87476,87478],{},[2210,87477,662],{},[8204,87479,87480],{},[2210,87481,686],{},[2092,87483,87484],{"encoding":2094},"4\\sqrt{7}",[55,87486,87487,87488,87508],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[1647,87489,87491],{"className":87490},[2059],[2061,87492,87493],{"xmlns":2063},[2065,87494,87495,87505],{},[2068,87496,87497,87499,87501,87503],{},[2071,87498,2273],{},[2071,87500,586],{},[2075,87502,2077],{},[2210,87504,646],{},[2092,87506,87507],{"encoding":2094},"dL = 2","), k udržení produkce stačí snížit kapitál o",[1647,87510,87512],{"className":87511},[2059],[2061,87513,87514],{"xmlns":2063,"display":31093},[2065,87515,87516,87565],{},[2068,87517,87518,87520,87522,87524,87526,87528,87530,87532,87534,87536,87538,87540,87542,87544,87546,87548,87550,87552,87554,87558,87560,87562],{},[2071,87519,2273],{},[2071,87521,10929],{},[2075,87523,2077],{},[2075,87525,2303],{},[2071,87527,2890],{},[2071,87529,4082],{},[2071,87531,543],{},[2071,87533,532],{},[2075,87535,2084],{"stretchy":2083},[2210,87537,662],{},[2075,87539,2361],{"separator":2360},[2210,87541,686],{},[2075,87543,2090],{"stretchy":2083},[2075,87545,3251],{},[2210,87547,646],{},[2075,87549,2077],{},[2075,87551,2303],{},[2210,87553,5672],{},[8204,87555,87556],{},[2210,87557,686],{},[2075,87559,2803],{},[2075,87561,2303],{},[2210,87563,87564],{},"21,17.",[2092,87566,87567],{"encoding":2094},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[84,87569,87571],{"id":87570},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[55,87573,87574,87575,835,87577,75,87579,87581,87582,87585,87586,87589],{},"Hlavními faktory produkce jsou ",[95,87576,79385],{},[95,87578,79401],{},[95,87580,79417],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[95,87583,87584],{},"jednofaktorový"," (pouze práce) a ",[95,87587,87588],{},"dvoufaktorový"," (práce + kapitál) model.",[55,87591,87592,87593,87596,87597,87599,87600,87602,87603,28930,87606,87625,87626,87643,87644,87661,87662,87684,87685,4445,87704,195],{},"V ",[95,87594,87595],{},"1F modelu"," se definuje ",[95,87598,11155],{}," (derivace produkce podle práce) a ",[95,87601,79320],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[95,87604,87605],{},"zákonu klesajících výnosů",[1647,87607,87609],{"className":87608},[2059],[2061,87610,87611],{"xmlns":2063},[2065,87612,87613,87623],{},[2068,87614,87615,87617],{},[2071,87616,2890],{},[2348,87618,87619,87621],{},[2071,87620,575],{},[2071,87622,586],{},[2092,87624,11176],{"encoding":2094}," nejprve roste, od inflexního bodu ",[1647,87627,87629],{"className":87628},[2059],[2061,87630,87631],{"xmlns":2063},[2065,87632,87633,87641],{},[2068,87634,87635],{},[2348,87636,87637,87639],{},[2071,87638,586],{},[2210,87640,630],{},[2092,87642,80029],{"encoding":2094}," klesá a v bodě ",[1647,87645,87647],{"className":87646},[2059],[2061,87648,87649],{"xmlns":2063},[2065,87650,87651,87659],{},[2068,87652,87653],{},[2348,87654,87655,87657],{},[2071,87656,586],{},[2210,87658,638],{},[2092,87660,14947],{"encoding":2094}," dosahuje nuly (maximum produkce). Platí ",[95,87663,87664,87665],{},"princip maximalizace ",[1647,87666,87668],{"className":87667},[2059],[2061,87669,87670],{"xmlns":2063},[2065,87671,87672,87682],{},[2068,87673,87674,87676],{},[2071,87675,4342],{},[2348,87677,87678,87680],{},[2071,87679,575],{},[2071,87681,586],{},[2092,87683,79104],{"encoding":2094},": v bodě maxima ",[1647,87686,87688],{"className":87687},[2059],[2061,87689,87690],{"xmlns":2063},[2065,87691,87692,87702],{},[2068,87693,87694,87696],{},[2071,87695,4342],{},[2348,87697,87698,87700],{},[2071,87699,575],{},[2071,87701,586],{},[2092,87703,79104],{"encoding":2094},[1647,87705,87707],{"className":87706},[2059],[2061,87708,87709],{"xmlns":2063},[2065,87710,87711,87731],{},[2068,87712,87713,87715,87721,87723,87725],{},[2071,87714,2890],{},[2348,87716,87717,87719],{},[2071,87718,575],{},[2071,87720,586],{},[2075,87722,2077],{},[2071,87724,4342],{},[2348,87726,87727,87729],{},[2071,87728,575],{},[2071,87730,586],{},[2092,87732,79134],{"encoding":2094},[55,87734,87735,87736,87739,87740,1445,87743,87772,87773,87790,87791,87794,87795,87824,87825,87827,87828,8189,87858,87880],{},"Ve ",[95,87737,87738],{},"2F modelu"," se obvykle používají ",[95,87741,87742],{},"Cobb-Douglasovy funkce",[1647,87744,87746],{"className":87745},[2059],[2061,87747,87748],{"xmlns":2063},[2065,87749,87750,87770],{},[2068,87751,87752,87754,87756,87758,87764],{},[2071,87753,2861],{},[2075,87755,2077],{},[2071,87757,4342],{},[2205,87759,87760,87762],{},[2071,87761,586],{},[2071,87763,69],{},[2205,87765,87766,87768],{},[2071,87767,10929],{},[2071,87769,2179],{},[2092,87771,79201],{"encoding":2094},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[1647,87774,87776],{"className":87775},[2059],[2061,87777,87778],{"xmlns":2063},[2065,87779,87780,87788],{},[2068,87781,87782,87784,87786],{},[2071,87783,69],{},[2075,87785,2176],{},[2071,87787,2179],{},[2092,87789,79295],{"encoding":2094}," rozlišujeme ",[95,87792,87793],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[1647,87796,87798],{"className":87797},[2059],[2061,87799,87800],{"xmlns":2063},[2065,87801,87802,87822],{},[2068,87803,87804,87806,87812,87814,87816],{},[2071,87805,2890],{},[2348,87807,87808,87810],{},[2071,87809,575],{},[2071,87811,586],{},[2075,87813,2361],{"separator":2360},[2071,87815,2890],{},[2348,87817,87818,87820],{},[2071,87819,575],{},[2071,87821,10929],{},[2092,87823,79232],{"encoding":2094}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[95,87826,10908],{}," jsou indiferenční křivky produkční funkce. Podíl ",[1647,87829,87831],{"className":87830},[2059],[2061,87832,87833],{"xmlns":2063},[2065,87834,87835,87855],{},[2068,87836,87837,87839,87845,87847,87849],{},[2071,87838,2890],{},[2348,87840,87841,87843],{},[2071,87842,575],{},[2071,87844,586],{},[2071,87846,4761],{"mathvariant":2450},[2071,87848,2890],{},[2348,87850,87851,87853],{},[2071,87852,575],{},[2071,87854,10929],{},[2092,87856,87857],{"encoding":2094},"MP_L\u002FMP_K",[95,87859,87860,87861,2090],{},"mezní míra technické substituce (",[1647,87862,87864],{"className":87863},[2059],[2061,87865,87866],{"xmlns":2063},[2065,87867,87868,87878],{},[2068,87869,87870,87872,87874,87876],{},[2071,87871,2890],{},[2071,87873,4082],{},[2071,87875,543],{},[2071,87877,532],{},[2092,87879,11729],{"encoding":2094}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[84,87882,54178],{"id":54177},[201,87884,87885,87888,87891,87894,87897,87900,87903,87906,87909,87912,87915],{},[92,87886,87887],{},"Jaké jsou faktory produkce?",[92,87889,87890],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[92,87892,87893],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[92,87895,87896],{},"Co udává mezní produkt práce?",[92,87898,87899],{},"Co musí respektovat průběh křivky produkce?",[92,87901,87902],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[92,87904,87905],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[92,87907,87908],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[92,87910,87911],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[92,87913,87914],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[92,87916,87917],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[84,87919,87921],{"id":87920},"úlohy-51517","Úlohy 5.1–5.17",[609,87923,44742],{"id":44741},[55,87925,87926,87929,87930,87952,87953,835,87973,835,87993,88013],{},[95,87927,87928],{},"5.1"," Je dána produkce ",[1647,87931,87933],{"className":87932},[2059],[2061,87934,87935],{"xmlns":2063},[2065,87936,87937,87949],{},[2068,87938,87939,87941,87943,87945],{},[2071,87940,2861],{},[2075,87942,2077],{},[2210,87944,2935],{},[8204,87946,87947],{},[2071,87948,586],{},[2092,87950,87951],{"encoding":2094},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[1647,87954,87956],{"className":87955},[2059],[2061,87957,87958],{"xmlns":2063},[2065,87959,87960,87970],{},[2068,87961,87962,87964,87966,87968],{},[2071,87963,2861],{},[2075,87965,2084],{"stretchy":2083},[2210,87967,638],{},[2075,87969,2090],{"stretchy":2083},[2092,87971,87972],{"encoding":2094},"Q(1)",[1647,87974,87976],{"className":87975},[2059],[2061,87977,87978],{"xmlns":2063},[2065,87979,87980,87990],{},[2068,87981,87982,87984,87986,87988],{},[2071,87983,2861],{},[2075,87985,2084],{"stretchy":2083},[2210,87987,662],{},[2075,87989,2090],{"stretchy":2083},[2092,87991,87992],{"encoding":2094},"Q(4)",[1647,87994,87996],{"className":87995},[2059],[2061,87997,87998],{"xmlns":2063},[2065,87999,88000,88010],{},[2068,88001,88002,88004,88006,88008],{},[2071,88003,2861],{},[2075,88005,2084],{"stretchy":2083},[2210,88007,4087],{},[2075,88009,2090],{"stretchy":2083},[2092,88011,88012],{"encoding":2094},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[55,88015,88016,87929,88019,88055,88056,88069,88070,88089,88090,88116,88117,2758,88130,88143],{},[95,88017,88018],{},"5.2",[1647,88020,88022],{"className":88021},[2059],[2061,88023,88024],{"xmlns":2063},[2065,88025,88026,88052],{},[2068,88027,88028,88030,88032,88034,88036,88042,88044,88046],{},[2071,88029,2861],{},[2075,88031,2077],{},[2075,88033,2303],{},[2210,88035,2866],{},[2205,88037,88038,88040],{},[2071,88039,586],{},[2210,88041,654],{},[2075,88043,2176],{},[2210,88045,4087],{},[2205,88047,88048,88050],{},[2071,88049,586],{},[2210,88051,646],{},[2092,88053,88054],{"encoding":2094},"Q = -0{,}1 L^{3} + 9 L^{2}",". (a) Rozhodněte, kdy produkce roste, resp. klesá. (b) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (c) Určete ",[1647,88057,88059],{"className":88058},[2059],[2061,88060,88061],{"xmlns":2063},[2065,88062,88063,88067],{},[2068,88064,88065],{},[2071,88066,586],{},[2092,88068,586],{"encoding":2094}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[1647,88071,88073],{"className":88072},[2059],[2061,88074,88075],{"xmlns":2063},[2065,88076,88077,88087],{},[2068,88078,88079,88081],{},[2071,88080,2890],{},[2348,88082,88083,88085],{},[2071,88084,575],{},[2071,88086,586],{},[2092,88088,11176],{"encoding":2094},". (f) Vypočtěte ",[1647,88091,88093],{"className":88092},[2059],[2061,88094,88095],{"xmlns":2063},[2065,88096,88097,88113],{},[2068,88098,88099,88101,88107,88109,88111],{},[2071,88100,2890],{},[2348,88102,88103,88105],{},[2071,88104,575],{},[2071,88106,586],{},[2075,88108,2084],{"stretchy":2083},[2210,88110,2935],{},[2075,88112,2090],{"stretchy":2083},[2092,88114,88115],{"encoding":2094},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[1647,88118,88120],{"className":88119},[2059],[2061,88121,88122],{"xmlns":2063},[2065,88123,88124,88128],{},[2068,88125,88126],{},[2210,88127,2935],{},[2092,88129,2935],{"encoding":2094},[1647,88131,88133],{"className":88132},[2059],[2061,88134,88135],{"xmlns":2063},[2065,88136,88137,88141],{},[2068,88138,88139],{},[2210,88140,46578],{},[2092,88142,46578],{"encoding":2094}," a porovnejte se skutečnou změnou produkce.",[55,88145,88146,88149,88150,88172,88173,88201,88202,88233,88234,195],{},[95,88147,88148],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[1647,88151,88153],{"className":88152},[2059],[2061,88154,88155],{"xmlns":2063},[2065,88156,88157,88169],{},[2068,88158,88159,88161,88163,88165],{},[2071,88160,2861],{},[2075,88162,2077],{},[2210,88164,16845],{},[8204,88166,88167],{},[2071,88168,586],{},[2092,88170,88171],{"encoding":2094},"Q = 500\\sqrt{L}",".\n(b) ",[1647,88174,88176],{"className":88175},[2059],[2061,88177,88178],{"xmlns":2063},[2065,88179,88180,88198],{},[2068,88181,88182,88184,88186,88188,88192,88194,88196],{},[2071,88183,2861],{},[2075,88185,2077],{},[2210,88187,33108],{},[8204,88189,88190],{},[2071,88191,586],{},[2075,88193,2303],{},[2210,88195,662],{},[2071,88197,586],{},[2092,88199,88200],{"encoding":2094},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[1647,88203,88205],{"className":88204},[2059],[2061,88206,88207],{"xmlns":2063},[2065,88208,88209,88230],{},[2068,88210,88211,88213,88215,88217,88219,88221,88224],{},[2071,88212,2861],{},[2075,88214,2077],{},[2210,88216,3194],{},[2071,88218,586],{},[2075,88220,2303],{},[2210,88222,88223],{},"0,01",[2205,88225,88226,88228],{},[2071,88227,586],{},[2210,88229,646],{},[2092,88231,88232],{"encoding":2094},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[1647,88235,88237],{"className":88236},[2059],[2061,88238,88239],{"xmlns":2063},[2065,88240,88241,88267],{},[2068,88242,88243,88245,88247,88249,88251,88257,88259,88261],{},[2071,88244,2861],{},[2075,88246,2077],{},[2075,88248,2303],{},[2210,88250,72681],{},[2205,88252,88253,88255],{},[2071,88254,586],{},[2210,88256,654],{},[2075,88258,2176],{},[2210,88260,4087],{},[2205,88262,88263,88265],{},[2071,88264,586],{},[2210,88266,646],{},[2092,88268,88269],{"encoding":2094},"Q = -0{,}3 L^{3} + 9 L^{2}",[55,88271,88272,88275,88276,2697,88295,76668,88312,195],{},[95,88273,88274],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[1647,88277,88279],{"className":88278},[2059],[2061,88280,88281],{"xmlns":2063},[2065,88282,88283,88293],{},[2068,88284,88285,88287],{},[2071,88286,4342],{},[2348,88288,88289,88291],{},[2071,88290,575],{},[2071,88292,586],{},[2092,88294,79104],{"encoding":2094},[1647,88296,88298],{"className":88297},[2059],[2061,88299,88300],{"xmlns":2063},[2065,88301,88302,88310],{},[2068,88303,88304],{},[2348,88305,88306,88308],{},[2071,88307,586],{},[2210,88309,630],{},[2092,88311,80029],{"encoding":2094},[1647,88313,88315],{"className":88314},[2059],[2061,88316,88317],{"xmlns":2063},[2065,88318,88319,88359],{},[2068,88320,88321,88323,88329,88331,88337,88339,88341,88343,88349,88351,88357],{},[2071,88322,4342],{},[2348,88324,88325,88327],{},[2071,88326,575],{},[2071,88328,586],{},[2075,88330,2084],{"stretchy":2083},[2348,88332,88333,88335],{},[2071,88334,586],{},[2210,88336,630],{},[2075,88338,2090],{"stretchy":2083},[2075,88340,2077],{},[2071,88342,2890],{},[2348,88344,88345,88347],{},[2071,88346,575],{},[2071,88348,586],{},[2075,88350,2084],{"stretchy":2083},[2348,88352,88353,88355],{},[2071,88354,586],{},[2210,88356,630],{},[2075,88358,2090],{"stretchy":2083},[2092,88360,88361],{"encoding":2094},"AP_L(L_0) = MP_L(L_0)",[55,88363,88364,87929,88367,24333,88403,88416,88417,88436],{},[95,88365,88366],{},"5.5",[1647,88368,88370],{"className":88369},[2059],[2061,88371,88372],{"xmlns":2063},[2065,88373,88374,88400],{},[2068,88375,88376,88378,88380,88382,88384,88390,88392,88394],{},[2071,88377,2861],{},[2075,88379,2077],{},[2075,88381,2303],{},[2210,88383,2911],{},[2205,88385,88386,88388],{},[2071,88387,586],{},[2210,88389,654],{},[2075,88391,2176],{},[2210,88393,3583],{},[2205,88395,88396,88398],{},[2071,88397,586],{},[2210,88399,646],{},[2092,88401,88402],{"encoding":2094},"Q = -0{,}2 L^{3} + 12 L^{2}",[1647,88404,88406],{"className":88405},[2059],[2061,88407,88408],{"xmlns":2063},[2065,88409,88410,88414],{},[2068,88411,88412],{},[2071,88413,586],{},[2092,88415,586],{"encoding":2094}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[1647,88418,88420],{"className":88419},[2059],[2061,88421,88422],{"xmlns":2063},[2065,88423,88424,88434],{},[2068,88425,88426,88428],{},[2071,88427,4342],{},[2348,88429,88430,88432],{},[2071,88431,575],{},[2071,88433,586],{},[2092,88435,79104],{"encoding":2094},") a stanovte, kolik jednotek produkce připadá na jednoho pracovníka. (b) Určete počet pracovníků s využitím principu maximalizace průměrného produktu práce. (c) Ověřte platnost principu maximalizujícího produkci a stanovte příslušné maximum produkce. (d) Porovnejte počet pracovníků v případech (a), (c). (e) Graficky interpretujte získané výsledky.",[609,88438,88440],{"id":88439},"dvoufaktorový-model","Dvoufaktorový model",[55,88442,88443,88446,88447,88172,88473,88201,88515,195],{},[95,88444,88445],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[1647,88448,88450],{"className":88449},[2059],[2061,88451,88452],{"xmlns":2063},[2065,88453,88454,88470],{},[2068,88455,88456,88458,88460,88462,88464],{},[2071,88457,2861],{},[2075,88459,2077],{},[2210,88461,686],{},[2071,88463,586],{},[2205,88465,88466,88468],{},[2071,88467,10929],{},[2210,88469,646],{},[2092,88471,88472],{"encoding":2094},"Q = 7 L K^{2}",[1647,88474,88476],{"className":88475},[2059],[2061,88477,88478],{"xmlns":2063},[2065,88479,88480,88512],{},[2068,88481,88482,88484,88486,88488,88500],{},[2071,88483,2861],{},[2075,88485,2077],{},[2210,88487,3194],{},[2205,88489,88490,88492],{},[2071,88491,586],{},[2068,88493,88494,88496,88498],{},[2210,88495,646],{},[2071,88497,4761],{"mathvariant":2450},[2210,88499,654],{},[2205,88501,88502,88504],{},[2071,88503,10929],{},[2068,88505,88506,88508,88510],{},[2210,88507,638],{},[2071,88509,4761],{"mathvariant":2450},[2210,88511,654],{},[2092,88513,88514],{"encoding":2094},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[1647,88516,88518],{"className":88517},[2059],[2061,88519,88520],{"xmlns":2063},[2065,88521,88522,88554],{},[2068,88523,88524,88526,88528,88530,88542],{},[2071,88525,2861],{},[2075,88527,2077],{},[2210,88529,3781],{},[2205,88531,88532,88534],{},[2071,88533,586],{},[2068,88535,88536,88538,88540],{},[2210,88537,654],{},[2071,88539,4761],{"mathvariant":2450},[2210,88541,670],{},[2205,88543,88544,88546],{},[2071,88545,10929],{},[2068,88547,88548,88550,88552],{},[2210,88549,646],{},[2071,88551,4761],{"mathvariant":2450},[2210,88553,670],{},[2092,88555,88556],{"encoding":2094},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[55,88558,88559,87929,88562,88604,88605,835,88623,88642,88643,88660],{},[95,88560,88561],{},"5.7",[1647,88563,88565],{"className":88564},[2059],[2061,88566,88567],{"xmlns":2063},[2065,88568,88569,88601],{},[2068,88570,88571,88573,88575,88577,88589],{},[2071,88572,2861],{},[2075,88574,2077],{},[2210,88576,2935],{},[2205,88578,88579,88581],{},[2071,88580,586],{},[2068,88582,88583,88585,88587],{},[2210,88584,638],{},[2071,88586,4761],{"mathvariant":2450},[2210,88588,646],{},[2205,88590,88591,88593],{},[2071,88592,10929],{},[2068,88594,88595,88597,88599],{},[2210,88596,638],{},[2071,88598,4761],{"mathvariant":2450},[2210,88600,646],{},[2092,88602,88603],{"encoding":2094},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[1647,88606,88608],{"className":88607},[2059],[2061,88609,88610],{"xmlns":2063},[2065,88611,88612,88620],{},[2068,88613,88614,88616,88618],{},[2071,88615,586],{},[2075,88617,2077],{},[2210,88619,22881],{},[2092,88621,88622],{"encoding":2094},"L = 400",[1647,88624,88626],{"className":88625},[2059],[2061,88627,88628],{"xmlns":2063},[2065,88629,88630,88639],{},[2068,88631,88632,88634,88636],{},[2071,88633,10929],{},[2075,88635,2077],{},[2210,88637,88638],{},"17576",[2092,88640,88641],{"encoding":2094},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[1647,88644,88646],{"className":88645},[2059],[2061,88647,88648],{"xmlns":2063},[2065,88649,88650,88658],{},[2068,88651,88652,88654,88656],{},[2071,88653,586],{},[2075,88655,2361],{"separator":2360},[2071,88657,10929],{},[2092,88659,83454],{"encoding":2094}," zdvojnásobí.",[55,88662,88663,88666,88667,88604,88698,835,88716,74054,88734,88764,88765,88795,88796,2758,88809,88823,88824,2758,88837,88850],{},[95,88664,88665],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[1647,88668,88670],{"className":88669},[2059],[2061,88671,88672],{"xmlns":2063},[2065,88673,88674,88695],{},[2068,88675,88676,88678,88680,88683,88689],{},[2071,88677,2861],{},[2075,88679,2077],{},[2210,88681,88682],{},"1,01",[2205,88684,88685,88687],{},[2071,88686,586],{},[2210,88688,26469],{},[2205,88690,88691,88693],{},[2071,88692,10929],{},[2210,88694,26528],{},[2092,88696,88697],{"encoding":2094},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[1647,88699,88701],{"className":88700},[2059],[2061,88702,88703],{"xmlns":2063},[2065,88704,88705,88713],{},[2068,88706,88707,88709,88711],{},[2071,88708,586],{},[2075,88710,2077],{},[2210,88712,33770],{},[2092,88714,88715],{"encoding":2094},"L = 250",[1647,88717,88719],{"className":88718},[2059],[2061,88720,88721],{"xmlns":2063},[2065,88722,88723,88731],{},[2068,88724,88725,88727,88729],{},[2071,88726,10929],{},[2075,88728,2077],{},[2210,88730,2854],{},[2092,88732,88733],{"encoding":2094},"K = 1000",[1647,88735,88737],{"className":88736},[2059],[2061,88738,88739],{"xmlns":2063},[2065,88740,88741,88761],{},[2068,88742,88743,88745,88751,88753,88755,88757,88759],{},[2071,88744,2890],{},[2348,88746,88747,88749],{},[2071,88748,575],{},[2071,88750,586],{},[2075,88752,2084],{"stretchy":2083},[2210,88754,33770],{},[2075,88756,2361],{"separator":2360},[2210,88758,2854],{},[2075,88760,2090],{"stretchy":2083},[2092,88762,88763],{"encoding":2094},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[1647,88766,88768],{"className":88767},[2059],[2061,88769,88770],{"xmlns":2063},[2065,88771,88772,88792],{},[2068,88773,88774,88776,88782,88784,88786,88788,88790],{},[2071,88775,2890],{},[2348,88777,88778,88780],{},[2071,88779,575],{},[2071,88781,10929],{},[2075,88783,2084],{"stretchy":2083},[2210,88785,33770],{},[2075,88787,2361],{"separator":2360},[2210,88789,2854],{},[2075,88791,2090],{"stretchy":2083},[2092,88793,88794],{"encoding":2094},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[1647,88797,88799],{"className":88798},[2059],[2061,88800,88801],{"xmlns":2063},[2065,88802,88803,88807],{},[2068,88804,88805],{},[2071,88806,586],{},[2092,88808,586],{"encoding":2094},[1647,88810,88812],{"className":88811},[2059],[2061,88813,88814],{"xmlns":2063},[2065,88815,88816,88821],{},[2068,88817,88818],{},[2210,88819,88820],{},"260",[2092,88822,88820],{"encoding":2094}," a současném poklesu ",[1647,88825,88827],{"className":88826},[2059],[2061,88828,88829],{"xmlns":2063},[2065,88830,88831,88835],{},[2068,88832,88833],{},[2071,88834,10929],{},[2092,88836,10929],{"encoding":2094},[1647,88838,88840],{"className":88839},[2059],[2061,88841,88842],{"xmlns":2063},[2065,88843,88844,88848],{},[2068,88845,88846],{},[2210,88847,16926],{},[2092,88849,16926],{"encoding":2094}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[55,88852,88853,88856,88857,195],{},[95,88854,88855],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[1647,88858,88860],{"className":88859},[2059],[2061,88861,88862],{"xmlns":2063},[2065,88863,88864,88884],{},[2068,88865,88866,88868,88870,88872,88878],{},[2071,88867,2861],{},[2075,88869,2077],{},[2210,88871,2935],{},[2205,88873,88874,88876],{},[2071,88875,586],{},[2210,88877,72681],{},[2205,88879,88880,88882],{},[2071,88881,10929],{},[2210,88883,5096],{},[2092,88885,88886],{"encoding":2094},"Q = 10 L^{0{,}3} K^{0{,}5}",[55,88888,88889,88892,88893,85050,88916,11525,88929,11156,88979,4007],{},[95,88890,88891],{},"5.10"," Dokažte, že pro homogenní funkci ",[1647,88894,88896],{"className":88895},[2059],[2061,88897,88898],{"xmlns":2063},[2065,88899,88900,88914],{},[2068,88901,88902,88904,88906,88908,88910,88912],{},[2071,88903,2861],{},[2075,88905,2084],{"stretchy":2083},[2071,88907,586],{},[2075,88909,2361],{"separator":2360},[2071,88911,10929],{},[2075,88913,2090],{"stretchy":2083},[2092,88915,11128],{"encoding":2094},[1647,88917,88919],{"className":88918},[2059],[2061,88920,88921],{"xmlns":2063},[2065,88922,88923,88927],{},[2068,88924,88925],{},[2071,88926,41153],{},[2092,88928,41153],{"encoding":2094},[1647,88930,88932],{"className":88931},[2059],[2061,88933,88934],{"xmlns":2063},[2065,88935,88936,88976],{},[2068,88937,88938,88940,88948,88950,88952,88960,88962,88964,88966,88968,88970,88972,88974],{},[2071,88939,586],{},[9252,88941,88942,88944,88946],{},[2071,88943,2861],{},[2071,88945,586],{},[2075,88947,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,88949,2176],{},[2071,88951,10929],{},[9252,88953,88954,88956,88958],{},[2071,88955,2861],{},[2071,88957,10929],{},[2075,88959,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,88961,2077],{},[2071,88963,41153],{},[2071,88965,2861],{},[2075,88967,2084],{"stretchy":2083},[2071,88969,586],{},[2075,88971,2361],{"separator":2360},[2071,88973,10929],{},[2075,88975,2090],{"stretchy":2083},[2092,88977,88978],{"encoding":2094},"L Q'_L + K Q'_K = n Q(L, K)",[3982,88980,85025],{},[55,88982,88983,88986],{},[95,88984,88985],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[55,88988,88989,87929,88992,89032,89033,835,89055,835,89077,89099],{},[95,88990,88991],{},"5.12",[1647,88993,88995],{"className":88994},[2059],[2061,88996,88997],{"xmlns":2063},[2065,88998,88999,89029],{},[2068,89000,89001,89003,89005,89017],{},[2071,89002,2861],{},[2075,89004,2077],{},[2205,89006,89007,89009],{},[2071,89008,586],{},[2068,89010,89011,89013,89015],{},[2210,89012,638],{},[2071,89014,4761],{"mathvariant":2450},[2210,89016,654],{},[2205,89018,89019,89021],{},[2071,89020,10929],{},[2068,89022,89023,89025,89027],{},[2210,89024,638],{},[2071,89026,4761],{"mathvariant":2450},[2210,89028,662],{},[2092,89030,89031],{"encoding":2094},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[1647,89034,89036],{"className":89035},[2059],[2061,89037,89038],{"xmlns":2063},[2065,89039,89040,89052],{},[2068,89041,89042,89048,89050],{},[2348,89043,89044,89046],{},[2071,89045,85266],{},[2210,89047,630],{},[2075,89049,2077],{},[2210,89051,638],{},[2092,89053,89054],{"encoding":2094},"q_0 = 1",[1647,89056,89058],{"className":89057},[2059],[2061,89059,89060],{"xmlns":2063},[2065,89061,89062,89074],{},[2068,89063,89064,89070,89072],{},[2348,89065,89066,89068],{},[2071,89067,85266],{},[2210,89069,638],{},[2075,89071,2077],{},[2210,89073,646],{},[2092,89075,89076],{"encoding":2094},"q_1 = 2",[1647,89078,89080],{"className":89079},[2059],[2061,89081,89082],{"xmlns":2063},[2065,89083,89084,89096],{},[2068,89085,89086,89092,89094],{},[2348,89087,89088,89090],{},[2071,89089,85266],{},[2210,89091,646],{},[2075,89093,2077],{},[2210,89095,654],{},[2092,89097,89098],{"encoding":2094},"q_2 = 3",". (c) Načrtněte izokvanty.",[55,89101,89102,87929,89105,89145,89146,835,89174,835,89202,835,89230,835,89259,835,89288,835,89317,835,89346,835,89375,195],{},[95,89103,89104],{},"5.13",[1647,89106,89108],{"className":89107},[2059],[2061,89109,89110],{"xmlns":2063},[2065,89111,89112,89142],{},[2068,89113,89114,89116,89118,89130],{},[2071,89115,2861],{},[2075,89117,2077],{},[2205,89119,89120,89122],{},[2071,89121,586],{},[2068,89123,89124,89126,89128],{},[2210,89125,638],{},[2071,89127,4761],{"mathvariant":2450},[2210,89129,654],{},[2205,89131,89132,89134],{},[2071,89133,10929],{},[2068,89135,89136,89138,89140],{},[2210,89137,638],{},[2071,89139,4761],{"mathvariant":2450},[2210,89141,646],{},[2092,89143,89144],{"encoding":2094},"Q = L^{1\u002F3} K^{1\u002F2}",". Rozhodněte, které ze zadaných bodů leží na téže izokvantě a v kladném případě stanovte, jaká produkce je na příslušné izokvantě dosažena (užijte kalkulátoru): ",[1647,89147,89149],{"className":89148},[2059],[2061,89150,89151],{"xmlns":2063},[2065,89152,89153,89171],{},[2068,89154,89155,89161,89163,89165,89167,89169],{},[2348,89156,89157,89159],{},[2071,89158,4342],{},[2210,89160,638],{},[2075,89162,2561],{"stretchy":2083},[2210,89164,638],{},[2075,89166,8512],{"separator":2360},[2210,89168,638],{},[2075,89170,2576],{"stretchy":2083},[2092,89172,89173],{"encoding":2094},"A_1[1; 1]",[1647,89175,89177],{"className":89176},[2059],[2061,89178,89179],{"xmlns":2063},[2065,89180,89181,89199],{},[2068,89182,89183,89189,89191,89193,89195,89197],{},[2348,89184,89185,89187],{},[2071,89186,4342],{},[2210,89188,646],{},[2075,89190,2561],{"stretchy":2083},[2210,89192,638],{},[2075,89194,8512],{"separator":2360},[2210,89196,5672],{},[2075,89198,2576],{"stretchy":2083},[2092,89200,89201],{"encoding":2094},"A_2[1; 8]",[1647,89203,89205],{"className":89204},[2059],[2061,89206,89207],{"xmlns":2063},[2065,89208,89209,89227],{},[2068,89210,89211,89217,89219,89221,89223,89225],{},[2348,89212,89213,89215],{},[2071,89214,4342],{},[2210,89216,654],{},[2075,89218,2561],{"stretchy":2083},[2210,89220,638],{},[2075,89222,8512],{"separator":2360},[2210,89224,71067],{},[2075,89226,2576],{"stretchy":2083},[2092,89228,89229],{"encoding":2094},"A_3[1; 27]",[1647,89231,89233],{"className":89232},[2059],[2061,89234,89235],{"xmlns":2063},[2065,89236,89237,89256],{},[2068,89238,89239,89245,89247,89249,89251,89254],{},[2348,89240,89241,89243],{},[2071,89242,4342],{},[2210,89244,662],{},[2075,89246,2561],{"stretchy":2083},[2210,89248,646],{},[2075,89250,8512],{"separator":2360},[2210,89252,89253],{},"0,353",[2075,89255,2576],{"stretchy":2083},[2092,89257,89258],{"encoding":2094},"A_4[2; 0{,}353]",[1647,89260,89262],{"className":89261},[2059],[2061,89263,89264],{"xmlns":2063},[2065,89265,89266,89285],{},[2068,89267,89268,89274,89276,89278,89280,89283],{},[2348,89269,89270,89272],{},[2071,89271,4342],{},[2210,89273,670],{},[2075,89275,2561],{"stretchy":2083},[2210,89277,646],{},[2075,89279,8512],{"separator":2360},[2210,89281,89282],{},"2,828",[2075,89284,2576],{"stretchy":2083},[2092,89286,89287],{"encoding":2094},"A_5[2; 2{,}828]",[1647,89289,89291],{"className":89290},[2059],[2061,89292,89293],{"xmlns":2063},[2065,89294,89295,89314],{},[2068,89296,89297,89303,89305,89307,89309,89312],{},[2348,89298,89299,89301],{},[2071,89300,4342],{},[2210,89302,678],{},[2075,89304,2561],{"stretchy":2083},[2210,89306,646],{},[2075,89308,8512],{"separator":2360},[2210,89310,89311],{},"9,545",[2075,89313,2576],{"stretchy":2083},[2092,89315,89316],{"encoding":2094},"A_6[2; 9{,}545]",[1647,89318,89320],{"className":89319},[2059],[2061,89321,89322],{"xmlns":2063},[2065,89323,89324,89343],{},[2068,89325,89326,89332,89334,89336,89338,89341],{},[2348,89327,89328,89330],{},[2071,89329,4342],{},[2210,89331,686],{},[2075,89333,2561],{"stretchy":2083},[2210,89335,69029],{},[2075,89337,8512],{"separator":2360},[2210,89339,89340],{},"0,544",[2075,89342,2576],{"stretchy":2083},[2092,89344,89345],{"encoding":2094},"A_7[1{,}5; 0{,}544]",[1647,89347,89349],{"className":89348},[2059],[2061,89350,89351],{"xmlns":2063},[2065,89352,89353,89372],{},[2068,89354,89355,89361,89363,89365,89367,89370],{},[2348,89356,89357,89359],{},[2071,89358,4342],{},[2210,89360,5672],{},[2075,89362,2561],{"stretchy":2083},[2210,89364,69029],{},[2075,89366,8512],{"separator":2360},[2210,89368,89369],{},"14,696",[2075,89371,2576],{"stretchy":2083},[2092,89373,89374],{"encoding":2094},"A_8[1{,}5; 14{,}696]",[1647,89376,89378],{"className":89377},[2059],[2061,89379,89380],{"xmlns":2063},[2065,89381,89382,89400],{},[2068,89383,89384,89390,89392,89394,89396,89398],{},[2348,89385,89386,89388],{},[2071,89387,4342],{},[2210,89389,4087],{},[2075,89391,2561],{"stretchy":2083},[2210,89393,646],{},[2075,89395,8512],{"separator":2360},[2210,89397,670],{},[2075,89399,2576],{"stretchy":2083},[2092,89401,89402],{"encoding":2094},"A_9[2; 5]",[55,89404,89405,89408],{},[95,89406,89407],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[55,89410,89411,89414,89415,89445,89446,89459,89460,89473,89474,73787,89493,89512,89513,195],{},[95,89412,89413],{},"5.15"," Produkce firmy je dána vztahem ",[1647,89416,89418],{"className":89417},[2059],[2061,89419,89420],{"xmlns":2063},[2065,89421,89422,89442],{},[2068,89423,89424,89426,89428,89430,89436],{},[2071,89425,2861],{},[2075,89427,2077],{},[2210,89429,646],{},[2205,89431,89432,89434],{},[2071,89433,586],{},[2210,89435,5096],{},[2205,89437,89438,89440],{},[2071,89439,10929],{},[2210,89441,26528],{},[2092,89443,89444],{"encoding":2094},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[1647,89447,89449],{"className":89448},[2059],[2061,89450,89451],{"xmlns":2063},[2065,89452,89453,89457],{},[2068,89454,89455],{},[2210,89456,3164],{},[2092,89458,3164],{"encoding":2094}," pracovníků a disponuje-li ",[1647,89461,89463],{"className":89462},[2059],[2061,89464,89465],{"xmlns":2063},[2065,89466,89467,89471],{},[2068,89468,89469],{},[2210,89470,68905],{},[2092,89472,68905],{"encoding":2094}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[1647,89475,89477],{"className":89476},[2059],[2061,89478,89479],{"xmlns":2063},[2065,89480,89481,89491],{},[2068,89482,89483,89485,89487,89489],{},[2071,89484,2890],{},[2071,89486,4082],{},[2071,89488,543],{},[2071,89490,532],{},[2092,89492,11729],{"encoding":2094},[1647,89494,89496],{"className":89495},[2059],[2061,89497,89498],{"xmlns":2063},[2065,89499,89500,89510],{},[2068,89501,89502,89504,89506,89508],{},[2071,89503,2890],{},[2071,89505,4082],{},[2071,89507,543],{},[2071,89509,532],{},[2092,89511,11729],{"encoding":2094}," na hladině dle (a) a výsledek ekonomicky interpretujte. (d) Odhadněte změnu kapitálu potřebné k udržení produkce na hladině dle (a), jestliže počet pracovníků poklesne na ",[1647,89514,89516],{"className":89515},[2059],[2061,89517,89518],{"xmlns":2063},[2065,89519,89520,89525],{},[2068,89521,89522],{},[2210,89523,89524],{},"95",[2092,89526,89524],{"encoding":2094},[55,89528,89529,87929,89532,75461,89564,89583,89584,89597,89598,89611,89612,89625],{},[95,89530,89531],{},"5.16",[1647,89533,89535],{"className":89534},[2059],[2061,89536,89537],{"xmlns":2063},[2065,89538,89539,89561],{},[2068,89540,89541,89543,89545,89551,89553,89555],{},[2071,89542,2861],{},[2075,89544,2077],{},[2205,89546,89547,89549],{},[2071,89548,10929],{},[2210,89550,646],{},[2075,89552,2176],{},[2210,89554,646],{},[2205,89556,89557,89559],{},[2071,89558,586],{},[2210,89560,646],{},[2092,89562,89563],{"encoding":2094},"Q = K^{2} + 2 L^{2}",[1647,89565,89567],{"className":89566},[2059],[2061,89568,89569],{"xmlns":2063},[2065,89570,89571,89581],{},[2068,89572,89573,89575,89577,89579],{},[2071,89574,2890],{},[2071,89576,4082],{},[2071,89578,543],{},[2071,89580,532],{},[2092,89582,11729],{"encoding":2094},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[1647,89585,89587],{"className":89586},[2059],[2061,89588,89589],{"xmlns":2063},[2065,89590,89591,89595],{},[2068,89592,89593],{},[2210,89594,3194],{},[2092,89596,3194],{"encoding":2094}," pracovníky a ",[1647,89599,89601],{"className":89600},[2059],[2061,89602,89603],{"xmlns":2063},[2065,89604,89605,89609],{},[2068,89606,89607],{},[2210,89608,82087],{},[2092,89610,82087],{"encoding":2094}," jednotkami kapitálu, jestliže se kapitál sníží na ",[1647,89613,89615],{"className":89614},[2059],[2061,89616,89617],{"xmlns":2063},[2065,89618,89619,89623],{},[2068,89620,89621],{},[2210,89622,50999],{},[2092,89624,50999],{"encoding":2094}," jednotek.",[55,89627,89628,89631,89632,11525,89662,195],{},[95,89629,89630],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[1647,89633,89635],{"className":89634},[2059],[2061,89636,89637],{"xmlns":2063},[2065,89638,89639,89659],{},[2068,89640,89641,89643,89645,89647,89653],{},[2071,89642,2861],{},[2075,89644,2077],{},[2071,89646,4342],{},[2205,89648,89649,89651],{},[2071,89650,586],{},[2071,89652,69],{},[2205,89654,89655,89657],{},[2071,89656,10929],{},[2071,89658,2179],{},[2092,89660,89661],{"encoding":2094},"Q = A L^{a} K^{b}",[1647,89663,89665],{"className":89664},[2059],[2061,89666,89667],{"xmlns":2063},[2065,89668,89669,89699],{},[2068,89670,89671,89673,89675,89677,89679,89681,89689,89691],{},[2071,89672,2890],{},[2071,89674,4082],{},[2071,89676,543],{},[2071,89678,532],{},[2075,89680,2077],{},[2400,89682,89683],{"scriptlevel":630,"displaystyle":2083},[2403,89684,89685,89687],{},[2071,89686,69],{},[2071,89688,2179],{},[2075,89690,3251],{},[2400,89692,89693],{"scriptlevel":630,"displaystyle":2083},[2403,89694,89695,89697],{},[2071,89696,10929],{},[2071,89698,586],{},[2092,89700,89701],{"encoding":2094},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[84,89703,321],{"id":320},[89,89705,89706,89739,89766,89775,89825,89856,89909,89932,89987,90060,90138,90181,90213,90246,90287,90359,90420,90486,90503,90576,90642,90694,90750,90784,90827],{},[92,89707,89708,89711,89712,41189,89725,89738],{},[95,89709,89710],{},"Faktory (vstupy) produkce:"," práce ",[1647,89713,89715],{"className":89714},[2059],[2061,89716,89717],{"xmlns":2063},[2065,89718,89719,89723],{},[2068,89720,89721],{},[2071,89722,586],{},[2092,89724,586],{"encoding":2094},[1647,89726,89728],{"className":89727},[2059],[2061,89729,89730],{"xmlns":2063},[2065,89731,89732,89736],{},[2068,89733,89734],{},[2071,89735,10929],{},[2092,89737,10929],{"encoding":2094},", půda.",[92,89740,89741,7102,89743,195],{},[95,89742,44742],{},[1647,89744,89746],{"className":89745},[2059],[2061,89747,89748],{"xmlns":2063},[2065,89749,89750,89764],{},[2068,89751,89752,89754,89756,89758,89760,89762],{},[2071,89753,2861],{},[2075,89755,2077],{},[2071,89757,2861],{},[2075,89759,2084],{"stretchy":2083},[2071,89761,586],{},[2075,89763,2090],{"stretchy":2083},[2092,89765,79015],{"encoding":2094},[92,89767,89768,11156,89770,13861,89773,195],{},[95,89769,78865],{},[3982,89771,89772],{},"production function",[95,89774,79518],{},[92,89776,89777,1445,89779,195],{},[95,89778,79564],{},[1647,89780,89782],{"className":89781},[2059],[2061,89783,89784],{"xmlns":2063},[2065,89785,89786,89822],{},[2068,89787,89788,89790,89796,89798,89800,89802,89804,89806,89808,89810,89816,89818,89820],{},[2071,89789,2890],{},[2348,89791,89792,89794],{},[2071,89793,575],{},[2071,89795,586],{},[2075,89797,2077],{},[2071,89799,2273],{},[2071,89801,2861],{},[2071,89803,4761],{"mathvariant":2450},[2071,89805,2273],{},[2071,89807,586],{},[2075,89809,2077],{},[2205,89811,89812,89814],{},[2071,89813,2861],{},[2075,89815,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,89817,2084],{"stretchy":2083},[2071,89819,586],{},[2075,89821,2090],{"stretchy":2083},[2092,89823,89824],{"encoding":2094},"MP_L = dQ\u002FdL = Q'(L)",[92,89826,89827,1445,89829,195],{},[95,89828,80499],{},[1647,89830,89832],{"className":89831},[2059],[2061,89833,89834],{"xmlns":2063},[2065,89835,89836,89854],{},[2068,89837,89838,89840,89846,89848,89850,89852],{},[2071,89839,4342],{},[2348,89841,89842,89844],{},[2071,89843,575],{},[2071,89845,586],{},[2075,89847,2077],{},[2071,89849,2861],{},[2071,89851,4761],{"mathvariant":2450},[2071,89853,586],{},[2092,89855,79083],{"encoding":2094},[92,89857,89858,89860,89861,11525,89878,195],{},[95,89859,79986],{}," — od určitého ",[1647,89862,89864],{"className":89863},[2059],[2061,89865,89866],{"xmlns":2063},[2065,89867,89868,89876],{},[2068,89869,89870],{},[2348,89871,89872,89874],{},[2071,89873,586],{},[2210,89875,630],{},[2092,89877,80029],{"encoding":2094},[1647,89879,89881],{"className":89880},[2059],[2061,89882,89883],{"xmlns":2063},[2065,89884,89885,89907],{},[2068,89886,89887,89897,89899,89901,89903,89905],{},[2205,89888,89889,89891],{},[2071,89890,2861],{},[2068,89892,89893,89895],{},[2075,89894,2452],{"mathvariant":2450},[2075,89896,2452],{"mathvariant":2450},[2075,89898,2084],{"stretchy":2083},[2071,89900,586],{},[2075,89902,2090],{"stretchy":2083},[2075,89904,3521],{},[2210,89906,630],{},[2092,89908,80175],{"encoding":2094},[92,89910,89911,1445,89914,89931],{},[95,89912,89913],{},"Inflexní bod",[1647,89915,89917],{"className":89916},[2059],[2061,89918,89919],{"xmlns":2063},[2065,89920,89921,89929],{},[2068,89922,89923],{},[2348,89924,89925,89927],{},[2071,89926,586],{},[2210,89928,630],{},[2092,89930,80029],{"encoding":2094}," — přechod z konvexity do konkavity.",[92,89933,89934,1445,89937,7102,89954,195],{},[95,89935,89936],{},"Bod maxima produkce",[1647,89938,89940],{"className":89939},[2059],[2061,89941,89942],{"xmlns":2063},[2065,89943,89944,89952],{},[2068,89945,89946],{},[2348,89947,89948,89950],{},[2071,89949,586],{},[2210,89951,638],{},[2092,89953,14947],{"encoding":2094},[1647,89955,89957],{"className":89956},[2059],[2061,89958,89959],{"xmlns":2063},[2065,89960,89961,89985],{},[2068,89962,89963,89965,89971,89973,89979,89981,89983],{},[2071,89964,2890],{},[2348,89966,89967,89969],{},[2071,89968,575],{},[2071,89970,586],{},[2075,89972,2084],{"stretchy":2083},[2348,89974,89975,89977],{},[2071,89976,586],{},[2210,89978,638],{},[2075,89980,2090],{"stretchy":2083},[2075,89982,2077],{},[2210,89984,630],{},[2092,89986,80248],{"encoding":2094},[92,89988,89989,90011,90012,11525,90031,195],{},[95,89990,89991,89992],{},"Princip maximalizace ",[1647,89993,89995],{"className":89994},[2059],[2061,89996,89997],{"xmlns":2063},[2065,89998,89999,90009],{},[2068,90000,90001,90003],{},[2071,90002,4342],{},[2348,90004,90005,90007],{},[2071,90006,575],{},[2071,90008,586],{},[2092,90010,79104],{"encoding":2094}," — v bodě maxima ",[1647,90013,90015],{"className":90014},[2059],[2061,90016,90017],{"xmlns":2063},[2065,90018,90019,90029],{},[2068,90020,90021,90023],{},[2071,90022,4342],{},[2348,90024,90025,90027],{},[2071,90026,575],{},[2071,90028,586],{},[2092,90030,79104],{"encoding":2094},[1647,90032,90034],{"className":90033},[2059],[2061,90035,90036],{"xmlns":2063},[2065,90037,90038,90058],{},[2068,90039,90040,90042,90048,90050,90052],{},[2071,90041,2890],{},[2348,90043,90044,90046],{},[2071,90045,575],{},[2071,90047,586],{},[2075,90049,2077],{},[2071,90051,4342],{},[2348,90053,90054,90056],{},[2071,90055,575],{},[2071,90057,586],{},[2092,90059,79134],{"encoding":2094},[92,90061,90062,1445,90065,835,90104,835,90121,195],{},[95,90063,90064],{},"Polynomiální produkční funkce",[1647,90066,90068],{"className":90067},[2059],[2061,90069,90070],{"xmlns":2063},[2065,90071,90072,90102],{},[2068,90073,90074,90076,90078,90080,90082,90084,90086,90092,90094,90096],{},[2071,90075,2861],{},[2075,90077,2084],{"stretchy":2083},[2071,90079,586],{},[2075,90081,2090],{"stretchy":2083},[2075,90083,2077],{},[2071,90085,69],{},[2205,90087,90088,90090],{},[2071,90089,586],{},[2210,90091,654],{},[2075,90093,2176],{},[2071,90095,2179],{},[2205,90097,90098,90100],{},[2071,90099,586],{},[2210,90101,646],{},[2092,90103,80366],{"encoding":2094},[1647,90105,90107],{"className":90106},[2059],[2061,90108,90109],{"xmlns":2063},[2065,90110,90111,90119],{},[2068,90112,90113,90115,90117],{},[2071,90114,69],{},[2075,90116,3521],{},[2210,90118,630],{},[2092,90120,47379],{"encoding":2094},[1647,90122,90124],{"className":90123},[2059],[2061,90125,90126],{"xmlns":2063},[2065,90127,90128,90136],{},[2068,90129,90130,90132,90134],{},[2071,90131,2179],{},[2075,90133,3482],{},[2210,90135,630],{},[2092,90137,21553],{"encoding":2094},[92,90139,90140,1445,90143,195],{},[95,90141,90142],{},"Diferenciál produkce",[1647,90144,90146],{"className":90145},[2059],[2061,90147,90148],{"xmlns":2063},[2065,90149,90150,90178],{},[2068,90151,90152,90154,90156,90158,90160,90162,90164,90166,90172,90174,90176],{},[2071,90153,2961],{"mathvariant":2450},[2071,90155,2861],{},[2075,90157,2803],{},[2071,90159,2273],{},[2071,90161,2861],{},[2075,90163,2077],{},[2071,90165,2890],{},[2348,90167,90168,90170],{},[2071,90169,575],{},[2071,90171,586],{},[2363,90173,3061],{},[2071,90175,2273],{},[2071,90177,586],{},[2092,90179,90180],{"encoding":2094},"\\Delta Q \\approx dQ = MP_L\\,dL",[92,90182,90183,7102,90185,195],{},[95,90184,88440],{},[1647,90186,90188],{"className":90187},[2059],[2061,90189,90190],{"xmlns":2063},[2065,90191,90192,90210],{},[2068,90193,90194,90196,90198,90200,90202,90204,90206,90208],{},[2071,90195,2861],{},[2075,90197,2077],{},[2071,90199,2861],{},[2075,90201,2084],{"stretchy":2083},[2071,90203,586],{},[2075,90205,2361],{"separator":2360},[2071,90207,10929],{},[2075,90209,2090],{"stretchy":2083},[2092,90211,90212],{"encoding":2094},"Q = Q(L, K)",[92,90214,90215,7102,90217,195],{},[95,90216,82535],{},[1647,90218,90220],{"className":90219},[2059],[2061,90221,90222],{"xmlns":2063},[2065,90223,90224,90244],{},[2068,90225,90226,90228,90230,90232,90238],{},[2071,90227,2861],{},[2075,90229,2077],{},[2071,90231,4342],{},[2205,90233,90234,90236],{},[2071,90235,586],{},[2071,90237,69],{},[2205,90239,90240,90242],{},[2071,90241,10929],{},[2071,90243,2179],{},[2092,90245,79201],{"encoding":2094},[92,90247,90248,7102,90251,90286],{},[95,90249,90250],{},"Ryzí Cobb-Douglas",[1647,90252,90254],{"className":90253},[2059],[2061,90255,90256],{"xmlns":2063},[2065,90257,90258,90284],{},[2068,90259,90260,90262,90264,90266,90272],{},[2071,90261,2861],{},[2075,90263,2077],{},[2071,90265,4342],{},[2205,90267,90268,90270],{},[2071,90269,586],{},[2071,90271,69],{},[2205,90273,90274,90276],{},[2071,90275,10929],{},[2068,90277,90278,90280,90282],{},[2210,90279,638],{},[2075,90281,2303],{},[2071,90283,69],{},[2092,90285,83361],{"encoding":2094}," (konstantní výnosy).",[92,90288,90289,7102,90291,195],{},[95,90290,84077],{},[1647,90292,90294],{"className":90293},[2059],[2061,90295,90296],{"xmlns":2063},[2065,90297,90298,90356],{},[2068,90299,90300,90302,90304,90306,90308,90310,90312,90314,90316,90318,90328,90330,90332,90342],{},[2071,90301,2861],{},[2075,90303,2077],{},[2071,90305,4342],{},[2075,90307,2561],{"stretchy":2083},[2075,90309,2084],{"stretchy":2083},[2210,90311,638],{},[2075,90313,2303],{},[2071,90315,69],{},[2075,90317,2090],{"stretchy":2083},[2205,90319,90320,90322],{},[2071,90321,586],{},[2068,90323,90324,90326],{},[2075,90325,2303],{},[2071,90327,2179],{},[2075,90329,2176],{},[2071,90331,69],{},[2205,90333,90334,90336],{},[2071,90335,10929],{},[2068,90337,90338,90340],{},[2075,90339,2303],{},[2071,90341,2179],{},[2205,90343,90344,90346],{},[2075,90345,2576],{"stretchy":2083},[2068,90347,90348,90350,90352,90354],{},[2075,90349,2303],{},[2210,90351,638],{},[2071,90353,4761],{"mathvariant":2450},[2071,90355,2179],{},[2092,90357,90358],{"encoding":2094},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[92,90360,90361,11156,90364,13861,90386,11156,90389,90419],{},[95,90362,90363],{},"Lineární",[1647,90365,90367],{"className":90366},[2059],[2061,90368,90369],{"xmlns":2063},[2065,90370,90371,90383],{},[2068,90372,90373,90375,90377,90379,90381],{},[2071,90374,69],{},[2071,90376,586],{},[2075,90378,2176],{},[2071,90380,2179],{},[2071,90382,10929],{},[2092,90384,90385],{"encoding":2094},"aL + bK",[95,90387,90388],{},"Leontiefova",[1647,90390,90392],{"className":90391},[2059],[2061,90393,90394],{"xmlns":2063},[2065,90395,90396,90416],{},[2068,90397,90398,90400,90402,90404,90406,90408,90410,90412,90414],{},[2071,90399,84305],{},[2075,90401,60670],{},[2075,90403,2084],{"stretchy":2083},[2071,90405,69],{},[2071,90407,586],{},[2075,90409,2361],{"separator":2360},[2071,90411,2179],{},[2071,90413,10929],{},[2075,90415,2090],{"stretchy":2083},[2092,90417,90418],{"encoding":2094},"\\min(aL, bK)",") produkční funkce.",[92,90421,90422,7102,90438,195],{},[95,90423,90424,90425],{},"Homogenita stupně ",[1647,90426,90428],{"className":90427},[2059],[2061,90429,90430],{"xmlns":2063},[2065,90431,90432,90436],{},[2068,90433,90434],{},[2071,90435,41153],{},[2092,90437,41153],{"encoding":2094},[1647,90439,90441],{"className":90440},[2059],[2061,90442,90443],{"xmlns":2063},[2065,90444,90445,90483],{},[2068,90446,90447,90449,90451,90453,90455,90457,90459,90461,90463,90465,90471,90473,90475,90477,90479,90481],{},[2071,90448,2861],{},[2075,90450,2084],{"stretchy":2083},[2071,90452,13774],{},[2071,90454,586],{},[2075,90456,2361],{"separator":2360},[2071,90458,13774],{},[2071,90460,10929],{},[2075,90462,2090],{"stretchy":2083},[2075,90464,2077],{},[2205,90466,90467,90469],{},[2071,90468,13774],{},[2071,90470,41153],{},[2071,90472,2861],{},[2075,90474,2084],{"stretchy":2083},[2071,90476,586],{},[2075,90478,2361],{"separator":2360},[2071,90480,10929],{},[2075,90482,2090],{"stretchy":2083},[2092,90484,90485],{"encoding":2094},"Q(rL, rK) = r^n Q(L, K)",[92,90487,90488,83459],{},[95,90489,83392,90490],{},[1647,90491,90493],{"className":90492},[2059],[2061,90494,90495],{"xmlns":2063},[2065,90496,90497,90501],{},[2068,90498,90499],{},[2071,90500,4342],{},[2092,90502,4342],{"encoding":2094},[92,90504,90505,90507,90508,90530,90531,90553,90554,4007],{},[95,90506,82894],{}," — konstantní (",[1647,90509,90511],{"className":90510},[2059],[2061,90512,90513],{"xmlns":2063},[2065,90514,90515,90527],{},[2068,90516,90517,90519,90521,90523,90525],{},[2071,90518,69],{},[2075,90520,2176],{},[2071,90522,2179],{},[2075,90524,2077],{},[2210,90526,638],{},[2092,90528,90529],{"encoding":2094},"a+b=1","), rostoucí (",[1647,90532,90534],{"className":90533},[2059],[2061,90535,90536],{"xmlns":2063},[2065,90537,90538,90550],{},[2068,90539,90540,90542,90544,90546,90548],{},[2071,90541,69],{},[2075,90543,2176],{},[2071,90545,2179],{},[2075,90547,3482],{},[2210,90549,638],{},[2092,90551,90552],{"encoding":2094},"a+b>1","), klesající (",[1647,90555,90557],{"className":90556},[2059],[2061,90558,90559],{"xmlns":2063},[2065,90560,90561,90573],{},[2068,90562,90563,90565,90567,90569,90571],{},[2071,90564,69],{},[2075,90566,2176],{},[2071,90568,2179],{},[2075,90570,3521],{},[2210,90572,638],{},[2092,90574,90575],{"encoding":2094},"a+b\u003C1",[92,90577,90578,1445,90580,835,90610,1445,90612,195],{},[95,90579,79564],{},[1647,90581,90583],{"className":90582},[2059],[2061,90584,90585],{"xmlns":2063},[2065,90586,90587,90607],{},[2068,90588,90589,90591,90597,90599],{},[2071,90590,2890],{},[2348,90592,90593,90595],{},[2071,90594,575],{},[2071,90596,586],{},[2075,90598,2077],{},[9252,90600,90601,90603,90605],{},[2071,90602,2861],{},[2071,90604,586],{},[2075,90606,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,90608,90609],{"encoding":2094},"MP_L = Q'_L",[95,90611,82467],{},[1647,90613,90615],{"className":90614},[2059],[2061,90616,90617],{"xmlns":2063},[2065,90618,90619,90639],{},[2068,90620,90621,90623,90629,90631],{},[2071,90622,2890],{},[2348,90624,90625,90627],{},[2071,90626,575],{},[2071,90628,10929],{},[2075,90630,2077],{},[9252,90632,90633,90635,90637],{},[2071,90634,2861],{},[2071,90636,10929],{},[2075,90638,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,90640,90641],{"encoding":2094},"MP_K = Q'_K",[92,90643,90644,1445,90646,195],{},[95,90645,84680],{},[1647,90647,90649],{"className":90648},[2059],[2061,90650,90651],{"xmlns":2063},[2065,90652,90653,90691],{},[2068,90654,90655,90657,90659,90661,90663,90669,90671,90673,90675,90677,90679,90685,90687,90689],{},[2071,90656,2273],{},[2071,90658,2861],{},[2075,90660,2077],{},[2071,90662,2890],{},[2348,90664,90665,90667],{},[2071,90666,575],{},[2071,90668,586],{},[2363,90670,3061],{},[2071,90672,2273],{},[2071,90674,586],{},[2075,90676,2176],{},[2071,90678,2890],{},[2348,90680,90681,90683],{},[2071,90682,575],{},[2071,90684,10929],{},[2363,90686,3061],{},[2071,90688,2273],{},[2071,90690,10929],{},[2092,90692,90693],{"encoding":2094},"dQ = MP_L\\,dL + MP_K\\,dK",[92,90695,90696,7102,90698,195],{},[95,90697,85025],{},[1647,90699,90701],{"className":90700},[2059],[2061,90702,90703],{"xmlns":2063},[2065,90704,90705,90747],{},[2068,90706,90707,90709,90717,90719,90721,90729,90731,90733,90735,90737,90739,90741,90743,90745],{},[2071,90708,586],{},[9252,90710,90711,90713,90715],{},[2071,90712,2861],{},[2071,90714,586],{},[2075,90716,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,90718,2176],{},[2071,90720,10929],{},[9252,90722,90723,90725,90727],{},[2071,90724,2861],{},[2071,90726,10929],{},[2075,90728,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,90730,2077],{},[2071,90732,41153],{},[2363,90734,3061],{},[2071,90736,2861],{},[2075,90738,2084],{"stretchy":2083},[2071,90740,586],{},[2075,90742,2361],{"separator":2360},[2071,90744,10929],{},[2075,90746,2090],{"stretchy":2083},[2092,90748,90749],{"encoding":2094},"L Q'_L + K Q'_K = n\\,Q(L,K)",[92,90751,90752,90755,90756,195],{},[95,90753,90754],{},"Izokvanta"," — křivka ",[1647,90757,90759],{"className":90758},[2059],[2061,90760,90761],{"xmlns":2063},[2065,90762,90763,90781],{},[2068,90764,90765,90767,90769,90771,90773,90775,90777,90779],{},[2071,90766,2861],{},[2075,90768,2084],{"stretchy":2083},[2071,90770,586],{},[2075,90772,2361],{"separator":2360},[2071,90774,10929],{},[2075,90776,2090],{"stretchy":2083},[2075,90778,2077],{},[2071,90780,85266],{},[2092,90782,90783],{"encoding":2094},"Q(L, K) = q",[92,90785,90786,1445,90788,195],{},[95,90787,85455],{},[1647,90789,90791],{"className":90790},[2059],[2061,90792,90793],{"xmlns":2063},[2065,90794,90795,90825],{},[2068,90796,90797,90799,90801,90803,90805,90807,90809,90815,90817,90819],{},[2071,90798,2890],{},[2071,90800,4082],{},[2071,90802,543],{},[2071,90804,532],{},[2075,90806,2077],{},[2071,90808,2890],{},[2348,90810,90811,90813],{},[2071,90812,575],{},[2071,90814,586],{},[2071,90816,4761],{"mathvariant":2450},[2071,90818,2890],{},[2348,90820,90821,90823],{},[2071,90822,575],{},[2071,90824,10929],{},[2092,90826,79276],{"encoding":2094},[92,90828,90829,1445,90832,195],{},[95,90830,90831],{},"Substituční vztah",[1647,90833,90835],{"className":90834},[2059],[2061,90836,90837],{"xmlns":2063},[2065,90838,90839,90863],{},[2068,90840,90841,90843,90845,90847,90849,90851,90853,90855,90857,90859,90861],{},[2071,90842,2961],{"mathvariant":2450},[2071,90844,10929],{},[2075,90846,2803],{},[2075,90848,2303],{},[2071,90850,2890],{},[2071,90852,4082],{},[2071,90854,543],{},[2071,90856,532],{},[2363,90858,3061],{},[2071,90860,2273],{},[2071,90862,586],{},[2092,90864,90865],{"encoding":2094},"\\Delta K \\approx -MRTS\\,dL",[84,90867,3866],{"id":3865},[89,90869,90870,90967,90974,90981],{},[92,90871,90872,1445,90874,90877,90878,835,90881,90884,90885,90888,90889,90908,90909,21387,90928,90931,90932,90951,90952,4007],{},[95,90873,55018],{},[69,90875,3901],{"className":90876,"dataFsResolvedFilePath":3899,"href":3900},[62]," (parciální derivace, totální diferenciál), ",[69,90879,2431],{"className":90880,"dataFsResolvedFilePath":4005,"href":4006},[62],[69,90882,12195],{"className":90883,"dataFsResolvedFilePath":12193,"href":12194},[62]," (optimalizace produkce s rozpočtovým omezením), ",[69,90886,12226],{"className":90887,"dataFsResolvedFilePath":10901,"href":10902},[62]," (paralela: izokvanty ↔ indiferenční křivky, ",[1647,90890,90892],{"className":90891},[2059],[2061,90893,90894],{"xmlns":2063},[2065,90895,90896,90906],{},[2068,90897,90898,90900,90902,90904],{},[2071,90899,2890],{},[2071,90901,4082],{},[2071,90903,543],{},[2071,90905,532],{},[2092,90907,11729],{"encoding":2094}," ↔ ",[1647,90910,90912],{"className":90911},[2059],[2061,90913,90914],{"xmlns":2063},[2065,90915,90916,90926],{},[2068,90917,90918,90920,90922,90924],{},[2071,90919,2890],{},[2071,90921,4082],{},[2071,90923,2849],{},[2071,90925,532],{},[2092,90927,11733],{"encoding":2094},[69,90929,3906],{"className":90930,"dataFsResolvedFilePath":3022,"href":3023},[62]," (analogie principu max ",[1647,90933,90935],{"className":90934},[2059],[2061,90936,90937],{"xmlns":2063},[2065,90938,90939,90949],{},[2068,90940,90941,90943],{},[2071,90942,4342],{},[2348,90944,90945,90947],{},[2071,90946,575],{},[2071,90948,586],{},[2092,90950,79104],{"encoding":2094}," ↔ min ",[1647,90953,90955],{"className":90954},[2059],[2061,90956,90957],{"xmlns":2063},[2065,90958,90959,90965],{},[2068,90960,90961,90963],{},[2071,90962,4342],{},[2071,90964,2849],{},[2092,90966,60030],{"encoding":2094},[92,90968,90969,1445,90971,195],{},[95,90970,3873],{},[69,90972,3913],{"className":90973,"dataFsResolvedFilePath":3911,"href":3912},[62],[92,90975,90976,1445,90978,195],{},[95,90977,17946],{},[69,90979,39735],{"className":90980,"dataFsResolvedFilePath":39733,"href":39734},[62],[92,90982,90983,1445,90985,195],{},[95,90984,17937],{},[69,90986,17941],{"className":90987,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":90989},[90990,90991,90992,90996,90998,91003,91004,91011,91012,91014,91015,91016,91018,91023,91024,91025,91029,91030],{"id":79299,"depth":7,"text":79300},{"id":79436,"depth":7,"text":79437},{"id":79539,"depth":7,"text":90993,"children":90994},"Mezní produkt práce (MPLMP_L)",[90995],{"id":79985,"depth":4,"text":79986},{"id":80474,"depth":7,"text":90997},"Průměrný produkt práce (APLAP_L)",{"id":80592,"depth":7,"text":80593,"children":90999},[91000,91001,91002],{"id":80828,"depth":4,"text":69971},{"id":81139,"depth":4,"text":81140},{"id":81859,"depth":4,"text":81860},{"id":82431,"depth":7,"text":82432},{"id":82534,"depth":7,"text":82535,"children":91005},[91006,91007,91009,91010],{"id":82893,"depth":4,"text":82894},{"id":83391,"depth":4,"text":91008},"Parametr efektivity AA",{"id":83462,"depth":4,"text":83463},{"id":41471,"depth":4,"text":83802},{"id":83989,"depth":7,"text":83990},{"id":84328,"depth":7,"text":91013},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":85019,"depth":7,"text":85020},{"id":79365,"depth":7,"text":10908},{"id":85430,"depth":7,"text":91017},"Mezní míra technické substituce (MRTSMRTS)",{"id":86296,"depth":7,"text":86297,"children":91019},[91020,91021,91022],{"id":86300,"depth":4,"text":86301},{"id":86943,"depth":4,"text":86944},{"id":87224,"depth":4,"text":87225},{"id":87570,"depth":7,"text":87571},{"id":54177,"depth":7,"text":54178},{"id":87920,"depth":7,"text":87921,"children":91026},[91027,91028],{"id":44741,"depth":4,"text":44742},{"id":88439,"depth":4,"text":88440},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fprodukce",{"title":78935,"description":156},[9647,9648],"topics\u002Fprodukce",[17,10944,91037,91038,91039,79365,91040,91041],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":91044,"title":742,"body":91045,"course":163,"courses":91380,"created":795,"description":156,"extension":166,"meta":91381,"navigation":168,"path":91382,"seo":91383,"sources":91384,"stem":91385,"tags":91386,"type":177,"updated":178,"__hash__":91391},"topics\u002Ftopics\u002Frizeni-rizik.md",{"type":48,"value":91046,"toc":91369},[91047,91050,91057,91063,91067,91131,91135,91185,91189,91194,91213,91217,91220,91224,91238,91242,91270,91274,91323,91325,91351,91356],[51,91048,742],{"id":91049},"řízení-rizik",[55,91051,91052],{},[58,91053],{"alt":91054,"className":91055,"src":91056},"rizeni-rizik-proces",[62,63],"\u002Fwiki-assets\u002Frizeni-rizik-proces.jpeg",[55,91058,91059,91060,195],{},"Komplexní proces identifikace, analýzy a ošetření rizik ohrožujících bezpečnost informací v organizaci. Tvoří jádro ",[69,91061,733],{"className":91062,"dataFsResolvedFilePath":731,"href":732},[62],[84,91064,91066],{"id":91065},"normativní-základ","Normativní základ",[323,91068,91069,91079],{},[326,91070,91071],{},[329,91072,91073,91076],{},[332,91074,91075],{},"Norma",[332,91077,91078],{},"Zaměření",[342,91080,91081,91091,91101,91111,91121],{},[329,91082,91083,91088],{},[347,91084,91085],{},[95,91086,91087],{},"ISO 31000:2019",[347,91089,91090],{},"Obecné smrnice pro management rizik",[329,91092,91093,91098],{},[347,91094,91095],{},[95,91096,91097],{},"ISO 31010:2020",[347,91099,91100],{},"Techniky posuzování rizik",[329,91102,91103,91108],{},[347,91104,91105],{},[95,91106,91107],{},"ISO\u002FIEC 27005:2019",[347,91109,91110],{},"Řízení rizik bezpečnosti informací",[329,91112,91113,91118],{},[347,91114,91115],{},[95,91116,91117],{},"NIST SP 800-30",[347,91119,91120],{},"Průvodce hodnocením rizik",[329,91122,91123,91128],{},[347,91124,91125],{},[95,91126,91127],{},"NIST SP 800-39",[347,91129,91130],{},"Proces řízení bezpečnostních rizik",[84,91132,91134],{"id":91133},"proces-řízení-rizik-isoiec-27005","Proces řízení rizik (ISO\u002FIEC 27005)",[201,91136,91137,91143,91149,91155,91161,91167,91173,91179],{},[92,91138,91139,91142],{},[95,91140,91141],{},"Stanovení kontextu"," — rozsah, kritéria, metodika, role",[92,91144,91145,91148],{},[95,91146,91147],{},"Identifikace rizik"," — aktiva, hrozby, zranitelnosti",[92,91150,91151,91154],{},[95,91152,91153],{},"Analýza rizik"," — kvantifikace nebo kvalitativní popis",[92,91156,91157,91160],{},[95,91158,91159],{},"Vyhodnocení rizik"," — prioritizace dle kritérií",[92,91162,91163,91166],{},[95,91164,91165],{},"Zvládání rizik"," — výběr opatření (redukce, přenos, retence, vyhnutí)",[92,91168,91169,91172],{},[95,91170,91171],{},"Akceptace rizik"," — formální rozhodnutí",[92,91174,91175,91178],{},[95,91176,91177],{},"Komunikace"," — sdílení informací o rizicích",[92,91180,91181,91184],{},[95,91182,91183],{},"Monitorování"," — průběžné přezkoumávání",[84,91186,91188],{"id":91187},"výpočet-hodnoty-rizika","Výpočet hodnoty rizika",[55,91190,91191],{},[95,91192,91193],{},"Riziko = dopadová hodnota aktiva × hrozba × zranitelnost",[89,91195,91196,91202,91207],{},[92,91197,91198,91201],{},[95,91199,91200],{},"Hrozba"," — potenciální příčina incidentu (stupnice 1–5)",[92,91203,91204,91206],{},[95,91205,18598],{}," — slabé místo aktiva (stupnice 1–5)",[92,91208,91209,91212],{},[95,91210,91211],{},"Dopad"," — hodnota aktiva při ztrátě CIA",[84,91214,91216],{"id":91215},"obecný-model-hodnocení-rizik","Obecný model hodnocení rizik",[55,91218,91219],{},"Hrozba → Systém → Zranitelnost → Zneužitelnost? → Riziko → Přijatelné? → Opatření\u002FZbytkové riziko",[84,91221,91223],{"id":91222},"klíčové-dokumenty","Klíčové dokumenty",[89,91225,91226,91232],{},[92,91227,91228,91231],{},[95,91229,91230],{},"RTP"," (Risk Treatment Plan) — plán zvládání rizik s opatřeními, prioritami, termíny, zdroji",[92,91233,91234,91237],{},[95,91235,91236],{},"PoA\u002FSoA"," (Statement of Applicability) — přehled aplikovaných a neaplikovaných opatření",[84,91239,91241],{"id":91240},"bezpečnostní-role-dle-zkb","Bezpečnostní role dle ZKB",[89,91243,91244,91250,91255,91260,91265],{},[92,91245,91246,91249],{},[95,91247,91248],{},"Výbor pro řízení KB"," — organizovaná skupina pro celkové řízení",[92,91251,91252,91254],{},[95,91253,18280],{}," — odpovědný za ISMS",[92,91256,91257,91259],{},[95,91258,18290],{}," — návrh a implementace opatření",[92,91261,91262,91264],{},[95,91263,18300],{}," — provádění auditů",[92,91266,91267,91269],{},[95,91268,18310],{}," — zajištění rozvoje a bezpečnosti aktiva",[84,91271,91273],{"id":91272},"tří-úrovňový-model-nist-sp-800-39","Tří-úrovňový model (NIST SP 800-39)",[323,91275,91276,91288],{},[326,91277,91278],{},[329,91279,91280,91283,91285],{},[332,91281,91282],{},"Úroveň",[332,91284,91078],{},[332,91286,91287],{},"Typ rizika",[342,91289,91290,91301,91312],{},[329,91291,91292,91295,91298],{},[347,91293,91294],{},"Stupeň 1",[347,91296,91297],{},"Organizace",[347,91299,91300],{},"Strategické riziko",[329,91302,91303,91306,91309],{},[347,91304,91305],{},"Stupeň 2",[347,91307,91308],{},"Poslání\u002Fobchodní procesy",[347,91310,91311],{},"Taktické riziko",[329,91313,91314,91317,91320],{},[347,91315,91316],{},"Stupeň 3",[347,91318,91319],{},"Informační systémy",[347,91321,91322],{},"Operační riziko",[84,91324,723],{"id":722},[89,91326,91327,91333,91339,91346],{},[92,91328,91329,91332],{},[69,91330,733],{"className":91331,"dataFsResolvedFilePath":731,"href":732},[62]," — řízení rizik jako součást systému",[92,91334,91335,91338],{},[69,91336,364],{"className":91337,"dataFsResolvedFilePath":18478,"href":18479},[62]," — kontinuita činnosti při materializaci rizik",[92,91340,91341,91345],{},[69,91342,91344],{"className":91343,"dataFsResolvedFilePath":778,"href":779},[62],"Disaster Recovery"," — obnova po havárii",[92,91347,91348,30711],{},[69,91349,751],{"className":91350,"dataFsResolvedFilePath":749,"href":750},[62],[84,91352,756,91353],{"id":755},[69,91354,762],{"className":91355,"dataFsResolvedFilePath":760,"href":761},[62],[89,91357,91358,91364],{},[92,91359,91360],{},[69,91361,91363],{"className":91362,"dataFsResolvedFilePath":18516,"href":18517},[62],"Risk Management — shrnutí přednášky",[92,91365,91366],{},[69,91367,18510],{"className":91368,"dataFsResolvedFilePath":18508,"href":18509},[62],{"title":156,"searchDepth":7,"depth":7,"links":91370},[91371,91372,91373,91374,91375,91376,91377,91378,91379],{"id":91065,"depth":7,"text":91066},{"id":91133,"depth":7,"text":91134},{"id":91187,"depth":7,"text":91188},{"id":91215,"depth":7,"text":91216},{"id":91222,"depth":7,"text":91223},{"id":91240,"depth":7,"text":91241},{"id":91272,"depth":7,"text":91273},{"id":722,"depth":7,"text":723},{"id":755,"depth":7,"text":793},[11],{},"\u002Ftopics\u002Frizeni-rizik",{"title":742,"description":156},[18548,18547],"topics\u002Frizeni-rizik",[11,91387,91388,91389,32,91390],"rizeni-rizik","iso-31000","iso-27005","hodnoceni-rizik","QgxHGq7BTBoSo7sPrQH8Uv8y26R9huxzIJnkKME8Y9Q",{"id":91393,"title":91394,"body":91395,"course":163,"courses":91628,"created":795,"description":156,"extension":166,"meta":91629,"navigation":168,"path":91630,"seo":91631,"sources":91632,"stem":91634,"tags":91635,"type":177,"updated":178,"__hash__":91640},"topics\u002Ftopics\u002Fsae.md","SAE — Budování bezpečnostního povědomí",{"type":48,"value":91396,"toc":91620},[91397,91400,91407,91410,91414,91513,91517,91552,91556,91576,91580,91583,91585,91605,91610],[51,91398,91394],{"id":91399},"sae-budování-bezpečnostního-povědomí",[55,91401,91402],{},[58,91403],{"alt":91404,"className":91405,"src":91406},"sae-pyramida",[62,63],"\u002Fwiki-assets\u002Fsae-pyramida.jpeg",[55,91408,91409],{},"Program definovaný doporučeními NIST řady SP 800, sloužící k budování a zvyšování bezpečnostního povědomí uživatelů ICT. Základní součást kybernetické hygieny.",[84,91411,91413],{"id":91412},"čtyři-úrovně-sae","Čtyři úrovně SAE",[323,91415,91416,91433],{},[326,91417,91418],{},[329,91419,91420,91422,91425,91427,91430],{},[332,91421,91282],{},[332,91423,91424],{},"Příznak",[332,91426,18638],{},[332,91428,91429],{},"Metody",[332,91431,91432],{},"Časový rámec",[342,91434,91435,91455,91475,91495],{},[329,91436,91437,91443,91446,91449,91452],{},[347,91438,91439,91442],{},[95,91440,91441],{},"Awareness"," (povědomí)",[347,91444,91445],{},"„Co\"",[347,91447,91448],{},"Rozpoznávání",[347,91450,91451],{},"Média, videa, plakáty",[347,91453,91454],{},"Krátkodobý",[329,91456,91457,91463,91466,91469,91472],{},[347,91458,91459,91462],{},[95,91460,91461],{},"Training"," (výcvik)",[347,91464,91465],{},"„Jak\"",[347,91467,91468],{},"Dovednosti",[347,91470,91471],{},"Přednášky, případovky, cvičení",[347,91473,91474],{},"Střednědobý",[329,91476,91477,91483,91486,91489,91492],{},[347,91478,91479,91482],{},[95,91480,91481],{},"Education"," (vzdělávání)",[347,91484,91485],{},"„Proč\"",[347,91487,91488],{},"Porozumění",[347,91490,91491],{},"Semináře, diskuze, výzkum",[347,91493,91494],{},"Dlouhodobý",[329,91496,91497,91502,91504,91507,91510],{},[347,91498,91499],{},[95,91500,91501],{},"Professional Development",[347,91503,10415],{},[347,91505,91506],{},"Profesní rozvoj",[347,91508,91509],{},"Certifikace, konference",[347,91511,91512],{},"Průběžný",[84,91514,91516],{"id":91515},"sae-plán-11-kroků","SAE plán (11 kroků)",[201,91518,91519,91522,91525,91528,91531,91534,91537,91540,91543,91546,91549],{},[92,91520,91521],{},"Role a odpovědnosti v programu",[92,91523,91524],{},"Stanovení cílů pro každou fázi",[92,91526,91527],{},"Rozdělení uživatelů (analýza)",[92,91529,91530],{},"Vytvoření školících materiálů dle skupin",[92,91532,91533],{},"Určení cíle pro každou skupinu",[92,91535,91536],{},"Témata pro každou relaci\u002Fkurz",[92,91538,91539],{},"Metody nasazení (metodiky)",[92,91541,91542],{},"Dokumentace a zpětná vazba",[92,91544,91545],{},"Vyhodnocení a aktualizace materiálů",[92,91547,91548],{},"Četnost opakování",[92,91550,91551],{},"Kalkulace",[84,91553,91555],{"id":91554},"modely-řízení","Modely řízení",[89,91557,91558,91564,91570],{},[92,91559,91560,91563],{},[95,91561,91562],{},"Centralizovaný"," — veškerá odpovědnost na CIO\u002FCISO",[92,91565,91566,91569],{},[95,91567,91568],{},"Částečně decentralizovaný"," — politiky centrálně, implementace distribuovaně",[92,91571,91572,91575],{},[95,91573,91574],{},"Plně decentralizovaný"," — pouze politika centrálně, vše ostatní delegováno",[84,91577,91579],{"id":91578},"doporučená-témata-dle-nzkb-vyhl-4092025-sb","Doporučená témata dle nZKB (vyhl. 409\u002F2025 Sb.)",[55,91581,91582],{},"25 témat včetně: bezpečné použití přenosných médií, cloud, hlášení incidentů, BYOD, aktuální hrozby, firewall, malware, hesla, MFA, sociální inženýrství, VPN, šifrování, zálohování aj.",[84,91584,723],{"id":722},[89,91586,91587,91593,91599],{},[92,91588,91589,91592],{},[69,91590,733],{"className":91591,"dataFsResolvedFilePath":731,"href":732},[62]," — SAE jako součást provozní bezpečnosti",[92,91594,91595,91598],{},[69,91596,751],{"className":91597,"dataFsResolvedFilePath":749,"href":750},[62]," — povědomí jako obrana č. 1",[92,91600,91601,91604],{},[69,91602,742],{"className":91603,"dataFsResolvedFilePath":740,"href":741},[62]," — snižování rizika lidského faktoru",[84,91606,756,91607],{"id":755},[69,91608,762],{"className":91609,"dataFsResolvedFilePath":760,"href":761},[62],[89,91611,91612],{},[92,91613,91614],{},[69,91615,91619],{"className":91616,"dataFsResolvedFilePath":91617,"href":91618},[62],"summaries\u002Fimork-sae.md","\u002Fwiki\u002Fimork-sae","SAE — shrnutí přednášky",{"title":156,"searchDepth":7,"depth":7,"links":91621},[91622,91623,91624,91625,91626,91627],{"id":91412,"depth":7,"text":91413},{"id":91515,"depth":7,"text":91516},{"id":91554,"depth":7,"text":91555},{"id":91578,"depth":7,"text":91579},{"id":722,"depth":7,"text":723},{"id":755,"depth":7,"text":793},[11],{},"\u002Ftopics\u002Fsae",{"title":91394,"description":156},[91633],"raw\u002Fimork\u002F2002 VUT_Bezp SAE-2025.pdf","topics\u002Fsae",[11,91636,91637,91638,32,91639],"sae","bezpecnostni-povedomi","skoleni","kyberneticka-hygiena","-1Y2p-b_s_2TkIYA9ZxuD7k_ZQ-t9uyKk4l8A4eMzr8",{"id":91642,"title":12411,"body":91643,"course":163,"courses":91958,"created":165,"description":156,"extension":166,"meta":91959,"navigation":168,"path":91960,"seo":91961,"sources":91962,"stem":91963,"tags":91964,"type":177,"updated":178,"__hash__":91970},"topics\u002Ftopics\u002Fteorie-chaosu.md",{"type":48,"value":91644,"toc":91941},[91645,91648,91655,91658,91660,91664,91691,91695,91706,91710,91713,91767,91771,91778,91781,91784,91788,91805,91809,91812,91850,91854,91857,91861,91864,91867,91871,91874,91876,91896,91898,91918,91920,91923,91928],[51,91646,12411],{"id":91647},"teorie-chaosu",[55,91649,91650],{},[58,91651],{"alt":91652,"className":91653,"src":91654},"chaos-lorenz-atraktor",[62,63],"\u002Fwiki-assets\u002Fchaos-lorenz-atraktor.jpeg",[55,91656,91657],{},"Zkoumá deterministické nelineární systémy, které se chovají nepravidelně a jsou extrémně citlivé na počáteční podmínky. Chaos ≠ náhoda — leží na spektru mezi řádem a náhodností.",[84,91659,321],{"id":320},[609,91661,91663],{"id":91662},"chaos","Chaos",[89,91665,91666,91676,91682],{},[92,91667,91668,91669,91672,91673],{},"Systém je ",[95,91670,91671],{},"deterministický"," (má pravidla), ale dlouhodobě ",[95,91674,91675],{},"těžko předvídatelný",[92,91677,91678,91679,91681],{},"Spektrum: řád → ",[95,91680,91662],{}," → náhodnost",[92,91683,91684,91685,75,91688],{},"Vzniká v dynamických systémech se ",[95,91686,91687],{},"zpětnou vazbou",[95,91689,91690],{},"nelinearitou",[609,91692,91694],{"id":91693},"motýlí-efekt","Motýlí efekt",[89,91696,91697,91700,91703],{},[92,91698,91699],{},"Extrémní citlivost na počáteční podmínky (Lorenz)",[92,91701,91702],{},"Malá změna na začátku → obrovský rozdíl v čase",[92,91704,91705],{},"Důsledek: dlouhodobá přesná předpověď je prakticky nemožná",[609,91707,91709],{"id":91708},"atraktory","Atraktory",[55,91711,91712],{},"Množina stavů, ke kterým systém směřuje nebo v nichž se pohybuje:",[323,91714,91715,91726],{},[326,91716,91717],{},[329,91718,91719,91721,91724],{},[332,91720,10393],{},[332,91722,91723],{},"Chování",[332,91725,3144],{},[342,91727,91728,91741,91754],{},[329,91729,91730,91735,91738],{},[347,91731,91732],{},[95,91733,91734],{},"Bodový",[347,91736,91737],{},"Ustálení v rovnováze",[347,91739,91740],{},"Kyvadlo s tlumením",[329,91742,91743,91748,91751],{},[347,91744,91745],{},[95,91746,91747],{},"Cyklický",[347,91749,91750],{},"Periodické opakování",[347,91752,91753],{},"Sezónní cykly",[329,91755,91756,91761,91764],{},[347,91757,91758],{},[95,91759,91760],{},"Chaotický (podivný)",[347,91762,91763],{},"Složitý pohyb bez přesného opakování",[347,91765,91766],{},"Strange attractor",[609,91768,91770],{"id":91769},"logistická-funkce","Logistická funkce",[55,91772,91773],{},[58,91774],{"alt":91775,"className":91776,"src":91777},"chaos-bifurkace",[62,63],"\u002Fwiki-assets\u002Fchaos-bifurkace.jpeg",[55,91779,91780],{},"x_{n+1} = r · xₙ · (1 − xₙ)",[55,91782,91783],{},"Jednoduchá rovnice, která podle parametru r generuje: stabilitu → oscilace → chaos. Klasická demonstrace teorie chaosu.",[609,91785,91787],{"id":91786},"fraktály","Fraktály",[89,91789,91790,91796,91799],{},[92,91791,91792,91795],{},[95,91793,91794],{},"Soběpodobné obrazce"," — podobný tvar v různých měřítkách (Mandelbrot)",[92,91797,91798],{},"Příklady: stromy, mraky, cenové grafy",[92,91800,91801,91804],{},[95,91802,91803],{},"Fraktální dimenze"," D = 2 − H — měří složitost\u002Fnepravidelnost útvaru",[609,91806,91808],{"id":91807},"hurstův-exponent-h","Hurstův exponent (H)",[55,91810,91811],{},"Analýza časových řad:",[323,91813,91814,91824],{},[326,91815,91816],{},[329,91817,91818,91821],{},[332,91819,91820],{},"Hodnota",[332,91822,91823],{},"Interpretace",[342,91825,91826,91834,91842],{},[329,91827,91828,91831],{},[347,91829,91830],{},"H = 0,5",[347,91832,91833],{},"Náhodný proces",[329,91835,91836,91839],{},[347,91837,91838],{},"H > 0,5",[347,91840,91841],{},"Persistence \u002F trendovost",[329,91843,91844,91847],{},[347,91845,91846],{},"H \u003C 0,5",[347,91848,91849],{},"Antipersistence",[609,91851,91853],{"id":91852},"elliottovy-vlny","Elliottovy vlny",[55,91855,91856],{},"Teorie tržních pohybů ve vlnách (impulsy + korekce). Ilustrace vnitřní struktury zdánlivě nepravidelného vývoje.",[84,91858,91860],{"id":91859},"zpětná-vazba","Zpětná vazba",[55,91862,91863],{},"Klíčový mechanismus chaosu: výstup systému zpětně ovlivňuje vstup → malé změny se zesilují.",[55,91865,91866],{},"V ekonomii: očekávání investorů → ceny → chování investorů → ceny.",[84,91868,91870],{"id":91869},"výskyt-chaosu","Výskyt chaosu",[55,91872,91873],{},"Matematika, fyzika, chemie, biologie, psychologie, ekonomie, finance, politika. Počasí, turbulence, finanční trhy, ekonomické cykly, sociální procesy.",[84,91875,723],{"id":722},[89,91877,91878,91884,91890],{},[92,91879,91880,91883],{},[69,91881,12420],{"className":91882,"dataFsResolvedFilePath":12418,"href":12419},[62]," — chaos omezuje dlouhodobou předpověditelnost",[92,91885,91886,91889],{},[69,91887,12261],{"className":91888,"dataFsResolvedFilePath":72,"href":73},[62]," — oba řeší nejistotu, ale jinak (neostrost vs. dynamická nepředvídatelnost)",[92,91891,91892,91895],{},[69,91893,12754],{"className":91894,"dataFsResolvedFilePath":79,"href":80},[62]," — mohou se učit vzory v chaotických datech",[84,91897,1913],{"id":1912},[201,91899,91900,91903,91906,91909,91912,91915],{},[92,91901,91902],{},"Co je to chaos?",[92,91904,91905],{},"Co je to atraktor?",[92,91907,91908],{},"Jaké jsou typy atraktoru?",[92,91910,91911],{},"Co je to fraktál?",[92,91913,91914],{},"Co jsou to Elliottovy vlny?",[92,91916,91917],{},"Kdo je zakladatelem teorie fraktálů?",[84,91919,1946],{"id":1945},[55,91921,91922],{},"Chaos, nahodilost a řád, rovnováha, atraktor, fraktál, soběpodobnost, soběpříbuznost.",[84,91924,756,91925],{"id":1952},[69,91926,136],{"className":91927,"dataFsResolvedFilePath":134,"href":135},[62],[89,91929,91930,91936],{},[92,91931,91932],{},[69,91933,91935],{"className":91934,"dataFsResolvedFilePath":59567,"href":59566},[62],"Teorie chaosu — shrnutí přednášky",[92,91937,91938,12482],{},[69,91939,1965],{"className":91940,"dataFsResolvedFilePath":1963,"href":1964},[62],{"title":156,"searchDepth":7,"depth":7,"links":91942},[91943,91952,91953,91954,91955,91956,91957],{"id":320,"depth":7,"text":321,"children":91944},[91945,91946,91947,91948,91949,91950,91951],{"id":91662,"depth":4,"text":91663},{"id":91693,"depth":4,"text":91694},{"id":91708,"depth":4,"text":91709},{"id":91769,"depth":4,"text":91770},{"id":91786,"depth":4,"text":91787},{"id":91807,"depth":4,"text":91808},{"id":91852,"depth":4,"text":91853},{"id":91859,"depth":7,"text":91860},{"id":91869,"depth":7,"text":91870},{"id":722,"depth":7,"text":723},{"id":1912,"depth":7,"text":1913},{"id":1945,"depth":7,"text":1946},{"id":1952,"depth":7,"text":2003},[14],{},"\u002Ftopics\u002Fteorie-chaosu",{"title":12411,"description":156},[59581,2009],"topics\u002Fteorie-chaosu",[14,91662,91708,91965,91966,91967,91968,91969],"fraktaly","hurst","motyli-efekt","logisticka-funkce","lorenz","9_KE3En_XZkN73ydbuFmiWlnjt-zr6FQ4aFJizQUcmg",{"id":91972,"title":262,"body":91973,"course":163,"courses":92314,"created":165,"description":156,"extension":166,"meta":92315,"navigation":168,"path":92316,"seo":92317,"sources":92318,"stem":92319,"tags":92320,"type":177,"updated":178,"__hash__":92324},"topics\u002Ftopics\u002Fumele-neuronove-site.md",{"type":48,"value":91974,"toc":92297},[91975,91978,91985,91988,91992,91996,92003,92023,92027,92085,92089,92115,92119,92127,92134,92151,92155,92172,92176,92190,92192,92218,92220,92240,92242,92265,92267,92270,92275],[51,91976,262],{"id":91977},"umělé-neuronové-sítě",[55,91979,91980],{},[58,91981],{"alt":91982,"className":91983,"src":91984},"nn-vicevrstva-sit",[62,63],"\u002Fwiki-assets\u002Fnn-vicevrstva-sit.jpeg",[55,91986,91987],{},"Výpočetní model inspirovaný biologickým nervovým systémem. Soustava propojených neuronů, které se z dat učí rozpoznávat vzory, klasifikovat a predikovat.",[84,91989,91991],{"id":91990},"stavební-kameny","Stavební kameny",[609,91993,91995],{"id":91994},"perceptron-umělý-neuron","Perceptron (umělý neuron)",[55,91997,91998],{},[58,91999],{"alt":92000,"className":92001,"src":92002},"nn-perceptron",[62,63],"\u002Fwiki-assets\u002Fnn-perceptron.jpeg",[89,92004,92005,92008,92011,92017],{},[92,92006,92007],{},"Vstupy i₁..iₙ × váhy w₁..wₙ → vážený součet + bias → aktivační funkce → výstup",[92,92009,92010],{},"Matematicky: a = Σ(iⱼ·wⱼ) + b, výstup m = f(a)",[92,92012,92013,92016],{},[95,92014,92015],{},"Váhy"," nesou naučenou znalost (kladné posilují, záporné tlumí)",[92,92018,92019,92022],{},[95,92020,92021],{},"Bias"," posouvá rozhodovací hranici",[609,92024,92026],{"id":92025},"aktivační-funkce","Aktivační funkce",[323,92028,92029,92043],{},[326,92030,92031],{},[329,92032,92033,92036,92038,92040],{},[332,92034,92035],{},"Funkce",[332,92037,58597],{},[332,92039,12343],{},[332,92041,92042],{},"Použití",[342,92044,92045,92058,92071],{},[329,92046,92047,92049,92052,92055],{},[347,92048,90363],{},[347,92050,92051],{},"m = a",[347,92053,92054],{},"ℝ",[347,92056,92057],{},"Jednoduchý, bez nelinearity",[329,92059,92060,92063,92066,92068],{},[347,92061,92062],{},"Logistický sigmoid",[347,92064,92065],{},"m = 1\u002F(1+e⁻ᵃ)",[347,92067,76592],{},[347,92069,92070],{},"Pravděpodobnost, binární klasifikace",[329,92072,92073,92076,92079,92082],{},[347,92074,92075],{},"Hyperbolický tangens",[347,92077,92078],{},"m = tanh(a)",[347,92080,92081],{},"(−1, 1)",[347,92083,92084],{},"Kladné i záporné aktivace",[609,92086,92088],{"id":92087},"vícevrstvá-síť","Vícevrstvá síť",[89,92090,92091,92097,92103,92109],{},[92,92092,92093,92096],{},[95,92094,92095],{},"Vstupní vrstva"," — přijímá data",[92,92098,92099,92102],{},[95,92100,92101],{},"Skryté vrstvy"," — vytvářejí vnitřní reprezentace, zachycují nelinearitu",[92,92104,92105,92108],{},[95,92106,92107],{},"Výstupní vrstva"," — konečné rozhodnutí nebo predikce",[92,92110,92111,92114],{},[95,92112,92113],{},"Deep learning"," — mnoho vrstev a parametrů, pro složité úlohy s velkým objemem dat",[84,92116,92118],{"id":92117},"učení","Učení",[609,92120,92121],{"id":297},[69,92122,92126],{"className":92123,"dataFsResolvedFilePath":92124,"href":92125},[62],"topics\u002Fbackpropagation.md","\u002Fwiki\u002Fbackpropagation","Backpropagation",[55,92128,92129],{},[58,92130],{"alt":92131,"className":92132,"src":92133},"nn-backpropagation",[62,63],"\u002Fwiki-assets\u002Fnn-backpropagation.jpeg",[201,92135,92136,92139,92142,92145,92148],{},[92,92137,92138],{},"Dopředný průchod — výpočet výstupu",[92,92140,92141],{},"Výpočet chyby (e = cíl − výstup)",[92,92143,92144],{},"Zpětné šíření chyby přes vrstvy",[92,92146,92147],{},"Úprava vah ve směru snížení chyby",[92,92149,92150],{},"Opakování (iterativní proces)",[609,92152,92154],{"id":92153},"praktický-postup","Praktický postup",[201,92156,92157,92160,92163,92166,92169],{},[92,92158,92159],{},"Připravit data (matice vstupů a výstupů)",[92,92161,92162],{},"Zvolit architekturu (počet vrstev, neuronů, aktivační funkce)",[92,92164,92165],{},"Rozdělit data na trénovací\u002Ftestovací (např. 75\u002F25 %)",[92,92167,92168],{},"Trénovat a sledovat průběh chyby",[92,92170,92171],{},"Kritéria ukončení: min chyba, max iterací, max čas",[609,92173,92175],{"id":92174},"kompromis-jednoduchost-vs-složitost","Kompromis jednoduchost vs. složitost",[89,92177,92178,92184],{},[92,92179,92180,92183],{},[95,92181,92182],{},"Podučený model"," — příliš jednoduchý, vysoká chyba",[92,92185,92186,92189],{},[95,92187,92188],{},"Přeučený model"," — naučí se i šum, nefunguje na nových datech",[84,92191,12660],{"id":12659},[89,92193,92194,92197,92200,92203,92206,92209,92215],{},[92,92195,92196],{},"Hodnocení bonity klienta (scoring)",[92,92198,92199],{},"Oceňování (nemovitosti, auta, produkty)",[92,92201,92202],{},"Vyhodnocení investic a rizika",[92,92204,92205],{},"Detekce podvodů (praní peněz, daňové anomálie)",[92,92207,92208],{},"Rozpoznávání obrazu, písma, zvuku, překlad",[92,92210,92211,92214],{},[69,92212,12420],{"className":92213,"dataFsResolvedFilePath":12418,"href":12419},[62]," časových řad (akcie, měny, komodity)",[92,92216,92217],{},"Diagnostika nemocí, autonomní systémy",[84,92219,723],{"id":722},[89,92221,92222,92228,92234],{},[92,92223,92224,92227],{},[69,92225,12398],{"className":92226,"dataFsResolvedFilePath":12396,"href":12397},[62]," — hybridní systém: fuzzy struktura + učení neuronové sítě",[92,92229,92230,92233],{},[69,92231,12261],{"className":92232,"dataFsResolvedFilePath":72,"href":73},[62]," — partner v ANFIS",[92,92235,92236,92239],{},[69,92237,12509],{"className":92238,"dataFsResolvedFilePath":9672,"href":9673},[62]," — mohou optimalizovat architekturu sítě",[84,92241,1913],{"id":1912},[201,92243,92244,92247,92250,92253,92256,92259,92262],{},[92,92245,92246],{},"Popište metodu a vysvětlete princip neuronových sítí.",[92,92248,92249],{},"Popište realizaci a výpočet neuronových sítí na počítači.",[92,92251,92252],{},"Jak lze využít neuronových sítí v praxi?",[92,92254,92255],{},"Kdy je vhodné použít neuronových sítí?",[92,92257,92258],{},"Jaký je správný postup kroků při výpočtu pomocí neuronových sítí?",[92,92260,92261],{},"Jaké vrstvy mají neuronové sítě?",[92,92263,92264],{},"Jaké jsou typy přenosových funkcí?",[84,92266,1946],{"id":1945},[55,92268,92269],{},"Neuronová síť, učení, testování, vstupní matice, přenosová funkce.",[84,92271,756,92272],{"id":1952},[69,92273,136],{"className":92274,"dataFsResolvedFilePath":134,"href":135},[62],[89,92276,92277,92282,92287,92292],{},[92,92278,92279],{},[69,92280,271],{"className":92281,"dataFsResolvedFilePath":269,"href":270},[62],[92,92283,92284],{},[69,92285,280],{"className":92286,"dataFsResolvedFilePath":278,"href":279},[62],[92,92288,92289],{},[69,92290,153],{"className":92291,"dataFsResolvedFilePath":151,"href":152},[62],[92,92293,92294,12482],{},[69,92295,1965],{"className":92296,"dataFsResolvedFilePath":1963,"href":1964},[62],{"title":156,"searchDepth":7,"depth":7,"links":92298},[92299,92304,92309,92310,92311,92312,92313],{"id":91990,"depth":7,"text":91991,"children":92300},[92301,92302,92303],{"id":91994,"depth":4,"text":91995},{"id":92025,"depth":4,"text":92026},{"id":92087,"depth":4,"text":92088},{"id":92117,"depth":7,"text":92118,"children":92305},[92306,92307,92308],{"id":297,"depth":4,"text":92126},{"id":92153,"depth":4,"text":92154},{"id":92174,"depth":4,"text":92175},{"id":12659,"depth":7,"text":12660},{"id":722,"depth":7,"text":723},{"id":1912,"depth":7,"text":1913},{"id":1945,"depth":7,"text":1946},{"id":1952,"depth":7,"text":2003},[14],{},"\u002Ftopics\u002Fumele-neuronove-site",{"title":262,"description":156},[293,294,172,2009],"topics\u002Fumele-neuronove-site",[14,23,92321,297,92322,92323,59584],"perceptron","deep-learning","klasifikace","2MvJHrE1Kihv1j7VlanYSB_CCyk_IdCCqYQ_wceZWs4",{"id":92326,"title":92327,"body":92328,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":101277,"navigation":168,"path":101278,"seo":101279,"sources":101280,"stem":101281,"tags":101282,"type":177,"updated":178,"__hash__":101285},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":48,"value":92329,"toc":101251},[92330,92333,92335,92534,92543,92547,92550,92603,92607,92619,92623,92626,92643,92766,92772,92916,92926,92930,92965,93003,93051,93108,93168,93210,93786,93790,93873,93982,94075,94333,94336,94389,94500,94582,94586,94597,94830,94885,94891,94931,94994,95005,95196,95302,95455,95503,95508,95622,95660,95786,95832,95859,95936,96011,96091,96221,96282,96370,96374,96377,96446,96529,96536,96596,96906,96910,96916,96969,96985,97036,97174,97250,97363,97680,97684,97691,97851,97910,97914,97936,98033,98154,98268,98291,98354,98411,98663,98671,98675,98682,98936,98986,99042,99045,99209,99213,99311,99313,99345,99349,99482,99724,99908,100076,100383,100516,100703,100715,100717,101152,101154],[51,92331,92327],{"id":92332},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[84,92334,13739],{"id":13738},[55,92336,92337,1445,92339,92370,92371,92374,92375,92405,92406,92424,92425,92465,92466,92469,92470,92483,92484,31280,92487,92500,92501,92514,92515,92528,92529,195],{},[95,92338,12226],{},[1647,92340,92342],{"className":92341},[2059],[2061,92343,92344],{"xmlns":2063},[2065,92345,92346,92368],{},[2068,92347,92348,92350,92352,92358,92360,92366],{},[2071,92349,10871],{},[2075,92351,2084],{"stretchy":2083},[2348,92353,92354,92356],{},[2071,92355,2861],{},[2210,92357,638],{},[2075,92359,2361],{"separator":2360},[2348,92361,92362,92364],{},[2071,92363,2861],{},[2210,92365,646],{},[2075,92367,2090],{"stretchy":2083},[2092,92369,19083],{"encoding":2094}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[95,92372,92373],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[1647,92376,92378],{"className":92377},[2059],[2061,92379,92380],{"xmlns":2063},[2065,92381,92382,92402],{},[2068,92383,92384,92386,92392,92394],{},[2071,92385,2890],{},[2348,92387,92388,92390],{},[2071,92389,10871],{},[2071,92391,20528],{},[2075,92393,2077],{},[9252,92395,92396,92398,92400],{},[2071,92397,10871],{},[2071,92399,20528],{},[2075,92401,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,92403,92404],{"encoding":2094},"MU_i = U'_i",", indiferenční křivky ",[1647,92407,92409],{"className":92408},[2059],[2061,92410,92411],{"xmlns":2063},[2065,92412,92413,92421],{},[2068,92414,92415,92417,92419],{},[2071,92416,10871],{},[2075,92418,2077],{},[2071,92420,2222],{},[2092,92422,92423],{"encoding":2094},"U = c"," a mezní míra komoditní substituce ",[1647,92426,92428],{"className":92427},[2059],[2061,92429,92430],{"xmlns":2063},[2065,92431,92432,92462],{},[2068,92433,92434,92436,92438,92440,92442,92444,92446,92452,92454,92456],{},[2071,92435,2890],{},[2071,92437,4082],{},[2071,92439,2849],{},[2071,92441,532],{},[2075,92443,2077],{},[2071,92445,2890],{},[2348,92447,92448,92450],{},[2071,92449,10871],{},[2210,92451,638],{},[2071,92453,4761],{"mathvariant":2450},[2071,92455,2890],{},[2348,92457,92458,92460],{},[2071,92459,10871],{},[2210,92461,646],{},[2092,92463,92464],{"encoding":2094},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[95,92467,92468],{},"teorii užitečnosti"," — funkce ",[1647,92471,92473],{"className":92472},[2059],[2061,92474,92475],{"xmlns":2063},[2065,92476,92477,92481],{},[2068,92478,92479],{},[2071,92480,10871],{},[2092,92482,10871],{"encoding":2094},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[95,92485,92486],{},"Optimalizaci spotřebitele",[1647,92488,92490],{"className":92489},[2059],[2061,92491,92492],{"xmlns":2063},[2065,92493,92494,92498],{},[2068,92495,92496],{},[2071,92497,10871],{},[2092,92499,10871],{"encoding":2094}," při rozpočtu, min ",[1647,92502,92504],{"className":92503},[2059],[2061,92505,92506],{"xmlns":2063},[2065,92507,92508,92512],{},[2068,92509,92510],{},[2071,92511,554],{},[2092,92513,554],{"encoding":2094}," při dané ",[1647,92516,92518],{"className":92517},[2059],[2061,92519,92520],{"xmlns":2063},[2065,92521,92522,92526],{},[2068,92523,92524],{},[2071,92525,10871],{},[2092,92527,10871],{"encoding":2094},", Lagrange, funkce poptávky) viz ",[69,92530,30805],{"className":92531,"dataFsResolvedFilePath":92532,"href":92533},[62],"topics\u002Foptimalizace-spotrebitele.md","\u002Fwiki\u002Foptimalizace-spotrebitele",[55,92535,92536,92537,92539,92540,195],{},"Kapitola 6 knihy ",[3982,92538,17941],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[69,92541,39784],{"className":92542,"dataFsResolvedFilePath":92532,"href":92533},[62],[84,92544,92546],{"id":92545},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[55,92548,92549],{},"Po prostudování této kapitoly byste měli umět:",[89,92551,92552,92558,92567,92572,92575,92581,92587,92590,92596],{},[92,92553,92554,92555,2361],{},"vyložit, co se rozumí termínem ",[95,92556,92557],{},"užitečnost",[92,92559,92560,92561,75,92564,2361],{},"definovat pojmy ",[95,92562,92563],{},"svazek zboží",[95,92565,92566],{},"funkce užitečnosti",[92,92568,79314,92569,79321],{},[95,92570,92571],{},"mezní užitečnosti",[92,92573,92574],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[92,92576,79341,92577,92580],{},[95,92578,92579],{},"Cobb-Douglasových"," funkcí užitečnosti,",[92,92582,79362,92583,92586],{},[95,92584,92585],{},"křivky užitečnosti"," (indiferenční křivky),",[92,92588,92589],{},"vyjmenovat jejich základní vlastnosti,",[92,92591,79314,92592,92595],{},[95,92593,92594],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[92,92597,92598,92599,92602],{},"řešit ",[95,92600,92601],{},"optimalizační úlohy"," s ohledem na užitečnost.",[84,92604,92606],{"id":92605},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[55,92608,92609,92610,92614,92615,92618],{},"Spotřebitel typicky přijímá tři typy rozhodnutí: (i) kolik kterého zboží či služby nakoupit, (ii) kolik času věnovat práci vs. odpočinku, (iii) zda spotřebovat více než důchod (půjčky) nebo méně (spoření). Teorie se soustředí na typ (i), který bezprostředně určuje ",[69,92611,92613],{"className":92612,"dataFsResolvedFilePath":13670,"href":13671},[62],"poptávku",". Centrálním pojmem je ",[95,92616,92617],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[609,92620,92622],{"id":92621},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[55,92624,92625],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[89,92627,92628,92634],{},[92,92629,92630,92633],{},[95,92631,92632],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[92,92635,92636,92639,92640,92642],{},[95,92637,92638],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[95,92641,92373],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1023,92644,92645],{},[55,92646,92647,92649,92650,92653,92654,1445,92667,92670,92671,75,92684,92703,92704,835,92730,92757,92758,92761,92762,92765],{},[1647,92648,4499],{}," Pozor — ordinalisté užitečnost ",[95,92651,92652],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[1647,92655,92657],{"className":92656},[2059],[2061,92658,92659],{"xmlns":2063},[2065,92660,92661,92665],{},[2068,92662,92663],{},[2071,92664,10871],{},[2092,92666,10871],{"encoding":2094},[95,92668,92669],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[1647,92672,92674],{"className":92673},[2059],[2061,92675,92676],{"xmlns":2063},[2065,92677,92678,92682],{},[2068,92679,92680],{},[2071,92681,10871],{},[2092,92683,10871],{"encoding":2094},[1647,92685,92687],{"className":92686},[2059],[2061,92688,92689],{"xmlns":2063},[2065,92690,92691,92700],{},[2068,92692,92693],{},[8473,92694,92695,92697],{"accent":2360},[2071,92696,10871],{},[2075,92698,92699],{},"~",[2092,92701,92702],{"encoding":2094},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[1647,92705,92707],{"className":92706},[2059],[2061,92708,92709],{"xmlns":2063},[2065,92710,92711,92727],{},[2068,92712,92713,92719,92721],{},[8473,92714,92715,92717],{"accent":2360},[2071,92716,10871],{},[2075,92718,92699],{},[2075,92720,2077],{},[2205,92722,92723,92725],{},[2071,92724,10871],{},[2210,92726,646],{},[2092,92728,92729],{"encoding":2094},"\\tilde U = U^2",[1647,92731,92733],{"className":92732},[2059],[2061,92734,92735],{"xmlns":2063},[2065,92736,92737,92754],{},[2068,92738,92739,92745,92747,92750,92752],{},[8473,92740,92741,92743],{"accent":2360},[2071,92742,10871],{},[2075,92744,92699],{},[2075,92746,2077],{},[2071,92748,92749],{},"ln",[2075,92751,60670],{},[2071,92753,10871],{},[2092,92755,92756],{"encoding":2094},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[95,92759,92760],{},"porovnání"," mezi svazky a ",[95,92763,92764],{},"poměry"," mezních veličin.",[55,92767,92768,92769,2777],{},"Ordinalistický přístup vychází z ",[95,92770,92771],{},"pěti hlavních předpokladů",[201,92773,92774,92780,92786,92904,92910],{},[92,92775,92776,92779],{},[95,92777,92778],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[92,92781,92782,92785],{},[95,92783,92784],{},"Ordinalita."," Spotřebitel dokáže uspořádat skupiny zboží podle míry uspokojení — rozhodne, který svazek je lepší, nebo zda jsou oba stejně dobré. Není však nutné, aby míru uspokojení vyjadřoval číselně.",[92,92787,92788,92791,92792,66211,92805,92818,92819,66211,92832,2999,92845,92848,92849,75,92868,67040,92886,195],{},[95,92789,92790],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[1647,92793,92795],{"className":92794},[2059],[2061,92796,92797],{"xmlns":2063},[2065,92798,92799,92803],{},[2068,92800,92801],{},[2071,92802,4342],{},[2092,92804,4342],{"encoding":2094},[1647,92806,92808],{"className":92807},[2059],[2061,92809,92810],{"xmlns":2063},[2065,92811,92812,92816],{},[2068,92813,92814],{},[2071,92815,25992],{},[2092,92817,25992],{"encoding":2094},", nebude jindy preferovat ",[1647,92820,92822],{"className":92821},[2059],[2061,92823,92824],{"xmlns":2063},[2065,92825,92826,92830],{},[2068,92827,92828],{},[2071,92829,25992],{},[2092,92831,25992],{"encoding":2094},[1647,92833,92835],{"className":92834},[2059],[2061,92836,92837],{"xmlns":2063},[2065,92838,92839,92843],{},[2068,92840,92841],{},[2071,92842,4342],{},[2092,92844,4342],{"encoding":2094},[95,92846,92847],{},"Tranzitivita",": pokud ",[1647,92850,92852],{"className":92851},[2059],[2061,92853,92854],{"xmlns":2063},[2065,92855,92856,92865],{},[2068,92857,92858,92860,92863],{},[2071,92859,4342],{},[2075,92861,92862],{},"≻",[2071,92864,25992],{},[2092,92866,92867],{"encoding":2094},"A \\succ B",[1647,92869,92871],{"className":92870},[2059],[2061,92872,92873],{"xmlns":2063},[2065,92874,92875,92883],{},[2068,92876,92877,92879,92881],{},[2071,92878,25992],{},[2075,92880,92862],{},[2071,92882,2849],{},[2092,92884,92885],{"encoding":2094},"B \\succ C",[1647,92887,92889],{"className":92888},[2059],[2061,92890,92891],{"xmlns":2063},[2065,92892,92893,92901],{},[2068,92894,92895,92897,92899],{},[2071,92896,4342],{},[2075,92898,92862],{},[2071,92900,2849],{},[2092,92902,92903],{"encoding":2094},"A \\succ C",[92,92905,92906,92909],{},[95,92907,92908],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[92,92911,92912,92915],{},[95,92913,92914],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[55,92917,92918,92919,92922,92923,195],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[3982,92920,92921],{},"preference"," a na příbuzné ",[3982,92924,92925],{},"funkci užitečnosti",[84,92927,92929],{"id":92928},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[55,92931,92932,92933,92946,92947,92950,92951,92964],{},"Uvažujme ",[1647,92934,92936],{"className":92935},[2059],[2061,92937,92938],{"xmlns":2063},[2065,92939,92940,92944],{},[2068,92941,92942],{},[2071,92943,41153],{},[2092,92945,41153],{"encoding":2094}," různých zboží. ",[95,92948,92949],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[1647,92952,92954],{"className":92953},[2059],[2061,92955,92956],{"xmlns":2063},[2065,92957,92958,92962],{},[2068,92959,92960],{},[2071,92961,41153],{},[2092,92963,41153],{"encoding":2094},"-tice",[55,92966,92967],{},[1647,92968,92970],{"className":92969},[2059],[2061,92971,92972],{"xmlns":2063},[2065,92973,92974,93000],{},[2068,92975,92976,92978,92984,92986,92988,92990,92996,92998],{},[2075,92977,2084],{"stretchy":2083},[2348,92979,92980,92982],{},[2071,92981,2861],{},[2210,92983,638],{},[2075,92985,2361],{"separator":2360},[2075,92987,10773],{},[2075,92989,2361],{"separator":2360},[2348,92991,92992,92994],{},[2071,92993,2861],{},[2071,92995,41153],{},[2075,92997,2090],{"stretchy":2083},[2075,92999,2361],{"separator":2360},[2092,93001,93002],{"encoding":2094},"(Q_1, \\dots, Q_n),",[55,93004,4397,93005,93022,93023,93036,93037,93040,93041,93044,93045,93048,93049,2777],{},[1647,93006,93008],{"className":93007},[2059],[2061,93009,93010],{"xmlns":2063},[2065,93011,93012,93020],{},[2068,93013,93014],{},[2348,93015,93016,93018],{},[2071,93017,2861],{},[2071,93019,20528],{},[2092,93021,51834],{"encoding":2094}," značí množství ",[1647,93024,93026],{"className":93025},[2059],[2061,93027,93028],{"xmlns":2063},[2065,93029,93030,93034],{},[2068,93031,93032],{},[2071,93033,20528],{},[2092,93035,20528],{"encoding":2094},"-tého zboží. Spotřebitel je schopen svazky ",[95,93038,93039],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[95,93042,93043],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[95,93046,93047],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[95,93050,92925],{},[1647,93052,93054],{"className":93053},[2059],[2061,93055,93056],{"xmlns":2063,"display":31093},[2065,93057,93058,93105],{},[23493,93059,93060],{"width":31098},[23498,93061,93062,93064,93098,93100],{},[23501,93063],{"width":31103},[23501,93065,93066],{},[2068,93067,93068,93070,93072,93074,93076,93082,93084,93086,93088,93094,93096],{},[2071,93069,10871],{},[2075,93071,2077],{},[2071,93073,10871],{},[2075,93075,2084],{"stretchy":2083},[2348,93077,93078,93080],{},[2071,93079,2861],{},[2210,93081,638],{},[2075,93083,2361],{"separator":2360},[2075,93085,10773],{},[2075,93087,2361],{"separator":2360},[2348,93089,93090,93092],{},[2071,93091,2861],{},[2071,93093,41153],{},[2075,93095,2090],{"stretchy":2083},[2075,93097,2361],{"separator":2360},[23501,93099],{"width":31103},[23501,93101,93102],{},[2363,93103,93104],{},"(6.1)",[2092,93106,93107],{"encoding":2094},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[55,93109,4397,93110,93140,93141,93163,93164,93167],{},[1647,93111,93113],{"className":93112},[2059],[2061,93114,93115],{"xmlns":2063},[2065,93116,93117,93137],{},[2068,93118,93119,93125,93127,93129,93131],{},[2348,93120,93121,93123],{},[2071,93122,2861],{},[2210,93124,638],{},[2075,93126,2361],{"separator":2360},[2075,93128,10773],{},[2075,93130,2361],{"separator":2360},[2348,93132,93133,93135],{},[2071,93134,2861],{},[2071,93136,41153],{},[2092,93138,93139],{"encoding":2094},"Q_1, \\dots, Q_n"," jsou množství jednotlivých zboží. Funkce užitečnosti (utility function) „umisťuje\" svazky na určitá místa v posloupnosti preference — sama žádnou konkrétní hodnotu uspokojení neměří. Dvě funkce ",[1647,93142,93144],{"className":93143},[2059],[2061,93145,93146],{"xmlns":2063},[2065,93147,93148,93160],{},[2068,93149,93150,93152,93154],{},[2071,93151,10871],{},[2075,93153,2361],{"separator":2360},[8473,93155,93156,93158],{"accent":2360},[2071,93157,10871],{},[2075,93159,92699],{},[2092,93161,93162],{"encoding":2094},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[95,93165,93166],{},"monotónní transformace"," zachovávající pořadí.",[55,93169,93170,93171,7102,93174,195],{},"Dále se omezíme na funkce pro ",[95,93172,93173],{},"dvě zboží",[1647,93175,93177],{"className":93176},[2059],[2061,93178,93179],{"xmlns":2063},[2065,93180,93181,93207],{},[2068,93182,93183,93185,93187,93189,93191,93197,93199,93205],{},[2071,93184,10871],{},[2075,93186,2077],{},[2071,93188,10871],{},[2075,93190,2084],{"stretchy":2083},[2348,93192,93193,93195],{},[2071,93194,2861],{},[2210,93196,638],{},[2075,93198,2361],{"separator":2360},[2348,93200,93201,93203],{},[2071,93202,2861],{},[2210,93204,646],{},[2075,93206,2090],{"stretchy":2083},[2092,93208,93209],{"encoding":2094},"U = U(Q_1, Q_2)",[1023,93211,93212,93287],{},[55,93213,93214,93216,93217,2777],{},[1647,93215,56993],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[1647,93218,93220],{"className":93219},[2059],[2061,93221,93222],{"xmlns":2063},[2065,93223,93224,93284],{},[2068,93225,93226,93228,93230,93232,93234,93240,93242,93248,93250,93256,93258,93260,93262],{},[2071,93227,10871],{},[2075,93229,2077],{},[2071,93231,10871],{},[2075,93233,2084],{"stretchy":2083},[2348,93235,93236,93238],{},[2071,93237,2861],{},[2210,93239,638],{},[2075,93241,2361],{"separator":2360},[2348,93243,93244,93246],{},[2071,93245,2861],{},[2210,93247,646],{},[2075,93249,2361],{"separator":2360},[2348,93251,93252,93254],{},[2071,93253,2861],{},[2210,93255,654],{},[2075,93257,2090],{"stretchy":2083},[2075,93259,2077],{},[2210,93261,646],{},[8204,93263,93264],{},[2068,93265,93266,93272,93278],{},[2348,93267,93268,93270],{},[2071,93269,2861],{},[2210,93271,638],{},[2348,93273,93274,93276],{},[2071,93275,2861],{},[2210,93277,646],{},[2348,93279,93280,93282],{},[2071,93281,2861],{},[2210,93283,654],{},[2092,93285,93286],{"encoding":2094},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[89,93288,93289,93482],{},[92,93290,93291,93292,93318,93319,14673,93345,75,93404,5676,93464,8512],{},"svazek ",[1647,93293,93295],{"className":93294},[2059],[2061,93296,93297],{"xmlns":2063},[2065,93298,93299,93315],{},[2068,93300,93301,93303,93305,93307,93309,93311,93313],{},[2075,93302,2084],{"stretchy":2083},[2210,93304,46153],{},[2075,93306,2361],{"separator":2360},[2210,93308,662],{},[2075,93310,2361],{"separator":2360},[2210,93312,46131],{},[2075,93314,2090],{"stretchy":2083},[2092,93316,93317],{"encoding":2094},"(16, 4, 64)"," je preferován před ",[1647,93320,93322],{"className":93321},[2059],[2061,93323,93324],{"xmlns":2063},[2065,93325,93326,93342],{},[2068,93327,93328,93330,93332,93334,93336,93338,93340],{},[2075,93329,2084],{"stretchy":2083},[2210,93331,4087],{},[2075,93333,2361],{"separator":2360},[2210,93335,4087],{},[2075,93337,2361],{"separator":2360},[2210,93339,71067],{},[2075,93341,2090],{"stretchy":2083},[2092,93343,93344],{"encoding":2094},"(9, 9, 27)",[1647,93346,93348],{"className":93347},[2059],[2061,93349,93350],{"xmlns":2063},[2065,93351,93352,93401],{},[2068,93353,93354,93356,93358,93360,93362,93364,93366,93368,93370,93372,93374,93388,93390,93392,93397,93399],{},[2071,93355,10871],{},[2075,93357,2084],{"stretchy":2083},[2210,93359,46153],{},[2075,93361,2361],{"separator":2360},[2210,93363,662],{},[2075,93365,2361],{"separator":2360},[2210,93367,46131],{},[2075,93369,2090],{"stretchy":2083},[2075,93371,2077],{},[2210,93373,646],{},[8204,93375,93376],{},[2068,93377,93378,93380,93382,93384,93386],{},[2210,93379,46153],{},[2075,93381,3251],{},[2210,93383,662],{},[2075,93385,3251],{},[2210,93387,46131],{},[2075,93389,2077],{},[2210,93391,646],{},[8204,93393,93394],{},[2210,93395,93396],{},"4096",[2075,93398,2077],{},[2210,93400,5704],{},[2092,93402,93403],{"encoding":2094},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[1647,93405,93407],{"className":93406},[2059],[2061,93408,93409],{"xmlns":2063},[2065,93410,93411,93461],{},[2068,93412,93413,93415,93417,93419,93421,93423,93425,93427,93429,93431,93433,93447,93449,93451,93456,93458],{},[2071,93414,10871],{},[2075,93416,2084],{"stretchy":2083},[2210,93418,4087],{},[2075,93420,2361],{"separator":2360},[2210,93422,4087],{},[2075,93424,2361],{"separator":2360},[2210,93426,71067],{},[2075,93428,2090],{"stretchy":2083},[2075,93430,2077],{},[2210,93432,646],{},[8204,93434,93435],{},[2068,93436,93437,93439,93441,93443,93445],{},[2210,93438,4087],{},[2075,93440,3251],{},[2210,93442,4087],{},[2075,93444,3251],{},[2210,93446,71067],{},[2075,93448,2077],{},[2210,93450,646],{},[8204,93452,93453],{},[2210,93454,93455],{},"2187",[2075,93457,5987],{},[2210,93459,93460],{},"93,53",[2092,93462,93463],{"encoding":2094},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[1647,93465,93467],{"className":93466},[2059],[2061,93468,93469],{"xmlns":2063},[2065,93470,93471,93479],{},[2068,93472,93473,93475,93477],{},[2210,93474,5704],{},[2075,93476,3482],{},[2210,93478,93460],{},[2092,93480,93481],{"encoding":2094},"128 > 93{,}53",[92,93483,93484,93485,75,93511,93537,93538,75,93578,93619,93620,93666,93667,75,93693,2917,93719,75,93737,93755,93756,195],{},"svazky ",[1647,93486,93488],{"className":93487},[2059],[2061,93489,93490],{"xmlns":2063},[2065,93491,93492,93508],{},[2068,93493,93494,93496,93498,93500,93502,93504,93506],{},[2075,93495,2084],{"stretchy":2083},[2210,93497,662],{},[2075,93499,2361],{"separator":2360},[2210,93501,5672],{},[2075,93503,2361],{"separator":2360},[2210,93505,646],{},[2075,93507,2090],{"stretchy":2083},[2092,93509,93510],{"encoding":2094},"(4, 8, 2)",[1647,93512,93514],{"className":93513},[2059],[2061,93515,93516],{"xmlns":2063},[2065,93517,93518,93534],{},[2068,93519,93520,93522,93524,93526,93528,93530,93532],{},[2075,93521,2084],{"stretchy":2083},[2210,93523,46131],{},[2075,93525,2361],{"separator":2360},[2210,93527,638],{},[2075,93529,2361],{"separator":2360},[2210,93531,662],{},[2075,93533,2090],{"stretchy":2083},[2092,93535,93536],{"encoding":2094},"(64, 1, 4)"," jsou indiferentní, protože ",[1647,93539,93541],{"className":93540},[2059],[2061,93542,93543],{"xmlns":2063},[2065,93544,93545,93575],{},[2068,93546,93547,93549,93551,93553,93555,93557,93559,93561,93563,93565,93567,93571,93573],{},[2071,93548,10871],{},[2075,93550,2084],{"stretchy":2083},[2210,93552,662],{},[2075,93554,2361],{"separator":2360},[2210,93556,5672],{},[2075,93558,2361],{"separator":2360},[2210,93560,646],{},[2075,93562,2090],{"stretchy":2083},[2075,93564,2077],{},[2210,93566,646],{},[8204,93568,93569],{},[2210,93570,46131],{},[2075,93572,2077],{},[2210,93574,46153],{},[2092,93576,93577],{"encoding":2094},"U(4,8,2) = 2\\sqrt{64} = 16",[1647,93579,93581],{"className":93580},[2059],[2061,93582,93583],{"xmlns":2063},[2065,93584,93585,93616],{},[2068,93586,93587,93589,93591,93593,93595,93597,93599,93601,93603,93605,93607,93612,93614],{},[2071,93588,10871],{},[2075,93590,2084],{"stretchy":2083},[2210,93592,46131],{},[2075,93594,2361],{"separator":2360},[2210,93596,638],{},[2075,93598,2361],{"separator":2360},[2210,93600,662],{},[2075,93602,2090],{"stretchy":2083},[2075,93604,2077],{},[2210,93606,646],{},[8204,93608,93609],{},[2210,93610,93611],{},"256",[2075,93613,2077],{},[2210,93615,76829],{},[2092,93617,93618],{"encoding":2094},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[1647,93621,93623],{"className":93622},[2059],[2061,93624,93625],{"xmlns":2063},[2065,93626,93627,93663],{},[2068,93628,93629,93631,93633,93635,93637,93639,93641,93643,93645,93647,93649,93651,93653,93655,93657,93659,93661],{},[2071,93630,10871],{},[2075,93632,2084],{"stretchy":2083},[2210,93634,662],{},[2075,93636,2361],{"separator":2360},[2210,93638,5672],{},[2075,93640,2361],{"separator":2360},[2210,93642,646],{},[2075,93644,2090],{"stretchy":2083},[2075,93646,2077],{},[2071,93648,10871],{},[2075,93650,2084],{"stretchy":2083},[2210,93652,46131],{},[2075,93654,2361],{"separator":2360},[2210,93656,638],{},[2075,93658,2361],{"separator":2360},[2210,93660,662],{},[2075,93662,2090],{"stretchy":2083},[2092,93664,93665],{"encoding":2094},"U(4,8,2) = U(64,1,4)","; ověření: ",[1647,93668,93670],{"className":93669},[2059],[2061,93671,93672],{"xmlns":2063},[2065,93673,93674,93690],{},[2068,93675,93676,93678,93680,93682,93684,93686,93688],{},[2210,93677,662],{},[2075,93679,3251],{},[2210,93681,5672],{},[2075,93683,3251],{},[2210,93685,646],{},[2075,93687,2077],{},[2210,93689,46131],{},[2092,93691,93692],{"encoding":2094},"4 \\cdot 8 \\cdot 2 = 64",[1647,93694,93696],{"className":93695},[2059],[2061,93697,93698],{"xmlns":2063},[2065,93699,93700,93716],{},[2068,93701,93702,93704,93706,93708,93710,93712,93714],{},[2210,93703,46131],{},[2075,93705,3251],{},[2210,93707,638],{},[2075,93709,3251],{},[2210,93711,662],{},[2075,93713,2077],{},[2210,93715,93611],{},[2092,93717,93718],{"encoding":2094},"64 \\cdot 1 \\cdot 4 = 256",[1647,93720,93722],{"className":93721},[2059],[2061,93723,93724],{"xmlns":2063},[2065,93725,93726,93734],{},[2068,93727,93728,93730,93732],{},[2071,93729,10871],{},[2075,93731,2077],{},[2210,93733,46153],{},[2092,93735,93736],{"encoding":2094},"U = 16",[1647,93738,93740],{"className":93739},[2059],[2061,93741,93742],{"xmlns":2063},[2065,93743,93744,93752],{},[2068,93745,93746,93748,93750],{},[2071,93747,10871],{},[2075,93749,2077],{},[2210,93751,76829],{},[2092,93753,93754],{"encoding":2094},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[1647,93757,93759],{"className":93758},[2059],[2061,93760,93761],{"xmlns":2063},[2065,93762,93763,93783],{},[2068,93764,93765,93771,93777],{},[2348,93766,93767,93769],{},[2071,93768,2861],{},[2210,93770,638],{},[2348,93772,93773,93775],{},[2071,93774,2861],{},[2210,93776,646],{},[2348,93778,93779,93781],{},[2071,93780,2861],{},[2210,93782,654],{},[2092,93784,93785],{"encoding":2094},"Q_1 Q_2 Q_3",[84,93787,93789],{"id":93788},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[55,93791,93792,93793,8189,93828,1445,93831,46105,93848,11156,93865,93868,93869,93872],{},"Pro funkci užitečnosti ",[1647,93794,93796],{"className":93795},[2059],[2061,93797,93798],{"xmlns":2063},[2065,93799,93800,93826],{},[2068,93801,93802,93804,93806,93808,93810,93816,93818,93824],{},[2071,93803,10871],{},[2075,93805,2077],{},[2071,93807,10871],{},[2075,93809,2084],{"stretchy":2083},[2348,93811,93812,93814],{},[2071,93813,2861],{},[2210,93815,638],{},[2075,93817,2361],{"separator":2360},[2348,93819,93820,93822],{},[2071,93821,2861],{},[2210,93823,646],{},[2075,93825,2090],{"stretchy":2083},[2092,93827,93209],{"encoding":2094},[95,93829,93830],{},"mezní užitečnost",[1647,93832,93834],{"className":93833},[2059],[2061,93835,93836],{"xmlns":2063},[2065,93837,93838,93846],{},[2068,93839,93840],{},[2348,93841,93842,93844],{},[2071,93843,2861],{},[2210,93845,638],{},[2092,93847,32029],{"encoding":2094},[1647,93849,93851],{"className":93850},[2059],[2061,93852,93853],{"xmlns":2063},[2065,93854,93855,93863],{},[2068,93856,93857],{},[2348,93858,93859,93861],{},[2071,93860,2861],{},[2210,93862,646],{},[2092,93864,32048],{"encoding":2094},[95,93866,93867],{},"marginal utility",") parciální ",[69,93870,2430],{"className":93871,"dataFsResolvedFilePath":4005,"href":4006},[62]," užitečnosti podle příslušné proměnné:",[1647,93874,93876],{"className":93875},[2059],[2061,93877,93878],{"xmlns":2063,"display":31093},[2065,93879,93880,93979],{},[23493,93881,93882],{"width":31098},[23498,93883,93884,93886,93972,93974],{},[23501,93885],{"width":31103},[23501,93887,93888],{},[2068,93889,93890,93892,93898,93900,93908,93910,93928,93930,93932,93934,93940,93942,93950,93952,93970],{},[2071,93891,2890],{},[2348,93893,93894,93896],{},[2071,93895,10871],{},[2210,93897,638],{},[2075,93899,2077],{},[9252,93901,93902,93904,93906],{},[2071,93903,10871],{},[2210,93905,638],{},[2075,93907,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,93909,2077],{},[2403,93911,93912,93918],{},[2068,93913,93914,93916],{},[2071,93915,11003],{"mathvariant":2450},[2071,93917,10871],{},[2068,93919,93920,93922],{},[2071,93921,11003],{"mathvariant":2450},[2348,93923,93924,93926],{},[2071,93925,2861],{},[2210,93927,638],{},[2075,93929,2361],{"separator":2360},[5965,93931],{"width":17019},[2071,93933,2890],{},[2348,93935,93936,93938],{},[2071,93937,10871],{},[2210,93939,646],{},[2075,93941,2077],{},[9252,93943,93944,93946,93948],{},[2071,93945,10871],{},[2210,93947,646],{},[2075,93949,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,93951,2077],{},[2403,93953,93954,93960],{},[2068,93955,93956,93958],{},[2071,93957,11003],{"mathvariant":2450},[2071,93959,10871],{},[2068,93961,93962,93964],{},[2071,93963,11003],{"mathvariant":2450},[2348,93965,93966,93968],{},[2071,93967,2861],{},[2210,93969,646],{},[2071,93971,195],{"mathvariant":2450},[23501,93973],{"width":31103},[23501,93975,93976],{},[2363,93977,93978],{},"(6.2)",[2092,93980,93981],{"encoding":2094},"MU_1 = U'_1 = \\frac{\\partial U}{\\partial Q_1}, \\quad MU_2 = U'_2 = \\frac{\\partial U}{\\partial Q_2}. \\tag{6.2}",[55,93983,93984,93985,94019,94020,94050,94051,1445,94054,195],{},"Pro pevné ",[1647,93986,93988],{"className":93987},[2059],[2061,93989,93990],{"xmlns":2063},[2065,93991,93992,94016],{},[2068,93993,93994,94000,94002,94004,94006,94012,94014],{},[2348,93995,93996,93998],{},[2071,93997,2861],{},[2210,93999,638],{},[2075,94001,2077],{},[2071,94003,69],{},[2075,94005,2361],{"separator":2360},[2348,94007,94008,94010],{},[2071,94009,2861],{},[2210,94011,646],{},[2075,94013,2077],{},[2071,94015,2179],{},[2092,94017,94018],{"encoding":2094},"Q_1 = a, Q_2 = b"," se hodnota ",[1647,94021,94023],{"className":94022},[2059],[2061,94024,94025],{"xmlns":2063},[2065,94026,94027,94047],{},[2068,94028,94029,94031,94037,94039,94041,94043,94045],{},[2071,94030,2890],{},[2348,94032,94033,94035],{},[2071,94034,10871],{},[2210,94036,638],{},[2075,94038,2084],{"stretchy":2083},[2071,94040,69],{},[2075,94042,2361],{"separator":2360},[2071,94044,2179],{},[2075,94046,2090],{"stretchy":2083},[2092,94048,94049],{"encoding":2094},"MU_1(a, b)"," nazývá mezní užitečnost ",[95,94052,94053],{},"v bodě (na hladině)",[1647,94055,94057],{"className":94056},[2059],[2061,94058,94059],{"xmlns":2063},[2065,94060,94061,94073],{},[2068,94062,94063,94065,94067,94069,94071],{},[2075,94064,2561],{"stretchy":2083},[2071,94066,69],{},[2075,94068,2361],{"separator":2360},[2071,94070,2179],{},[2075,94072,2576],{"stretchy":2083},[2092,94074,11954],{"encoding":2094},[1023,94076,94077],{},[55,94078,94079,94081,94082,94112,94141,94142,2683,94155,2697,94172,94193,94194,2744,94211,2758,94224,94241,94242,94264,94265,94294,94295,6560,94315,94332],{},[1647,94080,4243],{}," Intuice — co říká ",[1647,94083,94085],{"className":94084},[2059],[2061,94086,94087],{"xmlns":2063},[2065,94088,94089,94109],{},[2068,94090,94091,94093,94099,94101,94103,94105,94107],{},[2071,94092,2890],{},[2348,94094,94095,94097],{},[2071,94096,10871],{},[2210,94098,638],{},[2075,94100,2084],{"stretchy":2083},[2071,94102,69],{},[2075,94104,2361],{"separator":2360},[2071,94106,2179],{},[2075,94108,2090],{"stretchy":2083},[2092,94110,94111],{"encoding":2094},"MU_1(a,b)",[1647,94113,94115],{"className":94114},[2059],[2061,94116,94117],{"xmlns":2063},[2065,94118,94119,94139],{},[2068,94120,94121,94123,94129,94131,94133,94135,94137],{},[2071,94122,2890],{},[2348,94124,94125,94127],{},[2071,94126,10871],{},[2210,94128,638],{},[2075,94130,2084],{"stretchy":2083},[2071,94132,69],{},[2075,94134,2361],{"separator":2360},[2071,94136,2179],{},[2075,94138,2090],{"stretchy":2083},[2092,94140,94049],{"encoding":2094}," je rychlost změny ",[1647,94143,94145],{"className":94144},[2059],[2061,94146,94147],{"xmlns":2063},[2065,94148,94149,94153],{},[2068,94150,94151],{},[2071,94152,10871],{},[2092,94154,10871],{"encoding":2094},[1647,94156,94158],{"className":94157},[2059],[2061,94159,94160],{"xmlns":2063},[2065,94161,94162,94170],{},[2068,94163,94164],{},[2348,94165,94166,94168],{},[2071,94167,2861],{},[2210,94169,638],{},[2092,94171,32029],{"encoding":2094},[1647,94173,94175],{"className":94174},[2059],[2061,94176,94177],{"xmlns":2063},[2065,94178,94179,94191],{},[2068,94180,94181,94183,94185,94187,94189],{},[2075,94182,2561],{"stretchy":2083},[2071,94184,69],{},[2075,94186,2361],{"separator":2360},[2071,94188,2179],{},[2075,94190,2576],{"stretchy":2083},[2092,94192,11954],{"encoding":2094},". Přibližně: změní-li se ",[1647,94195,94197],{"className":94196},[2059],[2061,94198,94199],{"xmlns":2063},[2065,94200,94201,94209],{},[2068,94202,94203],{},[2348,94204,94205,94207],{},[2071,94206,2861],{},[2210,94208,638],{},[2092,94210,32029],{"encoding":2094},[1647,94212,94214],{"className":94213},[2059],[2061,94215,94216],{"xmlns":2063},[2065,94217,94218,94222],{},[2068,94219,94220],{},[2071,94221,69],{},[2092,94223,69],{"encoding":2094},[1647,94225,94227],{"className":94226},[2059],[2061,94228,94229],{"xmlns":2063},[2065,94230,94231,94239],{},[2068,94232,94233,94235,94237],{},[2071,94234,69],{},[2075,94236,2176],{},[2210,94238,638],{},[2092,94240,2776],{"encoding":2094}," při pevném ",[1647,94243,94245],{"className":94244},[2059],[2061,94246,94247],{"xmlns":2063},[2065,94248,94249,94261],{},[2068,94250,94251,94257,94259],{},[2348,94252,94253,94255],{},[2071,94254,2861],{},[2210,94256,646],{},[2075,94258,2077],{},[2071,94260,2179],{},[2092,94262,94263],{"encoding":2094},"Q_2 = b",", změní se užitečnost zhruba o ",[1647,94266,94268],{"className":94267},[2059],[2061,94269,94270],{"xmlns":2063},[2065,94271,94272,94292],{},[2068,94273,94274,94276,94282,94284,94286,94288,94290],{},[2071,94275,2890],{},[2348,94277,94278,94280],{},[2071,94279,10871],{},[2210,94281,638],{},[2075,94283,2084],{"stretchy":2083},[2071,94285,69],{},[2075,94287,2361],{"separator":2360},[2071,94289,2179],{},[2075,94291,2090],{"stretchy":2083},[2092,94293,94049],{"encoding":2094},". Stejně tak ",[1647,94296,94298],{"className":94297},[2059],[2061,94299,94300],{"xmlns":2063},[2065,94301,94302,94312],{},[2068,94303,94304,94306],{},[2071,94305,2890],{},[2348,94307,94308,94310],{},[2071,94309,10871],{},[2210,94311,646],{},[2092,94313,94314],{"encoding":2094},"MU_2",[1647,94316,94318],{"className":94317},[2059],[2061,94319,94320],{"xmlns":2063},[2065,94321,94322,94330],{},[2068,94323,94324],{},[2348,94325,94326,94328],{},[2071,94327,2861],{},[2210,94329,646],{},[2092,94331,32048],{"encoding":2094},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[609,94334,84680],{"id":94335},"totální-diferenciál",[55,94337,94338,94339,52636,94355,94385,94386,2777],{},"Přibližnou změnu užitečnosti ",[1647,94340,94342],{"className":94341},[2059],[2061,94343,94344],{"xmlns":2063},[2065,94345,94346,94352],{},[2068,94347,94348,94350],{},[2071,94349,2961],{"mathvariant":2450},[2071,94351,10871],{},[2092,94353,94354],{"encoding":2094},"\\Delta U",[1647,94356,94358],{"className":94357},[2059],[2061,94359,94360],{"xmlns":2063},[2065,94361,94362,94382],{},[2068,94363,94364,94366,94372,94374,94376],{},[2071,94365,2273],{"mathvariant":2450},[2348,94367,94368,94370],{},[2071,94369,2861],{},[2210,94371,638],{},[2075,94373,2361],{"separator":2360},[2071,94375,2273],{"mathvariant":2450},[2348,94377,94378,94380],{},[2071,94379,2861],{},[2210,94381,646],{},[2092,94383,94384],{"encoding":2094},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[95,94387,94388],{},"totálního diferenciálu",[1647,94390,94392],{"className":94391},[2059],[2061,94393,94394],{"xmlns":2063,"display":31093},[2065,94395,94396,94497],{},[23493,94397,94398],{"width":31098},[23498,94399,94400,94402,94490,94492],{},[23501,94401],{"width":31103},[23501,94403,94404],{},[2068,94405,94406,94408,94410,94412,94414,94416,94418,94426,94428,94434,94436,94444,94446,94452,94454,94456,94462,94464,94470,94472,94474,94480,94482,94488],{},[2071,94407,2961],{"mathvariant":2450},[2071,94409,10871],{},[2075,94411,2803],{},[2071,94413,2273],{"mathvariant":2450},[2071,94415,10871],{},[2075,94417,2077],{},[9252,94419,94420,94422,94424],{},[2071,94421,10871],{},[2210,94423,638],{},[2075,94425,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2071,94427,2273],{"mathvariant":2450},[2348,94429,94430,94432],{},[2071,94431,2861],{},[2210,94433,638],{},[2075,94435,2176],{},[9252,94437,94438,94440,94442],{},[2071,94439,10871],{},[2210,94441,646],{},[2075,94443,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2071,94445,2273],{"mathvariant":2450},[2348,94447,94448,94450],{},[2071,94449,2861],{},[2210,94451,646],{},[2075,94453,2077],{},[2071,94455,2890],{},[2348,94457,94458,94460],{},[2071,94459,10871],{},[2210,94461,638],{},[2071,94463,2273],{"mathvariant":2450},[2348,94465,94466,94468],{},[2071,94467,2861],{},[2210,94469,638],{},[2075,94471,2176],{},[2071,94473,2890],{},[2348,94475,94476,94478],{},[2071,94477,10871],{},[2210,94479,646],{},[2071,94481,2273],{"mathvariant":2450},[2348,94483,94484,94486],{},[2071,94485,2861],{},[2210,94487,646],{},[2071,94489,195],{"mathvariant":2450},[23501,94491],{"width":31103},[23501,94493,94494],{},[2363,94495,94496],{},"(6.3)",[2092,94498,94499],{"encoding":2094},"\\Delta U \\approx \\mathrm{d} U = U'_1 \\mathrm{d} Q_1 + U'_2 \\mathrm{d} Q_2 = MU_1 \\mathrm{d} Q_1 + MU_2 \\mathrm{d} Q_2. \\tag{6.3}",[55,94501,79940,94502,195],{},[1647,94503,94505],{"className":94504},[2059],[2061,94506,94507],{"xmlns":2063},[2065,94508,94509,94579],{},[2068,94510,94511,94513,94515,94517,94519,94521,94527,94529,94531,94537,94539,94545,94547,94549,94555,94557,94559,94561,94563,94569,94571,94577],{},[2071,94512,2961],{"mathvariant":2450},[2071,94514,10871],{},[2075,94516,2077],{},[2071,94518,10871],{},[2075,94520,2084],{"stretchy":2083},[2348,94522,94523,94525],{},[2071,94524,2861],{},[2210,94526,638],{},[2075,94528,2176],{},[2071,94530,2273],{"mathvariant":2450},[2348,94532,94533,94535],{},[2071,94534,2861],{},[2210,94536,638],{},[2075,94538,2361],{"separator":2360},[2348,94540,94541,94543],{},[2071,94542,2861],{},[2210,94544,646],{},[2075,94546,2176],{},[2071,94548,2273],{"mathvariant":2450},[2348,94550,94551,94553],{},[2071,94552,2861],{},[2210,94554,646],{},[2075,94556,2090],{"stretchy":2083},[2075,94558,2303],{},[2071,94560,10871],{},[2075,94562,2084],{"stretchy":2083},[2348,94564,94565,94567],{},[2071,94566,2861],{},[2210,94568,638],{},[2075,94570,2361],{"separator":2360},[2348,94572,94573,94575],{},[2071,94574,2861],{},[2210,94576,646],{},[2075,94578,2090],{"stretchy":2083},[2092,94580,94581],{"encoding":2094},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[84,94583,94585],{"id":94584},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[55,94587,94588,94589,94592,94593,94596],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[95,94590,94591],{},"rostoucí užitečnost"," (předpoklad 4) a ",[95,94594,94595],{},"klesající mezní užitečnost"," (předpoklad 5).",[55,94598,94599,94602,94603,46105,94629,94655,94656,835,94688,94720,94721,75,94775,94829],{},[95,94600,94601],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[1647,94604,94606],{"className":94605},[2059],[2061,94607,94608],{"xmlns":2063},[2065,94609,94610,94626],{},[2068,94611,94612,94618,94620],{},[2348,94613,94614,94616],{},[2071,94615,2861],{},[2210,94617,646],{},[2075,94619,2077],{},[2348,94621,94622,94624],{},[2071,94623,69],{},[2210,94625,630],{},[2092,94627,94628],{"encoding":2094},"Q_2 = a_0",[1647,94630,94632],{"className":94631},[2059],[2061,94633,94634],{"xmlns":2063},[2065,94635,94636,94652],{},[2068,94637,94638,94644,94646],{},[2348,94639,94640,94642],{},[2071,94641,2861],{},[2210,94643,638],{},[2075,94645,2077],{},[2348,94647,94648,94650],{},[2071,94649,2179],{},[2210,94651,630],{},[2092,94653,94654],{"encoding":2094},"Q_1 = b_0"," jsou funkce jedné proměnné ",[1647,94657,94659],{"className":94658},[2059],[2061,94660,94661],{"xmlns":2063},[2065,94662,94663,94685],{},[2068,94664,94665,94667,94669,94675,94677,94683],{},[2071,94666,10871],{},[2075,94668,2084],{"stretchy":2083},[2348,94670,94671,94673],{},[2071,94672,2861],{},[2210,94674,638],{},[2075,94676,2361],{"separator":2360},[2348,94678,94679,94681],{},[2071,94680,69],{},[2210,94682,630],{},[2075,94684,2090],{"stretchy":2083},[2092,94686,94687],{"encoding":2094},"U(Q_1, a_0)",[1647,94689,94691],{"className":94690},[2059],[2061,94692,94693],{"xmlns":2063},[2065,94694,94695,94717],{},[2068,94696,94697,94699,94701,94707,94709,94715],{},[2071,94698,10871],{},[2075,94700,2084],{"stretchy":2083},[2348,94702,94703,94705],{},[2071,94704,2179],{},[2210,94706,630],{},[2075,94708,2361],{"separator":2360},[2348,94710,94711,94713],{},[2071,94712,2861],{},[2210,94714,646],{},[2075,94716,2090],{"stretchy":2083},[2092,94718,94719],{"encoding":2094},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[1647,94722,94724],{"className":94723},[2059],[2061,94725,94726],{"xmlns":2063},[2065,94727,94728,94772],{},[2068,94729,94730,94768,94770],{},[2400,94731,94732],{"scriptlevel":630,"displaystyle":2360},[2403,94733,94734,94758],{},[2068,94735,94736,94738,94740,94742,94748,94750,94756],{},[2071,94737,2273],{"mathvariant":2450},[2071,94739,10871],{},[2075,94741,2084],{"stretchy":2083},[2348,94743,94744,94746],{},[2071,94745,2861],{},[2210,94747,638],{},[2075,94749,2361],{"separator":2360},[2348,94751,94752,94754],{},[2071,94753,69],{},[2210,94755,630],{},[2075,94757,2090],{"stretchy":2083},[2068,94759,94760,94762],{},[2071,94761,2273],{"mathvariant":2450},[2348,94763,94764,94766],{},[2071,94765,2861],{},[2210,94767,638],{},[2075,94769,3482],{},[2210,94771,630],{},[2092,94773,94774],{"encoding":2094},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[1647,94776,94778],{"className":94777},[2059],[2061,94779,94780],{"xmlns":2063},[2065,94781,94782,94826],{},[2068,94783,94784,94822,94824],{},[2400,94785,94786],{"scriptlevel":630,"displaystyle":2360},[2403,94787,94788,94812],{},[2068,94789,94790,94792,94794,94796,94802,94804,94810],{},[2071,94791,2273],{"mathvariant":2450},[2071,94793,10871],{},[2075,94795,2084],{"stretchy":2083},[2348,94797,94798,94800],{},[2071,94799,2179],{},[2210,94801,630],{},[2075,94803,2361],{"separator":2360},[2348,94805,94806,94808],{},[2071,94807,2861],{},[2210,94809,646],{},[2075,94811,2090],{"stretchy":2083},[2068,94813,94814,94816],{},[2071,94815,2273],{"mathvariant":2450},[2348,94817,94818,94820],{},[2071,94819,2861],{},[2210,94821,646],{},[2075,94823,3482],{},[2210,94825,630],{},[2092,94827,94828],{"encoding":2094},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[1647,94831,94833],{"className":94832},[2059],[2061,94834,94835],{"xmlns":2063,"display":31093},[2065,94836,94837,94882],{},[23493,94838,94839],{"width":31098},[23498,94840,94841,94843,94875,94877],{},[23501,94842],{"width":31103},[23501,94844,94845],{},[2068,94846,94847,94855,94857,94859,94861,94863,94871,94873],{},[9252,94848,94849,94851,94853],{},[2071,94850,10871],{},[2210,94852,638],{},[2075,94854,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,94856,3482],{},[2210,94858,630],{},[2075,94860,2361],{"separator":2360},[5965,94862],{"width":17019},[9252,94864,94865,94867,94869],{},[2071,94866,10871],{},[2210,94868,646],{},[2075,94870,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,94872,3482],{},[2210,94874,14195],{},[23501,94876],{"width":31103},[23501,94878,94879],{},[2363,94880,94881],{},"(6.4)",[2092,94883,94884],{"encoding":2094},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[55,94886,94887,94888,94890],{},"Tedy mezní užitečnosti obou zboží jsou ",[95,94889,56975],{}," — užitečnost roste s množstvím každého zboží.",[55,94892,94893,94896,94897,94927,94928,2777],{},[95,94894,94895],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[1647,94898,94900],{"className":94899},[2059],[2061,94901,94902],{"xmlns":2063},[2065,94903,94904,94924],{},[2068,94905,94906,94914,94916],{},[9252,94907,94908,94910,94912],{},[2071,94909,10871],{},[2210,94911,638],{},[2075,94913,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,94915,2361],{"separator":2360},[9252,94917,94918,94920,94922],{},[2071,94919,10871],{},[2210,94921,646],{},[2075,94923,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,94925,94926],{"encoding":2094},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[95,94929,94930],{},"záporné",[1647,94932,94934],{"className":94933},[2059],[2061,94935,94936],{"xmlns":2063,"display":31093},[2065,94937,94938,94991],{},[23493,94939,94940],{"width":31098},[23498,94941,94942,94944,94984,94986],{},[23501,94943],{"width":31103},[23501,94945,94946],{},[2068,94947,94948,94960,94962,94964,94966,94968,94980,94982],{},[9252,94949,94950,94952,94954],{},[2071,94951,10871],{},[2210,94953,2976],{},[2068,94955,94956,94958],{},[2075,94957,2452],{"mathvariant":2450},[2075,94959,2452],{"mathvariant":2450},[2075,94961,3521],{},[2210,94963,630],{},[2075,94965,2361],{"separator":2360},[5965,94967],{"width":17019},[9252,94969,94970,94972,94974],{},[2071,94971,10871],{},[2210,94973,35572],{},[2068,94975,94976,94978],{},[2075,94977,2452],{"mathvariant":2450},[2075,94979,2452],{"mathvariant":2450},[2075,94981,3521],{},[2210,94983,14195],{},[23501,94985],{"width":31103},[23501,94987,94988],{},[2363,94989,94990],{},"(6.5)",[2092,94992,94993],{"encoding":2094},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[55,94995,94996,94997,95000,95001,195],{},"Podmínka (6.5) je známa jako ",[95,94998,94999],{},"zákon klesající mezní užitečnosti (law of diminishing marginal utility)"," — mezní užitečnost každého zboží klesá s růstem jeho množství. Jde o analogii zákona klesajících výnosů z ",[69,95002,95004],{"className":95003,"dataFsResolvedFilePath":10942,"href":10943},[62],"produkční teorie",[55,95006,95007,95008,75,95040,95072,95073,75,95099,95125,95126,95154,95155,75,95157,95159,95160,95195],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[1647,95009,95011],{"className":95010},[2059],[2061,95012,95013],{"xmlns":2063},[2065,95014,95015,95037],{},[2068,95016,95017,95019,95021,95027,95029,95035],{},[2071,95018,10871],{},[2075,95020,2084],{"stretchy":2083},[2348,95022,95023,95025],{},[2071,95024,2861],{},[2210,95026,638],{},[2075,95028,2361],{"separator":2360},[2348,95030,95031,95033],{},[2071,95032,2179],{},[2210,95034,630],{},[2075,95036,2090],{"stretchy":2083},[2092,95038,95039],{"encoding":2094},"U(Q_1, b_0)",[1647,95041,95043],{"className":95042},[2059],[2061,95044,95045],{"xmlns":2063},[2065,95046,95047,95069],{},[2068,95048,95049,95051,95053,95059,95061,95067],{},[2071,95050,10871],{},[2075,95052,2084],{"stretchy":2083},[2348,95054,95055,95057],{},[2071,95056,69],{},[2210,95058,630],{},[2075,95060,2361],{"separator":2360},[2348,95062,95063,95065],{},[2071,95064,2861],{},[2210,95066,646],{},[2075,95068,2090],{"stretchy":2083},[2092,95070,95071],{"encoding":2094},"U(a_0, Q_2)"," v souřadnicových rovinách ",[1647,95074,95076],{"className":95075},[2059],[2061,95077,95078],{"xmlns":2063},[2065,95079,95080,95096],{},[2068,95081,95082,95084,95086,95088,95094],{},[2075,95083,2084],{"stretchy":2083},[2071,95085,10871],{},[2075,95087,2361],{"separator":2360},[2348,95089,95090,95092],{},[2071,95091,2861],{},[2210,95093,638],{},[2075,95095,2090],{"stretchy":2083},[2092,95097,95098],{"encoding":2094},"(U, Q_1)",[1647,95100,95102],{"className":95101},[2059],[2061,95103,95104],{"xmlns":2063},[2065,95105,95106,95122],{},[2068,95107,95108,95110,95112,95114,95120],{},[2075,95109,2084],{"stretchy":2083},[2071,95111,10871],{},[2075,95113,2361],{"separator":2360},[2348,95115,95116,95118],{},[2071,95117,2861],{},[2210,95119,646],{},[2075,95121,2090],{"stretchy":2083},[2092,95123,95124],{"encoding":2094},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[1647,95127,95129],{"className":95128},[2059],[2061,95130,95131],{"xmlns":2063},[2065,95132,95133,95151],{},[2068,95134,95135,95137,95139,95141,95143,95145,95147,95149],{},[2071,95136,10871],{},[2075,95138,2084],{"stretchy":2083},[2210,95140,630],{},[2075,95142,2361],{"separator":2360},[2210,95144,630],{},[2075,95146,2090],{"stretchy":2083},[2075,95148,2077],{},[2210,95150,630],{},[2092,95152,95153],{"encoding":2094},"U(0, 0) = 0","), jsou ",[95,95156,15392],{},[95,95158,42779],{},". Typický tvar grafu ",[1647,95161,95163],{"className":95162},[2059],[2061,95164,95165],{"xmlns":2063},[2065,95166,95167,95193],{},[2068,95168,95169,95171,95173,95175,95177,95183,95185,95191],{},[2071,95170,10871],{},[2075,95172,2077],{},[2071,95174,10871],{},[2075,95176,2084],{"stretchy":2083},[2348,95178,95179,95181],{},[2071,95180,2861],{},[2210,95182,638],{},[2075,95184,2361],{"separator":2360},[2348,95186,95187,95189],{},[2071,95188,2861],{},[2210,95190,646],{},[2075,95192,2090],{"stretchy":2083},[2092,95194,93209],{"encoding":2094}," — plocha v prostoru — je na obrázku 6.2.",[55,95197,95198],{},[3982,95199,95200,95201,94241,95229,95250,95251,94241,95279,95301],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[1647,95202,95204],{"className":95203},[2059],[2061,95205,95206],{"xmlns":2063},[2065,95207,95208,95226],{},[2068,95209,95210,95212,95214,95220,95222,95224],{},[2071,95211,10871],{},[2075,95213,2084],{"stretchy":2083},[2348,95215,95216,95218],{},[2071,95217,2861],{},[2210,95219,638],{},[2075,95221,2361],{"separator":2360},[2071,95223,2179],{},[2075,95225,2090],{"stretchy":2083},[2092,95227,95228],{"encoding":2094},"U(Q_1, b)",[1647,95230,95232],{"className":95231},[2059],[2061,95233,95234],{"xmlns":2063},[2065,95235,95236,95248],{},[2068,95237,95238,95244,95246],{},[2348,95239,95240,95242],{},[2071,95241,2861],{},[2210,95243,646],{},[2075,95245,2077],{},[2071,95247,2179],{},[2092,95249,94263],{"encoding":2094}," (vlevo) a ",[1647,95252,95254],{"className":95253},[2059],[2061,95255,95256],{"xmlns":2063},[2065,95257,95258,95276],{},[2068,95259,95260,95262,95264,95266,95268,95274],{},[2071,95261,10871],{},[2075,95263,2084],{"stretchy":2083},[2071,95265,69],{},[2075,95267,2361],{"separator":2360},[2348,95269,95270,95272],{},[2071,95271,2861],{},[2210,95273,646],{},[2075,95275,2090],{"stretchy":2083},[2092,95277,95278],{"encoding":2094},"U(a, Q_2)",[1647,95280,95282],{"className":95281},[2059],[2061,95283,95284],{"xmlns":2063},[2065,95285,95286,95298],{},[2068,95287,95288,95294,95296],{},[2348,95289,95290,95292],{},[2071,95291,2861],{},[2210,95293,638],{},[2075,95295,2077],{},[2071,95297,69],{},[2092,95299,95300],{"encoding":2094},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[55,95303,95304],{},[3982,95305,95306,95307,95342,95343,95373,95374,75,95397,95419,95420,195],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[1647,95308,95310],{"className":95309},[2059],[2061,95311,95312],{"xmlns":2063},[2065,95313,95314,95340],{},[2068,95315,95316,95318,95320,95322,95324,95330,95332,95338],{},[2071,95317,10871],{},[2075,95319,2077],{},[2071,95321,10871],{},[2075,95323,2084],{"stretchy":2083},[2348,95325,95326,95328],{},[2071,95327,2861],{},[2210,95329,638],{},[2075,95331,2361],{"separator":2360},[2348,95333,95334,95336],{},[2071,95335,2861],{},[2210,95337,646],{},[2075,95339,2090],{"stretchy":2083},[2092,95341,93209],{"encoding":2094}," nad rovinou ",[1647,95344,95346],{"className":95345},[2059],[2061,95347,95348],{"xmlns":2063},[2065,95349,95350,95370],{},[2068,95351,95352,95354,95360,95362,95368],{},[2075,95353,2084],{"stretchy":2083},[2348,95355,95356,95358],{},[2071,95357,2861],{},[2210,95359,638],{},[2075,95361,2361],{"separator":2360},[2348,95363,95364,95366],{},[2071,95365,2861],{},[2210,95367,646],{},[2075,95369,2090],{"stretchy":2083},[2092,95371,95372],{"encoding":2094},"(Q_1, Q_2)"," s řezy rovinami ",[1647,95375,95377],{"className":95376},[2059],[2061,95378,95379],{"xmlns":2063},[2065,95380,95381,95394],{},[2068,95382,95383,95389,95391],{},[2348,95384,95385,95387],{},[2071,95386,2861],{},[2210,95388,638],{},[2075,95390,2077],{},[2363,95392,95393],{},"const",[2092,95395,95396],{"encoding":2094},"Q_1 = \\text{const}",[1647,95398,95400],{"className":95399},[2059],[2061,95401,95402],{"xmlns":2063},[2065,95403,95404,95416],{},[2068,95405,95406,95412,95414],{},[2348,95407,95408,95410],{},[2071,95409,2861],{},[2210,95411,646],{},[2075,95413,2077],{},[2363,95415,95393],{},[2092,95417,95418],{"encoding":2094},"Q_2 = \\text{const}"," a s křivkou ",[1647,95421,95423],{"className":95422},[2059],[2061,95424,95425],{"xmlns":2063},[2065,95426,95427,95453],{},[2068,95428,95429,95431,95433,95439,95441,95447,95449,95451],{},[2071,95430,10871],{},[2075,95432,2084],{"stretchy":2083},[2348,95434,95435,95437],{},[2071,95436,2861],{},[2210,95438,638],{},[2075,95440,2361],{"separator":2360},[2348,95442,95443,95445],{},[2071,95444,2861],{},[2210,95446,646],{},[2075,95448,2090],{"stretchy":2083},[2075,95450,2077],{},[2071,95452,2222],{},[2092,95454,10896],{"encoding":2094},[609,95456,95458,95459],{"id":95457},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[1647,95460,95462],{"className":95461},[2059],[2061,95463,95464],{"xmlns":2063},[2065,95465,95466,95500],{},[2068,95467,95468,95470,95472,95486],{},[2071,95469,10871],{},[2075,95471,2077],{},[9252,95473,95474,95476,95478],{},[2071,95475,2861],{},[2210,95477,638],{},[2068,95479,95480,95482,95484],{},[2210,95481,638],{},[2071,95483,4761],{"mathvariant":2450},[2210,95485,646],{},[9252,95487,95488,95490,95492],{},[2071,95489,2861],{},[2210,95491,646],{},[2068,95493,95494,95496,95498],{},[2210,95495,638],{},[2071,95497,4761],{"mathvariant":2450},[2210,95499,654],{},[2092,95501,95502],{"encoding":2094},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[55,95504,95505],{},[95,95506,95507],{},"Ověření (6.4) a (6.5).",[1647,95509,95511],{"className":95510},[2059],[2061,95512,95513],{"xmlns":2063,"display":31093},[2065,95514,95515,95619],{},[2068,95516,95517,95525,95527,95535,95551,95565,95567,95569,95577,95579,95587,95601,95617],{},[9252,95518,95519,95521,95523],{},[2071,95520,10871],{},[2210,95522,638],{},[2075,95524,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,95526,2077],{},[2400,95528,95529],{"scriptlevel":630,"displaystyle":2083},[2403,95530,95531,95533],{},[2210,95532,638],{},[2210,95534,646],{},[9252,95536,95537,95539,95541],{},[2071,95538,2861],{},[2210,95540,638],{},[2068,95542,95543,95545,95547,95549],{},[2075,95544,2303],{},[2210,95546,638],{},[2071,95548,4761],{"mathvariant":2450},[2210,95550,646],{},[9252,95552,95553,95555,95557],{},[2071,95554,2861],{},[2210,95556,646],{},[2068,95558,95559,95561,95563],{},[2210,95560,638],{},[2071,95562,4761],{"mathvariant":2450},[2210,95564,654],{},[2075,95566,2361],{"separator":2360},[5965,95568],{"width":17019},[9252,95570,95571,95573,95575],{},[2071,95572,10871],{},[2210,95574,646],{},[2075,95576,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,95578,2077],{},[2400,95580,95581],{"scriptlevel":630,"displaystyle":2083},[2403,95582,95583,95585],{},[2210,95584,638],{},[2210,95586,654],{},[9252,95588,95589,95591,95593],{},[2071,95590,2861],{},[2210,95592,638],{},[2068,95594,95595,95597,95599],{},[2210,95596,638],{},[2071,95598,4761],{"mathvariant":2450},[2210,95600,646],{},[9252,95602,95603,95605,95607],{},[2071,95604,2861],{},[2210,95606,646],{},[2068,95608,95609,95611,95613,95615],{},[2075,95610,2303],{},[2210,95612,646],{},[2071,95614,4761],{"mathvariant":2450},[2210,95616,654],{},[2075,95618,2361],{"separator":2360},[2092,95620,95621],{"encoding":2094},"U'_1 = \\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F3}, \\quad U'_2 = \\tfrac{1}{3} Q_1^{1\u002F2} Q_2^{-2\u002F3},",[55,95623,95624,95625,95659],{},"zřejmě ",[1647,95626,95628],{"className":95627},[2059],[2061,95629,95630],{"xmlns":2063},[2065,95631,95632,95656],{},[2068,95633,95634,95642,95644,95652,95654],{},[9252,95635,95636,95638,95640],{},[2071,95637,10871],{},[2210,95639,638],{},[2075,95641,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,95643,2361],{"separator":2360},[9252,95645,95646,95648,95650],{},[2071,95647,10871],{},[2210,95649,646],{},[2075,95651,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,95653,3482],{},[2210,95655,630],{},[2092,95657,95658],{"encoding":2094},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[1647,95661,95663],{"className":95662},[2059],[2061,95664,95665],{"xmlns":2063,"display":31093},[2065,95666,95667,95783],{},[2068,95668,95669,95681,95683,95685,95693,95709,95723,95725,95727,95739,95741,95743,95751,95765,95781],{},[9252,95670,95671,95673,95675],{},[2071,95672,10871],{},[2210,95674,2976],{},[2068,95676,95677,95679],{},[2075,95678,2452],{"mathvariant":2450},[2075,95680,2452],{"mathvariant":2450},[2075,95682,2077],{},[2075,95684,2303],{},[2400,95686,95687],{"scriptlevel":630,"displaystyle":2083},[2403,95688,95689,95691],{},[2210,95690,638],{},[2210,95692,662],{},[9252,95694,95695,95697,95699],{},[2071,95696,2861],{},[2210,95698,638],{},[2068,95700,95701,95703,95705,95707],{},[2075,95702,2303],{},[2210,95704,654],{},[2071,95706,4761],{"mathvariant":2450},[2210,95708,646],{},[9252,95710,95711,95713,95715],{},[2071,95712,2861],{},[2210,95714,646],{},[2068,95716,95717,95719,95721],{},[2210,95718,638],{},[2071,95720,4761],{"mathvariant":2450},[2210,95722,654],{},[2075,95724,2361],{"separator":2360},[5965,95726],{"width":17019},[9252,95728,95729,95731,95733],{},[2071,95730,10871],{},[2210,95732,35572],{},[2068,95734,95735,95737],{},[2075,95736,2452],{"mathvariant":2450},[2075,95738,2452],{"mathvariant":2450},[2075,95740,2077],{},[2075,95742,2303],{},[2400,95744,95745],{"scriptlevel":630,"displaystyle":2083},[2403,95746,95747,95749],{},[2210,95748,646],{},[2210,95750,4087],{},[9252,95752,95753,95755,95757],{},[2071,95754,2861],{},[2210,95756,638],{},[2068,95758,95759,95761,95763],{},[2210,95760,638],{},[2071,95762,4761],{"mathvariant":2450},[2210,95764,646],{},[9252,95766,95767,95769,95771],{},[2071,95768,2861],{},[2210,95770,646],{},[2068,95772,95773,95775,95777,95779],{},[2075,95774,2303],{},[2210,95776,670],{},[2071,95778,4761],{"mathvariant":2450},[2210,95780,654],{},[2075,95782,2361],{"separator":2360},[2092,95784,95785],{"encoding":2094},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F3}, \\quad U''_{22} = -\\tfrac{2}{9} Q_1^{1\u002F2} Q_2^{-5\u002F3},",[55,95787,95788,95789,95831],{},"opět ",[1647,95790,95792],{"className":95791},[2059],[2061,95793,95794],{"xmlns":2063},[2065,95795,95796,95828],{},[2068,95797,95798,95810,95812,95824,95826],{},[9252,95799,95800,95802,95804],{},[2071,95801,10871],{},[2210,95803,2976],{},[2068,95805,95806,95808],{},[2075,95807,2452],{"mathvariant":2450},[2075,95809,2452],{"mathvariant":2450},[2075,95811,2361],{"separator":2360},[9252,95813,95814,95816,95818],{},[2071,95815,10871],{},[2210,95817,35572],{},[2068,95819,95820,95822],{},[2075,95821,2452],{"mathvariant":2450},[2075,95823,2452],{"mathvariant":2450},[2075,95825,3521],{},[2210,95827,630],{},[2092,95829,95830],{"encoding":2094},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[55,95833,95834],{},[95,95835,95836,95837,195],{},"(a) Mezní užitečnosti v bodě ",[1647,95838,95840],{"className":95839},[2059],[2061,95841,95842],{"xmlns":2063},[2065,95843,95844,95856],{},[2068,95845,95846,95848,95850,95852,95854],{},[2075,95847,2561],{"stretchy":2083},[2210,95849,3164],{},[2075,95851,2361],{"separator":2360},[2210,95853,8464],{},[2075,95855,2576],{"stretchy":2083},[2092,95857,95858],{"encoding":2094},"[100, 200]",[1647,95860,95862],{"className":95861},[2059],[2061,95863,95864],{"xmlns":2063,"display":31093},[2065,95865,95866,95933],{},[2068,95867,95868,95870,95876,95878,95880,95882,95884,95886,95888,95896,95898,95912,95914,95926,95928,95931],{},[2071,95869,2890],{},[2348,95871,95872,95874],{},[2071,95873,10871],{},[2210,95875,638],{},[2075,95877,2084],{"stretchy":2083},[2210,95879,3164],{},[2075,95881,2361],{"separator":2360},[2210,95883,8464],{},[2075,95885,2090],{"stretchy":2083},[2075,95887,2077],{},[2400,95889,95890],{"scriptlevel":630,"displaystyle":2083},[2403,95891,95892,95894],{},[2210,95893,638],{},[2210,95895,646],{},[2075,95897,3251],{},[2205,95899,95900,95902],{},[2210,95901,3164],{},[2068,95903,95904,95906,95908,95910],{},[2075,95905,2303],{},[2210,95907,638],{},[2071,95909,4761],{"mathvariant":2450},[2210,95911,646],{},[2075,95913,3251],{},[2205,95915,95916,95918],{},[2210,95917,8464],{},[2068,95919,95920,95922,95924],{},[2210,95921,638],{},[2071,95923,4761],{"mathvariant":2450},[2210,95925,654],{},[2075,95927,5987],{},[2210,95929,95930],{},"0,4204",[2075,95932,2361],{"separator":2360},[2092,95934,95935],{"encoding":2094},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[1647,95937,95939],{"className":95938},[2059],[2061,95940,95941],{"xmlns":2063,"display":31093},[2065,95942,95943,96008],{},[2068,95944,95945,95947,95953,95955,95957,95959,95961,95963,95965,95973,95975,95987,95989,96003,96005],{},[2071,95946,2890],{},[2348,95948,95949,95951],{},[2071,95950,10871],{},[2210,95952,646],{},[2075,95954,2084],{"stretchy":2083},[2210,95956,3164],{},[2075,95958,2361],{"separator":2360},[2210,95960,8464],{},[2075,95962,2090],{"stretchy":2083},[2075,95964,2077],{},[2400,95966,95967],{"scriptlevel":630,"displaystyle":2083},[2403,95968,95969,95971],{},[2210,95970,638],{},[2210,95972,654],{},[2075,95974,3251],{},[2205,95976,95977,95979],{},[2210,95978,3164],{},[2068,95980,95981,95983,95985],{},[2210,95982,638],{},[2071,95984,4761],{"mathvariant":2450},[2210,95986,646],{},[2075,95988,3251],{},[2205,95990,95991,95993],{},[2210,95992,8464],{},[2068,95994,95995,95997,95999,96001],{},[2075,95996,2303],{},[2210,95998,646],{},[2071,96000,4761],{"mathvariant":2450},[2210,96002,654],{},[2075,96004,5987],{},[2210,96006,96007],{},"0,63067.",[2092,96009,96010],{"encoding":2094},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[55,96012,96013,1445,96015,96050,96051,96072,96073,96090],{},[3982,96014,9302],{},[1647,96016,96018],{"className":96017},[2059],[2061,96019,96020],{"xmlns":2063},[2065,96021,96022,96047],{},[2068,96023,96024,96026,96032,96034,96036,96038,96040,96042,96044],{},[2071,96025,2890],{},[2348,96027,96028,96030],{},[2071,96029,10871],{},[2210,96031,646],{},[2075,96033,2084],{"stretchy":2083},[2210,96035,3164],{},[2075,96037,2361],{"separator":2360},[2210,96039,8464],{},[2075,96041,2090],{"stretchy":2083},[2075,96043,5987],{},[2210,96045,96046],{},"0,63067",[2092,96048,96049],{"encoding":2094},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[1647,96052,96054],{"className":96053},[2059],[2061,96055,96056],{"xmlns":2063},[2065,96057,96058,96070],{},[2068,96059,96060,96062,96064,96066,96068],{},[2075,96061,2561],{"stretchy":2083},[2210,96063,3164],{},[2075,96065,2361],{"separator":2360},[2210,96067,8464],{},[2075,96069,2576],{"stretchy":2083},[2092,96071,95858],{"encoding":2094}," roste užitečnost při jednotkové změně ",[1647,96074,96076],{"className":96075},[2059],[2061,96077,96078],{"xmlns":2063},[2065,96079,96080,96088],{},[2068,96081,96082],{},[2348,96083,96084,96086],{},[2071,96085,2861],{},[2210,96087,646],{},[2092,96089,32048],{"encoding":2094}," přibližně o 0,63067.",[55,96092,96093,96112,96113,43475,96134,96151,96152,96178,96179,96196,96197,3225],{},[95,96094,96095,96096,96111],{},"(b) Odhad změny ",[1647,96097,96099],{"className":96098},[2059],[2061,96100,96101],{"xmlns":2063},[2065,96102,96103,96109],{},[2068,96104,96105,96107],{},[2071,96106,2961],{"mathvariant":2450},[2071,96108,10871],{},[2092,96110,94354],{"encoding":2094}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[1647,96114,96116],{"className":96115},[2059],[2061,96117,96118],{"xmlns":2063},[2065,96119,96120,96132],{},[2068,96121,96122,96124,96126,96128,96130],{},[2075,96123,2561],{"stretchy":2083},[2210,96125,3164],{},[2075,96127,2361],{"separator":2360},[2210,96129,8464],{},[2075,96131,2576],{"stretchy":2083},[2092,96133,95858],{"encoding":2094},[1647,96135,96137],{"className":96136},[2059],[2061,96138,96139],{"xmlns":2063},[2065,96140,96141,96149],{},[2068,96142,96143],{},[2348,96144,96145,96147],{},[2071,96146,2861],{},[2210,96148,638],{},[2092,96150,32029],{"encoding":2094}," na 98 (tj. ",[1647,96153,96155],{"className":96154},[2059],[2061,96156,96157],{"xmlns":2063},[2065,96158,96159,96175],{},[2068,96160,96161,96163,96169,96171,96173],{},[2071,96162,2273],{"mathvariant":2450},[2348,96164,96165,96167],{},[2071,96166,2861],{},[2210,96168,638],{},[2075,96170,2077],{},[2075,96172,2303],{},[2210,96174,646],{},[2092,96176,96177],{"encoding":2094},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[1647,96180,96182],{"className":96181},[2059],[2061,96183,96184],{"xmlns":2063},[2065,96185,96186,96194],{},[2068,96187,96188],{},[2348,96189,96190,96192],{},[2071,96191,2861],{},[2210,96193,646],{},[2092,96195,32048],{"encoding":2094}," o 3 (tj. ",[1647,96198,96200],{"className":96199},[2059],[2061,96201,96202],{"xmlns":2063},[2065,96203,96204,96218],{},[2068,96205,96206,96208,96214,96216],{},[2071,96207,2273],{"mathvariant":2450},[2348,96209,96210,96212],{},[2071,96211,2861],{},[2210,96213,646],{},[2075,96215,2077],{},[2210,96217,654],{},[2092,96219,96220],{"encoding":2094},"\\mathrm{d} Q_2 = 3",[1647,96222,96224],{"className":96223},[2059],[2061,96225,96226],{"xmlns":2063,"display":31093},[2065,96227,96228,96279],{},[2068,96229,96230,96232,96234,96236,96238,96240,96242,96244,96246,96248,96250,96252,96254,96256,96258,96260,96262,96264,96266,96269,96271,96274,96276],{},[2071,96231,2961],{"mathvariant":2450},[2071,96233,10871],{},[2075,96235,2803],{},[2071,96237,2273],{"mathvariant":2450},[2071,96239,10871],{},[2075,96241,2077],{},[2210,96243,95930],{},[2075,96245,3251],{},[2075,96247,2084],{"stretchy":2083},[2075,96249,2303],{},[2210,96251,646],{},[2075,96253,2090],{"stretchy":2083},[2075,96255,2176],{},[2210,96257,96046],{},[2075,96259,3251],{},[2210,96261,654],{},[2075,96263,2077],{},[2075,96265,2303],{},[2210,96267,96268],{},"0,8408",[2075,96270,2176],{},[2210,96272,96273],{},"1,89201",[2075,96275,5987],{},[2210,96277,96278],{},"1,05.",[2092,96280,96281],{"encoding":2094},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[55,96283,96284,96285,96288,96289,96340,96341,195],{},"Užitečnost se tedy zvýší přibližně o ",[95,96286,96287],{},"1,05",". Skutečná změna je ",[1647,96290,96292],{"className":96291},[2059],[2061,96293,96294],{"xmlns":2063},[2065,96295,96296,96337],{},[2068,96297,96298,96300,96302,96304,96306,96308,96311,96313,96316,96318,96320,96322,96324,96326,96328,96330,96332,96334],{},[2071,96299,2961],{"mathvariant":2450},[2071,96301,10871],{},[2075,96303,2077],{},[2071,96305,10871],{},[2075,96307,2084],{"stretchy":2083},[2210,96309,96310],{},"98",[2075,96312,2361],{"separator":2360},[2210,96314,96315],{},"203",[2075,96317,2090],{"stretchy":2083},[2075,96319,2303],{},[2071,96321,10871],{},[2075,96323,2084],{"stretchy":2083},[2210,96325,3164],{},[2075,96327,2361],{"separator":2360},[2210,96329,8464],{},[2075,96331,2090],{"stretchy":2083},[2075,96333,5987],{},[2210,96335,96336],{},"1,031",[2092,96338,96339],{"encoding":2094},"\\Delta U = U(98, 203) - U(100, 200) \\doteq 1{,}031"," — relativní chyba odhadu je zhruba 2 %. Aproximace totálním diferenciálem je uspokojivá pro malé ",[1647,96342,96344],{"className":96343},[2059],[2061,96345,96346],{"xmlns":2063},[2065,96347,96348,96368],{},[2068,96349,96350,96352,96358,96360,96362],{},[2071,96351,2273],{"mathvariant":2450},[2348,96353,96354,96356],{},[2071,96355,2861],{},[2210,96357,638],{},[2075,96359,2361],{"separator":2360},[2071,96361,2273],{"mathvariant":2450},[2348,96363,96364,96366],{},[2071,96365,2861],{},[2210,96367,646],{},[2092,96369,94384],{"encoding":2094},[84,96371,96373],{"id":96372},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[55,96375,96376],{},"Nejčastěji používané funkce užitečnosti mají tvar",[1647,96378,96380],{"className":96379},[2059],[2061,96381,96382],{"xmlns":2063,"display":31093},[2065,96383,96384,96443],{},[23493,96385,96386],{"width":31098},[23498,96387,96388,96390,96436,96438],{},[23501,96389],{"width":31103},[23501,96391,96392],{},[2068,96393,96394,96396,96398,96404,96406,96412,96414,96416,96424,96426,96434],{},[2071,96395,10871],{},[2075,96397,2084],{"stretchy":2083},[2348,96399,96400,96402],{},[2071,96401,2861],{},[2210,96403,638],{},[2075,96405,2361],{"separator":2360},[2348,96407,96408,96410],{},[2071,96409,2861],{},[2210,96411,646],{},[2075,96413,2090],{"stretchy":2083},[2075,96415,2077],{},[9252,96417,96418,96420,96422],{},[2071,96419,2861],{},[2210,96421,638],{},[2071,96423,69],{},[2075,96425,3251],{},[9252,96427,96428,96430,96432],{},[2071,96429,2861],{},[2210,96431,646],{},[2071,96433,2179],{},[2075,96435,2361],{"separator":2360},[23501,96437],{"width":31103},[23501,96439,96440],{},[2363,96441,96442],{},"(6.6)",[2092,96444,96445],{"encoding":2094},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[55,96447,4397,96448,96466,96467,96469,96470,96474,96475,96505,96506,96528],{},[1647,96449,96451],{"className":96450},[2059],[2061,96452,96453],{"xmlns":2063},[2065,96454,96455,96463],{},[2068,96456,96457,96459,96461],{},[2071,96458,69],{},[2075,96460,2361],{"separator":2360},[2071,96462,2179],{},[2092,96464,96465],{"encoding":2094},"a, b"," jsou kladná čísla; nazývají se ",[95,96468,79170],{}," (v příbuznosti s produkčními funkcemi — viz ",[69,96471,96473],{"className":96472,"dataFsResolvedFilePath":10942,"href":10943},[62],"kapitola 5","). Obvykle se volí ",[1647,96476,96478],{"className":96477},[2059],[2061,96479,96480],{"xmlns":2063},[2065,96481,96482,96502],{},[2068,96483,96484,96486,96488,96490,96492,96494,96496,96498,96500],{},[2071,96485,69],{},[2075,96487,2361],{"separator":2360},[2071,96489,2179],{},[2075,96491,6593],{},[2075,96493,2084],{"stretchy":2083},[2210,96495,630],{},[2075,96497,2361],{"separator":2360},[2210,96499,638],{},[2075,96501,2090],{"stretchy":2083},[2092,96503,96504],{"encoding":2094},"a, b \\in (0, 1)",", často se klade ",[1647,96507,96509],{"className":96508},[2059],[2061,96510,96511],{"xmlns":2063},[2065,96512,96513,96525],{},[2068,96514,96515,96517,96519,96521,96523],{},[2071,96516,2179],{},[2075,96518,2077],{},[2210,96520,638],{},[2075,96522,2303],{},[2071,96524,69],{},[2092,96526,96527],{"encoding":2094},"b = 1 - a",", čímž (6.6) přejde na tvar",[55,96530,96531],{},[58,96532],{"alt":96533,"className":96534,"src":96535},"imek-cobb-douglas-3d-plus-ic",[62,63],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[1647,96537,96539],{"className":96538},[2059],[2061,96540,96541],{"xmlns":2063,"display":31093},[2065,96542,96543,96593],{},[2068,96544,96545,96547,96549,96555,96557,96563,96565,96567,96575,96577,96591],{},[2071,96546,10871],{},[2075,96548,2084],{"stretchy":2083},[2348,96550,96551,96553],{},[2071,96552,2861],{},[2210,96554,638],{},[2075,96556,2361],{"separator":2360},[2348,96558,96559,96561],{},[2071,96560,2861],{},[2210,96562,646],{},[2075,96564,2090],{"stretchy":2083},[2075,96566,2077],{},[9252,96568,96569,96571,96573],{},[2071,96570,2861],{},[2210,96572,638],{},[2071,96574,69],{},[2075,96576,3251],{},[9252,96578,96579,96581,96583],{},[2071,96580,2861],{},[2210,96582,646],{},[2068,96584,96585,96587,96589],{},[2210,96586,638],{},[2075,96588,2303],{},[2071,96590,69],{},[2071,96592,195],{"mathvariant":2450},[2092,96594,96595],{"encoding":2094},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1023,96597,96598,96647,96769,96903],{},[55,96599,96600,96602,96603],{},[1647,96601,56993],{}," Příklad 6.3 — ověření vlastností pro ",[1647,96604,96606],{"className":96605},[2059],[2061,96607,96608],{"xmlns":2063},[2065,96609,96610,96644],{},[2068,96611,96612,96614,96616,96630],{},[2071,96613,10871],{},[2075,96615,2077],{},[9252,96617,96618,96620,96622],{},[2071,96619,2861],{},[2210,96621,638],{},[2068,96623,96624,96626,96628],{},[2210,96625,638],{},[2071,96627,4761],{"mathvariant":2450},[2210,96629,662],{},[9252,96631,96632,96634,96636],{},[2071,96633,2861],{},[2210,96635,646],{},[2068,96637,96638,96640,96642],{},[2210,96639,654],{},[2071,96641,4761],{"mathvariant":2450},[2210,96643,662],{},[2092,96645,96646],{"encoding":2094},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[1647,96648,96650],{"className":96649},[2059],[2061,96651,96652],{"xmlns":2063,"display":31093},[2065,96653,96654,96766],{},[2068,96655,96656,96664,96666,96674,96690,96704,96706,96708,96710,96712,96720,96722,96730,96744,96760,96762,96764],{},[9252,96657,96658,96660,96662],{},[2071,96659,10871],{},[2210,96661,638],{},[2075,96663,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,96665,2077],{},[2400,96667,96668],{"scriptlevel":630,"displaystyle":2083},[2403,96669,96670,96672],{},[2210,96671,638],{},[2210,96673,662],{},[9252,96675,96676,96678,96680],{},[2071,96677,2861],{},[2210,96679,638],{},[2068,96681,96682,96684,96686,96688],{},[2075,96683,2303],{},[2210,96685,654],{},[2071,96687,4761],{"mathvariant":2450},[2210,96689,662],{},[9252,96691,96692,96694,96696],{},[2071,96693,2861],{},[2210,96695,646],{},[2068,96697,96698,96700,96702],{},[2210,96699,654],{},[2071,96701,4761],{"mathvariant":2450},[2210,96703,662],{},[2075,96705,3482],{},[2210,96707,630],{},[2075,96709,2361],{"separator":2360},[5965,96711],{"width":17019},[9252,96713,96714,96716,96718],{},[2071,96715,10871],{},[2210,96717,646],{},[2075,96719,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,96721,2077],{},[2400,96723,96724],{"scriptlevel":630,"displaystyle":2083},[2403,96725,96726,96728],{},[2210,96727,654],{},[2210,96729,662],{},[9252,96731,96732,96734,96736],{},[2071,96733,2861],{},[2210,96735,638],{},[2068,96737,96738,96740,96742],{},[2210,96739,638],{},[2071,96741,4761],{"mathvariant":2450},[2210,96743,662],{},[9252,96745,96746,96748,96750],{},[2071,96747,2861],{},[2210,96749,646],{},[2068,96751,96752,96754,96756,96758],{},[2075,96753,2303],{},[2210,96755,638],{},[2071,96757,4761],{"mathvariant":2450},[2210,96759,662],{},[2075,96761,3482],{},[2210,96763,630],{},[2075,96765,2361],{"separator":2360},[2092,96767,96768],{"encoding":2094},"U'_1 = \\tfrac{1}{4} Q_1^{-3\u002F4} Q_2^{3\u002F4} > 0, \\quad U'_2 = \\tfrac{3}{4} Q_1^{1\u002F4} Q_2^{-1\u002F4} > 0,",[1647,96770,96772],{"className":96771},[2059],[2061,96773,96774],{"xmlns":2063,"display":31093},[2065,96775,96776,96900],{},[2068,96777,96778,96790,96792,96794,96802,96818,96832,96834,96836,96838,96840,96852,96854,96856,96864,96878,96894,96896,96898],{},[9252,96779,96780,96782,96784],{},[2071,96781,10871],{},[2210,96783,2976],{},[2068,96785,96786,96788],{},[2075,96787,2452],{"mathvariant":2450},[2075,96789,2452],{"mathvariant":2450},[2075,96791,2077],{},[2075,96793,2303],{},[2400,96795,96796],{"scriptlevel":630,"displaystyle":2083},[2403,96797,96798,96800],{},[2210,96799,654],{},[2210,96801,46153],{},[9252,96803,96804,96806,96808],{},[2071,96805,2861],{},[2210,96807,638],{},[2068,96809,96810,96812,96814,96816],{},[2075,96811,2303],{},[2210,96813,686],{},[2071,96815,4761],{"mathvariant":2450},[2210,96817,662],{},[9252,96819,96820,96822,96824],{},[2071,96821,2861],{},[2210,96823,646],{},[2068,96825,96826,96828,96830],{},[2210,96827,654],{},[2071,96829,4761],{"mathvariant":2450},[2210,96831,662],{},[2075,96833,3521],{},[2210,96835,630],{},[2075,96837,2361],{"separator":2360},[5965,96839],{"width":17019},[9252,96841,96842,96844,96846],{},[2071,96843,10871],{},[2210,96845,35572],{},[2068,96847,96848,96850],{},[2075,96849,2452],{"mathvariant":2450},[2075,96851,2452],{"mathvariant":2450},[2075,96853,2077],{},[2075,96855,2303],{},[2400,96857,96858],{"scriptlevel":630,"displaystyle":2083},[2403,96859,96860,96862],{},[2210,96861,654],{},[2210,96863,46153],{},[9252,96865,96866,96868,96870],{},[2071,96867,2861],{},[2210,96869,638],{},[2068,96871,96872,96874,96876],{},[2210,96873,638],{},[2071,96875,4761],{"mathvariant":2450},[2210,96877,662],{},[9252,96879,96880,96882,96884],{},[2071,96881,2861],{},[2210,96883,646],{},[2068,96885,96886,96888,96890,96892],{},[2075,96887,2303],{},[2210,96889,670],{},[2071,96891,4761],{"mathvariant":2450},[2210,96893,662],{},[2075,96895,3521],{},[2210,96897,630],{},[2075,96899,2361],{"separator":2360},[2092,96901,96902],{"encoding":2094},"U''_{11} = -\\tfrac{3}{16} Q_1^{-7\u002F4} Q_2^{3\u002F4} \u003C 0, \\quad U''_{22} = -\\tfrac{3}{16} Q_1^{1\u002F4} Q_2^{-5\u002F4} \u003C 0,",[55,96904,96905],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[84,96907,96909],{"id":96908},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[55,96911,96912,96915],{},[95,96913,96914],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[1647,96917,96919],{"className":96918},[2059],[2061,96920,96921],{"xmlns":2063,"display":31093},[2065,96922,96923,96966],{},[23493,96924,96925],{"width":31098},[23498,96926,96927,96929,96959,96961],{},[23501,96928],{"width":31103},[23501,96930,96931],{},[2068,96932,96933,96935,96937,96943,96945,96951,96953,96955,96957],{},[2071,96934,10871],{},[2075,96936,2084],{"stretchy":2083},[2348,96938,96939,96941],{},[2071,96940,2861],{},[2210,96942,638],{},[2075,96944,2361],{"separator":2360},[2348,96946,96947,96949],{},[2071,96948,2861],{},[2210,96950,646],{},[2075,96952,2090],{"stretchy":2083},[2075,96954,2077],{},[2071,96956,2222],{},[2075,96958,2361],{"separator":2360},[23501,96960],{"width":31103},[23501,96962,96963],{},[2363,96964,96965],{},"(6.7)",[2092,96967,96968],{"encoding":2094},"U(Q_1, Q_2) = c, \\tag{6.7}",[55,96970,4397,96971,96984],{},[1647,96972,96974],{"className":96973},[2059],[2061,96975,96976],{"xmlns":2063},[2065,96977,96978,96982],{},[2068,96979,96980],{},[2071,96981,2222],{},[2092,96983,2222],{"encoding":2094}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[1647,96986,96988],{"className":96987},[2059],[2061,96989,96990],{"xmlns":2063,"display":31093},[2065,96991,96992,97033],{},[23493,96993,96994],{"width":31098},[23498,96995,96996,96998,97026,97028],{},[23501,96997],{"width":31103},[23501,96999,97000],{},[2068,97001,97002,97010,97012,97020,97022,97024],{},[9252,97003,97004,97006,97008],{},[2071,97005,2861],{},[2210,97007,638],{},[2071,97009,69],{},[2075,97011,3251],{},[9252,97013,97014,97016,97018],{},[2071,97015,2861],{},[2210,97017,646],{},[2071,97019,2179],{},[2075,97021,2077],{},[2071,97023,2222],{},[2071,97025,195],{"mathvariant":2450},[23501,97027],{"width":31103},[23501,97029,97030],{},[2363,97031,97032],{},"(6.8)",[2092,97034,97035],{"encoding":2094},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[55,97037,97038,97039,4445,97069,1445,97072,97085,97086,97121,97122,97139,97140,97169,97170,97173],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[1647,97040,97042],{"className":97041},[2059],[2061,97043,97044],{"xmlns":2063},[2065,97045,97046,97066],{},[2068,97047,97048,97050,97056,97058,97064],{},[2075,97049,2561],{"stretchy":2083},[2348,97051,97052,97054],{},[2071,97053,2861],{},[2210,97055,638],{},[2075,97057,2361],{"separator":2360},[2348,97059,97060,97062],{},[2071,97061,2861],{},[2210,97063,646],{},[2075,97065,2576],{"stretchy":2083},[2092,97067,97068],{"encoding":2094},"[Q_1, Q_2]",[95,97070,97071],{},"stejnou úrovní uspokojení",[1647,97073,97075],{"className":97074},[2059],[2061,97076,97077],{"xmlns":2063},[2065,97078,97079,97083],{},[2068,97080,97081],{},[2071,97082,2222],{},[2092,97084,2222],{"encoding":2094},". Křivky užitečnosti vznikají jako průsečnice plochy ",[1647,97087,97089],{"className":97088},[2059],[2061,97090,97091],{"xmlns":2063},[2065,97092,97093,97119],{},[2068,97094,97095,97097,97099,97101,97103,97109,97111,97117],{},[2071,97096,10871],{},[2075,97098,2077],{},[2071,97100,10871],{},[2075,97102,2084],{"stretchy":2083},[2348,97104,97105,97107],{},[2071,97106,2861],{},[2210,97108,638],{},[2075,97110,2361],{"separator":2360},[2348,97112,97113,97115],{},[2071,97114,2861],{},[2210,97116,646],{},[2075,97118,2090],{"stretchy":2083},[2092,97120,93209],{"encoding":2094}," s rovinami ",[1647,97123,97125],{"className":97124},[2059],[2061,97126,97127],{"xmlns":2063},[2065,97128,97129,97137],{},[2068,97130,97131,97133,97135],{},[2071,97132,10871],{},[2075,97134,2077],{},[2071,97136,2222],{},[2092,97138,92423],{"encoding":2094}," rovnoběžnými s rovinou ",[1647,97141,97143],{"className":97142},[2059],[2061,97144,97145],{"xmlns":2063},[2065,97146,97147,97167],{},[2068,97148,97149,97151,97157,97159,97165],{},[2075,97150,2084],{"stretchy":2083},[2348,97152,97153,97155],{},[2071,97154,2861],{},[2210,97156,638],{},[2075,97158,2361],{"separator":2360},[2348,97160,97161,97163],{},[2071,97162,2861],{},[2210,97164,646],{},[2075,97166,2090],{"stretchy":2083},[2092,97168,95372],{"encoding":2094}," (obrázek 6.2). Jsou v příbuznosti s ",[95,97171,97172],{},"izokvantami"," produkčních funkcí.",[55,97175,97176],{},[3982,97177,97178,97179,95250,97197,97215,97216,195],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[1647,97180,97182],{"className":97181},[2059],[2061,97183,97184],{"xmlns":2063},[2065,97185,97186,97194],{},[2068,97187,97188,97190,97192],{},[2071,97189,69],{},[2075,97191,3521],{},[2071,97193,2179],{},[2092,97195,97196],{"encoding":2094},"a \u003C b",[1647,97198,97200],{"className":97199},[2059],[2061,97201,97202],{"xmlns":2063},[2065,97203,97204,97212],{},[2068,97205,97206,97208,97210],{},[2071,97207,69],{},[2075,97209,3482],{},[2071,97211,2179],{},[2092,97213,97214],{"encoding":2094},"a > b"," (vpravo); různé hladiny ",[1647,97217,97219],{"className":97218},[2059],[2061,97220,97221],{"xmlns":2063},[2065,97222,97223,97247],{},[2068,97224,97225,97231,97233,97239,97241],{},[2348,97226,97227,97229],{},[2071,97228,2222],{},[2210,97230,630],{},[2075,97232,3521],{},[2348,97234,97235,97237],{},[2071,97236,2222],{},[2210,97238,638],{},[2075,97240,3521],{},[2348,97242,97243,97245],{},[2071,97244,2222],{},[2210,97246,646],{},[2092,97248,97249],{"encoding":2094},"c_0 \u003C c_1 \u003C c_2",[55,97251,97252],{},[3982,97253,97254,97255,97284,97285,97343,97344,97362],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[1647,97256,97258],{"className":97257},[2059],[2061,97259,97260],{"xmlns":2063},[2065,97261,97262,97282],{},[2068,97263,97264,97266,97272,97274,97280],{},[2075,97265,2084],{"stretchy":2083},[2348,97267,97268,97270],{},[2071,97269,2861],{},[2210,97271,638],{},[2075,97273,2361],{"separator":2360},[2348,97275,97276,97278],{},[2071,97277,2861],{},[2210,97279,646],{},[2075,97281,2090],{"stretchy":2083},[2092,97283,95372],{"encoding":2094},"; body ",[1647,97286,97288],{"className":97287},[2059],[2061,97289,97290],{"xmlns":2063},[2065,97291,97292,97340],{},[2068,97293,97294,97296,97298,97300,97306,97308,97314,97316,97318,97320,97322,97324,97330,97332,97338],{},[2071,97295,4342],{},[2075,97297,2077],{},[2075,97299,2561],{"stretchy":2083},[2348,97301,97302,97304],{},[2071,97303,69],{},[2210,97305,638],{},[2075,97307,2361],{"separator":2360},[2348,97309,97310,97312],{},[2071,97311,69],{},[2210,97313,646],{},[2075,97315,2576],{"stretchy":2083},[2075,97317,2361],{"separator":2360},[2071,97319,25992],{},[2075,97321,2077],{},[2075,97323,2561],{"stretchy":2083},[2348,97325,97326,97328],{},[2071,97327,2179],{},[2210,97329,638],{},[2075,97331,2361],{"separator":2360},[2348,97333,97334,97336],{},[2071,97335,2179],{},[2210,97337,646],{},[2075,97339,2576],{"stretchy":2083},[2092,97341,97342],{"encoding":2094},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[1647,97345,97347],{"className":97346},[2059],[2061,97348,97349],{"xmlns":2063},[2065,97350,97351,97359],{},[2068,97352,97353,97355,97357],{},[2071,97354,2849],{},[2075,97356,2361],{"separator":2360},[2071,97358,4271],{},[2092,97360,97361],{"encoding":2094},"C, D"," na vyšší hladině.",[1023,97364,97365],{},[55,97366,97367,97369,97370,97432,97433,97477,97478,97512,97513,28930,97531,97512,97585,28930,97603,97679],{},[1647,97368,56993],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[1647,97371,97373],{"className":97372},[2059],[2061,97374,97375],{"xmlns":2063},[2065,97376,97377,97429],{},[2068,97378,97379,97381,97383,97389,97391,97397,97399,97401,97415],{},[2071,97380,10871],{},[2075,97382,2084],{"stretchy":2083},[2348,97384,97385,97387],{},[2071,97386,2861],{},[2210,97388,638],{},[2075,97390,2361],{"separator":2360},[2348,97392,97393,97395],{},[2071,97394,2861],{},[2210,97396,646],{},[2075,97398,2090],{"stretchy":2083},[2075,97400,2077],{},[9252,97402,97403,97405,97407],{},[2071,97404,2861],{},[2210,97406,638],{},[2068,97408,97409,97411,97413],{},[2210,97410,638],{},[2071,97412,4761],{"mathvariant":2450},[2210,97414,662],{},[9252,97416,97417,97419,97421],{},[2071,97418,2861],{},[2210,97420,646],{},[2068,97422,97423,97425,97427],{},[2210,97424,654],{},[2071,97426,4761],{"mathvariant":2450},[2210,97428,662],{},[2092,97430,97431],{"encoding":2094},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[1647,97434,97436],{"className":97435},[2059],[2061,97437,97438],{"xmlns":2063},[2065,97439,97440,97474],{},[2068,97441,97442,97456,97470,97472],{},[9252,97443,97444,97446,97448],{},[2071,97445,2861],{},[2210,97447,638],{},[2068,97449,97450,97452,97454],{},[2210,97451,638],{},[2071,97453,4761],{"mathvariant":2450},[2210,97455,662],{},[9252,97457,97458,97460,97462],{},[2071,97459,2861],{},[2210,97461,646],{},[2068,97463,97464,97466,97468],{},[2210,97465,654],{},[2071,97467,4761],{"mathvariant":2450},[2210,97469,662],{},[2075,97471,2077],{},[2071,97473,2222],{},[2092,97475,97476],{"encoding":2094},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[1647,97479,97481],{"className":97480},[2059],[2061,97482,97483],{"xmlns":2063},[2065,97484,97485,97509],{},[2068,97486,97487,97493,97501,97503],{},[2348,97488,97489,97491],{},[2071,97490,2861],{},[2210,97492,638],{},[9252,97494,97495,97497,97499],{},[2071,97496,2861],{},[2210,97498,646],{},[2210,97500,654],{},[2075,97502,2077],{},[2205,97504,97505,97507],{},[2071,97506,2222],{},[2210,97508,662],{},[2092,97510,97511],{"encoding":2094},"Q_1 Q_2^{3} = c^{4}",". Pro ",[1647,97514,97516],{"className":97515},[2059],[2061,97517,97518],{"xmlns":2063},[2065,97519,97520,97528],{},[2068,97521,97522,97524,97526],{},[2071,97523,2222],{},[2075,97525,2077],{},[2210,97527,638],{},[2092,97529,97530],{"encoding":2094},"c = 1",[1647,97532,97534],{"className":97533},[2059],[2061,97535,97536],{"xmlns":2063},[2065,97537,97538,97582],{},[2068,97539,97540,97546,97548,97564,97566],{},[2348,97541,97542,97544],{},[2071,97543,2861],{},[2210,97545,646],{},[2075,97547,2077],{},[9252,97549,97550,97552,97554],{},[2071,97551,2861],{},[2210,97553,638],{},[2068,97555,97556,97558,97560,97562],{},[2075,97557,2303],{},[2210,97559,638],{},[2071,97561,4761],{"mathvariant":2450},[2210,97563,654],{},[2075,97565,2077],{},[2400,97567,97568],{"scriptlevel":630,"displaystyle":2360},[2403,97569,97570,97572],{},[2210,97571,638],{},[86496,97573,97574,97580],{},[2348,97575,97576,97578],{},[2071,97577,2861],{},[2210,97579,638],{},[2210,97581,654],{},[2092,97583,97584],{"encoding":2094},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[1647,97586,97588],{"className":97587},[2059],[2061,97589,97590],{"xmlns":2063},[2065,97591,97592,97600],{},[2068,97593,97594,97596,97598],{},[2071,97595,2222],{},[2075,97597,2077],{},[2210,97599,646],{},[2092,97601,97602],{"encoding":2094},"c = 2",[1647,97604,97606],{"className":97605},[2059],[2061,97607,97608],{"xmlns":2063},[2065,97609,97610,97676],{},[2068,97611,97612,97618,97620,97632,97634,97650,97652],{},[2348,97613,97614,97616],{},[2071,97615,2861],{},[2210,97617,646],{},[2075,97619,2077],{},[2205,97621,97622,97624],{},[2210,97623,646],{},[2068,97625,97626,97628,97630],{},[2210,97627,662],{},[2071,97629,4761],{"mathvariant":2450},[2210,97631,654],{},[2075,97633,3251],{},[9252,97635,97636,97638,97640],{},[2071,97637,2861],{},[2210,97639,638],{},[2068,97641,97642,97644,97646,97648],{},[2075,97643,2303],{},[2210,97645,638],{},[2071,97647,4761],{"mathvariant":2450},[2210,97649,654],{},[2075,97651,2077],{},[2400,97653,97654],{"scriptlevel":630,"displaystyle":2360},[2403,97655,97656,97666],{},[2068,97657,97658,97660],{},[2210,97659,646],{},[86496,97661,97662,97664],{},[2210,97663,646],{},[2210,97665,654],{},[86496,97667,97668,97674],{},[2348,97669,97670,97672],{},[2071,97671,2861],{},[2210,97673,638],{},[2210,97675,654],{},[2092,97677,97678],{"encoding":2094},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[609,97681,97683],{"id":97682},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[55,97685,97686],{},[58,97687],{"alt":97688,"className":97689,"src":97690},"imek-ic-4vlastnosti-anotovane",[62,63],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1023,97692,97693,97702,97749,97793,97799,97805],{},[55,97694,97695,97697,97698,97701],{},[1647,97696,4499],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[95,97699,97700],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[55,97703,97704],{},[1647,97705,97707],{"className":97706},[2059],[2061,97708,97709],{"xmlns":2063},[2065,97710,97711,97746],{},[2068,97712,97713,97716,97718,97720,97722,97724,97742,97744],{},[2071,97714,97715],{"mathvariant":2450},"tg",[2075,97717,60670],{},[2071,97719,21601],{},[2075,97721,2077],{},[2075,97723,2303],{},[2403,97725,97726,97734],{},[9252,97727,97728,97730,97732],{},[2071,97729,10871],{},[2210,97731,638],{},[2075,97733,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,97735,97736,97738,97740],{},[2071,97737,10871],{},[2210,97739,646],{},[2075,97741,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,97743,3521],{},[2210,97745,630],{},[2092,97747,97748],{"encoding":2094},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[55,97750,97751,97752,97792],{},"(derivace implicitně zadané funkce ",[1647,97753,97755],{"className":97754},[2059],[2061,97756,97757],{"xmlns":2063},[2065,97758,97759,97789],{},[2068,97760,97761,97763,97765,97771,97773,97779,97781,97783,97785,97787],{},[2071,97762,10871],{},[2075,97764,2084],{"stretchy":2083},[2348,97766,97767,97769],{},[2071,97768,2861],{},[2210,97770,638],{},[2075,97772,2361],{"separator":2360},[2348,97774,97775,97777],{},[2071,97776,2861],{},[2210,97778,646],{},[2075,97780,2090],{"stretchy":2083},[2075,97782,2303],{},[2071,97784,2222],{},[2075,97786,2077],{},[2210,97788,630],{},[2092,97790,97791],{"encoding":2094},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[55,97794,97795,97798],{},[95,97796,97797],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[55,97800,97801,97804],{},[95,97802,97803],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[55,97806,97807,97810,97811,97829,97830,97846,97847,97850],{},[95,97808,97809],{},"4° Konvexní."," Pro každé dva body ",[1647,97812,97814],{"className":97813},[2059],[2061,97815,97816],{"xmlns":2063},[2065,97817,97818,97826],{},[2068,97819,97820,97822,97824],{},[2071,97821,4342],{},[2075,97823,2361],{"separator":2360},[2071,97825,25992],{},[2092,97827,97828],{"encoding":2094},"A, B"," na téže křivce leží vnitřní body úsečky ",[1647,97831,97833],{"className":97832},[2059],[2061,97834,97835],{"xmlns":2063},[2065,97836,97837,97843],{},[2068,97838,97839,97841],{},[2071,97840,4342],{},[2071,97842,25992],{},[2092,97844,97845],{"encoding":2094},"AB"," ve ",[95,97848,97849],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[55,97852,97853],{},[3982,97854,97855,97856,97891,97892,195],{},"Obrázek 6.6 — klesající a konvexní průběh ",[1647,97857,97859],{"className":97858},[2059],[2061,97860,97861],{"xmlns":2063},[2065,97862,97863,97889],{},[2068,97864,97865,97867,97869,97875,97877,97883,97885,97887],{},[2071,97866,10871],{},[2075,97868,2084],{"stretchy":2083},[2348,97870,97871,97873],{},[2071,97872,2861],{},[2210,97874,638],{},[2075,97876,2361],{"separator":2360},[2348,97878,97879,97881],{},[2071,97880,2861],{},[2210,97882,646],{},[2075,97884,2090],{"stretchy":2083},[2075,97886,2077],{},[2071,97888,2222],{},[2092,97890,10896],{"encoding":2094}," s tečnou se sklonem ",[1647,97893,97895],{"className":97894},[2059],[2061,97896,97897],{"xmlns":2063},[2065,97898,97899,97907],{},[2068,97900,97901,97903,97905],{},[2071,97902,97715],{"mathvariant":2450},[2075,97904,60670],{},[2071,97906,21601],{},[2092,97908,97909],{"encoding":2094},"\\operatorname{tg}\\alpha",[84,97911,97913],{"id":97912},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[55,97915,97916,1445,97919,11156,97932,97935],{},[95,97917,97918],{},"Mezní míra komoditní substituce",[1647,97920,97922],{"className":97921},[2059],[2061,97923,97924],{"xmlns":2063},[2065,97925,97926,97930],{},[2068,97927,97928],{},[2363,97929,11733],{},[2092,97931,31265],{"encoding":2094},[95,97933,97934],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[1647,97937,97939],{"className":97938},[2059],[2061,97940,97941],{"xmlns":2063,"display":31093},[2065,97942,97943,98030],{},[23493,97944,97945],{"width":31098},[23498,97946,97947,97949,98023,98025],{},[23501,97948],{"width":31103},[23501,97950,97951],{},[2068,97952,97953,97955,97957,97959,97961,97967,97969,97975,97977,97979,98001,98003,98021],{},[2363,97954,11733],{},[2075,97956,2077],{},[2363,97958,11733],{},[2075,97960,2084],{"stretchy":2083},[2348,97962,97963,97965],{},[2071,97964,2861],{},[2210,97966,638],{},[2075,97968,2361],{"separator":2360},[2348,97970,97971,97973],{},[2071,97972,2861],{},[2210,97974,646],{},[2075,97976,2090],{"stretchy":2083},[2075,97978,2077],{},[2403,97980,97981,97991],{},[2068,97982,97983,97985],{},[2071,97984,2890],{},[2348,97986,97987,97989],{},[2071,97988,10871],{},[2210,97990,638],{},[2068,97992,97993,97995],{},[2071,97994,2890],{},[2348,97996,97997,97999],{},[2071,97998,10871],{},[2210,98000,646],{},[2075,98002,2077],{},[2403,98004,98005,98013],{},[9252,98006,98007,98009,98011],{},[2071,98008,10871],{},[2210,98010,638],{},[2075,98012,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,98014,98015,98017,98019],{},[2071,98016,10871],{},[2210,98018,646],{},[2075,98020,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2071,98022,195],{"mathvariant":2450},[23501,98024],{"width":31103},[23501,98026,98027],{},[2363,98028,98029],{},"(6.9)",[2092,98031,98032],{"encoding":2094},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[55,98034,98035,98036,98070,98071,98103,98104,98139,98140,98153],{},"Geometricky: ",[1647,98037,98039],{"className":98038},[2059],[2061,98040,98041],{"xmlns":2063},[2065,98042,98043,98067],{},[2068,98044,98045,98047],{},[2075,98046,2303],{},[2400,98048,98049],{"scriptlevel":630,"displaystyle":2083},[2403,98050,98051,98059],{},[9252,98052,98053,98055,98057],{},[2071,98054,10871],{},[2210,98056,638],{},[2075,98058,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,98060,98061,98063,98065],{},[2071,98062,10871],{},[2210,98064,646],{},[2075,98066,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,98068,98069],{"encoding":2094},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[1647,98072,98074],{"className":98073},[2059],[2061,98075,98076],{"xmlns":2063},[2065,98077,98078,98100],{},[2068,98079,98080,98086,98088,98090,98092,98098],{},[2348,98081,98082,98084],{},[2071,98083,2861],{},[2210,98085,646],{},[2075,98087,2077],{},[2071,98089,2080],{},[2075,98091,2084],{"stretchy":2083},[2348,98093,98094,98096],{},[2071,98095,2861],{},[2210,98097,638],{},[2075,98099,2090],{"stretchy":2083},[2092,98101,98102],{"encoding":2094},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[1647,98105,98107],{"className":98106},[2059],[2061,98108,98109],{"xmlns":2063},[2065,98110,98111,98137],{},[2068,98112,98113,98115,98117,98123,98125,98131,98133,98135],{},[2071,98114,10871],{},[2075,98116,2084],{"stretchy":2083},[2348,98118,98119,98121],{},[2071,98120,2861],{},[2210,98122,638],{},[2075,98124,2361],{"separator":2360},[2348,98126,98127,98129],{},[2071,98128,2861],{},[2210,98130,646],{},[2075,98132,2090],{"stretchy":2083},[2075,98134,2077],{},[2071,98136,2222],{},[2092,98138,10896],{"encoding":2094},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[1647,98141,98143],{"className":98142},[2059],[2061,98144,98145],{"xmlns":2063},[2065,98146,98147,98151],{},[2068,98148,98149],{},[2363,98150,11733],{},[2092,98152,31265],{"encoding":2094}," chápeme jako velikost kompenzace.",[1023,98155,98156],{},[55,98157,98158,98160,98161,8189,98193,98231,98232,98249,98250,98267],{},[1647,98159,4243],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[1647,98162,98164],{"className":98163},[2059],[2061,98165,98166],{"xmlns":2063},[2065,98167,98168,98190],{},[2068,98169,98170,98172,98174,98180,98182,98188],{},[2363,98171,11733],{},[2075,98173,2084],{"stretchy":2083},[2348,98175,98176,98178],{},[2071,98177,2861],{},[2210,98179,638],{},[2075,98181,2361],{"separator":2360},[2348,98183,98184,98186],{},[2071,98185,2861],{},[2210,98187,646],{},[2075,98189,2090],{"stretchy":2083},[2092,98191,98192],{"encoding":2094},"\\text{MRCS}(Q_1, Q_2)",[95,98194,98195,98196,32030,98213,98230],{},"míra, jakou je spotřebitel ochoten zaměnit ",[1647,98197,98199],{"className":98198},[2059],[2061,98200,98201],{"xmlns":2063},[2065,98202,98203,98211],{},[2068,98204,98205],{},[2348,98206,98207,98209],{},[2071,98208,2861],{},[2210,98210,638],{},[2092,98212,32029],{"encoding":2094},[1647,98214,98216],{"className":98215},[2059],[2061,98217,98218],{"xmlns":2063},[2065,98219,98220,98228],{},[2068,98221,98222],{},[2348,98223,98224,98226],{},[2071,98225,2861],{},[2210,98227,646],{},[2092,98229,32048],{"encoding":2094}," při zachování užitečnosti"," — tedy kolik jednotek ",[1647,98233,98235],{"className":98234},[2059],[2061,98236,98237],{"xmlns":2063},[2065,98238,98239,98247],{},[2068,98240,98241],{},[2348,98242,98243,98245],{},[2071,98244,2861],{},[2210,98246,646],{},[2092,98248,32048],{"encoding":2094}," „obětuje\" za jednu jednotku ",[1647,98251,98253],{"className":98252},[2059],[2061,98254,98255],{"xmlns":2063},[2065,98256,98257,98265],{},[2068,98258,98259],{},[2348,98260,98261,98263],{},[2071,98262,2861],{},[2210,98264,638],{},[2092,98266,32029],{"encoding":2094}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[55,98269,98270,98271,32971],{},"Pro obecnou změnu ",[1647,98272,98274],{"className":98273},[2059],[2061,98275,98276],{"xmlns":2063},[2065,98277,98278,98288],{},[2068,98279,98280,98282],{},[2071,98281,2273],{"mathvariant":2450},[2348,98283,98284,98286],{},[2071,98285,2861],{},[2210,98287,638],{},[2092,98289,98290],{"encoding":2094},"\\mathrm{d} Q_1",[1647,98292,98294],{"className":98293},[2059],[2061,98295,98296],{"xmlns":2063,"display":31093},[2065,98297,98298,98351],{},[23493,98299,98300],{"width":31098},[23498,98301,98302,98304,98344,98346],{},[23501,98303],{"width":31103},[23501,98305,98306],{},[2068,98307,98308,98310,98316,98318,98320,98326,98328,98330,98332,98334,98336,98342],{},[2071,98309,2961],{"mathvariant":2450},[2348,98311,98312,98314],{},[2071,98313,2861],{},[2210,98315,646],{},[2075,98317,2803],{},[2071,98319,2273],{"mathvariant":2450},[2348,98321,98322,98324],{},[2071,98323,2861],{},[2210,98325,646],{},[2075,98327,2077],{},[2075,98329,2303],{},[2363,98331,11733],{},[2075,98333,3251],{},[2071,98335,2273],{"mathvariant":2450},[2348,98337,98338,98340],{},[2071,98339,2861],{},[2210,98341,638],{},[2075,98343,2361],{"separator":2360},[23501,98345],{"width":31103},[23501,98347,98348],{},[2363,98349,98350],{},"(6.10)",[2092,98352,98353],{"encoding":2094},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[1647,98355,98357],{"className":98356},[2059],[2061,98358,98359],{"xmlns":2063,"display":31093},[2065,98360,98361,98408],{},[23493,98362,98363],{"width":31098},[23498,98364,98365,98367,98401,98403],{},[23501,98366],{"width":31103},[23501,98368,98369],{},[2068,98370,98371,98373,98379,98381,98383,98389,98391,98393,98399],{},[2071,98372,2273],{"mathvariant":2450},[2348,98374,98375,98377],{},[2071,98376,2861],{},[2210,98378,638],{},[2075,98380,2077],{},[2075,98382,2303],{},[2403,98384,98385,98387],{},[2210,98386,638],{},[2363,98388,11733],{},[2363,98390,3061],{},[2071,98392,2273],{"mathvariant":2450},[2348,98394,98395,98397],{},[2071,98396,2861],{},[2210,98398,646],{},[2071,98400,195],{"mathvariant":2450},[23501,98402],{"width":31103},[23501,98404,98405],{},[2363,98406,98407],{},"(6.11)",[2092,98409,98410],{"encoding":2094},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1023,98412,98413,98479,98596],{},[55,98414,98415,98417,98418,32971],{},[1647,98416,56993],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[1647,98419,98421],{"className":98420},[2059],[2061,98422,98423],{"xmlns":2063},[2065,98424,98425,98477],{},[2068,98426,98427,98429,98431,98437,98439,98445,98447,98449,98463],{},[2071,98428,10871],{},[2075,98430,2084],{"stretchy":2083},[2348,98432,98433,98435],{},[2071,98434,2861],{},[2210,98436,638],{},[2075,98438,2361],{"separator":2360},[2348,98440,98441,98443],{},[2071,98442,2861],{},[2210,98444,646],{},[2075,98446,2090],{"stretchy":2083},[2075,98448,2077],{},[9252,98450,98451,98453,98455],{},[2071,98452,2861],{},[2210,98454,638],{},[2068,98456,98457,98459,98461],{},[2210,98458,638],{},[2071,98460,4761],{"mathvariant":2450},[2210,98462,646],{},[9252,98464,98465,98467,98469],{},[2071,98466,2861],{},[2210,98468,646],{},[2068,98470,98471,98473,98475],{},[2210,98472,638],{},[2071,98474,4761],{"mathvariant":2450},[2210,98476,646],{},[2092,98478,32970],{"encoding":2094},[55,98480,98481],{},[1647,98482,98484],{"className":98483},[2059],[2061,98485,98486],{"xmlns":2063},[2065,98487,98488,98594],{},[2068,98489,98490,98492,98494,98576,98578,98592],{},[2363,98491,11733],{},[2075,98493,2077],{},[2403,98495,98496,98536],{},[2068,98497,98498,98506,98522],{},[2400,98499,98500],{"scriptlevel":630,"displaystyle":2083},[2403,98501,98502,98504],{},[2210,98503,638],{},[2210,98505,646],{},[9252,98507,98508,98510,98512],{},[2071,98509,2861],{},[2210,98511,638],{},[2068,98513,98514,98516,98518,98520],{},[2075,98515,2303],{},[2210,98517,638],{},[2071,98519,4761],{"mathvariant":2450},[2210,98521,646],{},[9252,98523,98524,98526,98528],{},[2071,98525,2861],{},[2210,98527,646],{},[2068,98529,98530,98532,98534],{},[2210,98531,638],{},[2071,98533,4761],{"mathvariant":2450},[2210,98535,646],{},[2068,98537,98538,98546,98560],{},[2400,98539,98540],{"scriptlevel":630,"displaystyle":2083},[2403,98541,98542,98544],{},[2210,98543,638],{},[2210,98545,646],{},[9252,98547,98548,98550,98552],{},[2071,98549,2861],{},[2210,98551,638],{},[2068,98553,98554,98556,98558],{},[2210,98555,638],{},[2071,98557,4761],{"mathvariant":2450},[2210,98559,646],{},[9252,98561,98562,98564,98566],{},[2071,98563,2861],{},[2210,98565,646],{},[2068,98567,98568,98570,98572,98574],{},[2075,98569,2303],{},[2210,98571,638],{},[2071,98573,4761],{"mathvariant":2450},[2210,98575,646],{},[2075,98577,2077],{},[2403,98579,98580,98586],{},[2348,98581,98582,98584],{},[2071,98583,2861],{},[2210,98585,646],{},[2348,98587,98588,98590],{},[2071,98589,2861],{},[2210,98591,638],{},[2071,98593,195],{"mathvariant":2450},[2092,98595,33089],{"encoding":2094},[55,98597,33092,98598,2999,98641,33140,98643,98662],{},[1647,98599,98601],{"className":98600},[2059],[2061,98602,98603],{"xmlns":2063},[2065,98604,98605,98639],{},[2068,98606,98607,98609,98611,98613,98615,98617,98619,98621,98629,98631],{},[2363,98608,11733],{},[2075,98610,2084],{"stretchy":2083},[2210,98612,33108],{},[2075,98614,2361],{"separator":2360},[2210,98616,16845],{},[2075,98618,2090],{"stretchy":2083},[2075,98620,2077],{},[2400,98622,98623],{"scriptlevel":630,"displaystyle":2083},[2403,98624,98625,98627],{},[2210,98626,16845],{},[2210,98628,33108],{},[2075,98630,2077],{},[2400,98632,98633],{"scriptlevel":630,"displaystyle":2083},[2403,98634,98635,98637],{},[2210,98636,670],{},[2210,98638,654],{},[2092,98640,33137],{"encoding":2094},[3982,98642,9302],{},[1647,98644,98646],{"className":98645},[2059],[2061,98647,98648],{"xmlns":2063},[2065,98649,98650,98660],{},[2068,98651,98652],{},[2400,98653,98654],{"scriptlevel":630,"displaystyle":2083},[2403,98655,98656,98658],{},[2210,98657,670],{},[2210,98659,654],{},[2092,98661,33160],{"encoding":2094}," jednotky, aby se užitečnost zachovala.",[55,98664,98665,98666,98670],{},"(Paralelou je ",[69,98667,98669],{"className":98668,"dataFsResolvedFilePath":10942,"href":10943},[62],"mezní míra technické substituce MRTS"," z produkční teorie.)",[84,98672,98674],{"id":98673},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[55,98676,98677,98678,98681],{},"Rámcově se v kapitole 6 studují ",[95,98679,98680],{},"dvě vázané optimalizační úlohy"," s užitečností:",[89,98683,98684,98820],{},[92,98685,98686,98688,98689,11288,98720,1445,98723,98772,98773,195],{},[95,98687,31279],{}," — maximalizace ",[1647,98690,98692],{"className":98691},[2059],[2061,98693,98694],{"xmlns":2063},[2065,98695,98696,98718],{},[2068,98697,98698,98700,98702,98708,98710,98716],{},[2071,98699,10871],{},[2075,98701,2084],{"stretchy":2083},[2348,98703,98704,98706],{},[2071,98705,2861],{},[2210,98707,638],{},[2075,98709,2361],{"separator":2360},[2348,98711,98712,98714],{},[2071,98713,2861],{},[2210,98715,646],{},[2075,98717,2090],{"stretchy":2083},[2092,98719,19083],{"encoding":2094},[95,98721,98722],{},"rozpočtovém omezení",[1647,98724,98726],{"className":98725},[2059],[2061,98727,98728],{"xmlns":2063},[2065,98729,98730,98770],{},[2068,98731,98732,98738,98740,98748,98754,98756,98764],{},[2205,98733,98734,98736],{},[2071,98735,9214],{},[2075,98737,4441],{},[2075,98739,2077],{},[9252,98741,98742,98744,98746],{},[2071,98743,575],{},[2210,98745,638],{},[2075,98747,4441],{},[2348,98749,98750,98752],{},[2071,98751,2861],{},[2210,98753,638],{},[2075,98755,2176],{},[9252,98757,98758,98760,98762],{},[2071,98759,575],{},[2210,98761,646],{},[2075,98763,4441],{},[2348,98765,98766,98768],{},[2071,98767,2861],{},[2210,98769,646],{},[2092,98771,20036],{"encoding":2094},". Výstupem je Marshallova poptávka ",[1647,98774,98776],{"className":98775},[2059],[2061,98777,98778],{"xmlns":2063},[2065,98779,98780,98818],{},[2068,98781,98782,98788,98790,98796,98798,98804,98806,98812,98814,98816],{},[2348,98783,98784,98786],{},[2071,98785,2861],{},[2071,98787,20528],{},[2075,98789,2077],{},[2348,98791,98792,98794],{},[2071,98793,4271],{},[2071,98795,20528],{},[2075,98797,2084],{"stretchy":2083},[2348,98799,98800,98802],{},[2071,98801,575],{},[2210,98803,638],{},[2075,98805,2361],{"separator":2360},[2348,98807,98808,98810],{},[2071,98809,575],{},[2210,98811,646],{},[2075,98813,2361],{"separator":2360},[2071,98815,9214],{},[2075,98817,2090],{"stretchy":2083},[2092,98819,39481],{"encoding":2094},[92,98821,98822,30928,98825,30971,98871,98888,98889,195],{},[95,98823,98824],{},"Duální úloha",[1647,98826,98828],{"className":98827},[2059],[2061,98829,98830],{"xmlns":2063},[2065,98831,98832,98868],{},[2068,98833,98834,98836,98838,98846,98852,98854,98862],{},[2071,98835,554],{},[2075,98837,2077],{},[9252,98839,98840,98842,98844],{},[2071,98841,575],{},[2210,98843,638],{},[2075,98845,4441],{},[2348,98847,98848,98850],{},[2071,98849,2861],{},[2210,98851,638],{},[2075,98853,2176],{},[9252,98855,98856,98858,98860],{},[2071,98857,575],{},[2210,98859,646],{},[2075,98861,4441],{},[2348,98863,98864,98866],{},[2071,98865,2861],{},[2210,98867,646],{},[2092,98869,98870],{"encoding":2094},"E = P_1^* Q_1 + P_2^* Q_2",[1647,98872,98874],{"className":98873},[2059],[2061,98875,98876],{"xmlns":2063},[2065,98877,98878,98886],{},[2068,98879,98880],{},[2205,98881,98882,98884],{},[2071,98883,10871],{},[2075,98885,4441],{},[2092,98887,30989],{"encoding":2094},". Výstupem je Hicksova poptávka ",[1647,98890,98892],{"className":98891},[2059],[2061,98893,98894],{"xmlns":2063},[2065,98895,98896,98934],{},[2068,98897,98898,98904,98906,98912,98914,98920,98922,98928,98930,98932],{},[2348,98899,98900,98902],{},[2071,98901,2861],{},[2071,98903,20528],{},[2075,98905,2077],{},[2348,98907,98908,98910],{},[2071,98909,4271],{},[2071,98911,20528],{},[2075,98913,2084],{"stretchy":2083},[2348,98915,98916,98918],{},[2071,98917,575],{},[2210,98919,638],{},[2075,98921,2361],{"separator":2360},[2348,98923,98924,98926],{},[2071,98925,575],{},[2210,98927,646],{},[2075,98929,2361],{"separator":2360},[2071,98931,10871],{},[2075,98933,2090],{"stretchy":2083},[2092,98935,20561],{"encoding":2094},[55,98937,98938,98939,98942,98943,1445,98946,98985],{},"Obě úlohy se řeší ",[69,98940,30994],{"className":98941,"dataFsResolvedFilePath":12193,"href":12194},[62]," a vedou na ",[95,98944,98945],{},"tentýž bod dotyku",[1647,98947,98949],{"className":98948},[2059],[2061,98950,98951],{"xmlns":2063},[2065,98952,98953,98983],{},[2068,98954,98955,98961,98963,98971,98973,98981],{},[2205,98956,98957,98959],{},[2071,98958,2861],{},[2075,98960,4441],{},[2075,98962,2561],{"stretchy":2083},[9252,98964,98965,98967,98969],{},[2071,98966,2861],{},[2210,98968,638],{},[2075,98970,4441],{},[2075,98972,2361],{"separator":2360},[9252,98974,98975,98977,98979],{},[2071,98976,2861],{},[2210,98978,646],{},[2075,98980,4441],{},[2075,98982,2576],{"stretchy":2083},[2092,98984,31354],{"encoding":2094}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[1647,98987,98989],{"className":98988},[2059],[2061,98990,98991],{"xmlns":2063,"display":31093},[2065,98992,98993,99039],{},[2068,98994,98995,98997,98999,99017,99019,99037],{},[2363,98996,11733],{},[2075,98998,2077],{},[2403,99000,99001,99009],{},[9252,99002,99003,99005,99007],{},[2071,99004,10871],{},[2210,99006,638],{},[2075,99008,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,99010,99011,99013,99015],{},[2071,99012,10871],{},[2210,99014,646],{},[2075,99016,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,99018,2077],{},[2403,99020,99021,99029],{},[9252,99022,99023,99025,99027],{},[2071,99024,575],{},[2210,99026,638],{},[2075,99028,4441],{},[9252,99030,99031,99033,99035],{},[2071,99032,575],{},[2210,99034,646],{},[2075,99036,4441],{},[2071,99038,195],{"mathvariant":2450},[2092,99040,99041],{"encoding":2094},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[55,99043,99044],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1023,99046,99047],{},[55,99048,99049,99051,99052,99055,99056,99059,99060,99087,99088,99122,99123,99157,99158,99201,99202,99205,99206,195],{},[1647,99050,4243],{}," Pro detailní postup viz ",[69,99053,39784],{"className":99054,"dataFsResolvedFilePath":92532,"href":92533},[62],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[95,99057,99058],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[1647,99061,99063],{"className":99062},[2059],[2061,99064,99065],{"xmlns":2063},[2065,99066,99067,99085],{},[2068,99068,99069,99071,99073,99079],{},[2071,99070,10871],{},[2075,99072,2077],{},[2348,99074,99075,99077],{},[2071,99076,2861],{},[2210,99078,638],{},[2348,99080,99081,99083],{},[2071,99082,2861],{},[2210,99084,646],{},[2092,99086,33253],{"encoding":2094}," s výsledkem ",[1647,99089,99091],{"className":99090},[2059],[2061,99092,99093],{"xmlns":2063},[2065,99094,99095,99119],{},[2068,99096,99097,99103,99105,99107,99109,99115,99117],{},[2348,99098,99099,99101],{},[2071,99100,2861],{},[2210,99102,638],{},[2075,99104,2077],{},[2210,99106,5091],{},[2075,99108,2361],{"separator":2360},[2348,99110,99111,99113],{},[2071,99112,2861],{},[2210,99114,646],{},[2075,99116,2077],{},[2210,99118,2935],{},[2092,99120,99121],{"encoding":2094},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[1647,99124,99126],{"className":99125},[2059],[2061,99127,99128],{"xmlns":2063},[2065,99129,99130,99154],{},[2068,99131,99132,99138,99140,99142,99144,99150,99152],{},[2348,99133,99134,99136],{},[2071,99135,2861],{},[2210,99137,638],{},[2075,99139,2077],{},[2210,99141,662],{},[2075,99143,2361],{"separator":2360},[2348,99145,99146,99148],{},[2071,99147,2861],{},[2210,99149,646],{},[2075,99151,2077],{},[2210,99153,638],{},[2092,99155,99156],{"encoding":2094},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[1647,99159,99161],{"className":99160},[2059],[2061,99162,99163],{"xmlns":2063},[2065,99164,99165,99199],{},[2068,99166,99167,99169,99171,99185],{},[2071,99168,10871],{},[2075,99170,2077],{},[9252,99172,99173,99175,99177],{},[2071,99174,2861],{},[2210,99176,638],{},[2068,99178,99179,99181,99183],{},[2210,99180,638],{},[2071,99182,4761],{"mathvariant":2450},[2210,99184,646],{},[9252,99186,99187,99189,99191],{},[2071,99188,2861],{},[2210,99190,646],{},[2068,99192,99193,99195,99197],{},[2210,99194,638],{},[2071,99196,4761],{"mathvariant":2450},[2210,99198,646],{},[2092,99200,36185],{"encoding":2094},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[95,99203,99204],{},"6.8–6.13"," jsou na stránce ",[69,99207,30793],{"className":99208,"dataFsResolvedFilePath":92532,"href":92533},[62],[84,99210,99212],{"id":99211},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[55,99214,99215,99216,99229,99230,99232,99233,99235,99236,99238,99239,99241,99242,99244,99245,99247,99248,1445,99250,99285,99286,99299,99300,99303,99304,99307,99308,195],{},"Každá ",[1647,99217,99219],{"className":99218},[2059],[2061,99220,99221],{"xmlns":2063},[2065,99222,99223,99227],{},[2068,99224,99225],{},[2071,99226,41153],{},[2092,99228,41153],{"encoding":2094},"-tice množství jednotlivých zboží je ",[95,99231,92563],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[95,99234,93047],{}," a současně ",[95,99237,92566],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[95,99240,92571],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[95,99243,56975],{}," (6.4) a druhé parciální derivace ",[95,99246,94930],{}," (6.5 — zákon klesající mezní užitečnosti). ",[95,99249,10858],{},[1647,99251,99253],{"className":99252},[2059],[2061,99254,99255],{"xmlns":2063},[2065,99256,99257,99283],{},[2068,99258,99259,99261,99263,99269,99271,99277,99279,99281],{},[2071,99260,10871],{},[2075,99262,2084],{"stretchy":2083},[2348,99264,99265,99267],{},[2071,99266,2861],{},[2210,99268,638],{},[2075,99270,2361],{"separator":2360},[2348,99272,99273,99275],{},[2071,99274,2861],{},[2210,99276,646],{},[2075,99278,2090],{"stretchy":2083},[2075,99280,2077],{},[2071,99282,2222],{},[2092,99284,10896],{"encoding":2094}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[1647,99287,99289],{"className":99288},[2059],[2061,99290,99291],{"xmlns":2063},[2065,99292,99293,99297],{},[2068,99294,99295],{},[2363,99296,11733],{},[2092,99298,31265],{"encoding":2094}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[95,99301,99302],{},"maximalizace užitečnosti"," a duální ",[95,99305,99306],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[69,99309,39784],{"className":99310,"dataFsResolvedFilePath":92532,"href":92533},[62],[84,99312,54178],{"id":54177},[201,99314,99315,99318,99321,99324,99327,99330,99333,99336,99339,99342],{},[92,99316,99317],{},"Co se zahrnuje pod termín užitečnost?",[92,99319,99320],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[92,99322,99323],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[92,99325,99326],{},"Jak se vypočítá mezní užitečnost?",[92,99328,99329],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[92,99331,99332],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[92,99334,99335],{},"Které jsou nejčastěji používané funkce užitečnosti?",[92,99337,99338],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[92,99340,99341],{},"Proč mají křivky užitečnosti záporný sklon?",[92,99343,99344],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[84,99346,99348],{"id":99347},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[55,99350,99351,99354,99355,87952,99397,835,99425,835,99453,99481],{},[95,99352,99353],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[1647,99356,99358],{"className":99357},[2059],[2061,99359,99360],{"xmlns":2063},[2065,99361,99362,99394],{},[2068,99363,99364,99366,99368,99374,99376,99378,99384,99386,99388],{},[2071,99365,10871],{},[2075,99367,2077],{},[2348,99369,99370,99372],{},[2071,99371,2861],{},[2210,99373,638],{},[2075,99375,2176],{},[2210,99377,69029],{},[2348,99379,99380,99382],{},[2071,99381,2861],{},[2210,99383,646],{},[2075,99385,2176],{},[2210,99387,646],{},[2348,99389,99390,99392],{},[2071,99391,2861],{},[2210,99393,654],{},[2092,99395,99396],{"encoding":2094},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[1647,99398,99400],{"className":99399},[2059],[2061,99401,99402],{"xmlns":2063},[2065,99403,99404,99422],{},[2068,99405,99406,99408,99410,99412,99414,99416,99418,99420],{},[2071,99407,10871],{},[2075,99409,2084],{"stretchy":2083},[2210,99411,662],{},[2075,99413,2361],{"separator":2360},[2210,99415,646],{},[2075,99417,2361],{"separator":2360},[2210,99419,646],{},[2075,99421,2090],{"stretchy":2083},[2092,99423,99424],{"encoding":2094},"U(4, 2, 2)",[1647,99426,99428],{"className":99427},[2059],[2061,99429,99430],{"xmlns":2063},[2065,99431,99432,99450],{},[2068,99433,99434,99436,99438,99440,99442,99444,99446,99448],{},[2071,99435,10871],{},[2075,99437,2084],{"stretchy":2083},[2210,99439,638],{},[2075,99441,2361],{"separator":2360},[2210,99443,662],{},[2075,99445,2361],{"separator":2360},[2210,99447,646],{},[2075,99449,2090],{"stretchy":2083},[2092,99451,99452],{"encoding":2094},"U(1, 4, 2)",[1647,99454,99456],{"className":99455},[2059],[2061,99457,99458],{"xmlns":2063},[2065,99459,99460,99478],{},[2068,99461,99462,99464,99466,99468,99470,99472,99474,99476],{},[2071,99463,10871],{},[2075,99465,2084],{"stretchy":2083},[2210,99467,646],{},[2075,99469,2361],{"separator":2360},[2210,99471,654],{},[2075,99473,2361],{"separator":2360},[2210,99475,638],{},[2075,99477,2090],{"stretchy":2083},[2092,99479,99480],{"encoding":2094},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[55,99483,99484,99487,99488,99540,99541,835,99567,835,99593,835,99619,835,99645,835,99671,835,99697,99723],{},[95,99485,99486],{},"6.2"," Je dána užitečnost ",[1647,99489,99491],{"className":99490},[2059],[2061,99492,99493],{"xmlns":2063},[2065,99494,99495,99537],{},[2068,99496,99497,99499,99501,99503,99517,99531],{},[2071,99498,10871],{},[2075,99500,2077],{},[2210,99502,646],{},[9252,99504,99505,99507,99509],{},[2071,99506,2861],{},[2210,99508,638],{},[2068,99510,99511,99513,99515],{},[2210,99512,638],{},[2071,99514,4761],{"mathvariant":2450},[2210,99516,654],{},[9252,99518,99519,99521,99523],{},[2071,99520,2861],{},[2210,99522,646],{},[2068,99524,99525,99527,99529],{},[2210,99526,638],{},[2071,99528,4761],{"mathvariant":2450},[2210,99530,646],{},[2348,99532,99533,99535],{},[2071,99534,2861],{},[2210,99536,654],{},[2092,99538,99539],{"encoding":2094},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[1647,99542,99544],{"className":99543},[2059],[2061,99545,99546],{"xmlns":2063},[2065,99547,99548,99564],{},[2068,99549,99550,99552,99554,99556,99558,99560,99562],{},[2075,99551,2084],{"stretchy":2083},[2210,99553,5652],{},[2075,99555,2361],{"separator":2360},[2210,99557,71067],{},[2075,99559,2361],{"separator":2360},[2210,99561,2935],{},[2075,99563,2090],{"stretchy":2083},[2092,99565,99566],{"encoding":2094},"(36, 27, 10)",[1647,99568,99570],{"className":99569},[2059],[2061,99571,99572],{"xmlns":2063},[2065,99573,99574,99590],{},[2068,99575,99576,99578,99580,99582,99584,99586,99588],{},[2075,99577,2084],{"stretchy":2083},[2210,99579,46131],{},[2075,99581,2361],{"separator":2360},[2210,99583,5672],{},[2075,99585,2361],{"separator":2360},[2210,99587,9121],{},[2075,99589,2090],{"stretchy":2083},[2092,99591,99592],{"encoding":2094},"(64, 8, 20)",[1647,99594,99596],{"className":99595},[2059],[2061,99597,99598],{"xmlns":2063},[2065,99599,99600,99616],{},[2068,99601,99602,99604,99606,99608,99610,99612,99614],{},[2075,99603,2084],{"stretchy":2083},[2210,99605,5091],{},[2075,99607,2361],{"separator":2360},[2210,99609,46131],{},[2075,99611,2361],{"separator":2360},[2210,99613,5672],{},[2075,99615,2090],{"stretchy":2083},[2092,99617,99618],{"encoding":2094},"(25, 64, 8)",[1647,99620,99622],{"className":99621},[2059],[2061,99623,99624],{"xmlns":2063},[2065,99625,99626,99642],{},[2068,99627,99628,99630,99632,99634,99636,99638,99640],{},[2075,99629,2084],{"stretchy":2083},[2210,99631,662],{},[2075,99633,2361],{"separator":2360},[2210,99635,76999],{},[2075,99637,2361],{"separator":2360},[2210,99639,678],{},[2075,99641,2090],{"stretchy":2083},[2092,99643,99644],{"encoding":2094},"(4, 125, 6)",[1647,99646,99648],{"className":99647},[2059],[2061,99649,99650],{"xmlns":2063},[2065,99651,99652,99668],{},[2068,99653,99654,99656,99658,99660,99662,99664,99666],{},[2075,99655,2084],{"stretchy":2083},[2210,99657,4087],{},[2075,99659,2361],{"separator":2360},[2210,99661,5298],{},[2075,99663,2361],{"separator":2360},[2210,99665,3583],{},[2075,99667,2090],{"stretchy":2083},[2092,99669,99670],{"encoding":2094},"(9, 40, 12)",[1647,99672,99674],{"className":99673},[2059],[2061,99675,99676],{"xmlns":2063},[2065,99677,99678,99694],{},[2068,99679,99680,99682,99684,99686,99688,99690,99692],{},[2075,99681,2084],{"stretchy":2083},[2210,99683,4087],{},[2075,99685,2361],{"separator":2360},[2210,99687,46131],{},[2075,99689,2361],{"separator":2360},[2210,99691,670],{},[2075,99693,2090],{"stretchy":2083},[2092,99695,99696],{"encoding":2094},"(9, 64, 5)",[1647,99698,99700],{"className":99699},[2059],[2061,99701,99702],{"xmlns":2063},[2065,99703,99704,99720],{},[2068,99705,99706,99708,99710,99712,99714,99716,99718],{},[2075,99707,2084],{"stretchy":2083},[2210,99709,46131],{},[2075,99711,2361],{"separator":2360},[2210,99713,5672],{},[2075,99715,2361],{"separator":2360},[2210,99717,2935],{},[2075,99719,2090],{"stretchy":2083},[2092,99721,99722],{"encoding":2094},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[55,99725,99726,99487,99729,99772,99773,99807,99808,6560,99838,99871,99872,99889,99890,99907],{},[95,99727,99728],{},"6.3",[1647,99730,99732],{"className":99731},[2059],[2061,99733,99734],{"xmlns":2063},[2065,99735,99736,99770],{},[2068,99737,99738,99740,99742,99756],{},[2071,99739,10871],{},[2075,99741,2077],{},[9252,99743,99744,99746,99748],{},[2071,99745,2861],{},[2210,99747,638],{},[2068,99749,99750,99752,99754],{},[2210,99751,638],{},[2071,99753,4761],{"mathvariant":2450},[2210,99755,646],{},[9252,99757,99758,99760,99762],{},[2071,99759,2861],{},[2210,99761,646],{},[2068,99763,99764,99766,99768],{},[2210,99765,638],{},[2071,99767,4761],{"mathvariant":2450},[2210,99769,646],{},[2092,99771,36185],{"encoding":2094},". (a) Vypočtěte užitečnost pro ",[1647,99774,99776],{"className":99775},[2059],[2061,99777,99778],{"xmlns":2063},[2065,99779,99780,99804],{},[2068,99781,99782,99788,99790,99792,99794,99800,99802],{},[2348,99783,99784,99786],{},[2071,99785,2861],{},[2210,99787,638],{},[2075,99789,2077],{},[2210,99791,3194],{},[2075,99793,2361],{"separator":2360},[2348,99795,99796,99798],{},[2071,99797,2861],{},[2210,99799,646],{},[2075,99801,2077],{},[2210,99803,50999],{},[2092,99805,99806],{"encoding":2094},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[1647,99809,99811],{"className":99810},[2059],[2061,99812,99813],{"xmlns":2063},[2065,99814,99815,99835],{},[2068,99816,99817,99819,99825,99827,99829],{},[2071,99818,2890],{},[2348,99820,99821,99823],{},[2071,99822,10871],{},[2210,99824,638],{},[2075,99826,2361],{"separator":2360},[2071,99828,2890],{},[2348,99830,99831,99833],{},[2071,99832,10871],{},[2210,99834,646],{},[2092,99836,99837],{"encoding":2094},"MU_1, MU_2",[1647,99839,99841],{"className":99840},[2059],[2061,99842,99843],{"xmlns":2063},[2065,99844,99845,99869],{},[2068,99846,99847,99853,99855,99857,99859,99865,99867],{},[2348,99848,99849,99851],{},[2071,99850,2861],{},[2210,99852,638],{},[2075,99854,2077],{},[2210,99856,3194],{},[2075,99858,2361],{"separator":2360},[2348,99860,99861,99863],{},[2071,99862,2861],{},[2210,99864,646],{},[2075,99866,2077],{},[2210,99868,50999],{},[2092,99870,99806],{"encoding":2094}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[1647,99873,99875],{"className":99874},[2059],[2061,99876,99877],{"xmlns":2063},[2065,99878,99879,99887],{},[2068,99880,99881],{},[2348,99882,99883,99885],{},[2071,99884,2861],{},[2210,99886,638],{},[2092,99888,32029],{"encoding":2094}," na 60 a poklesu ",[1647,99891,99893],{"className":99892},[2059],[2061,99894,99895],{"xmlns":2063},[2065,99896,99897,99905],{},[2068,99898,99899],{},[2348,99900,99901,99903],{},[2071,99902,2861],{},[2210,99904,646],{},[2092,99906,32048],{"encoding":2094}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[55,99909,99910,99913,99914,99975,99976,195],{},[95,99911,99912],{},"6.4"," Je dána funkce ",[1647,99915,99917],{"className":99916},[2059],[2061,99918,99919],{"xmlns":2063},[2065,99920,99921,99973],{},[2068,99922,99923,99925,99927,99933,99935,99941,99943,99945,99959],{},[2071,99924,10871],{},[2075,99926,2084],{"stretchy":2083},[2348,99928,99929,99931],{},[2071,99930,2861],{},[2210,99932,638],{},[2075,99934,2361],{"separator":2360},[2348,99936,99937,99939],{},[2071,99938,2861],{},[2210,99940,646],{},[2075,99942,2090],{"stretchy":2083},[2075,99944,2077],{},[9252,99946,99947,99949,99951],{},[2071,99948,2861],{},[2210,99950,638],{},[2068,99952,99953,99955,99957],{},[2210,99954,638],{},[2071,99956,4761],{"mathvariant":2450},[2210,99958,646],{},[9252,99960,99961,99963,99965],{},[2071,99962,2861],{},[2210,99964,646],{},[2068,99966,99967,99969,99971],{},[2210,99968,638],{},[2071,99970,4761],{"mathvariant":2450},[2210,99972,646],{},[2092,99974,32970],{"encoding":2094},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[1647,99977,99979],{"className":99978},[2059],[2061,99980,99981],{"xmlns":2063},[2065,99982,99983,100073],{},[2068,99984,99985,99987,99989,99995,99997,99999,100001,100003,100005,100007,100013,100015,100017,100019,100021,100023,100025,100027,100029,100035,100037,100039,100041,100043,100045,100047,100053,100055,100057,100059,100061,100063,100065,100071],{},[2071,99986,10871],{},[2075,99988,2084],{"stretchy":2083},[2348,99990,99991,99993],{},[2071,99992,2861],{},[2210,99994,638],{},[2075,99996,2361],{"separator":2360},[2210,99998,638],{},[2075,100000,2090],{"stretchy":2083},[2075,100002,2361],{"separator":2360},[2071,100004,10871],{},[2075,100006,2084],{"stretchy":2083},[2348,100008,100009,100011],{},[2071,100010,2861],{},[2210,100012,638],{},[2075,100014,2361],{"separator":2360},[2210,100016,646],{},[2075,100018,2090],{"stretchy":2083},[2075,100020,2361],{"separator":2360},[2071,100022,10871],{},[2075,100024,2084],{"stretchy":2083},[2210,100026,638],{},[2075,100028,2361],{"separator":2360},[2348,100030,100031,100033],{},[2071,100032,2861],{},[2210,100034,646],{},[2075,100036,2090],{"stretchy":2083},[2075,100038,2361],{"separator":2360},[2071,100040,10871],{},[2075,100042,2084],{"stretchy":2083},[2210,100044,646],{},[2075,100046,2361],{"separator":2360},[2348,100048,100049,100051],{},[2071,100050,2861],{},[2210,100052,646],{},[2075,100054,2090],{"stretchy":2083},[2075,100056,2361],{"separator":2360},[2071,100058,10871],{},[2075,100060,2084],{"stretchy":2083},[2210,100062,654],{},[2075,100064,2361],{"separator":2360},[2348,100066,100067,100069],{},[2071,100068,2861],{},[2210,100070,646],{},[2075,100072,2090],{"stretchy":2083},[2092,100074,100075],{"encoding":2094},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[55,100077,100078,99487,100081,100125,100126,100234,100235,835,100260,835,100285,100327,100328,835,100357,100382],{},[95,100079,100080],{},"6.5",[1647,100082,100084],{"className":100083},[2059],[2061,100085,100086],{"xmlns":2063},[2065,100087,100088,100122],{},[2068,100089,100090,100092,100094,100108],{},[2071,100091,10871],{},[2075,100093,2077],{},[9252,100095,100096,100098,100100],{},[2071,100097,2861],{},[2210,100099,638],{},[2068,100101,100102,100104,100106],{},[2210,100103,646],{},[2071,100105,4761],{"mathvariant":2450},[2210,100107,654],{},[9252,100109,100110,100112,100114],{},[2071,100111,2861],{},[2210,100113,646],{},[2068,100115,100116,100118,100120],{},[2210,100117,638],{},[2071,100119,4761],{"mathvariant":2450},[2210,100121,654],{},[2092,100123,100124],{"encoding":2094},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[1647,100127,100129],{"className":100128},[2059],[2061,100130,100131],{"xmlns":2063},[2065,100132,100133,100231],{},[2068,100134,100135,100137,100139,100145,100147,100153,100155,100157,100159,100161,100163,100165,100171,100173,100175,100177,100179,100181,100183,100189,100191,100193,100195,100197,100199,100201,100203,100205,100211,100213,100215,100217,100219,100221,100223,100229],{},[2071,100136,10871],{},[2075,100138,2084],{"stretchy":2083},[2348,100140,100141,100143],{},[2071,100142,2861],{},[2210,100144,638],{},[2075,100146,2361],{"separator":2360},[2348,100148,100149,100151],{},[2071,100150,2861],{},[2210,100152,646],{},[2075,100154,2090],{"stretchy":2083},[2075,100156,2077],{},[2210,100158,646],{},[2075,100160,2361],{"separator":2360},[2071,100162,10871],{},[2075,100164,2084],{"stretchy":2083},[2348,100166,100167,100169],{},[2071,100168,2861],{},[2210,100170,638],{},[2075,100172,2361],{"separator":2360},[2210,100174,654],{},[2075,100176,2090],{"stretchy":2083},[2075,100178,2361],{"separator":2360},[2071,100180,10871],{},[2075,100182,2084],{"stretchy":2083},[2348,100184,100185,100187],{},[2071,100186,2861],{},[2210,100188,638],{},[2075,100190,2361],{"separator":2360},[2210,100192,646],{},[2075,100194,2090],{"stretchy":2083},[2075,100196,2361],{"separator":2360},[2071,100198,10871],{},[2075,100200,2084],{"stretchy":2083},[2210,100202,646],{},[2075,100204,2361],{"separator":2360},[2348,100206,100207,100209],{},[2071,100208,2861],{},[2210,100210,646],{},[2075,100212,2090],{"stretchy":2083},[2075,100214,2361],{"separator":2360},[2071,100216,10871],{},[2075,100218,2084],{"stretchy":2083},[2210,100220,654],{},[2075,100222,2361],{"separator":2360},[2348,100224,100225,100227],{},[2071,100226,2861],{},[2210,100228,646],{},[2075,100230,2090],{"stretchy":2083},[2092,100232,100233],{"encoding":2094},"U(Q_1, Q_2) = 2, U(Q_1, 3), U(Q_1, 2), U(2, Q_2), U(3, Q_2)",". Leží některé z bodů ",[1647,100236,100238],{"className":100237},[2059],[2061,100239,100240],{"xmlns":2063},[2065,100241,100242,100257],{},[2068,100243,100244,100246,100248,100250,100252,100255],{},[2071,100245,4342],{},[2075,100247,2561],{"stretchy":2083},[2210,100249,69029],{},[2075,100251,8512],{"separator":2360},[2210,100253,100254],{},"3,555",[2075,100256,2576],{"stretchy":2083},[2092,100258,100259],{"encoding":2094},"A[1{,}5; 3{,}555]",[1647,100261,100263],{"className":100262},[2059],[2061,100264,100265],{"xmlns":2063},[2065,100266,100267,100282],{},[2068,100268,100269,100271,100273,100275,100277,100280],{},[2071,100270,25992],{},[2075,100272,2561],{"stretchy":2083},[2210,100274,57497],{},[2075,100276,8512],{"separator":2360},[2210,100278,100279],{},"1,28",[2075,100281,2576],{"stretchy":2083},[2092,100283,100284],{"encoding":2094},"B[2{,}5; 1{,}28]",[1647,100286,100288],{"className":100287},[2059],[2061,100289,100290],{"xmlns":2063},[2065,100291,100292,100324],{},[2068,100293,100294,100296,100298,100300,100302,100304,100306,100312,100314,100316,100318,100320,100322],{},[2071,100295,2849],{},[2075,100297,2561],{"stretchy":2083},[2210,100299,646],{},[2075,100301,8512],{"separator":2360},[2071,100303,10871],{},[2075,100305,2084],{"stretchy":2083},[2348,100307,100308,100310],{},[2071,100309,2861],{},[2210,100311,638],{},[2075,100313,2361],{"separator":2360},[2210,100315,654],{},[2075,100317,2090],{"stretchy":2083},[2075,100319,2077],{},[2210,100321,654],{},[2075,100323,2576],{"stretchy":2083},[2092,100325,100326],{"encoding":2094},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[1647,100329,100331],{"className":100330},[2059],[2061,100332,100333],{"xmlns":2063},[2065,100334,100335,100354],{},[2068,100336,100337,100339,100341,100343,100345,100347,100349,100352],{},[2071,100338,4271],{},[2075,100340,2561],{"stretchy":2083},[2210,100342,654],{},[2075,100344,8512],{"separator":2360},[2210,100346,638],{},[2075,100348,8512],{"separator":2360},[2210,100350,100351],{},"0,832",[2075,100353,2576],{"stretchy":2083},[2092,100355,100356],{"encoding":2094},"D[3; 1; 0{,}832]",[1647,100358,100360],{"className":100359},[2059],[2061,100361,100362],{"xmlns":2063},[2065,100363,100364,100379],{},[2068,100365,100366,100368,100370,100372,100374,100377],{},[2071,100367,554],{},[2075,100369,2561],{"stretchy":2083},[2210,100371,57497],{},[2075,100373,8512],{"separator":2360},[2210,100375,100376],{},"4,32",[2075,100378,2576],{"stretchy":2083},[2092,100380,100381],{"encoding":2094},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[55,100384,100385,99487,100388,100431,100432,6560,100445,100479,100480,100497,100498,100515],{},[95,100386,100387],{},"6.6",[1647,100389,100391],{"className":100390},[2059],[2061,100392,100393],{"xmlns":2063},[2065,100394,100395,100429],{},[2068,100396,100397,100399,100401,100415],{},[2071,100398,10871],{},[2075,100400,2077],{},[9252,100402,100403,100405,100407],{},[2071,100404,2861],{},[2210,100406,638],{},[2068,100408,100409,100411,100413],{},[2210,100410,646],{},[2071,100412,4761],{"mathvariant":2450},[2210,100414,654],{},[9252,100416,100417,100419,100421],{},[2071,100418,2861],{},[2210,100420,646],{},[2068,100422,100423,100425,100427],{},[2210,100424,638],{},[2071,100426,4761],{"mathvariant":2450},[2210,100428,654],{},[2092,100430,100124],{"encoding":2094},". (a) Najděte mezní míru komoditní substituce ",[1647,100433,100435],{"className":100434},[2059],[2061,100436,100437],{"xmlns":2063},[2065,100438,100439,100443],{},[2068,100440,100441],{},[2363,100442,11733],{},[2092,100444,31265],{"encoding":2094},[1647,100446,100448],{"className":100447},[2059],[2061,100449,100450],{"xmlns":2063},[2065,100451,100452,100476],{},[2068,100453,100454,100460,100462,100464,100466,100472,100474],{},[2348,100455,100456,100458],{},[2071,100457,2861],{},[2210,100459,638],{},[2075,100461,2077],{},[2210,100463,3164],{},[2075,100465,2361],{"separator":2360},[2348,100467,100468,100470],{},[2071,100469,2861],{},[2210,100471,646],{},[2075,100473,2077],{},[2210,100475,8464],{},[2092,100477,100478],{"encoding":2094},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[1647,100481,100483],{"className":100482},[2059],[2061,100484,100485],{"xmlns":2063},[2065,100486,100487,100495],{},[2068,100488,100489],{},[2348,100490,100491,100493],{},[2071,100492,2861],{},[2210,100494,638],{},[2092,100496,32029],{"encoding":2094},", poklesne-li ",[1647,100499,100501],{"className":100500},[2059],[2061,100502,100503],{"xmlns":2063},[2065,100504,100505,100513],{},[2068,100506,100507],{},[2348,100508,100509,100511],{},[2071,100510,2861],{},[2210,100512,646],{},[2092,100514,32048],{"encoding":2094}," o 5 vzhledem k hladině dle (b).",[55,100517,100518,100521,100522,100539,100540,100557,100558,100590,100591,100616,100617,100630,100631,835,100655,835,100679,195],{},[95,100519,100520],{},"6.7"," Míra uspokojení z nákupu množství ",[1647,100523,100525],{"className":100524},[2059],[2061,100526,100527],{"xmlns":2063},[2065,100528,100529,100537],{},[2068,100530,100531],{},[2348,100532,100533,100535],{},[2071,100534,2861],{},[2210,100536,638],{},[2092,100538,32029],{"encoding":2094}," nealko nápojů a množství ",[1647,100541,100543],{"className":100542},[2059],[2061,100544,100545],{"xmlns":2063},[2065,100546,100547,100555],{},[2068,100548,100549],{},[2348,100550,100551,100553],{},[2071,100552,2861],{},[2210,100554,646],{},[2092,100556,32048],{"encoding":2094}," hamburgerů za týden je dána funkcí užitečnosti ",[1647,100559,100561],{"className":100560},[2059],[2061,100562,100563],{"xmlns":2063},[2065,100564,100565,100587],{},[2068,100566,100567,100569,100571],{},[2071,100568,10871],{},[2075,100570,2077],{},[8204,100572,100573],{},[2068,100574,100575,100581],{},[2348,100576,100577,100579],{},[2071,100578,2861],{},[2210,100580,638],{},[2348,100582,100583,100585],{},[2071,100584,2861],{},[2210,100586,646],{},[2092,100588,100589],{"encoding":2094},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[1647,100592,100594],{"className":100593},[2059],[2061,100595,100596],{"xmlns":2063},[2065,100597,100598,100614],{},[2068,100599,100600,100606,100608],{},[2348,100601,100602,100604],{},[2071,100603,2861],{},[2210,100605,638],{},[2075,100607,2361],{"separator":2360},[2348,100609,100610,100612],{},[2071,100611,2861],{},[2210,100613,646],{},[2092,100615,38648],{"encoding":2094},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[1647,100618,100620],{"className":100619},[2059],[2061,100621,100622],{"xmlns":2063},[2065,100623,100624,100628],{},[2068,100625,100626],{},[2363,100627,11733],{},[2092,100629,31265],{"encoding":2094}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[1647,100632,100634],{"className":100633},[2059],[2061,100635,100636],{"xmlns":2063},[2065,100637,100638,100652],{},[2068,100639,100640,100642,100644,100646,100648,100650],{},[2363,100641,11733],{},[2075,100643,2084],{"stretchy":2083},[2210,100645,670],{},[2075,100647,2361],{"separator":2360},[2210,100649,9121],{},[2075,100651,2090],{"stretchy":2083},[2092,100653,100654],{"encoding":2094},"\\text{MRCS}(5, 20)",[1647,100656,100658],{"className":100657},[2059],[2061,100659,100660],{"xmlns":2063},[2065,100661,100662,100676],{},[2068,100663,100664,100666,100668,100670,100672,100674],{},[2363,100665,11733],{},[2075,100667,2084],{"stretchy":2083},[2210,100669,9121],{},[2075,100671,2361],{"separator":2360},[2210,100673,670],{},[2075,100675,2090],{"stretchy":2083},[2092,100677,100678],{"encoding":2094},"\\text{MRCS}(20, 5)",[1647,100680,100682],{"className":100681},[2059],[2061,100683,100684],{"xmlns":2063},[2065,100685,100686,100700],{},[2068,100687,100688,100690,100692,100694,100696,100698],{},[2363,100689,11733],{},[2075,100691,2084],{"stretchy":2083},[2210,100693,646],{},[2075,100695,2361],{"separator":2360},[2210,100697,3194],{},[2075,100699,2090],{"stretchy":2083},[2092,100701,100702],{"encoding":2094},"\\text{MRCS}(2, 50)",[1023,100704,100705],{},[55,100706,100707,100709,100710,195],{},[1647,100708,4659],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[69,100711,100714],{"className":100712,"dataFsResolvedFilePath":92532,"href":100713},[62],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[84,100716,321],{"id":320},[89,100718,100719,100725,100730,100736,100789,100799,100845,100900,100963,101020,101075,101114],{},[92,100720,100721,100724],{},[95,100722,100723],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[92,100726,100727,100729],{},[95,100728,92622],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[92,100731,100732,100735],{},[95,100733,100734],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[92,100737,100738,100740,100741,100754,100755,195],{},[95,100739,92949],{}," — uspořádaná ",[1647,100742,100744],{"className":100743},[2059],[2061,100745,100746],{"xmlns":2063},[2065,100747,100748,100752],{},[2068,100749,100750],{},[2071,100751,41153],{},[2092,100753,41153],{"encoding":2094},"-tice ",[1647,100756,100758],{"className":100757},[2059],[2061,100759,100760],{"xmlns":2063},[2065,100761,100762,100786],{},[2068,100763,100764,100766,100772,100774,100776,100778,100784],{},[2075,100765,2084],{"stretchy":2083},[2348,100767,100768,100770],{},[2071,100769,2861],{},[2210,100771,638],{},[2075,100773,2361],{"separator":2360},[2075,100775,10773],{},[2075,100777,2361],{"separator":2360},[2348,100779,100780,100782],{},[2071,100781,2861],{},[2071,100783,41153],{},[2075,100785,2090],{"stretchy":2083},[2092,100787,100788],{"encoding":2094},"(Q_1, \\dots, Q_n)",[92,100790,100791,100794,100795,100798],{},[95,100792,100793],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[95,100796,100797],{},"indiferentní svazky"," mají stejnou užitečnost.",[92,100800,100801,1445,100804,100844],{},[95,100802,100803],{},"Funkce užitečnosti",[1647,100805,100807],{"className":100806},[2059],[2061,100808,100809],{"xmlns":2063},[2065,100810,100811,100841],{},[2068,100812,100813,100815,100817,100819,100821,100827,100829,100831,100833,100839],{},[2071,100814,10871],{},[2075,100816,2077],{},[2071,100818,10871],{},[2075,100820,2084],{"stretchy":2083},[2348,100822,100823,100825],{},[2071,100824,2861],{},[2210,100826,638],{},[2075,100828,2361],{"separator":2360},[2075,100830,10773],{},[2075,100832,2361],{"separator":2360},[2348,100834,100835,100837],{},[2071,100836,2861],{},[2071,100838,41153],{},[2075,100840,2090],{"stretchy":2083},[2092,100842,100843],{"encoding":2094},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[92,100846,100847,1445,100850,100879,100880,1445,100883,100899],{},[95,100848,100849],{},"Mezní užitečnost",[1647,100851,100853],{"className":100852},[2059],[2061,100854,100855],{"xmlns":2063},[2065,100856,100857,100877],{},[2068,100858,100859,100861,100867,100869],{},[2071,100860,2890],{},[2348,100862,100863,100865],{},[2071,100864,10871],{},[2071,100866,20528],{},[2075,100868,2077],{},[9252,100870,100871,100873,100875],{},[2071,100872,10871],{},[2071,100874,20528],{},[2075,100876,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,100878,92404],{"encoding":2094}," — vzorec (6.2); ",[95,100881,100882],{},"totální diferenciál",[1647,100884,100886],{"className":100885},[2059],[2061,100887,100888],{"xmlns":2063},[2065,100889,100890,100896],{},[2068,100891,100892,100894],{},[2071,100893,2273],{"mathvariant":2450},[2071,100895,10871],{},[2092,100897,100898],{"encoding":2094},"\\mathrm{d} U"," — (6.3).",[92,100901,100902,100904,100905,100929,100930,100962],{},[95,100903,94585],{}," — (6.4) ",[1647,100906,100908],{"className":100907},[2059],[2061,100909,100910],{"xmlns":2063},[2065,100911,100912,100926],{},[2068,100913,100914,100922,100924],{},[9252,100915,100916,100918,100920],{},[2071,100917,10871],{},[2071,100919,20528],{},[2075,100921,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,100923,3482],{},[2210,100925,630],{},[2092,100927,100928],{"encoding":2094},"U'_i > 0",", (6.5) ",[1647,100931,100933],{"className":100932},[2059],[2061,100934,100935],{"xmlns":2063},[2065,100936,100937,100959],{},[2068,100938,100939,100955,100957],{},[9252,100940,100941,100943,100949],{},[2071,100942,10871],{},[2068,100944,100945,100947],{},[2071,100946,20528],{},[2071,100948,20528],{},[2068,100950,100951,100953],{},[2075,100952,2452],{"mathvariant":2450},[2075,100954,2452],{"mathvariant":2450},[2075,100956,3521],{},[2210,100958,630],{},[2092,100960,100961],{"encoding":2094},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[92,100964,100965,1445,100967,100998,100999,195],{},[95,100966,96373],{},[1647,100968,100970],{"className":100969},[2059],[2061,100971,100972],{"xmlns":2063},[2065,100973,100974,100996],{},[2068,100975,100976,100978,100980,100988],{},[2071,100977,10871],{},[2075,100979,2077],{},[9252,100981,100982,100984,100986],{},[2071,100983,2861],{},[2210,100985,638],{},[2071,100987,69],{},[9252,100989,100990,100992,100994],{},[2071,100991,2861],{},[2210,100993,646],{},[2071,100995,2179],{},[2092,100997,38829],{"encoding":2094}," — (6.6), speciálně ",[1647,101000,101002],{"className":101001},[2059],[2061,101003,101004],{"xmlns":2063},[2065,101005,101006,101018],{},[2068,101007,101008,101010,101012,101014,101016],{},[2071,101009,2179],{},[2075,101011,2077],{},[2210,101013,638],{},[2075,101015,2303],{},[2071,101017,69],{},[2092,101019,96527],{"encoding":2094},[92,101021,101022,1445,101025,101060,101061,101074],{},[95,101023,101024],{},"Křivky užitečnosti (indiferenční)",[1647,101026,101028],{"className":101027},[2059],[2061,101029,101030],{"xmlns":2063},[2065,101031,101032,101058],{},[2068,101033,101034,101036,101038,101044,101046,101052,101054,101056],{},[2071,101035,10871],{},[2075,101037,2084],{"stretchy":2083},[2348,101039,101040,101042],{},[2071,101041,2861],{},[2210,101043,638],{},[2075,101045,2361],{"separator":2360},[2348,101047,101048,101050],{},[2071,101049,2861],{},[2210,101051,646],{},[2075,101053,2090],{"stretchy":2083},[2075,101055,2077],{},[2071,101057,2222],{},[2092,101059,10896],{"encoding":2094}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[1647,101062,101064],{"className":101063},[2059],[2061,101065,101066],{"xmlns":2063},[2065,101067,101068,101072],{},[2068,101069,101070],{},[2071,101071,10871],{},[2092,101073,10871],{"encoding":2094},", konvexní.",[92,101076,101077,1445,101079,101113],{},[95,101078,97918],{},[1647,101080,101082],{"className":101081},[2059],[2061,101083,101084],{"xmlns":2063},[2065,101085,101086,101110],{},[2068,101087,101088,101090,101092,101094,101100,101102,101104],{},[2363,101089,11733],{},[2075,101091,2077],{},[2071,101093,2890],{},[2348,101095,101096,101098],{},[2071,101097,10871],{},[2210,101099,638],{},[2071,101101,4761],{"mathvariant":2450},[2071,101103,2890],{},[2348,101105,101106,101108],{},[2071,101107,10871],{},[2210,101109,646],{},[2092,101111,101112],{"encoding":2094},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[92,101115,101116,1445,101119,10897,101148,101151],{},[95,101117,101118],{},"Podmínka optimality",[1647,101120,101122],{"className":101121},[2059],[2061,101123,101124],{"xmlns":2063},[2065,101125,101126,101146],{},[2068,101127,101128,101130,101132,101138,101140],{},[2363,101129,11733],{},[2075,101131,2077],{},[2348,101133,101134,101136],{},[2071,101135,575],{},[2210,101137,638],{},[2071,101139,4761],{"mathvariant":2450},[2348,101141,101142,101144],{},[2071,101143,575],{},[2210,101145,646],{},[2092,101147,31025],{"encoding":2094},[69,101149,39784],{"className":101150,"dataFsResolvedFilePath":92532,"href":92533},[62]," pro plné odvození.",[84,101153,3866],{"id":3865},[89,101155,101156,101193,101234,101244],{},[92,101157,101158,1445,101161,101164,101165,101178,101179,101192],{},[95,101159,101160],{},"Navazující téma:",[69,101162,30805],{"className":101163,"dataFsResolvedFilePath":92532,"href":92533},[62]," (Lagrange, max ",[1647,101166,101168],{"className":101167},[2059],[2061,101169,101170],{"xmlns":2063},[2065,101171,101172,101176],{},[2068,101173,101174],{},[2071,101175,10871],{},[2092,101177,10871],{"encoding":2094},", min ",[1647,101180,101182],{"className":101181},[2059],[2061,101183,101184],{"xmlns":2063},[2065,101185,101186,101190],{},[2068,101187,101188],{},[2071,101189,554],{},[2092,101191,554],{"encoding":2094},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[92,101194,101195,1445,101198,12227,101201,90877,101204,101207,101208,101211,101212,21387,101230,101233],{},[95,101196,101197],{},"Související pojmy:",[69,101199,3901],{"className":101200,"dataFsResolvedFilePath":3899,"href":3900},[62],[69,101202,2431],{"className":101203,"dataFsResolvedFilePath":4005,"href":4006},[62],[69,101205,12221],{"className":101206,"dataFsResolvedFilePath":10942,"href":10943},[62]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[69,101209,13672],{"className":101210,"dataFsResolvedFilePath":13670,"href":13671},[62]," (Marshallovy poptávkové funkce ",[1647,101213,101215],{"className":101214},[2059],[2061,101216,101217],{"xmlns":2063},[2065,101218,101219,101227],{},[2068,101220,101221],{},[2348,101222,101223,101225],{},[2071,101224,4271],{},[2071,101226,20528],{},[2092,101228,101229],{"encoding":2094},"D_i",[69,101231,12195],{"className":101232,"dataFsResolvedFilePath":12193,"href":12194},[62]," (vázaná optimalizace — nástroj pro navazující téma).",[92,101235,101236,1445,101238,835,101241],{},[95,101237,39729],{},[69,101239,39735],{"className":101240,"dataFsResolvedFilePath":39733,"href":39734},[62],[69,101242,39739],{"className":101243,"dataFsResolvedFilePath":17950,"href":17951},[62],[92,101245,101246,1445,101248],{},[95,101247,17937],{},[69,101249,17941],{"className":101250,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":101252},[101253,101254,101255,101258,101259,101262,101266,101267,101270,101271,101272,101273,101274,101275,101276],{"id":13738,"depth":7,"text":13739},{"id":92545,"depth":7,"text":92546},{"id":92605,"depth":7,"text":92606,"children":101256},[101257],{"id":92621,"depth":4,"text":92622},{"id":92928,"depth":7,"text":92929},{"id":93788,"depth":7,"text":93789,"children":101260},[101261],{"id":94335,"depth":4,"text":84680},{"id":94584,"depth":7,"text":94585,"children":101263},[101264],{"id":95457,"depth":4,"text":101265},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":96372,"depth":7,"text":96373},{"id":96908,"depth":7,"text":96909,"children":101268},[101269],{"id":97682,"depth":4,"text":97683},{"id":97912,"depth":7,"text":97913},{"id":98673,"depth":7,"text":98674},{"id":99211,"depth":7,"text":99212},{"id":54177,"depth":7,"text":54178},{"id":99347,"depth":7,"text":99348},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fuzitecnost",{"title":92327,"description":156},[9647,18006],"topics\u002Fuzitecnost",[17,10903,101283,91039,12257,101284],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":101287,"title":3879,"body":101288,"course":17,"courses":163,"created":3932,"description":101560,"extension":166,"meta":101561,"navigation":168,"path":101562,"seo":101563,"sources":101564,"stem":101565,"tags":101566,"type":177,"updated":178,"__hash__":101572},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":48,"value":101289,"toc":101552},[101290,101293,101300,101307,101311,101321,101323,101357,101361,101404,101407,101465,101469,101499,101503,101523,101525],[51,101291,3879],{"id":101292},"základy-matematické-ekonomie",[55,101294,101295,101296,101299],{},"Úvodní pojmy a princip modelování v ",[69,101297,19120],{"className":101298,"dataFsResolvedFilePath":2034,"href":2035},[62],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[55,101301,101302],{},[58,101303],{"alt":101304,"className":101305,"src":101306},"imek-model-promenne",[62,63],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[84,101308,101310],{"id":101309},"co-je-matematická-ekonomie","Co je matematická ekonomie",[55,101312,101313,101316,101317,101320],{},[95,101314,101315],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[95,101318,101319],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[84,101322,321],{"id":320},[89,101324,101325,101331,101337,101343,101352],{},[92,101326,101327,101330],{},[95,101328,101329],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[92,101332,101333,101336],{},[95,101334,101335],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[92,101338,101339,101342],{},[95,101340,101341],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[92,101344,101345,7102,101348,101351],{},[95,101346,101347],{},"Ceteris paribus",[3982,101349,101350],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[92,101353,101354,101356],{},[95,101355,54930],{}," — odezva endogenních proměnných na změnu některé exogenní.",[84,101358,101360],{"id":101359},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[55,101362,101363,101403],{},[1647,101364,101366],{"className":101365},[2059],[2061,101367,101368],{"xmlns":2063},[2065,101369,101370,101400],{},[2068,101371,101372,101374,101376,101378,101380,101382,101384,101386,101388,101390,101392,101394,101396,101398],{},[2071,101373,2861],{},[2075,101375,2077],{},[2071,101377,4271],{},[2075,101379,2084],{"stretchy":2083},[2071,101381,575],{},[2075,101383,2361],{"separator":2360},[2071,101385,9214],{},[2075,101387,2361],{"separator":2360},[2071,101389,21033],{},[2075,101391,2361],{"separator":2360},[2071,101393,10871],{},[2075,101395,2361],{"separator":2360},[2075,101397,10773],{},[2075,101399,2090],{"stretchy":2083},[2092,101401,101402],{"encoding":2094},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[55,101405,101406],{},"Zjednodušení:",[89,101408,101409,101437],{},[92,101410,101411,1445,101414],{},[95,101412,101413],{},"Jednofaktorový model:",[1647,101415,101417],{"className":101416},[2059],[2061,101418,101419],{"xmlns":2063},[2065,101420,101421,101435],{},[2068,101422,101423,101425,101427,101429,101431,101433],{},[2071,101424,2861],{},[2075,101426,2077],{},[2071,101428,4271],{},[2075,101430,2084],{"stretchy":2083},[2071,101432,575],{},[2075,101434,2090],{"stretchy":2083},[2092,101436,4280],{"encoding":2094},[92,101438,101439,1445,101442],{},[95,101440,101441],{},"Inverzní zápis:",[1647,101443,101445],{"className":101444},[2059],[2061,101446,101447],{"xmlns":2063},[2065,101448,101449,101463],{},[2068,101450,101451,101453,101455,101457,101459,101461],{},[2071,101452,575],{},[2075,101454,2077],{},[2071,101456,4271],{},[2075,101458,2084],{"stretchy":2083},[2071,101460,2861],{},[2075,101462,2090],{"stretchy":2083},[2092,101464,4727],{"encoding":2094},[84,101466,101468],{"id":101467},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[201,101470,101471,101480],{},[92,101472,101473,101476,101477,4007],{},[95,101474,101475],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[69,101478,17975],{"className":101479,"dataFsResolvedFilePath":13670,"href":13671},[62],[92,101481,101482,101485,101486,101489,101490,101493,101494,101498],{},[95,101483,101484],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[69,101487,2430],{"className":101488,"dataFsResolvedFilePath":4005,"href":4006},[62]," pro 1D, ",[69,101491,17988],{"className":101492,"dataFsResolvedFilePath":3899,"href":3900},[62]," pro 2D, ",[69,101495,101497],{"className":101496,"dataFsResolvedFilePath":12193,"href":12194},[62],"lagrangeova-metoda"," pro vázané extrémy).",[84,101500,101502],{"id":101501},"konvence-z-přednášek","Konvence z přednášek",[89,101504,101505,101511,101517],{},[92,101506,101507,101508,101510],{},"Symbol ",[929,101509,2803],{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[92,101512,101513,101514,195],{},"Numerické výsledky ",[95,101515,101516],{},"na 3 desetinná místa",[92,101518,3980,101519,101522],{},[3982,101520,101521],{},"jednotková změna"," má standardní význam (změna o 1).",[84,101524,3866],{"id":3865},[89,101526,101527,101532,101540],{},[92,101528,101529,101531],{},[95,101530,3873],{}," —",[92,101533,101534,1445,101536],{},[95,101535,3884],{},[69,101537,101539],{"className":101538,"dataFsResolvedFilePath":4005,"href":4006},[62],"Derivace a diferenciál",[92,101541,101542,1445,101544,835,101548],{},[95,101543,3895],{},[69,101545,101547],{"className":101546,"dataFsResolvedFilePath":55057,"href":55058},[62],"Souhrn KS 1. blok",[69,101549,101551],{"className":101550,"dataFsResolvedFilePath":2034,"href":2035},[62],"kurz ImeK",{"title":156,"searchDepth":7,"depth":7,"links":101553},[101554,101555,101556,101557,101558,101559],{"id":101309,"depth":7,"text":101310},{"id":320,"depth":7,"text":321},{"id":101359,"depth":7,"text":101360},{"id":101467,"depth":7,"text":101468},{"id":101501,"depth":7,"text":101502},{"id":3865,"depth":7,"text":3866},"Úvodní pojmy a princip modelování v matematické ekonomii. Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",{},"\u002Ftopics\u002Fzaklady-matematicke-ekonomie",{"title":3879,"description":101560},[3938],"topics\u002Fzaklady-matematicke-ekonomie",[17,101567,101568,101569,101570,101571],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":101574,"title":101575,"body":101576,"course":17,"courses":163,"created":9642,"description":156,"extension":166,"meta":105848,"navigation":168,"path":105849,"seo":105850,"sources":105851,"stem":105852,"tags":105853,"type":177,"updated":178,"__hash__":105857},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":48,"value":101577,"toc":105831},[101578,101581,101675,101679,101701,101715,101767,101769,101773,101836,101879,101898,102061,102160,102163,102230,102234,102363,102402,102432,102544,102589,102655,102708,102784,102840,102842,102846,102910,102954,102974,103135,103138,103222,103319,103322,103388,103392,103441,103467,103572,103636,103641,103737,103784,103786,103789,103811,103853,103860,103893,103895,103966,104020,104129,104133,104222,104298,104562,104600,104602,104606,104609,104616,104927,104930,104988,105168,105197,105199,105203,105209,105347,105356,105358,105360,105785,105787,105789],[51,101579,101575],{"id":101580},"zdanění-trhu-dopady-daně-na-rovnováhu",[1023,101582,101583],{},[55,101584,101585,46920,101587,101600,101601,101604,101605,101607,101608,101611,101612,101633,101634,101657,101658,101661,101662,195],{},[1647,101586,4243],{},[1647,101588,101590],{"className":101589},[2059],[2061,101591,101592],{"xmlns":2063},[2065,101593,101594,101598],{},[2068,101595,101596],{},[2071,101597,543],{},[2092,101599,543],{"encoding":2094}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[95,101602,101603],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[95,101606,92613],{}," (je-li uložena spotřebiteli). Výsledné ",[95,101609,101610],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[1647,101613,101615],{"className":101614},[2059],[2061,101616,101617],{"xmlns":2063},[2065,101618,101619,101631],{},[2068,101620,101621],{},[2348,101622,101623,101625],{},[2071,101624,543],{},[2068,101626,101627,101629],{},[2071,101628,46969],{},[2071,101630,55],{},[2092,101632,46974],{"encoding":2094}," (spotřebitel) a ",[1647,101635,101637],{"className":101636},[2059],[2061,101638,101639],{"xmlns":2063},[2065,101640,101641,101655],{},[2068,101642,101643],{},[2348,101644,101645,101647],{},[2071,101646,543],{},[2068,101648,101649,101651,101653],{},[2071,101650,46992],{},[2071,101652,2073],{},[2071,101654,13774],{},[2092,101656,46999],{"encoding":2094}," (výrobce). Klíčovým zjištěním je ",[95,101659,101660],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[1647,101663,101665],{"className":101664},[2059],[2061,101666,101667],{"xmlns":2063},[2065,101668,101669,101673],{},[2068,101670,101671],{},[2071,101672,543],{},[2092,101674,543],{"encoding":2094},[84,101676,101678],{"id":101677},"dvě-formy-zdanění","Dvě formy zdanění",[55,101680,101681,101682,101700],{},"Uvažujme jednotkovou daň ",[1647,101683,101685],{"className":101684},[2059],[2061,101686,101687],{"xmlns":2063},[2065,101688,101689,101697],{},[2068,101690,101691,101693,101695],{},[2071,101692,543],{},[2075,101694,3482],{},[2210,101696,630],{},[2092,101698,101699],{"encoding":2094},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[89,101702,101703,101709],{},[92,101704,101705,101708],{},[95,101706,101707],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[92,101710,101711,101714],{},[95,101712,101713],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[55,101716,101717,101718,101731,101732,101735,101736,195],{},"V obou případech dochází k posunu jedné z křivek o ",[1647,101719,101721],{"className":101720},[2059],[2061,101722,101723],{"xmlns":2063},[2065,101724,101725,101729],{},[2068,101726,101727],{},[2071,101728,543],{},[2092,101730,543],{"encoding":2094}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[95,101733,101734],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[1647,101737,101739],{"className":101738},[2059],[2061,101740,101741],{"xmlns":2063},[2065,101742,101743,101765],{},[2068,101744,101745,101747,101749,101755,101757,101763],{},[2071,101746,554],{},[2075,101748,2561],{"stretchy":2083},[2205,101750,101751,101753],{},[2071,101752,2861],{},[2071,101754,554],{},[2075,101756,2361],{"separator":2360},[2205,101758,101759,101761],{},[2071,101760,575],{},[2071,101762,554],{},[2075,101764,2576],{"stretchy":2083},[2092,101766,45658],{"encoding":2094},[909,101768],{},[84,101770,101772],{"id":101771},"daň-uložená-výrobci","Daň uložená výrobci",[55,101774,101775,101776,101789,101790,101807,101808,101835],{},"Je-li daň ",[1647,101777,101779],{"className":101778},[2059],[2061,101780,101781],{"xmlns":2063},[2065,101782,101783,101787],{},[2068,101784,101785],{},[2071,101786,543],{},[2092,101788,543],{"encoding":2094}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[1647,101791,101793],{"className":101792},[2059],[2061,101794,101795],{"xmlns":2063},[2065,101796,101797,101805],{},[2068,101798,101799,101801,101803],{},[2071,101800,575],{},[2075,101802,2303],{},[2071,101804,543],{},[2092,101806,45413],{"encoding":2094}," (hrubá cena mínus odvod), plyne z rovnice ",[1647,101809,101811],{"className":101810},[2059],[2061,101812,101813],{"xmlns":2063},[2065,101814,101815,101833],{},[2068,101816,101817,101819,101821,101823,101825,101827,101829,101831],{},[2071,101818,575],{},[2075,101820,2303],{},[2071,101822,543],{},[2075,101824,2077],{},[2071,101826,532],{},[2075,101828,2084],{"stretchy":2083},[2071,101830,2861],{},[2075,101832,2090],{"stretchy":2083},[2092,101834,45442],{"encoding":2094}," nová funkce nabídky:",[1647,101837,101839],{"className":101838},[2059],[2061,101840,101841],{"xmlns":2063,"display":31093},[2065,101842,101843,101877],{},[2068,101844,101845,101847,101849,101855,101857,101859,101861,101863,101865,101867,101869,101871,101873,101875],{},[2071,101846,575],{},[2075,101848,2077],{},[2348,101850,101851,101853],{},[2071,101852,532],{},[2210,101854,638],{},[2075,101856,2084],{"stretchy":2083},[2071,101858,2861],{},[2075,101860,2090],{"stretchy":2083},[2075,101862,2077],{},[2071,101864,532],{},[2075,101866,2084],{"stretchy":2083},[2071,101868,2861],{},[2075,101870,2090],{"stretchy":2083},[2075,101872,2176],{},[2071,101874,543],{},[2071,101876,195],{"mathvariant":2450},[2092,101878,45487],{"encoding":2094},[55,101880,101881,101882,1445,101895,101897],{},"Nabídka se tedy posouvá o ",[1647,101883,101885],{"className":101884},[2059],[2061,101886,101887],{"xmlns":2063},[2065,101888,101889,101893],{},[2068,101890,101891],{},[2071,101892,543],{},[2092,101894,543],{"encoding":2094},[95,101896,45520],{}," (ekvivalentně doleva). Poptávka se nemění.",[55,101899,101900,101901,101941,101942,75,101970,101998,101999,102018,102019,102043,102044,4007],{},"Nový rovnovážný bod ",[1647,101902,101904],{"className":101903},[2059],[2061,101905,101906],{"xmlns":2063},[2065,101907,101908,101938],{},[2068,101909,101910,101916,101918,101926,101928,101936],{},[2348,101911,101912,101914],{},[2071,101913,554],{},[2210,101915,638],{},[2075,101917,2561],{"stretchy":2083},[9252,101919,101920,101922,101924],{},[2071,101921,2861],{},[2210,101923,638],{},[2071,101925,554],{},[2075,101927,2361],{"separator":2360},[9252,101929,101930,101932,101934],{},[2071,101931,575],{},[2210,101933,638],{},[2071,101935,554],{},[2075,101937,2576],{"stretchy":2083},[2092,101939,101940],{"encoding":2094},"E_1[Q_1^E, P_1^E]"," splňuje ",[1647,101943,101945],{"className":101944},[2059],[2061,101946,101947],{"xmlns":2063},[2065,101948,101949,101967],{},[2068,101950,101951,101959,101961],{},[9252,101952,101953,101955,101957],{},[2071,101954,2861],{},[2210,101956,638],{},[2071,101958,554],{},[2075,101960,3521],{},[2205,101962,101963,101965],{},[2071,101964,2861],{},[2071,101966,554],{},[2092,101968,101969],{"encoding":2094},"Q_1^E \u003C Q^E",[1647,101971,101973],{"className":101972},[2059],[2061,101974,101975],{"xmlns":2063},[2065,101976,101977,101995],{},[2068,101978,101979,101987,101989],{},[9252,101980,101981,101983,101985],{},[2071,101982,575],{},[2210,101984,638],{},[2071,101986,554],{},[2075,101988,3482],{},[2205,101990,101991,101993],{},[2071,101992,575],{},[2071,101994,554],{},[2092,101996,101997],{"encoding":2094},"P_1^E > P^E",". Spotřebitel platí ",[1647,102000,102002],{"className":102001},[2059],[2061,102003,102004],{"xmlns":2063},[2065,102005,102006,102016],{},[2068,102007,102008],{},[9252,102009,102010,102012,102014],{},[2071,102011,575],{},[2210,102013,638],{},[2071,102015,554],{},[2092,102017,52153],{"encoding":2094},", výrobci ale zůstává pouze čistá cena ",[1647,102020,102022],{"className":102021},[2059],[2061,102023,102024],{"xmlns":2063},[2065,102025,102026,102040],{},[2068,102027,102028,102036,102038],{},[9252,102029,102030,102032,102034],{},[2071,102031,575],{},[2210,102033,638],{},[2071,102035,554],{},[2075,102037,2303],{},[2071,102039,543],{},[2092,102041,102042],{"encoding":2094},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[1647,102045,102047],{"className":102046},[2059],[2061,102048,102049],{"xmlns":2063},[2065,102050,102051,102059],{},[2068,102052,102053],{},[2205,102054,102055,102057],{},[2071,102056,575],{},[2071,102058,554],{},[2092,102060,45757],{"encoding":2094},[55,102062,102063],{},[3982,102064,102065,102066,102096,102097,102110,102111,5756,102128,102141,102142,195],{},"Obrázek 2.17 (resp. 2.18): Posun ",[1647,102067,102069],{"className":102068},[2059],[2061,102070,102071],{"xmlns":2063},[2065,102072,102073,102093],{},[2068,102074,102075,102077,102079,102085,102087,102089,102091],{},[2071,102076,532],{},[2075,102078,3197],{},[2348,102080,102081,102083],{},[2071,102082,532],{},[2210,102084,638],{},[2075,102086,2077],{},[2071,102088,532],{},[2075,102090,2176],{},[2071,102092,543],{},[2092,102094,102095],{"encoding":2094},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[1647,102098,102100],{"className":102099},[2059],[2061,102101,102102],{"xmlns":2063},[2065,102103,102104,102108],{},[2068,102105,102106],{},[2071,102107,543],{},[2092,102109,543],{"encoding":2094},". Průsečík ",[1647,102112,102114],{"className":102113},[2059],[2061,102115,102116],{"xmlns":2063},[2065,102117,102118,102126],{},[2068,102119,102120],{},[2348,102121,102122,102124],{},[2071,102123,532],{},[2210,102125,638],{},[2092,102127,45288],{"encoding":2094},[1647,102129,102131],{"className":102130},[2059],[2061,102132,102133],{"xmlns":2063},[2065,102134,102135,102139],{},[2068,102136,102137],{},[2071,102138,4271],{},[2092,102140,4271],{"encoding":2094}," je nový rovnovážný bod ",[1647,102143,102145],{"className":102144},[2059],[2061,102146,102147],{"xmlns":2063},[2065,102148,102149,102157],{},[2068,102150,102151],{},[2348,102152,102153,102155],{},[2071,102154,554],{},[2210,102156,638],{},[2092,102158,102159],{"encoding":2094},"E_1",[609,102161,49599],{"id":102162},"příklad-29",[55,102164,102165,45946,102167,45981,102191,102211,102212,102229],{},[95,102166,42224],{},[1647,102168,102170],{"className":102169},[2059],[2061,102171,102172],{"xmlns":2063},[2065,102173,102174,102188],{},[2068,102175,102176,102178,102180,102182,102184,102186],{},[2071,102177,575],{},[2075,102179,2077],{},[2210,102181,3583],{},[2075,102183,2303],{},[2210,102185,646],{},[2071,102187,2861],{},[2092,102189,102190],{"encoding":2094},"P = 12 - 2Q",[1647,102192,102194],{"className":102193},[2059],[2061,102195,102196],{"xmlns":2063},[2065,102197,102198,102208],{},[2068,102199,102200,102202,102204,102206],{},[2071,102201,575],{},[2075,102203,2077],{},[2210,102205,662],{},[2071,102207,2861],{},[2092,102209,102210],{"encoding":2094},"P = 4Q",". Na výrobce je uložena jednotková daň ",[1647,102213,102215],{"className":102214},[2059],[2061,102216,102217],{"xmlns":2063},[2065,102218,102219,102227],{},[2068,102220,102221,102223,102225],{},[2071,102222,543],{},[2075,102224,2077],{},[2210,102226,678],{},[2092,102228,45559],{"encoding":2094}," Kč.",[55,102231,102232],{},[95,102233,42256],{},[55,102235,102236,102239,102240,5656,102266,5676,102286,835,102308,102338,102339,195],{},[3982,102237,102238],{},"Bez daně."," Z rovnosti ",[1647,102241,102243],{"className":102242},[2059],[2061,102244,102245],{"xmlns":2063},[2065,102246,102247,102263],{},[2068,102248,102249,102251,102253,102255,102257,102259,102261],{},[2210,102250,3583],{},[2075,102252,2303],{},[2210,102254,646],{},[2071,102256,2861],{},[2075,102258,2077],{},[2210,102260,662],{},[2071,102262,2861],{},[2092,102264,102265],{"encoding":2094},"12 - 2Q = 4Q",[1647,102267,102269],{"className":102268},[2059],[2061,102270,102271],{"xmlns":2063},[2065,102272,102273,102283],{},[2068,102274,102275,102277,102279,102281],{},[2210,102276,678],{},[2071,102278,2861],{},[2075,102280,2077],{},[2210,102282,3583],{},[2092,102284,102285],{"encoding":2094},"6Q = 12",[1647,102287,102289],{"className":102288},[2059],[2061,102290,102291],{"xmlns":2063},[2065,102292,102293,102305],{},[2068,102294,102295,102301,102303],{},[2205,102296,102297,102299],{},[2071,102298,2861],{},[2071,102300,554],{},[2075,102302,2077],{},[2210,102304,646],{},[2092,102306,102307],{"encoding":2094},"Q^E = 2",[1647,102309,102311],{"className":102310},[2059],[2061,102312,102313],{"xmlns":2063},[2065,102314,102315,102335],{},[2068,102316,102317,102323,102325,102327,102329,102331,102333],{},[2205,102318,102319,102321],{},[2071,102320,575],{},[2071,102322,554],{},[2075,102324,2077],{},[2210,102326,662],{},[2075,102328,3251],{},[2210,102330,646],{},[2075,102332,2077],{},[2210,102334,5672],{},[2092,102336,102337],{"encoding":2094},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[1647,102340,102342],{"className":102341},[2059],[2061,102343,102344],{"xmlns":2063},[2065,102345,102346,102360],{},[2068,102347,102348,102350,102352,102354,102356,102358],{},[2071,102349,554],{},[2075,102351,2561],{"stretchy":2083},[2210,102353,646],{},[2075,102355,2361],{"separator":2360},[2210,102357,5672],{},[2075,102359,2576],{"stretchy":2083},[2092,102361,102362],{"encoding":2094},"E[2, 8]",[55,102364,102365,102368,102369,102401],{},[3982,102366,102367],{},"S daní uloženou výrobci."," Nová nabídka je ",[1647,102370,102372],{"className":102371},[2059],[2061,102373,102374],{"xmlns":2063},[2065,102375,102376,102398],{},[2068,102377,102378,102384,102386,102388,102390,102392,102394,102396],{},[2348,102379,102380,102382],{},[2071,102381,532],{},[2210,102383,638],{},[2075,102385,2777],{},[2071,102387,575],{},[2075,102389,2077],{},[2210,102391,662],{},[2071,102393,2861],{},[2075,102395,2176],{},[2210,102397,678],{},[2092,102399,102400],{"encoding":2094},"S_1: P = 4Q + 6",". Z rovnice",[1647,102403,102405],{"className":102404},[2059],[2061,102406,102407],{"xmlns":2063,"display":31093},[2065,102408,102409,102429],{},[2068,102410,102411,102413,102415,102417,102419,102421,102423,102425,102427],{},[2210,102412,3583],{},[2075,102414,2303],{},[2210,102416,646],{},[2071,102418,2861],{},[2075,102420,2077],{},[2210,102422,662],{},[2071,102424,2861],{},[2075,102426,2176],{},[2210,102428,678],{},[2092,102430,102431],{"encoding":2094},"12 - 2Q = 4Q + 6",[55,102433,102434,102435,5676,102455,835,102479,102515,102516,195],{},"plyne ",[1647,102436,102438],{"className":102437},[2059],[2061,102439,102440],{"xmlns":2063},[2065,102441,102442,102452],{},[2068,102443,102444,102446,102448,102450],{},[2210,102445,678],{},[2071,102447,2861],{},[2075,102449,2077],{},[2210,102451,678],{},[2092,102453,102454],{"encoding":2094},"6Q = 6",[1647,102456,102458],{"className":102457},[2059],[2061,102459,102460],{"xmlns":2063},[2065,102461,102462,102476],{},[2068,102463,102464,102472,102474],{},[9252,102465,102466,102468,102470],{},[2071,102467,2861],{},[2210,102469,638],{},[2071,102471,554],{},[2075,102473,2077],{},[2210,102475,638],{},[2092,102477,102478],{"encoding":2094},"Q_1^E = 1",[1647,102480,102482],{"className":102481},[2059],[2061,102483,102484],{"xmlns":2063},[2065,102485,102486,102512],{},[2068,102487,102488,102496,102498,102500,102502,102504,102506,102508,102510],{},[9252,102489,102490,102492,102494],{},[2071,102491,575],{},[2210,102493,638],{},[2071,102495,554],{},[2075,102497,2077],{},[2210,102499,662],{},[2075,102501,3251],{},[2210,102503,638],{},[2075,102505,2176],{},[2210,102507,678],{},[2075,102509,2077],{},[2210,102511,2935],{},[2092,102513,102514],{"encoding":2094},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[1647,102517,102519],{"className":102518},[2059],[2061,102520,102521],{"xmlns":2063},[2065,102522,102523,102541],{},[2068,102524,102525,102531,102533,102535,102537,102539],{},[2348,102526,102527,102529],{},[2071,102528,554],{},[2210,102530,638],{},[2075,102532,2561],{"stretchy":2083},[2210,102534,638],{},[2075,102536,2361],{"separator":2360},[2210,102538,2935],{},[2075,102540,2576],{"stretchy":2083},[2092,102542,102543],{"encoding":2094},"E_1[1, 10]",[55,102545,102546,102549,102550,102574,102575,102588],{},[3982,102547,102548],{},"Rozklad daňového břemene."," Spotřebitel platí ",[1647,102551,102553],{"className":102552},[2059],[2061,102554,102555],{"xmlns":2063},[2065,102556,102557,102571],{},[2068,102558,102559,102567,102569],{},[9252,102560,102561,102563,102565],{},[2071,102562,575],{},[2210,102564,638],{},[2071,102566,554],{},[2075,102568,2077],{},[2210,102570,2935],{},[2092,102572,102573],{"encoding":2094},"P_1^E = 10"," Kč namísto původních ",[1647,102576,102578],{"className":102577},[2059],[2061,102579,102580],{"xmlns":2063},[2065,102581,102582,102586],{},[2068,102583,102584],{},[2210,102585,5672],{},[2092,102587,5672],{"encoding":2094},", navýšení je",[1647,102590,102592],{"className":102591},[2059],[2061,102593,102594],{"xmlns":2063,"display":31093},[2065,102595,102596,102652],{},[2068,102597,102598,102608,102610,102618,102620,102626,102628,102630,102632,102634,102636,102638,102640,102650],{},[2348,102599,102600,102602],{},[2071,102601,543],{},[2068,102603,102604,102606],{},[2071,102605,46969],{},[2071,102607,55],{},[2075,102609,2077],{},[9252,102611,102612,102614,102616],{},[2071,102613,575],{},[2210,102615,638],{},[2071,102617,554],{},[2075,102619,2303],{},[2205,102621,102622,102624],{},[2071,102623,575],{},[2071,102625,554],{},[2075,102627,2077],{},[2210,102629,2935],{},[2075,102631,2303],{},[2210,102633,5672],{},[2075,102635,2077],{},[2210,102637,646],{},[2363,102639,2365],{},[2068,102641,102642,102644],{},[2363,102643,10929],{},[8473,102645,102646,102648],{"accent":2360},[2363,102647,2222],{},[2075,102649,27796],{},[2071,102651,195],{"mathvariant":2450},[2092,102653,102654],{"encoding":2094},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[55,102656,102657,102658,102574,102694,102707],{},"Výrobci zůstává čistá cena ",[1647,102659,102661],{"className":102660},[2059],[2061,102662,102663],{"xmlns":2063},[2065,102664,102665,102691],{},[2068,102666,102667,102675,102677,102679,102681,102683,102685,102687,102689],{},[9252,102668,102669,102671,102673],{},[2071,102670,575],{},[2210,102672,638],{},[2071,102674,554],{},[2075,102676,2303],{},[2071,102678,543],{},[2075,102680,2077],{},[2210,102682,2935],{},[2075,102684,2303],{},[2210,102686,678],{},[2075,102688,2077],{},[2210,102690,662],{},[2092,102692,102693],{"encoding":2094},"P_1^E - T = 10 - 6 = 4",[1647,102695,102697],{"className":102696},[2059],[2061,102698,102699],{"xmlns":2063},[2065,102700,102701,102705],{},[2068,102702,102703],{},[2210,102704,5672],{},[2092,102706,5672],{"encoding":2094},", pokles je",[1647,102709,102711],{"className":102710},[2059],[2061,102712,102713],{"xmlns":2063,"display":31093},[2065,102714,102715,102781],{},[2068,102716,102717,102729,102731,102737,102739,102741,102749,102751,102753,102755,102757,102759,102761,102763,102765,102767,102769,102779],{},[2348,102718,102719,102721],{},[2071,102720,543],{},[2068,102722,102723,102725,102727],{},[2071,102724,46992],{},[2071,102726,2073],{},[2071,102728,13774],{},[2075,102730,2077],{},[2205,102732,102733,102735],{},[2071,102734,575],{},[2071,102736,554],{},[2075,102738,2303],{},[2075,102740,2084],{"stretchy":2083},[9252,102742,102743,102745,102747],{},[2071,102744,575],{},[2210,102746,638],{},[2071,102748,554],{},[2075,102750,2303],{},[2071,102752,543],{},[2075,102754,2090],{"stretchy":2083},[2075,102756,2077],{},[2210,102758,5672],{},[2075,102760,2303],{},[2210,102762,662],{},[2075,102764,2077],{},[2210,102766,662],{},[2363,102768,2365],{},[2068,102770,102771,102773],{},[2363,102772,10929],{},[8473,102774,102775,102777],{"accent":2360},[2363,102776,2222],{},[2075,102778,27796],{},[2071,102780,195],{"mathvariant":2450},[2092,102782,102783],{"encoding":2094},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[55,102785,102786,102787,102839],{},"Kontrola: ",[1647,102788,102790],{"className":102789},[2059],[2061,102791,102792],{"xmlns":2063},[2065,102793,102794,102836],{},[2068,102795,102796,102806,102808,102820,102822,102824,102826,102828,102830,102832,102834],{},[2348,102797,102798,102800],{},[2071,102799,543],{},[2068,102801,102802,102804],{},[2071,102803,46969],{},[2071,102805,55],{},[2075,102807,2176],{},[2348,102809,102810,102812],{},[2071,102811,543],{},[2068,102813,102814,102816,102818],{},[2071,102815,46992],{},[2071,102817,2073],{},[2071,102819,13774],{},[2075,102821,2077],{},[2210,102823,646],{},[2075,102825,2176],{},[2210,102827,662],{},[2075,102829,2077],{},[2210,102831,678],{},[2075,102833,2077],{},[2071,102835,543],{},[2092,102837,102838],{"encoding":2094},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[909,102841],{},[84,102843,102845],{"id":102844},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[55,102847,101775,102848,102861,102862,102880,102881,102909],{},[1647,102849,102851],{"className":102850},[2059],[2061,102852,102853],{"xmlns":2063},[2065,102854,102855,102859],{},[2068,102856,102857],{},[2071,102858,543],{},[2092,102860,543],{"encoding":2094}," uložena spotřebiteli, pak spotřebitel platí celkem ",[1647,102863,102865],{"className":102864},[2059],[2061,102866,102867],{"xmlns":2063},[2065,102868,102869,102877],{},[2068,102870,102871,102873,102875],{},[2071,102872,575],{},[2075,102874,2176],{},[2071,102876,543],{},[2092,102878,102879],{"encoding":2094},"P + T"," (cena prodejce plus daň). Z podmínky ",[1647,102882,102884],{"className":102883},[2059],[2061,102885,102886],{"xmlns":2063},[2065,102887,102888,102906],{},[2068,102889,102890,102892,102894,102896,102898,102900,102902,102904],{},[2071,102891,575],{},[2075,102893,2176],{},[2071,102895,543],{},[2075,102897,2077],{},[2071,102899,4271],{},[2075,102901,2084],{"stretchy":2083},[2071,102903,2861],{},[2075,102905,2090],{"stretchy":2083},[2092,102907,102908],{"encoding":2094},"P + T = D(Q)"," plyne nová funkce poptávky:",[1647,102911,102913],{"className":102912},[2059],[2061,102914,102915],{"xmlns":2063,"display":31093},[2065,102916,102917,102951],{},[2068,102918,102919,102921,102923,102929,102931,102933,102935,102937,102939,102941,102943,102945,102947,102949],{},[2071,102920,575],{},[2075,102922,2077],{},[2348,102924,102925,102927],{},[2071,102926,4271],{},[2210,102928,646],{},[2075,102930,2084],{"stretchy":2083},[2071,102932,2861],{},[2075,102934,2090],{"stretchy":2083},[2075,102936,2077],{},[2071,102938,4271],{},[2075,102940,2084],{"stretchy":2083},[2071,102942,2861],{},[2075,102944,2090],{"stretchy":2083},[2075,102946,2303],{},[2071,102948,543],{},[2071,102950,195],{"mathvariant":2450},[2092,102952,102953],{"encoding":2094},"P = D_2(Q) = D(Q) - T.",[55,102955,102956,102957,1445,102970,102973],{},"Poptávka se tedy posouvá o ",[1647,102958,102960],{"className":102959},[2059],[2061,102961,102962],{"xmlns":2063},[2065,102963,102964,102968],{},[2068,102965,102966],{},[2071,102967,543],{},[2092,102969,543],{"encoding":2094},[95,102971,102972],{},"svisle dolů",". Nabídka se nemění.",[55,102975,101900,102976,101941,103016,75,103044,103072,103073,103092,103093,103117,103118,4007],{},[1647,102977,102979],{"className":102978},[2059],[2061,102980,102981],{"xmlns":2063},[2065,102982,102983,103013],{},[2068,102984,102985,102991,102993,103001,103003,103011],{},[2348,102986,102987,102989],{},[2071,102988,554],{},[2210,102990,646],{},[2075,102992,2561],{"stretchy":2083},[9252,102994,102995,102997,102999],{},[2071,102996,2861],{},[2210,102998,646],{},[2071,103000,554],{},[2075,103002,2361],{"separator":2360},[9252,103004,103005,103007,103009],{},[2071,103006,575],{},[2210,103008,646],{},[2071,103010,554],{},[2075,103012,2576],{"stretchy":2083},[2092,103014,103015],{"encoding":2094},"E_2[Q_2^E, P_2^E]",[1647,103017,103019],{"className":103018},[2059],[2061,103020,103021],{"xmlns":2063},[2065,103022,103023,103041],{},[2068,103024,103025,103033,103035],{},[9252,103026,103027,103029,103031],{},[2071,103028,2861],{},[2210,103030,646],{},[2071,103032,554],{},[2075,103034,3521],{},[2205,103036,103037,103039],{},[2071,103038,2861],{},[2071,103040,554],{},[2092,103042,103043],{"encoding":2094},"Q_2^E \u003C Q^E",[1647,103045,103047],{"className":103046},[2059],[2061,103048,103049],{"xmlns":2063},[2065,103050,103051,103069],{},[2068,103052,103053,103061,103063],{},[9252,103054,103055,103057,103059],{},[2071,103056,575],{},[2210,103058,646],{},[2071,103060,554],{},[2075,103062,3521],{},[2205,103064,103065,103067],{},[2071,103066,575],{},[2071,103068,554],{},[2092,103070,103071],{"encoding":2094},"P_2^E \u003C P^E",". Výrobce obdrží ",[1647,103074,103076],{"className":103075},[2059],[2061,103077,103078],{"xmlns":2063},[2065,103079,103080,103090],{},[2068,103081,103082],{},[9252,103083,103084,103086,103088],{},[2071,103085,575],{},[2210,103087,646],{},[2071,103089,554],{},[2092,103091,52214],{"encoding":2094},", spotřebitel platí celkem ",[1647,103094,103096],{"className":103095},[2059],[2061,103097,103098],{"xmlns":2063},[2065,103099,103100,103114],{},[2068,103101,103102,103110,103112],{},[9252,103103,103104,103106,103108],{},[2071,103105,575],{},[2210,103107,646],{},[2071,103109,554],{},[2075,103111,2176],{},[2071,103113,543],{},[2092,103115,103116],{"encoding":2094},"P_2^E + T"," (tato částka je vyšší než původní ",[1647,103119,103121],{"className":103120},[2059],[2061,103122,103123],{"xmlns":2063},[2065,103124,103125,103133],{},[2068,103126,103127],{},[2205,103128,103129,103131],{},[2071,103130,575],{},[2071,103132,554],{},[2092,103134,45757],{"encoding":2094},[55,103136,103137],{},"Daňové břemeno:",[1647,103139,103141],{"className":103140},[2059],[2061,103142,103143],{"xmlns":2063,"display":31093},[2065,103144,103145,103219],{},[2068,103146,103147,103157,103159,103161,103169,103171,103173,103175,103177,103183,103185,103187,103199,103201,103207,103209,103217],{},[2348,103148,103149,103151],{},[2071,103150,543],{},[2068,103152,103153,103155],{},[2071,103154,46969],{},[2071,103156,55],{},[2075,103158,2077],{},[2075,103160,2084],{"stretchy":2083},[9252,103162,103163,103165,103167],{},[2071,103164,575],{},[2210,103166,646],{},[2071,103168,554],{},[2075,103170,2176],{},[2071,103172,543],{},[2075,103174,2090],{"stretchy":2083},[2075,103176,2303],{},[2205,103178,103179,103181],{},[2071,103180,575],{},[2071,103182,554],{},[2075,103184,2361],{"separator":2360},[5965,103186],{"width":5967},[2348,103188,103189,103191],{},[2071,103190,543],{},[2068,103192,103193,103195,103197],{},[2071,103194,46992],{},[2071,103196,2073],{},[2071,103198,13774],{},[2075,103200,2077],{},[2205,103202,103203,103205],{},[2071,103204,575],{},[2071,103206,554],{},[2075,103208,2303],{},[9252,103210,103211,103213,103215],{},[2071,103212,575],{},[2210,103214,646],{},[2071,103216,554],{},[2071,103218,195],{"mathvariant":2450},[2092,103220,103221],{"encoding":2094},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[55,103223,103224],{},[3982,103225,103226,103227,103257,103258,102110,103271,5756,103288,102141,103301,195],{},"Obrázek 2.19: Posun ",[1647,103228,103230],{"className":103229},[2059],[2061,103231,103232],{"xmlns":2063},[2065,103233,103234,103254],{},[2068,103235,103236,103238,103240,103246,103248,103250,103252],{},[2071,103237,4271],{},[2075,103239,3197],{},[2348,103241,103242,103244],{},[2071,103243,4271],{},[2210,103245,646],{},[2075,103247,2077],{},[2071,103249,4271],{},[2075,103251,2303],{},[2071,103253,543],{},[2092,103255,103256],{"encoding":2094},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[1647,103259,103261],{"className":103260},[2059],[2061,103262,103263],{"xmlns":2063},[2065,103264,103265,103269],{},[2068,103266,103267],{},[2071,103268,543],{},[2092,103270,543],{"encoding":2094},[1647,103272,103274],{"className":103273},[2059],[2061,103275,103276],{"xmlns":2063},[2065,103277,103278,103286],{},[2068,103279,103280],{},[2348,103281,103282,103284],{},[2071,103283,4271],{},[2210,103285,646],{},[2092,103287,42618],{"encoding":2094},[1647,103289,103291],{"className":103290},[2059],[2061,103292,103293],{"xmlns":2063},[2065,103294,103295,103299],{},[2068,103296,103297],{},[2071,103298,532],{},[2092,103300,532],{"encoding":2094},[1647,103302,103304],{"className":103303},[2059],[2061,103305,103306],{"xmlns":2063},[2065,103307,103308,103316],{},[2068,103309,103310],{},[2348,103311,103312,103314],{},[2071,103313,554],{},[2210,103315,646],{},[2092,103317,103318],{"encoding":2094},"E_2",[609,103320,49679],{"id":103321},"příklad-210",[55,103323,103324,103326,103327,45981,103350,103369,103370,103387],{},[95,103325,42224],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[1647,103328,103330],{"className":103329},[2059],[2061,103331,103332],{"xmlns":2063},[2065,103333,103334,103348],{},[2068,103335,103336,103338,103340,103342,103344,103346],{},[2071,103337,575],{},[2075,103339,2077],{},[2210,103341,3583],{},[2075,103343,2303],{},[2210,103345,646],{},[2071,103347,2861],{},[2092,103349,102190],{"encoding":2094},[1647,103351,103353],{"className":103352},[2059],[2061,103354,103355],{"xmlns":2063},[2065,103356,103357,103367],{},[2068,103358,103359,103361,103363,103365],{},[2071,103360,575],{},[2075,103362,2077],{},[2210,103364,662],{},[2071,103366,2861],{},[2092,103368,102210],{"encoding":2094},". Daň ",[1647,103371,103373],{"className":103372},[2059],[2061,103374,103375],{"xmlns":2063},[2065,103376,103377,103385],{},[2068,103378,103379,103381,103383],{},[2071,103380,543],{},[2075,103382,2077],{},[2210,103384,678],{},[2092,103386,45559],{"encoding":2094}," Kč je tentokrát uložena na spotřebitele.",[55,103389,103390],{},[95,103391,42256],{},[55,103393,103394,103395,102401],{},"Nová poptávka je ",[1647,103396,103398],{"className":103397},[2059],[2061,103399,103400],{"xmlns":2063},[2065,103401,103402,103438],{},[2068,103403,103404,103410,103412,103414,103416,103418,103420,103422,103424,103426,103428,103430,103432,103434,103436],{},[2348,103405,103406,103408],{},[2071,103407,4271],{},[2210,103409,646],{},[2075,103411,2777],{},[2071,103413,575],{},[2075,103415,2077],{},[2210,103417,3583],{},[2075,103419,2303],{},[2210,103421,646],{},[2071,103423,2861],{},[2075,103425,2303],{},[2210,103427,678],{},[2075,103429,2077],{},[2210,103431,678],{},[2075,103433,2303],{},[2210,103435,646],{},[2071,103437,2861],{},[2092,103439,103440],{"encoding":2094},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[1647,103442,103444],{"className":103443},[2059],[2061,103445,103446],{"xmlns":2063,"display":31093},[2065,103447,103448,103464],{},[2068,103449,103450,103452,103454,103456,103458,103460,103462],{},[2210,103451,678],{},[2075,103453,2303],{},[2210,103455,646],{},[2071,103457,2861],{},[2075,103459,2077],{},[2210,103461,662],{},[2071,103463,2861],{},[2092,103465,103466],{"encoding":2094},"6 - 2Q = 4Q",[55,103468,102434,103469,5676,103488,835,103512,102515,103544,195],{},[1647,103470,103472],{"className":103471},[2059],[2061,103473,103474],{"xmlns":2063},[2065,103475,103476,103486],{},[2068,103477,103478,103480,103482,103484],{},[2210,103479,678],{},[2071,103481,2861],{},[2075,103483,2077],{},[2210,103485,678],{},[2092,103487,102454],{"encoding":2094},[1647,103489,103491],{"className":103490},[2059],[2061,103492,103493],{"xmlns":2063},[2065,103494,103495,103509],{},[2068,103496,103497,103505,103507],{},[9252,103498,103499,103501,103503],{},[2071,103500,2861],{},[2210,103502,646],{},[2071,103504,554],{},[2075,103506,2077],{},[2210,103508,638],{},[2092,103510,103511],{"encoding":2094},"Q_2^E = 1",[1647,103513,103515],{"className":103514},[2059],[2061,103516,103517],{"xmlns":2063},[2065,103518,103519,103541],{},[2068,103520,103521,103529,103531,103533,103535,103537,103539],{},[9252,103522,103523,103525,103527],{},[2071,103524,575],{},[2210,103526,646],{},[2071,103528,554],{},[2075,103530,2077],{},[2210,103532,662],{},[2075,103534,3251],{},[2210,103536,638],{},[2075,103538,2077],{},[2210,103540,662],{},[2092,103542,103543],{"encoding":2094},"P_2^E = 4 \\cdot 1 = 4",[1647,103545,103547],{"className":103546},[2059],[2061,103548,103549],{"xmlns":2063},[2065,103550,103551,103569],{},[2068,103552,103553,103559,103561,103563,103565,103567],{},[2348,103554,103555,103557],{},[2071,103556,554],{},[2210,103558,646],{},[2075,103560,2561],{"stretchy":2083},[2210,103562,638],{},[2075,103564,2361],{"separator":2360},[2210,103566,662],{},[2075,103568,2576],{"stretchy":2083},[2092,103570,103571],{"encoding":2094},"E_2[1, 4]",[55,103573,103574,103575,103611,103612,102229],{},"Spotřebitel platí celkem ",[1647,103576,103578],{"className":103577},[2059],[2061,103579,103580],{"xmlns":2063},[2065,103581,103582,103608],{},[2068,103583,103584,103592,103594,103596,103598,103600,103602,103604,103606],{},[9252,103585,103586,103588,103590],{},[2071,103587,575],{},[2210,103589,646],{},[2071,103591,554],{},[2075,103593,2176],{},[2071,103595,543],{},[2075,103597,2077],{},[2210,103599,662],{},[2075,103601,2176],{},[2210,103603,678],{},[2075,103605,2077],{},[2210,103607,2935],{},[2092,103609,103610],{"encoding":2094},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[1647,103613,103615],{"className":103614},[2059],[2061,103616,103617],{"xmlns":2063},[2065,103618,103619,103633],{},[2068,103620,103621,103629,103631],{},[9252,103622,103623,103625,103627],{},[2071,103624,575],{},[2210,103626,646],{},[2071,103628,554],{},[2075,103630,2077],{},[2210,103632,662],{},[2092,103634,103635],{"encoding":2094},"P_2^E = 4",[55,103637,103638],{},[3982,103639,103640],{},"Rozklad daňového břemene:",[1647,103642,103644],{"className":103643},[2059],[2061,103645,103646],{"xmlns":2063,"display":31093},[2065,103647,103648,103734],{},[2068,103649,103650,103660,103662,103664,103666,103668,103670,103672,103674,103676,103678,103680,103682,103692,103694,103696,103708,103710,103712,103714,103716,103718,103720,103722,103732],{},[2348,103651,103652,103654],{},[2071,103653,543],{},[2068,103655,103656,103658],{},[2071,103657,46969],{},[2071,103659,55],{},[2075,103661,2077],{},[2075,103663,2084],{"stretchy":2083},[2210,103665,662],{},[2075,103667,2176],{},[2210,103669,678],{},[2075,103671,2090],{"stretchy":2083},[2075,103673,2303],{},[2210,103675,5672],{},[2075,103677,2077],{},[2210,103679,646],{},[2363,103681,2365],{},[2068,103683,103684,103686],{},[2363,103685,10929],{},[8473,103687,103688,103690],{"accent":2360},[2363,103689,2222],{},[2075,103691,27796],{},[2075,103693,2361],{"separator":2360},[5965,103695],{"width":5967},[2348,103697,103698,103700],{},[2071,103699,543],{},[2068,103701,103702,103704,103706],{},[2071,103703,46992],{},[2071,103705,2073],{},[2071,103707,13774],{},[2075,103709,2077],{},[2210,103711,5672],{},[2075,103713,2303],{},[2210,103715,662],{},[2075,103717,2077],{},[2210,103719,662],{},[2363,103721,2365],{},[2068,103723,103724,103726],{},[2363,103725,10929],{},[8473,103727,103728,103730],{"accent":2360},[2363,103729,2222],{},[2075,103731,27796],{},[2071,103733,195],{"mathvariant":2450},[2092,103735,103736],{"encoding":2094},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[55,103738,103739,103740,195],{},"Opět ",[1647,103741,103743],{"className":103742},[2059],[2061,103744,103745],{"xmlns":2063},[2065,103746,103747,103781],{},[2068,103748,103749,103759,103761,103773,103775,103777,103779],{},[2348,103750,103751,103753],{},[2071,103752,543],{},[2068,103754,103755,103757],{},[2071,103756,46969],{},[2071,103758,55],{},[2075,103760,2176],{},[2348,103762,103763,103765],{},[2071,103764,543],{},[2068,103766,103767,103769,103771],{},[2071,103768,46992],{},[2071,103770,2073],{},[2071,103772,13774],{},[2075,103774,2077],{},[2210,103776,678],{},[2075,103778,2077],{},[2071,103780,543],{},[2092,103782,103783],{"encoding":2094},"T_{sp} + T_{vyr} = 6 = T",[909,103785],{},[84,103787,46950],{"id":103788},"daňové-břemeno",[55,103790,103791,11156,103793,103796,103797,103810],{},[95,103792,46950],{},[3982,103794,103795],{},"tax burden",") je rozdělení zaplacené daně ",[1647,103798,103800],{"className":103799},[2059],[2061,103801,103802],{"xmlns":2063},[2065,103803,103804,103808],{},[2068,103805,103806],{},[2071,103807,543],{},[2092,103809,543],{"encoding":2094}," mezi spotřebitele a výrobce:",[1647,103812,103814],{"className":103813},[2059],[2061,103815,103816],{"xmlns":2063,"display":31093},[2065,103817,103818,103850],{},[2068,103819,103820,103822,103824,103834,103836,103848],{},[2071,103821,543],{},[2075,103823,2077],{},[2348,103825,103826,103828],{},[2071,103827,543],{},[2068,103829,103830,103832],{},[2071,103831,46969],{},[2071,103833,55],{},[2075,103835,2176],{},[2348,103837,103838,103840],{},[2071,103839,543],{},[2068,103841,103842,103844,103846],{},[2071,103843,46992],{},[2071,103845,2073],{},[2071,103847,13774],{},[2071,103849,195],{"mathvariant":2450},[2092,103851,103852],{"encoding":2094},"T = T_{sp} + T_{vyr}.",[55,103854,103855],{},[58,103856],{"alt":103857,"className":103858,"src":103859},"imek-dan-rozklad-bremene-sklony",[62,63],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1023,103861,103862],{},[55,103863,103864,103866,103867,75,103880,195],{},[1647,103865,4243],{}," Intuice — proč se daňové břemeno dělí\nKdyby byla poptávka dokonale elastická (vodorovná), spotřebitelé by při jakémkoliv navýšení ceny úplně přestali nakupovat — celou daň by musel zaplatit výrobce. Naopak při dokonale neelastické poptávce (svislá křivka) spotřebitelé nakupují stále stejné množství a celou daň přenesou na ně. V realitě jsou obě křivky nějak skloněné a daňové břemeno se dělí v poměru, který je dán relativními sklony ",[1647,103868,103870],{"className":103869},[2059],[2061,103871,103872],{"xmlns":2063},[2065,103873,103874,103878],{},[2068,103875,103876],{},[2071,103877,4271],{},[2092,103879,4271],{"encoding":2094},[1647,103881,103883],{"className":103882},[2059],[2061,103884,103885],{"xmlns":2063},[2065,103886,103887,103891],{},[2068,103888,103889],{},[2071,103890,532],{},[2092,103892,532],{"encoding":2094},[609,103894,2519],{"id":2518},[55,103896,103897,103898,103919,103920,103933,103934,103951,103952,103965],{},"V grafu ",[1647,103899,103901],{"className":103900},[2059],[2061,103902,103903],{"xmlns":2063},[2065,103904,103905,103917],{},[2068,103906,103907,103909,103911,103913,103915],{},[2075,103908,2084],{"stretchy":2083},[2071,103910,2861],{},[2075,103912,2361],{"separator":2360},[2071,103914,575],{},[2075,103916,2090],{"stretchy":2083},[2092,103918,41982],{"encoding":2094}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[1647,103921,103923],{"className":103922},[2059],[2061,103924,103925],{"xmlns":2063},[2065,103926,103927,103931],{},[2068,103928,103929],{},[2071,103930,543],{},[2092,103932,543],{"encoding":2094},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[1647,103935,103937],{"className":103936},[2059],[2061,103938,103939],{"xmlns":2063},[2065,103940,103941,103949],{},[2068,103942,103943],{},[2205,103944,103945,103947],{},[2071,103946,575],{},[2071,103948,554],{},[2092,103950,45757],{"encoding":2094},", rozdělí se úsečka ",[1647,103953,103955],{"className":103954},[2059],[2061,103956,103957],{"xmlns":2063},[2065,103958,103959,103963],{},[2068,103960,103961],{},[2071,103962,543],{},[2092,103964,543],{"encoding":2094}," na dvě části:",[89,103967,103968,103993],{},[92,103969,103970,103971,103992],{},"horní část odpovídá ",[1647,103972,103974],{"className":103973},[2059],[2061,103975,103976],{"xmlns":2063},[2065,103977,103978,103990],{},[2068,103979,103980],{},[2348,103981,103982,103984],{},[2071,103983,543],{},[2068,103985,103986,103988],{},[2071,103987,46969],{},[2071,103989,55],{},[2092,103991,46974],{"encoding":2094}," (o kolik vzrostla cena placená spotřebitelem),",[92,103994,103995,103996,104019],{},"dolní část odpovídá ",[1647,103997,103999],{"className":103998},[2059],[2061,104000,104001],{"xmlns":2063},[2065,104002,104003,104017],{},[2068,104004,104005],{},[2348,104006,104007,104009],{},[2071,104008,543],{},[2068,104010,104011,104013,104015],{},[2071,104012,46992],{},[2071,104014,2073],{},[2071,104016,13774],{},[2092,104018,46999],{"encoding":2094}," (o kolik klesla cena přijímaná výrobcem).",[55,104021,104022],{},[3982,104023,104024,104025,2758,104038,104059,104060,104083,104084,75,104105,104128],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[1647,104026,104028],{"className":104027},[2059],[2061,104029,104030],{"xmlns":2063},[2065,104031,104032,104036],{},[2068,104033,104034],{},[2071,104035,543],{},[2092,104037,543],{"encoding":2094},[1647,104039,104041],{"className":104040},[2059],[2061,104042,104043],{"xmlns":2063},[2065,104044,104045,104057],{},[2068,104046,104047],{},[2348,104048,104049,104051],{},[2071,104050,543],{},[2068,104052,104053,104055],{},[2071,104054,46969],{},[2071,104056,55],{},[2092,104058,46974],{"encoding":2094}," (nahoře) a ",[1647,104061,104063],{"className":104062},[2059],[2061,104064,104065],{"xmlns":2063},[2065,104066,104067,104081],{},[2068,104068,104069],{},[2348,104070,104071,104073],{},[2071,104072,543],{},[2068,104074,104075,104077,104079],{},[2071,104076,46992],{},[2071,104078,2073],{},[2071,104080,13774],{},[2092,104082,46999],{"encoding":2094}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[1647,104085,104087],{"className":104086},[2059],[2061,104088,104089],{"xmlns":2063},[2065,104090,104091,104103],{},[2068,104092,104093],{},[2348,104094,104095,104097],{},[2071,104096,543],{},[2068,104098,104099,104101],{},[2071,104100,46969],{},[2071,104102,55],{},[2092,104104,46974],{"encoding":2094},[1647,104106,104108],{"className":104107},[2059],[2061,104109,104110],{"xmlns":2063},[2065,104111,104112,104126],{},[2068,104113,104114],{},[2348,104115,104116,104118],{},[2071,104117,543],{},[2068,104119,104120,104122,104124],{},[2071,104121,46992],{},[2071,104123,2073],{},[2071,104125,13774],{},[2092,104127,46999],{"encoding":2094}," je v obou případech stejná.",[609,104130,104132],{"id":104131},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[55,104134,104135,104136,104139,104140,11156,104163,104180,104181,11156,104204,104221],{},"Platí obecně: ",[95,104137,104138],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[1647,104141,104143],{"className":104142},[2059],[2061,104144,104145],{"xmlns":2063},[2065,104146,104147,104161],{},[2068,104148,104149,104151,104153,104155,104157,104159],{},[2071,104150,575],{},[2075,104152,2077],{},[2071,104154,69],{},[2071,104156,2861],{},[2075,104158,2176],{},[2071,104160,2179],{},[2092,104162,41352],{"encoding":2094},[1647,104164,104166],{"className":104165},[2059],[2061,104167,104168],{"xmlns":2063},[2065,104169,104170,104178],{},[2068,104171,104172,104174,104176],{},[2071,104173,69],{},[2075,104175,3521],{},[2210,104177,630],{},[2092,104179,47379],{"encoding":2094},") a lineární nabídku ",[1647,104182,104184],{"className":104183},[2059],[2061,104185,104186],{"xmlns":2063},[2065,104187,104188,104202],{},[2068,104189,104190,104192,104194,104196,104198,104200],{},[2071,104191,575],{},[2075,104193,2077],{},[2071,104195,2222],{},[2071,104197,2861],{},[2075,104199,2176],{},[2071,104201,2273],{},[2092,104203,44533],{"encoding":2094},[1647,104205,104207],{"className":104206},[2059],[2061,104208,104209],{"xmlns":2063},[2065,104210,104211,104219],{},[2068,104212,104213,104215,104217],{},[2071,104214,2222],{},[2075,104216,3482],{},[2210,104218,630],{},[2092,104220,44551],{"encoding":2094},") lze rozklad odvodit pomocí multiplikátorů a platí",[1647,104223,104225],{"className":104224},[2059],[2061,104226,104227],{"xmlns":2063,"display":31093},[2065,104228,104229,104295],{},[2068,104230,104231,104255,104257,104267,104269,104293],{},[2403,104232,104233,104243],{},[2348,104234,104235,104237],{},[2071,104236,543],{},[2068,104238,104239,104241],{},[2071,104240,46969],{},[2071,104242,55],{},[2348,104244,104245,104247],{},[2071,104246,543],{},[2068,104248,104249,104251,104253],{},[2071,104250,46992],{},[2071,104252,2073],{},[2071,104254,13774],{},[2075,104256,2077],{},[2403,104258,104259,104261],{},[2071,104260,2222],{},[2068,104262,104263,104265],{},[2075,104264,2303],{},[2071,104266,69],{},[2075,104268,2077],{},[2403,104270,104271,104283],{},[2068,104272,104273,104276,104279,104281],{},[2071,104274,104275],{"mathvariant":2450},"∣",[2363,104277,104278],{},"sklon ",[2071,104280,532],{},[2071,104282,104275],{"mathvariant":2450},[2068,104284,104285,104287,104289,104291],{},[2071,104286,104275],{"mathvariant":2450},[2363,104288,104278],{},[2071,104290,4271],{},[2071,104292,104275],{"mathvariant":2450},[2071,104294,195],{"mathvariant":2450},[2092,104296,104297],{"encoding":2094},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1023,104299,104300,104305],{},[55,104301,104302,104304],{},[1647,104303,4659],{}," Postup výpočtu rozkladu",[201,104306,104307,104342,104395,104474],{},[92,104308,104309,104310,104341],{},"Spočti rovnovážný bod ",[1647,104311,104313],{"className":104312},[2059],[2061,104314,104315],{"xmlns":2063},[2065,104316,104317,104339],{},[2068,104318,104319,104321,104323,104329,104331,104337],{},[2071,104320,554],{},[2075,104322,2561],{"stretchy":2083},[2205,104324,104325,104327],{},[2071,104326,2861],{},[2071,104328,554],{},[2075,104330,2361],{"separator":2360},[2205,104332,104333,104335],{},[2071,104334,575],{},[2071,104336,554],{},[2075,104338,2576],{"stretchy":2083},[2092,104340,45658],{"encoding":2094}," bez daně.",[92,104343,104344,104345,2462,104370,4007],{},"Urči posunutou křivku (",[1647,104346,104348],{"className":104347},[2059],[2061,104349,104350],{"xmlns":2063},[2065,104351,104352,104368],{},[2068,104353,104354,104360,104362,104364,104366],{},[2348,104355,104356,104358],{},[2071,104357,532],{},[2210,104359,638],{},[2075,104361,2077],{},[2071,104363,532],{},[2075,104365,2176],{},[2071,104367,543],{},[2092,104369,47048],{"encoding":2094},[1647,104371,104373],{"className":104372},[2059],[2061,104374,104375],{"xmlns":2063},[2065,104376,104377,104393],{},[2068,104378,104379,104385,104387,104389,104391],{},[2348,104380,104381,104383],{},[2071,104382,4271],{},[2210,104384,646],{},[2075,104386,2077],{},[2071,104388,4271],{},[2075,104390,2303],{},[2071,104392,543],{},[2092,104394,47079],{"encoding":2094},[92,104396,104397,104398,3997,104417,13861,104436,3997,104455,4007],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[1647,104399,104401],{"className":104400},[2059],[2061,104402,104403],{"xmlns":2063},[2065,104404,104405,104415],{},[2068,104406,104407],{},[9252,104408,104409,104411,104413],{},[2071,104410,2861],{},[2210,104412,638],{},[2071,104414,554],{},[2092,104416,52132],{"encoding":2094},[1647,104418,104420],{"className":104419},[2059],[2061,104421,104422],{"xmlns":2063},[2065,104423,104424,104434],{},[2068,104425,104426],{},[9252,104427,104428,104430,104432],{},[2071,104429,2861],{},[2210,104431,646],{},[2071,104433,554],{},[2092,104435,52194],{"encoding":2094},[1647,104437,104439],{"className":104438},[2059],[2061,104440,104441],{"xmlns":2063},[2065,104442,104443,104453],{},[2068,104444,104445],{},[9252,104446,104447,104449,104451],{},[2071,104448,575],{},[2210,104450,638],{},[2071,104452,554],{},[2092,104454,52153],{"encoding":2094},[1647,104456,104458],{"className":104457},[2059],[2061,104459,104460],{"xmlns":2063},[2065,104461,104462,104472],{},[2068,104463,104464],{},[9252,104465,104466,104468,104470],{},[2071,104467,575],{},[2210,104469,646],{},[2071,104471,554],{},[2092,104473,52214],{"encoding":2094},[92,104475,104476,104477,75,104498,104521,104522,195],{},"Dopočítej ",[1647,104478,104480],{"className":104479},[2059],[2061,104481,104482],{"xmlns":2063},[2065,104483,104484,104496],{},[2068,104485,104486],{},[2348,104487,104488,104490],{},[2071,104489,543],{},[2068,104491,104492,104494],{},[2071,104493,46969],{},[2071,104495,55],{},[2092,104497,46974],{"encoding":2094},[1647,104499,104501],{"className":104500},[2059],[2061,104502,104503],{"xmlns":2063},[2065,104504,104505,104519],{},[2068,104506,104507],{},[2348,104508,104509,104511],{},[2071,104510,543],{},[2068,104512,104513,104515,104517],{},[2071,104514,46992],{},[2071,104516,2073],{},[2071,104518,13774],{},[2092,104520,46999],{"encoding":2094}," z definice, vždy ověř ",[1647,104523,104525],{"className":104524},[2059],[2061,104526,104527],{"xmlns":2063},[2065,104528,104529,104559],{},[2068,104530,104531,104541,104543,104555,104557],{},[2348,104532,104533,104535],{},[2071,104534,543],{},[2068,104536,104537,104539],{},[2071,104538,46969],{},[2071,104540,55],{},[2075,104542,2176],{},[2348,104544,104545,104547],{},[2071,104546,543],{},[2068,104548,104549,104551,104553],{},[2071,104550,46992],{},[2071,104552,2073],{},[2071,104554,13774],{},[2075,104556,2077],{},[2071,104558,543],{},[2092,104560,104561],{"encoding":2094},"T_{sp} + T_{vyr} = T",[1023,104563,104564],{},[55,104565,104566,104568,104569,104572,104573,75,104586,104599],{},[1647,104567,4499],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[95,104570,104571],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[1647,104574,104576],{"className":104575},[2059],[2061,104577,104578],{"xmlns":2063},[2065,104579,104580,104584],{},[2068,104581,104582],{},[2071,104583,4271],{},[2092,104585,4271],{"encoding":2094},[1647,104587,104589],{"className":104588},[2059],[2061,104590,104591],{"xmlns":2063},[2065,104592,104593,104597],{},[2068,104594,104595],{},[2071,104596,532],{},[2092,104598,532],{"encoding":2094},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[909,104601],{},[84,104603,104605],{"id":104604},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[55,104607,104608],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[55,104610,104611],{},[58,104612],{"alt":104613,"className":104614,"src":104615},"imek-dan-ekvivalence-vyrobce-spotrebitel",[62,63],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[323,104617,104618,104630],{},[326,104619,104620],{},[329,104621,104622,104624,104627],{},[332,104623,58594],{},[332,104625,104626],{},"(a) daň výrobci",[332,104628,104629],{},"(b) daň spotřebiteli",[342,104631,104632,104687,104754,104814],{},[329,104633,104634,104637,104662],{},[347,104635,104636],{},"Rovnovážné množství",[347,104638,104639],{},[1647,104640,104642],{"className":104641},[2059],[2061,104643,104644],{"xmlns":2063},[2065,104645,104646,104660],{},[2068,104647,104648,104656,104658],{},[9252,104649,104650,104652,104654],{},[2071,104651,2861],{},[2210,104653,638],{},[2071,104655,554],{},[2075,104657,2077],{},[2210,104659,638],{},[2092,104661,102478],{"encoding":2094},[347,104663,104664],{},[1647,104665,104667],{"className":104666},[2059],[2061,104668,104669],{"xmlns":2063},[2065,104670,104671,104685],{},[2068,104672,104673,104681,104683],{},[9252,104674,104675,104677,104679],{},[2071,104676,2861],{},[2210,104678,646],{},[2071,104680,554],{},[2075,104682,2077],{},[2210,104684,638],{},[2092,104686,103511],{"encoding":2094},[329,104688,104689,104692,104717],{},[347,104690,104691],{},"Cena placená spotřebitelem",[347,104693,104694],{},[1647,104695,104697],{"className":104696},[2059],[2061,104698,104699],{"xmlns":2063},[2065,104700,104701,104715],{},[2068,104702,104703,104711,104713],{},[9252,104704,104705,104707,104709],{},[2071,104706,575],{},[2210,104708,638],{},[2071,104710,554],{},[2075,104712,2077],{},[2210,104714,2935],{},[2092,104716,102573],{"encoding":2094},[347,104718,104719],{},[1647,104720,104722],{"className":104721},[2059],[2061,104723,104724],{"xmlns":2063},[2065,104725,104726,104752],{},[2068,104727,104728,104736,104738,104740,104742,104744,104746,104748,104750],{},[9252,104729,104730,104732,104734],{},[2071,104731,575],{},[2210,104733,646],{},[2071,104735,554],{},[2075,104737,2176],{},[2071,104739,543],{},[2075,104741,2077],{},[2210,104743,662],{},[2075,104745,2176],{},[2210,104747,678],{},[2075,104749,2077],{},[2210,104751,2935],{},[2092,104753,103610],{"encoding":2094},[329,104755,104756,104759,104789],{},[347,104757,104758],{},"Cena přijímaná výrobcem",[347,104760,104761],{},[1647,104762,104764],{"className":104763},[2059],[2061,104765,104766],{"xmlns":2063},[2065,104767,104768,104786],{},[2068,104769,104770,104778,104780,104782,104784],{},[9252,104771,104772,104774,104776],{},[2071,104773,575],{},[2210,104775,638],{},[2071,104777,554],{},[2075,104779,2303],{},[2071,104781,543],{},[2075,104783,2077],{},[2210,104785,662],{},[2092,104787,104788],{"encoding":2094},"P_1^E - T = 4",[347,104790,104791],{},[1647,104792,104794],{"className":104793},[2059],[2061,104795,104796],{"xmlns":2063},[2065,104797,104798,104812],{},[2068,104799,104800,104808,104810],{},[9252,104801,104802,104804,104806],{},[2071,104803,575],{},[2210,104805,646],{},[2071,104807,554],{},[2075,104809,2077],{},[2210,104811,662],{},[2092,104813,103635],{"encoding":2094},[329,104815,104816,104819,104873],{},[347,104817,104818],{},"Rozklad břemene",[347,104820,104821,835,104846],{},[1647,104822,104824],{"className":104823},[2059],[2061,104825,104826],{"xmlns":2063},[2065,104827,104828,104844],{},[2068,104829,104830,104840,104842],{},[2348,104831,104832,104834],{},[2071,104833,543],{},[2068,104835,104836,104838],{},[2071,104837,46969],{},[2071,104839,55],{},[2075,104841,2077],{},[2210,104843,646],{},[2092,104845,47270],{"encoding":2094},[1647,104847,104849],{"className":104848},[2059],[2061,104850,104851],{"xmlns":2063},[2065,104852,104853,104871],{},[2068,104854,104855,104867,104869],{},[2348,104856,104857,104859],{},[2071,104858,543],{},[2068,104860,104861,104863,104865],{},[2071,104862,46992],{},[2071,104864,2073],{},[2071,104866,13774],{},[2075,104868,2077],{},[2210,104870,662],{},[2092,104872,47299],{"encoding":2094},[347,104874,104875,835,104900],{},[1647,104876,104878],{"className":104877},[2059],[2061,104879,104880],{"xmlns":2063},[2065,104881,104882,104898],{},[2068,104883,104884,104894,104896],{},[2348,104885,104886,104888],{},[2071,104887,543],{},[2068,104889,104890,104892],{},[2071,104891,46969],{},[2071,104893,55],{},[2075,104895,2077],{},[2210,104897,646],{},[2092,104899,47270],{"encoding":2094},[1647,104901,104903],{"className":104902},[2059],[2061,104904,104905],{"xmlns":2063},[2065,104906,104907,104925],{},[2068,104908,104909,104921,104923],{},[2348,104910,104911,104913],{},[2071,104912,543],{},[2068,104914,104915,104917,104919],{},[2071,104916,46992],{},[2071,104918,2073],{},[2071,104920,13774],{},[2075,104922,2077],{},[2210,104924,662],{},[2092,104926,47299],{"encoding":2094},[55,104928,104929],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[1647,104931,104933],{"className":104932},[2059],[2061,104934,104935],{"xmlns":2063,"display":31093},[2065,104936,104937,104985],{},[2068,104938,104939,104947,104949,104957,104959,104961,104969,104971,104973,104975,104983],{},[9252,104940,104941,104943,104945],{},[2071,104942,2861],{},[2210,104944,638],{},[2071,104946,554],{},[2075,104948,2077],{},[9252,104950,104951,104953,104955],{},[2071,104952,2861],{},[2210,104954,646],{},[2071,104956,554],{},[2075,104958,2361],{"separator":2360},[5965,104960],{"width":5967},[9252,104962,104963,104965,104967],{},[2071,104964,575],{},[2210,104966,638],{},[2071,104968,554],{},[2075,104970,2303],{},[2071,104972,543],{},[2075,104974,2077],{},[9252,104976,104977,104979,104981],{},[2071,104978,575],{},[2210,104980,646],{},[2071,104982,554],{},[2071,104984,195],{"mathvariant":2450},[2092,104986,104987],{"encoding":2094},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1023,104989,104990,105009,105163],{},[55,104991,104992,104994,104995,105008],{},[1647,104993,4659],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[1647,104996,104998],{"className":104997},[2059],[2061,104999,105000],{"xmlns":2063},[2065,105001,105002,105006],{},[2068,105003,105004],{},[2071,105005,543],{},[2092,105007,543],{"encoding":2094}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[89,105010,105011,105043,105079,105116],{},[92,105012,105013,105014,2361],{},"rovnovážná množství obou režimů, ",[1647,105015,105017],{"className":105016},[2059],[2061,105018,105019],{"xmlns":2063},[2065,105020,105021,105041],{},[2068,105022,105023,105031,105033],{},[9252,105024,105025,105027,105029],{},[2071,105026,2861],{},[2210,105028,638],{},[2071,105030,554],{},[2075,105032,2077],{},[9252,105034,105035,105037,105039],{},[2071,105036,2861],{},[2210,105038,646],{},[2071,105040,554],{},[2092,105042,47202],{"encoding":2094},[92,105044,105045,105046,2361],{},"čistá cena přijímaná výrobcem, ",[1647,105047,105049],{"className":105048},[2059],[2061,105050,105051],{"xmlns":2063},[2065,105052,105053,105077],{},[2068,105054,105055,105063,105065,105067,105069],{},[9252,105056,105057,105059,105061],{},[2071,105058,575],{},[2210,105060,638],{},[2071,105062,554],{},[2075,105064,2303],{},[2071,105066,543],{},[2075,105068,2077],{},[9252,105070,105071,105073,105075],{},[2071,105072,575],{},[2210,105074,646],{},[2071,105076,554],{},[2092,105078,47236],{"encoding":2094},[92,105080,105081,105082,2361],{},"celková cena placená spotřebitelem, ",[1647,105083,105085],{"className":105084},[2059],[2061,105086,105087],{"xmlns":2063},[2065,105088,105089,105113],{},[2068,105090,105091,105099,105101,105109,105111],{},[9252,105092,105093,105095,105097],{},[2071,105094,575],{},[2210,105096,638],{},[2071,105098,554],{},[2075,105100,2077],{},[9252,105102,105103,105105,105107],{},[2071,105104,575],{},[2210,105106,646],{},[2071,105108,554],{},[2075,105110,2176],{},[2071,105112,543],{},[2092,105114,105115],{"encoding":2094},"P_1^E = P_2^E + T",[92,105117,105118,105119,75,105140,195],{},"rozklad daňového břemene ",[1647,105120,105122],{"className":105121},[2059],[2061,105123,105124],{"xmlns":2063},[2065,105125,105126,105138],{},[2068,105127,105128],{},[2348,105129,105130,105132],{},[2071,105131,543],{},[2068,105133,105134,105136],{},[2071,105135,46969],{},[2071,105137,55],{},[2092,105139,46974],{"encoding":2094},[1647,105141,105143],{"className":105142},[2059],[2061,105144,105145],{"xmlns":2063},[2065,105146,105147,105161],{},[2068,105148,105149],{},[2348,105150,105151,105153],{},[2071,105152,543],{},[2068,105154,105155,105157,105159],{},[2071,105156,46992],{},[2071,105158,2073],{},[2071,105160,13774],{},[2092,105162,46999],{"encoding":2094},[55,105164,105165,105166,195],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[95,105167,38223],{},[55,105169,105170,105171,75,105184,4007],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[1647,105172,105174],{"className":105173},[2059],[2061,105175,105176],{"xmlns":2063},[2065,105177,105178,105182],{},[2068,105179,105180],{},[2071,105181,4271],{},[2092,105183,4271],{"encoding":2094},[1647,105185,105187],{"className":105186},[2059],[2061,105188,105189],{"xmlns":2063},[2065,105190,105191,105195],{},[2068,105192,105193],{},[2071,105194,532],{},[2092,105196,532],{"encoding":2094},[909,105198],{},[84,105200,105202],{"id":105201},"úlohy","Úlohy",[55,105204,105205,105206,3225],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[69,105207,17975],{"className":105208,"dataFsResolvedFilePath":13670,"href":13671},[62],[89,105210,105211,105241,105272],{},[92,105212,105213,105216,105217,105240],{},[95,105214,105215],{},"Úloha 2.4"," — Poptávka ",[1647,105218,105220],{"className":105219},[2059],[2061,105221,105222],{"xmlns":2063},[2065,105223,105224,105238],{},[2068,105225,105226,105228,105230,105232,105234,105236],{},[2071,105227,575],{},[2075,105229,2077],{},[2210,105231,3583],{},[2075,105233,2303],{},[2210,105235,646],{},[2071,105237,2861],{},[2092,105239,102190],{"encoding":2094},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[92,105242,105243,105246,105247,105271],{},[95,105244,105245],{},"Úloha 2.9"," — Nabídka ",[1647,105248,105250],{"className":105249},[2059],[2061,105251,105252],{"xmlns":2063},[2065,105253,105254,105268],{},[2068,105255,105256,105258,105260,105262,105264,105266],{},[2071,105257,575],{},[2075,105259,2077],{},[2210,105261,5096],{},[2071,105263,2861],{},[2075,105265,2176],{},[2210,105267,39270],{},[2092,105269,105270],{"encoding":2094},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[92,105273,105274,105277,105278,75,105304,105328,105329,105346],{},[95,105275,105276],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[1647,105279,105281],{"className":105280},[2059],[2061,105282,105283],{"xmlns":2063},[2065,105284,105285,105301],{},[2068,105286,105287,105289,105291,105293,105295,105297,105299],{},[2071,105288,575],{},[2075,105290,2077],{},[2075,105292,2303],{},[2210,105294,662],{},[2071,105296,2861],{},[2075,105298,2176],{},[2210,105300,50999],{},[2092,105302,105303],{"encoding":2094},"P = -4Q + 80",[1647,105305,105307],{"className":105306},[2059],[2061,105308,105309],{"xmlns":2063},[2065,105310,105311,105325],{},[2068,105312,105313,105315,105317,105319,105321,105323],{},[2071,105314,575],{},[2075,105316,2077],{},[2210,105318,654],{},[2071,105320,2861],{},[2075,105322,2176],{},[2210,105324,2935],{},[2092,105326,105327],{"encoding":2094},"P = 3Q + 10",": rovnováha, daň ",[1647,105330,105332],{"className":105331},[2059],[2061,105333,105334],{"xmlns":2063},[2065,105335,105336,105344],{},[2068,105337,105338,105340,105342],{},[2071,105339,543],{},[2075,105341,2077],{},[2210,105343,686],{},[2092,105345,52111],{"encoding":2094}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[55,105348,105349,105350,105352,105353,105355],{},"Související úvodní příklady posunu křivek při zdanění: ",[95,105351,49524],{}," (posun poptávky při zdanění kupujícího) a ",[95,105354,49558],{}," (posun nabídky při zdanění výrobce).",[909,105357],{},[84,105359,321],{"id":320},[89,105361,105362,105381,105439,105496,105579,105625,105668,105713,105779],{},[92,105363,105364,1445,105367,105380],{},[95,105365,105366],{},"Jednotková daň",[1647,105368,105370],{"className":105369},[2059],[2061,105371,105372],{"xmlns":2063},[2065,105373,105374,105378],{},[2068,105375,105376],{},[2071,105377,543],{},[2092,105379,543],{"encoding":2094}," — fixní částka na každou prodanou jednotku zboží",[92,105382,105383,105385,105386,105424,105425,105438],{},[95,105384,101772],{}," — posun nabídky ",[1647,105387,105389],{"className":105388},[2059],[2061,105390,105391],{"xmlns":2063},[2065,105392,105393,105421],{},[2068,105394,105395,105401,105403,105405,105407,105409,105411,105413,105415,105417,105419],{},[2348,105396,105397,105399],{},[2071,105398,532],{},[2210,105400,638],{},[2075,105402,2084],{"stretchy":2083},[2071,105404,2861],{},[2075,105406,2090],{"stretchy":2083},[2075,105408,2077],{},[2071,105410,532],{},[2075,105412,2084],{"stretchy":2083},[2071,105414,2861],{},[2075,105416,2090],{"stretchy":2083},[2075,105418,2176],{},[2071,105420,543],{},[2092,105422,105423],{"encoding":2094},"S_1(Q) = S(Q) + T"," (o ",[1647,105426,105428],{"className":105427},[2059],[2061,105429,105430],{"xmlns":2063},[2065,105431,105432,105436],{},[2068,105433,105434],{},[2071,105435,543],{},[2092,105437,543],{"encoding":2094}," svisle nahoru)",[92,105440,105441,105443,105444,105424,105482,105495],{},[95,105442,102845],{}," — posun poptávky ",[1647,105445,105447],{"className":105446},[2059],[2061,105448,105449],{"xmlns":2063},[2065,105450,105451,105479],{},[2068,105452,105453,105459,105461,105463,105465,105467,105469,105471,105473,105475,105477],{},[2348,105454,105455,105457],{},[2071,105456,4271],{},[2210,105458,646],{},[2075,105460,2084],{"stretchy":2083},[2071,105462,2861],{},[2075,105464,2090],{"stretchy":2083},[2075,105466,2077],{},[2071,105468,4271],{},[2075,105470,2084],{"stretchy":2083},[2071,105472,2861],{},[2075,105474,2090],{"stretchy":2083},[2075,105476,2303],{},[2071,105478,543],{},[2092,105480,105481],{"encoding":2094},"D_2(Q) = D(Q) - T",[1647,105483,105485],{"className":105484},[2059],[2061,105486,105487],{"xmlns":2063},[2065,105488,105489,105493],{},[2068,105490,105491],{},[2071,105492,543],{},[2092,105494,543],{"encoding":2094}," svisle dolů)",[92,105497,105498,7102,105501,46105,105540],{},[95,105499,105500],{},"Rovnovážný bod s daní",[1647,105502,105504],{"className":105503},[2059],[2061,105505,105506],{"xmlns":2063},[2065,105507,105508,105538],{},[2068,105509,105510,105516,105518,105526,105528,105536],{},[2348,105511,105512,105514],{},[2071,105513,554],{},[2210,105515,638],{},[2075,105517,2561],{"stretchy":2083},[9252,105519,105520,105522,105524],{},[2071,105521,2861],{},[2210,105523,638],{},[2071,105525,554],{},[2075,105527,2361],{"separator":2360},[9252,105529,105530,105532,105534],{},[2071,105531,575],{},[2210,105533,638],{},[2071,105535,554],{},[2075,105537,2576],{"stretchy":2083},[2092,105539,101940],{"encoding":2094},[1647,105541,105543],{"className":105542},[2059],[2061,105544,105545],{"xmlns":2063},[2065,105546,105547,105577],{},[2068,105548,105549,105555,105557,105565,105567,105575],{},[2348,105550,105551,105553],{},[2071,105552,554],{},[2210,105554,646],{},[2075,105556,2561],{"stretchy":2083},[9252,105558,105559,105561,105563],{},[2071,105560,2861],{},[2210,105562,646],{},[2071,105564,554],{},[2075,105566,2361],{"separator":2360},[9252,105568,105569,105571,105573],{},[2071,105570,575],{},[2210,105572,646],{},[2071,105574,554],{},[2075,105576,2576],{"stretchy":2083},[2092,105578,103015],{"encoding":2094},[92,105580,105581,11156,105583,105585,105586],{},[95,105582,46950],{},[3982,105584,103795],{},") — rozklad ",[1647,105587,105589],{"className":105588},[2059],[2061,105590,105591],{"xmlns":2063},[2065,105592,105593,105623],{},[2068,105594,105595,105597,105599,105609,105611],{},[2071,105596,543],{},[2075,105598,2077],{},[2348,105600,105601,105603],{},[2071,105602,543],{},[2068,105604,105605,105607],{},[2071,105606,46969],{},[2071,105608,55],{},[2075,105610,2176],{},[2348,105612,105613,105615],{},[2071,105614,543],{},[2068,105616,105617,105619,105621],{},[2071,105618,46992],{},[2071,105620,2073],{},[2071,105622,13774],{},[2092,105624,47138],{"encoding":2094},[92,105626,105627,105650,105651,2090],{},[95,105628,105629],{},[1647,105630,105632],{"className":105631},[2059],[2061,105633,105634],{"xmlns":2063},[2065,105635,105636,105648],{},[2068,105637,105638],{},[2348,105639,105640,105642],{},[2071,105641,543],{},[2068,105643,105644,105646],{},[2071,105645,46969],{},[2071,105647,55],{},[2092,105649,46974],{"encoding":2094}," — část daně nesená spotřebitelem (navýšení ceny nad ",[1647,105652,105654],{"className":105653},[2059],[2061,105655,105656],{"xmlns":2063},[2065,105657,105658,105666],{},[2068,105659,105660],{},[2205,105661,105662,105664],{},[2071,105663,575],{},[2071,105665,554],{},[2092,105667,45757],{"encoding":2094},[92,105669,105670,105695,105696,2090],{},[95,105671,105672],{},[1647,105673,105675],{"className":105674},[2059],[2061,105676,105677],{"xmlns":2063},[2065,105678,105679,105693],{},[2068,105680,105681],{},[2348,105682,105683,105685],{},[2071,105684,543],{},[2068,105686,105687,105689,105691],{},[2071,105688,46992],{},[2071,105690,2073],{},[2071,105692,13774],{},[2092,105694,46999],{"encoding":2094}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[1647,105697,105699],{"className":105698},[2059],[2061,105700,105701],{"xmlns":2063},[2065,105702,105703,105711],{},[2068,105704,105705],{},[2205,105706,105707,105709],{},[2071,105708,575],{},[2071,105710,554],{},[2092,105712,45757],{"encoding":2094},[92,105714,105715,7102,105717,835,105746],{},[95,105716,54770],{},[1647,105718,105720],{"className":105719},[2059],[2061,105721,105722],{"xmlns":2063},[2065,105723,105724,105744],{},[2068,105725,105726,105734,105736],{},[9252,105727,105728,105730,105732],{},[2071,105729,2861],{},[2210,105731,638],{},[2071,105733,554],{},[2075,105735,2077],{},[9252,105737,105738,105740,105742],{},[2071,105739,2861],{},[2210,105741,646],{},[2071,105743,554],{},[2092,105745,47202],{"encoding":2094},[1647,105747,105749],{"className":105748},[2059],[2061,105750,105751],{"xmlns":2063},[2065,105752,105753,105777],{},[2068,105754,105755,105763,105765,105767,105769],{},[9252,105756,105757,105759,105761],{},[2071,105758,575],{},[2210,105760,638],{},[2071,105762,554],{},[2075,105764,2303],{},[2071,105766,543],{},[2075,105768,2077],{},[9252,105770,105771,105773,105775],{},[2071,105772,575],{},[2210,105774,646],{},[2071,105776,554],{},[2092,105778,47236],{"encoding":2094},[92,105780,105781,105784],{},[95,105782,105783],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[909,105786],{},[84,105788,3866],{"id":3865},[89,105790,105791,105799,105817,105824],{},[92,105792,105793,1445,105796],{},[95,105794,105795],{},"Kontext (hub):",[69,105797,41053],{"className":105798,"dataFsResolvedFilePath":13670,"href":13671},[62],[92,105800,105801,1445,105803,105806,105807,21387,105809,105812,105813,105816],{},[95,105802,55018],{},[69,105804,13513],{"className":105805,"dataFsResolvedFilePath":49268,"href":49269},[62]," (daň vyvolává ztrátu blahobytu — ",[3982,105808,59332],{},[69,105810,2431],{"className":105811,"dataFsResolvedFilePath":4005,"href":4006},[62]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[69,105814,3913],{"className":105815,"dataFsResolvedFilePath":3911,"href":3912},[62]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[92,105818,105819,1445,105821],{},[95,105820,55053],{},[69,105822,55059],{"className":105823,"dataFsResolvedFilePath":55057,"href":55058},[62],[92,105825,105826,1445,105828],{},[95,105827,17937],{},[69,105829,17941],{"className":105830,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":105832},[105833,105834,105837,105840,105844,105845,105846,105847],{"id":101677,"depth":7,"text":101678},{"id":101771,"depth":7,"text":101772,"children":105835},[105836],{"id":102162,"depth":4,"text":49599},{"id":102844,"depth":7,"text":102845,"children":105838},[105839],{"id":103321,"depth":4,"text":49679},{"id":103788,"depth":7,"text":46950,"children":105841},[105842,105843],{"id":2518,"depth":4,"text":2519},{"id":104131,"depth":4,"text":104132},{"id":104604,"depth":7,"text":104605},{"id":105201,"depth":7,"text":105202},{"id":320,"depth":7,"text":321},{"id":3865,"depth":7,"text":3866},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":101575,"description":156},[9647,3938],"topics\u002Fzdaneni-trhu",[17,55120,105854,105855,105856,17975],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",{"id":105859,"title":105860,"body":105861,"course":17,"courses":163,"created":3932,"description":105868,"extension":166,"meta":106000,"navigation":168,"path":106001,"seo":106002,"sources":106003,"stem":106004,"tags":106005,"type":106007,"updated":178,"__hash__":106008},"summaries\u002Fsummaries\u002Fimek-blok-01.md","KS 1. blok — Kalkul a mikroekonomie",{"type":48,"value":105862,"toc":105995},[105863,105866,105869,105886,105890,105935,105939,105971,105975],[51,105864,105860],{"id":105865},"ks-1-blok-kalkul-a-mikroekonomie",[55,105867,105868],{},"Rozcestník prvního přednáškového bloku Mgr. Martiny Bobalové, Ph.D. (57 stran). Obsah byl rozdělen do menších tematických stránek, které lze studovat samostatně.",[1023,105870,105871],{},[55,105872,105873,105876,105877,105879,105880,105882,105883,105885],{},[95,105874,105875],{},"Konvence z přednášek:"," symbol ",[929,105878,2803],{}," pro přibližné rovnosti, výsledky ",[95,105881,101516],{},", pojem ",[3982,105884,101521],{}," znamená změnu o 1.",[84,105887,105889],{"id":105888},"témata-bloku-doporučené-pořadí","Témata bloku — doporučené pořadí",[201,105891,105892,105898,105904,105911,105917,105923,105929],{},[92,105893,105894,105897],{},[69,105895,3879],{"className":105896,"dataFsResolvedFilePath":3877,"href":3878},[62]," — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika, principy řešení",[92,105899,105900,105903],{},[69,105901,13684],{"className":105902,"dataFsResolvedFilePath":4005,"href":4006},[62]," — funkce, polynomy, derivace (geom.\u002Finženýrská interpretace), tečna, diferenciál jako lineární odhad přírůstku, podmínky extrémů",[92,105905,105906,105910],{},[69,105907,105909],{"className":105908,"dataFsResolvedFilePath":3888,"href":3889},[62],"Integrál (neurčitý a určitý)"," — primitivní funkce, určitý integrál jako plocha, rekonstrukce TR z MR a TC z MC",[92,105912,105913,105916],{},[69,105914,3901],{"className":105915,"dataFsResolvedFilePath":3899,"href":3900},[62]," — parciální derivace, diferenciál 2D, implicitní funkce, volné extrémy 2D, indiferenční křivky \u002F izokvanty",[92,105918,105919,105922],{},[69,105920,12195],{"className":105921,"dataFsResolvedFilePath":12193,"href":12194},[62]," — vázané extrémy, multiplikátor jako náklady příležitosti",[92,105924,105925,105928],{},[69,105926,13672],{"className":105927,"dataFsResolvedFilePath":13670,"href":13671},[62]," — modely D, S, tržní rovnováha, multiplikátory, přebytky, zdanění",[92,105930,105931,105934],{},[69,105932,3906],{"className":105933,"dataFsResolvedFilePath":3022,"href":3023},[62]," — TR\u002FAR\u002FMR, TC\u002FAC\u002FMC\u002FAVC\u002FAFC, body zvratu, maximalizace zisku, konstrukce nabídky firmy",[84,105936,105938],{"id":105937},"vazby-do-dalších-bloků","Vazby do dalších bloků",[89,105940,105941,105947,105957],{},[92,105942,105943,105946],{},[69,105944,3913],{"className":105945,"dataFsResolvedFilePath":3911,"href":3912},[62]," (Blok 2) — navazuje na příjem (vliv elasticity na TR) a využívá derivace.",[92,105948,105949,105952,105953,195],{},[69,105950,12221],{"className":105951,"dataFsResolvedFilePath":10942,"href":10943},[62]," (Blok 2) — využívá ",[69,105954,105956],{"className":105955,"dataFsResolvedFilePath":3899,"href":3900},[62],"parciální derivace",[92,105958,105959,105962,105963,75,105967,195],{},[69,105960,12226],{"className":105961,"dataFsResolvedFilePath":10901,"href":10902},[62]," (Blok 3) — využívá ",[69,105964,105966],{"className":105965,"dataFsResolvedFilePath":12193,"href":12194},[62],"Lagrange",[69,105968,105970],{"className":105969,"dataFsResolvedFilePath":3899,"href":3900},[62],"2D kalkul",[84,105972,105974],{"id":105973},"související","Související",[89,105976,105977,105983,105989],{},[92,105978,105979],{},[69,105980,105982],{"className":105981,"dataFsResolvedFilePath":2034,"href":2035},[62],"Kurz ImeK",[92,105984,105985,105988],{},[69,105986,39735],{"className":105987,"dataFsResolvedFilePath":39733,"href":39734},[62]," — Elasticita a produkce",[92,105990,105991,105994],{},[69,105992,39739],{"className":105993,"dataFsResolvedFilePath":17950,"href":17951},[62]," — Užitečnost a národní důchod",{"title":156,"searchDepth":7,"depth":7,"links":105996},[105997,105998,105999],{"id":105888,"depth":7,"text":105889},{"id":105937,"depth":7,"text":105938},{"id":105973,"depth":7,"text":105974},{},"\u002Fsummaries\u002Fimek-blok-01",{"title":105860,"description":105868},[3938],"summaries\u002Fimek-blok-01",[17,106006,2430,13721,42,17975,3024,39],"kalkul","summary","L44rKXw_S6gzhoDZz59NET2mlCeh4JKwVNZq9bCCveU",{"id":106010,"title":106011,"body":106012,"course":17,"courses":163,"created":3932,"description":106019,"extension":166,"meta":106485,"navigation":168,"path":106486,"seo":106487,"sources":106488,"stem":106489,"tags":106490,"type":106007,"updated":178,"__hash__":106492},"summaries\u002Fsummaries\u002Fimek-blok-02.md","KS 2. blok — Elasticita a produkce",{"type":48,"value":106013,"toc":106479},[106014,106017,106020,106022,106109,106113,106438,106442,106470,106472],[51,106015,106011],{"id":106016},"ks-2-blok-elasticita-a-produkce",[55,106018,106019],{},"Rozcestník druhého přednáškového bloku (19 stran). Pokrývá dvě hlavní témata, každé se samostatnou stránkou.",[84,106021,105889],{"id":105888},[201,106023,106024,106058],{},[92,106025,106026,106029,106030,106043,106044,106057],{},[69,106027,3913],{"className":106028,"dataFsResolvedFilePath":3911,"href":3912},[62]," — motivační hypotéza (procentní růst ",[1647,106031,106033],{"className":106032},[2059],[2061,106034,106035],{"xmlns":2063},[2065,106036,106037,106041],{},[2068,106038,106039],{},[2071,106040,2861],{},[2092,106042,2861],{"encoding":2094}," ≥ procentní pokles ",[1647,106045,106047],{"className":106046},[2059],[2061,106048,106049],{"xmlns":2063},[2065,106050,106051,106055],{},[2068,106052,106053],{},[2071,106054,575],{},[2092,106056,575],{"encoding":2094},"), cenová\u002Fkřížová\u002Fdůchodová elasticita poptávky, cenová elasticita nabídky, vícefaktorový model, pravidla pro TR, klasifikace (elastická \u002F jednotkově elastická \u002F neelastická).",[92,106059,106060,106064,106065,56618,106085,106108],{},[69,106061,106063],{"className":106062,"dataFsResolvedFilePath":10942,"href":10943},[62],"Produkce — produkční funkce"," — jednofaktorový a dvoufaktorový model ",[1647,106066,106068],{"className":106067},[2059],[2061,106069,106070],{"xmlns":2063},[2065,106071,106072,106082],{},[2068,106073,106074,106076,106078,106080],{},[2071,106075,2861],{},[2075,106077,2084],{"stretchy":2083},[2071,106079,586],{},[2075,106081,2090],{"stretchy":2083},[2092,106083,106084],{"encoding":2094},"Q(L)",[1647,106086,106088],{"className":106087},[2059],[2061,106089,106090],{"xmlns":2063},[2065,106091,106092,106106],{},[2068,106093,106094,106096,106098,106100,106102,106104],{},[2071,106095,2861],{},[2075,106097,2084],{"stretchy":2083},[2071,106099,586],{},[2075,106101,2361],{"separator":2360},[2071,106103,10929],{},[2075,106105,2090],{"stretchy":2083},[2092,106107,11128],{"encoding":2094},", Cobb-Douglas, CES, lineární, Leontiefova funkce, mezní produkty, izokvanty, MRTS, výnosy z rozsahu, Eulerova věta.",[84,106110,106112],{"id":106111},"klíčové-vzorce-na-jeden-pohled","Klíčové vzorce na jeden pohled",[89,106114,106115,106158,106199,106255,106332,106393],{},[92,106116,106117,106118],{},"Cenová elasticita poptávky: ",[1647,106119,106121],{"className":106120},[2059],[2061,106122,106123],{"xmlns":2063},[2065,106124,106125,106155],{},[2068,106126,106127,106129,106131,106133,106141,106143,106149,106151,106153],{},[2071,106128,554],{},[2075,106130,2077],{},[2075,106132,2303],{},[2400,106134,106135],{"scriptlevel":630,"displaystyle":2360},[2403,106136,106137,106139],{},[2071,106138,575],{},[2071,106140,2861],{},[2363,106142,3061],{},[2205,106144,106145,106147],{},[2071,106146,2861],{},[2075,106148,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,106150,2084],{"stretchy":2083},[2071,106152,575],{},[2075,106154,2090],{"stretchy":2083},[2092,106156,106157],{"encoding":2094},"E = -\\dfrac{P}{Q}\\, Q'(P)",[92,106159,106160,106161],{},"Cenová elasticita nabídky: ",[1647,106162,106164],{"className":106163},[2059],[2061,106165,106166],{"xmlns":2063},[2065,106167,106168,106196],{},[2068,106169,106170,106172,106174,106182,106184,106190,106192,106194],{},[2071,106171,554],{},[2075,106173,2077],{},[2400,106175,106176],{"scriptlevel":630,"displaystyle":2360},[2403,106177,106178,106180],{},[2071,106179,575],{},[2071,106181,2861],{},[2363,106183,3061],{},[2205,106185,106186,106188],{},[2071,106187,2861],{},[2075,106189,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,106191,2084],{"stretchy":2083},[2071,106193,575],{},[2075,106195,2090],{"stretchy":2083},[2092,106197,106198],{"encoding":2094},"E = \\dfrac{P}{Q}\\, Q'(P)",[92,106200,106201,106202,106236,106237,2090],{},"Cobb-Douglas: ",[1647,106203,106205],{"className":106204},[2059],[2061,106206,106207],{"xmlns":2063},[2065,106208,106209,106233],{},[2068,106210,106211,106213,106215,106217,106219,106225,106227],{},[2071,106212,2861],{},[2075,106214,2077],{},[2071,106216,4342],{},[2363,106218,3061],{},[2205,106220,106221,106223],{},[2071,106222,586],{},[2071,106224,69],{},[2363,106226,3061],{},[2205,106228,106229,106231],{},[2071,106230,10929],{},[2071,106232,2179],{},[2092,106234,106235],{"encoding":2094},"Q = A\\, L^a\\, K^b"," (rostoucí\u002Fkonstantní\u002Fklesající výnosy podle ",[1647,106238,106240],{"className":106239},[2059],[2061,106241,106242],{"xmlns":2063},[2065,106243,106244,106252],{},[2068,106245,106246,106248,106250],{},[2071,106247,69],{},[2075,106249,2176],{},[2071,106251,2179],{},[2092,106253,106254],{"encoding":2094},"a + b",[92,106256,106257,106258],{},"CES: ",[1647,106259,106261],{"className":106260},[2059],[2061,106262,106263],{"xmlns":2063},[2065,106264,106265,106329],{},[2068,106266,106267,106269,106271,106273],{},[2071,106268,2861],{},[2075,106270,2077],{},[2071,106272,4342],{},[2205,106274,106275,106319],{},[2068,106276,106277,106279,106281,106283,106285,106287,106289,106291,106301,106303,106305,106307,106317],{},[2075,106278,2561],{"fence":2360},[2075,106280,2084],{"stretchy":2083},[2210,106282,638],{},[2075,106284,2303],{},[2071,106286,69],{},[2075,106288,2090],{"stretchy":2083},[2363,106290,3061],{},[2205,106292,106293,106295],{},[2071,106294,586],{},[2068,106296,106297,106299],{},[2075,106298,2303],{},[2071,106300,2179],{},[2075,106302,2176],{},[2071,106304,69],{},[2363,106306,3061],{},[2205,106308,106309,106311],{},[2071,106310,10929],{},[2068,106312,106313,106315],{},[2075,106314,2303],{},[2071,106316,2179],{},[2075,106318,2576],{"fence":2360},[2068,106320,106321,106323,106325,106327],{},[2075,106322,2303],{},[2210,106324,638],{},[2071,106326,4761],{"mathvariant":2450},[2071,106328,2179],{},[2092,106330,106331],{"encoding":2094},"Q = A \\left[(1-a)\\, L^{-b} + a\\, K^{-b}\\right]^{-1\u002Fb}",[92,106333,106334,106335],{},"MRTS: ",[1647,106336,106338],{"className":106337},[2059],[2061,106339,106340],{"xmlns":2063},[2065,106341,106342,106390],{},[2068,106343,106344,106368,106370],{},[2400,106345,106346],{"scriptlevel":630,"displaystyle":2360},[2403,106347,106348,106358],{},[2068,106349,106350,106352],{},[2071,106351,2890],{},[2348,106353,106354,106356],{},[2071,106355,575],{},[2071,106357,586],{},[2068,106359,106360,106362],{},[2071,106361,2890],{},[2348,106363,106364,106366],{},[2071,106365,575],{},[2071,106367,10929],{},[2075,106369,2077],{},[2400,106371,106372],{"scriptlevel":630,"displaystyle":2360},[2403,106373,106374,106382],{},[9252,106375,106376,106378,106380],{},[2071,106377,2861],{},[2071,106379,586],{},[2075,106381,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,106383,106384,106386,106388],{},[2071,106385,2861],{},[2071,106387,10929],{},[2075,106389,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,106391,106392],{"encoding":2094},"\\dfrac{MP_L}{MP_K} = \\dfrac{Q'_L}{Q'_K}",[92,106394,106395,106396],{},"Eulerova věta (n = 1): ",[1647,106397,106399],{"className":106398},[2059],[2061,106400,106401],{"xmlns":2063},[2065,106402,106403,106435],{},[2068,106404,106405,106407,106409,106411,106417,106419,106421,106423,106425,106431,106433],{},[2071,106406,586],{},[2075,106408,3251],{},[2071,106410,2890],{},[2348,106412,106413,106415],{},[2071,106414,575],{},[2071,106416,586],{},[2075,106418,2176],{},[2071,106420,10929],{},[2075,106422,3251],{},[2071,106424,2890],{},[2348,106426,106427,106429],{},[2071,106428,575],{},[2071,106430,10929],{},[2075,106432,2077],{},[2071,106434,2861],{},[2092,106436,106437],{"encoding":2094},"L \\cdot MP_L + K \\cdot MP_K = Q",[84,106439,106441],{"id":106440},"vazby","Vazby",[89,106443,106444,106461],{},[92,106445,106446,1445,106449,106453,106454,75,106457,106460],{},[95,106447,106448],{},"Předchozí blok:",[69,106450,106452],{"className":106451,"dataFsResolvedFilePath":55057,"href":55058},[62],"KS 1. blok"," — kalkul (zejm. ",[69,106455,2430],{"className":106456,"dataFsResolvedFilePath":4005,"href":4006},[62],[69,106458,17988],{"className":106459,"dataFsResolvedFilePath":3899,"href":3900},[62]," je nutný předpoklad)",[92,106462,106463,1445,106466,106469],{},[95,106464,106465],{},"Navazující blok:",[69,106467,39739],{"className":106468,"dataFsResolvedFilePath":17950,"href":17951},[62]," — užitečnost (paralela izokvanty ↔ indiferenční křivky)",[84,106471,105974],{"id":105973},[89,106473,106474],{},[92,106475,106476],{},[69,106477,105982],{"className":106478,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":106480},[106481,106482,106483,106484],{"id":105888,"depth":7,"text":105889},{"id":106111,"depth":7,"text":106112},{"id":106440,"depth":7,"text":106441},{"id":105973,"depth":7,"text":105974},{},"\u002Fsummaries\u002Fimek-blok-02",{"title":106011,"description":106019},[9648],"summaries\u002Fimek-blok-02",[17,3984,10944,91039,106491,79365,91040],"ces","mb17Curl0KaUEMv7ngk7L4dH249715rS9GMlaUzLIdI",{"id":106494,"title":106495,"body":106496,"course":17,"courses":163,"created":3932,"description":106503,"extension":166,"meta":107021,"navigation":168,"path":107022,"seo":107023,"sources":107024,"stem":107025,"tags":107026,"type":106007,"updated":178,"__hash__":107027},"summaries\u002Fsummaries\u002Fimek-blok-03.md","KS 3. blok — Užitečnost a národní důchod",{"type":48,"value":106497,"toc":107015},[106498,106501,106504,106506,106605,106607,106974,106976,107006,107008],[51,106499,106495],{"id":106500},"ks-3-blok-užitečnost-a-národní-důchod",[55,106502,106503],{},"Rozcestník třetího přednáškového bloku (25 stran). Most mezi mikroekonomií (rozhodování spotřebitele) a makroekonomií (modely národní ekonomiky).",[84,106505,105889],{"id":105888},[201,106507,106508,106534],{},[92,106509,106510,106513,106514,106530,106531,106533],{},[69,106511,12226],{"className":106512,"dataFsResolvedFilePath":10901,"href":10902},[62]," — pojetí kardinalistické vs. ordinalistické, model užitečnosti, mezní užitečnost (",[1647,106515,106517],{"className":106516},[2059],[2061,106518,106519],{"xmlns":2063},[2065,106520,106521,106527],{},[2068,106522,106523,106525],{},[2071,106524,2890],{},[2071,106526,10871],{},[2092,106528,106529],{"encoding":2094},"MU","), Cobb-Douglasova funkce užitečnosti, indiferenční křivky, ",[95,106532,11733],{},", maximalizace užitečnosti při rozpočtovém omezení (Lagrange), minimalizace výdajů (duální úloha), Marshallova vs. Hicksova poptávka.",[92,106535,106536,106539,106540,106568,106569,106595,106596,835,106598,835,106600,835,106602,106604],{},[69,106537,20596],{"className":106538,"dataFsResolvedFilePath":13901,"href":13902},[62]," — GNP ",[1647,106541,106543],{"className":106542},[2059],[2061,106544,106545],{"xmlns":2063},[2065,106546,106547,106565],{},[2068,106548,106549,106551,106553,106555,106557,106559,106561,106563],{},[2075,106550,2077],{},[2071,106552,2849],{},[2075,106554,2176],{},[2071,106556,13919],{},[2075,106558,2176],{},[2071,106560,13845],{},[2075,106562,2176],{},[2071,106564,14055],{},[2092,106566,106567],{"encoding":2094},"= C + I + G + X",", lineární model spotřeby, mezní sklon ke spotřebě\u002Fúsporám (",[1647,106570,106572],{"className":106571},[2059],[2061,106573,106574],{"xmlns":2063},[2065,106575,106576,106592],{},[2068,106577,106578,106580,106582,106584,106586,106588,106590],{},[2071,106579,2890],{},[2071,106581,575],{},[2071,106583,2849],{},[2075,106585,2361],{"separator":2360},[2071,106587,2890],{},[2071,106589,575],{},[2071,106591,532],{},[2092,106593,106594],{"encoding":2094},"MPC, MPS","), modely ",[95,106597,20663],{},[95,106599,20667],{},[95,106601,20671],{},[95,106603,13744],{},", multiplikátory (autonomní spotřeby, investic, mezního sklonu).",[84,106606,106112],{"id":106111},[89,106608,106609,106671,106722,106785,106834,106897],{},[92,106610,106611,106612,106670],{},"MRCS: ",[1647,106613,106615],{"className":106614},[2059],[2061,106616,106617],{"xmlns":2063},[2065,106618,106619,106667],{},[2068,106620,106621,106645,106647],{},[2400,106622,106623],{"scriptlevel":630,"displaystyle":2360},[2403,106624,106625,106635],{},[2068,106626,106627,106629],{},[2071,106628,2890],{},[2348,106630,106631,106633],{},[2071,106632,10871],{},[2210,106634,638],{},[2068,106636,106637,106639],{},[2071,106638,2890],{},[2348,106640,106641,106643],{},[2071,106642,10871],{},[2210,106644,646],{},[2075,106646,2077],{},[2400,106648,106649],{"scriptlevel":630,"displaystyle":2360},[2403,106650,106651,106659],{},[9252,106652,106653,106655,106657],{},[2071,106654,10871],{},[2210,106656,638],{},[2075,106658,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[9252,106660,106661,106663,106665],{},[2071,106662,10871],{},[2210,106664,646],{},[2075,106666,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,106668,106669],{"encoding":2094},"\\dfrac{MU_1}{MU_2} = \\dfrac{U'_1}{U'_2}"," (poměr mezních užitečností = poměr cen v optimu)",[92,106672,19986,106673],{},[1647,106674,106676],{"className":106675},[2059],[2061,106677,106678],{"xmlns":2063},[2065,106679,106680,106720],{},[2068,106681,106682,106688,106690,106698,106704,106706,106714],{},[2205,106683,106684,106686],{},[2071,106685,9214],{},[2075,106687,4441],{},[2075,106689,2077],{},[9252,106691,106692,106694,106696],{},[2071,106693,575],{},[2210,106695,638],{},[2075,106697,4441],{},[2348,106699,106700,106702],{},[2071,106701,2861],{},[2210,106703,638],{},[2075,106705,2176],{},[9252,106707,106708,106710,106712],{},[2071,106709,575],{},[2210,106711,646],{},[2075,106713,4441],{},[2348,106715,106716,106718],{},[2071,106717,2861],{},[2210,106719,646],{},[2092,106721,20036],{"encoding":2094},[92,106723,106724,106725,106748,106749],{},"Lineární spotřeba: ",[1647,106726,106728],{"className":106727},[2059],[2061,106729,106730],{"xmlns":2063},[2065,106731,106732,106746],{},[2068,106733,106734,106736,106738,106740,106742,106744],{},[2071,106735,2849],{},[2075,106737,2077],{},[2071,106739,69],{},[2071,106741,9214],{},[2075,106743,2176],{},[2071,106745,2179],{},[2092,106747,21659],{"encoding":2094},", redukovaný tvar C-I: ",[1647,106750,106752],{"className":106751},[2059],[2061,106753,106754],{"xmlns":2063},[2065,106755,106756,106782],{},[2068,106757,106758,106760,106762],{},[2071,106759,9214],{},[2075,106761,2077],{},[2400,106763,106764],{"scriptlevel":630,"displaystyle":2360},[2403,106765,106766,106774],{},[2068,106767,106768,106770,106772],{},[2071,106769,2179],{},[2075,106771,2176],{},[2071,106773,13919],{},[2068,106775,106776,106778,106780],{},[2210,106777,638],{},[2075,106779,2303],{},[2071,106781,69],{},[2092,106783,106784],{"encoding":2094},"Y = \\dfrac{b + I}{1 - a}",[92,106786,106787,106788],{},"Multiplikátor investic \u002F autonomní spotřeby: ",[1647,106789,106791],{"className":106790},[2059],[2061,106792,106793],{"xmlns":2063},[2065,106794,106795,106831],{},[2068,106796,106797,106805,106807,106815,106817],{},[9252,106798,106799,106801,106803],{},[2071,106800,9214],{},[2071,106802,13919],{},[2075,106804,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,106806,2077],{},[9252,106808,106809,106811,106813],{},[2071,106810,9214],{},[2071,106812,2179],{},[2075,106814,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,106816,2077],{},[2400,106818,106819],{"scriptlevel":630,"displaystyle":2360},[2403,106820,106821,106823],{},[2210,106822,638],{},[2068,106824,106825,106827,106829],{},[2210,106826,638],{},[2075,106828,2303],{},[2071,106830,69],{},[2092,106832,106833],{"encoding":2094},"Y'_I = Y'_b = \\dfrac{1}{1 - a}",[92,106835,106836,106837],{},"IS: ",[1647,106838,106840],{"className":106839},[2059],[2061,106841,106842],{"xmlns":2063},[2065,106843,106844,106894],{},[2068,106845,106846,106848,106850,106864,106866,106868,106870,106884,106886,106888,106890,106892],{},[2071,106847,9214],{},[2075,106849,2077],{},[2400,106851,106852],{"scriptlevel":630,"displaystyle":2360},[2403,106853,106854,106856],{},[2071,106855,2222],{},[2068,106857,106858,106860,106862],{},[2210,106859,638],{},[2075,106861,2303],{},[2071,106863,69],{},[2363,106865,3061],{},[2071,106867,13774],{},[2075,106869,2176],{},[2400,106871,106872],{"scriptlevel":630,"displaystyle":2360},[2403,106873,106874,106876],{},[2210,106875,638],{},[2068,106877,106878,106880,106882],{},[2210,106879,638],{},[2075,106881,2303],{},[2071,106883,69],{},[2075,106885,2084],{"stretchy":2083},[2071,106887,2179],{},[2075,106889,2176],{},[2071,106891,2273],{},[2075,106893,2090],{"stretchy":2083},[2092,106895,106896],{"encoding":2094},"Y = \\dfrac{c}{1-a}\\, r + \\dfrac{1}{1-a}(b + d)",[92,106898,106899,106900],{},"LM: ",[1647,106901,106903],{"className":106902},[2059],[2061,106904,106905],{"xmlns":2063},[2065,106906,106907,106971],{},[2068,106908,106909,106911,106913,106915,106931,106933,106935,106937,106953,106955],{},[2071,106910,9214],{},[2075,106912,2077],{},[2075,106914,2303],{},[2400,106916,106917],{"scriptlevel":630,"displaystyle":2360},[2403,106918,106919,106925],{},[2348,106920,106921,106923],{},[2071,106922,14972],{},[2210,106924,646],{},[2348,106926,106927,106929],{},[2071,106928,14972],{},[2210,106930,638],{},[2363,106932,3061],{},[2071,106934,13774],{},[2075,106936,2303],{},[2400,106938,106939],{"scriptlevel":630,"displaystyle":2360},[2403,106940,106941,106947],{},[2348,106942,106943,106945],{},[2071,106944,14972],{},[2210,106946,654],{},[2348,106948,106949,106951],{},[2071,106950,14972],{},[2210,106952,638],{},[2075,106954,2176],{},[2400,106956,106957],{"scriptlevel":630,"displaystyle":2360},[2403,106958,106959,106965],{},[2205,106960,106961,106963],{},[2071,106962,2890],{},[2075,106964,4441],{},[2348,106966,106967,106969],{},[2071,106968,14972],{},[2210,106970,638],{},[2092,106972,106973],{"encoding":2094},"Y = -\\dfrac{k_2}{k_1}\\, r - \\dfrac{k_3}{k_1} + \\dfrac{M^*}{k_1}",[84,106975,106441],{"id":106440},[89,106977,106978,106986,106991],{},[92,106979,106980,1445,106982,106985],{},[95,106981,106448],{},[69,106983,39735],{"className":106984,"dataFsResolvedFilePath":39733,"href":39734},[62]," — produkce (paralela izokvanty ↔ indiferenční křivky)",[92,106987,106988,106990],{},[95,106989,3884],{}," — (poslední blok kurzu)",[92,106992,106993,1445,106996,835,106999,2744,107002],{},[95,106994,106995],{},"Předpoklady:",[69,106997,105966],{"className":106998,"dataFsResolvedFilePath":12193,"href":12194},[62],[69,107000,105970],{"className":107001,"dataFsResolvedFilePath":3899,"href":3900},[62],[69,107003,107005],{"className":107004,"dataFsResolvedFilePath":55057,"href":55058},[62],"Bloku 1",[84,107007,105974],{"id":105973},[89,107009,107010],{},[92,107011,107012],{},[69,107013,105982],{"className":107014,"dataFsResolvedFilePath":2034,"href":2035},[62],{"title":156,"searchDepth":7,"depth":7,"links":107016},[107017,107018,107019,107020],{"id":105888,"depth":7,"text":105889},{"id":106111,"depth":7,"text":106112},{"id":106440,"depth":7,"text":106441},{"id":105973,"depth":7,"text":105974},{},"\u002Fsummaries\u002Fimek-blok-03",{"title":106495,"description":106503},[18006],"summaries\u002Fimek-blok-03",[17,10903,42,18009,30502],"Wm7uyoEKQfsPBb_MtycXHkrbnPMQuof03eH-QI7XEyQ",{"id":107029,"title":107030,"body":107031,"course":17,"courses":163,"created":3932,"description":107345,"extension":166,"meta":107346,"navigation":168,"path":107347,"seo":107348,"sources":107349,"stem":107351,"tags":107352,"type":106007,"updated":178,"__hash__":107354},"summaries\u002Fsummaries\u002Fimek-detail-predmetu.md","Matematická ekonomie — Detail předmětu",{"type":48,"value":107032,"toc":107333},[107033,107036,107043,107047,107138,107142,107145,107161,107165,107176,107180,107194,107197,107201,107212,107216,107272,107275,107278,107282,107319,107323,107326,107330],[51,107034,107030],{"id":107035},"matematická-ekonomie-detail-předmětu",[55,107037,107038,107039,195],{},"Viz ",[69,107040,107042],{"className":107041,"dataFsResolvedFilePath":2034,"href":2035},[62],"přehled kurzu",[84,107044,107046],{"id":107045},"administrativa","Administrativa",[323,107048,107049,107058],{},[326,107050,107051],{},[329,107052,107053,107056],{},[332,107054,107055],{},"Atribut",[332,107057,91820],{},[342,107059,107060,107066,107074,107082,107090,107098,107106,107114,107122,107130],{},[329,107061,107062,107064],{},[347,107063,18226],{},[347,107065,2036],{},[329,107067,107068,107071],{},[347,107069,107070],{},"Fakulta",[347,107072,107073],{},"FP VUT",[329,107075,107076,107079],{},[347,107077,107078],{},"Akademický rok",[347,107080,107081],{},"2025\u002F2026",[329,107083,107084,107087],{},[347,107085,107086],{},"Garant",[347,107088,107089],{},"doc. RNDr. Bedřich Půža, CSc.",[329,107091,107092,107095],{},[347,107093,107094],{},"Garantující ústav",[347,107096,107097],{},"Ústav informatiky FP",[329,107099,107100,107103],{},[347,107101,107102],{},"Vyučující (KS)",[347,107104,107105],{},"Mgr. Martina Bobalová, Ph.D.",[329,107107,107108,107111],{},[347,107109,107110],{},"Jazyk výuky",[347,107112,107113],{},"čeština",[329,107115,107116,107119],{},[347,107117,107118],{},"Ukončení",[347,107120,107121],{},"zkouška",[329,107123,107124,107127],{},[347,107125,107126],{},"Semestr",[347,107128,107129],{},"letní",[329,107131,107132,107135],{},[347,107133,107134],{},"Konzultace v KS",[347,107136,107137],{},"20 hod. nepovinná",[84,107139,107141],{"id":107140},"cíl-a-anotace","Cíl a anotace",[55,107143,107144],{},"Cílem je hlouběji proniknout do kauzální podstaty ekonomických vztahů, rozvíjet schopnost vyjadřovat ekonomické vztahy exaktními prostředky a provádět jejich analýzy. Předmět navazuje na mikro- a makroekonomii — syntetizuje je prostředky matematiky s potenciálem pro komputerizaci. Těžištěm je matematické modelování základních ekonomických zákonitostí:",[89,107146,107147,107150,107153,107155,107157,107159],{},[92,107148,107149],{},"analýza poptávky a nabídky",[92,107151,107152],{},"příjem, náklady, zisk",[92,107154,3984],{},[92,107156,10944],{},[92,107158,92557],{},[92,107160,21186],{},[84,107162,107164],{"id":107163},"průběh-zkoušky","Průběh zkoušky",[55,107166,107167,107168,107171,107172,107175],{},"Zkouška = ",[95,107169,107170],{},"písemná"," (60 min, těžiště hodnocení) + ",[95,107173,107174],{},"ústní"," (~10 min, upřesnění klasifikace).",[609,107177,107179],{"id":107178},"zadání-písemné-části","Zadání písemné části",[201,107181,107182,107185,107188,107191],{},[92,107183,107184],{},"Rozhodovací úloha o ekonomické funkci — 10 b.",[92,107186,107187],{},"Definice, formulace vlastnosti, interpretace ekonomické veličiny — 20 b.",[92,107189,107190],{},"Výpočetní úloha — 30 b.",[92,107192,107193],{},"Výpočetní úloha — 40 b.",[55,107195,107196],{},"Celkem 100 b. Doporučeno mít kalkulátor (přípustný je i dobrý odhad).",[609,107198,107200],{"id":107199},"dílčí-podmínky-pro-ae","Dílčí podmínky pro A–E",[89,107202,107203,107206,107209],{},[92,107204,107205],{},"≥ 11 bodů v součtu úloh 1 + 2",[92,107207,107208],{},"≥ 10 bodů v úloze 3",[92,107210,107211],{},"≥ 10 bodů v úloze 4",[609,107213,107215],{"id":107214},"stupnice","Stupnice",[323,107217,107218,107228],{},[326,107219,107220],{},[329,107221,107222,107225],{},[332,107223,107224],{},"Známka",[332,107226,107227],{},"Body",[342,107229,107230,107237,107244,107251,107258,107265],{},[329,107231,107232,107234],{},[347,107233,4342],{},[347,107235,107236],{},"90–100",[329,107238,107239,107241],{},[347,107240,25992],{},[347,107242,107243],{},"80–89",[329,107245,107246,107248],{},[347,107247,2849],{},[347,107249,107250],{},"70–79",[329,107252,107253,107255],{},[347,107254,4271],{},[347,107256,107257],{},"60–69",[329,107259,107260,107262],{},[347,107261,554],{},[347,107263,107264],{},"50–59",[329,107266,107267,107269],{},[347,107268,10177],{},[347,107270,107271],{},"0–49 nebo nesplnění podmínek",[55,107273,107274],{},"Student může odmítnout klasifikaci B–E před uzavřením; pak je F a může jít na další termín.",[55,107276,107277],{},"Účast na přednáškách není kontrolována.",[84,107279,107281],{"id":107280},"literatura","Literatura",[89,107283,107284,107291,107298,107305,107312],{},[92,107285,107286,107287,107290],{},"Mezník, I. ",[3982,107288,107289],{},"Úvod do matematické ekonomie pro ekonomy"," — FP VUT \u002F CERM, Brno 2017 (CZ, doporučeno)",[92,107292,107293,107294,107297],{},"Chiang, A. C. ",[3982,107295,107296],{},"Fundamental Methods of Mathematical Economics"," — McGraw-Hill, 1984",[92,107299,107300,107301,107304],{},"Jacques, J. ",[3982,107302,107303],{},"Mathematics for Economics and Business"," — Addison-Wesley, 1995",[92,107306,107307,107308,107311],{},"Koch, J. U. & Ostrosky, L. A. ",[3982,107309,107310],{},"Introduction to Mathematical Economics"," — McGraw-Hill, 1994",[92,107313,107314,107315,107318],{},"McKenna, C. J. & Rees, R. ",[3982,107316,107317],{},"Economics: A Mathematical Introduction"," — Oxford UP, 1992",[84,107320,107322],{"id":107321},"prerekvizity","Prerekvizity",[55,107324,107325],{},"Standardní kurz inženýrské matematiky, mikroekonomie a makroekonomie na bakalářské úrovni.",[84,107327,107329],{"id":107328},"elearning","eLearning",[55,107331,107332],{},"Moodle VUT — aktuální otevřený kurz.",{"title":156,"searchDepth":7,"depth":7,"links":107334},[107335,107336,107337,107342,107343,107344],{"id":107045,"depth":7,"text":107046},{"id":107140,"depth":7,"text":107141},{"id":107163,"depth":7,"text":107164,"children":107338},[107339,107340,107341],{"id":107178,"depth":4,"text":107179},{"id":107199,"depth":4,"text":107200},{"id":107214,"depth":4,"text":107215},{"id":107280,"depth":7,"text":107281},{"id":107321,"depth":7,"text":107322},{"id":107328,"depth":7,"text":107329},"Viz přehled kurzu.",{},"\u002Fsummaries\u002Fimek-detail-predmetu",{"title":107030,"description":107345},[107350],"raw\u002Fimek\u002FDetail předmětu.md","summaries\u002Fimek-detail-predmetu",[17,107353],"zkouska","HbE7Shpid43OlvVaEKLZsPSS1RryulK33e-e-2LTZvI",{"id":107356,"title":107357,"body":107358,"course":17,"courses":163,"created":9642,"description":108322,"extension":166,"meta":108323,"navigation":168,"path":108324,"seo":108325,"sources":108326,"stem":108327,"tags":108328,"type":106007,"updated":178,"__hash__":108332},"summaries\u002Fsummaries\u002Fimek-kniha.md","Kniha — *Úvod do matematické ekonomie pro ekonomy*",{"type":48,"value":107359,"toc":108302},[107360,107366,107381,107389,107393,107400,107409,107418,107425,107525,107531,107538,107579,107584,107591,107820,107825,107832,108017,108022,108029,108071,108076,108080,108083,108204,108208,108248,108252,108268,108270],[51,107361,107363,107364],{"id":107362},"kniha-úvod-do-matematické-ekonomie-pro-ekonomy","Kniha — ",[3982,107365,107289],{},[55,107367,107368,107369,107372,107373,107376,107377,107380],{},"Doporučená literatura k předmětu ",[69,107370,17941],{"className":107371,"href":2035,"dataFsResolvedFilePath":2034},[62],", autor ",[95,107374,107375],{},"I. Mezník",", vydavatelství FP VUT \u002F CERM, Brno 2017. Studentské naskenované fotografie pokrývají ",[95,107378,107379],{},"kapitoly 2 až 7"," (stran 34–144, celkem 107 unikátních stran).",[55,107382,107383,107384,195],{},"Text je hlavním zdrojem obsahu pro většinu topiců ImeK — kniha poskytuje podrobný matematický a ekonomický výklad, všechny pracovní příklady (s plnými řešeními), soubory úloh k samostatnému řešení i otázky k sebehodnocení. Obsah byl strojově přepsán do strukturovaných českých studijních materiálů v ",[69,107385,107388],{"className":107386,"href":107387},[62],"\u002Fwiki\u002F#Pokrytí topiců","#Pokrytí topiců",[84,107390,107392],{"id":107391},"pokrytí-podle-kapitol","Pokrytí podle kapitol",[609,107394,107396,107397],{"id":107395},"kapitola-2-poptávka-nabídka-tržní-rovnováha-str-3463","Kapitola 2 — Poptávka, nabídka, tržní rovnováha ",[3982,107398,107399],{},"(str. 34–63)",[55,107401,107402,107403,75,107406,195],{},"Obecný vícefaktorový a jednofaktorový model poptávky a nabídky, zákon klesající poptávky, lineární modely, posun poptávky a nabídky (Engelova funkce, zdanění), tržní rovnováha jako průsečík D a S, pravidla komparativní statiky, multiplikátory pro mikroekonomické proměnné, přebytek spotřebitele a výrobce. Obsahuje ",[95,107404,107405],{},"Příklady 2.1–2.13",[95,107407,107408],{},"Úlohy 2.1–2.18",[55,107410,107411,107412,835,107415,195],{},"Topiky: ",[69,107413,17975],{"className":107414,"href":13671,"dataFsResolvedFilePath":13670},[62],[69,107416,49270],{"className":107417,"href":49269,"dataFsResolvedFilePath":49268},[62],[609,107419,107421,107422],{"id":107420},"kapitola-3-příjem-náklady-zisk-nabídka-firmy-str-6681","Kapitola 3 — Příjem, náklady, zisk, nabídka firmy ",[3982,107423,107424],{},"(str. 66–81)",[55,107426,107427,107428,107449,107450,107477,107478,107499,107500,107519,107520,835,107523,195],{},"Celkový, průměrný a mezní příjem (TR, AR, MR); celkové, fixní, variabilní, průměrné a mezní náklady (TC, FC, TVC, AC, AFC, AVC, MC); princip minimalizace průměrných nákladů (",[1647,107429,107431],{"className":107430},[2059],[2061,107432,107433],{"xmlns":2063},[2065,107434,107435,107447],{},[2068,107436,107437,107439,107441,107443,107445],{},[2071,107438,4342],{},[2071,107440,2849],{},[2075,107442,2077],{},[2071,107444,2890],{},[2071,107446,2849],{},[2092,107448,59693],{"encoding":2094}," v minimu); zisk ",[1647,107451,107453],{"className":107452},[2059],[2061,107454,107455],{"xmlns":2063},[2065,107456,107457,107475],{},[2068,107458,107459,107461,107463,107465,107467,107469,107471,107473],{},[2071,107460,575],{},[2071,107462,4082],{},[2075,107464,2077],{},[2071,107466,543],{},[2071,107468,4082],{},[2075,107470,2303],{},[2071,107472,543],{},[2071,107474,2849],{},[2092,107476,59670],{"encoding":2094}," a body zvratu; princip maximalizace zisku (",[1647,107479,107481],{"className":107480},[2059],[2061,107482,107483],{"xmlns":2063},[2065,107484,107485,107497],{},[2068,107486,107487,107489,107491,107493,107495],{},[2071,107488,2890],{},[2071,107490,4082],{},[2075,107492,2077],{},[2071,107494,2890],{},[2071,107496,2849],{},[2092,107498,59741],{"encoding":2094},"); konstrukce křivky nabídky firmy (",[1647,107501,107503],{"className":107502},[2059],[2061,107504,107505],{"xmlns":2063},[2065,107506,107507,107517],{},[2068,107508,107509,107511,107513,107515],{},[2071,107510,575],{},[2075,107512,2077],{},[2071,107514,2890],{},[2071,107516,2849],{},[2092,107518,72721],{"encoding":2094}," nad minimem AVC). ",[95,107521,107522],{},"Příklady 3.1–3.12",[95,107524,73701],{},[55,107526,107527,107528,195],{},"Topic: ",[69,107529,3024],{"className":107530,"href":3023,"dataFsResolvedFilePath":3022},[62],[609,107532,107534,107535],{"id":107533},"kapitola-4-elasticita-str-8396","Kapitola 4 — Elasticita ",[3982,107536,107537],{},"(str. 83–96)",[55,107539,107540,107541,107554,107555,107572,107573,835,107576,195],{},"Pojem elasticity jako míry citlivosti na procentní změnu, cenová elasticita poptávky i nabídky, tři pravidla o vztahu ",[1647,107542,107544],{"className":107543},[2059],[2061,107545,107546],{"xmlns":2063},[2065,107547,107548,107552],{},[2068,107549,107550],{},[2071,107551,554],{},[2092,107553,554],{"encoding":2094}," a celkového příjmu (u lineární poptávky max TR v bodě ",[1647,107556,107558],{"className":107557},[2059],[2061,107559,107560],{"xmlns":2063},[2065,107561,107562,107570],{},[2068,107563,107564,107566,107568],{},[2071,107565,554],{},[2075,107567,2077],{},[2210,107569,638],{},[2092,107571,4632],{"encoding":2094},"), křížová a důchodová elasticita. ",[95,107574,107575],{},"Příklady 4.1–4.8",[95,107577,107578],{},"Úlohy 4.1–4.21",[55,107580,107527,107581,195],{},[69,107582,3984],{"className":107583,"href":3912,"dataFsResolvedFilePath":3911},[62],[609,107585,107587,107588],{"id":107586},"kapitola-5-produkce-str-97111","Kapitola 5 — Produkce ",[3982,107589,107590],{},"(str. 97–111)",[55,107592,107593,107594,107613,107614,107633,107634,107653,107654,11156,107673,107702,107703,107727,107728,107757,107758,107775,107776,2999,107815,835,107818,195],{},"Jednofaktorový model ",[1647,107595,107597],{"className":107596},[2059],[2061,107598,107599],{"xmlns":2063},[2065,107600,107601,107611],{},[2068,107602,107603,107605,107607,107609],{},[2071,107604,2861],{},[2075,107606,2084],{"stretchy":2083},[2071,107608,586],{},[2075,107610,2090],{"stretchy":2083},[2092,107612,106084],{"encoding":2094}," s mezním produktem práce ",[1647,107615,107617],{"className":107616},[2059],[2061,107618,107619],{"xmlns":2063},[2065,107620,107621,107631],{},[2068,107622,107623,107625],{},[2071,107624,2890],{},[2348,107626,107627,107629],{},[2071,107628,575],{},[2071,107630,586],{},[2092,107632,11176],{"encoding":2094},", průměrným produktem ",[1647,107635,107637],{"className":107636},[2059],[2061,107638,107639],{"xmlns":2063},[2065,107640,107641,107651],{},[2068,107642,107643,107645],{},[2071,107644,4342],{},[2348,107646,107647,107649],{},[2071,107648,575],{},[2071,107650,586],{},[2092,107652,79104],{"encoding":2094}," a principem maximalizace ",[1647,107655,107657],{"className":107656},[2059],[2061,107658,107659],{"xmlns":2063},[2065,107660,107661,107671],{},[2068,107662,107663,107665],{},[2071,107664,4342],{},[2348,107666,107667,107669],{},[2071,107668,575],{},[2071,107670,586],{},[2092,107672,79104],{"encoding":2094},[1647,107674,107676],{"className":107675},[2059],[2061,107677,107678],{"xmlns":2063},[2065,107679,107680,107700],{},[2068,107681,107682,107684,107690,107692,107694],{},[2071,107683,2890],{},[2348,107685,107686,107688],{},[2071,107687,575],{},[2071,107689,586],{},[2075,107691,2077],{},[2071,107693,4342],{},[2348,107695,107696,107698],{},[2071,107697,575],{},[2071,107699,586],{},[2092,107701,79134],{"encoding":2094}," v max); dvoufaktorový model ",[1647,107704,107706],{"className":107705},[2059],[2061,107707,107708],{"xmlns":2063},[2065,107709,107710,107724],{},[2068,107711,107712,107714,107716,107718,107720,107722],{},[2071,107713,2861],{},[2075,107715,2084],{"stretchy":2083},[2071,107717,586],{},[2075,107719,2361],{"separator":2360},[2071,107721,10929],{},[2075,107723,2090],{"stretchy":2083},[2092,107725,107726],{"encoding":2094},"Q(L,K)","; Cobb-Douglasova produkční funkce ",[1647,107729,107731],{"className":107730},[2059],[2061,107732,107733],{"xmlns":2063},[2065,107734,107735,107755],{},[2068,107736,107737,107739,107741,107743,107749],{},[2071,107738,2861],{},[2075,107740,2077],{},[2071,107742,4342],{},[2205,107744,107745,107747],{},[2071,107746,586],{},[2071,107748,69],{},[2205,107750,107751,107753],{},[2071,107752,10929],{},[2071,107754,2179],{},[2092,107756,79201],{"encoding":2094},", výnosy z rozsahu podle ",[1647,107759,107761],{"className":107760},[2059],[2061,107762,107763],{"xmlns":2063},[2065,107764,107765,107773],{},[2068,107766,107767,107769,107771],{},[2071,107768,69],{},[2075,107770,2176],{},[2071,107772,2179],{},[2092,107774,106254],{"encoding":2094},"; CES funkce; Eulerova věta; izokvanty; mezní míra technické substituce ",[1647,107777,107779],{"className":107778},[2059],[2061,107780,107781],{"xmlns":2063},[2065,107782,107783,107813],{},[2068,107784,107785,107787,107789,107791,107793,107795,107797,107803,107805,107807],{},[2071,107786,2890],{},[2071,107788,4082],{},[2071,107790,543],{},[2071,107792,532],{},[2075,107794,2077],{},[2071,107796,2890],{},[2348,107798,107799,107801],{},[2071,107800,575],{},[2071,107802,586],{},[2071,107804,4761],{"mathvariant":2450},[2071,107806,2890],{},[2348,107808,107809,107811],{},[2071,107810,575],{},[2071,107812,10929],{},[2092,107814,79276],{"encoding":2094},[95,107816,107817],{},"Příklady 5.1–5.6",[95,107819,87921],{},[55,107821,107527,107822,195],{},[69,107823,10944],{"className":107824,"href":10943,"dataFsResolvedFilePath":10942},[62],[609,107826,107828,107829],{"id":107827},"kapitola-6-užitečnost-str-113131","Kapitola 6 — Užitečnost ",[3982,107830,107831],{},"(str. 113–131)",[55,107833,107834,107835,107871,107872,107901,107902,75,107925,107956,107957,107996,107997,108010,108011,835,108014,195],{},"Pojetí užitečnosti (kardinalistický vs. ordinalistický přístup, předpoklady spotřebitele); funkce užitečnosti ",[1647,107836,107838],{"className":107837},[2059],[2061,107839,107840],{"xmlns":2063},[2065,107841,107842,107868],{},[2068,107843,107844,107846,107848,107854,107856,107858,107860,107866],{},[2071,107845,10871],{},[2075,107847,2084],{"stretchy":2083},[2348,107849,107850,107852],{},[2071,107851,2861],{},[2210,107853,638],{},[2075,107855,2361],{"separator":2360},[2075,107857,10773],{},[2075,107859,2361],{"separator":2360},[2348,107861,107862,107864],{},[2071,107863,2861],{},[2071,107865,41153],{},[2075,107867,2090],{"stretchy":2083},[2092,107869,107870],{"encoding":2094},"U(Q_1, \\dots, Q_n)",", mezní užitečnost ",[1647,107873,107875],{"className":107874},[2059],[2061,107876,107877],{"xmlns":2063},[2065,107878,107879,107899],{},[2068,107880,107881,107883,107889,107891],{},[2071,107882,2890],{},[2348,107884,107885,107887],{},[2071,107886,10871],{},[2071,107888,20528],{},[2075,107890,2077],{},[9252,107892,107893,107895,107897],{},[2071,107894,10871],{},[2071,107896,20528],{},[2075,107898,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2092,107900,92404],{"encoding":2094},", vlastnosti ",[1647,107903,107905],{"className":107904},[2059],[2061,107906,107907],{"xmlns":2063},[2065,107908,107909,107923],{},[2068,107910,107911,107919,107921],{},[9252,107912,107913,107915,107917],{},[2071,107914,10871],{},[2071,107916,20528],{},[2075,107918,2452],{"mathvariant":2450,"lspace":2451,"rspace":2451},[2075,107920,3482],{},[2210,107922,630],{},[2092,107924,100928],{"encoding":2094},[1647,107926,107928],{"className":107927},[2059],[2061,107929,107930],{"xmlns":2063},[2065,107931,107932,107954],{},[2068,107933,107934,107950,107952],{},[9252,107935,107936,107938,107944],{},[2071,107937,10871],{},[2068,107939,107940,107942],{},[2071,107941,20528],{},[2071,107943,20528],{},[2068,107945,107946,107948],{},[2075,107947,2452],{"mathvariant":2450},[2075,107949,2452],{"mathvariant":2450},[2075,107951,3521],{},[2210,107953,630],{},[2092,107955,100961],{"encoding":2094}," (zákon klesající mezní užitečnosti); Cobb-Douglasova funkce užitečnosti; indiferenční křivky a jejich 4 vlastnosti; mezní míra komoditní substituce ",[1647,107958,107960],{"className":107959},[2059],[2061,107961,107962],{"xmlns":2063},[2065,107963,107964,107994],{},[2068,107965,107966,107968,107970,107972,107974,107976,107978,107984,107986,107988],{},[2071,107967,2890],{},[2071,107969,4082],{},[2071,107971,2849],{},[2071,107973,532],{},[2075,107975,2077],{},[2071,107977,2890],{},[2348,107979,107980,107982],{},[2071,107981,10871],{},[2210,107983,638],{},[2071,107985,4761],{"mathvariant":2450},[2071,107987,2890],{},[2348,107989,107990,107992],{},[2071,107991,10871],{},[2210,107993,646],{},[2092,107995,92464],{"encoding":2094},"; optimalizace spotřebitele Lagrangeovou metodou (maximalizace ",[1647,107998,108000],{"className":107999},[2059],[2061,108001,108002],{"xmlns":2063},[2065,108003,108004,108008],{},[2068,108005,108006],{},[2071,108007,10871],{},[2092,108009,10871],{"encoding":2094}," za rozpočtového omezení i duální minimalizace výdajů). ",[95,108012,108013],{},"Příklady 6.1–6.8",[95,108015,108016],{},"Úlohy 6.1–6.13",[55,108018,107527,108019,195],{},[69,108020,10903],{"className":108021,"href":10902,"dataFsResolvedFilePath":10901},[62],[609,108023,108025,108026],{"id":108024},"kapitola-7-národní-důchod-str-133144","Kapitola 7 — Národní důchod ",[3982,108027,108028],{},"(str. 133–144)",[55,108030,108031,108032,108049,108050,108067,108068,195],{},"Zjednodušený makroekonomický model, GNP a národní důchod, funkce spotřeby a úspor, mezní sklon ke spotřebě ",[1647,108033,108035],{"className":108034},[2059],[2061,108036,108037],{"xmlns":2063},[2065,108038,108039,108047],{},[2068,108040,108041,108043,108045],{},[2071,108042,2890],{},[2071,108044,575],{},[2071,108046,2849],{},[2092,108048,20784],{"encoding":2094}," a k úsporám ",[1647,108051,108053],{"className":108052},[2059],[2061,108054,108055],{"xmlns":2063},[2065,108056,108057,108065],{},[2068,108058,108059,108061,108063],{},[2071,108060,2890],{},[2071,108062,575],{},[2071,108064,532],{},[2092,108066,22398],{"encoding":2094},"; modely národní ekonomiky C-I (uzavřená bez vlády), C-I-G (s vládou), C-I-G-X (otevřená); multiplikátory pro makroekonomické proměnné; IS-LM analýza — křivky IS a LM, rovnovážný důchod a úroková míra. ",[95,108069,108070],{},"Příklady 7.1–7.6",[55,108072,107527,108073,195],{},[69,108074,17961],{"className":108075,"href":13902,"dataFsResolvedFilePath":13901},[62],[84,108077,108079],{"id":108078},"pokrytí-topiců","Pokrytí topiců",[55,108081,108082],{},"Obsah knihy byl sloučen s již existujícími přednáškovými shrnutími do následujících topic pages:",[323,108084,108085,108098],{},[326,108086,108087],{},[329,108088,108089,108092,108095],{},[332,108090,108091],{},"Topic",[332,108093,108094],{},"Zdroj (kniha)",[332,108096,108097],{},"Další zdroje",[342,108099,108100,108116,108128,108143,108159,108174,108189],{},[329,108101,108102,108107,108110],{},[347,108103,108104],{},[69,108105,17975],{"className":108106,"href":13671,"dataFsResolvedFilePath":13670},[62],[347,108108,108109],{},"Kap. 2",[347,108111,108112],{},[69,108113,108115],{"className":108114,"href":55058,"dataFsResolvedFilePath":55057},[62],"imek-blok-01",[329,108117,108118,108123,108126],{},[347,108119,108120],{},[69,108121,49270],{"className":108122,"href":49269,"dataFsResolvedFilePath":49268},[62],[347,108124,108125],{},"Kap. 2.5–2.6 (nové)",[347,108127,10415],{},[329,108129,108130,108135,108138],{},[347,108131,108132],{},[69,108133,3024],{"className":108134,"href":3023,"dataFsResolvedFilePath":3022},[62],[347,108136,108137],{},"Kap. 3",[347,108139,108140],{},[69,108141,108115],{"className":108142,"href":55058,"dataFsResolvedFilePath":55057},[62],[329,108144,108145,108150,108153],{},[347,108146,108147],{},[69,108148,3984],{"className":108149,"href":3912,"dataFsResolvedFilePath":3911},[62],[347,108151,108152],{},"Kap. 4",[347,108154,108155],{},[69,108156,108158],{"className":108157,"href":39734,"dataFsResolvedFilePath":39733},[62],"imek-blok-02",[329,108160,108161,108166,108169],{},[347,108162,108163],{},[69,108164,10944],{"className":108165,"href":10943,"dataFsResolvedFilePath":10942},[62],[347,108167,108168],{},"Kap. 5",[347,108170,108171],{},[69,108172,108158],{"className":108173,"href":39734,"dataFsResolvedFilePath":39733},[62],[329,108175,108176,108181,108184],{},[347,108177,108178],{},[69,108179,10903],{"className":108180,"href":10902,"dataFsResolvedFilePath":10901},[62],[347,108182,108183],{},"Kap. 6",[347,108185,108186],{},[69,108187,17952],{"className":108188,"href":17951,"dataFsResolvedFilePath":17950},[62],[329,108190,108191,108196,108199],{},[347,108192,108193],{},[69,108194,17961],{"className":108195,"href":13902,"dataFsResolvedFilePath":13901},[62],[347,108197,108198],{},"Kap. 7",[347,108200,108201],{},[69,108202,17952],{"className":108203,"href":17951,"dataFsResolvedFilePath":17950},[62],[84,108205,108207],{"id":108206},"co-kniha-neobsahuje-v-naskenovaných-stránkách","Co kniha neobsahuje (v naskenovaných stránkách)",[89,108209,108210,108233],{},[92,108211,108212,108215,108216,835,108220,835,108223,835,108226,835,108229,108232],{},[95,108213,108214],{},"Kapitola 1"," (str. 1–33) — pravděpodobně úvod \u002F matematický aparát (funkce, derivace, integrály, Lagrange). Teorie je pokryta v ",[69,108217,108219],{"className":108218,"href":3878,"dataFsResolvedFilePath":3877},[62],"zaklady-matematicke-ekonomie",[69,108221,2430],{"className":108222,"href":4006,"dataFsResolvedFilePath":4005},[62],[69,108224,13721],{"className":108225,"href":3889,"dataFsResolvedFilePath":3888},[62],[69,108227,17988],{"className":108228,"href":3900,"dataFsResolvedFilePath":3899},[62],[69,108230,101497],{"className":108231,"href":12194,"dataFsResolvedFilePath":12193},[62]," ze zdrojů ve vysokoškolských blocích.",[92,108234,108235,108236,108239,108240,108243,108244,108247],{},"Chybějící strany ve skenech: ",[95,108237,108238],{},"64, 65"," (konec teorie \u002F úvod kap. 3), ",[95,108241,108242],{},"82"," (začátek kap. 4), ",[95,108245,108246],{},"112"," (úvod kap. 6). Obsah byl pokud možno dovozen z kontextu sousedních stran a z přednášek.",[84,108249,108251],{"id":108250},"vlastní-úlohy-otázky","Vlastní úlohy \u002F otázky",[55,108253,108254,108255,75,108258,108261,108262,75,108265,108267],{},"Kniha obsahuje rozsáhlé soubory ",[95,108256,108257],{},"úloh k samostatnému řešení",[95,108259,108260],{},"otázek k sebehodnocení"," ke každé kapitole. Všechny jsou zachované verbatim v příslušných topic pages (sekce ",[3982,108263,108264],{},"Úlohy X.x",[3982,108266,54178],{},") a představují vysoce kvalitní studijní materiál pro přípravu ke zkoušce.",[84,108269,3866],{"id":3865},[89,108271,108272,108279,108288],{},[92,108273,108274,1445,108276],{},[95,108275,17937],{},[69,108277,17941],{"className":108278,"href":2035,"dataFsResolvedFilePath":2034},[62],[92,108280,108281,1445,108284,108287],{},[95,108282,108283],{},"Manifest skenu:",[929,108285,108286],{},"raw\u002Fimek\u002Fkniha_scanned\u002F_manifest.md"," (mapování fotografií → stránky)",[92,108289,108290,1445,108293,835,108296,835,108299],{},[95,108291,108292],{},"Přednášková shrnutí:",[69,108294,108115],{"className":108295,"href":55058,"dataFsResolvedFilePath":55057},[62],[69,108297,108158],{"className":108298,"href":39734,"dataFsResolvedFilePath":39733},[62],[69,108300,17952],{"className":108301,"href":17951,"dataFsResolvedFilePath":17950},[62],{"title":156,"searchDepth":7,"depth":7,"links":108303},[108304,108318,108319,108320,108321],{"id":107391,"depth":7,"text":107392,"children":108305},[108306,108308,108310,108312,108314,108316],{"id":107395,"depth":4,"text":108307},"Kapitola 2 — Poptávka, nabídka, tržní rovnováha (str. 34–63)",{"id":107420,"depth":4,"text":108309},"Kapitola 3 — Příjem, náklady, zisk, nabídka firmy (str. 66–81)",{"id":107533,"depth":4,"text":108311},"Kapitola 4 — Elasticita (str. 83–96)",{"id":107586,"depth":4,"text":108313},"Kapitola 5 — Produkce (str. 97–111)",{"id":107827,"depth":4,"text":108315},"Kapitola 6 — Užitečnost (str. 113–131)",{"id":108024,"depth":4,"text":108317},"Kapitola 7 — Národní důchod (str. 133–144)",{"id":108078,"depth":7,"text":108079},{"id":108206,"depth":7,"text":108207},{"id":108250,"depth":7,"text":108251},{"id":3865,"depth":7,"text":3866},"Doporučená literatura k předmětu Matematická ekonomie, autor I. Mezník, vydavatelství FP VUT \u002F CERM, Brno 2017. Studentské naskenované fotografie pokrývají kapitoly 2 až 7 (stran 34–144, celkem 107 unikátních stran).",{},"\u002Fsummaries\u002Fimek-kniha",{"title":107357,"description":108322},[9647],"summaries\u002Fimek-kniha",[17,108329,108330,108331,39,34],"kniha","meznik","uvod-do-matematicke-ekonomie","y96KAueM4SX4d38JcXzZsLYGyBeElKYfkrfMaVP4EJQ",{"id":108334,"title":108335,"body":108336,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":108542,"navigation":168,"path":108543,"seo":108544,"sources":108545,"stem":108546,"tags":108547,"type":106007,"updated":178,"__hash__":108551},"summaries\u002Fsummaries\u002Fimork-ai-utoky.md","AI útoky a kybernetická kriminalita",{"type":48,"value":108337,"toc":108532},[108338,108341,108344,108347,108371,108375,108435,108438,108441,108445,108475,108479,108482,108486,108508,108512],[51,108339,108335],{"id":108340},"ai-útoky-a-kybernetická-kriminalita",[84,108342,18762],{"id":108343},"wormgpt",[55,108345,108346],{},"Black-hat AI nástroj pro generování škodlivého obsahu:",[89,108348,108349,108356,108359,108365],{},[92,108350,108351,108352,108355],{},"Založen na ",[95,108353,108354],{},"GPT-J"," (EleutherAI, 2021)",[92,108357,108358],{},"Trénován na datech o malwaru",[92,108360,108361,108364],{},[95,108362,108363],{},"Žádné etické zábrany"," — bez guardrails",[92,108366,108367,108368],{},"Cena: ",[95,108369,108370],{},"60 EUR\u002Fměsíc",[84,108372,108374],{"id":108373},"jak-ai-mění-kybernetickou-kriminalitu","Jak AI mění kybernetickou kriminalitu",[323,108376,108377,108385],{},[326,108378,108379],{},[329,108380,108381,108383],{},[332,108382,520],{},[332,108384,91211],{},[342,108386,108387,108395,108403,108411,108419,108427],{},[329,108388,108389,108392],{},[347,108390,108391],{},"Snadné použití",[347,108393,108394],{},"Nízká bariéra vstupu pro útočníky",[329,108396,108397,108400],{},[347,108398,108399],{},"Klamání",[347,108401,108402],{},"Přesvědčivější phishing a sociální inženýrství",[329,108404,108405,108408],{},[347,108406,108407],{},"Škálovatelnost",[347,108409,108410],{},"Masové generování personalizovaných útoků",[329,108412,108413,108416],{},[347,108414,108415],{},"Rychlost",[347,108417,108418],{},"Automatizace celého řetězce útoku",[329,108420,108421,108424],{},[347,108422,108423],{},"Snížené riziko",[347,108425,108426],{},"Útočník se méně exponuje",[329,108428,108429,108432],{},[347,108430,108431],{},"Nákladová efektivita",[347,108433,108434],{},"Nízké náklady na útok vs. vysoký zisk",[84,108436,108437],{"id":18838},"BEC (Business Email Compromise)",[55,108439,108440],{},"Podvodné emaily cílící na firemní procesy — jedna z nejnákladnějších forem kybernetické kriminality.",[609,108442,108444],{"id":108443},"_5-typů-bec-dle-fbi","5 typů BEC dle FBI",[201,108446,108447,108453,108459,108465,108470],{},[92,108448,108449,108452],{},[95,108450,108451],{},"Impersonace právníka"," — vydávání se za advokáta při naléhavé transakci",[92,108454,108455,108458],{},[95,108456,108457],{},"CEO fraud"," — falešné pokyny od vedení k převodu financí",[92,108460,108461,108464],{},[95,108462,108463],{},"Krádež dat"," — získání citlivých informací (HR, mzdy)",[92,108466,108467,108469],{},[95,108468,18856],{}," — přístup k legitimnímu emailovému účtu",[92,108471,108472,108474],{},[95,108473,18859],{}," — podvržení platebních údajů na fakturách",[609,108476,108478],{"id":108477},"man-in-the-email","Man-in-the-email",[55,108480,108481],{},"Útočník se vloží do emailové konverzace mezi dvěma stranami a manipuluje obsah zpráv.",[84,108483,108485],{"id":108484},"obrana","Obrana",[201,108487,108488,108496,108502],{},[92,108489,108490,108495],{},[95,108491,108492],{},[69,108493,18339],{"className":108494,"dataFsResolvedFilePath":91617,"href":91618},[62]," (Security Awareness Education) — #1 priorita",[92,108497,108498,108501],{},[95,108499,108500],{},"Proaktivní obrana"," — detekce AI-generovaného obsahu, monitoring anomálií",[92,108503,108504,108507],{},[95,108505,108506],{},"Technologické povědomí"," — průběžné vzdělávání o nových hrozbách",[84,108509,108511],{"id":108510},"proč-phishing-přetrvává","Proč phishing přetrvává",[89,108513,108514,108520,108526],{},[92,108515,108516,108519],{},[95,108517,108518],{},"Lidská zranitelnost"," — psychologické manipulace fungují",[92,108521,108522,108525],{},[95,108523,108524],{},"Všudypřítomnost emailu"," — každý ho používá",[92,108527,108528,108531],{},[95,108529,108530],{},"Ziskovost"," — vysoká návratnost investice pro útočníky",{"title":156,"searchDepth":7,"depth":7,"links":108533},[108534,108535,108536,108540,108541],{"id":108343,"depth":7,"text":18762},{"id":108373,"depth":7,"text":108374},{"id":18838,"depth":7,"text":108437,"children":108537},[108538,108539],{"id":108443,"depth":4,"text":108444},{"id":108477,"depth":4,"text":108478},{"id":108484,"depth":7,"text":108485},{"id":108510,"depth":7,"text":108511},{},"\u002Fsummaries\u002Fimork-ai-utoky",{"title":108335,"description":156},[19008],"summaries\u002Fimork-ai-utoky",[11,108548,108343,108549,19015,108550],"ai","bec","kyberneticka-kriminalita","fjRffZ1TYLcv9-Ijz6k4WhQrq5Ah8pM4M4XLFoQEhHY",{"id":108553,"title":108554,"body":108555,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":108868,"navigation":168,"path":108869,"seo":108870,"sources":108871,"stem":108873,"tags":108874,"type":106007,"updated":178,"__hash__":108878},"summaries\u002Fsummaries\u002Fimork-akademicke-prostredi.md","ImorK — ISMS v akademickém prostředí",{"type":48,"value":108556,"toc":108856},[108557,108560,108564,108570,108584,108591,108595,108633,108643,108647,108690,108694,108726,108730,108744,108748,108751,108765,108768,108772,108775,108789,108793,108796,108800,108803,108849,108853],[51,108558,108554],{"id":108559},"imork-isms-v-akademickém-prostředí",[84,108561,108563],{"id":108562},"specifika-univerzitního-kampusu","Specifika univerzitního kampusu",[55,108565,108566,108567,2777],{},"Univerzita má ",[95,108568,108569],{},"dvojí roli",[89,108571,108572,108578],{},[92,108573,108574,108577],{},[95,108575,108576],{},"Zaměstnavatel"," — zaměstnanci, akademici, výzkumníci",[92,108579,108580,108583],{},[95,108581,108582],{},"ISP (poskytovatel služeb)"," — studenti, hosté, konference",[55,108585,108586,108587,108590],{},"Tato dualita přináší unikátní výzvy pro ",[69,108588,733],{"className":108589,"dataFsResolvedFilePath":731,"href":732},[62]," — vysoká fluktuace uživatelů, otevřené prostředí, rozmanité požadavky na přístup.",[84,108592,108594],{"id":108593},"síťová-segmentace","Síťová segmentace",[323,108596,108597,108607],{},[326,108598,108599],{},[329,108600,108601,108604],{},[332,108602,108603],{},"Segment",[332,108605,108606],{},"Účel",[342,108608,108609,108617,108625],{},[329,108610,108611,108614],{},[347,108612,108613],{},"Zaměstnanecká síť",[347,108615,108616],{},"Interní systémy, citlivá data",[329,108618,108619,108622],{},[347,108620,108621],{},"Laboratorní síť",[347,108623,108624],{},"Výzkum, experimenty",[329,108626,108627,108630],{},[347,108628,108629],{},"WiFi (eduroam aj.)",[347,108631,108632],{},"Studenti, hosté",[55,108634,108635,108636,108639,108640,195],{},"Klíčové principy: ",[95,108637,108638],{},"AAA"," (Authentication, Authorization, Accounting) a centrální ",[95,108641,108642],{},"logging",[84,108644,108646],{"id":108645},"standardy-ansibicsi","Standardy ANSI\u002FBICSI",[323,108648,108649,108658],{},[326,108650,108651],{},[329,108652,108653,108656],{},[332,108654,108655],{},"Standard",[332,108657,523],{},[342,108659,108660,108670,108680],{},[329,108661,108662,108667],{},[347,108663,108664],{},[95,108665,108666],{},"BICSI 001-2017",[347,108668,108669],{},"Vzdělávací instituce — kabeláž a infrastruktura",[329,108671,108672,108677],{},[347,108673,108674],{},[95,108675,108676],{},"BICSI 007-2020",[347,108678,108679],{},"Inteligentní budovy",[329,108681,108682,108687],{},[347,108683,108684],{},[95,108685,108686],{},"BICSI 008-2018",[347,108688,108689],{},"Bezdrátové sítě (WLAN)",[84,108691,108693],{"id":108692},"klasifikace-dat-5-úrovní","Klasifikace dat (5 úrovní)",[201,108695,108696,108702,108708,108714,108720],{},[92,108697,108698,108701],{},[95,108699,108700],{},"Veřejná"," — volně dostupné informace",[92,108703,108704,108707],{},[95,108705,108706],{},"Duševní vlastnictví"," — výzkum, publikace před zveřejněním",[92,108709,108710,108713],{},[95,108711,108712],{},"Plány areálu"," — fyzická bezpečnost",[92,108715,108716,108719],{},[95,108717,108718],{},"Přístupová data"," — identity, hesla, certifikáty",[92,108721,108722,108725],{},[95,108723,108724],{},"Finanční a osobní údaje"," — nejvyšší ochrana",[84,108727,108729],{"id":108728},"bezpečnostní-politika-cíle","Bezpečnostní politika — cíle",[89,108731,108732,108735,108738,108741],{},[92,108733,108734],{},"Ochrana informačních aktiv",[92,108736,108737],{},"Zajištění kontinuity vzdělávacího procesu",[92,108739,108740],{},"Soulad s legislativou (ZKB, GDPR)",[92,108742,108743],{},"Ochrana výzkumných dat a duševního vlastnictví",[84,108745,108747],{"id":108746},"implementace-iso-27001-iso-20000","Implementace ISO 27001 + ISO 20000",[55,108749,108750],{},"Kombinovaná implementace:",[89,108752,108753,108759],{},[92,108754,108755,108758],{},[95,108756,108757],{},"ISO 27001"," — systém řízení informační bezpečnosti",[92,108760,108761,108764],{},[95,108762,108763],{},"ISO 20000"," — systém řízení IT služeb (ITSM)",[55,108766,108767],{},"Kroky: gap analýza → návrh politiky → implementace opatření → interní audit → certifikace.",[84,108769,108771],{"id":108770},"identity-management","Identity management",[55,108773,108774],{},"Správa identit v univerzitním prostředí:",[89,108776,108777,108780,108783,108786],{},[92,108778,108779],{},"Životní cyklus identity (nástup → studium → absolvent\u002Fodchod)",[92,108781,108782],{},"Single Sign-On (SSO)",[92,108784,108785],{},"Federace identit (eduID, eduroam)",[92,108787,108788],{},"Přidělování rolí a oprávnění",[84,108790,108792],{"id":108791},"regulace-vis-vyhl-3602020-sb","Regulace VIS (Vyhl. 360\u002F2020 Sb.)",[55,108794,108795],{},"Vyhláška o významných informačních systémech — relevantní pro univerzity provozující IS s velkým počtem uživatelů nebo citlivými daty.",[84,108797,108799],{"id":108798},"tlp-protokol-traffic-light-protocol","TLP protokol (Traffic Light Protocol)",[55,108801,108802],{},"Klasifikace sdílení informací o bezpečnostních hrozbách:",[323,108804,108805,108815],{},[326,108806,108807],{},[329,108808,108809,108812],{},[332,108810,108811],{},"Barva",[332,108813,108814],{},"Sdílení",[342,108816,108817,108825,108833,108841],{},[329,108818,108819,108822],{},[347,108820,108821],{},"🔴 TLP:RED",[347,108823,108824],{},"Pouze přímí příjemci",[329,108826,108827,108830],{},[347,108828,108829],{},"🟠 TLP:AMBER",[347,108831,108832],{},"Omezená komunita",[329,108834,108835,108838],{},[347,108836,108837],{},"🟢 TLP:GREEN",[347,108839,108840],{},"Širší komunita",[329,108842,108843,108846],{},[347,108844,108845],{},"⚪ TLP:CLEAR",[347,108847,108848],{},"Veřejné",[84,108850,108852],{"id":108851},"enisa-cyberhead","ENISA CyberHEAD",[55,108854,108855],{},"Databáze ENISA zaměřená na kybernetickou bezpečnost ve vysokoškolském vzdělávání (Cybersecurity Higher Education Database) — mapuje programy, kurzy a kompetence napříč EU.",{"title":156,"searchDepth":7,"depth":7,"links":108857},[108858,108859,108860,108861,108862,108863,108864,108865,108866,108867],{"id":108562,"depth":7,"text":108563},{"id":108593,"depth":7,"text":108594},{"id":108645,"depth":7,"text":108646},{"id":108692,"depth":7,"text":108693},{"id":108728,"depth":7,"text":108729},{"id":108746,"depth":7,"text":108747},{"id":108770,"depth":7,"text":108771},{"id":108791,"depth":7,"text":108792},{"id":108798,"depth":7,"text":108799},{"id":108851,"depth":7,"text":108852},{},"\u002Fsummaries\u002Fimork-akademicke-prostredi",{"title":108554,"description":156},[108872],"raw\u002Fimork\u002F2004 VUT_Bezp akademici-2021.pdf","summaries\u002Fimork-akademicke-prostredi",[11,20,108875,108876,108877],"univerzity","kampus","wifi","Zg8xovWQTxYfvBj7GcSVkjlAWlIrXxpGv9Ns1XFrmbk",{"id":108880,"title":18955,"body":108881,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":109476,"navigation":168,"path":109477,"seo":109478,"sources":109479,"stem":109480,"tags":109481,"type":106007,"updated":178,"__hash__":109486},"summaries\u002Fsummaries\u002Fimork-anatomie-utoku.md",{"type":48,"value":108882,"toc":109455},[108883,108886,108890,108904,108906,108975,108977,109008,109012,109026,109029,109032,109036,109104,109108,109133,109137,109140,109144,109180,109184,109187,109191,109194,109214,109218,109225,109250,109254,109386,109390,109393,109438,109440,109448,109452],[51,108884,18955],{"id":108885},"anatomie-kybernetického-útoku",[84,108887,108889],{"id":108888},"útočný-povrch-attack-surface","Útočný povrch (Attack Surface)",[89,108891,108892,108898],{},[92,108893,108894,108897],{},[95,108895,108896],{},"Digitální"," — síťová rozhraní, aplikace, služby, API",[92,108899,108900,108903],{},[95,108901,108902],{},"Fyzický"," — USB porty, přístupové body, zařízení",[84,108905,321],{"id":320},[323,108907,108908,108916],{},[326,108909,108910],{},[329,108911,108912,108914],{},[332,108913,334],{},[332,108915,45728],{},[342,108917,108918,108928,108938,108948,108957,108966],{},[329,108919,108920,108925],{},[347,108921,108922],{},[95,108923,108924],{},"Threat Agent",[347,108926,108927],{},"Aktér provádějící útok (hacker, insider, APT skupina)",[329,108929,108930,108935],{},[347,108931,108932],{},[95,108933,108934],{},"Attack Vector",[347,108936,108937],{},"Cesta\u002Fmetoda průniku do systému",[329,108939,108940,108945],{},[347,108941,108942],{},[95,108943,108944],{},"Vulnerability",[347,108946,108947],{},"Zranitelnost — slabina v systému",[329,108949,108950,108954],{},[347,108951,108952],{},[95,108953,18604],{},[347,108955,108956],{},"Kód\u002Ftechnika zneužívající zranitelnost",[329,108958,108959,108963],{},[347,108960,108961],{},[95,108962,18610],{},[347,108964,108965],{},"Škodlivý obsah doručený exploitem",[329,108967,108968,108972],{},[347,108969,108970],{},[95,108971,18616],{},[347,108973,108974],{},"Kód spuštěný po úspěšném exploitu",[84,108976,18710],{"id":18709},[201,108978,108979,108985,108990,108996,109002],{},[92,108980,108981,108984],{},[95,108982,108983],{},"Email s přílohou"," — nejčastější vektor, sociální inženýrství",[92,108986,108987,108989],{},[95,108988,18718],{}," — legitimní software s malwarem",[92,108991,108992,108995],{},[95,108993,108994],{},"Drive-by download"," — stažení malwaru při návštěvě webu",[92,108997,108998,109001],{},[95,108999,109000],{},"Vyměnitelná média"," — USB (BadUSB) — fyzický vektor",[92,109003,109004,109007],{},[95,109005,109006],{},"Watering hole"," — kompromitace často navštěvovaného webu cílové skupiny",[84,109009,109011],{"id":109010},"plošný-vs-cílený-útok","Plošný vs. cílený útok",[89,109013,109014,109020],{},[92,109015,109016,109019],{},[95,109017,109018],{},"Plošný útok"," — masový, automatizovaný, netargeted (spam, phishing kampaně)",[92,109021,109022,109025],{},[95,109023,109024],{},"Cílený útok"," — zaměřený na konkrétní organizaci\u002Fosobu, sofistikovaný",[84,109027,109028],{"id":18669},"APT (Advanced Persistent Threat)",[55,109030,109031],{},"Pokročilá přetrvávající hrozba — dlouhodobý, cílený útok financovaný státem nebo organizovaným zločinem.",[609,109033,109035],{"id":109034},"_4-fáze-apt","4 fáze APT",[201,109037,109038,109051,109072,109088],{},[92,109039,109040,109042,109043],{},[95,109041,18687],{}," (Preparation\u002FReconnaissance)",[89,109044,109045,109048],{},[92,109046,109047],{},"Průzkum cíle (OSINT, sociální sítě, technický recon)",[92,109049,109050],{},"Výběr vektoru útoku",[92,109052,109053,109056,109057],{},[95,109054,109055],{},"Infiltrace"," (Infiltration)",[89,109058,109059,109066,109069],{},[92,109060,109061,109065],{},[69,109062,109064],{"className":109063,"dataFsResolvedFilePath":18961,"href":18962},[62],"Spear phishing"," — cílený phishing",[92,109067,109068],{},"Malvertising — škodlivá reklama",[92,109070,109071],{},"Počáteční kompromitace systému",[92,109073,109074,109076,109077],{},[95,109075,18699],{}," (Compromise)",[89,109078,109079,109082,109085],{},[92,109080,109081],{},"Laterální pohyb (lateral movement) — šíření v síti",[92,109083,109084],{},"Eskalace oprávnění",[92,109086,109087],{},"Instalace backdoorů",[92,109089,109090,109092,109093],{},[95,109091,18705],{}," (Completion)",[89,109094,109095,109098,109101],{},[92,109096,109097],{},"Exfiltrace dat",[92,109099,109100],{},"Dlouhodobý přístup",[92,109102,109103],{},"Případná destrukce\u002Fsabotáž",[84,109105,109107],{"id":109106},"softwarové-útoky","Softwarové útoky",[89,109109,109110,109116,109122,109127],{},[92,109111,109112,109115],{},[95,109113,109114],{},"Adware"," — nevyžádaná reklama",[92,109117,109118,109121],{},[95,109119,109120],{},"Spyware"," — sledování aktivity uživatele",[92,109123,109124,109126],{},[95,109125,18744],{}," — sebereplikující škodlivý kód",[92,109128,109129,109132],{},[95,109130,109131],{},"Trojany"," — malware maskovaný jako legitimní software",[84,109134,109136],{"id":109135},"sociální-inženýrství","Sociální inženýrství",[55,109138,109139],{},"Nejoblíbenější metoda útoku — manipulace s lidskou důvěrou a emocemi (strach, zvědavost, autorita, časový tlak). Obchází technická opatření tím, že cílí na nejslabší článek — člověka.",[84,109141,109143],{"id":109142},"phishing-vs-spear-phishing","Phishing vs. Spear Phishing",[323,109145,109146,109154],{},[326,109147,109148],{},[329,109149,109150,109152],{},[332,109151,10393],{},[332,109153,340],{},[342,109155,109156,109170],{},[329,109157,109158,109163],{},[347,109159,109160],{},[95,109161,109162],{},"Phishing",[347,109164,109165,109166,109169],{},"Masový útok — ",[95,109167,109168],{},"83 % útočníků"," předstírá příslušnost ke známé značce",[329,109171,109172,109177],{},[347,109173,109174],{},[95,109175,109176],{},"Spear Phishing",[347,109178,109179],{},"Cílený útok na konkrétní osoby\u002Forganizace — personalizované zprávy",[609,109181,109183],{"id":109182},"struktura-phisherské-organizace","Struktura phisherské organizace",[55,109185,109186],{},"Organizovaná skupina s dělbou rolí — tvůrci stránek, spameři, muly pro praní peněz, koordinátoři.",[84,109188,109190],{"id":109189},"typy-malwaru-rozšířeno","Typy malwaru — rozšířeno",[55,109192,109193],{},"Doplnění k základním softwarovým útokům:",[89,109195,109196,109202,109208],{},[92,109197,109198,109201],{},[95,109199,109200],{},"Cryptojacking"," — neoprávněné využití výpočetního výkonu oběti pro těžbu kryptoměn",[92,109203,109204,109207],{},[95,109205,109206],{},"Trojský kůň"," — maskuje se jako legitimní software, otevírá zadní vrátka",[92,109209,109210,109213],{},[95,109211,109212],{},"Červi (worms)"," — samostatné šíření po síti bez interakce uživatele (na rozdíl od virů)",[84,109215,109217],{"id":109216},"watering-hole-supply-chain-útoky","Watering hole \u002F Supply chain útoky",[55,109219,109220,109221,3225],{},"Pokročilé útoky na dodavatelský řetězec a průmyslové řídicí systémy (",[69,109222,109224],{"className":109223,"dataFsResolvedFilePath":18446,"href":18447},[62],"ICS",[89,109226,109227,109232,109238,109244],{},[92,109228,109229,109231],{},[95,109230,109006],{}," — kompromitace webu často navštěvovaného cílovou skupinou",[92,109233,109234,109237],{},[95,109235,109236],{},"Supply chain"," — infiltrace přes důvěryhodného dodavatele softwaru\u002Fhardwaru",[92,109239,109240,109243],{},[95,109241,109242],{},"Steganografie v obrázcích"," — ukrytí škodlivého kódu v obrazových souborech",[92,109245,109246,109249],{},[95,109247,109248],{},"Zneužití výjimek jako dešifrovacích klíčů"," — využití exception handlerů pro aktivaci payloadu",[84,109251,109253],{"id":109252},"útoky-podle-isoosi-vrstev","Útoky podle ISO\u002FOSI vrstev",[323,109255,109256,109272],{},[326,109257,109258],{},[329,109259,109260,109263,109266,109269],{},[332,109261,109262],{},"Vrstva",[332,109264,109265],{},"Protokoly",[332,109267,109268],{},"Techniky útoku",[332,109270,109271],{},"Mitigace",[342,109273,109274,109290,109306,109322,109338,109354,109370],{},[329,109275,109276,109281,109284,109287],{},[347,109277,109278],{},[95,109279,109280],{},"L1 (fyzická)",[347,109282,109283],{},"Ethernet, Wi-Fi",[347,109285,109286],{},"Odposlech, rušení",[347,109288,109289],{},"Fyzická bezpečnost, stínění",[329,109291,109292,109297,109300,109303],{},[347,109293,109294],{},[95,109295,109296],{},"L2 (linková)",[347,109298,109299],{},"ARP, MAC",[347,109301,109302],{},"ARP spoofing, MAC flooding",[347,109304,109305],{},"Port security, DHCP snooping",[329,109307,109308,109313,109316,109319],{},[347,109309,109310],{},[95,109311,109312],{},"L3 (síťová)",[347,109314,109315],{},"IP, ICMP",[347,109317,109318],{},"IP spoofing, ICMP flood",[347,109320,109321],{},"Filtrování, ACL",[329,109323,109324,109329,109332,109335],{},[347,109325,109326],{},[95,109327,109328],{},"L4 (transportní)",[347,109330,109331],{},"TCP, UDP",[347,109333,109334],{},"SYN flood, UDP flood",[347,109336,109337],{},"SYN cookies, rate limiting",[329,109339,109340,109345,109348,109351],{},[347,109341,109342],{},[95,109343,109344],{},"L5 (relační)",[347,109346,109347],{},"NetBIOS, RPC",[347,109349,109350],{},"Session hijacking",[347,109352,109353],{},"Šifrování sessions",[329,109355,109356,109361,109364,109367],{},[347,109357,109358],{},[95,109359,109360],{},"L6 (prezentační)",[347,109362,109363],{},"SSL\u002FTLS",[347,109365,109366],{},"SSL stripping, POODLE",[347,109368,109369],{},"Aktualizace, HSTS",[329,109371,109372,109377,109380,109383],{},[347,109373,109374],{},[95,109375,109376],{},"L7 (aplikační)",[347,109378,109379],{},"HTTP, DNS, SMTP",[347,109381,109382],{},"[[imork-www",[347,109384,109385],{},"XSS]], [[imork-www",[84,109387,109389],{"id":109388},"amplifikační-útoky","Amplifikační útoky",[55,109391,109392],{},"DDoS útoky využívající asymetrii mezi malým požadavkem a velkou odpovědí:",[323,109394,109395,109406],{},[326,109396,109397],{},[329,109398,109399,109401,109404],{},[332,109400,10393],{},[332,109402,109403],{},"Amplifikační faktor",[332,109405,87],{},[342,109407,109408,109421],{},[329,109409,109410,109415,109418],{},[347,109411,109412],{},[95,109413,109414],{},"DNS amplification",[347,109416,109417],{},"1:70",[347,109419,109420],{},"Malý DNS dotaz → velká odpověď (ANY record)",[329,109422,109423,109428,109431],{},[347,109424,109425],{},[95,109426,109427],{},"NTP amplification",[347,109429,109430],{},"1:556",[347,109432,109433,109434,109437],{},"Příkaz ",[929,109435,109436],{},"monlist"," → obrovská odpověď",[609,109439,108485],{"id":108484},[89,109441,109442],{},[92,109443,109444,109447],{},[95,109445,109446],{},"BCP38"," (RFC 2827) — filtrování zdrojových IP adres na hranici sítě (ingress filtering), zamezení IP spoofingu",[84,109449,109451],{"id":109450},"mitre-attck","MITRE ATT&CK",[55,109453,109454],{},"Znalostní báze taktik a technik kybernetických útoků — referenční framework pro popis chování útočníků.",{"title":156,"searchDepth":7,"depth":7,"links":109456},[109457,109458,109459,109460,109461,109464,109465,109466,109469,109470,109471,109472,109475],{"id":108888,"depth":7,"text":108889},{"id":320,"depth":7,"text":321},{"id":18709,"depth":7,"text":18710},{"id":109010,"depth":7,"text":109011},{"id":18669,"depth":7,"text":109028,"children":109462},[109463],{"id":109034,"depth":4,"text":109035},{"id":109106,"depth":7,"text":109107},{"id":109135,"depth":7,"text":109136},{"id":109142,"depth":7,"text":109143,"children":109467},[109468],{"id":109182,"depth":4,"text":109183},{"id":109189,"depth":7,"text":109190},{"id":109216,"depth":7,"text":109217},{"id":109252,"depth":7,"text":109253},{"id":109388,"depth":7,"text":109389,"children":109473},[109474],{"id":108484,"depth":4,"text":108485},{"id":109450,"depth":7,"text":109451},{},"\u002Fsummaries\u002Fimork-anatomie-utoku",{"title":18955,"description":156},[19007],"summaries\u002Fimork-anatomie-utoku",[11,19011,19013,109482,19015,109483,109484,109485],"exploit","socialni-inzenyrstvi","malware","supply-chain","uyh1iT5L9T1JAdGrSpU7KFcF6aLiKI26GbUzKuDQN6g",{"id":109488,"title":109489,"body":109490,"course":11,"courses":163,"created":795,"description":109497,"extension":166,"meta":109643,"navigation":168,"path":109644,"seo":109645,"sources":109646,"stem":109648,"tags":109649,"type":106007,"updated":178,"__hash__":109655},"summaries\u002Fsummaries\u002Fimork-audio-hack.md","Případovka: Audio Hack",{"type":48,"value":109491,"toc":109634},[109492,109495,109498,109502,109537,109541,109559,109563,109575,109579,109598,109600,109622,109629],[51,109493,109489],{"id":109494},"případovka-audio-hack",[55,109496,109497],{},"Případová studie z 16. listopadu 2022. Demonstrace fyzické zranitelnosti hardwaru prostřednictvím zvukového signálu.",[84,109499,109501],{"id":109500},"incident","Incident",[89,109503,109504,109518,109528,109534],{},[92,109505,109506],{},[201,109507,109508],{"start":40},[92,109509,109510,109511,7102,109514,109517],{},"album zpěvačky ",[95,109512,109513],{},"Janet Jackson",[3982,109515,109516],{},"Rhythm Nation 1814"," (1989)",[92,109519,109520,109521,109524,109525],{},"Skladba ",[95,109522,109523],{},"Rhythm Nation"," způsobovala u některých notebooků ",[95,109526,109527],{},"pád systému",[92,109529,109530,109531],{},"Příčina: zvuk rezonuje s ",[95,109532,109533],{},"mechanickými pevnými disky s 5400 ot\u002Fmin",[92,109535,109536],{},"Známý efekt — křik v datovém centru měřitelně zvyšuje latenci disků",[84,109538,109540],{"id":109539},"cve-2022-38392","CVE-2022-38392",[89,109542,109543,109549],{},[92,109544,109545,109546],{},"Produkt: ",[95,109547,109548],{},"Seagate STDT40000100",[92,109550,109551,109552,109555,109556],{},"Popis: HDD s 5400 ot\u002Fmin (~2005) umožňují fyzicky blízkým útočníkům způsobit ",[95,109553,109554],{},"DoS"," (selhání zařízení) prostřednictvím ",[95,109557,109558],{},"rezonančního frekvenčního útoku",[84,109560,109562],{"id":109561},"řešení","Řešení",[201,109564,109565,109568],{},[92,109566,109567],{},"Filtr ve zvukovém kanálu — detekce a odstranění rušivých frekvencí",[92,109569,109570,109571,109574],{},"Přechod na technologii ",[95,109572,109573],{},"SSD"," (bez pohyblivých částí)",[84,109576,109578],{"id":109577},"význam-pro-bezpečnost","Význam pro bezpečnost",[89,109580,109581,109592,109595],{},[92,109582,109583,109584,109588,109589],{},"Demonstruje, že ",[69,109585,109587],{"className":109586,"dataFsResolvedFilePath":749,"href":750},[62],"kybernetická bezpečnost"," zahrnuje i ",[95,109590,109591],{},"fyzické vektory útoku",[92,109593,109594],{},"Rezonanční frekvence jako nekonvenční DoS vektor",[92,109596,109597],{},"CVE databáze eviduje i fyzické zranitelnosti HW",[84,109599,723],{"id":722},[89,109601,109602,109609,109615],{},[92,109603,109604,109608],{},[69,109605,109607],{"className":109606,"dataFsResolvedFilePath":18953,"href":18954},[62],"Anatomie útoku"," — fyzická útočná plocha",[92,109610,109611,109614],{},[69,109612,18494],{"className":109613,"dataFsResolvedFilePath":18492,"href":18493},[62]," — fyzická ochrana médií",[92,109616,109617,109621],{},[69,109618,109620],{"className":109619,"dataFsResolvedFilePath":18446,"href":18447},[62],"MCN"," — spolehlivost a dostupnost infrastruktury",[84,109623,109625,109626],{"id":109624},"zdroj-v-kurzu-imork","Zdroj v kurzu ",[69,109627,762],{"className":109628,"dataFsResolvedFilePath":760,"href":761},[62],[89,109630,109631],{},[92,109632,109633],{},"Případovka 2207 — Audio Hack (2022)",{"title":156,"searchDepth":7,"depth":7,"links":109635},[109636,109637,109638,109639,109640,109641],{"id":109500,"depth":7,"text":109501},{"id":109539,"depth":7,"text":109540},{"id":109561,"depth":7,"text":109562},{"id":109577,"depth":7,"text":109578},{"id":722,"depth":7,"text":723},{"id":109624,"depth":7,"text":109642},"Zdroj v kurzu ImorK",{},"\u002Fsummaries\u002Fimork-audio-hack",{"title":109489,"description":109497},[109647],"raw\u002Fimork\u002F2207 VUT_Bezp_Případovka Audio Hack-2022.pdf","summaries\u002Fimork-audio-hack",[11,109650,109651,109652,109653,109654],"zranitelnost","fyzicky-utok","hdd","cve","dos","-zqMNRcmjGIOFNhxf7tKJ9FRRfRECwhUuFNmeMB82X8",{"id":109657,"title":109658,"body":109659,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":109869,"navigation":168,"path":109870,"seo":109871,"sources":109872,"stem":109874,"tags":109875,"type":106007,"updated":178,"__hash__":109878},"summaries\u002Fsummaries\u002Fimork-automotive.md","Automotive bezpečnost",{"type":48,"value":109660,"toc":109858},[109661,109664,109671,109675,109681,109706,109710,109713,109717,109749,109753,109756,109760,109763,109775,109779,109785,109825,109829,109836,109851,109855],[51,109662,109658],{"id":109663},"automotive-bezpečnost",[55,109665,109666],{},[58,109667],{"alt":109668,"className":109669,"src":109670},"imork-automotive-vrstvy",[62,63],"\u002Fwiki-assets\u002Fimork-automotive-vrstvy.jpeg",[84,109672,109674],{"id":109673},"can-bus","CAN Bus",[55,109676,109677,109680],{},[95,109678,109679],{},"CAN"," (Controller Area Network) — komunikační sběrnice pro vozidla:",[89,109682,109683,109690,109696,109699],{},[92,109684,109685,109686,109689],{},"Vyvinuta firmou ",[95,109687,109688],{},"Bosch"," v roce 1983",[92,109691,109692,109693],{},"Normalizována jako ",[95,109694,109695],{},"ISO 11898",[92,109697,109698],{},"Povinná v EU od roku 2001",[92,109700,109701,109702,109705],{},"Moderní vozidlo obsahuje až ",[95,109703,109704],{},"70 ECU"," (Electronic Control Unit)",[609,109707,109709],{"id":109708},"can-hacking-tool-cht","CAN Hacking Tool (CHT)",[55,109711,109712],{},"Nástroj pro bezpečnostní testování a demonstraci zranitelností CAN sběrnice.",[84,109714,109716],{"id":109715},"vektory-útoku","Vektory útoku",[89,109718,109719,109725,109731,109737,109743],{},[92,109720,109721,109724],{},[95,109722,109723],{},"OBD-II konektor"," — přímý fyzický přístup ke sběrnici",[92,109726,109727,109730],{},[95,109728,109729],{},"Bluetooth"," — bezdrátový útok přes hands-free a infotainment",[92,109732,109733,109736],{},[95,109734,109735],{},"WiFi"," — připojení přes hotspot vozidla",[92,109738,109739,109742],{},[95,109740,109741],{},"Infotainment systém"," — vstupní brána do vnitřní sítě vozidla",[92,109744,109745,109748],{},[95,109746,109747],{},"Relay útoky na keyless entry"," — prodloužení signálu klíčenky",[84,109750,109752],{"id":109751},"_4-bezpečnostní-vrstvy","4 bezpečnostní vrstvy",[55,109754,109755],{},"Vícevrstvý model ochrany automobilových systémů (hardware, síťová, aplikační, datová vrstva).",[84,109757,109759],{"id":109758},"ochrana-soukromí","Ochrana soukromí",[55,109761,109762],{},"Problematika soukromí v kontextu:",[89,109764,109765,109768],{},[92,109766,109767],{},"Navigačních systémů (sledování polohy)",[92,109769,109770,109771,109774],{},"Systému ",[95,109772,109773],{},"eCall"," (automatické tísňové volání)",[84,109776,109778],{"id":109777},"tisax","TISAX",[55,109780,109781,109784],{},[95,109782,109783],{},"Trusted Information Security Assessment Exchange"," — standard pro automobilový průmysl:",[89,109786,109787,109797,109800,109807],{},[92,109788,109789,109790,109793,109794],{},"Vytvořen sdruženími ",[95,109791,109792],{},"VDA"," (Verband der Automobilindustrie) a ",[95,109795,109796],{},"ENX",[92,109798,109799],{},"Založen na ISO 27001",[92,109801,109802,109803,109806],{},"Obsahuje ",[95,109804,109805],{},"model zralosti"," (maturity model)",[92,109808,109809,42768,109812],{},[95,109810,109811],{},"4 moduly",[201,109813,109814,109816,109819,109822],{},[92,109815,733],{},[92,109817,109818],{},"Ochrana dat (data protection)",[92,109820,109821],{},"Připojení třetích stran",[92,109823,109824],{},"Ochrana prototypů",[84,109826,109828],{"id":109827},"un-regulation-no-155","UN Regulation No. 155",[55,109830,109831,109832,109835],{},"Od ",[95,109833,109834],{},"července 2024"," povinná kybernetická ochrana pro všechna nová vozidla v EU:",[89,109837,109838,109841,109844],{},[92,109839,109840],{},"Požadavky na celý životní cyklus vozidla",[92,109842,109843],{},"Povinnost implementace CSMS (Cyber Security Management System)",[92,109845,109846,109847,109850],{},"Podmínka pro ",[95,109848,109849],{},"homologaci"," vozidla",[84,109852,109854],{"id":109853},"penetrační-testování","Penetrační testování",[55,109856,109857],{},"Testování bezpečnosti automobilových systémů jako součást procesu homologace a certifikace.",{"title":156,"searchDepth":7,"depth":7,"links":109859},[109860,109863,109864,109865,109866,109867,109868],{"id":109673,"depth":7,"text":109674,"children":109861},[109862],{"id":109708,"depth":4,"text":109709},{"id":109715,"depth":7,"text":109716},{"id":109751,"depth":7,"text":109752},{"id":109758,"depth":7,"text":109759},{"id":109777,"depth":7,"text":109778},{"id":109827,"depth":7,"text":109828},{"id":109853,"depth":7,"text":109854},{},"\u002Fsummaries\u002Fimork-automotive",{"title":109658,"description":156},[109873],"raw\u002Fimork\u002F2010 VUT_Bezp Automotive-2023.pdf","summaries\u002Fimork-automotive",[11,20,109876,109673,109777,109877],"automotive","iso-11898","tjhs2XZkpXo2HJS6RjfsESJJmOEtX5YL5FEVcIwdAfE",{"id":109880,"title":109881,"body":109882,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":110453,"navigation":168,"path":110454,"seo":110455,"sources":110456,"stem":110457,"tags":110458,"type":106007,"updated":178,"__hash__":110462},"summaries\u002Fsummaries\u002Fimork-bcm.md","Business Continuity Management (BCM)",{"type":48,"value":109883,"toc":110422},[109884,109887,109889,109906,109910,109918,109920,109942,109946,109954,109958,109961,110041,110045,110048,110085,110089,110092,110096,110122,110126,110130,110144,110148,110163,110167,110187,110191,110195,110221,110225,110251,110255,110269,110273,110277,110315,110319,110326,110330,110334,110354,110358,110372,110376,110382,110401,110408,110412,110415,110419],[51,109885,109881],{"id":109886},"business-continuity-management-bcm",[84,109888,45728],{"id":45727},[89,109890,109891,109896,109901],{},[92,109892,109893,109895],{},[95,109894,364],{}," (Business Continuity Management) — řízení kontinuity činností organizace",[92,109897,109898,109900],{},[95,109899,377],{}," (Business Impact Analysis) — analýza dopadů na podnikání; identifikuje kritické procesy a stanoví priority obnovy",[92,109902,109903,109905],{},[95,109904,390],{}," (Minimum Business Continuity Objective) — minimální úroveň služeb, kterou musí organizace udržet",[84,109907,109909],{"id":109908},"vztah-bcm-k-řízení-rizik","Vztah BCM k řízení rizik",[55,109911,109912,109913,109917],{},"BCM je součástí ",[69,109914,109916],{"className":109915,"dataFsResolvedFilePath":18516,"href":18517},[62],"podnikového řízení rizik",". Zatímco risk management se zaměřuje na prevenci, BCM řeší situace, kdy k incidentu dojde.",[84,109919,426],{"id":425},[201,109921,109922,109927,109932,109937],{},[92,109923,109924,109926],{},[95,109925,447],{}," — stanovení politiky BCM, analýza BIA, strategie kontinuity",[92,109928,109929,109931],{},[95,109930,457],{}," — implementace postupů, školení, dokumentace",[92,109933,109934,109936],{},[95,109935,467],{}," — interní audity, přezkum vedením, testování plánů",[92,109938,109939,109941],{},[95,109940,477],{}," — nápravná opatření, zlepšování",[84,109943,109945],{"id":109944},"isoiec-270312011","ISO\u002FIEC 27031:2011",[55,109947,109948,109949,109953],{},"Připravenost ICT pro kontinuitu podnikání — propojení mezi ",[69,109950,109952],{"className":109951,"dataFsResolvedFilePath":18446,"href":18447},[62],"kritickou infrastrukturou"," a BCMS.",[84,109955,109957],{"id":109956},"iso-223012019-požadavky-na-bcms","ISO 22301:2019 — Požadavky na BCMS",[55,109959,109960],{},"Kapitoly mapované na PDCA:",[323,109962,109963,109975],{},[326,109964,109965],{},[329,109966,109967,109970,109972],{},[332,109968,109969],{},"Kapitola",[332,109971,438],{},[332,109973,109974],{},"PDCA fáze",[342,109976,109977,109986,109995,110004,110014,110023,110032],{},[329,109978,109979,109981,109984],{},[347,109980,662],{},[347,109982,109983],{},"Kontext organizace",[347,109985,447],{},[329,109987,109988,109990,109993],{},[347,109989,670],{},[347,109991,109992],{},"Leadership",[347,109994,447],{},[329,109996,109997,109999,110002],{},[347,109998,678],{},[347,110000,110001],{},"Plánování",[347,110003,447],{},[329,110005,110006,110008,110011],{},[347,110007,686],{},[347,110009,110010],{},"Podpora",[347,110012,110013],{},"Plan\u002FDo",[329,110015,110016,110018,110021],{},[347,110017,5672],{},[347,110019,110020],{},"Provoz (BIA, strategie, plány)",[347,110022,457],{},[329,110024,110025,110027,110030],{},[347,110026,4087],{},[347,110028,110029],{},"Hodnocení výkonnosti",[347,110031,467],{},[329,110033,110034,110036,110039],{},[347,110035,2935],{},[347,110037,110038],{},"Zlepšování",[347,110040,477],{},[84,110042,110044],{"id":110043},"steeple-analýza","STEEPLE analýza",[55,110046,110047],{},"Analýza vnějšího prostředí pro BCM plánování:",[89,110049,110050,110055,110060,110065,110070,110075,110080],{},[92,110051,110052,110054],{},[95,110053,532],{}," — Social (sociální faktory)",[92,110056,110057,110059],{},[95,110058,543],{}," — Technological (technologické)",[92,110061,110062,110064],{},[95,110063,554],{}," — Economic (ekonomické)",[92,110066,110067,110069],{},[95,110068,554],{}," — Ethical (etické)",[92,110071,110072,110074],{},[95,110073,575],{}," — Political (politické)",[92,110076,110077,110079],{},[95,110078,586],{}," — Legislative (legislativní)",[92,110081,110082,110084],{},[95,110083,554],{}," — Environmental (environmentální)",[84,110086,110088],{"id":110087},"rozsah-bcm-plánování","Rozsah BCM plánování",[55,110090,110091],{},"Určení hranic BCMS — které procesy, lokality, produkty a služby jsou zahrnuty.",[84,110093,110095],{"id":110094},"přínosy-bcm","Přínosy BCM",[89,110097,110098,110104,110110,110116],{},[92,110099,110100,110103],{},[95,110101,110102],{},"Regulatorní soulad"," — splnění požadavků legislativy a norem",[92,110105,110106,110109],{},[95,110107,110108],{},"Konkurenční výhoda"," — důvěra zákazníků a partnerů",[92,110111,110112,110115],{},[95,110113,110114],{},"Finanční přínosy"," — snížení ztrát z výpadků",[92,110117,110118,110121],{},[95,110119,110120],{},"Reputace"," — ochrana dobrého jména organizace",[84,110123,110125],{"id":110124},"bia-podrobně","BIA podrobně",[609,110127,110129],{"id":110128},"dva-způsoby-provedení-bia","Dva způsoby provedení BIA",[201,110131,110132,110138],{},[92,110133,110134,110137],{},[95,110135,110136],{},"Bottom-up"," — od provozních manažerů směrem nahoru; detailní znalost procesů, ale časově náročné",[92,110139,110140,110143],{},[95,110141,110142],{},"Top-down"," — od vyššího managementu; rychlejší, ale může opomenout provozní detaily",[609,110145,110147],{"id":110146},"principy-bia","Principy BIA",[89,110149,110150,110157],{},[92,110151,110152,110153,110156],{},"Orientace na ",[95,110154,110155],{},"dopad",", ne na příčinu — nezkoumá, co se stane, ale jaké budou následky",[92,110158,110159,110162],{},[95,110160,110161],{},"Kalendář klíčových ročních událostí"," — identifikace období se zvýšenou kritičností (uzávěrky, sezónní špičky)",[84,110164,110166],{"id":110165},"mapování-procesů","Mapování procesů",[89,110168,110169,110175,110181],{},[92,110170,110171,110174],{},[95,110172,110173],{},"Víceúrovňové mapování"," — od strategických procesů po operativní detaily",[92,110176,110177,110180],{},[95,110178,110179],{},"Identifikace zdrojů"," — lidé, technologie, prostory, dodavatelé potřební pro každý proces",[92,110182,110183,110186],{},[95,110184,110185],{},"SPoF"," (Single Point of Failure) — identifikace jediných bodů selhání, jejichž výpadek zastaví celý proces",[84,110188,110190],{"id":110189},"strategie-kontinuity","Strategie kontinuity",[609,110192,110194],{"id":110193},"_4-kroky-strategie","4 kroky strategie",[201,110196,110197,110203,110209,110215],{},[92,110198,110199,110202],{},[95,110200,110201],{},"Reakce na incident"," — okamžitá odezva, aktivace krizového řízení",[92,110204,110205,110208],{},[95,110206,110207],{},"Obnova kritických činností"," — prioritní obnovení klíčových procesů dle BIA",[92,110210,110211,110214],{},[95,110212,110213],{},"Vztahy se stakeholdery"," — komunikace se zainteresovanými stranami",[92,110216,110217,110220],{},[95,110218,110219],{},"Nekritické činnosti"," — postupná obnova ostatních procesů",[609,110222,110224],{"id":110223},"_4-scénáře-narušení","4 scénáře narušení",[201,110226,110227,110233,110239,110245],{},[92,110228,110229,110232],{},[95,110230,110231],{},"Zamezení přístupu"," — nedostupnost budov\u002Fprostor (požár, povodeň)",[92,110234,110235,110238],{},[95,110236,110237],{},"Nedostatek pracovníků"," — pandemie, hromadná absence",[92,110240,110241,110244],{},[95,110242,110243],{},"Selhání technologie"," — výpadek ICT, kybernetický útok",[92,110246,110247,110250],{},[95,110248,110249],{},"Selhání dodavatele"," — přerušení dodavatelského řetězce",[609,110252,110254],{"id":110253},"další-aspekty","Další aspekty",[89,110256,110257,110263],{},[92,110258,110259,110262],{},[95,110260,110261],{},"Riziko nahromadění práce"," — kumulace nedokončených úkolů během výpadku, které mohou přetížit organizaci po obnově",[92,110264,110265,110268],{},[95,110266,110267],{},"Komunikační strategie"," — interní (zaměstnanci, vedení) i externí (zákazníci, úřady, média); řízení komunikace s médii",[84,110270,110272],{"id":110271},"implementace-plánů","Implementace plánů",[609,110274,110276],{"id":110275},"obsah-plánu-kontinuity","Obsah plánu kontinuity",[89,110278,110279,110285,110291,110297,110303,110309],{},[92,110280,110281,110284],{},[95,110282,110283],{},"Účel a rozsah"," — co plán pokrývá",[92,110286,110287,110290],{},[95,110288,110289],{},"Role a odpovědnosti"," — kdo za co odpovídá",[92,110292,110293,110296],{},[95,110294,110295],{},"Aktivační kritéria"," — kdy se plán spouští",[92,110298,110299,110302],{},[95,110300,110301],{},"DRP"," (Disaster Recovery Plan) — obnova IT infrastruktury",[92,110304,110305,110308],{},[95,110306,110307],{},"Kontaktní seznamy"," — krizové kontakty",[92,110310,110311,110314],{},[95,110312,110313],{},"Priority obnovy"," — pořadí obnovovaných procesů dle BIA",[609,110316,110318],{"id":110317},"dlouhodobá-obnova","Dlouhodobá obnova",[55,110320,110321,110322,110325],{},"Dlouhodobá obnova je řízena jako ",[95,110323,110324],{},"samostatný projekt"," — návrat do normálního provozu, obnova plné kapacity, vyhodnocení.",[84,110327,110329],{"id":110328},"testování-bcm","Testování BCM",[609,110331,110333],{"id":110332},"formy-testování","Formy testování",[201,110335,110336,110342,110348],{},[92,110337,110338,110341],{},[95,110339,110340],{},"Přezkoumání u stolu"," (Tabletop review) — teoretické procházení scénářů",[92,110343,110344,110347],{},[95,110345,110346],{},"Procházení plánu"," (Walkthrough) — krokové ověření postupů s účastníky",[92,110349,110350,110353],{},[95,110351,110352],{},"Úplné testování"," (Full exercise) — simulace reálného incidentu",[609,110355,110357],{"id":110356},"zásady-testování","Zásady testování",[89,110359,110360,110366],{},[92,110361,110362,110365],{},[95,110363,110364],{},"Neočekávané testy"," — testování bez předchozího varování pro ověření reálné připravenosti",[92,110367,110368,110371],{},[95,110369,110370],{},"Direktivní řízení pod tlakem"," — v krizové situaci přechod na centralizované rozhodování",[84,110373,110375],{"id":110374},"vkb-vyhláška-o-kybernetické-bezpečnosti","VKB (Vyhláška o kybernetické bezpečnosti)",[55,110377,110378,110379,2777],{},"Požadavky dle ",[95,110380,110381],{},"§15 vyhlášky č. 82\u002F2018 Sb.",[89,110383,110384,110389,110395],{},[92,110385,110386,110388],{},[95,110387,390],{}," — minimální úroveň služeb pro kontinuitu",[92,110390,110391,110394],{},[95,110392,110393],{},"Doba obnovení"," (RTO) — maximální přípustná doba výpadku",[92,110396,110397,110400],{},[95,110398,110399],{},"Bod obnovení dat"," (RPO) — maximální přípustná ztráta dat",[55,110402,110403,110404,110407],{},"Příloha č. 5, bod ",[95,110405,110406],{},"1.23 Politika řízení kontinuity"," — požadavky na dokumentaci a řízení BCM.",[84,110409,110411],{"id":110410},"bcmaas-bcm-as-a-service","BCMaaS (BCM as a Service)",[55,110413,110414],{},"Cloudový model poskytování BCM — outsourcing plánování a řízení kontinuity jako služby, vhodný zejména pro menší organizace bez vlastních kapacit.",[84,110416,110418],{"id":110417},"integrace-bcm-do-kultury-organizace","Integrace BCM do kultury organizace",[55,110420,110421],{},"BCM nesmí být izolovaný projekt — musí být součástí firemní kultury, pravidelně testován a aktualizován.",{"title":156,"searchDepth":7,"depth":7,"links":110423},[110424,110425,110426,110427,110428,110429,110430,110431,110432,110436,110437,110442,110446,110450,110451,110452],{"id":45727,"depth":7,"text":45728},{"id":109908,"depth":7,"text":109909},{"id":425,"depth":7,"text":426},{"id":109944,"depth":7,"text":109945},{"id":109956,"depth":7,"text":109957},{"id":110043,"depth":7,"text":110044},{"id":110087,"depth":7,"text":110088},{"id":110094,"depth":7,"text":110095},{"id":110124,"depth":7,"text":110125,"children":110433},[110434,110435],{"id":110128,"depth":4,"text":110129},{"id":110146,"depth":4,"text":110147},{"id":110165,"depth":7,"text":110166},{"id":110189,"depth":7,"text":110190,"children":110438},[110439,110440,110441],{"id":110193,"depth":4,"text":110194},{"id":110223,"depth":4,"text":110224},{"id":110253,"depth":4,"text":110254},{"id":110271,"depth":7,"text":110272,"children":110443},[110444,110445],{"id":110275,"depth":4,"text":110276},{"id":110317,"depth":4,"text":110318},{"id":110328,"depth":7,"text":110329,"children":110447},[110448,110449],{"id":110332,"depth":4,"text":110333},{"id":110356,"depth":4,"text":110357},{"id":110374,"depth":7,"text":110375},{"id":110410,"depth":7,"text":110411},{"id":110417,"depth":7,"text":110418},{},"\u002Fsummaries\u002Fimork-bcm",{"title":109881,"description":156},[800],"summaries\u002Fimork-bcm",[11,804,805,806,807,110459,110460,110461],"drp","bcmaas","vyhlaska-82-2018","J_vmr-AYHd_z5z6kZzejOKie3Z9rHKr5LTfURqhjruI",{"id":110464,"title":18526,"body":110465,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":110943,"navigation":168,"path":110944,"seo":110945,"sources":110946,"stem":110948,"tags":110949,"type":106007,"updated":178,"__hash__":110956},"summaries\u002Fsummaries\u002Fimork-bezpecnostni-strategie.md",{"type":48,"value":110466,"toc":110921},[110467,110470,110477,110480,110484,110488,110494,110498,110504,110508,110528,110532,110588,110592,110596,110599,110613,110617,110667,110671,110723,110727,110793,110797,110804,110808,110828,110830,110849,110853,110856,110860,110866,110869,110883,110885,110911,110916],[51,110468,18526],{"id":110469},"bezpečnostní-strategie",[55,110471,110472],{},[58,110473],{"alt":110474,"className":110475,"src":110476},"imork-strategie-hierarchie",[62,63],"\u002Fwiki-assets\u002Fimork-strategie-hierarchie.jpeg",[55,110478,110479],{},"Přednáška pokrývající bezpečnostní strategie na třech úrovních: EU → ČR → organizace. Strategické řízení, modely vyspělosti a konkrétní rámce.",[84,110481,110483],{"id":110482},"strategické-koncepty","Strategické koncepty",[609,110485,110487],{"id":110486},"strategický-čtverec","Strategický čtverec",[55,110489,110490,110491],{},"Čtyři dimenze strategického plánování: ",[95,110492,110493],{},"Vize\u002Fcíle → Strategie → Nástroje → Zdroje",[609,110495,110497],{"id":110496},"strategický-trojúhelník","Strategický trojúhelník",[55,110499,110500,110501],{},"Zjednodušený model: ",[95,110502,110503],{},"Strategický cíl ↔ Nástroje ↔ Zdroje",[609,110505,110507],{"id":110506},"strategická-analýza-metody","Strategická analýza — metody",[89,110509,110510,110513,110516,110519,110522,110525],{},[92,110511,110512],{},"Analýza poslání, vize a strategických cílů",[92,110514,110515],{},"Analýza funkčních\u002Fpodnikatelských oblastí",[92,110517,110518],{},"Analýza vnějšího a vnitřního prostředí",[92,110520,110521],{},"Analýza konkurenčního prostředí",[92,110523,110524],{},"Analýza zdrojů a kapacity organizace",[92,110526,110527],{},"Návrh konkurenční a prováděcích strategií",[609,110529,110531],{"id":110530},"poslání-vs-vize","Poslání vs. vize",[323,110533,110534,110546],{},[326,110535,110536],{},[329,110537,110538,110541,110544],{},[332,110539,110540],{},"Koncept",[332,110542,110543],{},"Směr",[332,110545,340],{},[342,110547,110548,110562,110576],{},[329,110549,110550,110556,110559],{},[347,110551,110552,110555],{},[95,110553,110554],{},"Poslání"," (mission)",[347,110557,110558],{},"Ven (zákazník)",[347,110560,110561],{},"Smysl a účel existence organizace",[329,110563,110564,110570,110573],{},[347,110565,110566,110569],{},[95,110567,110568],{},"Vize"," (vision)",[347,110571,110572],{},"Dovnitř (management)",[347,110574,110575],{},"Strategická představa budoucnosti",[329,110577,110578,110583,110585],{},[347,110579,110580],{},[95,110581,110582],{},"Strategické cíle",[347,110584,10415],{},[347,110586,110587],{},"Milníky k naplňování vize",[84,110589,110591],{"id":110590},"bezpečnostní-strategie-eu","Bezpečnostní strategie EU",[609,110593,110595],{"id":110594},"enisa-national-capabilities-assessment-framework-2020","ENISA — National Capabilities Assessment Framework (2020)",[55,110597,110598],{},"Měření vyspělosti schopností členských států v kybernetické bezpečnosti. 4 klastry:",[201,110600,110601,110604,110607,110610],{},[92,110602,110603],{},"Řízení a normy kybernetické bezpečnosti",[92,110605,110606],{},"Budování schopností a zvyšování povědomí",[92,110608,110609],{},"Právní a regulatorní povinnosti",[92,110611,110612],{},"Spolupráce",[609,110614,110616],{"id":110615},"_15-společných-strategických-cílů-ncss","15 společných strategických cílů NCSS",[201,110618,110619,110622,110625,110628,110631,110637,110640,110643,110646,110649,110652,110655,110658,110661,110664],{},[92,110620,110621],{},"Vnitrostátní pohotovostní plány",[92,110623,110624],{},"Základní bezpečnostní opatření",[92,110626,110627],{},"Cvičení v oblasti kybernetické bezpečnosti",[92,110629,110630],{},"Schopnost reakce na incident",[92,110632,110633,110634,2090],{},"Zvyšování povědomí uživatelů (",[69,110635,18339],{"className":110636,"dataFsResolvedFilePath":18337,"href":18338},[62],[92,110638,110639],{},"Programy odborné přípravy a vzdělávání",[92,110641,110642],{},"Podpora VaV",[92,110644,110645],{},"Pobídky soukromému sektoru",[92,110647,110648],{},"Ochrana KII, OES a DSP",[92,110650,110651],{},"Boj proti kyberkriminalitě",[92,110653,110654],{},"Mechanismy hlášení incidentů",[92,110656,110657],{},"Ochrana osobních údajů",[92,110659,110660],{},"Partnerství veřejný-soukromý sektor (PPP)",[92,110662,110663],{},"Spolupráce veřejných agentur",[92,110665,110666],{},"Mezinárodní spolupráce",[609,110668,110670],{"id":110669},"pětistupňová-škála-vyspělosti-enisa","Pětistupňová škála vyspělosti ENISA",[323,110672,110673,110681],{},[326,110674,110675],{},[329,110676,110677,110679],{},[332,110678,91282],{},[332,110680,340],{},[342,110682,110683,110691,110699,110707,110715],{},[329,110684,110685,110688],{},[347,110686,110687],{},"1 — Počáteční",[347,110689,110690],{},"Nemá jasně definovaný přístup",[329,110692,110693,110696],{},[347,110694,110695],{},"2 — Raná definice",[347,110697,110698],{},"Definován vnitrostátní přístup",[329,110700,110701,110704],{},[347,110702,110703],{},"3 — Vytvoření",[347,110705,110706],{},"Jasně určen akční plán",[329,110708,110709,110712],{},[347,110710,110711],{},"4 — Optimalizace",[347,110713,110714],{},"Plán pravidelně přezkoumáván",[329,110716,110717,110720],{},[347,110718,110719],{},"5 — Adaptabilita",[347,110721,110722],{},"Strategie je dynamická a adaptivní",[609,110724,110726],{"id":110725},"cmmc-cybersecurity-maturity-model-certification","CMMC — Cybersecurity Maturity Model Certification",[323,110728,110729,110741],{},[326,110730,110731],{},[329,110732,110733,110735,110738],{},[332,110734,91282],{},[332,110736,110737],{},"Procesy",[332,110739,110740],{},"Postupy",[342,110742,110743,110753,110763,110773,110783],{},[329,110744,110745,110747,110750],{},[347,110746,638],{},[347,110748,110749],{},"Provedené",[347,110751,110752],{},"Základní kybernetická hygiena",[329,110754,110755,110757,110760],{},[347,110756,646],{},[347,110758,110759],{},"Zdokumentované",[347,110761,110762],{},"Pokročilá kybernetická hygiena",[329,110764,110765,110767,110770],{},[347,110766,654],{},[347,110768,110769],{},"Řízené",[347,110771,110772],{},"Správná kybernetická hygiena",[329,110774,110775,110777,110780],{},[347,110776,662],{},[347,110778,110779],{},"Přezkoumávané",[347,110781,110782],{},"Proaktivní",[329,110784,110785,110787,110790],{},[347,110786,670],{},[347,110788,110789],{},"Optimalizační",[347,110791,110792],{},"Pokročilé\u002Fpokrokové",[84,110794,110796],{"id":110795},"bezpečnostní-strategie-čr-20212025","Bezpečnostní strategie ČR (2021–2025)",[55,110798,110799,110800,110803],{},"Vytvořena ",[95,110801,110802],{},"NÚKIBem",", převedena do Akčního plánu.",[609,110805,110807],{"id":110806},"tři-vize","Tři vize",[201,110809,110810,110816,110822],{},[92,110811,110812,110815],{},[95,110813,110814],{},"Sebevědomě v kyberprostoru"," — společný přístup, bezpečná infrastruktura, strategická komunikace",[92,110817,110818,110821],{},[95,110819,110820],{},"Silná a spolehlivá spojenectví"," — mezinárodní spolupráce, právní rámec, expertíza",[92,110823,110824,110827],{},[95,110825,110826],{},"Odolná společnost 4.0"," — zabezpečení digitální společnosti, vzdělávání, rozšiřování expertní základny",[609,110829,321],{"id":320},[89,110831,110832,110837,110843],{},[92,110833,110834,110836],{},[95,110835,110826],{}," — společnost využívající výhody technologií s minimalizací rizik",[92,110838,110839,110842],{},[95,110840,110841],{},"Digitální hygiena"," — zásady a návyky pro bezpečný pohyb ve virtuálním prostředí",[92,110844,110845,110848],{},[95,110846,110847],{},"Pyramidální model"," — Společnost → Pracovníci VS → Pracovníci NB → Experti KB",[609,110850,110852],{"id":110851},"akční-plán-čr-členění","Akční plán ČR — členění",[55,110854,110855],{},"A. Efektivita struktur a procesů | B. Mezinárodní spolupráce | C. Ochrana KII a VIS | D. Spolupráce se soukromým sektorem | E. VaV a spotřebitelská důvěra | F. Vzdělávání a osvěta | G. Schopnosti Policie ČR | H. Právní úprava",[84,110857,110859],{"id":110858},"bezpečnostní-strategie-organizace","Bezpečnostní strategie organizace",[55,110861,110862,110863],{},"Odvozuje se hierarchicky: ",[95,110864,110865],{},"EU → ČR → Organizace",[55,110867,110868],{},"Úspěšná strategie musí být:",[89,110870,110871,110874,110877,110880],{},[92,110872,110873],{},"Řádně zdokumentovaná",[92,110875,110876],{},"Analyticky podložená",[92,110878,110879],{},"Logicky zdůvodněná",[92,110881,110882],{},"Projednaná a přijatá",[84,110884,723],{"id":722},[89,110886,110887,110893,110899,110905],{},[92,110888,110889,110892],{},[69,110890,733],{"className":110891,"dataFsResolvedFilePath":731,"href":732},[62]," — strategické řízení bezpečnosti jako jádro ISMS",[92,110894,110895,110898],{},[69,110896,742],{"className":110897,"dataFsResolvedFilePath":740,"href":741},[62]," — strategická analýza hrozeb",[92,110900,110901,110904],{},[69,110902,18339],{"className":110903,"dataFsResolvedFilePath":18337,"href":18338},[62]," — strategický cíl č. 5 (zvyšování povědomí)",[92,110906,110907,110910],{},[69,110908,18510],{"className":110909,"dataFsResolvedFilePath":18508,"href":18509},[62]," — governance a role",[84,110912,109625,110913],{"id":109624},[69,110914,762],{"className":110915,"dataFsResolvedFilePath":760,"href":761},[62],[89,110917,110918],{},[92,110919,110920],{},"Přednáška 2101 — Bezpečnostní strategie (2022)",{"title":156,"searchDepth":7,"depth":7,"links":110922},[110923,110929,110935,110940,110941,110942],{"id":110482,"depth":7,"text":110483,"children":110924},[110925,110926,110927,110928],{"id":110486,"depth":4,"text":110487},{"id":110496,"depth":4,"text":110497},{"id":110506,"depth":4,"text":110507},{"id":110530,"depth":4,"text":110531},{"id":110590,"depth":7,"text":110591,"children":110930},[110931,110932,110933,110934],{"id":110594,"depth":4,"text":110595},{"id":110615,"depth":4,"text":110616},{"id":110669,"depth":4,"text":110670},{"id":110725,"depth":4,"text":110726},{"id":110795,"depth":7,"text":110796,"children":110936},[110937,110938,110939],{"id":110806,"depth":4,"text":110807},{"id":320,"depth":4,"text":321},{"id":110851,"depth":4,"text":110852},{"id":110858,"depth":7,"text":110859},{"id":722,"depth":7,"text":723},{"id":109624,"depth":7,"text":109642},{},"\u002Fsummaries\u002Fimork-bezpecnostni-strategie",{"title":18526,"description":156},[110947],"raw\u002Fimork\u002F2101 VUT_Bezpečnostní strategie-2022.pdf","summaries\u002Fimork-bezpecnostni-strategie",[11,20,110950,110951,110952,110953,110954,110955],"strategie","enisa","ncss","cmmc","nukib","eu","f_mvGFmBrRkDa1X3-U-t6mrp3qv7lsx84Kk8ORqZ8R8",{"id":110958,"title":110959,"body":110960,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":111134,"navigation":168,"path":111135,"seo":111136,"sources":111137,"stem":111138,"tags":111139,"type":106007,"updated":178,"__hash__":111141},"summaries\u002Fsummaries\u002Fimork-detail-predmetu.md","ImorK — Detail předmětu",{"type":48,"value":110961,"toc":111128},[110962,110965,110969,111035,111039,111050,111054,111102,111106],[51,110963,110959],{"id":110964},"imork-detail-předmětu",[84,110966,110968],{"id":110967},"základní-informace","Základní informace",[323,110970,110971,110980],{},[326,110972,110973],{},[329,110974,110975,110978],{},[332,110976,110977],{},"Položka",[332,110979,91820],{},[342,110981,110982,110990,110997,111004,111012,111020,111028],{},[329,110983,110984,110987],{},[347,110985,110986],{},"Název",[347,110988,110989],{},"Management oborových řešení",[329,110991,110992,110994],{},[347,110993,18226],{},[347,110995,110996],{},"[[imork",[329,110998,110999,111001],{},[347,111000,107086],{},[347,111002,111003],{},"Ing. Petr Novák",[329,111005,111006,111009],{},[347,111007,111008],{},"Vyučující",[347,111010,111011],{},"Ing. Petr Sedlák",[329,111013,111014,111017],{},[347,111015,111016],{},"Prerekvizita",[347,111018,111019],{},"ImibePA",[329,111021,111022,111025],{},[347,111023,111024],{},"Zakončení",[347,111026,111027],{},"Zkouška",[329,111029,111030,111033],{},[347,111031,111032],{},"Přednášek",[347,111034,46578],{},[84,111036,111038],{"id":111037},"zaměření-předmětu","Zaměření předmětu",[55,111040,111041,111042,111045,111046,111049],{},"Předmět se zabývá implementací ",[69,111043,733],{"className":111044,"dataFsResolvedFilePath":731,"href":732},[62]," (Information Security Management System) v různých odvětvích. Základem je rodina norem ",[95,111047,111048],{},"ISO\u002FIEC 27000",", která poskytuje rámec pro řízení informační bezpečnosti napříč sektory.",[84,111051,111053],{"id":111052},"témata-přednášek","Témata přednášek",[201,111055,111056,111059,111064,111070,111076,111079,111082,111085,111088,111090,111093,111096,111099],{},[92,111057,111058],{},"Manažerská informační bezpečnost",[92,111060,111061,18472],{},[69,111062,18339],{"className":111063,"dataFsResolvedFilePath":18337,"href":18338},[62],[92,111065,111066],{},[69,111067,111069],{"className":111068,"dataFsResolvedFilePath":740,"href":741},[62],"Risk management",[92,111071,111072,111075],{},[69,111073,733],{"className":111074,"dataFsResolvedFilePath":731,"href":732},[62]," v akademickém prostředí",[92,111077,111078],{},"ISMS ve finančním sektoru",[92,111080,111081],{},"ISMS ve zdravotnictví",[92,111083,111084],{},"ISMS v energetice",[92,111086,111087],{},"ISMS u ISP (poskytovatelů internetových služeb)",[92,111089,751],{},[92,111091,111092],{},"GDPR a ochrana osobních údajů",[92,111094,111095],{},"Bezpečnost webových aplikací",[92,111097,111098],{},"Bezpečnost e-mailu",[92,111100,111101],{},"Bezpečnost mobilních zařízení",[84,111103,111105],{"id":111104},"klíčové-normy","Klíčové normy",[89,111107,111108,111113,111118,111123],{},[92,111109,111110,111112],{},[95,111111,18125],{}," — požadavky na ISMS",[92,111114,111115,111117],{},[95,111116,18131],{}," — soubor opatření",[92,111119,111120,111122],{},[95,111121,18137],{}," — řízení rizik",[92,111124,111125,111127],{},[95,111126,18147],{}," — governance informační bezpečnosti",{"title":156,"searchDepth":7,"depth":7,"links":111129},[111130,111131,111132,111133],{"id":110967,"depth":7,"text":110968},{"id":111037,"depth":7,"text":111038},{"id":111052,"depth":7,"text":111053},{"id":111104,"depth":7,"text":111105},{},"\u002Fsummaries\u002Fimork-detail-predmetu",{"title":110959,"description":156},[18549],"summaries\u002Fimork-detail-predmetu",[11,20,18554,111140],"oborova-reseni","HA7cJ7q4IpBLhhghqroPOp-4m9R1lKaT7wEz-w0jlC8",{"id":111143,"title":111144,"body":111145,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":111309,"navigation":168,"path":111310,"seo":111311,"sources":111312,"stem":111314,"tags":111315,"type":106007,"updated":178,"__hash__":111320},"summaries\u002Fsummaries\u002Fimork-digitalni-identita.md","Digitální identita a digitální stopa",{"type":48,"value":111146,"toc":111299},[111147,111150,111154,111165,111169,111216,111221,111225,111242,111246,111261,111263,111289,111294],[51,111148,111144],{"id":111149},"digitální-identita-a-digitální-stopa",[84,111151,111153],{"id":111152},"digitální-identita-digital-identity","Digitální identita (Digital Identity)",[89,111155,111156,111159,111162],{},[92,111157,111158],{},"Digitální reprezentace osoby v informačních systémech a na internetu",[92,111160,111161],{},"Zahrnuje: uživatelské jméno, heslo, datum narození, bankovní údaje, fyzickou adresu, zdravotní anamnézu",[92,111163,111164],{},"Dynamická, víceúčelová a znovupoužitelná",[609,111166,111168],{"id":111167},"ověření-identity-3-faktory","Ověření identity — 3 faktory",[323,111170,111171,111181],{},[326,111172,111173],{},[329,111174,111175,111177,111179],{},[332,111176,520],{},[332,111178,340],{},[332,111180,3144],{},[342,111182,111183,111194,111205],{},[329,111184,111185,111188,111191],{},[347,111186,111187],{},"Znalosti",[347,111189,111190],{},"Něco, co uživatel zná",[347,111192,111193],{},"Heslo, PIN",[329,111195,111196,111199,111202],{},[347,111197,111198],{},"Vlastnictví",[347,111200,111201],{},"Něco, co uživatel má",[347,111203,111204],{},"Token, karta",[329,111206,111207,111210,111213],{},[347,111208,111209],{},"Biometrie",[347,111211,111212],{},"Něco, co uživatel je",[347,111214,111215],{},"Otisk prstu, obličej",[89,111217,111218],{},[92,111219,111220],{},"Další metody: ID přihlašování, digitální (elektronický) podpis",[84,111222,111224],{"id":111223},"digitální-stopa-digital-footprint","Digitální stopa (Digital Footprint)",[89,111226,111227,111230,111236],{},[92,111228,111229],{},"Informace zanechaná uživatelem v síťovém prostředí při používání internetu",[92,111231,111232,111235],{},[95,111233,111234],{},"Aktivní stopa"," — vědomá činnost (příspěvky, registrace, sdílení)",[92,111237,111238,111241],{},[95,111239,111240],{},"Pasivní stopa"," — nevědomá (cookies, IP adresy, metadata, síťová aktivita)",[609,111243,111245],{"id":111244},"rizika","Rizika",[89,111247,111248,111251,111254],{},[92,111249,111250],{},"Ztráta soukromí",[92,111252,111253],{},"Zneužití digitální identity",[92,111255,111256,111257,111260],{},"Odstranění digitální stopy je prakticky ",[95,111258,111259],{},"nerealizovatelné"," — lze pouze minimalizovat (např. TOR)",[84,111262,723],{"id":722},[89,111264,111265,111271,111277,111283],{},[92,111266,111267,111270],{},[69,111268,18494],{"className":111269,"dataFsResolvedFilePath":30745,"href":30746},[62]," — technologie ochrany osobních údajů",[92,111272,111273,111276],{},[69,111274,18971],{"className":111275,"dataFsResolvedFilePath":18969,"href":18970},[62]," — online identita a webové služby",[92,111278,111279,111282],{},[69,111280,30731],{"className":111281,"dataFsResolvedFilePath":30729,"href":30730},[62]," — ověřování identity odesílatele",[92,111284,111285,111288],{},[69,111286,18339],{"className":111287,"dataFsResolvedFilePath":91617,"href":91618},[62]," — budování povědomí o digitální stopě",[84,111290,109625,111291],{"id":109624},[69,111292,762],{"className":111293,"dataFsResolvedFilePath":760,"href":761},[62],[89,111295,111296],{},[92,111297,111298],{},"Přednáška PRIS 2208 — Digitální identita a stopa",{"title":156,"searchDepth":7,"depth":7,"links":111300},[111301,111304,111307,111308],{"id":111152,"depth":7,"text":111153,"children":111302},[111303],{"id":111167,"depth":4,"text":111168},{"id":111223,"depth":7,"text":111224,"children":111305},[111306],{"id":111244,"depth":4,"text":111245},{"id":722,"depth":7,"text":723},{"id":109624,"depth":7,"text":109642},{},"\u002Fsummaries\u002Fimork-digitalni-identita",{"title":111144,"description":156},[111313],"raw\u002Fimork\u002FPRIS 2208 VUT_Bezp Digi identita a stopa.pdf","summaries\u002Fimork-digitalni-identita",[11,111316,111317,111318,111319],"digitalni-identita","digitalni-stopa","soukromi","autentizace","JlgGM2RoX6hA7QNj991s8oYfHyiVj55huoXyL7O18G0",{"id":111322,"title":111323,"body":111324,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":111556,"navigation":168,"path":111557,"seo":111558,"sources":111559,"stem":111561,"tags":111562,"type":106007,"updated":178,"__hash__":111565},"summaries\u002Fsummaries\u002Fimork-doprava.md","ISMS v dopravě (železnice)",{"type":48,"value":111325,"toc":111543},[111326,111329,111333,111340,111344,111347,111351,111421,111423,111426,111430,111433,111437,111468,111472,111475,111479,111522,111526,111529,111533],[51,111327,111323],{"id":111328},"isms-v-dopravě-železnice",[84,111330,111332],{"id":111331},"železnice-jako-kritická-infrastruktura","Železnice jako kritická infrastruktura",[55,111334,111335,111336,111339],{},"Železniční doprava je součástí kritické infrastruktury státu. Systém ",[95,111337,111338],{},"CIWIN"," (Critical Infrastructure Warning Information Network) slouží k výměně informací o hrozbách mezi členskými státy EU.",[609,111341,111343],{"id":111342},"třístupňový-procesní-model-ki","Třístupňový procesní model KI",[55,111345,111346],{},"Tři úrovně řízení bezpečnosti kritické infrastruktury v železniční dopravě.",[84,111348,111350],{"id":111349},"relevantní-normy","Relevantní normy",[323,111352,111353,111361],{},[326,111354,111355],{},[329,111356,111357,111359],{},[332,111358,91075],{},[332,111360,523],{},[342,111362,111363,111373,111382,111391,111401,111411],{},[329,111364,111365,111370],{},[347,111366,111367],{},[95,111368,111369],{},"NIS Directive",[347,111371,111372],{},"Směrnice EU o bezpečnosti sítí a informačních systémů",[329,111374,111375,111380],{},[347,111376,111377],{},[95,111378,111379],{},"ISO 27k",[347,111381,18253],{},[329,111383,111384,111388],{},[347,111385,111386],{},[95,111387,18193],{},[347,111389,111390],{},"Kybernetický bezpečnostní rámec",[329,111392,111393,111398],{},[347,111394,111395],{},[95,111396,111397],{},"ISA\u002FIEC 62443",[347,111399,111400],{},"Bezpečnost průmyslových řídicích systémů",[329,111402,111403,111408],{},[347,111404,111405],{},[95,111406,111407],{},"CLC\u002FTS 50701",[347,111409,111410],{},"Kybernetická bezpečnost železnic",[329,111412,111413,111418],{},[347,111414,111415],{},[95,111416,111417],{},"EN 50155",[347,111419,111420],{},"Palubní elektronika kolejových vozidel",[84,111422,742],{"id":91049},[55,111424,111425],{},"Řízení rizik dle ISO 27005 aplikované na železniční prostředí.",[84,111427,111429],{"id":111428},"_8-základních-železničních-služeb","8 základních železničních služeb",[55,111431,111432],{},"Definice klíčových služeb železniční dopravy (osobní přeprava, nákladní přeprava, řízení provozu, signalizace, údržba aj.).",[84,111434,111436],{"id":111435},"taxonomie-aktiv","Taxonomie aktiv",[89,111438,111439,111445,111451,111457,111463],{},[92,111440,111441,111444],{},[95,111442,111443],{},"Služby"," — přepravní a podpůrné",[92,111446,111447,111450],{},[95,111448,111449],{},"Systémy"," — ICT, OT, zabezpečovací technika",[92,111452,111453,111456],{},[95,111454,111455],{},"Fyzická aktiva"," — infrastruktura, vozidla",[92,111458,111459,111462],{},[95,111460,111461],{},"Lidé"," — zaměstnanci, cestující",[92,111464,111465,111467],{},[95,111466,12717],{}," — provozní, osobní, bezpečnostní",[84,111469,111471],{"id":111470},"kategorie-hrozeb","Kategorie hrozeb",[55,111473,111474],{},"Rozdělení hrozeb specifických pro železniční sektor.",[84,111476,111478],{"id":111477},"_7-scénářů-kybernetických-rizik","7 scénářů kybernetických rizik",[201,111480,111481,111487,111493,111498,111504,111510,111516],{},[92,111482,111483,111486],{},[95,111484,111485],{},"Narušení signalizace"," — manipulace se zabezpečovacím zařízením",[92,111488,111489,111492],{},[95,111490,111491],{},"Sabotáž řízení provozu"," — útok na dispečerské systémy",[92,111494,111495,111497],{},[95,111496,18756],{}," — zašifrování kritických systémů",[92,111499,111500,111503],{},[95,111501,111502],{},"Krádež osobních údajů"," — data cestujících",[92,111505,111506,111509],{},[95,111507,111508],{},"Průnik do databází"," — provozní a bezpečnostní data",[92,111511,111512,111515],{},[95,111513,111514],{},"DDoS na prodej jízdenek"," — znepřístupnění ticketového systému",[92,111517,111518,111521],{},[95,111519,111520],{},"Destrukce datového centra"," — fyzický nebo kybernetický útok",[84,111523,111525],{"id":111524},"enisa-railway-cybersecurity-2021","ENISA Railway Cybersecurity (2021)",[55,111527,111528],{},"Komplexní dokument ENISA zaměřený na kybernetickou bezpečnost železniční dopravy v EU.",[84,111530,111532],{"id":111531},"průmyslová-řešení","Průmyslová řešení",[55,111534,111535,111536,75,111539,111542],{},"Řešení od výrobců ",[95,111537,111538],{},"Moxa",[95,111540,111541],{},"Hirschmann"," — průmyslové síťové prvky odolné vůči prostředí železniční dopravy.",{"title":156,"searchDepth":7,"depth":7,"links":111544},[111545,111548,111549,111550,111551,111552,111553,111554,111555],{"id":111331,"depth":7,"text":111332,"children":111546},[111547],{"id":111342,"depth":4,"text":111343},{"id":111349,"depth":7,"text":111350},{"id":91049,"depth":7,"text":742},{"id":111428,"depth":7,"text":111429},{"id":111435,"depth":7,"text":111436},{"id":111470,"depth":7,"text":111471},{"id":111477,"depth":7,"text":111478},{"id":111524,"depth":7,"text":111525},{"id":111531,"depth":7,"text":111532},{},"\u002Fsummaries\u002Fimork-doprava",{"title":111323,"description":156},[111560],"raw\u002Fimork\u002F2009 VUT_Bezp Doprava-2022.pdf","summaries\u002Fimork-doprava",[11,20,45203,111563,111564,110951],"zeleznice","kriticka-infrastruktura","34VWx7IiQub9XzBq--CQa4CskttJ3cE78kCMI1B8gUM",{"id":111567,"title":604,"body":111568,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":111812,"navigation":168,"path":111813,"seo":111814,"sources":111815,"stem":111816,"tags":111817,"type":106007,"updated":178,"__hash__":111823},"summaries\u002Fsummaries\u002Fimork-dr.md",{"type":48,"value":111569,"toc":111802},[111570,111572,111576,111583,111585,111597,111601,111615,111619,111622,111626,111680,111684,111687,111707,111711,111778,111782],[51,111571,604],{"id":603},[84,111573,111575],{"id":111574},"vztah-k-bcm","Vztah k BCM",[55,111577,111578,111579,111582],{},"DR je součástí ",[69,111580,367],{"className":111581,"dataFsResolvedFilePath":770,"href":771},[62],". Zaměřuje se na obnovu IT systémů a dat po havárii.",[84,111584,1453],{"id":1452},[89,111586,111587,111592],{},[92,111588,111589,111591],{},[95,111590,403],{}," (Recovery Point Objective) — maximální přípustná ztráta dat (časový úsek, za který se data ztratí)",[92,111593,111594,111596],{},[95,111595,416],{}," (Recovery Time Objective) — maximální přípustná doba obnovy systému do provozuschopného stavu",[84,111598,111600],{"id":111599},"normy-a-standardy","Normy a standardy",[89,111602,111603,111609],{},[92,111604,111605,111608],{},[95,111606,111607],{},"ISO\u002FIEC 24762:2008"," — směrnice pro obnovu ICT služeb po havárii",[92,111610,111611,111614],{},[95,111612,111613],{},"NIST SP 800-184"," — průvodce obnovou po kybernetické události",[84,111616,111618],{"id":111617},"_10-kroků-pro-optimální-dr-plán","10 kroků pro optimální DR plán",[55,111620,111621],{},"Strukturovaný postup tvorby DR plánu zahrnující analýzu rizik, identifikaci kritických systémů, definici RPO\u002FRTO, výběr strategie, testování a průběžnou aktualizaci.",[84,111623,111625],{"id":111624},"_3-přístupy-ke-cloudovému-dr","3 přístupy ke cloudovému DR",[323,111627,111628,111639],{},[326,111629,111630],{},[329,111631,111632,111635,111637],{},[332,111633,111634],{},"Přístup",[332,111636,340],{},[332,111638,416],{},[342,111640,111641,111654,111667],{},[329,111642,111643,111648,111651],{},[347,111644,111645],{},[95,111646,111647],{},"Cold",[347,111649,111650],{},"Data zálohována, infrastruktura se staví až při havárii",[347,111652,111653],{},"Hodiny–dny",[329,111655,111656,111661,111664],{},[347,111657,111658],{},[95,111659,111660],{},"Warm",[347,111662,111663],{},"Částečně aktivní prostředí, rychlejší aktivace",[347,111665,111666],{},"Minuty–hodiny",[329,111668,111669,111674,111677],{},[347,111670,111671],{},[95,111672,111673],{},"Hot",[347,111675,111676],{},"Plně zrcadlené prostředí, okamžitý přepnutí",[347,111678,111679],{},"Sekundy–minuty",[84,111681,111683],{"id":111682},"draas-disaster-recovery-as-a-service","DRaaS (Disaster Recovery as a Service)",[55,111685,111686],{},"Tři modely poskytování:",[89,111688,111689,111695,111701],{},[92,111690,111691,111694],{},[95,111692,111693],{},"Managed"," — poskytovatel řídí celý DR proces",[92,111696,111697,111700],{},[95,111698,111699],{},"Assisted"," — sdílená odpovědnost mezi zákazníkem a poskytovatelem",[92,111702,111703,111706],{},[95,111704,111705],{},"Self-service"," — zákazník si sám spravuje DR v cloudovém prostředí",[84,111708,111710],{"id":111709},"_7-dr-úrovní-tiers","7 DR úrovní (Tiers)",[323,111712,111713,111721],{},[326,111714,111715],{},[329,111716,111717,111719],{},[332,111718,621],{},[332,111720,340],{},[342,111722,111723,111729,111736,111743,111750,111757,111764,111771],{},[329,111724,111725,111727],{},[347,111726,630],{},[347,111728,633],{},[329,111730,111731,111733],{},[347,111732,638],{},[347,111734,111735],{},"Záloha na vzdálené médium (pickup truck)",[329,111737,111738,111740],{},[347,111739,646],{},[347,111741,111742],{},"Záloha na vzdálené médium + hot site",[329,111744,111745,111747],{},[347,111746,654],{},[347,111748,111749],{},"Elektronický vaulting",[329,111751,111752,111754],{},[347,111753,662],{},[347,111755,111756],{},"Point-in-time kopie",[329,111758,111759,111761],{},[347,111760,670],{},[347,111762,111763],{},"Integrity transakcí",[329,111765,111766,111768],{},[347,111767,678],{},[347,111769,111770],{},"Minimální\u002Fžádná ztráta dat",[329,111772,111773,111775],{},[347,111774,686],{},[347,111776,111777],{},"Automatizace obnovy s využitím AI",[84,111779,111781],{"id":111780},"výstupy-dr-plánu","Výstupy DR plánu",[89,111783,111784,111790,111796],{},[92,111785,111786,111789],{},[95,111787,111788],{},"Obnova systémů"," — postupy pro obnovení serverů, databází, aplikací",[92,111791,111792,111795],{},[95,111793,111794],{},"Obnova LAN"," — rekonstrukce lokální síťové infrastruktury",[92,111797,111798,111801],{},[95,111799,111800],{},"Obnova vzdálené konektivity"," — WAN, VPN, externí přístupy",{"title":156,"searchDepth":7,"depth":7,"links":111803},[111804,111805,111806,111807,111808,111809,111810,111811],{"id":111574,"depth":7,"text":111575},{"id":1452,"depth":7,"text":1453},{"id":111599,"depth":7,"text":111600},{"id":111617,"depth":7,"text":111618},{"id":111624,"depth":7,"text":111625},{"id":111682,"depth":7,"text":111683},{"id":111709,"depth":7,"text":111710},{"id":111780,"depth":7,"text":111781},{},"\u002Fsummaries\u002Fimork-dr",{"title":604,"description":156},[801],"summaries\u002Fimork-dr",[11,111818,808,111819,111820,111821,111822],"dr","rpo","rto","cloud","draas","nIPOldGccGwF_BB0JHV_YNviY26-MXG-4KnGZNynBnw",{"id":111825,"title":111826,"body":111827,"course":11,"courses":163,"created":795,"description":112236,"extension":166,"meta":112237,"navigation":168,"path":112238,"seo":112239,"sources":112240,"stem":112242,"tags":112243,"type":106007,"updated":178,"__hash__":112249},"summaries\u002Fsummaries\u002Fimork-ehealth.md","eHealth v ČR",{"type":48,"value":111828,"toc":112221},[111829,111832,111838,111842,111848,111852,111871,111875,111878,111926,111930,111941,111945,111992,111996,111999,112035,112039,112042,112046,112082,112086,112100,112104,112135,112139,112142,112185,112187],[51,111830,111826],{"id":111831},"ehealth-v-čr",[55,111833,111834,111835,195],{},"Případová studie (22 slidů, 4.10.2021) zaměřená na elektronizaci zdravotnictví v České republice a v Evropě. Součást kurzu ",[69,111836,762],{"className":111837,"href":761,"dataFsResolvedFilePath":760},[62],[84,111839,111841],{"id":111840},"co-je-ehealth","Co je eHealth",[55,111843,111844,111847],{},[95,111845,111846],{},"eHealth"," = elektronizace zdravotnictví — využití ICT pro podporu zdravotní péče, prevence, výzkumu a administrativy.",[609,111849,111851],{"id":111850},"wireless-body-area-network-wban","Wireless Body Area Network (WBAN)",[89,111853,111854,111857,111860,111863],{},[92,111855,111856],{},"Síť senzorů umístěných přímo na těle pacienta",[92,111858,111859],{},"Kontinuální monitorování zdravotního stavu",[92,111861,111862],{},"Přenos dat do zdravotnických systémů v reálném čase",[92,111864,111865,111866,111870],{},"Propojení s konceptem ",[69,111867,111869],{"className":111868,"href":750,"dataFsResolvedFilePath":749},[62],"kybernetické bezpečnosti"," — ochrana citlivých zdravotních dat",[84,111872,111874],{"id":111873},"národní-plán-rozvoje-ehealth","Národní plán rozvoje eHealth",[55,111876,111877],{},"Klíčové oblasti národního plánu:",[323,111879,111880,111888],{},[326,111881,111882],{},[329,111883,111884,111886],{},[332,111885,523],{},[332,111887,340],{},[342,111889,111890,111898,111906,111914],{},[329,111891,111892,111895],{},[347,111893,111894],{},"Elektronická dokumentace",[347,111896,111897],{},"Digitalizace zdravotních záznamů",[329,111899,111900,111903],{},[347,111901,111902],{},"ePreskripce",[347,111904,111905],{},"Elektronické předepisování léků",[329,111907,111908,111911],{},[347,111909,111910],{},"Registry",[347,111912,111913],{},"Centrální evidence pacientů a zdravotních dat",[329,111915,111916,111923],{},[347,111917,111918],{},[69,111919,111922],{"className":111920,"href":111921},[62,63],"\u002Fwiki\u002Fimork-zdravotnictvi\\","Telemedicína",[347,111924,111925],{},"Vzdálená diagnostika a konzultace",[84,111927,111929],{"id":111928},"projekt-epsos-eu","Projekt epSOS (EU)",[89,111931,111932,111935,111938],{},[92,111933,111934],{},"Celoevropský projekt pro přeshraniční výměnu zdravotních dat",[92,111936,111937],{},"Interoperabilita mezi národními systémy eHealth",[92,111939,111940],{},"Sdílení Patient Summary a ePrescription mezi členskými státy",[84,111942,111944],{"id":111943},"_6-principů-ehealth","6 principů eHealth",[201,111946,111947,111953,111964,111974,111980,111986],{},[92,111948,111949,111952],{},[95,111950,111951],{},"Důvěryhodnost"," — systém musí být spolehlivý a ověřitelný",[92,111954,111955,111958,111959,111963],{},[95,111956,111957],{},"Zákonnost"," — soulad s legislativou (",[69,111960,111962],{"className":111961,"href":18493,"dataFsResolvedFilePath":18492},[62],"ochrana osobních údajů",", GDPR)",[92,111965,111966,7102,111969,111973],{},[95,111967,111968],{},"Bezpečnost",[69,111970,111972],{"className":111971,"href":750,"dataFsResolvedFilePath":749},[62],"ochrana"," před neoprávněným přístupem",[92,111975,111976,111979],{},[95,111977,111978],{},"Jednoduchost"," — snadné používání pro zdravotníky i pacienty",[92,111981,111982,111985],{},[95,111983,111984],{},"Flexibilita"," — přizpůsobitelnost novým požadavkům",[92,111987,111988,111991],{},[95,111989,111990],{},"Otevřenost"," — kompatibilita a standardizace",[84,111993,111995],{"id":111994},"architektura-domu-ehealth","Architektura „domu\" eHealth",[55,111997,111998],{},"Vrstvový model architektury eHealth (od základů ke střeše):",[201,112000,112001,112007,112013,112018,112024,112029],{},[92,112002,112003,112006],{},[95,112004,112005],{},"Legislativa"," — právní rámec (základ)",[92,112008,112009,112012],{},[95,112010,112011],{},"Standardy"," — technické a datové normy",[92,112014,112015,112017],{},[95,112016,111910],{}," — centrální databáze",[92,112019,112020,112023],{},[95,112021,112022],{},"EHR"," (Electronic Health Record) — elektronické zdravotní záznamy",[92,112025,112026,112028],{},[95,112027,111443],{}," — aplikace a procesy nad daty",[92,112030,112031,112034],{},[95,112032,112033],{},"Portál"," — uživatelské rozhraní (střecha)",[84,112036,112038],{"id":112037},"nsez-po-roce-2016","NSeZ po roce 2016",[55,112040,112041],{},"Národní strategie elektronického zdravotnictví (NSeZ) — aktualizovaná koncepce po roce 2016 definující směr rozvoje eHealth v ČR.",[84,112043,112045],{"id":112044},"infrastruktura-elektronického-zdravotnictví-3-vrstvy","Infrastruktura elektronického zdravotnictví — 3 vrstvy",[323,112047,112048,112056],{},[326,112049,112050],{},[329,112051,112052,112054],{},[332,112053,109262],{},[332,112055,438],{},[342,112057,112058,112066,112074],{},[329,112059,112060,112063],{},[347,112061,112062],{},"eGovernment",[347,112064,112065],{},"Sdílená státní infrastruktura (základní registry, datové schránky)",[329,112067,112068,112071],{},[347,112069,112070],{},"Základní komponenty",[347,112072,112073],{},"Stavební bloky eHealth (identifikace, autorizace, standardy)",[329,112075,112076,112079],{},[347,112077,112078],{},"Služby EZ",[347,112080,112081],{},"Koncové služby pro pacienty a zdravotníky",[84,112083,112085],{"id":112084},"zahraniční-vzory","Zahraniční vzory",[89,112087,112088,112094],{},[92,112089,112090,112093],{},[95,112091,112092],{},"Slovensko"," — implementace eHealth s národním zdravotnickým portálem",[92,112095,112096,112099],{},[95,112097,112098],{},"Estonsko"," — vzorový příklad digitalizace zdravotnictví, propojení s e-governmentem",[84,112101,112103],{"id":112102},"_5-trendů-digitální-medicíny","5 trendů digitální medicíny",[201,112105,112106,112112,112118,112124,112130],{},[92,112107,112108,112111],{},[95,112109,112110],{},"AI v diagnostice"," — strojové učení pro analýzu snímků a dat",[92,112113,112114,112117],{},[95,112115,112116],{},"Inteligentní našeptávač"," — podpora rozhodování lékařů",[92,112119,112120,112123],{},[95,112121,112122],{},"Dokumentace online"," — přechod na plně digitální záznamy",[92,112125,112126,112129],{},[95,112127,112128],{},"Digitální náramky"," — wearables pro monitorování zdraví",[92,112131,112132,112134],{},[95,112133,111922],{}," — vzdálené konzultace a monitoring",[84,112136,112138],{"id":112137},"wifi-infrastruktura-ve-zdravotnictví","WiFi infrastruktura ve zdravotnictví",[55,112140,112141],{},"Tři kategorie bezdrátových sítí podle účelu:",[323,112143,112144,112153],{},[326,112145,112146],{},[329,112147,112148,112151],{},[332,112149,112150],{},"Kategorie",[332,112152,108606],{},[342,112154,112155,112165,112175],{},[329,112156,112157,112162],{},[347,112158,112159],{},[95,112160,112161],{},"Medical",[347,112163,112164],{},"Kritické zdravotnické přístroje, nejvyšší spolehlivost",[329,112166,112167,112172],{},[347,112168,112169],{},[95,112170,112171],{},"Enterprise",[347,112173,112174],{},"Administrativní systémy nemocnice",[329,112176,112177,112182],{},[347,112178,112179],{},[95,112180,112181],{},"Consumer",[347,112183,112184],{},"Připojení pacientů a návštěvníků",[84,112186,254],{"id":253},[89,112188,112189,112200,112206,112212],{},[92,112190,112191,112195,112196,112199],{},[69,112192,112194],{"className":112193,"href":18181,"dataFsResolvedFilePath":18180},[62],"Bezpečnost ve zdravotnictví"," — širší kontext ",[69,112197,111869],{"className":112198,"href":750,"dataFsResolvedFilePath":749},[62]," v nemocnicích",[92,112201,112202,112205],{},[69,112203,18494],{"className":112204,"href":18493,"dataFsResolvedFilePath":18492},[62]," — GDPR a zdravotní data",[92,112207,112208,112211],{},[69,112209,733],{"className":112210,"href":732,"dataFsResolvedFilePath":731},[62]," — řízení bezpečnosti informací ve zdravotnických organizacích",[92,112213,112214,112220],{},[69,112215,112219],{"className":112216,"href":112217,"dataFsResolvedFilePath":112218},[62],"\u002Fwiki\u002Fimork-digitalni-identita","summaries\u002Fimork-digitalni-identita.md","Digitální identita"," — autentizace ve zdravotnických systémech",{"title":156,"searchDepth":7,"depth":7,"links":112222},[112223,112226,112227,112228,112229,112230,112231,112232,112233,112234,112235],{"id":111840,"depth":7,"text":111841,"children":112224},[112225],{"id":111850,"depth":4,"text":111851},{"id":111873,"depth":7,"text":111874},{"id":111928,"depth":7,"text":111929},{"id":111943,"depth":7,"text":111944},{"id":111994,"depth":7,"text":111995},{"id":112037,"depth":7,"text":112038},{"id":112044,"depth":7,"text":112045},{"id":112084,"depth":7,"text":112085},{"id":112102,"depth":7,"text":112103},{"id":112137,"depth":7,"text":112138},{"id":253,"depth":7,"text":254},"Případová studie (22 slidů, 4.10.2021) zaměřená na elektronizaci zdravotnictví v České republice a v Evropě. Součást kurzu ImorK.",{},"\u002Fsummaries\u002Fimork-ehealth",{"title":111826,"description":112236},[112241],"raw\u002Fimork\u002F2105 VUT_Bezp_Případovka eHealth_2021.pdf","summaries\u002Fimork-ehealth",[11,112244,112245,112246,112247,112248],"ehealth","zdravotnictvi","telemedicina","ehr","elektronicka-preskripce","Z0z27C8H27kSKFJYsem19yyPS3B4O1-SHwvEI5SJBy8",{"id":112251,"title":30759,"body":112252,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":112740,"navigation":168,"path":112741,"seo":112742,"sources":112743,"stem":112744,"tags":112745,"type":106007,"updated":178,"__hash__":112751},"summaries\u002Fsummaries\u002Fimork-email.md",{"type":48,"value":112253,"toc":112715},[112254,112257,112261,112281,112285,112288,112292,112295,112299,112424,112428,112454,112458,112461,112465,112468,112472,112475,112479,112505,112509,112512,112523,112527,112531,112534,112554,112558,112565,112569,112572,112576,112596,112600,112604,112607,112611,112653,112657,112674,112678,112692,112696],[51,112255,30759],{"id":112256},"bezpečnost-emailových-služeb",[84,112258,112260],{"id":112259},"principy-emailu","Principy emailu",[89,112262,112263,112269,112275],{},[92,112264,112265,112268],{},[95,112266,112267],{},"SMTP"," (Simple Mail Transfer Protocol) — odesílání a přenos zpráv",[92,112270,112271,112274],{},[95,112272,112273],{},"POP3"," (Post Office Protocol v3) — stahování zpráv (maže ze serveru)",[92,112276,112277,112280],{},[95,112278,112279],{},"IMAP"," (Internet Message Access Protocol) — přístup ke zprávám na serveru",[84,112282,112284],{"id":112283},"mime-standard","MIME standard",[55,112286,112287],{},"Multipurpose Internet Mail Extensions — umožňuje přenos příloh, formátovaného textu a multimédií v emailu.",[84,112289,112291],{"id":112290},"nist-sp-800-45","NIST SP 800-45",[55,112293,112294],{},"Průvodce zabezpečením emailových služeb — doporučení pro konfiguraci a provoz.",[84,112296,112298],{"id":112297},"_9-bezpečnostních-protokolů-emailu","9 bezpečnostních protokolů emailu",[323,112300,112301,112313],{},[326,112302,112303],{},[329,112304,112305,112308,112311],{},[332,112306,112307],{},"#",[332,112309,112310],{},"Protokol",[332,112312,92035],{},[342,112314,112315,112327,112339,112351,112363,112375,112387,112400,112412],{},[329,112316,112317,112319,112324],{},[347,112318,638],{},[347,112320,112321],{},[95,112322,112323],{},"SSL\u002FTLS pro HTTPS",[347,112325,112326],{},"Šifrování webového přístupu k emailu",[329,112328,112329,112331,112336],{},[347,112330,646],{},[347,112332,112333],{},[95,112334,112335],{},"SMTPS",[347,112337,112338],{},"Šifrování SMTP komunikace",[329,112340,112341,112343,112348],{},[347,112342,654],{},[347,112344,112345],{},[95,112346,112347],{},"STARTTLS",[347,112349,112350],{},"Upgrade nešifrovaného spojení na šifrované",[329,112352,112353,112355,112360],{},[347,112354,662],{},[347,112356,112357],{},[95,112358,112359],{},"MTA-STS",[347,112361,112362],{},"Vynucení TLS mezi mail servery",[329,112364,112365,112367,112372],{},[347,112366,670],{},[347,112368,112369],{},[95,112370,112371],{},"SPF",[347,112373,112374],{},"Ověření oprávněného odesílatele (DNS záznam)",[329,112376,112377,112379,112384],{},[347,112378,678],{},[347,112380,112381],{},[95,112382,112383],{},"DKIM",[347,112385,112386],{},"Digitální podpis zprávy doménou",[329,112388,112389,112391,112397],{},[347,112390,686],{},[347,112392,112393,112396],{},[95,112394,112395],{},"DMARC"," (+ BIMI)",[347,112398,112399],{},"Politika pro SPF\u002FDKIM selhání + vizuální ověření",[329,112401,112402,112404,112409],{},[347,112403,5672],{},[347,112405,112406],{},[95,112407,112408],{},"S\u002FMIME",[347,112410,112411],{},"End-to-end šifrování a podpis (certifikáty)",[329,112413,112414,112416,112421],{},[347,112415,4087],{},[347,112417,112418],{},[95,112419,112420],{},"OpenPGP",[347,112422,112423],{},"End-to-end šifrování a podpis (klíče)",[84,112425,112427],{"id":112426},"doporučení-pro-šifrování","Doporučení pro šifrování",[89,112429,112430,112436,112442,112448],{},[92,112431,112432,112435],{},[95,112433,112434],{},"Symetrické",": AES 128\u002F192\u002F256",[92,112437,112438,112441],{},[95,112439,112440],{},"Podpisy",": DSS (Digital Signature Standard)",[92,112443,112444,112447],{},[95,112445,112446],{},"Asymetrické",": RSA 2048+ bitů",[92,112449,112450,112453],{},[95,112451,112452],{},"Hash",": SHA-256",[84,112455,112457],{"id":112456},"zabezpečení-os-mailového-serveru","Zabezpečení OS mailového serveru",[55,112459,112460],{},"Hardening operačního systému — minimalizace služeb, aktualizace, správa oprávnění.",[84,112462,112464],{"id":112463},"dmz-architektura","DMZ architektura",[55,112466,112467],{},"Mail server umístěn v demilitarizované zóně — oddělení od vnitřní sítě i internetu.",[84,112469,112471],{"id":112470},"mail-gateway","Mail gateway",[55,112473,112474],{},"Vstupní bod pro email — filtrování spamu, malwaru, kontrola politik.",[84,112476,112478],{"id":112477},"pgp-openpgp","PGP \u002F OpenPGP",[89,112480,112481,112487,112493,112499],{},[92,112482,112483,112486],{},[95,112484,112485],{},"RSA asymetrické šifrování"," — veřejný klíč pro šifrování, soukromý pro dešifrování",[92,112488,112489,112492],{},[95,112490,112491],{},"RFC 2440"," — specifikace OpenPGP Message Format",[92,112494,112495,112498],{},[95,112496,112497],{},"EFAIL zranitelnost (2018)"," — útok na šifrované emaily přes HTML rendering; útočník mohl exfiltrovat obsah šifrované zprávy",[92,112500,112501,112504],{},[95,112502,112503],{},"MDC"," (Modification Detection Code) — ochrana integrity zpráv proti EFAIL útoku",[84,112506,112508],{"id":112507},"digitální-certifikáty","Digitální certifikáty",[55,112510,112511],{},"Elektronické dokumenty prokazující vlastnictví veřejného klíče:",[89,112513,112514,112517,112520],{},[92,112515,112516],{},"Vydávány certifikační autoritou (CA)",[92,112518,112519],{},"Obsahují: veřejný klíč, identitu vlastníka, dobu platnosti, podpis CA",[92,112521,112522],{},"Základ pro důvěryhodnou komunikaci (S\u002FMIME, TLS)",[84,112524,112526],{"id":112525},"emailové-hrozby-21-století","Emailové hrozby 21. století",[609,112528,112530],{"id":112529},"komplexní-přístup-k-ochraně","Komplexní přístup k ochraně",[55,112532,112533],{},"Trojí úroveň:",[201,112535,112536,112542,112548],{},[92,112537,112538,112541],{},[95,112539,112540],{},"Perimetr"," — ochrana na hranici sítě (spam filtry, gateway)",[92,112543,112544,112547],{},[95,112545,112546],{},"Vnitřní síť"," — detekce hrozeb uvnitř organizace",[92,112549,112550,112553],{},[95,112551,112552],{},"Mimo organizaci"," — ochrana značky, monitoring podvodných domén",[609,112555,112557],{"id":112556},"cloud-migration-rizika","Cloud migration rizika",[55,112559,112560,112561,112564],{},"Přechod na cloudové emailové služby (např. ",[95,112562,112563],{},"Office 365",") přináší nové vektory útoku — sdílená infrastruktura, API zranitelnosti.",[609,112566,112568],{"id":112567},"email-jako-vektor-č-1","Email jako vektor č. 1",[55,112570,112571],{},"Email zůstává primárním vektorem kybernetických útoků — vstupní brána pro phishing, malware, BEC.",[84,112573,112575],{"id":112574},"bec-přes-email-business-email-compromise","BEC přes email (Business Email Compromise)",[89,112577,112578,112584,112590],{},[92,112579,112580,112583],{},[95,112581,112582],{},"Impersonace"," — útočník se vydává za vedoucího pracovníka nebo obchodního partnera",[92,112585,112586,112589],{},[95,112587,112588],{},"Kompromitace dodavatelského řetězce"," — zneužití důvěry mezi organizacemi",[92,112591,112592,112595],{},[95,112593,112594],{},"Ztráta citlivých dat"," — exfiltrace informací přes kompromitovaný email",[84,112597,112599],{"id":112598},"ochrana-a-obrana","Ochrana a obrana",[609,112601,112603],{"id":112602},"sae-simulační-nástroje","SAE + simulační nástroje",[55,112605,112606],{},"Školení bezpečnostního povědomí (Security Awareness Education) doplněná o simulované phishingové kampaně.",[609,112608,112610],{"id":112609},"tři-zóny-ochrany","Tři zóny ochrany",[323,112612,112613,112623],{},[326,112614,112615],{},[329,112616,112617,112620],{},[332,112618,112619],{},"Zóna",[332,112621,112622],{},"Opatření",[342,112624,112625,112634,112643],{},[329,112626,112627,112631],{},[347,112628,112629],{},[95,112630,112540],{},[347,112632,112633],{},"Spam\u002Fphishing filtrování, antimalware gateway",[329,112635,112636,112640],{},[347,112637,112638],{},[95,112639,112546],{},[347,112641,112642],{},"Detekce anomálií, monitorování neobvyklého chování",[329,112644,112645,112650],{},[347,112646,112647],{},[95,112648,112649],{},"Za perimetrem",[347,112651,112652],{},"Monitoring podvodných webů, [[imork-email",[84,112654,112656],{"id":112655},"mimecast","Mimecast",[89,112658,112659,112665,112671],{},[92,112660,112661,112664],{},[95,112662,112663],{},"Cloudová emailová brána"," — SaaS architektura",[92,112666,112667,112670],{},[95,112668,112669],{},"Email Security 3.0"," — pokročilá ochrana proti cíleným útokům, impersonaci a malwaru",[92,112672,112673],{},"Integrace s existující infrastrukturou (Office 365, Google Workspace)",[84,112675,112677],{"id":112676},"sandboxing","Sandboxing",[89,112679,112680,112686,112689],{},[92,112681,112682,112685],{},[95,112683,112684],{},"Emulace hrozeb"," — spuštění podezřelých příloh a odkazů v izolovaném virtuálním prostředí",[92,112687,112688],{},"Detekce neznámého malwaru, který projde signaturovou kontrolou",[92,112690,112691],{},"Izolace zabraňuje šíření hrozby do produkční sítě",[84,112693,112695],{"id":112694},"vrstvy-zabezpečení-infrastruktury","Vrstvy zabezpečení infrastruktury",[201,112697,112698,112704,112709],{},[92,112699,112700,112703],{},[95,112701,112702],{},"Firewall"," — síťová filtrace",[92,112705,112706,112708],{},[95,112707,18812],{}," — hardening, aktualizace",[92,112710,112711,112714],{},[95,112712,112713],{},"Endpoint"," — ochrana koncových stanic",{"title":156,"searchDepth":7,"depth":7,"links":112716},[112717,112718,112719,112720,112721,112722,112723,112724,112725,112726,112727,112732,112733,112737,112738,112739],{"id":112259,"depth":7,"text":112260},{"id":112283,"depth":7,"text":112284},{"id":112290,"depth":7,"text":112291},{"id":112297,"depth":7,"text":112298},{"id":112426,"depth":7,"text":112427},{"id":112456,"depth":7,"text":112457},{"id":112463,"depth":7,"text":112464},{"id":112470,"depth":7,"text":112471},{"id":112477,"depth":7,"text":112478},{"id":112507,"depth":7,"text":112508},{"id":112525,"depth":7,"text":112526,"children":112728},[112729,112730,112731],{"id":112529,"depth":4,"text":112530},{"id":112556,"depth":4,"text":112557},{"id":112567,"depth":4,"text":112568},{"id":112574,"depth":7,"text":112575},{"id":112598,"depth":7,"text":112599,"children":112734},[112735,112736],{"id":112602,"depth":4,"text":112603},{"id":112609,"depth":4,"text":112610},{"id":112655,"depth":7,"text":112656},{"id":112676,"depth":7,"text":112677},{"id":112694,"depth":7,"text":112695},{},"\u002Fsummaries\u002Fimork-email",{"title":30759,"description":156},[30781],"summaries\u002Fimork-email",[11,112746,30784,112747,112748,112749,112750,108549],"email","spf","dkim","dmarc","pgp","__MSmS1lrmaxXAI-afCGO6ozg5OGx49hHkBQqq1CERY",{"id":112753,"title":111084,"body":112754,"course":11,"courses":163,"created":795,"description":156,"extension":166,"meta":112977,"navigation":168,"path":112978,"seo":112979,"sources":112980,"stem":112982,"tags":112983,"type":106007,"updated":178,"__hash__":112988},"summaries\u002Fsummaries\u002Fimork-energetika.md",{"type":48,"value":112755,"toc":112963},[112756,112759,112766,112770,112773,112787,112791,112811,112815,112819,112822,112826,112829,112833,112836,112840,112843,112857,112861,112927,112931,112938,112942,112945,112958,112960],[51,112757,111084],{"id":112758},"isms-v-energetice",[55,112760,112761],{},[58,112762],{"alt":112763,"className":112764,"src":112765},"imork-energetika-vrstvy",[62,63],"\u002Fwiki-assets\u002Fimork-energetika-vrstvy.jpeg",[84,112767,112769],{"id":112768},"energetická-strategie","Energetická strategie",[55,112771,112772],{},"Současný trend v energetice směřuje k:",[89,112774,112775,112778,112784],{},[92,112776,112777],{},"Decentralizované výrobě energie",[92,112779,112780,112783],{},[69,112781,18414],{"className":112782,"dataFsResolvedFilePath":18412,"href":18413},[62]," (chytré sítě)",[92,112785,112786],{},"Obnovitelným zdrojům energie",[84,112788,112790],{"id":112789},"tři-klíčové-faktory-pro-ib-v-energetice","Tři klíčové faktory pro IB v energetice",[201,112792,112793,112799,112805],{},[92,112794,112795,112798],{},[95,112796,112797],{},"Strategické vstupy"," — smart grids a jejich závislost na ICT",[92,112800,112801,112804],{},[95,112802,112803],{},"Vývoj SBC"," (Single Board Computer) — miniaturizace řídících jednotek",[92,112806,112807,112810],{},[95,112808,112809],{},"Kybernetický prostor"," — propojení fyzické a digitální infrastruktury",[84,112812,112814],{"id":112813},"normy","Normy",[609,112816,112818],{"id":112817},"isoiec-tr-270192020","ISO\u002FIEC TR 27019:2020",[55,112820,112821],{},"Specifická norma pro řízení informační bezpečnosti v energetickém sektoru — rozšíření ISO 27001 pro energetiku.",[609,112823,112825],{"id":112824},"iec-61850","IEC 61850",[55,112827,112828],{},"Standard pro komunikaci v elektrických stanicích a elektrárnách. Definuje protokoly a datové modely pro automatizaci rozvodných sítí.",[609,112830,112832],{"id":112831},"iec-tc-57-wg-15","IEC TC 57 WG 15",[55,112834,112835],{},"Pracovní skupina zaměřená na bezpečnost dat v energetických komunikačních systémech.",[84,112837,112839],{"id":112838},"duální-infrastruktura","Duální infrastruktura",[55,112841,112842],{},"Energetický sektor disponuje dvěma propojenými vrstvami:",[89,112844,112845,112851],{},[92,112846,112847,112850],{},[95,112848,112849],{},"Fyzická infrastruktura"," — výrobny, rozvodny, přenosová vedení",[92,112852,112853,112856],{},[95,112854,112855],{},"Digitální infrastruktura"," — SCADA, řídicí systémy, komunikační sítě",[84,112858,112860],{"id":112859},"automatizační-systémy","Automatizační systémy",[323,112862,112863,112873],{},[326,112864,112865],{},[329,112866,112867,112869,112871],{},[332,112868,18226],{},[332,112870,110986],{},[332,112872,92035],{},[342,112874,112875,112888,112901,112914],{},[329,112876,112877,112882,112885],{},[347,112878,112879],{},[95,112880,112881],{},"PLC",[347,112883,112884],{},"Programmable Logic Controller",[347,112886,112887],{},"Programovatelný logický automat",[329,112889,112890,112895,112898],{},[347,112891,112892],{},[95,112893,112894],{},"SBC",[347,112896,112897],{},"Single Board Computer",[347,112899,112900],{},"Jednodeskový počítač",[329,112902,112903,112908,112911],{},[347,112904,112905],{},[95,112906,112907],{},"RTU",[347,112909,112910],{},"Remote Terminal Unit",[347,112912,112913],{},"Vzdálená terminálová jednotka",[329,112915,112916,112921,112924],{},[347,112917,112918],{},[95,112919,112920],{},"IED",[347,112922,112923],{},"Intelligent Electronic Device",[347,112925,112926],{},"Inteligentní elektronické zařízení",[84,112928,112930],{"id":112929},"architektura-elektrárny","Architektura elektrárny",[55,112932,112933,112934,112937],{},"Definovány ",[95,112935,112936],{},"3 úrovně"," v architektuře řízení elektrárny (station level, bay level, process level).",[84,112939,112941],{"id":112940},"bezpečnostní-principy","Bezpečnostní principy",[55,112943,112944],{},"V energetice se uplatňuje rozšířený model:",[89,112946,112947,112953],{},[92,112948,112949,112952],{},[95,112950,112951],{},"CIA"," (Confidentiality, Integrity, Availability)",[92,112954,112955,112957],{},[95,112956,18107],{}," (nepopiratelnost) — zvláště důležitá u řídících příkazů",[84,112959,109854],{"id":109853},[55,112961,112962],{},"Příklad penetračního testování energetické infrastruktury — ověření odolnosti SCADA systémů a řídicích jednotek proti kybernetickým útokům.",{"title":156,"searchDepth":7,"depth":7,"links":112964},[112965,112966,112967,112972,112973,112974,112975,112976],{"id":112768,"depth":7,"text":112769},{"id":112789,"depth":7,"text":112790},{"id":112813,"depth":7,"text":112814,"children":112968},[112969,112970,112971],{"id":112817,"depth":4,"text":112818},{"id":112824,"depth":4,"text":112825},{"id":112831,"depth":4,"text":112832},{"id":112838,"depth":7,"text":112839},{"id":112859,"depth":7,"text":112860},{"id":112929,"depth":7,"text":112930},{"id":112940,"depth":7,"text":112941},{"id":109853,"depth":7,"text":109854},{},"\u002Fsummaries\u002Fimork-energetika",{"title":111084,"description":156},[112981],"raw\u002Fimork\u002F2007 VUT_Bezp energetika-2023.pdf","summaries\u002Fimork-energetika",[11,20,112984,112985,112824,112986,112987],"energetika","smart-grid","scada","plc","DnqVpih9-Ouq3-rQRiWHYjMB-13HSw8NMpmFWMh2cm4",1777154859720]