[{"data":1,"prerenderedAt":105008},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-elasticita":1626,"course-stats-imek":7394,"course-topics-imek":7398,"backlinks-elasticita":104981,"related-elasticita":105006},{"courses":4,"counts":1622},[5,679,1148],{"id":6,"title":7,"body":8,"course":658,"courseName":659,"courses":659,"created":660,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":663,"navigation":664,"path":665,"seo":666,"sources":667,"stem":669,"tags":670,"type":676,"updated":677,"__hash__":678},"courses\u002Fcourses\u002Fimork.md","Management oborových řešení (ImorK)",{"type":9,"value":10,"toc":640},"minimark",[11,15,114,119,147,151,193,197,202,251,255,338,342,371,375,395,399,455,459,533,537,548,552,604,608],[12,13,7],"h1",{"id":14},"management-oborových-řešení-imork",[16,17,18,29],"table",{},[19,20,21],"thead",{},[22,23,24,27],"tr",{},[25,26],"th",{},[25,28],{},[30,31,32,44,54,64,74,84,94,104],"tbody",{},[22,33,34,41],{},[35,36,37],"td",{},[38,39,40],"strong",{},"Zkratka",[35,42,43],{},"ImorK",[22,45,46,51],{},[35,47,48],{},[38,49,50],{},"Fakulta",[35,52,53],{},"Fakulta podnikatelská, VUT v Brně",[22,55,56,61],{},[35,57,58],{},[38,59,60],{},"Semestr",[35,62,63],{},"letní 2025\u002F2026",[22,65,66,71],{},[35,67,68],{},[38,69,70],{},"Ukončení",[35,72,73],{},"zkouška",[22,75,76,81],{},[35,77,78],{},[38,79,80],{},"Garant",[35,82,83],{},"Ing. Lukáš Novák, Ph.D.",[22,85,86,91],{},[35,87,88],{},[38,89,90],{},"Vyučující",[35,92,93],{},"Ing. Petr Sedlák",[22,95,96,101],{},[35,97,98],{},[38,99,100],{},"Ústav",[35,102,103],{},"Ústav informatiky",[22,105,106,111],{},[35,107,108],{},[38,109,110],{},"Prerekvizita",[35,112,113],{},"Management informační bezpečnosti (ImibePA)",[115,116,118],"h2",{"id":117},"cíle-předmětu","Cíle předmětu",[120,121,122,129,135,141],"ul",{},[123,124,125,126],"li",{},"Znalosti o specifických problémech a odlišnostech při ",[38,127,128],{},"oborovém řešení informační bezpečnosti",[123,130,131,132],{},"Porozumění jednotlivých řešení na úrovni ",[38,133,134],{},"případových studií",[123,136,137,138],{},"Přehled o rozdílných aspektech v závislosti na oborové řešení ",[38,139,140],{},"ISMS",[123,142,143,144],{},"Metodika pro budování bezpečných IS na bázi norem řady ",[38,145,146],{},"ISO\u002FIEC 27000",[115,148,150],{"id":149},"osnova","Osnova",[152,153,154,157,160,163,166,169,172,175,178,181,184,187,190],"ol",{},[123,155,156],{},"Bezpečnost v kyberprostoru",[123,158,159],{},"Budování bezpečnostního povědomí — SAE",[123,161,162],{},"Manažerská informační bezpečnost",[123,164,165],{},"Problematika GDPR",[123,167,168],{},"ISMS v ISVS",[123,170,171],{},"ISMS v univerzitním prostředí",[123,173,174],{},"ISMS ve zdravotnictví",[123,176,177],{},"ISMS v energetice",[123,179,180],{},"ISMS poskytovatelů konektivity (ISP)",[123,182,183],{},"Bezpečnost konvergovaných sítí",[123,185,186],{},"Řízení bezpečnosti www aplikací",[123,188,189],{},"Řízení bezpečnosti mailových aplikací",[123,191,192],{},"Řízení mobilní bezpečnosti",[115,194,196],{"id":195},"shrnutí-zdrojů","Shrnutí zdrojů",[198,199,201],"h3",{"id":200},"přednášky","Přednášky",[120,203,204,215,224,233,242],{},[123,205,206,214],{},[207,208,213],"a",{"className":209,"dataFsResolvedFilePath":211,"href":212},[210],"wikilink","summaries\u002Fimork-detail-predmetu.md","\u002Fwiki\u002Fimork-detail-predmetu","Detail předmětu"," — sylabus kurzu, hodnocení, literatura",[123,216,217,223],{},[207,218,222],{"className":219,"dataFsResolvedFilePath":220,"href":221},[210],"summaries\u002Fimork-manazerska-bezpecnost.md","\u002Fwiki\u002Fimork-manazerska-bezpecnost","Manažerská bezpečnost"," — governance, SIEM, log management, bezpečnostní role",[123,225,226,232],{},[207,227,231],{"className":228,"dataFsResolvedFilePath":229,"href":230},[210],"summaries\u002Fimork-bezpecnostni-strategie.md","\u002Fwiki\u002Fimork-bezpecnostni-strategie","Bezpečnostní strategie"," — tvorba a implementace bezpečnostní strategie",[123,234,235,241],{},[207,236,240],{"className":237,"dataFsResolvedFilePath":238,"href":239},[210],"summaries\u002Fimork-sae.md","\u002Fwiki\u002Fimork-sae","SAE"," — budování bezpečnostního povědomí (NIST SP 800-50\u002F16)",[123,243,244,250],{},[207,245,249],{"className":246,"dataFsResolvedFilePath":247,"href":248},[210],"summaries\u002Fimork-risk-management.md","\u002Fwiki\u002Fimork-risk-management","Risk Management"," — ISO 31000, ISO 27005, RTP, PoA\u002FSoA",[198,252,254],{"id":253},"oborová-isms","Oborová ISMS",[120,256,257,266,275,284,293,302,311,320,329],{},[123,258,259,265],{},[207,260,264],{"className":261,"dataFsResolvedFilePath":262,"href":263},[210],"summaries\u002Fimork-akademicke-prostredi.md","\u002Fwiki\u002Fimork-akademicke-prostredi","Akademické prostředí"," — kampus, WiFi, identita, VIS",[123,267,268,274],{},[207,269,273],{"className":270,"dataFsResolvedFilePath":271,"href":272},[210],"summaries\u002Fimork-financni-sektor.md","\u002Fwiki\u002Fimork-financni-sektor","Finanční sektor"," — DORA, MiCA, DLT\u002Fblockchain",[123,276,277,283],{},[207,278,282],{"className":279,"dataFsResolvedFilePath":280,"href":281},[210],"summaries\u002Fimork-zdravotnictvi.md","\u002Fwiki\u002Fimork-zdravotnictvi","Zdravotnictví"," — HIPAA, ISO 27799, PACS, DICOM, eHealth",[123,285,286,292],{},[207,287,291],{"className":288,"dataFsResolvedFilePath":289,"href":290},[210],"summaries\u002Fimork-energetika.md","\u002Fwiki\u002Fimork-energetika","Energetika"," — ISO 27019, IEC 61850, PLC\u002FSBC\u002FRTU",[123,294,295,301],{},[207,296,300],{"className":297,"dataFsResolvedFilePath":298,"href":299},[210],"summaries\u002Fimork-smart-grid.md","\u002Fwiki\u002Fimork-smart-grid","Smart Grid"," — NISTIR 7628, IEC 62351, prosumers",[123,303,304,310],{},[207,305,309],{"className":306,"dataFsResolvedFilePath":307,"href":308},[210],"summaries\u002Fimork-doprava.md","\u002Fwiki\u002Fimork-doprava","Doprava (železnice)"," — CLC\u002FTS 50701, kritická infrastruktura",[123,312,313,319],{},[207,314,318],{"className":315,"dataFsResolvedFilePath":316,"href":317},[210],"summaries\u002Fimork-automotive.md","\u002Fwiki\u002Fimork-automotive","Automotive"," — CAN bus, TISAX, UN Reg. 155",[123,321,322,328],{},[207,323,327],{"className":324,"dataFsResolvedFilePath":325,"href":326},[210],"summaries\u002Fimork-isp.md","\u002Fwiki\u002Fimork-isp","ISP\u002Ftelekomunikace"," — ISO 27011, NGN, 5G bezpečnost",[123,330,331,337],{},[207,332,336],{"className":333,"dataFsResolvedFilePath":334,"href":335},[210],"summaries\u002Fimork-mcn.md","\u002Fwiki\u002Fimork-mcn","Mission Critical Networks"," — NCPI, model hrozeb, dostupnost",[198,339,341],{"id":340},"bezpečnost-aplikací-a-dat","Bezpečnost aplikací a dat",[120,343,344,353,362],{},[123,345,346,352],{},[207,347,351],{"className":348,"dataFsResolvedFilePath":349,"href":350},[210],"summaries\u002Fimork-www.md","\u002Fwiki\u002Fimork-www","Bezpečnost webu"," — OWASP, SQL injection, XSS, Solid",[123,354,355,361],{},[207,356,360],{"className":357,"dataFsResolvedFilePath":358,"href":359},[210],"summaries\u002Fimork-email.md","\u002Fwiki\u002Fimork-email","Bezpečnost emailu"," — SPF, DKIM, DMARC, S\u002FMIME, šifrování",[123,363,364,370],{},[207,365,369],{"className":366,"dataFsResolvedFilePath":367,"href":368},[210],"summaries\u002Fimork-ochrana-dat.md","\u002Fwiki\u002Fimork-ochrana-dat","Ochrana dat"," — NAC, IDS\u002FIPS, SIEM, DLP, IPv6",[198,372,374],{"id":373},"kontinuita-a-obnova","Kontinuita a obnova",[120,376,377,386],{},[123,378,379,385],{},[207,380,384],{"className":381,"dataFsResolvedFilePath":382,"href":383},[210],"summaries\u002Fimork-bcm.md","\u002Fwiki\u002Fimork-bcm","BCM"," — ISO 22301, BIA, STEEPLE, PDCA",[123,387,388,394],{},[207,389,393],{"className":390,"dataFsResolvedFilePath":391,"href":392},[210],"summaries\u002Fimork-dr.md","\u002Fwiki\u002Fimork-dr","Disaster Recovery"," — RPO\u002FRTO, cloud DR, 7 tiers, DRaaS",[198,396,398],{"id":397},"kybernetické-útoky","Kybernetické útoky",[120,400,401,410,419,428,437,446],{},[123,402,403,409],{},[207,404,408],{"className":405,"dataFsResolvedFilePath":406,"href":407},[210],"summaries\u002Fimork-anatomie-utoku.md","\u002Fwiki\u002Fimork-anatomie-utoku","Anatomie útoku"," — APT, vektory, exploit\u002Fpayload",[123,411,412,418],{},[207,413,417],{"className":414,"dataFsResolvedFilePath":415,"href":416},[210],"summaries\u002Fimork-ai-utoky.md","\u002Fwiki\u002Fimork-ai-utoky","AI útoky"," — WormGPT, BEC, phishing",[123,420,421,427],{},[207,422,426],{"className":423,"dataFsResolvedFilePath":424,"href":425},[210],"summaries\u002Fimork-sitove-utoky.md","\u002Fwiki\u002Fimork-sitove-utoky","Síťové útoky"," — DDoS, spoofing, Emotet→Trickbot→Ryuk",[123,429,430,436],{},[207,431,435],{"className":432,"dataFsResolvedFilePath":433,"href":434},[210],"summaries\u002Fimork-ransomware.md","\u002Fwiki\u002Fimork-ransomware","Ransomware"," — historie 1989–2024, RaaS, NISTIR 8374, IR plán",[123,438,439,445],{},[207,440,444],{"className":441,"dataFsResolvedFilePath":442,"href":443},[210],"summaries\u002Fimork-rizeny-hacking.md","\u002Fwiki\u002Fimork-rizeny-hacking","Řízený hacking \u002F APT"," — APT skupiny, informační válka, OSINT",[123,447,448,454],{},[207,449,453],{"className":450,"dataFsResolvedFilePath":451,"href":452},[210],"summaries\u002Fimork-internetova-bezpecnost.md","\u002Fwiki\u002Fimork-internetova-bezpecnost","Internetová bezpečnost"," — kyberprostor, OSINT, behaviorální biometrika",[198,456,458],{"id":457},"případové-studie","Případové studie",[120,460,461,470,479,488,497,506,515,524],{},[123,462,463,469],{},[207,464,468],{"className":465,"dataFsResolvedFilePath":466,"href":467},[210],"summaries\u002Fimork-nemocnice.md","\u002Fwiki\u002Fimork-nemocnice","Útoky na nemocnice"," — Benešov (70M Kč), FN Brno (350M Kč), Nymburk",[123,471,472,478],{},[207,473,477],{"className":474,"dataFsResolvedFilePath":475,"href":476},[210],"summaries\u002Fimork-kradez-dat.md","\u002Fwiki\u002Fimork-kradez-dat","Krádež dat"," — PII, černý trh, IoT botnety, ISO 27701, GDPR",[123,480,481,487],{},[207,482,486],{"className":483,"dataFsResolvedFilePath":484,"href":485},[210],"summaries\u002Fimork-sprava-login.md","\u002Fwiki\u002Fimork-sprava-login","Správa login"," — privilegované účty, NIST SP 800-63, biometrika",[123,489,490,496],{},[207,491,495],{"className":492,"dataFsResolvedFilePath":493,"href":494},[210],"summaries\u002Fimork-ehealth.md","\u002Fwiki\u002Fimork-ehealth","eHealth"," — elektronizace zdravotnictví, telemedicína, NSeZ",[123,498,499,505],{},[207,500,504],{"className":501,"dataFsResolvedFilePath":502,"href":503},[210],"summaries\u002Fimork-tor.md","\u002Fwiki\u002Fimork-tor","TOR"," — anonymizace, onion routing, NSA X-Keyscore",[123,507,508,514],{},[207,509,513],{"className":510,"dataFsResolvedFilePath":511,"href":512},[210],"summaries\u002Fimork-payment.md","\u002Fwiki\u002Fimork-payment","Bezpečnost plateb"," — PCI DSS v4.0, NFC\u002Ftokenizace, EMV, darknet",[123,516,517,523],{},[207,518,522],{"className":519,"dataFsResolvedFilePath":520,"href":521},[210],"summaries\u002Fimork-mobilni-bezpecnost.md","\u002Fwiki\u002Fimork-mobilni-bezpecnost","Mobilní bezpečnost"," — SIMJaker, SIM swapping, 5G, Common Criteria",[123,525,526,532],{},[207,527,531],{"className":528,"dataFsResolvedFilePath":529,"href":530},[210],"summaries\u002Fimork-audio-hack.md","\u002Fwiki\u002Fimork-audio-hack","Audio Hack"," — fyzická zranitelnost HDD, CVE-2022-38392, rezonanční útok",[198,534,536],{"id":535},"další","Další",[120,538,539],{},[123,540,541,547],{},[207,542,546],{"className":543,"dataFsResolvedFilePath":544,"href":545},[210],"summaries\u002Fimork-digitalni-identita.md","\u002Fwiki\u002Fimork-digitalni-identita","Digitální identita a stopa"," — online identita, footprint",[115,549,551],{"id":550},"témata","Témata",[120,553,554,562,571,580,588,596],{},[123,555,556,561],{},[207,557,140],{"className":558,"dataFsResolvedFilePath":559,"href":560},[210],"topics\u002Fisms.md","\u002Fwiki\u002Fisms"," — systém řízení bezpečnosti informací",[123,563,564,570],{},[207,565,569],{"className":566,"dataFsResolvedFilePath":567,"href":568},[210],"topics\u002Frizeni-rizik.md","\u002Fwiki\u002Frizeni-rizik","Řízení rizik"," — proces identifikace a ošetření rizik",[123,572,573,579],{},[207,574,578],{"className":575,"dataFsResolvedFilePath":576,"href":577},[210],"topics\u002Fkyberneticka-bezpecnost.md","\u002Fwiki\u002Fkyberneticka-bezpecnost","Kybernetická bezpečnost"," — hrozby, útoky, obrana",[123,581,582,587],{},[207,583,240],{"className":584,"dataFsResolvedFilePath":585,"href":586},[210],"topics\u002Fsae.md","\u002Fwiki\u002Fsae"," — budování bezpečnostního povědomí",[123,589,590,595],{},[207,591,384],{"className":592,"dataFsResolvedFilePath":593,"href":594},[210],"topics\u002Fbcm.md","\u002Fwiki\u002Fbcm"," — řízení kontinuity činnosti",[123,597,598,603],{},[207,599,369],{"className":600,"dataFsResolvedFilePath":601,"href":602},[210],"topics\u002Fochrana-dat.md","\u002Fwiki\u002Fochrana-dat"," — technologická řešení ochrany",[115,605,607],{"id":606},"doporučená-literatura","Doporučená literatura",[120,609,610,618,625,631,634,637],{},[123,611,612,613,617],{},"JORDÁN, V. a ONDRÁK, V.: ",[614,615,616],"em",{},"Integrovaná podniková infrastruktura."," Brno: CERM, 2016. ISBN 978-80-214-5241-1",[123,619,620,621,624],{},"SEDLÁK, P. a KONEČNÝ, M.: ",[614,622,623],{},"Přeměna ISMS v manažerské informatice."," Brno: CERM, 2023. ISBN 978-80-7623-110-8",[123,626,620,627,630],{},[614,628,629],{},"Kybernetická (ne)bezpečnost."," Brno: CERM, 2021. ISBN 978-80-7623-068-2",[123,632,633],{},"ČSN EN ISO\u002FIEC 27011 — Bezpečnost pro telekomunikační organizace",[123,635,636],{},"ČSN EN ISO\u002FIEC 27019 — Bezpečnost pro energetický průmysl",[123,638,639],{},"ČSN EN ISO\u002FIEC 27799 — Bezpečnost ve zdravotnictví",{"title":641,"searchDepth":642,"depth":642,"links":643},"",2,[644,645,646,656,657],{"id":117,"depth":642,"text":118},{"id":149,"depth":642,"text":150},{"id":195,"depth":642,"text":196,"children":647},[648,650,651,652,653,654,655],{"id":200,"depth":649,"text":201},3,{"id":253,"depth":649,"text":254},{"id":340,"depth":649,"text":341},{"id":373,"depth":649,"text":374},{"id":397,"depth":649,"text":398},{"id":457,"depth":649,"text":458},{"id":535,"depth":649,"text":536},{"id":550,"depth":642,"text":551},{"id":606,"depth":642,"text":607},"imork",null,"2026-04-12","md",false,{},true,"\u002Fcourses\u002Fimork",{"title":7,"description":641},[668],"raw\u002Fimork\u002FDetail předmětu.md","courses\u002Fimork",[658,671,672,673,674,675],"isms","informacni-bezpecnost","kyberneticka-bezpecnost","oborova-reseni","iso-27000","course","2026-04-25","6MdSdXZJ3FNW9uPHrGzZPucQlKskWh23itOKhDSZfGs",{"id":680,"title":681,"body":682,"course":1128,"courseName":659,"courses":659,"created":1129,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":1130,"navigation":664,"path":1131,"seo":1132,"sources":1133,"stem":1139,"tags":1140,"type":676,"updated":677,"__hash__":1147},"courses\u002Fcourses\u002Fimek.md","Matematická ekonomie (ImeK)",{"type":9,"value":683,"toc":1112},[684,687,719,723,731,735,738,748,831,841,861,871,947,951,962,966,969,994,1000,1011,1017,1020,1024,1061,1065,1068,1072],[12,685,681],{"id":686},"matematická-ekonomie-imek",[120,688,689,695,701,707,713],{},[123,690,691,694],{},[38,692,693],{},"Fakulta:"," FP VUT",[123,696,697,700],{},[38,698,699],{},"Garant:"," doc. RNDr. Bedřich Půža, CSc.",[123,702,703,706],{},[38,704,705],{},"Vyučující (kombinované studium):"," Mgr. Martina Bobalová, Ph.D.",[123,708,709,712],{},[38,710,711],{},"Ukončení:"," zkouška (písemná 60 min + ústní ~10 min)",[123,714,715,718],{},[38,716,717],{},"Semestr:"," letní 2025\u002F2026",[115,720,722],{"id":721},"cíl-předmětu","Cíl předmětu",[724,725,726,727,730],"p",{},"Hlouběji proniknout do kauzální podstaty ekonomických vztahů, rozvoj schopnosti vyjadřovat ekonomické vztahy ",[38,728,729],{},"exaktními prostředky"," a provádět jejich analýzy. Matematické modelování mikroekonomie a makroekonomie pomocí prostředků inženýrské matematiky (derivace, integrály, Lagrangeova metoda).",[115,732,734],{"id":733},"obsah-kurzu","Obsah kurzu",[724,736,737],{},"Kurz je v kombinovaném studiu rozčleněn do tří přednáškových bloků:",[198,739,741,742],{"id":740},"blok-1-kalkul-poptávkanabídka-příjemnákladyzisk","Blok 1 — ",[207,743,747],{"className":744,"dataFsResolvedFilePath":745,"href":746},[210],"summaries\u002Fimek-blok-01.md","\u002Fwiki\u002Fimek-blok-01","Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",[120,749,750,759,768,777,786,795,804,813,822],{},[123,751,752,758],{},[207,753,757],{"className":754,"dataFsResolvedFilePath":755,"href":756},[210],"topics\u002Fzaklady-matematicke-ekonomie.md","\u002Fwiki\u002Fzaklady-matematicke-ekonomie","Základy matematické ekonomie"," — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika",[123,760,761,767],{},[207,762,766],{"className":763,"dataFsResolvedFilePath":764,"href":765},[210],"topics\u002Fderivace.md","\u002Fwiki\u002Fderivace","Derivace, diferenciál a extrémy 1D"," — geometrická a inženýrská interpretace, mezní veličiny",[123,769,770,776],{},[207,771,775],{"className":772,"dataFsResolvedFilePath":773,"href":774},[210],"topics\u002Fintegral.md","\u002Fwiki\u002Fintegral","Integrál"," — neurčitý a určitý, rekonstrukce TR z MR a TC z MC",[123,778,779,785],{},[207,780,784],{"className":781,"dataFsResolvedFilePath":782,"href":783},[210],"topics\u002Ffunkce-vice-promennych.md","\u002Fwiki\u002Ffunkce-vice-promennych","Funkce více proměnných"," — parciální derivace, diferenciál 2D, implicitní funkce, volné extrémy",[123,787,788,794],{},[207,789,793],{"className":790,"dataFsResolvedFilePath":791,"href":792},[210],"topics\u002Flagrangeova-metoda.md","\u002Fwiki\u002Flagrangeova-metoda","Lagrangeova metoda"," — vázané extrémy, multiplikátor jako náklady příležitosti",[123,796,797,803],{},[207,798,802],{"className":799,"dataFsResolvedFilePath":800,"href":801},[210],"topics\u002Fpoptavka-nabidka.md","\u002Fwiki\u002Fpoptavka-nabidka","Poptávka, nabídka a tržní rovnováha"," — modely D a S, rovnováha, multiplikátory",[123,805,806,812],{},[207,807,811],{"className":808,"dataFsResolvedFilePath":809,"href":810},[210],"topics\u002Fzdaneni-trhu.md","\u002Fwiki\u002Fzdaneni-trhu","Zdanění trhu"," — daň výrobci vs. spotřebiteli, rozklad daňového břemene, ekvivalence",[123,814,815,821],{},[207,816,820],{"className":817,"dataFsResolvedFilePath":818,"href":819},[210],"topics\u002Fprebytek-spotrebitele-vyrobce.md","\u002Fwiki\u002Fprebytek-spotrebitele-vyrobce","Přebytek spotřebitele a výrobce"," — CS, PS, plochy pod\u002Fnad křivkami",[123,823,824,830],{},[207,825,829],{"className":826,"dataFsResolvedFilePath":827,"href":828},[210],"topics\u002Fprijem-naklady-zisk.md","\u002Fwiki\u002Fprijem-naklady-zisk","Příjem, náklady a zisk"," — TR, AR, MR, TC, AC, MC, body zvratu, konstrukce nabídky firmy",[198,832,834,835],{"id":833},"blok-2-elasticita-a-produkce","Blok 2 — ",[207,836,840],{"className":837,"dataFsResolvedFilePath":838,"href":839},[210],"summaries\u002Fimek-blok-02.md","\u002Fwiki\u002Fimek-blok-02","Elasticita a produkce",[120,842,843,852],{},[123,844,845,851],{},[207,846,850],{"className":847,"dataFsResolvedFilePath":848,"href":849},[210],"topics\u002Felasticita.md","\u002Fwiki\u002Felasticita","Cenová, křížová a důchodová elasticita"," (jedno- i vícefaktorový model)",[123,853,854,860],{},[207,855,859],{"className":856,"dataFsResolvedFilePath":857,"href":858},[210],"topics\u002Fprodukce.md","\u002Fwiki\u002Fprodukce","Produkční funkce"," — Cobb-Douglasova, CES, lineární, Leontiefova, izokvanty, MRTS, Eulerova věta",[198,862,864,865],{"id":863},"blok-3-užitečnost-a-národní-důchod","Blok 3 — ",[207,866,870],{"className":867,"dataFsResolvedFilePath":868,"href":869},[210],"summaries\u002Fimek-blok-03.md","\u002Fwiki\u002Fimek-blok-03","Užitečnost a národní důchod",[120,872,873,906,929,938],{},[123,874,875,881,882,905],{},[207,876,880],{"className":877,"dataFsResolvedFilePath":878,"href":879},[210],"topics\u002Fuzitecnost.md","\u002Fwiki\u002Fuzitecnost","Užitečnost"," — pojem, mezní užitečnost, Cobb-Douglasova ",[883,884,887],"span",{"className":885},[886],"katex",[888,889,891],"math",{"xmlns":890},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[892,893,894,901],"semantics",{},[895,896,897],"mrow",{},[898,899,900],"mi",{},"U",[902,903,900],"annotation",{"encoding":904},"application\u002Fx-tex",", indiferenční křivky, MRCS",[123,907,908,914,915,928],{},[207,909,913],{"className":910,"dataFsResolvedFilePath":911,"href":912},[210],"topics\u002Foptimalizace-spotrebitele.md","\u002Fwiki\u002Foptimalizace-spotrebitele","Optimalizace spotřebitele"," — Lagrangeova maximalizace ",[883,916,918],{"className":917},[886],[888,919,920],{"xmlns":890},[892,921,922,926],{},[895,923,924],{},[898,925,900],{},[902,927,900],{"encoding":904},", duální minimalizace výdajů, Marshallova\u002FHicksova poptávka",[123,930,931,937],{},[207,932,936],{"className":933,"dataFsResolvedFilePath":934,"href":935},[210],"topics\u002Fnarodni-duchod.md","\u002Fwiki\u002Fnarodni-duchod","Národní důchod"," — GNP, spotřeba\u002Fúspory, MPC\u002FMPS, modely C-I, C-I-G, C-I-G-X",[123,939,940,946],{},[207,941,945],{"className":942,"dataFsResolvedFilePath":943,"href":944},[210],"topics\u002Fis-lm.md","\u002Fwiki\u002Fis-lm","IS-LM analýza"," — simultánní rovnováha trhu zboží a peněz, fiskální\u002Fmonetární politika",[115,948,950],{"id":949},"reference-a-přehledy","Reference a přehledy",[120,952,953],{},[123,954,955,961],{},[207,956,960],{"className":957,"dataFsResolvedFilePath":958,"href":959},[210],"outputs\u002Fimek-vzorce-prehled.md","\u002Fwiki\u002Fimek-vzorce-prehled","Kompletní přehled vzorců"," — všechny klíčové vzorce kurzu v definičním tvaru, se zdrojem a intuicí. Referenční list pro přípravu na zkoušku.",[115,963,965],{"id":964},"hodnocení-zkoušky","Hodnocení zkoušky",[724,967,968],{},"Písemná část (60 min) — 4 úlohy:",[152,970,971,977,983,989],{},[123,972,973,974],{},"Rozhodovací úloha o ekonomické funkci — ",[38,975,976],{},"10 bodů",[123,978,979,980],{},"Definice, formulace vlastnosti, interpretace ekonomické veličiny — ",[38,981,982],{},"20 bodů",[123,984,985,986],{},"Výpočetní úloha — ",[38,987,988],{},"30 bodů",[123,990,985,991],{},[38,992,993],{},"40 bodů",[724,995,996,999],{},[38,997,998],{},"Dílčí podmínky"," (nutné pro A–E):",[120,1001,1002,1005,1008],{},[123,1003,1004],{},"≥ 11 bodů ze součtu úloh 1 a 2",[123,1006,1007],{},"≥ 10 bodů z úlohy 3",[123,1009,1010],{},"≥ 10 bodů z úlohy 4",[724,1012,1013,1016],{},[38,1014,1015],{},"Stupnice:"," A (90–100), B (80–89), C (70–79), D (60–69), E (50–59), F (0–49 nebo nesplnění podmínek).",[724,1018,1019],{},"Doporučeno mít kalkulátor.",[115,1021,1023],{"id":1022},"literatura","Literatura",[120,1025,1026,1033,1040,1047,1054],{},[123,1027,1028,1029,1032],{},"I. Mezník, ",[614,1030,1031],{},"Úvod do matematické ekonomie pro ekonomy",", FP VUT \u002F CERM, Brno 2017 (CZ)",[123,1034,1035,1036,1039],{},"A.C. Chiang, ",[614,1037,1038],{},"Fundamental Methods of Mathematical Economics",", McGraw-Hill, 1984",[123,1041,1042,1043,1046],{},"J.U. Koch, L.A. Ostrosky, ",[614,1044,1045],{},"Introduction to Mathematical Economics",", McGraw-Hill, 1994",[123,1048,1049,1050,1053],{},"C.J. McKenna, R. Rees, ",[614,1051,1052],{},"Economics: A Mathematical Introduction",", Oxford UP, 1992",[123,1055,1056,1057,1060],{},"J. Jacques, ",[614,1058,1059],{},"Mathematics for Economics and Business",", Addison-Wesley, 1995",[115,1062,1064],{"id":1063},"prerekvizity","Prerekvizity",[724,1066,1067],{},"Standardní kurz inženýrské matematiky, mikroekonomie a makroekonomie na bakalářské úrovni.",[115,1069,1071],{"id":1070},"přehled-zdrojů","Přehled zdrojů",[120,1073,1074,1082,1089,1096,1103],{},[123,1075,1076,1081],{},[207,1077,213],{"className":1078,"dataFsResolvedFilePath":1079,"href":1080},[210],"summaries\u002Fimek-detail-predmetu.md","\u002Fwiki\u002Fimek-detail-predmetu"," — sylabus a administrativní informace",[123,1083,1084,1088],{},[207,1085,1087],{"className":1086,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok"," — 57 stran, matematický aparát + mikroekonomie",[123,1090,1091,1095],{},[207,1092,1094],{"className":1093,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok"," — 19 stran, elasticita a produkce",[123,1097,1098,1102],{},[207,1099,1101],{"className":1100,"dataFsResolvedFilePath":868,"href":869},[210],"KS 3. blok"," — 25 stran, užitečnost a národní důchod",[123,1104,1105,1111],{},[207,1106,1110],{"className":1107,"dataFsResolvedFilePath":1108,"href":1109},[210],"summaries\u002Fimek-kniha.md","\u002Fwiki\u002Fimek-kniha","Kniha Mezník — Úvod do matematické ekonomie"," — naskenované kap. 2–7 (107 stran), kompletní teorie + Příklady + Úlohy k samostatnému řešení",{"title":641,"searchDepth":642,"depth":642,"links":1113},[1114,1115,1123,1124,1125,1126,1127],{"id":721,"depth":642,"text":722},{"id":733,"depth":642,"text":734,"children":1116},[1117,1119,1121],{"id":740,"depth":649,"text":1118},"Blok 1 — Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",{"id":833,"depth":649,"text":1120},"Blok 2 — Elasticita a produkce",{"id":863,"depth":649,"text":1122},"Blok 3 — Užitečnost a národní důchod",{"id":949,"depth":642,"text":950},{"id":964,"depth":642,"text":965},{"id":1022,"depth":642,"text":1023},{"id":1063,"depth":642,"text":1064},{"id":1070,"depth":642,"text":1071},"imek","2026-04-20",{},"\u002Fcourses\u002Fimek",{"title":681,"description":641},[1134,1135,1136,1137,1138],"raw\u002Fimek\u002FDetail předmětu.md","raw\u002Fimek\u002FKS_prvni_blok.pdf","raw\u002Fimek\u002FKS_druhy_blok.pdf","raw\u002Fimek\u002FKS_treti_blok.pdf","raw\u002Fimek\u002Fkniha_scanned\u002F","courses\u002Fimek",[1128,1141,1142,1143,1144,1145,1146],"ekonomie","mikroekonomie","makroekonomie","lagrange","derivace","integraly","x73RNX_N_uAS3i63VHeCgVFPJa4tJKL2z8kq4DIN24M",{"id":1149,"title":1150,"body":1151,"course":1601,"courseName":659,"courses":659,"created":1602,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":1603,"navigation":664,"path":1604,"seo":1605,"sources":1606,"stem":1612,"tags":1613,"type":676,"updated":677,"__hash__":1621},"courses\u002Fcourses\u002Fipmrk.md","Pokročilé metody v rozhodování (IpmrK)",{"type":9,"value":1152,"toc":1593},[1153,1156,1230,1232,1235,1237,1321,1325,1354,1358,1423,1425,1474,1476],[12,1154,1150],{"id":1155},"pokročilé-metody-v-rozhodování-ipmrk",[16,1157,1158,1166],{},[19,1159,1160],{},[22,1161,1162,1164],{},[25,1163],{},[25,1165],{},[30,1167,1168,1177,1186,1195,1203,1211,1221],{},[22,1169,1170,1174],{},[35,1171,1172],{},[38,1173,40],{},[35,1175,1176],{},"IpmrK",[22,1178,1179,1183],{},[35,1180,1181],{},[38,1182,50],{},[35,1184,1185],{},"Fakulta podnikatelská VUT v Brně",[22,1187,1188,1192],{},[35,1189,1190],{},[38,1191,80],{},[35,1193,1194],{},"prof. Ing. Petr Dostál, CSc.",[22,1196,1197,1201],{},[35,1198,1199],{},[38,1200,100],{},[35,1202,103],{},[22,1204,1205,1209],{},[35,1206,1207],{},[38,1208,60],{},[35,1210,63],{},[22,1212,1213,1218],{},[35,1214,1215],{},[38,1216,1217],{},"Jazyk",[35,1219,1220],{},"čeština",[22,1222,1223,1227],{},[35,1224,1225],{},[38,1226,70],{},[35,1228,1229],{},"zkouška (písemný test 0–20 bodů, ECTS) + seminární práce (8–12 stran)",[115,1231,722],{"id":721},[724,1233,1234],{},"Seznámit se s pokročilými a nestandardními metodami analytických a simulačních technik v ekonomii a financích. Důraz na teorii i aplikaci do manažerské praxe.",[115,1236,150],{"id":149},[152,1238,1239,1242,1251,1257,1263,1271,1277,1285,1290,1298,1306,1315,1318],{},[123,1240,1241],{},"Úvod",[123,1243,1244,1250],{},[207,1245,1249],{"className":1246,"dataFsResolvedFilePath":1247,"href":1248},[210],"topics\u002Ffuzzy-logika.md","\u002Fwiki\u002Ffuzzy-logika","Fuzzy logika"," — teorie",[123,1252,1253,1256],{},[207,1254,1249],{"className":1255,"dataFsResolvedFilePath":1247,"href":1248},[210]," + aplikace — Excel",[123,1258,1259,1262],{},[207,1260,1249],{"className":1261,"dataFsResolvedFilePath":1247,"href":1248},[210]," — aplikace MATLAB",[123,1264,1265,1250],{},[207,1266,1270],{"className":1267,"dataFsResolvedFilePath":1268,"href":1269},[210],"topics\u002Fumele-neuronove-site.md","\u002Fwiki\u002Fumele-neuronove-site","Umělé neuronové sítě",[123,1272,1273,1276],{},[207,1274,1270],{"className":1275,"dataFsResolvedFilePath":1268,"href":1269},[210]," + aplikace MATLAB",[123,1278,1279,1250],{},[207,1280,1284],{"className":1281,"dataFsResolvedFilePath":1282,"href":1283},[210],"topics\u002Fgeneticke-algoritmy.md","\u002Fwiki\u002Fgeneticke-algoritmy","Genetické algoritmy",[123,1286,1287,1276],{},[207,1288,1284],{"className":1289,"dataFsResolvedFilePath":1282,"href":1283},[210],[123,1291,1292],{},[207,1293,1297],{"className":1294,"dataFsResolvedFilePath":1295,"href":1296},[210],"topics\u002Fteorie-chaosu.md","\u002Fwiki\u002Fteorie-chaosu","Teorie chaosu",[123,1299,1300],{},[207,1301,1305],{"className":1302,"dataFsResolvedFilePath":1303,"href":1304},[210],"topics\u002Fdatamining.md","\u002Fwiki\u002Fdatamining","Datamining",[123,1307,1308,1314],{},[207,1309,1313],{"className":1310,"dataFsResolvedFilePath":1311,"href":1312},[210],"topics\u002Fpredikce.md","\u002Fwiki\u002Fpredikce","Predikce",", kapitálový trh",[123,1316,1317],{},"Řízení výroby a řízení rizik",[123,1319,1320],{},"Rozhodování",[115,1322,1324],{"id":1323},"hodnocení","Hodnocení",[120,1326,1327,1333],{},[123,1328,1329,1332],{},[38,1330,1331],{},"Zkouška",": písemný test, 0–20 bodů. A: 20–18, B: 17–16, C: 15–14, D: 13–12, E: 11–10, F: 9–0.",[123,1334,1335,1338,1339,1343,1344,1348,1349,1353],{},[38,1336,1337],{},"Seminární práce",": 8–12 stran, individuální zaměření na problematiku z praxe, řešení pomocí ",[207,1340,1342],{"className":1341,"dataFsResolvedFilePath":1247,"href":1248},[210],"fuzzy logiky",", ",[207,1345,1347],{"className":1346,"dataFsResolvedFilePath":1268,"href":1269},[210],"umělých neuronových sítí"," nebo ",[207,1350,1352],{"className":1351,"dataFsResolvedFilePath":1282,"href":1283},[210],"genetických algoritmů",". Nutná úspěšná obhajoba.",[115,1355,1357],{"id":1356},"hlavní-témata","Hlavní témata",[120,1359,1360,1366,1372,1378,1387,1393,1402,1408,1417],{},[123,1361,1362,1365],{},[207,1363,1249],{"className":1364,"dataFsResolvedFilePath":1247,"href":1248},[210]," — modelování rozhodování s vágními pojmy",[123,1367,1368,1371],{},[207,1369,1270],{"className":1370,"dataFsResolvedFilePath":1268,"href":1269},[210]," — učení z dat, klasifikace, predikce",[123,1373,1374,1377],{},[207,1375,1284],{"className":1376,"dataFsResolvedFilePath":1282,"href":1283},[210]," — evoluční optimalizace",[123,1379,1380,1386],{},[207,1381,1385],{"className":1382,"dataFsResolvedFilePath":1383,"href":1384},[210],"topics\u002Fevolucni-algoritmy.md","\u002Fwiki\u002Fevolucni-algoritmy","Evoluční algoritmy"," — metaheuristiky, rojové algoritmy, prohledávací metody",[123,1388,1389,1392],{},[207,1390,1297],{"className":1391,"dataFsResolvedFilePath":1295,"href":1296},[210]," — nelineární dynamické systémy",[123,1394,1395,1401],{},[207,1396,1400],{"className":1397,"dataFsResolvedFilePath":1398,"href":1399},[210],"topics\u002Foptimalizace.md","\u002Fwiki\u002Foptimalizace","Optimalizace"," — hledání minima\u002Fmaxima, MATLAB Optimization Toolbox",[123,1403,1404,1407],{},[207,1405,1305],{"className":1406,"dataFsResolvedFilePath":1303,"href":1304},[210]," — dolování z dat, klastrování, rozhodovací stromy, Witness Miner",[123,1409,1410,1416],{},[207,1411,1415],{"className":1412,"dataFsResolvedFilePath":1413,"href":1414},[210],"topics\u002Fanfis.md","\u002Fwiki\u002Fanfis","ANFIS"," — hybridní propojení fuzzy logiky a neuronových sítí",[123,1418,1419,1422],{},[207,1420,1313],{"className":1421,"dataFsResolvedFilePath":1311,"href":1312},[210]," — prognózování časových řad v ekonomii a financích",[115,1424,607],{"id":606},[120,1426,1427,1434,1440,1447,1454,1460,1467],{},[123,1428,1429,1430,1433],{},"DOSTÁL, P. ",[614,1431,1432],{},"Pokročilé metody analýz a modelování v podnikatelství a veřejné správě",", CERM, 2008",[123,1435,1429,1436,1439],{},[614,1437,1438],{},"Advanced Decision making in Business and Public Services",", CERM, 2011",[123,1441,1442,1443,1446],{},"DOSTÁL, P., RAIS, K., SOJKA, Z. ",[614,1444,1445],{},"Pokročilé metody manažerského rozhodování",", Grada, 2005",[123,1448,1449,1450,1453],{},"ALTROCK, C. ",[614,1451,1452],{},"Fuzzy Logic & Neurofuzzy",", 1996",[123,1455,1456,1457,1453],{},"GATELY, E. ",[614,1458,1459],{},"Neural Network for Financial Forecasting",[123,1461,1462,1463,1466],{},"DAVIS, L. ",[614,1464,1465],{},"Handbook of Genetic Algorithms",", 1991",[123,1468,1469,1470,1473],{},"PETERS, E. ",[614,1471,1472],{},"Fractal Market Analysis",", 1994",[115,1475,196],{"id":195},[120,1477,1478,1486,1495,1504,1513,1522,1531,1540,1549,1557,1566,1575,1584],{},[123,1479,1480,1485],{},[207,1481,213],{"className":1482,"dataFsResolvedFilePath":1483,"href":1484},[210],"summaries\u002Fipmrk-detail-predmetu.md","\u002Fwiki\u002Fipmrk-detail-predmetu"," — základní informace o kurzu",[123,1487,1488,1494],{},[207,1489,1493],{"className":1490,"dataFsResolvedFilePath":1491,"href":1492},[210],"summaries\u002Fipmrk-fuzzy-excel.md","\u002Fwiki\u002Fipmrk-fuzzy-excel","Fuzzy logika — Excel"," — princip fuzzy logiky, funkce členství, pravidla, implementace",[123,1496,1497,1503],{},[207,1498,1502],{"className":1499,"dataFsResolvedFilePath":1500,"href":1501},[210],"summaries\u002Fipmrk-fuzzy-matlab.md","\u002Fwiki\u002Fipmrk-fuzzy-matlab","Fuzzy logika — MATLAB"," — architektura fuzzy systému, návrh modelu",[123,1505,1506,1512],{},[207,1507,1511],{"className":1508,"dataFsResolvedFilePath":1509,"href":1510},[210],"summaries\u002Fipmrk-nn-teorie.md","\u002Fwiki\u002Fipmrk-nn-teorie","Neuronové sítě — teorie"," — perceptron, aktivační funkce, backpropagation",[123,1514,1515,1521],{},[207,1516,1520],{"className":1517,"dataFsResolvedFilePath":1518,"href":1519},[210],"summaries\u002Fipmrk-nn-vypocet.md","\u002Fwiki\u002Fipmrk-nn-vypocet","Neuronové sítě — výpočet"," — ruční učení neuronu, vícevrstvé sítě, trénování",[123,1523,1524,1530],{},[207,1525,1529],{"className":1526,"dataFsResolvedFilePath":1527,"href":1528},[210],"summaries\u002Fipmrk-nn-aplikace.md","\u002Fwiki\u002Fipmrk-nn-aplikace","Neuronové sítě — aplikace"," — ANFIS, scoring, predikce, deep learning",[123,1532,1533,1539],{},[207,1534,1538],{"className":1535,"dataFsResolvedFilePath":1536,"href":1537},[210],"summaries\u002Fipmrk-ga-teorie.md","\u002Fwiki\u002Fipmrk-ga-teorie","Genetické algoritmy — teorie"," — chromozomy, selekce, křížení, mutace",[123,1541,1542,1548],{},[207,1543,1547],{"className":1544,"dataFsResolvedFilePath":1545,"href":1546},[210],"summaries\u002Fipmrk-ga-vyuziti.md","\u002Fwiki\u002Fipmrk-ga-vyuziti","Genetické algoritmy — využití"," — optimalizace, TSP, knapsack, klastrování",[123,1550,1551,1556],{},[207,1552,1297],{"className":1553,"dataFsResolvedFilePath":1554,"href":1555},[210],"summaries\u002Fipmrk-chaos.md","\u002Fwiki\u002Fipmrk-chaos"," — atraktory, fraktály, motýlí efekt, Hurstův exponent",[123,1558,1559,1565],{},[207,1560,1564],{"className":1561,"dataFsResolvedFilePath":1562,"href":1563},[210],"summaries\u002Fipmrk-kniha.md","\u002Fwiki\u002Fipmrk-kniha","Kniha — Pokročilé metody"," — celá učebnice, 7 kapitol, kontrolní otázky, nová témata (evoluční alg., optimalizace, datamining)",[123,1567,1568,1574],{},[207,1569,1573],{"className":1570,"dataFsResolvedFilePath":1571,"href":1572},[210],"summaries\u002Fipmrk-evolucni-algoritmy.md","\u002Fwiki\u002Fipmrk-evolucni-algoritmy","Evoluční algoritmy — principy a přehled"," — pseudokódy, vzorce SA\u002FTabu\u002FACO\u002FPSO\u002FDE\u002FSOMA\u002FAIS\u002FABC\u002FGSO",[123,1576,1577,1583],{},[207,1578,1582],{"className":1579,"dataFsResolvedFilePath":1580,"href":1581},[210],"summaries\u002Fipmrk-optimalizace.md","\u002Fwiki\u002Fipmrk-optimalizace","Optimalizace — MATLAB Optimization Toolbox"," — kompletní syntaxe fmincon\u002Ffminsearch\u002Flinprog\u002Fintlinprog\u002Fga",[123,1585,1586,1592],{},[207,1587,1591],{"className":1588,"dataFsResolvedFilePath":1589,"href":1590},[210],"summaries\u002Fipmrk-datamining.md","\u002Fwiki\u002Fipmrk-datamining","Datamining — techniky a nástroje"," — CRISP-DM, Link analýza, k-means, rozhodovací stromy, Apriori, Witness Miner, MATLAB kód",{"title":641,"searchDepth":642,"depth":642,"links":1594},[1595,1596,1597,1598,1599,1600],{"id":721,"depth":642,"text":722},{"id":149,"depth":642,"text":150},{"id":1323,"depth":642,"text":1324},{"id":1356,"depth":642,"text":1357},{"id":606,"depth":642,"text":607},{"id":195,"depth":642,"text":196},"ipmrk","2026-04-10",{},"\u002Fcourses\u002Fipmrk",{"title":1150,"description":641},[1607,1608,1609,1610,1611],"raw\u002Fipmrk\u002FDetail předmětu.md","raw\u002Fipmrk\u002Fkniha.md","raw\u002Fipmrk\u002Fevolucni-algoritmy-online.md","raw\u002Fipmrk\u002Foptimalizace-online.md","raw\u002Fipmrk\u002Fdatamining-online.md","courses\u002Fipmrk",[1601,1614,1615,1616,1617,1618,1619,1620],"fuzzy","neuronove-site","geneticke-algoritmy","evolucni-algoritmy","chaos","optimalizace","datamining","_iX_YpjZn-5NmPhFSn_DHNExx_u1xi12WJEbWAHjXpg",{"ipmrk":1623,"imork":1624,"imek":1625},25,41,21,{"page":1627,"collection":7393},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":7381,"navigation":664,"path":7382,"seo":7383,"sources":7384,"stem":7385,"tags":7386,"type":7391,"updated":677,"__hash__":7392},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":1631,"toc":7353},[1632,1635,1660,1664,1692,1696,1744,1839,1883,1887,1914,1921,1925,1935,1947,1951,1980,1989,2049,2055,2058,2064,2093,2099,2197,2364,2660,2664,2744,2750,2754,2855,2921,3092,3096,3176,3207,3234,3240,3273,3351,3438,3442,3505,3511,3514,3520,3634,3719,3764,3768,3814,3823,4140,4145,4169,4198,4265,4362,4366,4373,4380,4452,4572,4656,4659,4665,4993,4997,5160,5168,5304,5312,5550,5558,5561,5566,5823,5827,6001,6135,6172,6218,6221,6351,6441,6459,6463,6470,6476,6537,6540,6564,6567,6573,6576,6582,6585,6589,6628,6687,6876,6880,6954,6960,6967,6971,6977,7120,7124,7130,7166,7171,7348],[12,1633,1629],{"id":1634},"elasticita-poptávky-a-nabídky",[1636,1637,1638],"blockquote",{},[724,1639,1640,1643,1644,1647,1648,1651,1652,1655,1656,1659],{},[883,1641,1642],{},"!abstract"," TL;DR\n",[38,1645,1646],{},"Elasticita"," 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: ",[38,1649,1650],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,1653,1654],{},"křížově-cenovou elasticitu"," a ",[38,1657,1658],{},"důchodovou elasticitu",".",[115,1661,1663],{"id":1662},"úvod-motivace","Úvod — motivace",[724,1665,1666,1667,1670,1671,1674,1675,1678,1679,1682,1683,1686,1687,1691],{},"Termín ",[614,1668,1669],{},"elasticita"," (alternativně ",[614,1672,1673],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,1676,1677],{},"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 ",[614,1680,1681],{},"cenové elasticity poptávky"," (resp. ",[614,1684,1685],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,1688,1690],{"className":1689,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace",").",[198,1693,1695],{"id":1694},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,1697,1698,1699,1722,1723,1743],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,1700,1702],{"className":1701},[886],[888,1703,1704],{"xmlns":890},[892,1705,1706,1719],{},[895,1707,1708,1711,1715],{},[898,1709,1710],{},"P",[1712,1713,1714],"mo",{},"=",[1716,1717,1718],"mn",{},"10",[902,1720,1721],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,1724,1726],{"className":1725},[886],[888,1727,1728],{"xmlns":890},[892,1729,1730,1740],{},[895,1731,1732,1735,1737],{},[898,1733,1734],{},"Q",[1712,1736,1714],{},[1716,1738,1739],{},"100",[902,1741,1742],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,1745,1746,1796],{},[123,1747,1748,1751,1752,1795],{},[38,1749,1750],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,1753,1755],{"className":1754},[886],[888,1756,1757],{"xmlns":890},[892,1758,1759,1792],{},[895,1760,1761,1765,1768,1770,1773,1776,1778,1781,1784,1787,1789],{},[1762,1763,1764],"mtext",{},"  ",[1712,1766,1767],{},"⇒",[1762,1769,1764],{},[898,1771,1772],{},"T",[898,1774,1775],{},"R",[1712,1777,1714],{},[1716,1779,1780],{},"9",[1712,1782,1783],{},"⋅",[1716,1785,1786],{},"110",[1712,1788,1714],{},[1716,1790,1791],{},"990",[902,1793,1794],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,1797,1798,1801,1802,1838],{},[38,1799,1800],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,1803,1805],{"className":1804},[886],[888,1806,1807],{"xmlns":890},[892,1808,1809,1835],{},[895,1810,1811,1813,1815,1817,1819,1821,1823,1825,1827,1830,1832],{},[1762,1812,1764],{},[1712,1814,1767],{},[1762,1816,1764],{},[898,1818,1772],{},[898,1820,1775],{},[1712,1822,1714],{},[1716,1824,1780],{},[1712,1826,1783],{},[1716,1828,1829],{},"120",[1712,1831,1714],{},[1716,1833,1834],{},"1080",[902,1836,1837],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,1840,1841,1842,1845,1846,1849,1850,1853,1854,1857,1858,1861,1862,1878,1879,1882],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,1843,1844],{},"nerozumné",", na Trhu 2 ",[38,1847,1848],{},"rozumné",". Trh 2 je ",[38,1851,1852],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,1855,1856],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,1859,1860],{},"neelastická"," a vyššího ",[883,1863,1865],{"className":1864},[886],[888,1866,1867],{"xmlns":890},[892,1868,1869,1875],{},[895,1870,1871,1873],{},[898,1872,1772],{},[898,1874,1775],{},[902,1876,1877],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,1880,1881],{},"zvýšením"," ceny.",[198,1884,1886],{"id":1885},"hypotéza-41","Hypotéza 4.1",[1636,1888,1889],{},[724,1890,1891,1892],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,1893,1895],{"className":1894},[886],[888,1896,1897],{"xmlns":890},[892,1898,1899,1911],{},[895,1900,1901,1905,1908],{},[1712,1902,1904],{"stretchy":1903},"false","(",[1716,1906,1907],{},"4.1",[1712,1909,1910],{"stretchy":1903},")",[902,1912,1913],{"encoding":904},"(4.1)",[724,1915,1916,1917,1920],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,1918,1919],{},"procentní změny"," obou faktorů.",[115,1922,1924],{"id":1923},"pojem-elasticity","Pojem elasticity",[724,1926,1927,1928,1930,1931,1934],{},"Obecně ",[38,1929,1669],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,1932,1933],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1636,1936,1937],{},[724,1938,1939,1942,1943,1946],{},[883,1940,1941],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,1944,1945],{},"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.",[115,1948,1950],{"id":1949},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,1952,1953,1954,1979],{},"Nechť ",[883,1955,1957],{"className":1956},[886],[888,1958,1959],{"xmlns":890},[892,1960,1961,1976],{},[895,1962,1963,1965,1967,1970,1972,1974],{},[898,1964,1734],{},[1712,1966,1714],{},[898,1968,1969],{},"D",[1712,1971,1904],{"stretchy":1903},[898,1973,1710],{},[1712,1975,1910],{"stretchy":1903},[902,1977,1978],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,1981,1982],{},[883,1983,1988],{"className":1984,"title":1986,"style":1987},[1985],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,1990,1991,1992,1655,2010,2026,2027,2048],{},"Znaménko minus je korekce: změny ",[883,1993,1995],{"className":1994},[886],[888,1996,1997],{"xmlns":890},[892,1998,1999,2007],{},[895,2000,2001,2005],{},[898,2002,2004],{"mathvariant":2003},"normal","Δ",[898,2006,1734],{},[902,2008,2009],{"encoding":904},"\\Delta Q",[883,2011,2013],{"className":2012},[886],[888,2014,2015],{"xmlns":890},[892,2016,2017,2023],{},[895,2018,2019,2021],{},[898,2020,2004],{"mathvariant":2003},[898,2022,1710],{},[902,2024,2025],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,2028,2030],{"className":2029},[886],[888,2031,2032],{"xmlns":890},[892,2033,2034,2045],{},[895,2035,2036],{},[2037,2038,2039,2042],"msup",{},[898,2040,2041],{},"E",[898,2043,2044],{},"A",[902,2046,2047],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,2050,2051],{},[883,2052,2054],{"className":2053,"title":1986,"style":1987},[1985],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,2056,2057],{},"Po dosazení:",[724,2059,2060],{},[883,2061,2063],{"className":2062,"title":1986,"style":1987},[1985],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,2065,2066,2067,2089,2090,2092],{},"Limitním přechodem ",[883,2068,2070],{"className":2069},[886],[888,2071,2072],{"xmlns":890},[892,2073,2074,2086],{},[895,2075,2076,2078,2080,2083],{},[898,2077,2004],{"mathvariant":2003},[898,2079,1710],{},[1712,2081,2082],{},"→",[1716,2084,2085],{},"0",[902,2087,2088],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,2091,1681],{}," (price elasticity of demand):",[724,2094,2095],{},[883,2096,2098],{"className":2097,"title":1986,"style":1987},[1985],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,2100,2101,2102,2125,2126,2149,2150,2174,2175,2196],{},"kde ",[883,2103,2105],{"className":2104},[886],[888,2106,2107],{"xmlns":890},[892,2108,2109,2123],{},[895,2110,2111,2113,2115,2117,2119,2121],{},[898,2112,1734],{},[1712,2114,1714],{},[898,2116,1969],{},[1712,2118,1904],{"stretchy":1903},[898,2120,1710],{},[1712,2122,1910],{"stretchy":1903},[902,2124,1978],{"encoding":904},". Pro pevnou cenu ",[883,2127,2129],{"className":2128},[886],[888,2130,2131],{"xmlns":890},[892,2132,2133,2146],{},[895,2134,2135,2137,2139],{},[898,2136,1710],{},[1712,2138,1714],{},[2037,2140,2141,2143],{},[898,2142,1710],{},[1712,2144,2145],{},"∗",[902,2147,2148],{"encoding":904},"P = P^*"," se ",[883,2151,2153],{"className":2152},[886],[888,2154,2155],{"xmlns":890},[892,2156,2157,2171],{},[895,2158,2159,2161,2163,2169],{},[898,2160,2041],{},[1712,2162,1904],{"stretchy":1903},[2037,2164,2165,2167],{},[898,2166,1710],{},[1712,2168,2145],{},[1712,2170,1910],{"stretchy":1903},[902,2172,2173],{"encoding":904},"E(P^*)"," nazývá ",[614,2176,2177,2178],{},"elasticita poptávky při ceně ",[883,2179,2181],{"className":2180},[886],[888,2182,2183],{"xmlns":890},[892,2184,2185,2193],{},[895,2186,2187],{},[2037,2188,2189,2191],{},[898,2190,1710],{},[1712,2192,2145],{},[902,2194,2195],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1636,2198,2199],{},[724,2200,2201,2204,2205,2226,2227,2258,2259,2288,2289,1343,2308,1343,2326,2344,2345,2360,2361,1659],{},[883,2202,2203],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,2206,2207,2208],{},"explicitní ",[883,2209,2211],{"className":2210},[886],[888,2212,2213],{"xmlns":890},[892,2214,2215,2223],{},[895,2216,2217,2220],{},[1712,2218,2219],{},"−",[1716,2221,2222],{},"1",[902,2224,2225],{"encoding":904},"-1"," právě proto, že ",[883,2228,2230],{"className":2229},[886],[888,2231,2232],{"xmlns":890},[892,2233,2234,2255],{},[895,2235,2236,2244,2246,2248,2250,2253],{},[2037,2237,2238,2240],{},[898,2239,1734],{},[1712,2241,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},"0em","′",[1712,2245,1904],{"stretchy":1903},[898,2247,1710],{},[1712,2249,1910],{"stretchy":1903},[1712,2251,2252],{},"\u003C",[1716,2254,2085],{},[902,2256,2257],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,2260,2262],{"className":2261},[886],[888,2263,2264],{"xmlns":890},[892,2265,2266,2285],{},[895,2267,2268,2270,2272,2278,2280,2283],{},[898,2269,2041],{},[1712,2271,1904],{"stretchy":1903},[2037,2273,2274,2276],{},[898,2275,1710],{},[1712,2277,2145],{},[1712,2279,1910],{"stretchy":1903},[1712,2281,2282],{},"≥",[1716,2284,2085],{},[902,2286,2287],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,2290,2292],{"className":2291},[886],[888,2293,2294],{"xmlns":890},[892,2295,2296,2305],{},[895,2297,2298,2300,2303],{},[898,2299,2041],{},[1712,2301,2302],{},">",[1716,2304,2222],{},[902,2306,2307],{"encoding":904},"E > 1",[883,2309,2311],{"className":2310},[886],[888,2312,2313],{"xmlns":890},[892,2314,2315,2323],{},[895,2316,2317,2319,2321],{},[898,2318,2041],{},[1712,2320,2252],{},[1716,2322,2222],{},[902,2324,2325],{"encoding":904},"E \u003C 1",[883,2327,2329],{"className":2328},[886],[888,2330,2331],{"xmlns":890},[892,2332,2333,2341],{},[895,2334,2335,2337,2339],{},[898,2336,2041],{},[1712,2338,1714],{},[1716,2340,2222],{},[902,2342,2343],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,2346,2348],{"className":2347},[886],[888,2349,2350],{"xmlns":890},[892,2351,2352,2358],{},[895,2353,2354,2356],{},[1712,2355,2219],{},[1716,2357,2222],{},[902,2359,2225],{"encoding":904}," 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 ",[38,2362,2363],{},"absolutní hodnotou",[1636,2365,2366,2386],{},[724,2367,2368,2371,2372,2385],{},[883,2369,2370],{},"!tip"," Postup: jak spočítat ",[883,2373,2375],{"className":2374},[886],[888,2376,2377],{"xmlns":890},[892,2378,2379,2383],{},[895,2380,2381],{},[898,2382,2041],{},[902,2384,2041],{"encoding":904}," v bodě",[152,2387,2388,2440,2481,2534,2603],{},[123,2389,2390,2391,2414,2415,2439],{},"Zapište ",[883,2392,2394],{"className":2393},[886],[888,2395,2396],{"xmlns":890},[892,2397,2398,2412],{},[895,2399,2400,2402,2404,2406,2408,2410],{},[898,2401,1734],{},[1712,2403,1714],{},[898,2405,1969],{},[1712,2407,1904],{"stretchy":1903},[898,2409,1710],{},[1712,2411,1910],{"stretchy":1903},[902,2413,1978],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,2416,2418],{"className":2417},[886],[888,2419,2420],{"xmlns":890},[892,2421,2422,2436],{},[895,2423,2424,2426,2428,2430,2432,2434],{},[898,2425,1710],{},[1712,2427,1714],{},[898,2429,1969],{},[1712,2431,1904],{"stretchy":1903},[898,2433,1734],{},[1712,2435,1910],{"stretchy":1903},[902,2437,2438],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,2441,2442,2443,1659],{},"Spočítejte derivaci ",[883,2444,2446],{"className":2445},[886],[888,2447,2448],{"xmlns":890},[892,2449,2450,2478],{},[895,2451,2452,2458,2460,2462,2464,2466,2469,2471,2474,2476],{},[2037,2453,2454,2456],{},[898,2455,1734],{},[1712,2457,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,2459,1904],{"stretchy":1903},[898,2461,1710],{},[1712,2463,1910],{"stretchy":1903},[1712,2465,1714],{},[898,2467,2468],{"mathvariant":2003},"d",[898,2470,1734],{},[898,2472,2473],{"mathvariant":2003},"\u002F",[898,2475,2468],{"mathvariant":2003},[898,2477,1710],{},[902,2479,2480],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,2482,2483,2484,2501,2502,1659],{},"Dosaďte zadanou cenu ",[883,2485,2487],{"className":2486},[886],[888,2488,2489],{"xmlns":890},[892,2490,2491,2499],{},[895,2492,2493],{},[2037,2494,2495,2497],{},[898,2496,1710],{},[1712,2498,2145],{},[902,2500,2195],{"encoding":904}," a dopočítejte odpovídající ",[883,2503,2505],{"className":2504},[886],[888,2506,2507],{"xmlns":890},[892,2508,2509,2531],{},[895,2510,2511,2517,2519,2521,2523,2529],{},[2037,2512,2513,2515],{},[898,2514,1734],{},[1712,2516,2145],{},[1712,2518,1714],{},[898,2520,1969],{},[1712,2522,1904],{"stretchy":1903},[2037,2524,2525,2527],{},[898,2526,1710],{},[1712,2528,2145],{},[1712,2530,1910],{"stretchy":1903},[902,2532,2533],{"encoding":904},"Q^* = D(P^*)",[123,2535,2536,2537,1659],{},"Dosaďte do (4.5): ",[883,2538,2540],{"className":2539},[886],[888,2541,2542],{"xmlns":890},[892,2543,2544,2600],{},[895,2545,2546,2548,2550,2556,2558,2560,2562,2581,2584,2590,2592,2598],{},[898,2547,2041],{},[1712,2549,1904],{"stretchy":1903},[2037,2551,2552,2554],{},[898,2553,1710],{},[1712,2555,2145],{},[1712,2557,1910],{"stretchy":1903},[1712,2559,1714],{},[1712,2561,2219],{},[2563,2564,2566],"mstyle",{"scriptlevel":2085,"displaystyle":2565},"true",[2567,2568,2569,2575],"mfrac",{},[2037,2570,2571,2573],{},[898,2572,1710],{},[1712,2574,2145],{},[2037,2576,2577,2579],{},[898,2578,1734],{},[1712,2580,2145],{},[1762,2582,2583],{}," ",[2037,2585,2586,2588],{},[898,2587,1734],{},[1712,2589,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,2591,1904],{"stretchy":1903},[2037,2593,2594,2596],{},[898,2595,1710],{},[1712,2597,2145],{},[1712,2599,1910],{"stretchy":1903},[902,2601,2602],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,2604,2605,2606,2623,2624,2641,2642,2659],{},"Klasifikujte: ",[883,2607,2609],{"className":2608},[886],[888,2610,2611],{"xmlns":890},[892,2612,2613,2621],{},[895,2614,2615,2617,2619],{},[898,2616,2041],{},[1712,2618,2302],{},[1716,2620,2222],{},[902,2622,2307],{"encoding":904}," elastická, ",[883,2625,2627],{"className":2626},[886],[888,2628,2629],{"xmlns":890},[892,2630,2631,2639],{},[895,2632,2633,2635,2637],{},[898,2634,2041],{},[1712,2636,1714],{},[1716,2638,2222],{},[902,2640,2343],{"encoding":904}," jednotková, ",[883,2643,2645],{"className":2644},[886],[888,2646,2647],{"xmlns":890},[892,2648,2649,2657],{},[895,2650,2651,2653,2655],{},[898,2652,2041],{},[1712,2654,2252],{},[1716,2656,2222],{},[902,2658,2325],{"encoding":904}," neelastická.",[198,2661,2663],{"id":2662},"interpretace-46","Interpretace (4.6)",[1636,2665,2666],{},[724,2667,2668,2669,2692,2693,2706,2707,2724,2725],{},"Číslo ",[883,2670,2672],{"className":2671},[886],[888,2673,2674],{"xmlns":890},[892,2675,2676,2690],{},[895,2677,2678,2680,2682,2688],{},[898,2679,2041],{},[1712,2681,1904],{"stretchy":1903},[2037,2683,2684,2686],{},[898,2685,1710],{},[1712,2687,2145],{},[1712,2689,1910],{"stretchy":1903},[902,2691,2173],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,2694,2696],{"className":2695},[886],[888,2697,2698],{"xmlns":890},[892,2699,2700,2704],{},[895,2701,2702],{},[898,2703,1734],{},[902,2705,1734],{"encoding":904},", jestliže se cena ",[883,2708,2710],{"className":2709},[886],[888,2711,2712],{"xmlns":890},[892,2713,2714,2722],{},[895,2715,2716],{},[2037,2717,2718,2720],{},[898,2719,1710],{},[1712,2721,2145],{},[902,2723,2195],{"encoding":904}," změní o 1 %. ",[883,2726,2728],{"className":2727},[886],[888,2729,2730],{"xmlns":890},[892,2731,2732,2741],{},[895,2733,2734,2736,2739],{},[1712,2735,1904],{"stretchy":1903},[1716,2737,2738],{},"4.6",[1712,2740,1910],{"stretchy":1903},[902,2742,2743],{"encoding":904},"(4.6)",[724,2745,2746,2749],{},[38,2747,2748],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,2751,2753],{"id":2752},"příklad-41","Příklad 4.1",[724,2755,2756,2757,2793,2794,1343,2820,2854],{},"Poptávka ",[883,2758,2760],{"className":2759},[886],[888,2761,2762],{"xmlns":890},[892,2763,2764,2790],{},[895,2765,2766,2768,2770,2772,2774,2776,2778,2780,2783,2785,2788],{},[898,2767,1710],{},[1712,2769,1714],{},[898,2771,1969],{},[1712,2773,1904],{"stretchy":1903},[898,2775,1734],{},[1712,2777,1910],{"stretchy":1903},[1712,2779,1714],{},[1716,2781,2782],{},"50",[1712,2784,2219],{},[1716,2786,2787],{},"2",[898,2789,1734],{},[902,2791,2792],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,2795,2797],{"className":2796},[886],[888,2798,2799],{"xmlns":890},[892,2800,2801,2817],{},[895,2802,2803,2805,2807,2810,2812,2815],{},[898,2804,1734],{},[1712,2806,1714],{},[1716,2808,2809],{},"25",[1712,2811,2219],{},[1716,2813,2814],{},"0,5",[898,2816,1710],{},[902,2818,2819],{"encoding":904},"Q = 25 - 0{,}5P",[883,2821,2823],{"className":2822},[886],[888,2824,2825],{"xmlns":890},[892,2826,2827,2851],{},[895,2828,2829,2845,2847,2849],{},[2563,2830,2831],{"scriptlevel":2085,"displaystyle":2565},[2567,2832,2833,2839],{},[895,2834,2835,2837],{},[898,2836,2468],{"mathvariant":2003},[898,2838,1734],{},[895,2840,2841,2843],{},[898,2842,2468],{"mathvariant":2003},[898,2844,1710],{},[1712,2846,1714],{},[1712,2848,2219],{},[1716,2850,2814],{},[902,2852,2853],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",":",[724,2856,2857],{},[883,2858,2860],{"className":2859},[886],[888,2861,2862],{"xmlns":890},[892,2863,2864,2918],{},[895,2865,2866,2868,2870,2872,2886,2888,2890,2892,2894,2896,2898,2916],{},[898,2867,2041],{},[1712,2869,1714],{},[1712,2871,2219],{},[2567,2873,2874,2876],{},[898,2875,1710],{},[895,2877,2878,2880,2882,2884],{},[1716,2879,2809],{},[1712,2881,2219],{},[1716,2883,2814],{},[898,2885,1710],{},[1712,2887,1783],{},[1712,2889,1904],{"stretchy":1903},[1712,2891,2219],{},[1716,2893,2814],{},[1712,2895,1910],{"stretchy":1903},[1712,2897,1714],{},[2567,2899,2900,2906],{},[895,2901,2902,2904],{},[1716,2903,2814],{},[898,2905,1710],{},[895,2907,2908,2910,2912,2914],{},[1716,2909,2809],{},[1712,2911,2219],{},[1716,2913,2814],{},[898,2915,1710],{},[898,2917,1659],{"mathvariant":2003},[902,2919,2920],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,2922,2923,2924,1343,2948,1343,2979,1343,3003,3028,3029,3052,3053,3072,3073,1691],{},"Potom ",[883,2925,2927],{"className":2926},[886],[888,2928,2929],{"xmlns":890},[892,2930,2931,2945],{},[895,2932,2933,2935,2937,2939,2941,2943],{},[898,2934,2041],{},[1712,2936,1904],{"stretchy":1903},[1716,2938,2085],{},[1712,2940,1910],{"stretchy":1903},[1712,2942,1714],{},[1716,2944,2085],{},[902,2946,2947],{"encoding":904},"E(0)=0",[883,2949,2951],{"className":2950},[886],[888,2952,2953],{"xmlns":890},[892,2954,2955,2976],{},[895,2956,2957,2959,2961,2963,2965,2967],{},[898,2958,2041],{},[1712,2960,1904],{"stretchy":1903},[1716,2962,1718],{},[1712,2964,1910],{"stretchy":1903},[1712,2966,1714],{},[2563,2968,2969],{"scriptlevel":2085,"displaystyle":1903},[2567,2970,2971,2973],{},[1716,2972,2222],{},[1716,2974,2975],{},"4",[902,2977,2978],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,2980,2982],{"className":2981},[886],[888,2983,2984],{"xmlns":890},[892,2985,2986,3000],{},[895,2987,2988,2990,2992,2994,2996,2998],{},[898,2989,2041],{},[1712,2991,1904],{"stretchy":1903},[1716,2993,2809],{},[1712,2995,1910],{"stretchy":1903},[1712,2997,1714],{},[1716,2999,2222],{},[902,3001,3002],{"encoding":904},"E(25)=1",[883,3004,3006],{"className":3005},[886],[888,3007,3008],{"xmlns":890},[892,3009,3010,3025],{},[895,3011,3012,3014,3016,3019,3021,3023],{},[898,3013,2041],{},[1712,3015,1904],{"stretchy":1903},[1716,3017,3018],{},"40",[1712,3020,1910],{"stretchy":1903},[1712,3022,1714],{},[1716,3024,2975],{},[902,3026,3027],{"encoding":904},"E(40)=4",". Např. ",[883,3030,3032],{"className":3031},[886],[888,3033,3034],{"xmlns":890},[892,3035,3036,3050],{},[895,3037,3038,3040,3042,3044,3046,3048],{},[898,3039,2041],{},[1712,3041,1904],{"stretchy":1903},[1716,3043,3018],{},[1712,3045,1910],{"stretchy":1903},[1712,3047,1714],{},[1716,3049,2975],{},[902,3051,3027],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,3054,3056],{"className":3055},[886],[888,3057,3058],{"xmlns":890},[892,3059,3060,3069],{},[895,3061,3062,3064,3066],{},[898,3063,1734],{},[1712,3065,1714],{},[1716,3067,3068],{},"5",[902,3070,3071],{"encoding":904},"Q=5"," na ",[883,3074,3076],{"className":3075},[886],[888,3077,3078],{"xmlns":890},[892,3079,3080,3089],{},[895,3081,3082,3084,3086],{},[898,3083,1734],{},[1712,3085,1714],{},[1716,3087,3088],{},"4,8",[902,3090,3091],{"encoding":904},"Q=4{,}8",[198,3093,3095],{"id":3094},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,3097,3098,3156],{},[123,3099,3100,3103,3104,3121,3122,1659],{},[38,3101,3102],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,3105,3107],{"className":3106},[886],[888,3108,3109],{"xmlns":890},[892,3110,3111,3119],{},[895,3112,3113],{},[2037,3114,3115,3117],{},[898,3116,2041],{},[898,3118,2044],{},[902,3120,2047],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,3123,3125],{"className":3124},[886],[888,3126,3127],{"xmlns":890},[892,3128,3129,3153],{},[895,3130,3131,3134,3136,3139,3141,3143,3146,3148,3150],{},[1712,3132,3133],{"stretchy":1903},"⟨",[898,3135,1710],{},[1712,3137,3138],{"separator":2565},",",[1762,3140,2583],{},[898,3142,1710],{},[1712,3144,3145],{},"+",[898,3147,2004],{"mathvariant":2003},[898,3149,1710],{},[1712,3151,3152],{"stretchy":1903},"⟩",[902,3154,3155],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,3157,3158,3161,3162,3175],{},[38,3159,3160],{},"Bodová"," (okamžitá) elasticita: ",[883,3163,3165],{"className":3164},[886],[888,3166,3167],{"xmlns":890},[892,3168,3169,3173],{},[895,3170,3171],{},[898,3172,2041],{},[902,3174,2041],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,3177,3179,3180,3193,3194],{"id":3178},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,3181,3183],{"className":3182},[886],[888,3184,3185],{"xmlns":890},[892,3186,3187,3191],{},[895,3188,3189],{},[898,3190,1710],{},[902,3192,1710],{"encoding":904}," jako funkce ",[883,3195,3197],{"className":3196},[886],[888,3198,3199],{"xmlns":890},[892,3200,3201,3205],{},[895,3202,3203],{},[898,3204,1734],{},[902,3206,1734],{"encoding":904},[724,3208,3209,3210,3233],{},"Pokud je poptávka zadaná ve tvaru ",[883,3211,3213],{"className":3212},[886],[888,3214,3215],{"xmlns":890},[892,3216,3217,3231],{},[895,3218,3219,3221,3223,3225,3227,3229],{},[898,3220,1710],{},[1712,3222,1714],{},[898,3224,1969],{},[1712,3226,1904],{"stretchy":1903},[898,3228,1734],{},[1712,3230,1910],{"stretchy":1903},[902,3232,2438],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,3235,3236],{},[883,3237,3239],{"className":3238,"title":1986,"style":1987},[1985],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,3241,3242,3245,3246,3272],{},[38,3243,3244],{},"Příklad 4.3."," ",[883,3247,3249],{"className":3248},[886],[888,3250,3251],{"xmlns":890},[892,3252,3253,3269],{},[895,3254,3255,3257,3259,3261,3263],{},[898,3256,1710],{},[1712,3258,1714],{},[1716,3260,1739],{},[1712,3262,2219],{},[2037,3264,3265,3267],{},[898,3266,1734],{},[1716,3268,2787],{},[902,3270,3271],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,3274,3275],{},[883,3276,3278],{"className":3277},[886],[888,3279,3280],{"xmlns":890},[892,3281,3282,3348],{},[895,3283,3284,3286,3288,3290,3306,3308,3320,3322,3346],{},[898,3285,2041],{},[1712,3287,1714],{},[1712,3289,2219],{},[2567,3291,3292,3304],{},[895,3293,3294,3296,3298],{},[1716,3295,1739],{},[1712,3297,2219],{},[2037,3299,3300,3302],{},[898,3301,1734],{},[1716,3303,2787],{},[898,3305,1734],{},[1712,3307,1783],{},[2567,3309,3310,3312],{},[1716,3311,2222],{},[895,3313,3314,3316,3318],{},[1712,3315,2219],{},[1716,3317,2787],{},[898,3319,1734],{},[1712,3321,1714],{},[2567,3323,3324,3336],{},[895,3325,3326,3328,3330],{},[1716,3327,1739],{},[1712,3329,2219],{},[2037,3331,3332,3334],{},[898,3333,1734],{},[1716,3335,2787],{},[895,3337,3338,3340],{},[1716,3339,2787],{},[2037,3341,3342,3344],{},[898,3343,1734],{},[1716,3345,2787],{},[898,3347,1659],{"mathvariant":2003},[902,3349,3350],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,3352,3353,3354,3381,3382,3401,3402,1659],{},"Z rovnice ",[883,3355,3357],{"className":3356},[886],[888,3358,3359],{"xmlns":890},[892,3360,3361,3378],{},[895,3362,3363,3365,3367,3373,3375],{},[1716,3364,1739],{},[1712,3366,2219],{},[2037,3368,3369,3371],{},[898,3370,1734],{},[1716,3372,2787],{},[1712,3374,1714],{},[1716,3376,3377],{},"36",[902,3379,3380],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,3383,3385],{"className":3384},[886],[888,3386,3387],{"xmlns":890},[892,3388,3389,3398],{},[895,3390,3391,3393,3395],{},[898,3392,1734],{},[1712,3394,1714],{},[1716,3396,3397],{},"8",[902,3399,3400],{"encoding":904},"Q = 8",", tedy ",[883,3403,3405],{"className":3404},[886],[888,3406,3407],{"xmlns":890},[892,3408,3409,3435],{},[895,3410,3411,3413,3415,3417,3419,3421,3430,3432],{},[898,3412,2041],{},[1712,3414,1904],{"stretchy":1903},[1716,3416,3397],{},[1712,3418,1910],{"stretchy":1903},[1712,3420,1714],{},[2563,3422,3423],{"scriptlevel":2085,"displaystyle":1903},[2567,3424,3425,3427],{},[1716,3426,3377],{},[1716,3428,3429],{},"128",[1712,3431,1714],{},[1716,3433,3434],{},"0,281",[902,3436,3437],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,3439,3441],{"id":3440},"přibližné-změny","Přibližné změny",[724,3443,3444,3445,3481,3482,3504],{},"Diferenciál ",[883,3446,3448],{"className":3447},[886],[888,3449,3450],{"xmlns":890},[892,3451,3452,3478],{},[895,3453,3454,3456,3458,3460,3466,3468,3470,3472,3474,3476],{},[898,3455,2468],{"mathvariant":2003},[898,3457,1734],{},[1712,3459,1714],{},[2037,3461,3462,3464],{},[898,3463,1734],{},[1712,3465,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,3467,1904],{"stretchy":1903},[898,3469,1710],{},[1712,3471,1910],{"stretchy":1903},[1762,3473,2583],{},[898,3475,2468],{"mathvariant":2003},[898,3477,1710],{},[902,3479,3480],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,3483,3485],{"className":3484},[886],[888,3486,3487],{"xmlns":890},[892,3488,3489,3501],{},[895,3490,3491,3493,3495,3497,3499],{},[898,3492,2468],{"mathvariant":2003},[898,3494,1710],{},[1712,3496,1714],{},[898,3498,2004],{"mathvariant":2003},[898,3500,1710],{},[902,3502,3503],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,3506,3507],{},[883,3508,3510],{"className":3509,"title":1986,"style":1987},[1985],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,3512,3513],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,3515,3516],{},[883,3517,3519],{"className":3518,"title":1986,"style":1987},[1985],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,3521,3522,3245,3525,3560,3561,3580,3581,3615,3616,3633],{},[38,3523,3524],{},"Příklad 4.5.",[883,3526,3528],{"className":3527},[886],[888,3529,3530],{"xmlns":890},[892,3531,3532,3557],{},[895,3533,3534,3536,3538,3540,3546,3548,3550,3552,3554],{},[898,3535,1710],{},[1712,3537,1714],{},[1712,3539,2219],{},[2037,3541,3542,3544],{},[898,3543,1734],{},[1716,3545,2787],{},[1712,3547,2219],{},[1716,3549,2975],{},[898,3551,1734],{},[1712,3553,3145],{},[1716,3555,3556],{},"96",[902,3558,3559],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,3562,3564],{"className":3563},[886],[888,3565,3566],{"xmlns":890},[892,3567,3568,3577],{},[895,3569,3570,3572,3574],{},[898,3571,1710],{},[1712,3573,1714],{},[1716,3575,3576],{},"51",[902,3578,3579],{"encoding":904},"P=51",". Z rovnice ",[883,3582,3584],{"className":3583},[886],[888,3585,3586],{"xmlns":890},[892,3587,3588,3612],{},[895,3589,3590,3592,3594,3596,3602,3604,3606,3608,3610],{},[1716,3591,3576],{},[1712,3593,1714],{},[1712,3595,2219],{},[2037,3597,3598,3600],{},[898,3599,1734],{},[1716,3601,2787],{},[1712,3603,2219],{},[1716,3605,2975],{},[898,3607,1734],{},[1712,3609,3145],{},[1716,3611,3556],{},[902,3613,3614],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,3617,3619],{"className":3618},[886],[888,3620,3621],{"xmlns":890},[892,3622,3623,3631],{},[895,3624,3625,3627,3629],{},[898,3626,1734],{},[1712,3628,1714],{},[1716,3630,3068],{},[902,3632,3071],{"encoding":904},". Elasticita:",[724,3635,3636],{},[883,3637,3639],{"className":3638},[886],[888,3640,3641],{"xmlns":890},[892,3642,3643,3716],{},[895,3644,3645,3647,3649,3687,3689,3693,3695,3697,3699,3701,3703,3710,3713],{},[898,3646,2041],{},[1712,3648,1714],{},[2567,3650,3651,3671],{},[895,3652,3653,3655,3661,3663,3665,3667,3669],{},[1712,3654,2219],{},[2037,3656,3657,3659],{},[898,3658,1734],{},[1716,3660,2787],{},[1712,3662,2219],{},[1716,3664,2975],{},[898,3666,1734],{},[1712,3668,3145],{},[1716,3670,3556],{},[895,3672,3673,3675,3677,3679,3681,3683,3685],{},[898,3674,1734],{},[1712,3676,1904],{"stretchy":1903},[1716,3678,2787],{},[898,3680,1734],{},[1712,3682,3145],{},[1716,3684,2975],{},[1712,3686,1910],{"stretchy":1903},[1712,3688,3138],{"separator":2565},[3690,3691],"mspace",{"width":3692},"2em",[898,3694,2041],{},[1712,3696,1904],{"stretchy":1903},[1716,3698,3068],{},[1712,3700,1910],{"stretchy":1903},[1712,3702,1714],{},[2567,3704,3705,3707],{},[1716,3706,3576],{},[1716,3708,3709],{},"70",[1712,3711,3712],{},"≐",[1716,3714,3715],{},"0,728.",[902,3717,3718],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,3720,3721,3722,1659],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,3723,3725],{"className":3724},[886],[888,3726,3727],{"xmlns":890},[892,3728,3729,3761],{},[895,3730,3731,3733,3735,3738,3741,3743,3746,3748,3750,3752,3754,3757,3759],{},[898,3732,2004],{"mathvariant":2003},[898,3734,1734],{},[898,3736,3737],{"mathvariant":2003},"%",[1712,3739,3740],{},"≈",[1712,3742,2219],{},[1716,3744,3745],{},"0,728",[1712,3747,1783],{},[1716,3749,2787],{},[1712,3751,1714],{},[1712,3753,2219],{},[1716,3755,3756],{},"1,456",[1762,3758,2583],{},[898,3760,3737],{"mathvariant":2003},[902,3762,3763],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,3765,3767],{"id":3766},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,3769,3770,3771,3794,3795,2854],{},"V závislosti na hodnotě ",[883,3772,3774],{"className":3773},[886],[888,3775,3776],{"xmlns":890},[892,3777,3778,3792],{},[895,3779,3780,3782,3784,3790],{},[898,3781,2041],{},[1712,3783,1904],{"stretchy":1903},[2037,3785,3786,3788],{},[898,3787,1710],{},[1712,3789,2145],{},[1712,3791,1910],{"stretchy":1903},[902,3793,2173],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,3796,3798],{"className":3797},[886],[888,3799,3800],{"xmlns":890},[892,3801,3802,3811],{},[895,3803,3804,3806,3809],{},[1712,3805,1904],{"stretchy":1903},[1716,3807,3808],{},"4.7",[1712,3810,1910],{"stretchy":1903},[902,3812,3813],{"encoding":904},"(4.7)",[724,3815,3816],{},[3817,3818],"img",{"alt":3819,"className":3820,"src":3822},"imek-typy-elasticity-5panelu",[210,3821],"wikilink-broken","\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,3824,3825,3864],{},[19,3826,3827],{},[22,3828,3829,3855,3858,3861],{},[25,3830,3831,3832],{},"Hodnota ",[883,3833,3835],{"className":3834},[886],[888,3836,3837],{"xmlns":890},[892,3838,3839,3853],{},[895,3840,3841,3843,3845,3851],{},[898,3842,2041],{},[1712,3844,1904],{"stretchy":1903},[2037,3846,3847,3849],{},[898,3848,1710],{},[1712,3850,2145],{},[1712,3852,1910],{"stretchy":1903},[902,3854,2173],{"encoding":904},[25,3856,3857],{},"Typ poptávky",[25,3859,3860],{},"Termín",[25,3862,3863],{},"Význam",[30,3865,3866,3899,3961,4036,4093],{},[22,3867,3868,3888,3893,3896],{},[35,3869,3870],{},[883,3871,3873],{"className":3872},[886],[888,3874,3875],{"xmlns":890},[892,3876,3877,3885],{},[895,3878,3879,3881,3883],{},[898,3880,2041],{},[1712,3882,1714],{},[1716,3884,2085],{},[902,3886,3887],{"encoding":904},"E = 0",[35,3889,3890],{},[38,3891,3892],{},"dokonale neelastická",[35,3894,3895],{},"perfectly inelastic",[35,3897,3898],{},"množství se nemění bez ohledu na cenu",[22,3900,3901,3925,3929,3932],{},[35,3902,3903],{},[883,3904,3906],{"className":3905},[886],[888,3907,3908],{"xmlns":890},[892,3909,3910,3922],{},[895,3911,3912,3914,3916,3918,3920],{},[1716,3913,2085],{},[1712,3915,2252],{},[898,3917,2041],{},[1712,3919,2252],{},[1716,3921,2222],{},[902,3923,3924],{"encoding":904},"0 \u003C E \u003C 1",[35,3926,3927],{},[38,3928,1860],{},[35,3930,3931],{},"inelastic",[35,3933,3934,3947,3948],{},[883,3935,3937],{"className":3936},[886],[888,3938,3939],{"xmlns":890},[892,3940,3941,3945],{},[895,3942,3943],{},[898,3944,1734],{},[902,3946,1734],{"encoding":904}," se mění pomaleji než ",[883,3949,3951],{"className":3950},[886],[888,3952,3953],{"xmlns":890},[892,3954,3955,3959],{},[895,3956,3957],{},[898,3958,1710],{},[902,3960,1710],{"encoding":904},[22,3962,3963,3982,3987,3990],{},[35,3964,3965],{},[883,3966,3968],{"className":3967},[886],[888,3969,3970],{"xmlns":890},[892,3971,3972,3980],{},[895,3973,3974,3976,3978],{},[898,3975,2041],{},[1712,3977,1714],{},[1716,3979,2222],{},[902,3981,2343],{"encoding":904},[35,3983,3984],{},[38,3985,3986],{},"jednotkově elastická",[35,3988,3989],{},"unit elastic",[35,3991,3992,4005,4006,4019,4020,4035],{},[883,3993,3995],{"className":3994},[886],[888,3996,3997],{"xmlns":890},[892,3998,3999,4003],{},[895,4000,4001],{},[898,4002,1734],{},[902,4004,1734],{"encoding":904}," i ",[883,4007,4009],{"className":4008},[886],[888,4010,4011],{"xmlns":890},[892,4012,4013,4017],{},[895,4014,4015],{},[898,4016,1710],{},[902,4018,1710],{"encoding":904}," se mění stejně rychle; ",[883,4021,4023],{"className":4022},[886],[888,4024,4025],{"xmlns":890},[892,4026,4027,4033],{},[895,4028,4029,4031],{},[898,4030,1772],{},[898,4032,1775],{},[902,4034,1877],{"encoding":904}," má maximum",[22,4037,4038,4057,4061,4064],{},[35,4039,4040],{},[883,4041,4043],{"className":4042},[886],[888,4044,4045],{"xmlns":890},[892,4046,4047,4055],{},[895,4048,4049,4051,4053],{},[898,4050,2041],{},[1712,4052,2302],{},[1716,4054,2222],{},[902,4056,2307],{"encoding":904},[35,4058,4059],{},[38,4060,1856],{},[35,4062,4063],{},"elastic",[35,4065,4066,4079,4080],{},[883,4067,4069],{"className":4068},[886],[888,4070,4071],{"xmlns":890},[892,4072,4073,4077],{},[895,4074,4075],{},[898,4076,1734],{},[902,4078,1734],{"encoding":904}," se mění rychleji než ",[883,4081,4083],{"className":4082},[886],[888,4084,4085],{"xmlns":890},[892,4086,4087,4091],{},[895,4088,4089],{},[898,4090,1710],{},[902,4092,1710],{"encoding":904},[22,4094,4095,4116,4121,4124],{},[35,4096,4097],{},[883,4098,4100],{"className":4099},[886],[888,4101,4102],{"xmlns":890},[892,4103,4104,4113],{},[895,4105,4106,4108,4110],{},[898,4107,2041],{},[1712,4109,2082],{},[898,4111,4112],{"mathvariant":2003},"∞",[902,4114,4115],{"encoding":904},"E \\to \\infty",[35,4117,4118],{},[38,4119,4120],{},"dokonale elastická",[35,4122,4123],{},"perfectly elastic",[35,4125,4126,4127],{},"sebemenší změna ceny úplně mění ",[883,4128,4130],{"className":4129},[886],[888,4131,4132],{"xmlns":890},[892,4133,4134,4138],{},[895,4135,4136],{},[898,4137,1734],{},[902,4139,1734],{"encoding":904},[724,4141,4142],{},[38,4143,4144],{},"Pravidlo růstu elasticity s cenou:",[1636,4146,4147],{},[724,4148,4149,4150],{},"S rostoucí cenou elasticita poptávky roste. ",[883,4151,4153],{"className":4152},[886],[888,4154,4155],{"xmlns":890},[892,4156,4157,4166],{},[895,4158,4159,4161,4164],{},[1712,4160,1904],{"stretchy":1903},[1716,4162,4163],{},"4.8",[1712,4165,1910],{"stretchy":1903},[902,4167,4168],{"encoding":904},"(4.8)",[724,4170,4171,4172,4175,4176,4179,4180,4197],{},"Z toho plyne, že při ",[614,4173,4174],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,4177,4178],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,4181,4183],{"className":4182},[886],[888,4184,4185],{"xmlns":890},[892,4186,4187,4195],{},[895,4188,4189],{},[2037,4190,4191,4193],{},[898,4192,1710],{},[1712,4194,2145],{},[902,4196,2195],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1636,4199,4200,4205],{},[724,4201,4202,4204],{},[883,4203,2370],{}," Postup: jak klasifikovat poptávku",[152,4206,4207,4234,4237],{},[123,4208,4209,4210,4233],{},"Spočítejte ",[883,4211,4213],{"className":4212},[886],[888,4214,4215],{"xmlns":890},[892,4216,4217,4231],{},[895,4218,4219,4221,4223,4229],{},[898,4220,2041],{},[1712,4222,1904],{"stretchy":1903},[2037,4224,4225,4227],{},[898,4226,1710],{},[1712,4228,2145],{},[1712,4230,1910],{"stretchy":1903},[902,4232,2173],{"encoding":904}," dle (4.5).",[123,4235,4236],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,4238,4239,4240,4264],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,4241,4243],{"className":4242},[886],[888,4244,4245],{"xmlns":890},[892,4246,4247,4261],{},[895,4248,4249,4251,4253,4255,4257,4259],{},[898,4250,2041],{},[1712,4252,1904],{"stretchy":1903},[898,4254,1710],{},[1712,4256,1910],{"stretchy":1903},[1712,4258,1714],{},[1716,4260,2222],{},[902,4262,4263],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,4266,4267,4270,4271,4288,4289,4307,4308,4335,4336,1659],{},[38,4268,4269],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,4272,4274],{"className":4273},[886],[888,4275,4276],{"xmlns":890},[892,4277,4278,4286],{},[895,4279,4280,4282,4284],{},[898,4281,2041],{},[1712,4283,1714],{},[1716,4285,2222],{},[902,4287,2343],{"encoding":904}," pro ",[883,4290,4292],{"className":4291},[886],[888,4293,4294],{"xmlns":890},[892,4295,4296,4304],{},[895,4297,4298,4300,4302],{},[898,4299,1710],{},[1712,4301,1714],{},[1716,4303,2809],{},[902,4305,4306],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,4309,4311],{"className":4310},[886],[888,4312,4313],{"xmlns":890},[892,4314,4315,4332],{},[895,4316,4317,4319,4322,4324,4326,4328,4330],{},[898,4318,1710],{},[1712,4320,4321],{},"∈",[1712,4323,3133],{"stretchy":1903},[1716,4325,2085],{},[1712,4327,3138],{"separator":2565},[1716,4329,2809],{},[1712,4331,1910],{"stretchy":1903},[902,4333,4334],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,4337,4339],{"className":4338},[886],[888,4340,4341],{"xmlns":890},[892,4342,4343,4359],{},[895,4344,4345,4347,4349,4351,4353,4355,4357],{},[898,4346,1710],{},[1712,4348,4321],{},[1712,4350,1904],{"stretchy":1903},[1716,4352,2809],{},[1712,4354,3138],{"separator":2565},[1716,4356,2782],{},[1712,4358,3152],{"stretchy":1903},[902,4360,4361],{"encoding":904},"P \\in (25, 50\\rangle",[115,4363,4365],{"id":4364},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,4367,4368],{},[3817,4369],{"alt":4370,"className":4371,"src":4372},"imek-elasticita-tr",[210,3821],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,4374,4375],{},[3817,4376],{"alt":4377,"className":4378,"src":4379},"imek-elasticita-podel-linearni-poptavky",[210,3821],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,4381,4382,4383,4433,4434,4451],{},"Pro celkový příjem platí ",[883,4384,4386],{"className":4385},[886],[888,4387,4388],{"xmlns":890},[892,4389,4390,4430],{},[895,4391,4392,4394,4396,4398,4400,4402,4404,4406,4408,4410,4412,4414,4416,4418,4420,4422,4424,4426,4428],{},[898,4393,1772],{},[898,4395,1775],{},[1712,4397,1714],{},[898,4399,1772],{},[898,4401,1775],{},[1712,4403,1904],{"stretchy":1903},[898,4405,1734],{},[1712,4407,1910],{"stretchy":1903},[1712,4409,1714],{},[898,4411,1710],{},[1712,4413,1783],{},[898,4415,1734],{},[1712,4417,1714],{},[898,4419,1734],{},[1712,4421,1783],{},[898,4423,1969],{},[1712,4425,1904],{"stretchy":1903},[898,4427,1734],{},[1712,4429,1910],{"stretchy":1903},[902,4431,4432],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,4435,4437],{"className":4436},[886],[888,4438,4439],{"xmlns":890},[892,4440,4441,4448],{},[895,4442,4443,4446],{},[898,4444,4445],{},"M",[898,4447,1775],{},[902,4449,4450],{"encoding":904},"MR"," odvodíme:",[724,4453,4454],{},[883,4455,4457],{"className":4456},[886],[888,4458,4459],{"xmlns":890},[892,4460,4461,4569],{},[895,4462,4463,4465,4467,4469,4471,4477,4479,4481,4483,4485,4487,4489,4491,4493,4495,4497,4499,4505,4507,4509,4511,4513,4515,4517,4519,4533,4535,4537],{},[898,4464,4445],{},[898,4466,1775],{},[1712,4468,1714],{},[898,4470,1772],{},[2037,4472,4473,4475],{},[898,4474,1775],{},[1712,4476,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,4478,1904],{"stretchy":1903},[898,4480,1734],{},[1712,4482,1910],{"stretchy":1903},[1712,4484,1714],{},[898,4486,1969],{},[1712,4488,1904],{"stretchy":1903},[898,4490,1734],{},[1712,4492,1910],{"stretchy":1903},[1712,4494,3145],{},[898,4496,1734],{},[1762,4498,2583],{},[2037,4500,4501,4503],{},[898,4502,1969],{},[1712,4504,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,4506,1904],{"stretchy":1903},[898,4508,1734],{},[1712,4510,1910],{"stretchy":1903},[1712,4512,1714],{},[898,4514,1710],{},[1712,4516,3145],{},[898,4518,1734],{},[2567,4520,4521,4527],{},[895,4522,4523,4525],{},[898,4524,2468],{"mathvariant":2003},[898,4526,1710],{},[895,4528,4529,4531],{},[898,4530,2468],{"mathvariant":2003},[898,4532,1734],{},[1712,4534,1714],{},[898,4536,1710],{},[895,4538,4539,4541,4543,4545,4551,4553,4567],{},[1712,4540,1904],{"fence":2565},[1716,4542,2222],{},[1712,4544,3145],{},[2567,4546,4547,4549],{},[898,4548,1734],{},[898,4550,1710],{},[1712,4552,1783],{},[2567,4554,4555,4561],{},[895,4556,4557,4559],{},[898,4558,2468],{"mathvariant":2003},[898,4560,1710],{},[895,4562,4563,4565],{},[898,4564,2468],{"mathvariant":2003},[898,4566,1734],{},[1712,4568,1910],{"fence":2565},[902,4570,4571],{"encoding":904},"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)",[724,4573,4574],{},[883,4575,4577],{"className":4576},[886],[888,4578,4579],{"xmlns":890},[892,4580,4581,4653],{},[895,4582,4583,4585,4587,4629,4631,4633],{},[1712,4584,1714],{},[898,4586,1710],{},[895,4588,4589,4591,4593,4595,4627],{},[1712,4590,1904],{"fence":2565},[1716,4592,2222],{},[1712,4594,3145],{},[2567,4596,4597,4599],{},[1716,4598,2222],{},[895,4600,4601,4609,4611],{},[2563,4602,4603],{"scriptlevel":2085,"displaystyle":1903},[2567,4604,4605,4607],{},[898,4606,1710],{},[898,4608,1734],{},[1712,4610,1783],{},[2563,4612,4613],{"scriptlevel":2085,"displaystyle":1903},[2567,4614,4615,4621],{},[895,4616,4617,4619],{},[898,4618,2468],{"mathvariant":2003},[898,4620,1734],{},[895,4622,4623,4625],{},[898,4624,2468],{"mathvariant":2003},[898,4626,1710],{},[1712,4628,1910],{"fence":2565},[1712,4630,1714],{},[898,4632,1710],{},[895,4634,4635,4637,4639,4641,4651],{},[1712,4636,1904],{"fence":2565},[1716,4638,2222],{},[1712,4640,3145],{},[2567,4642,4643,4645],{},[1716,4644,2222],{},[895,4646,4647,4649],{},[1712,4648,2219],{},[898,4650,2041],{},[1712,4652,1910],{"fence":2565},[902,4654,4655],{"encoding":904},"= P\\left(1 + \\frac{1}{\\tfrac{P}{Q}\\cdot\\tfrac{\\mathrm{d}Q}{\\mathrm{d}P}}\\right) = P\\left(1 + \\frac{1}{-E}\\right)",[724,4657,4658],{},"a tedy",[724,4660,4661],{},[883,4662,4664],{"className":4663,"title":1986,"style":1987},[1985],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1636,4666,4667,4736,4986],{},[724,4668,4669,4671,4672,4706,4707,4722,4723,2854],{},[883,4670,1941],{}," Intuice: vztah ",[883,4673,4675],{"className":4674},[886],[888,4676,4677],{"xmlns":890},[892,4678,4679,4703],{},[895,4680,4681,4683,4685,4687,4689,4691,4693,4695,4697,4699,4701],{},[898,4682,4445],{},[898,4684,1775],{},[1712,4686,1714],{},[898,4688,1710],{},[1712,4690,1904],{"stretchy":1903},[1716,4692,2222],{},[1712,4694,2219],{},[1716,4696,2222],{},[898,4698,2473],{"mathvariant":2003},[898,4700,2041],{},[1712,4702,1910],{"stretchy":1903},[902,4704,4705],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,4708,4710],{"className":4709},[886],[888,4711,4712],{"xmlns":890},[892,4713,4714,4720],{},[895,4715,4716,4718],{},[898,4717,4445],{},[898,4719,1775],{},[902,4721,4450],{"encoding":904}," jednoznačně určuje hodnota ",[883,4724,4726],{"className":4725},[886],[888,4727,4728],{"xmlns":890},[892,4729,4730,4734],{},[895,4731,4732],{},[898,4733,2041],{},[902,4735,2041],{"encoding":904},[120,4737,4738,4848,4917],{},[123,4739,4740,4757,4758,3245,4772,3245,4798,3245,4811,4831,4832,4847],{},[883,4741,4743],{"className":4742},[886],[888,4744,4745],{"xmlns":890},[892,4746,4747,4755],{},[895,4748,4749,4751,4753],{},[898,4750,2041],{},[1712,4752,2302],{},[1716,4754,2222],{},[902,4756,2307],{"encoding":904}," (elastická) ",[883,4759,4761],{"className":4760},[886],[888,4762,4763],{"xmlns":890},[892,4764,4765,4769],{},[895,4766,4767],{},[1712,4768,1767],{},[902,4770,4771],{"encoding":904},"\\Rightarrow",[883,4773,4775],{"className":4774},[886],[888,4776,4777],{"xmlns":890},[892,4778,4779,4795],{},[895,4780,4781,4783,4785,4787,4789,4791,4793],{},[1716,4782,2222],{},[1712,4784,2219],{},[1716,4786,2222],{},[898,4788,2473],{"mathvariant":2003},[898,4790,2041],{},[1712,4792,2302],{},[1716,4794,2085],{},[902,4796,4797],{"encoding":904},"1 - 1\u002FE > 0",[883,4799,4801],{"className":4800},[886],[888,4802,4803],{"xmlns":890},[892,4804,4805,4809],{},[895,4806,4807],{},[1712,4808,1767],{},[902,4810,4771],{"encoding":904},[883,4812,4814],{"className":4813},[886],[888,4815,4816],{"xmlns":890},[892,4817,4818,4828],{},[895,4819,4820,4822,4824,4826],{},[898,4821,4445],{},[898,4823,1775],{},[1712,4825,2302],{},[1716,4827,2085],{},[902,4829,4830],{"encoding":904},"MR > 0"," — ",[883,4833,4835],{"className":4834},[886],[888,4836,4837],{"xmlns":890},[892,4838,4839,4845],{},[895,4840,4841,4843],{},[898,4842,1772],{},[898,4844,1775],{},[902,4846,1877],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,4849,4850,4867,4868,3245,4881,4831,4901,4916],{},[883,4851,4853],{"className":4852},[886],[888,4854,4855],{"xmlns":890},[892,4856,4857,4865],{},[895,4858,4859,4861,4863],{},[898,4860,2041],{},[1712,4862,1714],{},[1716,4864,2222],{},[902,4866,2343],{"encoding":904}," (jednotková) ",[883,4869,4871],{"className":4870},[886],[888,4872,4873],{"xmlns":890},[892,4874,4875,4879],{},[895,4876,4877],{},[1712,4878,1767],{},[902,4880,4771],{"encoding":904},[883,4882,4884],{"className":4883},[886],[888,4885,4886],{"xmlns":890},[892,4887,4888,4898],{},[895,4889,4890,4892,4894,4896],{},[898,4891,4445],{},[898,4893,1775],{},[1712,4895,1714],{},[1716,4897,2085],{},[902,4899,4900],{"encoding":904},"MR = 0",[883,4902,4904],{"className":4903},[886],[888,4905,4906],{"xmlns":890},[892,4907,4908,4914],{},[895,4909,4910,4912],{},[898,4911,1772],{},[898,4913,1775],{},[902,4915,1877],{"encoding":904}," je extrém (maximum).",[123,4918,4919,4936,4937,3245,4950,4831,4970,4985],{},[883,4920,4922],{"className":4921},[886],[888,4923,4924],{"xmlns":890},[892,4925,4926,4934],{},[895,4927,4928,4930,4932],{},[898,4929,2041],{},[1712,4931,2252],{},[1716,4933,2222],{},[902,4935,2325],{"encoding":904}," (neelastická) ",[883,4938,4940],{"className":4939},[886],[888,4941,4942],{"xmlns":890},[892,4943,4944,4948],{},[895,4945,4946],{},[1712,4947,1767],{},[902,4949,4771],{"encoding":904},[883,4951,4953],{"className":4952},[886],[888,4954,4955],{"xmlns":890},[892,4956,4957,4967],{},[895,4958,4959,4961,4963,4965],{},[898,4960,4445],{},[898,4962,1775],{},[1712,4964,2252],{},[1716,4966,2085],{},[902,4968,4969],{"encoding":904},"MR \u003C 0",[883,4971,4973],{"className":4972},[886],[888,4974,4975],{"xmlns":890},[892,4976,4977,4983],{},[895,4978,4979,4981],{},[898,4980,1772],{},[898,4982,1775],{},[902,4984,1877],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,4987,4988,4989,1659],{},"Viz také ",[207,4990,4992],{"className":4991,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk",[198,4994,4996],{"id":4995},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,4998,4999,5019,5020,5046,5047,5062,5063,5076,5077,5090,5091,5104,5105,5121,5122,3245,5137,5140,5141,5121,5157,1659],{},[38,5000,5001,5002,1691],{},"(a) Poptávka elastická (",[883,5003,5005],{"className":5004},[886],[888,5006,5007],{"xmlns":890},[892,5008,5009,5017],{},[895,5010,5011,5013,5015],{},[898,5012,2041],{},[1712,5014,2302],{},[1716,5016,2222],{},[902,5018,2307],{"encoding":904}," Z (4.12) plyne ",[883,5021,5023],{"className":5022},[886],[888,5024,5025],{"xmlns":890},[892,5026,5027,5043],{},[895,5028,5029,5031,5033,5035,5037,5039,5041],{},[898,5030,4445],{},[898,5032,1775],{},[1712,5034,1904],{"stretchy":1903},[898,5036,1734],{},[1712,5038,1910],{"stretchy":1903},[1712,5040,2302],{},[1716,5042,2085],{},[902,5044,5045],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,5048,5050],{"className":5049},[886],[888,5051,5052],{"xmlns":890},[892,5053,5054,5060],{},[895,5055,5056,5058],{},[898,5057,1772],{},[898,5059,1775],{},[902,5061,1877],{"encoding":904}," je rostoucí funkcí ",[883,5064,5066],{"className":5065},[886],[888,5067,5068],{"xmlns":890},[892,5069,5070,5074],{},[895,5071,5072],{},[898,5073,1734],{},[902,5075,1734],{"encoding":904},". Avšak růst ",[883,5078,5080],{"className":5079},[886],[888,5081,5082],{"xmlns":890},[892,5083,5084,5088],{},[895,5085,5086],{},[898,5087,1734],{},[902,5089,1734],{"encoding":904}," je odezvou na pokles ceny ",[883,5092,5094],{"className":5093},[886],[888,5095,5096],{"xmlns":890},[892,5097,5098,5102],{},[895,5099,5100],{},[898,5101,1710],{},[902,5103,1710],{"encoding":904},". Tudíž s ",[614,5106,5107,5108],{},"poklesem ceny ",[883,5109,5111],{"className":5110},[886],[888,5112,5113],{"xmlns":890},[892,5114,5115,5119],{},[895,5116,5117],{},[898,5118,1710],{},[902,5120,1710],{"encoding":904}," celkový příjem ",[883,5123,5125],{"className":5124},[886],[888,5126,5127],{"xmlns":890},[892,5128,5129,5135],{},[895,5130,5131,5133],{},[898,5132,1772],{},[898,5134,1775],{},[902,5136,1877],{"encoding":904},[614,5138,5139],{},"roste"," a s ",[614,5142,5143,5144],{},"růstem ceny ",[883,5145,5147],{"className":5146},[886],[888,5148,5149],{"xmlns":890},[892,5150,5151,5155],{},[895,5152,5153],{},[898,5154,1710],{},[902,5156,1710],{"encoding":904},[614,5158,5159],{},"klesá",[1636,5161,5162],{},[724,5163,5164,5167],{},[38,5165,5166],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,5169,5170,5019,5190,1343,5216,5231,5232,5245,5246,5259,5260,5273,5274,5121,5287,3245,5302,1659],{},[38,5171,5172,5173,1691],{},"(b) Poptávka neelastická (",[883,5174,5176],{"className":5175},[886],[888,5177,5178],{"xmlns":890},[892,5179,5180,5188],{},[895,5181,5182,5184,5186],{},[898,5183,2041],{},[1712,5185,2252],{},[1716,5187,2222],{},[902,5189,2325],{"encoding":904},[883,5191,5193],{"className":5192},[886],[888,5194,5195],{"xmlns":890},[892,5196,5197,5213],{},[895,5198,5199,5201,5203,5205,5207,5209,5211],{},[898,5200,4445],{},[898,5202,1775],{},[1712,5204,1904],{"stretchy":1903},[898,5206,1734],{},[1712,5208,1910],{"stretchy":1903},[1712,5210,2252],{},[1716,5212,2085],{},[902,5214,5215],{"encoding":904},"MR(Q) \u003C 0",[883,5217,5219],{"className":5218},[886],[888,5220,5221],{"xmlns":890},[892,5222,5223,5229],{},[895,5224,5225,5227],{},[898,5226,1772],{},[898,5228,1775],{},[902,5230,1877],{"encoding":904}," je klesající funkce ",[883,5233,5235],{"className":5234},[886],[888,5236,5237],{"xmlns":890},[892,5238,5239,5243],{},[895,5240,5241],{},[898,5242,1734],{},[902,5244,1734],{"encoding":904},", tj. s růstem ",[883,5247,5249],{"className":5248},[886],[888,5250,5251],{"xmlns":890},[892,5252,5253,5257],{},[895,5254,5255],{},[898,5256,1734],{},[902,5258,1734],{"encoding":904}," (s poklesem ceny ",[883,5261,5263],{"className":5262},[886],[888,5264,5265],{"xmlns":890},[892,5266,5267,5271],{},[895,5268,5269],{},[898,5270,1710],{},[902,5272,1710],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,5275,5277],{"className":5276},[886],[888,5278,5279],{"xmlns":890},[892,5280,5281,5285],{},[895,5282,5283],{},[898,5284,1710],{},[902,5286,1710],{"encoding":904},[883,5288,5290],{"className":5289},[886],[888,5291,5292],{"xmlns":890},[892,5293,5294,5300],{},[895,5295,5296,5298],{},[898,5297,1772],{},[898,5299,1775],{},[902,5301,1877],{"encoding":904},[614,5303,5139],{},[1636,5305,5306],{},[724,5307,5308,5311],{},[38,5309,5310],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,5313,5314,5019,5334,5353,5354,5369,5370,5440,5441,1655,5469,5502,5503,3401,5531,5546,5547,1659],{},[38,5315,5316,5317,1691],{},"(c) Jednotková elasticita (",[883,5318,5320],{"className":5319},[886],[888,5321,5322],{"xmlns":890},[892,5323,5324,5332],{},[895,5325,5326,5328,5330],{},[898,5327,2041],{},[1712,5329,1714],{},[1716,5331,2222],{},[902,5333,2343],{"encoding":904},[883,5335,5337],{"className":5336},[886],[888,5338,5339],{"xmlns":890},[892,5340,5341,5351],{},[895,5342,5343,5345,5347,5349],{},[898,5344,4445],{},[898,5346,1775],{},[1712,5348,1714],{},[1716,5350,2085],{},[902,5352,4900],{"encoding":904}," — nutná podmínka extrému ",[883,5355,5357],{"className":5356},[886],[888,5358,5359],{"xmlns":890},[892,5360,5361,5367],{},[895,5362,5363,5365],{},[898,5364,1772],{},[898,5366,1775],{},[902,5368,1877],{"encoding":904},". Dále ",[883,5371,5373],{"className":5372},[886],[888,5374,5375],{"xmlns":890},[892,5376,5377,5437],{},[895,5378,5379,5381,5391,5393,5395,5401,5403,5409,5411,5413,5415,5417,5419,5421,5431,5433,5435],{},[898,5380,1772],{},[2037,5382,5383,5385],{},[898,5384,1775],{},[895,5386,5387,5389],{},[1712,5388,2243],{"mathvariant":2003},[1712,5390,2243],{"mathvariant":2003},[1712,5392,1714],{},[898,5394,4445],{},[2037,5396,5397,5399],{},[898,5398,1775],{},[1712,5400,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,5402,1714],{},[2037,5404,5405,5407],{},[898,5406,1969],{},[1712,5408,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,5410,1904],{"stretchy":1903},[898,5412,1734],{},[1712,5414,1910],{"stretchy":1903},[1712,5416,3145],{},[898,5418,1734],{},[1762,5420,2583],{},[2037,5422,5423,5425],{},[898,5424,1969],{},[895,5426,5427,5429],{},[1712,5428,2243],{"mathvariant":2003},[1712,5430,2243],{"mathvariant":2003},[1712,5432,1904],{"stretchy":1903},[898,5434,1734],{},[1712,5436,1910],{"stretchy":1903},[902,5438,5439],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,5442,5444],{"className":5443},[886],[888,5445,5446],{"xmlns":890},[892,5447,5448,5466],{},[895,5449,5450,5456,5458,5460,5462,5464],{},[2037,5451,5452,5454],{},[898,5453,1969],{},[1712,5455,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,5457,1904],{"stretchy":1903},[898,5459,1734],{},[1712,5461,1910],{"stretchy":1903},[1712,5463,2252],{},[1716,5465,2085],{},[902,5467,5468],{"encoding":904},"D'(Q) \u003C 0",[883,5470,5472],{"className":5471},[886],[888,5473,5474],{"xmlns":890},[892,5475,5476,5499],{},[895,5477,5478,5488,5490,5492,5494,5497],{},[2037,5479,5480,5482],{},[898,5481,1969],{},[895,5483,5484,5486],{},[1712,5485,2243],{"mathvariant":2003},[1712,5487,2243],{"mathvariant":2003},[1712,5489,1904],{"stretchy":1903},[898,5491,1734],{},[1712,5493,1910],{"stretchy":1903},[1712,5495,5496],{},"≤",[1716,5498,2085],{},[902,5500,5501],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,5504,5506],{"className":5505},[886],[888,5507,5508],{"xmlns":890},[892,5509,5510,5528],{},[895,5511,5512,5514,5524,5526],{},[898,5513,1772],{},[2037,5515,5516,5518],{},[898,5517,1775],{},[895,5519,5520,5522],{},[1712,5521,2243],{"mathvariant":2003},[1712,5523,2243],{"mathvariant":2003},[1712,5525,2252],{},[1716,5527,2085],{},[902,5529,5530],{"encoding":904},"TR'' \u003C 0",[883,5532,5534],{"className":5533},[886],[888,5535,5536],{"xmlns":890},[892,5537,5538,5544],{},[895,5539,5540,5542],{},[898,5541,1772],{},[898,5543,1775],{},[902,5545,1877],{"encoding":904}," nabývá ",[38,5548,5549],{},"maxima",[1636,5551,5552],{},[724,5553,5554,5557],{},[38,5555,5556],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,5559,5560],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,5562,5563],{},[38,5564,5565],{},"Souhrnná tabulka Pravidel 1–3:",[16,5567,5568,5672],{},[19,5569,5570],{},[22,5571,5572,5575,5590,5607,5638,5669],{},[25,5573,5574],{},"Charakter poptávky",[25,5576,5577],{},[883,5578,5580],{"className":5579},[886],[888,5581,5582],{"xmlns":890},[892,5583,5584,5588],{},[895,5585,5586],{},[898,5587,2041],{},[902,5589,2041],{"encoding":904},[25,5591,5592],{},[883,5593,5595],{"className":5594},[886],[888,5596,5597],{"xmlns":890},[892,5598,5599,5605],{},[895,5600,5601,5603],{},[898,5602,4445],{},[898,5604,1775],{},[902,5606,4450],{"encoding":904},[25,5608,5609,5610,3245,5623],{},"Pokles ceny ",[883,5611,5613],{"className":5612},[886],[888,5614,5615],{"xmlns":890},[892,5616,5617,5621],{},[895,5618,5619],{},[1712,5620,1767],{},[902,5622,4771],{"encoding":904},[883,5624,5626],{"className":5625},[886],[888,5627,5628],{"xmlns":890},[892,5629,5630,5636],{},[895,5631,5632,5634],{},[898,5633,1772],{},[898,5635,1775],{},[902,5637,1877],{"encoding":904},[25,5639,5640,5641,3245,5654],{},"Růst ceny ",[883,5642,5644],{"className":5643},[886],[888,5645,5646],{"xmlns":890},[892,5647,5648,5652],{},[895,5649,5650],{},[1712,5651,1767],{},[902,5653,4771],{"encoding":904},[883,5655,5657],{"className":5656},[886],[888,5658,5659],{"xmlns":890},[892,5660,5661,5667],{},[895,5662,5663,5665],{},[898,5664,1772],{},[898,5666,1775],{},[902,5668,1877],{"encoding":904},[25,5670,5671],{},"Doporučení",[30,5673,5674,5723,5774],{},[22,5675,5676,5678,5696,5714,5716,5718],{},[35,5677,1856],{},[35,5679,5680],{},[883,5681,5683],{"className":5682},[886],[888,5684,5685],{"xmlns":890},[892,5686,5687,5693],{},[895,5688,5689,5691],{},[1712,5690,2302],{},[1716,5692,2222],{},[902,5694,5695],{"encoding":904},"> 1",[35,5697,5698],{},[883,5699,5701],{"className":5700},[886],[888,5702,5703],{"xmlns":890},[892,5704,5705,5711],{},[895,5706,5707,5709],{},[1712,5708,2302],{},[1716,5710,2085],{},[902,5712,5713],{"encoding":904},"> 0",[35,5715,5139],{},[35,5717,5159],{},[35,5719,5720],{},[38,5721,5722],{},"snížit cenu",[22,5724,5725,5728,5746,5764,5767,5769],{},[35,5726,5727],{},"jednotková",[35,5729,5730],{},[883,5731,5733],{"className":5732},[886],[888,5734,5735],{"xmlns":890},[892,5736,5737,5743],{},[895,5738,5739,5741],{},[1712,5740,1714],{},[1716,5742,2222],{},[902,5744,5745],{"encoding":904},"= 1",[35,5747,5748],{},[883,5749,5751],{"className":5750},[886],[888,5752,5753],{"xmlns":890},[892,5754,5755,5761],{},[895,5756,5757,5759],{},[1712,5758,1714],{},[1716,5760,2085],{},[902,5762,5763],{"encoding":904},"= 0",[35,5765,5766],{},"maximum",[35,5768,5766],{},[35,5770,5771],{},[38,5772,5773],{},"držet cenu",[22,5775,5776,5778,5796,5814,5816,5818],{},[35,5777,1860],{},[35,5779,5780],{},[883,5781,5783],{"className":5782},[886],[888,5784,5785],{"xmlns":890},[892,5786,5787,5793],{},[895,5788,5789,5791],{},[1712,5790,2252],{},[1716,5792,2222],{},[902,5794,5795],{"encoding":904},"\u003C 1",[35,5797,5798],{},[883,5799,5801],{"className":5800},[886],[888,5802,5803],{"xmlns":890},[892,5804,5805,5811],{},[895,5806,5807,5809],{},[1712,5808,2252],{},[1716,5810,2085],{},[902,5812,5813],{"encoding":904},"\u003C 0",[35,5815,5159],{},[35,5817,5139],{},[35,5819,5820],{},[38,5821,5822],{},"zvýšit cenu",[198,5824,5826],{"id":5825},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,5828,5829,5830,5855,5856,5878,5879,5892,5893,5906,5907,5920,5921,3401,5948,6000],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,5831,5833],{"className":5832},[886],[888,5834,5835],{"xmlns":890},[892,5836,5837,5853],{},[895,5838,5839,5841,5843,5845,5847],{},[898,5840,1710],{},[1712,5842,1714],{},[1716,5844,1739],{},[1712,5846,2219],{},[2037,5848,5849,5851],{},[898,5850,1734],{},[1716,5852,2787],{},[902,5854,3271],{"encoding":904},". Reálné cenové rozpětí je ",[883,5857,5859],{"className":5858},[886],[888,5860,5861],{"xmlns":890},[892,5862,5863,5875],{},[895,5864,5865,5867,5869,5871,5873],{},[1712,5866,3133],{"stretchy":1903},[1716,5868,2222],{},[1712,5870,3138],{"separator":2565},[1716,5872,1739],{},[1712,5874,3152],{"stretchy":1903},[902,5876,5877],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,5880,5882],{"className":5881},[886],[888,5883,5884],{"xmlns":890},[892,5885,5886,5890],{},[895,5887,5888],{},[898,5889,1734],{},[902,5891,1734],{"encoding":904}," jako funkci ",[883,5894,5896],{"className":5895},[886],[888,5897,5898],{"xmlns":890},[892,5899,5900,5904],{},[895,5901,5902],{},[898,5903,1710],{},[902,5905,1710],{"encoding":904},"; pro nezáporné ",[883,5908,5910],{"className":5909},[886],[888,5911,5912],{"xmlns":890},[892,5913,5914,5918],{},[895,5915,5916],{},[898,5917,1734],{},[902,5919,1734],{"encoding":904}," je ",[883,5922,5924],{"className":5923},[886],[888,5925,5926],{"xmlns":890},[892,5927,5928,5945],{},[895,5929,5930,5932,5934],{},[898,5931,1734],{},[1712,5933,1714],{},[5935,5936,5937],"msqrt",{},[895,5938,5939,5941,5943],{},[1716,5940,1739],{},[1712,5942,2219],{},[898,5944,1710],{},[902,5946,5947],{"encoding":904},"Q = \\sqrt{100 - P}",[883,5949,5951],{"className":5950},[886],[888,5952,5953],{"xmlns":890},[892,5954,5955,5997],{},[895,5956,5957,5973,5975,5977],{},[2563,5958,5959],{"scriptlevel":2085,"displaystyle":2565},[2567,5960,5961,5967],{},[895,5962,5963,5965],{},[898,5964,2468],{"mathvariant":2003},[898,5966,1734],{},[895,5968,5969,5971],{},[898,5970,2468],{"mathvariant":2003},[898,5972,1710],{},[1712,5974,1714],{},[1712,5976,2219],{},[2563,5978,5979],{"scriptlevel":2085,"displaystyle":2565},[2567,5980,5981,5983],{},[1716,5982,2222],{},[895,5984,5985,5987],{},[1716,5986,2787],{},[5935,5988,5989],{},[895,5990,5991,5993,5995],{},[1716,5992,1739],{},[1712,5994,2219],{},[898,5996,1710],{},[902,5998,5999],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,6002,6003],{},[883,6004,6006],{"className":6005},[886],[888,6007,6008],{"xmlns":890},[892,6009,6010,6132],{},[895,6011,6012,6014,6016,6018,6020,6022,6024,6030,6032,6046,6048,6050,6064,6066,6092,6094,6112,6114,6130],{},[898,6013,2041],{},[1712,6015,1904],{"stretchy":1903},[898,6017,1710],{},[1712,6019,1910],{"stretchy":1903},[1712,6021,1714],{},[1712,6023,2219],{},[2567,6025,6026,6028],{},[898,6027,1710],{},[898,6029,1734],{},[1712,6031,1783],{},[2567,6033,6034,6040],{},[895,6035,6036,6038],{},[898,6037,2468],{"mathvariant":2003},[898,6039,1734],{},[895,6041,6042,6044],{},[898,6043,2468],{"mathvariant":2003},[898,6045,1710],{},[1712,6047,1714],{},[1712,6049,2219],{},[2567,6051,6052,6054],{},[898,6053,1710],{},[5935,6055,6056],{},[895,6057,6058,6060,6062],{},[1716,6059,1739],{},[1712,6061,2219],{},[898,6063,1710],{},[1712,6065,1783],{},[895,6067,6068,6070,6072,6090],{},[1712,6069,1904],{"fence":2565},[1712,6071,2219],{},[2567,6073,6074,6076],{},[1716,6075,2222],{},[895,6077,6078,6080],{},[1716,6079,2787],{},[5935,6081,6082],{},[895,6083,6084,6086,6088],{},[1716,6085,1739],{},[1712,6087,2219],{},[898,6089,1710],{},[1712,6091,1910],{"fence":2565},[1712,6093,1714],{},[2567,6095,6096,6098],{},[898,6097,1710],{},[895,6099,6100,6102,6104,6106,6108,6110],{},[1716,6101,2787],{},[1712,6103,1904],{"stretchy":1903},[1716,6105,1739],{},[1712,6107,2219],{},[898,6109,1710],{},[1712,6111,1910],{"stretchy":1903},[1712,6113,1714],{},[2567,6115,6116,6122],{},[895,6117,6118,6120],{},[1716,6119,2814],{},[898,6121,1710],{},[895,6123,6124,6126,6128],{},[1716,6125,1739],{},[1712,6127,2219],{},[898,6129,1710],{},[898,6131,1659],{"mathvariant":2003},[902,6133,6134],{"encoding":904},"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}.",[724,6136,6137,6138,2854],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,6139,6141],{"className":6140},[886],[888,6142,6143],{"xmlns":890},[892,6144,6145,6169],{},[895,6146,6147,6165,6167],{},[2563,6148,6149],{"scriptlevel":2085,"displaystyle":2565},[2567,6150,6151,6157],{},[895,6152,6153,6155],{},[1716,6154,2814],{},[898,6156,1710],{},[895,6158,6159,6161,6163],{},[1716,6160,1739],{},[1712,6162,2219],{},[898,6164,1710],{},[1712,6166,1714],{},[1716,6168,2222],{},[902,6170,6171],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,6173,6174],{},[883,6175,6177],{"className":6176},[886],[888,6178,6179],{"xmlns":890},[892,6180,6181,6215],{},[895,6182,6183,6189,6191,6199,6201,6204,6213],{},[2037,6184,6185,6187],{},[898,6186,1710],{},[1712,6188,2145],{},[1712,6190,1714],{},[2567,6192,6193,6196],{},[1716,6194,6195],{},"200",[1716,6197,6198],{},"3",[1712,6200,3712],{},[1716,6202,6203],{},"66,",[6205,6206,6207,6210],"mover",{"accent":2565},[1716,6208,6209],{},"6",[1712,6211,6212],{"stretchy":2565},"‾",[898,6214,1659],{"mathvariant":2003},[902,6216,6217],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,6219,6220],{},"S využitím vlastnosti (4.8):",[120,6222,6223,6269,6311],{},[123,6224,6225,6226,6261,6262,6264,6265,6268],{},"Při cenách ",[883,6227,6229],{"className":6228},[886],[888,6230,6231],{"xmlns":890},[892,6232,6233,6258],{},[895,6234,6235,6237,6239,6241,6243,6246,6248,6250,6256],{},[898,6236,1710],{},[1712,6238,4321],{},[1712,6240,3133],{"stretchy":1903},[1716,6242,2222],{},[1712,6244,6245],{"separator":2565},";",[1762,6247,2583],{},[1716,6249,6203],{},[6205,6251,6252,6254],{"accent":2565},[1716,6253,6209],{},[1712,6255,6212],{"stretchy":2565},[1712,6257,1910],{"stretchy":1903},[902,6259,6260],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,6263,1860],{}," — dle ",[614,6266,6267],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,6270,6225,6271,6261,6305,6264,6307,6310],{},[883,6272,6274],{"className":6273},[886],[888,6275,6276],{"xmlns":890},[892,6277,6278,6302],{},[895,6279,6280,6282,6284,6286,6288,6294,6296,6298,6300],{},[898,6281,1710],{},[1712,6283,4321],{},[1712,6285,1904],{"stretchy":1903},[1716,6287,6203],{},[6205,6289,6290,6292],{"accent":2565},[1716,6291,6209],{},[1712,6293,6212],{"stretchy":2565},[1712,6295,6245],{"separator":2565},[1762,6297,2583],{},[1716,6299,1739],{},[1712,6301,3152],{"stretchy":1903},[902,6303,6304],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,6306,1856],{},[614,6308,6309],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,6312,6313,6314,6317,6318,6346,6347,6350],{},"Dle ",[614,6315,6316],{},"Pravidla 3"," je při ceně ",[883,6319,6321],{"className":6320},[886],[888,6322,6323],{"xmlns":890},[892,6324,6325,6343],{},[895,6326,6327,6333,6335,6337],{},[2037,6328,6329,6331],{},[898,6330,1710],{},[1712,6332,2145],{},[1712,6334,1714],{},[1716,6336,6203],{},[6205,6338,6339,6341],{"accent":2565},[1716,6340,6209],{},[1712,6342,6212],{"stretchy":2565},[902,6344,6345],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,6348,6349],{},"maxima celkového příjmu"," ve výši",[724,6352,6353],{},[883,6354,6356],{"className":6355},[886],[888,6357,6358],{"xmlns":890},[892,6359,6360,6438],{},[895,6361,6362,6364,6366,6368,6374,6376,6378,6384,6386,6400,6402,6408,6410,6418,6420,6433,6435],{},[898,6363,1772],{},[898,6365,1775],{},[1712,6367,1904],{"stretchy":1903},[2037,6369,6370,6372],{},[898,6371,1710],{},[1712,6373,2145],{},[1712,6375,1910],{"stretchy":1903},[1712,6377,1714],{},[2037,6379,6380,6382],{},[898,6381,1710],{},[1712,6383,2145],{},[1712,6385,1783],{},[5935,6387,6388],{},[895,6389,6390,6392,6394],{},[1716,6391,1739],{},[1712,6393,2219],{},[2037,6395,6396,6398],{},[898,6397,1710],{},[1712,6399,2145],{},[1712,6401,1714],{},[2567,6403,6404,6406],{},[1716,6405,6195],{},[1716,6407,6198],{},[1712,6409,1783],{},[5935,6411,6412],{},[2567,6413,6414,6416],{},[1716,6415,1739],{},[1716,6417,6198],{},[1712,6419,1714],{},[2567,6421,6422,6425],{},[1716,6423,6424],{},"2000",[895,6426,6427,6429],{},[1716,6428,6198],{},[5935,6430,6431],{},[1716,6432,6198],{},[1712,6434,3712],{},[1716,6436,6437],{},"384,9.",[902,6439,6440],{"encoding":904},"TR(P^*) = P^*\\cdot\\sqrt{100 - P^*} = \\frac{200}{3}\\cdot\\sqrt{\\frac{100}{3}} = \\frac{2000}{3\\sqrt{3}} \\doteq 384{,}9.",[724,6442,6443,6444,1659],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,6445,6447],{"className":6446},[886],[888,6448,6449],{"xmlns":890},[892,6450,6451,6457],{},[895,6452,6453,6455],{},[898,6454,1772],{},[898,6456,1775],{},[902,6458,1877],{"encoding":904},[115,6460,6462],{"id":6461},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,6464,6465,6466,6469],{},"Analogicky se definuje ",[38,6467,6468],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,6471,6472],{},[883,6473,6475],{"className":6474,"title":1986,"style":1987},[1985],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,6477,2101,6478,6503,6504,6536],{},[883,6479,6481],{"className":6480},[886],[888,6482,6483],{"xmlns":890},[892,6484,6485,6500],{},[895,6486,6487,6489,6491,6494,6496,6498],{},[898,6488,1734],{},[1712,6490,1714],{},[898,6492,6493],{},"S",[1712,6495,1904],{"stretchy":1903},[898,6497,1710],{},[1712,6499,1910],{"stretchy":1903},[902,6501,6502],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,6505,6507],{"className":6506},[886],[888,6508,6509],{"xmlns":890},[892,6510,6511,6533],{},[895,6512,6513,6529,6531],{},[2563,6514,6515],{"scriptlevel":2085,"displaystyle":2565},[2567,6516,6517,6523],{},[895,6518,6519,6521],{},[898,6520,2468],{"mathvariant":2003},[898,6522,1734],{},[895,6524,6525,6527],{},[898,6526,2468],{"mathvariant":2003},[898,6528,1710],{},[1712,6530,2302],{},[1716,6532,2085],{},[902,6534,6535],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,6538,6539],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1636,6541,6542],{},[724,6543,6544,6545],{},"S rostoucí cenou elasticita nabídky roste. ",[883,6546,6548],{"className":6547},[886],[888,6549,6550],{"xmlns":890},[892,6551,6552,6561],{},[895,6553,6554,6556,6559],{},[1712,6555,1904],{"stretchy":1903},[1716,6557,6558],{},"4.14",[1712,6560,1910],{"stretchy":1903},[902,6562,6563],{"encoding":904},"(4.14)",[724,6565,6566],{},"Pro nominální změny platí",[724,6568,6569],{},[883,6570,6572],{"className":6571,"title":1986,"style":1987},[1985],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,6574,6575],{},"a pro procentní změny",[724,6577,6578],{},[883,6579,6581],{"className":6580,"title":1986,"style":1987},[1985],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,6583,6584],{},"(bez znaménka minus).",[198,6586,6588],{"id":6587},"příklad-47","Příklad 4.7",[724,6590,6591,6592,2854],{},"Nabídka ",[883,6593,6595],{"className":6594},[886],[888,6596,6597],{"xmlns":890},[892,6598,6599,6625],{},[895,6600,6601,6603,6605,6608,6614,6616,6618,6620,6622],{},[898,6602,1734],{},[1712,6604,1714],{},[1716,6606,6607],{},"0,1",[2037,6609,6610,6612],{},[898,6611,1710],{},[1716,6613,2787],{},[1712,6615,3145],{},[1716,6617,3068],{},[898,6619,1710],{},[1712,6621,3145],{},[1716,6623,6624],{},"150",[902,6626,6627],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,6629,6630],{},[883,6631,6633],{"className":6632},[886],[888,6634,6635],{"xmlns":890},[892,6636,6637,6684],{},[895,6638,6639,6641,6643,6667,6669,6671,6674,6676,6678,6680,6682],{},[898,6640,2041],{},[1712,6642,1714],{},[2567,6644,6645,6647],{},[898,6646,1710],{},[895,6648,6649,6651,6657,6659,6661,6663,6665],{},[1716,6650,6607],{},[2037,6652,6653,6655],{},[898,6654,1710],{},[1716,6656,2787],{},[1712,6658,3145],{},[1716,6660,3068],{},[898,6662,1710],{},[1712,6664,3145],{},[1716,6666,6624],{},[1762,6668,2583],{},[1712,6670,1904],{"stretchy":1903},[1716,6672,6673],{},"0,2",[898,6675,1710],{},[1712,6677,3145],{},[1716,6679,3068],{},[1712,6681,1910],{"stretchy":1903},[898,6683,1659],{"mathvariant":2003},[902,6685,6686],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,6688,2923,6689,1343,6719,1343,6746,6782,6783,6808,6809,6827,6828,1659],{},[883,6690,6692],{"className":6691},[886],[888,6693,6694],{"xmlns":890},[892,6695,6696,6716],{},[895,6697,6698,6700,6702,6704,6706,6708],{},[898,6699,2041],{},[1712,6701,1904],{"stretchy":1903},[1716,6703,1718],{},[1712,6705,1910],{"stretchy":1903},[1712,6707,1714],{},[2563,6709,6710],{"scriptlevel":2085,"displaystyle":1903},[2567,6711,6712,6714],{},[1716,6713,2222],{},[1716,6715,6198],{},[902,6717,6718],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,6720,6722],{"className":6721},[886],[888,6723,6724],{"xmlns":890},[892,6725,6726,6743],{},[895,6727,6728,6730,6732,6737,6739,6741],{},[898,6729,2041],{},[1712,6731,1904],{"stretchy":1903},[5935,6733,6734],{},[1716,6735,6736],{},"1500",[1712,6738,1910],{"stretchy":1903},[1712,6740,1714],{},[1716,6742,2222],{},[902,6744,6745],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,6747,6749],{"className":6748},[886],[888,6750,6751],{"xmlns":890},[892,6752,6753,6779],{},[895,6754,6755,6757,6759,6761,6763,6765,6774,6776],{},[898,6756,2041],{},[1712,6758,1904],{"stretchy":1903},[1716,6760,1739],{},[1712,6762,1910],{"stretchy":1903},[1712,6764,1714],{},[2563,6766,6767],{"scriptlevel":2085,"displaystyle":1903},[2567,6768,6769,6771],{},[1716,6770,2782],{},[1716,6772,6773],{},"33",[1712,6775,3712],{},[1716,6777,6778],{},"1,515",[902,6780,6781],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,6784,6786],{"className":6785},[886],[888,6787,6788],{"xmlns":890},[892,6789,6790,6805],{},[895,6791,6792,6794,6796,6800,6802],{},[898,6793,1710],{},[1712,6795,2302],{},[5935,6797,6798],{},[1716,6799,6736],{},[1712,6801,3740],{},[1716,6803,6804],{},"38,7",[902,6806,6807],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,6810,6812],{"className":6811},[886],[888,6813,6814],{"xmlns":890},[892,6815,6816,6824],{},[895,6817,6818,6820,6822],{},[898,6819,1710],{},[1712,6821,2252],{},[1716,6823,6804],{},[902,6825,6826],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,6829,6831],{"className":6830},[886],[888,6832,6833],{"xmlns":890},[892,6834,6835,6873],{},[895,6836,6837,6839,6841,6843,6845,6853,6855,6858,6860,6863,6869,6871],{},[898,6838,2004],{"mathvariant":2003},[898,6840,1734],{},[898,6842,3737],{"mathvariant":2003},[1712,6844,3740],{},[2563,6846,6847],{"scriptlevel":2085,"displaystyle":1903},[2567,6848,6849,6851],{},[1716,6850,2222],{},[1716,6852,6198],{},[1712,6854,1783],{},[1716,6856,6857],{},"20",[1712,6859,1714],{},[1716,6861,6862],{},"6,",[6205,6864,6865,6867],{"accent":2565},[1716,6866,6209],{},[1712,6868,6212],{"stretchy":2565},[1762,6870,2583],{},[898,6872,3737],{"mathvariant":2003},[902,6874,6875],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,6877,6879],{"id":6878},"vícefaktorový-model","Vícefaktorový model",[724,6881,6882,6883,6896,6897,3245,6900,6913,6914,3245,6917,6936,6937,3245,6940,2854],{},"Předpokládejme, že poptávané množství ",[883,6884,6886],{"className":6885},[886],[888,6887,6888],{"xmlns":890},[892,6889,6890,6894],{},[895,6891,6892],{},[898,6893,1734],{},[902,6895,1734],{"encoding":904}," závisí na ",[38,6898,6899],{},"ceně základního zboží",[883,6901,6903],{"className":6902},[886],[888,6904,6905],{"xmlns":890},[892,6906,6907,6911],{},[895,6908,6909],{},[898,6910,1710],{},[902,6912,1710],{"encoding":904},", na ",[38,6915,6916],{},"ceně alternativního zboží",[883,6918,6920],{"className":6919},[886],[888,6921,6922],{"xmlns":890},[892,6923,6924,6933],{},[895,6925,6926],{},[6927,6928,6929,6931],"msub",{},[898,6930,1710],{},[898,6932,2044],{},[902,6934,6935],{"encoding":904},"P_A"," a na ",[38,6938,6939],{},"důchodu",[883,6941,6943],{"className":6942},[886],[888,6944,6945],{"xmlns":890},[892,6946,6947,6952],{},[895,6948,6949],{},[898,6950,6951],{},"Y",[902,6953,6951],{"encoding":904},[724,6955,6956],{},[883,6957,6959],{"className":6958,"title":1986,"style":1987},[1985],"Q = D(P, P_A, Y). \\tag{4.17}",[724,6961,6962,6963,6966],{},"V analogii jednofaktorového modelu pracujeme s ",[38,6964,6965],{},"parciálními derivacemi"," funkce poptávky.",[198,6968,6970],{"id":6969},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,6972,6973],{},[883,6974,6976],{"className":6975,"title":1986,"style":1987},[1985],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,6978,2101,6979,7000,7001,7014,7015,7037,7038,3245,7041,7087,7088,7101,7102,7119],{},[883,6980,6982],{"className":6981},[886],[888,6983,6984],{"xmlns":890},[892,6985,6986,6997],{},[895,6987,6988],{},[6989,6990,6991,6993,6995],"msubsup",{},[898,6992,1734],{},[898,6994,1710],{},[1712,6996,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,6998,6999],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,7002,7004],{"className":7003},[886],[888,7005,7006],{"xmlns":890},[892,7007,7008,7012],{},[895,7009,7010],{},[898,7011,1710],{},[902,7013,1710],{"encoding":904},". Vždy ",[883,7016,7018],{"className":7017},[886],[888,7019,7020],{"xmlns":890},[892,7021,7022,7034],{},[895,7023,7024,7030,7032],{},[6927,7025,7026,7028],{},[898,7027,2041],{},[898,7029,1710],{},[1712,7031,2282],{},[1716,7033,2085],{},[902,7035,7036],{"encoding":904},"E_P \\ge 0",". ",[614,7039,7040],{},"Interpretace:",[883,7042,7044],{"className":7043},[886],[888,7045,7046],{"xmlns":890},[892,7047,7048,7084],{},[895,7049,7050,7056,7058,7064,7066,7074,7076,7082],{},[6927,7051,7052,7054],{},[898,7053,2041],{},[898,7055,1710],{},[1712,7057,1904],{"stretchy":1903},[2037,7059,7060,7062],{},[898,7061,1710],{},[1712,7063,2145],{},[1712,7065,3138],{"separator":2565},[6989,7067,7068,7070,7072],{},[898,7069,1710],{},[898,7071,2044],{},[1712,7073,2145],{},[1712,7075,3138],{"separator":2565},[2037,7077,7078,7080],{},[898,7079,6951],{},[1712,7081,2145],{},[1712,7083,1910],{"stretchy":1903},[902,7085,7086],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,7089,7091],{"className":7090},[886],[888,7092,7093],{"xmlns":890},[892,7094,7095,7099],{},[895,7096,7097],{},[898,7098,1734],{},[902,7100,1734],{"encoding":904}," při 1% změně ",[883,7103,7105],{"className":7104},[886],[888,7106,7107],{"xmlns":890},[892,7108,7109,7117],{},[895,7110,7111],{},[2037,7112,7113,7115],{},[898,7114,1710],{},[1712,7116,2145],{},[902,7118,2195],{"encoding":904},", ceteris paribus.",[198,7121,7123],{"id":7122},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,7125,7126],{},[883,7127,7129],{"className":7128,"title":1986,"style":1987},[1985],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,7131,7132,7087,7134,7147,7148,7165],{},[614,7133,7040],{},[883,7135,7137],{"className":7136},[886],[888,7138,7139],{"xmlns":890},[892,7140,7141,7145],{},[895,7142,7143],{},[898,7144,1734],{},[902,7146,1734],{"encoding":904}," základního zboží při 1% změně ceny ",[883,7149,7151],{"className":7150},[886],[888,7152,7153],{"xmlns":890},[892,7154,7155,7163],{},[895,7156,7157],{},[6927,7158,7159,7161],{},[898,7160,1710],{},[898,7162,2044],{},[902,7164,6935],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,7167,7168],{},[38,7169,7170],{},"Znaménko závisí na povaze alternativního zboží:",[120,7172,7173,7261],{},[123,7174,7175,7176,7179,7180,7197,7198,3245,7211,1659],{},"Je-li alternativní zboží ",[38,7177,7178],{},"komplement",", růst ",[883,7181,7183],{"className":7182},[886],[888,7184,7185],{"xmlns":890},[892,7186,7187,7195],{},[895,7188,7189],{},[6927,7190,7191,7193],{},[898,7192,1710],{},[898,7194,2044],{},[902,7196,6935],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,7199,7201],{"className":7200},[886],[888,7202,7203],{"xmlns":890},[892,7204,7205,7209],{},[895,7206,7207],{},[898,7208,1734],{},[902,7210,1734],{"encoding":904},[883,7212,7214],{"className":7213},[886],[888,7215,7216],{"xmlns":890},[892,7217,7218,7258],{},[895,7219,7220,7222,7224,7236,7238,7240,7242,7244,7254,7256],{},[1712,7221,1767],{},[1762,7223,1764],{},[6989,7225,7226,7228,7234],{},[898,7227,1734],{},[6927,7229,7230,7232],{},[898,7231,1710],{},[898,7233,2044],{},[1712,7235,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,7237,2252],{},[1716,7239,2085],{},[1712,7241,3138],{"separator":2565},[1762,7243,1764],{},[6927,7245,7246,7248],{},[898,7247,2041],{},[6927,7249,7250,7252],{},[898,7251,1710],{},[898,7253,2044],{},[1712,7255,2252],{},[1716,7257,2085],{},[902,7259,7260],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,7262,7175,7263,7179,7266,7283,7284,7297,7298,1659],{},[38,7264,7265],{},"substitut",[883,7267,7269],{"className":7268},[886],[888,7270,7271],{"xmlns":890},[892,7272,7273,7281],{},[895,7274,7275],{},[6927,7276,7277,7279],{},[898,7278,1710],{},[898,7280,2044],{},[902,7282,6935],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,7285,7287],{"className":7286},[886],[888,7288,7289],{"xmlns":890},[892,7290,7291,7295],{},[895,7292,7293],{},[898,7294,1734],{},[902,7296,1734],{"encoding":904}," roste ",[883,7299,7301],{"className":7300},[886],[888,7302,7303],{"xmlns":890},[892,7304,7305,7345],{},[895,7306,7307,7309,7311,7323,7325,7327,7329,7331,7341,7343],{},[1712,7308,1767],{},[1762,7310,1764],{},[6989,7312,7313,7315,7321],{},[898,7314,1734],{},[6927,7316,7317,7319],{},[898,7318,1710],{},[898,7320,2044],{},[1712,7322,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,7324,2302],{},[1716,7326,2085],{},[1712,7328,3138],{"separator":2565},[1762,7330,1764],{},[6927,7332,7333,7335],{},[898,7334,2041],{},[6927,7336,7337,7339],{},[898,7338,1710],{},[898,7340,2044],{},[1712,7342,2302],{},[1716,7344,2085],{},[902,7346,7347],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,7349,7352],{"className":7350,"title":7351,"style":1987},[1985],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":7354},[7355,7359,7360,7368,7369,7373,7376],{"id":1662,"depth":642,"text":1663,"children":7356},[7357,7358],{"id":1694,"depth":649,"text":1695},{"id":1885,"depth":649,"text":1886},{"id":1923,"depth":642,"text":1924},{"id":1949,"depth":642,"text":1950,"children":7361},[7362,7363,7364,7365,7367],{"id":2662,"depth":649,"text":2663},{"id":2752,"depth":649,"text":2753},{"id":3094,"depth":649,"text":3095},{"id":3178,"depth":649,"text":7366},"Výpočet, je-li dáno PP jako funkce QQ",{"id":3440,"depth":649,"text":3441},{"id":3766,"depth":642,"text":3767},{"id":4364,"depth":642,"text":4365,"children":7370},[7371,7372],{"id":4995,"depth":649,"text":4996},{"id":5825,"depth":649,"text":5826},{"id":6461,"depth":642,"text":6462,"children":7374},[7375],{"id":6587,"depth":649,"text":6588},{"id":6878,"depth":642,"text":6879,"children":7377},[7378,7379],{"id":6969,"depth":649,"text":6970},{"id":7122,"depth":649,"text":7123},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":1629,"description":641},[1138,1136],"topics\u002Felasticita",[1128,1669,7387,7388,7389,7390],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","topic","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM","topics",{"zapisku":1625,"topics":7395,"summaries":7396,"outputs":7397},15,5,1,[7399,9257,14440,15997,16869,21153,22760,32640,41634,55701,59993,79337,91449,100408,100696],{"id":7400,"title":7401,"body":7402,"course":1128,"courses":659,"created":1129,"description":9246,"extension":661,"meta":9247,"navigation":664,"path":9248,"seo":9249,"sources":9250,"stem":9251,"tags":9252,"type":7391,"updated":677,"__hash__":9256},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":7403,"toc":9229},[7404,7407,7428,7432,7511,7514,7639,7783,7785,7865,7869,7930,7980,7987,7991,8125,8175,8179,8220,8286,8355,8363,8367,8405,8477,8481,8559,8607,8650,8654,8658,8728,8732,8782,8859,8866,8869,8922,9190,9194],[12,7405,7401],{"id":7406},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,7408,7409,7410,7416,7417,7420,7421,7424,7425,1659],{},"Matematický aparát kurzu ",[207,7411,7415],{"className":7412,"dataFsResolvedFilePath":7413,"href":7414},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","ImeK",". Bez derivace se neobejdou ",[38,7418,7419],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,7422,7423],{},"maximalizace zisku"," ani ",[38,7426,7427],{},"minimalizace nákladů",[115,7429,7431],{"id":7430},"funkce-a-polynomy","Funkce a polynomy",[724,7433,7434,7435,7462,7463,7476,7477,7490,7491,1659],{},"Funkce jedné proměnné ",[883,7436,7438],{"className":7437},[886],[888,7439,7440],{"xmlns":890},[892,7441,7442,7459],{},[895,7443,7444,7447,7449,7452,7454,7457],{},[898,7445,7446],{},"y",[1712,7448,1714],{},[898,7450,7451],{},"f",[1712,7453,1904],{"stretchy":1903},[898,7455,7456],{},"x",[1712,7458,1910],{"stretchy":1903},[902,7460,7461],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,7464,7466],{"className":7465},[886],[888,7467,7468],{"xmlns":890},[892,7469,7470,7474],{},[895,7471,7472],{},[898,7473,7456],{},[902,7475,7456],{"encoding":904}," (nezávislá) → ",[883,7478,7480],{"className":7479},[886],[888,7481,7482],{"xmlns":890},[892,7483,7484,7488],{},[895,7485,7486],{},[898,7487,7446],{},[902,7489,7446],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,7492,7494],{"className":7493},[886],[888,7495,7496],{"xmlns":890},[892,7497,7498,7508],{},[895,7499,7500,7502,7504,7506],{},[898,7501,7451],{},[1712,7503,1904],{"stretchy":1903},[898,7505,207],{},[1712,7507,1910],{"stretchy":1903},[902,7509,7510],{"encoding":904},"f(a)",[724,7512,7513],{},"Polynomy:",[120,7515,7516,7548,7589],{},[123,7517,7518],{},[152,7519,7520],{},[123,7521,7522,7523],{},"stupně: ",[883,7524,7526],{"className":7525},[886],[888,7527,7528],{"xmlns":890},[892,7529,7530,7545],{},[895,7531,7532,7534,7536,7538,7540,7542],{},[898,7533,7446],{},[1712,7535,1714],{},[898,7537,207],{},[898,7539,7456],{},[1712,7541,3145],{},[898,7543,7544],{},"b",[902,7546,7547],{"encoding":904},"y = ax + b",[123,7549,7550],{},[152,7551,7552],{"start":642},[123,7553,7522,7554],{},[883,7555,7557],{"className":7556},[886],[888,7558,7559],{"xmlns":890},[892,7560,7561,7586],{},[895,7562,7563,7565,7567,7569,7575,7577,7579,7581,7583],{},[898,7564,7446],{},[1712,7566,1714],{},[898,7568,207],{},[2037,7570,7571,7573],{},[898,7572,7456],{},[1716,7574,2787],{},[1712,7576,3145],{},[898,7578,7544],{},[898,7580,7456],{},[1712,7582,3145],{},[898,7584,7585],{},"c",[902,7587,7588],{"encoding":904},"y = ax^2 + bx + c",[123,7590,7591],{},[152,7592,7593],{"start":649},[123,7594,7522,7595],{},[883,7596,7598],{"className":7597},[886],[888,7599,7600],{"xmlns":890},[892,7601,7602,7636],{},[895,7603,7604,7606,7608,7610,7616,7618,7620,7626,7628,7630,7632,7634],{},[898,7605,7446],{},[1712,7607,1714],{},[898,7609,207],{},[2037,7611,7612,7614],{},[898,7613,7456],{},[1716,7615,6198],{},[1712,7617,3145],{},[898,7619,7544],{},[2037,7621,7622,7624],{},[898,7623,7456],{},[1716,7625,2787],{},[1712,7627,3145],{},[898,7629,7585],{},[898,7631,7456],{},[1712,7633,3145],{},[898,7635,2468],{},[902,7637,7638],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,7640,7641,3245,7644,7698,7699,7736,7737,1659],{},[38,7642,7643],{},"Příklad rozkladu:",[883,7645,7647],{"className":7646},[886],[888,7648,7649],{"xmlns":890},[892,7650,7651,7695],{},[895,7652,7653,7655,7657,7663,7665,7667,7669,7671,7673,7675,7677,7679,7681,7683,7685,7687,7689,7691,7693],{},[898,7654,7446],{},[1712,7656,1714],{},[2037,7658,7659,7661],{},[898,7660,7456],{},[1716,7662,2787],{},[1712,7664,2219],{},[1716,7666,3068],{},[898,7668,7456],{},[1712,7670,3145],{},[1716,7672,6209],{},[1712,7674,1714],{},[1712,7676,1904],{"stretchy":1903},[898,7678,7456],{},[1712,7680,2219],{},[1716,7682,2787],{},[1712,7684,1910],{"stretchy":1903},[1712,7686,1904],{"stretchy":1903},[898,7688,7456],{},[1712,7690,2219],{},[1716,7692,6198],{},[1712,7694,1910],{"stretchy":1903},[902,7696,7697],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,7700,7702],{"className":7701},[886],[888,7703,7704],{"xmlns":890},[892,7705,7706,7733],{},[895,7707,7708,7714,7716,7718,7720,7723,7729,7731],{},[6927,7709,7710,7712],{},[898,7711,7456],{},[1716,7713,2222],{},[1712,7715,1714],{},[1716,7717,2787],{},[1712,7719,3138],{"separator":2565},[1762,7721,7722],{}," ",[6927,7724,7725,7727],{},[898,7726,7456],{},[1716,7728,2787],{},[1712,7730,1714],{},[1716,7732,6198],{},[902,7734,7735],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,7738,7740],{"className":7739},[886],[888,7741,7742],{"xmlns":890},[892,7743,7744,7780],{},[895,7745,7746,7748,7750,7752,7754,7756,7764,7770,7772],{},[898,7747,7446],{},[1712,7749,1714],{},[1712,7751,1904],{"stretchy":1903},[898,7753,7456],{},[1712,7755,2219],{},[2563,7757,7758],{"scriptlevel":2085,"displaystyle":1903},[2567,7759,7760,7762],{},[1716,7761,3068],{},[1716,7763,2787],{},[2037,7765,7766,7768],{},[1712,7767,1910],{"stretchy":1903},[1716,7769,2787],{},[1712,7771,2219],{},[2563,7773,7774],{"scriptlevel":2085,"displaystyle":1903},[2567,7775,7776,7778],{},[1716,7777,2222],{},[1716,7779,2975],{},[902,7781,7782],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,7784,1690],{"id":1145},[724,7786,7787,7788,1348,7812,7840,7841,1659],{},"Označení ",[883,7789,7791],{"className":7790},[886],[888,7792,7793],{"xmlns":890},[892,7794,7795,7809],{},[895,7796,7797,7803,7805,7807],{},[2037,7798,7799,7801],{},[898,7800,7451],{},[1712,7802,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,7804,1904],{"stretchy":1903},[898,7806,7456],{},[1712,7808,1910],{"stretchy":1903},[902,7810,7811],{"encoding":904},"f'(x)",[883,7813,7815],{"className":7814},[886],[888,7816,7817],{"xmlns":890},[892,7818,7819,7837],{},[895,7820,7821],{},[2563,7822,7823],{"scriptlevel":2085,"displaystyle":2565},[2567,7824,7825,7831],{},[895,7826,7827,7829],{},[898,7828,2468],{},[898,7830,7446],{},[895,7832,7833,7835],{},[898,7834,2468],{},[898,7836,7456],{},[902,7838,7839],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,7842,7844],{"className":7843},[886],[888,7845,7846],{"xmlns":890},[892,7847,7848,7862],{},[895,7849,7850,7856,7858,7860],{},[2037,7851,7852,7854],{},[898,7853,7451],{},[1712,7855,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,7857,1904],{"stretchy":1903},[898,7859,207],{},[1712,7861,1910],{"stretchy":1903},[902,7863,7864],{"encoding":904},"f'(a)",[198,7866,7868],{"id":7867},"geometrická-interpretace","Geometrická interpretace",[724,7870,7871,7894,7895,7898,7899,7929],{},[883,7872,7874],{"className":7873},[886],[888,7875,7876],{"xmlns":890},[892,7877,7878,7892],{},[895,7879,7880,7886,7888,7890],{},[2037,7881,7882,7884],{},[898,7883,7451],{},[1712,7885,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,7887,1904],{"stretchy":1903},[898,7889,207],{},[1712,7891,1910],{"stretchy":1903},[902,7893,7864],{"encoding":904}," = ",[38,7896,7897],{},"sklon tečny"," ke grafu funkce v bodě ",[883,7900,7902],{"className":7901},[886],[888,7903,7904],{"xmlns":890},[892,7905,7906,7926],{},[895,7907,7908,7911,7913,7915,7917,7919,7921,7923],{},[1712,7909,7910],{"stretchy":1903},"[",[898,7912,207],{},[1712,7914,3138],{"separator":2565},[898,7916,7451],{},[1712,7918,1904],{"stretchy":1903},[898,7920,207],{},[1712,7922,1910],{"stretchy":1903},[1712,7924,7925],{"stretchy":1903},"]",[902,7927,7928],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,7931,7932],{},[883,7933,7935],{"className":7934},[886],[888,7936,7937],{"xmlns":890},[892,7938,7939,7977],{},[895,7940,7941,7943,7945,7947,7949,7951,7953,7955,7961,7963,7965,7967,7969,7971,7973,7975],{},[898,7942,7446],{},[1712,7944,2219],{},[898,7946,7451],{},[1712,7948,1904],{"stretchy":1903},[898,7950,207],{},[1712,7952,1910],{"stretchy":1903},[1712,7954,1714],{},[2037,7956,7957,7959],{},[898,7958,7451],{},[1712,7960,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,7962,1904],{"stretchy":1903},[898,7964,207],{},[1712,7966,1910],{"stretchy":1903},[1712,7968,1904],{"stretchy":1903},[898,7970,7456],{},[1712,7972,2219],{},[898,7974,207],{},[1712,7976,1910],{"stretchy":1903},[902,7978,7979],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,7981,7982],{},[3817,7983],{"alt":7984,"className":7985,"src":7986},"imek-derivace-tecna",[210,3821],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,7988,7990],{"id":7989},"inženýrská-interpretace","Inženýrská interpretace",[724,7992,7993,7894,8016,3245,8019,8032,8033,8046,8047,8065,8066,8079,8080,8093,8094,3072,8107,2854],{},[883,7994,7996],{"className":7995},[886],[888,7997,7998],{"xmlns":890},[892,7999,8000,8014],{},[895,8001,8002,8008,8010,8012],{},[2037,8003,8004,8006],{},[898,8005,7451],{},[1712,8007,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,8009,1904],{"stretchy":1903},[898,8011,207],{},[1712,8013,1910],{"stretchy":1903},[902,8015,7864],{"encoding":904},[38,8017,8018],{},"rychlost změny",[883,8020,8022],{"className":8021},[886],[888,8023,8024],{"xmlns":890},[892,8025,8026,8030],{},[895,8027,8028],{},[898,8029,7446],{},[902,8031,7446],{"encoding":904}," vzhledem k ",[883,8034,8036],{"className":8035},[886],[888,8037,8038],{"xmlns":890},[892,8039,8040,8044],{},[895,8041,8042],{},[898,8043,7456],{},[902,8045,7456],{"encoding":904}," v bodě ",[883,8048,8050],{"className":8049},[886],[888,8051,8052],{"xmlns":890},[892,8053,8054,8062],{},[895,8055,8056,8058,8060],{},[898,8057,7456],{},[1712,8059,1714],{},[898,8061,207],{},[902,8063,8064],{"encoding":904},"x = a","; přibližná změna ",[883,8067,8069],{"className":8068},[886],[888,8070,8071],{"xmlns":890},[892,8072,8073,8077],{},[895,8074,8075],{},[898,8076,7446],{},[902,8078,7446],{"encoding":904}," při změně ",[883,8081,8083],{"className":8082},[886],[888,8084,8085],{"xmlns":890},[892,8086,8087,8091],{},[895,8088,8089],{},[898,8090,7456],{},[902,8092,7456],{"encoding":904}," z ",[883,8095,8097],{"className":8096},[886],[888,8098,8099],{"xmlns":890},[892,8100,8101,8105],{},[895,8102,8103],{},[898,8104,207],{},[902,8106,207],{"encoding":904},[883,8108,8110],{"className":8109},[886],[888,8111,8112],{"xmlns":890},[892,8113,8114,8122],{},[895,8115,8116,8118,8120],{},[898,8117,207],{},[1712,8119,3145],{},[1716,8121,2222],{},[902,8123,8124],{"encoding":904},"a+1",[724,8126,8127],{},[883,8128,8130],{"className":8129},[886],[888,8131,8132],{"xmlns":890},[892,8133,8134,8172],{},[895,8135,8136,8138,8140,8142,8144,8146,8148,8150,8152,8154,8156,8158,8160,8166,8168,8170],{},[898,8137,7451],{},[1712,8139,1904],{"stretchy":1903},[898,8141,207],{},[1712,8143,3145],{},[1716,8145,2222],{},[1712,8147,1910],{"stretchy":1903},[1712,8149,3740],{},[898,8151,7451],{},[1712,8153,1904],{"stretchy":1903},[898,8155,207],{},[1712,8157,1910],{"stretchy":1903},[1712,8159,3145],{},[2037,8161,8162,8164],{},[898,8163,7451],{},[1712,8165,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,8167,1904],{"stretchy":1903},[898,8169,207],{},[1712,8171,1910],{"stretchy":1903},[902,8173,8174],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,8176,8178],{"id":8177},"příklad-mezní-náklady","Příklad — mezní náklady",[724,8180,8181,8182,1659],{},"Celkové náklady ",[883,8183,8185],{"className":8184},[886],[888,8186,8187],{"xmlns":890},[892,8188,8189,8217],{},[895,8190,8191,8193,8196,8198,8201,8203,8205,8207,8209,8211],{},[898,8192,1772],{},[898,8194,8195],{},"C",[1712,8197,1714],{},[1716,8199,8200],{},"1000",[1712,8202,3145],{},[1716,8204,2787],{},[898,8206,1734],{},[1712,8208,3145],{},[1716,8210,6607],{},[2037,8212,8213,8215],{},[898,8214,1734],{},[1716,8216,2787],{},[902,8218,8219],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,8221,8222,8223,8259,8260,1659],{},"Mezní náklady: ",[883,8224,8226],{"className":8225},[886],[888,8227,8228],{"xmlns":890},[892,8229,8230,8256],{},[895,8231,8232,8234,8236,8238,8240,8246,8248,8250,8252,8254],{},[898,8233,4445],{},[898,8235,8195],{},[1712,8237,1714],{},[898,8239,1772],{},[2037,8241,8242,8244],{},[898,8243,8195],{},[1712,8245,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,8247,1714],{},[1716,8249,2787],{},[1712,8251,3145],{},[1716,8253,6673],{},[898,8255,1734],{},[902,8257,8258],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,8261,8263],{"className":8262},[886],[888,8264,8265],{"xmlns":890},[892,8266,8267,8283],{},[895,8268,8269,8271,8273,8275,8277,8279,8281],{},[898,8270,4445],{},[898,8272,8195],{},[1712,8274,1904],{"stretchy":1903},[1716,8276,1718],{},[1712,8278,1910],{"stretchy":1903},[1712,8280,1714],{},[1716,8282,2975],{},[902,8284,8285],{"encoding":904},"MC(10) = 4",[724,8287,8288,3245,8291,7037,8339,3245,8342,1659],{},[38,8289,8290],{},"Skutečný přírůstek:",[883,8292,8294],{"className":8293},[886],[888,8295,8296],{"xmlns":890},[892,8297,8298,8336],{},[895,8299,8300,8302,8304,8306,8308,8310,8312,8314,8317,8319,8321,8323,8325,8327,8329,8331,8333],{},[898,8301,2004],{"mathvariant":2003},[898,8303,1772],{},[898,8305,8195],{},[1712,8307,1714],{},[898,8309,1772],{},[898,8311,8195],{},[1712,8313,1904],{"stretchy":1903},[1716,8315,8316],{},"11",[1712,8318,1910],{"stretchy":1903},[1712,8320,2219],{},[898,8322,1772],{},[898,8324,8195],{},[1712,8326,1904],{"stretchy":1903},[1716,8328,1718],{},[1712,8330,1910],{"stretchy":1903},[1712,8332,1714],{},[1716,8334,8335],{},"4,2",[902,8337,8338],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,8340,8341],{},"Přibližný (lineární):",[883,8343,8345],{"className":8344},[886],[888,8346,8347],{"xmlns":890},[892,8348,8349,8353],{},[895,8350,8351],{},[1716,8352,2975],{},[902,8354,2975],{"encoding":904},[724,8356,8357,8358,8362],{},"(Viz aplikace v ",[207,8359,8361],{"className":8360,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,8364,8366],{"id":8365},"diferenciál","Diferenciál",[724,8368,8369],{},[883,8370,8372],{"className":8371},[886],[888,8373,8374],{"xmlns":890},[892,8375,8376,8402],{},[895,8377,8378,8380,8382,8384,8390,8392,8394,8396,8398,8400],{},[898,8379,2468],{},[898,8381,7451],{},[1712,8383,1714],{},[2037,8385,8386,8388],{},[898,8387,7451],{},[1712,8389,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,8391,1904],{"stretchy":1903},[898,8393,7456],{},[1712,8395,1910],{"stretchy":1903},[1762,8397,2583],{},[898,8399,2468],{},[898,8401,7456],{},[902,8403,8404],{"encoding":904},"df = f'(x)\\, dx",[724,8406,8407,8408,8424,8425,8473,8474,1659],{},"Pro malá ",[883,8409,8411],{"className":8410},[886],[888,8412,8413],{"xmlns":890},[892,8414,8415,8421],{},[895,8416,8417,8419],{},[898,8418,2468],{},[898,8420,7456],{},[902,8422,8423],{"encoding":904},"dx"," platí: ",[883,8426,8428],{"className":8427},[886],[888,8429,8430],{"xmlns":890},[892,8431,8432,8470],{},[895,8433,8434,8436,8438,8440,8442,8444,8446,8448,8450,8452,8454,8456,8458,8460,8462,8464,8466,8468],{},[898,8435,2004],{"mathvariant":2003},[898,8437,7451],{},[1712,8439,1714],{},[898,8441,7451],{},[1712,8443,1904],{"stretchy":1903},[898,8445,7456],{},[1712,8447,3145],{},[898,8449,2468],{},[898,8451,7456],{},[1712,8453,1910],{"stretchy":1903},[1712,8455,2219],{},[898,8457,7451],{},[1712,8459,1904],{"stretchy":1903},[898,8461,7456],{},[1712,8463,1910],{"stretchy":1903},[1712,8465,3740],{},[898,8467,2468],{},[898,8469,7451],{},[902,8471,8472],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,8475,8476],{},"lineární odhad přírůstku",[198,8478,8480],{"id":8479},"příklad","Příklad",[724,8482,8483,8513,8514,8537,8538,8558],{},[883,8484,8486],{"className":8485},[886],[888,8487,8488],{"xmlns":890},[892,8489,8490,8510],{},[895,8491,8492,8494,8496,8498,8500,8502,8504],{},[898,8493,1772],{},[898,8495,8195],{},[1712,8497,1714],{},[1716,8499,1739],{},[1712,8501,3145],{},[1716,8503,6607],{},[2037,8505,8506,8508],{},[898,8507,1734],{},[1716,8509,2787],{},[902,8511,8512],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,8515,8517],{"className":8516},[886],[888,8518,8519],{"xmlns":890},[892,8520,8521,8534],{},[895,8522,8523,8525,8527,8529,8531],{},[898,8524,1734],{},[1712,8526,2854],{},[1716,8528,2782],{},[1712,8530,2082],{},[1716,8532,8533],{},"60",[902,8535,8536],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,8539,8541],{"className":8540},[886],[888,8542,8543],{"xmlns":890},[892,8544,8545,8555],{},[895,8546,8547,8549,8551,8553],{},[898,8548,2468],{},[898,8550,1734],{},[1712,8552,1714],{},[1716,8554,1718],{},[902,8556,8557],{"encoding":904},"dQ = 10","):",[724,8560,8561],{},[883,8562,8564],{"className":8563},[886],[888,8565,8566],{"xmlns":890},[892,8567,8568,8604],{},[895,8569,8570,8572,8574,8576,8578,8580,8582,8584,8586,8588,8590,8592,8594,8596,8598,8600,8602],{},[898,8571,2468],{},[898,8573,1772],{},[898,8575,8195],{},[1712,8577,1714],{},[1716,8579,6673],{},[898,8581,1734],{},[1712,8583,1783],{},[898,8585,2468],{},[898,8587,1734],{},[1712,8589,1714],{},[1716,8591,6673],{},[1712,8593,1783],{},[1716,8595,2782],{},[1712,8597,1783],{},[1716,8599,1718],{},[1712,8601,1714],{},[1716,8603,1739],{},[902,8605,8606],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,8608,8609,8610,8632,8633,8649],{},"Přesná změna: ",[883,8611,8613],{"className":8612},[886],[888,8614,8615],{"xmlns":890},[892,8616,8617,8629],{},[895,8618,8619,8621,8623,8625,8627],{},[898,8620,2004],{"mathvariant":2003},[898,8622,1772],{},[898,8624,8195],{},[1712,8626,1714],{},[1716,8628,1786],{},[902,8630,8631],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,8634,8636],{"className":8635},[886],[888,8637,8638],{"xmlns":890},[892,8639,8640,8646],{},[895,8641,8642,8644],{},[898,8643,1772],{},[898,8645,8195],{},[902,8647,8648],{"encoding":904},"TC"," je konvexní.",[115,8651,8653],{"id":8652},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,8655,8657],{"id":8656},"nutná-podmínka","Nutná podmínka",[724,8659,8660,8661,8046,8681,8694,8695,8723,8724,8727],{},"Má-li ",[883,8662,8664],{"className":8663},[886],[888,8665,8666],{"xmlns":890},[892,8667,8668,8678],{},[895,8669,8670,8672,8674,8676],{},[898,8671,7451],{},[1712,8673,1904],{"stretchy":1903},[898,8675,7456],{},[1712,8677,1910],{"stretchy":1903},[902,8679,8680],{"encoding":904},"f(x)",[883,8682,8684],{"className":8683},[886],[888,8685,8686],{"xmlns":890},[892,8687,8688,8692],{},[895,8689,8690],{},[898,8691,207],{},[902,8693,207],{"encoding":904}," extrém, pak ",[883,8696,8698],{"className":8697},[886],[888,8699,8700],{"xmlns":890},[892,8701,8702,8720],{},[895,8703,8704,8710,8712,8714,8716,8718],{},[2037,8705,8706,8708],{},[898,8707,7451],{},[1712,8709,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,8711,1904],{"stretchy":1903},[898,8713,207],{},[1712,8715,1910],{"stretchy":1903},[1712,8717,1714],{},[1716,8719,2085],{},[902,8721,8722],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,8725,8726],{},"stacionární"," (podezřelé) body.",[198,8729,8731],{"id":8730},"postačující-podmínka","Postačující podmínka",[724,8733,8734,8735,8748,8749,2854],{},"Pro stacionární bod ",[883,8736,8738],{"className":8737},[886],[888,8739,8740],{"xmlns":890},[892,8741,8742,8746],{},[895,8743,8744],{},[898,8745,207],{},[902,8747,207],{"encoding":904},", je-li ",[883,8750,8752],{"className":8751},[886],[888,8753,8754],{"xmlns":890},[892,8755,8756,8779],{},[895,8757,8758,8768,8770,8772,8774,8777],{},[2037,8759,8760,8762],{},[898,8761,7451],{},[895,8763,8764,8766],{},[1712,8765,2243],{"mathvariant":2003},[1712,8767,2243],{"mathvariant":2003},[1712,8769,1904],{"stretchy":1903},[898,8771,207],{},[1712,8773,1910],{"stretchy":1903},[1712,8775,8776],{"mathvariant":2003},"≠",[1716,8778,2085],{},[902,8780,8781],{"encoding":904},"f''(a) \\neq 0",[120,8783,8784,8822],{},[123,8785,8786,8818,8819],{},[883,8787,8789],{"className":8788},[886],[888,8790,8791],{"xmlns":890},[892,8792,8793,8815],{},[895,8794,8795,8805,8807,8809,8811,8813],{},[2037,8796,8797,8799],{},[898,8798,7451],{},[895,8800,8801,8803],{},[1712,8802,2243],{"mathvariant":2003},[1712,8804,2243],{"mathvariant":2003},[1712,8806,1904],{"stretchy":1903},[898,8808,207],{},[1712,8810,1910],{"stretchy":1903},[1712,8812,2302],{},[1716,8814,2085],{},[902,8816,8817],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,8820,8821],{},"lokální minimum",[123,8823,8824,8818,8856],{},[883,8825,8827],{"className":8826},[886],[888,8828,8829],{"xmlns":890},[892,8830,8831,8853],{},[895,8832,8833,8843,8845,8847,8849,8851],{},[2037,8834,8835,8837],{},[898,8836,7451],{},[895,8838,8839,8841],{},[1712,8840,2243],{"mathvariant":2003},[1712,8842,2243],{"mathvariant":2003},[1712,8844,1904],{"stretchy":1903},[898,8846,207],{},[1712,8848,1910],{"stretchy":1903},[1712,8850,2252],{},[1716,8852,2085],{},[902,8854,8855],{"encoding":904},"f''(a) \u003C 0",[38,8857,8858],{},"lokální maximum",[724,8860,8861],{},[3817,8862],{"alt":8863,"className":8864,"src":8865},"imek-extremy-1d",[210,3821],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,8867,8480],{"id":8868},"příklad-1",[724,8870,8871],{},[883,8872,8874],{"className":8873},[886],[888,8875,8876],{"xmlns":890},[892,8877,8878,8919],{},[895,8879,8880,8882,8884,8886,8888,8890,8892,8898,8900,8902,8908,8910,8913,8915,8917],{},[898,8881,7451],{},[1712,8883,1904],{"stretchy":1903},[898,8885,7456],{},[1712,8887,1910],{"stretchy":1903},[1712,8889,1714],{},[1716,8891,2787],{},[2037,8893,8894,8896],{},[898,8895,7456],{},[1716,8897,6198],{},[1712,8899,2219],{},[1716,8901,6198],{},[2037,8903,8904,8906],{},[898,8905,7456],{},[1716,8907,2787],{},[1712,8909,2219],{},[1716,8911,8912],{},"12",[898,8914,7456],{},[1712,8916,3145],{},[1716,8918,6198],{},[902,8920,8921],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,8923,8924,9035,9075,9136],{},[123,8925,8926,8998,8999],{},[883,8927,8929],{"className":8928},[886],[888,8930,8931],{"xmlns":890},[892,8932,8933,8995],{},[895,8934,8935,8941,8943,8945,8947,8949,8951,8957,8959,8961,8963,8965,8967,8969,8971,8973,8975,8977,8979,8981,8983,8985,8987,8989,8991,8993],{},[2037,8936,8937,8939],{},[898,8938,7451],{},[1712,8940,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,8942,1904],{"stretchy":1903},[898,8944,7456],{},[1712,8946,1910],{"stretchy":1903},[1712,8948,1714],{},[1716,8950,6209],{},[2037,8952,8953,8955],{},[898,8954,7456],{},[1716,8956,2787],{},[1712,8958,2219],{},[1716,8960,6209],{},[898,8962,7456],{},[1712,8964,2219],{},[1716,8966,8912],{},[1712,8968,1714],{},[1716,8970,6209],{},[1712,8972,1904],{"stretchy":1903},[898,8974,7456],{},[1712,8976,3145],{},[1716,8978,2222],{},[1712,8980,1910],{"stretchy":1903},[1712,8982,1904],{"stretchy":1903},[898,8984,7456],{},[1712,8986,2219],{},[1716,8988,2787],{},[1712,8990,1910],{"stretchy":1903},[1712,8992,1714],{},[1716,8994,2085],{},[902,8996,8997],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,9000,9002],{"className":9001},[886],[888,9003,9004],{"xmlns":890},[892,9005,9006,9032],{},[895,9007,9008,9014,9016,9018,9020,9022,9028,9030],{},[6927,9009,9010,9012],{},[898,9011,7456],{},[1716,9013,2222],{},[1712,9015,1714],{},[1712,9017,2219],{},[1716,9019,2222],{},[1712,9021,3138],{"separator":2565},[6927,9023,9024,9026],{},[898,9025,7456],{},[1716,9027,2787],{},[1712,9029,1714],{},[1716,9031,2787],{},[902,9033,9034],{"encoding":904},"x_1 = -1, x_2 = 2",[123,9036,9037],{},[883,9038,9040],{"className":9039},[886],[888,9041,9042],{"xmlns":890},[892,9043,9044,9072],{},[895,9045,9046,9056,9058,9060,9062,9064,9066,9068,9070],{},[2037,9047,9048,9050],{},[898,9049,7451],{},[895,9051,9052,9054],{},[1712,9053,2243],{"mathvariant":2003},[1712,9055,2243],{"mathvariant":2003},[1712,9057,1904],{"stretchy":1903},[898,9059,7456],{},[1712,9061,1910],{"stretchy":1903},[1712,9063,1714],{},[1716,9065,8912],{},[898,9067,7456],{},[1712,9069,2219],{},[1716,9071,6209],{},[902,9073,9074],{"encoding":904},"f''(x) = 12x - 6",[123,9076,9077,8818,9118,9120,9121],{},[883,9078,9080],{"className":9079},[886],[888,9081,9082],{"xmlns":890},[892,9083,9084,9115],{},[895,9085,9086,9096,9098,9100,9102,9104,9106,9108,9111,9113],{},[2037,9087,9088,9090],{},[898,9089,7451],{},[895,9091,9092,9094],{},[1712,9093,2243],{"mathvariant":2003},[1712,9095,2243],{"mathvariant":2003},[1712,9097,1904],{"stretchy":1903},[1712,9099,2219],{},[1716,9101,2222],{},[1712,9103,1910],{"stretchy":1903},[1712,9105,1714],{},[1712,9107,2219],{},[1716,9109,9110],{},"18",[1712,9112,2252],{},[1716,9114,2085],{},[902,9116,9117],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,9119,5766],{}," v ",[883,9122,9124],{"className":9123},[886],[888,9125,9126],{"xmlns":890},[892,9127,9128,9134],{},[895,9129,9130,9132],{},[1712,9131,2219],{},[1716,9133,2222],{},[902,9135,2225],{"encoding":904},[123,9137,9138,8818,9174,9120,9177],{},[883,9139,9141],{"className":9140},[886],[888,9142,9143],{"xmlns":890},[892,9144,9145,9171],{},[895,9146,9147,9157,9159,9161,9163,9165,9167,9169],{},[2037,9148,9149,9151],{},[898,9150,7451],{},[895,9152,9153,9155],{},[1712,9154,2243],{"mathvariant":2003},[1712,9156,2243],{"mathvariant":2003},[1712,9158,1904],{"stretchy":1903},[1716,9160,2787],{},[1712,9162,1910],{"stretchy":1903},[1712,9164,1714],{},[1716,9166,9110],{},[1712,9168,2302],{},[1716,9170,2085],{},[902,9172,9173],{"encoding":904},"f''(2) = 18 > 0",[38,9175,9176],{},"minimum",[883,9178,9180],{"className":9179},[886],[888,9181,9182],{"xmlns":890},[892,9183,9184,9188],{},[895,9185,9186],{},[1716,9187,2787],{},[902,9189,2787],{"encoding":904},[115,9191,9193],{"id":9192},"navigace","Navigace",[120,9195,9196,9204,9212],{},[123,9197,9198,3245,9201],{},[38,9199,9200],{},"Předchozí:",[207,9202,757],{"className":9203,"dataFsResolvedFilePath":755,"href":756},[210],[123,9205,9206,3245,9209],{},[38,9207,9208],{},"Navazující:",[207,9210,775],{"className":9211,"dataFsResolvedFilePath":773,"href":774},[210],[123,9213,9214,3245,9217,9220,9221,9224,9225,9228],{},[38,9215,9216],{},"Souvislosti:",[207,9218,784],{"className":9219,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,9222,4992],{"className":9223,"dataFsResolvedFilePath":827,"href":828},[210]," (aplikace mezních veličin), ",[207,9226,1646],{"className":9227,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":9230},[9231,9232,9237,9240,9245],{"id":7430,"depth":642,"text":7431},{"id":1145,"depth":642,"text":1690,"children":9233},[9234,9235,9236],{"id":7867,"depth":649,"text":7868},{"id":7989,"depth":649,"text":7990},{"id":8177,"depth":649,"text":8178},{"id":8365,"depth":642,"text":8366,"children":9238},[9239],{"id":8479,"depth":649,"text":8480},{"id":8652,"depth":642,"text":8653,"children":9241},[9242,9243,9244],{"id":8656,"depth":649,"text":8657},{"id":8730,"depth":649,"text":8731},{"id":8868,"depth":649,"text":8480},{"id":9192,"depth":642,"text":9193},"Matematický aparát kurzu ImeK. Bez derivace se neobejdou mezní veličiny (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde maximalizace zisku ani minimalizace 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:642,"links":14411},[14412,14416,14417,14424,14425,14429,14432],{"id":1662,"depth":642,"text":1663,"children":14413},[14414,14415],{"id":1694,"depth":649,"text":1695},{"id":1885,"depth":649,"text":1886},{"id":1923,"depth":642,"text":1924},{"id":1949,"depth":642,"text":1950,"children":14418},[14419,14420,14421,14422,14423],{"id":2662,"depth":649,"text":2663},{"id":2752,"depth":649,"text":2753},{"id":3094,"depth":649,"text":3095},{"id":3178,"depth":649,"text":7366},{"id":3440,"depth":649,"text":3441},{"id":3766,"depth":642,"text":3767},{"id":4364,"depth":642,"text":4365,"children":14426},[14427,14428],{"id":4995,"depth":649,"text":4996},{"id":5825,"depth":649,"text":5826},{"id":6461,"depth":642,"text":6462,"children":14430},[14431],{"id":6587,"depth":649,"text":6588},{"id":6878,"depth":642,"text":6879,"children":14433},[14434,14435],{"id":6969,"depth":649,"text":6970},{"id":7122,"depth":649,"text":7123},{},{"title":1629,"description":641},[1138,1136],[1128,1669,7387,7388,7389,7390],{"id":14441,"title":14442,"body":14443,"course":1128,"courses":659,"created":1129,"description":15985,"extension":661,"meta":15986,"navigation":664,"path":15987,"seo":15988,"sources":15989,"stem":15990,"tags":15991,"type":7391,"updated":677,"__hash__":15996},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":14444,"toc":15970},[14445,14448,14522,14529,14533,14597,14686,14690,14717,14784,14839,14843,14870,14963,14965,14997,15168,15172,15242,15290,15294,15355,15461,15476,15480,15482,15510,15575,15577,15584,15672,15697,15895,15899,15935,15937],[12,14446,14442],{"id":14447},"kalkul-funkcí-více-proměnných",[724,14449,14450,14451,14454,14455,1343,14484,1659],{},"Většina ekonomických veličin závisí na ",[38,14452,14453],{},"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 ",[883,14456,14458],{"className":14457},[886],[888,14459,14460],{"xmlns":890},[892,14461,14462,14481],{},[895,14463,14464,14467,14469,14471,14473,14475,14477,14479],{},[898,14465,14466],{},"z",[1712,14468,1714],{},[898,14470,7451],{},[1712,14472,1904],{"stretchy":1903},[898,14474,7456],{},[1712,14476,3138],{"separator":2565},[898,14478,7446],{},[1712,14480,1910],{"stretchy":1903},[902,14482,14483],{"encoding":904},"z = f(x, y)",[883,14485,14487],{"className":14486},[886],[888,14488,14489],{"xmlns":890},[892,14490,14491,14519],{},[895,14492,14493,14496,14498,14500,14502,14504,14506,14508,14510,14512,14514,14516],{},[898,14494,14495],{},"w",[1712,14497,1714],{},[898,14499,7451],{},[1712,14501,1904],{"stretchy":1903},[898,14503,7456],{},[1712,14505,3138],{"separator":2565},[898,14507,7446],{},[1712,14509,3138],{"separator":2565},[898,14511,14466],{},[1712,14513,1910],{"stretchy":1903},[1712,14515,3138],{"separator":2565},[1712,14517,14518],{},"…",[902,14520,14521],{"encoding":904},"w = f(x, y, z), \\ldots",[724,14523,14524],{},[3817,14525],{"alt":14526,"className":14527,"src":14528},"imek-funkce-2d-vrstevnice",[210,3821],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,14530,14532],{"id":14531},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,14534,14535,14536,14563,14564,14592,14593,14596],{},"Pro ",[883,14537,14539],{"className":14538},[886],[888,14540,14541],{"xmlns":890},[892,14542,14543,14561],{},[895,14544,14545,14547,14549,14551,14553,14555,14557,14559],{},[898,14546,14466],{},[1712,14548,1714],{},[898,14550,7451],{},[1712,14552,1904],{"stretchy":1903},[898,14554,7456],{},[1712,14556,3138],{"separator":2565},[898,14558,7446],{},[1712,14560,1910],{"stretchy":1903},[902,14562,14483],{"encoding":904}," se křivkou s předpisem ",[883,14565,14567],{"className":14566},[886],[888,14568,14569],{"xmlns":890},[892,14570,14571,14589],{},[895,14572,14573,14575,14577,14579,14581,14583,14585,14587],{},[898,14574,7451],{},[1712,14576,1904],{"stretchy":1903},[898,14578,7456],{},[1712,14580,3138],{"separator":2565},[898,14582,7446],{},[1712,14584,1910],{"stretchy":1903},[1712,14586,1714],{},[898,14588,7585],{},[902,14590,14591],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,14594,14595],{},"vrstevnice"," funkce. V ekonomii:",[120,14598,14599,14646],{},[123,14600,14601,14604,14605,14641,14642,1659],{},[38,14602,14603],{},"Indiferenční křivky"," užitečnosti ",[883,14606,14608],{"className":14607},[886],[888,14609,14610],{"xmlns":890},[892,14611,14612,14638],{},[895,14613,14614,14616,14618,14624,14626,14632,14634,14636],{},[898,14615,900],{},[1712,14617,1904],{"stretchy":1903},[6927,14619,14620,14622],{},[898,14621,1734],{},[1716,14623,2222],{},[1712,14625,3138],{"separator":2565},[6927,14627,14628,14630],{},[898,14629,1734],{},[1716,14631,2787],{},[1712,14633,1910],{"stretchy":1903},[1712,14635,1714],{},[898,14637,7585],{},[902,14639,14640],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,14643,14645],{"className":14644,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,14647,14648,14651,14652,14641,14682,1659],{},[38,14649,14650],{},"Izokvanty"," produkce ",[883,14653,14655],{"className":14654},[886],[888,14656,14657],{"xmlns":890},[892,14658,14659,14679],{},[895,14660,14661,14663,14665,14668,14670,14673,14675,14677],{},[898,14662,1734],{},[1712,14664,1904],{"stretchy":1903},[898,14666,14667],{},"L",[1712,14669,3138],{"separator":2565},[898,14671,14672],{},"K",[1712,14674,1910],{"stretchy":1903},[1712,14676,1714],{},[898,14678,7585],{},[902,14680,14681],{"encoding":904},"Q(L, K) = c",[207,14683,14685],{"className":14684,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,14687,14689],{"id":14688},"parciální-derivace","Parciální derivace",[724,14691,14535,14692,14716],{},[883,14693,14695],{"className":14694},[886],[888,14696,14697],{"xmlns":890},[892,14698,14699,14713],{},[895,14700,14701,14703,14705,14707,14709,14711],{},[898,14702,7451],{},[1712,14704,1904],{"stretchy":1903},[898,14706,7456],{},[1712,14708,3138],{"separator":2565},[898,14710,7446],{},[1712,14712,1910],{"stretchy":1903},[902,14714,14715],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,14718,14719],{},[883,14720,14722],{"className":14721},[886],[888,14723,14724],{"xmlns":890},[892,14725,14726,14781],{},[895,14727,14728,14736,14738,14753,14755,14757,14765,14767],{},[6989,14729,14730,14732,14734],{},[898,14731,7451],{},[898,14733,7456],{},[1712,14735,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,14737,1714],{},[2567,14739,14740,14747],{},[895,14741,14742,14745],{},[898,14743,14744],{"mathvariant":2003},"∂",[898,14746,7451],{},[895,14748,14749,14751],{},[898,14750,14744],{"mathvariant":2003},[898,14752,7456],{},[1712,14754,3138],{"separator":2565},[3690,14756],{"width":3692},[6989,14758,14759,14761,14763],{},[898,14760,7451],{},[898,14762,7446],{},[1712,14764,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,14766,1714],{},[2567,14768,14769,14775],{},[895,14770,14771,14773],{},[898,14772,14744],{"mathvariant":2003},[898,14774,7451],{},[895,14776,14777,14779],{},[898,14778,14744],{"mathvariant":2003},[898,14780,7446],{},[902,14782,14783],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,14785,14786,14787,1659],{},"Hodnoty v bodě: ",[883,14788,14790],{"className":14789},[886],[888,14791,14792],{"xmlns":890},[892,14793,14794,14836],{},[895,14795,14796,14804,14806,14808,14810,14812,14814,14816,14818,14826,14828,14830,14832,14834],{},[6989,14797,14798,14800,14802],{},[898,14799,7451],{},[898,14801,7456],{},[1712,14803,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,14805,1904],{"stretchy":1903},[898,14807,207],{},[1712,14809,3138],{"separator":2565},[898,14811,7544],{},[1712,14813,1910],{"stretchy":1903},[1712,14815,3138],{"separator":2565},[1762,14817,7722],{},[6989,14819,14820,14822,14824],{},[898,14821,7451],{},[898,14823,7446],{},[1712,14825,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,14827,1904],{"stretchy":1903},[898,14829,207],{},[1712,14831,3138],{"separator":2565},[898,14833,7544],{},[1712,14835,1910],{"stretchy":1903},[902,14837,14838],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,14840,14842],{"id":14841},"ekonomické-značení","Ekonomické značení",[724,14844,14845,14846,2854],{},"Pro produkční funkci ",[883,14847,14849],{"className":14848},[886],[888,14850,14851],{"xmlns":890},[892,14852,14853,14867],{},[895,14854,14855,14857,14859,14861,14863,14865],{},[898,14856,1734],{},[1712,14858,1904],{"stretchy":1903},[898,14860,14667],{},[1712,14862,3138],{"separator":2565},[898,14864,14672],{},[1712,14866,1910],{"stretchy":1903},[902,14868,14869],{"encoding":904},"Q(L, K)",[120,14871,14872,14918],{},[123,14873,14874,7894,14894,14897,14898,1910],{},[883,14875,14877],{"className":14876},[886],[888,14878,14879],{"xmlns":890},[892,14880,14881,14891],{},[895,14882,14883],{},[6989,14884,14885,14887,14889],{},[898,14886,1734],{},[898,14888,14667],{},[1712,14890,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,14892,14893],{"encoding":904},"Q'_L",[38,14895,14896],{},"mezní produkt práce"," (",[883,14899,14901],{"className":14900},[886],[888,14902,14903],{"xmlns":890},[892,14904,14905,14915],{},[895,14906,14907,14909],{},[898,14908,4445],{},[6927,14910,14911,14913],{},[898,14912,1710],{},[898,14914,14667],{},[902,14916,14917],{"encoding":904},"MP_L",[123,14919,14920,7894,14940,14897,14943,1910],{},[883,14921,14923],{"className":14922},[886],[888,14924,14925],{"xmlns":890},[892,14926,14927,14937],{},[895,14928,14929],{},[6989,14930,14931,14933,14935],{},[898,14932,1734],{},[898,14934,14672],{},[1712,14936,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,14938,14939],{"encoding":904},"Q'_K",[38,14941,14942],{},"mezní produkt kapitálu",[883,14944,14946],{"className":14945},[886],[888,14947,14948],{"xmlns":890},[892,14949,14950,14960],{},[895,14951,14952,14954],{},[898,14953,4445],{},[6927,14955,14956,14958],{},[898,14957,1710],{},[898,14959,14672],{},[902,14961,14962],{"encoding":904},"MP_K",[198,14964,7990],{"id":7989},[724,14966,14967,2854],{},[883,14968,14970],{"className":14969},[886],[888,14971,14972],{"xmlns":890},[892,14973,14974,14994],{},[895,14975,14976,14984,14986,14988,14990,14992],{},[6989,14977,14978,14980,14982],{},[898,14979,7451],{},[898,14981,7456],{},[1712,14983,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,14985,1904],{"stretchy":1903},[898,14987,207],{},[1712,14989,3138],{"separator":2565},[898,14991,7544],{},[1712,14993,1910],{"stretchy":1903},[902,14995,14996],{"encoding":904},"f'_x(a, b)",[120,14998,14999,15057],{},[123,15000,15001,15002,15015,15016,15029,15030,15056],{},"rychlost změny ",[883,15003,15005],{"className":15004},[886],[888,15006,15007],{"xmlns":890},[892,15008,15009,15013],{},[895,15010,15011],{},[898,15012,7451],{},[902,15014,7451],{"encoding":904}," vůči ",[883,15017,15019],{"className":15018},[886],[888,15020,15021],{"xmlns":890},[892,15022,15023,15027],{},[895,15024,15025],{},[898,15026,7456],{},[902,15028,7456],{"encoding":904}," při ",[883,15031,15033],{"className":15032},[886],[888,15034,15035],{"xmlns":890},[892,15036,15037,15053],{},[895,15038,15039,15041,15043,15045,15047,15049,15051],{},[898,15040,7456],{},[1712,15042,1714],{},[898,15044,207],{},[1712,15046,3138],{"separator":2565},[898,15048,7446],{},[1712,15050,1714],{},[898,15052,7544],{},[902,15054,15055],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,15058,15059,15060,8079,15073,15086,15087,15105,15106,1659],{},"přibližná změna ",[883,15061,15063],{"className":15062},[886],[888,15064,15065],{"xmlns":890},[892,15066,15067,15071],{},[895,15068,15069],{},[898,15070,7451],{},[902,15072,7451],{"encoding":904},[883,15074,15076],{"className":15075},[886],[888,15077,15078],{"xmlns":890},[892,15079,15080,15084],{},[895,15081,15082],{},[898,15083,7456],{},[902,15085,7456],{"encoding":904}," o 1 (a pevném ",[883,15088,15090],{"className":15089},[886],[888,15091,15092],{"xmlns":890},[892,15093,15094,15102],{},[895,15095,15096,15098,15100],{},[898,15097,7446],{},[1712,15099,1714],{},[898,15101,7544],{},[902,15103,15104],{"encoding":904},"y = b","): ",[883,15107,15109],{"className":15108},[886],[888,15110,15111],{"xmlns":890},[892,15112,15113,15165],{},[895,15114,15115,15117,15119,15121,15123,15125,15127,15129,15131,15133,15135,15137,15139,15141,15143,15145,15147,15155,15157,15159,15161,15163],{},[898,15116,7451],{},[1712,15118,1904],{"stretchy":1903},[898,15120,207],{},[1712,15122,3145],{},[1716,15124,2222],{},[1712,15126,3138],{"separator":2565},[898,15128,7544],{},[1712,15130,1910],{"stretchy":1903},[1712,15132,3740],{},[898,15134,7451],{},[1712,15136,1904],{"stretchy":1903},[898,15138,207],{},[1712,15140,3138],{"separator":2565},[898,15142,7544],{},[1712,15144,1910],{"stretchy":1903},[1712,15146,3145],{},[6989,15148,15149,15151,15153],{},[898,15150,7451],{},[898,15152,7456],{},[1712,15154,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15156,1904],{"stretchy":1903},[898,15158,207],{},[1712,15160,3138],{"separator":2565},[898,15162,7544],{},[1712,15164,1910],{"stretchy":1903},[902,15166,15167],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,15169,15171],{"id":15170},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,15173,15174],{},[883,15175,15177],{"className":15176},[886],[888,15178,15179],{"xmlns":890},[892,15180,15181,15239],{},[895,15182,15183,15185,15187,15189,15197,15199,15201,15203,15205,15207,15209,15211,15213,15215,15223,15225,15227,15229,15231,15233,15235,15237],{},[898,15184,2468],{},[898,15186,7451],{},[1712,15188,1714],{},[6989,15190,15191,15193,15195],{},[898,15192,7451],{},[898,15194,7456],{},[1712,15196,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15198,1904],{"stretchy":1903},[898,15200,7456],{},[1712,15202,3138],{"separator":2565},[898,15204,7446],{},[1712,15206,1910],{"stretchy":1903},[1762,15208,2583],{},[898,15210,2468],{},[898,15212,7456],{},[1712,15214,3145],{},[6989,15216,15217,15219,15221],{},[898,15218,7451],{},[898,15220,7446],{},[1712,15222,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15224,1904],{"stretchy":1903},[898,15226,7456],{},[1712,15228,3138],{"separator":2565},[898,15230,7446],{},[1712,15232,1910],{"stretchy":1903},[1762,15234,2583],{},[898,15236,2468],{},[898,15238,7446],{},[902,15240,15241],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,15243,8407,15244,15266,15267,15289],{},[883,15245,15247],{"className":15246},[886],[888,15248,15249],{"xmlns":890},[892,15250,15251,15263],{},[895,15252,15253,15255,15257,15259,15261],{},[898,15254,2468],{},[898,15256,7456],{},[1712,15258,3138],{"separator":2565},[898,15260,2468],{},[898,15262,7446],{},[902,15264,15265],{"encoding":904},"dx, dy"," platí ",[883,15268,15270],{"className":15269},[886],[888,15271,15272],{"xmlns":890},[892,15273,15274,15286],{},[895,15275,15276,15278,15280,15282,15284],{},[898,15277,2004],{"mathvariant":2003},[898,15279,7451],{},[1712,15281,3740],{},[898,15283,2468],{},[898,15285,7451],{},[902,15287,15288],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,15291,15293],{"id":15292},"implicitní-funkce","Implicitní funkce",[724,15295,15296,15297,15326,15327,15340,15341,15354],{},"Je-li vztah dán rovnicí ",[883,15298,15300],{"className":15299},[886],[888,15301,15302],{"xmlns":890},[892,15303,15304,15323],{},[895,15305,15306,15309,15311,15313,15315,15317,15319,15321],{},[898,15307,15308],{},"F",[1712,15310,1904],{"stretchy":1903},[898,15312,7456],{},[1712,15314,3138],{"separator":2565},[898,15316,7446],{},[1712,15318,1910],{"stretchy":1903},[1712,15320,1714],{},[1716,15322,2085],{},[902,15324,15325],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,15328,15330],{"className":15329},[886],[888,15331,15332],{"xmlns":890},[892,15333,15334,15338],{},[895,15335,15336],{},[898,15337,7446],{},[902,15339,7446],{"encoding":904}," podle ",[883,15342,15344],{"className":15343},[886],[888,15345,15346],{"xmlns":890},[892,15347,15348,15352],{},[895,15349,15350],{},[898,15351,7456],{},[902,15353,7456],{"encoding":904}," (nebo naopak):",[724,15356,15357],{},[883,15358,15360],{"className":15359},[886],[888,15361,15362],{"xmlns":890},[892,15363,15364,15458],{},[895,15365,15366,15372,15374,15388,15390,15392,15410,15412,15414,15420,15422,15436,15438,15440],{},[2037,15367,15368,15370],{},[898,15369,7446],{},[1712,15371,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15373,1714],{},[2567,15375,15376,15382],{},[895,15377,15378,15380],{},[898,15379,2468],{},[898,15381,7446],{},[895,15383,15384,15386],{},[898,15385,2468],{},[898,15387,7456],{},[1712,15389,1714],{},[1712,15391,2219],{},[2567,15393,15394,15402],{},[6989,15395,15396,15398,15400],{},[898,15397,15308],{},[898,15399,7456],{},[1712,15401,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,15403,15404,15406,15408],{},[898,15405,15308],{},[898,15407,7446],{},[1712,15409,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15411,3138],{"separator":2565},[3690,15413],{"width":3692},[2037,15415,15416,15418],{},[898,15417,7456],{},[1712,15419,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15421,1714],{},[2567,15423,15424,15430],{},[895,15425,15426,15428],{},[898,15427,2468],{},[898,15429,7456],{},[895,15431,15432,15434],{},[898,15433,2468],{},[898,15435,7446],{},[1712,15437,1714],{},[1712,15439,2219],{},[2567,15441,15442,15450],{},[6989,15443,15444,15446,15448],{},[898,15445,15308],{},[898,15447,7446],{},[1712,15449,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,15451,15452,15454,15456],{},[898,15453,15308],{},[898,15455,7456],{},[1712,15457,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,15459,15460],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,15462,15463,15464,15467,15468,1655,15472,1659],{},"Tato vzorec dává ",[38,15465,15466],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,15469,15471],{"className":15470,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,15473,15475],{"className":15474,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,15477,15479],{"id":15478},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,15481,8657],{"id":8656},[724,15483,15484,15485,15509],{},"V bodě extrému ",[883,15486,15488],{"className":15487},[886],[888,15489,15490],{"xmlns":890},[892,15491,15492,15506],{},[895,15493,15494,15496,15498,15500,15502,15504],{},[898,15495,2044],{},[1712,15497,7910],{"stretchy":1903},[898,15499,207],{},[1712,15501,3138],{"separator":2565},[898,15503,7544],{},[1712,15505,7925],{"stretchy":1903},[902,15507,15508],{"encoding":904},"A[a, b]"," musí platit současně:",[724,15511,15512],{},[883,15513,15515],{"className":15514},[886],[888,15516,15517],{"xmlns":890},[892,15518,15519,15572],{},[895,15520,15521,15529,15531,15533,15535,15537,15539,15541,15543,15545,15548,15550,15558,15560,15562,15564,15566,15568,15570],{},[6989,15522,15523,15525,15527],{},[898,15524,7451],{},[898,15526,7456],{},[1712,15528,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15530,1904],{"stretchy":1903},[898,15532,207],{},[1712,15534,3138],{"separator":2565},[898,15536,7544],{},[1712,15538,1910],{"stretchy":1903},[1712,15540,1714],{},[1716,15542,2085],{},[1762,15544,1764],{},[1712,15546,15547],{},"∧",[1762,15549,1764],{},[6989,15551,15552,15554,15556],{},[898,15553,7451],{},[898,15555,7446],{},[1712,15557,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,15559,1904],{"stretchy":1903},[898,15561,207],{},[1712,15563,3138],{"separator":2565},[898,15565,7544],{},[1712,15567,1910],{"stretchy":1903},[1712,15569,1714],{},[1716,15571,2085],{},[902,15573,15574],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,15576,8731],{"id":8730},[724,15578,15579,15580,15583],{},"Definujeme ",[38,15581,15582],{},"diskriminant"," (Hessián zjednodušeně):",[724,15585,15586],{},[883,15587,15589],{"className":15588},[886],[888,15590,15591],{"xmlns":890},[892,15592,15593,15669],{},[895,15594,15595,15597,15599,15601,15603,15605,15607,15609,15625,15627,15643,15645,15647,15663],{},[898,15596,1969],{},[1712,15598,1904],{"stretchy":1903},[898,15600,7456],{},[1712,15602,3138],{"separator":2565},[898,15604,7446],{},[1712,15606,1910],{"stretchy":1903},[1712,15608,1714],{},[6989,15610,15611,15613,15619],{},[898,15612,7451],{},[895,15614,15615,15617],{},[898,15616,7456],{},[898,15618,7456],{},[895,15620,15621,15623],{},[1712,15622,2243],{"mathvariant":2003},[1712,15624,2243],{"mathvariant":2003},[1712,15626,1783],{},[6989,15628,15629,15631,15637],{},[898,15630,7451],{},[895,15632,15633,15635],{},[898,15634,7446],{},[898,15636,7446],{},[895,15638,15639,15641],{},[1712,15640,2243],{"mathvariant":2003},[1712,15642,2243],{"mathvariant":2003},[1712,15644,2219],{},[1712,15646,1904],{"stretchy":1903},[6989,15648,15649,15651,15657],{},[898,15650,7451],{},[895,15652,15653,15655],{},[898,15654,7456],{},[898,15656,7446],{},[895,15658,15659,15661],{},[1712,15660,2243],{"mathvariant":2003},[1712,15662,2243],{"mathvariant":2003},[2037,15664,15665,15667],{},[1712,15666,1910],{"stretchy":1903},[1716,15668,2787],{},[902,15670,15671],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,15673,15674,15675,2854],{},"V podezřelém bodě ",[883,15676,15678],{"className":15677},[886],[888,15679,15680],{"xmlns":890},[892,15681,15682,15694],{},[895,15683,15684,15686,15688,15690,15692],{},[1712,15685,7910],{"stretchy":1903},[898,15687,207],{},[1712,15689,3138],{"separator":2565},[898,15691,7544],{},[1712,15693,7925],{"stretchy":1903},[902,15695,15696],{"encoding":904},"[a, b]",[152,15698,15699,15826,15862],{},[123,15700,15701,15731,15732],{},[38,15702,15703,2854],{},[883,15704,15706],{"className":15705},[886],[888,15707,15708],{"xmlns":890},[892,15709,15710,15728],{},[895,15711,15712,15714,15716,15718,15720,15722,15724,15726],{},[898,15713,1969],{},[1712,15715,1904],{"stretchy":1903},[898,15717,207],{},[1712,15719,3138],{"separator":2565},[898,15721,7544],{},[1712,15723,1910],{"stretchy":1903},[1712,15725,2302],{},[1716,15727,2085],{},[902,15729,15730],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,15733,15734,15780],{},[123,15735,15736,8818,15778],{},[883,15737,15739],{"className":15738},[886],[888,15740,15741],{"xmlns":890},[892,15742,15743,15775],{},[895,15744,15745,15761,15763,15765,15767,15769,15771,15773],{},[6989,15746,15747,15749,15755],{},[898,15748,7451],{},[895,15750,15751,15753],{},[898,15752,7456],{},[898,15754,7456],{},[895,15756,15757,15759],{},[1712,15758,2243],{"mathvariant":2003},[1712,15760,2243],{"mathvariant":2003},[1712,15762,1904],{"stretchy":1903},[898,15764,207],{},[1712,15766,3138],{"separator":2565},[898,15768,7544],{},[1712,15770,1910],{"stretchy":1903},[1712,15772,2302],{},[1716,15774,2085],{},[902,15776,15777],{"encoding":904},"f''_{xx}(a, b) > 0",[38,15779,9176],{},[123,15781,15782,8818,15824],{},[883,15783,15785],{"className":15784},[886],[888,15786,15787],{"xmlns":890},[892,15788,15789,15821],{},[895,15790,15791,15807,15809,15811,15813,15815,15817,15819],{},[6989,15792,15793,15795,15801],{},[898,15794,7451],{},[895,15796,15797,15799],{},[898,15798,7456],{},[898,15800,7456],{},[895,15802,15803,15805],{},[1712,15804,2243],{"mathvariant":2003},[1712,15806,2243],{"mathvariant":2003},[1712,15808,1904],{"stretchy":1903},[898,15810,207],{},[1712,15812,3138],{"separator":2565},[898,15814,7544],{},[1712,15816,1910],{"stretchy":1903},[1712,15818,2252],{},[1716,15820,2085],{},[902,15822,15823],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,15825,5766],{},[123,15827,15828,3245,15858,15861],{},[38,15829,15830,2854],{},[883,15831,15833],{"className":15832},[886],[888,15834,15835],{"xmlns":890},[892,15836,15837,15855],{},[895,15838,15839,15841,15843,15845,15847,15849,15851,15853],{},[898,15840,1969],{},[1712,15842,1904],{"stretchy":1903},[898,15844,207],{},[1712,15846,3138],{"separator":2565},[898,15848,7544],{},[1712,15850,1910],{"stretchy":1903},[1712,15852,2252],{},[1716,15854,2085],{},[902,15856,15857],{"encoding":904},"D(a, b) \u003C 0",[38,15859,15860],{},"sedlo"," (v daném bodě extrém není).",[123,15863,15864,15894],{},[38,15865,15866,2854],{},[883,15867,15869],{"className":15868},[886],[888,15870,15871],{"xmlns":890},[892,15872,15873,15891],{},[895,15874,15875,15877,15879,15881,15883,15885,15887,15889],{},[898,15876,1969],{},[1712,15878,1904],{"stretchy":1903},[898,15880,207],{},[1712,15882,3138],{"separator":2565},[898,15884,7544],{},[1712,15886,1910],{"stretchy":1903},[1712,15888,1714],{},[1716,15890,2085],{},[902,15892,15893],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,15896,15898],{"id":15897},"vázané-extrémy","Vázané extrémy",[724,15900,15901,15902,15931,15932,1659],{},"Pro extrémy s omezující podmínkou ",[883,15903,15905],{"className":15904},[886],[888,15906,15907],{"xmlns":890},[892,15908,15909,15928],{},[895,15910,15911,15914,15916,15918,15920,15922,15924,15926],{},[898,15912,15913],{},"g",[1712,15915,1904],{"stretchy":1903},[898,15917,7456],{},[1712,15919,3138],{"separator":2565},[898,15921,7446],{},[1712,15923,1910],{"stretchy":1903},[1712,15925,1714],{},[1716,15927,2085],{},[902,15929,15930],{"encoding":904},"g(x, y) = 0"," se používá ",[207,15933,793],{"className":15934,"dataFsResolvedFilePath":791,"href":792},[210],[115,15936,9193],{"id":9192},[120,15938,15939,15946,15953],{},[123,15940,15941,3245,15943],{},[38,15942,9200],{},[207,15944,775],{"className":15945,"dataFsResolvedFilePath":773,"href":774},[210],[123,15947,15948,3245,15950],{},[38,15949,9208],{},[207,15951,793],{"className":15952,"dataFsResolvedFilePath":791,"href":792},[210],[123,15954,15955,3245,15957,15961,15962,15965,15966,15969],{},[38,15956,9216],{},[207,15958,15960],{"className":15959,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,15963,880],{"className":15964,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,15967,1646],{"className":15968,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":15971},[15972,15973,15977,15978,15979,15983,15984],{"id":14531,"depth":642,"text":14532},{"id":14688,"depth":642,"text":14689,"children":15974},[15975,15976],{"id":14841,"depth":649,"text":14842},{"id":7989,"depth":649,"text":7990},{"id":15170,"depth":642,"text":15171},{"id":15292,"depth":642,"text":15293},{"id":15478,"depth":642,"text":15479,"children":15980},[15981,15982],{"id":8656,"depth":649,"text":8657},{"id":8730,"depth":649,"text":8731},{"id":15897,"depth":642,"text":15898},{"id":9192,"depth":642,"text":9193},"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":14442,"description":15985},[1135],"topics\u002Ffunkce-vice-promennych",[1128,15992,9253,15993,15994,15995],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":15998,"title":775,"body":15999,"course":1128,"courses":659,"created":1129,"description":16855,"extension":661,"meta":16856,"navigation":664,"path":16857,"seo":16858,"sources":16859,"stem":16860,"tags":16861,"type":7391,"updated":677,"__hash__":16868},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":16000,"toc":16845},[16001,16004,16015,16019,16064,16144,16148,16224,16266,16273,16277,16281,16310,16368,16415,16453,16457,16507,16559,16611,16655,16658,16661,16733,16736,16808,16815,16817],[12,16002,775],{"id":16003},"integrál",[724,16005,16006,16007,16010,16011,16014],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,16008,16009],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,16012,16013],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,16016,16018],{"id":16017},"neurčitý-integrál","Neurčitý integrál",[724,16020,16021],{},[883,16022,16024],{"className":16023},[886],[888,16025,16026],{"xmlns":890},[892,16027,16028,16061],{},[895,16029,16030,16032,16034,16036,16038,16040,16043,16045,16047,16049,16051,16053,16055,16057,16059],{},[898,16031,15308],{},[1712,16033,1904],{"stretchy":1903},[898,16035,7456],{},[1712,16037,1910],{"stretchy":1903},[1712,16039,1714],{},[1712,16041,16042],{},"∫",[898,16044,7451],{},[1712,16046,1904],{"stretchy":1903},[898,16048,7456],{},[1712,16050,1910],{"stretchy":1903},[1762,16052,2583],{},[898,16054,2468],{},[898,16056,7456],{},[1712,16058,3145],{},[898,16060,8195],{},[902,16062,16063],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,16065,2101,16066,7037,16100,5920,16113,16116,16117,1343,16130,16143],{},[883,16067,16069],{"className":16068},[886],[888,16070,16071],{"xmlns":890},[892,16072,16073,16097],{},[895,16074,16075,16081,16083,16085,16087,16089,16091,16093,16095],{},[2037,16076,16077,16079],{},[898,16078,15308],{},[1712,16080,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,16082,1904],{"stretchy":1903},[898,16084,7456],{},[1712,16086,1910],{"stretchy":1903},[1712,16088,1714],{},[898,16090,7451],{},[1712,16092,1904],{"stretchy":1903},[898,16094,7456],{},[1712,16096,1910],{"stretchy":1903},[902,16098,16099],{"encoding":904},"F'(x) = f(x)",[883,16101,16103],{"className":16102},[886],[888,16104,16105],{"xmlns":890},[892,16106,16107,16111],{},[895,16108,16109],{},[898,16110,15308],{},[902,16112,15308],{"encoding":904},[38,16114,16115],{},"primitivní funkce"," k ",[883,16118,16120],{"className":16119},[886],[888,16121,16122],{"xmlns":890},[892,16123,16124,16128],{},[895,16125,16126],{},[898,16127,7451],{},[902,16129,7451],{"encoding":904},[883,16131,16133],{"className":16132},[886],[888,16134,16135],{"xmlns":890},[892,16136,16137,16141],{},[895,16138,16139],{},[898,16140,8195],{},[902,16142,8195],{"encoding":904}," konstanta.",[115,16145,16147],{"id":16146},"určitý-integrál","Určitý integrál",[724,16149,16150],{},[883,16151,16153],{"className":16152},[886],[888,16154,16155],{"xmlns":890},[892,16156,16157,16221],{},[895,16158,16159,16167,16169,16171,16173,16175,16177,16179,16181,16183,16185,16187,16189,16191,16193,16201,16203,16205,16207,16209,16211,16213,16215,16217,16219],{},[6989,16160,16161,16163,16165],{},[1712,16162,16042],{},[898,16164,207],{},[898,16166,7544],{},[898,16168,7451],{},[1712,16170,1904],{"stretchy":1903},[898,16172,7456],{},[1712,16174,1910],{"stretchy":1903},[1762,16176,2583],{},[898,16178,2468],{},[898,16180,7456],{},[1712,16182,1714],{},[1712,16184,7910],{"stretchy":1903},[898,16186,15308],{},[1712,16188,1904],{"stretchy":1903},[898,16190,7456],{},[1712,16192,1910],{"stretchy":1903},[6989,16194,16195,16197,16199],{},[1712,16196,7925],{"stretchy":1903},[898,16198,207],{},[898,16200,7544],{},[1712,16202,1714],{},[898,16204,15308],{},[1712,16206,1904],{"stretchy":1903},[898,16208,7544],{},[1712,16210,1910],{"stretchy":1903},[1712,16212,2219],{},[898,16214,15308],{},[1712,16216,1904],{"stretchy":1903},[898,16218,207],{},[1712,16220,1910],{"stretchy":1903},[902,16222,16223],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,16225,16226,16227,3245,16230,16243,16244,16265],{},"Geometricky ",[38,16228,16229],{},"plocha pod grafem",[883,16231,16233],{"className":16232},[886],[888,16234,16235],{"xmlns":890},[892,16236,16237,16241],{},[895,16238,16239],{},[898,16240,7451],{},[902,16242,7451],{"encoding":904}," na intervalu ",[883,16245,16247],{"className":16246},[886],[888,16248,16249],{"xmlns":890},[892,16250,16251,16263],{},[895,16252,16253,16255,16257,16259,16261],{},[1712,16254,7910],{"stretchy":1903},[898,16256,207],{},[1712,16258,3138],{"separator":2565},[898,16260,7544],{},[1712,16262,7925],{"stretchy":1903},[902,16264,15696],{"encoding":904}," (orientovaná).",[724,16267,16268],{},[3817,16269],{"alt":16270,"className":16271,"src":16272},"imek-integral-plocha",[210,3821],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,16274,16276],{"id":16275},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,16278,16280],{"id":16279},"příklad-tr-z-mr","Příklad — TR z MR",[724,16282,16283,16284,1659],{},"Mezní příjem ",[883,16285,16287],{"className":16286},[886],[888,16288,16289],{"xmlns":890},[892,16290,16291,16307],{},[895,16292,16293,16295,16297,16299,16301,16303,16305],{},[898,16294,4445],{},[898,16296,1775],{},[1712,16298,1714],{},[1716,16300,1739],{},[1712,16302,2219],{},[1716,16304,2787],{},[898,16306,1734],{},[902,16308,16309],{"encoding":904},"MR = 100 - 2Q",[724,16311,16312],{},[883,16313,16315],{"className":16314},[886],[888,16316,16317],{"xmlns":890},[892,16318,16319,16365],{},[895,16320,16321,16323,16325,16327,16329,16331,16333,16335,16337,16339,16341,16343,16345,16347,16349,16351,16353,16355,16361,16363],{},[898,16322,1772],{},[898,16324,1775],{},[1712,16326,1714],{},[1712,16328,16042],{},[1712,16330,1904],{"stretchy":1903},[1716,16332,1739],{},[1712,16334,2219],{},[1716,16336,2787],{},[898,16338,1734],{},[1712,16340,1910],{"stretchy":1903},[1762,16342,2583],{},[898,16344,2468],{},[898,16346,1734],{},[1712,16348,1714],{},[1716,16350,1739],{},[898,16352,1734],{},[1712,16354,2219],{},[2037,16356,16357,16359],{},[898,16358,1734],{},[1716,16360,2787],{},[1712,16362,3145],{},[898,16364,7585],{},[902,16366,16367],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,16369,16370,16371,8818,16397,2854],{},"Okrajová podmínka ",[883,16372,16374],{"className":16373},[886],[888,16375,16376],{"xmlns":890},[892,16377,16378,16394],{},[895,16379,16380,16382,16384,16386,16388,16390,16392],{},[898,16381,1772],{},[898,16383,1775],{},[1712,16385,1904],{"stretchy":1903},[1716,16387,2085],{},[1712,16389,1910],{"stretchy":1903},[1712,16391,1714],{},[1716,16393,2085],{},[902,16395,16396],{"encoding":904},"TR(0) = 0",[883,16398,16400],{"className":16399},[886],[888,16401,16402],{"xmlns":890},[892,16403,16404,16412],{},[895,16405,16406,16408,16410],{},[898,16407,7585],{},[1712,16409,1714],{},[1716,16411,2085],{},[902,16413,16414],{"encoding":904},"c = 0",[724,16416,16417],{},[883,16418,16420],{"className":16419},[886],[888,16421,16422],{"xmlns":890},[892,16423,16424,16450],{},[895,16425,16426,16428,16430,16432,16434,16436,16438,16440,16442,16444],{},[898,16427,1772],{},[898,16429,1775],{},[1712,16431,1904],{"stretchy":1903},[898,16433,1734],{},[1712,16435,1910],{"stretchy":1903},[1712,16437,1714],{},[1716,16439,1739],{},[898,16441,1734],{},[1712,16443,2219],{},[2037,16445,16446,16448],{},[898,16447,1734],{},[1716,16449,2787],{},[902,16451,16452],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,16454,16456],{"id":16455},"příklad-tc-z-mc","Příklad — TC z MC",[724,16458,16459,16460,16486,16487,1659],{},"Mezní náklady ",[883,16461,16463],{"className":16462},[886],[888,16464,16465],{"xmlns":890},[892,16466,16467,16483],{},[895,16468,16469,16471,16473,16475,16477,16479,16481],{},[898,16470,4445],{},[898,16472,8195],{},[1712,16474,1714],{},[1716,16476,2787],{},[1712,16478,3145],{},[1716,16480,6673],{},[898,16482,1734],{},[902,16484,16485],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,16488,16490],{"className":16489},[886],[888,16491,16492],{"xmlns":890},[892,16493,16494,16504],{},[895,16495,16496,16498,16500,16502],{},[898,16497,15308],{},[898,16499,8195],{},[1712,16501,1714],{},[1716,16503,1739],{},[902,16505,16506],{"encoding":904},"FC = 100",[724,16508,16509],{},[883,16510,16512],{"className":16511},[886],[888,16513,16514],{"xmlns":890},[892,16515,16516,16556],{},[895,16517,16518,16520,16522,16524,16526,16528,16530,16532,16534,16536,16538,16540,16542,16544,16546,16552,16554],{},[898,16519,1772],{},[898,16521,8195],{},[1712,16523,1714],{},[1712,16525,16042],{},[898,16527,4445],{},[898,16529,8195],{},[1762,16531,2583],{},[898,16533,2468],{},[898,16535,1734],{},[1712,16537,1714],{},[1716,16539,2787],{},[898,16541,1734],{},[1712,16543,3145],{},[1716,16545,6607],{},[2037,16547,16548,16550],{},[898,16549,1734],{},[1716,16551,2787],{},[1712,16553,3145],{},[898,16555,7585],{},[902,16557,16558],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,16560,16370,16561,8818,16593,2854],{},[883,16562,16564],{"className":16563},[886],[888,16565,16566],{"xmlns":890},[892,16567,16568,16590],{},[895,16569,16570,16572,16574,16576,16578,16580,16582,16584,16586,16588],{},[898,16571,1772],{},[898,16573,8195],{},[1712,16575,1904],{"stretchy":1903},[1716,16577,2085],{},[1712,16579,1910],{"stretchy":1903},[1712,16581,1714],{},[898,16583,15308],{},[898,16585,8195],{},[1712,16587,1714],{},[1716,16589,1739],{},[902,16591,16592],{"encoding":904},"TC(0) = FC = 100",[883,16594,16596],{"className":16595},[886],[888,16597,16598],{"xmlns":890},[892,16599,16600,16608],{},[895,16601,16602,16604,16606],{},[898,16603,7585],{},[1712,16605,1714],{},[1716,16607,1739],{},[902,16609,16610],{"encoding":904},"c = 100",[724,16612,16613],{},[883,16614,16616],{"className":16615},[886],[888,16617,16618],{"xmlns":890},[892,16619,16620,16652],{},[895,16621,16622,16624,16626,16628,16630,16632,16634,16636,16638,16640,16642,16644,16646],{},[898,16623,1772],{},[898,16625,8195],{},[1712,16627,1904],{"stretchy":1903},[898,16629,1734],{},[1712,16631,1910],{"stretchy":1903},[1712,16633,1714],{},[1716,16635,1739],{},[1712,16637,3145],{},[1716,16639,2787],{},[898,16641,1734],{},[1712,16643,3145],{},[1716,16645,6607],{},[2037,16647,16648,16650],{},[898,16649,1734],{},[1716,16651,2787],{},[902,16653,16654],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,16656,820],{"id":16657},"přebytek-spotřebitele-a-výrobce",[724,16659,16660],{},"Přebytek spotřebitele:",[724,16662,16663],{},[883,16664,16666],{"className":16665},[886],[888,16667,16668],{"xmlns":890},[892,16669,16670,16730],{},[895,16671,16672,16674,16676,16678,16684,16686,16688,16700,16702,16704,16706,16708,16710,16712,16714,16716,16722,16724],{},[898,16673,8195],{},[898,16675,6493],{},[1712,16677,1904],{"stretchy":1903},[6927,16679,16680,16682],{},[898,16681,1734],{},[1716,16683,2085],{},[1712,16685,1910],{"stretchy":1903},[1712,16687,1714],{},[6989,16689,16690,16692,16694],{},[1712,16691,16042],{},[1716,16693,2085],{},[6927,16695,16696,16698],{},[898,16697,1734],{},[1716,16699,2085],{},[898,16701,1969],{},[1712,16703,1904],{"stretchy":1903},[898,16705,1734],{},[1712,16707,1910],{"stretchy":1903},[1762,16709,2583],{},[898,16711,2468],{},[898,16713,1734],{},[1712,16715,2219],{},[6927,16717,16718,16720],{},[898,16719,1710],{},[1716,16721,2085],{},[1762,16723,2583],{},[6927,16725,16726,16728],{},[898,16727,1734],{},[1716,16729,2085],{},[902,16731,16732],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,16734,16735],{},"Přebytek výrobce:",[724,16737,16738],{},[883,16739,16741],{"className":16740},[886],[888,16742,16743],{"xmlns":890},[892,16744,16745,16805],{},[895,16746,16747,16749,16751,16753,16759,16761,16763,16769,16771,16777,16779,16791,16793,16795,16797,16799,16801,16803],{},[898,16748,1710],{},[898,16750,6493],{},[1712,16752,1904],{"stretchy":1903},[6927,16754,16755,16757],{},[898,16756,1734],{},[1716,16758,2085],{},[1712,16760,1910],{"stretchy":1903},[1712,16762,1714],{},[6927,16764,16765,16767],{},[898,16766,1710],{},[1716,16768,2085],{},[1762,16770,2583],{},[6927,16772,16773,16775],{},[898,16774,1734],{},[1716,16776,2085],{},[1712,16778,2219],{},[6989,16780,16781,16783,16785],{},[1712,16782,16042],{},[1716,16784,2085],{},[6927,16786,16787,16789],{},[898,16788,1734],{},[1716,16790,2085],{},[898,16792,6493],{},[1712,16794,1904],{"stretchy":1903},[898,16796,1734],{},[1712,16798,1910],{"stretchy":1903},[1762,16800,2583],{},[898,16802,2468],{},[898,16804,1734],{},[902,16806,16807],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,16809,16810,16811,1659],{},"Detailně viz ",[207,16812,16814],{"className":16813,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,16816,9193],{"id":9192},[120,16818,16819,16826,16833],{},[123,16820,16821,3245,16823],{},[38,16822,9200],{},[207,16824,766],{"className":16825,"dataFsResolvedFilePath":764,"href":765},[210],[123,16827,16828,3245,16830],{},[38,16829,9208],{},[207,16831,784],{"className":16832,"dataFsResolvedFilePath":782,"href":783},[210],[123,16834,16835,3245,16837,16840,16841,16844],{},[38,16836,9216],{},[207,16838,4992],{"className":16839,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,16842,16814],{"className":16843,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":16846},[16847,16848,16849,16854],{"id":16017,"depth":642,"text":16018},{"id":16146,"depth":642,"text":16147},{"id":16275,"depth":642,"text":16276,"children":16850},[16851,16852,16853],{"id":16279,"depth":649,"text":16280},{"id":16455,"depth":649,"text":16456},{"id":16657,"depth":649,"text":820},{"id":9192,"depth":642,"text":9193},"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":775,"description":16855},[1135],"topics\u002Fintegral",[1128,16862,16863,16864,16865,16866,16867],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":16870,"title":16871,"body":16872,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":21141,"navigation":664,"path":21142,"seo":21143,"sources":21144,"stem":21145,"tags":21146,"type":7391,"updated":677,"__hash__":21152},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":16873,"toc":21129},[16874,16877,16881,17025,17032,17036,17106,17144,17247,17251,17281,17347,17394,17397,17466,17469,17504,17540,17544,17592,17599,17645,17691,17694,17773,17870,17953,17957,18001,18031,18037,18066,18088,18138,18191,18257,18260,18326,18355,18414,18430,18517,18615,18746,18750,18907,19056,19436,19440,19443,19502,19505,19591,19619,19657,19660,19697,19737,19771,19773,19810,19842,19940,19945,20069,20121,20203,20342,20346,20466,20473,20584,20591,20595,21070,21072],[12,16875,16871],{"id":16876},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,16878,16880],{"id":16879},"tldr","TL;DR",[724,16882,16883,16886,16887,14897,16890,16903,16904,16918,16919,16922,16923,1343,16926,16929,16930,1343,16933,16936,16937,3245,16940,16970,16971,16974,16975,1343,16989,17002,17003,17006,17007,1691],{},[38,16884,16885],{},"IS-LM"," je makroekonomický model se ",[38,16888,16889],{},"dvěma neznámými",[883,16891,16893],{"className":16892},[886],[888,16894,16895],{"xmlns":890},[892,16896,16897,16901],{},[895,16898,16899],{},[898,16900,6951],{},[902,16902,6951],{"encoding":904}," — národní důchod a ",[883,16905,16907],{"className":16906},[886],[888,16908,16909],{"xmlns":890},[892,16910,16911,16916],{},[895,16912,16913],{},[898,16914,16915],{},"r",[902,16917,16915],{"encoding":904}," — úroková míra) a ",[38,16920,16921],{},"dvěma trhy",": trhem zboží (křivka ",[38,16924,16925],{},"IS",[614,16927,16928],{},"Investment = Savings",") a trhem peněz (křivka ",[38,16931,16932],{},"LM",[614,16934,16935],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,16938,16939],{},"simultánní rovnováhu",[883,16941,16943],{"className":16942},[886],[888,16944,16945],{"xmlns":890},[892,16946,16947,16967],{},[895,16948,16949,16951,16957,16959,16965],{},[1712,16950,1904],{"stretchy":1903},[2037,16952,16953,16955],{},[898,16954,6951],{},[898,16956,2041],{},[1712,16958,3138],{"separator":2565},[2037,16960,16961,16963],{},[898,16962,16915],{},[898,16964,2041],{},[1712,16966,1910],{"stretchy":1903},[902,16968,16969],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,16972,16973],{},"fiskální politiky"," (posun IS změnou ",[883,16976,16978],{"className":16977},[886],[888,16979,16980],{"xmlns":890},[892,16981,16982,16987],{},[895,16983,16984],{},[898,16985,16986],{},"G",[902,16988,16986],{"encoding":904},[883,16990,16992],{"className":16991},[886],[888,16993,16994],{"xmlns":890},[892,16995,16996,17000],{},[895,16997,16998],{},[898,16999,1772],{},[902,17001,1772],{"encoding":904},") a ",[38,17004,17005],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,17008,17010],{"className":17009},[886],[888,17011,17012],{"xmlns":890},[892,17013,17014,17022],{},[895,17015,17016],{},[2037,17017,17018,17020],{},[898,17019,4445],{},[1712,17021,2145],{},[902,17023,17024],{"encoding":904},"M^*",[724,17026,17027],{},[3817,17028],{"alt":17029,"className":17030,"src":17031},"imek-is-lm-model",[210,3821],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,17033,17035],{"id":17034},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,17037,17038,17039,17043,17044,14897,17047,17070,17071,17074,17075,17091,17092,17105],{},"V modelech ",[207,17040,17042],{"className":17041,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,17045,17046],{},"investice pokládány za konstantní",[883,17048,17050],{"className":17049},[886],[888,17051,17052],{"xmlns":890},[892,17053,17054,17067],{},[895,17055,17056,17059,17061],{},[898,17057,17058],{},"I",[1712,17060,1714],{},[2037,17062,17063,17065],{},[898,17064,17058],{},[1712,17066,2145],{},[902,17068,17069],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,17072,17073],{},"ceně peněz",", tedy na ",[38,17076,17077,17078],{},"úrokové míře ",[883,17079,17081],{"className":17080},[886],[888,17082,17083],{"xmlns":890},[892,17084,17085,17089],{},[895,17086,17087],{},[898,17088,16915],{},[902,17090,16915],{"encoding":904},": čím vyšší ",[883,17093,17095],{"className":17094},[886],[888,17096,17097],{"xmlns":890},[892,17098,17099,17103],{},[895,17100,17101],{},[898,17102,16915],{},[902,17104,16915],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,17107,17108,17138],{},[123,17109,17110,3245,17113,17137],{},[38,17111,17112],{},"funkci investic",[883,17114,17116],{"className":17115},[886],[888,17117,17118],{"xmlns":890},[892,17119,17120,17134],{},[895,17121,17122,17124,17126,17128,17130,17132],{},[898,17123,17058],{},[1712,17125,1714],{},[898,17127,17058],{},[1712,17129,1904],{"stretchy":1903},[898,17131,16915],{},[1712,17133,1910],{"stretchy":1903},[902,17135,17136],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,17139,17140,17143],{},[38,17141,17142],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1636,17145,17146],{},[724,17147,17148,17150,17151,17170,17171,17198,17199,17212,17213,17242,17243,17246],{},[883,17149,2203],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,17152,17154],{"className":17153},[886],[888,17155,17156],{"xmlns":890},[892,17157,17158,17167],{},[895,17159,17160,17162,17165],{},[898,17161,8195],{},[1762,17163,17164],{},"-",[898,17166,17058],{},[902,17168,17169],{"encoding":904},"C\\text{-}I"," až ",[883,17172,17174],{"className":17173},[886],[888,17175,17176],{"xmlns":890},[892,17177,17178,17195],{},[895,17179,17180,17182,17184,17186,17188,17190,17192],{},[898,17181,8195],{},[1762,17183,17164],{},[898,17185,17058],{},[1762,17187,17164],{},[898,17189,16986],{},[1762,17191,17164],{},[898,17193,17194],{},"X",[902,17196,17197],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,17200,17202],{"className":17201},[886],[888,17203,17204],{"xmlns":890},[892,17205,17206,17210],{},[895,17207,17208],{},[898,17209,6951],{},[902,17211,6951],{"encoding":904},". V IS-LM jsou ",[38,17214,17215,17216,1655,17229],{},"dvě neznámé ",[883,17217,17219],{"className":17218},[886],[888,17220,17221],{"xmlns":890},[892,17222,17223,17227],{},[895,17224,17225],{},[898,17226,6951],{},[902,17228,6951],{"encoding":904},[883,17230,17232],{"className":17231},[886],[888,17233,17234],{"xmlns":890},[892,17235,17236,17240],{},[895,17237,17238],{},[898,17239,16915],{},[902,17241,16915],{"encoding":904},", a proto potřebujeme ",[38,17244,17245],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,17248,17250],{"id":17249},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,17252,17253,17254,17267,17268,2854],{},"Lineární závislost investic ",[883,17255,17257],{"className":17256},[886],[888,17258,17259],{"xmlns":890},[892,17260,17261,17265],{},[895,17262,17263],{},[898,17264,17058],{},[902,17266,17058],{"encoding":904}," na úrokové míře ",[883,17269,17271],{"className":17270},[886],[888,17272,17273],{"xmlns":890},[892,17274,17275,17279],{},[895,17276,17277],{},[898,17278,16915],{},[902,17280,16915],{"encoding":904},[724,17282,17283],{},[883,17284,17286],{"className":17285},[886],[888,17287,17288],{"xmlns":890},[892,17289,17290,17344],{},[895,17291,17292,17294,17296,17298,17300,17302,17304,17306,17308,17310,17312,17314,17316,17318,17320,17322,17324,17326,17328,17330,17332,17335,17337,17339,17342],{},[898,17293,17058],{},[1712,17295,1714],{},[898,17297,17058],{},[1712,17299,1904],{"stretchy":1903},[898,17301,16915],{},[1712,17303,1910],{"stretchy":1903},[1712,17305,1714],{},[898,17307,7585],{},[898,17309,16915],{},[1712,17311,3145],{},[898,17313,2468],{},[1712,17315,3138],{"separator":2565},[3690,17317],{"width":3692},[898,17319,7585],{},[1712,17321,2252],{},[1716,17323,2085],{},[1712,17325,3138],{"separator":2565},[1762,17327,7722],{},[898,17329,2468],{},[1712,17331,2302],{},[1716,17333,17334],{},"0.",[3690,17336],{"width":3692},[1712,17338,1904],{"stretchy":1903},[1716,17340,17341],{},"7.11",[1712,17343,1910],{"stretchy":1903},[902,17345,17346],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,17348,17349,17370],{},[123,17350,17351,17369],{},[883,17352,17354],{"className":17353},[886],[888,17355,17356],{"xmlns":890},[892,17357,17358,17366],{},[895,17359,17360,17362,17364],{},[898,17361,2468],{},[1712,17363,2302],{},[1716,17365,2085],{},[902,17367,17368],{"encoding":904},"d > 0"," zřejmé,",[123,17371,17372,17390,17391,1659],{},[883,17373,17375],{"className":17374},[886],[888,17376,17377],{"xmlns":890},[892,17378,17379,17387],{},[895,17380,17381,17383,17385],{},[898,17382,7585],{},[1712,17384,2252],{},[1716,17386,2085],{},[902,17388,17389],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,17392,17393],{},"klesající",[724,17395,17396],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,17398,17399],{},[883,17400,17402],{"className":17401},[886],[888,17403,17404],{"xmlns":890},[892,17405,17406,17463],{},[895,17407,17408,17410,17412,17414,17416,17418,17420,17422,17424,17426,17428,17430,17432,17434,17436,17438,17440,17442,17444,17446,17448,17450,17452,17454,17456,17458,17461],{},[898,17409,8195],{},[1712,17411,1714],{},[898,17413,8195],{},[1712,17415,1904],{"stretchy":1903},[898,17417,6951],{},[1712,17419,1910],{"stretchy":1903},[1712,17421,1714],{},[898,17423,207],{},[898,17425,6951],{},[1712,17427,3145],{},[898,17429,7544],{},[1712,17431,3138],{"separator":2565},[3690,17433],{"width":3692},[1716,17435,2085],{},[1712,17437,2252],{},[898,17439,207],{},[1712,17441,2252],{},[1716,17443,2222],{},[1712,17445,3138],{"separator":2565},[1762,17447,7722],{},[898,17449,7544],{},[1712,17451,2302],{},[1716,17453,17334],{},[3690,17455],{"width":3692},[1712,17457,1904],{"stretchy":1903},[1716,17459,17460],{},"7.12",[1712,17462,1910],{"stretchy":1903},[902,17464,17465],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,17467,17468],{},"Podmínka rovnováhy na trhu zboží:",[724,17470,17471],{},[883,17472,17474],{"className":17473},[886],[888,17475,17476],{"xmlns":890},[892,17477,17478,17501],{},[895,17479,17480,17482,17484,17486,17488,17490,17492,17494,17496,17499],{},[898,17481,6951],{},[1712,17483,1714],{},[898,17485,8195],{},[1712,17487,3145],{},[898,17489,17058],{},[898,17491,1659],{"mathvariant":2003},[3690,17493],{"width":3692},[1712,17495,1904],{"stretchy":1903},[1716,17497,17498],{},"7.13",[1712,17500,1910],{"stretchy":1903},[902,17502,17503],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,17505,17506,17507,3245,17510,17536,17537,1659],{},"To dává ",[38,17508,17509],{},"tři rovnice o čtyřech neznámých",[883,17511,17513],{"className":17512},[886],[888,17514,17515],{"xmlns":890},[892,17516,17517,17533],{},[895,17518,17519,17521,17523,17525,17527,17529,17531],{},[898,17520,6951],{},[1712,17522,3138],{"separator":2565},[898,17524,8195],{},[1712,17526,3138],{"separator":2565},[898,17528,17058],{},[1712,17530,3138],{"separator":2565},[898,17532,16915],{},[902,17534,17535],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,17538,17539],{},"rovnováhy na trhu peněz",[115,17541,17543],{"id":17542},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,17545,17546,17547,3381,17569,17587,17588,17591],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,17548,17550],{"className":17549},[886],[888,17551,17552],{"xmlns":890},[892,17553,17554,17566],{},[895,17555,17556,17558,17560,17562,17564],{},[898,17557,6951],{},[1712,17559,1714],{},[898,17561,8195],{},[1712,17563,3145],{},[898,17565,6493],{},[902,17567,17568],{"encoding":904},"Y = C + S",[883,17570,17572],{"className":17571},[886],[888,17573,17574],{"xmlns":890},[892,17575,17576,17584],{},[895,17577,17578,17580,17582],{},[898,17579,17058],{},[1712,17581,1714],{},[898,17583,6493],{},[902,17585,17586],{"encoding":904},"I = S"," (plánované ",[38,17589,17590],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,17593,17594],{},[3817,17595],{"alt":17596,"className":17597,"src":17598},"imek-odvozeni-is-4panelu",[210,3821],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,17600,17601],{},[883,17602,17604],{"className":17603},[886],[888,17605,17606],{"xmlns":890},[892,17607,17608,17642],{},[895,17609,17610,17612,17614,17616,17618,17620,17622,17624,17626,17628,17630,17632,17634,17636,17638,17640],{},[898,17611,6951],{},[1712,17613,1714],{},[1712,17615,1904],{"stretchy":1903},[898,17617,207],{},[898,17619,6951],{},[1712,17621,3145],{},[898,17623,7544],{},[1712,17625,1910],{"stretchy":1903},[1712,17627,3145],{},[1712,17629,1904],{"stretchy":1903},[898,17631,7585],{},[898,17633,16915],{},[1712,17635,3145],{},[898,17637,2468],{},[1712,17639,1910],{"stretchy":1903},[1712,17641,3138],{"separator":2565},[902,17643,17644],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,17646,17647],{},[883,17648,17650],{"className":17649},[886],[888,17651,17652],{"xmlns":890},[892,17653,17654,17688],{},[895,17655,17656,17658,17660,17662,17664,17666,17668,17670,17672,17674,17676,17678,17680,17682,17684,17686],{},[1712,17657,1904],{"stretchy":1903},[1716,17659,2222],{},[1712,17661,2219],{},[898,17663,207],{},[1712,17665,1910],{"stretchy":1903},[898,17667,6951],{},[1712,17669,2219],{},[898,17671,7585],{},[898,17673,16915],{},[1712,17675,2219],{},[898,17677,7544],{},[1712,17679,2219],{},[898,17681,2468],{},[1712,17683,1714],{},[1716,17685,2085],{},[1712,17687,3138],{"separator":2565},[902,17689,17690],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,17692,17693],{},"odkud",[724,17695,17696],{},[883,17697,17699],{"className":17698},[886],[888,17700,17701],{"xmlns":890},[892,17702,17703,17770],{},[895,17704,17705,17761,17763,17765,17768],{},[17706,17707,17709],"menclose",{"notation":17708},"box",[2563,17710,17711],{"scriptlevel":2085,"displaystyle":1903},[2563,17712,17713],{"scriptlevel":2085,"displaystyle":1903},[2563,17714,17715],{"scriptlevel":2085,"displaystyle":2565},[895,17716,17717,17719,17721,17723,17735,17737,17739,17741,17759],{},[1762,17718,2583],{},[898,17720,6951],{},[1712,17722,1714],{},[2567,17724,17725,17727],{},[898,17726,7585],{},[895,17728,17729,17731,17733],{},[1716,17730,2222],{},[1712,17732,2219],{},[898,17734,207],{},[1762,17736,2583],{},[898,17738,16915],{},[1712,17740,3145],{},[2567,17742,17743,17751],{},[895,17744,17745,17747,17749],{},[898,17746,7544],{},[1712,17748,3145],{},[898,17750,2468],{},[895,17752,17753,17755,17757],{},[1716,17754,2222],{},[1712,17756,2219],{},[898,17758,207],{},[1762,17760,2583],{},[3690,17762],{"width":3692},[1712,17764,1904],{"stretchy":1903},[1716,17766,17767],{},"7.14",[1712,17769,1910],{"stretchy":1903},[902,17771,17772],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,17774,17775,17776,14897,17779,17782,17783,17786,17787,17789,17790,17812,17813,17841,17842,17863,17864,17866,17867,17869],{},"Tento vztah se nazývá ",[38,17777,17778],{},"funkce IS",[614,17780,17781],{},"IS schedule",") a její graf ",[38,17784,17785],{},"křivka IS",". Křivka je ",[38,17788,17393],{}," přímka v rovině ",[883,17791,17793],{"className":17792},[886],[888,17794,17795],{"xmlns":890},[892,17796,17797,17809],{},[895,17798,17799,17801,17803,17805,17807],{},[1712,17800,1904],{"stretchy":1903},[898,17802,16915],{},[1712,17804,3138],{"separator":2565},[898,17806,6951],{},[1712,17808,1910],{"stretchy":1903},[902,17810,17811],{"encoding":904},"(r, Y)",", neboť ",[883,17814,17816],{"className":17815},[886],[888,17817,17818],{"xmlns":890},[892,17819,17820,17838],{},[895,17821,17822,17834,17836],{},[2567,17823,17824,17826],{},[898,17825,7585],{},[895,17827,17828,17830,17832],{},[1716,17829,2222],{},[1712,17831,2219],{},[898,17833,207],{},[1712,17835,2252],{},[1716,17837,2085],{},[902,17839,17840],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,17843,17845],{"className":17844},[886],[888,17846,17847],{"xmlns":890},[892,17848,17849,17861],{},[895,17850,17851,17853,17855,17857,17859],{},[1712,17852,1904],{"stretchy":1903},[898,17854,16915],{},[1712,17856,3138],{"separator":2565},[898,17858,6951],{},[1712,17860,1910],{"stretchy":1903},[902,17862,17811],{"encoding":904},", pro které plánované ",[38,17865,17058],{},"nvestment = ",[38,17868,6493],{},"avings.",[1636,17871,17872],{},[724,17873,17874,17876,17877,17890,17891,3245,17894,17907,17908,17921,17922,1655,17935,17948,17949,17952],{},[883,17875,1941],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,17878,17880],{"className":17879},[886],[888,17881,17882],{"xmlns":890},[892,17883,17884,17888],{},[895,17885,17886],{},[898,17887,16915],{},[902,17889,16915],{"encoding":904}," → levnější úvěr → ",[38,17892,17893],{},"více investic",[883,17895,17897],{"className":17896},[886],[888,17898,17899],{"xmlns":890},[892,17900,17901,17905],{},[895,17902,17903],{},[898,17904,17058],{},[902,17906,17058],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,17909,17911],{"className":17910},[886],[888,17912,17913],{"xmlns":890},[892,17914,17915,17919],{},[895,17916,17917],{},[898,17918,6951],{},[902,17920,6951],{"encoding":904},". Vztah mezi ",[883,17923,17925],{"className":17924},[886],[888,17926,17927],{"xmlns":890},[892,17928,17929,17933],{},[895,17930,17931],{},[898,17932,16915],{},[902,17934,16915],{"encoding":904},[883,17936,17938],{"className":17937},[886],[888,17939,17940],{"xmlns":890},[892,17941,17942,17946],{},[895,17943,17944],{},[898,17945,6951],{},[902,17947,6951],{"encoding":904}," na trhu zboží je proto ",[38,17950,17951],{},"nepřímý"," (klesající křivka).",[115,17954,17956],{"id":17955},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,17958,17959,17960,17978,17979,7037,17997,18000],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,17961,17963],{"className":17962},[886],[888,17964,17965],{"xmlns":890},[892,17966,17967,17975],{},[895,17968,17969],{},[2037,17970,17971,17973],{},[898,17972,4445],{},[898,17974,1969],{},[902,17976,17977],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,17980,17982],{"className":17981},[886],[888,17983,17984],{"xmlns":890},[892,17985,17986,17994],{},[895,17987,17988],{},[2037,17989,17990,17992],{},[898,17991,4445],{},[898,17993,6493],{},[902,17995,17996],{"encoding":904},"M^S",[38,17998,17999],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,18002,18003],{},[883,18004,18006],{"className":18005},[886],[888,18007,18008],{"xmlns":890},[892,18009,18010,18028],{},[895,18011,18012,18018,18020,18026],{},[2037,18013,18014,18016],{},[898,18015,4445],{},[898,18017,6493],{},[1712,18019,1714],{},[2037,18021,18022,18024],{},[898,18023,4445],{},[1712,18025,2145],{},[898,18027,1659],{"mathvariant":2003},[902,18029,18030],{"encoding":904},"M^S = M^*.",[724,18032,18033,18036],{},[38,18034,18035],{},"Poptávka"," po penězích má tři zdroje:",[120,18038,18039,18048,18057],{},[123,18040,18041,14897,18044,18047],{},[38,18042,18043],{},"transakční poptávka",[614,18045,18046],{},"transactions demand",") — peníze pro nákup zboží,",[123,18049,18050,14897,18053,18056],{},[38,18051,18052],{},"opatrnostní poptávka",[614,18054,18055],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,18058,18059,14897,18062,18065],{},[38,18060,18061],{},"spekulační poptávka",[614,18063,18064],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,18067,18068,18069,18087],{},"Součet transakční a opatrnostní poptávky ",[883,18070,18072],{"className":18071},[886],[888,18073,18074],{"xmlns":890},[892,18075,18076,18084],{},[895,18077,18078],{},[6927,18079,18080,18082],{},[898,18081,14667],{},[1716,18083,2222],{},[902,18085,18086],{"encoding":904},"L_1"," je úměrný důchodu:",[724,18089,18090],{},[883,18091,18093],{"className":18092},[886],[888,18094,18095],{"xmlns":890},[892,18096,18097,18135],{},[895,18098,18099,18105,18107,18114,18116,18118,18120,18122,18124,18130,18132],{},[6927,18100,18101,18103],{},[898,18102,14667],{},[1716,18104,2222],{},[1712,18106,1714],{},[6927,18108,18109,18112],{},[898,18110,18111],{},"k",[1716,18113,2222],{},[898,18115,6951],{},[1712,18117,3138],{"separator":2565},[3690,18119],{"width":3692},[1716,18121,2085],{},[1712,18123,2252],{},[6927,18125,18126,18128],{},[898,18127,18111],{},[1716,18129,2222],{},[1712,18131,2252],{},[1716,18133,18134],{},"1.",[902,18136,18137],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,18139,18140,18141,18159,18160,1343,18173,18190],{},"Spekulační poptávka ",[883,18142,18144],{"className":18143},[886],[888,18145,18146],{"xmlns":890},[892,18147,18148,18156],{},[895,18149,18150],{},[6927,18151,18152,18154],{},[898,18153,14667],{},[1716,18155,2787],{},[902,18157,18158],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,18161,18163],{"className":18162},[886],[888,18164,18165],{"xmlns":890},[892,18166,18167,18171],{},[895,18168,18169],{},[898,18170,16915],{},[902,18172,16915],{"encoding":904},[883,18174,18176],{"className":18175},[886],[888,18177,18178],{"xmlns":890},[892,18179,18180,18188],{},[895,18181,18182],{},[6927,18183,18184,18186],{},[898,18185,14667],{},[1716,18187,2787],{},[902,18189,18158],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,18192,18193],{},[883,18194,18196],{"className":18195},[886],[888,18197,18198],{"xmlns":890},[892,18199,18200,18254],{},[895,18201,18202,18208,18210,18216,18218,18220,18226,18228,18230,18236,18238,18240,18242,18244,18250,18252],{},[6927,18203,18204,18206],{},[898,18205,14667],{},[1716,18207,2787],{},[1712,18209,1714],{},[6927,18211,18212,18214],{},[898,18213,18111],{},[1716,18215,2787],{},[898,18217,16915],{},[1712,18219,3145],{},[6927,18221,18222,18224],{},[898,18223,18111],{},[1716,18225,6198],{},[1712,18227,3138],{"separator":2565},[3690,18229],{"width":3692},[6927,18231,18232,18234],{},[898,18233,18111],{},[1716,18235,2787],{},[1712,18237,2252],{},[1716,18239,2085],{},[1712,18241,3138],{"separator":2565},[1762,18243,7722],{},[6927,18245,18246,18248],{},[898,18247,18111],{},[1716,18249,6198],{},[1712,18251,2302],{},[1716,18253,17334],{},[902,18255,18256],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,18258,18259],{},"Celková poptávka po penězích:",[724,18261,18262],{},[883,18263,18265],{"className":18264},[886],[888,18266,18267],{"xmlns":890},[892,18268,18269,18323],{},[895,18270,18271,18277,18279,18285,18287,18293,18295,18301,18303,18305,18311,18313,18315,18321],{},[2037,18272,18273,18275],{},[898,18274,4445],{},[898,18276,1969],{},[1712,18278,1714],{},[6927,18280,18281,18283],{},[898,18282,14667],{},[1716,18284,2222],{},[1712,18286,3145],{},[6927,18288,18289,18291],{},[898,18290,14667],{},[1716,18292,2787],{},[1712,18294,1714],{},[6927,18296,18297,18299],{},[898,18298,18111],{},[1716,18300,2222],{},[898,18302,6951],{},[1712,18304,3145],{},[6927,18306,18307,18309],{},[898,18308,18111],{},[1716,18310,2787],{},[898,18312,16915],{},[1712,18314,3145],{},[6927,18316,18317,18319],{},[898,18318,18111],{},[1716,18320,6198],{},[898,18322,1659],{"mathvariant":2003},[902,18324,18325],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,18327,18328,18329,2854],{},"Podmínka rovnováhy na trhu peněz ",[883,18330,18332],{"className":18331},[886],[888,18333,18334],{"xmlns":890},[892,18335,18336,18352],{},[895,18337,18338,18344,18346],{},[2037,18339,18340,18342],{},[898,18341,4445],{},[898,18343,1969],{},[1712,18345,1714],{},[2037,18347,18348,18350],{},[898,18349,4445],{},[1712,18351,2145],{},[902,18353,18354],{"encoding":904},"M^D = M^*",[724,18356,18357],{},[883,18358,18360],{"className":18359},[886],[888,18361,18362],{"xmlns":890},[892,18363,18364,18411],{},[895,18365,18366,18372,18374,18380,18382,18384,18390,18392,18394,18400,18402,18404,18406,18409],{},[2037,18367,18368,18370],{},[898,18369,4445],{},[1712,18371,2145],{},[1712,18373,1714],{},[6927,18375,18376,18378],{},[898,18377,18111],{},[1716,18379,2222],{},[898,18381,6951],{},[1712,18383,3145],{},[6927,18385,18386,18388],{},[898,18387,18111],{},[1716,18389,2787],{},[898,18391,16915],{},[1712,18393,3145],{},[6927,18395,18396,18398],{},[898,18397,18111],{},[1716,18399,6198],{},[1712,18401,3138],{"separator":2565},[3690,18403],{"width":3692},[1712,18405,1904],{"stretchy":1903},[1716,18407,18408],{},"7.15",[1712,18410,1910],{"stretchy":1903},[902,18412,18413],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,18415,18416,18417,8558],{},"po úpravě (vyjádření ",[883,18418,18420],{"className":18419},[886],[888,18421,18422],{"xmlns":890},[892,18423,18424,18428],{},[895,18425,18426],{},[898,18427,6951],{},[902,18429,6951],{"encoding":904},[724,18431,18432],{},[883,18433,18435],{"className":18434},[886],[888,18436,18437],{"xmlns":890},[892,18438,18439,18514],{},[895,18440,18441,18505,18507,18509,18512],{},[17706,18442,18443],{"notation":17708},[2563,18444,18445],{"scriptlevel":2085,"displaystyle":1903},[2563,18446,18447],{"scriptlevel":2085,"displaystyle":1903},[2563,18448,18449],{"scriptlevel":2085,"displaystyle":2565},[895,18450,18451,18453,18455,18457,18459,18473,18475,18477,18479,18503],{},[1762,18452,2583],{},[898,18454,6951],{},[1712,18456,1714],{},[1712,18458,2219],{},[2567,18460,18461,18467],{},[6927,18462,18463,18465],{},[898,18464,18111],{},[1716,18466,2787],{},[6927,18468,18469,18471],{},[898,18470,18111],{},[1716,18472,2222],{},[1762,18474,2583],{},[898,18476,16915],{},[1712,18478,3145],{},[2567,18480,18481,18497],{},[895,18482,18483,18489,18491],{},[2037,18484,18485,18487],{},[898,18486,4445],{},[1712,18488,2145],{},[1712,18490,2219],{},[6927,18492,18493,18495],{},[898,18494,18111],{},[1716,18496,6198],{},[6927,18498,18499,18501],{},[898,18500,18111],{},[1716,18502,2222],{},[1762,18504,2583],{},[3690,18506],{"width":3692},[1712,18508,1904],{"stretchy":1903},[1716,18510,18511],{},"7.16",[1712,18513,1910],{"stretchy":1903},[902,18515,18516],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,18518,17775,18519,14897,18522,18525,18526,17786,18529,17789,18532,17812,18553,18585,18586,18608,18609,18611,18612,18614],{},[38,18520,18521],{},"funkce LM",[614,18523,18524],{},"LM schedule","), její graf ",[38,18527,18528],{},"křivka LM",[38,18530,18531],{},"rostoucí",[883,18533,18535],{"className":18534},[886],[888,18536,18537],{"xmlns":890},[892,18538,18539,18551],{},[895,18540,18541,18543,18545,18547,18549],{},[1712,18542,1904],{"stretchy":1903},[898,18544,16915],{},[1712,18546,3138],{"separator":2565},[898,18548,6951],{},[1712,18550,1910],{"stretchy":1903},[902,18552,17811],{"encoding":904},[883,18554,18556],{"className":18555},[886],[888,18557,18558],{"xmlns":890},[892,18559,18560,18582],{},[895,18561,18562,18564,18578,18580],{},[1712,18563,2219],{},[2567,18565,18566,18572],{},[6927,18567,18568,18570],{},[898,18569,18111],{},[1716,18571,2787],{},[6927,18573,18574,18576],{},[898,18575,18111],{},[1716,18577,2222],{},[1712,18579,2302],{},[1716,18581,2085],{},[902,18583,18584],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,18587,18589],{"className":18588},[886],[888,18590,18591],{"xmlns":890},[892,18592,18593,18605],{},[895,18594,18595,18601,18603],{},[6927,18596,18597,18599],{},[898,18598,18111],{},[1716,18600,2787],{},[1712,18602,2252],{},[1716,18604,2085],{},[902,18606,18607],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,18610,14667],{},"iquidity of ",[38,18613,4445],{},"oney.",[1636,18616,18617],{},[724,18618,18619,18621,18622,18635,18636,18664,18665,18682,18683,18696,18697,18714,18715,1655,18728,18741,18742,18745],{},[883,18620,1941],{}," Intuice — proč LM roste\nVyšší důchod ",[883,18623,18625],{"className":18624},[886],[888,18626,18627],{"xmlns":890},[892,18628,18629,18633],{},[895,18630,18631],{},[898,18632,6951],{},[902,18634,6951],{"encoding":904}," → větší transakční poptávka po penězích ",[883,18637,18639],{"className":18638},[886],[888,18640,18641],{"xmlns":890},[892,18642,18643,18661],{},[895,18644,18645,18651,18653,18659],{},[6927,18646,18647,18649],{},[898,18648,14667],{},[1716,18650,2222],{},[1712,18652,1714],{},[6927,18654,18655,18657],{},[898,18656,18111],{},[1716,18658,2222],{},[898,18660,6951],{},[902,18662,18663],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,18666,18668],{"className":18667},[886],[888,18669,18670],{"xmlns":890},[892,18671,18672,18680],{},[895,18673,18674],{},[2037,18675,18676,18678],{},[898,18677,4445],{},[1712,18679,2145],{},[902,18681,17024],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,18684,18686],{"className":18685},[886],[888,18687,18688],{"xmlns":890},[892,18689,18690,18694],{},[895,18691,18692],{},[898,18693,16915],{},[902,18695,16915],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,18698,18700],{"className":18699},[886],[888,18701,18702],{"xmlns":890},[892,18703,18704,18712],{},[895,18705,18706],{},[6927,18707,18708,18710],{},[898,18709,14667],{},[1716,18711,2787],{},[902,18713,18158],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,18716,18718],{"className":18717},[886],[888,18719,18720],{"xmlns":890},[892,18721,18722,18726],{},[895,18723,18724],{},[898,18725,6951],{},[902,18727,6951],{"encoding":904},[883,18729,18731],{"className":18730},[886],[888,18732,18733],{"xmlns":890},[892,18734,18735,18739],{},[895,18736,18737],{},[898,18738,16915],{},[902,18740,16915],{"encoding":904}," na trhu peněz je proto ",[38,18743,18744],{},"přímý"," (rostoucí křivka).",[115,18747,18749],{"id":18748},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,18751,18752,18753,18756,18757,3245,18760,1655,18778,3245,18781,18799,18800,18818,18819,18837,18838,18854,18855,1655,18870,18885,18886,1659],{},"Řešením ",[38,18754,18755],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,18758,18759],{},"rovnovážný důchod",[883,18761,18763],{"className":18762},[886],[888,18764,18765],{"xmlns":890},[892,18766,18767,18775],{},[895,18768,18769],{},[2037,18770,18771,18773],{},[898,18772,6951],{},[898,18774,2041],{},[902,18776,18777],{"encoding":904},"Y^E",[38,18779,18780],{},"rovnovážnou úrokovou míru",[883,18782,18784],{"className":18783},[886],[888,18785,18786],{"xmlns":890},[892,18787,18788,18796],{},[895,18789,18790],{},[2037,18791,18792,18794],{},[898,18793,16915],{},[898,18795,2041],{},[902,18797,18798],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,18801,18803],{"className":18802},[886],[888,18804,18805],{"xmlns":890},[892,18806,18807,18815],{},[895,18808,18809],{},[2037,18810,18811,18813],{},[898,18812,17058],{},[898,18814,2041],{},[902,18816,18817],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,18820,18822],{"className":18821},[886],[888,18823,18824],{"xmlns":890},[892,18825,18826,18834],{},[895,18827,18828],{},[2037,18829,18830,18832],{},[898,18831,8195],{},[898,18833,2041],{},[902,18835,18836],{"encoding":904},"C^E",". Graficky jde o ",[38,18839,18840,18841],{},"průsečík ",[883,18842,18844],{"className":18843},[886],[888,18845,18846],{"xmlns":890},[892,18847,18848,18852],{},[895,18849,18850],{},[898,18851,2041],{},[902,18853,2041],{"encoding":904}," křivek ",[883,18856,18858],{"className":18857},[886],[888,18859,18860],{"xmlns":890},[892,18861,18862,18868],{},[895,18863,18864,18866],{},[898,18865,17058],{},[898,18867,6493],{},[902,18869,16925],{"encoding":904},[883,18871,18873],{"className":18872},[886],[888,18874,18875],{"xmlns":890},[892,18876,18877,18883],{},[895,18878,18879,18881],{},[898,18880,14667],{},[898,18882,4445],{},[902,18884,16932],{"encoding":904}," v rovině ",[883,18887,18889],{"className":18888},[886],[888,18890,18891],{"xmlns":890},[892,18892,18893,18905],{},[895,18894,18895,18897,18899,18901,18903],{},[1712,18896,1904],{"stretchy":1903},[898,18898,16915],{},[1712,18900,3138],{"separator":2565},[898,18902,6951],{},[1712,18904,1910],{"stretchy":1903},[902,18906,17811],{"encoding":904},[724,18908,18909],{},[614,18910,18911,18912,18933,18934,18949,18950,18965,18966,18979,18980,18997,18998,17002,19011,18997,19028,19041,19042,19055],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,18913,18915],{"className":18914},[886],[888,18916,18917],{"xmlns":890},[892,18918,18919,18931],{},[895,18920,18921,18923,18925,18927,18929],{},[1712,18922,1904],{"stretchy":1903},[898,18924,16915],{},[1712,18926,3138],{"separator":2565},[898,18928,6951],{},[1712,18930,1910],{"stretchy":1903},[902,18932,17811],{"encoding":904},". Rostoucí přímka ",[883,18935,18937],{"className":18936},[886],[888,18938,18939],{"xmlns":890},[892,18940,18941,18947],{},[895,18942,18943,18945],{},[898,18944,14667],{},[898,18946,4445],{},[902,18948,16932],{"encoding":904}," a klesající přímka ",[883,18951,18953],{"className":18952},[886],[888,18954,18955],{"xmlns":890},[892,18956,18957,18963],{},[895,18958,18959,18961],{},[898,18960,17058],{},[898,18962,6493],{},[902,18964,16925],{"encoding":904}," se protínají v bodě ",[883,18967,18969],{"className":18968},[886],[888,18970,18971],{"xmlns":890},[892,18972,18973,18977],{},[895,18974,18975],{},[898,18976,2041],{},[902,18978,2041],{"encoding":904}," se souřadnicemi ",[883,18981,18983],{"className":18982},[886],[888,18984,18985],{"xmlns":890},[892,18986,18987,18995],{},[895,18988,18989],{},[2037,18990,18991,18993],{},[898,18992,16915],{},[898,18994,2041],{},[902,18996,18798],{"encoding":904}," (na ose ",[883,18999,19001],{"className":19000},[886],[888,19002,19003],{"xmlns":890},[892,19004,19005,19009],{},[895,19006,19007],{},[898,19008,16915],{},[902,19010,16915],{"encoding":904},[883,19012,19014],{"className":19013},[886],[888,19015,19016],{"xmlns":890},[892,19017,19018,19026],{},[895,19019,19020],{},[2037,19021,19022,19024],{},[898,19023,6951],{},[898,19025,2041],{},[902,19027,18777],{"encoding":904},[883,19029,19031],{"className":19030},[886],[888,19032,19033],{"xmlns":890},[892,19034,19035,19039],{},[895,19036,19037],{},[898,19038,6951],{},[902,19040,6951],{"encoding":904},"); tečkované čáry z ",[883,19043,19045],{"className":19044},[886],[888,19046,19047],{"xmlns":890},[892,19048,19049,19053],{},[895,19050,19051],{},[898,19052,2041],{},[902,19054,2041],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1636,19057,19058,19063],{},[724,19059,19060,19062],{},[883,19061,2370],{}," Postup — jak najít IS-LM rovnováhu",[152,19064,19065,19141,19209,19267,19340],{},[123,19066,19067,19070,19071,1655,19091,19111,19112,1655,19125,19138,19139,1659],{},[38,19068,19069],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,19072,19074],{"className":19073},[886],[888,19075,19076],{"xmlns":890},[892,19077,19078,19088],{},[895,19079,19080,19082,19084,19086],{},[898,19081,8195],{},[1712,19083,1904],{"stretchy":1903},[898,19085,6951],{},[1712,19087,1910],{"stretchy":1903},[902,19089,19090],{"encoding":904},"C(Y)",[883,19092,19094],{"className":19093},[886],[888,19095,19096],{"xmlns":890},[892,19097,19098,19108],{},[895,19099,19100,19102,19104,19106],{},[898,19101,17058],{},[1712,19103,1904],{"stretchy":1903},[898,19105,16915],{},[1712,19107,1910],{"stretchy":1903},[902,19109,19110],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,19113,19115],{"className":19114},[886],[888,19116,19117],{"xmlns":890},[892,19118,19119,19123],{},[895,19120,19121],{},[898,19122,6951],{},[902,19124,6951],{"encoding":904},[883,19126,19128],{"className":19127},[886],[888,19129,19130],{"xmlns":890},[892,19131,19132,19136],{},[895,19133,19134],{},[898,19135,16915],{},[902,19137,16915],{"encoding":904}," — dostaneš rovnici ",[38,19140,16925],{},[123,19142,19143,19146,19147,1655,19164,19181,19182,19138,19207,1659],{},[38,19144,19145],{},"Z trhu peněz (7.15)"," dosaď ",[883,19148,19150],{"className":19149},[886],[888,19151,19152],{"xmlns":890},[892,19153,19154,19162],{},[895,19155,19156],{},[6927,19157,19158,19160],{},[898,19159,14667],{},[1716,19161,2222],{},[902,19163,18086],{"encoding":904},[883,19165,19167],{"className":19166},[886],[888,19168,19169],{"xmlns":890},[892,19170,19171,19179],{},[895,19172,19173],{},[6927,19174,19175,19177],{},[898,19176,14667],{},[1716,19178,2787],{},[902,19180,18158],{"encoding":904}," a vztah ",[883,19183,19185],{"className":19184},[886],[888,19186,19187],{"xmlns":890},[892,19188,19189,19205],{},[895,19190,19191,19197,19199],{},[2037,19192,19193,19195],{},[898,19194,4445],{},[898,19196,1969],{},[1712,19198,1714],{},[2037,19200,19201,19203],{},[898,19202,4445],{},[1712,19204,2145],{},[902,19206,18354],{"encoding":904},[38,19208,16932],{},[123,19210,19211,19214,19215,1655,19228,19241,19242,19266],{},[38,19212,19213],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,19216,19218],{"className":19217},[886],[888,19219,19220],{"xmlns":890},[892,19221,19222,19226],{},[895,19223,19224],{},[898,19225,6951],{},[902,19227,6951],{"encoding":904},[883,19229,19231],{"className":19230},[886],[888,19232,19233],{"xmlns":890},[892,19234,19235,19239],{},[895,19236,19237],{},[898,19238,16915],{},[902,19240,16915],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,19243,19245],{"className":19244},[886],[888,19246,19247],{"xmlns":890},[892,19248,19249,19263],{},[895,19250,19251,19253,19255,19257,19259,19261],{},[898,19252,6951],{},[1712,19254,1714],{},[898,19256,7451],{},[1712,19258,1904],{"stretchy":1903},[898,19260,16915],{},[1712,19262,1910],{"stretchy":1903},[902,19264,19265],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,19268,19269,3245,19272,1655,19306,1659],{},[38,19270,19271],{},"Zpětně dopočítej",[883,19273,19275],{"className":19274},[886],[888,19276,19277],{"xmlns":890},[892,19278,19279,19303],{},[895,19280,19281,19287,19289,19291,19293,19299,19301],{},[2037,19282,19283,19285],{},[898,19284,8195],{},[898,19286,2041],{},[1712,19288,1714],{},[898,19290,207],{},[1762,19292,2583],{},[2037,19294,19295,19297],{},[898,19296,6951],{},[898,19298,2041],{},[1712,19300,3145],{},[898,19302,7544],{},[902,19304,19305],{"encoding":904},"C^E = a\\,Y^E + b",[883,19307,19309],{"className":19308},[886],[888,19310,19311],{"xmlns":890},[892,19312,19313,19337],{},[895,19314,19315,19321,19323,19325,19327,19333,19335],{},[2037,19316,19317,19319],{},[898,19318,17058],{},[898,19320,2041],{},[1712,19322,1714],{},[898,19324,7585],{},[1762,19326,2583],{},[2037,19328,19329,19331],{},[898,19330,16915],{},[898,19332,2041],{},[1712,19334,3145],{},[898,19336,2468],{},[902,19338,19339],{"encoding":904},"I^E = c\\,r^E + d",[123,19341,19342,19345,19346,19380,19381,19435],{},[38,19343,19344],{},"Ověř:"," musí platit ",[883,19347,19349],{"className":19348},[886],[888,19350,19351],{"xmlns":890},[892,19352,19353,19377],{},[895,19354,19355,19361,19363,19369,19371],{},[2037,19356,19357,19359],{},[898,19358,6951],{},[898,19360,2041],{},[1712,19362,1714],{},[2037,19364,19365,19367],{},[898,19366,8195],{},[898,19368,2041],{},[1712,19370,3145],{},[2037,19372,19373,19375],{},[898,19374,17058],{},[898,19376,2041],{},[902,19378,19379],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,19382,19384],{"className":19383},[886],[888,19385,19386],{"xmlns":890},[892,19387,19388,19432],{},[895,19389,19390,19396,19398,19404,19410,19412,19418,19424,19426],{},[2037,19391,19392,19394],{},[898,19393,4445],{},[1712,19395,2145],{},[1712,19397,1714],{},[6927,19399,19400,19402],{},[898,19401,18111],{},[1716,19403,2222],{},[2037,19405,19406,19408],{},[898,19407,6951],{},[898,19409,2041],{},[1712,19411,3145],{},[6927,19413,19414,19416],{},[898,19415,18111],{},[1716,19417,2787],{},[2037,19419,19420,19422],{},[898,19421,16915],{},[898,19423,2041],{},[1712,19425,3145],{},[6927,19427,19428,19430],{},[898,19429,18111],{},[1716,19431,6198],{},[902,19433,19434],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,19437,19439],{"id":19438},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,19441,19442],{},"Pro trh zboží jsou dány:",[120,19444,19445,19473],{},[123,19446,19447,19448,3138],{},"spotřeba ",[883,19449,19451],{"className":19450},[886],[888,19452,19453],{"xmlns":890},[892,19454,19455,19470],{},[895,19456,19457,19459,19461,19464,19466,19468],{},[898,19458,8195],{},[1712,19460,1714],{},[1716,19462,19463],{},"0,8",[898,19465,6951],{},[1712,19467,3145],{},[1716,19469,1739],{},[902,19471,19472],{"encoding":904},"C = 0{,}8Y + 100",[123,19474,19475,19476,1659],{},"investice ",[883,19477,19479],{"className":19478},[886],[888,19480,19481],{"xmlns":890},[892,19482,19483,19499],{},[895,19484,19485,19487,19489,19491,19493,19495,19497],{},[898,19486,17058],{},[1712,19488,1714],{},[1712,19490,2219],{},[1716,19492,6857],{},[898,19494,16915],{},[1712,19496,3145],{},[1716,19498,8200],{},[902,19500,19501],{"encoding":904},"I = -20r + 1000",[724,19503,19504],{},"Pro trh peněz:",[120,19506,19507,19533,19565],{},[123,19508,19509,3138],{},[883,19510,19512],{"className":19511},[886],[888,19513,19514],{"xmlns":890},[892,19515,19516,19530],{},[895,19517,19518,19524,19526,19528],{},[6927,19519,19520,19522],{},[898,19521,14667],{},[1716,19523,2222],{},[1712,19525,1714],{},[1716,19527,6607],{},[898,19529,6951],{},[902,19531,19532],{"encoding":904},"L_1 = 0{,}1Y",[123,19534,19535,3138],{},[883,19536,19538],{"className":19537},[886],[888,19539,19540],{"xmlns":890},[892,19541,19542,19562],{},[895,19543,19544,19550,19552,19554,19556,19558,19560],{},[6927,19545,19546,19548],{},[898,19547,14667],{},[1716,19549,2787],{},[1712,19551,1714],{},[1712,19553,2219],{},[1716,19555,2809],{},[898,19557,16915],{},[1712,19559,3145],{},[1716,19561,6424],{},[902,19563,19564],{"encoding":904},"L_2 = -25r + 2000",[123,19566,19567,19568,1659],{},"nabídka peněz ",[883,19569,19571],{"className":19570},[886],[888,19572,19573],{"xmlns":890},[892,19574,19575,19588],{},[895,19576,19577,19583,19585],{},[2037,19578,19579,19581],{},[898,19580,4445],{},[1712,19582,2145],{},[1712,19584,1714],{},[1716,19586,19587],{},"2375",[902,19589,19590],{"encoding":904},"M^* = 2375",[724,19592,19593,19596,19597,2854],{},[38,19594,19595],{},"Funkce IS"," — dosazením do (7.13) ",[883,19598,19600],{"className":19599},[886],[888,19601,19602],{"xmlns":890},[892,19603,19604,19616],{},[895,19605,19606,19608,19610,19612,19614],{},[898,19607,6951],{},[1712,19609,1714],{},[898,19611,8195],{},[1712,19613,3145],{},[898,19615,17058],{},[902,19617,19618],{"encoding":904},"Y = C + I",[724,19620,19621],{},[883,19622,19624],{"className":19623},[886],[888,19625,19626],{"xmlns":890},[892,19627,19628,19654],{},[895,19629,19630,19632,19634,19636,19638,19640,19642,19644,19646,19648,19650,19652],{},[898,19631,6951],{},[1712,19633,1714],{},[1716,19635,19463],{},[898,19637,6951],{},[1712,19639,3145],{},[1716,19641,1739],{},[1712,19643,2219],{},[1716,19645,6857],{},[898,19647,16915],{},[1712,19649,3145],{},[1716,19651,8200],{},[1712,19653,3138],{"separator":2565},[902,19655,19656],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,19658,19659],{},"tj.",[724,19661,19662],{},[883,19663,19665],{"className":19664},[886],[888,19666,19667],{"xmlns":890},[892,19668,19669,19694],{},[895,19670,19671,19673,19675,19677,19679,19681,19683,19686,19688,19690,19692],{},[1716,19672,6673],{},[898,19674,6951],{},[1712,19676,3145],{},[1716,19678,6857],{},[898,19680,16915],{},[1712,19682,1714],{},[1716,19684,19685],{},"1100.",[3690,19687],{"width":3692},[1712,19689,1904],{"stretchy":1903},[1762,19691,16925],{},[1712,19693,1910],{"stretchy":1903},[902,19695,19696],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,19698,19699,19702,19703,2854],{},[38,19700,19701],{},"Funkce LM"," — dosazením do (7.15) ",[883,19704,19706],{"className":19705},[886],[888,19707,19708],{"xmlns":890},[892,19709,19710,19734],{},[895,19711,19712,19718,19720,19726,19728],{},[2037,19713,19714,19716],{},[898,19715,4445],{},[1712,19717,2145],{},[1712,19719,1714],{},[6927,19721,19722,19724],{},[898,19723,14667],{},[1716,19725,2222],{},[1712,19727,3145],{},[6927,19729,19730,19732],{},[898,19731,14667],{},[1716,19733,2787],{},[902,19735,19736],{"encoding":904},"M^* = L_1 + L_2",[724,19738,19739],{},[883,19740,19742],{"className":19741},[886],[888,19743,19744],{"xmlns":890},[892,19745,19746,19768],{},[895,19747,19748,19750,19752,19754,19756,19758,19760,19762,19764,19766],{},[1716,19749,19587],{},[1712,19751,1714],{},[1716,19753,6607],{},[898,19755,6951],{},[1712,19757,2219],{},[1716,19759,2809],{},[898,19761,16915],{},[1712,19763,3145],{},[1716,19765,6424],{},[1712,19767,3138],{"separator":2565},[902,19769,19770],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,19772,19659],{},[724,19774,19775],{},[883,19776,19778],{"className":19777},[886],[888,19779,19780],{"xmlns":890},[892,19781,19782,19807],{},[895,19783,19784,19786,19788,19790,19792,19794,19796,19799,19801,19803,19805],{},[1716,19785,6607],{},[898,19787,6951],{},[1712,19789,2219],{},[1716,19791,2809],{},[898,19793,16915],{},[1712,19795,1714],{},[1716,19797,19798],{},"375.",[3690,19800],{"width":3692},[1712,19802,1904],{"stretchy":1903},[1762,19804,16932],{},[1712,19806,1910],{"stretchy":1903},[902,19808,19809],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,19811,19812,19815,19816,19841],{},[38,19813,19814],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,19817,19819],{"className":19818},[886],[888,19820,19821],{"xmlns":890},[892,19822,19823,19838],{},[895,19824,19825,19827,19829,19832,19834,19836],{},[898,19826,6951],{},[1712,19828,1714],{},[1716,19830,19831],{},"5500",[1712,19833,2219],{},[1716,19835,1739],{},[898,19837,16915],{},[902,19839,19840],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,19843,19844],{},[883,19845,19847],{"className":19846},[886],[888,19848,19849],{"xmlns":890},[892,19850,19851,19937],{},[895,19852,19853,19855,19857,19859,19861,19863,19865,19867,19869,19871,19873,19875,19878,19880,19883,19885,19888,19890,19892,19894,19896,19898,19900,19902,19904,19906,19908,19910,19913,19915,19917,19920,19922,19924,19926,19932,19934],{},[1716,19854,6607],{},[1712,19856,1904],{"stretchy":1903},[1716,19858,19831],{},[1712,19860,2219],{},[1716,19862,1739],{},[898,19864,16915],{},[1712,19866,1910],{"stretchy":1903},[1712,19868,2219],{},[1716,19870,2809],{},[898,19872,16915],{},[1712,19874,1714],{},[1716,19876,19877],{},"375",[1762,19879,1764],{},[1712,19881,19882],{},"⟹",[1762,19884,1764],{},[1716,19886,19887],{},"550",[1712,19889,2219],{},[1716,19891,1718],{},[898,19893,16915],{},[1712,19895,2219],{},[1716,19897,2809],{},[898,19899,16915],{},[1712,19901,1714],{},[1716,19903,19877],{},[1762,19905,1764],{},[1712,19907,19882],{},[1762,19909,1764],{},[1716,19911,19912],{},"35",[898,19914,16915],{},[1712,19916,1714],{},[1716,19918,19919],{},"175",[1762,19921,1764],{},[1712,19923,19882],{},[1762,19925,1764],{},[2037,19927,19928,19930],{},[898,19929,16915],{},[898,19931,2041],{},[1712,19933,1714],{},[1716,19935,19936],{},"5.",[902,19938,19939],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,19941,19942],{},[38,19943,19944],{},"Zpětné dosazení:",[120,19946,19947,19993,20030],{},[123,19948,19949,3138],{},[883,19950,19952],{"className":19951},[886],[888,19953,19954],{"xmlns":890},[892,19955,19956,19990],{},[895,19957,19958,19964,19966,19968,19970,19972,19974,19976,19978,19980,19982,19985,19987],{},[2037,19959,19960,19962],{},[898,19961,6951],{},[898,19963,2041],{},[1712,19965,1714],{},[1716,19967,19831],{},[1712,19969,2219],{},[1716,19971,1739],{},[1712,19973,1783],{},[1716,19975,3068],{},[1712,19977,1714],{},[1716,19979,19831],{},[1712,19981,2219],{},[1716,19983,19984],{},"500",[1712,19986,1714],{},[1716,19988,19989],{},"5000",[902,19991,19992],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,19994,19995,3138],{},[883,19996,19998],{"className":19997},[886],[888,19999,20000],{"xmlns":890},[892,20001,20002,20027],{},[895,20003,20004,20010,20012,20014,20016,20018,20020,20022,20024],{},[2037,20005,20006,20008],{},[898,20007,8195],{},[898,20009,2041],{},[1712,20011,1714],{},[1716,20013,19463],{},[1712,20015,1783],{},[1716,20017,19989],{},[1712,20019,3145],{},[1716,20021,1739],{},[1712,20023,1714],{},[1716,20025,20026],{},"4100",[902,20028,20029],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,20031,20032,1659],{},[883,20033,20035],{"className":20034},[886],[888,20036,20037],{"xmlns":890},[892,20038,20039,20066],{},[895,20040,20041,20047,20049,20051,20053,20055,20057,20059,20061,20063],{},[2037,20042,20043,20045],{},[898,20044,17058],{},[898,20046,2041],{},[1712,20048,1714],{},[1712,20050,2219],{},[1716,20052,6857],{},[1712,20054,1783],{},[1716,20056,3068],{},[1712,20058,3145],{},[1716,20060,8200],{},[1712,20062,1714],{},[1716,20064,20065],{},"900",[902,20067,20068],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,20070,20071,3245,20074,20120],{},[38,20072,20073],{},"Ověření:",[883,20075,20077],{"className":20076},[886],[888,20078,20079],{"xmlns":890},[892,20080,20081,20117],{},[895,20082,20083,20089,20091,20097,20099,20101,20103,20105,20107,20109,20111],{},[2037,20084,20085,20087],{},[898,20086,8195],{},[898,20088,2041],{},[1712,20090,3145],{},[2037,20092,20093,20095],{},[898,20094,17058],{},[898,20096,2041],{},[1712,20098,1714],{},[1716,20100,20026],{},[1712,20102,3145],{},[1716,20104,20065],{},[1712,20106,1714],{},[1716,20108,19989],{},[1712,20110,1714],{},[2037,20112,20113,20115],{},[898,20114,6951],{},[898,20116,2041],{},[902,20118,20119],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,20122,20123],{},[883,20124,20126],{"className":20125},[886],[888,20127,20128],{"xmlns":890},[892,20129,20130,20200],{},[895,20131,20132],{},[17706,20133,20134],{"notation":17708},[2563,20135,20136],{"scriptlevel":2085,"displaystyle":1903},[2563,20137,20138],{"scriptlevel":2085,"displaystyle":1903},[2563,20139,20140],{"scriptlevel":2085,"displaystyle":2565},[895,20141,20142,20144,20150,20152,20154,20156,20159,20165,20167,20169,20171,20173,20179,20181,20183,20185,20187,20193,20195,20198],{},[1762,20143,2583],{},[2037,20145,20146,20148],{},[898,20147,6951],{},[898,20149,2041],{},[1712,20151,1714],{},[1716,20153,19989],{},[1712,20155,3138],{"separator":2565},[3690,20157],{"width":20158},"1em",[2037,20160,20161,20163],{},[898,20162,16915],{},[898,20164,2041],{},[1712,20166,1714],{},[1716,20168,3068],{},[1712,20170,3138],{"separator":2565},[3690,20172],{"width":20158},[2037,20174,20175,20177],{},[898,20176,8195],{},[898,20178,2041],{},[1712,20180,1714],{},[1716,20182,20026],{},[1712,20184,3138],{"separator":2565},[3690,20186],{"width":20158},[2037,20188,20189,20191],{},[898,20190,17058],{},[898,20192,2041],{},[1712,20194,1714],{},[1716,20196,20197],{},"900.",[1762,20199,2583],{},[902,20201,20202],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,20204,20205],{},[614,20206,20207,20208,20221,20222,20235,20236,20251,20252,20265,20266,20281,20282,20295,20296,20309,20310,1659],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,20209,20211],{"className":20210},[886],[888,20212,20213],{"xmlns":890},[892,20214,20215,20219],{},[895,20216,20217],{},[898,20218,6951],{},[902,20220,6951],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,20223,20225],{"className":20224},[886],[888,20226,20227],{"xmlns":890},[892,20228,20229,20233],{},[895,20230,20231],{},[898,20232,16915],{},[902,20234,16915],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,20237,20239],{"className":20238},[886],[888,20240,20241],{"xmlns":890},[892,20242,20243,20249],{},[895,20244,20245,20247],{},[898,20246,14667],{},[898,20248,4445],{},[902,20250,16932],{"encoding":904}," stoupá z oblasti nízkých ",[883,20253,20255],{"className":20254},[886],[888,20256,20257],{"xmlns":890},[892,20258,20259,20263],{},[895,20260,20261],{},[898,20262,16915],{},[902,20264,16915],{"encoding":904},", přímka ",[883,20267,20269],{"className":20268},[886],[888,20270,20271],{"xmlns":890},[892,20272,20273,20279],{},[895,20274,20275,20277],{},[898,20276,17058],{},[898,20278,6493],{},[902,20280,16925],{"encoding":904}," klesá a protíná osu ",[883,20283,20285],{"className":20284},[886],[888,20286,20287],{"xmlns":890},[892,20288,20289,20293],{},[895,20290,20291],{},[898,20292,16915],{},[902,20294,16915],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,20297,20299],{"className":20298},[886],[888,20300,20301],{"xmlns":890},[892,20302,20303,20307],{},[895,20304,20305],{},[898,20306,2041],{},[902,20308,2041],{"encoding":904}," leží v bodě ",[883,20311,20313],{"className":20312},[886],[888,20314,20315],{"xmlns":890},[892,20316,20317,20339],{},[895,20318,20319,20321,20323,20325,20327,20329,20331,20333,20335,20337],{},[1712,20320,7910],{"stretchy":1903},[898,20322,16915],{},[1712,20324,1714],{},[1716,20326,3068],{},[1712,20328,3138],{"separator":2565},[1762,20330,7722],{},[898,20332,6951],{},[1712,20334,1714],{},[1716,20336,19989],{},[1712,20338,7925],{"stretchy":1903},[902,20340,20341],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,20343,20345],{"id":20344},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,20347,20348,20351,20352,20365,20366,4831,20379,20382,20383,20401,20402,20419,20420,20437,20438,20451,20452,20465],{},[38,20349,20350],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,20353,20355],{"className":20354},[886],[888,20356,20357],{"xmlns":890},[892,20358,20359,20363],{},[895,20360,20361],{},[898,20362,16986],{},[902,20364,16986],{"encoding":904}," nebo snížení daní ",[883,20367,20369],{"className":20368},[886],[888,20370,20371],{"xmlns":890},[892,20372,20373,20377],{},[895,20374,20375],{},[898,20376,1772],{},[902,20378,1772],{"encoding":904},[38,20380,20381],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,20384,20386],{"className":20385},[886],[888,20387,20388],{"xmlns":890},[892,20389,20390,20398],{},[895,20391,20392],{},[2037,20393,20394,20396],{},[898,20395,2041],{},[1712,20397,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,20399,20400],{"encoding":904},"E'"," má vyšší ",[883,20403,20405],{"className":20404},[886],[888,20406,20407],{"xmlns":890},[892,20408,20409,20417],{},[895,20410,20411],{},[2037,20412,20413,20415],{},[898,20414,6951],{},[898,20416,2041],{},[902,20418,18777],{"encoding":904}," i vyšší ",[883,20421,20423],{"className":20422},[886],[888,20424,20425],{"xmlns":890},[892,20426,20427,20435],{},[895,20428,20429],{},[2037,20430,20431,20433],{},[898,20432,16915],{},[898,20434,2041],{},[902,20436,18798],{"encoding":904}," (vyšší ",[883,20439,20441],{"className":20440},[886],[888,20442,20443],{"xmlns":890},[892,20444,20445,20449],{},[895,20446,20447],{},[898,20448,6951],{},[902,20450,6951],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,20453,20455],{"className":20454},[886],[888,20456,20457],{"xmlns":890},[892,20458,20459,20463],{},[895,20460,20461],{},[898,20462,16915],{},[902,20464,16915],{"encoding":904}," nahoru).",[724,20467,20468],{},[3817,20469],{"alt":20470,"className":20471,"src":20472},"imek-posun-is-lm-politiky",[210,3821],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,20474,20475,20478,20479,20496,20497,20500,20501,20518,20519,20536,20537,20550,20551,20570,20571,1691],{},[38,20476,20477],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,20480,20482],{"className":20481},[886],[888,20483,20484],{"xmlns":890},[892,20485,20486,20494],{},[895,20487,20488],{},[2037,20489,20490,20492],{},[898,20491,4445],{},[1712,20493,2145],{},[902,20495,17024],{"encoding":904}," národní bankou — ",[38,20498,20499],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,20502,20504],{"className":20503},[886],[888,20505,20506],{"xmlns":890},[892,20507,20508,20516],{},[895,20509,20510],{},[2037,20511,20512,20514],{},[898,20513,16915],{},[898,20515,2041],{},[902,20517,18798],{"encoding":904}," a vyšší ",[883,20520,20522],{"className":20521},[886],[888,20523,20524],{"xmlns":890},[892,20525,20526,20534],{},[895,20527,20528],{},[2037,20529,20530,20532],{},[898,20531,6951],{},[898,20533,2041],{},[902,20535,18777],{"encoding":904}," (nižší ",[883,20538,20540],{"className":20539},[886],[888,20541,20542],{"xmlns":890},[892,20543,20544,20548],{},[895,20545,20546],{},[898,20547,16915],{},[902,20549,16915],{"encoding":904}," povzbuzuje investice ",[883,20552,20554],{"className":20553},[886],[888,20555,20556],{"xmlns":890},[892,20557,20558,20568],{},[895,20559,20560,20562,20564,20566],{},[898,20561,17058],{},[1712,20563,1904],{"stretchy":1903},[898,20565,16915],{},[1712,20567,1910],{"stretchy":1903},[902,20569,19110],{"encoding":904},", ty zvedají ",[883,20572,20574],{"className":20573},[886],[888,20575,20576],{"xmlns":890},[892,20577,20578,20582],{},[895,20579,20580],{},[898,20581,6951],{},[902,20583,6951],{"encoding":904},[724,20585,20586,20587,20590],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,20588,20589],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,20592,20594],{"id":20593},"klíčové-pojmy","Klíčové pojmy",[120,20596,20597,20670,20716,20798,20848,20915,20972,21013,21046],{},[123,20598,20599,4831,20632,1343,20649,20666,20667,20669],{},[38,20600,20601,20602],{},"Funkce investic ",[883,20603,20605],{"className":20604},[886],[888,20606,20607],{"xmlns":890},[892,20608,20609,20629],{},[895,20610,20611,20613,20615,20617,20619,20621,20623,20625,20627],{},[898,20612,17058],{},[1712,20614,1904],{"stretchy":1903},[898,20616,16915],{},[1712,20618,1910],{"stretchy":1903},[1712,20620,1714],{},[898,20622,7585],{},[898,20624,16915],{},[1712,20626,3145],{},[898,20628,2468],{},[902,20630,20631],{"encoding":904},"I(r) = cr + d",[883,20633,20635],{"className":20634},[886],[888,20636,20637],{"xmlns":890},[892,20638,20639,20647],{},[895,20640,20641,20643,20645],{},[898,20642,7585],{},[1712,20644,2252],{},[1716,20646,2085],{},[902,20648,17389],{"encoding":904},[883,20650,20652],{"className":20651},[886],[888,20653,20654],{"xmlns":890},[892,20655,20656,20664],{},[895,20657,20658,20660,20662],{},[898,20659,2468],{},[1712,20661,2302],{},[1716,20663,2085],{},[902,20665,17368],{"encoding":904},"; ",[38,20668,17393],{}," funkce úrokové míry.",[123,20671,20672,20675,20676,20697,20698,20715],{},[38,20673,20674],{},"Trh zboží"," — rovnováha ",[883,20677,20679],{"className":20678},[886],[888,20680,20681],{"xmlns":890},[892,20682,20683,20695],{},[895,20684,20685,20687,20689,20691,20693],{},[898,20686,6951],{},[1712,20688,1714],{},[898,20690,8195],{},[1712,20692,3145],{},[898,20694,17058],{},[902,20696,19618],{"encoding":904},", ekvivalentně ",[883,20699,20701],{"className":20700},[886],[888,20702,20703],{"xmlns":890},[892,20704,20705,20713],{},[895,20706,20707,20709,20711],{},[898,20708,17058],{},[1712,20710,1714],{},[898,20712,6493],{},[902,20714,17586],{"encoding":904}," (investice = úspory).",[123,20717,20718,14897,20721,20723,20724,20774,20775,17789,20777,1659],{},[38,20719,20720],{},"Křivka IS",[614,20722,16928],{},") — ",[883,20725,20727],{"className":20726},[886],[888,20728,20729],{"xmlns":890},[892,20730,20731,20771],{},[895,20732,20733,20735,20737,20749,20751,20753],{},[898,20734,6951],{},[1712,20736,1714],{},[2567,20738,20739,20741],{},[898,20740,7585],{},[895,20742,20743,20745,20747],{},[1716,20744,2222],{},[1712,20746,2219],{},[898,20748,207],{},[898,20750,16915],{},[1712,20752,3145],{},[2567,20754,20755,20763],{},[895,20756,20757,20759,20761],{},[898,20758,7544],{},[1712,20760,3145],{},[898,20762,2468],{},[895,20764,20765,20767,20769],{},[1716,20766,2222],{},[1712,20768,2219],{},[898,20770,207],{},[902,20772,20773],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,20776,17393],{},[883,20778,20780],{"className":20779},[886],[888,20781,20782],{"xmlns":890},[892,20783,20784,20796],{},[895,20785,20786,20788,20790,20792,20794],{},[1712,20787,1904],{"stretchy":1903},[898,20789,16915],{},[1712,20791,3138],{"separator":2565},[898,20793,6951],{},[1712,20795,1910],{"stretchy":1903},[902,20797,17811],{"encoding":904},[123,20799,20800,20675,20803,20829,20830,1659],{},[38,20801,20802],{},"Trh peněz",[883,20804,20806],{"className":20805},[886],[888,20807,20808],{"xmlns":890},[892,20809,20810,20826],{},[895,20811,20812,20818,20820],{},[2037,20813,20814,20816],{},[898,20815,4445],{},[898,20817,1969],{},[1712,20819,1714],{},[2037,20821,20822,20824],{},[898,20823,4445],{},[898,20825,6493],{},[902,20827,20828],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,20831,20833],{"className":20832},[886],[888,20834,20835],{"xmlns":890},[892,20836,20837,20845],{},[895,20838,20839],{},[2037,20840,20841,20843],{},[898,20842,4445],{},[1712,20844,2145],{},[902,20846,20847],{"encoding":904},"M^* ",[123,20849,20850,4831,20853,1659],{},[38,20851,20852],{},"Transakční, opatrnostní, spekulační poptávka",[883,20854,20856],{"className":20855},[886],[888,20857,20858],{"xmlns":890},[892,20859,20860,20912],{},[895,20861,20862,20868,20870,20876,20878,20884,20886,20892,20894,20896,20902,20904,20906],{},[2037,20863,20864,20866],{},[898,20865,4445],{},[898,20867,1969],{},[1712,20869,1714],{},[6927,20871,20872,20874],{},[898,20873,14667],{},[1716,20875,2222],{},[1712,20877,3145],{},[6927,20879,20880,20882],{},[898,20881,14667],{},[1716,20883,2787],{},[1712,20885,1714],{},[6927,20887,20888,20890],{},[898,20889,18111],{},[1716,20891,2222],{},[898,20893,6951],{},[1712,20895,3145],{},[6927,20897,20898,20900],{},[898,20899,18111],{},[1716,20901,2787],{},[898,20903,16915],{},[1712,20905,3145],{},[6927,20907,20908,20910],{},[898,20909,18111],{},[1716,20911,6198],{},[902,20913,20914],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,20916,20917,14897,20920,20723,20922,20968,20969,20971],{},[38,20918,20919],{},"Křivka LM",[614,20921,16935],{},[883,20923,20925],{"className":20924},[886],[888,20926,20927],{"xmlns":890},[892,20928,20929,20965],{},[895,20930,20931,20937,20939,20945,20947,20949,20955,20957,20959],{},[2037,20932,20933,20935],{},[898,20934,4445],{},[1712,20936,2145],{},[1712,20938,1714],{},[6927,20940,20941,20943],{},[898,20942,18111],{},[1716,20944,2222],{},[898,20946,6951],{},[1712,20948,3145],{},[6927,20950,20951,20953],{},[898,20952,18111],{},[1716,20954,2787],{},[898,20956,16915],{},[1712,20958,3145],{},[6927,20960,20961,20963],{},[898,20962,18111],{},[1716,20964,6198],{},[902,20966,20967],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,20970,18531],{}," přímka.",[123,20973,20974,20977,20978,21012],{},[38,20975,20976],{},"Simultánní rovnováha"," — průsečík ",[883,20979,20981],{"className":20980},[886],[888,20982,20983],{"xmlns":890},[892,20984,20985,21009],{},[895,20986,20987,20989,20991,20993,20999,21001,21007],{},[898,20988,2041],{},[1712,20990,1714],{},[1712,20992,1904],{"stretchy":1903},[2037,20994,20995,20997],{},[898,20996,16915],{},[898,20998,2041],{},[1712,21000,3138],{"separator":2565},[2037,21002,21003,21005],{},[898,21004,6951],{},[898,21006,2041],{},[1712,21008,1910],{"stretchy":1903},[902,21010,21011],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,21014,21015,21018,21019,1343,21032,21045],{},[38,21016,21017],{},"Fiskální politika"," — nástroje ",[883,21020,21022],{"className":21021},[886],[888,21023,21024],{"xmlns":890},[892,21025,21026,21030],{},[895,21027,21028],{},[898,21029,16986],{},[902,21031,16986],{"encoding":904},[883,21033,21035],{"className":21034},[886],[888,21036,21037],{"xmlns":890},[892,21038,21039,21043],{},[895,21040,21041],{},[898,21042,1772],{},[902,21044,1772],{"encoding":904}," posouvající křivku IS.",[123,21047,21048,21051,21052,21069],{},[38,21049,21050],{},"Monetární politika"," — nástroj ",[883,21053,21055],{"className":21054},[886],[888,21056,21057],{"xmlns":890},[892,21058,21059,21067],{},[895,21060,21061],{},[2037,21062,21063,21065],{},[898,21064,4445],{},[1712,21066,2145],{},[902,21068,17024],{"encoding":904}," posouvající křivku LM.",[115,21071,9193],{"id":9192},[120,21073,21074,21083,21092,21102],{},[123,21075,21076,3245,21079],{},[38,21077,21078],{},"Kurz:",[207,21080,21082],{"className":21081,"dataFsResolvedFilePath":7413,"href":7414},[210],"Matematická ekonomie",[123,21084,21085,3245,21088],{},[38,21086,21087],{},"Přednáška:",[207,21089,21091],{"className":21090,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,21093,21094,3245,21097,21101],{},[38,21095,21096],{},"Nadřazené téma:",[207,21098,21100],{"className":21099,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,21103,21104,21107],{},[38,21105,21106],{},"Související:",[120,21108,21109,21116,21122],{},[123,21110,21111,21115],{},[207,21112,21114],{"className":21113,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,21117,21118,21121],{},[207,21119,1145],{"className":21120,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,21123,21124,21128],{},[207,21125,21127],{"className":21126,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":21130},[21131,21132,21133,21134,21135,21136,21137,21138,21139,21140],{"id":16879,"depth":642,"text":16880},{"id":17034,"depth":642,"text":17035},{"id":17249,"depth":642,"text":17250},{"id":17542,"depth":642,"text":17543},{"id":17955,"depth":642,"text":17956},{"id":18748,"depth":642,"text":18749},{"id":19438,"depth":642,"text":19439},{"id":20344,"depth":642,"text":20345},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fis-lm",{"title":16871,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,21147,1143,21148,21149,21150,21151,21100],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":21154,"title":21155,"body":21156,"course":659,"courses":22749,"created":1129,"description":22750,"extension":661,"meta":22751,"navigation":664,"path":22752,"seo":22753,"sources":22754,"stem":22755,"tags":22756,"type":7391,"updated":677,"__hash__":22759},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":21157,"toc":22737},[21158,21161,21257,21264,21284,21288,21293,21356,21375,21377,21380,21516,21518,21728,21762,21899,21903,21967,21983,22011,22015,22113,22117,22121,22174,22280,22494,22498,22541,22647,22699,22701],[12,21159,21155],{"id":21160},"lagrangeova-metoda-vázané-extrémy",[724,21162,21163,21164,1682,21187,21219,21220,21223,21224,21251,21252,21256],{},"Hledáme extrém funkce ",[883,21165,21167],{"className":21166},[886],[888,21168,21169],{"xmlns":890},[892,21170,21171,21185],{},[895,21172,21173,21175,21177,21179,21181,21183],{},[898,21174,7451],{},[1712,21176,1904],{"stretchy":1903},[898,21178,7456],{},[1712,21180,3138],{"separator":2565},[898,21182,7446],{},[1712,21184,1910],{"stretchy":1903},[902,21186,14715],{"encoding":904},[883,21188,21190],{"className":21189},[886],[888,21191,21192],{"xmlns":890},[892,21193,21194,21216],{},[895,21195,21196,21198,21200,21206,21208,21214],{},[898,21197,900],{},[1712,21199,1904],{"stretchy":1903},[6927,21201,21202,21204],{},[898,21203,1734],{},[1716,21205,2222],{},[1712,21207,3138],{"separator":2565},[6927,21209,21210,21212],{},[898,21211,1734],{},[1716,21213,2787],{},[1712,21215,1910],{"stretchy":1903},[902,21217,21218],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,21221,21222],{},"podmíněný"," rovnicí ",[883,21225,21227],{"className":21226},[886],[888,21228,21229],{"xmlns":890},[892,21230,21231,21249],{},[895,21232,21233,21235,21237,21239,21241,21243,21245,21247],{},[898,21234,15913],{},[1712,21236,1904],{"stretchy":1903},[898,21238,7456],{},[1712,21240,3138],{"separator":2565},[898,21242,7446],{},[1712,21244,1910],{"stretchy":1903},[1712,21246,1714],{},[1716,21248,2085],{},[902,21250,15930],{"encoding":904},". V ",[207,21253,21255],{"className":21254,"dataFsResolvedFilePath":7413,"href":7414},[210],"matematické ekonomii"," se používá pro:",[724,21258,21259],{},[3817,21260],{"alt":21261,"className":21262,"src":21263},"imek-lagrange-tecnost",[210,3821],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,21265,21266,21275,21281],{},[123,21267,21268,21271,21272,1910],{},[38,21269,21270],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,21273,14645],{"className":21274,"dataFsResolvedFilePath":878,"href":879},[210],[123,21276,21277,21280],{},[38,21278,21279],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,21282,21283],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,21285,21287],{"id":21286},"princip","Princip",[724,21289,15579,21290,2854],{},[38,21291,21292],{},"Lagrangeovu funkci",[724,21294,21295],{},[883,21296,21298],{"className":21297},[886],[888,21299,21300],{"xmlns":890},[892,21301,21302,21353],{},[895,21303,21304,21306,21308,21310,21312,21314,21316,21319,21321,21323,21325,21327,21329,21331,21333,21335,21337,21339,21341,21343,21345,21347,21349,21351],{},[898,21305,14667],{},[1712,21307,1904],{"stretchy":1903},[898,21309,7456],{},[1712,21311,3138],{"separator":2565},[898,21313,7446],{},[1712,21315,3138],{"separator":2565},[898,21317,21318],{},"λ",[1712,21320,1910],{"stretchy":1903},[1712,21322,1714],{},[898,21324,7451],{},[1712,21326,1904],{"stretchy":1903},[898,21328,7456],{},[1712,21330,3138],{"separator":2565},[898,21332,7446],{},[1712,21334,1910],{"stretchy":1903},[1712,21336,3145],{},[898,21338,21318],{},[1762,21340,2583],{},[898,21342,15913],{},[1712,21344,1904],{"stretchy":1903},[898,21346,7456],{},[1712,21348,3138],{"separator":2565},[898,21350,7446],{},[1712,21352,1910],{"stretchy":1903},[902,21354,21355],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,21357,2101,21358,5920,21372,1659],{},[883,21359,21361],{"className":21360},[886],[888,21362,21363],{"xmlns":890},[892,21364,21365,21369],{},[895,21366,21367],{},[898,21368,21318],{},[902,21370,21371],{"encoding":904},"\\lambda",[38,21373,21374],{},"Lagrangeův multiplikátor",[115,21376,8657],{"id":8656},[724,21378,21379],{},"Řešíme soustavu:",[724,21381,21382,21430,21478],{},[883,21383,21385],{"className":21384},[886],[888,21386,21387],{"xmlns":890},[892,21388,21389,21427],{},[895,21390,21391,21399,21401,21409,21411,21413,21415,21423,21425],{},[6989,21392,21393,21395,21397],{},[898,21394,14667],{},[898,21396,7456],{},[1712,21398,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21400,1714],{},[6989,21402,21403,21405,21407],{},[898,21404,7451],{},[898,21406,7456],{},[1712,21408,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21410,3145],{},[898,21412,21318],{},[1762,21414,2583],{},[6989,21416,21417,21419,21421],{},[898,21418,15913],{},[898,21420,7456],{},[1712,21422,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21424,1714],{},[1716,21426,2085],{},[902,21428,21429],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,21431,21433],{"className":21432},[886],[888,21434,21435],{"xmlns":890},[892,21436,21437,21475],{},[895,21438,21439,21447,21449,21457,21459,21461,21463,21471,21473],{},[6989,21440,21441,21443,21445],{},[898,21442,14667],{},[898,21444,7446],{},[1712,21446,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21448,1714],{},[6989,21450,21451,21453,21455],{},[898,21452,7451],{},[898,21454,7446],{},[1712,21456,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21458,3145],{},[898,21460,21318],{},[1762,21462,2583],{},[6989,21464,21465,21467,21469],{},[898,21466,15913],{},[898,21468,7446],{},[1712,21470,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21472,1714],{},[1716,21474,2085],{},[902,21476,21477],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,21479,21481],{"className":21480},[886],[888,21482,21483],{"xmlns":890},[892,21484,21485,21513],{},[895,21486,21487,21495,21497,21499,21501,21503,21505,21507,21509,21511],{},[6989,21488,21489,21491,21493],{},[898,21490,14667],{},[898,21492,21318],{},[1712,21494,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21496,1714],{},[898,21498,15913],{},[1712,21500,1904],{"stretchy":1903},[898,21502,7456],{},[1712,21504,3138],{"separator":2565},[898,21506,7446],{},[1712,21508,1910],{"stretchy":1903},[1712,21510,1714],{},[1716,21512,2085],{},[902,21514,21515],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,21517,8731],{"id":8730},[724,21519,21520],{},[883,21521,21523],{"className":21522},[886],[888,21524,21525],{"xmlns":890},[892,21526,21527,21725],{},[895,21528,21529,21531,21533,21535,21537,21539,21541,21543,21545,21547,21549,21565,21567,21569,21585,21587,21589,21597,21603,21605,21607,21623,21625,21627,21643,21645,21647,21655,21661,21663,21665,21667,21683,21685,21687,21703,21705,21707,21715,21717],{},[898,21530,1969],{},[1712,21532,1904],{"stretchy":1903},[898,21534,7456],{},[1712,21536,3138],{"separator":2565},[898,21538,7446],{},[1712,21540,3138],{"separator":2565},[898,21542,21318],{},[1712,21544,1910],{"stretchy":1903},[1712,21546,1714],{},[1712,21548,1904],{"stretchy":1903},[6989,21550,21551,21553,21559],{},[898,21552,7451],{},[895,21554,21555,21557],{},[898,21556,7456],{},[898,21558,7456],{},[895,21560,21561,21563],{},[1712,21562,2243],{"mathvariant":2003},[1712,21564,2243],{"mathvariant":2003},[1712,21566,3145],{},[898,21568,21318],{},[6989,21570,21571,21573,21579],{},[898,21572,15913],{},[895,21574,21575,21577],{},[898,21576,7456],{},[898,21578,7456],{},[895,21580,21581,21583],{},[1712,21582,2243],{"mathvariant":2003},[1712,21584,2243],{"mathvariant":2003},[1712,21586,1910],{"stretchy":1903},[1712,21588,1904],{"stretchy":1903},[6989,21590,21591,21593,21595],{},[898,21592,15913],{},[898,21594,7446],{},[1712,21596,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[2037,21598,21599,21601],{},[1712,21600,1910],{"stretchy":1903},[1716,21602,2787],{},[1712,21604,3145],{},[1712,21606,1904],{"stretchy":1903},[6989,21608,21609,21611,21617],{},[898,21610,7451],{},[895,21612,21613,21615],{},[898,21614,7446],{},[898,21616,7446],{},[895,21618,21619,21621],{},[1712,21620,2243],{"mathvariant":2003},[1712,21622,2243],{"mathvariant":2003},[1712,21624,3145],{},[898,21626,21318],{},[6989,21628,21629,21631,21637],{},[898,21630,15913],{},[895,21632,21633,21635],{},[898,21634,7446],{},[898,21636,7446],{},[895,21638,21639,21641],{},[1712,21640,2243],{"mathvariant":2003},[1712,21642,2243],{"mathvariant":2003},[1712,21644,1910],{"stretchy":1903},[1712,21646,1904],{"stretchy":1903},[6989,21648,21649,21651,21653],{},[898,21650,15913],{},[898,21652,7456],{},[1712,21654,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[2037,21656,21657,21659],{},[1712,21658,1910],{"stretchy":1903},[1716,21660,2787],{},[1712,21662,2219],{},[1716,21664,2787],{},[1712,21666,1904],{"stretchy":1903},[6989,21668,21669,21671,21677],{},[898,21670,7451],{},[895,21672,21673,21675],{},[898,21674,7456],{},[898,21676,7446],{},[895,21678,21679,21681],{},[1712,21680,2243],{"mathvariant":2003},[1712,21682,2243],{"mathvariant":2003},[1712,21684,3145],{},[898,21686,21318],{},[6989,21688,21689,21691,21697],{},[898,21690,15913],{},[895,21692,21693,21695],{},[898,21694,7456],{},[898,21696,7446],{},[895,21698,21699,21701],{},[1712,21700,2243],{"mathvariant":2003},[1712,21702,2243],{"mathvariant":2003},[1712,21704,1910],{"stretchy":1903},[1762,21706,2583],{},[6989,21708,21709,21711,21713],{},[898,21710,15913],{},[898,21712,7456],{},[1712,21714,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,21716,2583],{},[6989,21718,21719,21721,21723],{},[898,21720,15913],{},[898,21722,7446],{},[1712,21724,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,21726,21727],{"encoding":904},"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",[724,21729,21730,21731,21761],{},"Je-li ",[883,21732,21734],{"className":21733},[886],[888,21735,21736],{"xmlns":890},[892,21737,21738,21758],{},[895,21739,21740,21742,21744,21746,21748,21750,21756],{},[1712,21741,7910],{"stretchy":1903},[898,21743,207],{},[1712,21745,3138],{"separator":2565},[898,21747,7544],{},[1712,21749,3138],{"separator":2565},[6927,21751,21752,21754],{},[898,21753,21318],{},[1716,21755,2085],{},[1712,21757,7925],{"stretchy":1903},[902,21759,21760],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,21763,21764,21832],{},[123,21765,21766,8818,21802,21804,21805],{},[883,21767,21769],{"className":21768},[886],[888,21770,21771],{"xmlns":890},[892,21772,21773,21799],{},[895,21774,21775,21777,21779,21781,21783,21785,21787,21793,21795,21797],{},[898,21776,1969],{},[1712,21778,1904],{"stretchy":1903},[898,21780,207],{},[1712,21782,3138],{"separator":2565},[898,21784,7544],{},[1712,21786,3138],{"separator":2565},[6927,21788,21789,21791],{},[898,21790,21318],{},[1716,21792,2085],{},[1712,21794,1910],{"stretchy":1903},[1712,21796,2252],{},[1716,21798,2085],{},[902,21800,21801],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,21803,5766],{}," vázané podmínkou ",[883,21806,21808],{"className":21807},[886],[888,21809,21810],{"xmlns":890},[892,21811,21812,21830],{},[895,21813,21814,21816,21818,21820,21822,21824,21826,21828],{},[898,21815,15913],{},[1712,21817,1904],{"stretchy":1903},[898,21819,7456],{},[1712,21821,3138],{"separator":2565},[898,21823,7446],{},[1712,21825,1910],{"stretchy":1903},[1712,21827,1714],{},[1716,21829,2085],{},[902,21831,15930],{"encoding":904},[123,21833,21834,8818,21870,21804,21872],{},[883,21835,21837],{"className":21836},[886],[888,21838,21839],{"xmlns":890},[892,21840,21841,21867],{},[895,21842,21843,21845,21847,21849,21851,21853,21855,21861,21863,21865],{},[898,21844,1969],{},[1712,21846,1904],{"stretchy":1903},[898,21848,207],{},[1712,21850,3138],{"separator":2565},[898,21852,7544],{},[1712,21854,3138],{"separator":2565},[6927,21856,21857,21859],{},[898,21858,21318],{},[1716,21860,2085],{},[1712,21862,1910],{"stretchy":1903},[1712,21864,2302],{},[1716,21866,2085],{},[902,21868,21869],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,21871,9176],{},[883,21873,21875],{"className":21874},[886],[888,21876,21877],{"xmlns":890},[892,21878,21879,21897],{},[895,21880,21881,21883,21885,21887,21889,21891,21893,21895],{},[898,21882,15913],{},[1712,21884,1904],{"stretchy":1903},[898,21886,7456],{},[1712,21888,3138],{"separator":2565},[898,21890,7446],{},[1712,21892,1910],{"stretchy":1903},[1712,21894,1714],{},[1716,21896,2085],{},[902,21898,15930],{"encoding":904},[115,21900,21902],{"id":21901},"význam-multiplikátoru","Význam multiplikátoru",[724,21904,21905],{},[883,21906,21908],{"className":21907},[886],[888,21909,21910],{"xmlns":890},[892,21911,21912,21964],{},[895,21913,21914,21916,21918,21940,21942],{},[898,21915,21318],{},[1712,21917,1714],{},[2567,21919,21920,21928],{},[6989,21921,21922,21924,21926],{},[898,21923,7451],{},[898,21925,7456],{},[1712,21927,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[895,21929,21930,21932],{},[1712,21931,2219],{},[6989,21933,21934,21936,21938],{},[898,21935,15913],{},[898,21937,7456],{},[1712,21939,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,21941,1714],{},[2567,21943,21944,21952],{},[6989,21945,21946,21948,21950],{},[898,21947,7451],{},[898,21949,7446],{},[1712,21951,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[895,21953,21954,21956],{},[1712,21955,2219],{},[6989,21957,21958,21960,21962],{},[898,21959,15913],{},[898,21961,7446],{},[1712,21963,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,21965,21966],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,21968,21969,21982],{},[883,21970,21972],{"className":21971},[886],[888,21973,21974],{"xmlns":890},[892,21975,21976,21980],{},[895,21977,21978],{},[898,21979,21318],{},[902,21981,21371],{"encoding":904}," udává:",[120,21984,21985,21991],{},[123,21986,21987,21988],{},"konstantní ",[38,21989,21990],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,21992,21993,21996,21997,22010],{},[38,21994,21995],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,21998,22000],{"className":21999},[886],[888,22001,22002],{"xmlns":890},[892,22003,22004,22008],{},[895,22005,22006],{},[898,22007,7451],{},[902,22009,7451],{"encoding":904},", uvolní-li se omezení o jednotku",[115,22012,22014],{"id":22013},"alternativní-postup","Alternativní postup",[724,22016,22017,22018,22045,22046,22070,22071,22095,22096,22109,22110,1659],{},"Lze-li z ",[883,22019,22021],{"className":22020},[886],[888,22022,22023],{"xmlns":890},[892,22024,22025,22043],{},[895,22026,22027,22029,22031,22033,22035,22037,22039,22041],{},[898,22028,15913],{},[1712,22030,1904],{"stretchy":1903},[898,22032,7456],{},[1712,22034,3138],{"separator":2565},[898,22036,7446],{},[1712,22038,1910],{"stretchy":1903},[1712,22040,1714],{},[1716,22042,2085],{},[902,22044,15930],{"encoding":904}," vyjádřit ",[883,22047,22049],{"className":22048},[886],[888,22050,22051],{"xmlns":890},[892,22052,22053,22067],{},[895,22054,22055,22057,22059,22061,22063,22065],{},[898,22056,7446],{},[1712,22058,1714],{},[898,22060,7446],{},[1712,22062,1904],{"stretchy":1903},[898,22064,7456],{},[1712,22066,1910],{"stretchy":1903},[902,22068,22069],{"encoding":904},"y = y(x)"," (nebo ",[883,22072,22074],{"className":22073},[886],[888,22075,22076],{"xmlns":890},[892,22077,22078,22092],{},[895,22079,22080,22082,22084,22086,22088,22090],{},[898,22081,7456],{},[1712,22083,1714],{},[898,22085,7456],{},[1712,22087,1904],{"stretchy":1903},[898,22089,7446],{},[1712,22091,1910],{"stretchy":1903},[902,22093,22094],{"encoding":904},"x = x(y)","), dosadíme do ",[883,22097,22099],{"className":22098},[886],[888,22100,22101],{"xmlns":890},[892,22102,22103,22107],{},[895,22104,22105],{},[898,22106,7451],{},[902,22108,7451],{"encoding":904}," a převedeme na ",[38,22111,22112],{},"extrém funkce jedné proměnné",[115,22114,22116],{"id":22115},"použití-v-imek","Použití v ImeK",[198,22118,22120],{"id":22119},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,22122,22123,22124,1659],{},"Rozpočtové omezení: ",[883,22125,22127],{"className":22126},[886],[888,22128,22129],{"xmlns":890},[892,22130,22131,22171],{},[895,22132,22133,22139,22141,22149,22155,22157,22165],{},[2037,22134,22135,22137],{},[898,22136,6951],{},[1712,22138,2145],{},[1712,22140,1714],{},[6989,22142,22143,22145,22147],{},[898,22144,1710],{},[1716,22146,2222],{},[1712,22148,2145],{},[6927,22150,22151,22153],{},[898,22152,1734],{},[1716,22154,2222],{},[1712,22156,3145],{},[6989,22158,22159,22161,22163],{},[898,22160,1710],{},[1716,22162,2787],{},[1712,22164,2145],{},[6927,22166,22167,22169],{},[898,22168,1734],{},[1716,22170,2787],{},[902,22172,22173],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,22175,22176],{},[883,22177,22179],{"className":22178},[886],[888,22180,22181],{"xmlns":890},[892,22182,22183,22277],{},[895,22184,22185,22187,22189,22195,22197,22203,22205,22207,22209,22211,22213,22215,22221,22223,22229,22231,22233,22235,22237,22243,22245,22253,22259,22261,22269,22275],{},[898,22186,14667],{},[1712,22188,1904],{"stretchy":1903},[6927,22190,22191,22193],{},[898,22192,1734],{},[1716,22194,2222],{},[1712,22196,3138],{"separator":2565},[6927,22198,22199,22201],{},[898,22200,1734],{},[1716,22202,2787],{},[1712,22204,3138],{"separator":2565},[898,22206,21318],{},[1712,22208,1910],{"stretchy":1903},[1712,22210,1714],{},[898,22212,900],{},[1712,22214,1904],{"stretchy":1903},[6927,22216,22217,22219],{},[898,22218,1734],{},[1716,22220,2222],{},[1712,22222,3138],{"separator":2565},[6927,22224,22225,22227],{},[898,22226,1734],{},[1716,22228,2787],{},[1712,22230,1910],{"stretchy":1903},[1712,22232,3145],{},[898,22234,21318],{},[1712,22236,1904],{"stretchy":1903},[2037,22238,22239,22241],{},[898,22240,6951],{},[1712,22242,2145],{},[1712,22244,2219],{},[6989,22246,22247,22249,22251],{},[898,22248,1710],{},[1716,22250,2222],{},[1712,22252,2145],{},[6927,22254,22255,22257],{},[898,22256,1734],{},[1716,22258,2222],{},[1712,22260,2219],{},[6989,22262,22263,22265,22267],{},[898,22264,1710],{},[1716,22266,2787],{},[1712,22268,2145],{},[6927,22270,22271,22273],{},[898,22272,1734],{},[1716,22274,2787],{},[1712,22276,1910],{"stretchy":1903},[902,22278,22279],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,22281,22282,22283,1343,22315,1343,22347,22396,22397,22451,22452,1659],{},"Soustava: ",[883,22284,22286],{"className":22285},[886],[888,22287,22288],{"xmlns":890},[892,22289,22290,22312],{},[895,22291,22292,22300,22302,22304],{},[6989,22293,22294,22296,22298],{},[898,22295,900],{},[1716,22297,2222],{},[1712,22299,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,22301,1714],{},[898,22303,21318],{},[6989,22305,22306,22308,22310],{},[898,22307,1710],{},[1716,22309,2222],{},[1712,22311,2145],{},[902,22313,22314],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,22316,22318],{"className":22317},[886],[888,22319,22320],{"xmlns":890},[892,22321,22322,22344],{},[895,22323,22324,22332,22334,22336],{},[6989,22325,22326,22328,22330],{},[898,22327,900],{},[1716,22329,2787],{},[1712,22331,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,22333,1714],{},[898,22335,21318],{},[6989,22337,22338,22340,22342],{},[898,22339,1710],{},[1716,22341,2787],{},[1712,22343,2145],{},[902,22345,22346],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,22348,22350],{"className":22349},[886],[888,22351,22352],{"xmlns":890},[892,22353,22354,22394],{},[895,22355,22356,22362,22364,22372,22378,22380,22388],{},[2037,22357,22358,22360],{},[898,22359,6951],{},[1712,22361,2145],{},[1712,22363,1714],{},[6989,22365,22366,22368,22370],{},[898,22367,1710],{},[1716,22369,2222],{},[1712,22371,2145],{},[6927,22373,22374,22376],{},[898,22375,1734],{},[1716,22377,2222],{},[1712,22379,3145],{},[6989,22381,22382,22384,22386],{},[898,22383,1710],{},[1716,22385,2787],{},[1712,22387,2145],{},[6927,22389,22390,22392],{},[898,22391,1734],{},[1716,22393,2787],{},[902,22395,22173],{"encoding":904},". Z prvních dvou: ",[883,22398,22400],{"className":22399},[886],[888,22401,22402],{"xmlns":890},[892,22403,22404,22448],{},[895,22405,22406,22426,22428],{},[2563,22407,22408],{"scriptlevel":2085,"displaystyle":1903},[2567,22409,22410,22418],{},[6989,22411,22412,22414,22416],{},[898,22413,900],{},[1716,22415,2222],{},[1712,22417,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,22419,22420,22422,22424],{},[898,22421,900],{},[1716,22423,2787],{},[1712,22425,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,22427,1714],{},[2563,22429,22430],{"scriptlevel":2085,"displaystyle":1903},[2567,22431,22432,22440],{},[6989,22433,22434,22436,22438],{},[898,22435,1710],{},[1716,22437,2222],{},[1712,22439,2145],{},[6989,22441,22442,22444,22446],{},[898,22443,1710],{},[1716,22445,2787],{},[1712,22447,2145],{},[902,22449,22450],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,22453,22455],{"className":22454},[886],[888,22456,22457],{"xmlns":890},[892,22458,22459,22491],{},[895,22460,22461,22463,22465,22467,22469,22471],{},[898,22462,4445],{},[898,22464,1775],{},[898,22466,8195],{},[898,22468,6493],{},[1712,22470,1714],{},[2563,22472,22473],{"scriptlevel":2085,"displaystyle":1903},[2567,22474,22475,22483],{},[6989,22476,22477,22479,22481],{},[898,22478,1710],{},[1716,22480,2222],{},[1712,22482,2145],{},[6989,22484,22485,22487,22489],{},[898,22486,1710],{},[1716,22488,2787],{},[1712,22490,2145],{},[902,22492,22493],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,22495,22497],{"id":22496},"minimalizace-výdajů","Minimalizace výdajů",[724,22499,22500,22501,1659],{},"Podmínka dané užitečnosti ",[883,22502,22504],{"className":22503},[886],[888,22505,22506],{"xmlns":890},[892,22507,22508,22538],{},[895,22509,22510,22516,22518,22520,22522,22528,22530,22536],{},[2037,22511,22512,22514],{},[898,22513,900],{},[1712,22515,2145],{},[1712,22517,1714],{},[898,22519,900],{},[1712,22521,1904],{"stretchy":1903},[6927,22523,22524,22526],{},[898,22525,1734],{},[1716,22527,2222],{},[1712,22529,3138],{"separator":2565},[6927,22531,22532,22534],{},[898,22533,1734],{},[1716,22535,2787],{},[1712,22537,1910],{"stretchy":1903},[902,22539,22540],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,22542,22543],{},[883,22544,22546],{"className":22545},[886],[888,22547,22548],{"xmlns":890},[892,22549,22550,22644],{},[895,22551,22552,22554,22556,22562,22564,22570,22572,22574,22576,22578,22586,22592,22594,22602,22608,22610,22612,22614,22620,22622,22624,22626,22632,22634,22640,22642],{},[898,22553,14667],{},[1712,22555,1904],{"stretchy":1903},[6927,22557,22558,22560],{},[898,22559,1734],{},[1716,22561,2222],{},[1712,22563,3138],{"separator":2565},[6927,22565,22566,22568],{},[898,22567,1734],{},[1716,22569,2787],{},[1712,22571,3138],{"separator":2565},[898,22573,21318],{},[1712,22575,1910],{"stretchy":1903},[1712,22577,1714],{},[6989,22579,22580,22582,22584],{},[898,22581,1710],{},[1716,22583,2222],{},[1712,22585,2145],{},[6927,22587,22588,22590],{},[898,22589,1734],{},[1716,22591,2222],{},[1712,22593,3145],{},[6989,22595,22596,22598,22600],{},[898,22597,1710],{},[1716,22599,2787],{},[1712,22601,2145],{},[6927,22603,22604,22606],{},[898,22605,1734],{},[1716,22607,2787],{},[1712,22609,3145],{},[898,22611,21318],{},[1712,22613,1904],{"stretchy":1903},[2037,22615,22616,22618],{},[898,22617,900],{},[1712,22619,2145],{},[1712,22621,2219],{},[898,22623,900],{},[1712,22625,1904],{"stretchy":1903},[6927,22627,22628,22630],{},[898,22629,1734],{},[1716,22631,2222],{},[1712,22633,3138],{"separator":2565},[6927,22635,22636,22638],{},[898,22637,1734],{},[1716,22639,2787],{},[1712,22641,1910],{"stretchy":1903},[1712,22643,1910],{"stretchy":1903},[902,22645,22646],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,22648,22649,22650,1659],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,22651,22653],{"className":22652},[886],[888,22654,22655],{"xmlns":890},[892,22656,22657,22696],{},[895,22658,22659,22666,22668,22674,22676,22682,22684,22690,22692,22694],{},[6927,22660,22661,22663],{},[898,22662,1734],{},[898,22664,22665],{},"i",[1712,22667,1714],{},[6927,22669,22670,22672],{},[898,22671,1969],{},[898,22673,22665],{},[1712,22675,1904],{"stretchy":1903},[6927,22677,22678,22680],{},[898,22679,1710],{},[1716,22681,2222],{},[1712,22683,3138],{"separator":2565},[6927,22685,22686,22688],{},[898,22687,1710],{},[1716,22689,2787],{},[1712,22691,3138],{"separator":2565},[898,22693,900],{},[1712,22695,1910],{"stretchy":1903},[902,22697,22698],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,22700,9193],{"id":9192},[120,22702,22703,22710,22717,22726],{},[123,22704,22705,3245,22707],{},[38,22706,9200],{},[207,22708,784],{"className":22709,"dataFsResolvedFilePath":782,"href":783},[210],[123,22711,22712,3245,22714],{},[38,22713,9208],{},[207,22715,16814],{"className":22716,"dataFsResolvedFilePath":800,"href":801},[210],[123,22718,22719,3245,22722,22725],{},[38,22720,22721],{},"Aplikace v kurzu:",[207,22723,880],{"className":22724,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,22727,22728,3245,22730,1343,22733,22736],{},[38,22729,9216],{},[207,22731,936],{"className":22732,"dataFsResolvedFilePath":934,"href":935},[210],[207,22734,1400],{"className":22735,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":22738},[22739,22740,22741,22742,22743,22744,22748],{"id":21286,"depth":642,"text":21287},{"id":8656,"depth":642,"text":8657},{"id":8730,"depth":642,"text":8731},{"id":21901,"depth":642,"text":21902},{"id":22013,"depth":642,"text":22014},{"id":22115,"depth":642,"text":22116,"children":22745},[22746,22747],{"id":22119,"depth":649,"text":22120},{"id":22496,"depth":649,"text":22497},{"id":9192,"depth":642,"text":9193},[1128,1601],"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":21155,"description":22750},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,22757,22758],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":22761,"title":936,"body":22762,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":32630,"navigation":664,"path":32631,"seo":32632,"sources":32633,"stem":32634,"tags":32635,"type":7391,"updated":677,"__hash__":32639},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":22763,"toc":32592},[22764,22767,22769,22892,23027,23031,23034,23147,23151,23179,23226,23229,23295,23340,23343,23369,23400,23404,23408,23452,23496,23558,23613,23616,23620,23623,23670,23767,23873,23879,23956,23985,24124,24128,24157,24207,24354,24444,24448,24474,24512,24539,24577,24639,24714,24792,24850,24916,24960,24964,25022,25071,25116,25329,25449,25455,25459,25482,25486,25493,25497,25528,25563,25567,25617,25705,25747,25768,25830,25890,25894,25965,26033,26105,26220,26268,26272,26275,26316,26355,26378,26492,26656,26664,26691,26721,26724,26801,26954,27038,27377,27381,27505,27641,27777,27830,27833,28083,28164,28168,28171,28229,28261,28264,28313,28316,28387,28583,28587,28738,28968,29006,29059,29105,29108,29164,29213,29417,29507,29511,29527,29534,29703,29707,29778,29859,29940,30019,30165,30253,30257,30440,30571,30616,30713,30717,31456,31458,32509,32511],[12,22765,936],{"id":22766},"národní-důchod",[115,22768,16880],{"id":16879},[724,22770,22771,22772,3245,22776,22779,22780,3245,22783,22796,22797,22800,22801,22804,22805,22808,22809,22811,22812,3245,22814,22831,22832,22849,22850,22853,22854,1691],{},"Kapitola 7 ",[207,22773,22775],{"className":22774,"dataFsResolvedFilePath":7413,"href":7414},[210],"Matematické ekonomie",[38,22777,22778],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,22781,22782],{},"národním důchodem",[883,22784,22786],{"className":22785},[886],[888,22787,22788],{"xmlns":890},[892,22789,22790,22794],{},[895,22791,22792],{},[898,22793,6951],{},[902,22795,6951],{"encoding":904},". Budují se postupně bohatší modely — ",[38,22798,22799],{},"C-I"," (jen spotřeba a investice) → ",[38,22802,22803],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,22806,22807],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,22810,16885],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,22813,18759],{},[883,22815,22817],{"className":22816},[886],[888,22818,22819],{"xmlns":890},[892,22820,22821,22829],{},[895,22822,22823],{},[2037,22824,22825,22827],{},[898,22826,6951],{},[898,22828,2041],{},[902,22830,18777],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,22833,22835],{"className":22834},[886],[888,22836,22837],{"xmlns":890},[892,22838,22839,22847],{},[895,22840,22841],{},[2037,22842,22843,22845],{},[898,22844,6951],{},[898,22846,2041],{},[902,22848,18777],{"encoding":904}," na exogenní veličiny popisují ",[38,22851,22852],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,22855,22857],{"className":22856},[886],[888,22858,22859],{"xmlns":890},[892,22860,22861,22889],{},[895,22862,22863,22865,22867,22869,22871,22873,22875,22877,22879,22881,22883,22885,22887],{},[1716,22864,2222],{},[898,22866,2473],{"mathvariant":2003},[1712,22868,1904],{"stretchy":1903},[1716,22870,2222],{},[1712,22872,2219],{},[898,22874,207],{},[1712,22876,1910],{"stretchy":1903},[1712,22878,1714],{},[1716,22880,2222],{},[898,22882,2473],{"mathvariant":2003},[898,22884,4445],{},[898,22886,1710],{},[898,22888,6493],{},[902,22890,22891],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1636,22893,22894],{},[724,22895,22896,22898,22899,22902,22903,22921,22922,22952,22953,23000,23001,23003,23004,23026],{},[883,22897,1941],{}," Intuice\n",[38,22900,22901],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,22904,22906],{"className":22905},[886],[888,22907,22908],{"xmlns":890},[892,22909,22910,22918],{},[895,22911,22912,22914,22916],{},[898,22913,4445],{},[898,22915,1710],{},[898,22917,8195],{},[902,22919,22920],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,22923,22925],{"className":22924},[886],[888,22926,22927],{"xmlns":890},[892,22928,22929,22949],{},[895,22930,22931,22933,22935,22937,22939,22941,22943,22945,22947],{},[898,22932,4445],{},[898,22934,1710],{},[898,22936,6493],{},[1712,22938,1714],{},[1716,22940,2222],{},[1712,22942,2219],{},[898,22944,4445],{},[898,22946,1710],{},[898,22948,8195],{},[902,22950,22951],{"encoding":904},"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 ",[883,22954,22956],{"className":22955},[886],[888,22957,22958],{"xmlns":890},[892,22959,22960,22997],{},[895,22961,22962,22964,22966,22968,22970,22976,22978,22981,22983,22985,22987,22989,22991,22993,22995],{},[1716,22963,2222],{},[1712,22965,3145],{},[898,22967,207],{},[1712,22969,3145],{},[2037,22971,22972,22974],{},[898,22973,207],{},[1716,22975,2787],{},[1712,22977,3145],{},[1712,22979,22980],{},"⋯",[1712,22982,1714],{},[1716,22984,2222],{},[898,22986,2473],{"mathvariant":2003},[1712,22988,1904],{"stretchy":1903},[1716,22990,2222],{},[1712,22992,2219],{},[898,22994,207],{},[1712,22996,1910],{"stretchy":1903},[902,22998,22999],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,23002,16885],{}," 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 ",[883,23005,23007],{"className":23006},[886],[888,23008,23009],{"xmlns":890},[892,23010,23011,23023],{},[895,23012,23013,23015,23017,23019,23021],{},[1712,23014,1904],{"stretchy":1903},[898,23016,6951],{},[1712,23018,3138],{"separator":2565},[898,23020,16915],{},[1712,23022,1910],{"stretchy":1903},[902,23024,23025],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,23028,23030],{"id":23029},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,23032,23033],{},"Po prostudování kapitoly by čtenář měl umět:",[120,23035,23036,23039,23042,23045,23048,23051,23054,23144],{},[123,23037,23038],{},"popsat zjednodušený model národní ekonomiky,",[123,23040,23041],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,23043,23044],{},"popsat lineární model spotřeby a úspor,",[123,23046,23047],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,23049,23050],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,23052,23053],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,23055,23056,23057,1343,23074,1343,23096,1655,23121,23143],{},"popsat modely ",[883,23058,23060],{"className":23059},[886],[888,23061,23062],{"xmlns":890},[892,23063,23064,23072],{},[895,23065,23066,23068,23070],{},[898,23067,8195],{},[1762,23069,17164],{},[898,23071,17058],{},[902,23073,17169],{"encoding":904},[883,23075,23077],{"className":23076},[886],[888,23078,23079],{"xmlns":890},[892,23080,23081,23093],{},[895,23082,23083,23085,23087,23089,23091],{},[898,23084,8195],{},[1762,23086,17164],{},[898,23088,17058],{},[1762,23090,17164],{},[898,23092,16986],{},[902,23094,23095],{"encoding":904},"C\\text{-}I\\text{-}G",[883,23097,23099],{"className":23098},[886],[888,23100,23101],{"xmlns":890},[892,23102,23103,23119],{},[895,23104,23105,23107,23109,23111,23113,23115,23117],{},[898,23106,8195],{},[1762,23108,17164],{},[898,23110,17058],{},[1762,23112,17164],{},[898,23114,16986],{},[1762,23116,17164],{},[898,23118,17194],{},[902,23120,17197],{"encoding":904},[883,23122,23124],{"className":23123},[886],[888,23125,23126],{"xmlns":890},[892,23127,23128,23140],{},[895,23129,23130,23132,23134,23136,23138],{},[898,23131,17058],{},[898,23133,6493],{},[1762,23135,17164],{},[898,23137,14667],{},[898,23139,4445],{},[902,23141,23142],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,23145,23146],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,23148,23150],{"id":23149},"gnp-a-národní-důchod","GNP a národní důchod",[724,23152,23153,3245,23156,14897,23175,23178],{},[38,23154,23155],{},"Hrubý národní produkt",[883,23157,23159],{"className":23158},[886],[888,23160,23161],{"xmlns":890},[892,23162,23163,23172],{},[895,23164,23165,23167,23170],{},[898,23166,16986],{},[898,23168,23169],{},"N",[898,23171,1710],{},[902,23173,23174],{"encoding":904},"GNP",[614,23176,23177],{},"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:",[724,23180,23181],{},[883,23182,23184],{"className":23183},[886],[888,23185,23186],{"xmlns":890},[892,23187,23188,23223],{},[895,23189,23190,23192,23194,23196,23198,23200,23202,23204,23206,23208,23210,23212,23214,23216,23218,23221],{},[898,23191,16986],{},[898,23193,23169],{},[898,23195,1710],{},[1712,23197,1714],{},[898,23199,8195],{},[1712,23201,3145],{},[898,23203,17058],{},[1712,23205,3145],{},[898,23207,16986],{},[1712,23209,3145],{},[898,23211,17194],{},[1712,23213,3138],{"separator":2565},[3690,23215],{"width":3692},[1712,23217,1904],{"stretchy":1903},[1716,23219,23220],{},"7.1",[1712,23222,1910],{"stretchy":1903},[902,23224,23225],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,23227,23228],{},"kde",[120,23230,23231,23247,23263,23279],{},[123,23232,23233,23246],{},[883,23234,23236],{"className":23235},[886],[888,23237,23238],{"xmlns":890},[892,23239,23240,23244],{},[895,23241,23242],{},[898,23243,8195],{},[902,23245,8195],{"encoding":904}," — výdaje domácností na spotřebu,",[123,23248,23249,23262],{},[883,23250,23252],{"className":23251},[886],[888,23253,23254],{"xmlns":890},[892,23255,23256,23260],{},[895,23257,23258],{},[898,23259,17058],{},[902,23261,17058],{"encoding":904}," — hrubé domácí investice,",[123,23264,23265,23278],{},[883,23266,23268],{"className":23267},[886],[888,23269,23270],{"xmlns":890},[892,23271,23272,23276],{},[895,23273,23274],{},[898,23275,16986],{},[902,23277,16986],{"encoding":904}," — vládní výdaje,",[123,23280,23281,23294],{},[883,23282,23284],{"className":23283},[886],[888,23285,23286],{"xmlns":890},[892,23287,23288,23292],{},[895,23289,23290],{},[898,23291,17194],{},[902,23293,17194],{"encoding":904}," — čistý export.",[724,23296,23297,23298,23315,23316,23319,23320,3245,23323,14897,23336,23339],{},"K měření ",[883,23299,23301],{"className":23300},[886],[888,23302,23303],{"xmlns":890},[892,23304,23305,23313],{},[895,23306,23307,23309,23311],{},[898,23308,16986],{},[898,23310,23169],{},[898,23312,1710],{},[902,23314,23174],{"encoding":904}," se užívá ",[38,23317,23318],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,23321,23322],{},"národní důchod",[883,23324,23326],{"className":23325},[886],[888,23327,23328],{"xmlns":890},[892,23329,23330,23334],{},[895,23331,23332],{},[898,23333,6951],{},[902,23335,6951],{"encoding":904},[614,23337,23338],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,23341,23342],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,23344,23345],{},[883,23346,23348],{"className":23347},[886],[888,23349,23350],{"xmlns":890},[892,23351,23352,23366],{},[895,23353,23354,23356,23358,23360,23362,23364],{},[898,23355,16986],{},[898,23357,23169],{},[898,23359,1710],{},[1712,23361,3740],{},[898,23363,6951],{},[1712,23365,3138],{"separator":2565},[902,23367,23368],{"encoding":904},"GNP \\approx Y,",[724,23370,23371,23372,14897,23375,23378,23379,23392,23393,23396,23397,1659],{},"a užívá se společného názvu ",[38,23373,23374],{},"důchod",[614,23376,23377],{},"income",") s označením ",[883,23380,23382],{"className":23381},[886],[888,23383,23384],{"xmlns":890},[892,23385,23386,23390],{},[895,23387,23388],{},[898,23389,6951],{},[902,23391,6951],{"encoding":904},". Domácnosti důchod použijí ke ",[38,23394,23395],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,23398,23399],{},"úspor",[115,23401,23403],{"id":23402},"spotřeba-a-úspory","Spotřeba a úspory",[198,23405,23407],{"id":23406},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,23409,23410,23411,23424,23425,23438,23439,2854],{},"Jak spotřeba ",[883,23412,23414],{"className":23413},[886],[888,23415,23416],{"xmlns":890},[892,23417,23418,23422],{},[895,23419,23420],{},[898,23421,8195],{},[902,23423,8195],{"encoding":904},", tak úspory ",[883,23426,23428],{"className":23427},[886],[888,23429,23430],{"xmlns":890},[892,23431,23432,23436],{},[895,23433,23434],{},[898,23435,6493],{},[902,23437,6493],{"encoding":904}," závisejí na důchodu ",[883,23440,23442],{"className":23441},[886],[888,23443,23444],{"xmlns":890},[892,23445,23446,23450],{},[895,23447,23448],{},[898,23449,6951],{},[902,23451,6951],{"encoding":904},[724,23453,23454],{},[883,23455,23457],{"className":23456},[886],[888,23458,23459],{"xmlns":890},[892,23460,23461,23493],{},[895,23462,23463,23465,23467,23469,23471,23473,23475,23477,23479,23481,23483,23485,23487,23489,23491],{},[898,23464,8195],{},[1712,23466,1714],{},[898,23468,8195],{},[1712,23470,1904],{"stretchy":1903},[898,23472,6951],{},[1712,23474,1910],{"stretchy":1903},[1712,23476,3138],{"separator":2565},[3690,23478],{"width":3692},[898,23480,6493],{},[1712,23482,1714],{},[898,23484,6493],{},[1712,23486,1904],{"stretchy":1903},[898,23488,6951],{},[1712,23490,1910],{"stretchy":1903},[898,23492,1659],{"mathvariant":2003},[902,23494,23495],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,23497,23498,5920,23517,14897,23520,23523,23524,5920,23544,14897,23547,23550,23551,1655,23554,23557],{},[883,23499,23501],{"className":23500},[886],[888,23502,23503],{"xmlns":890},[892,23504,23505,23515],{},[895,23506,23507,23509,23511,23513],{},[898,23508,8195],{},[1712,23510,1904],{"stretchy":1903},[898,23512,6951],{},[1712,23514,1910],{"stretchy":1903},[902,23516,19090],{"encoding":904},[38,23518,23519],{},"funkce spotřeby",[614,23521,23522],{},"consumption function","), ",[883,23525,23527],{"className":23526},[886],[888,23528,23529],{"xmlns":890},[892,23530,23531,23541],{},[895,23532,23533,23535,23537,23539],{},[898,23534,6493],{},[1712,23536,1904],{"stretchy":1903},[898,23538,6951],{},[1712,23540,1910],{"stretchy":1903},[902,23542,23543],{"encoding":904},"S(Y)",[38,23545,23546],{},"funkce úspor",[614,23548,23549],{},"savings function","); jejich grafy se nazývají ",[38,23552,23553],{},"křivka spotřeby",[38,23555,23556],{},"křivka úspor",". Platí základní identita",[724,23559,23560],{},[883,23561,23563],{"className":23562},[886],[888,23564,23565],{"xmlns":890},[892,23566,23567,23610],{},[895,23568,23569,23571,23573,23575,23577,23579,23581,23583,23585,23587,23589,23591,23593,23595,23597,23599,23601,23603,23605,23608],{},[898,23570,6951],{},[1712,23572,1714],{},[898,23574,8195],{},[1712,23576,3145],{},[898,23578,6493],{},[1712,23580,1714],{},[898,23582,8195],{},[1712,23584,1904],{"stretchy":1903},[898,23586,6951],{},[1712,23588,1910],{"stretchy":1903},[1712,23590,3145],{},[898,23592,6493],{},[1712,23594,1904],{"stretchy":1903},[898,23596,6951],{},[1712,23598,1910],{"stretchy":1903},[898,23600,1659],{"mathvariant":2003},[3690,23602],{"width":3692},[1712,23604,1904],{"stretchy":1903},[1716,23606,23607],{},"7.2",[1712,23609,1910],{"stretchy":1903},[902,23611,23612],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,23614,23615],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,23617,23619],{"id":23618},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,23621,23622],{},"Nejjednodušší model předpokládá lineární tvar",[724,23624,23625],{},[883,23626,23628],{"className":23627},[886],[888,23629,23630],{"xmlns":890},[892,23631,23632,23667],{},[895,23633,23634,23636,23638,23640,23642,23644,23646,23648,23650,23652,23654,23656,23658,23660,23662,23665],{},[898,23635,8195],{},[1712,23637,1714],{},[898,23639,8195],{},[1712,23641,1904],{"stretchy":1903},[898,23643,6951],{},[1712,23645,1910],{"stretchy":1903},[1712,23647,1714],{},[898,23649,207],{},[898,23651,6951],{},[1712,23653,3145],{},[898,23655,7544],{},[1712,23657,3138],{"separator":2565},[3690,23659],{"width":3692},[1712,23661,1904],{"stretchy":1903},[1716,23663,23664],{},"7.3",[1712,23666,1910],{"stretchy":1903},[902,23668,23669],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,23671,2101,23672,1655,23690,23712,23713,23753,23754,1659],{},[883,23673,23675],{"className":23674},[886],[888,23676,23677],{"xmlns":890},[892,23678,23679,23687],{},[895,23680,23681,23683,23685],{},[898,23682,7544],{},[1712,23684,2302],{},[1716,23686,2085],{},[902,23688,23689],{"encoding":904},"b > 0",[883,23691,23693],{"className":23692},[886],[888,23694,23695],{"xmlns":890},[892,23696,23697,23709],{},[895,23698,23699,23701,23703,23705,23707],{},[1716,23700,2085],{},[1712,23702,2252],{},[898,23704,207],{},[1712,23706,2252],{},[1716,23708,2222],{},[902,23710,23711],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,23714,23716],{"className":23715},[886],[888,23717,23718],{"xmlns":890},[892,23719,23720,23750],{},[895,23721,23722,23724,23726,23733,23735,23738,23740,23742,23744,23746,23748],{},[898,23723,207],{},[1712,23725,1714],{},[895,23727,23728,23731],{},[898,23729,23730],{"mathvariant":2003},"t",[898,23732,15913],{"mathvariant":2003},[1762,23734,2583],{},[898,23736,23737],{},"α",[1712,23739,1714],{},[898,23741,2004],{"mathvariant":2003},[898,23743,8195],{},[898,23745,2473],{"mathvariant":2003},[898,23747,2004],{"mathvariant":2003},[898,23749,6951],{},[902,23751,23752],{"encoding":904},"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 ",[883,23755,23757],{"className":23756},[886],[888,23758,23759],{"xmlns":890},[892,23760,23761,23765],{},[895,23762,23763],{},[898,23764,6951],{},[902,23766,6951],{"encoding":904},[724,23768,23769],{},[614,23770,23771,23772,23796,23797,23835,23836,23852,23853,1659],{},"Obrázek 7.1 — Přímka spotřeby ",[883,23773,23775],{"className":23774},[886],[888,23776,23777],{"xmlns":890},[892,23778,23779,23793],{},[895,23780,23781,23783,23785,23787,23789,23791],{},[898,23782,8195],{},[1712,23784,1714],{},[898,23786,207],{},[898,23788,6951],{},[1712,23790,3145],{},[898,23792,7544],{},[902,23794,23795],{"encoding":904},"C = aY + b"," se směrnicí ",[883,23798,23800],{"className":23799},[886],[888,23801,23802],{"xmlns":890},[892,23803,23804,23832],{},[895,23805,23806,23808,23810,23816,23818,23820,23822,23824,23826,23828,23830],{},[898,23807,207],{},[1712,23809,1714],{},[895,23811,23812,23814],{},[898,23813,23730],{"mathvariant":2003},[898,23815,15913],{"mathvariant":2003},[1762,23817,2583],{},[898,23819,23737],{},[1712,23821,1714],{},[898,23823,2004],{"mathvariant":2003},[898,23825,8195],{},[898,23827,2473],{"mathvariant":2003},[898,23829,2004],{"mathvariant":2003},[898,23831,6951],{},[902,23833,23834],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,23837,23839],{"className":23838},[886],[888,23840,23841],{"xmlns":890},[892,23842,23843,23849],{},[895,23844,23845,23847],{},[898,23846,2004],{"mathvariant":2003},[898,23848,8195],{},[902,23850,23851],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,23854,23856],{"className":23855},[886],[888,23857,23858],{"xmlns":890},[892,23859,23860,23870],{},[895,23861,23862,23864,23866,23868],{},[898,23863,2004],{"mathvariant":2003},[898,23865,6951],{},[1712,23867,1714],{},[1716,23869,2222],{},[902,23871,23872],{"encoding":904},"\\Delta Y = 1",[724,23874,23875,23876,2854],{},"Dosazením do (7.2) plyne ",[38,23877,23878],{},"lineární model úspor",[724,23880,23881],{},[883,23882,23884],{"className":23883},[886],[888,23885,23886],{"xmlns":890},[892,23887,23888,23953],{},[895,23889,23890,23892,23894,23896,23898,23900,23902,23904,23906,23908,23910,23912,23914,23916,23918,23920,23922,23924,23926,23928,23930,23932,23934,23936,23938,23940,23942,23944,23946,23948,23951],{},[898,23891,6493],{},[1712,23893,1714],{},[898,23895,6951],{},[1712,23897,2219],{},[898,23899,8195],{},[1712,23901,1904],{"stretchy":1903},[898,23903,6951],{},[1712,23905,1910],{"stretchy":1903},[1712,23907,1714],{},[898,23909,6951],{},[1712,23911,2219],{},[1712,23913,1904],{"stretchy":1903},[898,23915,207],{},[898,23917,6951],{},[1712,23919,3145],{},[898,23921,7544],{},[1712,23923,1910],{"stretchy":1903},[1712,23925,1714],{},[1712,23927,1904],{"stretchy":1903},[1716,23929,2222],{},[1712,23931,2219],{},[898,23933,207],{},[1712,23935,1910],{"stretchy":1903},[898,23937,6951],{},[1712,23939,2219],{},[898,23941,7544],{},[898,23943,1659],{"mathvariant":2003},[3690,23945],{"width":3692},[1712,23947,1904],{"stretchy":1903},[1716,23949,23950],{},"7.4",[1712,23952,1910],{"stretchy":1903},[902,23954,23955],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,23957,23958,23959,1691],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,23960,23962],{"className":23961},[886],[888,23963,23964],{"xmlns":890},[892,23965,23966,23982],{},[895,23967,23968,23970,23972,23974,23976,23978,23980],{},[1716,23969,2085],{},[1712,23971,2252],{},[1716,23973,2222],{},[1712,23975,2219],{},[898,23977,207],{},[1712,23979,2252],{},[1716,23981,2222],{},[902,23983,23984],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,23986,23987],{},[614,23988,23989,23990,1655,24013,24045,24046,8046,24059,24089,24090,8046,24108,1659],{},"Obrázek 7.2 — Přímky ",[883,23991,23993],{"className":23992},[886],[888,23994,23995],{"xmlns":890},[892,23996,23997,24011],{},[895,23998,23999,24001,24003,24005,24007,24009],{},[898,24000,8195],{},[1712,24002,1714],{},[898,24004,207],{},[898,24006,6951],{},[1712,24008,3145],{},[898,24010,7544],{},[902,24012,23795],{"encoding":904},[883,24014,24016],{"className":24015},[886],[888,24017,24018],{"xmlns":890},[892,24019,24020,24042],{},[895,24021,24022,24024,24026,24028,24030,24032,24034,24036,24038,24040],{},[898,24023,6493],{},[1712,24025,1714],{},[1712,24027,1904],{"stretchy":1903},[1716,24029,2222],{},[1712,24031,2219],{},[898,24033,207],{},[1712,24035,1910],{"stretchy":1903},[898,24037,6951],{},[1712,24039,2219],{},[898,24041,7544],{},[902,24043,24044],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,24047,24049],{"className":24048},[886],[888,24050,24051],{"xmlns":890},[892,24052,24053,24057],{},[895,24054,24055],{},[898,24056,6951],{},[902,24058,6951],{"encoding":904},[883,24060,24062],{"className":24061},[886],[888,24063,24064],{"xmlns":890},[892,24065,24066,24086],{},[895,24067,24068,24070,24072,24074,24076,24078,24080,24082,24084],{},[898,24069,6951],{},[1712,24071,1714],{},[898,24073,7544],{},[898,24075,2473],{"mathvariant":2003},[1712,24077,1904],{"stretchy":1903},[1716,24079,2222],{},[1712,24081,2219],{},[898,24083,207],{},[1712,24085,1910],{"stretchy":1903},[902,24087,24088],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,24091,24093],{"className":24092},[886],[888,24094,24095],{"xmlns":890},[892,24096,24097,24105],{},[895,24098,24099,24101,24103],{},[898,24100,8195],{},[1712,24102,3138],{"separator":2565},[898,24104,6493],{},[902,24106,24107],{"encoding":904},"C, S",[883,24109,24111],{"className":24110},[886],[888,24112,24113],{"xmlns":890},[892,24114,24115,24121],{},[895,24116,24117,24119],{},[1712,24118,2219],{},[898,24120,7544],{},[902,24122,24123],{"encoding":904},"-b",[198,24125,24127],{"id":24126},"příklad-71","Příklad 7.1",[724,24129,24130,24131,24156],{},"Pro spotřebu ",[883,24132,24134],{"className":24133},[886],[888,24135,24136],{"xmlns":890},[892,24137,24138,24153],{},[895,24139,24140,24142,24144,24147,24149,24151],{},[898,24141,8195],{},[1712,24143,1714],{},[1716,24145,24146],{},"0,4",[898,24148,6951],{},[1712,24150,3145],{},[1716,24152,1718],{},[902,24154,24155],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,24158,24159],{},[883,24160,24162],{"className":24161},[886],[888,24163,24164],{"xmlns":890},[892,24165,24166,24204],{},[895,24167,24168,24170,24172,24174,24176,24178,24180,24182,24184,24186,24188,24190,24192,24194,24197,24199,24201],{},[898,24169,6493],{},[1712,24171,1714],{},[898,24173,6951],{},[1712,24175,2219],{},[898,24177,8195],{},[1712,24179,1714],{},[898,24181,6951],{},[1712,24183,2219],{},[1716,24185,24146],{},[898,24187,6951],{},[1712,24189,2219],{},[1716,24191,1718],{},[1712,24193,1714],{},[1716,24195,24196],{},"0,6",[898,24198,6951],{},[1712,24200,2219],{},[1716,24202,24203],{},"10.",[902,24205,24206],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,24208,24209],{},[614,24210,24211,24212,1655,24235,24259,24260,5920,24273,24297,24298,5920,24315,24331,24332,1659],{},"Obrázek 7.3 — Přímky ",[883,24213,24215],{"className":24214},[886],[888,24216,24217],{"xmlns":890},[892,24218,24219,24233],{},[895,24220,24221,24223,24225,24227,24229,24231],{},[898,24222,8195],{},[1712,24224,1714],{},[1716,24226,24146],{},[898,24228,6951],{},[1712,24230,3145],{},[1716,24232,1718],{},[902,24234,24155],{"encoding":904},[883,24236,24238],{"className":24237},[886],[888,24239,24240],{"xmlns":890},[892,24241,24242,24256],{},[895,24243,24244,24246,24248,24250,24252,24254],{},[898,24245,6493],{},[1712,24247,1714],{},[1716,24249,24196],{},[898,24251,6951],{},[1712,24253,2219],{},[1716,24255,1718],{},[902,24257,24258],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,24261,24263],{"className":24262},[886],[888,24264,24265],{"xmlns":890},[892,24266,24267,24271],{},[895,24268,24269],{},[898,24270,6951],{},[902,24272,6951],{"encoding":904},[883,24274,24276],{"className":24275},[886],[888,24277,24278],{"xmlns":890},[892,24279,24280,24294],{},[895,24281,24282,24284,24287],{},[1712,24283,3740],{},[1716,24285,24286],{},"16,",[6205,24288,24289,24291],{"accent":2565},[1716,24290,6209],{},[1712,24292,24293],{},"ˉ",[902,24295,24296],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,24299,24301],{"className":24300},[886],[888,24302,24303],{"xmlns":890},[892,24304,24305,24313],{},[895,24306,24307,24309,24311],{},[898,24308,8195],{},[1712,24310,3138],{"separator":2565},[898,24312,6493],{},[902,24314,24107],{"encoding":904},[883,24316,24318],{"className":24317},[886],[888,24319,24320],{"xmlns":890},[892,24321,24322,24328],{},[895,24323,24324,24326],{},[1712,24325,2219],{},[1716,24327,1718],{},[902,24329,24330],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,24333,24335],{"className":24334},[886],[888,24336,24337],{"xmlns":890},[892,24338,24339,24351],{},[895,24340,24341,24343,24345,24347,24349],{},[1712,24342,1904],{"stretchy":1903},[1716,24344,2085],{},[1712,24346,3138],{"separator":2565},[1716,24348,1718],{},[1712,24350,1910],{"stretchy":1903},[902,24352,24353],{"encoding":904},"(0, 10)",[724,24355,24356,24357,5920,24375,24405,24406,14897,24409,24412,24413,5920,24437,14897,24440,24443],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,24358,24360],{"className":24359},[886],[888,24361,24362],{"xmlns":890},[892,24363,24364,24372],{},[895,24365,24366,24368,24370],{},[898,24367,6951],{},[1712,24369,1714],{},[1716,24371,2085],{},[902,24373,24374],{"encoding":904},"Y = 0",[883,24376,24378],{"className":24377},[886],[888,24379,24380],{"xmlns":890},[892,24381,24382,24402],{},[895,24383,24384,24386,24388,24390,24392,24394,24396,24398,24400],{},[898,24385,6493],{},[1712,24387,1904],{"stretchy":1903},[1716,24389,2085],{},[1712,24391,1910],{"stretchy":1903},[1712,24393,1714],{},[1712,24395,2219],{},[898,24397,7544],{},[1712,24399,2252],{},[1716,24401,2085],{},[902,24403,24404],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,24407,24408],{},"autonomních úsporách",[614,24410,24411],{},"autonomous savings","). Analogicky ",[883,24414,24416],{"className":24415},[886],[888,24417,24418],{"xmlns":890},[892,24419,24420,24434],{},[895,24421,24422,24424,24426,24428,24430,24432],{},[898,24423,8195],{},[1712,24425,1904],{"stretchy":1903},[1716,24427,2085],{},[1712,24429,1910],{"stretchy":1903},[1712,24431,1714],{},[898,24433,7544],{},[902,24435,24436],{"encoding":904},"C(0) = b",[38,24438,24439],{},"autonomní spotřeba",[614,24441,24442],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,24445,24447],{"id":24446},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,24449,24450,3245,24453,14897,24470,24473],{},[38,24451,24452],{},"Mezní sklon ke spotřebě",[883,24454,24456],{"className":24455},[886],[888,24457,24458],{"xmlns":890},[892,24459,24460,24468],{},[895,24461,24462,24464,24466],{},[898,24463,4445],{},[898,24465,1710],{},[898,24467,8195],{},[902,24469,22920],{"encoding":904},[614,24471,24472],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,24475,24476],{},[883,24477,24479],{"className":24478},[886],[888,24480,24481],{"xmlns":890},[892,24482,24483,24509],{},[895,24484,24485,24487,24489,24491,24493,24507],{},[898,24486,4445],{},[898,24488,1710],{},[898,24490,8195],{},[1712,24492,1714],{},[2567,24494,24495,24501],{},[895,24496,24497,24499],{},[898,24498,2468],{"mathvariant":2003},[898,24500,8195],{},[895,24502,24503,24505],{},[898,24504,2468],{"mathvariant":2003},[898,24506,6951],{},[898,24508,1659],{"mathvariant":2003},[902,24510,24511],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,24513,24514,3245,24517,14897,24535,24538],{},[38,24515,24516],{},"Mezní sklon k úsporám",[883,24518,24520],{"className":24519},[886],[888,24521,24522],{"xmlns":890},[892,24523,24524,24532],{},[895,24525,24526,24528,24530],{},[898,24527,4445],{},[898,24529,1710],{},[898,24531,6493],{},[902,24533,24534],{"encoding":904},"MPS",[614,24536,24537],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,24540,24541],{},[883,24542,24544],{"className":24543},[886],[888,24545,24546],{"xmlns":890},[892,24547,24548,24574],{},[895,24549,24550,24552,24554,24556,24558,24572],{},[898,24551,4445],{},[898,24553,1710],{},[898,24555,6493],{},[1712,24557,1714],{},[2567,24559,24560,24566],{},[895,24561,24562,24564],{},[898,24563,2468],{"mathvariant":2003},[898,24565,6493],{},[895,24567,24568,24570],{},[898,24569,2468],{"mathvariant":2003},[898,24571,6951],{},[898,24573,1659],{"mathvariant":2003},[902,24575,24576],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,24578,24579,24580,24638],{},"Z (7.2) plyne ",[883,24581,24583],{"className":24582},[886],[888,24584,24585],{"xmlns":890},[892,24586,24587,24635],{},[895,24588,24589,24603,24605,24619,24621],{},[2567,24590,24591,24597],{},[895,24592,24593,24595],{},[898,24594,2468],{"mathvariant":2003},[898,24596,6951],{},[895,24598,24599,24601],{},[898,24600,2468],{"mathvariant":2003},[898,24602,6951],{},[1712,24604,1714],{},[2567,24606,24607,24613],{},[895,24608,24609,24611],{},[898,24610,2468],{"mathvariant":2003},[898,24612,8195],{},[895,24614,24615,24617],{},[898,24616,2468],{"mathvariant":2003},[898,24618,6951],{},[1712,24620,3145],{},[2567,24622,24623,24629],{},[895,24624,24625,24627],{},[898,24626,2468],{"mathvariant":2003},[898,24628,6493],{},[895,24630,24631,24633],{},[898,24632,2468],{"mathvariant":2003},[898,24634,6951],{},[902,24636,24637],{"encoding":904},"\\frac{\\mathrm{d}Y}{\\mathrm{d}Y} = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} + \\frac{\\mathrm{d}S}{\\mathrm{d}Y}",", a tedy",[724,24640,24641],{},[883,24642,24644],{"className":24643},[886],[888,24645,24646],{"xmlns":890},[892,24647,24648,24711],{},[895,24649,24650,24702,24704,24706,24709],{},[17706,24651,24652],{"notation":17708},[2563,24653,24654],{"scriptlevel":2085,"displaystyle":1903},[2563,24655,24656],{"scriptlevel":2085,"displaystyle":1903},[2563,24657,24658],{"scriptlevel":2085,"displaystyle":2565},[895,24659,24660,24662,24664,24666,24668,24670,24672,24674,24676,24678,24680,24682,24684,24686,24688,24690,24692,24694,24696,24698,24700],{},[898,24661,4445],{},[898,24663,1710],{},[898,24665,8195],{},[1712,24667,3145],{},[898,24669,4445],{},[898,24671,1710],{},[898,24673,6493],{},[1712,24675,1714],{},[1716,24677,2222],{},[1712,24679,3138],{"separator":2565},[3690,24681],{"width":3692},[898,24683,4445],{},[898,24685,1710],{},[898,24687,6493],{},[1712,24689,1714],{},[1716,24691,2222],{},[1712,24693,2219],{},[898,24695,4445],{},[898,24697,1710],{},[898,24699,8195],{},[898,24701,1659],{"mathvariant":2003},[3690,24703],{"width":3692},[1712,24705,1904],{"stretchy":1903},[1716,24707,24708],{},"7.5",[1712,24710,1910],{"stretchy":1903},[902,24712,24713],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,24715,24716,3245,24719,24742,24743,1655,24765,24791],{},[38,24717,24718],{},"Pro lineární model",[883,24720,24722],{"className":24721},[886],[888,24723,24724],{"xmlns":890},[892,24725,24726,24740],{},[895,24727,24728,24730,24732,24734,24736,24738],{},[898,24729,8195],{},[1712,24731,1714],{},[898,24733,207],{},[898,24735,6951],{},[1712,24737,3145],{},[898,24739,7544],{},[902,24741,23795],{"encoding":904}," vychází ",[883,24744,24746],{"className":24745},[886],[888,24747,24748],{"xmlns":890},[892,24749,24750,24762],{},[895,24751,24752,24754,24756,24758,24760],{},[898,24753,4445],{},[898,24755,1710],{},[898,24757,8195],{},[1712,24759,1714],{},[898,24761,207],{},[902,24763,24764],{"encoding":904},"MPC = a",[883,24766,24768],{"className":24767},[886],[888,24769,24770],{"xmlns":890},[892,24771,24772,24788],{},[895,24773,24774,24776,24778,24780,24782,24784,24786],{},[898,24775,4445],{},[898,24777,1710],{},[898,24779,6493],{},[1712,24781,1714],{},[1716,24783,2222],{},[1712,24785,2219],{},[898,24787,207],{},[902,24789,24790],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,24793,24794,24797,24798,24820,24821,24849],{},[38,24795,24796],{},"Interpretace diferenciálem."," Pro pevné ",[883,24799,24801],{"className":24800},[886],[888,24802,24803],{"xmlns":890},[892,24804,24805,24817],{},[895,24806,24807,24809,24811],{},[898,24808,6951],{},[1712,24810,1714],{},[2037,24812,24813,24815],{},[898,24814,6951],{},[1712,24816,2145],{},[902,24818,24819],{"encoding":904},"Y = Y^*"," udává ",[883,24822,24824],{"className":24823},[886],[888,24825,24826],{"xmlns":890},[892,24827,24828,24846],{},[895,24829,24830,24832,24834,24836,24838,24844],{},[898,24831,4445],{},[898,24833,1710],{},[898,24835,8195],{},[1712,24837,1904],{"stretchy":1903},[2037,24839,24840,24842],{},[898,24841,6951],{},[1712,24843,2145],{},[1712,24845,1910],{"stretchy":1903},[902,24847,24848],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,24851,24852],{},[883,24853,24855],{"className":24854},[886],[888,24856,24857],{"xmlns":890},[892,24858,24859,24913],{},[895,24860,24861,24863,24865,24867,24869,24871,24873,24879,24881,24883,24885,24887,24889,24891,24893,24895,24897,24899,24901,24903,24905,24907,24909,24911],{},[898,24862,2004],{"mathvariant":2003},[898,24864,8195],{},[1712,24866,3740],{},[898,24868,2468],{"mathvariant":2003},[898,24870,8195],{},[1712,24872,1714],{},[2037,24874,24875,24877],{},[898,24876,8195],{},[1712,24878,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,24880,1904],{"stretchy":1903},[898,24882,6951],{},[1712,24884,1910],{"stretchy":1903},[1762,24886,2583],{},[898,24888,2468],{"mathvariant":2003},[898,24890,6951],{},[1712,24892,1714],{},[898,24894,4445],{},[898,24896,1710],{},[898,24898,8195],{},[1712,24900,1904],{"stretchy":1903},[898,24902,6951],{},[1712,24904,1910],{"stretchy":1903},[1762,24906,2583],{},[898,24908,2468],{"mathvariant":2003},[898,24910,6951],{},[898,24912,1659],{"mathvariant":2003},[902,24914,24915],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,24917,24918,24919,24955,24956,24959],{},"Analogicky ",[883,24920,24922],{"className":24921},[886],[888,24923,24924],{"xmlns":890},[892,24925,24926,24952],{},[895,24927,24928,24930,24932,24934,24936,24938,24940,24942,24944,24946,24948,24950],{},[898,24929,2004],{"mathvariant":2003},[898,24931,6493],{},[1712,24933,3740],{},[898,24935,4445],{},[898,24937,1710],{},[898,24939,6493],{},[1712,24941,1904],{"stretchy":1903},[898,24943,6951],{},[1712,24945,1910],{"stretchy":1903},[1762,24947,2583],{},[898,24949,2468],{"mathvariant":2003},[898,24951,6951],{},[902,24953,24954],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,24957,1145],{"className":24958,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,24961,24963],{"id":24962},"příklad-72","Příklad 7.2",[724,24965,24130,24966,25001,25002,25021],{},[883,24967,24969],{"className":24968},[886],[888,24970,24971],{"xmlns":890},[892,24972,24973,24998],{},[895,24974,24975,24977,24979,24982,24988,24990,24992,24994,24996],{},[898,24976,8195],{},[1712,24978,1714],{},[1716,24980,24981],{},"0,001",[2037,24983,24984,24986],{},[898,24985,6951],{},[1716,24987,2787],{},[1712,24989,3145],{},[1716,24991,6673],{},[898,24993,6951],{},[1712,24995,3145],{},[1716,24997,2782],{},[902,24999,25000],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,25003,25005],{"className":25004},[886],[888,25006,25007],{"xmlns":890},[892,25008,25009,25018],{},[895,25010,25011,25013,25015],{},[898,25012,6951],{},[1712,25014,2252],{},[1716,25016,25017],{},"400",[902,25019,25020],{"encoding":904},"Y \u003C 400",") platí",[724,25023,25024],{},[883,25025,25027],{"className":25026},[886],[888,25028,25029],{"xmlns":890},[892,25030,25031,25068],{},[895,25032,25033,25035,25037,25039,25041,25055,25057,25060,25062,25064,25066],{},[898,25034,4445],{},[898,25036,1710],{},[898,25038,8195],{},[1712,25040,1714],{},[2567,25042,25043,25049],{},[895,25044,25045,25047],{},[898,25046,2468],{"mathvariant":2003},[898,25048,8195],{},[895,25050,25051,25053],{},[898,25052,2468],{"mathvariant":2003},[898,25054,6951],{},[1712,25056,1714],{},[1716,25058,25059],{},"0,002",[898,25061,6951],{},[1712,25063,3145],{},[1716,25065,6673],{},[1712,25067,3138],{"separator":2565},[902,25069,25070],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,25072,25073],{},[883,25074,25076],{"className":25075},[886],[888,25077,25078],{"xmlns":890},[892,25079,25080,25113],{},[895,25081,25082,25084,25086,25088,25090,25092,25094,25096,25098,25100,25102,25104,25106,25108,25110],{},[898,25083,4445],{},[898,25085,1710],{},[898,25087,6493],{},[1712,25089,1714],{},[1716,25091,2222],{},[1712,25093,2219],{},[898,25095,4445],{},[898,25097,1710],{},[898,25099,8195],{},[1712,25101,1714],{},[1712,25103,2219],{},[1716,25105,25059],{},[898,25107,6951],{},[1712,25109,3145],{},[1716,25111,25112],{},"0,8.",[902,25114,25115],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,25117,25118,25198,25277],{},[123,25119,25120,1343,25148,25176,25177,5920,25195,1659],{},[883,25121,25123],{"className":25122},[886],[888,25124,25125],{"xmlns":890},[892,25126,25127,25145],{},[895,25128,25129,25131,25133,25135,25137,25139,25141,25143],{},[898,25130,4445],{},[898,25132,1710],{},[898,25134,8195],{},[1712,25136,1904],{"stretchy":1903},[1716,25138,1739],{},[1712,25140,1910],{"stretchy":1903},[1712,25142,1714],{},[1716,25144,24146],{},[902,25146,25147],{"encoding":904},"MPC(100) = 0{,}4",[883,25149,25151],{"className":25150},[886],[888,25152,25153],{"xmlns":890},[892,25154,25155,25173],{},[895,25156,25157,25159,25161,25163,25165,25167,25169,25171],{},[898,25158,4445],{},[898,25160,1710],{},[898,25162,6493],{},[1712,25164,1904],{"stretchy":1903},[1716,25166,1739],{},[1712,25168,1910],{"stretchy":1903},[1712,25170,1714],{},[1716,25172,24196],{},[902,25174,25175],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,25178,25180],{"className":25179},[886],[888,25181,25182],{"xmlns":890},[892,25183,25184,25192],{},[895,25185,25186,25188,25190],{},[898,25187,6951],{},[1712,25189,1714],{},[1716,25191,1739],{},[902,25193,25194],{"encoding":904},"Y = 100",[38,25196,25197],{},"větší sklon k úsporám",[123,25199,25200,1343,25228,25176,25256,5920,25274,1659],{},[883,25201,25203],{"className":25202},[886],[888,25204,25205],{"xmlns":890},[892,25206,25207,25225],{},[895,25208,25209,25211,25213,25215,25217,25219,25221,25223],{},[898,25210,4445],{},[898,25212,1710],{},[898,25214,8195],{},[1712,25216,1904],{"stretchy":1903},[1716,25218,6195],{},[1712,25220,1910],{"stretchy":1903},[1712,25222,1714],{},[1716,25224,24196],{},[902,25226,25227],{"encoding":904},"MPC(200) = 0{,}6",[883,25229,25231],{"className":25230},[886],[888,25232,25233],{"xmlns":890},[892,25234,25235,25253],{},[895,25236,25237,25239,25241,25243,25245,25247,25249,25251],{},[898,25238,4445],{},[898,25240,1710],{},[898,25242,6493],{},[1712,25244,1904],{"stretchy":1903},[1716,25246,6195],{},[1712,25248,1910],{"stretchy":1903},[1712,25250,1714],{},[1716,25252,24146],{},[902,25254,25255],{"encoding":904},"MPS(200) = 0{,}4",[883,25257,25259],{"className":25258},[886],[888,25260,25261],{"xmlns":890},[892,25262,25263,25271],{},[895,25264,25265,25267,25269],{},[898,25266,6951],{},[1712,25268,1714],{},[1716,25270,6195],{},[902,25272,25273],{"encoding":904},"Y = 200",[38,25275,25276],{},"větší sklon ke spotřebě",[123,25278,25279,25280,25298,25299,1691],{},"Přesně při ",[883,25281,25283],{"className":25282},[886],[888,25284,25285],{"xmlns":890},[892,25286,25287,25295],{},[895,25288,25289,25291,25293],{},[898,25290,6951],{},[1712,25292,1714],{},[1716,25294,6624],{},[902,25296,25297],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,25300,25302],{"className":25301},[886],[888,25303,25304],{"xmlns":890},[892,25305,25306,25326],{},[895,25307,25308,25310,25312,25314,25316,25318,25320,25322,25324],{},[898,25309,4445],{},[898,25311,1710],{},[898,25313,8195],{},[1712,25315,1714],{},[898,25317,4445],{},[898,25319,1710],{},[898,25321,6493],{},[1712,25323,1714],{},[1716,25325,2814],{},[902,25327,25328],{"encoding":904},"MPC = MPS = 0{,}5",[724,25330,25331,25332,25349,25350,25364,25365,3072,25378,25392,25393,25406,25407,25448],{},"Interpretace: při ",[883,25333,25335],{"className":25334},[886],[888,25336,25337],{"xmlns":890},[892,25338,25339,25347],{},[895,25340,25341,25343,25345],{},[898,25342,6951],{},[1712,25344,1714],{},[1716,25346,1739],{},[902,25348,25194],{"encoding":904}," se spotřeba mění ",[883,25351,25353],{"className":25352},[886],[888,25354,25355],{"xmlns":890},[892,25356,25357,25361],{},[895,25358,25359],{},[1716,25360,24146],{},[902,25362,25363],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,25366,25368],{"className":25367},[886],[888,25369,25370],{"xmlns":890},[892,25371,25372,25376],{},[895,25373,25374],{},[1716,25375,1739],{},[902,25377,1739],{"encoding":904},[883,25379,25381],{"className":25380},[886],[888,25382,25383],{"xmlns":890},[892,25384,25385,25390],{},[895,25386,25387],{},[1716,25388,25389],{},"101",[902,25391,25389],{"encoding":904},", změní se spotřeba přibližně o ",[883,25394,25396],{"className":25395},[886],[888,25397,25398],{"xmlns":890},[892,25399,25400,25404],{},[895,25401,25402],{},[1716,25403,24146],{},[902,25405,25363],{"encoding":904},". Skutečná změna ",[883,25408,25410],{"className":25409},[886],[888,25411,25412],{"xmlns":890},[892,25413,25414,25445],{},[895,25415,25416,25418,25420,25422,25424,25426,25428,25430,25432,25434,25436,25438,25440,25442],{},[898,25417,2004],{"mathvariant":2003},[898,25419,8195],{},[1712,25421,1714],{},[898,25423,8195],{},[1712,25425,1904],{"stretchy":1903},[1716,25427,25389],{},[1712,25429,1910],{"stretchy":1903},[1712,25431,2219],{},[898,25433,8195],{},[1712,25435,1904],{"stretchy":1903},[1716,25437,1739],{},[1712,25439,1910],{"stretchy":1903},[1712,25441,1714],{},[1716,25443,25444],{},"0,401",[902,25446,25447],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,25450,25451,25452],{},"Obecný trend: ",[38,25453,25454],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,25456,25458],{"id":25457},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,25460,25461,25462,14897,25465,25468,25469,14897,25472,17002,25475,14897,25478,25481],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,25463,25464],{},"makroekonomická rovnováha",[614,25466,25467],{},"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 ",[38,25470,25471],{},"agregátní poptávky",[614,25473,25474],{},"aggregate demand",[38,25476,25477],{},"agregátní nabídky",[614,25479,25480],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,25483,25485],{"id":25484},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,25487,25488],{},[3817,25489],{"alt":25490,"className":25491,"src":25492},"imek-keynesian-kriz",[210,3821],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,25494,25496],{"id":25495},"zadání-modelu","Zadání modelu",[724,25498,25499,25500,25513,25514,25527],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,25501,25503],{"className":25502},[886],[888,25504,25505],{"xmlns":890},[892,25506,25507,25511],{},[895,25508,25509],{},[898,25510,8195],{},[902,25512,8195],{"encoding":904}," a investice ",[883,25515,25517],{"className":25516},[886],[888,25518,25519],{"xmlns":890},[892,25520,25521,25525],{},[895,25522,25523],{},[898,25524,17058],{},[902,25526,17058],{"encoding":904},". Podmínka rovnováhy:",[724,25529,25530],{},[883,25531,25533],{"className":25532},[886],[888,25534,25535],{"xmlns":890},[892,25536,25537,25560],{},[895,25538,25539,25541,25543,25545,25547,25549,25551,25553,25555,25558],{},[898,25540,6951],{},[1712,25542,1714],{},[898,25544,8195],{},[1712,25546,3145],{},[898,25548,17058],{},[898,25550,1659],{"mathvariant":2003},[3690,25552],{"width":3692},[1712,25554,1904],{"stretchy":1903},[1716,25556,25557],{},"7.6",[1712,25559,1910],{"stretchy":1903},[902,25561,25562],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,25564,25566],{"id":25565},"soustava-rovnic","Soustava rovnic",[724,25568,25569,25570,25591,25592,25616],{},"Pro pevně zadané (plánované) investice ",[883,25571,25573],{"className":25572},[886],[888,25574,25575],{"xmlns":890},[892,25576,25577,25589],{},[895,25578,25579,25581,25583],{},[898,25580,17058],{},[1712,25582,1714],{},[2037,25584,25585,25587],{},[898,25586,17058],{},[1712,25588,2145],{},[902,25590,17069],{"encoding":904}," a funkci spotřeby ",[883,25593,25595],{"className":25594},[886],[888,25596,25597],{"xmlns":890},[892,25598,25599,25613],{},[895,25600,25601,25603,25605,25607,25609,25611],{},[898,25602,8195],{},[1712,25604,1714],{},[898,25606,8195],{},[1712,25608,1904],{"stretchy":1903},[898,25610,6951],{},[1712,25612,1910],{"stretchy":1903},[902,25614,25615],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,25618,25619],{},[883,25620,25622],{"className":25621},[886],[888,25623,25624],{"xmlns":890},[892,25625,25626,25702],{},[895,25627,25628,25693,25695,25697,25700],{},[25629,25630,25633,25665],"mtable",{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},"0.25em","right left",[25634,25635,25636,25643],"mtr",{},[25637,25638,25639],"mtd",{},[2563,25640,25641],{"scriptlevel":2085,"displaystyle":2565},[898,25642,6951],{},[25637,25644,25645],{},[2563,25646,25647],{"scriptlevel":2085,"displaystyle":2565},[895,25648,25649,25651,25653,25655,25657,25663],{},[895,25650],{},[1712,25652,1714],{},[898,25654,8195],{},[1712,25656,3145],{},[2037,25658,25659,25661],{},[898,25660,17058],{},[1712,25662,2145],{},[1712,25664,3138],{"separator":2565},[25634,25666,25667,25673],{},[25637,25668,25669],{},[2563,25670,25671],{"scriptlevel":2085,"displaystyle":2565},[898,25672,8195],{},[25637,25674,25675],{},[2563,25676,25677],{"scriptlevel":2085,"displaystyle":2565},[895,25678,25679,25681,25683,25685,25687,25689,25691],{},[895,25680],{},[1712,25682,1714],{},[898,25684,8195],{},[1712,25686,1904],{"stretchy":1903},[898,25688,6951],{},[1712,25690,1910],{"stretchy":1903},[1712,25692,3138],{"separator":2565},[3690,25694],{"width":3692},[1712,25696,1904],{"stretchy":1903},[1716,25698,25699],{},"7.7",[1712,25701,1910],{"stretchy":1903},[902,25703,25704],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,25706,25707,25708,3245,25710,1655,25727,3245,25730,1659],{},"jejímž řešením jsou ",[38,25709,18759],{},[883,25711,25713],{"className":25712},[886],[888,25714,25715],{"xmlns":890},[892,25716,25717,25725],{},[895,25718,25719],{},[2037,25720,25721,25723],{},[898,25722,6951],{},[898,25724,2041],{},[902,25726,18777],{"encoding":904},[38,25728,25729],{},"rovnovážná spotřeba",[883,25731,25733],{"className":25732},[886],[888,25734,25735],{"xmlns":890},[892,25736,25737,25745],{},[895,25738,25739],{},[2037,25740,25741,25743],{},[898,25742,8195],{},[898,25744,2041],{},[902,25746,18836],{"encoding":904},[198,25748,25750,25751],{"id":25749},"výpočet-yeye","Výpočet ",[883,25752,25754],{"className":25753},[886],[888,25755,25756],{"xmlns":890},[892,25757,25758,25766],{},[895,25759,25760],{},[2037,25761,25762,25764],{},[898,25763,6951],{},[898,25765,2041],{},[902,25767,18777],{"encoding":904},[724,25769,25770,25771,25794,25795,5502,25827],{},"Pro lineární spotřebu ",[883,25772,25774],{"className":25773},[886],[888,25775,25776],{"xmlns":890},[892,25777,25778,25792],{},[895,25779,25780,25782,25784,25786,25788,25790],{},[898,25781,8195],{},[1712,25783,1714],{},[898,25785,207],{},[898,25787,6951],{},[1712,25789,3145],{},[898,25791,7544],{},[902,25793,23795],{"encoding":904}," plyne z (7.7) rovnice ",[883,25796,25798],{"className":25797},[886],[888,25799,25800],{"xmlns":890},[892,25801,25802,25824],{},[895,25803,25804,25806,25808,25810,25812,25814,25816,25818],{},[898,25805,6951],{},[1712,25807,1714],{},[898,25809,207],{},[898,25811,6951],{},[1712,25813,3145],{},[898,25815,7544],{},[1712,25817,3145],{},[2037,25819,25820,25822],{},[898,25821,17058],{},[1712,25823,2145],{},[902,25825,25826],{"encoding":904},"Y = aY + b + I^*",[38,25828,25829],{},"redukovaný tvar",[724,25831,25832],{},[883,25833,25835],{"className":25834},[886],[888,25836,25837],{"xmlns":890},[892,25838,25839,25887],{},[895,25840,25841],{},[17706,25842,25843],{"notation":17708},[2563,25844,25845],{"scriptlevel":2085,"displaystyle":1903},[2563,25846,25847],{"scriptlevel":2085,"displaystyle":1903},[2563,25848,25849],{"scriptlevel":2085,"displaystyle":2565},[895,25850,25851,25853,25859,25861,25883,25885],{},[1762,25852,2583],{},[2037,25854,25855,25857],{},[898,25856,6951],{},[898,25858,2041],{},[1712,25860,1714],{},[2567,25862,25863,25875],{},[895,25864,25865,25867,25869],{},[898,25866,7544],{},[1712,25868,3145],{},[2037,25870,25871,25873],{},[898,25872,17058],{},[1712,25874,2145],{},[895,25876,25877,25879,25881],{},[1716,25878,2222],{},[1712,25880,2219],{},[898,25882,207],{},[898,25884,1659],{"mathvariant":2003},[1762,25886,2583],{},[902,25888,25889],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,25891,25893],{"id":25892},"příklad-73","Příklad 7.3",[724,25895,25896,25897,5920,25914,1655,25938,25964],{},"V modelu ",[883,25898,25900],{"className":25899},[886],[888,25901,25902],{"xmlns":890},[892,25903,25904,25912],{},[895,25905,25906,25908,25910],{},[898,25907,8195],{},[1762,25909,17164],{},[898,25911,17058],{},[902,25913,17169],{"encoding":904},[883,25915,25917],{"className":25916},[886],[888,25918,25919],{"xmlns":890},[892,25920,25921,25935],{},[895,25922,25923,25925,25927,25929,25931,25933],{},[898,25924,8195],{},[1712,25926,1714],{},[1716,25928,24196],{},[898,25930,6951],{},[1712,25932,3145],{},[1716,25934,1718],{},[902,25936,25937],{"encoding":904},"C = 0{,}6Y + 10",[883,25939,25941],{"className":25940},[886],[888,25942,25943],{"xmlns":890},[892,25944,25945,25961],{},[895,25946,25947,25949,25951,25953,25955],{},[898,25948,17058],{},[1712,25950,1714],{},[1716,25952,8912],{},[1712,25954,1714],{},[2037,25956,25957,25959],{},[898,25958,17058],{},[1712,25960,2145],{},[902,25962,25963],{"encoding":904},"I = 12 = I^*",". Soustava",[724,25966,25967],{},[883,25968,25970],{"className":25969},[886],[888,25971,25972],{"xmlns":890},[892,25973,25974,26030],{},[25629,25975,25976,26002],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,25977,25978,25984],{},[25637,25979,25980],{},[2563,25981,25982],{"scriptlevel":2085,"displaystyle":2565},[898,25983,6951],{},[25637,25985,25986],{},[2563,25987,25988],{"scriptlevel":2085,"displaystyle":2565},[895,25989,25990,25992,25994,25996,25998,26000],{},[895,25991],{},[1712,25993,1714],{},[898,25995,8195],{},[1712,25997,3145],{},[1716,25999,8912],{},[1712,26001,3138],{"separator":2565},[25634,26003,26004,26010],{},[25637,26005,26006],{},[2563,26007,26008],{"scriptlevel":2085,"displaystyle":2565},[898,26009,8195],{},[25637,26011,26012],{},[2563,26013,26014],{"scriptlevel":2085,"displaystyle":2565},[895,26015,26016,26018,26020,26022,26024,26026,26028],{},[895,26017],{},[1712,26019,1714],{},[1716,26021,24196],{},[898,26023,6951],{},[1712,26025,3145],{},[1716,26027,1718],{},[1712,26029,3138],{"separator":2565},[902,26031,26032],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,26034,26035,26036,1343,26059,26082,26083,1691],{},"má řešení ",[883,26037,26039],{"className":26038},[886],[888,26040,26041],{"xmlns":890},[892,26042,26043,26056],{},[895,26044,26045,26051,26053],{},[2037,26046,26047,26049],{},[898,26048,6951],{},[898,26050,2041],{},[1712,26052,1714],{},[1716,26054,26055],{},"55",[902,26057,26058],{"encoding":904},"Y^E = 55",[883,26060,26062],{"className":26061},[886],[888,26063,26064],{"xmlns":890},[892,26065,26066,26079],{},[895,26067,26068,26074,26076],{},[2037,26069,26070,26072],{},[898,26071,8195],{},[898,26073,2041],{},[1712,26075,1714],{},[1716,26077,26078],{},"43",[902,26080,26081],{"encoding":904},"C^E = 43"," (a ",[883,26084,26086],{"className":26085},[886],[888,26087,26088],{"xmlns":890},[892,26089,26090,26102],{},[895,26091,26092,26098,26100],{},[2037,26093,26094,26096],{},[898,26095,6493],{},[898,26097,2041],{},[1712,26099,1714],{},[1716,26101,8912],{},[902,26103,26104],{"encoding":904},"S^E = 12",[724,26106,26107],{},[614,26108,26109,26110,26132,26133,17002,26154,26177,26178,1659],{},"Obrázek 7.5 — Přímky ",[883,26111,26113],{"className":26112},[886],[888,26114,26115],{"xmlns":890},[892,26116,26117,26129],{},[895,26118,26119,26121,26123,26125,26127],{},[898,26120,8195],{},[1712,26122,1714],{},[898,26124,6951],{},[1712,26126,2219],{},[1716,26128,8912],{},[902,26130,26131],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,26134,26136],{"className":26135},[886],[888,26137,26138],{"xmlns":890},[892,26139,26140,26152],{},[895,26141,26142,26144,26146,26148,26150],{},[898,26143,6951],{},[1712,26145,1714],{},[898,26147,8195],{},[1712,26149,3145],{},[898,26151,17058],{},[902,26153,19618],{"encoding":904},[883,26155,26157],{"className":26156},[886],[888,26158,26159],{"xmlns":890},[892,26160,26161,26175],{},[895,26162,26163,26165,26167,26169,26171,26173],{},[898,26164,8195],{},[1712,26166,1714],{},[1716,26168,24196],{},[898,26170,6951],{},[1712,26172,3145],{},[1716,26174,1718],{},[902,26176,25937],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,26179,26181],{"className":26180},[886],[888,26182,26183],{"xmlns":890},[892,26184,26185,26217],{},[895,26186,26187,26189,26195,26197,26203,26205,26207,26209,26211,26213,26215],{},[1712,26188,7910],{"stretchy":1903},[2037,26190,26191,26193],{},[898,26192,6951],{},[898,26194,2041],{},[1712,26196,3138],{"separator":2565},[2037,26198,26199,26201],{},[898,26200,8195],{},[898,26202,2041],{},[1712,26204,7925],{"stretchy":1903},[1712,26206,1714],{},[1712,26208,7910],{"stretchy":1903},[1716,26210,26055],{},[1712,26212,3138],{"separator":2565},[1716,26214,26078],{},[1712,26216,7925],{"stretchy":1903},[902,26218,26219],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,26221,26222,26225,26226,26243,26244,1659],{},[38,26223,26224],{},"Komentář k přechodu."," Model ",[883,26227,26229],{"className":26228},[886],[888,26230,26231],{"xmlns":890},[892,26232,26233,26241],{},[895,26234,26235,26237,26239],{},[898,26236,8195],{},[1762,26238,17164],{},[898,26240,17058],{},[902,26242,17169],{"encoding":904}," 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 ",[38,26245,26246,26247],{},"model ",[883,26248,26250],{"className":26249},[886],[888,26251,26252],{"xmlns":890},[892,26253,26254,26266],{},[895,26255,26256,26258,26260,26262,26264],{},[898,26257,8195],{},[1762,26259,17164],{},[898,26261,17058],{},[1762,26263,17164],{},[898,26265,16986],{},[902,26267,23095],{"encoding":904},[115,26269,26271],{"id":26270},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,26273,25496],{"id":26274},"zadání-modelu-1",[724,26276,26277,26278,26295,26296,3245,26299,14897,26312,26315],{},"Rozšíření modelu ",[883,26279,26281],{"className":26280},[886],[888,26282,26283],{"xmlns":890},[892,26284,26285,26293],{},[895,26286,26287,26289,26291],{},[898,26288,8195],{},[1762,26290,17164],{},[898,26292,17058],{},[902,26294,17169],{"encoding":904}," o ",[38,26297,26298],{},"vládní výdaje",[883,26300,26302],{"className":26301},[886],[888,26303,26304],{"xmlns":890},[892,26305,26306,26310],{},[895,26307,26308],{},[898,26309,16986],{},[902,26311,16986],{"encoding":904},[614,26313,26314],{},"government expenditure","). Podmínka rovnováhy:",[724,26317,26318],{},[883,26319,26321],{"className":26320},[886],[888,26322,26323],{"xmlns":890},[892,26324,26325,26352],{},[895,26326,26327,26329,26331,26333,26335,26337,26339,26341,26343,26345,26347,26350],{},[898,26328,6951],{},[1712,26330,1714],{},[898,26332,8195],{},[1712,26334,3145],{},[898,26336,17058],{},[1712,26338,3145],{},[898,26340,16986],{},[898,26342,1659],{"mathvariant":2003},[3690,26344],{"width":3692},[1712,26346,1904],{"stretchy":1903},[1716,26348,26349],{},"7.8",[1712,26351,1910],{"stretchy":1903},[902,26353,26354],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,26356,26357,26358,3245,26361,14897,26374,26377],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,26359,26360],{},"zdaněním domácností",[883,26362,26364],{"className":26363},[886],[888,26365,26366],{"xmlns":890},[892,26367,26368,26372],{},[895,26369,26370],{},[898,26371,1772],{},[902,26373,1772],{"encoding":904},[614,26375,26376],{},"taxation","). Zdanění bývá:",[120,26379,26380,26413,26438],{},[123,26381,26382,26383,3138],{},"úměrné důchodu: ",[883,26384,26386],{"className":26385},[886],[888,26387,26388],{"xmlns":890},[892,26389,26390,26410],{},[895,26391,26392,26394,26396,26398,26400,26402,26404,26406,26408],{},[898,26393,1772],{},[1712,26395,1714],{},[898,26397,1772],{},[1712,26399,1904],{"stretchy":1903},[898,26401,6951],{},[1712,26403,1910],{"stretchy":1903},[1712,26405,1714],{},[898,26407,23730],{},[898,26409,6951],{},[902,26411,26412],{"encoding":904},"T = T(Y) = tY",[123,26414,26415,26416,3138],{},"fixní: ",[883,26417,26419],{"className":26418},[886],[888,26420,26421],{"xmlns":890},[892,26422,26423,26435],{},[895,26424,26425,26427,26429],{},[898,26426,1772],{},[1712,26428,1714],{},[2037,26430,26431,26433],{},[898,26432,1772],{},[1712,26434,2145],{},[902,26436,26437],{"encoding":904},"T = T^*",[123,26439,26440,26441,26469,26470,1659],{},"kombinované: ",[883,26442,26444],{"className":26443},[886],[888,26445,26446],{"xmlns":890},[892,26447,26448,26466],{},[895,26449,26450,26452,26454,26460,26462,26464],{},[898,26451,1772],{},[1712,26453,1714],{},[2037,26455,26456,26458],{},[898,26457,1772],{},[1712,26459,2145],{},[1712,26461,3145],{},[898,26463,23730],{},[898,26465,6951],{},[902,26467,26468],{"encoding":904},"T = T^* + tY",", kde ",[883,26471,26473],{"className":26472},[886],[888,26474,26475],{"xmlns":890},[892,26476,26477,26489],{},[895,26478,26479,26481,26483,26485,26487],{},[1716,26480,2085],{},[1712,26482,5496],{},[898,26484,23730],{},[1712,26486,2252],{},[1716,26488,2222],{},[902,26490,26491],{"encoding":904},"0 \\le t \u003C 1",[1636,26493,26494],{},[724,26495,26496,26498,26499,26520,26521,26524,26525,26538,26539,17002,26565,3245,26568,26594,26595,26623,26624,1655,26637,26655],{},[883,26497,2203],{}," Pozor na disponibilní důchod\nV modelu ",[883,26500,26502],{"className":26501},[886],[888,26503,26504],{"xmlns":890},[892,26505,26506,26518],{},[895,26507,26508,26510,26512,26514,26516],{},[898,26509,8195],{},[1762,26511,17164],{},[898,26513,17058],{},[1762,26515,17164],{},[898,26517,16986],{},[902,26519,23095],{"encoding":904}," je nutné ",[38,26522,26523],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,26526,26528],{"className":26527},[886],[888,26529,26530],{"xmlns":890},[892,26531,26532,26536],{},[895,26533,26534],{},[898,26535,6951],{},[902,26537,6951],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,26540,26542],{"className":26541},[886],[888,26543,26544],{"xmlns":890},[892,26545,26546,26562],{},[895,26547,26548,26550,26552,26554,26556,26558,26560],{},[898,26549,6951],{},[1712,26551,1714],{},[898,26553,8195],{},[1712,26555,3145],{},[898,26557,17058],{},[1712,26559,3145],{},[898,26561,16986],{},[902,26563,26564],{"encoding":904},"Y = C + I + G",[38,26566,26567],{},"disponibilní důchod",[883,26569,26571],{"className":26570},[886],[888,26572,26573],{"xmlns":890},[892,26574,26575,26591],{},[895,26576,26577,26583,26585,26587,26589],{},[6927,26578,26579,26581],{},[898,26580,6951],{},[898,26582,1969],{},[1712,26584,1714],{},[898,26586,6951],{},[1712,26588,2219],{},[898,26590,1772],{},[902,26592,26593],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,26596,26598],{"className":26597},[886],[888,26599,26600],{"xmlns":890},[892,26601,26602,26620],{},[895,26603,26604,26606,26608,26610,26612,26618],{},[898,26605,8195],{},[1712,26607,1714],{},[898,26609,8195],{},[1712,26611,1904],{"stretchy":1903},[6927,26613,26614,26616],{},[898,26615,6951],{},[898,26617,1969],{},[1712,26619,1910],{"stretchy":1903},[902,26621,26622],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,26625,26627],{"className":26626},[886],[888,26628,26629],{"xmlns":890},[892,26630,26631,26635],{},[895,26632,26633],{},[898,26634,6951],{},[902,26636,6951],{"encoding":904},[883,26638,26640],{"className":26639},[886],[888,26641,26642],{"xmlns":890},[892,26643,26644,26652],{},[895,26645,26646],{},[6927,26647,26648,26650],{},[898,26649,6951],{},[898,26651,1969],{},[902,26653,26654],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,26657,26658,14897,26661,1910],{},[38,26659,26660],{},"Disponibilní důchod",[614,26662,26663],{},"disposable income",[724,26665,26666],{},[883,26667,26669],{"className":26668},[886],[888,26670,26671],{"xmlns":890},[892,26672,26673,26689],{},[895,26674,26675,26681,26683,26685,26687],{},[6927,26676,26677,26679],{},[898,26678,6951],{},[898,26680,1969],{},[1712,26682,1714],{},[898,26684,6951],{},[1712,26686,2219],{},[898,26688,1772],{},[902,26690,26593],{"encoding":904},[724,26692,26693,26694,1659],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,26695,26697],{"className":26696},[886],[888,26698,26699],{"xmlns":890},[892,26700,26701,26719],{},[895,26702,26703,26705,26707,26709,26711,26717],{},[898,26704,8195],{},[1712,26706,1714],{},[898,26708,8195],{},[1712,26710,1904],{"stretchy":1903},[6927,26712,26713,26715],{},[898,26714,6951],{},[898,26716,1969],{},[1712,26718,1910],{"stretchy":1903},[902,26720,26622],{"encoding":904},[198,26722,25566],{"id":26723},"soustava-rovnic-1",[724,26725,26726,26727,1343,26748,26770,26771,2854],{},"Pro pevně zadané ",[883,26728,26730],{"className":26729},[886],[888,26731,26732],{"xmlns":890},[892,26733,26734,26746],{},[895,26735,26736,26738,26740],{},[898,26737,17058],{},[1712,26739,1714],{},[2037,26741,26742,26744],{},[898,26743,17058],{},[1712,26745,2145],{},[902,26747,17069],{"encoding":904},[883,26749,26751],{"className":26750},[886],[888,26752,26753],{"xmlns":890},[892,26754,26755,26767],{},[895,26756,26757,26759,26761],{},[898,26758,16986],{},[1712,26760,1714],{},[2037,26762,26763,26765],{},[898,26764,16986],{},[1712,26766,2145],{},[902,26768,26769],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,26772,26774],{"className":26773},[886],[888,26775,26776],{"xmlns":890},[892,26777,26778,26798],{},[895,26779,26780,26782,26784,26786,26788,26794,26796],{},[898,26781,6951],{},[1712,26783,3138],{"separator":2565},[898,26785,8195],{},[1712,26787,3138],{"separator":2565},[6927,26789,26790,26792],{},[898,26791,6951],{},[898,26793,1969],{},[1712,26795,3138],{"separator":2565},[898,26797,1772],{},[902,26799,26800],{"encoding":904},"Y, C, Y_D, T",[724,26802,26803],{},[883,26804,26806],{"className":26805},[886],[888,26807,26808],{"xmlns":890},[892,26809,26810,26951],{},[895,26811,26812,26942,26944,26946,26949],{},[25629,26813,26814,26852,26880,26912],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,26815,26816,26822],{},[25637,26817,26818],{},[2563,26819,26820],{"scriptlevel":2085,"displaystyle":2565},[898,26821,6951],{},[25637,26823,26824],{},[2563,26825,26826],{"scriptlevel":2085,"displaystyle":2565},[895,26827,26828,26830,26832,26834,26836,26842,26844,26850],{},[895,26829],{},[1712,26831,1714],{},[898,26833,8195],{},[1712,26835,3145],{},[2037,26837,26838,26840],{},[898,26839,17058],{},[1712,26841,2145],{},[1712,26843,3145],{},[2037,26845,26846,26848],{},[898,26847,16986],{},[1712,26849,2145],{},[1712,26851,3138],{"separator":2565},[25634,26853,26854,26860],{},[25637,26855,26856],{},[2563,26857,26858],{"scriptlevel":2085,"displaystyle":2565},[898,26859,1772],{},[25637,26861,26862],{},[2563,26863,26864],{"scriptlevel":2085,"displaystyle":2565},[895,26865,26866,26868,26870,26872,26874,26876,26878],{},[895,26867],{},[1712,26869,1714],{},[898,26871,1772],{},[1712,26873,1904],{"stretchy":1903},[898,26875,6951],{},[1712,26877,1910],{"stretchy":1903},[1712,26879,3138],{"separator":2565},[25634,26881,26882,26888],{},[25637,26883,26884],{},[2563,26885,26886],{"scriptlevel":2085,"displaystyle":2565},[898,26887,8195],{},[25637,26889,26890],{},[2563,26891,26892],{"scriptlevel":2085,"displaystyle":2565},[895,26893,26894,26896,26898,26900,26902,26908,26910],{},[895,26895],{},[1712,26897,1714],{},[898,26899,8195],{},[1712,26901,1904],{"stretchy":1903},[6927,26903,26904,26906],{},[898,26905,6951],{},[898,26907,1969],{},[1712,26909,1910],{"stretchy":1903},[1712,26911,3138],{"separator":2565},[25634,26913,26914,26924],{},[25637,26915,26916],{},[2563,26917,26918],{"scriptlevel":2085,"displaystyle":2565},[6927,26919,26920,26922],{},[898,26921,6951],{},[898,26923,1969],{},[25637,26925,26926],{},[2563,26927,26928],{"scriptlevel":2085,"displaystyle":2565},[895,26929,26930,26932,26934,26936,26938,26940],{},[895,26931],{},[1712,26933,1714],{},[898,26935,6951],{},[1712,26937,2219],{},[898,26939,1772],{},[1712,26941,3138],{"separator":2565},[3690,26943],{"width":3692},[1712,26945,1904],{"stretchy":1903},[1716,26947,26948],{},"7.9",[1712,26950,1910],{"stretchy":1903},[902,26952,26953],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,26955,26956,26957,27001,27002,1659],{},"s řešeními ",[883,26958,26960],{"className":26959},[886],[888,26961,26962],{"xmlns":890},[892,26963,26964,26998],{},[895,26965,26966,26972,26974,26980,26982,26988,26990],{},[2037,26967,26968,26970],{},[898,26969,6951],{},[898,26971,2041],{},[1712,26973,3138],{"separator":2565},[2037,26975,26976,26978],{},[898,26977,8195],{},[898,26979,2041],{},[1712,26981,3138],{"separator":2565},[2037,26983,26984,26986],{},[898,26985,1772],{},[898,26987,2041],{},[1712,26989,3138],{"separator":2565},[6989,26991,26992,26994,26996],{},[898,26993,6951],{},[898,26995,1969],{},[898,26997,2041],{},[902,26999,27000],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,27003,27005],{"className":27004},[886],[888,27006,27007],{"xmlns":890},[892,27008,27009,27035],{},[895,27010,27011,27017,27019,27027,27029],{},[2037,27012,27013,27015],{},[898,27014,6493],{},[898,27016,2041],{},[1712,27018,1714],{},[6989,27020,27021,27023,27025],{},[898,27022,6951],{},[898,27024,1969],{},[898,27026,2041],{},[1712,27028,2219],{},[2037,27030,27031,27033],{},[898,27032,8195],{},[898,27034,2041],{},[902,27036,27037],{"encoding":904},"S^E = Y_D^E - C^E",[1636,27039,27040,27045],{},[724,27041,27042,27044],{},[883,27043,2370],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,27046,27047,27070,27153,27208,27298],{},[123,27048,27049,27052,27053,1659],{},[38,27050,27051],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,27054,27056],{"className":27055},[886],[888,27057,27058],{"xmlns":890},[892,27059,27060,27068],{},[895,27061,27062],{},[6927,27063,27064,27066],{},[898,27065,6951],{},[898,27067,1969],{},[902,27069,26654],{"encoding":904},[123,27071,27072,27121,27122,27139,27140,1659],{},[38,27073,27074,27075,27095,27096],{},"Dosaď ",[883,27076,27078],{"className":27077},[886],[888,27079,27080],{"xmlns":890},[892,27081,27082,27092],{},[895,27083,27084,27086,27088,27090],{},[898,27085,1772],{},[1712,27087,1904],{"stretchy":1903},[898,27089,6951],{},[1712,27091,1910],{"stretchy":1903},[902,27093,27094],{"encoding":904},"T(Y)"," do ",[883,27097,27099],{"className":27098},[886],[888,27100,27101],{"xmlns":890},[892,27102,27103,27119],{},[895,27104,27105,27111,27113,27115,27117],{},[6927,27106,27107,27109],{},[898,27108,6951],{},[898,27110,1969],{},[1712,27112,1714],{},[898,27114,6951],{},[1712,27116,2219],{},[898,27118,1772],{},[902,27120,26593],{"encoding":904}," — dostaneš ",[883,27123,27125],{"className":27124},[886],[888,27126,27127],{"xmlns":890},[892,27128,27129,27137],{},[895,27130,27131],{},[6927,27132,27133,27135],{},[898,27134,6951],{},[898,27136,1969],{},[902,27138,26654],{"encoding":904}," jako lineární funkci ",[883,27141,27143],{"className":27142},[886],[888,27144,27145],{"xmlns":890},[892,27146,27147,27151],{},[895,27148,27149],{},[898,27150,6951],{},[902,27152,6951],{"encoding":904},[123,27154,27155,27121,27182,27139,27195,1659],{},[38,27156,27074,27157,27181],{},[883,27158,27160],{"className":27159},[886],[888,27161,27162],{"xmlns":890},[892,27163,27164,27178],{},[895,27165,27166,27172,27174,27176],{},[6927,27167,27168,27170],{},[898,27169,6951],{},[898,27171,1969],{},[1712,27173,1904],{"stretchy":1903},[898,27175,6951],{},[1712,27177,1910],{"stretchy":1903},[902,27179,27180],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,27183,27185],{"className":27184},[886],[888,27186,27187],{"xmlns":890},[892,27188,27189,27193],{},[895,27190,27191],{},[898,27192,8195],{},[902,27194,8195],{"encoding":904},[883,27196,27198],{"className":27197},[886],[888,27199,27200],{"xmlns":890},[892,27201,27202,27206],{},[895,27203,27204],{},[898,27205,6951],{},[902,27207,6951],{"encoding":904},[123,27209,27210,3245,27232,27266,27267,27280,27281,1659],{},[38,27211,27074,27212,27231],{},[883,27213,27215],{"className":27214},[886],[888,27216,27217],{"xmlns":890},[892,27218,27219,27229],{},[895,27220,27221,27223,27225,27227],{},[898,27222,8195],{},[1712,27224,1904],{"stretchy":1903},[898,27226,6951],{},[1712,27228,1910],{"stretchy":1903},[902,27230,19090],{"encoding":904}," do podmínky rovnováhy",[883,27233,27235],{"className":27234},[886],[888,27236,27237],{"xmlns":890},[892,27238,27239,27263],{},[895,27240,27241,27243,27245,27247,27249,27255,27257],{},[898,27242,6951],{},[1712,27244,1714],{},[898,27246,8195],{},[1712,27248,3145],{},[2037,27250,27251,27253],{},[898,27252,17058],{},[1712,27254,2145],{},[1712,27256,3145],{},[2037,27258,27259,27261],{},[898,27260,16986],{},[1712,27262,2145],{},[902,27264,27265],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,27268,27270],{"className":27269},[886],[888,27271,27272],{"xmlns":890},[892,27273,27274,27278],{},[895,27275,27276],{},[898,27277,6951],{},[902,27279,6951],{"encoding":904},", odtud ",[883,27282,27284],{"className":27283},[886],[888,27285,27286],{"xmlns":890},[892,27287,27288,27296],{},[895,27289,27290],{},[2037,27291,27292,27294],{},[898,27293,6951],{},[898,27295,2041],{},[902,27297,18777],{"encoding":904},[123,27299,27300,27303,27304,1343,27322,1343,27342,1343,27359,1659],{},[38,27301,27302],{},"Zpětným dosazením"," dopočítej ",[883,27305,27307],{"className":27306},[886],[888,27308,27309],{"xmlns":890},[892,27310,27311,27319],{},[895,27312,27313],{},[2037,27314,27315,27317],{},[898,27316,1772],{},[898,27318,2041],{},[902,27320,27321],{"encoding":904},"T^E",[883,27323,27325],{"className":27324},[886],[888,27326,27327],{"xmlns":890},[892,27328,27329,27339],{},[895,27330,27331],{},[6989,27332,27333,27335,27337],{},[898,27334,6951],{},[898,27336,1969],{},[898,27338,2041],{},[902,27340,27341],{"encoding":904},"Y_D^E",[883,27343,27345],{"className":27344},[886],[888,27346,27347],{"xmlns":890},[892,27348,27349,27357],{},[895,27350,27351],{},[2037,27352,27353,27355],{},[898,27354,8195],{},[898,27356,2041],{},[902,27358,18836],{"encoding":904},[883,27360,27362],{"className":27361},[886],[888,27363,27364],{"xmlns":890},[892,27365,27366,27374],{},[895,27367,27368],{},[2037,27369,27370,27372],{},[898,27371,6493],{},[898,27373,2041],{},[902,27375,27376],{"encoding":904},"S^E",[198,27378,27380],{"id":27379},"příklad-74","Příklad 7.4",[724,27382,25896,27383,27404,27405,1343,27436,1343,27460,1343,27482,27504],{},[883,27384,27386],{"className":27385},[886],[888,27387,27388],{"xmlns":890},[892,27389,27390,27402],{},[895,27391,27392,27394,27396,27398,27400],{},[898,27393,8195],{},[1762,27395,17164],{},[898,27397,17058],{},[1762,27399,17164],{},[898,27401,16986],{},[902,27403,23095],{"encoding":904}," jsou dány ",[883,27406,27408],{"className":27407},[886],[888,27409,27410],{"xmlns":890},[892,27411,27412,27433],{},[895,27413,27414,27416,27418,27421,27423,27429,27431],{},[898,27415,8195],{},[1712,27417,1714],{},[1716,27419,27420],{},"0,9",[1762,27422,2583],{},[6927,27424,27425,27427],{},[898,27426,6951],{},[898,27428,1969],{},[1712,27430,3145],{},[1716,27432,3709],{},[902,27434,27435],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,27437,27439],{"className":27438},[886],[888,27440,27441],{"xmlns":890},[892,27442,27443,27457],{},[895,27444,27445,27447,27449,27451,27453,27455],{},[898,27446,1772],{},[1712,27448,1714],{},[1716,27450,6673],{},[898,27452,6951],{},[1712,27454,3145],{},[1716,27456,2809],{},[902,27458,27459],{"encoding":904},"T = 0{,}2Y + 25",[883,27461,27463],{"className":27462},[886],[888,27464,27465],{"xmlns":890},[892,27466,27467,27479],{},[895,27468,27469,27475,27477],{},[2037,27470,27471,27473],{},[898,27472,17058],{},[1712,27474,2145],{},[1712,27476,1714],{},[1716,27478,19912],{},[902,27480,27481],{"encoding":904},"I^* = 35",[883,27483,27485],{"className":27484},[886],[888,27486,27487],{"xmlns":890},[892,27488,27489,27501],{},[895,27490,27491,27497,27499],{},[2037,27492,27493,27495],{},[898,27494,16986],{},[1712,27496,2145],{},[1712,27498,1714],{},[1716,27500,6857],{},[902,27502,27503],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,27506,27507],{},[883,27508,27510],{"className":27509},[886],[888,27511,27512],{"xmlns":890},[892,27513,27514,27638],{},[25629,27515,27516,27546,27574,27608],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,27517,27518,27524],{},[25637,27519,27520],{},[2563,27521,27522],{"scriptlevel":2085,"displaystyle":2565},[898,27523,6951],{},[25637,27525,27526],{},[2563,27527,27528],{"scriptlevel":2085,"displaystyle":2565},[895,27529,27530,27532,27534,27536,27538,27540,27542,27544],{},[895,27531],{},[1712,27533,1714],{},[898,27535,8195],{},[1712,27537,3145],{},[1716,27539,19912],{},[1712,27541,3145],{},[1716,27543,6857],{},[1712,27545,3138],{"separator":2565},[25634,27547,27548,27554],{},[25637,27549,27550],{},[2563,27551,27552],{"scriptlevel":2085,"displaystyle":2565},[898,27553,1772],{},[25637,27555,27556],{},[2563,27557,27558],{"scriptlevel":2085,"displaystyle":2565},[895,27559,27560,27562,27564,27566,27568,27570,27572],{},[895,27561],{},[1712,27563,1714],{},[1716,27565,6673],{},[898,27567,6951],{},[1712,27569,3145],{},[1716,27571,2809],{},[1712,27573,3138],{"separator":2565},[25634,27575,27576,27582],{},[25637,27577,27578],{},[2563,27579,27580],{"scriptlevel":2085,"displaystyle":2565},[898,27581,8195],{},[25637,27583,27584],{},[2563,27585,27586],{"scriptlevel":2085,"displaystyle":2565},[895,27587,27588,27590,27592,27594,27596,27602,27604,27606],{},[895,27589],{},[1712,27591,1714],{},[1716,27593,27420],{},[1762,27595,2583],{},[6927,27597,27598,27600],{},[898,27599,6951],{},[898,27601,1969],{},[1712,27603,3145],{},[1716,27605,3709],{},[1712,27607,3138],{"separator":2565},[25634,27609,27610,27620],{},[25637,27611,27612],{},[2563,27613,27614],{"scriptlevel":2085,"displaystyle":2565},[6927,27615,27616,27618],{},[898,27617,6951],{},[898,27619,1969],{},[25637,27621,27622],{},[2563,27623,27624],{"scriptlevel":2085,"displaystyle":2565},[895,27625,27626,27628,27630,27632,27634,27636],{},[895,27627],{},[1712,27629,1714],{},[898,27631,6951],{},[1712,27633,2219],{},[898,27635,1772],{},[898,27637,1659],{"mathvariant":2003},[902,27639,27640],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,27642,27643,27646,27647,27701,27702,27748,27749,2854],{},[38,27644,27645],{},"Řešení."," Z definice ",[883,27648,27650],{"className":27649},[886],[888,27651,27652],{"xmlns":890},[892,27653,27654,27698],{},[895,27655,27656,27662,27664,27666,27668,27670,27672,27674,27676,27678,27680,27682,27684,27686,27688,27690,27692,27694,27696],{},[6927,27657,27658,27660],{},[898,27659,6951],{},[898,27661,1969],{},[1712,27663,1714],{},[898,27665,6951],{},[1712,27667,2219],{},[898,27669,1772],{},[1712,27671,1714],{},[898,27673,6951],{},[1712,27675,2219],{},[1712,27677,1904],{"stretchy":1903},[1716,27679,6673],{},[898,27681,6951],{},[1712,27683,3145],{},[1716,27685,2809],{},[1712,27687,1910],{"stretchy":1903},[1712,27689,1714],{},[1716,27691,19463],{},[898,27693,6951],{},[1712,27695,2219],{},[1716,27697,2809],{},[902,27699,27700],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,27703,27705],{"className":27704},[886],[888,27706,27707],{"xmlns":890},[892,27708,27709,27745],{},[895,27710,27711,27713,27715,27717,27719,27721,27723,27725,27727,27729,27731,27733,27735,27738,27740,27742],{},[898,27712,8195],{},[1712,27714,1714],{},[1716,27716,27420],{},[1712,27718,1904],{"stretchy":1903},[1716,27720,19463],{},[898,27722,6951],{},[1712,27724,2219],{},[1716,27726,2809],{},[1712,27728,1910],{"stretchy":1903},[1712,27730,3145],{},[1716,27732,3709],{},[1712,27734,1714],{},[1716,27736,27737],{},"0,72",[898,27739,6951],{},[1712,27741,3145],{},[1716,27743,27744],{},"47,5",[902,27746,27747],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,27750,27752],{"className":27751},[886],[888,27753,27754],{"xmlns":890},[892,27755,27756,27774],{},[895,27757,27758,27760,27762,27764,27766,27768,27770,27772],{},[898,27759,6951],{},[1712,27761,1714],{},[1716,27763,27737],{},[898,27765,6951],{},[1712,27767,3145],{},[1716,27769,27744],{},[1712,27771,3145],{},[1716,27773,26055],{},[902,27775,27776],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,27778,27779],{},[883,27780,27782],{"className":27781},[886],[888,27783,27784],{"xmlns":890},[892,27785,27786,27827],{},[895,27787,27788,27791,27793,27795,27798,27800,27802,27804,27810,27812,27822,27824],{},[1716,27789,27790],{},"0,28",[898,27792,6951],{},[1712,27794,1714],{},[1716,27796,27797],{},"102,5",[1762,27799,1764],{},[1712,27801,19882],{},[1762,27803,1764],{},[2037,27805,27806,27808],{},[898,27807,6951],{},[898,27809,2041],{},[1712,27811,1714],{},[2563,27813,27814],{"scriptlevel":2085,"displaystyle":1903},[2567,27815,27816,27819],{},[1716,27817,27818],{},"5125",[1716,27820,27821],{},"14",[1712,27823,3712],{},[1716,27825,27826],{},"366,071.",[902,27828,27829],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,27831,27832],{},"Rovnovážné veličiny:",[120,27834,27835,27870,27922,27976,28024],{},[123,27836,27837,3138],{},[883,27838,27840],{"className":27839},[886],[888,27841,27842],{"xmlns":890},[892,27843,27844,27867],{},[895,27845,27846,27852,27854,27862,27864],{},[2037,27847,27848,27850],{},[898,27849,6951],{},[898,27851,2041],{},[1712,27853,1714],{},[2563,27855,27856],{"scriptlevel":2085,"displaystyle":1903},[2567,27857,27858,27860],{},[1716,27859,27818],{},[1716,27861,27821],{},[1712,27863,3712],{},[1716,27865,27866],{},"366,071",[902,27868,27869],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,27871,27872,3138],{},[883,27873,27875],{"className":27874},[886],[888,27876,27877],{"xmlns":890},[892,27878,27879,27919],{},[895,27880,27881,27887,27889,27891,27893,27899,27901,27903,27905,27914,27916],{},[2037,27882,27883,27885],{},[898,27884,1772],{},[898,27886,2041],{},[1712,27888,1714],{},[1716,27890,6673],{},[1762,27892,2583],{},[2037,27894,27895,27897],{},[898,27896,6951],{},[898,27898,2041],{},[1712,27900,3145],{},[1716,27902,2809],{},[1712,27904,1714],{},[2563,27906,27907],{"scriptlevel":2085,"displaystyle":1903},[2567,27908,27909,27912],{},[1716,27910,27911],{},"1375",[1716,27913,27821],{},[1712,27915,3712],{},[1716,27917,27918],{},"98,214",[902,27920,27921],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,27923,27924,3138],{},[883,27925,27927],{"className":27926},[886],[888,27928,27929],{"xmlns":890},[892,27930,27931,27973],{},[895,27932,27933,27941,27943,27949,27951,27957,27959,27968,27970],{},[6989,27934,27935,27937,27939],{},[898,27936,6951],{},[898,27938,1969],{},[898,27940,2041],{},[1712,27942,1714],{},[2037,27944,27945,27947],{},[898,27946,6951],{},[898,27948,2041],{},[1712,27950,2219],{},[2037,27952,27953,27955],{},[898,27954,1772],{},[898,27956,2041],{},[1712,27958,1714],{},[2563,27960,27961],{"scriptlevel":2085,"displaystyle":1903},[2567,27962,27963,27966],{},[1716,27964,27965],{},"3750",[1716,27967,27821],{},[1712,27969,3712],{},[1716,27971,27972],{},"267,857",[902,27974,27975],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,27977,27978,3138],{},[883,27979,27981],{"className":27980},[886],[888,27982,27983],{"xmlns":890},[892,27984,27985,28021],{},[895,27986,27987,27993,27995,28001,28003,28005,28007,28016,28018],{},[2037,27988,27989,27991],{},[898,27990,8195],{},[898,27992,2041],{},[1712,27994,1714],{},[2037,27996,27997,27999],{},[898,27998,6951],{},[898,28000,2041],{},[1712,28002,2219],{},[1716,28004,26055],{},[1712,28006,1714],{},[2563,28008,28009],{"scriptlevel":2085,"displaystyle":1903},[2567,28010,28011,28014],{},[1716,28012,28013],{},"4355",[1716,28015,27821],{},[1712,28017,3712],{},[1716,28019,28020],{},"311,071",[902,28022,28023],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,28025,28026,28082],{},[883,28027,28029],{"className":28028},[886],[888,28030,28031],{"xmlns":890},[892,28032,28033,28079],{},[895,28034,28035,28041,28043,28051,28053,28059,28061,28063,28072,28074,28076],{},[2037,28036,28037,28039],{},[898,28038,6493],{},[898,28040,2041],{},[1712,28042,1714],{},[6989,28044,28045,28047,28049],{},[898,28046,6951],{},[898,28048,1969],{},[898,28050,2041],{},[1712,28052,2219],{},[2037,28054,28055,28057],{},[898,28056,8195],{},[898,28058,2041],{},[1712,28060,1714],{},[1712,28062,2219],{},[2563,28064,28065],{"scriptlevel":2085,"displaystyle":1903},[2567,28066,28067,28070],{},[1716,28068,28069],{},"605",[1716,28071,27821],{},[1712,28073,3712],{},[1712,28075,2219],{},[1716,28077,28078],{},"43,214",[902,28080,28081],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,28084,28085,26225,28087,28108,28109,28112,28113,28136,28137,1659],{},[38,28086,26224],{},[883,28088,28090],{"className":28089},[886],[888,28091,28092],{"xmlns":890},[892,28093,28094,28106],{},[895,28095,28096,28098,28100,28102,28104],{},[898,28097,8195],{},[1762,28099,17164],{},[898,28101,17058],{},[1762,28103,17164],{},[898,28105,16986],{},[902,28107,23095],{"encoding":904}," stále uvažuje ",[38,28110,28111],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,28114,28116],{"className":28115},[886],[888,28117,28118],{"xmlns":890},[892,28119,28120,28133],{},[895,28121,28122,28124,28126,28129,28131],{},[898,28123,17194],{},[1712,28125,1714],{},[898,28127,28128],{},"B",[1712,28130,2219],{},[898,28132,4445],{},[902,28134,28135],{"encoding":904},"X = B - M"," dává ",[38,28138,26246,28139],{},[883,28140,28142],{"className":28141},[886],[888,28143,28144],{"xmlns":890},[892,28145,28146,28162],{},[895,28147,28148,28150,28152,28154,28156,28158,28160],{},[898,28149,8195],{},[1762,28151,17164],{},[898,28153,17058],{},[1762,28155,17164],{},[898,28157,16986],{},[1762,28159,17164],{},[898,28161,17194],{},[902,28163,17197],{"encoding":904},[115,28165,28167],{"id":28166},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,28169,25496],{"id":28170},"zadání-modelu-2",[724,28172,28173,28174,3245,28177,26469,28198,28211,28212,17002,28215,28228],{},"Rozšíření o ",[38,28175,28176],{},"čistý export",[883,28178,28180],{"className":28179},[886],[888,28181,28182],{"xmlns":890},[892,28183,28184,28196],{},[895,28185,28186,28188,28190,28192,28194],{},[898,28187,17194],{},[1712,28189,1714],{},[898,28191,28128],{},[1712,28193,2219],{},[898,28195,4445],{},[902,28197,28135],{"encoding":904},[883,28199,28201],{"className":28200},[886],[888,28202,28203],{"xmlns":890},[892,28204,28205,28209],{},[895,28206,28207],{},[898,28208,28128],{},[902,28210,28128],{"encoding":904}," je hrubý export (",[614,28213,28214],{},"brutto export",[883,28216,28218],{"className":28217},[886],[888,28219,28220],{"xmlns":890},[892,28221,28222,28226],{},[895,28223,28224],{},[898,28225,4445],{},[902,28227,4445],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,28230,28231],{},[883,28232,28234],{"className":28233},[886],[888,28235,28236],{"xmlns":890},[892,28237,28238,28258],{},[895,28239,28240,28242,28244,28246,28248,28254,28256],{},[898,28241,4445],{},[1712,28243,1714],{},[898,28245,4445],{},[1712,28247,1904],{"stretchy":1903},[6927,28249,28250,28252],{},[898,28251,6951],{},[898,28253,1969],{},[1712,28255,1910],{"stretchy":1903},[898,28257,1659],{"mathvariant":2003},[902,28259,28260],{"encoding":904},"M = M(Y_D).",[724,28262,28263],{},"Podmínka rovnováhy:",[724,28265,28266],{},[883,28267,28269],{"className":28268},[886],[888,28270,28271],{"xmlns":890},[892,28272,28273,28310],{},[895,28274,28275,28277,28279,28281,28283,28285,28287,28289,28291,28293,28295,28297,28299,28301,28303,28306,28308],{},[898,28276,6951],{},[1712,28278,1714],{},[898,28280,8195],{},[1712,28282,3145],{},[898,28284,17058],{},[1712,28286,3145],{},[898,28288,16986],{},[1712,28290,3145],{},[898,28292,28128],{},[1712,28294,2219],{},[898,28296,4445],{},[898,28298,1659],{"mathvariant":2003},[3690,28300],{"width":3692},[1712,28302,1904],{"stretchy":1903},[1716,28304,28305],{},"7.10",[1762,28307,207],{},[1712,28309,1910],{"stretchy":1903},[902,28311,28312],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,28314,25566],{"id":28315},"soustava-rovnic-2",[724,28317,26726,28318,28352,28353,2854],{},[883,28319,28321],{"className":28320},[886],[888,28322,28323],{"xmlns":890},[892,28324,28325,28349],{},[895,28326,28327,28333,28335,28341,28343],{},[2037,28328,28329,28331],{},[898,28330,17058],{},[1712,28332,2145],{},[1712,28334,3138],{"separator":2565},[2037,28336,28337,28339],{},[898,28338,16986],{},[1712,28340,2145],{},[1712,28342,3138],{"separator":2565},[2037,28344,28345,28347],{},[898,28346,28128],{},[1712,28348,2145],{},[902,28350,28351],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,28354,28356],{"className":28355},[886],[888,28357,28358],{"xmlns":890},[892,28359,28360,28384],{},[895,28361,28362,28364,28366,28368,28370,28372,28374,28380,28382],{},[898,28363,6951],{},[1712,28365,3138],{"separator":2565},[898,28367,8195],{},[1712,28369,3138],{"separator":2565},[898,28371,1772],{},[1712,28373,3138],{"separator":2565},[6927,28375,28376,28378],{},[898,28377,6951],{},[898,28379,1969],{},[1712,28381,3138],{"separator":2565},[898,28383,4445],{},[902,28385,28386],{"encoding":904},"Y, C, T, Y_D, M",[724,28388,28389],{},[883,28390,28392],{"className":28391},[886],[888,28393,28394],{"xmlns":890},[892,28395,28396,28580],{},[895,28397,28398,28572,28574,28576,28578],{},[25629,28399,28400,28432,28462,28490,28522],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,28401,28402,28408],{},[25637,28403,28404],{},[2563,28405,28406],{"scriptlevel":2085,"displaystyle":2565},[898,28407,8195],{},[25637,28409,28410],{},[2563,28411,28412],{"scriptlevel":2085,"displaystyle":2565},[895,28413,28414,28416,28418,28420,28422,28428,28430],{},[895,28415],{},[1712,28417,1714],{},[898,28419,8195],{},[1712,28421,1904],{"stretchy":1903},[6927,28423,28424,28426],{},[898,28425,6951],{},[898,28427,1969],{},[1712,28429,1910],{"stretchy":1903},[1712,28431,3138],{"separator":2565},[25634,28433,28434,28444],{},[25637,28435,28436],{},[2563,28437,28438],{"scriptlevel":2085,"displaystyle":2565},[6927,28439,28440,28442],{},[898,28441,6951],{},[898,28443,1969],{},[25637,28445,28446],{},[2563,28447,28448],{"scriptlevel":2085,"displaystyle":2565},[895,28449,28450,28452,28454,28456,28458,28460],{},[895,28451],{},[1712,28453,1714],{},[898,28455,6951],{},[1712,28457,2219],{},[898,28459,1772],{},[1712,28461,3138],{"separator":2565},[25634,28463,28464,28470],{},[25637,28465,28466],{},[2563,28467,28468],{"scriptlevel":2085,"displaystyle":2565},[898,28469,1772],{},[25637,28471,28472],{},[2563,28473,28474],{"scriptlevel":2085,"displaystyle":2565},[895,28475,28476,28478,28480,28482,28484,28486,28488],{},[895,28477],{},[1712,28479,1714],{},[898,28481,1772],{},[1712,28483,1904],{"stretchy":1903},[898,28485,6951],{},[1712,28487,1910],{"stretchy":1903},[1712,28489,3138],{"separator":2565},[25634,28491,28492,28498],{},[25637,28493,28494],{},[2563,28495,28496],{"scriptlevel":2085,"displaystyle":2565},[898,28497,4445],{},[25637,28499,28500],{},[2563,28501,28502],{"scriptlevel":2085,"displaystyle":2565},[895,28503,28504,28506,28508,28510,28512,28518,28520],{},[895,28505],{},[1712,28507,1714],{},[898,28509,4445],{},[1712,28511,1904],{"stretchy":1903},[6927,28513,28514,28516],{},[898,28515,6951],{},[898,28517,1969],{},[1712,28519,1910],{"stretchy":1903},[1712,28521,3138],{"separator":2565},[25634,28523,28524,28530],{},[25637,28525,28526],{},[2563,28527,28528],{"scriptlevel":2085,"displaystyle":2565},[898,28529,6951],{},[25637,28531,28532],{},[2563,28533,28534],{"scriptlevel":2085,"displaystyle":2565},[895,28535,28536,28538,28540,28542,28544,28550,28552,28558,28560,28566,28568,28570],{},[895,28537],{},[1712,28539,1714],{},[898,28541,8195],{},[1712,28543,3145],{},[2037,28545,28546,28548],{},[898,28547,17058],{},[1712,28549,2145],{},[1712,28551,3145],{},[2037,28553,28554,28556],{},[898,28555,16986],{},[1712,28557,2145],{},[1712,28559,3145],{},[2037,28561,28562,28564],{},[898,28563,28128],{},[1712,28565,2145],{},[1712,28567,2219],{},[898,28569,4445],{},[898,28571,1659],{"mathvariant":2003},[3690,28573],{"width":3692},[1712,28575,1904],{"stretchy":1903},[1716,28577,28305],{},[1712,28579,1910],{"stretchy":1903},[902,28581,28582],{"encoding":904},"\\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)",[198,28584,28586],{"id":28585},"příklad-75","Příklad 7.5",[724,28588,28589,28590,1343,28622,1343,28649,1343,28670,1343,28692,1343,28714,28737],{},"Dáno: ",[883,28591,28593],{"className":28592},[886],[888,28594,28595],{"xmlns":890},[892,28596,28597,28619],{},[895,28598,28599,28601,28603,28606,28608,28614,28616],{},[898,28600,8195],{},[1712,28602,1714],{},[1716,28604,28605],{},"0,75",[1762,28607,2583],{},[6927,28609,28610,28612],{},[898,28611,6951],{},[898,28613,1969],{},[1712,28615,3145],{},[1716,28617,28618],{},"750",[902,28620,28621],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,28623,28625],{"className":28624},[886],[888,28626,28627],{"xmlns":890},[892,28628,28629,28646],{},[895,28630,28631,28633,28635,28638,28640],{},[898,28632,4445],{},[1712,28634,1714],{},[1716,28636,28637],{},"0,15",[1762,28639,2583],{},[6927,28641,28642,28644],{},[898,28643,6951],{},[898,28645,1969],{},[902,28647,28648],{"encoding":904},"M = 0{,}15\\,Y_D",[883,28650,28652],{"className":28651},[886],[888,28653,28654],{"xmlns":890},[892,28655,28656,28667],{},[895,28657,28658,28660,28662,28665],{},[898,28659,1772],{},[1712,28661,1714],{},[1716,28663,28664],{},"0,25",[898,28666,6951],{},[902,28668,28669],{"encoding":904},"T = 0{,}25Y",[883,28671,28673],{"className":28672},[886],[888,28674,28675],{"xmlns":890},[892,28676,28677,28689],{},[895,28678,28679,28685,28687],{},[2037,28680,28681,28683],{},[898,28682,17058],{},[1712,28684,2145],{},[1712,28686,1714],{},[1716,28688,19984],{},[902,28690,28691],{"encoding":904},"I^* = 500",[883,28693,28695],{"className":28694},[886],[888,28696,28697],{"xmlns":890},[892,28698,28699,28711],{},[895,28700,28701,28707,28709],{},[2037,28702,28703,28705],{},[898,28704,16986],{},[1712,28706,2145],{},[1712,28708,1714],{},[1716,28710,6624],{},[902,28712,28713],{"encoding":904},"G^* = 150",[883,28715,28717],{"className":28716},[886],[888,28718,28719],{"xmlns":890},[892,28720,28721,28734],{},[895,28722,28723,28729,28731],{},[2037,28724,28725,28727],{},[898,28726,28128],{},[1712,28728,2145],{},[1712,28730,1714],{},[1716,28732,28733],{},"800",[902,28735,28736],{"encoding":904},"B^* = 800",". Soustava:",[724,28739,28740],{},[883,28741,28743],{"className":28742},[886],[888,28744,28745],{"xmlns":890},[892,28746,28747,28965],{},[25629,28748,28749,28795,28837,28873,28915],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,28750,28751,28767],{},[25637,28752,28753],{},[2563,28754,28755],{"scriptlevel":2085,"displaystyle":2565},[895,28756,28757,28759,28761,28763,28765],{},[1712,28758,1904],{"stretchy":1903},[898,28760,16915],{},[1716,28762,2222],{},[1712,28764,1910],{"stretchy":1903},[1762,28766,7722],{},[25637,28768,28769],{},[2563,28770,28771],{"scriptlevel":2085,"displaystyle":2565},[895,28772,28773,28775,28777,28779,28781,28783,28789,28791,28793],{},[895,28774],{},[898,28776,8195],{},[1712,28778,1714],{},[1716,28780,28605],{},[1762,28782,2583],{},[6927,28784,28785,28787],{},[898,28786,6951],{},[898,28788,1969],{},[1712,28790,3145],{},[1716,28792,28618],{},[1712,28794,3138],{"separator":2565},[25634,28796,28797,28813],{},[25637,28798,28799],{},[2563,28800,28801],{"scriptlevel":2085,"displaystyle":2565},[895,28802,28803,28805,28807,28809,28811],{},[1712,28804,1904],{"stretchy":1903},[898,28806,16915],{},[1716,28808,2787],{},[1712,28810,1910],{"stretchy":1903},[1762,28812,7722],{},[25637,28814,28815],{},[2563,28816,28817],{"scriptlevel":2085,"displaystyle":2565},[895,28818,28819,28821,28827,28829,28831,28833,28835],{},[895,28820],{},[6927,28822,28823,28825],{},[898,28824,6951],{},[898,28826,1969],{},[1712,28828,1714],{},[898,28830,6951],{},[1712,28832,2219],{},[898,28834,1772],{},[1712,28836,3138],{"separator":2565},[25634,28838,28839,28855],{},[25637,28840,28841],{},[2563,28842,28843],{"scriptlevel":2085,"displaystyle":2565},[895,28844,28845,28847,28849,28851,28853],{},[1712,28846,1904],{"stretchy":1903},[898,28848,16915],{},[1716,28850,6198],{},[1712,28852,1910],{"stretchy":1903},[1762,28854,7722],{},[25637,28856,28857],{},[2563,28858,28859],{"scriptlevel":2085,"displaystyle":2565},[895,28860,28861,28863,28865,28867,28869,28871],{},[895,28862],{},[898,28864,1772],{},[1712,28866,1714],{},[1716,28868,28664],{},[898,28870,6951],{},[1712,28872,3138],{"separator":2565},[25634,28874,28875,28891],{},[25637,28876,28877],{},[2563,28878,28879],{"scriptlevel":2085,"displaystyle":2565},[895,28880,28881,28883,28885,28887,28889],{},[1712,28882,1904],{"stretchy":1903},[898,28884,16915],{},[1716,28886,2975],{},[1712,28888,1910],{"stretchy":1903},[1762,28890,7722],{},[25637,28892,28893],{},[2563,28894,28895],{"scriptlevel":2085,"displaystyle":2565},[895,28896,28897,28899,28901,28903,28905,28907,28913],{},[895,28898],{},[898,28900,4445],{},[1712,28902,1714],{},[1716,28904,28637],{},[1762,28906,2583],{},[6927,28908,28909,28911],{},[898,28910,6951],{},[898,28912,1969],{},[1712,28914,3138],{"separator":2565},[25634,28916,28917,28933],{},[25637,28918,28919],{},[2563,28920,28921],{"scriptlevel":2085,"displaystyle":2565},[895,28922,28923,28925,28927,28929,28931],{},[1712,28924,1904],{"stretchy":1903},[898,28926,16915],{},[1716,28928,3068],{},[1712,28930,1910],{"stretchy":1903},[1762,28932,7722],{},[25637,28934,28935],{},[2563,28936,28937],{"scriptlevel":2085,"displaystyle":2565},[895,28938,28939,28941,28943,28945,28947,28949,28951,28953,28955,28957,28959,28961,28963],{},[895,28940],{},[898,28942,6951],{},[1712,28944,1714],{},[898,28946,8195],{},[1712,28948,3145],{},[1716,28950,19984],{},[1712,28952,3145],{},[1716,28954,6624],{},[1712,28956,3145],{},[1716,28958,28733],{},[1712,28960,2219],{},[898,28962,4445],{},[898,28964,1659],{"mathvariant":2003},[902,28966,28967],{"encoding":904},"\\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}",[724,28969,28970,28971,29005],{},"Postupná substituce — z (r3) do (r2): ",[883,28972,28974],{"className":28973},[886],[888,28975,28976],{"xmlns":890},[892,28977,28978,29002],{},[895,28979,28980,28986,28988,28990,28992,28994,28996,28998,29000],{},[6927,28981,28982,28984],{},[898,28983,6951],{},[898,28985,1969],{},[1712,28987,1714],{},[898,28989,6951],{},[1712,28991,2219],{},[1716,28993,28664],{},[898,28995,6951],{},[1712,28997,1714],{},[1716,28999,28605],{},[898,29001,6951],{},[902,29003,29004],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,29007,29008],{},[883,29009,29011],{"className":29010},[886],[888,29012,29013],{"xmlns":890},[892,29014,29015,29056],{},[895,29016,29017,29019,29021,29023,29025,29027,29029,29031,29033,29035,29037,29039,29041,29043,29045,29048,29050,29052,29054],{},[1712,29018,1904],{"stretchy":1903},[898,29020,16915],{},[1716,29022,6209],{},[1712,29024,1910],{"stretchy":1903},[1762,29026,7722],{},[898,29028,8195],{},[1712,29030,1714],{},[1716,29032,28605],{},[1712,29034,1783],{},[1716,29036,28605],{},[898,29038,6951],{},[1712,29040,3145],{},[1716,29042,28618],{},[1712,29044,1714],{},[1716,29046,29047],{},"0,5625",[898,29049,6951],{},[1712,29051,3145],{},[1716,29053,28618],{},[1712,29055,3138],{"separator":2565},[902,29057,29058],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,29060,29061],{},[883,29062,29064],{"className":29063},[886],[888,29065,29066],{"xmlns":890},[892,29067,29068,29102],{},[895,29069,29070,29072,29074,29077,29079,29081,29083,29085,29087,29089,29091,29093,29095,29098,29100],{},[1712,29071,1904],{"stretchy":1903},[898,29073,16915],{},[1716,29075,29076],{},"7",[1712,29078,1910],{"stretchy":1903},[1762,29080,7722],{},[898,29082,4445],{},[1712,29084,1714],{},[1716,29086,28637],{},[1712,29088,1783],{},[1716,29090,28605],{},[898,29092,6951],{},[1712,29094,1714],{},[1716,29096,29097],{},"0,1125",[898,29099,6951],{},[898,29101,1659],{"mathvariant":2003},[902,29103,29104],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,29106,29107],{},"Dosazením do (r5):",[724,29109,29110],{},[883,29111,29113],{"className":29112},[886],[888,29114,29115],{"xmlns":890},[892,29116,29117,29161],{},[895,29118,29119,29121,29123,29125,29127,29129,29131,29133,29135,29137,29139,29141,29143,29145,29147,29149,29151,29154,29156,29158],{},[898,29120,6951],{},[1712,29122,1714],{},[1716,29124,29047],{},[898,29126,6951],{},[1712,29128,3145],{},[1716,29130,28618],{},[1712,29132,3145],{},[1716,29134,19984],{},[1712,29136,3145],{},[1716,29138,6624],{},[1712,29140,3145],{},[1716,29142,28733],{},[1712,29144,2219],{},[1716,29146,29097],{},[898,29148,6951],{},[1712,29150,1714],{},[1716,29152,29153],{},"0,45",[898,29155,6951],{},[1712,29157,3145],{},[1716,29159,29160],{},"2200.",[902,29162,29163],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,29165,29166,29167,3401,29189,29212],{},"Odtud ",[883,29168,29170],{"className":29169},[886],[888,29171,29172],{"xmlns":890},[892,29173,29174,29186],{},[895,29175,29176,29179,29181,29183],{},[1716,29177,29178],{},"0,55",[898,29180,6951],{},[1712,29182,1714],{},[1716,29184,29185],{},"2200",[902,29187,29188],{"encoding":904},"0{,}55Y = 2200",[883,29190,29192],{"className":29191},[886],[888,29193,29194],{"xmlns":890},[892,29195,29196,29209],{},[895,29197,29198,29204,29206],{},[2037,29199,29200,29202],{},[898,29201,6951],{},[898,29203,2041],{},[1712,29205,1714],{},[1716,29207,29208],{},"4000",[902,29210,29211],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,29214,29215,29238,29270,29305,29338,29374],{},[123,29216,29217,3138],{},[883,29218,29220],{"className":29219},[886],[888,29221,29222],{"xmlns":890},[892,29223,29224,29236],{},[895,29225,29226,29232,29234],{},[2037,29227,29228,29230],{},[898,29229,6951],{},[898,29231,2041],{},[1712,29233,1714],{},[1716,29235,29208],{},[902,29237,29211],{"encoding":904},[123,29239,29240,3138],{},[883,29241,29243],{"className":29242},[886],[888,29244,29245],{"xmlns":890},[892,29246,29247,29267],{},[895,29248,29249,29255,29257,29259,29261,29263,29265],{},[2037,29250,29251,29253],{},[898,29252,1772],{},[898,29254,2041],{},[1712,29256,1714],{},[1716,29258,28664],{},[1712,29260,1783],{},[1716,29262,29208],{},[1712,29264,1714],{},[1716,29266,8200],{},[902,29268,29269],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,29271,29272,3138],{},[883,29273,29275],{"className":29274},[886],[888,29276,29277],{"xmlns":890},[892,29278,29279,29302],{},[895,29280,29281,29289,29291,29293,29295,29297,29299],{},[6989,29282,29283,29285,29287],{},[898,29284,6951],{},[898,29286,1969],{},[898,29288,2041],{},[1712,29290,1714],{},[1716,29292,28605],{},[1712,29294,1783],{},[1716,29296,29208],{},[1712,29298,1714],{},[1716,29300,29301],{},"3000",[902,29303,29304],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,29306,29307,3138],{},[883,29308,29310],{"className":29309},[886],[888,29311,29312],{"xmlns":890},[892,29313,29314,29335],{},[895,29315,29316,29322,29324,29326,29328,29330,29332],{},[2037,29317,29318,29320],{},[898,29319,4445],{},[898,29321,2041],{},[1712,29323,1714],{},[1716,29325,28637],{},[1712,29327,1783],{},[1716,29329,29301],{},[1712,29331,1714],{},[1716,29333,29334],{},"450",[902,29336,29337],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,29339,29340,3138],{},[883,29341,29343],{"className":29342},[886],[888,29344,29345],{"xmlns":890},[892,29346,29347,29371],{},[895,29348,29349,29355,29357,29359,29361,29363,29365,29367,29369],{},[2037,29350,29351,29353],{},[898,29352,8195],{},[898,29354,2041],{},[1712,29356,1714],{},[1716,29358,28605],{},[1712,29360,1783],{},[1716,29362,29301],{},[1712,29364,3145],{},[1716,29366,28618],{},[1712,29368,1714],{},[1716,29370,29301],{},[902,29372,29373],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,29375,29376,29416],{},[883,29377,29379],{"className":29378},[886],[888,29380,29381],{"xmlns":890},[892,29382,29383,29413],{},[895,29384,29385,29391,29393,29401,29403,29409,29411],{},[2037,29386,29387,29389],{},[898,29388,6493],{},[898,29390,2041],{},[1712,29392,1714],{},[6989,29394,29395,29397,29399],{},[898,29396,6951],{},[898,29398,1969],{},[898,29400,2041],{},[1712,29402,2219],{},[2037,29404,29405,29407],{},[898,29406,8195],{},[898,29408,2041],{},[1712,29410,1714],{},[1716,29412,2085],{},[902,29414,29415],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,29418,29419,29421,29422,1343,29439,1655,29460,29485,29486,29489,29490,29503,29504,1659],{},[38,29420,26224],{}," Modely ",[883,29423,29425],{"className":29424},[886],[888,29426,29427],{"xmlns":890},[892,29428,29429,29437],{},[895,29430,29431,29433,29435],{},[898,29432,8195],{},[1762,29434,17164],{},[898,29436,17058],{},[902,29438,17169],{"encoding":904},[883,29440,29442],{"className":29441},[886],[888,29443,29444],{"xmlns":890},[892,29445,29446,29458],{},[895,29447,29448,29450,29452,29454,29456],{},[898,29449,8195],{},[1762,29451,17164],{},[898,29453,17058],{},[1762,29455,17164],{},[898,29457,16986],{},[902,29459,23095],{"encoding":904},[883,29461,29463],{"className":29462},[886],[888,29464,29465],{"xmlns":890},[892,29466,29467,29483],{},[895,29468,29469,29471,29473,29475,29477,29479,29481],{},[898,29470,8195],{},[1762,29472,17164],{},[898,29474,17058],{},[1762,29476,17164],{},[898,29478,16986],{},[1762,29480,17164],{},[898,29482,17194],{},[902,29484,17197],{"encoding":904}," pokládají investice za ",[38,29487,29488],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,29491,29493],{"className":29492},[886],[888,29494,29495],{"xmlns":890},[892,29496,29497,29501],{},[895,29498,29499],{},[898,29500,16915],{},[902,29502,16915],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,29505,29506],{},"model IS-LM",[115,29508,29510],{"id":29509},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,29512,29513,29514,29518,29519,29522,29523,29526],{},"V článku ",[207,29515,29517],{"className":29516,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,29520,29521],{},"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 ",[38,29524,29525],{},"výraznější"," než v mikroekonomických modelech.",[724,29528,29529],{},[3817,29530],{"alt":29531,"className":29532,"src":29533},"imek-multiplikatorovy-efekt-chain",[210,3821],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,29535,17038,29536,1343,29553,1343,29574,29599,29600,29603,29604,29622,29623,29641,29642,29660,29661,29664,29665,1343,29682,29699,29700,29702],{},[883,29537,29539],{"className":29538},[886],[888,29540,29541],{"xmlns":890},[892,29542,29543,29551],{},[895,29544,29545,29547,29549],{},[898,29546,8195],{},[1762,29548,17164],{},[898,29550,17058],{},[902,29552,17169],{"encoding":904},[883,29554,29556],{"className":29555},[886],[888,29557,29558],{"xmlns":890},[892,29559,29560,29572],{},[895,29561,29562,29564,29566,29568,29570],{},[898,29563,8195],{},[1762,29565,17164],{},[898,29567,17058],{},[1762,29569,17164],{},[898,29571,16986],{},[902,29573,23095],{"encoding":904},[883,29575,29577],{"className":29576},[886],[888,29578,29579],{"xmlns":890},[892,29580,29581,29597],{},[895,29582,29583,29585,29587,29589,29591,29593,29595],{},[898,29584,8195],{},[1762,29586,17164],{},[898,29588,17058],{},[1762,29590,17164],{},[898,29592,16986],{},[1762,29594,17164],{},[898,29596,17194],{},[902,29598,17197],{"encoding":904}," se vyšetřuje vliv změn ",[38,29601,29602],{},"exogenních"," veličin (plánovaných investic ",[883,29605,29607],{"className":29606},[886],[888,29608,29609],{"xmlns":890},[892,29610,29611,29619],{},[895,29612,29613],{},[2037,29614,29615,29617],{},[898,29616,17058],{},[1712,29618,2145],{},[902,29620,29621],{"encoding":904},"I^*",", vládních výdajů ",[883,29624,29626],{"className":29625},[886],[888,29627,29628],{"xmlns":890},[892,29629,29630,29638],{},[895,29631,29632],{},[2037,29633,29634,29636],{},[898,29635,16986],{},[1712,29637,2145],{},[902,29639,29640],{"encoding":904},"G^*",", exportu ",[883,29643,29645],{"className":29644},[886],[888,29646,29647],{"xmlns":890},[892,29648,29649,29657],{},[895,29650,29651],{},[2037,29652,29653,29655],{},[898,29654,28128],{},[1712,29656,2145],{},[902,29658,29659],{"encoding":904},"B^*",") na změny ",[38,29662,29663],{},"endogenních"," rovnovážných veličin (",[883,29666,29668],{"className":29667},[886],[888,29669,29670],{"xmlns":890},[892,29671,29672,29680],{},[895,29673,29674],{},[2037,29675,29676,29678],{},[898,29677,6951],{},[898,29679,2041],{},[902,29681,18777],{"encoding":904},[883,29683,29685],{"className":29684},[886],[888,29686,29687],{"xmlns":890},[892,29688,29689,29697],{},[895,29690,29691],{},[2037,29692,29693,29695],{},[898,29694,8195],{},[898,29696,2041],{},[902,29698,18836],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,29701,22852],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,29704,29706],{"id":29705},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,29708,25770,29709,29732,29733,29777],{},[883,29710,29712],{"className":29711},[886],[888,29713,29714],{"xmlns":890},[892,29715,29716,29730],{},[895,29717,29718,29720,29722,29724,29726,29728],{},[898,29719,8195],{},[1712,29721,1714],{},[898,29723,207],{},[898,29725,6951],{},[1712,29727,3145],{},[898,29729,7544],{},[902,29731,23795],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,29734,29736],{"className":29735},[886],[888,29737,29738],{"xmlns":890},[892,29739,29740,29774],{},[895,29741,29742,29748,29750],{},[2037,29743,29744,29746],{},[898,29745,6951],{},[898,29747,2041],{},[1712,29749,1714],{},[2563,29751,29752],{"scriptlevel":2085,"displaystyle":2565},[2567,29753,29754,29766],{},[895,29755,29756,29758,29760],{},[898,29757,7544],{},[1712,29759,3145],{},[2037,29761,29762,29764],{},[898,29763,17058],{},[1712,29765,2145],{},[895,29767,29768,29770,29772],{},[1716,29769,2222],{},[1712,29771,2219],{},[898,29773,207],{},[902,29775,29776],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,29779,29780],{},[883,29781,29783],{"className":29782},[886],[888,29784,29785],{"xmlns":890},[892,29786,29787,29856],{},[895,29788,29789,29807,29809,29839,29841],{},[2567,29790,29791,29801],{},[895,29792,29793,29795],{},[898,29794,14744],{"mathvariant":2003},[2037,29796,29797,29799],{},[898,29798,6951],{},[898,29800,2041],{},[895,29802,29803,29805],{},[898,29804,14744],{"mathvariant":2003},[898,29806,207],{},[1712,29808,1714],{},[2567,29810,29811,29823],{},[895,29812,29813,29815,29817],{},[898,29814,7544],{},[1712,29816,3145],{},[2037,29818,29819,29821],{},[898,29820,17058],{},[1712,29822,2145],{},[895,29824,29825,29827,29829,29831,29833],{},[1712,29826,1904],{"stretchy":1903},[1716,29828,2222],{},[1712,29830,2219],{},[898,29832,207],{},[2037,29834,29835,29837],{},[1712,29836,1910],{"stretchy":1903},[1716,29838,2787],{},[3690,29840],{"width":3692},[895,29842,29843,29846,29853],{},[1762,29844,29845],{},"(multiplik",[6205,29847,29848,29850],{"accent":2565},[1762,29849,207],{},[1712,29851,29852],{},"ˊ",[1762,29854,29855],{},"tor MPC)",[902,29857,29858],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,29860,29861],{},[883,29862,29864],{"className":29863},[886],[888,29865,29866],{"xmlns":890},[892,29867,29868,29937],{},[895,29869,29870,29888,29890,29902,29904],{},[2567,29871,29872,29882],{},[895,29873,29874,29876],{},[898,29875,14744],{"mathvariant":2003},[2037,29877,29878,29880],{},[898,29879,6951],{},[898,29881,2041],{},[895,29883,29884,29886],{},[898,29885,14744],{"mathvariant":2003},[898,29887,7544],{},[1712,29889,1714],{},[2567,29891,29892,29894],{},[1716,29893,2222],{},[895,29895,29896,29898,29900],{},[1716,29897,2222],{},[1712,29899,2219],{},[898,29901,207],{},[3690,29903],{"width":3692},[895,29905,29906,29908,29914,29917,29924,29927,29934],{},[1762,29907,29845],{},[6205,29909,29910,29912],{"accent":2565},[1762,29911,207],{},[1712,29913,29852],{},[1762,29915,29916],{},"tor autonomn",[6205,29918,29919,29922],{"accent":2565},[1762,29920,29921],{},"ı",[1712,29923,29852],{},[1762,29925,29926],{}," spot",[6205,29928,29929,29931],{"accent":2565},[1762,29930,16915],{},[1712,29932,29933],{},"ˇ",[1762,29935,29936],{},"eby)",[902,29938,29939],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,29941,29942],{},[883,29943,29945],{"className":29944},[886],[888,29946,29947],{"xmlns":890},[892,29948,29949,30016],{},[895,29950,29951,29973,29975,29987,29989,30001,30003],{},[2567,29952,29953,29963],{},[895,29954,29955,29957],{},[898,29956,14744],{"mathvariant":2003},[2037,29958,29959,29961],{},[898,29960,6951],{},[898,29962,2041],{},[895,29964,29965,29967],{},[898,29966,14744],{"mathvariant":2003},[2037,29968,29969,29971],{},[898,29970,17058],{},[1712,29972,2145],{},[1712,29974,1714],{},[2567,29976,29977,29979],{},[1716,29978,2222],{},[895,29980,29981,29983,29985],{},[1716,29982,2222],{},[1712,29984,2219],{},[898,29986,207],{},[1712,29988,1714],{},[2567,29990,29991,29993],{},[1716,29992,2222],{},[895,29994,29995,29997,29999],{},[898,29996,4445],{},[898,29998,1710],{},[898,30000,6493],{},[3690,30002],{"width":3692},[895,30004,30005,30007,30013],{},[1762,30006,29845],{},[6205,30008,30009,30011],{"accent":2565},[1762,30010,207],{},[1712,30012,29852],{},[1762,30014,30015],{},"tor investic)",[902,30017,30018],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1636,30020,30021],{},[724,30022,30023,30025,30026,30029,30030,30043,30044,30061,30062,30080,30081,30125,30126,26295,30143,30146,30147,30164],{},[883,30024,1941],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,30027,30028],{},"důchodem","; z něj se utratí ",[883,30031,30033],{"className":30032},[886],[888,30034,30035],{"xmlns":890},[892,30036,30037,30041],{},[895,30038,30039],{},[898,30040,207],{},[902,30042,207],{"encoding":904}," Kč (= ",[883,30045,30047],{"className":30046},[886],[888,30048,30049],{"xmlns":890},[892,30050,30051,30059],{},[895,30052,30053,30055,30057],{},[898,30054,4445],{},[898,30056,1710],{},[898,30058,8195],{},[902,30060,22920],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,30063,30065],{"className":30064},[886],[888,30066,30067],{"xmlns":890},[892,30068,30069,30077],{},[895,30070,30071],{},[2037,30072,30073,30075],{},[898,30074,207],{},[1716,30076,2787],{},[902,30078,30079],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,30082,30084],{"className":30083},[886],[888,30085,30086],{"xmlns":890},[892,30087,30088,30122],{},[895,30089,30090,30092,30094,30096,30098,30104,30106,30108,30110],{},[1716,30091,2222],{},[1712,30093,3145],{},[898,30095,207],{},[1712,30097,3145],{},[2037,30099,30100,30102],{},[898,30101,207],{},[1716,30103,2787],{},[1712,30105,3145],{},[1712,30107,22980],{},[1712,30109,1714],{},[2567,30111,30112,30114],{},[1716,30113,2222],{},[895,30115,30116,30118,30120],{},[1716,30117,2222],{},[1712,30119,2219],{},[898,30121,207],{},[902,30123,30124],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,30127,30129],{"className":30128},[886],[888,30130,30131],{"xmlns":890},[892,30132,30133,30141],{},[895,30134,30135],{},[2037,30136,30137,30139],{},[898,30138,6951],{},[898,30140,2041],{},[902,30142,18777],{"encoding":904},[38,30144,30145],{},"více"," než korunu — čím vyšší ",[883,30148,30150],{"className":30149},[886],[888,30151,30152],{"xmlns":890},[892,30153,30154,30162],{},[895,30155,30156,30158,30160],{},[898,30157,4445],{},[898,30159,1710],{},[898,30161,8195],{},[902,30163,22920],{"encoding":904},", tím silnější multiplikační efekt.",[724,30166,30167,30170,30171,30197,30198,30201,30202,1655,30223,30248,30249,1659],{},[38,30168,30169],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,30172,30174],{"className":30173},[886],[888,30175,30176],{"xmlns":890},[892,30177,30178,30194],{},[895,30179,30180],{},[2563,30181,30182],{"scriptlevel":2085,"displaystyle":1903},[2567,30183,30184,30186],{},[1716,30185,2222],{},[895,30187,30188,30190,30192],{},[1716,30189,2222],{},[1712,30191,2219],{},[898,30193,207],{},[902,30195,30196],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,30199,30200],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,30203,30205],{"className":30204},[886],[888,30206,30207],{"xmlns":890},[892,30208,30209,30221],{},[895,30210,30211,30213,30215,30217,30219],{},[898,30212,8195],{},[1762,30214,17164],{},[898,30216,17058],{},[1762,30218,17164],{},[898,30220,16986],{},[902,30222,23095],{"encoding":904},[883,30224,30226],{"className":30225},[886],[888,30227,30228],{"xmlns":890},[892,30229,30230,30246],{},[895,30231,30232,30234,30236,30238,30240,30242,30244],{},[898,30233,8195],{},[1762,30235,17164],{},[898,30237,17058],{},[1762,30239,17164],{},[898,30241,16986],{},[1762,30243,17164],{},[898,30245,17194],{},[902,30247,17197],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,30250,30252],{"className":30251,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,30254,30256],{"id":30255},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,30258,17038,30259,1343,30276,1655,30297,17043,30322,14897,30325,30346,30347,3245,30350,30363,30364,3481,30393,30410,30411,30414,30415,30417,30418,30439],{},[883,30260,30262],{"className":30261},[886],[888,30263,30264],{"xmlns":890},[892,30265,30266,30274],{},[895,30267,30268,30270,30272],{},[898,30269,8195],{},[1762,30271,17164],{},[898,30273,17058],{},[902,30275,17169],{"encoding":904},[883,30277,30279],{"className":30278},[886],[888,30280,30281],{"xmlns":890},[892,30282,30283,30295],{},[895,30284,30285,30287,30289,30291,30293],{},[898,30286,8195],{},[1762,30288,17164],{},[898,30290,17058],{},[1762,30292,17164],{},[898,30294,16986],{},[902,30296,23095],{"encoding":904},[883,30298,30300],{"className":30299},[886],[888,30301,30302],{"xmlns":890},[892,30303,30304,30320],{},[895,30305,30306,30308,30310,30312,30314,30316,30318],{},[898,30307,8195],{},[1762,30309,17164],{},[898,30311,17058],{},[1762,30313,17164],{},[898,30315,16986],{},[1762,30317,17164],{},[898,30319,17194],{},[902,30321,17197],{"encoding":904},[38,30323,30324],{},"investice konstantní",[883,30326,30328],{"className":30327},[886],[888,30329,30330],{"xmlns":890},[892,30331,30332,30344],{},[895,30333,30334,30336,30338],{},[898,30335,17058],{},[1712,30337,1714],{},[2037,30339,30340,30342],{},[898,30341,17058],{},[1712,30343,2145],{},[902,30345,17069],{"encoding":904},"). Reálnější je předpoklad, že ",[38,30348,30349],{},"investice závisejí na úrokové míře",[883,30351,30353],{"className":30352},[886],[888,30354,30355],{"xmlns":890},[892,30356,30357,30361],{},[895,30358,30359],{},[898,30360,16915],{},[902,30362,16915],{"encoding":904}," — klesající funkce ",[883,30365,30367],{"className":30366},[886],[888,30368,30369],{"xmlns":890},[892,30370,30371,30391],{},[895,30372,30373,30375,30377,30379,30381,30383,30385,30387,30389],{},[898,30374,17058],{},[1712,30376,1904],{"stretchy":1903},[898,30378,16915],{},[1712,30380,1910],{"stretchy":1903},[1712,30382,1714],{},[898,30384,7585],{},[898,30386,16915],{},[1712,30388,3145],{},[898,30390,2468],{},[902,30392,20631],{"encoding":904},[883,30394,30396],{"className":30395},[886],[888,30397,30398],{"xmlns":890},[892,30399,30400,30408],{},[895,30401,30402,30404,30406],{},[898,30403,7585],{},[1712,30405,2252],{},[1716,30407,2085],{},[902,30409,17389],{"encoding":904},". Přidáním ",[38,30412,30413],{},"trhu peněz"," k trhu zboží vzniká model ",[38,30416,16885],{}," se dvěma neznámými ",[883,30419,30421],{"className":30420},[886],[888,30422,30423],{"xmlns":890},[892,30424,30425,30437],{},[895,30426,30427,30429,30431,30433,30435],{},[1712,30428,1904],{"stretchy":1903},[898,30430,6951],{},[1712,30432,3138],{"separator":2565},[898,30434,16915],{},[1712,30436,1910],{"stretchy":1903},[902,30438,23025],{"encoding":904}," a dvěma rovnicemi:",[120,30441,30442,30492],{},[123,30443,30444,14897,30446,30448,30449,30470,30471,1659],{},[38,30445,20720],{},[614,30447,16928],{},") — klesající přímka v rovině ",[883,30450,30452],{"className":30451},[886],[888,30453,30454],{"xmlns":890},[892,30455,30456,30468],{},[895,30457,30458,30460,30462,30464,30466],{},[1712,30459,1904],{"stretchy":1903},[898,30461,16915],{},[1712,30463,3138],{"separator":2565},[898,30465,6951],{},[1712,30467,1910],{"stretchy":1903},[902,30469,17811],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,30472,30474],{"className":30473},[886],[888,30475,30476],{"xmlns":890},[892,30477,30478,30490],{},[895,30479,30480,30482,30484,30486,30488],{},[898,30481,6951],{},[1712,30483,1714],{},[898,30485,8195],{},[1712,30487,3145],{},[898,30489,17058],{},[902,30491,19618],{"encoding":904},[123,30493,30494,14897,30496,30498,30499,26469,30524,30570],{},[38,30495,20919],{},[614,30497,16935],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,30500,30502],{"className":30501},[886],[888,30503,30504],{"xmlns":890},[892,30505,30506,30522],{},[895,30507,30508,30514,30516],{},[2037,30509,30510,30512],{},[898,30511,4445],{},[898,30513,1969],{},[1712,30515,1714],{},[2037,30517,30518,30520],{},[898,30519,4445],{},[1712,30521,2145],{},[902,30523,18354],{"encoding":904},[883,30525,30527],{"className":30526},[886],[888,30528,30529],{"xmlns":890},[892,30530,30531,30567],{},[895,30532,30533,30539,30541,30547,30549,30551,30557,30559,30561],{},[2037,30534,30535,30537],{},[898,30536,4445],{},[898,30538,1969],{},[1712,30540,1714],{},[6927,30542,30543,30545],{},[898,30544,18111],{},[1716,30546,2222],{},[898,30548,6951],{},[1712,30550,3145],{},[6927,30552,30553,30555],{},[898,30554,18111],{},[1716,30556,2787],{},[898,30558,16915],{},[1712,30560,3145],{},[6927,30562,30563,30565],{},[898,30564,18111],{},[1716,30566,6198],{},[902,30568,30569],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,30572,30573,3245,30576,30609,30610,30612,30613,30615],{},[38,30574,30575],{},"Simultánní rovnovážný bod",[883,30577,30579],{"className":30578},[886],[888,30580,30581],{"xmlns":890},[892,30582,30583,30607],{},[895,30584,30585,30587,30589,30591,30597,30599,30605],{},[898,30586,2041],{},[1712,30588,1714],{},[1712,30590,1904],{"stretchy":1903},[2037,30592,30593,30595],{},[898,30594,16915],{},[898,30596,2041],{},[1712,30598,3138],{"separator":2565},[2037,30600,30601,30603],{},[898,30602,6951],{},[898,30604,2041],{},[1712,30606,1910],{"stretchy":1903},[902,30608,21011],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,30611,16973],{}," (posun IS) a ",[38,30614,17005],{}," (posun LM).",[724,30617,30618],{},[38,30619,30620,30621,1343,30643,1343,30665,1343,30687,30709,30710,1659],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,30622,30624],{"className":30623},[886],[888,30625,30626],{"xmlns":890},[892,30627,30628,30640],{},[895,30629,30630,30636,30638],{},[2037,30631,30632,30634],{},[898,30633,6951],{},[898,30635,2041],{},[1712,30637,1714],{},[1716,30639,19989],{},[902,30641,30642],{"encoding":904},"Y^E = 5000",[883,30644,30646],{"className":30645},[886],[888,30647,30648],{"xmlns":890},[892,30649,30650,30662],{},[895,30651,30652,30658,30660],{},[2037,30653,30654,30656],{},[898,30655,16915],{},[898,30657,2041],{},[1712,30659,1714],{},[1716,30661,3068],{},[902,30663,30664],{"encoding":904},"r^E = 5",[883,30666,30668],{"className":30667},[886],[888,30669,30670],{"xmlns":890},[892,30671,30672,30684],{},[895,30673,30674,30680,30682],{},[2037,30675,30676,30678],{},[898,30677,8195],{},[898,30679,2041],{},[1712,30681,1714],{},[1716,30683,20026],{},[902,30685,30686],{"encoding":904},"C^E = 4100",[883,30688,30690],{"className":30689},[886],[888,30691,30692],{"xmlns":890},[892,30693,30694,30706],{},[895,30695,30696,30702,30704],{},[2037,30697,30698,30700],{},[898,30699,17058],{},[898,30701,2041],{},[1712,30703,1714],{},[1716,30705,20065],{},[902,30707,30708],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,30711,945],{"className":30712,"dataFsResolvedFilePath":943,"href":944},[210],[115,30714,30716],{"id":30715},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,30718,30719,30783,30894,31037,31279,31347],{},[123,30720,30721,30724,30725,30747,30748,30782],{},[38,30722,30723],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,30726,30728],{"className":30727},[886],[888,30729,30730],{"xmlns":890},[892,30731,30732,30744],{},[895,30733,30734,30736,30738,30740,30742],{},[898,30735,16986],{},[898,30737,23169],{},[898,30739,1710],{},[1712,30741,3740],{},[898,30743,6951],{},[902,30745,30746],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,30749,30751],{"className":30750},[886],[888,30752,30753],{"xmlns":890},[892,30754,30755,30779],{},[895,30756,30757,30759,30761,30763,30765,30767,30769,30771,30773,30775,30777],{},[898,30758,16986],{},[898,30760,23169],{},[898,30762,1710],{},[1712,30764,1714],{},[898,30766,8195],{},[1712,30768,3145],{},[898,30770,17058],{},[1712,30772,3145],{},[898,30774,16986],{},[1712,30776,3145],{},[898,30778,17194],{},[902,30780,30781],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,30784,30785,30787,30788,30809,30810,1343,30833,30864,30865,30878,30879,1659],{},[38,30786,23403],{}," splňují ",[883,30789,30791],{"className":30790},[886],[888,30792,30793],{"xmlns":890},[892,30794,30795,30807],{},[895,30796,30797,30799,30801,30803,30805],{},[898,30798,6951],{},[1712,30800,1714],{},[898,30802,8195],{},[1712,30804,3145],{},[898,30806,6493],{},[902,30808,17568],{"encoding":904}," (7.2); lineární model ",[883,30811,30813],{"className":30812},[886],[888,30814,30815],{"xmlns":890},[892,30816,30817,30831],{},[895,30818,30819,30821,30823,30825,30827,30829],{},[898,30820,8195],{},[1712,30822,1714],{},[898,30824,207],{},[898,30826,6951],{},[1712,30828,3145],{},[898,30830,7544],{},[902,30832,23795],{"encoding":904},[883,30834,30836],{"className":30835},[886],[888,30837,30838],{"xmlns":890},[892,30839,30840,30862],{},[895,30841,30842,30844,30846,30848,30850,30852,30854,30856,30858,30860],{},[898,30843,6493],{},[1712,30845,1714],{},[1712,30847,1904],{"stretchy":1903},[1716,30849,2222],{},[1712,30851,2219],{},[898,30853,207],{},[1712,30855,1910],{"stretchy":1903},[898,30857,6951],{},[1712,30859,2219],{},[898,30861,7544],{},[902,30863,24044],{"encoding":904}," s autonomní spotřebou ",[883,30866,30868],{"className":30867},[886],[888,30869,30870],{"xmlns":890},[892,30871,30872,30876],{},[895,30873,30874],{},[898,30875,7544],{},[902,30877,7544],{"encoding":904}," a autonomními úsporami ",[883,30880,30882],{"className":30881},[886],[888,30883,30884],{"xmlns":890},[892,30885,30886,30892],{},[895,30887,30888,30890],{},[1712,30889,2219],{},[898,30891,7544],{},[902,30893,24123],{"encoding":904},[123,30895,30896,3245,30899,1343,30929,30959,30960,30990,30991,1343,31012,1659],{},[38,30897,30898],{},"Mezní sklony",[883,30900,30902],{"className":30901},[886],[888,30903,30904],{"xmlns":890},[892,30905,30906,30926],{},[895,30907,30908,30910,30912,30914,30916,30918,30920,30922,30924],{},[898,30909,4445],{},[898,30911,1710],{},[898,30913,8195],{},[1712,30915,1714],{},[898,30917,2468],{"mathvariant":2003},[898,30919,8195],{},[898,30921,2473],{"mathvariant":2003},[898,30923,2468],{"mathvariant":2003},[898,30925,6951],{},[902,30927,30928],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,30930,30932],{"className":30931},[886],[888,30933,30934],{"xmlns":890},[892,30935,30936,30956],{},[895,30937,30938,30940,30942,30944,30946,30948,30950,30952,30954],{},[898,30939,4445],{},[898,30941,1710],{},[898,30943,6493],{},[1712,30945,1714],{},[898,30947,2468],{"mathvariant":2003},[898,30949,6493],{},[898,30951,2473],{"mathvariant":2003},[898,30953,2468],{"mathvariant":2003},[898,30955,6951],{},[902,30957,30958],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,30961,30963],{"className":30962},[886],[888,30964,30965],{"xmlns":890},[892,30966,30967,30987],{},[895,30968,30969,30971,30973,30975,30977,30979,30981,30983,30985],{},[898,30970,4445],{},[898,30972,1710],{},[898,30974,8195],{},[1712,30976,3145],{},[898,30978,4445],{},[898,30980,1710],{},[898,30982,6493],{},[1712,30984,1714],{},[1716,30986,2222],{},[902,30988,30989],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,30992,30994],{"className":30993},[886],[888,30995,30996],{"xmlns":890},[892,30997,30998,31010],{},[895,30999,31000,31002,31004,31006,31008],{},[898,31001,4445],{},[898,31003,1710],{},[898,31005,8195],{},[1712,31007,1714],{},[898,31009,207],{},[902,31011,24764],{"encoding":904},[883,31013,31015],{"className":31014},[886],[888,31016,31017],{"xmlns":890},[892,31018,31019,31035],{},[895,31020,31021,31023,31025,31027,31029,31031,31033],{},[898,31022,4445],{},[898,31024,1710],{},[898,31026,6493],{},[1712,31028,1714],{},[1716,31030,2222],{},[1712,31032,2219],{},[898,31034,207],{},[902,31036,24790],{"encoding":904},[123,31038,31039,31042,31043],{},[38,31040,31041],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,31044,31045,31133,31202],{},[123,31046,31047,31064,31065,31086,31087,3138],{},[883,31048,31050],{"className":31049},[886],[888,31051,31052],{"xmlns":890},[892,31053,31054,31062],{},[895,31055,31056,31058,31060],{},[898,31057,8195],{},[1762,31059,17164],{},[898,31061,17058],{},[902,31063,17169],{"encoding":904},": ",[883,31066,31068],{"className":31067},[886],[888,31069,31070],{"xmlns":890},[892,31071,31072,31084],{},[895,31073,31074,31076,31078,31080,31082],{},[898,31075,6951],{},[1712,31077,1714],{},[898,31079,8195],{},[1712,31081,3145],{},[898,31083,17058],{},[902,31085,19618],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,31088,31090],{"className":31089},[886],[888,31091,31092],{"xmlns":890},[892,31093,31094,31130],{},[895,31095,31096,31102,31104,31106,31108,31110,31116,31118,31120,31122,31124,31126,31128],{},[2037,31097,31098,31100],{},[898,31099,6951],{},[898,31101,2041],{},[1712,31103,1714],{},[1712,31105,1904],{"stretchy":1903},[898,31107,7544],{},[1712,31109,3145],{},[2037,31111,31112,31114],{},[898,31113,17058],{},[1712,31115,2145],{},[1712,31117,1910],{"stretchy":1903},[898,31119,2473],{"mathvariant":2003},[1712,31121,1904],{"stretchy":1903},[1716,31123,2222],{},[1712,31125,2219],{},[898,31127,207],{},[1712,31129,1910],{"stretchy":1903},[902,31131,31132],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,31134,31135,31156,31157,31176,31177,3138],{},[883,31136,31138],{"className":31137},[886],[888,31139,31140],{"xmlns":890},[892,31141,31142,31154],{},[895,31143,31144,31146,31148,31150,31152],{},[898,31145,8195],{},[1762,31147,17164],{},[898,31149,17058],{},[1762,31151,17164],{},[898,31153,16986],{},[902,31155,23095],{"encoding":904},": přidává vládu, zdanění ",[883,31158,31160],{"className":31159},[886],[888,31161,31162],{"xmlns":890},[892,31163,31164,31174],{},[895,31165,31166,31168,31170,31172],{},[898,31167,1772],{},[1712,31169,1904],{"stretchy":1903},[898,31171,6951],{},[1712,31173,1910],{"stretchy":1903},[902,31175,27094],{"encoding":904}," a disponibilní důchod ",[883,31178,31180],{"className":31179},[886],[888,31181,31182],{"xmlns":890},[892,31183,31184,31200],{},[895,31185,31186,31192,31194,31196,31198],{},[6927,31187,31188,31190],{},[898,31189,6951],{},[898,31191,1969],{},[1712,31193,1714],{},[898,31195,6951],{},[1712,31197,2219],{},[898,31199,1772],{},[902,31201,26593],{"encoding":904},[123,31203,31204,31229,31230,26469,31251,1659],{},[883,31205,31207],{"className":31206},[886],[888,31208,31209],{"xmlns":890},[892,31210,31211,31227],{},[895,31212,31213,31215,31217,31219,31221,31223,31225],{},[898,31214,8195],{},[1762,31216,17164],{},[898,31218,17058],{},[1762,31220,17164],{},[898,31222,16986],{},[1762,31224,17164],{},[898,31226,17194],{},[902,31228,17197],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,31231,31233],{"className":31232},[886],[888,31234,31235],{"xmlns":890},[892,31236,31237,31249],{},[895,31238,31239,31241,31243,31245,31247],{},[898,31240,17194],{},[1712,31242,1714],{},[898,31244,28128],{},[1712,31246,2219],{},[898,31248,4445],{},[902,31250,28135],{"encoding":904},[883,31252,31254],{"className":31253},[886],[888,31255,31256],{"xmlns":890},[892,31257,31258,31276],{},[895,31259,31260,31262,31264,31266,31268,31274],{},[898,31261,4445],{},[1712,31263,1714],{},[898,31265,4445],{},[1712,31267,1904],{"stretchy":1903},[6927,31269,31270,31272],{},[898,31271,6951],{},[898,31273,1969],{},[1712,31275,1910],{"stretchy":1903},[902,31277,31278],{"encoding":904},"M = M(Y_D)",[123,31280,31281,31284,31285,3245,31288,31346],{},[38,31282,31283],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,31286,31287],{},"multiplikátor investic",[883,31289,31291],{"className":31290},[886],[888,31292,31293],{"xmlns":890},[892,31294,31295,31343],{},[895,31296,31297,31299,31305,31307,31309,31315,31317,31319,31321,31323,31325,31327,31329,31331,31333,31335,31337,31339,31341],{},[898,31298,14744],{"mathvariant":2003},[2037,31300,31301,31303],{},[898,31302,6951],{},[898,31304,2041],{},[898,31306,2473],{"mathvariant":2003},[898,31308,14744],{"mathvariant":2003},[2037,31310,31311,31313],{},[898,31312,17058],{},[1712,31314,2145],{},[1712,31316,1714],{},[1716,31318,2222],{},[898,31320,2473],{"mathvariant":2003},[1712,31322,1904],{"stretchy":1903},[1716,31324,2222],{},[1712,31326,2219],{},[898,31328,207],{},[1712,31330,1910],{"stretchy":1903},[1712,31332,1714],{},[1716,31334,2222],{},[898,31336,2473],{"mathvariant":2003},[898,31338,4445],{},[898,31340,1710],{},[898,31342,6493],{},[902,31344,31345],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,31348,31349,31351,31352,31367,31368,23523,31385,31400,31401,31426,31427,1659],{},[38,31350,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,31353,31355],{"className":31354},[886],[888,31356,31357],{"xmlns":890},[892,31358,31359,31365],{},[895,31360,31361,31363],{},[898,31362,17058],{},[898,31364,6493],{},[902,31366,16925],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,31369,31371],{"className":31370},[886],[888,31372,31373],{"xmlns":890},[892,31374,31375,31383],{},[895,31376,31377,31379,31381],{},[898,31378,17058],{},[1712,31380,1714],{},[898,31382,6493],{},[902,31384,17586],{"encoding":904},[883,31386,31388],{"className":31387},[886],[888,31389,31390],{"xmlns":890},[892,31391,31392,31398],{},[895,31393,31394,31396],{},[898,31395,14667],{},[898,31397,4445],{},[902,31399,16932],{"encoding":904}," rovnováhu trhu peněz (",[883,31402,31404],{"className":31403},[886],[888,31405,31406],{"xmlns":890},[892,31407,31408,31424],{},[895,31409,31410,31416,31418],{},[2037,31411,31412,31414],{},[898,31413,4445],{},[898,31415,1969],{},[1712,31417,1714],{},[2037,31419,31420,31422],{},[898,31421,4445],{},[1712,31423,2145],{},[902,31425,18354],{"encoding":904},"); průsečík dává ",[883,31428,31430],{"className":31429},[886],[888,31431,31432],{"xmlns":890},[892,31433,31434,31454],{},[895,31435,31436,31438,31444,31446,31452],{},[1712,31437,1904],{"stretchy":1903},[2037,31439,31440,31442],{},[898,31441,6951],{},[898,31443,2041],{},[1712,31445,3138],{"separator":2565},[2037,31447,31448,31450],{},[898,31449,16915],{},[898,31451,2041],{},[1712,31453,1910],{"stretchy":1903},[902,31455,16969],{"encoding":904},[115,31457,20594],{"id":20593},[120,31459,31460,31498,31538,31628,31710,31764,31820,31879,31914,31919,31991,32066,32152,32214,32282,32340,32393,32432],{},[123,31461,31462,4831,31465,30782],{},[38,31463,31464],{},"Hrubý národní produkt (GNP)",[883,31466,31468],{"className":31467},[886],[888,31469,31470],{"xmlns":890},[892,31471,31472,31496],{},[895,31473,31474,31476,31478,31480,31482,31484,31486,31488,31490,31492,31494],{},[898,31475,16986],{},[898,31477,23169],{},[898,31479,1710],{},[1712,31481,1714],{},[898,31483,8195],{},[1712,31485,3145],{},[898,31487,17058],{},[1712,31489,3145],{},[898,31491,16986],{},[1712,31493,3145],{},[898,31495,17194],{},[902,31497,30781],{"encoding":904},[123,31499,31500,31516,31517,1659],{},[38,31501,31502,31503],{},"Národní důchod ",[883,31504,31506],{"className":31505},[886],[888,31507,31508],{"xmlns":890},[892,31509,31510,31514],{},[895,31511,31512],{},[898,31513,6951],{},[902,31515,6951],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,31518,31520],{"className":31519},[886],[888,31521,31522],{"xmlns":890},[892,31523,31524,31536],{},[895,31525,31526,31528,31530,31532,31534],{},[898,31527,16986],{},[898,31529,23169],{},[898,31531,1710],{},[1712,31533,3740],{},[898,31535,6951],{},[902,31537,30746],{"encoding":904},[123,31539,31540,31566,31567,1343,31590,1343,31611,1659],{},[38,31541,31542,31543],{},"Funkce spotřeby ",[883,31544,31546],{"className":31545},[886],[888,31547,31548],{"xmlns":890},[892,31549,31550,31564],{},[895,31551,31552,31554,31556,31558,31560,31562],{},[898,31553,8195],{},[1712,31555,1714],{},[898,31557,8195],{},[1712,31559,1904],{"stretchy":1903},[898,31561,6951],{},[1712,31563,1910],{"stretchy":1903},[902,31565,25615],{"encoding":904}," — lineární model ",[883,31568,31570],{"className":31569},[886],[888,31571,31572],{"xmlns":890},[892,31573,31574,31588],{},[895,31575,31576,31578,31580,31582,31584,31586],{},[898,31577,8195],{},[1712,31579,1714],{},[898,31581,207],{},[898,31583,6951],{},[1712,31585,3145],{},[898,31587,7544],{},[902,31589,23795],{"encoding":904},[883,31591,31593],{"className":31592},[886],[888,31594,31595],{"xmlns":890},[892,31596,31597,31609],{},[895,31598,31599,31601,31603,31605,31607],{},[1716,31600,2085],{},[1712,31602,2252],{},[898,31604,207],{},[1712,31606,2252],{},[1716,31608,2222],{},[902,31610,23711],{"encoding":904},[883,31612,31614],{"className":31613},[886],[888,31615,31616],{"xmlns":890},[892,31617,31618,31626],{},[895,31619,31620,31622,31624],{},[898,31621,7544],{},[1712,31623,2302],{},[1716,31625,2085],{},[902,31627,23689],{"encoding":904},[123,31629,31630,4831,31657,31678,31679,1659],{},[38,31631,31632,31633],{},"Funkce úspor ",[883,31634,31636],{"className":31635},[886],[888,31637,31638],{"xmlns":890},[892,31639,31640,31654],{},[895,31641,31642,31644,31646,31648,31650,31652],{},[898,31643,6493],{},[1712,31645,1714],{},[898,31647,6493],{},[1712,31649,1904],{"stretchy":1903},[898,31651,6951],{},[1712,31653,1910],{"stretchy":1903},[902,31655,31656],{"encoding":904},"S = S(Y)",[883,31658,31660],{"className":31659},[886],[888,31661,31662],{"xmlns":890},[892,31663,31664,31676],{},[895,31665,31666,31668,31670,31672,31674],{},[898,31667,6951],{},[1712,31669,1714],{},[898,31671,8195],{},[1712,31673,3145],{},[898,31675,6493],{},[902,31677,17568],{"encoding":904},"; lineární ",[883,31680,31682],{"className":31681},[886],[888,31683,31684],{"xmlns":890},[892,31685,31686,31708],{},[895,31687,31688,31690,31692,31694,31696,31698,31700,31702,31704,31706],{},[898,31689,6493],{},[1712,31691,1714],{},[1712,31693,1904],{"stretchy":1903},[1716,31695,2222],{},[1712,31697,2219],{},[898,31699,207],{},[1712,31701,1910],{"stretchy":1903},[898,31703,6951],{},[1712,31705,2219],{},[898,31707,7544],{},[902,31709,24044],{"encoding":904},[123,31711,31712,4831,31715,1343,31738,1659],{},[38,31713,31714],{},"Autonomní spotřeba\u002Fúspory",[883,31716,31718],{"className":31717},[886],[888,31719,31720],{"xmlns":890},[892,31721,31722,31736],{},[895,31723,31724,31726,31728,31730,31732,31734],{},[898,31725,8195],{},[1712,31727,1904],{"stretchy":1903},[1716,31729,2085],{},[1712,31731,1910],{"stretchy":1903},[1712,31733,1714],{},[898,31735,7544],{},[902,31737,24436],{"encoding":904},[883,31739,31741],{"className":31740},[886],[888,31742,31743],{"xmlns":890},[892,31744,31745,31761],{},[895,31746,31747,31749,31751,31753,31755,31757,31759],{},[898,31748,6493],{},[1712,31750,1904],{"stretchy":1903},[1716,31752,2085],{},[1712,31754,1910],{"stretchy":1903},[1712,31756,1714],{},[1712,31758,2219],{},[898,31760,7544],{},[902,31762,31763],{"encoding":904},"S(0) = -b",[123,31765,31766,31798,31799,1691],{},[38,31767,31768,31769],{},"Mezní sklon ke spotřebě ",[883,31770,31772],{"className":31771},[886],[888,31773,31774],{"xmlns":890},[892,31775,31776,31796],{},[895,31777,31778,31780,31782,31784,31786,31788,31790,31792,31794],{},[898,31779,4445],{},[898,31781,1710],{},[898,31783,8195],{},[1712,31785,1714],{},[898,31787,2468],{"mathvariant":2003},[898,31789,8195],{},[898,31791,2473],{"mathvariant":2003},[898,31793,2468],{"mathvariant":2003},[898,31795,6951],{},[902,31797,30928],{"encoding":904}," (v lineárním modelu ",[883,31800,31802],{"className":31801},[886],[888,31803,31804],{"xmlns":890},[892,31805,31806,31818],{},[895,31807,31808,31810,31812,31814,31816],{},[898,31809,4445],{},[898,31811,1710],{},[898,31813,8195],{},[1712,31815,1714],{},[898,31817,207],{},[902,31819,24764],{"encoding":904},[123,31821,31822,31798,31854,1691],{},[38,31823,31824,31825],{},"Mezní sklon k úsporám ",[883,31826,31828],{"className":31827},[886],[888,31829,31830],{"xmlns":890},[892,31831,31832,31852],{},[895,31833,31834,31836,31838,31840,31842,31844,31846,31848,31850],{},[898,31835,4445],{},[898,31837,1710],{},[898,31839,6493],{},[1712,31841,1714],{},[898,31843,2468],{"mathvariant":2003},[898,31845,6493],{},[898,31847,2473],{"mathvariant":2003},[898,31849,2468],{"mathvariant":2003},[898,31851,6951],{},[902,31853,30958],{"encoding":904},[883,31855,31857],{"className":31856},[886],[888,31858,31859],{"xmlns":890},[892,31860,31861,31877],{},[895,31862,31863,31865,31867,31869,31871,31873,31875],{},[898,31864,4445],{},[898,31866,1710],{},[898,31868,6493],{},[1712,31870,1714],{},[1716,31872,2222],{},[1712,31874,2219],{},[898,31876,207],{},[902,31878,24790],{"encoding":904},[123,31880,31881,3245,31884,31913],{},[38,31882,31883],{},"Vztah",[883,31885,31887],{"className":31886},[886],[888,31888,31889],{"xmlns":890},[892,31890,31891,31911],{},[895,31892,31893,31895,31897,31899,31901,31903,31905,31907,31909],{},[898,31894,4445],{},[898,31896,1710],{},[898,31898,8195],{},[1712,31900,3145],{},[898,31902,4445],{},[898,31904,1710],{},[898,31906,6493],{},[1712,31908,1714],{},[1716,31910,2222],{},[902,31912,30989],{"encoding":904}," (7.5).",[123,31915,31916,31918],{},[38,31917,25458],{}," — rovnováha agregátní poptávky a nabídky.",[123,31920,31921,31924,31925,20666,31946,1659],{},[38,31922,31923],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,31926,31928],{"className":31927},[886],[888,31929,31930],{"xmlns":890},[892,31931,31932,31944],{},[895,31933,31934,31936,31938,31940,31942],{},[898,31935,6951],{},[1712,31937,1714],{},[898,31939,8195],{},[1712,31941,3145],{},[898,31943,17058],{},[902,31945,19618],{"encoding":904},[883,31947,31949],{"className":31948},[886],[888,31950,31951],{"xmlns":890},[892,31952,31953,31989],{},[895,31954,31955,31961,31963,31965,31967,31969,31975,31977,31979,31981,31983,31985,31987],{},[2037,31956,31957,31959],{},[898,31958,6951],{},[898,31960,2041],{},[1712,31962,1714],{},[1712,31964,1904],{"stretchy":1903},[898,31966,7544],{},[1712,31968,3145],{},[2037,31970,31971,31973],{},[898,31972,17058],{},[1712,31974,2145],{},[1712,31976,1910],{"stretchy":1903},[898,31978,2473],{"mathvariant":2003},[1712,31980,1904],{"stretchy":1903},[1716,31982,2222],{},[1712,31984,2219],{},[898,31986,207],{},[1712,31988,1910],{"stretchy":1903},[902,31990,31132],{"encoding":904},[123,31992,31993,31996,31997,1343,32016,20666,32041,1659],{},[38,31994,31995],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,31998,32000],{"className":31999},[886],[888,32001,32002],{"xmlns":890},[892,32003,32004,32014],{},[895,32005,32006,32008,32010,32012],{},[898,32007,1772],{},[1712,32009,1904],{"stretchy":1903},[898,32011,6951],{},[1712,32013,1910],{"stretchy":1903},[902,32015,27094],{"encoding":904},[883,32017,32019],{"className":32018},[886],[888,32020,32021],{"xmlns":890},[892,32022,32023,32039],{},[895,32024,32025,32031,32033,32035,32037],{},[6927,32026,32027,32029],{},[898,32028,6951],{},[898,32030,1969],{},[1712,32032,1714],{},[898,32034,6951],{},[1712,32036,2219],{},[898,32038,1772],{},[902,32040,26593],{"encoding":904},[883,32042,32044],{"className":32043},[886],[888,32045,32046],{"xmlns":890},[892,32047,32048,32064],{},[895,32049,32050,32052,32054,32056,32058,32060,32062],{},[898,32051,6951],{},[1712,32053,1714],{},[898,32055,8195],{},[1712,32057,3145],{},[898,32059,17058],{},[1712,32061,3145],{},[898,32063,16986],{},[902,32065,26564],{"encoding":904},[123,32067,32068,32071,32072,32093,32094,20666,32118,1659],{},[38,32069,32070],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,32073,32075],{"className":32074},[886],[888,32076,32077],{"xmlns":890},[892,32078,32079,32091],{},[895,32080,32081,32083,32085,32087,32089],{},[898,32082,17194],{},[1712,32084,1714],{},[898,32086,28128],{},[1712,32088,2219],{},[898,32090,4445],{},[902,32092,28135],{"encoding":904},", importem ",[883,32095,32097],{"className":32096},[886],[888,32098,32099],{"xmlns":890},[892,32100,32101,32115],{},[895,32102,32103,32105,32107,32113],{},[898,32104,4445],{},[1712,32106,1904],{"stretchy":1903},[6927,32108,32109,32111],{},[898,32110,6951],{},[898,32112,1969],{},[1712,32114,1910],{"stretchy":1903},[902,32116,32117],{"encoding":904},"M(Y_D)",[883,32119,32121],{"className":32120},[886],[888,32122,32123],{"xmlns":890},[892,32124,32125,32149],{},[895,32126,32127,32129,32131,32133,32135,32137,32139,32141,32143,32145,32147],{},[898,32128,6951],{},[1712,32130,1714],{},[898,32132,8195],{},[1712,32134,3145],{},[898,32136,17058],{},[1712,32138,3145],{},[898,32140,16986],{},[1712,32142,3145],{},[898,32144,28128],{},[1712,32146,2219],{},[898,32148,4445],{},[902,32150,32151],{"encoding":904},"Y = C + I + G + B - M",[123,32153,32154,4831,32157,31346],{},[38,32155,32156],{},"Multiplikátor investic",[883,32158,32160],{"className":32159},[886],[888,32161,32162],{"xmlns":890},[892,32163,32164,32212],{},[895,32165,32166,32168,32174,32176,32178,32184,32186,32188,32190,32192,32194,32196,32198,32200,32202,32204,32206,32208,32210],{},[898,32167,14744],{"mathvariant":2003},[2037,32169,32170,32172],{},[898,32171,6951],{},[898,32173,2041],{},[898,32175,2473],{"mathvariant":2003},[898,32177,14744],{"mathvariant":2003},[2037,32179,32180,32182],{},[898,32181,17058],{},[1712,32183,2145],{},[1712,32185,1714],{},[1716,32187,2222],{},[898,32189,2473],{"mathvariant":2003},[1712,32191,1904],{"stretchy":1903},[1716,32193,2222],{},[1712,32195,2219],{},[898,32197,207],{},[1712,32199,1910],{"stretchy":1903},[1712,32201,1714],{},[1716,32203,2222],{},[898,32205,2473],{"mathvariant":2003},[898,32207,4445],{},[898,32209,1710],{},[898,32211,6493],{},[902,32213,31345],{"encoding":904},[123,32215,32216,4831,32247,1343,32264,32281],{},[38,32217,20601,32218],{},[883,32219,32221],{"className":32220},[886],[888,32222,32223],{"xmlns":890},[892,32224,32225,32245],{},[895,32226,32227,32229,32231,32233,32235,32237,32239,32241,32243],{},[898,32228,17058],{},[1712,32230,1904],{"stretchy":1903},[898,32232,16915],{},[1712,32234,1910],{"stretchy":1903},[1712,32236,1714],{},[898,32238,7585],{},[898,32240,16915],{},[1712,32242,3145],{},[898,32244,2468],{},[902,32246,20631],{"encoding":904},[883,32248,32250],{"className":32249},[886],[888,32251,32252],{"xmlns":890},[892,32253,32254,32262],{},[895,32255,32256,32258,32260],{},[898,32257,7585],{},[1712,32259,2252],{},[1716,32261,2085],{},[902,32263,17389],{"encoding":904},[883,32265,32267],{"className":32266},[886],[888,32268,32269],{"xmlns":890},[892,32270,32271,32279],{},[895,32272,32273,32275,32277],{},[898,32274,2468],{},[1712,32276,2302],{},[1716,32278,2085],{},[902,32280,17368],{"encoding":904},"; klesající.",[123,32283,32284,32286,32287,32289,32290,32339],{},[38,32285,20720],{}," — rovnováha na trhu zboží (",[614,32288,16928],{},"); ",[883,32291,32293],{"className":32292},[886],[888,32294,32295],{"xmlns":890},[892,32296,32297,32337],{},[895,32298,32299,32301,32303,32315,32317,32319],{},[898,32300,6951],{},[1712,32302,1714],{},[2567,32304,32305,32307],{},[898,32306,7585],{},[895,32308,32309,32311,32313],{},[1716,32310,2222],{},[1712,32312,2219],{},[898,32314,207],{},[898,32316,16915],{},[1712,32318,3145],{},[2567,32320,32321,32329],{},[895,32322,32323,32325,32327],{},[898,32324,7544],{},[1712,32326,3145],{},[898,32328,2468],{},[895,32330,32331,32333,32335],{},[1716,32332,2222],{},[1712,32334,2219],{},[898,32336,207],{},[902,32338,20773],{"encoding":904}," (7.14); klesající.",[123,32341,32342,32344,32345,32289,32347,32392],{},[38,32343,20919],{}," — rovnováha na trhu peněz (",[614,32346,16935],{},[883,32348,32350],{"className":32349},[886],[888,32351,32352],{"xmlns":890},[892,32353,32354,32390],{},[895,32355,32356,32362,32364,32370,32372,32374,32380,32382,32384],{},[2037,32357,32358,32360],{},[898,32359,4445],{},[1712,32361,2145],{},[1712,32363,1714],{},[6927,32365,32366,32368],{},[898,32367,18111],{},[1716,32369,2222],{},[898,32371,6951],{},[1712,32373,3145],{},[6927,32375,32376,32378],{},[898,32377,18111],{},[1716,32379,2787],{},[898,32381,16915],{},[1712,32383,3145],{},[6927,32385,32386,32388],{},[898,32387,18111],{},[1716,32389,6198],{},[902,32391,20967],{"encoding":904}," (7.15); rostoucí.",[123,32394,32395,4831,32398,1659],{},[38,32396,32397],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,32399,32401],{"className":32400},[886],[888,32402,32403],{"xmlns":890},[892,32404,32405,32429],{},[895,32406,32407,32413,32415,32421,32423],{},[2037,32408,32409,32411],{},[898,32410,4445],{},[898,32412,1969],{},[1712,32414,1714],{},[6927,32416,32417,32419],{},[898,32418,14667],{},[1716,32420,2222],{},[1712,32422,3145],{},[6927,32424,32425,32427],{},[898,32426,14667],{},[1716,32428,2787],{},[902,32430,32431],{"encoding":904},"M^D = L_1 + L_2",[123,32433,32434,20977,32436,18854,32449,1655,32464,32479,32480,1659],{},[38,32435,945],{},[883,32437,32439],{"className":32438},[886],[888,32440,32441],{"xmlns":890},[892,32442,32443,32447],{},[895,32444,32445],{},[898,32446,2041],{},[902,32448,2041],{"encoding":904},[883,32450,32452],{"className":32451},[886],[888,32453,32454],{"xmlns":890},[892,32455,32456,32462],{},[895,32457,32458,32460],{},[898,32459,17058],{},[898,32461,6493],{},[902,32463,16925],{"encoding":904},[883,32465,32467],{"className":32466},[886],[888,32468,32469],{"xmlns":890},[892,32470,32471,32477],{},[895,32472,32473,32475],{},[898,32474,14667],{},[898,32476,4445],{},[902,32478,16932],{"encoding":904}," určuje ",[883,32481,32483],{"className":32482},[886],[888,32484,32485],{"xmlns":890},[892,32486,32487,32507],{},[895,32488,32489,32491,32497,32499,32505],{},[1712,32490,1904],{"stretchy":1903},[2037,32492,32493,32495],{},[898,32494,6951],{},[898,32496,2041],{},[1712,32498,3138],{"separator":2565},[2037,32500,32501,32503],{},[898,32502,16915],{},[898,32504,2041],{},[1712,32506,1910],{"stretchy":1903},[902,32508,16969],{"encoding":904},[115,32510,9193],{"id":9192},[120,32512,32513,32520,32527],{},[123,32514,32515,3245,32517],{},[38,32516,21078],{},[207,32518,21082],{"className":32519,"dataFsResolvedFilePath":7413,"href":7414},[210],[123,32521,32522,3245,32524],{},[38,32523,21087],{},[207,32525,21091],{"className":32526,"dataFsResolvedFilePath":868,"href":869},[210],[123,32528,32529,32531],{},[38,32530,21106],{},[120,32532,32533,32539,32545,32551],{},[123,32534,32535,32538],{},[207,32536,21147],{"className":32537,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,32540,32541,32544],{},[207,32542,21114],{"className":32543,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,32546,32547,32550],{},[207,32548,8361],{"className":32549,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,32552,32553,32556,32557,1343,32574,32591],{},[207,32554,1145],{"className":32555,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,32558,32560],{"className":32559},[886],[888,32561,32562],{"xmlns":890},[892,32563,32564,32572],{},[895,32565,32566,32568,32570],{},[898,32567,4445],{},[898,32569,1710],{},[898,32571,8195],{},[902,32573,22920],{"encoding":904},[883,32575,32577],{"className":32576},[886],[888,32578,32579],{"xmlns":890},[892,32580,32581,32589],{},[895,32582,32583,32585,32587],{},[898,32584,4445],{},[898,32586,1710],{},[898,32588,6493],{},[902,32590,24534],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":32593},[32594,32595,32596,32597,32602,32605,32606,32613,32618,32623,32626,32627,32628,32629],{"id":16879,"depth":642,"text":16880},{"id":23029,"depth":642,"text":23030},{"id":23149,"depth":642,"text":23150},{"id":23402,"depth":642,"text":23403,"children":32598},[32599,32600,32601],{"id":23406,"depth":649,"text":23407},{"id":23618,"depth":649,"text":23619},{"id":24126,"depth":649,"text":24127},{"id":24446,"depth":642,"text":24447,"children":32603},[32604],{"id":24962,"depth":649,"text":24963},{"id":25457,"depth":642,"text":25458},{"id":25484,"depth":642,"text":25485,"children":32607},[32608,32609,32610,32612],{"id":25495,"depth":649,"text":25496},{"id":25565,"depth":649,"text":25566},{"id":25749,"depth":649,"text":32611},"Výpočet YEY^E",{"id":25892,"depth":649,"text":25893},{"id":26270,"depth":642,"text":26271,"children":32614},[32615,32616,32617],{"id":26274,"depth":649,"text":25496},{"id":26723,"depth":649,"text":25566},{"id":27379,"depth":649,"text":27380},{"id":28166,"depth":642,"text":28167,"children":32619},[32620,32621,32622],{"id":28170,"depth":649,"text":25496},{"id":28315,"depth":649,"text":25566},{"id":28585,"depth":649,"text":28586},{"id":29509,"depth":642,"text":29510,"children":32624},[32625],{"id":29705,"depth":649,"text":29706},{"id":30255,"depth":642,"text":30256},{"id":30715,"depth":642,"text":30716},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,21100,1143,32636,32637,32638,21147,22758],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":32641,"title":32642,"body":32643,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":41623,"navigation":664,"path":41624,"seo":41625,"sources":41626,"stem":41627,"tags":41628,"type":7391,"updated":677,"__hash__":41633},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":32644,"toc":41592},[32645,32648,32650,32879,32883,32936,33006,33118,33277,33281,33397,33401,33404,33526,33529,33722,33746,33814,33978,33996,34062,34440,34444,34451,34695,34751,34755,34820,34938,35070,35102,35222,35304,35307,35429,35622,35843,35847,35887,35992,36049,36149,36326,36456,36509,36512,36599,36603,36779,36783,36786,36871,36874,36931,37036,37040,37161,37164,37347,37350,37458,37667,37987,38035,38108,38182,38184,38408,38643,38911,38915,38918,39023,39080,39114,39161,39194,39278,39280,39512,39645,39722,39844,39999,40003,40144,40151,40375,40386,40390,40394,40499,40641,40751,40850,40854,41013,41123,41125,41518,41520],[12,32646,32642],{"id":32647},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,32649,16880],{"id":16879},[724,32651,32652,32654,32655,32689,32690,32693,32694,32725,32726,32772,32773,32776,32777,32819,32820,32838,32839,32843,32844,32874,32875,32878],{},[38,32653,913],{}," řeší, jaký svazek zboží ",[883,32656,32658],{"className":32657},[886],[888,32659,32660],{"xmlns":890},[892,32661,32662,32686],{},[895,32663,32664,32666,32674,32676,32684],{},[1712,32665,7910],{"stretchy":1903},[6989,32667,32668,32670,32672],{},[898,32669,1734],{},[1716,32671,2222],{},[1712,32673,2145],{},[1712,32675,3138],{"separator":2565},[6989,32677,32678,32680,32682],{},[898,32679,1734],{},[1716,32681,2787],{},[1712,32683,2145],{},[1712,32685,7925],{"stretchy":1903},[902,32687,32688],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,32691,32692],{},"primární úloha"," — maximalizace užitečnosti ",[883,32695,32697],{"className":32696},[886],[888,32698,32699],{"xmlns":890},[892,32700,32701,32723],{},[895,32702,32703,32705,32707,32713,32715,32721],{},[898,32704,900],{},[1712,32706,1904],{"stretchy":1903},[6927,32708,32709,32711],{},[898,32710,1734],{},[1716,32712,2222],{},[1712,32714,3138],{"separator":2565},[6927,32716,32717,32719],{},[898,32718,1734],{},[1716,32720,2787],{},[1712,32722,1910],{"stretchy":1903},[902,32724,21218],{"encoding":904}," při rozpočtovém omezení ",[883,32727,32729],{"className":32728},[886],[888,32730,32731],{"xmlns":890},[892,32732,32733,32769],{},[895,32734,32735,32741,32743,32749,32755,32757,32763],{},[2037,32736,32737,32739],{},[898,32738,6951],{},[1712,32740,2145],{},[1712,32742,1714],{},[6927,32744,32745,32747],{},[898,32746,1710],{},[1716,32748,2222],{},[6927,32750,32751,32753],{},[898,32752,1734],{},[1716,32754,2222],{},[1712,32756,3145],{},[6927,32758,32759,32761],{},[898,32760,1710],{},[1716,32762,2787],{},[6927,32764,32765,32767],{},[898,32766,1734],{},[1716,32768,2787],{},[902,32770,32771],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,32774,32775],{},"duální úloha"," — minimalizace výdajů ",[883,32778,32780],{"className":32779},[886],[888,32781,32782],{"xmlns":890},[892,32783,32784,32816],{},[895,32785,32786,32788,32790,32796,32802,32804,32810],{},[898,32787,2041],{},[1712,32789,1714],{},[6927,32791,32792,32794],{},[898,32793,1710],{},[1716,32795,2222],{},[6927,32797,32798,32800],{},[898,32799,1734],{},[1716,32801,2222],{},[1712,32803,3145],{},[6927,32805,32806,32808],{},[898,32807,1710],{},[1716,32809,2787],{},[6927,32811,32812,32814],{},[898,32813,1734],{},[1716,32815,2787],{},[902,32817,32818],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,32821,32823],{"className":32822},[886],[888,32824,32825],{"xmlns":890},[892,32826,32827,32835],{},[895,32828,32829],{},[2037,32830,32831,32833],{},[898,32832,900],{},[1712,32834,2145],{},[902,32836,32837],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,32840,32842],{"className":32841,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,32845,32847],{"className":32846},[886],[888,32848,32849],{"xmlns":890},[892,32850,32851,32871],{},[895,32852,32853,32855,32857,32863,32865],{},[1762,32854,15475],{},[1712,32856,1714],{},[6927,32858,32859,32861],{},[898,32860,1710],{},[1716,32862,2222],{},[898,32864,2473],{"mathvariant":2003},[6927,32866,32867,32869],{},[898,32868,1710],{},[1716,32870,2787],{},[902,32872,32873],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,32876,32877],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,32880,32882],{"id":32881},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,32884,32885,32886,32904,32905,32935],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,32887,32889],{"className":32888},[886],[888,32890,32891],{"xmlns":890},[892,32892,32893,32901],{},[895,32894,32895],{},[2037,32896,32897,32899],{},[898,32898,6951],{},[1712,32900,2145],{},[902,32902,32903],{"encoding":904},"Y^*"," a ceny ",[883,32906,32908],{"className":32907},[886],[888,32909,32910],{"xmlns":890},[892,32911,32912,32932],{},[895,32913,32914,32922,32924],{},[6989,32915,32916,32918,32920],{},[898,32917,1710],{},[1716,32919,2222],{},[1712,32921,2145],{},[1712,32923,3138],{"separator":2565},[6989,32925,32926,32928,32930],{},[898,32927,1710],{},[1716,32929,2787],{},[1712,32931,2145],{},[902,32933,32934],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,32937,32939],{"className":32938},[886],[888,32940,32942],{"xmlns":890,"display":32941},"block",[892,32943,32944,33003],{},[25629,32945,32947],{"width":32946},"100%",[25634,32948,32949,32952,32996,32998],{},[25637,32950],{"width":32951},"50%",[25637,32953,32954],{},[895,32955,32956,32962,32964,32972,32978,32980,32988,32994],{},[2037,32957,32958,32960],{},[898,32959,6951],{},[1712,32961,2145],{},[1712,32963,1714],{},[6989,32965,32966,32968,32970],{},[898,32967,1710],{},[1716,32969,2222],{},[1712,32971,2145],{},[6927,32973,32974,32976],{},[898,32975,1734],{},[1716,32977,2222],{},[1712,32979,3145],{},[6989,32981,32982,32984,32986],{},[898,32983,1710],{},[1716,32985,2787],{},[1712,32987,2145],{},[6927,32989,32990,32992],{},[898,32991,1734],{},[1716,32993,2787],{},[1712,32995,3138],{"separator":2565},[25637,32997],{"width":32951},[25637,32999,33000],{},[1762,33001,33002],{},"(6.12)",[902,33004,33005],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,33007,33008,33009,33012,33013,1655,33049,33085,33086,33099,33100,33114,33115,1659],{},"geometricky ",[38,33010,33011],{},"rozpočtová přímka (budget line)"," procházející body ",[883,33014,33016],{"className":33015},[886],[888,33017,33018],{"xmlns":890},[892,33019,33020,33046],{},[895,33021,33022,33024,33030,33032,33040,33042,33044],{},[1712,33023,7910],{"stretchy":1903},[2037,33025,33026,33028],{},[898,33027,6951],{},[1712,33029,2145],{},[898,33031,2473],{"mathvariant":2003},[6989,33033,33034,33036,33038],{},[898,33035,1710],{},[1716,33037,2222],{},[1712,33039,2145],{},[1712,33041,3138],{"separator":2565},[1716,33043,2085],{},[1712,33045,7925],{"stretchy":1903},[902,33047,33048],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,33050,33052],{"className":33051},[886],[888,33053,33054],{"xmlns":890},[892,33055,33056,33082],{},[895,33057,33058,33060,33062,33064,33070,33072,33080],{},[1712,33059,7910],{"stretchy":1903},[1716,33061,2085],{},[1712,33063,3138],{"separator":2565},[2037,33065,33066,33068],{},[898,33067,6951],{},[1712,33069,2145],{},[898,33071,2473],{"mathvariant":2003},[6989,33073,33074,33076,33078],{},[898,33075,1710],{},[1716,33077,2787],{},[1712,33079,2145],{},[1712,33081,7925],{"stretchy":1903},[902,33083,33084],{"encoding":904},"[0, Y^*\u002FP_2^*]",". Spotřebitel chce v rámci této přímky (a pod ní) najít svazek s nejvyšší dostupnou užitečností. Teorie před optimalizací — tvar funkce ",[883,33087,33089],{"className":33088},[886],[888,33090,33091],{"xmlns":890},[892,33092,33093,33097],{},[895,33094,33095],{},[898,33096,900],{},[902,33098,900],{"encoding":904},", indiferenční křivky a ",[883,33101,33103],{"className":33102},[886],[888,33104,33105],{"xmlns":890},[892,33106,33107,33111],{},[895,33108,33109],{},[1762,33110,15475],{},[902,33112,33113],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,33116,880],{"className":33117,"dataFsResolvedFilePath":878,"href":879},[210],[1636,33119,33120],{},[724,33121,33122,33124,33125,33128,33129,33142,33143,33145,33146,33159,33160,3245,33163,33203,33204,33221,33222,33239,33240,33257,33258,33276],{},[883,33123,2203],{}," Pozor — dvě úlohy, totéž řešení\n",[38,33126,33127],{},"Primární úloha"," (max ",[883,33130,33132],{"className":33131},[886],[888,33133,33134],{"xmlns":890},[892,33135,33136,33140],{},[895,33137,33138],{},[898,33139,900],{},[902,33141,900],{"encoding":904}," při pevném rozpočtu) a ",[38,33144,32775],{}," (min ",[883,33147,33149],{"className":33148},[886],[888,33150,33151],{"xmlns":890},[892,33152,33153,33157],{},[895,33154,33155],{},[898,33156,2041],{},[902,33158,2041],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,33161,33162],{},"tentýž bod",[883,33164,33166],{"className":33165},[886],[888,33167,33168],{"xmlns":890},[892,33169,33170,33200],{},[895,33171,33172,33178,33180,33188,33190,33198],{},[2037,33173,33174,33176],{},[898,33175,1734],{},[1712,33177,2145],{},[1712,33179,7910],{"stretchy":1903},[6989,33181,33182,33184,33186],{},[898,33183,1734],{},[1716,33185,2222],{},[1712,33187,2145],{},[1712,33189,3138],{"separator":2565},[6989,33191,33192,33194,33196],{},[898,33193,1734],{},[1716,33195,2787],{},[1712,33197,2145],{},[1712,33199,7925],{"stretchy":1903},[902,33201,33202],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,33205,33207],{"className":33206},[886],[888,33208,33209],{"xmlns":890},[892,33210,33211,33219],{},[895,33212,33213],{},[2037,33214,33215,33217],{},[898,33216,6951],{},[1712,33218,2145],{},[902,33220,32903],{"encoding":904}," a hledáme maximální ",[883,33223,33225],{"className":33224},[886],[888,33226,33227],{"xmlns":890},[892,33228,33229,33237],{},[895,33230,33231],{},[2037,33232,33233,33235],{},[898,33234,900],{},[1712,33236,2145],{},[902,33238,32837],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,33241,33243],{"className":33242},[886],[888,33244,33245],{"xmlns":890},[892,33246,33247,33255],{},[895,33248,33249],{},[2037,33250,33251,33253],{},[898,33252,900],{},[1712,33254,2145],{},[902,33256,32837],{"encoding":904}," a hledáme minimální ",[883,33259,33261],{"className":33260},[886],[888,33262,33263],{"xmlns":890},[892,33264,33265,33273],{},[895,33266,33267],{},[2037,33268,33269,33271],{},[898,33270,2041],{},[1712,33272,2145],{},[902,33274,33275],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,33278,33280],{"id":33279},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,33282,33283,33284,33315,33316,33392,33393,1659],{},"Úlohou je najít maximum ",[883,33285,33287],{"className":33286},[886],[888,33288,33289],{"xmlns":890},[892,33290,33291,33313],{},[895,33292,33293,33295,33297,33303,33305,33311],{},[898,33294,900],{},[1712,33296,1904],{"stretchy":1903},[6927,33298,33299,33301],{},[898,33300,1734],{},[1716,33302,2222],{},[1712,33304,3138],{"separator":2565},[6927,33306,33307,33309],{},[898,33308,1734],{},[1716,33310,2787],{},[1712,33312,1910],{"stretchy":1903},[902,33314,21218],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,33317,33319],{"className":33318},[886],[888,33320,33321],{"xmlns":890},[892,33322,33323,33389],{},[895,33324,33325,33327,33329,33335,33337,33343,33345,33347,33353,33355,33363,33369,33371,33379,33385,33387],{},[898,33326,15913],{},[1712,33328,1904],{"stretchy":1903},[6927,33330,33331,33333],{},[898,33332,1734],{},[1716,33334,2222],{},[1712,33336,3138],{"separator":2565},[6927,33338,33339,33341],{},[898,33340,1734],{},[1716,33342,2787],{},[1712,33344,1910],{"stretchy":1903},[1712,33346,1714],{},[2037,33348,33349,33351],{},[898,33350,6951],{},[1712,33352,2145],{},[1712,33354,2219],{},[6989,33356,33357,33359,33361],{},[898,33358,1710],{},[1716,33360,2222],{},[1712,33362,2145],{},[6927,33364,33365,33367],{},[898,33366,1734],{},[1716,33368,2222],{},[1712,33370,2219],{},[6989,33372,33373,33375,33377],{},[898,33374,1710],{},[1716,33376,2787],{},[1712,33378,2145],{},[6927,33380,33381,33383],{},[898,33382,1734],{},[1716,33384,2787],{},[1712,33386,1714],{},[1716,33388,2085],{},[902,33390,33391],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,33394,33396],{"className":33395,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,33398,33400],{"id":33399},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,33402,33403],{},"Sestavíme",[883,33405,33407],{"className":33406},[886],[888,33408,33409],{"xmlns":890,"display":32941},[892,33410,33411,33523],{},[25629,33412,33413],{"width":32946},[25634,33414,33415,33417,33516,33518],{},[25637,33416],{"width":32951},[25637,33418,33419],{},[895,33420,33421,33424,33426,33432,33434,33440,33442,33444,33446,33448,33450,33452,33458,33460,33466,33468,33470,33472,33474,33480,33482,33490,33496,33498,33506,33512,33514],{},[898,33422,14667],{"mathvariant":33423},"script",[1712,33425,1904],{"stretchy":1903},[6927,33427,33428,33430],{},[898,33429,1734],{},[1716,33431,2222],{},[1712,33433,3138],{"separator":2565},[6927,33435,33436,33438],{},[898,33437,1734],{},[1716,33439,2787],{},[1712,33441,3138],{"separator":2565},[898,33443,21318],{},[1712,33445,1910],{"stretchy":1903},[1712,33447,1714],{},[898,33449,900],{},[1712,33451,1904],{"stretchy":1903},[6927,33453,33454,33456],{},[898,33455,1734],{},[1716,33457,2222],{},[1712,33459,3138],{"separator":2565},[6927,33461,33462,33464],{},[898,33463,1734],{},[1716,33465,2787],{},[1712,33467,1910],{"stretchy":1903},[1712,33469,3145],{},[898,33471,21318],{},[1712,33473,1904],{"stretchy":1903},[2037,33475,33476,33478],{},[898,33477,6951],{},[1712,33479,2145],{},[1712,33481,2219],{},[6989,33483,33484,33486,33488],{},[898,33485,1710],{},[1716,33487,2222],{},[1712,33489,2145],{},[6927,33491,33492,33494],{},[898,33493,1734],{},[1716,33495,2222],{},[1712,33497,2219],{},[6989,33499,33500,33502,33504],{},[898,33501,1710],{},[1716,33503,2787],{},[1712,33505,2145],{},[6927,33507,33508,33510],{},[898,33509,1734],{},[1716,33511,2787],{},[1712,33513,1910],{"stretchy":1903},[898,33515,1659],{"mathvariant":2003},[25637,33517],{"width":32951},[25637,33519,33520],{},[1762,33521,33522],{},"(6.13)",[902,33524,33525],{"encoding":904},"\\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}",[724,33527,33528],{},"Soustava prvního řádu:",[883,33530,33532],{"className":33531},[886],[888,33533,33534],{"xmlns":890,"display":32941},[892,33535,33536,33719],{},[25629,33537,33538],{"width":32946},[25634,33539,33540,33542,33712,33714],{},[25637,33541],{"width":32951},[25637,33543,33544],{},[25629,33545,33546,33596,33646],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,33547,33548,33560],{},[25637,33549,33550],{},[2563,33551,33552],{"scriptlevel":2085,"displaystyle":2565},[6989,33553,33554,33556,33558],{},[898,33555,14667],{"mathvariant":33423},[1716,33557,2222],{},[1712,33559,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,33561,33562],{},[2563,33563,33564],{"scriptlevel":2085,"displaystyle":2565},[895,33565,33566,33568,33570,33578,33580,33582,33590,33592,33594],{},[895,33567],{},[1712,33569,1714],{},[6989,33571,33572,33574,33576],{},[898,33573,900],{},[1716,33575,2222],{},[1712,33577,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,33579,2219],{},[898,33581,21318],{},[6989,33583,33584,33586,33588],{},[898,33585,1710],{},[1716,33587,2222],{},[1712,33589,2145],{},[1712,33591,1714],{},[1716,33593,2085],{},[1712,33595,3138],{"separator":2565},[25634,33597,33598,33610],{},[25637,33599,33600],{},[2563,33601,33602],{"scriptlevel":2085,"displaystyle":2565},[6989,33603,33604,33606,33608],{},[898,33605,14667],{"mathvariant":33423},[1716,33607,2787],{},[1712,33609,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,33611,33612],{},[2563,33613,33614],{"scriptlevel":2085,"displaystyle":2565},[895,33615,33616,33618,33620,33628,33630,33632,33640,33642,33644],{},[895,33617],{},[1712,33619,1714],{},[6989,33621,33622,33624,33626],{},[898,33623,900],{},[1716,33625,2787],{},[1712,33627,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,33629,2219],{},[898,33631,21318],{},[6989,33633,33634,33636,33638],{},[898,33635,1710],{},[1716,33637,2787],{},[1712,33639,2145],{},[1712,33641,1714],{},[1716,33643,2085],{},[1712,33645,3138],{"separator":2565},[25634,33647,33648,33660],{},[25637,33649,33650],{},[2563,33651,33652],{"scriptlevel":2085,"displaystyle":2565},[6989,33653,33654,33656,33658],{},[898,33655,14667],{"mathvariant":33423},[898,33657,21318],{},[1712,33659,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,33661,33662],{},[2563,33663,33664],{"scriptlevel":2085,"displaystyle":2565},[895,33665,33666,33668,33670,33676,33678,33686,33692,33694,33702,33708,33710],{},[895,33667],{},[1712,33669,1714],{},[2037,33671,33672,33674],{},[898,33673,6951],{},[1712,33675,2145],{},[1712,33677,2219],{},[6989,33679,33680,33682,33684],{},[898,33681,1710],{},[1716,33683,2222],{},[1712,33685,2145],{},[6927,33687,33688,33690],{},[898,33689,1734],{},[1716,33691,2222],{},[1712,33693,2219],{},[6989,33695,33696,33698,33700],{},[898,33697,1710],{},[1716,33699,2787],{},[1712,33701,2145],{},[6927,33703,33704,33706],{},[898,33705,1734],{},[1716,33707,2787],{},[1712,33709,1714],{},[1716,33711,17334],{},[25637,33713],{"width":32951},[25637,33715,33716],{},[1762,33717,33718],{},"(6.14)",[902,33720,33721],{"encoding":904},"\\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}",[724,33723,33724,33725,33728,33729,33742,33743,2854],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,33726,33727],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,33730,33732],{"className":33731},[886],[888,33733,33734],{"xmlns":890},[892,33735,33736,33740],{},[895,33737,33738],{},[898,33739,21318],{},[902,33741,21371],{"encoding":904}," dostáváme ",[38,33744,33745],{},"podmínku optimality",[883,33747,33749],{"className":33748},[886],[888,33750,33751],{"xmlns":890,"display":32941},[892,33752,33753,33811],{},[895,33754,33755],{},[17706,33756,33757],{"notation":17708},[2563,33758,33759],{"scriptlevel":2085,"displaystyle":1903},[2563,33760,33761],{"scriptlevel":2085,"displaystyle":1903},[2563,33762,33763],{"scriptlevel":2085,"displaystyle":2565},[895,33764,33765,33767,33769,33771,33789,33791,33809],{},[1762,33766,1764],{},[1762,33768,15475],{},[1712,33770,1714],{},[2567,33772,33773,33781],{},[6989,33774,33775,33777,33779],{},[898,33776,900],{},[1716,33778,2222],{},[1712,33780,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,33782,33783,33785,33787],{},[898,33784,900],{},[1716,33786,2787],{},[1712,33788,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,33790,1714],{},[2567,33792,33793,33801],{},[6989,33794,33795,33797,33799],{},[898,33796,1710],{},[1716,33798,2222],{},[1712,33800,2145],{},[6989,33802,33803,33805,33807],{},[898,33804,1710],{},[1716,33806,2787],{},[1712,33808,2145],{},[1762,33810,1764],{},[902,33812,33813],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1636,33815,33816],{},[724,33817,33818,33820,33821,33855,33856,33859,33860,33878,33879,33897,33898,33928,33929,33946,33947,33977],{},[883,33819,1941],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,33822,33824],{"className":33823},[886],[888,33825,33826],{"xmlns":890},[892,33827,33828,33852],{},[895,33829,33830,33832,33834,33842,33844],{},[1762,33831,15475],{},[1712,33833,1714],{},[6989,33835,33836,33838,33840],{},[898,33837,1710],{},[1716,33839,2222],{},[1712,33841,2145],{},[898,33843,2473],{"mathvariant":2003},[6989,33845,33846,33848,33850],{},[898,33847,1710],{},[1716,33849,2787],{},[1712,33851,2145],{},[902,33853,33854],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,33857,33858],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,33861,33863],{"className":33862},[886],[888,33864,33865],{"xmlns":890},[892,33866,33867,33875],{},[895,33868,33869],{},[6927,33870,33871,33873],{},[898,33872,1734],{},[1716,33874,2222],{},[902,33876,33877],{"encoding":904},"Q_1"," za ",[883,33880,33882],{"className":33881},[886],[888,33883,33884],{"xmlns":890},[892,33885,33886,33894],{},[895,33887,33888],{},[6927,33889,33890,33892],{},[898,33891,1734],{},[1716,33893,2787],{},[902,33895,33896],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,33899,33901],{"className":33900},[886],[888,33902,33903],{"xmlns":890},[892,33904,33905,33925],{},[895,33906,33907,33909,33911,33917,33919],{},[1762,33908,15475],{},[1712,33910,2302],{},[6927,33912,33913,33915],{},[898,33914,1710],{},[1716,33916,2222],{},[898,33918,2473],{"mathvariant":2003},[6927,33920,33921,33923],{},[898,33922,1710],{},[1716,33924,2787],{},[902,33926,33927],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,33930,33932],{"className":33931},[886],[888,33933,33934],{"xmlns":890},[892,33935,33936,33944],{},[895,33937,33938],{},[6927,33939,33940,33942],{},[898,33941,1734],{},[1716,33943,2222],{},[902,33945,33877],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,33948,33950],{"className":33949},[886],[888,33951,33952],{"xmlns":890},[892,33953,33954,33974],{},[895,33955,33956,33958,33960,33966,33968],{},[1762,33957,15475],{},[1712,33959,2252],{},[6927,33961,33962,33964],{},[898,33963,1710],{},[1716,33965,2222],{},[898,33967,2473],{"mathvariant":2003},[6927,33969,33970,33972],{},[898,33971,1710],{},[1716,33973,2787],{},[902,33975,33976],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,33979,33981,33982,33995],{"id":33980},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,33983,33985],{"className":33984},[886],[888,33986,33987],{"xmlns":890},[892,33988,33989,33993],{},[895,33990,33991],{},[898,33992,21318],{},[902,33994,21371],{"encoding":904}," — mezní užitečnost důchodu",[724,33997,33998,33999,34017,34018,34021,34022,34039,34040,34057,34058,34061],{},"Lagrangeův multiplikátor ",[883,34000,34002],{"className":34001},[886],[888,34003,34004],{"xmlns":890},[892,34005,34006,34014],{},[895,34007,34008],{},[2037,34009,34010,34012],{},[898,34011,21318],{},[1712,34013,2145],{},[902,34015,34016],{"encoding":904},"\\lambda^*"," představuje ",[38,34019,34020],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,34023,34025],{"className":34024},[886],[888,34026,34027],{"xmlns":890},[892,34028,34029,34037],{},[895,34030,34031],{},[2037,34032,34033,34035],{},[898,34034,900],{},[1712,34036,2145],{},[902,34038,32837],{"encoding":904}," při jednotkové změně důchodu ",[883,34041,34043],{"className":34042},[886],[888,34044,34045],{"xmlns":890},[892,34046,34047,34055],{},[895,34048,34049],{},[2037,34050,34051,34053],{},[898,34052,6951],{},[1712,34054,2145],{},[902,34056,32903],{"encoding":904},". Je to ",[38,34059,34060],{},"stínová cena"," rozpočtového omezení.",[1636,34063,34064,34069],{},[724,34065,34066,34068],{},[883,34067,2370],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,34070,34071,34131,34218,34254,34341],{},[123,34072,34073,34076,34077,1659],{},[38,34074,34075],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,34078,34080],{"className":34079},[886],[888,34081,34082],{"xmlns":890},[892,34083,34084,34128],{},[895,34085,34086,34092,34094,34102,34108,34110,34118,34124,34126],{},[2037,34087,34088,34090],{},[898,34089,6951],{},[1712,34091,2145],{},[1712,34093,2219],{},[6989,34095,34096,34098,34100],{},[898,34097,1710],{},[1716,34099,2222],{},[1712,34101,2145],{},[6927,34103,34104,34106],{},[898,34105,1734],{},[1716,34107,2222],{},[1712,34109,2219],{},[6989,34111,34112,34114,34116],{},[898,34113,1710],{},[1716,34115,2787],{},[1712,34117,2145],{},[6927,34119,34120,34122],{},[898,34121,1734],{},[1716,34123,2787],{},[1712,34125,1714],{},[1716,34127,2085],{},[902,34129,34130],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,34132,34133,3245,34136,1659],{},[38,34134,34135],{},"Sestav Lagrangeovu funkci",[883,34137,34139],{"className":34138},[886],[888,34140,34141],{"xmlns":890},[892,34142,34143,34215],{},[895,34144,34145,34147,34149,34151,34153,34159,34161,34167,34169,34171,34173,34175,34181,34183,34191,34197,34199,34207,34213],{},[898,34146,14667],{"mathvariant":33423},[1712,34148,1714],{},[898,34150,900],{},[1712,34152,1904],{"stretchy":1903},[6927,34154,34155,34157],{},[898,34156,1734],{},[1716,34158,2222],{},[1712,34160,3138],{"separator":2565},[6927,34162,34163,34165],{},[898,34164,1734],{},[1716,34166,2787],{},[1712,34168,1910],{"stretchy":1903},[1712,34170,3145],{},[898,34172,21318],{},[1712,34174,1904],{"stretchy":1903},[2037,34176,34177,34179],{},[898,34178,6951],{},[1712,34180,2145],{},[1712,34182,2219],{},[6989,34184,34185,34187,34189],{},[898,34186,1710],{},[1716,34188,2222],{},[1712,34190,2145],{},[6927,34192,34193,34195],{},[898,34194,1734],{},[1716,34196,2222],{},[1712,34198,2219],{},[6989,34200,34201,34203,34205],{},[898,34202,1710],{},[1716,34204,2787],{},[1712,34206,2145],{},[6927,34208,34209,34211],{},[898,34210,1734],{},[1716,34212,2787],{},[1712,34214,1910],{"stretchy":1903},[902,34216,34217],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,34219,34220,15340,34223,34253],{},[38,34221,34222],{},"Spočítej parciální derivace",[883,34224,34226],{"className":34225},[886],[888,34227,34228],{"xmlns":890},[892,34229,34230,34250],{},[895,34231,34232,34238,34240,34246,34248],{},[6927,34233,34234,34236],{},[898,34235,1734],{},[1716,34237,2222],{},[1712,34239,3138],{"separator":2565},[6927,34241,34242,34244],{},[898,34243,1734],{},[1716,34245,2787],{},[1712,34247,3138],{"separator":2565},[898,34249,21318],{},[902,34251,34252],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,34255,34256,34272,34273,34306,34307,1655,34324,1659],{},[38,34257,34258,34259],{},"Vyluč ",[883,34260,34262],{"className":34261},[886],[888,34263,34264],{"xmlns":890},[892,34265,34266,34270],{},[895,34267,34268],{},[898,34269,21318],{},[902,34271,21371],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,34274,34276],{"className":34275},[886],[888,34277,34278],{"xmlns":890},[892,34279,34280,34304],{},[895,34281,34282,34284,34286,34294,34296],{},[1762,34283,15475],{},[1712,34285,1714],{},[6989,34287,34288,34290,34292],{},[898,34289,1710],{},[1716,34291,2222],{},[1712,34293,2145],{},[898,34295,2473],{"mathvariant":2003},[6989,34297,34298,34300,34302],{},[898,34299,1710],{},[1716,34301,2787],{},[1712,34303,2145],{},[902,34305,33854],{"encoding":904},", která dá vztah mezi ",[883,34308,34310],{"className":34309},[886],[888,34311,34312],{"xmlns":890},[892,34313,34314,34322],{},[895,34315,34316],{},[6927,34317,34318,34320],{},[898,34319,1734],{},[1716,34321,2222],{},[902,34323,33877],{"encoding":904},[883,34325,34327],{"className":34326},[886],[888,34328,34329],{"xmlns":890},[892,34330,34331,34339],{},[895,34332,34333],{},[6927,34334,34335,34337],{},[898,34336,1734],{},[1716,34338,2787],{},[902,34340,33896],{"encoding":904},[123,34342,34343,34346,34347,34377,34378,34395,34396,1659],{},[38,34344,34345],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,34348,34350],{"className":34349},[886],[888,34351,34352],{"xmlns":890},[892,34353,34354,34374],{},[895,34355,34356,34364,34366],{},[6989,34357,34358,34360,34362],{},[898,34359,1734],{},[1716,34361,2222],{},[1712,34363,2145],{},[1712,34365,3138],{"separator":2565},[6989,34367,34368,34370,34372],{},[898,34369,1734],{},[1716,34371,2787],{},[1712,34373,2145],{},[902,34375,34376],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,34379,34381],{"className":34380},[886],[888,34382,34383],{"xmlns":890},[892,34384,34385,34393],{},[895,34386,34387],{},[2037,34388,34389,34391],{},[898,34390,21318],{},[1712,34392,2145],{},[902,34394,34016],{"encoding":904}," a maximální užitečnost ",[883,34397,34399],{"className":34398},[886],[888,34400,34401],{"xmlns":890},[892,34402,34403,34437],{},[895,34404,34405,34411,34413,34415,34417,34425,34427,34435],{},[2037,34406,34407,34409],{},[898,34408,900],{},[1712,34410,2145],{},[1712,34412,1714],{},[898,34414,900],{},[1712,34416,1904],{"stretchy":1903},[6989,34418,34419,34421,34423],{},[898,34420,1734],{},[1716,34422,2222],{},[1712,34424,2145],{},[1712,34426,3138],{"separator":2565},[6989,34428,34429,34431,34433],{},[898,34430,1734],{},[1716,34432,2787],{},[1712,34434,2145],{},[1712,34436,1910],{"stretchy":1903},[902,34438,34439],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,34441,34443],{"id":34442},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,34445,34446],{},[3817,34447],{"alt":34448,"className":34449,"src":34450},"imek-uzitecnost-optimum",[210,3821],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,34452,34453],{},[614,34454,34455,34456,34505,34506,1655,34534,34562,34563,34597,34598,34637,34638,34656,34657,34675,34676,34694],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,34457,34459],{"className":34458},[886],[888,34460,34461],{"xmlns":890},[892,34462,34463,34503],{},[895,34464,34465,34471,34473,34481,34487,34489,34497],{},[2037,34466,34467,34469],{},[898,34468,6951],{},[1712,34470,2145],{},[1712,34472,1714],{},[6989,34474,34475,34477,34479],{},[898,34476,1710],{},[1716,34478,2222],{},[1712,34480,2145],{},[6927,34482,34483,34485],{},[898,34484,1734],{},[1716,34486,2222],{},[1712,34488,3145],{},[6989,34490,34491,34493,34495],{},[898,34492,1710],{},[1716,34494,2787],{},[1712,34496,2145],{},[6927,34498,34499,34501],{},[898,34500,1734],{},[1716,34502,2787],{},[902,34504,22173],{"encoding":904}," protíná osy v ",[883,34507,34509],{"className":34508},[886],[888,34510,34511],{"xmlns":890},[892,34512,34513,34531],{},[895,34514,34515,34521,34523],{},[2037,34516,34517,34519],{},[898,34518,6951],{},[1712,34520,2145],{},[898,34522,2473],{"mathvariant":2003},[6989,34524,34525,34527,34529],{},[898,34526,1710],{},[1716,34528,2222],{},[1712,34530,2145],{},[902,34532,34533],{"encoding":904},"Y^*\u002FP_1^*",[883,34535,34537],{"className":34536},[886],[888,34538,34539],{"xmlns":890},[892,34540,34541,34559],{},[895,34542,34543,34549,34551],{},[2037,34544,34545,34547],{},[898,34546,6951],{},[1712,34548,2145],{},[898,34550,2473],{"mathvariant":2003},[6989,34552,34553,34555,34557],{},[898,34554,1710],{},[1716,34556,2787],{},[1712,34558,2145],{},[902,34560,34561],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,34564,34566],{"className":34565},[886],[888,34567,34568],{"xmlns":890},[892,34569,34570,34594],{},[895,34571,34572,34578,34580,34586,34588],{},[6927,34573,34574,34576],{},[898,34575,7585],{},[1716,34577,2222],{},[1712,34579,2252],{},[2037,34581,34582,34584],{},[898,34583,7585],{},[1712,34585,2145],{},[1712,34587,2252],{},[6927,34589,34590,34592],{},[898,34591,7585],{},[1716,34593,2787],{},[902,34595,34596],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,34599,34601],{"className":34600},[886],[888,34602,34603],{"xmlns":890},[892,34604,34605,34635],{},[895,34606,34607,34613,34615,34623,34625,34633],{},[2037,34608,34609,34611],{},[898,34610,1734],{},[1712,34612,2145],{},[1712,34614,7910],{"stretchy":1903},[6989,34616,34617,34619,34621],{},[898,34618,1734],{},[1716,34620,2222],{},[1712,34622,2145],{},[1712,34624,3138],{"separator":2565},[6989,34626,34627,34629,34631],{},[898,34628,1734],{},[1716,34630,2787],{},[1712,34632,2145],{},[1712,34634,7925],{"stretchy":1903},[902,34636,33202],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,34639,34641],{"className":34640},[886],[888,34642,34643],{"xmlns":890},[892,34644,34645,34653],{},[895,34646,34647],{},[2037,34648,34649,34651],{},[898,34650,7585],{},[1712,34652,2145],{},[902,34654,34655],{"encoding":904},"c^*",". Křivka ",[883,34658,34660],{"className":34659},[886],[888,34661,34662],{"xmlns":890},[892,34663,34664,34672],{},[895,34665,34666],{},[6927,34667,34668,34670],{},[898,34669,7585],{},[1716,34671,2222],{},[902,34673,34674],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,34677,34679],{"className":34678},[886],[888,34680,34681],{"xmlns":890},[892,34682,34683,34691],{},[895,34684,34685],{},[6927,34686,34687,34689],{},[898,34688,7585],{},[1716,34690,2787],{},[902,34692,34693],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,34696,34697,34698,34701,34702,34720,34721,34750],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,34699,34700],{},"dotýkají",", tj. mají v bodě ",[883,34703,34705],{"className":34704},[886],[888,34706,34707],{"xmlns":890},[892,34708,34709,34717],{},[895,34710,34711],{},[2037,34712,34713,34715],{},[898,34714,1734],{},[1712,34716,2145],{},[902,34718,34719],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,34722,34724],{"className":34723},[886],[888,34725,34726],{"xmlns":890},[892,34727,34728,34748],{},[895,34729,34730,34732,34734,34740,34742],{},[1762,34731,15475],{},[1712,34733,1714],{},[6927,34735,34736,34738],{},[898,34737,1710],{},[1716,34739,2222],{},[898,34741,2473],{"mathvariant":2003},[6927,34743,34744,34746],{},[898,34745,1710],{},[1716,34747,2787],{},[902,34749,32873],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,34752,34754],{"id":34753},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,34756,14535,34757,34819],{},[883,34758,34760],{"className":34759},[886],[888,34761,34762],{"xmlns":890},[892,34763,34764,34816],{},[895,34765,34766,34768,34770,34776,34778,34784,34786,34788,34802],{},[898,34767,900],{},[1712,34769,1904],{"stretchy":1903},[6927,34771,34772,34774],{},[898,34773,1734],{},[1716,34775,2222],{},[1712,34777,3138],{"separator":2565},[6927,34779,34780,34782],{},[898,34781,1734],{},[1716,34783,2787],{},[1712,34785,1910],{"stretchy":1903},[1712,34787,1714],{},[6989,34789,34790,34792,34794],{},[898,34791,1734],{},[1716,34793,2222],{},[895,34795,34796,34798,34800],{},[1716,34797,2222],{},[898,34799,2473],{"mathvariant":2003},[1716,34801,2787],{},[6989,34803,34804,34806,34808],{},[898,34805,1734],{},[1716,34807,2787],{},[895,34809,34810,34812,34814],{},[1716,34811,2222],{},[898,34813,2473],{"mathvariant":2003},[1716,34815,2787],{},[902,34817,34818],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,34821,34822],{},[883,34823,34825],{"className":34824},[886],[888,34826,34827],{"xmlns":890},[892,34828,34829,34935],{},[895,34830,34831,34833,34835,34917,34919,34933],{},[1762,34832,15475],{},[1712,34834,1714],{},[2567,34836,34837,34877],{},[895,34838,34839,34847,34863],{},[2563,34840,34841],{"scriptlevel":2085,"displaystyle":1903},[2567,34842,34843,34845],{},[1716,34844,2222],{},[1716,34846,2787],{},[6989,34848,34849,34851,34853],{},[898,34850,1734],{},[1716,34852,2222],{},[895,34854,34855,34857,34859,34861],{},[1712,34856,2219],{},[1716,34858,2222],{},[898,34860,2473],{"mathvariant":2003},[1716,34862,2787],{},[6989,34864,34865,34867,34869],{},[898,34866,1734],{},[1716,34868,2787],{},[895,34870,34871,34873,34875],{},[1716,34872,2222],{},[898,34874,2473],{"mathvariant":2003},[1716,34876,2787],{},[895,34878,34879,34887,34901],{},[2563,34880,34881],{"scriptlevel":2085,"displaystyle":1903},[2567,34882,34883,34885],{},[1716,34884,2222],{},[1716,34886,2787],{},[6989,34888,34889,34891,34893],{},[898,34890,1734],{},[1716,34892,2222],{},[895,34894,34895,34897,34899],{},[1716,34896,2222],{},[898,34898,2473],{"mathvariant":2003},[1716,34900,2787],{},[6989,34902,34903,34905,34907],{},[898,34904,1734],{},[1716,34906,2787],{},[895,34908,34909,34911,34913,34915],{},[1712,34910,2219],{},[1716,34912,2222],{},[898,34914,2473],{"mathvariant":2003},[1716,34916,2787],{},[1712,34918,1714],{},[2567,34920,34921,34927],{},[6927,34922,34923,34925],{},[898,34924,1734],{},[1716,34926,2787],{},[6927,34928,34929,34931],{},[898,34930,1734],{},[1716,34932,2222],{},[898,34934,1659],{"mathvariant":2003},[902,34936,34937],{"encoding":904},"\\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}.",[724,34939,34940,34941,7037,34986,34988,34989,35009,35010,35040,35041,1659],{},"Tedy ",[883,34942,34944],{"className":34943},[886],[888,34945,34946],{"xmlns":890},[892,34947,34948,34983],{},[895,34949,34950,34952,34954,34957,34959,34961,34963,34965,34973,34975],{},[1762,34951,15475],{},[1712,34953,1904],{"stretchy":1903},[1716,34955,34956],{},"300",[1712,34958,3138],{"separator":2565},[1716,34960,19984],{},[1712,34962,1910],{"stretchy":1903},[1712,34964,1714],{},[2563,34966,34967],{"scriptlevel":2085,"displaystyle":1903},[2567,34968,34969,34971],{},[1716,34970,19984],{},[1716,34972,34956],{},[1712,34974,1714],{},[2563,34976,34977],{"scriptlevel":2085,"displaystyle":1903},[2567,34978,34979,34981],{},[1716,34980,3068],{},[1716,34982,6198],{},[902,34984,34985],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,34987,7040],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,34990,34992],{"className":34991},[886],[888,34993,34994],{"xmlns":890},[892,34995,34996,35006],{},[895,34997,34998],{},[2563,34999,35000],{"scriptlevel":2085,"displaystyle":1903},[2567,35001,35002,35004],{},[1716,35003,3068],{},[1716,35005,6198],{},[902,35007,35008],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,35011,35013],{"className":35012},[886],[888,35014,35015],{"xmlns":890},[892,35016,35017,35037],{},[895,35018,35019,35021,35023,35029,35031],{},[1762,35020,15475],{},[1712,35022,1714],{},[6927,35024,35025,35027],{},[898,35026,1734],{},[1716,35028,2787],{},[898,35030,2473],{"mathvariant":2003},[6927,35032,35033,35035],{},[898,35034,1734],{},[1716,35036,2222],{},[902,35038,35039],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,35042,35044],{"className":35043},[886],[888,35045,35046],{"xmlns":890},[892,35047,35048,35068],{},[895,35049,35050,35052,35054,35060,35062],{},[1762,35051,15475],{},[1712,35053,1714],{},[6927,35055,35056,35058],{},[898,35057,1710],{},[1716,35059,2222],{},[898,35061,2473],{"mathvariant":2003},[6927,35063,35064,35066],{},[898,35065,1710],{},[1716,35067,2787],{},[902,35069,32873],{"encoding":904},[115,35071,35073,35074],{"id":35072},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,35075,35077],{"className":35076},[886],[888,35078,35079],{"xmlns":890},[892,35080,35081,35099],{},[895,35082,35083,35085,35087,35093],{},[898,35084,900],{},[1712,35086,1714],{},[6927,35088,35089,35091],{},[898,35090,1734],{},[1716,35092,2222],{},[6927,35094,35095,35097],{},[898,35096,1734],{},[1716,35098,2787],{},[902,35100,35101],{"encoding":904},"U = Q_1 Q_2",[724,35103,35104,35105,1343,35151,1343,35175,1343,35199,35221],{},"Je dána ",[883,35106,35108],{"className":35107},[886],[888,35109,35110],{"xmlns":890},[892,35111,35112,35148],{},[895,35113,35114,35116,35118,35124,35126,35132,35134,35136,35142],{},[898,35115,900],{},[1712,35117,1904],{"stretchy":1903},[6927,35119,35120,35122],{},[898,35121,1734],{},[1716,35123,2222],{},[1712,35125,3138],{"separator":2565},[6927,35127,35128,35130],{},[898,35129,1734],{},[1716,35131,2787],{},[1712,35133,1910],{"stretchy":1903},[1712,35135,1714],{},[6927,35137,35138,35140],{},[898,35139,1734],{},[1716,35141,2222],{},[6927,35143,35144,35146],{},[898,35145,1734],{},[1716,35147,2787],{},[902,35149,35150],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,35152,35154],{"className":35153},[886],[888,35155,35156],{"xmlns":890},[892,35157,35158,35172],{},[895,35159,35160,35168,35170],{},[6989,35161,35162,35164,35166],{},[898,35163,1710],{},[1716,35165,2222],{},[1712,35167,2145],{},[1712,35169,1714],{},[1716,35171,2787],{},[902,35173,35174],{"encoding":904},"P_1^* = 2",[883,35176,35178],{"className":35177},[886],[888,35179,35180],{"xmlns":890},[892,35181,35182,35196],{},[895,35183,35184,35192,35194],{},[6989,35185,35186,35188,35190],{},[898,35187,1710],{},[1716,35189,2787],{},[1712,35191,2145],{},[1712,35193,1714],{},[1716,35195,3068],{},[902,35197,35198],{"encoding":904},"P_2^* = 5",[883,35200,35202],{"className":35201},[886],[888,35203,35204],{"xmlns":890},[892,35205,35206,35218],{},[895,35207,35208,35214,35216],{},[2037,35209,35210,35212],{},[898,35211,6951],{},[1712,35213,2145],{},[1712,35215,1714],{},[1716,35217,1739],{},[902,35219,35220],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,35223,35225],{"className":35224},[886],[888,35226,35227],{"xmlns":890,"display":32941},[892,35228,35229,35301],{},[895,35230,35231,35233,35235,35241,35243,35249,35251,35253,35255,35257,35263,35269,35271,35273,35275,35277,35279,35281,35287,35289,35291,35297,35299],{},[898,35232,14667],{"mathvariant":33423},[1712,35234,1904],{"stretchy":1903},[6927,35236,35237,35239],{},[898,35238,1734],{},[1716,35240,2222],{},[1712,35242,3138],{"separator":2565},[6927,35244,35245,35247],{},[898,35246,1734],{},[1716,35248,2787],{},[1712,35250,3138],{"separator":2565},[898,35252,21318],{},[1712,35254,1910],{"stretchy":1903},[1712,35256,1714],{},[6927,35258,35259,35261],{},[898,35260,1734],{},[1716,35262,2222],{},[6927,35264,35265,35267],{},[898,35266,1734],{},[1716,35268,2787],{},[1712,35270,3145],{},[898,35272,21318],{},[1712,35274,1904],{"stretchy":1903},[1716,35276,1739],{},[1712,35278,2219],{},[1716,35280,2787],{},[6927,35282,35283,35285],{},[898,35284,1734],{},[1716,35286,2222],{},[1712,35288,2219],{},[1716,35290,3068],{},[6927,35292,35293,35295],{},[898,35294,1734],{},[1716,35296,2787],{},[1712,35298,1910],{"stretchy":1903},[898,35300,1659],{"mathvariant":2003},[902,35302,35303],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,35305,35306],{},"Soustava:",[883,35308,35310],{"className":35309},[886],[888,35311,35312],{"xmlns":890,"display":32941},[892,35313,35314,35426],{},[25629,35315,35316,35350,35384],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,35317,35318,35336],{},[25637,35319,35320],{},[2563,35321,35322],{"scriptlevel":2085,"displaystyle":2565},[895,35323,35324,35330,35332,35334],{},[6927,35325,35326,35328],{},[898,35327,1734],{},[1716,35329,2787],{},[1712,35331,2219],{},[1716,35333,2787],{},[898,35335,21318],{},[25637,35337,35338],{},[2563,35339,35340],{"scriptlevel":2085,"displaystyle":2565},[895,35341,35342,35344,35346,35348],{},[895,35343],{},[1712,35345,1714],{},[1716,35347,2085],{},[1712,35349,3138],{"separator":2565},[25634,35351,35352,35370],{},[25637,35353,35354],{},[2563,35355,35356],{"scriptlevel":2085,"displaystyle":2565},[895,35357,35358,35364,35366,35368],{},[6927,35359,35360,35362],{},[898,35361,1734],{},[1716,35363,2222],{},[1712,35365,2219],{},[1716,35367,3068],{},[898,35369,21318],{},[25637,35371,35372],{},[2563,35373,35374],{"scriptlevel":2085,"displaystyle":2565},[895,35375,35376,35378,35380,35382],{},[895,35377],{},[1712,35379,1714],{},[1716,35381,2085],{},[1712,35383,3138],{"separator":2565},[25634,35385,35386,35414],{},[25637,35387,35388],{},[2563,35389,35390],{"scriptlevel":2085,"displaystyle":2565},[895,35391,35392,35394,35396,35398,35404,35406,35408],{},[1716,35393,1739],{},[1712,35395,2219],{},[1716,35397,2787],{},[6927,35399,35400,35402],{},[898,35401,1734],{},[1716,35403,2222],{},[1712,35405,2219],{},[1716,35407,3068],{},[6927,35409,35410,35412],{},[898,35411,1734],{},[1716,35413,2787],{},[25637,35415,35416],{},[2563,35417,35418],{"scriptlevel":2085,"displaystyle":2565},[895,35419,35420,35422,35424],{},[895,35421],{},[1712,35423,1714],{},[1716,35425,17334],{},[902,35427,35428],{"encoding":904},"\\begin{aligned}\nQ_2 - 2 \\lambda &= 0, \\\\\nQ_1 - 5 \\lambda &= 0, \\\\\n100 - 2 Q_1 - 5 Q_2 &= 0.\n\\end{aligned}",[724,35430,35431,35432,1343,35456,35480,35481,3401,35521,35539,35540,35590,35591,1659],{},"Z prvních dvou rovnic ",[883,35433,35435],{"className":35434},[886],[888,35436,35437],{"xmlns":890},[892,35438,35439,35453],{},[895,35440,35441,35447,35449,35451],{},[6927,35442,35443,35445],{},[898,35444,1734],{},[1716,35446,2787],{},[1712,35448,1714],{},[1716,35450,2787],{},[898,35452,21318],{},[902,35454,35455],{"encoding":904},"Q_2 = 2\\lambda",[883,35457,35459],{"className":35458},[886],[888,35460,35461],{"xmlns":890},[892,35462,35463,35477],{},[895,35464,35465,35471,35473,35475],{},[6927,35466,35467,35469],{},[898,35468,1734],{},[1716,35470,2222],{},[1712,35472,1714],{},[1716,35474,3068],{},[898,35476,21318],{},[902,35478,35479],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,35482,35484],{"className":35483},[886],[888,35485,35486],{"xmlns":890},[892,35487,35488,35518],{},[895,35489,35490,35492,35494,35496,35498,35500,35502,35504,35506,35508,35510,35512,35514,35516],{},[1716,35491,1739],{},[1712,35493,1714],{},[1716,35495,2787],{},[1712,35497,1783],{},[1716,35499,3068],{},[898,35501,21318],{},[1712,35503,3145],{},[1716,35505,3068],{},[1712,35507,1783],{},[1716,35509,2787],{},[898,35511,21318],{},[1712,35513,1714],{},[1716,35515,6857],{},[898,35517,21318],{},[902,35519,35520],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,35522,35524],{"className":35523},[886],[888,35525,35526],{"xmlns":890},[892,35527,35528,35536],{},[895,35529,35530,35532,35534],{},[898,35531,21318],{},[1712,35533,1714],{},[1716,35535,3068],{},[902,35537,35538],{"encoding":904},"\\lambda = 5",". Odtud ",[38,35541,35542,1343,35566],{},[883,35543,35545],{"className":35544},[886],[888,35546,35547],{"xmlns":890},[892,35548,35549,35563],{},[895,35550,35551,35559,35561],{},[6989,35552,35553,35555,35557],{},[898,35554,1734],{},[1716,35556,2222],{},[1712,35558,2145],{},[1712,35560,1714],{},[1716,35562,2809],{},[902,35564,35565],{"encoding":904},"Q_1^* = 25",[883,35567,35569],{"className":35568},[886],[888,35570,35571],{"xmlns":890},[892,35572,35573,35587],{},[895,35574,35575,35583,35585],{},[6989,35576,35577,35579,35581],{},[898,35578,1734],{},[1716,35580,2787],{},[1712,35582,2145],{},[1712,35584,1714],{},[1716,35586,1718],{},[902,35588,35589],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,35592,35594],{"className":35593},[886],[888,35595,35596],{"xmlns":890},[892,35597,35598,35619],{},[895,35599,35600,35606,35608,35610,35612,35614,35616],{},[2037,35601,35602,35604],{},[898,35603,900],{},[1712,35605,2145],{},[1712,35607,1714],{},[1716,35609,2809],{},[1712,35611,1783],{},[1716,35613,1718],{},[1712,35615,1714],{},[1716,35617,35618],{},"250",[902,35620,35621],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,35623,35624],{},[614,35625,35626,35627,33012,35665,1655,35689,35713,35714,35744,35745,35769,35770,35792,35793,1659],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,35628,35630],{"className":35629},[886],[888,35631,35632],{"xmlns":890},[892,35633,35634,35662],{},[895,35635,35636,35638,35640,35642,35648,35650,35652,35658,35660],{},[1716,35637,1739],{},[1712,35639,2219],{},[1716,35641,2787],{},[6927,35643,35644,35646],{},[898,35645,1734],{},[1716,35647,2222],{},[1712,35649,2219],{},[1716,35651,3068],{},[6927,35653,35654,35656],{},[898,35655,1734],{},[1716,35657,2787],{},[1712,35659,1714],{},[1716,35661,2085],{},[902,35663,35664],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,35666,35668],{"className":35667},[886],[888,35669,35670],{"xmlns":890},[892,35671,35672,35686],{},[895,35673,35674,35676,35678,35680,35682,35684],{},[898,35675,2044],{},[1712,35677,7910],{"stretchy":1903},[1716,35679,2085],{},[1712,35681,3138],{"separator":2565},[1716,35683,6857],{},[1712,35685,7925],{"stretchy":1903},[902,35687,35688],{"encoding":904},"A[0, 20]",[883,35690,35692],{"className":35691},[886],[888,35693,35694],{"xmlns":890},[892,35695,35696,35710],{},[895,35697,35698,35700,35702,35704,35706,35708],{},[898,35699,28128],{},[1712,35701,7910],{"stretchy":1903},[1716,35703,2782],{},[1712,35705,3138],{"separator":2565},[1716,35707,2085],{},[1712,35709,7925],{"stretchy":1903},[902,35711,35712],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,35715,35717],{"className":35716},[886],[888,35718,35719],{"xmlns":890},[892,35720,35721,35741],{},[895,35722,35723,35729,35731,35733,35735],{},[6927,35724,35725,35727],{},[898,35726,1734],{},[1716,35728,2787],{},[1712,35730,1714],{},[1716,35732,35618],{},[898,35734,2473],{"mathvariant":2003},[6927,35736,35737,35739],{},[898,35738,1734],{},[1716,35740,2222],{},[902,35742,35743],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,35746,35748],{"className":35747},[886],[888,35749,35750],{"xmlns":890},[892,35751,35752,35766],{},[895,35753,35754,35756,35758,35760,35762,35764],{},[898,35755,2041],{},[1712,35757,7910],{"stretchy":1903},[1716,35759,2809],{},[1712,35761,3138],{"separator":2565},[1716,35763,1718],{},[1712,35765,7925],{"stretchy":1903},[902,35767,35768],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,35771,35773],{"className":35772},[886],[888,35774,35775],{"xmlns":890},[892,35776,35777,35789],{},[895,35778,35779,35781],{},[1712,35780,2219],{},[2563,35782,35783],{"scriptlevel":2085,"displaystyle":1903},[2567,35784,35785,35787],{},[1716,35786,2787],{},[1716,35788,3068],{},[902,35790,35791],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,35794,35796],{"className":35795},[886],[888,35797,35798],{"xmlns":890},[892,35799,35800,35840],{},[895,35801,35802,35804,35806,35808,35810,35812,35814,35816,35818,35820,35828,35830,35832],{},[1712,35803,2219],{},[1762,35805,15475],{},[1712,35807,1904],{"stretchy":1903},[1716,35809,2809],{},[1712,35811,3138],{"separator":2565},[1716,35813,1718],{},[1712,35815,1910],{"stretchy":1903},[1712,35817,1714],{},[1712,35819,2219],{},[2563,35821,35822],{"scriptlevel":2085,"displaystyle":1903},[2567,35823,35824,35826],{},[1716,35825,1718],{},[1716,35827,2809],{},[1712,35829,1714],{},[1712,35831,2219],{},[2563,35833,35834],{"scriptlevel":2085,"displaystyle":1903},[2567,35835,35836,35838],{},[1716,35837,2787],{},[1716,35839,3068],{},[902,35841,35842],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,35844,35846],{"id":35845},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,35848,35849,35850,33878,35880,35883,35884,2854],{},"Považujeme-li v úloze ",[883,35851,35853],{"className":35852},[886],[888,35854,35855],{"xmlns":890},[892,35856,35857,35877],{},[895,35858,35859,35865,35867,35873,35875],{},[6927,35860,35861,35863],{},[898,35862,1710],{},[1716,35864,2222],{},[1712,35866,3138],{"separator":2565},[6927,35868,35869,35871],{},[898,35870,1710],{},[1716,35872,2787],{},[1712,35874,3138],{"separator":2565},[898,35876,6951],{},[902,35878,35879],{"encoding":904},"P_1, P_2, Y",[38,35881,35882],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,35885,35886],{},"Marshallovy poptávkové funkce",[883,35888,35890],{"className":35889},[886],[888,35891,35892],{"xmlns":890,"display":32941},[892,35893,35894,35989],{},[25629,35895,35896],{"width":32946},[25634,35897,35898,35900,35982,35984],{},[25637,35899],{"width":32951},[25637,35901,35902],{},[895,35903,35904,35910,35912,35918,35920,35926,35928,35934,35936,35938,35940,35942,35944,35950,35952,35958,35960,35966,35968,35974,35976,35978,35980],{},[6927,35905,35906,35908],{},[898,35907,1734],{},[1716,35909,2222],{},[1712,35911,1714],{},[6927,35913,35914,35916],{},[898,35915,1969],{},[1716,35917,2222],{},[1712,35919,1904],{"stretchy":1903},[6927,35921,35922,35924],{},[898,35923,1710],{},[1716,35925,2222],{},[1712,35927,3138],{"separator":2565},[6927,35929,35930,35932],{},[898,35931,1710],{},[1716,35933,2787],{},[1712,35935,3138],{"separator":2565},[898,35937,6951],{},[1712,35939,1910],{"stretchy":1903},[1712,35941,3138],{"separator":2565},[3690,35943],{"width":20158},[6927,35945,35946,35948],{},[898,35947,1734],{},[1716,35949,2787],{},[1712,35951,1714],{},[6927,35953,35954,35956],{},[898,35955,1969],{},[1716,35957,2787],{},[1712,35959,1904],{"stretchy":1903},[6927,35961,35962,35964],{},[898,35963,1710],{},[1716,35965,2222],{},[1712,35967,3138],{"separator":2565},[6927,35969,35970,35972],{},[898,35971,1710],{},[1716,35973,2787],{},[1712,35975,3138],{"separator":2565},[898,35977,6951],{},[1712,35979,1910],{"stretchy":1903},[1712,35981,3138],{"separator":2565},[25637,35983],{"width":32951},[25637,35985,35986],{},[1762,35987,35988],{},"(6.15)",[902,35990,35991],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,35993,35995],{"className":35994},[886],[888,35996,35997],{"xmlns":890,"display":32941},[892,35998,35999,36046],{},[25629,36000,36001],{"width":32946},[25634,36002,36003,36005,36039,36041],{},[25637,36004],{"width":32951},[25637,36006,36007],{},[895,36008,36009,36011,36013,36015,36017,36023,36025,36031,36033,36035,36037],{},[898,36010,21318],{},[1712,36012,1714],{},[898,36014,21318],{},[1712,36016,1904],{"stretchy":1903},[6927,36018,36019,36021],{},[898,36020,1710],{},[1716,36022,2222],{},[1712,36024,3138],{"separator":2565},[6927,36026,36027,36029],{},[898,36028,1710],{},[1716,36030,2787],{},[1712,36032,3138],{"separator":2565},[898,36034,6951],{},[1712,36036,1910],{"stretchy":1903},[898,36038,1659],{"mathvariant":2003},[25637,36040],{"width":32951},[25637,36042,36043],{},[1762,36044,36045],{},"(6.16)",[902,36047,36048],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,36050,36051,36081,36082,36148],{},[38,36052,36053,36054,1659],{},"Odvození pro ",[883,36055,36057],{"className":36056},[886],[888,36058,36059],{"xmlns":890},[892,36060,36061,36079],{},[895,36062,36063,36065,36067,36073],{},[898,36064,900],{},[1712,36066,1714],{},[6927,36068,36069,36071],{},[898,36070,1734],{},[1716,36072,2222],{},[6927,36074,36075,36077],{},[898,36076,1734],{},[1716,36078,2787],{},[902,36080,35101],{"encoding":904}," Lagrangeova funkce ",[883,36083,36085],{"className":36084},[886],[888,36086,36087],{"xmlns":890},[892,36088,36089,36145],{},[895,36090,36091,36093,36095,36101,36107,36109,36111,36113,36115,36117,36123,36129,36131,36137,36143],{},[898,36092,14667],{"mathvariant":33423},[1712,36094,1714],{},[6927,36096,36097,36099],{},[898,36098,1734],{},[1716,36100,2222],{},[6927,36102,36103,36105],{},[898,36104,1734],{},[1716,36106,2787],{},[1712,36108,3145],{},[898,36110,21318],{},[1712,36112,1904],{"stretchy":1903},[898,36114,6951],{},[1712,36116,2219],{},[6927,36118,36119,36121],{},[898,36120,1710],{},[1716,36122,2222],{},[6927,36124,36125,36127],{},[898,36126,1734],{},[1716,36128,2222],{},[1712,36130,2219],{},[6927,36132,36133,36135],{},[898,36134,1710],{},[1716,36136,2787],{},[6927,36138,36139,36141],{},[898,36140,1734],{},[1716,36142,2787],{},[1712,36144,1910],{"stretchy":1903},[902,36146,36147],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,36150,36152],{"className":36151},[886],[888,36153,36154],{"xmlns":890,"display":32941},[892,36155,36156,36323],{},[25629,36157,36158],{"width":32946},[25634,36159,36160,36162,36316,36318],{},[25637,36161],{"width":32951},[25637,36163,36164],{},[25629,36165,36166,36212,36258],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,36167,36168,36180],{},[25637,36169,36170],{},[2563,36171,36172],{"scriptlevel":2085,"displaystyle":2565},[6989,36173,36174,36176,36178],{},[898,36175,14667],{"mathvariant":33423},[1716,36177,2222],{},[1712,36179,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,36181,36182],{},[2563,36183,36184],{"scriptlevel":2085,"displaystyle":2565},[895,36185,36186,36188,36190,36196,36198,36200,36206,36208,36210],{},[895,36187],{},[1712,36189,1714],{},[6927,36191,36192,36194],{},[898,36193,1734],{},[1716,36195,2787],{},[1712,36197,2219],{},[898,36199,21318],{},[6927,36201,36202,36204],{},[898,36203,1710],{},[1716,36205,2222],{},[1712,36207,1714],{},[1716,36209,2085],{},[1712,36211,3138],{"separator":2565},[25634,36213,36214,36226],{},[25637,36215,36216],{},[2563,36217,36218],{"scriptlevel":2085,"displaystyle":2565},[6989,36219,36220,36222,36224],{},[898,36221,14667],{"mathvariant":33423},[1716,36223,2787],{},[1712,36225,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,36227,36228],{},[2563,36229,36230],{"scriptlevel":2085,"displaystyle":2565},[895,36231,36232,36234,36236,36242,36244,36246,36252,36254,36256],{},[895,36233],{},[1712,36235,1714],{},[6927,36237,36238,36240],{},[898,36239,1734],{},[1716,36241,2222],{},[1712,36243,2219],{},[898,36245,21318],{},[6927,36247,36248,36250],{},[898,36249,1710],{},[1716,36251,2787],{},[1712,36253,1714],{},[1716,36255,2085],{},[1712,36257,3138],{"separator":2565},[25634,36259,36260,36272],{},[25637,36261,36262],{},[2563,36263,36264],{"scriptlevel":2085,"displaystyle":2565},[6989,36265,36266,36268,36270],{},[898,36267,14667],{"mathvariant":33423},[898,36269,21318],{},[1712,36271,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,36273,36274],{},[2563,36275,36276],{"scriptlevel":2085,"displaystyle":2565},[895,36277,36278,36280,36282,36284,36286,36292,36298,36300,36306,36312,36314],{},[895,36279],{},[1712,36281,1714],{},[898,36283,6951],{},[1712,36285,2219],{},[6927,36287,36288,36290],{},[898,36289,1710],{},[1716,36291,2222],{},[6927,36293,36294,36296],{},[898,36295,1734],{},[1716,36297,2222],{},[1712,36299,2219],{},[6927,36301,36302,36304],{},[898,36303,1710],{},[1716,36305,2787],{},[6927,36307,36308,36310],{},[898,36309,1734],{},[1716,36311,2787],{},[1712,36313,1714],{},[1716,36315,17334],{},[25637,36317],{"width":32951},[25637,36319,36320],{},[1762,36321,36322],{},"(6.17)",[902,36324,36325],{"encoding":904},"\\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}",[724,36327,36328,36329,36357,36358,36386,36387,36455],{},"Z prvních dvou: ",[883,36330,36332],{"className":36331},[886],[888,36333,36334],{"xmlns":890},[892,36335,36336,36354],{},[895,36337,36338,36344,36346,36352],{},[6927,36339,36340,36342],{},[898,36341,1734],{},[1716,36343,2787],{},[1712,36345,1714],{},[6927,36347,36348,36350],{},[898,36349,1710],{},[1716,36351,2222],{},[898,36353,21318],{},[902,36355,36356],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,36359,36361],{"className":36360},[886],[888,36362,36363],{"xmlns":890},[892,36364,36365,36383],{},[895,36366,36367,36373,36375,36381],{},[6927,36368,36369,36371],{},[898,36370,1734],{},[1716,36372,2222],{},[1712,36374,1714],{},[6927,36376,36377,36379],{},[898,36378,1710],{},[1716,36380,2787],{},[898,36382,21318],{},[902,36384,36385],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,36388,36390],{"className":36389},[886],[888,36391,36392],{"xmlns":890},[892,36393,36394,36452],{},[895,36395,36396,36398,36400,36406,36408,36414,36416,36418,36424,36426,36432,36434,36436,36438,36444,36450],{},[898,36397,6951],{},[1712,36399,1714],{},[6927,36401,36402,36404],{},[898,36403,1710],{},[1716,36405,2222],{},[1712,36407,1783],{},[6927,36409,36410,36412],{},[898,36411,1710],{},[1716,36413,2787],{},[898,36415,21318],{},[1712,36417,3145],{},[6927,36419,36420,36422],{},[898,36421,1710],{},[1716,36423,2787],{},[1712,36425,1783],{},[6927,36427,36428,36430],{},[898,36429,1710],{},[1716,36431,2222],{},[898,36433,21318],{},[1712,36435,1714],{},[1716,36437,2787],{},[6927,36439,36440,36442],{},[898,36441,1710],{},[1716,36443,2222],{},[6927,36445,36446,36448],{},[898,36447,1710],{},[1716,36449,2787],{},[898,36451,21318],{},[902,36453,36454],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,36457,36459],{"className":36458},[886],[888,36460,36461],{"xmlns":890,"display":32941},[892,36462,36463,36506],{},[25629,36464,36465],{"width":32946},[25634,36466,36467,36469,36499,36501],{},[25637,36468],{"width":32951},[25637,36470,36471],{},[895,36472,36473,36475,36477,36497],{},[898,36474,21318],{},[1712,36476,1714],{},[2567,36478,36479,36481],{},[898,36480,6951],{},[895,36482,36483,36485,36491],{},[1716,36484,2787],{},[6927,36486,36487,36489],{},[898,36488,1710],{},[1716,36490,2222],{},[6927,36492,36493,36495],{},[898,36494,1710],{},[1716,36496,2787],{},[898,36498,1659],{"mathvariant":2003},[25637,36500],{"width":32951},[25637,36502,36503],{},[1762,36504,36505],{},"(6.20)",[902,36507,36508],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,36510,36511],{},"Zpětně:",[883,36513,36515],{"className":36514},[886],[888,36516,36517],{"xmlns":890,"display":32941},[892,36518,36519,36596],{},[25629,36520,36521],{"width":32946},[25634,36522,36523,36525,36589,36591],{},[25637,36524],{"width":32951},[25637,36526,36527],{},[17706,36528,36529],{"notation":17708},[2563,36530,36531],{"scriptlevel":2085,"displaystyle":1903},[2563,36532,36533],{"scriptlevel":2085,"displaystyle":1903},[2563,36534,36535],{"scriptlevel":2085,"displaystyle":2565},[895,36536,36537,36539,36545,36547,36561,36563,36565,36571,36573,36587],{},[1762,36538,1764],{},[6927,36540,36541,36543],{},[898,36542,1734],{},[1716,36544,2222],{},[1712,36546,1714],{},[2567,36548,36549,36551],{},[898,36550,6951],{},[895,36552,36553,36555],{},[1716,36554,2787],{},[6927,36556,36557,36559],{},[898,36558,1710],{},[1716,36560,2222],{},[1712,36562,3138],{"separator":2565},[3690,36564],{"width":20158},[6927,36566,36567,36569],{},[898,36568,1734],{},[1716,36570,2787],{},[1712,36572,1714],{},[2567,36574,36575,36577],{},[898,36576,6951],{},[895,36578,36579,36581],{},[1716,36580,2787],{},[6927,36582,36583,36585],{},[898,36584,1710],{},[1716,36586,2787],{},[1762,36588,1764],{},[25637,36590],{"width":32951},[25637,36592,36593],{},[1762,36594,36595],{},"(6.21)",[902,36597,36598],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,36600,36602],{"id":36601},"engelova-funkce","Engelova funkce",[724,36604,14535,36605,36608,36609,36612,36613,24742,36630,1343,36660,36690,36691,36725,36726,1343,36752,36778],{},[38,36606,36607],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,36610,36611],{},"Engelovou funkcí",": pro ",[883,36614,36616],{"className":36615},[886],[888,36617,36618],{"xmlns":890},[892,36619,36620,36628],{},[895,36621,36622,36624,36626],{},[898,36623,6951],{},[1712,36625,1714],{},[1716,36627,1739],{},[902,36629,25194],{"encoding":904},[883,36631,36633],{"className":36632},[886],[888,36634,36635],{"xmlns":890},[892,36636,36637,36657],{},[895,36638,36639,36645,36647,36649,36651],{},[6927,36640,36641,36643],{},[898,36642,1734],{},[1716,36644,2222],{},[1712,36646,1714],{},[1716,36648,2782],{},[898,36650,2473],{"mathvariant":2003},[6927,36652,36653,36655],{},[898,36654,1710],{},[1716,36656,2222],{},[902,36658,36659],{"encoding":904},"Q_1 = 50\u002FP_1",[883,36661,36663],{"className":36662},[886],[888,36664,36665],{"xmlns":890},[892,36666,36667,36687],{},[895,36668,36669,36675,36677,36679,36681],{},[6927,36670,36671,36673],{},[898,36672,1734],{},[1716,36674,2787],{},[1712,36676,1714],{},[1716,36678,2782],{},[898,36680,2473],{"mathvariant":2003},[6927,36682,36683,36685],{},[898,36684,1710],{},[1716,36686,2787],{},[902,36688,36689],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,36692,36694],{"className":36693},[886],[888,36695,36696],{"xmlns":890},[892,36697,36698,36722],{},[895,36699,36700,36706,36708,36710,36712,36718,36720],{},[6927,36701,36702,36704],{},[898,36703,1710],{},[1716,36705,2222],{},[1712,36707,1714],{},[1716,36709,1718],{},[1712,36711,3138],{"separator":2565},[6927,36713,36714,36716],{},[898,36715,1710],{},[1716,36717,2787],{},[1712,36719,1714],{},[1716,36721,6857],{},[902,36723,36724],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,36727,36729],{"className":36728},[886],[888,36730,36731],{"xmlns":890},[892,36732,36733,36749],{},[895,36734,36735,36741,36743,36745,36747],{},[6927,36736,36737,36739],{},[898,36738,1734],{},[1716,36740,2222],{},[1712,36742,1714],{},[898,36744,6951],{},[898,36746,2473],{"mathvariant":2003},[1716,36748,6857],{},[902,36750,36751],{"encoding":904},"Q_1 = Y\u002F20",[883,36753,36755],{"className":36754},[886],[888,36756,36757],{"xmlns":890},[892,36758,36759,36775],{},[895,36760,36761,36767,36769,36771,36773],{},[6927,36762,36763,36765],{},[898,36764,1734],{},[1716,36766,2787],{},[1712,36768,1714],{},[898,36770,6951],{},[898,36772,2473],{"mathvariant":2003},[1716,36774,3018],{},[902,36776,36777],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,36780,36782],{"id":36781},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,36784,36785],{},"Výdaje spotřebitele jsou",[883,36787,36789],{"className":36788},[886],[888,36790,36791],{"xmlns":890,"display":32941},[892,36792,36793,36868],{},[25629,36794,36795],{"width":32946},[25634,36796,36797,36799,36861,36863],{},[25637,36798],{"width":32951},[25637,36800,36801],{},[895,36802,36803,36805,36807,36809,36811,36817,36819,36825,36827,36829,36837,36843,36845,36853,36859],{},[898,36804,2041],{},[1712,36806,1714],{},[898,36808,2041],{},[1712,36810,1904],{"stretchy":1903},[6927,36812,36813,36815],{},[898,36814,1734],{},[1716,36816,2222],{},[1712,36818,3138],{"separator":2565},[6927,36820,36821,36823],{},[898,36822,1734],{},[1716,36824,2787],{},[1712,36826,1910],{"stretchy":1903},[1712,36828,1714],{},[6989,36830,36831,36833,36835],{},[898,36832,1710],{},[1716,36834,2222],{},[1712,36836,2145],{},[6927,36838,36839,36841],{},[898,36840,1734],{},[1716,36842,2222],{},[1712,36844,3145],{},[6989,36846,36847,36849,36851],{},[898,36848,1710],{},[1716,36850,2787],{},[1712,36852,2145],{},[6927,36854,36855,36857],{},[898,36856,1734],{},[1716,36858,2787],{},[1712,36860,3138],{"separator":2565},[25637,36862],{"width":32951},[25637,36864,36865],{},[1762,36866,36867],{},"(6.22)",[902,36869,36870],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,36872,36873],{},"a je pevně zadána hladina užitečnosti",[883,36875,36877],{"className":36876},[886],[888,36878,36879],{"xmlns":890,"display":32941},[892,36880,36881,36928],{},[25629,36882,36883],{"width":32946},[25634,36884,36885,36887,36921,36923],{},[25637,36886],{"width":32951},[25637,36888,36889],{},[895,36890,36891,36897,36899,36901,36903,36909,36911,36917,36919],{},[2037,36892,36893,36895],{},[898,36894,900],{},[1712,36896,2145],{},[1712,36898,1714],{},[898,36900,900],{},[1712,36902,1904],{"stretchy":1903},[6927,36904,36905,36907],{},[898,36906,1734],{},[1716,36908,2222],{},[1712,36910,3138],{"separator":2565},[6927,36912,36913,36915],{},[898,36914,1734],{},[1716,36916,2787],{},[1712,36918,1910],{"stretchy":1903},[898,36920,1659],{"mathvariant":2003},[25637,36922],{"width":32951},[25637,36924,36925],{},[1762,36926,36927],{},"(6.23)",[902,36929,36930],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,36932,36933,36936,36937,36969,36970,1659],{},[38,36934,36935],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,36938,36940],{"className":36939},[886],[888,36941,36942],{"xmlns":890},[892,36943,36944,36966],{},[895,36945,36946,36948,36950,36956,36958,36964],{},[898,36947,2041],{},[1712,36949,1904],{"stretchy":1903},[6927,36951,36952,36954],{},[898,36953,1734],{},[1716,36955,2222],{},[1712,36957,3138],{"separator":2565},[6927,36959,36960,36962],{},[898,36961,1734],{},[1716,36963,2787],{},[1712,36965,1910],{"stretchy":1903},[902,36967,36968],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,36971,36973],{"className":36972},[886],[888,36974,36975],{"xmlns":890},[892,36976,36977,37033],{},[895,36978,36979,36981,36983,36989,36991,36997,36999,37001,37007,37009,37011,37013,37019,37021,37027,37029,37031],{},[898,36980,15913],{},[1712,36982,1904],{"stretchy":1903},[6927,36984,36985,36987],{},[898,36986,1734],{},[1716,36988,2222],{},[1712,36990,3138],{"separator":2565},[6927,36992,36993,36995],{},[898,36994,1734],{},[1716,36996,2787],{},[1712,36998,1910],{"stretchy":1903},[1712,37000,1714],{},[2037,37002,37003,37005],{},[898,37004,900],{},[1712,37006,2145],{},[1712,37008,2219],{},[898,37010,900],{},[1712,37012,1904],{"stretchy":1903},[6927,37014,37015,37017],{},[898,37016,1734],{},[1716,37018,2222],{},[1712,37020,3138],{"separator":2565},[6927,37022,37023,37025],{},[898,37024,1734],{},[1716,37026,2787],{},[1712,37028,1910],{"stretchy":1903},[1712,37030,1714],{},[1716,37032,2085],{},[902,37034,37035],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,37037,37039],{"id":37038},"lagrangeova-funkce","Lagrangeova funkce",[883,37041,37043],{"className":37042},[886],[888,37044,37045],{"xmlns":890,"display":32941},[892,37046,37047,37158],{},[25629,37048,37049],{"width":32946},[25634,37050,37051,37053,37151,37153],{},[25637,37052],{"width":32951},[25637,37054,37055],{},[895,37056,37057,37059,37061,37067,37069,37075,37077,37079,37081,37083,37091,37097,37099,37107,37113,37115,37117,37119,37125,37127,37129,37131,37137,37139,37145,37147,37149],{},[898,37058,14667],{"mathvariant":33423},[1712,37060,1904],{"stretchy":1903},[6927,37062,37063,37065],{},[898,37064,1734],{},[1716,37066,2222],{},[1712,37068,3138],{"separator":2565},[6927,37070,37071,37073],{},[898,37072,1734],{},[1716,37074,2787],{},[1712,37076,3138],{"separator":2565},[898,37078,21318],{},[1712,37080,1910],{"stretchy":1903},[1712,37082,1714],{},[6989,37084,37085,37087,37089],{},[898,37086,1710],{},[1716,37088,2222],{},[1712,37090,2145],{},[6927,37092,37093,37095],{},[898,37094,1734],{},[1716,37096,2222],{},[1712,37098,3145],{},[6989,37100,37101,37103,37105],{},[898,37102,1710],{},[1716,37104,2787],{},[1712,37106,2145],{},[6927,37108,37109,37111],{},[898,37110,1734],{},[1716,37112,2787],{},[1712,37114,3145],{},[898,37116,21318],{},[1712,37118,1904],{"stretchy":1903},[2037,37120,37121,37123],{},[898,37122,900],{},[1712,37124,2145],{},[1712,37126,2219],{},[898,37128,900],{},[1712,37130,1904],{"stretchy":1903},[6927,37132,37133,37135],{},[898,37134,1734],{},[1716,37136,2222],{},[1712,37138,3138],{"separator":2565},[6927,37140,37141,37143],{},[898,37142,1734],{},[1716,37144,2787],{},[1712,37146,1910],{"stretchy":1903},[1712,37148,1910],{"stretchy":1903},[898,37150,1659],{"mathvariant":2003},[25637,37152],{"width":32951},[25637,37154,37155],{},[1762,37156,37157],{},"(6.24)",[902,37159,37160],{"encoding":904},"\\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}",[724,37162,37163],{},"Soustava podmínek prvního řádu:",[883,37165,37167],{"className":37166},[886],[888,37168,37169],{"xmlns":890,"display":32941},[892,37170,37171,37344],{},[25629,37172,37173],{"width":32946},[25634,37174,37175,37177,37337,37339],{},[25637,37176],{"width":32951},[25637,37178,37179],{},[25629,37180,37181,37231,37281],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,37182,37183,37195],{},[25637,37184,37185],{},[2563,37186,37187],{"scriptlevel":2085,"displaystyle":2565},[6989,37188,37189,37191,37193],{},[898,37190,14667],{"mathvariant":33423},[1716,37192,2222],{},[1712,37194,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,37196,37197],{},[2563,37198,37199],{"scriptlevel":2085,"displaystyle":2565},[895,37200,37201,37203,37205,37213,37215,37217,37225,37227,37229],{},[895,37202],{},[1712,37204,1714],{},[6989,37206,37207,37209,37211],{},[898,37208,1710],{},[1716,37210,2222],{},[1712,37212,2145],{},[1712,37214,2219],{},[898,37216,21318],{},[6989,37218,37219,37221,37223],{},[898,37220,900],{},[1716,37222,2222],{},[1712,37224,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,37226,1714],{},[1716,37228,2085],{},[1712,37230,3138],{"separator":2565},[25634,37232,37233,37245],{},[25637,37234,37235],{},[2563,37236,37237],{"scriptlevel":2085,"displaystyle":2565},[6989,37238,37239,37241,37243],{},[898,37240,14667],{"mathvariant":33423},[1716,37242,2787],{},[1712,37244,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,37246,37247],{},[2563,37248,37249],{"scriptlevel":2085,"displaystyle":2565},[895,37250,37251,37253,37255,37263,37265,37267,37275,37277,37279],{},[895,37252],{},[1712,37254,1714],{},[6989,37256,37257,37259,37261],{},[898,37258,1710],{},[1716,37260,2787],{},[1712,37262,2145],{},[1712,37264,2219],{},[898,37266,21318],{},[6989,37268,37269,37271,37273],{},[898,37270,900],{},[1716,37272,2787],{},[1712,37274,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,37276,1714],{},[1716,37278,2085],{},[1712,37280,3138],{"separator":2565},[25634,37282,37283,37295],{},[25637,37284,37285],{},[2563,37286,37287],{"scriptlevel":2085,"displaystyle":2565},[6989,37288,37289,37291,37293],{},[898,37290,14667],{"mathvariant":33423},[898,37292,21318],{},[1712,37294,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,37296,37297],{},[2563,37298,37299],{"scriptlevel":2085,"displaystyle":2565},[895,37300,37301,37303,37305,37311,37313,37315,37317,37323,37325,37331,37333,37335],{},[895,37302],{},[1712,37304,1714],{},[2037,37306,37307,37309],{},[898,37308,900],{},[1712,37310,2145],{},[1712,37312,2219],{},[898,37314,900],{},[1712,37316,1904],{"stretchy":1903},[6927,37318,37319,37321],{},[898,37320,1734],{},[1716,37322,2222],{},[1712,37324,3138],{"separator":2565},[6927,37326,37327,37329],{},[898,37328,1734],{},[1716,37330,2787],{},[1712,37332,1910],{"stretchy":1903},[1712,37334,1714],{},[1716,37336,17334],{},[25637,37338],{"width":32951},[25637,37340,37341],{},[1762,37342,37343],{},"(6.25)",[902,37345,37346],{"encoding":904},"\\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}",[724,37348,37349],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,37351,37353],{"className":37352},[886],[888,37354,37355],{"xmlns":890,"display":32941},[892,37356,37357,37455],{},[25629,37358,37359],{"width":32946},[25634,37360,37361,37363,37448,37450],{},[25637,37362],{"width":32951},[25637,37364,37365],{},[895,37366,37367,37369,37371,37377,37379,37385,37387,37389,37391,37393,37395,37397,37446],{},[898,37368,1969],{},[1712,37370,1904],{"stretchy":1903},[6927,37372,37373,37375],{},[898,37374,1734],{},[1716,37376,2222],{},[1712,37378,3138],{"separator":2565},[6927,37380,37381,37383],{},[898,37382,1734],{},[1716,37384,2787],{},[1712,37386,3138],{"separator":2565},[898,37388,21318],{},[1712,37390,1910],{"stretchy":1903},[1712,37392,1714],{},[1712,37394,2219],{},[898,37396,21318],{},[895,37398,37399,37401,37413,37415,37428,37430,37432,37444],{},[1712,37400,1904],{"fence":2565},[6989,37402,37403,37405,37407],{},[898,37404,900],{},[1716,37406,8316],{},[895,37408,37409,37411],{},[1712,37410,2243],{"mathvariant":2003},[1712,37412,2243],{"mathvariant":2003},[1712,37414,3145],{},[6989,37416,37417,37419,37422],{},[898,37418,900],{},[1716,37420,37421],{},"22",[895,37423,37424,37426],{},[1712,37425,2243],{"mathvariant":2003},[1712,37427,2243],{"mathvariant":2003},[1712,37429,3145],{},[1716,37431,2787],{},[6989,37433,37434,37436,37438],{},[898,37435,900],{},[1716,37437,8912],{},[895,37439,37440,37442],{},[1712,37441,2243],{"mathvariant":2003},[1712,37443,2243],{"mathvariant":2003},[1712,37445,1910],{"fence":2565},[898,37447,1659],{"mathvariant":2003},[25637,37449],{"width":32951},[25637,37451,37452],{},[1762,37453,37454],{},"(6.26)",[902,37456,37457],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,37459,37460,37463,37464,37503,37504,37543,37544,37594,37595,37621,37622,37639,37640,37666],{},[38,37461,37462],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,37465,37467],{"className":37466},[886],[888,37468,37469],{"xmlns":890},[892,37470,37471,37501],{},[895,37472,37473,37479,37481,37489,37491,37499],{},[2037,37474,37475,37477],{},[898,37476,1734],{},[1712,37478,2145],{},[1712,37480,7910],{"stretchy":1903},[6989,37482,37483,37485,37487],{},[898,37484,1734],{},[1716,37486,2222],{},[1712,37488,2145],{},[1712,37490,3138],{"separator":2565},[6989,37492,37493,37495,37497],{},[898,37494,1734],{},[1716,37496,2787],{},[1712,37498,2145],{},[1712,37500,7925],{"stretchy":1903},[902,37502,33202],{"encoding":904}," dotyku křivky užitečnosti ",[883,37505,37507],{"className":37506},[886],[888,37508,37509],{"xmlns":890},[892,37510,37511,37541],{},[895,37512,37513,37519,37521,37523,37525,37531,37533,37539],{},[2037,37514,37515,37517],{},[898,37516,900],{},[1712,37518,2145],{},[1712,37520,1714],{},[898,37522,900],{},[1712,37524,1904],{"stretchy":1903},[6927,37526,37527,37529],{},[898,37528,1734],{},[1716,37530,2222],{},[1712,37532,3138],{"separator":2565},[6927,37534,37535,37537],{},[898,37536,1734],{},[1716,37538,2787],{},[1712,37540,1910],{"stretchy":1903},[902,37542,22540],{"encoding":904}," s přímkou výdajů ",[883,37545,37547],{"className":37546},[886],[888,37548,37549],{"xmlns":890},[892,37550,37551,37591],{},[895,37552,37553,37559,37561,37569,37575,37577,37585],{},[2037,37554,37555,37557],{},[898,37556,2041],{},[1712,37558,2145],{},[1712,37560,1714],{},[6989,37562,37563,37565,37567],{},[898,37564,1710],{},[1716,37566,2222],{},[1712,37568,2145],{},[6927,37570,37571,37573],{},[898,37572,1734],{},[1716,37574,2222],{},[1712,37576,3145],{},[6989,37578,37579,37581,37583],{},[898,37580,1710],{},[1716,37582,2787],{},[1712,37584,2145],{},[6927,37586,37587,37589],{},[898,37588,1734],{},[1716,37590,2787],{},[902,37592,37593],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,37596,37598],{"className":37597},[886],[888,37599,37600],{"xmlns":890},[892,37601,37602,37618],{},[895,37603,37604,37610,37612],{},[6927,37605,37606,37608],{},[898,37607,2041],{},[1716,37609,2085],{},[1712,37611,2252],{},[2037,37613,37614,37616],{},[898,37615,2041],{},[1712,37617,2145],{},[902,37619,37620],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,37623,37625],{"className":37624},[886],[888,37626,37627],{"xmlns":890},[892,37628,37629,37637],{},[895,37630,37631],{},[2037,37632,37633,37635],{},[898,37634,900],{},[1712,37636,2145],{},[902,37638,32837],{"encoding":904},", hladina ",[883,37641,37643],{"className":37642},[886],[888,37644,37645],{"xmlns":890},[892,37646,37647,37663],{},[895,37648,37649,37655,37657],{},[6927,37650,37651,37653],{},[898,37652,2041],{},[1716,37654,2222],{},[1712,37656,2302],{},[2037,37658,37659,37661],{},[898,37660,2041],{},[1712,37662,2145],{},[902,37664,37665],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1636,37668,37669,37674],{},[724,37670,37671,37673],{},[883,37672,2370],{}," Postup — duální úloha (minimalizace výdajů)",[152,37675,37676,37726,37812,37852,37927],{},[123,37677,37678,3245,37681,37725],{},[38,37679,37680],{},"Zapiš vazbu",[883,37682,37684],{"className":37683},[886],[888,37685,37686],{"xmlns":890},[892,37687,37688,37722],{},[895,37689,37690,37696,37698,37700,37702,37708,37710,37716,37718,37720],{},[2037,37691,37692,37694],{},[898,37693,900],{},[1712,37695,2145],{},[1712,37697,2219],{},[898,37699,900],{},[1712,37701,1904],{"stretchy":1903},[6927,37703,37704,37706],{},[898,37705,1734],{},[1716,37707,2222],{},[1712,37709,3138],{"separator":2565},[6927,37711,37712,37714],{},[898,37713,1734],{},[1716,37715,2787],{},[1712,37717,1910],{"stretchy":1903},[1712,37719,1714],{},[1716,37721,2085],{},[902,37723,37724],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,37727,37728,3245,37730,1659],{},[38,37729,34135],{},[883,37731,37733],{"className":37732},[886],[888,37734,37735],{"xmlns":890},[892,37736,37737,37809],{},[895,37738,37739,37741,37743,37751,37757,37759,37767,37773,37775,37777,37779,37785,37787,37789,37791,37797,37799,37805,37807],{},[898,37740,14667],{"mathvariant":33423},[1712,37742,1714],{},[6989,37744,37745,37747,37749],{},[898,37746,1710],{},[1716,37748,2222],{},[1712,37750,2145],{},[6927,37752,37753,37755],{},[898,37754,1734],{},[1716,37756,2222],{},[1712,37758,3145],{},[6989,37760,37761,37763,37765],{},[898,37762,1710],{},[1716,37764,2787],{},[1712,37766,2145],{},[6927,37768,37769,37771],{},[898,37770,1734],{},[1716,37772,2787],{},[1712,37774,3145],{},[898,37776,21318],{},[1712,37778,1904],{"stretchy":1903},[2037,37780,37781,37783],{},[898,37782,900],{},[1712,37784,2145],{},[1712,37786,2219],{},[898,37788,900],{},[1712,37790,1904],{"stretchy":1903},[6927,37792,37793,37795],{},[898,37794,1734],{},[1716,37796,2222],{},[1712,37798,3138],{"separator":2565},[6927,37800,37801,37803],{},[898,37802,1734],{},[1716,37804,2787],{},[1712,37806,1910],{"stretchy":1903},[1712,37808,1910],{"stretchy":1903},[902,37810,37811],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,37813,37814,37817,37818,37851],{},[38,37815,37816],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,37819,37821],{"className":37820},[886],[888,37822,37823],{"xmlns":890},[892,37824,37825,37849],{},[895,37826,37827,37829,37831,37839,37841],{},[1762,37828,15475],{},[1712,37830,1714],{},[6989,37832,37833,37835,37837],{},[898,37834,1710],{},[1716,37836,2222],{},[1712,37838,2145],{},[898,37840,2473],{"mathvariant":2003},[6989,37842,37843,37845,37847],{},[898,37844,1710],{},[1716,37846,2787],{},[1712,37848,2145],{},[902,37850,33854],{"encoding":904}," (stejná jako u maximalizace!).",[123,37853,37854,3245,37857,37897,37898,1659],{},[38,37855,37856],{},"Dosaď do vazby",[883,37858,37860],{"className":37859},[886],[888,37861,37862],{"xmlns":890},[892,37863,37864,37894],{},[895,37865,37866,37868,37870,37876,37878,37884,37886,37888],{},[898,37867,900],{},[1712,37869,1904],{"stretchy":1903},[6927,37871,37872,37874],{},[898,37873,1734],{},[1716,37875,2222],{},[1712,37877,3138],{"separator":2565},[6927,37879,37880,37882],{},[898,37881,1734],{},[1716,37883,2787],{},[1712,37885,1910],{"stretchy":1903},[1712,37887,1714],{},[2037,37889,37890,37892],{},[898,37891,900],{},[1712,37893,2145],{},[902,37895,37896],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,37899,37901],{"className":37900},[886],[888,37902,37903],{"xmlns":890},[892,37904,37905,37925],{},[895,37906,37907,37915,37917],{},[6989,37908,37909,37911,37913],{},[898,37910,1734],{},[1716,37912,2222],{},[1712,37914,2145],{},[1712,37916,3138],{"separator":2565},[6989,37918,37919,37921,37923],{},[898,37920,1734],{},[1716,37922,2787],{},[1712,37924,2145],{},[902,37926,34376],{"encoding":904},[123,37928,37929,3245,37932,37986],{},[38,37930,37931],{},"Vypočítej minimální výdaje",[883,37933,37935],{"className":37934},[886],[888,37936,37937],{"xmlns":890},[892,37938,37939,37983],{},[895,37940,37941,37947,37949,37957,37965,37967,37975],{},[2037,37942,37943,37945],{},[898,37944,2041],{},[1712,37946,2145],{},[1712,37948,1714],{},[6989,37950,37951,37953,37955],{},[898,37952,1710],{},[1716,37954,2222],{},[1712,37956,2145],{},[6989,37958,37959,37961,37963],{},[898,37960,1734],{},[1716,37962,2222],{},[1712,37964,2145],{},[1712,37966,3145],{},[6989,37968,37969,37971,37973],{},[898,37970,1710],{},[1716,37972,2787],{},[1712,37974,2145],{},[6989,37976,37977,37979,37981],{},[898,37978,1734],{},[1716,37980,2787],{},[1712,37982,2145],{},[902,37984,37985],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,37988,37990,37991],{"id":37989},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,37992,37994],{"className":37993},[886],[888,37995,37996],{"xmlns":890},[892,37997,37998,38032],{},[895,37999,38000,38002,38004,38018],{},[898,38001,900],{},[1712,38003,1714],{},[6989,38005,38006,38008,38010],{},[898,38007,1734],{},[1716,38009,2222],{},[895,38011,38012,38014,38016],{},[1716,38013,2222],{},[898,38015,2473],{"mathvariant":2003},[1716,38017,2787],{},[6989,38019,38020,38022,38024],{},[898,38021,1734],{},[1716,38023,2787],{},[895,38025,38026,38028,38030],{},[1716,38027,2222],{},[898,38029,2473],{"mathvariant":2003},[1716,38031,2787],{},[902,38033,38034],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,38036,38037,38038,1343,38060,1343,38084,35221],{},"Dáno ",[883,38039,38041],{"className":38040},[886],[888,38042,38043],{"xmlns":890},[892,38044,38045,38057],{},[895,38046,38047,38053,38055],{},[2037,38048,38049,38051],{},[898,38050,900],{},[1712,38052,2145],{},[1712,38054,1714],{},[1716,38056,2787],{},[902,38058,38059],{"encoding":904},"U^* = 2",[883,38061,38063],{"className":38062},[886],[888,38064,38065],{"xmlns":890},[892,38066,38067,38081],{},[895,38068,38069,38077,38079],{},[6989,38070,38071,38073,38075],{},[898,38072,1710],{},[1716,38074,2222],{},[1712,38076,2145],{},[1712,38078,1714],{},[1716,38080,28664],{},[902,38082,38083],{"encoding":904},"P_1^* = 0{,}25",[883,38085,38087],{"className":38086},[886],[888,38088,38089],{"xmlns":890},[892,38090,38091,38105],{},[895,38092,38093,38101,38103],{},[6989,38094,38095,38097,38099],{},[898,38096,1710],{},[1716,38098,2787],{},[1712,38100,2145],{},[1712,38102,1714],{},[1716,38104,2222],{},[902,38106,38107],{"encoding":904},"P_2^* = 1",[883,38109,38111],{"className":38110},[886],[888,38112,38113],{"xmlns":890,"display":32941},[892,38114,38115,38179],{},[895,38116,38117,38119,38121,38123,38129,38131,38137,38139,38141,38143,38145,38147,38161,38175,38177],{},[898,38118,14667],{"mathvariant":33423},[1712,38120,1714],{},[1716,38122,28664],{},[6927,38124,38125,38127],{},[898,38126,1734],{},[1716,38128,2222],{},[1712,38130,3145],{},[6927,38132,38133,38135],{},[898,38134,1734],{},[1716,38136,2787],{},[1712,38138,3145],{},[898,38140,21318],{},[1712,38142,1904],{"stretchy":1903},[1716,38144,2787],{},[1712,38146,2219],{},[6989,38148,38149,38151,38153],{},[898,38150,1734],{},[1716,38152,2222],{},[895,38154,38155,38157,38159],{},[1716,38156,2222],{},[898,38158,2473],{"mathvariant":2003},[1716,38160,2787],{},[6989,38162,38163,38165,38167],{},[898,38164,1734],{},[1716,38166,2787],{},[895,38168,38169,38171,38173],{},[1716,38170,2222],{},[898,38172,2473],{"mathvariant":2003},[1716,38174,2787],{},[1712,38176,1910],{"stretchy":1903},[898,38178,1659],{"mathvariant":2003},[902,38180,38181],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,38183,35306],{},[883,38185,38187],{"className":38186},[886],[888,38188,38189],{"xmlns":890,"display":32941},[892,38190,38191,38405],{},[25629,38192,38193,38269,38345],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,38194,38195,38207],{},[25637,38196,38197],{},[2563,38198,38199],{"scriptlevel":2085,"displaystyle":2565},[6989,38200,38201,38203,38205],{},[898,38202,14667],{"mathvariant":33423},[1716,38204,2222],{},[1712,38206,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,38208,38209],{},[2563,38210,38211],{"scriptlevel":2085,"displaystyle":2565},[895,38212,38213,38215,38217,38219,38221,38223,38225,38233,38249,38263,38265,38267],{},[895,38214],{},[1712,38216,1714],{},[1716,38218,28664],{},[1712,38220,2219],{},[898,38222,21318],{},[1712,38224,1783],{},[2563,38226,38227],{"scriptlevel":2085,"displaystyle":1903},[2567,38228,38229,38231],{},[1716,38230,2222],{},[1716,38232,2787],{},[6989,38234,38235,38237,38239],{},[898,38236,1734],{},[1716,38238,2222],{},[895,38240,38241,38243,38245,38247],{},[1712,38242,2219],{},[1716,38244,2222],{},[898,38246,2473],{"mathvariant":2003},[1716,38248,2787],{},[6989,38250,38251,38253,38255],{},[898,38252,1734],{},[1716,38254,2787],{},[895,38256,38257,38259,38261],{},[1716,38258,2222],{},[898,38260,2473],{"mathvariant":2003},[1716,38262,2787],{},[1712,38264,1714],{},[1716,38266,2085],{},[1712,38268,3138],{"separator":2565},[25634,38270,38271,38283],{},[25637,38272,38273],{},[2563,38274,38275],{"scriptlevel":2085,"displaystyle":2565},[6989,38276,38277,38279,38281],{},[898,38278,14667],{"mathvariant":33423},[1716,38280,2787],{},[1712,38282,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,38284,38285],{},[2563,38286,38287],{"scriptlevel":2085,"displaystyle":2565},[895,38288,38289,38291,38293,38295,38297,38299,38301,38309,38323,38339,38341,38343],{},[895,38290],{},[1712,38292,1714],{},[1716,38294,2222],{},[1712,38296,2219],{},[898,38298,21318],{},[1712,38300,1783],{},[2563,38302,38303],{"scriptlevel":2085,"displaystyle":1903},[2567,38304,38305,38307],{},[1716,38306,2222],{},[1716,38308,2787],{},[6989,38310,38311,38313,38315],{},[898,38312,1734],{},[1716,38314,2222],{},[895,38316,38317,38319,38321],{},[1716,38318,2222],{},[898,38320,2473],{"mathvariant":2003},[1716,38322,2787],{},[6989,38324,38325,38327,38329],{},[898,38326,1734],{},[1716,38328,2787],{},[895,38330,38331,38333,38335,38337],{},[1712,38332,2219],{},[1716,38334,2222],{},[898,38336,2473],{"mathvariant":2003},[1716,38338,2787],{},[1712,38340,1714],{},[1716,38342,2085],{},[1712,38344,3138],{"separator":2565},[25634,38346,38347,38359],{},[25637,38348,38349],{},[2563,38350,38351],{"scriptlevel":2085,"displaystyle":2565},[6989,38352,38353,38355,38357],{},[898,38354,14667],{"mathvariant":33423},[898,38356,21318],{},[1712,38358,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,38360,38361],{},[2563,38362,38363],{"scriptlevel":2085,"displaystyle":2565},[895,38364,38365,38367,38369,38371,38373,38387,38401,38403],{},[895,38366],{},[1712,38368,1714],{},[1716,38370,2787],{},[1712,38372,2219],{},[6989,38374,38375,38377,38379],{},[898,38376,1734],{},[1716,38378,2222],{},[895,38380,38381,38383,38385],{},[1716,38382,2222],{},[898,38384,2473],{"mathvariant":2003},[1716,38386,2787],{},[6989,38388,38389,38391,38393],{},[898,38390,1734],{},[1716,38392,2787],{},[895,38394,38395,38397,38399],{},[1716,38396,2222],{},[898,38398,2473],{"mathvariant":2003},[1716,38400,2787],{},[1712,38402,1714],{},[1716,38404,17334],{},[902,38406,38407],{"encoding":904},"\\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}",[724,38409,38410,38411,22451,38441,38469,38470,3401,38532,1343,38582,38604,38605,1659],{},"Podílem prvních dvou rovnic: ",[883,38412,38414],{"className":38413},[886],[888,38415,38416],{"xmlns":890},[892,38417,38418,38438],{},[895,38419,38420,38422,38424,38430,38432],{},[1716,38421,28664],{},[1712,38423,1714],{},[6927,38425,38426,38428],{},[898,38427,1734],{},[1716,38429,2787],{},[898,38431,2473],{"mathvariant":2003},[6927,38433,38434,38436],{},[898,38435,1734],{},[1716,38437,2222],{},[902,38439,38440],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,38442,38444],{"className":38443},[886],[888,38445,38446],{"xmlns":890},[892,38447,38448,38466],{},[895,38449,38450,38456,38458,38460],{},[6927,38451,38452,38454],{},[898,38453,1734],{},[1716,38455,2787],{},[1712,38457,1714],{},[1716,38459,28664],{},[6927,38461,38462,38464],{},[898,38463,1734],{},[1716,38465,2222],{},[902,38467,38468],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,38471,38473],{"className":38472},[886],[888,38474,38475],{"xmlns":890},[892,38476,38477,38529],{},[895,38478,38479,38493,38495,38497,38503,38515,38517,38519,38525,38527],{},[6989,38480,38481,38483,38485],{},[898,38482,1734],{},[1716,38484,2222],{},[895,38486,38487,38489,38491],{},[1716,38488,2222],{},[898,38490,2473],{"mathvariant":2003},[1716,38492,2787],{},[1712,38494,1904],{"stretchy":1903},[1716,38496,28664],{},[6927,38498,38499,38501],{},[898,38500,1734],{},[1716,38502,2222],{},[2037,38504,38505,38507],{},[1712,38506,1910],{"stretchy":1903},[895,38508,38509,38511,38513],{},[1716,38510,2222],{},[898,38512,2473],{"mathvariant":2003},[1716,38514,2787],{},[1712,38516,1714],{},[1716,38518,2814],{},[6927,38520,38521,38523],{},[898,38522,1734],{},[1716,38524,2222],{},[1712,38526,1714],{},[1716,38528,2787],{},[902,38530,38531],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,38533,38534,1343,38558],{},[883,38535,38537],{"className":38536},[886],[888,38538,38539],{"xmlns":890},[892,38540,38541,38555],{},[895,38542,38543,38551,38553],{},[6989,38544,38545,38547,38549],{},[898,38546,1734],{},[1716,38548,2222],{},[1712,38550,2145],{},[1712,38552,1714],{},[1716,38554,2975],{},[902,38556,38557],{"encoding":904},"Q_1^* = 4",[883,38559,38561],{"className":38560},[886],[888,38562,38563],{"xmlns":890},[892,38564,38565,38579],{},[895,38566,38567,38575,38577],{},[6989,38568,38569,38571,38573],{},[898,38570,1734],{},[1716,38572,2787],{},[1712,38574,2145],{},[1712,38576,1714],{},[1716,38578,2222],{},[902,38580,38581],{"encoding":904},"Q_2^* = 1",[883,38583,38585],{"className":38584},[886],[888,38586,38587],{"xmlns":890},[892,38588,38589,38601],{},[895,38590,38591,38597,38599],{},[2037,38592,38593,38595],{},[898,38594,21318],{},[1712,38596,2145],{},[1712,38598,1714],{},[1716,38600,2222],{},[902,38602,38603],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,38606,38608],{"className":38607},[886],[888,38609,38610],{"xmlns":890},[892,38611,38612,38640],{},[895,38613,38614,38620,38622,38624,38626,38628,38630,38632,38634,38636,38638],{},[2037,38615,38616,38618],{},[898,38617,2041],{},[1712,38619,2145],{},[1712,38621,1714],{},[1716,38623,28664],{},[1712,38625,1783],{},[1716,38627,2975],{},[1712,38629,3145],{},[1716,38631,2222],{},[1712,38633,1783],{},[1716,38635,2222],{},[1712,38637,1714],{},[1716,38639,2787],{},[902,38641,38642],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,38644,38645,38648,38649,1343,38715,1343,38781,38847,38848,38885,38886,38908,38909,1659],{},[614,38646,38647],{},"Ověření postačující podmínky"," (6.26): ",[883,38650,38652],{"className":38651},[886],[888,38653,38654],{"xmlns":890},[892,38655,38656,38712],{},[895,38657,38658,38670,38672,38674,38682,38698],{},[6989,38659,38660,38662,38664],{},[898,38661,900],{},[1716,38663,8316],{},[895,38665,38666,38668],{},[1712,38667,2243],{"mathvariant":2003},[1712,38669,2243],{"mathvariant":2003},[1712,38671,1714],{},[1712,38673,2219],{},[2563,38675,38676],{"scriptlevel":2085,"displaystyle":1903},[2567,38677,38678,38680],{},[1716,38679,2222],{},[1716,38681,2975],{},[6989,38683,38684,38686,38688],{},[898,38685,1734],{},[1716,38687,2222],{},[895,38689,38690,38692,38694,38696],{},[1712,38691,2219],{},[1716,38693,6198],{},[898,38695,2473],{"mathvariant":2003},[1716,38697,2787],{},[6989,38699,38700,38702,38704],{},[898,38701,1734],{},[1716,38703,2787],{},[895,38705,38706,38708,38710],{},[1716,38707,2222],{},[898,38709,2473],{"mathvariant":2003},[1716,38711,2787],{},[902,38713,38714],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,38716,38718],{"className":38717},[886],[888,38719,38720],{"xmlns":890},[892,38721,38722,38778],{},[895,38723,38724,38736,38738,38740,38748,38762],{},[6989,38725,38726,38728,38730],{},[898,38727,900],{},[1716,38729,37421],{},[895,38731,38732,38734],{},[1712,38733,2243],{"mathvariant":2003},[1712,38735,2243],{"mathvariant":2003},[1712,38737,1714],{},[1712,38739,2219],{},[2563,38741,38742],{"scriptlevel":2085,"displaystyle":1903},[2567,38743,38744,38746],{},[1716,38745,2222],{},[1716,38747,2975],{},[6989,38749,38750,38752,38754],{},[898,38751,1734],{},[1716,38753,2222],{},[895,38755,38756,38758,38760],{},[1716,38757,2222],{},[898,38759,2473],{"mathvariant":2003},[1716,38761,2787],{},[6989,38763,38764,38766,38768],{},[898,38765,1734],{},[1716,38767,2787],{},[895,38769,38770,38772,38774,38776],{},[1712,38771,2219],{},[1716,38773,6198],{},[898,38775,2473],{"mathvariant":2003},[1716,38777,2787],{},[902,38779,38780],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,38782,38784],{"className":38783},[886],[888,38785,38786],{"xmlns":890},[892,38787,38788,38844],{},[895,38789,38790,38802,38804,38812,38828],{},[6989,38791,38792,38794,38796],{},[898,38793,900],{},[1716,38795,8912],{},[895,38797,38798,38800],{},[1712,38799,2243],{"mathvariant":2003},[1712,38801,2243],{"mathvariant":2003},[1712,38803,1714],{},[2563,38805,38806],{"scriptlevel":2085,"displaystyle":1903},[2567,38807,38808,38810],{},[1716,38809,2222],{},[1716,38811,2975],{},[6989,38813,38814,38816,38818],{},[898,38815,1734],{},[1716,38817,2222],{},[895,38819,38820,38822,38824,38826],{},[1712,38821,2219],{},[1716,38823,2222],{},[898,38825,2473],{"mathvariant":2003},[1716,38827,2787],{},[6989,38829,38830,38832,38834],{},[898,38831,1734],{},[1716,38833,2787],{},[895,38835,38836,38838,38840,38842],{},[1712,38837,2219],{},[1716,38839,2222],{},[898,38841,2473],{"mathvariant":2003},[1716,38843,2787],{},[902,38845,38846],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,38849,38851],{"className":38850},[886],[888,38852,38853],{"xmlns":890},[892,38854,38855,38882],{},[895,38856,38857,38859,38861,38863,38865,38867,38869,38871,38873,38875,38878,38880],{},[898,38858,1969],{},[1712,38860,1904],{"stretchy":1903},[1716,38862,2975],{},[1712,38864,3138],{"separator":2565},[1716,38866,2222],{},[1712,38868,3138],{"separator":2565},[1716,38870,2222],{},[1712,38872,1910],{"stretchy":1903},[1712,38874,1714],{},[1716,38876,38877],{},"0,28125",[1712,38879,2302],{},[1716,38881,2085],{},[902,38883,38884],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,38887,38889],{"className":38888},[886],[888,38890,38891],{"xmlns":890},[892,38892,38893,38905],{},[895,38894,38895,38897,38899,38901,38903],{},[1712,38896,7910],{"stretchy":1903},[1716,38898,2975],{},[1712,38900,3138],{"separator":2565},[1716,38902,2222],{},[1712,38904,7925],{"stretchy":1903},[902,38906,38907],{"encoding":904},"[4, 1]"," je vázané ",[38,38910,9176],{},[115,38912,38914],{"id":38913},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,38916,38917],{},"Obecně:",[883,38919,38921],{"className":38920},[886],[888,38922,38923],{"xmlns":890,"display":32941},[892,38924,38925,39020],{},[25629,38926,38927],{"width":32946},[25634,38928,38929,38931,39013,39015],{},[25637,38930],{"width":32951},[25637,38932,38933],{},[895,38934,38935,38941,38943,38949,38951,38957,38959,38965,38967,38969,38971,38973,38975,38981,38983,38989,38991,38997,38999,39005,39007,39009,39011],{},[6927,38936,38937,38939],{},[898,38938,1734],{},[1716,38940,2222],{},[1712,38942,1714],{},[6927,38944,38945,38947],{},[898,38946,1969],{},[1716,38948,2222],{},[1712,38950,1904],{"stretchy":1903},[6927,38952,38953,38955],{},[898,38954,1710],{},[1716,38956,2222],{},[1712,38958,3138],{"separator":2565},[6927,38960,38961,38963],{},[898,38962,1710],{},[1716,38964,2787],{},[1712,38966,3138],{"separator":2565},[898,38968,900],{},[1712,38970,1910],{"stretchy":1903},[1712,38972,3138],{"separator":2565},[3690,38974],{"width":20158},[6927,38976,38977,38979],{},[898,38978,1734],{},[1716,38980,2787],{},[1712,38982,1714],{},[6927,38984,38985,38987],{},[898,38986,1969],{},[1716,38988,2787],{},[1712,38990,1904],{"stretchy":1903},[6927,38992,38993,38995],{},[898,38994,1710],{},[1716,38996,2222],{},[1712,38998,3138],{"separator":2565},[6927,39000,39001,39003],{},[898,39002,1710],{},[1716,39004,2787],{},[1712,39006,3138],{"separator":2565},[898,39008,900],{},[1712,39010,1910],{"stretchy":1903},[1712,39012,3138],{"separator":2565},[25637,39014],{"width":32951},[25637,39016,39017],{},[1762,39018,39019],{},"(6.27)",[902,39021,39022],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,39024,39026],{"className":39025},[886],[888,39027,39028],{"xmlns":890,"display":32941},[892,39029,39030,39077],{},[25629,39031,39032],{"width":32946},[25634,39033,39034,39036,39070,39072],{},[25637,39035],{"width":32951},[25637,39037,39038],{},[895,39039,39040,39042,39044,39046,39048,39054,39056,39062,39064,39066,39068],{},[898,39041,21318],{},[1712,39043,1714],{},[898,39045,21318],{},[1712,39047,1904],{"stretchy":1903},[6927,39049,39050,39052],{},[898,39051,1710],{},[1716,39053,2222],{},[1712,39055,3138],{"separator":2565},[6927,39057,39058,39060],{},[898,39059,1710],{},[1716,39061,2787],{},[1712,39063,3138],{"separator":2565},[898,39065,900],{},[1712,39067,1910],{"stretchy":1903},[898,39069,1659],{"mathvariant":2003},[25637,39071],{"width":32951},[25637,39073,39074],{},[1762,39075,39076],{},"(6.28)",[902,39078,39079],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,39081,39082,39083,3245,39086,39099,39100,39113],{},"Hicksova poptávka závisí na ",[38,39084,39085],{},"hladině užitečnosti",[883,39087,39089],{"className":39088},[886],[888,39090,39091],{"xmlns":890},[892,39092,39093,39097],{},[895,39094,39095],{},[898,39096,900],{},[902,39098,900],{"encoding":904}," (nikoli na důchodu ",[883,39101,39103],{"className":39102},[886],[888,39104,39105],{"xmlns":890},[892,39106,39107,39111],{},[895,39108,39109],{},[898,39110,6951],{},[902,39112,6951],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,39115,39117,39118],{"id":39116},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,39119,39121],{"className":39120},[886],[888,39122,39123],{"xmlns":890},[892,39124,39125,39159],{},[895,39126,39127,39129,39131,39145],{},[898,39128,900],{},[1712,39130,1714],{},[6989,39132,39133,39135,39137],{},[898,39134,1734],{},[1716,39136,2222],{},[895,39138,39139,39141,39143],{},[1716,39140,2222],{},[898,39142,2473],{"mathvariant":2003},[1716,39144,2787],{},[6989,39146,39147,39149,39151],{},[898,39148,1734],{},[1716,39150,2787],{},[895,39152,39153,39155,39157],{},[1716,39154,2222],{},[898,39156,2473],{"mathvariant":2003},[1716,39158,2787],{},[902,39160,38034],{"encoding":904},[724,39162,39163,39193],{},[883,39164,39166],{"className":39165},[886],[888,39167,39168],{"xmlns":890},[892,39169,39170,39190],{},[895,39171,39172,39178,39180,39186,39188],{},[6927,39173,39174,39176],{},[898,39175,1710],{},[1716,39177,2222],{},[1712,39179,3138],{"separator":2565},[6927,39181,39182,39184],{},[898,39183,1710],{},[1716,39185,2787],{},[1712,39187,3138],{"separator":2565},[898,39189,900],{},[902,39191,39192],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,39195,39197],{"className":39196},[886],[888,39198,39199],{"xmlns":890,"display":32941},[892,39200,39201,39275],{},[895,39202,39203,39205,39207,39213,39219,39221,39227,39233,39235,39237,39239,39241,39243,39257,39271,39273],{},[898,39204,14667],{"mathvariant":33423},[1712,39206,1714],{},[6927,39208,39209,39211],{},[898,39210,1710],{},[1716,39212,2222],{},[6927,39214,39215,39217],{},[898,39216,1734],{},[1716,39218,2222],{},[1712,39220,3145],{},[6927,39222,39223,39225],{},[898,39224,1710],{},[1716,39226,2787],{},[6927,39228,39229,39231],{},[898,39230,1734],{},[1716,39232,2787],{},[1712,39234,3145],{},[898,39236,21318],{},[1712,39238,1904],{"stretchy":1903},[898,39240,900],{},[1712,39242,2219],{},[6989,39244,39245,39247,39249],{},[898,39246,1734],{},[1716,39248,2222],{},[895,39250,39251,39253,39255],{},[1716,39252,2222],{},[898,39254,2473],{"mathvariant":2003},[1716,39256,2787],{},[6989,39258,39259,39261,39263],{},[898,39260,1734],{},[1716,39262,2787],{},[895,39264,39265,39267,39269],{},[1716,39266,2222],{},[898,39268,2473],{"mathvariant":2003},[1716,39270,2787],{},[1712,39272,1910],{"stretchy":1903},[898,39274,1659],{"mathvariant":2003},[902,39276,39277],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,39279,35306],{},[883,39281,39283],{"className":39282},[886],[888,39284,39285],{"xmlns":890,"display":32941},[892,39286,39287,39509],{},[25629,39288,39289,39369,39449],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,39290,39291,39303],{},[25637,39292,39293],{},[2563,39294,39295],{"scriptlevel":2085,"displaystyle":2565},[6989,39296,39297,39299,39301],{},[898,39298,14667],{"mathvariant":33423},[1716,39300,2222],{},[1712,39302,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,39304,39305],{},[2563,39306,39307],{"scriptlevel":2085,"displaystyle":2565},[895,39308,39309,39311,39313,39319,39321,39323,39325,39333,39349,39363,39365,39367],{},[895,39310],{},[1712,39312,1714],{},[6927,39314,39315,39317],{},[898,39316,1710],{},[1716,39318,2222],{},[1712,39320,2219],{},[898,39322,21318],{},[1712,39324,1783],{},[2563,39326,39327],{"scriptlevel":2085,"displaystyle":1903},[2567,39328,39329,39331],{},[1716,39330,2222],{},[1716,39332,2787],{},[6989,39334,39335,39337,39339],{},[898,39336,1734],{},[1716,39338,2222],{},[895,39340,39341,39343,39345,39347],{},[1712,39342,2219],{},[1716,39344,2222],{},[898,39346,2473],{"mathvariant":2003},[1716,39348,2787],{},[6989,39350,39351,39353,39355],{},[898,39352,1734],{},[1716,39354,2787],{},[895,39356,39357,39359,39361],{},[1716,39358,2222],{},[898,39360,2473],{"mathvariant":2003},[1716,39362,2787],{},[1712,39364,1714],{},[1716,39366,2085],{},[1712,39368,3138],{"separator":2565},[25634,39370,39371,39383],{},[25637,39372,39373],{},[2563,39374,39375],{"scriptlevel":2085,"displaystyle":2565},[6989,39376,39377,39379,39381],{},[898,39378,14667],{"mathvariant":33423},[1716,39380,2787],{},[1712,39382,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,39384,39385],{},[2563,39386,39387],{"scriptlevel":2085,"displaystyle":2565},[895,39388,39389,39391,39393,39399,39401,39403,39405,39413,39427,39443,39445,39447],{},[895,39390],{},[1712,39392,1714],{},[6927,39394,39395,39397],{},[898,39396,1710],{},[1716,39398,2787],{},[1712,39400,2219],{},[898,39402,21318],{},[1712,39404,1783],{},[2563,39406,39407],{"scriptlevel":2085,"displaystyle":1903},[2567,39408,39409,39411],{},[1716,39410,2222],{},[1716,39412,2787],{},[6989,39414,39415,39417,39419],{},[898,39416,1734],{},[1716,39418,2222],{},[895,39420,39421,39423,39425],{},[1716,39422,2222],{},[898,39424,2473],{"mathvariant":2003},[1716,39426,2787],{},[6989,39428,39429,39431,39433],{},[898,39430,1734],{},[1716,39432,2787],{},[895,39434,39435,39437,39439,39441],{},[1712,39436,2219],{},[1716,39438,2222],{},[898,39440,2473],{"mathvariant":2003},[1716,39442,2787],{},[1712,39444,1714],{},[1716,39446,2085],{},[1712,39448,3138],{"separator":2565},[25634,39450,39451,39463],{},[25637,39452,39453],{},[2563,39454,39455],{"scriptlevel":2085,"displaystyle":2565},[6989,39456,39457,39459,39461],{},[898,39458,14667],{"mathvariant":33423},[898,39460,21318],{},[1712,39462,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[25637,39464,39465],{},[2563,39466,39467],{"scriptlevel":2085,"displaystyle":2565},[895,39468,39469,39471,39473,39475,39477,39491,39505,39507],{},[895,39470],{},[1712,39472,1714],{},[898,39474,900],{},[1712,39476,2219],{},[6989,39478,39479,39481,39483],{},[898,39480,1734],{},[1716,39482,2222],{},[895,39484,39485,39487,39489],{},[1716,39486,2222],{},[898,39488,2473],{"mathvariant":2003},[1716,39490,2787],{},[6989,39492,39493,39495,39497],{},[898,39494,1734],{},[1716,39496,2787],{},[895,39498,39499,39501,39503],{},[1716,39500,2222],{},[898,39502,2473],{"mathvariant":2003},[1716,39504,2787],{},[1712,39506,1714],{},[1716,39508,17334],{},[902,39510,39511],{"encoding":904},"\\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}",[724,39513,39514,39515,39585,39586,39644],{},"Podílem rovnic: ",[883,39516,39518],{"className":39517},[886],[888,39519,39520],{"xmlns":890},[892,39521,39522,39582],{},[895,39523,39524,39530,39532,39538,39540,39546,39548,39554,39556,39562,39568,39570,39576],{},[6927,39525,39526,39528],{},[898,39527,1710],{},[1716,39529,2222],{},[898,39531,2473],{"mathvariant":2003},[6927,39533,39534,39536],{},[898,39535,1710],{},[1716,39537,2787],{},[1712,39539,1714],{},[6927,39541,39542,39544],{},[898,39543,1734],{},[1716,39545,2787],{},[898,39547,2473],{"mathvariant":2003},[6927,39549,39550,39552],{},[898,39551,1734],{},[1716,39553,2222],{},[1712,39555,1767],{},[6927,39557,39558,39560],{},[898,39559,1710],{},[1716,39561,2222],{},[6927,39563,39564,39566],{},[898,39565,1734],{},[1716,39567,2222],{},[1712,39569,1714],{},[6927,39571,39572,39574],{},[898,39573,1710],{},[1716,39575,2787],{},[6927,39577,39578,39580],{},[898,39579,1734],{},[1716,39581,2787],{},[902,39583,39584],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,39587,39589],{"className":39588},[886],[888,39590,39591],{"xmlns":890},[892,39592,39593,39641],{},[895,39594,39595,39597,39599,39605,39611,39613,39619,39625,39627,39629,39635],{},[898,39596,2041],{},[1712,39598,1714],{},[6927,39600,39601,39603],{},[898,39602,1710],{},[1716,39604,2222],{},[6927,39606,39607,39609],{},[898,39608,1734],{},[1716,39610,2222],{},[1712,39612,3145],{},[6927,39614,39615,39617],{},[898,39616,1710],{},[1716,39618,2787],{},[6927,39620,39621,39623],{},[898,39622,1734],{},[1716,39624,2787],{},[1712,39626,1714],{},[1716,39628,2787],{},[6927,39630,39631,39633],{},[898,39632,1710],{},[1716,39634,2222],{},[6927,39636,39637,39639],{},[898,39638,1734],{},[1716,39640,2222],{},[902,39642,39643],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,39646,39648],{"className":39647},[886],[888,39649,39650],{"xmlns":890,"display":32941},[892,39651,39652,39719],{},[25629,39653,39654],{"width":32946},[25634,39655,39656,39658,39712,39714],{},[25637,39657],{"width":32951},[25637,39659,39660],{},[895,39661,39662,39668,39670,39684,39686,39688,39694,39696,39710],{},[6927,39663,39664,39666],{},[898,39665,1734],{},[1716,39667,2222],{},[1712,39669,1714],{},[2567,39671,39672,39674],{},[898,39673,2041],{},[895,39675,39676,39678],{},[1716,39677,2787],{},[6927,39679,39680,39682],{},[898,39681,1710],{},[1716,39683,2222],{},[1712,39685,3138],{"separator":2565},[3690,39687],{"width":20158},[6927,39689,39690,39692],{},[898,39691,1734],{},[1716,39693,2787],{},[1712,39695,1714],{},[2567,39697,39698,39700],{},[898,39699,2041],{},[895,39701,39702,39704],{},[1716,39703,2787],{},[6927,39705,39706,39708],{},[898,39707,1710],{},[1716,39709,2787],{},[898,39711,1659],{"mathvariant":2003},[25637,39713],{"width":32951},[25637,39715,39716],{},[1762,39717,39718],{},"(6.29)",[902,39720,39721],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,39723,39724,39725,22451,39807,39843],{},"Ze třetí rovnice ",[883,39726,39728],{"className":39727},[886],[888,39729,39730],{"xmlns":890},[892,39731,39732,39804],{},[895,39733,39734,39736,39738,39776,39778],{},[898,39735,900],{},[1712,39737,1714],{},[5935,39739,39740],{},[895,39741,39742,39758,39760],{},[2563,39743,39744],{"scriptlevel":2085,"displaystyle":1903},[2567,39745,39746,39748],{},[898,39747,2041],{},[895,39749,39750,39752],{},[1716,39751,2787],{},[6927,39753,39754,39756],{},[898,39755,1710],{},[1716,39757,2222],{},[1712,39759,1783],{},[2563,39761,39762],{"scriptlevel":2085,"displaystyle":1903},[2567,39763,39764,39766],{},[898,39765,2041],{},[895,39767,39768,39770],{},[1716,39769,2787],{},[6927,39771,39772,39774],{},[898,39773,1710],{},[1716,39775,2787],{},[1712,39777,1714],{},[2563,39779,39780],{"scriptlevel":2085,"displaystyle":1903},[2567,39781,39782,39784],{},[898,39783,2041],{},[895,39785,39786,39788],{},[1716,39787,2787],{},[5935,39789,39790],{},[895,39791,39792,39798],{},[6927,39793,39794,39796],{},[898,39795,1710],{},[1716,39797,2222],{},[6927,39799,39800,39802],{},[898,39801,1710],{},[1716,39803,2787],{},[902,39805,39806],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,39808,39810],{"className":39809},[886],[888,39811,39812],{"xmlns":890},[892,39813,39814,39840],{},[895,39815,39816,39818,39820,39822,39824],{},[898,39817,2041],{},[1712,39819,1714],{},[1716,39821,2787],{},[898,39823,900],{},[5935,39825,39826],{},[895,39827,39828,39834],{},[6927,39829,39830,39832],{},[898,39831,1710],{},[1716,39833,2222],{},[6927,39835,39836,39838],{},[898,39837,1710],{},[1716,39839,2787],{},[902,39841,39842],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,39845,39847],{"className":39846},[886],[888,39848,39849],{"xmlns":890,"display":32941},[892,39850,39851,39996],{},[25629,39852,39853],{"width":32946},[25634,39854,39855,39857,39989,39991],{},[25637,39856],{"width":32951},[25637,39858,39859],{},[17706,39860,39861],{"notation":17708},[2563,39862,39863],{"scriptlevel":2085,"displaystyle":1903},[2563,39864,39865],{"scriptlevel":2085,"displaystyle":1903},[2563,39866,39867],{"scriptlevel":2085,"displaystyle":2565},[895,39868,39869,39871,39877,39879,39881,39897,39899,39905,39907,39913,39915,39921,39923,39925,39927,39929,39931,39937,39939,39941,39957,39959,39965,39967,39973,39975,39981,39983,39985,39987],{},[1762,39870,1764],{},[6927,39872,39873,39875],{},[898,39874,1734],{},[1716,39876,2222],{},[1712,39878,1714],{},[898,39880,900],{},[5935,39882,39883],{},[2567,39884,39885,39891],{},[6927,39886,39887,39889],{},[898,39888,1710],{},[1716,39890,2787],{},[6927,39892,39893,39895],{},[898,39894,1710],{},[1716,39896,2222],{},[1712,39898,1714],{},[6927,39900,39901,39903],{},[898,39902,1969],{},[1716,39904,2222],{},[1712,39906,1904],{"stretchy":1903},[6927,39908,39909,39911],{},[898,39910,1710],{},[1716,39912,2222],{},[1712,39914,3138],{"separator":2565},[6927,39916,39917,39919],{},[898,39918,1710],{},[1716,39920,2787],{},[1712,39922,3138],{"separator":2565},[898,39924,900],{},[1712,39926,1910],{"stretchy":1903},[1712,39928,3138],{"separator":2565},[3690,39930],{"width":20158},[6927,39932,39933,39935],{},[898,39934,1734],{},[1716,39936,2787],{},[1712,39938,1714],{},[898,39940,900],{},[5935,39942,39943],{},[2567,39944,39945,39951],{},[6927,39946,39947,39949],{},[898,39948,1710],{},[1716,39950,2222],{},[6927,39952,39953,39955],{},[898,39954,1710],{},[1716,39956,2787],{},[1712,39958,1714],{},[6927,39960,39961,39963],{},[898,39962,1969],{},[1716,39964,2787],{},[1712,39966,1904],{"stretchy":1903},[6927,39968,39969,39971],{},[898,39970,1710],{},[1716,39972,2222],{},[1712,39974,3138],{"separator":2565},[6927,39976,39977,39979],{},[898,39978,1710],{},[1716,39980,2787],{},[1712,39982,3138],{"separator":2565},[898,39984,900],{},[1712,39986,1910],{"stretchy":1903},[1762,39988,1764],{},[25637,39990],{"width":32951},[25637,39992,39993],{},[1762,39994,39995],{},"(6.30)",[902,39997,39998],{"encoding":904},"\\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}",[115,40000,40002],{"id":40001},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,40004,40005,40006,40019,40020,40037,40038,40051,40052,40069,40070,40073,40074,40113,40114,40143],{},"Primární (max ",[883,40007,40009],{"className":40008},[886],[888,40010,40011],{"xmlns":890},[892,40012,40013,40017],{},[895,40014,40015],{},[898,40016,900],{},[902,40018,900],{"encoding":904}," při rozpočtu ",[883,40021,40023],{"className":40022},[886],[888,40024,40025],{"xmlns":890},[892,40026,40027,40035],{},[895,40028,40029],{},[2037,40030,40031,40033],{},[898,40032,6951],{},[1712,40034,2145],{},[902,40036,32903],{"encoding":904},") a duální (min ",[883,40039,40041],{"className":40040},[886],[888,40042,40043],{"xmlns":890},[892,40044,40045,40049],{},[895,40046,40047],{},[898,40048,2041],{},[902,40050,2041],{"encoding":904}," při užitečnosti ",[883,40053,40055],{"className":40054},[886],[888,40056,40057],{"xmlns":890},[892,40058,40059,40067],{},[895,40060,40061],{},[2037,40062,40063,40065],{},[898,40064,900],{},[1712,40066,2145],{},[902,40068,32837],{"encoding":904},") úloha jsou ",[38,40071,40072],{},"ekvivalentní",": mají tentýž bod optima ",[883,40075,40077],{"className":40076},[886],[888,40078,40079],{"xmlns":890},[892,40080,40081,40111],{},[895,40082,40083,40089,40091,40099,40101,40109],{},[2037,40084,40085,40087],{},[898,40086,1734],{},[1712,40088,2145],{},[1712,40090,7910],{"stretchy":1903},[6989,40092,40093,40095,40097],{},[898,40094,1734],{},[1716,40096,2222],{},[1712,40098,2145],{},[1712,40100,3138],{"separator":2565},[6989,40102,40103,40105,40107],{},[898,40104,1734],{},[1716,40106,2787],{},[1712,40108,2145],{},[1712,40110,7925],{"stretchy":1903},[902,40112,33202],{"encoding":904}," a v obou platí ",[883,40115,40117],{"className":40116},[886],[888,40118,40119],{"xmlns":890},[892,40120,40121,40141],{},[895,40122,40123,40125,40127,40133,40135],{},[1762,40124,15475],{},[1712,40126,1714],{},[6927,40128,40129,40131],{},[898,40130,1710],{},[1716,40132,2222],{},[898,40134,2473],{"mathvariant":2003},[6927,40136,40137,40139],{},[898,40138,1710],{},[1716,40140,2787],{},[902,40142,32873],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,40145,40146],{},[3817,40147],{"alt":40148,"className":40149,"src":40150},"imek-primarni-vs-dualni",[210,3821],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,40152,40153,40264],{},[123,40154,40155,40158,40159,40172,40173,40213,40214,1659],{},[38,40156,40157],{},"Primární"," (Marshall): zadáno ",[883,40160,40162],{"className":40161},[886],[888,40163,40164],{"xmlns":890},[892,40165,40166,40170],{},[895,40167,40168],{},[898,40169,6951],{},[902,40171,6951],{"encoding":904},", hledáme maximální ",[883,40174,40176],{"className":40175},[886],[888,40177,40178],{"xmlns":890},[892,40179,40180,40210],{},[895,40181,40182,40188,40190,40196,40198,40204,40206,40208],{},[2037,40183,40184,40186],{},[898,40185,900],{},[1712,40187,2145],{},[1712,40189,1904],{"stretchy":1903},[6927,40191,40192,40194],{},[898,40193,1710],{},[1716,40195,2222],{},[1712,40197,3138],{"separator":2565},[6927,40199,40200,40202],{},[898,40201,1710],{},[1716,40203,2787],{},[1712,40205,3138],{"separator":2565},[898,40207,6951],{},[1712,40209,1910],{"stretchy":1903},[902,40211,40212],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,40215,40217],{"className":40216},[886],[888,40218,40219],{"xmlns":890},[892,40220,40221,40261],{},[895,40222,40223,40229,40231,40239,40241,40247,40249,40255,40257,40259],{},[6927,40224,40225,40227],{},[898,40226,1734],{},[898,40228,22665],{},[1712,40230,1714],{},[6989,40232,40233,40235,40237],{},[898,40234,1969],{},[898,40236,22665],{},[898,40238,4445],{},[1712,40240,1904],{"stretchy":1903},[6927,40242,40243,40245],{},[898,40244,1710],{},[1716,40246,2222],{},[1712,40248,3138],{"separator":2565},[6927,40250,40251,40253],{},[898,40252,1710],{},[1716,40254,2787],{},[1712,40256,3138],{"separator":2565},[898,40258,6951],{},[1712,40260,1910],{"stretchy":1903},[902,40262,40263],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,40265,40266,40269,40270,40283,40284,40213,40324,1659],{},[38,40267,40268],{},"Duální"," (Hicks): zadáno ",[883,40271,40273],{"className":40272},[886],[888,40274,40275],{"xmlns":890},[892,40276,40277,40281],{},[895,40278,40279],{},[898,40280,900],{},[902,40282,900],{"encoding":904},", hledáme minimální ",[883,40285,40287],{"className":40286},[886],[888,40288,40289],{"xmlns":890},[892,40290,40291,40321],{},[895,40292,40293,40299,40301,40307,40309,40315,40317,40319],{},[2037,40294,40295,40297],{},[898,40296,2041],{},[1712,40298,2145],{},[1712,40300,1904],{"stretchy":1903},[6927,40302,40303,40305],{},[898,40304,1710],{},[1716,40306,2222],{},[1712,40308,3138],{"separator":2565},[6927,40310,40311,40313],{},[898,40312,1710],{},[1716,40314,2787],{},[1712,40316,3138],{"separator":2565},[898,40318,900],{},[1712,40320,1910],{"stretchy":1903},[902,40322,40323],{"encoding":904},"E^*(P_1, P_2, U)",[883,40325,40327],{"className":40326},[886],[888,40328,40329],{"xmlns":890},[892,40330,40331,40372],{},[895,40332,40333,40339,40341,40350,40352,40358,40360,40366,40368,40370],{},[6927,40334,40335,40337],{},[898,40336,1734],{},[898,40338,22665],{},[1712,40340,1714],{},[6989,40342,40343,40345,40347],{},[898,40344,1969],{},[898,40346,22665],{},[898,40348,40349],{},"H",[1712,40351,1904],{"stretchy":1903},[6927,40353,40354,40356],{},[898,40355,1710],{},[1716,40357,2222],{},[1712,40359,3138],{"separator":2565},[6927,40361,40362,40364],{},[898,40363,1710],{},[1716,40365,2787],{},[1712,40367,3138],{"separator":2565},[898,40369,900],{},[1712,40371,1910],{"stretchy":1903},[902,40373,40374],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,40376,40377,40378,40381,40382,40385],{},"Proč se studují obě? Marshallova poptávka je ",[38,40379,40380],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,40383,40384],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,40387,40389],{"id":40388},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,40391,40393],{"id":40392},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,40395,40396,40399,40400,40432,40433,40471,40472,40498],{},[38,40397,40398],{},"6.8"," Jsou dány užitečnost ",[883,40401,40403],{"className":40402},[886],[888,40404,40405],{"xmlns":890},[892,40406,40407,40429],{},[895,40408,40409,40411,40413,40421],{},[898,40410,900],{},[1712,40412,1714],{},[6989,40414,40415,40417,40419],{},[898,40416,1734],{},[1716,40418,2222],{},[1716,40420,2814],{},[6989,40422,40423,40425,40427],{},[898,40424,1734],{},[1716,40426,2787],{},[1716,40428,2814],{},[902,40430,40431],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,40434,40436],{"className":40435},[886],[888,40437,40438],{"xmlns":890},[892,40439,40440,40468],{},[895,40441,40442,40450,40452,40454,40456,40464,40466],{},[6989,40443,40444,40446,40448],{},[898,40445,1710],{},[1716,40447,2222],{},[1712,40449,2145],{},[1712,40451,1714],{},[1716,40453,2975],{},[1712,40455,3138],{"separator":2565},[6989,40457,40458,40460,40462],{},[898,40459,1710],{},[1716,40461,2787],{},[1712,40463,2145],{},[1712,40465,1714],{},[1716,40467,1718],{},[902,40469,40470],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,40473,40475],{"className":40474},[886],[888,40476,40477],{"xmlns":890},[892,40478,40479,40495],{},[895,40480,40481,40487,40489],{},[6927,40482,40483,40485],{},[898,40484,1734],{},[1716,40486,2222],{},[1712,40488,3138],{"separator":2565},[6927,40490,40491,40493],{},[898,40492,1734],{},[1716,40494,2787],{},[902,40496,40497],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,40500,40501,40504,40505,40547,40548,40579,40580,40602,40603,1659],{},[38,40502,40503],{},"6.9"," Jsou dány rozpočtové omezení ",[883,40506,40508],{"className":40507},[886],[888,40509,40510],{"xmlns":890},[892,40511,40512,40544],{},[895,40513,40514,40516,40518,40524,40530,40532,40538],{},[898,40515,6951],{},[1712,40517,1714],{},[6927,40519,40520,40522],{},[898,40521,1710],{},[1716,40523,2222],{},[6927,40525,40526,40528],{},[898,40527,1734],{},[1716,40529,2222],{},[1712,40531,3145],{},[6927,40533,40534,40536],{},[898,40535,1710],{},[1716,40537,2787],{},[6927,40539,40540,40542],{},[898,40541,1734],{},[1716,40543,2787],{},[902,40545,40546],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,40549,40551],{"className":40550},[886],[888,40552,40553],{"xmlns":890},[892,40554,40555,40577],{},[895,40556,40557,40559,40561,40569],{},[898,40558,900],{},[1712,40560,1714],{},[6989,40562,40563,40565,40567],{},[898,40564,1734],{},[1716,40566,2222],{},[1716,40568,2814],{},[6989,40570,40571,40573,40575],{},[898,40572,1734],{},[1716,40574,2787],{},[1716,40576,2814],{},[902,40578,40431],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,40581,40583],{"className":40582},[886],[888,40584,40585],{"xmlns":890},[892,40586,40587,40599],{},[895,40588,40589,40595,40597],{},[2037,40590,40591,40593],{},[898,40592,6951],{},[1712,40594,2145],{},[1712,40596,1714],{},[1716,40598,19984],{},[902,40600,40601],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,40604,40606],{"className":40605},[886],[888,40607,40608],{"xmlns":890},[892,40609,40610,40638],{},[895,40611,40612,40620,40622,40624,40626,40634,40636],{},[6989,40613,40614,40616,40618],{},[898,40615,1710],{},[1716,40617,2222],{},[1712,40619,2145],{},[1712,40621,1714],{},[1716,40623,3068],{},[1712,40625,3138],{"separator":2565},[6989,40627,40628,40630,40632],{},[898,40629,1710],{},[1716,40631,2787],{},[1712,40633,2145],{},[1712,40635,1714],{},[1716,40637,1718],{},[902,40639,40640],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,40642,40643,40646,40647,26469,40679,40709,40710,1659],{},[38,40644,40645],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,40648,40650],{"className":40649},[886],[888,40651,40652],{"xmlns":890},[892,40653,40654,40676],{},[895,40655,40656,40658,40660,40668],{},[898,40657,900],{},[1712,40659,1714],{},[6989,40661,40662,40664,40666],{},[898,40663,1734],{},[1716,40665,2222],{},[898,40667,207],{},[6989,40669,40670,40672,40674],{},[898,40671,1734],{},[1716,40673,2787],{},[898,40675,7544],{},[902,40677,40678],{"encoding":904},"U = Q_1^a Q_2^b",[883,40680,40682],{"className":40681},[886],[888,40683,40684],{"xmlns":890},[892,40685,40686,40706],{},[895,40687,40688,40690,40692,40694,40696,40698,40700,40702,40704],{},[898,40689,207],{},[1712,40691,3138],{"separator":2565},[898,40693,7544],{},[1712,40695,4321],{},[1712,40697,3133],{"stretchy":1903},[1716,40699,2085],{},[1712,40701,3138],{"separator":2565},[1716,40703,2222],{},[1712,40705,3152],{"stretchy":1903},[902,40707,40708],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,40711,40713],{"className":40712},[886],[888,40714,40715],{"xmlns":890},[892,40716,40717,40749],{},[895,40718,40719,40721,40723,40729,40735,40737,40743],{},[898,40720,6951],{},[1712,40722,1714],{},[6927,40724,40725,40727],{},[898,40726,1710],{},[1716,40728,2222],{},[6927,40730,40731,40733],{},[898,40732,1734],{},[1716,40734,2222],{},[1712,40736,3145],{},[6927,40738,40739,40741],{},[898,40740,1710],{},[1716,40742,2787],{},[6927,40744,40745,40747],{},[898,40746,1734],{},[1716,40748,2787],{},[902,40750,40546],{"encoding":904},[724,40752,40753,40756,40757,26469,40791,40709,40809,1659],{},[38,40754,40755],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,40758,40760],{"className":40759},[886],[888,40761,40762],{"xmlns":890},[892,40763,40764,40788],{},[895,40765,40766,40768,40770,40778,40780],{},[898,40767,900],{},[1712,40769,1714],{},[6989,40771,40772,40774,40776],{},[898,40773,1734],{},[1716,40775,2222],{},[898,40777,207],{},[1712,40779,3145],{},[6989,40781,40782,40784,40786],{},[898,40783,1734],{},[1716,40785,2787],{},[898,40787,207],{},[902,40789,40790],{"encoding":904},"U = Q_1^a + Q_2^a",[883,40792,40794],{"className":40793},[886],[888,40795,40796],{"xmlns":890},[892,40797,40798,40806],{},[895,40799,40800,40802,40804],{},[898,40801,207],{},[1712,40803,8776],{"mathvariant":2003},[1716,40805,2085],{},[902,40807,40808],{"encoding":904},"a \\neq 0",[883,40810,40812],{"className":40811},[886],[888,40813,40814],{"xmlns":890},[892,40815,40816,40848],{},[895,40817,40818,40820,40822,40828,40834,40836,40842],{},[898,40819,6951],{},[1712,40821,1714],{},[6927,40823,40824,40826],{},[898,40825,1710],{},[1716,40827,2222],{},[6927,40829,40830,40832],{},[898,40831,1734],{},[1716,40833,2222],{},[1712,40835,3145],{},[6927,40837,40838,40840],{},[898,40839,1710],{},[1716,40841,2787],{},[6927,40843,40844,40846],{},[898,40845,1734],{},[1716,40847,2787],{},[902,40849,40546],{"encoding":904},[198,40851,40853],{"id":40852},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,40855,40856,40399,40859,1343,40886,40908,40909,1343,40932,40956,40957,40982,40983,1659],{},[38,40857,40858],{},"6.12",[883,40860,40862],{"className":40861},[886],[888,40863,40864],{"xmlns":890},[892,40865,40866,40884],{},[895,40867,40868,40870,40872,40878],{},[898,40869,900],{},[1712,40871,1714],{},[6927,40873,40874,40876],{},[898,40875,1734],{},[1716,40877,2222],{},[6927,40879,40880,40882],{},[898,40881,1734],{},[1716,40883,2787],{},[902,40885,35101],{"encoding":904},[883,40887,40889],{"className":40888},[886],[888,40890,40891],{"xmlns":890},[892,40892,40893,40905],{},[895,40894,40895,40901,40903],{},[2037,40896,40897,40899],{},[898,40898,900],{},[1712,40900,2145],{},[1712,40902,1714],{},[1716,40904,1718],{},[902,40906,40907],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,40910,40912],{"className":40911},[886],[888,40913,40914],{"xmlns":890},[892,40915,40916,40930],{},[895,40917,40918,40926,40928],{},[6989,40919,40920,40922,40924],{},[898,40921,1710],{},[1716,40923,2222],{},[1712,40925,2145],{},[1712,40927,1714],{},[1716,40929,2787],{},[902,40931,35174],{"encoding":904},[883,40933,40935],{"className":40934},[886],[888,40936,40937],{"xmlns":890},[892,40938,40939,40953],{},[895,40940,40941,40949,40951],{},[6989,40942,40943,40945,40947],{},[898,40944,1710],{},[1716,40946,2787],{},[1712,40948,2145],{},[1712,40950,1714],{},[1716,40952,2975],{},[902,40954,40955],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,40958,40960],{"className":40959},[886],[888,40961,40962],{"xmlns":890},[892,40963,40964,40980],{},[895,40965,40966,40972,40974],{},[6927,40967,40968,40970],{},[898,40969,1734],{},[1716,40971,2222],{},[1712,40973,3138],{"separator":2565},[6927,40975,40976,40978],{},[898,40977,1734],{},[1716,40979,2787],{},[902,40981,40497],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,40984,40986],{"className":40985},[886],[888,40987,40988],{"xmlns":890},[892,40989,40990,41010],{},[895,40991,40992,40994,40996,41002,41004],{},[898,40993,900],{},[1712,40995,1714],{},[6927,40997,40998,41000],{},[898,40999,1734],{},[1716,41001,2222],{},[1712,41003,1783],{},[6927,41005,41006,41008],{},[898,41007,1734],{},[1716,41009,2787],{},[902,41011,41012],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,41014,41015,41018,41019,41060,41061,41083,41084,1659],{},[38,41016,41017],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,41020,41022],{"className":41021},[886],[888,41023,41024],{"xmlns":890},[892,41025,41026,41058],{},[895,41027,41028,41030,41032,41038,41044,41046,41052],{},[898,41029,2041],{},[1712,41031,1714],{},[6927,41033,41034,41036],{},[898,41035,1710],{},[1716,41037,2222],{},[6927,41039,41040,41042],{},[898,41041,1734],{},[1716,41043,2222],{},[1712,41045,3145],{},[6927,41047,41048,41050],{},[898,41049,1710],{},[1716,41051,2787],{},[6927,41053,41054,41056],{},[898,41055,1734],{},[1716,41057,2787],{},[902,41059,32818],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,41062,41064],{"className":41063},[886],[888,41065,41066],{"xmlns":890},[892,41067,41068,41080],{},[895,41069,41070,41076,41078],{},[2037,41071,41072,41074],{},[898,41073,900],{},[1712,41075,2145],{},[1712,41077,1714],{},[1716,41079,2809],{},[902,41081,41082],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,41085,41087],{"className":41086},[886],[888,41088,41089],{"xmlns":890},[892,41090,41091,41120],{},[895,41092,41093,41101,41103,41105,41107,41115,41117],{},[6989,41094,41095,41097,41099],{},[898,41096,1710],{},[1716,41098,2222],{},[1712,41100,2145],{},[1712,41102,1714],{},[1716,41104,6857],{},[1712,41106,3138],{"separator":2565},[6989,41108,41109,41111,41113],{},[898,41110,1710],{},[1716,41112,2787],{},[1712,41114,2145],{},[1712,41116,1714],{},[1716,41118,41119],{},"15",[902,41121,41122],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,41124,20594],{"id":20593},[120,41126,41127,41184,41223,41243,41278,41332,41337,41343,41439,41484],{},[123,41128,41129,3245,41132,41181,41182,1659],{},[38,41130,41131],{},"Rozpočtové omezení (budget constraint)",[883,41133,41135],{"className":41134},[886],[888,41136,41137],{"xmlns":890},[892,41138,41139,41179],{},[895,41140,41141,41147,41149,41157,41163,41165,41173],{},[2037,41142,41143,41145],{},[898,41144,6951],{},[1712,41146,2145],{},[1712,41148,1714],{},[6989,41150,41151,41153,41155],{},[898,41152,1710],{},[1716,41154,2222],{},[1712,41156,2145],{},[6927,41158,41159,41161],{},[898,41160,1734],{},[1716,41162,2222],{},[1712,41164,3145],{},[6989,41166,41167,41169,41171],{},[898,41168,1710],{},[1716,41170,2787],{},[1712,41172,2145],{},[6927,41174,41175,41177],{},[898,41176,1734],{},[1716,41178,2787],{},[902,41180,22173],{"encoding":904}," — (6.12); ",[38,41183,33011],{},[123,41185,41186,41189,41190,1659],{},[38,41187,41188],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,41191,41193],{"className":41192},[886],[888,41194,41195],{"xmlns":890},[892,41196,41197,41221],{},[895,41198,41199,41201,41203,41211,41213],{},[1762,41200,15475],{},[1712,41202,1714],{},[6989,41204,41205,41207,41209],{},[898,41206,1710],{},[1716,41208,2222],{},[1712,41210,2145],{},[898,41212,2473],{"mathvariant":2003},[6989,41214,41215,41217,41219],{},[898,41216,1710],{},[1716,41218,2787],{},[1712,41220,2145],{},[902,41222,33854],{"encoding":904},[123,41224,41225,41240,41241,1659],{},[38,41226,33998,41227],{},[883,41228,41230],{"className":41229},[886],[888,41231,41232],{"xmlns":890},[892,41233,41234,41238],{},[895,41235,41236],{},[898,41237,21318],{},[902,41239,21371],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,41242,34020],{},[123,41244,41245,41248,41249,1659],{},[38,41246,41247],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,41250,41252],{"className":41251},[886],[888,41253,41254],{"xmlns":890},[892,41255,41256,41276],{},[895,41257,41258,41260,41262,41268,41270],{},[1762,41259,15475],{},[1712,41261,1714],{},[6927,41263,41264,41266],{},[898,41265,1710],{},[1716,41267,2222],{},[898,41269,2473],{"mathvariant":2003},[6927,41271,41272,41274],{},[898,41273,1710],{},[1716,41275,2787],{},[902,41277,32873],{"encoding":904},[123,41279,41280,4831,41283,41331],{},[38,41281,41282],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,41284,41286],{"className":41285},[886],[888,41287,41288],{"xmlns":890},[892,41289,41290,41328],{},[895,41291,41292,41298,41300,41306,41308,41314,41316,41322,41324,41326],{},[6927,41293,41294,41296],{},[898,41295,1734],{},[898,41297,22665],{},[1712,41299,1714],{},[6927,41301,41302,41304],{},[898,41303,1969],{},[898,41305,22665],{},[1712,41307,1904],{"stretchy":1903},[6927,41309,41310,41312],{},[898,41311,1710],{},[1716,41313,2222],{},[1712,41315,3138],{"separator":2565},[6927,41317,41318,41320],{},[898,41319,1710],{},[1716,41321,2787],{},[1712,41323,3138],{"separator":2565},[898,41325,6951],{},[1712,41327,1910],{"stretchy":1903},[902,41329,41330],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,41333,41334,41336],{},[38,41335,36602],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,41338,41339,41342],{},[38,41340,41341],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,41344,41345,4831,41347,41394,41395,41438],{},[38,41346,38914],{},[883,41348,41350],{"className":41349},[886],[888,41351,41352],{"xmlns":890},[892,41353,41354,41392],{},[895,41355,41356,41362,41364,41370,41372,41378,41380,41386,41388,41390],{},[6927,41357,41358,41360],{},[898,41359,1734],{},[898,41361,22665],{},[1712,41363,1714],{},[6927,41365,41366,41368],{},[898,41367,1969],{},[898,41369,22665],{},[1712,41371,1904],{"stretchy":1903},[6927,41373,41374,41376],{},[898,41375,1710],{},[1716,41377,2222],{},[1712,41379,3138],{"separator":2565},[6927,41381,41382,41384],{},[898,41383,1710],{},[1716,41385,2787],{},[1712,41387,3138],{"separator":2565},[898,41389,900],{},[1712,41391,1910],{"stretchy":1903},[902,41393,22698],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,41396,41398],{"className":41397},[886],[888,41399,41400],{"xmlns":890},[892,41401,41402,41436],{},[895,41403,41404,41406,41408,41422],{},[898,41405,900],{},[1712,41407,1714],{},[6989,41409,41410,41412,41414],{},[898,41411,1734],{},[1716,41413,2222],{},[895,41415,41416,41418,41420],{},[1716,41417,2222],{},[898,41419,2473],{"mathvariant":2003},[1716,41421,2787],{},[6989,41423,41424,41426,41428],{},[898,41425,1734],{},[1716,41427,2787],{},[895,41429,41430,41432,41434],{},[1716,41431,2222],{},[898,41433,2473],{"mathvariant":2003},[1716,41435,2787],{},[902,41437,38034],{"encoding":904},": (6.30).",[123,41440,41441,41483],{},[38,41442,41443,41444],{},"Bod dotyku ",[883,41445,41447],{"className":41446},[886],[888,41448,41449],{"xmlns":890},[892,41450,41451,41481],{},[895,41452,41453,41459,41461,41469,41471,41479],{},[2037,41454,41455,41457],{},[898,41456,1734],{},[1712,41458,2145],{},[1712,41460,7910],{"stretchy":1903},[6989,41462,41463,41465,41467],{},[898,41464,1734],{},[1716,41466,2222],{},[1712,41468,2145],{},[1712,41470,3138],{"separator":2565},[6989,41472,41473,41475,41477],{},[898,41474,1734],{},[1716,41476,2787],{},[1712,41478,2145],{},[1712,41480,7925],{"stretchy":1903},[902,41482,33202],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,41485,41486,41489,41490,41503,41504,41517],{},[38,41487,41488],{},"Dualita"," — ekvivalence max ",[883,41491,41493],{"className":41492},[886],[888,41494,41495],{"xmlns":890},[892,41496,41497,41501],{},[895,41498,41499],{},[898,41500,900],{},[902,41502,900],{"encoding":904}," a min ",[883,41505,41507],{"className":41506},[886],[888,41508,41509],{"xmlns":890},[892,41510,41511,41515],{},[895,41512,41513],{},[898,41514,2041],{},[902,41516,2041],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,41519,9193],{"id":9192},[120,41521,41522,41545,41561,41574,41585],{},[123,41523,41524,3245,41527,41530,41531,41544],{},[38,41525,41526],{},"Teorie před optimalizací:",[207,41528,880],{"className":41529,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,41532,41534],{"className":41533},[886],[888,41535,41536],{"xmlns":890},[892,41537,41538,41542],{},[895,41539,41540],{},[898,41541,900],{},[902,41543,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,41546,41547,3245,41550,41553,41554,41557,41558,1659],{},[38,41548,41549],{},"Matematický aparát:",[207,41551,793],{"className":41552,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,41555,784],{"className":41556,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,41559,1690],{"className":41560,"dataFsResolvedFilePath":764,"href":765},[210],[123,41562,41563,3245,41566,41569,41570,41573],{},[38,41564,41565],{},"Paralely:",[207,41567,15960],{"className":41568,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,41571,16814],{"className":41572,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,41575,41576,3245,41579,1343,41582],{},[38,41577,41578],{},"Přednášky:",[207,41580,1094],{"className":41581,"dataFsResolvedFilePath":838,"href":839},[210],[207,41583,1101],{"className":41584,"dataFsResolvedFilePath":868,"href":869},[210],[123,41586,41587,3245,41589],{},[38,41588,21078],{},[207,41590,21082],{"className":41591,"dataFsResolvedFilePath":7413,"href":7414},[210],{"title":641,"searchDepth":642,"depth":642,"links":41593},[41594,41595,41596,41601,41602,41603,41605,41608,41611,41613,41614,41616,41617,41621,41622],{"id":16879,"depth":642,"text":16880},{"id":32881,"depth":642,"text":32882},{"id":33279,"depth":642,"text":33280,"children":41597},[41598,41599],{"id":33399,"depth":649,"text":33400},{"id":33980,"depth":649,"text":41600},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":34442,"depth":642,"text":34443},{"id":34753,"depth":642,"text":34754},{"id":35072,"depth":642,"text":41604},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":35845,"depth":642,"text":35846,"children":41606},[41607],{"id":36601,"depth":649,"text":36602},{"id":36781,"depth":642,"text":36782,"children":41609},[41610],{"id":37038,"depth":649,"text":37039},{"id":37989,"depth":642,"text":41612},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":38913,"depth":642,"text":38914},{"id":39116,"depth":642,"text":41615},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":40001,"depth":642,"text":40002},{"id":40388,"depth":642,"text":40389,"children":41618},[41619,41620],{"id":40392,"depth":649,"text":40393},{"id":40852,"depth":649,"text":40853},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":32642,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,41629,1144,14645,41630,41631,41632],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":41635,"title":802,"body":41636,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":55689,"navigation":664,"path":55690,"seo":55691,"sources":55692,"stem":55693,"tags":55694,"type":7391,"updated":677,"__hash__":55700},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":41637,"toc":55645},[41638,41641,41667,41671,41678,41830,41844,41847,41849,41936,41940,41976,42049,42070,42195,42205,42218,42222,42227,42257,42319,42328,42332,42394,42401,42422,42540,42618,42622,42625,42684,42799,42804,42836,42898,42946,43001,43005,43026,43050,43098,43102,43114,43118,43228,43232,43248,43289,43300,43459,43469,43474,43478,43600,43610,43617,43621,43699,43710,43790,43796,43803,43942,43949,43952,44009,44013,44091,44137,44181,44187,44300,44304,44307,44502,44506,44743,44746,44900,45053,45055,45057,45137,45140,45245,45314,45323,45327,45330,45391,45400,45404,45437,45515,45554,45558,45607,45661,45665,45694,45723,45775,45782,45836,45914,45918,45961,46028,46072,46176,46195,46197,46201,46309,46313,46381,46430,46437,46522,46526,46598,46603,46651,46840,46844,46849,47025,47030,47089,47194,47198,47225,47229,47236,47400,47487,47492,47494,47497,47597,47747,47819,47893,47895,47899,47913,47917,48050,48105,48217,48294,48298,48355,48458,48517,48678,48682,48757,48829,48927,48985,49079,49132,49153,49207,49212,49290,49338,49425,49463,49551,49704,49740,49794,49797,49799,49801,49850,49857,49865,49952,49961,50048,50055,50057,50061,50286,50288,50292,50296,50365,50416,50619,50625,50636,50704,50710,51132,51136,51200,51224,51420,51426,51440,51508,51511,51551,51775,51843,52145,52554,52631,52797,52803,52806,52881,53334,53385,53791,53896,54559,54562,54639,54647,54721,54752,54754,54758,54802,54804,54806,54810,55040,55044,55135,55140,55234,55239,55412,55416,55534,55539,55588,55590,55592],[12,41639,802],{"id":41640},"poptávka-nabídka-a-tržní-rovnováha",[1636,41642,41643],{},[724,41644,41645,41647,41648,41651,41652,41655,41656,41659,41660,41662,41663,41666],{},[883,41646,1941],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,41649,41650],{},"poptávka",") a výrobce (",[38,41653,41654],{},"nabídka","), jejich interakci v ",[38,41657,41658],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,41661,22852],{},"). Uzavírá ji pojem ",[38,41664,41665],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,41668,41670],{"id":41669},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,41672,41673,41674,41677],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,41675,41676],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,41679,41680,41697,41739,41755],{},[123,41681,41682,41683,41696],{},"cena ",[883,41684,41686],{"className":41685},[886],[888,41687,41688],{"xmlns":890},[892,41689,41690,41694],{},[895,41691,41692],{},[898,41693,1710],{},[902,41695,1710],{"encoding":904}," zkoumaného zboží,",[123,41698,41699,41700,3138],{},"ceny alternativních zboží ",[883,41701,41703],{"className":41702},[886],[888,41704,41705],{"xmlns":890},[892,41706,41707,41736],{},[895,41708,41709,41715,41717,41723,41725,41727,41729],{},[6927,41710,41711,41713],{},[898,41712,1710],{},[1716,41714,2222],{},[1712,41716,3138],{"separator":2565},[6927,41718,41719,41721],{},[898,41720,1710],{},[1716,41722,2787],{},[1712,41724,3138],{"separator":2565},[1712,41726,14518],{},[1712,41728,3138],{"separator":2565},[6927,41730,41731,41733],{},[898,41732,1710],{},[898,41734,41735],{},"n",[902,41737,41738],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,41740,41741,41742,3138],{},"důchod ",[883,41743,41745],{"className":41744},[886],[888,41746,41747],{"xmlns":890},[892,41748,41749,41753],{},[895,41750,41751],{},[898,41752,6951],{},[902,41754,6951],{"encoding":904},[123,41756,41757,41758,41771,41772,41785,41786,41799,41800,41814,41815,41829],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,41759,41761],{"className":41760},[886],[888,41762,41763],{"xmlns":890},[892,41764,41765,41769],{},[895,41766,41767],{},[898,41768,14667],{},[902,41770,14667],{"encoding":904},", kapitál ",[883,41773,41775],{"className":41774},[886],[888,41776,41777],{"xmlns":890},[892,41778,41779,41783],{},[895,41780,41781],{},[898,41782,14672],{},[902,41784,14672],{"encoding":904},", půda ",[883,41787,41789],{"className":41788},[886],[888,41790,41791],{"xmlns":890},[892,41792,41793,41797],{},[895,41794,41795],{},[898,41796,2041],{},[902,41798,2041],{"encoding":904},"), technologie, počet výrobců ",[883,41801,41803],{"className":41802},[886],[888,41804,41805],{"xmlns":890},[892,41806,41807,41812],{},[895,41808,41809],{},[898,41810,41811],{},"O",[902,41813,41811],{"encoding":904},", počasí ",[883,41816,41818],{"className":41817},[886],[888,41819,41820],{"xmlns":890},[892,41821,41822,41827],{},[895,41823,41824],{},[898,41825,41826],{},"W",[902,41828,41826],{"encoding":904}," atd.",[724,41831,41832,41833,41836,41837,41840,41841,1659],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,41834,41835],{},"ceteris paribus","), hovoříme o ",[38,41838,41839],{},"jednofaktorovém modelu","; jinak jde o model ",[38,41842,41843],{},"vícefaktorový",[41845,41846],"hr",{},[115,41848,18035],{"id":41650},[1636,41850,41851],{},[724,41852,41853,41855,41856,41869,41870,41883,41884,41887,41888,41911,41912,1659],{},[883,41854,1941],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,41857,41859],{"className":41858},[886],[888,41860,41861],{"xmlns":890},[892,41862,41863,41867],{},[895,41864,41865],{},[898,41866,1734],{},[902,41868,1734],{"encoding":904}," na ceně ",[883,41871,41873],{"className":41872},[886],[888,41874,41875],{"xmlns":890},[892,41876,41877,41881],{},[895,41878,41879],{},[898,41880,1710],{},[902,41882,1710],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,41885,41886],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,41889,41891],{"className":41890},[886],[888,41892,41893],{"xmlns":890},[892,41894,41895,41909],{},[895,41896,41897,41899,41901,41903,41905,41907],{},[898,41898,1734],{},[1712,41900,1714],{},[898,41902,1969],{},[1712,41904,1904],{"stretchy":1903},[898,41906,1710],{},[1712,41908,1910],{"stretchy":1903},[902,41910,1978],{"encoding":904}," a jeho lineární verzí ",[883,41913,41915],{"className":41914},[886],[888,41916,41917],{"xmlns":890},[892,41918,41919,41933],{},[895,41920,41921,41923,41925,41927,41929,41931],{},[898,41922,1710],{},[1712,41924,1714],{},[898,41926,207],{},[898,41928,1734],{},[1712,41930,3145],{},[898,41932,7544],{},[902,41934,41935],{"encoding":904},"P = aQ + b",[198,41937,41939],{"id":41938},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,41941,41942,41943,41956,41957,41970,41971,14897,41973,8558],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,41944,41946],{"className":41945},[886],[888,41947,41948],{"xmlns":890},[892,41949,41950,41954],{},[895,41951,41952],{},[898,41953,1734],{},[902,41955,1734],{"encoding":904}," závisí na ceně ",[883,41958,41960],{"className":41959},[886],[888,41961,41962],{"xmlns":890},[892,41963,41964,41968],{},[895,41965,41966],{},[898,41967,1710],{},[902,41969,1710],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,41972,32877],{},[614,41974,41975],{},"demand function",[883,41977,41979],{"className":41978},[886],[888,41980,41981],{"xmlns":890,"display":32941},[892,41982,41983,42046],{},[25629,41984,41985],{"width":32946},[25634,41986,41987,41989,42039,42041],{},[25637,41988],{"width":32951},[25637,41990,41991],{},[895,41992,41993,41995,41997,41999,42001,42003,42005,42011,42013,42019,42021,42023,42025,42031,42033,42035,42037],{},[898,41994,1734],{},[1712,41996,1714],{},[898,41998,1969],{},[1712,42000,1904],{"stretchy":1903},[898,42002,1710],{},[1712,42004,3138],{"separator":2565},[6927,42006,42007,42009],{},[898,42008,1710],{},[1716,42010,2222],{},[1712,42012,3138],{"separator":2565},[6927,42014,42015,42017],{},[898,42016,1710],{},[1716,42018,2787],{},[1712,42020,3138],{"separator":2565},[1712,42022,14518],{},[1712,42024,3138],{"separator":2565},[6927,42026,42027,42029],{},[898,42028,1710],{},[898,42030,41735],{},[1712,42032,3138],{"separator":2565},[898,42034,6951],{},[1712,42036,1910],{"stretchy":1903},[898,42038,1659],{"mathvariant":2003},[25637,42040],{"width":32951},[25637,42042,42043],{},[1762,42044,42045],{},"(2.1)",[902,42047,42048],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,42050,42051,42052,42055,42056,42069],{},"Důležitou vlastností je ",[38,42053,42054],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,42057,42059],{"className":42058},[886],[888,42060,42061],{"xmlns":890},[892,42062,42063,42067],{},[895,42064,42065],{},[898,42066,16915],{},[902,42068,16915],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,42071,42073],{"className":42072},[886],[888,42074,42075],{"xmlns":890,"display":32941},[892,42076,42077,42192],{},[25629,42078,42079],{"width":32946},[25634,42080,42081,42083,42185,42187],{},[25637,42082],{"width":32951},[25637,42084,42085],{},[895,42086,42087,42089,42091,42093,42095,42097,42099,42101,42103,42109,42111,42113,42119,42121,42123,42125,42127,42133,42135,42137,42139,42141,42143,42145,42147,42149,42151,42157,42159,42165,42167,42169,42171,42177,42179,42181,42183],{},[898,42088,1734],{},[1712,42090,1714],{},[898,42092,1969],{},[1712,42094,1904],{"stretchy":1903},[898,42096,16915],{},[898,42098,1710],{},[1712,42100,3138],{"separator":2565},[898,42102,16915],{},[6927,42104,42105,42107],{},[898,42106,1710],{},[1716,42108,2222],{},[1712,42110,3138],{"separator":2565},[898,42112,16915],{},[6927,42114,42115,42117],{},[898,42116,1710],{},[1716,42118,2787],{},[1712,42120,3138],{"separator":2565},[1712,42122,14518],{},[1712,42124,3138],{"separator":2565},[898,42126,16915],{},[6927,42128,42129,42131],{},[898,42130,1710],{},[898,42132,41735],{},[1712,42134,3138],{"separator":2565},[898,42136,16915],{},[898,42138,6951],{},[1712,42140,1910],{"stretchy":1903},[1712,42142,1714],{},[898,42144,1969],{},[1712,42146,1904],{"stretchy":1903},[898,42148,1710],{},[1712,42150,3138],{"separator":2565},[6927,42152,42153,42155],{},[898,42154,1710],{},[1716,42156,2222],{},[1712,42158,3138],{"separator":2565},[6927,42160,42161,42163],{},[898,42162,1710],{},[1716,42164,2787],{},[1712,42166,3138],{"separator":2565},[1712,42168,14518],{},[1712,42170,3138],{"separator":2565},[6927,42172,42173,42175],{},[898,42174,1710],{},[898,42176,41735],{},[1712,42178,3138],{"separator":2565},[898,42180,6951],{},[1712,42182,1910],{"stretchy":1903},[898,42184,1659],{"mathvariant":2003},[25637,42186],{"width":32951},[25637,42188,42189],{},[1762,42190,42191],{},"(2.2)",[902,42193,42194],{"encoding":904},"Q = D(rP, rP_1, rP_2, \\dots, rP_n, rY) = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.2}",[1636,42196,42197],{},[724,42198,42199,42201,42202,1659],{},[883,42200,2203],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,42203,42204],{},"v jednofaktorových modelech neplatí",[724,42206,42207,42208,1343,42211,1655,42214,42217],{},"Rozlišuje se poptávka ",[38,42209,42210],{},"individuální",[38,42212,42213],{},"tržní",[38,42215,42216],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,42219,42221],{"id":42220},"jednofaktorové-modely","Jednofaktorové modely",[42223,42224,42226],"h4",{"id":42225},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,42228,42229,42230,42243,42244,2854],{},"Poptávané množství ",[883,42231,42233],{"className":42232},[886],[888,42234,42235],{"xmlns":890},[892,42236,42237,42241],{},[895,42238,42239],{},[898,42240,1734],{},[902,42242,1734],{"encoding":904}," závisí pouze na ceně ",[883,42245,42247],{"className":42246},[886],[888,42248,42249],{"xmlns":890},[892,42250,42251,42255],{},[895,42252,42253],{},[898,42254,1710],{},[902,42256,1710],{"encoding":904},[883,42258,42260],{"className":42259},[886],[888,42261,42262],{"xmlns":890,"display":32941},[892,42263,42264,42316],{},[25629,42265,42266],{"width":32946},[25634,42267,42268,42270,42309,42311],{},[25637,42269],{"width":32951},[25637,42271,42272],{},[895,42273,42274,42276,42278,42280,42282,42284,42286,42288,42290,42293,42295,42297,42299,42301,42303,42305,42307],{},[898,42275,1734],{},[1712,42277,1714],{},[898,42279,1969],{},[1712,42281,1904],{"stretchy":1903},[898,42283,1710],{},[1712,42285,1910],{"stretchy":1903},[1712,42287,3138],{"separator":2565},[3690,42289],{"width":3692},[1762,42291,42292],{},"resp.",[3690,42294],{"width":3692},[898,42296,1710],{},[1712,42298,1714],{},[898,42300,1969],{},[1712,42302,1904],{"stretchy":1903},[898,42304,1734],{},[1712,42306,1910],{"stretchy":1903},[898,42308,1659],{"mathvariant":2003},[25637,42310],{"width":32951},[25637,42312,42313],{},[1762,42314,42315],{},"(2.3)",[902,42317,42318],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,42320,42321,42322,14897,42325,1691],{},"Graf této funkce se nazývá ",[38,42323,42324],{},"křivka poptávky",[614,42326,42327],{},"demand curve",[42223,42329,42331],{"id":42330},"zákon-klesající-poptávky","Zákon klesající poptávky",[1636,42333,42334],{},[724,42335,42336],{},[38,42337,42338,42339,42352,42353,42366,42367,42352,42380,42393],{},"Roste-li cena ",[883,42340,42342],{"className":42341},[886],[888,42343,42344],{"xmlns":890},[892,42345,42346,42350],{},[895,42347,42348],{},[898,42349,1710],{},[902,42351,1710],{"encoding":904},", pak množství ",[883,42354,42356],{"className":42355},[886],[888,42357,42358],{"xmlns":890},[892,42359,42360,42364],{},[895,42361,42362],{},[898,42363,1734],{},[902,42365,1734],{"encoding":904}," klesá; klesá-li cena ",[883,42368,42370],{"className":42369},[886],[888,42371,42372],{"xmlns":890},[892,42373,42374,42378],{},[895,42375,42376],{},[898,42377,1710],{},[902,42379,1710],{"encoding":904},[883,42381,42383],{"className":42382},[886],[888,42384,42385],{"xmlns":890},[892,42386,42387,42391],{},[895,42388,42389],{},[898,42390,1734],{},[902,42392,1734],{"encoding":904}," roste.",[724,42395,42396,42397,42400],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,42398,42399],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1636,42402,42403,42408],{},[724,42404,42405,42407],{},[883,42406,1941],{}," Intuice — proč zákon platí",[120,42409,42410,42416],{},[123,42411,42412,42415],{},[38,42413,42414],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,42417,42418,42421],{},[38,42419,42420],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,42423,42424,42425,42438,42439,42452,42453,42479,42480,42506,42507,5920,42533,42536,42537,1659],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,42426,42428],{"className":42427},[886],[888,42429,42430],{"xmlns":890},[892,42431,42432,42436],{},[895,42433,42434],{},[898,42435,1710],{},[902,42437,1710],{"encoding":904}," se vynáší na svislou osu, množství ",[883,42440,42442],{"className":42441},[886],[888,42443,42444],{"xmlns":890},[892,42445,42446,42450],{},[895,42447,42448],{},[898,42449,1734],{},[902,42451,1734],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,42454,42456],{"className":42455},[886],[888,42457,42458],{"xmlns":890},[892,42459,42460,42476],{},[895,42461,42462,42464,42466,42468,42474],{},[1712,42463,7910],{"stretchy":1903},[1716,42465,2085],{},[1712,42467,3138],{"separator":2565},[6927,42469,42470,42472],{},[898,42471,1710],{},[1716,42473,2085],{},[1712,42475,7925],{"stretchy":1903},[902,42477,42478],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,42481,42483],{"className":42482},[886],[888,42484,42485],{"xmlns":890},[892,42486,42487,42503],{},[895,42488,42489,42491,42497,42499,42501],{},[1712,42490,7910],{"stretchy":1903},[6927,42492,42493,42495],{},[898,42494,1734],{},[1716,42496,2085],{},[1712,42498,3138],{"separator":2565},[1716,42500,2085],{},[1712,42502,7925],{"stretchy":1903},[902,42504,42505],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,42508,42510],{"className":42509},[886],[888,42511,42512],{"xmlns":890},[892,42513,42514,42530],{},[895,42515,42516,42518,42520,42522,42528],{},[1712,42517,1904],{"stretchy":1903},[1716,42519,2085],{},[1712,42521,3138],{"separator":2565},[6927,42523,42524,42526],{},[898,42525,1710],{},[1716,42527,2085],{},[1712,42529,1910],{"stretchy":1903},[902,42531,42532],{"encoding":904},"(0, P_0)",[38,42534,42535],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,42538,42539],{},"konvexní",[724,42541,42542],{},[614,42543,42544,42545,42567,42568,1655,42593,1659],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,42546,42548],{"className":42547},[886],[888,42549,42550],{"xmlns":890},[892,42551,42552,42564],{},[895,42553,42554,42556,42558,42560,42562],{},[1712,42555,1904],{"stretchy":1903},[898,42557,1734],{},[1712,42559,3138],{"separator":2565},[898,42561,1710],{},[1712,42563,1910],{"stretchy":1903},[902,42565,42566],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,42569,42571],{"className":42570},[886],[888,42572,42573],{"xmlns":890},[892,42574,42575,42591],{},[895,42576,42577,42579,42581,42583,42589],{},[1712,42578,7910],{"stretchy":1903},[1716,42580,2085],{},[1712,42582,3138],{"separator":2565},[6927,42584,42585,42587],{},[898,42586,1710],{},[1716,42588,2085],{},[1712,42590,7925],{"stretchy":1903},[902,42592,42478],{"encoding":904},[883,42594,42596],{"className":42595},[886],[888,42597,42598],{"xmlns":890},[892,42599,42600,42616],{},[895,42601,42602,42604,42610,42612,42614],{},[1712,42603,7910],{"stretchy":1903},[6927,42605,42606,42608],{},[898,42607,1734],{},[1716,42609,2085],{},[1712,42611,3138],{"separator":2565},[1716,42613,2085],{},[1712,42615,7925],{"stretchy":1903},[902,42617,42505],{"encoding":904},[42223,42619,42621],{"id":42620},"lineární-model-poptávky","Lineární model poptávky",[724,42623,42624],{},"Nejjednodušší závislostí je",[883,42626,42628],{"className":42627},[886],[888,42629,42630],{"xmlns":890,"display":32941},[892,42631,42632,42681],{},[25629,42633,42634],{"width":32946},[25634,42635,42636,42638,42674,42676],{},[25637,42637],{"width":32951},[25637,42639,42640],{},[895,42641,42642,42644,42646,42648,42650,42652,42654,42656,42658,42660,42662,42664,42666,42668,42670,42672],{},[898,42643,1710],{},[1712,42645,1714],{},[898,42647,207],{},[898,42649,1734],{},[1712,42651,3145],{},[898,42653,7544],{},[1712,42655,3138],{"separator":2565},[3690,42657],{"width":3692},[898,42659,207],{},[1712,42661,2252],{},[1716,42663,2085],{},[1712,42665,3138],{"separator":2565},[1762,42667,7722],{},[898,42669,7544],{},[1712,42671,2302],{},[1716,42673,17334],{},[25637,42675],{"width":32951},[25637,42677,42678],{},[1762,42679,42680],{},"(2.4)",[902,42682,42683],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,42685,42686,42687,26469,42723,1655,42747,5855,42773,42795,42796,1659],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,42688,42690],{"className":42689},[886],[888,42691,42692],{"xmlns":890},[892,42693,42694,42720],{},[895,42695,42696,42698,42700,42708,42710,42712],{},[898,42697,1734],{},[1712,42699,1714],{},[2563,42701,42702],{"scriptlevel":2085,"displaystyle":1903},[2567,42703,42704,42706],{},[1716,42705,2222],{},[898,42707,207],{},[898,42709,1710],{},[1712,42711,2219],{},[2563,42713,42714],{"scriptlevel":2085,"displaystyle":1903},[2567,42715,42716,42718],{},[898,42717,7544],{},[898,42719,207],{},[902,42721,42722],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,42724,42726],{"className":42725},[886],[888,42727,42728],{"xmlns":890},[892,42729,42730,42744],{},[895,42731,42732,42740,42742],{},[2563,42733,42734],{"scriptlevel":2085,"displaystyle":1903},[2567,42735,42736,42738],{},[1716,42737,2222],{},[898,42739,207],{},[1712,42741,2252],{},[1716,42743,2085],{},[902,42745,42746],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,42748,42750],{"className":42749},[886],[888,42751,42752],{"xmlns":890},[892,42753,42754,42770],{},[895,42755,42756,42758,42766,42768],{},[1712,42757,2219],{},[2563,42759,42760],{"scriptlevel":2085,"displaystyle":1903},[2567,42761,42762,42764],{},[898,42763,7544],{},[898,42765,207],{},[1712,42767,2302],{},[1716,42769,2085],{},[902,42771,42772],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,42774,42776],{"className":42775},[886],[888,42777,42778],{"xmlns":890},[892,42779,42780,42792],{},[895,42781,42782,42784,42786,42788,42790],{},[1712,42783,1904],{"stretchy":1903},[1716,42785,2085],{},[1712,42787,3138],{"separator":2565},[898,42789,7544],{},[1712,42791,1910],{"stretchy":1903},[902,42793,42794],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,42797,42798],{},"nedokonalé konkurenci",[42800,42801,42803],"h5",{"id":42802},"příklad-21","Příklad 2.1",[724,42805,42806,42809,42810,1659],{},[38,42807,42808],{},"Zadání:"," Lineární poptávka ",[883,42811,42813],{"className":42812},[886],[888,42814,42815],{"xmlns":890},[892,42816,42817,42833],{},[895,42818,42819,42821,42823,42825,42827,42829,42831],{},[898,42820,1710],{},[1712,42822,1714],{},[1712,42824,2219],{},[1716,42826,2787],{},[898,42828,1734],{},[1712,42830,3145],{},[1716,42832,8533],{},[902,42834,42835],{"encoding":904},"P = -2Q + 60",[724,42837,42838,42841,42842,42864,42865,1659],{},[38,42839,42840],{},"Řešení:"," Reálné cenové rozpětí je ",[883,42843,42845],{"className":42844},[886],[888,42846,42847],{"xmlns":890},[892,42848,42849,42861],{},[895,42850,42851,42853,42855,42857,42859],{},[1712,42852,1904],{"stretchy":1903},[1716,42854,2085],{},[1712,42856,3138],{"separator":2565},[1716,42858,8533],{},[1712,42860,1910],{"stretchy":1903},[902,42862,42863],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,42866,42868],{"className":42867},[886],[888,42869,42870],{"xmlns":890},[892,42871,42872,42895],{},[895,42873,42874,42876,42878,42880,42888,42890,42892],{},[898,42875,1734],{},[1712,42877,1714],{},[1712,42879,2219],{},[2563,42881,42882],{"scriptlevel":2085,"displaystyle":1903},[2567,42883,42884,42886],{},[1716,42885,2222],{},[1716,42887,2787],{},[898,42889,1710],{},[1712,42891,3145],{},[1716,42893,42894],{},"30",[902,42896,42897],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,42899,42900,42923],{},[19,42901,42902],{},[22,42903,42904,42919,42921],{},[25,42905,42906],{},[883,42907,42909],{"className":42908},[886],[888,42910,42911],{"xmlns":890},[892,42912,42913,42917],{},[895,42914,42915],{},[898,42916,1710],{},[902,42918,1710],{"encoding":904},[25,42920,3018],{},[25,42922,6857],{},[30,42924,42925],{},[22,42926,42927,42942,42944],{},[35,42928,42929],{},[883,42930,42932],{"className":42931},[886],[888,42933,42934],{"xmlns":890},[892,42935,42936,42940],{},[895,42937,42938],{},[898,42939,1734],{},[902,42941,1734],{"encoding":904},[35,42943,1718],{},[35,42945,6857],{},[724,42947,42948],{},[614,42949,42950,42951,1655,42973,1659],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,42952,42954],{"className":42953},[886],[888,42955,42956],{"xmlns":890},[892,42957,42958,42970],{},[895,42959,42960,42962,42964,42966,42968],{},[1712,42961,7910],{"stretchy":1903},[1716,42963,2085],{},[1712,42965,3138],{"separator":2565},[898,42967,7544],{},[1712,42969,7925],{"stretchy":1903},[902,42971,42972],{"encoding":904},"[0, b]",[883,42974,42976],{"className":42975},[886],[888,42977,42978],{"xmlns":890},[892,42979,42980,42998],{},[895,42981,42982,42984,42986,42988,42990,42992,42994,42996],{},[1712,42983,7910],{"stretchy":1903},[1712,42985,2219],{},[898,42987,7544],{},[898,42989,2473],{"mathvariant":2003},[898,42991,207],{},[1712,42993,3138],{"separator":2565},[1716,42995,2085],{},[1712,42997,7925],{"stretchy":1903},[902,42999,43000],{"encoding":904},"[-b\u002Fa, 0]",[42223,43002,43004],{"id":43003},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,43006,43007,43008,43025],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,43009,43011],{"className":43010},[886],[888,43012,43013],{"xmlns":890},[892,43014,43015,43023],{},[895,43016,43017],{},[2037,43018,43019,43021],{},[898,43020,1710],{},[1712,43022,2145],{},[902,43024,2195],{"encoding":904},", je funkce poptávky konstantní:",[883,43027,43029],{"className":43028},[886],[888,43030,43031],{"xmlns":890,"display":32941},[892,43032,43033,43047],{},[895,43034,43035,43037,43039,43045],{},[898,43036,1710],{},[1712,43038,1714],{},[2037,43040,43041,43043],{},[898,43042,1710],{},[1712,43044,2145],{},[898,43046,1659],{"mathvariant":2003},[902,43048,43049],{"encoding":904},"P = P^*.",[724,43051,43052],{},[614,43053,43054,43055,43076,43077,1659],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,43056,43058],{"className":43057},[886],[888,43059,43060],{"xmlns":890},[892,43061,43062,43074],{},[895,43063,43064,43066,43068,43070,43072],{},[1712,43065,1904],{"stretchy":1903},[898,43067,1734],{},[1712,43069,3138],{"separator":2565},[898,43071,1710],{},[1712,43073,1910],{"stretchy":1903},[902,43075,42566],{"encoding":904}," na úrovni ",[883,43078,43080],{"className":43079},[886],[888,43081,43082],{"xmlns":890},[892,43083,43084,43096],{},[895,43085,43086,43088,43090],{},[898,43087,1710],{},[1712,43089,1714],{},[2037,43091,43092,43094],{},[898,43093,1710],{},[1712,43095,2145],{},[902,43097,2148],{"encoding":904},[42223,43099,43101],{"id":43100},"giffenův-statek","Giffenův statek",[724,43103,43104,43105,43107,43108,43110,43111,1659],{},"Existují zboží, u nichž je křivka poptávky ",[38,43106,18531],{}," — tzv. ",[38,43109,43101],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,43112,43113],{},"podřadnému zboží",[42800,43115,43117],{"id":43116},"příklad-22","Příklad 2.2",[724,43119,43120,43123,43124,43142,43143,43165,43166,43184,43185,43203,43204,43227],{},[38,43121,43122],{},"Zadání a popis:"," Křivka ",[883,43125,43127],{"className":43126},[886],[888,43128,43129],{"xmlns":890},[892,43130,43131,43139],{},[895,43132,43133],{},[6927,43134,43135,43137],{},[898,43136,1969],{},[1716,43138,2222],{},[902,43140,43141],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,43144,43146],{"className":43145},[886],[888,43147,43148],{"xmlns":890},[892,43149,43150,43162],{},[895,43151,43152,43154,43156,43158,43160],{},[1712,43153,1904],{"stretchy":1903},[1716,43155,2085],{},[1712,43157,3138],{"separator":2565},[1716,43159,41119],{},[1712,43161,1910],{"stretchy":1903},[902,43163,43164],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,43167,43169],{"className":43168},[886],[888,43170,43171],{"xmlns":890},[892,43172,43173,43181],{},[895,43174,43175],{},[6927,43176,43177,43179],{},[898,43178,1734],{},[1716,43180,2085],{},[902,43182,43183],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,43186,43188],{"className":43187},[886],[888,43189,43190],{"xmlns":890},[892,43191,43192,43200],{},[895,43193,43194],{},[6927,43195,43196,43198],{},[898,43197,1969],{},[1716,43199,2787],{},[902,43201,43202],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,43205,43207],{"className":43206},[886],[888,43208,43209],{"xmlns":890},[892,43210,43211,43224],{},[895,43212,43213,43215,43217,43219,43222],{},[1712,43214,7910],{"stretchy":1903},[1716,43216,2085],{},[1712,43218,3138],{"separator":2565},[1716,43220,43221],{},"21",[1712,43223,7925],{"stretchy":1903},[902,43225,43226],{"encoding":904},"[0, 21]"," centů.",[198,43229,43231],{"id":43230},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,43233,43234,43235,2854],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,43236,43238],{"className":43237},[886],[888,43239,43240],{"xmlns":890},[892,43241,43242,43246],{},[895,43243,43244],{},[898,43245,6951],{},[902,43247,6951],{"encoding":904},[883,43249,43251],{"className":43250},[886],[888,43252,43253],{"xmlns":890,"display":32941},[892,43254,43255,43286],{},[25629,43256,43257],{"width":32946},[25634,43258,43259,43261,43279,43281],{},[25637,43260],{"width":32951},[25637,43262,43263],{},[895,43264,43265,43267,43269,43271,43273,43275,43277],{},[898,43266,1734],{},[1712,43268,1714],{},[898,43270,2041],{},[1712,43272,1904],{"stretchy":1903},[898,43274,6951],{},[1712,43276,1910],{"stretchy":1903},[898,43278,1659],{"mathvariant":2003},[25637,43280],{"width":32951},[25637,43282,43283],{},[1762,43284,43285],{},"(2.5)",[902,43287,43288],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,43290,43291,43292,43295,43296,43299],{},"Funkce se nazývá ",[38,43293,43294],{},"Engelova",", její graf ",[38,43297,43298],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,43301,43302,43434],{},[123,43303,43304,4831,43307,43320,43321,43334,43335,43352,43353],{},[38,43305,43306],{},"Normální (superior) zboží",[883,43308,43310],{"className":43309},[886],[888,43311,43312],{"xmlns":890},[892,43313,43314,43318],{},[895,43315,43316],{},[898,43317,1734],{},[902,43319,1734],{"encoding":904}," roste s ",[883,43322,43324],{"className":43323},[886],[888,43325,43326],{"xmlns":890},[892,43327,43328,43332],{},[895,43329,43330],{},[898,43331,6951],{},[902,43333,6951],{"encoding":904},", nepřesáhne hodnotu ",[883,43336,43338],{"className":43337},[886],[888,43339,43340],{"xmlns":890},[892,43341,43342,43350],{},[895,43343,43344],{},[6927,43345,43346,43348],{},[898,43347,1734],{},[1716,43349,2085],{},[902,43351,43183],{"encoding":904},":\n",[120,43354,43355,43387],{},[123,43356,43357,43360,43361,43364,43365,1659],{},[38,43358,43359],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,43362,43363],{},"konkávní"," křivka, autonomní spotřeba ",[883,43366,43368],{"className":43367},[886],[888,43369,43370],{"xmlns":890},[892,43371,43372,43384],{},[895,43373,43374,43380,43382],{},[6927,43375,43376,43378],{},[898,43377,1734],{},[1716,43379,2222],{},[1712,43381,2302],{},[1716,43383,2085],{},[902,43385,43386],{"encoding":904},"Q_1 > 0",[123,43388,43389,43392,43393,43411,43412,43414,43415,3245,43432,1659],{},[38,43390,43391],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,43394,43396],{"className":43395},[886],[888,43397,43398],{"xmlns":890},[892,43399,43400,43408],{},[895,43401,43402],{},[6927,43403,43404,43406],{},[898,43405,6951],{},[1716,43407,2222],{},[902,43409,43410],{"encoding":904},"Y_1",", křivka je nejprve ",[38,43413,42539],{}," a od ",[883,43416,43418],{"className":43417},[886],[888,43419,43420],{"xmlns":890},[892,43421,43422,43430],{},[895,43423,43424],{},[6927,43425,43426,43428],{},[898,43427,6951],{},[1716,43429,2222],{},[902,43431,43410],{"encoding":904},[38,43433,43363],{},[123,43435,43436,43439,43440,43458],{},[38,43437,43438],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,43441,43443],{"className":43442},[886],[888,43444,43445],{"xmlns":890},[892,43446,43447,43455],{},[895,43448,43449],{},[6927,43450,43451,43453],{},[898,43452,6951],{},[1716,43454,2085],{},[902,43456,43457],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,43460,43461,43462,43465,43466,1691],{},"Mírou citlivosti je ",[614,43463,43464],{},"důchodová elasticita"," (viz ",[207,43467,1669],{"className":43468,"dataFsResolvedFilePath":848,"href":849},[210],[724,43470,43471],{},[614,43472,43473],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[42223,43475,43477],{"id":43476},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1636,43479,43480,43551,43594],{},[724,43481,43482,43484,43485,3245,43488,3245,43501,3481,43503,43516,43517,43520,43521,1659],{},[883,43483,2203],{}," Pozor — nezbytné ≠ podřadné\n",[38,43486,43487],{},"Nezbytné zboží:",[883,43489,43491],{"className":43490},[886],[888,43492,43493],{"xmlns":890},[892,43494,43495,43499],{},[895,43496,43497],{},[898,43498,1734],{},[902,43500,1734],{"encoding":904},[38,43502,5139],{},[883,43504,43506],{"className":43505},[886],[888,43507,43508],{"xmlns":890},[892,43509,43510,43514],{},[895,43511,43512],{},[898,43513,6951],{},[902,43515,6951],{"encoding":904},", ale ",[38,43518,43519],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,43522,43524],{"className":43523},[886],[888,43525,43526],{"xmlns":890},[892,43527,43528,43548],{},[895,43529,43530,43536,43538,43540,43542,43544,43546],{},[6927,43531,43532,43534],{},[898,43533,2041],{},[898,43535,6951],{},[1712,43537,4321],{},[1712,43539,1904],{"stretchy":1903},[1716,43541,2085],{},[1712,43543,3138],{"separator":2565},[1716,43545,2222],{},[1712,43547,1910],{"stretchy":1903},[902,43549,43550],{"encoding":904},"E_Y \\in (0, 1)",[724,43552,43553,3245,43556,3245,43569,43571,43572,1659],{},[38,43554,43555],{},"Podřadné zboží:",[883,43557,43559],{"className":43558},[886],[888,43560,43561],{"xmlns":890},[892,43562,43563,43567],{},[895,43564,43565],{},[898,43566,1734],{},[902,43568,1734],{"encoding":904},[38,43570,5159],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,43573,43575],{"className":43574},[886],[888,43576,43577],{"xmlns":890},[892,43578,43579,43591],{},[895,43580,43581,43587,43589],{},[6927,43582,43583,43585],{},[898,43584,2041],{},[898,43586,6951],{},[1712,43588,2252],{},[1716,43590,2085],{},[902,43592,43593],{"encoding":904},"E_Y \u003C 0",[724,43595,43596,43597,1659],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,43598,43599],{},"méně kusů, ne jen proporčně méně",[724,43601,43602,43605,43606,43609],{},[38,43603,43604],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,43607,43608],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,43611,43612],{},[3817,43613],{"alt":43614,"className":43615,"src":43616},"imek-engelovy-krivky-3typy",[210,3821],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[42800,43618,43620],{"id":43619},"české-příklady","České příklady",[16,43622,43623,43633],{},[19,43624,43625],{},[22,43626,43627,43630],{},[25,43628,43629],{},"Podřadné",[25,43631,43632],{},"Nahradí se za",[30,43634,43635,43643,43651,43659,43667,43675,43683,43691],{},[22,43636,43637,43640],{},[35,43638,43639],{},"Instantní polévky, ramen",[35,43641,43642],{},"Čerstvé jídlo, restaurace",[22,43644,43645,43648],{},[35,43646,43647],{},"MHD (autobus, tramvaj)",[35,43649,43650],{},"Vlastní auto, Uber, taxi",[22,43652,43653,43656],{},[35,43654,43655],{},"Mražené polotovary, pizza z mrazáku",[35,43657,43658],{},"Čerstvé suroviny, hotovky",[22,43660,43661,43664],{},[35,43662,43663],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,43665,43666],{},"Značkové produkty",[22,43668,43669,43672],{},[35,43670,43671],{},"Paštika Májka, obyčejný měkký salám",[35,43673,43674],{},"Kvalitní uzeniny, šunka od kosti",[22,43676,43677,43680],{},[35,43678,43679],{},"Second hand oblečení",[35,43681,43682],{},"Nové oblečení, značky",[22,43684,43685,43688],{},[35,43686,43687],{},"Krabicové víno, nejlevnější pivo",[35,43689,43690],{},"Lahvové víno, řemeslná piva",[22,43692,43693,43696],{},[35,43694,43695],{},"Ojetá auta nižších tříd",[35,43697,43698],{},"Nová auta, prémiové značky",[1636,43700,43701],{},[724,43702,43703,43705,43706,43709],{},[883,43704,2370],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,43707,43708],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,43711,43712,43715,43716,14897,43719,43741,43742,14897,43745,43766,43767,43785,43786,43789],{},[38,43713,43714],{},"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 ",[38,43717,43718],{},"luxus",[883,43720,43722],{"className":43721},[886],[888,43723,43724],{"xmlns":890},[892,43725,43726,43738],{},[895,43727,43728,43734,43736],{},[6927,43729,43730,43732],{},[898,43731,2041],{},[898,43733,6951],{},[1712,43735,2302],{},[1716,43737,2222],{},[902,43739,43740],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,43743,43744],{},"podřadné",[883,43746,43748],{"className":43747},[886],[888,43749,43750],{"xmlns":890},[892,43751,43752,43764],{},[895,43753,43754,43760,43762],{},[6927,43755,43756,43758],{},[898,43757,2041],{},[898,43759,6951],{},[1712,43761,2252],{},[1716,43763,2085],{},[902,43765,43593],{"encoding":904},"). Proto je ",[883,43768,43770],{"className":43769},[886],[888,43771,43772],{"xmlns":890},[892,43773,43774,43782],{},[895,43775,43776],{},[6927,43777,43778,43780],{},[898,43779,2041],{},[898,43781,6951],{},[902,43783,43784],{"encoding":904},"E_Y"," vždy ",[38,43787,43788],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,43791,43792,43793,43795],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,43794,43101],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,43797,43799,43800,1910],{"id":43798},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,43801,43802],{},"shift of demand",[724,43804,43805,43806,43824,43825,43842,43843,43856,43857,3072,43870,43892,43893,43910,43911,43937,43938,43941],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,43807,43809],{"className":43808},[886],[888,43810,43811],{"xmlns":890},[892,43812,43813,43821],{},[895,43814,43815],{},[6927,43816,43817,43819],{},[898,43818,1710],{},[1716,43820,2085],{},[902,43822,43823],{"encoding":904},"P_0"," odpovídá množství ",[883,43826,43828],{"className":43827},[886],[888,43829,43830],{"xmlns":890},[892,43831,43832,43840],{},[895,43833,43834],{},[6927,43835,43836,43838],{},[898,43837,1734],{},[1716,43839,2085],{},[902,43841,43183],{"encoding":904}," na křivce ",[883,43844,43846],{"className":43845},[886],[888,43847,43848],{"xmlns":890},[892,43849,43850,43854],{},[895,43851,43852],{},[898,43853,1969],{},[902,43855,1969],{"encoding":904},"; vzroste-li důchod z ",[883,43858,43860],{"className":43859},[886],[888,43861,43862],{"xmlns":890},[892,43863,43864,43868],{},[895,43865,43866],{},[898,43867,6951],{},[902,43869,6951],{"encoding":904},[883,43871,43873],{"className":43872},[886],[888,43874,43875],{"xmlns":890},[892,43876,43877,43889],{},[895,43878,43879,43885,43887],{},[6927,43880,43881,43883],{},[898,43882,6951],{},[1716,43884,2222],{},[1712,43886,2302],{},[898,43888,6951],{},[902,43890,43891],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,43894,43896],{"className":43895},[886],[888,43897,43898],{"xmlns":890},[892,43899,43900,43908],{},[895,43901,43902],{},[6927,43903,43904,43906],{},[898,43905,1710],{},[1716,43907,2085],{},[902,43909,43823],{"encoding":904}," odpovídá vyšší ",[883,43912,43914],{"className":43913},[886],[888,43915,43916],{"xmlns":890},[892,43917,43918,43934],{},[895,43919,43920,43926,43928],{},[6927,43921,43922,43924],{},[898,43923,1734],{},[1716,43925,2222],{},[1712,43927,2302],{},[6927,43929,43930,43932],{},[898,43931,1734],{},[1716,43933,2085],{},[902,43935,43936],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,43939,43940],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,43943,43944],{},[3817,43945],{"alt":43946,"className":43947,"src":43948},"imek-posun-vs-pohyb-po-krivce",[210,3821],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,43950,43951],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,43953,43954],{},[614,43955,43956,43957,18885,43987,44008],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,43958,43960],{"className":43959},[886],[888,43961,43962],{"xmlns":890},[892,43963,43964,43984],{},[895,43965,43966,43972,43974,43976,43978],{},[6927,43967,43968,43970],{},[898,43969,1969],{},[1716,43971,2787],{},[1712,43973,3138],{"separator":2565},[898,43975,1969],{},[1712,43977,3138],{"separator":2565},[6927,43979,43980,43982],{},[898,43981,1969],{},[1716,43983,2222],{},[902,43985,43986],{"encoding":904},"D_2, D, D_1",[883,43988,43990],{"className":43989},[886],[888,43991,43992],{"xmlns":890},[892,43993,43994,44006],{},[895,43995,43996,43998,44000,44002,44004],{},[1712,43997,1904],{"stretchy":1903},[898,43999,1734],{},[1712,44001,3138],{"separator":2565},[898,44003,1710],{},[1712,44005,1910],{"stretchy":1903},[902,44007,42566],{"encoding":904},", šipky naznačují posuny.",[42800,44010,44012],{"id":44011},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,44014,44015,44017,44018,44041,44042,44059,44060,44077,44078,1659],{},[38,44016,42808],{}," Poptávce ",[883,44019,44021],{"className":44020},[886],[888,44022,44023],{"xmlns":890},[892,44024,44025,44039],{},[895,44026,44027,44029,44031,44033,44035,44037],{},[898,44028,1710],{},[1712,44030,1714],{},[898,44032,1969],{},[1712,44034,1904],{"stretchy":1903},[898,44036,1734],{},[1712,44038,1910],{"stretchy":1903},[902,44040,2438],{"encoding":904}," odpovídá ceně ",[883,44043,44045],{"className":44044},[886],[888,44046,44047],{"xmlns":890},[892,44048,44049,44057],{},[895,44050,44051],{},[6927,44052,44053,44055],{},[898,44054,1710],{},[1716,44056,2085],{},[902,44058,43823],{"encoding":904}," množství ",[883,44061,44063],{"className":44062},[886],[888,44064,44065],{"xmlns":890},[892,44066,44067,44075],{},[895,44068,44069],{},[6927,44070,44071,44073],{},[898,44072,1734],{},[1716,44074,2085],{},[902,44076,43183],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,44079,44081],{"className":44080},[886],[888,44082,44083],{"xmlns":890},[892,44084,44085,44089],{},[895,44086,44087],{},[898,44088,1772],{},[902,44090,1772],{"encoding":904},[724,44092,44093,44095,44096,44113,44114,44136],{},[38,44094,42840],{}," Kupující nakupuje množství ",[883,44097,44099],{"className":44098},[886],[888,44100,44101],{"xmlns":890},[892,44102,44103,44111],{},[895,44104,44105],{},[6927,44106,44107,44109],{},[898,44108,1734],{},[1716,44110,2222],{},[902,44112,33877],{"encoding":904},", které odpovídá ceně ",[883,44115,44117],{"className":44116},[886],[888,44118,44119],{"xmlns":890},[892,44120,44121,44133],{},[895,44122,44123,44129,44131],{},[6927,44124,44125,44127],{},[898,44126,1710],{},[1716,44128,2085],{},[1712,44130,3145],{},[898,44132,1772],{},[902,44134,44135],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,44138,44140],{"className":44139},[886],[888,44141,44142],{"xmlns":890,"display":32941},[892,44143,44144,44178],{},[895,44145,44146,44148,44150,44156,44158,44160,44162,44164,44166,44168,44170,44172,44174,44176],{},[898,44147,1710],{},[1712,44149,1714],{},[6927,44151,44152,44154],{},[898,44153,1969],{},[1716,44155,2222],{},[1712,44157,1904],{"stretchy":1903},[898,44159,1734],{},[1712,44161,1910],{"stretchy":1903},[1712,44163,1714],{},[898,44165,1969],{},[1712,44167,1904],{"stretchy":1903},[898,44169,1734],{},[1712,44171,1910],{"stretchy":1903},[1712,44173,2219],{},[898,44175,1772],{},[1712,44177,3138],{"separator":2565},[902,44179,44180],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,44182,44183,44184,1659],{},"tj. dojde k ",[38,44185,44186],{},"posunu poptávky doleva",[724,44188,44189],{},[614,44190,44191,44192,44213,44214,1343,44231,1343,44244,44265,44266,1655,44283,1659],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,44193,44195],{"className":44194},[886],[888,44196,44197],{"xmlns":890},[892,44198,44199,44211],{},[895,44200,44201,44203,44205,44207,44209],{},[1712,44202,1904],{"stretchy":1903},[898,44204,1734],{},[1712,44206,3138],{"separator":2565},[898,44208,1710],{},[1712,44210,1910],{"stretchy":1903},[902,44212,42566],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,44215,44217],{"className":44216},[886],[888,44218,44219],{"xmlns":890},[892,44220,44221,44229],{},[895,44222,44223],{},[6927,44224,44225,44227],{},[898,44226,1710],{},[1716,44228,2085],{},[902,44230,43823],{"encoding":904},[883,44232,44234],{"className":44233},[886],[888,44235,44236],{"xmlns":890},[892,44237,44238,44242],{},[895,44239,44240],{},[898,44241,1772],{},[902,44243,1772],{"encoding":904},[883,44245,44247],{"className":44246},[886],[888,44248,44249],{"xmlns":890},[892,44250,44251,44263],{},[895,44252,44253,44259,44261],{},[6927,44254,44255,44257],{},[898,44256,1710],{},[1716,44258,2085],{},[1712,44260,3145],{},[898,44262,1772],{},[902,44264,44135],{"encoding":904},"; na vodorovné ",[883,44267,44269],{"className":44268},[886],[888,44270,44271],{"xmlns":890},[892,44272,44273,44281],{},[895,44274,44275],{},[6927,44276,44277,44279],{},[898,44278,1734],{},[1716,44280,2222],{},[902,44282,33877],{"encoding":904},[883,44284,44286],{"className":44285},[886],[888,44287,44288],{"xmlns":890},[892,44289,44290,44298],{},[895,44291,44292],{},[6927,44293,44294,44296],{},[898,44295,1734],{},[1716,44297,2085],{},[902,44299,43183],{"encoding":904},[198,44301,44303],{"id":44302},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,44305,44306],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,44308,44310],{"className":44309},[886],[888,44311,44312],{"xmlns":890,"display":32941},[892,44313,44314,44499],{},[25629,44315,44316],{"width":32946},[25634,44317,44318,44320,44492,44494],{},[25637,44319],{"width":32951},[25637,44321,44322],{},[25629,44323,44324,44408],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,44325,44326,44336],{},[25637,44327,44328],{},[2563,44329,44330],{"scriptlevel":2085,"displaystyle":2565},[6927,44331,44332,44334],{},[898,44333,1734],{},[1716,44335,2222],{},[25637,44337,44338],{},[2563,44339,44340],{"scriptlevel":2085,"displaystyle":2565},[895,44341,44342,44344,44346,44352,44354,44360,44362,44368,44370,44372,44378,44380,44386,44392,44394,44400,44406],{},[895,44343],{},[1712,44345,1714],{},[6927,44347,44348,44350],{},[898,44349,1969],{},[1716,44351,2222],{},[1712,44353,1904],{"stretchy":1903},[6927,44355,44356,44358],{},[898,44357,1710],{},[1716,44359,2222],{},[1712,44361,3138],{"separator":2565},[6927,44363,44364,44366],{},[898,44365,1710],{},[1716,44367,2787],{},[1712,44369,1910],{"stretchy":1903},[1712,44371,1714],{},[6927,44373,44374,44376],{},[898,44375,207],{},[1716,44377,2222],{},[1712,44379,3145],{},[6927,44381,44382,44384],{},[898,44383,7544],{},[1716,44385,2222],{},[6927,44387,44388,44390],{},[898,44389,1710],{},[1716,44391,2222],{},[1712,44393,3145],{},[6927,44395,44396,44398],{},[898,44397,7585],{},[1716,44399,2222],{},[6927,44401,44402,44404],{},[898,44403,1710],{},[1716,44405,2787],{},[1712,44407,3138],{"separator":2565},[25634,44409,44410,44420],{},[25637,44411,44412],{},[2563,44413,44414],{"scriptlevel":2085,"displaystyle":2565},[6927,44415,44416,44418],{},[898,44417,1734],{},[1716,44419,2787],{},[25637,44421,44422],{},[2563,44423,44424],{"scriptlevel":2085,"displaystyle":2565},[895,44425,44426,44428,44430,44436,44438,44444,44446,44452,44454,44456,44462,44464,44470,44476,44478,44484,44490],{},[895,44427],{},[1712,44429,1714],{},[6927,44431,44432,44434],{},[898,44433,1969],{},[1716,44435,2787],{},[1712,44437,1904],{"stretchy":1903},[6927,44439,44440,44442],{},[898,44441,1710],{},[1716,44443,2222],{},[1712,44445,3138],{"separator":2565},[6927,44447,44448,44450],{},[898,44449,1710],{},[1716,44451,2787],{},[1712,44453,1910],{"stretchy":1903},[1712,44455,1714],{},[6927,44457,44458,44460],{},[898,44459,207],{},[1716,44461,2787],{},[1712,44463,3145],{},[6927,44465,44466,44468],{},[898,44467,7544],{},[1716,44469,2787],{},[6927,44471,44472,44474],{},[898,44473,1710],{},[1716,44475,2222],{},[1712,44477,3145],{},[6927,44479,44480,44482],{},[898,44481,7585],{},[1716,44483,2787],{},[6927,44485,44486,44488],{},[898,44487,1710],{},[1716,44489,2787],{},[898,44491,1659],{"mathvariant":2003},[25637,44493],{"width":32951},[25637,44495,44496],{},[1762,44497,44498],{},"(2.6)",[902,44500,44501],{"encoding":904},"\\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}",[42223,44503,44505],{"id":44504},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,44507,44508,44555,44602],{},[123,44509,44510,1343,44532,44554],{},[883,44511,44513],{"className":44512},[886],[888,44514,44515],{"xmlns":890},[892,44516,44517,44529],{},[895,44518,44519,44525,44527],{},[6927,44520,44521,44523],{},[898,44522,207],{},[1716,44524,2222],{},[1712,44526,2302],{},[1716,44528,2085],{},[902,44530,44531],{"encoding":904},"a_1 > 0",[883,44533,44535],{"className":44534},[886],[888,44536,44537],{"xmlns":890},[892,44538,44539,44551],{},[895,44540,44541,44547,44549],{},[6927,44542,44543,44545],{},[898,44544,207],{},[1716,44546,2787],{},[1712,44548,2302],{},[1716,44550,2085],{},[902,44552,44553],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,44556,44557,1343,44579,44601],{},[883,44558,44560],{"className":44559},[886],[888,44561,44562],{"xmlns":890},[892,44563,44564,44576],{},[895,44565,44566,44572,44574],{},[6927,44567,44568,44570],{},[898,44569,7544],{},[1716,44571,2222],{},[1712,44573,2252],{},[1716,44575,2085],{},[902,44577,44578],{"encoding":904},"b_1 \u003C 0",[883,44580,44582],{"className":44581},[886],[888,44583,44584],{"xmlns":890},[892,44585,44586,44598],{},[895,44587,44588,44594,44596],{},[6927,44589,44590,44592],{},[898,44591,7585],{},[1716,44593,2787],{},[1712,44595,2252],{},[1716,44597,2085],{},[902,44599,44600],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,44603,44604,44605,1343,44622,44640,44641],{},"zkřížené koeficienty ",[883,44606,44608],{"className":44607},[886],[888,44609,44610],{"xmlns":890},[892,44611,44612,44620],{},[895,44613,44614],{},[6927,44615,44616,44618],{},[898,44617,7585],{},[1716,44619,2222],{},[902,44621,34674],{"encoding":904},[883,44623,44625],{"className":44624},[886],[888,44626,44627],{"xmlns":890},[892,44628,44629,44637],{},[895,44630,44631],{},[6927,44632,44633,44635],{},[898,44634,7544],{},[1716,44636,2787],{},[902,44638,44639],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,44642,44643,44693],{},[123,44644,44645,44648,44649,1343,44671,3138],{},[38,44646,44647],{},"substituty"," (máslo vs. margarín): ",[883,44650,44652],{"className":44651},[886],[888,44653,44654],{"xmlns":890},[892,44655,44656,44668],{},[895,44657,44658,44664,44666],{},[6927,44659,44660,44662],{},[898,44661,7585],{},[1716,44663,2222],{},[1712,44665,2302],{},[1716,44667,2085],{},[902,44669,44670],{"encoding":904},"c_1 > 0",[883,44672,44674],{"className":44673},[886],[888,44675,44676],{"xmlns":890},[892,44677,44678,44690],{},[895,44679,44680,44686,44688],{},[6927,44681,44682,44684],{},[898,44683,7544],{},[1716,44685,2787],{},[1712,44687,2302],{},[1716,44689,2085],{},[902,44691,44692],{"encoding":904},"b_2 > 0",[123,44694,44695,44698,44699,1343,44721,1659],{},[38,44696,44697],{},"komplementy"," (auto vs. benzín): ",[883,44700,44702],{"className":44701},[886],[888,44703,44704],{"xmlns":890},[892,44705,44706,44718],{},[895,44707,44708,44714,44716],{},[6927,44709,44710,44712],{},[898,44711,7585],{},[1716,44713,2222],{},[1712,44715,2252],{},[1716,44717,2085],{},[902,44719,44720],{"encoding":904},"c_1 \u003C 0",[883,44722,44724],{"className":44723},[886],[888,44725,44726],{"xmlns":890},[892,44727,44728,44740],{},[895,44729,44730,44736,44738],{},[6927,44731,44732,44734],{},[898,44733,7544],{},[1716,44735,2787],{},[1712,44737,2252],{},[1716,44739,2085],{},[902,44741,44742],{"encoding":904},"b_2 \u003C 0",[724,44744,44745],{},"Schematicky:",[724,44747,44748,44751],{},[38,44749,44750],{},"Substituty",[883,44752,44754],{"className":44753},[886],[888,44755,44756],{"xmlns":890},[892,44757,44758,44897],{},[895,44759,44760,44766,44768,44783,44785,44805,44807,44827,44829,44831,44837,44839,44853,44855,44875,44877],{},[6927,44761,44762,44764],{},[898,44763,1734],{},[1716,44765,2222],{},[1712,44767,1714],{},[898,44769,44770],{},[44771,44772,44773,44781],"munder",{},[1712,44774,44775],{},[6927,44776,44777,44779],{},[898,44778,207],{},[1716,44780,2222],{},[1712,44782,3145],{"lspace":2242,"rspace":2242},[1712,44784,3145],{},[898,44786,44787],{},[44771,44788,44789,44803],{},[1712,44790,44791,44797],{},[6927,44792,44793,44795],{},[898,44794,7544],{},[1716,44796,2222],{},[6927,44798,44799,44801],{},[898,44800,1710],{},[1716,44802,2222],{},[1712,44804,2219],{"lspace":2242,"rspace":2242},[1712,44806,3145],{},[898,44808,44809],{},[44771,44810,44811,44825],{},[1712,44812,44813,44819],{},[6927,44814,44815,44817],{},[898,44816,7585],{},[1716,44818,2222],{},[6927,44820,44821,44823],{},[898,44822,1710],{},[1716,44824,2787],{},[1712,44826,3145],{"lspace":2242,"rspace":2242},[1712,44828,3138],{"separator":2565},[3690,44830],{"width":3692},[6927,44832,44833,44835],{},[898,44834,1734],{},[1716,44836,2787],{},[1712,44838,1714],{},[898,44840,44841],{},[44771,44842,44843,44851],{},[1712,44844,44845],{},[6927,44846,44847,44849],{},[898,44848,207],{},[1716,44850,2787],{},[1712,44852,3145],{"lspace":2242,"rspace":2242},[1712,44854,3145],{},[898,44856,44857],{},[44771,44858,44859,44873],{},[1712,44860,44861,44867],{},[6927,44862,44863,44865],{},[898,44864,7544],{},[1716,44866,2787],{},[6927,44868,44869,44871],{},[898,44870,1710],{},[1716,44872,2222],{},[1712,44874,3145],{"lspace":2242,"rspace":2242},[1712,44876,3145],{},[898,44878,44879],{},[44771,44880,44881,44895],{},[1712,44882,44883,44889],{},[6927,44884,44885,44887],{},[898,44886,7585],{},[1716,44888,2787],{},[6927,44890,44891,44893],{},[898,44892,1710],{},[1716,44894,2787],{},[1712,44896,2219],{"lspace":2242,"rspace":2242},[902,44898,44899],{"encoding":904},"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}",[724,44901,44902,44905],{},[38,44903,44904],{},"Komplementy",[883,44906,44908],{"className":44907},[886],[888,44909,44910],{"xmlns":890},[892,44911,44912,45050],{},[895,44913,44914,44920,44922,44936,44938,44958,44960,44980,44982,44984,44990,44992,45006,45008,45028,45030],{},[6927,44915,44916,44918],{},[898,44917,1734],{},[1716,44919,2222],{},[1712,44921,1714],{},[898,44923,44924],{},[44771,44925,44926,44934],{},[1712,44927,44928],{},[6927,44929,44930,44932],{},[898,44931,207],{},[1716,44933,2222],{},[1712,44935,3145],{"lspace":2242,"rspace":2242},[1712,44937,3145],{},[898,44939,44940],{},[44771,44941,44942,44956],{},[1712,44943,44944,44950],{},[6927,44945,44946,44948],{},[898,44947,7544],{},[1716,44949,2222],{},[6927,44951,44952,44954],{},[898,44953,1710],{},[1716,44955,2222],{},[1712,44957,2219],{"lspace":2242,"rspace":2242},[1712,44959,3145],{},[898,44961,44962],{},[44771,44963,44964,44978],{},[1712,44965,44966,44972],{},[6927,44967,44968,44970],{},[898,44969,7585],{},[1716,44971,2222],{},[6927,44973,44974,44976],{},[898,44975,1710],{},[1716,44977,2787],{},[1712,44979,2219],{"lspace":2242,"rspace":2242},[1712,44981,3138],{"separator":2565},[3690,44983],{"width":3692},[6927,44985,44986,44988],{},[898,44987,1734],{},[1716,44989,2787],{},[1712,44991,1714],{},[898,44993,44994],{},[44771,44995,44996,45004],{},[1712,44997,44998],{},[6927,44999,45000,45002],{},[898,45001,207],{},[1716,45003,2787],{},[1712,45005,3145],{"lspace":2242,"rspace":2242},[1712,45007,3145],{},[898,45009,45010],{},[44771,45011,45012,45026],{},[1712,45013,45014,45020],{},[6927,45015,45016,45018],{},[898,45017,7544],{},[1716,45019,2787],{},[6927,45021,45022,45024],{},[898,45023,1710],{},[1716,45025,2222],{},[1712,45027,2219],{"lspace":2242,"rspace":2242},[1712,45029,3145],{},[898,45031,45032],{},[44771,45033,45034,45048],{},[1712,45035,45036,45042],{},[6927,45037,45038,45040],{},[898,45039,7585],{},[1716,45041,2787],{},[6927,45043,45044,45046],{},[898,45045,1710],{},[1716,45047,2787],{},[1712,45049,2219],{"lspace":2242,"rspace":2242},[902,45051,45052],{"encoding":904},"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}",[41845,45054],{},[115,45056,17999],{"id":41654},[1636,45058,45059],{},[724,45060,45061,45063,45064,41869,45077,41883,45090,45093,45094,3481,45118,45136],{},[883,45062,1941],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,45065,45067],{"className":45066},[886],[888,45068,45069],{"xmlns":890},[892,45070,45071,45075],{},[895,45072,45073],{},[898,45074,1734],{},[902,45076,1734],{"encoding":904},[883,45078,45080],{"className":45079},[886],[888,45081,45082],{"xmlns":890},[892,45083,45084,45088],{},[895,45085,45086],{},[898,45087,1710],{},[902,45089,1710],{"encoding":904},[38,45091,45092],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,45095,45097],{"className":45096},[886],[888,45098,45099],{"xmlns":890},[892,45100,45101,45115],{},[895,45102,45103,45105,45107,45109,45111,45113],{},[898,45104,1710],{},[1712,45106,1714],{},[898,45108,7585],{},[898,45110,1734],{},[1712,45112,3145],{},[898,45114,2468],{},[902,45116,45117],{"encoding":904},"P = cQ + d",[883,45119,45121],{"className":45120},[886],[888,45122,45123],{"xmlns":890},[892,45124,45125,45133],{},[895,45126,45127,45129,45131],{},[898,45128,7585],{},[1712,45130,2302],{},[1716,45132,2085],{},[902,45134,45135],{"encoding":904},"c > 0"," je standardní aproximací.",[198,45138,41939],{"id":45139},"obecný-vícefaktorový-model-1",[724,45141,45142,14897,45145,45148,45149,45162,45163,41771,45176,41785,45189,45202,45203,45217,45218,41814,45231,45244],{},[38,45143,45144],{},"Nabízené množství",[614,45146,45147],{},"quantity supplied",") závisí na ceně ",[883,45150,45152],{"className":45151},[886],[888,45153,45154],{"xmlns":890},[892,45155,45156,45160],{},[895,45157,45158],{},[898,45159,1710],{},[902,45161,1710],{"encoding":904},", cenách výrobních faktorů (práce ",[883,45164,45166],{"className":45165},[886],[888,45167,45168],{"xmlns":890},[892,45169,45170,45174],{},[895,45171,45172],{},[898,45173,14667],{},[902,45175,14667],{"encoding":904},[883,45177,45179],{"className":45178},[886],[888,45180,45181],{"xmlns":890},[892,45182,45183,45187],{},[895,45184,45185],{},[898,45186,14672],{},[902,45188,14672],{"encoding":904},[883,45190,45192],{"className":45191},[886],[888,45193,45194],{"xmlns":890},[892,45195,45196,45200],{},[895,45197,45198],{},[898,45199,2041],{},[902,45201,2041],{"encoding":904},"), očekávání ",[883,45204,45206],{"className":45205},[886],[888,45207,45208],{"xmlns":890},[892,45209,45210,45215],{},[895,45211,45212],{},[898,45213,45214],{},"V",[902,45216,45214],{"encoding":904},", počtu výrobců ",[883,45219,45221],{"className":45220},[886],[888,45222,45223],{"xmlns":890},[892,45224,45225,45229],{},[895,45226,45227],{},[898,45228,41811],{},[902,45230,41811],{"encoding":904},[883,45232,45234],{"className":45233},[886],[888,45235,45236],{"xmlns":890},[892,45237,45238,45242],{},[895,45239,45240],{},[898,45241,41826],{},[902,45243,41826],{"encoding":904}," a dalších:",[883,45246,45248],{"className":45247},[886],[888,45249,45250],{"xmlns":890,"display":32941},[892,45251,45252,45311],{},[25629,45253,45254],{"width":32946},[25634,45255,45256,45258,45304,45306],{},[25637,45257],{"width":32951},[25637,45259,45260],{},[895,45261,45262,45264,45266,45268,45270,45272,45274,45276,45278,45280,45282,45284,45286,45288,45290,45292,45294,45296,45298,45300,45302],{},[898,45263,1734],{},[1712,45265,1714],{},[898,45267,6493],{},[1712,45269,1904],{"stretchy":1903},[898,45271,1710],{},[1712,45273,3138],{"separator":2565},[898,45275,14667],{},[1712,45277,3138],{"separator":2565},[898,45279,14672],{},[1712,45281,3138],{"separator":2565},[898,45283,2041],{},[1712,45285,3138],{"separator":2565},[898,45287,45214],{},[1712,45289,3138],{"separator":2565},[898,45291,41811],{},[1712,45293,3138],{"separator":2565},[898,45295,41826],{},[1712,45297,3138],{"separator":2565},[1712,45299,14518],{},[1712,45301,1910],{"stretchy":1903},[898,45303,1659],{"mathvariant":2003},[25637,45305],{"width":32951},[25637,45307,45308],{},[1762,45309,45310],{},"(2.7)",[902,45312,45313],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,45315,43291,45316,14897,45319,45322],{},[38,45317,45318],{},"funkce nabídky",[614,45320,45321],{},"supply function",") v širším slova smyslu.",[198,45324,45326],{"id":45325},"jednofaktorový-model","Jednofaktorový model",[724,45328,45329],{},"V nejpřirozenějším jednofaktorovém modelu",[883,45331,45333],{"className":45332},[886],[888,45334,45335],{"xmlns":890,"display":32941},[892,45336,45337,45388],{},[25629,45338,45339],{"width":32946},[25634,45340,45341,45343,45381,45383],{},[25637,45342],{"width":32951},[25637,45344,45345],{},[895,45346,45347,45349,45351,45353,45355,45357,45359,45361,45363,45365,45367,45369,45371,45373,45375,45377,45379],{},[898,45348,1734],{},[1712,45350,1714],{},[898,45352,6493],{},[1712,45354,1904],{"stretchy":1903},[898,45356,1710],{},[1712,45358,1910],{"stretchy":1903},[1712,45360,3138],{"separator":2565},[3690,45362],{"width":3692},[1762,45364,42292],{},[3690,45366],{"width":3692},[898,45368,1710],{},[1712,45370,1714],{},[898,45372,6493],{},[1712,45374,1904],{"stretchy":1903},[898,45376,1734],{},[1712,45378,1910],{"stretchy":1903},[898,45380,1659],{"mathvariant":2003},[25637,45382],{"width":32951},[25637,45384,45385],{},[1762,45386,45387],{},"(2.8)",[902,45389,45390],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,45392,45393,45394,14897,45397,1691],{},"Graf je ",[38,45395,45396],{},"křivka nabídky",[614,45398,45399],{},"supply curve",[42223,45401,45403],{"id":45402},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1636,45405,45406],{},[724,45407,45408],{},[38,45409,42338,45410,45423,45424,42393],{},[883,45411,45413],{"className":45412},[886],[888,45414,45415],{"xmlns":890},[892,45416,45417,45421],{},[895,45418,45419],{},[898,45420,1710],{},[902,45422,1710],{"encoding":904},", pak nabízené množství ",[883,45425,45427],{"className":45426},[886],[888,45428,45429],{"xmlns":890},[892,45430,45431,45435],{},[895,45432,45433],{},[898,45434,1734],{},[902,45436,1734],{"encoding":904},[724,45438,45439,45440,45465,45466,45496,45497,45514],{},"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 ",[883,45441,45443],{"className":45442},[886],[888,45444,45445],{"xmlns":890},[892,45446,45447,45463],{},[895,45448,45449,45451,45453,45455,45461],{},[1712,45450,7910],{"stretchy":1903},[1716,45452,2085],{},[1712,45454,3138],{"separator":2565},[6927,45456,45457,45459],{},[898,45458,1710],{},[1716,45460,2085],{},[1712,45462,7925],{"stretchy":1903},[902,45464,42478],{"encoding":904}," na svislé ose (případně z ",[883,45467,45469],{"className":45468},[886],[888,45470,45471],{"xmlns":890},[892,45472,45473,45493],{},[895,45474,45475,45477,45483,45485,45491],{},[1712,45476,7910],{"stretchy":1903},[6927,45478,45479,45481],{},[898,45480,1734],{},[1716,45482,2222],{},[1712,45484,3138],{"separator":2565},[6927,45486,45487,45489],{},[898,45488,1710],{},[1716,45490,2222],{},[1712,45492,7925],{"stretchy":1903},[902,45494,45495],{"encoding":904},"[Q_1, P_1]","), kde ",[883,45498,45500],{"className":45499},[886],[888,45501,45502],{"xmlns":890},[892,45503,45504,45512],{},[895,45505,45506],{},[6927,45507,45508,45510],{},[898,45509,1710],{},[1716,45511,2085],{},[902,45513,43823],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,45516,45517],{},[614,45518,45519,45520,9120,45533,1659],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,45521,45523],{"className":45522},[886],[888,45524,45525],{"xmlns":890},[892,45526,45527,45531],{},[895,45528,45529],{},[898,45530,6493],{},[902,45532,6493],{"encoding":904},[883,45534,45536],{"className":45535},[886],[888,45537,45538],{"xmlns":890},[892,45539,45540,45552],{},[895,45541,45542,45544,45546,45548,45550],{},[1712,45543,1904],{"stretchy":1903},[898,45545,1734],{},[1712,45547,3138],{"separator":2565},[898,45549,1710],{},[1712,45551,1910],{"stretchy":1903},[902,45553,42566],{"encoding":904},[42223,45555,45557],{"id":45556},"lineární-model-nabídky","Lineární model nabídky",[883,45559,45561],{"className":45560},[886],[888,45562,45563],{"xmlns":890,"display":32941},[892,45564,45565,45604],{},[25629,45566,45567],{"width":32946},[25634,45568,45569,45571,45597,45599],{},[25637,45570],{"width":32951},[25637,45572,45573],{},[895,45574,45575,45577,45579,45581,45583,45585,45587,45589,45591,45593,45595],{},[898,45576,1710],{},[1712,45578,1714],{},[898,45580,7585],{},[898,45582,1734],{},[1712,45584,3145],{},[898,45586,2468],{},[1712,45588,3138],{"separator":2565},[3690,45590],{"width":3692},[898,45592,7585],{},[1712,45594,2302],{},[1716,45596,17334],{},[25637,45598],{"width":32951},[25637,45600,45601],{},[1762,45602,45603],{},"(2.9)",[902,45605,45606],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,45608,45609,45610,45646,45647,45660],{},"Alternativně ",[883,45611,45613],{"className":45612},[886],[888,45614,45615],{"xmlns":890},[892,45616,45617,45643],{},[895,45618,45619,45621,45623,45631,45633,45635],{},[898,45620,1734],{},[1712,45622,1714],{},[2563,45624,45625],{"scriptlevel":2085,"displaystyle":1903},[2567,45626,45627,45629],{},[1716,45628,2222],{},[898,45630,7585],{},[898,45632,1710],{},[1712,45634,2219],{},[2563,45636,45637],{"scriptlevel":2085,"displaystyle":1903},[2567,45638,45639,45641],{},[898,45640,2468],{},[898,45642,7585],{},[902,45644,45645],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,45648,45650],{"className":45649},[886],[888,45651,45652],{"xmlns":890},[892,45653,45654,45658],{},[895,45655,45656],{},[898,45657,1710],{},[902,45659,1710],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[42800,45662,45664],{"id":45663},"příklad-25","Příklad 2.5",[724,45666,45667,45669,45670,1659],{},[38,45668,42808],{}," Lineární nabídka ",[883,45671,45673],{"className":45672},[886],[888,45674,45675],{"xmlns":890},[892,45676,45677,45691],{},[895,45678,45679,45681,45683,45685,45687,45689],{},[898,45680,1710],{},[1712,45682,1714],{},[1716,45684,2814],{},[898,45686,1734],{},[1712,45688,3145],{},[1716,45690,2809],{},[902,45692,45693],{"encoding":904},"P = 0{,}5Q + 25",[724,45695,45696,45698,45699,1659],{},[38,45697,42840],{}," Alternativní tvar ",[883,45700,45702],{"className":45701},[886],[888,45703,45704],{"xmlns":890},[892,45705,45706,45720],{},[895,45707,45708,45710,45712,45714,45716,45718],{},[898,45709,1734],{},[1712,45711,1714],{},[1716,45713,2787],{},[898,45715,1710],{},[1712,45717,2219],{},[1716,45719,2782],{},[902,45721,45722],{"encoding":904},"Q = 2P - 50",[16,45724,45725,45750],{},[19,45726,45727],{},[22,45728,45729,45744,45746,45748],{},[25,45730,45731],{},[883,45732,45734],{"className":45733},[886],[888,45735,45736],{"xmlns":890},[892,45737,45738,45742],{},[895,45739,45740],{},[898,45741,1710],{},[902,45743,1710],{"encoding":904},[25,45745,42894],{},[25,45747,19912],{},[25,45749,3018],{},[30,45751,45752],{},[22,45753,45754,45769,45771,45773],{},[35,45755,45756],{},[883,45757,45759],{"className":45758},[886],[888,45760,45761],{"xmlns":890},[892,45762,45763,45767],{},[895,45764,45765],{},[898,45766,1734],{},[902,45768,1734],{"encoding":904},[35,45770,1718],{},[35,45772,6857],{},[35,45774,42894],{},[198,45776,45778,45779,1910],{"id":45777},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,45780,45781],{},"shift of supply",[724,45783,45784,45785,45788,45789,45806,45807,45832,45833,1659],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,45786,45787],{},"doprava",": při stejné ceně ",[883,45790,45792],{"className":45791},[886],[888,45793,45794],{"xmlns":890},[892,45795,45796,45804],{},[895,45797,45798],{},[6927,45799,45800,45802],{},[898,45801,1710],{},[1716,45803,2085],{},[902,45805,43823],{"encoding":904}," vyrobí výrobce větší ",[883,45808,45810],{"className":45809},[886],[888,45811,45812],{"xmlns":890},[892,45813,45814,45830],{},[895,45815,45816,45822,45824],{},[6927,45817,45818,45820],{},[898,45819,1734],{},[1716,45821,2222],{},[1712,45823,2302],{},[6927,45825,45826,45828],{},[898,45827,1734],{},[1716,45829,2085],{},[902,45831,43936],{"encoding":904},"); zdražení vstupů posune křivku ",[38,45834,45835],{},"doleva",[724,45837,45838],{},[614,45839,45840,45841,45854,45855,45873,45874,45892,45893,1659],{},"Obrázek 2.11: Původní ",[883,45842,45844],{"className":45843},[886],[888,45845,45846],{"xmlns":890},[892,45847,45848,45852],{},[895,45849,45850],{},[898,45851,6493],{},[902,45853,6493],{"encoding":904},", posunuté ",[883,45856,45858],{"className":45857},[886],[888,45859,45860],{"xmlns":890},[892,45861,45862,45870],{},[895,45863,45864],{},[6927,45865,45866,45868],{},[898,45867,6493],{},[1716,45869,2222],{},[902,45871,45872],{"encoding":904},"S_1"," (doprava) a ",[883,45875,45877],{"className":45876},[886],[888,45878,45879],{"xmlns":890},[892,45880,45881,45889],{},[895,45882,45883],{},[6927,45884,45885,45887],{},[898,45886,6493],{},[1716,45888,2787],{},[902,45890,45891],{"encoding":904},"S_2"," (doleva) v ",[883,45894,45896],{"className":45895},[886],[888,45897,45898],{"xmlns":890},[892,45899,45900,45912],{},[895,45901,45902,45904,45906,45908,45910],{},[1712,45903,1904],{"stretchy":1903},[898,45905,1734],{},[1712,45907,3138],{"separator":2565},[898,45909,1710],{},[1712,45911,1910],{"stretchy":1903},[902,45913,42566],{"encoding":904},[42800,45915,45917],{"id":45916},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,45919,45920,45922,45923,45947,45948,1659],{},[38,45921,42808],{}," Nabídka ",[883,45924,45926],{"className":45925},[886],[888,45927,45928],{"xmlns":890},[892,45929,45930,45944],{},[895,45931,45932,45934,45936,45938,45940,45942],{},[898,45933,1710],{},[1712,45935,1714],{},[898,45937,6493],{},[1712,45939,1904],{"stretchy":1903},[898,45941,1734],{},[1712,45943,1910],{"stretchy":1903},[902,45945,45946],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,45949,45951],{"className":45950},[886],[888,45952,45953],{"xmlns":890},[892,45954,45955,45959],{},[895,45956,45957],{},[898,45958,1772],{},[902,45960,1772],{"encoding":904},[724,45962,45963,45965,45966,45979,45980,45998,45999,46027],{},[38,45964,42840],{}," Spotřebitel zaplatí ",[883,45967,45969],{"className":45968},[886],[888,45970,45971],{"xmlns":890},[892,45972,45973,45977],{},[895,45974,45975],{},[898,45976,1710],{},[902,45978,1710],{"encoding":904},", výrobce obdrží ",[883,45981,45983],{"className":45982},[886],[888,45984,45985],{"xmlns":890},[892,45986,45987,45995],{},[895,45988,45989,45991,45993],{},[898,45990,1710],{},[1712,45992,2219],{},[898,45994,1772],{},[902,45996,45997],{"encoding":904},"P - T",". Z podmínky ",[883,46000,46002],{"className":46001},[886],[888,46003,46004],{"xmlns":890},[892,46005,46006,46024],{},[895,46007,46008,46010,46012,46014,46016,46018,46020,46022],{},[898,46009,1710],{},[1712,46011,2219],{},[898,46013,1772],{},[1712,46015,1714],{},[898,46017,6493],{},[1712,46019,1904],{"stretchy":1903},[898,46021,1734],{},[1712,46023,1910],{"stretchy":1903},[902,46025,46026],{"encoding":904},"P - T = S(Q)"," plyne",[883,46029,46031],{"className":46030},[886],[888,46032,46033],{"xmlns":890,"display":32941},[892,46034,46035,46069],{},[895,46036,46037,46039,46041,46047,46049,46051,46053,46055,46057,46059,46061,46063,46065,46067],{},[898,46038,1710],{},[1712,46040,1714],{},[6927,46042,46043,46045],{},[898,46044,6493],{},[1716,46046,2222],{},[1712,46048,1904],{"stretchy":1903},[898,46050,1734],{},[1712,46052,1910],{"stretchy":1903},[1712,46054,1714],{},[898,46056,6493],{},[1712,46058,1904],{"stretchy":1903},[898,46060,1734],{},[1712,46062,1910],{"stretchy":1903},[1712,46064,3145],{},[898,46066,1772],{},[898,46068,1659],{"mathvariant":2003},[902,46070,46071],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,46073,46074,46075,46088,46089,3245,46102,46105,46106,1655,46126,5920,46144,1659],{},"Křivka ",[883,46076,46078],{"className":46077},[886],[888,46079,46080],{"xmlns":890},[892,46081,46082,46086],{},[895,46083,46084],{},[898,46085,6493],{},[902,46087,6493],{"encoding":904}," se tedy posune o ",[883,46090,46092],{"className":46091},[886],[888,46093,46094],{"xmlns":890},[892,46095,46096,46100],{},[895,46097,46098],{},[898,46099,1772],{},[902,46101,1772],{"encoding":904},[38,46103,46104],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,46107,46109],{"className":46108},[886],[888,46110,46111],{"xmlns":890},[892,46112,46113,46123],{},[895,46114,46115,46117,46119,46121],{},[898,46116,1710],{},[1712,46118,1714],{},[1716,46120,2787],{},[898,46122,1734],{},[902,46124,46125],{"encoding":904},"P = 2Q",[883,46127,46129],{"className":46128},[886],[888,46130,46131],{"xmlns":890},[892,46132,46133,46141],{},[895,46134,46135,46137,46139],{},[898,46136,1772],{},[1712,46138,1714],{},[1716,46140,6209],{},[902,46142,46143],{"encoding":904},"T = 6",[883,46145,46147],{"className":46146},[886],[888,46148,46149],{"xmlns":890},[892,46150,46151,46173],{},[895,46152,46153,46159,46161,46163,46165,46167,46169,46171],{},[6927,46154,46155,46157],{},[898,46156,6493],{},[1716,46158,2222],{},[1712,46160,2854],{},[898,46162,1710],{},[1712,46164,1714],{},[1716,46166,2787],{},[898,46168,1734],{},[1712,46170,3145],{},[1716,46172,6209],{},[902,46174,46175],{"encoding":904},"S_1: P = 2Q + 6",[724,46177,46178],{},[614,46179,46180,46181,46194],{},"Obrázek 2.12: Posun nabídky o ",[883,46182,46184],{"className":46183},[886],[888,46185,46186],{"xmlns":890},[892,46187,46188,46192],{},[895,46189,46190],{},[898,46191,1772],{},[902,46193,1772],{"encoding":904}," svisle nahoru.",[41845,46196],{},[115,46198,46200],{"id":46199},"tržní-rovnováha","Tržní rovnováha",[1636,46202,46203],{},[724,46204,46205,46207,46208,3245,46211,46243,46244,1343,46267,46290,46291,46294,46295,46308],{},[883,46206,1941],{}," TL;DR\nV ",[38,46209,46210],{},"rovnovážném bodě",[883,46212,46214],{"className":46213},[886],[888,46215,46216],{"xmlns":890},[892,46217,46218,46240],{},[895,46219,46220,46222,46224,46230,46232,46238],{},[898,46221,2041],{},[1712,46223,7910],{"stretchy":1903},[2037,46225,46226,46228],{},[898,46227,1734],{},[898,46229,2041],{},[1712,46231,3138],{"separator":2565},[2037,46233,46234,46236],{},[898,46235,1710],{},[898,46237,2041],{},[1712,46239,7925],{"stretchy":1903},[902,46241,46242],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,46245,46247],{"className":46246},[886],[888,46248,46249],{"xmlns":890},[892,46250,46251,46265],{},[895,46252,46253,46255,46257,46259,46261,46263],{},[898,46254,1710],{},[1712,46256,1714],{},[898,46258,1969],{},[1712,46260,1904],{"stretchy":1903},[898,46262,1734],{},[1712,46264,1910],{"stretchy":1903},[902,46266,2438],{"encoding":904},[883,46268,46270],{"className":46269},[886],[888,46271,46272],{"xmlns":890},[892,46273,46274,46288],{},[895,46275,46276,46278,46280,46282,46284,46286],{},[898,46277,1710],{},[1712,46279,1714],{},[898,46281,6493],{},[1712,46283,1904],{"stretchy":1903},[898,46285,1734],{},[1712,46287,1910],{"stretchy":1903},[902,46289,45946],{"encoding":904},". Čtyři ",[38,46292,46293],{},"pravidla komparativní statiky"," popisují, jak se ",[883,46296,46298],{"className":46297},[886],[888,46299,46300],{"xmlns":890},[892,46301,46302,46306],{},[895,46303,46304],{},[898,46305,2041],{},[902,46307,2041],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,46310,46312],{"id":46311},"definice","Definice",[724,46314,46315,14897,46317,46320,46321,3245,46324,46342,46343,46374,46375,14897,46378,1691],{},[38,46316,46200],{},[614,46318,46319],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,46322,46323],{},"rovnovážné ceně",[883,46325,46327],{"className":46326},[886],[888,46328,46329],{"xmlns":890},[892,46330,46331,46339],{},[895,46332,46333],{},[2037,46334,46335,46337],{},[898,46336,1710],{},[898,46338,2041],{},[902,46340,46341],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,46344,46346],{"className":46345},[886],[888,46347,46348],{"xmlns":890},[892,46349,46350,46372],{},[895,46351,46352,46354,46356,46362,46364,46370],{},[898,46353,2041],{},[1712,46355,7910],{"stretchy":1903},[2037,46357,46358,46360],{},[898,46359,1734],{},[898,46361,2041],{},[1712,46363,3138],{"separator":2565},[2037,46365,46366,46368],{},[898,46367,1710],{},[898,46369,2041],{},[1712,46371,7925],{"stretchy":1903},[902,46373,46242],{"encoding":904}," se nazývá ",[38,46376,46377],{},"rovnovážný bod",[614,46379,46380],{},"equilibrium point",[724,46382,46383,46384,1343,46407,1659],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,46385,46387],{"className":46386},[886],[888,46388,46389],{"xmlns":890},[892,46390,46391,46405],{},[895,46392,46393,46395,46397,46399,46401,46403],{},[898,46394,1710],{},[1712,46396,1714],{},[898,46398,1969],{},[1712,46400,1904],{"stretchy":1903},[898,46402,1734],{},[1712,46404,1910],{"stretchy":1903},[902,46406,2438],{"encoding":904},[883,46408,46410],{"className":46409},[886],[888,46411,46412],{"xmlns":890},[892,46413,46414,46428],{},[895,46415,46416,46418,46420,46422,46424,46426],{},[898,46417,1710],{},[1712,46419,1714],{},[898,46421,6493],{},[1712,46423,1904],{"stretchy":1903},[898,46425,1734],{},[1712,46427,1910],{"stretchy":1903},[902,46429,45946],{"encoding":904},[724,46431,46432],{},[3817,46433],{"alt":46434,"className":46435,"src":46436},"imek-poptavka-nabidka-rovnovaha",[210,3821],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,46438,46439],{},[614,46440,46441,46442,46455,46456,18885,46469,46490,46491,1659],{},"Obrázek 2.13: Klesající ",[883,46443,46445],{"className":46444},[886],[888,46446,46447],{"xmlns":890},[892,46448,46449,46453],{},[895,46450,46451],{},[898,46452,1969],{},[902,46454,1969],{"encoding":904}," a rostoucí ",[883,46457,46459],{"className":46458},[886],[888,46460,46461],{"xmlns":890},[892,46462,46463,46467],{},[895,46464,46465],{},[898,46466,6493],{},[902,46468,6493],{"encoding":904},[883,46470,46472],{"className":46471},[886],[888,46473,46474],{"xmlns":890},[892,46475,46476,46488],{},[895,46477,46478,46480,46482,46484,46486],{},[1712,46479,1904],{"stretchy":1903},[898,46481,1734],{},[1712,46483,3138],{"separator":2565},[898,46485,1710],{},[1712,46487,1910],{"stretchy":1903},[902,46489,42566],{"encoding":904}," protínající se v ",[883,46492,46494],{"className":46493},[886],[888,46495,46496],{"xmlns":890},[892,46497,46498,46520],{},[895,46499,46500,46502,46504,46510,46512,46518],{},[898,46501,2041],{},[1712,46503,7910],{"stretchy":1903},[2037,46505,46506,46508],{},[898,46507,1734],{},[898,46509,2041],{},[1712,46511,3138],{"separator":2565},[2037,46513,46514,46516],{},[898,46515,1710],{},[898,46517,2041],{},[1712,46519,7925],{"stretchy":1903},[902,46521,46242],{"encoding":904},[198,46523,46525],{"id":46524},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,46527,46528,46530,46531,46565,46566,1659],{},[38,46529,42808],{}," Poptávka ",[883,46532,46534],{"className":46533},[886],[888,46535,46536],{"xmlns":890},[892,46537,46538,46562],{},[895,46539,46540,46542,46544,46546,46552,46554,46556,46558,46560],{},[898,46541,1710],{},[1712,46543,1714],{},[1712,46545,2219],{},[2037,46547,46548,46550],{},[898,46549,1734],{},[1716,46551,2787],{},[1712,46553,2219],{},[1716,46555,1718],{},[898,46557,1734],{},[1712,46559,3145],{},[1716,46561,6624],{},[902,46563,46564],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,46567,46569],{"className":46568},[886],[888,46570,46571],{"xmlns":890},[892,46572,46573,46595],{},[895,46574,46575,46577,46579,46585,46587,46589,46591,46593],{},[898,46576,1710],{},[1712,46578,1714],{},[2037,46580,46581,46583],{},[898,46582,1734],{},[1716,46584,2787],{},[1712,46586,3145],{},[1716,46588,27821],{},[898,46590,1734],{},[1712,46592,3145],{},[1716,46594,37421],{},[902,46596,46597],{"encoding":904},"P = Q^2 + 14Q + 22",[724,46599,46600,46602],{},[38,46601,42840],{}," Z rovnosti",[883,46604,46606],{"className":46605},[886],[888,46607,46608],{"xmlns":890,"display":32941},[892,46609,46610,46648],{},[895,46611,46612,46614,46620,46622,46624,46626,46628,46630,46632,46638,46640,46642,46644,46646],{},[1712,46613,2219],{},[2037,46615,46616,46618],{},[898,46617,1734],{},[1716,46619,2787],{},[1712,46621,2219],{},[1716,46623,1718],{},[898,46625,1734],{},[1712,46627,3145],{},[1716,46629,6624],{},[1712,46631,1714],{},[2037,46633,46634,46636],{},[898,46635,1734],{},[1716,46637,2787],{},[1712,46639,3145],{},[1716,46641,27821],{},[898,46643,1734],{},[1712,46645,3145],{},[1716,46647,37421],{},[902,46649,46650],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,46652,46653,46654,46689,46690,46723,46724,46741,46742,46755,46756,1343,46778,46815,46816,1659],{},"dostaneme ",[883,46655,46657],{"className":46656},[886],[888,46658,46659],{"xmlns":890},[892,46660,46661,46686],{},[895,46662,46663,46665,46671,46673,46676,46678,46680,46682,46684],{},[1716,46664,2787],{},[2037,46666,46667,46669],{},[898,46668,1734],{},[1716,46670,2787],{},[1712,46672,3145],{},[1716,46674,46675],{},"24",[898,46677,1734],{},[1712,46679,2219],{},[1716,46681,3429],{},[1712,46683,1714],{},[1716,46685,2085],{},[902,46687,46688],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,46691,46693],{"className":46692},[886],[888,46694,46695],{"xmlns":890},[892,46696,46697,46720],{},[895,46698,46699,46705,46707,46709,46711,46713,46716,46718],{},[2037,46700,46701,46703],{},[898,46702,1734],{},[1716,46704,2787],{},[1712,46706,3145],{},[1716,46708,8912],{},[898,46710,1734],{},[1712,46712,2219],{},[1716,46714,46715],{},"64",[1712,46717,1714],{},[1716,46719,2085],{},[902,46721,46722],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,46725,46727],{"className":46726},[886],[888,46728,46729],{"xmlns":890},[892,46730,46731,46738],{},[895,46732,46733,46735],{},[1712,46734,2219],{},[1716,46736,46737],{},"16",[902,46739,46740],{"encoding":904},"-16"," (nevyhovuje) a ",[883,46743,46745],{"className":46744},[886],[888,46746,46747],{"xmlns":890},[892,46748,46749,46753],{},[895,46750,46751],{},[1716,46752,2975],{},[902,46754,2975],{"encoding":904},". Tedy ",[883,46757,46759],{"className":46758},[886],[888,46760,46761],{"xmlns":890},[892,46762,46763,46775],{},[895,46764,46765,46771,46773],{},[2037,46766,46767,46769],{},[898,46768,1734],{},[898,46770,2041],{},[1712,46772,1714],{},[1716,46774,2975],{},[902,46776,46777],{"encoding":904},"Q^E = 4",[883,46779,46781],{"className":46780},[886],[888,46782,46783],{"xmlns":890},[892,46784,46785,46812],{},[895,46786,46787,46793,46795,46797,46799,46801,46803,46805,46807,46809],{},[2037,46788,46789,46791],{},[898,46790,1710],{},[898,46792,2041],{},[1712,46794,1714],{},[1712,46796,2219],{},[1716,46798,46737],{},[1712,46800,2219],{},[1716,46802,3018],{},[1712,46804,3145],{},[1716,46806,6624],{},[1712,46808,1714],{},[1716,46810,46811],{},"94",[902,46813,46814],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,46817,46819],{"className":46818},[886],[888,46820,46821],{"xmlns":890},[892,46822,46823,46837],{},[895,46824,46825,46827,46829,46831,46833,46835],{},[898,46826,2041],{},[1712,46828,7910],{"stretchy":1903},[1716,46830,2975],{},[1712,46832,3138],{"separator":2565},[1716,46834,46811],{},[1712,46836,7925],{"stretchy":1903},[902,46838,46839],{"encoding":904},"E[4, 94]",[198,46841,46843],{"id":46842},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,46845,46846,46848],{},[38,46847,42808],{}," Poptávky a nabídky dvou zboží",[883,46850,46852],{"className":46851},[886],[888,46853,46854],{"xmlns":890,"display":32941},[892,46855,46856,47022],{},[25629,46857,46860,46948],{"rowspacing":25631,"columnalign":46858,"columnspacing":46859},"right left right left","0em 1em 0em",[25634,46861,46862,46872,46904,46914],{},[25637,46863,46864],{},[2563,46865,46866],{"scriptlevel":2085,"displaystyle":2565},[6927,46867,46868,46870],{},[898,46869,1734],{},[1716,46871,2222],{},[25637,46873,46874],{},[2563,46875,46876],{"scriptlevel":2085,"displaystyle":2565},[895,46877,46878,46880,46882,46884,46886,46888,46894,46896,46902],{},[895,46879],{},[1712,46881,1714],{},[1716,46883,3018],{},[1712,46885,2219],{},[1716,46887,3068],{},[6927,46889,46890,46892],{},[898,46891,1710],{},[1716,46893,2222],{},[1712,46895,2219],{},[6927,46897,46898,46900],{},[898,46899,1710],{},[1716,46901,2787],{},[1712,46903,3138],{"separator":2565},[25637,46905,46906],{},[2563,46907,46908],{"scriptlevel":2085,"displaystyle":2565},[6927,46909,46910,46912],{},[898,46911,1734],{},[1716,46913,2787],{},[25637,46915,46916],{},[2563,46917,46918],{"scriptlevel":2085,"displaystyle":2565},[895,46919,46920,46922,46924,46926,46928,46930,46936,46938,46940,46946],{},[895,46921],{},[1712,46923,1714],{},[1716,46925,2782],{},[1712,46927,2219],{},[1716,46929,2787],{},[6927,46931,46932,46934],{},[898,46933,1710],{},[1716,46935,2222],{},[1712,46937,2219],{},[1716,46939,2975],{},[6927,46941,46942,46944],{},[898,46943,1710],{},[1716,46945,2787],{},[1712,46947,3138],{"separator":2565},[25634,46949,46950,46960,46986,46996],{},[25637,46951,46952],{},[2563,46953,46954],{"scriptlevel":2085,"displaystyle":2565},[6927,46955,46956,46958],{},[898,46957,1734],{},[1716,46959,2222],{},[25637,46961,46962],{},[2563,46963,46964],{"scriptlevel":2085,"displaystyle":2565},[895,46965,46966,46968,46970,46972,46974,46976,46978,46984],{},[895,46967],{},[1712,46969,1714],{},[1712,46971,2219],{},[1716,46973,6198],{},[1712,46975,3145],{},[1716,46977,2975],{},[6927,46979,46980,46982],{},[898,46981,1710],{},[1716,46983,2222],{},[1712,46985,3138],{"separator":2565},[25637,46987,46988],{},[2563,46989,46990],{"scriptlevel":2085,"displaystyle":2565},[6927,46991,46992,46994],{},[898,46993,1734],{},[1716,46995,2787],{},[25637,46997,46998],{},[2563,46999,47000],{"scriptlevel":2085,"displaystyle":2565},[895,47001,47002,47004,47006,47008,47010,47012,47014,47020],{},[895,47003],{},[1712,47005,1714],{},[1712,47007,2219],{},[1716,47009,29076],{},[1712,47011,3145],{},[1716,47013,6198],{},[6927,47015,47016,47018],{},[898,47017,1710],{},[1716,47019,2787],{},[898,47021,1659],{"mathvariant":2003},[902,47023,47024],{"encoding":904},"\\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}",[724,47026,47027,47029],{},[38,47028,42840],{}," Z rovností poptávek a nabídek dostaneme",[883,47031,47033],{"className":47032},[886],[888,47034,47035],{"xmlns":890,"display":32941},[892,47036,47037,47086],{},[895,47038,47039,47041,47047,47049,47055,47057,47059,47061,47063,47065,47071,47073,47075,47081,47083],{},[1716,47040,1780],{},[6927,47042,47043,47045],{},[898,47044,1710],{},[1716,47046,2222],{},[1712,47048,3145],{},[6927,47050,47051,47053],{},[898,47052,1710],{},[1716,47054,2787],{},[1712,47056,1714],{},[1716,47058,26078],{},[1712,47060,3138],{"separator":2565},[3690,47062],{"width":3692},[1716,47064,2787],{},[6927,47066,47067,47069],{},[898,47068,1710],{},[1716,47070,2222],{},[1712,47072,3145],{},[1716,47074,29076],{},[6927,47076,47077,47079],{},[898,47078,1710],{},[1716,47080,2787],{},[1712,47082,1714],{},[1716,47084,47085],{},"57.",[902,47087,47088],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,47090,47091,47092,1343,47116,47140,47141,1343,47166,47190,47191,47193],{},"Řešením je ",[883,47093,47095],{"className":47094},[886],[888,47096,47097],{"xmlns":890},[892,47098,47099,47113],{},[895,47100,47101,47109,47111],{},[6989,47102,47103,47105,47107],{},[898,47104,1710],{},[1716,47106,2222],{},[898,47108,2041],{},[1712,47110,1714],{},[1716,47112,2975],{},[902,47114,47115],{"encoding":904},"P_1^E = 4",[883,47117,47119],{"className":47118},[886],[888,47120,47121],{"xmlns":890},[892,47122,47123,47137],{},[895,47124,47125,47133,47135],{},[6989,47126,47127,47129,47131],{},[898,47128,1710],{},[1716,47130,2787],{},[898,47132,2041],{},[1712,47134,1714],{},[1716,47136,29076],{},[902,47138,47139],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,47142,47144],{"className":47143},[886],[888,47145,47146],{"xmlns":890},[892,47147,47148,47163],{},[895,47149,47150,47158,47160],{},[6989,47151,47152,47154,47156],{},[898,47153,1734],{},[1716,47155,2222],{},[898,47157,2041],{},[1712,47159,1714],{},[1716,47161,47162],{},"13",[902,47164,47165],{"encoding":904},"Q_1^E = 13",[883,47167,47169],{"className":47168},[886],[888,47170,47171],{"xmlns":890},[892,47172,47173,47187],{},[895,47174,47175,47183,47185],{},[6989,47176,47177,47179,47181],{},[898,47178,1734],{},[1716,47180,2787],{},[898,47182,2041],{},[1712,47184,1714],{},[1716,47186,27821],{},[902,47188,47189],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,47192,44697],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,47195,47197],{"id":47196},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,47199,47200,47201,47218,47219,14897,47222,1691],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,47202,47204],{"className":47203},[886],[888,47205,47206],{"xmlns":890},[892,47207,47208,47216],{},[895,47209,47210],{},[2037,47211,47212,47214],{},[898,47213,1710],{},[898,47215,2041],{},[902,47217,46341],{"encoding":904},"; mechanismus popisuje ",[38,47220,47221],{},"teorém pavučiny",[614,47223,47224],{},"cobweb model",[198,47226,47228],{"id":47227},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,47230,47231],{},[3817,47232],{"alt":47233,"className":47234,"src":47235},"imek-komparativni-statika-4pripady",[210,3821],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1636,47237,47238,47279,47319,47359],{},[724,47239,47240,47243,47244,4005,47261,1659],{},[38,47241,47242],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,47245,47247],{"className":47246},[886],[888,47248,47249],{"xmlns":890},[892,47250,47251,47259],{},[895,47252,47253],{},[2037,47254,47255,47257],{},[898,47256,1710],{},[898,47258,2041],{},[902,47260,46341],{"encoding":904},[883,47262,47264],{"className":47263},[886],[888,47265,47266],{"xmlns":890},[892,47267,47268,47276],{},[895,47269,47270],{},[2037,47271,47272,47274],{},[898,47273,1734],{},[898,47275,2041],{},[902,47277,47278],{"encoding":904},"Q^E",[724,47280,47281,47284,47285,4005,47302,1659],{},[38,47282,47283],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,47286,47288],{"className":47287},[886],[888,47289,47290],{"xmlns":890},[892,47291,47292,47300],{},[895,47293,47294],{},[2037,47295,47296,47298],{},[898,47297,1710],{},[898,47299,2041],{},[902,47301,46341],{"encoding":904},[883,47303,47305],{"className":47304},[886],[888,47306,47307],{"xmlns":890},[892,47308,47309,47317],{},[895,47310,47311],{},[2037,47312,47313,47315],{},[898,47314,1734],{},[898,47316,2041],{},[902,47318,47278],{"encoding":904},[724,47320,47321,47324,47325,7179,47342,1659],{},[38,47322,47323],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,47326,47328],{"className":47327},[886],[888,47329,47330],{"xmlns":890},[892,47331,47332,47340],{},[895,47333,47334],{},[2037,47335,47336,47338],{},[898,47337,1710],{},[898,47339,2041],{},[902,47341,46341],{"encoding":904},[883,47343,47345],{"className":47344},[886],[888,47346,47347],{"xmlns":890},[892,47348,47349,47357],{},[895,47350,47351],{},[2037,47352,47353,47355],{},[898,47354,1734],{},[898,47356,2041],{},[902,47358,47278],{"encoding":904},[724,47360,47361,47364,47365,47382,47383,1659],{},[38,47362,47363],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,47366,47368],{"className":47367},[886],[888,47369,47370],{"xmlns":890},[892,47371,47372,47380],{},[895,47373,47374],{},[2037,47375,47376,47378],{},[898,47377,1710],{},[898,47379,2041],{},[902,47381,46341],{"encoding":904},", pokles ",[883,47384,47386],{"className":47385},[886],[888,47387,47388],{"xmlns":890},[892,47389,47390,47398],{},[895,47391,47392],{},[2037,47393,47394,47396],{},[898,47395,1734],{},[898,47397,2041],{},[902,47399,47278],{"encoding":904},[16,47401,47402,47447],{},[19,47403,47404],{},[22,47405,47406,47409,47428],{},[25,47407,47408],{},"Změna",[25,47410,47411],{},[883,47412,47414],{"className":47413},[886],[888,47415,47416],{"xmlns":890},[892,47417,47418,47426],{},[895,47419,47420],{},[2037,47421,47422,47424],{},[898,47423,1710],{},[898,47425,2041],{},[902,47427,46341],{"encoding":904},[25,47429,47430],{},[883,47431,47433],{"className":47432},[886],[888,47434,47435],{"xmlns":890},[892,47436,47437,47445],{},[895,47438,47439],{},[2037,47440,47441,47443],{},[898,47442,1734],{},[898,47444,2041],{},[902,47446,47278],{"encoding":904},[30,47448,47449,47459,47469,47478],{},[22,47450,47451,47454,47457],{},[35,47452,47453],{},"Růst poptávky",[35,47455,47456],{},"↑",[35,47458,47456],{},[22,47460,47461,47464,47467],{},[35,47462,47463],{},"Pokles poptávky",[35,47465,47466],{},"↓",[35,47468,47466],{},[22,47470,47471,47474,47476],{},[35,47472,47473],{},"Růst nabídky",[35,47475,47466],{},[35,47477,47456],{},[22,47479,47480,47483,47485],{},[35,47481,47482],{},"Pokles nabídky",[35,47484,47456],{},[35,47486,47466],{},[724,47488,47489],{},[614,47490,47491],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[41845,47493],{},[115,47495,811],{"id":47496},"zdanění-trhu",[1636,47498,47499,47588],{},[724,47500,47501,47503,47504,47517,47518,7037,47531,47534,47535,41651,47558,47583,47584,47587],{},[883,47502,1941],{}," TL;DR\nJednotková daň ",[883,47505,47507],{"className":47506},[886],[888,47508,47509],{"xmlns":890},[892,47510,47511,47515],{},[895,47512,47513],{},[898,47514,1772],{},[902,47516,1772],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,47519,47521],{"className":47520},[886],[888,47522,47523],{"xmlns":890},[892,47524,47525,47529],{},[895,47526,47527],{},[898,47528,1772],{},[902,47530,1772],{"encoding":904},[38,47532,47533],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,47536,47538],{"className":47537},[886],[888,47539,47540],{"xmlns":890},[892,47541,47542,47555],{},[895,47543,47544],{},[6927,47545,47546,47548],{},[898,47547,1772],{},[895,47549,47550,47553],{},[898,47551,47552],{},"s",[898,47554,724],{},[902,47556,47557],{"encoding":904},"T_{sp}",[883,47559,47561],{"className":47560},[886],[888,47562,47563],{"xmlns":890},[892,47564,47565,47580],{},[895,47566,47567],{},[6927,47568,47569,47571],{},[898,47570,1772],{},[895,47572,47573,47576,47578],{},[898,47574,47575],{},"v",[898,47577,7446],{},[898,47579,16915],{},[902,47581,47582],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,47585,47586],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,47589,47590],{},[614,47591,47592,47593,1659],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,47594,47596],{"className":47595,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,47598,47599,47600,47603,47604,47630,47631,47634,47635,47661,47662,47679,47680,47720,47721,1655,47734,1659],{},"Existují dvě formy zdanění — daň uložená ",[38,47601,47602],{},"výrobci"," (posun nabídky ",[883,47605,47607],{"className":47606},[886],[888,47608,47609],{"xmlns":890},[892,47610,47611,47627],{},[895,47612,47613,47619,47621,47623,47625],{},[6927,47614,47615,47617],{},[898,47616,6493],{},[1716,47618,2222],{},[1712,47620,1714],{},[898,47622,6493],{},[1712,47624,3145],{},[898,47626,1772],{},[902,47628,47629],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,47632,47633],{},"spotřebiteli"," (posun poptávky ",[883,47636,47638],{"className":47637},[886],[888,47639,47640],{"xmlns":890},[892,47641,47642,47658],{},[895,47643,47644,47650,47652,47654,47656],{},[6927,47645,47646,47648],{},[898,47647,1969],{},[1716,47649,2787],{},[1712,47651,1714],{},[898,47653,1969],{},[1712,47655,2219],{},[898,47657,1772],{},[902,47659,47660],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,47663,47665],{"className":47664},[886],[888,47666,47667],{"xmlns":890},[892,47668,47669,47677],{},[895,47670,47671],{},[2037,47672,47673,47675],{},[898,47674,1734],{},[898,47676,2041],{},[902,47678,47278],{"encoding":904}," klesá a vzniká rozklad daně ",[883,47681,47683],{"className":47682},[886],[888,47684,47685],{"xmlns":890},[892,47686,47687,47717],{},[895,47688,47689,47691,47693,47703,47705],{},[898,47690,1772],{},[1712,47692,1714],{},[6927,47694,47695,47697],{},[898,47696,1772],{},[895,47698,47699,47701],{},[898,47700,47552],{},[898,47702,724],{},[1712,47704,3145],{},[6927,47706,47707,47709],{},[898,47708,1772],{},[895,47710,47711,47713,47715],{},[898,47712,47575],{},[898,47714,7446],{},[898,47716,16915],{},[902,47718,47719],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,47722,47724],{"className":47723},[886],[888,47725,47726],{"xmlns":890},[892,47727,47728,47732],{},[895,47729,47730],{},[898,47731,1969],{},[902,47733,1969],{"encoding":904},[883,47735,47737],{"className":47736},[886],[888,47738,47739],{"xmlns":890},[892,47740,47741,47745],{},[895,47742,47743],{},[898,47744,6493],{},[902,47746,6493],{"encoding":904},[724,47748,47749,47750,47753,47754,1655,47784,47818],{},"Zásadním výsledkem kapitoly je ",[38,47751,47752],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,47755,47757],{"className":47756},[886],[888,47758,47759],{"xmlns":890},[892,47760,47761,47781],{},[895,47762,47763,47771,47773],{},[6989,47764,47765,47767,47769],{},[898,47766,1734],{},[1716,47768,2222],{},[898,47770,2041],{},[1712,47772,1714],{},[6989,47774,47775,47777,47779],{},[898,47776,1734],{},[1716,47778,2787],{},[898,47780,2041],{},[902,47782,47783],{"encoding":904},"Q_1^E = Q_2^E",[883,47785,47787],{"className":47786},[886],[888,47788,47789],{"xmlns":890},[892,47790,47791,47815],{},[895,47792,47793,47801,47803,47805,47807],{},[6989,47794,47795,47797,47799],{},[898,47796,1710],{},[1716,47798,2222],{},[898,47800,2041],{},[1712,47802,2219],{},[898,47804,1772],{},[1712,47806,1714],{},[6989,47808,47809,47811,47813],{},[898,47810,1710],{},[1716,47812,2787],{},[898,47814,2041],{},[902,47816,47817],{"encoding":904},"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.",[724,47820,47821,47822,47825,47826,47852,47853,47881,47882,47885,47886,47889,47890,1659],{},"Podrobný výklad, Příklady ",[38,47823,47824],{},"2.9"," (daň výrobci, ",[883,47827,47829],{"className":47828},[886],[888,47830,47831],{"xmlns":890},[892,47832,47833,47849],{},[895,47834,47835,47845,47847],{},[6927,47836,47837,47839],{},[898,47838,1772],{},[895,47840,47841,47843],{},[898,47842,47552],{},[898,47844,724],{},[1712,47846,1714],{},[1716,47848,2787],{},[902,47850,47851],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,47854,47856],{"className":47855},[886],[888,47857,47858],{"xmlns":890},[892,47859,47860,47878],{},[895,47861,47862,47874,47876],{},[6927,47863,47864,47866],{},[898,47865,1772],{},[895,47867,47868,47870,47872],{},[898,47869,47575],{},[898,47871,7446],{},[898,47873,16915],{},[1712,47875,1714],{},[1716,47877,2975],{},[902,47879,47880],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,47883,47884],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,47887,47888],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,47891,47596],{"className":47892,"dataFsResolvedFilePath":809,"href":810},[210],[41845,47894],{},[115,47896,47898],{"id":47897},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1636,47900,47901],{},[724,47902,47903,47905,47906,47909,47910,47912],{},[883,47904,1941],{}," TL;DR\nMultiplikátory jsou ",[38,47907,47908],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,47911,41835],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,47914,47916],{"id":47915},"redukovaný-tvar","Redukovaný tvar",[724,47918,47919,47920,14897,47943,1343,47961,17002,47978,14897,48001,48018,48019,48049],{},"Pro lineární model ",[883,47921,47923],{"className":47922},[886],[888,47924,47925],{"xmlns":890},[892,47926,47927,47941],{},[895,47928,47929,47931,47933,47935,47937,47939],{},[898,47930,1710],{},[1712,47932,1714],{},[898,47934,207],{},[898,47936,1734],{},[1712,47938,3145],{},[898,47940,7544],{},[902,47942,41935],{"encoding":904},[883,47944,47946],{"className":47945},[886],[888,47947,47948],{"xmlns":890},[892,47949,47950,47958],{},[895,47951,47952,47954,47956],{},[898,47953,207],{},[1712,47955,2252],{},[1716,47957,2085],{},[902,47959,47960],{"encoding":904},"a \u003C 0",[883,47962,47964],{"className":47963},[886],[888,47965,47966],{"xmlns":890},[892,47967,47968,47976],{},[895,47969,47970,47972,47974],{},[898,47971,7544],{},[1712,47973,2302],{},[1716,47975,2085],{},[902,47977,23689],{"encoding":904},[883,47979,47981],{"className":47980},[886],[888,47982,47983],{"xmlns":890},[892,47984,47985,47999],{},[895,47986,47987,47989,47991,47993,47995,47997],{},[898,47988,1710],{},[1712,47990,1714],{},[898,47992,7585],{},[898,47994,1734],{},[1712,47996,3145],{},[898,47998,2468],{},[902,48000,45117],{"encoding":904},[883,48002,48004],{"className":48003},[886],[888,48005,48006],{"xmlns":890},[892,48007,48008,48016],{},[895,48009,48010,48012,48014],{},[898,48011,7585],{},[1712,48013,2302],{},[1716,48015,2085],{},[902,48017,45135],{"encoding":904},") dává podmínka rovnováhy ",[883,48020,48022],{"className":48021},[886],[888,48023,48024],{"xmlns":890},[892,48025,48026,48046],{},[895,48027,48028,48030,48032,48034,48036,48038,48040,48042,48044],{},[898,48029,207],{},[898,48031,1734],{},[1712,48033,3145],{},[898,48035,7544],{},[1712,48037,1714],{},[898,48039,7585],{},[898,48041,1734],{},[1712,48043,3145],{},[898,48045,2468],{},[902,48047,48048],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,48051,48053],{"className":48052},[886],[888,48054,48055],{"xmlns":890,"display":32941},[892,48056,48057,48102],{},[25629,48058,48059],{"width":32946},[25634,48060,48061,48063,48095,48097],{},[25637,48062],{"width":32951},[25637,48064,48065],{},[895,48066,48067,48073,48075,48093],{},[2037,48068,48069,48071],{},[898,48070,1734],{},[898,48072,2041],{},[1712,48074,1714],{},[2567,48076,48077,48085],{},[895,48078,48079,48081,48083],{},[898,48080,7544],{},[1712,48082,2219],{},[898,48084,2468],{},[895,48086,48087,48089,48091],{},[898,48088,7585],{},[1712,48090,2219],{},[898,48092,207],{},[898,48094,1659],{"mathvariant":2003},[25637,48096],{"width":32951},[25637,48098,48099],{},[1762,48100,48101],{},"(2.10)",[902,48103,48104],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,48106,48107,48108,14897,48110,48113,48114,48131,48132,3245,48135,48161,48162,48175,48176,48194,48195,1691],{},"Vztah (2.10) je ",[38,48109,25829],{},[614,48111,48112],{},"reduced form",") pro ",[883,48115,48117],{"className":48116},[886],[888,48118,48119],{"xmlns":890},[892,48120,48121,48129],{},[895,48122,48123],{},[2037,48124,48125,48127],{},[898,48126,1734],{},[898,48128,2041],{},[902,48130,47278],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,48133,48134],{},"parametrů",[883,48136,48138],{"className":48137},[886],[888,48139,48140],{"xmlns":890},[892,48141,48142,48158],{},[895,48143,48144,48146,48148,48150,48152,48154,48156],{},[898,48145,207],{},[1712,48147,3138],{"separator":2565},[898,48149,7544],{},[1712,48151,3138],{"separator":2565},[898,48153,7585],{},[1712,48155,3138],{"separator":2565},[898,48157,2468],{},[902,48159,48160],{"encoding":904},"a, b, c, d",". Aby ",[883,48163,48165],{"className":48164},[886],[888,48166,48167],{"xmlns":890},[892,48168,48169,48173],{},[895,48170,48171],{},[898,48172,2041],{},[902,48174,2041],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,48177,48179],{"className":48178},[886],[888,48180,48181],{"xmlns":890},[892,48182,48183,48191],{},[895,48184,48185,48187,48189],{},[898,48186,7544],{},[1712,48188,2302],{},[898,48190,2468],{},[902,48192,48193],{"encoding":904},"b > d"," (neboť ",[883,48196,48198],{"className":48197},[886],[888,48199,48200],{"xmlns":890},[892,48201,48202,48214],{},[895,48203,48204,48206,48208,48210,48212],{},[898,48205,7585],{},[1712,48207,2219],{},[898,48209,207],{},[1712,48211,2302],{},[1716,48213,2085],{},[902,48215,48216],{"encoding":904},"c - a > 0",[724,48218,48219],{},[614,48220,48221,48222,48235,48236,48249,48250,23523,48263,46815,48280,48293],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,48223,48225],{"className":48224},[886],[888,48226,48227],{"xmlns":890},[892,48228,48229,48233],{},[895,48230,48231],{},[898,48232,7544],{},[902,48234,7544],{"encoding":904}," na ose ",[883,48237,48239],{"className":48238},[886],[888,48240,48241],{"xmlns":890},[892,48242,48243,48247],{},[895,48244,48245],{},[898,48246,1710],{},[902,48248,1710],{"encoding":904},") a nabídka (úsek ",[883,48251,48253],{"className":48252},[886],[888,48254,48255],{"xmlns":890},[892,48256,48257,48261],{},[895,48258,48259],{},[898,48260,2468],{},[902,48262,2468],{"encoding":904},[883,48264,48266],{"className":48265},[886],[888,48267,48268],{"xmlns":890},[892,48269,48270,48278],{},[895,48271,48272,48274,48276],{},[898,48273,7544],{},[1712,48275,2302],{},[898,48277,2468],{},[902,48279,48193],{"encoding":904},[883,48281,48283],{"className":48282},[886],[888,48284,48285],{"xmlns":890},[892,48286,48287,48291],{},[895,48288,48289],{},[898,48290,2041],{},[902,48292,2041],{"encoding":904}," v 1. kvadrantu.",[198,48295,48297],{"id":48296},"definice-multiplikátorů","Definice multiplikátorů",[724,48299,48300,48301,48326,48327,48340,48341,48354],{},"V komparativní statice jsou ",[883,48302,48304],{"className":48303},[886],[888,48305,48306],{"xmlns":890},[892,48307,48308,48324],{},[895,48309,48310,48312,48314,48316,48318,48320,48322],{},[898,48311,207],{},[1712,48313,3138],{"separator":2565},[898,48315,7544],{},[1712,48317,3138],{"separator":2565},[898,48319,7585],{},[1712,48321,3138],{"separator":2565},[898,48323,2468],{},[902,48325,48160],{"encoding":904}," exogenní proměnné a ",[883,48328,48330],{"className":48329},[886],[888,48331,48332],{"xmlns":890},[892,48333,48334,48338],{},[895,48335,48336],{},[898,48337,1734],{},[902,48339,1734],{"encoding":904}," endogenní. Přibližná změna ",[883,48342,48344],{"className":48343},[886],[888,48345,48346],{"xmlns":890},[892,48347,48348,48352],{},[895,48349,48350],{},[898,48351,1734],{},[902,48353,1734],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,48356,48358],{"className":48357},[886],[888,48359,48360],{"xmlns":890,"display":32941},[892,48361,48362,48455],{},[25629,48363,48364],{"width":32946},[25634,48365,48366,48368,48448,48450],{},[25637,48367],{"width":32951},[25637,48369,48370],{},[895,48371,48372,48374,48376,48378,48380,48382,48384,48392,48394,48396,48398,48400,48408,48410,48412,48414,48416,48424,48426,48428,48430,48432,48440,48442,48444,48446],{},[898,48373,2004],{"mathvariant":2003},[898,48375,1734],{},[1712,48377,3740],{},[898,48379,2468],{},[898,48381,1734],{},[1712,48383,1714],{},[6989,48385,48386,48388,48390],{},[898,48387,1734],{},[898,48389,207],{},[1712,48391,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,48393,2583],{},[898,48395,2468],{},[898,48397,207],{},[1712,48399,3145],{},[6989,48401,48402,48404,48406],{},[898,48403,1734],{},[898,48405,7544],{},[1712,48407,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,48409,2583],{},[898,48411,2468],{},[898,48413,7544],{},[1712,48415,3145],{},[6989,48417,48418,48420,48422],{},[898,48419,1734],{},[898,48421,7585],{},[1712,48423,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,48425,2583],{},[898,48427,2468],{},[898,48429,7585],{},[1712,48431,3145],{},[6989,48433,48434,48436,48438],{},[898,48435,1734],{},[898,48437,2468],{},[1712,48439,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,48441,2583],{},[898,48443,2468],{},[898,48445,2468],{},[898,48447,1659],{"mathvariant":2003},[25637,48449],{"width":32951},[25637,48451,48452],{},[1762,48453,48454],{},"(2.11)",[902,48456,48457],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,48459,48460,48461,48511,48512,14897,48514,8558],{},"Parciální derivace ",[883,48462,48464],{"className":48463},[886],[888,48465,48466],{"xmlns":890},[892,48467,48468,48508],{},[895,48469,48470,48478,48480,48488,48490,48498,48500],{},[6989,48471,48472,48474,48476],{},[898,48473,1734],{},[898,48475,207],{},[1712,48477,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48479,3138],{"separator":2565},[6989,48481,48482,48484,48486],{},[898,48483,1734],{},[898,48485,7544],{},[1712,48487,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48489,3138],{"separator":2565},[6989,48491,48492,48494,48496],{},[898,48493,1734],{},[898,48495,7585],{},[1712,48497,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48499,3138],{"separator":2565},[6989,48501,48502,48504,48506],{},[898,48503,1734],{},[898,48505,2468],{},[1712,48507,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,48509,48510],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,48513,22852],{},[614,48515,48516],{},"multipliers",[883,48518,48520],{"className":48519},[886],[888,48521,48522],{"xmlns":890,"display":32941},[892,48523,48524,48675],{},[25629,48525,48526],{"width":32946},[25634,48527,48528,48530,48668,48670],{},[25637,48529],{"width":32951},[25637,48531,48532],{},[895,48533,48534,48542,48544,48570,48572,48574,48582,48584,48596,48598,48600,48608,48610,48612,48638,48640,48642,48650,48652,48654,48666],{},[6989,48535,48536,48538,48540],{},[898,48537,1734],{},[898,48539,207],{},[1712,48541,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48543,1714],{},[2567,48545,48546,48554],{},[895,48547,48548,48550,48552],{},[898,48549,7544],{},[1712,48551,2219],{},[898,48553,2468],{},[895,48555,48556,48558,48560,48562,48564],{},[1712,48557,1904],{"stretchy":1903},[898,48559,7585],{},[1712,48561,2219],{},[898,48563,207],{},[2037,48565,48566,48568],{},[1712,48567,1910],{"stretchy":1903},[1716,48569,2787],{},[1712,48571,3138],{"separator":2565},[3690,48573],{"width":20158},[6989,48575,48576,48578,48580],{},[898,48577,1734],{},[898,48579,7544],{},[1712,48581,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48583,1714],{},[2567,48585,48586,48588],{},[1716,48587,2222],{},[895,48589,48590,48592,48594],{},[898,48591,7585],{},[1712,48593,2219],{},[898,48595,207],{},[1712,48597,3138],{"separator":2565},[3690,48599],{"width":20158},[6989,48601,48602,48604,48606],{},[898,48603,1734],{},[898,48605,7585],{},[1712,48607,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48609,1714],{},[1712,48611,2219],{},[2567,48613,48614,48622],{},[895,48615,48616,48618,48620],{},[898,48617,7544],{},[1712,48619,2219],{},[898,48621,2468],{},[895,48623,48624,48626,48628,48630,48632],{},[1712,48625,1904],{"stretchy":1903},[898,48627,7585],{},[1712,48629,2219],{},[898,48631,207],{},[2037,48633,48634,48636],{},[1712,48635,1910],{"stretchy":1903},[1716,48637,2787],{},[1712,48639,3138],{"separator":2565},[3690,48641],{"width":20158},[6989,48643,48644,48646,48648],{},[898,48645,1734],{},[898,48647,2468],{},[1712,48649,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48651,1714],{},[1712,48653,2219],{},[2567,48655,48656,48658],{},[1716,48657,2222],{},[895,48659,48660,48662,48664],{},[898,48661,7585],{},[1712,48663,2219],{},[898,48665,207],{},[898,48667,1659],{"mathvariant":2003},[25637,48669],{"width":32951},[25637,48671,48672],{},[1762,48673,48674],{},"(2.12)",[902,48676,48677],{"encoding":904},"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}",[198,48679,48681],{"id":48680},"znaménka-a-interpretace","Znaménka a interpretace",[724,48683,48684,48685,1343,48702,1343,48719,1343,48736,48753,48754,8558],{},"Za podmínek ",[883,48686,48688],{"className":48687},[886],[888,48689,48690],{"xmlns":890},[892,48691,48692,48700],{},[895,48693,48694,48696,48698],{},[898,48695,207],{},[1712,48697,2252],{},[1716,48699,2085],{},[902,48701,47960],{"encoding":904},[883,48703,48705],{"className":48704},[886],[888,48706,48707],{"xmlns":890},[892,48708,48709,48717],{},[895,48710,48711,48713,48715],{},[898,48712,7544],{},[1712,48714,2302],{},[1716,48716,2085],{},[902,48718,23689],{"encoding":904},[883,48720,48722],{"className":48721},[886],[888,48723,48724],{"xmlns":890},[892,48725,48726,48734],{},[895,48727,48728,48730,48732],{},[898,48729,7585],{},[1712,48731,2302],{},[1716,48733,2085],{},[902,48735,45135],{"encoding":904},[883,48737,48739],{"className":48738},[886],[888,48740,48741],{"xmlns":890},[892,48742,48743,48751],{},[895,48744,48745,48747,48749],{},[898,48746,7544],{},[1712,48748,2302],{},[898,48750,2468],{},[902,48752,48193],{"encoding":904}," platí (znaménka se ",[38,48755,48756],{},"nemění",[883,48758,48760],{"className":48759},[886],[888,48761,48762],{"xmlns":890,"display":32941},[892,48763,48764,48826],{},[895,48765,48766,48774,48776,48778,48780,48782,48790,48792,48794,48796,48798,48806,48808,48810,48812,48814,48822,48824],{},[6989,48767,48768,48770,48772],{},[898,48769,1734],{},[898,48771,207],{},[1712,48773,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48775,2302],{},[1716,48777,2085],{},[1712,48779,3138],{"separator":2565},[3690,48781],{"width":3692},[6989,48783,48784,48786,48788],{},[898,48785,1734],{},[898,48787,7544],{},[1712,48789,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48791,2302],{},[1716,48793,2085],{},[1712,48795,3138],{"separator":2565},[3690,48797],{"width":3692},[6989,48799,48800,48802,48804],{},[898,48801,1734],{},[898,48803,7585],{},[1712,48805,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48807,2252],{},[1716,48809,2085],{},[1712,48811,3138],{"separator":2565},[3690,48813],{"width":3692},[6989,48815,48816,48818,48820],{},[898,48817,1734],{},[898,48819,2468],{},[1712,48821,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48823,2252],{},[1716,48825,17334],{},[902,48827,48828],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,48830,48831,48890],{},[123,48832,48833,3245,48836,48856,48857,48874,48875,1343,48888,1659],{},[38,48834,48835],{},"Kvantitativní smysl:",[883,48837,48839],{"className":48838},[886],[888,48840,48841],{"xmlns":890},[892,48842,48843,48853],{},[895,48844,48845],{},[6989,48846,48847,48849,48851],{},[898,48848,1734],{},[898,48850,7456],{},[1712,48852,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,48854,48855],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,48858,48860],{"className":48859},[886],[888,48861,48862],{"xmlns":890},[892,48863,48864,48872],{},[895,48865,48866],{},[2037,48867,48868,48870],{},[898,48869,1734],{},[898,48871,2041],{},[902,48873,47278],{"encoding":904}," při jednotkové změně parametru ",[883,48876,48878],{"className":48877},[886],[888,48879,48880],{"xmlns":890},[892,48881,48882,48886],{},[895,48883,48884],{},[898,48885,7456],{},[902,48887,7456],{"encoding":904},[614,48889,41835],{},[123,48891,48892,48895,48896,48913,48914,1659],{},[38,48893,48894],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,48897,48899],{"className":48898},[886],[888,48900,48901],{"xmlns":890},[892,48902,48903,48911],{},[895,48904,48905],{},[2037,48906,48907,48909],{},[898,48908,1734],{},[898,48910,2041],{},[902,48912,47278],{"encoding":904}," na růst ",[883,48915,48917],{"className":48916},[886],[888,48918,48919],{"xmlns":890},[892,48920,48921,48925],{},[895,48922,48923],{},[898,48924,7456],{},[902,48926,7456],{"encoding":904},[724,48928,48929,48930,48943,48944,48194,48961,1691],{},"Např. růst ",[883,48931,48933],{"className":48932},[886],[888,48934,48935],{"xmlns":890},[892,48936,48937,48941],{},[895,48938,48939],{},[898,48940,7585],{},[902,48942,7585],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,48945,48947],{"className":48946},[886],[888,48948,48949],{"xmlns":890},[892,48950,48951,48959],{},[895,48952,48953],{},[2037,48954,48955,48957],{},[898,48956,1734],{},[898,48958,2041],{},[902,48960,47278],{"encoding":904},[883,48962,48964],{"className":48963},[886],[888,48965,48966],{"xmlns":890},[892,48967,48968,48982],{},[895,48969,48970,48978,48980],{},[6989,48971,48972,48974,48976],{},[898,48973,1734],{},[898,48975,7585],{},[1712,48977,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,48979,2252],{},[1716,48981,2085],{},[902,48983,48984],{"encoding":904},"Q'_c \u003C 0",[724,48986,48987],{},[614,48988,48989,48990,49010,49011,49035,49036,49058,49059,1659],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,48991,48993],{"className":48992},[886],[888,48994,48995],{"xmlns":890},[892,48996,48997,49007],{},[895,48998,48999,49001,49003,49005],{},[898,49000,7585],{},[898,49002,1734],{},[1712,49004,3145],{},[898,49006,2468],{},[902,49008,49009],{"encoding":904},"cQ + d"," na strmější ",[883,49012,49014],{"className":49013},[886],[888,49015,49016],{"xmlns":890},[892,49017,49018,49032],{},[895,49019,49020,49026,49028,49030],{},[6927,49021,49022,49024],{},[898,49023,7585],{},[1716,49025,2222],{},[898,49027,1734],{},[1712,49029,3145],{},[898,49031,2468],{},[902,49033,49034],{"encoding":904},"c_1 Q + d"," (při ",[883,49037,49039],{"className":49038},[886],[888,49040,49041],{"xmlns":890},[892,49042,49043,49055],{},[895,49044,49045,49051,49053],{},[6927,49046,49047,49049],{},[898,49048,7585],{},[1716,49050,2222],{},[1712,49052,2302],{},[898,49054,7585],{},[902,49056,49057],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,49060,49062],{"className":49061},[886],[888,49063,49064],{"xmlns":890},[892,49065,49066,49076],{},[895,49067,49068,49074],{},[2037,49069,49070,49072],{},[898,49071,1734],{},[898,49073,2041],{},[1712,49075,47466],{},[902,49077,49078],{"encoding":904},"Q^E \\downarrow",[724,49080,49081,49082,49114,49115,1659],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,49083,49085],{"className":49084},[886],[888,49086,49087],{"xmlns":890},[892,49088,49089,49111],{},[895,49090,49091,49093,49095,49097,49105,49107,49109],{},[898,49092,2004],{"mathvariant":2003},[898,49094,1734],{},[1712,49096,3740],{},[6989,49098,49099,49101,49103],{},[898,49100,1734],{},[898,49102,7544],{},[1712,49104,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,49106,2583],{},[898,49108,2468],{},[898,49110,7544],{},[902,49112,49113],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,49116,49118],{"className":49117},[886],[888,49119,49120],{"xmlns":890},[892,49121,49122,49130],{},[895,49123,49124],{},[2037,49125,49126,49128],{},[898,49127,1710],{},[898,49129,2041],{},[902,49131,46341],{"encoding":904},[198,49133,49135,49136],{"id":49134},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,49137,49139],{"className":49138},[886],[888,49140,49141],{"xmlns":890},[892,49142,49143,49151],{},[895,49144,49145],{},[2037,49146,49147,49149],{},[898,49148,1734],{},[898,49150,2041],{},[902,49152,47278],{"encoding":904},[724,49154,49155,46530,49157,46565,49183,1659],{},[38,49156,42808],{},[883,49158,49160],{"className":49159},[886],[888,49161,49162],{"xmlns":890},[892,49163,49164,49180],{},[895,49165,49166,49168,49170,49172,49174,49176,49178],{},[898,49167,1710],{},[1712,49169,1714],{},[1712,49171,2219],{},[1716,49173,6198],{},[898,49175,1734],{},[1712,49177,3145],{},[1716,49179,3018],{},[902,49181,49182],{"encoding":904},"P = -3Q + 40",[883,49184,49186],{"className":49185},[886],[888,49187,49188],{"xmlns":890},[892,49189,49190,49204],{},[895,49191,49192,49194,49196,49198,49200,49202],{},[898,49193,1710],{},[1712,49195,1714],{},[1716,49197,2814],{},[898,49199,1734],{},[1712,49201,3145],{},[1716,49203,1718],{},[902,49205,49206],{"encoding":904},"P = 0{,}5Q + 10",[724,49208,49209,49211],{},[38,49210,42840],{}," Rovnovážné množství",[883,49213,49215],{"className":49214},[886],[888,49216,49217],{"xmlns":890,"display":32941},[892,49218,49219,49287],{},[895,49220,49221,49227,49229,49247,49249,49273,49275,49282,49284],{},[2037,49222,49223,49225],{},[898,49224,1734],{},[898,49226,2041],{},[1712,49228,1714],{},[2567,49230,49231,49239],{},[895,49232,49233,49235,49237],{},[898,49234,7544],{},[1712,49236,2219],{},[898,49238,2468],{},[895,49240,49241,49243,49245],{},[898,49242,7585],{},[1712,49244,2219],{},[898,49246,207],{},[1712,49248,1714],{},[2567,49250,49251,49259],{},[895,49252,49253,49255,49257],{},[1716,49254,3018],{},[1712,49256,2219],{},[1716,49258,1718],{},[895,49260,49261,49263,49265,49267,49269,49271],{},[1716,49262,2814],{},[1712,49264,2219],{},[1712,49266,1904],{"stretchy":1903},[1712,49268,2219],{},[1716,49270,6198],{},[1712,49272,1910],{"stretchy":1903},[1712,49274,1714],{},[2567,49276,49277,49279],{},[1716,49278,42894],{},[1716,49280,49281],{},"3,5",[1712,49283,3740],{},[1716,49285,49286],{},"8,571.",[902,49288,49289],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,49291,49292,49337],{},[38,49293,49294,49295,8093,49308,3072,49322,49336],{},"(a) Změna ",[883,49296,49298],{"className":49297},[886],[888,49299,49300],{"xmlns":890},[892,49301,49302,49306],{},[895,49303,49304],{},[898,49305,7585],{},[902,49307,7585],{"encoding":904},[883,49309,49311],{"className":49310},[886],[888,49312,49313],{"xmlns":890},[892,49314,49315,49319],{},[895,49316,49317],{},[1716,49318,2814],{},[902,49320,49321],{"encoding":904},"0{,}5",[883,49323,49325],{"className":49324},[886],[888,49326,49327],{"xmlns":890},[892,49328,49329,49333],{},[895,49330,49331],{},[1716,49332,24196],{},[902,49334,49335],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,49339,49341],{"className":49340},[886],[888,49342,49343],{"xmlns":890,"display":32941},[892,49344,49345,49422],{},[895,49346,49347,49355,49357,49359,49361,49363,49365,49391,49393,49395,49397,49399,49401,49411,49413,49415,49417,49419],{},[6989,49348,49349,49351,49353],{},[898,49350,1734],{},[898,49352,7585],{},[1712,49354,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,49356,2583],{},[898,49358,2468],{},[898,49360,7585],{},[1712,49362,1714],{},[1712,49364,2219],{},[2567,49366,49367,49375],{},[895,49368,49369,49371,49373],{},[898,49370,7544],{},[1712,49372,2219],{},[898,49374,2468],{},[895,49376,49377,49379,49381,49383,49385],{},[1712,49378,1904],{"stretchy":1903},[898,49380,7585],{},[1712,49382,2219],{},[898,49384,207],{},[2037,49386,49387,49389],{},[1712,49388,1910],{"stretchy":1903},[1716,49390,2787],{},[1762,49392,2583],{},[898,49394,2468],{},[898,49396,7585],{},[1712,49398,1714],{},[1712,49400,2219],{},[2567,49402,49403,49405],{},[1716,49404,42894],{},[2037,49406,49407,49409],{},[1716,49408,49281],{},[1716,49410,2787],{},[1712,49412,1783],{},[1716,49414,6607],{},[1712,49416,3740],{},[1712,49418,2219],{},[1716,49420,49421],{},"0,245.",[902,49423,49424],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,49426,49427,49428,1659],{},"Nové rovnovážné množství ",[883,49429,49431],{"className":49430},[886],[888,49432,49433],{"xmlns":890},[892,49434,49435,49460],{},[895,49436,49437,49445,49447,49450,49452,49455,49457],{},[6989,49438,49439,49441,49443],{},[898,49440,1734],{},[1716,49442,2222],{},[898,49444,2041],{},[1712,49446,3740],{},[1716,49448,49449],{},"8,571",[1712,49451,2219],{},[1716,49453,49454],{},"0,245",[1712,49456,1714],{},[1716,49458,49459],{},"8,326",[902,49461,49462],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,49464,49465,49550],{},[38,49466,49467,49468,1343,49488,1343,49510,1343,49530,1659],{},"(b) Současné změny ",[883,49469,49471],{"className":49470},[886],[888,49472,49473],{"xmlns":890},[892,49474,49475,49485],{},[895,49476,49477,49479,49481,49483],{},[898,49478,2468],{},[898,49480,207],{},[1712,49482,1714],{},[1716,49484,2814],{},[902,49486,49487],{"encoding":904},"da = 0{,}5",[883,49489,49491],{"className":49490},[886],[888,49492,49493],{"xmlns":890},[892,49494,49495,49507],{},[895,49496,49497,49499,49501,49503,49505],{},[898,49498,2468],{},[898,49500,7544],{},[1712,49502,1714],{},[1712,49504,2219],{},[1716,49506,3068],{},[902,49508,49509],{"encoding":904},"db = -5",[883,49511,49513],{"className":49512},[886],[888,49514,49515],{"xmlns":890},[892,49516,49517,49527],{},[895,49518,49519,49521,49523,49525],{},[898,49520,2468],{},[898,49522,7585],{},[1712,49524,1714],{},[1716,49526,6607],{},[902,49528,49529],{"encoding":904},"dc = 0{,}1",[883,49531,49533],{"className":49532},[886],[888,49534,49535],{"xmlns":890},[892,49536,49537,49547],{},[895,49538,49539,49541,49543,49545],{},[898,49540,2468],{},[898,49542,2468],{},[1712,49544,1714],{},[1716,49546,2222],{},[902,49548,49549],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,49552,49554],{"className":49553},[886],[888,49555,49556],{"xmlns":890,"display":32941},[892,49557,49558,49701],{},[25629,49559,49560,49642,49678],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,49561,49562,49572],{},[25637,49563,49564],{},[2563,49565,49566],{"scriptlevel":2085,"displaystyle":2565},[895,49567,49568,49570],{},[898,49569,2004],{"mathvariant":2003},[898,49571,1734],{},[25637,49573,49574],{},[2563,49575,49576],{"scriptlevel":2085,"displaystyle":2565},[895,49577,49578,49580,49582,49592,49594,49596,49598,49604,49606,49608,49610,49612,49614,49616,49626,49628,49630,49632,49638,49640],{},[895,49579],{},[1712,49581,3740],{},[2567,49583,49584,49586],{},[1716,49585,42894],{},[2037,49587,49588,49590],{},[1716,49589,49281],{},[1716,49591,2787],{},[1712,49593,1783],{},[1716,49595,2814],{},[1712,49597,3145],{},[2567,49599,49600,49602],{},[1716,49601,2222],{},[1716,49603,49281],{},[1712,49605,1783],{},[1712,49607,1904],{"stretchy":1903},[1712,49609,2219],{},[1716,49611,3068],{},[1712,49613,1910],{"stretchy":1903},[1712,49615,2219],{},[2567,49617,49618,49620],{},[1716,49619,42894],{},[2037,49621,49622,49624],{},[1716,49623,49281],{},[1716,49625,2787],{},[1712,49627,1783],{},[1716,49629,6607],{},[1712,49631,2219],{},[2567,49633,49634,49636],{},[1716,49635,2222],{},[1716,49637,49281],{},[1712,49639,1783],{},[1716,49641,2222],{},[25634,49643,49644,49650],{},[25637,49645,49646],{},[2563,49647,49648],{"scriptlevel":2085,"displaystyle":2565},[895,49649],{},[25637,49651,49652],{},[2563,49653,49654],{"scriptlevel":2085,"displaystyle":2565},[895,49655,49656,49658,49660,49663,49665,49668,49670,49673,49675],{},[895,49657],{},[1712,49659,1714],{},[1716,49661,49662],{},"1,2245",[1712,49664,2219],{},[1716,49666,49667],{},"1,4286",[1712,49669,2219],{},[1716,49671,49672],{},"0,2449",[1712,49674,2219],{},[1716,49676,49677],{},"0,2857",[25634,49679,49680,49686],{},[25637,49681,49682],{},[2563,49683,49684],{"scriptlevel":2085,"displaystyle":2565},[895,49685],{},[25637,49687,49688],{},[2563,49689,49690],{"scriptlevel":2085,"displaystyle":2565},[895,49691,49692,49694,49696,49698],{},[895,49693],{},[1712,49695,3740],{},[1712,49697,2219],{},[1716,49699,49700],{},"0,735.",[902,49702,49703],{"encoding":904},"\\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}",[724,49705,34940,49706,1659],{},[883,49707,49709],{"className":49708},[886],[888,49710,49711],{"xmlns":890},[892,49712,49713,49737],{},[895,49714,49715,49723,49725,49727,49729,49732,49734],{},[6989,49716,49717,49719,49721],{},[898,49718,1734],{},[1716,49720,2222],{},[898,49722,2041],{},[1712,49724,3740],{},[1716,49726,49449],{},[1712,49728,2219],{},[1716,49730,49731],{},"0,735",[1712,49733,1714],{},[1716,49735,49736],{},"7,836",[902,49738,49739],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1636,49741,49742],{},[724,49743,49744,49746,49747,49770,49771,49793],{},[883,49745,2203],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,49748,49750],{"className":49749},[886],[888,49751,49752],{"xmlns":890},[892,49753,49754,49767],{},[895,49755,49756,49758,49760,49762,49764],{},[898,49757,2004],{"mathvariant":2003},[898,49759,1734],{},[1712,49761,3740],{},[1712,49763,2219],{},[1716,49765,49766],{},"2,69",[902,49768,49769],{"encoding":904},"\\Delta Q \\approx -2{,}69",", ta však neodpovídá přepočtu parciálních derivací podle (2.11) a (2.12). Správná hodnota při uvedených změnách je ",[883,49772,49774],{"className":49773},[886],[888,49775,49776],{"xmlns":890},[892,49777,49778,49790],{},[895,49779,49780,49782,49784,49786,49788],{},[898,49781,2004],{"mathvariant":2003},[898,49783,1734],{},[1712,49785,3740],{},[1712,49787,2219],{},[1716,49789,49731],{},[902,49791,49792],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,49795,49796],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[41845,49798],{},[115,49800,820],{"id":16657},[1636,49802,49803],{},[724,49804,49805,1643,49807,14897,49810,17002,49826,14897,49829,49845,49846,1659],{},[883,49806,1941],{},[38,49808,49809],{},"Přebytek spotřebitele",[883,49811,49813],{"className":49812},[886],[888,49814,49815],{"xmlns":890},[892,49816,49817,49823],{},[895,49818,49819,49821],{},[898,49820,8195],{},[898,49822,6493],{},[902,49824,49825],{"encoding":904},"CS",[38,49827,49828],{},"přebytek výrobce",[883,49830,49832],{"className":49831},[886],[888,49833,49834],{"xmlns":890},[892,49835,49836,49842],{},[895,49837,49838,49840],{},[898,49839,1710],{},[898,49841,6493],{},[902,49843,49844],{"encoding":904},"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 ",[207,49847,49849],{"className":49848,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,49851,49852],{},[3817,49853],{"alt":49854,"className":49855,"src":49856},"imek-prebytky-cs-ps",[210,3821],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,49858,49859,14897,49861,49864],{},[38,49860,49809],{},[614,49862,49863],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,49866,49868],{"className":49867},[886],[888,49869,49870],{"xmlns":890,"display":32941},[892,49871,49872,49949],{},[25629,49873,49874],{"width":32946},[25634,49875,49876,49878,49942,49944],{},[25637,49877],{"width":32951},[25637,49879,49880],{},[895,49881,49882,49884,49886,49888,49894,49896,49898,49910,49912,49914,49916,49918,49920,49922,49924,49926,49932,49934,49940],{},[898,49883,8195],{},[898,49885,6493],{},[1712,49887,1904],{"stretchy":1903},[6927,49889,49890,49892],{},[898,49891,1734],{},[1716,49893,2085],{},[1712,49895,1910],{"stretchy":1903},[1712,49897,1714],{},[6989,49899,49900,49902,49904],{},[1712,49901,16042],{},[1716,49903,2085],{},[6927,49905,49906,49908],{},[898,49907,1734],{},[1716,49909,2085],{},[898,49911,1969],{},[1712,49913,1904],{"stretchy":1903},[898,49915,1734],{},[1712,49917,1910],{"stretchy":1903},[1762,49919,2583],{},[898,49921,2468],{},[898,49923,1734],{},[1712,49925,2219],{},[6927,49927,49928,49930],{},[898,49929,1710],{},[1716,49931,2085],{},[1762,49933,2583],{},[6927,49935,49936,49938],{},[898,49937,1734],{},[1716,49939,2085],{},[898,49941,1659],{"mathvariant":2003},[25637,49943],{"width":32951},[25637,49945,49946],{},[1762,49947,49948],{},"(2.14)",[902,49950,49951],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,49953,49954,14897,49957,49960],{},[38,49955,49956],{},"Přebytek výrobce",[614,49958,49959],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,49962,49964],{"className":49963},[886],[888,49965,49966],{"xmlns":890,"display":32941},[892,49967,49968,50045],{},[25629,49969,49970],{"width":32946},[25634,49971,49972,49974,50038,50040],{},[25637,49973],{"width":32951},[25637,49975,49976],{},[895,49977,49978,49980,49982,49984,49990,49992,49994,50000,50002,50008,50010,50022,50024,50026,50028,50030,50032,50034,50036],{},[898,49979,1710],{},[898,49981,6493],{},[1712,49983,1904],{"stretchy":1903},[6927,49985,49986,49988],{},[898,49987,1734],{},[1716,49989,2085],{},[1712,49991,1910],{"stretchy":1903},[1712,49993,1714],{},[6927,49995,49996,49998],{},[898,49997,1710],{},[1716,49999,2085],{},[1762,50001,2583],{},[6927,50003,50004,50006],{},[898,50005,1734],{},[1716,50007,2085],{},[1712,50009,2219],{},[6989,50011,50012,50014,50016],{},[1712,50013,16042],{},[1716,50015,2085],{},[6927,50017,50018,50020],{},[898,50019,1734],{},[1716,50021,2085],{},[898,50023,6493],{},[1712,50025,1904],{"stretchy":1903},[898,50027,1734],{},[1712,50029,1910],{"stretchy":1903},[1762,50031,2583],{},[898,50033,2468],{},[898,50035,1734],{},[898,50037,1659],{"mathvariant":2003},[25637,50039],{"width":32951},[25637,50041,50042],{},[1762,50043,50044],{},"(2.15)",[902,50046,50047],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,50049,50050,50051,1659],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,50052,50054],{"className":50053,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[41845,50056],{},[115,50058,50060],{"id":50059},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,50062,50063,50094,50099,50105,50133,50139,50168,50174,50254,50280],{},[123,50064,50065,50067,50068,50093],{},[38,50066,42803],{}," — lineární poptávka ",[883,50069,50071],{"className":50070},[886],[888,50072,50073],{"xmlns":890},[892,50074,50075,50091],{},[895,50076,50077,50079,50081,50083,50085,50087,50089],{},[898,50078,1710],{},[1712,50080,1714],{},[1712,50082,2219],{},[1716,50084,2787],{},[898,50086,1734],{},[1712,50088,3145],{},[1716,50090,8533],{},[902,50092,42835],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,50095,50096,50098],{},[38,50097,43117],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,50100,50101,50104],{},[38,50102,50103],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,50106,50107,50109,50110,1659],{},[38,50108,45664],{}," — lineární nabídka ",[883,50111,50113],{"className":50112},[886],[888,50114,50115],{"xmlns":890},[892,50116,50117,50131],{},[895,50118,50119,50121,50123,50125,50127,50129],{},[898,50120,1710],{},[1712,50122,1714],{},[1716,50124,2814],{},[898,50126,1734],{},[1712,50128,3145],{},[1716,50130,2809],{},[902,50132,45693],{"encoding":904},[123,50134,50135,50138],{},[38,50136,50137],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,50140,50141,50144,50145,1659],{},[38,50142,50143],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,50146,50148],{"className":50147},[886],[888,50149,50150],{"xmlns":890},[892,50151,50152,50166],{},[895,50153,50154,50156,50158,50160,50162,50164],{},[898,50155,2041],{},[1712,50157,7910],{"stretchy":1903},[1716,50159,2975],{},[1712,50161,3138],{"separator":2565},[1716,50163,46811],{},[1712,50165,7925],{"stretchy":1903},[902,50167,46839],{"encoding":904},[123,50169,50170,50173],{},[38,50171,50172],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,50175,50176,50179,50180,50197,50198,1343,50223,50250,50251,8362],{},[38,50177,50178],{},"Příklad 2.9"," — daň ",[883,50181,50183],{"className":50182},[886],[888,50184,50185],{"xmlns":890},[892,50186,50187,50195],{},[895,50188,50189,50191,50193],{},[898,50190,1772],{},[1712,50192,1714],{},[1716,50194,6209],{},[902,50196,46143],{"encoding":904}," na výrobce; rozklad ",[883,50199,50201],{"className":50200},[886],[888,50202,50203],{"xmlns":890},[892,50204,50205,50221],{},[895,50206,50207,50217,50219],{},[6927,50208,50209,50211],{},[898,50210,1772],{},[895,50212,50213,50215],{},[898,50214,47552],{},[898,50216,724],{},[1712,50218,1714],{},[1716,50220,2787],{},[902,50222,47851],{"encoding":904},[883,50224,50226],{"className":50225},[886],[888,50227,50228],{"xmlns":890},[892,50229,50230,50248],{},[895,50231,50232,50244,50246],{},[6927,50233,50234,50236],{},[898,50235,1772],{},[895,50237,50238,50240,50242],{},[898,50239,47575],{},[898,50241,7446],{},[898,50243,16915],{},[1712,50245,1714],{},[1716,50247,2975],{},[902,50249,47880],{"encoding":904},". (Viz ",[207,50252,47596],{"className":50253,"dataFsResolvedFilePath":809,"href":810},[210],[123,50255,50256,50179,50259,50276,50277,8362],{},[38,50257,50258],{},"Příklad 2.10",[883,50260,50262],{"className":50261},[886],[888,50263,50264],{"xmlns":890},[892,50265,50266,50274],{},[895,50267,50268,50270,50272],{},[898,50269,1772],{},[1712,50271,1714],{},[1716,50273,6209],{},[902,50275,46143],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,50278,47596],{"className":50279,"dataFsResolvedFilePath":809,"href":810},[210],[123,50281,50282,50285],{},[38,50283,50284],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[41845,50287],{},[115,50289,50291],{"id":50290},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,50293,50295],{"id":50294},"základní-analýza-poptávky","Základní analýza poptávky",[724,50297,50298,50301,50302,50337,50338,50364],{},[38,50299,50300],{},"2.1"," Je dána poptávka ",[883,50303,50305],{"className":50304},[886],[888,50306,50307],{"xmlns":890},[892,50308,50309,50334],{},[895,50310,50311,50313,50315,50317,50319,50321,50323,50325,50328,50330,50332],{},[898,50312,1734],{},[1712,50314,1714],{},[898,50316,1969],{},[1712,50318,1904],{"stretchy":1903},[898,50320,1710],{},[1712,50322,1910],{"stretchy":1903},[1712,50324,1714],{},[1716,50326,50327],{},"75",[1712,50329,2219],{},[1716,50331,3068],{},[898,50333,1710],{},[902,50335,50336],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,50339,50341],{"className":50340},[886],[888,50342,50343],{"xmlns":890},[892,50344,50345,50361],{},[895,50346,50347,50349,50351,50353,50355,50357,50359],{},[1716,50348,2085],{},[1712,50350,3138],{"separator":2565},[1716,50352,3068],{},[1712,50354,3138],{"separator":2565},[1716,50356,1718],{},[1712,50358,3138],{"separator":2565},[1716,50360,41119],{},[902,50362,50363],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,50366,50367,50370,50371,50389,50390,8558],{},[38,50368,50369],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,50372,50374],{"className":50373},[886],[888,50375,50376],{"xmlns":890},[892,50377,50378,50386],{},[895,50379,50380,50382,50384],{},[898,50381,1710],{},[1712,50383,3138],{"separator":2565},[898,50385,1734],{},[902,50387,50388],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,50391,50393],{"className":50392},[886],[888,50394,50395],{"xmlns":890},[892,50396,50397,50413],{},[895,50398,50399,50401,50403,50405,50407,50409,50411],{},[898,50400,207],{},[1712,50402,3138],{"separator":2565},[898,50404,7544],{},[1712,50406,3138],{"separator":2565},[898,50408,7585],{},[1712,50410,2302],{},[1716,50412,2085],{},[902,50414,50415],{"encoding":904},"a, b, c > 0",[120,50417,50418,50451,50482,50517,50548,50583],{},[123,50419,50420,50421],{},"(a) ",[883,50422,50424],{"className":50423},[886],[888,50425,50426],{"xmlns":890},[892,50427,50428,50448],{},[895,50429,50430,50432,50434],{},[898,50431,1734],{},[1712,50433,1714],{},[2563,50435,50436],{"scriptlevel":2085,"displaystyle":2565},[2567,50437,50438,50440],{},[898,50439,207],{},[895,50441,50442,50444,50446],{},[898,50443,1710],{},[1712,50445,3145],{},[898,50447,7585],{},[902,50449,50450],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,50452,50453,50454],{},"(b) ",[883,50455,50457],{"className":50456},[886],[888,50458,50459],{"xmlns":890},[892,50460,50461,50479],{},[895,50462,50463,50465,50467],{},[898,50464,1734],{},[1712,50466,1714],{},[5935,50468,50469],{},[895,50470,50471,50473,50475,50477],{},[898,50472,207],{},[1712,50474,2219],{},[898,50476,7544],{},[898,50478,1734],{},[902,50480,50481],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,50483,50484,50485],{},"(c) ",[883,50486,50488],{"className":50487},[886],[888,50489,50490],{"xmlns":890},[892,50491,50492,50514],{},[895,50493,50494,50496,50498],{},[898,50495,1734],{},[1712,50497,1714],{},[2563,50499,50500],{"scriptlevel":2085,"displaystyle":2565},[2567,50501,50502,50512],{},[895,50503,50504,50506,50508],{},[898,50505,207],{},[1712,50507,2219],{},[5935,50509,50510],{},[898,50511,1710],{},[898,50513,7544],{},[902,50515,50516],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,50518,50519,50520],{},"(d) ",[883,50521,50523],{"className":50522},[886],[888,50524,50525],{"xmlns":890},[892,50526,50527,50545],{},[895,50528,50529,50531,50533,50535,50537,50539],{},[898,50530,1710],{},[1712,50532,1714],{},[898,50534,207],{},[1712,50536,2219],{},[898,50538,7544],{},[2037,50540,50541,50543],{},[898,50542,1734],{},[1716,50544,2787],{},[902,50546,50547],{"encoding":904},"P = a - bQ^2",[123,50549,50550,50551],{},"(e) ",[883,50552,50554],{"className":50553},[886],[888,50555,50556],{"xmlns":890},[892,50557,50558,50580],{},[895,50559,50560,50562,50564,50566,50576,50578],{},[898,50561,1734],{},[1712,50563,1714],{},[898,50565,7544],{},[2037,50567,50568,50570],{},[898,50569,1710],{},[895,50571,50572,50574],{},[1712,50573,2219],{},[898,50575,207],{},[1712,50577,3145],{},[898,50579,7585],{},[902,50581,50582],{"encoding":904},"Q = bP^{-a} + c",[123,50584,50585,50586],{},"(f) ",[883,50587,50589],{"className":50588},[886],[888,50590,50591],{"xmlns":890},[892,50592,50593,50616],{},[895,50594,50595,50597,50599,50601,50603],{},[898,50596,1734],{},[1712,50598,1714],{},[898,50600,207],{},[1712,50602,1783],{},[2037,50604,50605,50608],{},[898,50606,50607],{},"e",[895,50609,50610,50612,50614],{},[1712,50611,2219],{},[898,50613,7544],{},[898,50615,1710],{},[902,50617,50618],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,50620,50621,50624],{},[38,50622,50623],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,50626,50627,50630,50633],{},[123,50628,50629],{},"(a) Cena substitutu.",[123,50631,50632],{},"(b) Cena komplementu.",[123,50634,50635],{},"(c) Výdaje na reklamu.",[724,50637,50638,50301,50640,50674,50675,50703],{},[38,50639,29517],{},[883,50641,50643],{"className":50642},[886],[888,50644,50645],{"xmlns":890},[892,50646,50647,50671],{},[895,50648,50649,50651,50653,50655,50657,50659,50661,50663,50665,50667,50669],{},[898,50650,1710],{},[1712,50652,1714],{},[898,50654,1969],{},[1712,50656,1904],{"stretchy":1903},[898,50658,1734],{},[1712,50660,1910],{"stretchy":1903},[1712,50662,1714],{},[1716,50664,8912],{},[1712,50666,2219],{},[1716,50668,2787],{},[898,50670,1734],{},[902,50672,50673],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,50676,50678],{"className":50677},[886],[888,50679,50680],{"xmlns":890},[892,50681,50682,50700],{},[895,50683,50684,50686,50688,50694,50696,50698],{},[898,50685,1710],{},[1712,50687,1714],{},[2037,50689,50690,50692],{},[898,50691,1969],{},[1712,50693,2145],{},[1712,50695,1904],{"stretchy":1903},[898,50697,1734],{},[1712,50699,1910],{"stretchy":1903},[902,50701,50702],{"encoding":904},"P = D^*(Q)",", na kterou se změní původní poptávka v důsledku uložení daně 6 Kč na kupujícího na každou jednotku zboží. Graficky interpretujte.",[724,50705,50706,50709],{},[38,50707,50708],{},"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:",[120,50711,50712,50796,50872,50958,51046],{},[123,50713,50420,50714,1343,50754,1659],{},[883,50715,50717],{"className":50716},[886],[888,50718,50719],{"xmlns":890},[892,50720,50721,50751],{},[895,50722,50723,50729,50731,50733,50735,50737,50743,50745],{},[6927,50724,50725,50727],{},[898,50726,28128],{},[1716,50728,2222],{},[1712,50730,1714],{},[1716,50732,6857],{},[1712,50734,2219],{},[1716,50736,2975],{},[6927,50738,50739,50741],{},[898,50740,2044],{},[1716,50742,2222],{},[1712,50744,3145],{},[6927,50746,50747,50749],{},[898,50748,2044],{},[1716,50750,2787],{},[902,50752,50753],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,50755,50757],{"className":50756},[886],[888,50758,50759],{"xmlns":890},[892,50760,50761,50793],{},[895,50762,50763,50769,50771,50773,50775,50777,50783,50785,50787],{},[6927,50764,50765,50767],{},[898,50766,28128],{},[1716,50768,2787],{},[1712,50770,1714],{},[1716,50772,1718],{},[1712,50774,3145],{},[1716,50776,2787],{},[6927,50778,50779,50781],{},[898,50780,2044],{},[1716,50782,2222],{},[1712,50784,2219],{},[1716,50786,2975],{},[6927,50788,50789,50791],{},[898,50790,2044],{},[1716,50792,2787],{},[902,50794,50795],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,50797,50453,50798,1343,50840,1659],{},[883,50799,50801],{"className":50800},[886],[888,50802,50803],{"xmlns":890},[892,50804,50805,50837],{},[895,50806,50807,50813,50815,50817,50819,50821,50827,50829,50831],{},[6927,50808,50809,50811],{},[898,50810,28128],{},[1716,50812,2222],{},[1712,50814,1714],{},[1716,50816,2782],{},[1712,50818,2219],{},[1716,50820,1718],{},[6927,50822,50823,50825],{},[898,50824,2044],{},[1716,50826,2222],{},[1712,50828,2219],{},[1716,50830,6209],{},[6927,50832,50833,50835],{},[898,50834,2044],{},[1716,50836,2787],{},[902,50838,50839],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,50841,50843],{"className":50842},[886],[888,50844,50845],{"xmlns":890},[892,50846,50847,50869],{},[895,50848,50849,50855,50857,50859,50861,50863],{},[6927,50850,50851,50853],{},[898,50852,28128],{},[1716,50854,2787],{},[1712,50856,1714],{},[1716,50858,41119],{},[1712,50860,2219],{},[1716,50862,1718],{},[6927,50864,50865,50867],{},[898,50866,2044],{},[1716,50868,2787],{},[902,50870,50871],{"encoding":904},"B_2 = 15 - 10A_2",[123,50873,50484,50874,1343,50916,1659],{},[883,50875,50877],{"className":50876},[886],[888,50878,50879],{"xmlns":890},[892,50880,50881,50913],{},[895,50882,50883,50889,50891,50893,50895,50897,50903,50905,50907],{},[6927,50884,50885,50887],{},[898,50886,28128],{},[1716,50888,2222],{},[1712,50890,1714],{},[1716,50892,42894],{},[1712,50894,2219],{},[1716,50896,2787],{},[6927,50898,50899,50901],{},[898,50900,2044],{},[1716,50902,2222],{},[1712,50904,2219],{},[1716,50906,2975],{},[6927,50908,50909,50911],{},[898,50910,2044],{},[1716,50912,2787],{},[902,50914,50915],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,50917,50919],{"className":50918},[886],[888,50920,50921],{"xmlns":890},[892,50922,50923,50955],{},[895,50924,50925,50931,50933,50935,50937,50939,50945,50947,50949],{},[6927,50926,50927,50929],{},[898,50928,28128],{},[1716,50930,2787],{},[1712,50932,1714],{},[1716,50934,41119],{},[1712,50936,3145],{},[1716,50938,2787],{},[6927,50940,50941,50943],{},[898,50942,2044],{},[1716,50944,2222],{},[1712,50946,2219],{},[1716,50948,2787],{},[6927,50950,50951,50953],{},[898,50952,2044],{},[1716,50954,2787],{},[902,50956,50957],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,50959,50519,50960,1343,51004,1659],{},[883,50961,50963],{"className":50962},[886],[888,50964,50965],{"xmlns":890},[892,50966,50967,51001],{},[895,50968,50969,50975,50977,50979,50981,50983,50985,50991,50993,50995],{},[6927,50970,50971,50973],{},[898,50972,28128],{},[1716,50974,2222],{},[1712,50976,1714],{},[1712,50978,2219],{},[1716,50980,6857],{},[1712,50982,2219],{},[1716,50984,2787],{},[6927,50986,50987,50989],{},[898,50988,2044],{},[1716,50990,2222],{},[1712,50992,3145],{},[1716,50994,6198],{},[6927,50996,50997,50999],{},[898,50998,2044],{},[1716,51000,2787],{},[902,51002,51003],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,51005,51007],{"className":51006},[886],[888,51008,51009],{"xmlns":890},[892,51010,51011,51043],{},[895,51012,51013,51019,51021,51023,51025,51027,51033,51035,51037],{},[6927,51014,51015,51017],{},[898,51016,28128],{},[1716,51018,2787],{},[1712,51020,1714],{},[1716,51022,1718],{},[1712,51024,3145],{},[1716,51026,2787],{},[6927,51028,51029,51031],{},[898,51030,2044],{},[1716,51032,2222],{},[1712,51034,2219],{},[1716,51036,2787],{},[6927,51038,51039,51041],{},[898,51040,2044],{},[1716,51042,2787],{},[902,51044,51045],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,51047,50550,51048,1343,51090,1659],{},[883,51049,51051],{"className":51050},[886],[888,51052,51053],{"xmlns":890},[892,51054,51055,51087],{},[895,51056,51057,51063,51065,51067,51069,51071,51077,51079,51081],{},[6927,51058,51059,51061],{},[898,51060,28128],{},[1716,51062,2222],{},[1712,51064,1714],{},[1716,51066,6857],{},[1712,51068,3145],{},[1716,51070,2787],{},[6927,51072,51073,51075],{},[898,51074,2044],{},[1716,51076,2222],{},[1712,51078,3145],{},[1716,51080,2975],{},[6927,51082,51083,51085],{},[898,51084,2044],{},[1716,51086,2787],{},[902,51088,51089],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,51091,51093],{"className":51092},[886],[888,51094,51095],{"xmlns":890},[892,51096,51097,51129],{},[895,51098,51099,51105,51107,51109,51111,51113,51119,51121,51123],{},[6927,51100,51101,51103],{},[898,51102,28128],{},[1716,51104,2787],{},[1712,51106,1714],{},[1716,51108,3018],{},[1712,51110,2219],{},[1716,51112,6198],{},[6927,51114,51115,51117],{},[898,51116,2044],{},[1716,51118,2222],{},[1712,51120,3145],{},[1716,51122,3068],{},[6927,51124,51125,51127],{},[898,51126,2044],{},[1716,51128,2787],{},[902,51130,51131],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,51133,51135],{"id":51134},"základní-analýza-nabídky","Základní analýza nabídky",[724,51137,51138,51141,51142,51176,51177,51199],{},[38,51139,51140],{},"2.6"," Je dána nabídka ",[883,51143,51145],{"className":51144},[886],[888,51146,51147],{"xmlns":890},[892,51148,51149,51173],{},[895,51150,51151,51153,51155,51157,51159,51161,51163,51165,51167,51169,51171],{},[898,51152,1710],{},[1712,51154,1714],{},[898,51156,6493],{},[1712,51158,1904],{"stretchy":1903},[898,51160,1734],{},[1712,51162,1910],{"stretchy":1903},[1712,51164,1714],{},[1716,51166,6857],{},[1712,51168,3145],{},[1716,51170,6673],{},[898,51172,1734],{},[902,51174,51175],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,51178,51180],{"className":51179},[886],[888,51181,51182],{"xmlns":890},[892,51183,51184,51196],{},[895,51185,51186,51188,51190,51192,51194],{},[1716,51187,2809],{},[1712,51189,3138],{"separator":2565},[1716,51191,42894],{},[1712,51193,3138],{"separator":2565},[1716,51195,19912],{},[902,51197,51198],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,51201,51202,51205,51206,51223],{},[38,51203,51204],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,51207,51209],{"className":51208},[886],[888,51210,51211],{"xmlns":890},[892,51212,51213,51221],{},[895,51214,51215,51217,51219],{},[898,51216,1710],{},[1712,51218,3138],{"separator":2565},[898,51220,1734],{},[902,51222,50388],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,51225,51226,51252,51280,51313,51347,51383],{},[123,51227,50420,51228],{},[883,51229,51231],{"className":51230},[886],[888,51232,51233],{"xmlns":890},[892,51234,51235,51249],{},[895,51236,51237,51239,51241,51243,51245,51247],{},[898,51238,1710],{},[1712,51240,1714],{},[1716,51242,42894],{},[1712,51244,3145],{},[1716,51246,2787],{},[898,51248,1734],{},[902,51250,51251],{"encoding":904},"P = 30 + 2Q",[123,51253,50453,51254],{},[883,51255,51257],{"className":51256},[886],[888,51258,51259],{"xmlns":890},[892,51260,51261,51277],{},[895,51262,51263,51265,51267,51269,51271,51273,51275],{},[898,51264,1734],{},[1712,51266,1714],{},[1712,51268,2219],{},[1716,51270,6198],{},[1712,51272,3145],{},[1716,51274,8912],{},[898,51276,1710],{},[902,51278,51279],{"encoding":904},"Q = -3 + 12P",[123,51281,50484,51282],{},[883,51283,51285],{"className":51284},[886],[888,51286,51287],{"xmlns":890},[892,51288,51289,51311],{},[895,51290,51291,51293,51295,51301,51303,51305,51307,51309],{},[898,51292,1710],{},[1712,51294,1714],{},[2037,51296,51297,51299],{},[898,51298,1734],{},[1716,51300,2787],{},[1712,51302,3145],{},[1716,51304,27821],{},[898,51306,1734],{},[1712,51308,3145],{},[1716,51310,37421],{},[902,51312,46597],{"encoding":904},[123,51314,50519,51315],{},[883,51316,51318],{"className":51317},[886],[888,51319,51320],{"xmlns":890},[892,51321,51322,51344],{},[895,51323,51324,51326,51328,51334,51336,51338,51340,51342],{},[898,51325,1710],{},[1712,51327,1714],{},[2037,51329,51330,51332],{},[898,51331,1734],{},[1716,51333,2787],{},[1712,51335,3145],{},[1716,51337,2787],{},[898,51339,1734],{},[1712,51341,3145],{},[1716,51343,8912],{},[902,51345,51346],{"encoding":904},"P = Q^2 + 2Q + 12",[123,51348,50550,51349],{},[883,51350,51352],{"className":51351},[886],[888,51353,51354],{"xmlns":890},[892,51355,51356,51380],{},[895,51357,51358,51360,51362,51364,51366,51368,51370,51372,51374],{},[898,51359,1734],{},[1712,51361,1714],{},[1716,51363,6624],{},[1712,51365,3145],{},[1716,51367,3068],{},[898,51369,1710],{},[1712,51371,3145],{},[1716,51373,6607],{},[2037,51375,51376,51378],{},[898,51377,1710],{},[1716,51379,2787],{},[902,51381,51382],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,51384,50585,51385],{},[883,51386,51388],{"className":51387},[886],[888,51389,51390],{"xmlns":890},[892,51391,51392,51417],{},[895,51393,51394,51396,51398,51400,51402,51404,51406,51408,51411],{},[898,51395,1734],{},[1712,51397,1714],{},[1716,51399,29076],{},[1712,51401,3145],{},[1716,51403,6607],{},[898,51405,1710],{},[1712,51407,3145],{},[1716,51409,51410],{},"0,004",[2037,51412,51413,51415],{},[898,51414,1710],{},[1716,51416,2787],{},[902,51418,51419],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,51421,51422,51425],{},[38,51423,51424],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,51427,51428,51431,51434,51437],{},[123,51429,51430],{},"(a) Sníží ceny surovin — vstupů.",[123,51432,51433],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,51435,51436],{},"(c) Zvýší ceny všech energií.",[123,51438,51439],{},"(d) Sníží daňové odvody státu.",[724,51441,51442,51141,51444,51478,51479,51507],{},[38,51443,47824],{},[883,51445,51447],{"className":51446},[886],[888,51448,51449],{"xmlns":890},[892,51450,51451,51475],{},[895,51452,51453,51455,51457,51459,51461,51463,51465,51467,51469,51471,51473],{},[898,51454,1710],{},[1712,51456,1714],{},[898,51458,6493],{},[1712,51460,1904],{"stretchy":1903},[898,51462,1734],{},[1712,51464,1910],{"stretchy":1903},[1712,51466,1714],{},[1716,51468,2814],{},[898,51470,1734],{},[1712,51472,3145],{},[1716,51474,41119],{},[902,51476,51477],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,51480,51482],{"className":51481},[886],[888,51483,51484],{"xmlns":890},[892,51485,51486,51504],{},[895,51487,51488,51490,51492,51498,51500,51502],{},[898,51489,1710],{},[1712,51491,1714],{},[2037,51493,51494,51496],{},[898,51495,6493],{},[1712,51497,2145],{},[1712,51499,1904],{"stretchy":1903},[898,51501,1734],{},[1712,51503,1910],{"stretchy":1903},[902,51505,51506],{"encoding":904},"P = S^*(Q)",", na kterou se změní původní nabídka v důsledku uložení daně 5 Kč na výrobce na každou jednotku zboží. Graficky interpretujte.",[198,51509,46200],{"id":51510},"tržní-rovnováha-1",[724,51512,51513,51515,51516,51533,51534,2854],{},[38,51514,47884],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,51517,51519],{"className":51518},[886],[888,51520,51521],{"xmlns":890},[892,51522,51523,51531],{},[895,51524,51525],{},[2037,51526,51527,51529],{},[898,51528,1734],{},[898,51530,2041],{},[902,51532,47278],{"encoding":904}," a rovnovážnou cenu ",[883,51535,51537],{"className":51536},[886],[888,51538,51539],{"xmlns":890},[892,51540,51541,51549],{},[895,51542,51543],{},[2037,51544,51545,51547],{},[898,51546,1710],{},[898,51548,2041],{},[902,51550,46341],{"encoding":904},[120,51552,51553,51606,51657,51716],{},[123,51554,50420,51555,1343,51582,1659],{},[883,51556,51558],{"className":51557},[886],[888,51559,51560],{"xmlns":890},[892,51561,51562,51579],{},[895,51563,51564,51566,51568,51570,51572,51574,51576],{},[898,51565,1710],{},[1712,51567,1714],{},[1712,51569,2219],{},[1716,51571,3068],{},[898,51573,1734],{},[1712,51575,3145],{},[1716,51577,51578],{},"80",[902,51580,51581],{"encoding":904},"P = -5Q + 80",[883,51583,51585],{"className":51584},[886],[888,51586,51587],{"xmlns":890},[892,51588,51589,51603],{},[895,51590,51591,51593,51595,51597,51599,51601],{},[898,51592,1710],{},[1712,51594,1714],{},[1716,51596,2787],{},[898,51598,1734],{},[1712,51600,3145],{},[1716,51602,1718],{},[902,51604,51605],{"encoding":904},"P = 2Q + 10",[123,51607,50453,51608,1343,51634,1659],{},[883,51609,51611],{"className":51610},[886],[888,51612,51613],{"xmlns":890},[892,51614,51615,51631],{},[895,51616,51617,51619,51621,51623,51625,51627,51629],{},[898,51618,1734],{},[1712,51620,1714],{},[1712,51622,2219],{},[1716,51624,2814],{},[898,51626,1710],{},[1712,51628,3145],{},[1716,51630,2809],{},[902,51632,51633],{"encoding":904},"Q = -0{,}5P + 25",[883,51635,51637],{"className":51636},[886],[888,51638,51639],{"xmlns":890},[892,51640,51641,51655],{},[895,51642,51643,51645,51647,51649,51651,51653],{},[898,51644,1734],{},[1712,51646,1714],{},[1716,51648,2787],{},[898,51650,1710],{},[1712,51652,2219],{},[1716,51654,2782],{},[902,51656,45722],{"encoding":904},[123,51658,50484,51659,1343,51685,1659],{},[883,51660,51662],{"className":51661},[886],[888,51663,51664],{"xmlns":890},[892,51665,51666,51682],{},[895,51667,51668,51670,51672,51674,51676,51678,51680],{},[898,51669,1710],{},[1712,51671,1714],{},[1712,51673,2219],{},[1716,51675,2975],{},[898,51677,1734],{},[1712,51679,3145],{},[1716,51681,1829],{},[902,51683,51684],{"encoding":904},"P = -4Q + 120",[883,51686,51688],{"className":51687},[886],[888,51689,51690],{"xmlns":890},[892,51691,51692,51713],{},[895,51693,51694,51696,51698,51706,51708,51710],{},[898,51695,1710],{},[1712,51697,1714],{},[2563,51699,51700],{"scriptlevel":2085,"displaystyle":1903},[2567,51701,51702,51704],{},[1716,51703,2222],{},[1716,51705,6198],{},[898,51707,1734],{},[1712,51709,3145],{},[1716,51711,51712],{},"29",[902,51714,51715],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,51717,50519,51718,1343,51747,1659],{},[883,51719,51721],{"className":51720},[886],[888,51722,51723],{"xmlns":890},[892,51724,51725,51744],{},[895,51726,51727,51729,51731,51733,51739,51741],{},[898,51728,1710],{},[1712,51730,1714],{},[1712,51732,2219],{},[2037,51734,51735,51737],{},[898,51736,1734],{},[1716,51738,2787],{},[1712,51740,3145],{},[1716,51742,51743],{},"52",[902,51745,51746],{"encoding":904},"P = -Q^2 + 52",[883,51748,51750],{"className":51749},[886],[888,51751,51752],{"xmlns":890},[892,51753,51754,51772],{},[895,51755,51756,51758,51760,51762,51768,51770],{},[898,51757,1710],{},[1712,51759,1714],{},[1716,51761,2787],{},[2037,51763,51764,51766],{},[898,51765,1734],{},[1716,51767,2787],{},[1712,51769,3145],{},[1716,51771,1718],{},[902,51773,51774],{"encoding":904},"P = 2Q^2 + 10",[724,51776,51777,51780,51781,51811,51812,51842],{},[38,51778,51779],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,51782,51784],{"className":51783},[886],[888,51785,51786],{"xmlns":890},[892,51787,51788,51808],{},[895,51789,51790,51798,51800],{},[6989,51791,51792,51794,51796],{},[898,51793,1734],{},[1716,51795,2222],{},[898,51797,2041],{},[1712,51799,3138],{"separator":2565},[6989,51801,51802,51804,51806],{},[898,51803,1734],{},[1716,51805,2787],{},[898,51807,2041],{},[902,51809,51810],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,51813,51815],{"className":51814},[886],[888,51816,51817],{"xmlns":890},[892,51818,51819,51839],{},[895,51820,51821,51829,51831],{},[6989,51822,51823,51825,51827],{},[898,51824,1710],{},[1716,51826,2222],{},[898,51828,2041],{},[1712,51830,3138],{"separator":2565},[6989,51832,51833,51835,51837],{},[898,51834,1710],{},[1716,51836,2787],{},[898,51838,2041],{},[902,51840,51841],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,51844,51845,51997],{},[123,51846,50420,51847,1343,51887,1343,51929,1343,51963,1659],{},[883,51848,51850],{"className":51849},[886],[888,51851,51852],{"xmlns":890},[892,51853,51854,51884],{},[895,51855,51856,51862,51864,51866,51868,51870,51876,51878],{},[6927,51857,51858,51860],{},[898,51859,1734],{},[1716,51861,2222],{},[1712,51863,1714],{},[1716,51865,1718],{},[1712,51867,2219],{},[1716,51869,2787],{},[6927,51871,51872,51874],{},[898,51873,1710],{},[1716,51875,2222],{},[1712,51877,3145],{},[6927,51879,51880,51882],{},[898,51881,1710],{},[1716,51883,2787],{},[902,51885,51886],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,51888,51890],{"className":51889},[886],[888,51891,51892],{"xmlns":890},[892,51893,51894,51926],{},[895,51895,51896,51902,51904,51906,51908,51910,51916,51918,51920],{},[6927,51897,51898,51900],{},[898,51899,1734],{},[1716,51901,2787],{},[1712,51903,1714],{},[1716,51905,3068],{},[1712,51907,3145],{},[1716,51909,2787],{},[6927,51911,51912,51914],{},[898,51913,1710],{},[1716,51915,2222],{},[1712,51917,2219],{},[1716,51919,2787],{},[6927,51921,51922,51924],{},[898,51923,1710],{},[1716,51925,2787],{},[902,51927,51928],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,51930,51932],{"className":51931},[886],[888,51933,51934],{"xmlns":890},[892,51935,51936,51960],{},[895,51937,51938,51944,51946,51948,51950,51952,51954],{},[6927,51939,51940,51942],{},[898,51941,1734],{},[1716,51943,2222],{},[1712,51945,1714],{},[1712,51947,2219],{},[1716,51949,6198],{},[1712,51951,3145],{},[1716,51953,2787],{},[6927,51955,51956,51958],{},[898,51957,1710],{},[1716,51959,2222],{},[902,51961,51962],{"encoding":904},"Q_1 = -3 + 2P_1",[883,51964,51966],{"className":51965},[886],[888,51967,51968],{"xmlns":890},[892,51969,51970,51994],{},[895,51971,51972,51978,51980,51982,51984,51986,51988],{},[6927,51973,51974,51976],{},[898,51975,1734],{},[1716,51977,2787],{},[1712,51979,1714],{},[1712,51981,2219],{},[1716,51983,2787],{},[1712,51985,3145],{},[1716,51987,6198],{},[6927,51989,51990,51992],{},[898,51991,1710],{},[1716,51993,2787],{},[902,51995,51996],{"encoding":904},"Q_2 = -2 + 3P_2",[123,51998,50453,51999,1343,52039,1343,52081,1343,52113,1659],{},[883,52000,52002],{"className":52001},[886],[888,52003,52004],{"xmlns":890},[892,52005,52006,52036],{},[895,52007,52008,52014,52016,52018,52020,52022,52028,52030],{},[6927,52009,52010,52012],{},[898,52011,1734],{},[1716,52013,2222],{},[1712,52015,1714],{},[1716,52017,1739],{},[1712,52019,2219],{},[1716,52021,2787],{},[6927,52023,52024,52026],{},[898,52025,1710],{},[1716,52027,2222],{},[1712,52029,3145],{},[6927,52031,52032,52034],{},[898,52033,1710],{},[1716,52035,2787],{},[902,52037,52038],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,52040,52042],{"className":52041},[886],[888,52043,52044],{"xmlns":890},[892,52045,52046,52078],{},[895,52047,52048,52054,52056,52058,52060,52062,52068,52070,52072],{},[6927,52049,52050,52052],{},[898,52051,1734],{},[1716,52053,2787],{},[1712,52055,1714],{},[1716,52057,3068],{},[1712,52059,3145],{},[1716,52061,2787],{},[6927,52063,52064,52066],{},[898,52065,1710],{},[1716,52067,2222],{},[1712,52069,2219],{},[1716,52071,6198],{},[6927,52073,52074,52076],{},[898,52075,1710],{},[1716,52077,2787],{},[902,52079,52080],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,52082,52084],{"className":52083},[886],[888,52085,52086],{"xmlns":890},[892,52087,52088,52110],{},[895,52089,52090,52096,52098,52100,52102,52104],{},[6927,52091,52092,52094],{},[898,52093,1734],{},[1716,52095,2222],{},[1712,52097,1714],{},[1712,52099,2219],{},[1716,52101,1718],{},[1712,52103,3145],{},[6927,52105,52106,52108],{},[898,52107,1710],{},[1716,52109,2222],{},[902,52111,52112],{"encoding":904},"Q_1 = -10 + P_1",[883,52114,52116],{"className":52115},[886],[888,52117,52118],{"xmlns":890},[892,52119,52120,52142],{},[895,52121,52122,52128,52130,52132,52134,52136],{},[6927,52123,52124,52126],{},[898,52125,1734],{},[1716,52127,2787],{},[1712,52129,1714],{},[1716,52131,3068],{},[1712,52133,3145],{},[1716,52135,6209],{},[6927,52137,52138,52140],{},[898,52139,1710],{},[1716,52141,2787],{},[902,52143,52144],{"encoding":904},"Q_2 = 5 + 6P_2",[724,52146,52147,52150,52151,1343,52199,1343,52245,52295,52296,1343,52328,1343,52362,26469,52396,1655,52414,52432,52433,52446,52447,52473,52474,51811,52514,1659],{},[38,52148,52149],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,52152,52154],{"className":52153},[886],[888,52155,52156],{"xmlns":890},[892,52157,52158,52196],{},[895,52159,52160,52166,52168,52170,52172,52178,52180,52182,52188,52190],{},[6927,52161,52162,52164],{},[898,52163,1734],{},[1716,52165,2222],{},[1712,52167,1714],{},[1716,52169,41119],{},[1712,52171,2219],{},[6927,52173,52174,52176],{},[898,52175,1710],{},[1716,52177,2222],{},[1712,52179,3145],{},[1716,52181,2787],{},[6927,52183,52184,52186],{},[898,52185,1710],{},[1716,52187,2787],{},[1712,52189,3145],{},[6927,52191,52192,52194],{},[898,52193,1710],{},[1716,52195,6198],{},[902,52197,52198],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,52200,52202],{"className":52201},[886],[888,52203,52204],{"xmlns":890},[892,52205,52206,52242],{},[895,52207,52208,52214,52216,52218,52220,52226,52228,52234,52236],{},[6927,52209,52210,52212],{},[898,52211,1734],{},[1716,52213,2787],{},[1712,52215,1714],{},[1716,52217,1780],{},[1712,52219,3145],{},[6927,52221,52222,52224],{},[898,52223,1710],{},[1716,52225,2222],{},[1712,52227,2219],{},[6927,52229,52230,52232],{},[898,52231,1710],{},[1716,52233,2787],{},[1712,52235,2219],{},[6927,52237,52238,52240],{},[898,52239,1710],{},[1716,52241,6198],{},[902,52243,52244],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,52246,52248],{"className":52247},[886],[888,52249,52250],{"xmlns":890},[892,52251,52252,52292],{},[895,52253,52254,52260,52262,52264,52266,52268,52274,52276,52282,52284,52286],{},[6927,52255,52256,52258],{},[898,52257,1734],{},[1716,52259,6198],{},[1712,52261,1714],{},[1716,52263,3397],{},[1712,52265,3145],{},[1716,52267,2787],{},[6927,52269,52270,52272],{},[898,52271,1710],{},[1716,52273,2222],{},[1712,52275,2219],{},[6927,52277,52278,52280],{},[898,52279,1710],{},[1716,52281,2787],{},[1712,52283,2219],{},[1716,52285,2975],{},[6927,52287,52288,52290],{},[898,52289,1710],{},[1716,52291,6198],{},[902,52293,52294],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,52297,52299],{"className":52298},[886],[888,52300,52301],{"xmlns":890},[892,52302,52303,52325],{},[895,52304,52305,52311,52313,52315,52317,52319],{},[6927,52306,52307,52309],{},[898,52308,1734],{},[1716,52310,2222],{},[1712,52312,1714],{},[1712,52314,2219],{},[1716,52316,29076],{},[1712,52318,3145],{},[6927,52320,52321,52323],{},[898,52322,1710],{},[1716,52324,2222],{},[902,52326,52327],{"encoding":904},"Q_1 = -7 + P_1",[883,52329,52331],{"className":52330},[886],[888,52332,52333],{"xmlns":890},[892,52334,52335,52359],{},[895,52336,52337,52343,52345,52347,52349,52351,52353],{},[6927,52338,52339,52341],{},[898,52340,1734],{},[1716,52342,2787],{},[1712,52344,1714],{},[1712,52346,2219],{},[1716,52348,2975],{},[1712,52350,3145],{},[1716,52352,2975],{},[6927,52354,52355,52357],{},[898,52356,1710],{},[1716,52358,2787],{},[902,52360,52361],{"encoding":904},"Q_2 = -4 + 4P_2",[883,52363,52365],{"className":52364},[886],[888,52366,52367],{"xmlns":890},[892,52368,52369,52393],{},[895,52370,52371,52377,52379,52381,52383,52385,52387],{},[6927,52372,52373,52375],{},[898,52374,1734],{},[1716,52376,6198],{},[1712,52378,1714],{},[1712,52380,2219],{},[1716,52382,3068],{},[1712,52384,3145],{},[1716,52386,2787],{},[6927,52388,52389,52391],{},[898,52390,1710],{},[1716,52392,6198],{},[902,52394,52395],{"encoding":904},"Q_3 = -5 + 2P_3",[883,52397,52399],{"className":52398},[886],[888,52400,52401],{"xmlns":890},[892,52402,52403,52411],{},[895,52404,52405],{},[6927,52406,52407,52409],{},[898,52408,1734],{},[898,52410,22665],{},[902,52412,52413],{"encoding":904},"Q_i",[883,52415,52417],{"className":52416},[886],[888,52418,52419],{"xmlns":890},[892,52420,52421,52429],{},[895,52422,52423],{},[6927,52424,52425,52427],{},[898,52426,1710],{},[898,52428,22665],{},[902,52430,52431],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,52434,52436],{"className":52435},[886],[888,52437,52438],{"xmlns":890},[892,52439,52440,52444],{},[895,52441,52442],{},[898,52443,22665],{},[902,52445,22665],{"encoding":904},"-tého zboží, ",[883,52448,52450],{"className":52449},[886],[888,52451,52452],{"xmlns":890},[892,52453,52454,52470],{},[895,52455,52456,52458,52460,52462,52464,52466,52468],{},[898,52457,22665],{},[1712,52459,1714],{},[1716,52461,2222],{},[1712,52463,3138],{"separator":2565},[1716,52465,2787],{},[1712,52467,3138],{"separator":2565},[1716,52469,6198],{},[902,52471,52472],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,52475,52477],{"className":52476},[886],[888,52478,52479],{"xmlns":890},[892,52480,52481,52511],{},[895,52482,52483,52491,52493,52501,52503],{},[6989,52484,52485,52487,52489],{},[898,52486,1734],{},[1716,52488,2222],{},[898,52490,2041],{},[1712,52492,3138],{"separator":2565},[6989,52494,52495,52497,52499],{},[898,52496,1734],{},[1716,52498,2787],{},[898,52500,2041],{},[1712,52502,3138],{"separator":2565},[6989,52504,52505,52507,52509],{},[898,52506,1734],{},[1716,52508,6198],{},[898,52510,2041],{},[902,52512,52513],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,52515,52517],{"className":52516},[886],[888,52518,52519],{"xmlns":890},[892,52520,52521,52551],{},[895,52522,52523,52531,52533,52541,52543],{},[6989,52524,52525,52527,52529],{},[898,52526,1710],{},[1716,52528,2222],{},[898,52530,2041],{},[1712,52532,3138],{"separator":2565},[6989,52534,52535,52537,52539],{},[898,52536,1710],{},[1716,52538,2787],{},[898,52540,2041],{},[1712,52542,3138],{"separator":2565},[6989,52544,52545,52547,52549],{},[898,52546,1710],{},[1716,52548,6198],{},[898,52550,2041],{},[902,52552,52553],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,52555,52556,52559,52560,52596,52597,1659],{},[38,52557,52558],{},"2.13"," Jsou dány poptávka ",[883,52561,52563],{"className":52562},[886],[888,52564,52565],{"xmlns":890},[892,52566,52567,52593],{},[895,52568,52569,52571,52573,52575,52577,52579,52581,52583,52585,52587,52589,52591],{},[898,52570,1710],{},[1712,52572,1714],{},[898,52574,1969],{},[1712,52576,1904],{"stretchy":1903},[898,52578,1734],{},[1712,52580,1910],{"stretchy":1903},[1712,52582,1714],{},[1712,52584,2219],{},[1716,52586,2975],{},[898,52588,1734],{},[1712,52590,3145],{},[1716,52592,51578],{},[902,52594,52595],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,52598,52600],{"className":52599},[886],[888,52601,52602],{"xmlns":890},[892,52603,52604,52628],{},[895,52605,52606,52608,52610,52612,52614,52616,52618,52620,52622,52624,52626],{},[898,52607,1710],{},[1712,52609,1714],{},[898,52611,6493],{},[1712,52613,1904],{"stretchy":1903},[898,52615,1734],{},[1712,52617,1910],{"stretchy":1903},[1712,52619,1714],{},[1716,52621,6198],{},[898,52623,1734],{},[1712,52625,3145],{},[1716,52627,1718],{},[902,52629,52630],{"encoding":904},"P = S(Q) = 3Q + 10",[120,52632,52633,52670,52734,52794],{},[123,52634,52635,52636,51533,52653,1659],{},"(a) Určete rovnovážné množství ",[883,52637,52639],{"className":52638},[886],[888,52640,52641],{"xmlns":890},[892,52642,52643,52651],{},[895,52644,52645],{},[2037,52646,52647,52649],{},[898,52648,1734],{},[898,52650,2041],{},[902,52652,47278],{"encoding":904},[883,52654,52656],{"className":52655},[886],[888,52657,52658],{"xmlns":890},[892,52659,52660,52668],{},[895,52661,52662],{},[2037,52663,52664,52666],{},[898,52665,1710],{},[898,52667,2041],{},[902,52669,46341],{"encoding":904},[123,52671,52672,52673,52691,52692,52712,52713,52733],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,52674,52676],{"className":52675},[886],[888,52677,52678],{"xmlns":890},[892,52679,52680,52688],{},[895,52681,52682,52684,52686],{},[898,52683,1772],{},[1712,52685,1714],{},[1716,52687,29076],{},[902,52689,52690],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,52693,52695],{"className":52694},[886],[888,52696,52697],{"xmlns":890},[892,52698,52699,52709],{},[895,52700,52701],{},[6989,52702,52703,52705,52707],{},[898,52704,1734],{},[1716,52706,2222],{},[898,52708,2041],{},[902,52710,52711],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,52714,52716],{"className":52715},[886],[888,52717,52718],{"xmlns":890},[892,52719,52720,52730],{},[895,52721,52722],{},[6989,52723,52724,52726,52728],{},[898,52725,1710],{},[1716,52727,2222],{},[898,52729,2041],{},[902,52731,52732],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,52735,52736,52737,52691,52754,52712,52774,52733],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,52738,52740],{"className":52739},[886],[888,52741,52742],{"xmlns":890},[892,52743,52744,52752],{},[895,52745,52746,52748,52750],{},[898,52747,1772],{},[1712,52749,1714],{},[1716,52751,29076],{},[902,52753,52690],{"encoding":904},[883,52755,52757],{"className":52756},[886],[888,52758,52759],{"xmlns":890},[892,52760,52761,52771],{},[895,52762,52763],{},[6989,52764,52765,52767,52769],{},[898,52766,1734],{},[1716,52768,2787],{},[898,52770,2041],{},[902,52772,52773],{"encoding":904},"Q_2^E",[883,52775,52777],{"className":52776},[886],[888,52778,52779],{"xmlns":890},[892,52780,52781,52791],{},[895,52782,52783],{},[6989,52784,52785,52787,52789],{},[898,52786,1710],{},[1716,52788,2787],{},[898,52790,2041],{},[902,52792,52793],{"encoding":904},"P_2^E",[123,52795,52796],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,52798,52799,52800,1659],{},"Viz též ",[207,52801,47596],{"className":52802,"dataFsResolvedFilePath":809,"href":810},[210],[198,52804,47898],{"id":52805},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,52807,52808,52559,52811,52596,52847,1659],{},[38,52809,52810],{},"2.14",[883,52812,52814],{"className":52813},[886],[888,52815,52816],{"xmlns":890},[892,52817,52818,52844],{},[895,52819,52820,52822,52824,52826,52828,52830,52832,52834,52836,52838,52840,52842],{},[898,52821,1710],{},[1712,52823,1714],{},[898,52825,207],{},[898,52827,1734],{},[1712,52829,3145],{},[898,52831,7544],{},[1712,52833,1714],{},[1712,52835,2219],{},[1716,52837,2787],{},[898,52839,1734],{},[1712,52841,3145],{},[1716,52843,2782],{},[902,52845,52846],{"encoding":904},"P = aQ + b = -2Q + 50",[883,52848,52850],{"className":52849},[886],[888,52851,52852],{"xmlns":890},[892,52853,52854,52878],{},[895,52855,52856,52858,52860,52862,52864,52866,52868,52870,52872,52874,52876],{},[898,52857,1710],{},[1712,52859,1714],{},[898,52861,7585],{},[898,52863,1734],{},[1712,52865,3145],{},[898,52867,2468],{},[1712,52869,1714],{},[1716,52871,24196],{},[898,52873,1734],{},[1712,52875,3145],{},[1716,52877,6857],{},[902,52879,52880],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,52882,52883,52919,52922,53008,53061,53141,53195],{},[123,52884,52635,52885,51533,52902,1659],{},[883,52886,52888],{"className":52887},[886],[888,52889,52890],{"xmlns":890},[892,52891,52892,52900],{},[895,52893,52894],{},[2037,52895,52896,52898],{},[898,52897,1734],{},[898,52899,2041],{},[902,52901,47278],{"encoding":904},[883,52903,52905],{"className":52904},[886],[888,52906,52907],{"xmlns":890},[892,52908,52909,52917],{},[895,52910,52911],{},[2037,52912,52913,52915],{},[898,52914,1710],{},[898,52916,2041],{},[902,52918,46341],{"encoding":904},[123,52920,52921],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,52923,52924,52925,52942,52943,8093,52956,3072,52972,52988,52989,1659],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,52926,52928],{"className":52927},[886],[888,52929,52930],{"xmlns":890},[892,52931,52932,52940],{},[895,52933,52934],{},[2037,52935,52936,52938],{},[898,52937,1734],{},[898,52939,2041],{},[902,52941,47278],{"encoding":904}," odpovídající změně ",[883,52944,52946],{"className":52945},[886],[888,52947,52948],{"xmlns":890},[892,52949,52950,52954],{},[895,52951,52952],{},[898,52953,207],{},[902,52955,207],{"encoding":904},[883,52957,52959],{"className":52958},[886],[888,52960,52961],{"xmlns":890},[892,52962,52963,52969],{},[895,52964,52965,52967],{},[1712,52966,2219],{},[1716,52968,2787],{},[902,52970,52971],{"encoding":904},"-2",[883,52973,52975],{"className":52974},[886],[888,52976,52977],{"xmlns":890},[892,52978,52979,52985],{},[895,52980,52981,52983],{},[1712,52982,2219],{},[1716,52984,6198],{},[902,52986,52987],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52990,52992],{"className":52991},[886],[888,52993,52994],{"xmlns":890},[892,52995,52996,53006],{},[895,52997,52998],{},[6989,52999,53000,53002,53004],{},[898,53001,1734],{},[1716,53003,2222],{},[898,53005,2041],{},[902,53007,52711],{"encoding":904},[123,53009,53010,53011,52942,53028,53041,53042,1659],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,53012,53014],{"className":53013},[886],[888,53015,53016],{"xmlns":890},[892,53017,53018,53026],{},[895,53019,53020],{},[2037,53021,53022,53024],{},[898,53023,1734],{},[898,53025,2041],{},[902,53027,47278],{"encoding":904},[883,53029,53031],{"className":53030},[886],[888,53032,53033],{"xmlns":890},[892,53034,53035,53039],{},[895,53036,53037],{},[898,53038,7544],{},[902,53040,7544],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,53043,53045],{"className":53044},[886],[888,53046,53047],{"xmlns":890},[892,53048,53049,53059],{},[895,53050,53051],{},[6989,53052,53053,53055,53057],{},[898,53054,1734],{},[1716,53056,2787],{},[898,53058,2041],{},[902,53060,52773],{"encoding":904},[123,53062,53063,53064,52942,53081,8093,53094,3072,53107,52988,53121,1659],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,53065,53067],{"className":53066},[886],[888,53068,53069],{"xmlns":890},[892,53070,53071,53079],{},[895,53072,53073],{},[2037,53074,53075,53077],{},[898,53076,1734],{},[898,53078,2041],{},[902,53080,47278],{"encoding":904},[883,53082,53084],{"className":53083},[886],[888,53085,53086],{"xmlns":890},[892,53087,53088,53092],{},[895,53089,53090],{},[898,53091,7585],{},[902,53093,7585],{"encoding":904},[883,53095,53097],{"className":53096},[886],[888,53098,53099],{"xmlns":890},[892,53100,53101,53105],{},[895,53102,53103],{},[1716,53104,24196],{},[902,53106,49335],{"encoding":904},[883,53108,53110],{"className":53109},[886],[888,53111,53112],{"xmlns":890},[892,53113,53114,53118],{},[895,53115,53116],{},[1716,53117,19463],{},[902,53119,53120],{"encoding":904},"0{,}8",[883,53122,53124],{"className":53123},[886],[888,53125,53126],{"xmlns":890},[892,53127,53128,53138],{},[895,53129,53130],{},[6989,53131,53132,53134,53136],{},[898,53133,1734],{},[1716,53135,6198],{},[898,53137,2041],{},[902,53139,53140],{"encoding":904},"Q_3^E",[123,53142,53143,53144,52942,53161,53174,53175,1659],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,53145,53147],{"className":53146},[886],[888,53148,53149],{"xmlns":890},[892,53150,53151,53159],{},[895,53152,53153],{},[2037,53154,53155,53157],{},[898,53156,1734],{},[898,53158,2041],{},[902,53160,47278],{"encoding":904},[883,53162,53164],{"className":53163},[886],[888,53165,53166],{"xmlns":890},[892,53167,53168,53172],{},[895,53169,53170],{},[898,53171,2468],{},[902,53173,2468],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,53176,53178],{"className":53177},[886],[888,53179,53180],{"xmlns":890},[892,53181,53182,53192],{},[895,53183,53184],{},[6989,53185,53186,53188,53190],{},[898,53187,1734],{},[1716,53189,2975],{},[898,53191,2041],{},[902,53193,53194],{"encoding":904},"Q_4^E",[123,53196,53197,53198,53215,53216,53229,53230,26295,53243,1343,53258,26295,53271,1655,53285,26295,53298,53313,53314,1659],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,53199,53201],{"className":53200},[886],[888,53202,53203],{"xmlns":890},[892,53204,53205,53213],{},[895,53206,53207],{},[2037,53208,53209,53211],{},[898,53210,1734],{},[898,53212,2041],{},[902,53214,47278],{"encoding":904}," odpovídající změnám ",[883,53217,53219],{"className":53218},[886],[888,53220,53221],{"xmlns":890},[892,53222,53223,53227],{},[895,53224,53225],{},[898,53226,207],{},[902,53228,207],{"encoding":904}," o 1, ",[883,53231,53233],{"className":53232},[886],[888,53234,53235],{"xmlns":890},[892,53236,53237,53241],{},[895,53238,53239],{},[898,53240,7544],{},[902,53242,7544],{"encoding":904},[883,53244,53246],{"className":53245},[886],[888,53247,53248],{"xmlns":890},[892,53249,53250,53256],{},[895,53251,53252,53254],{},[1712,53253,2219],{},[1716,53255,1718],{},[902,53257,24330],{"encoding":904},[883,53259,53261],{"className":53260},[886],[888,53262,53263],{"xmlns":890},[892,53264,53265,53269],{},[895,53266,53267],{},[898,53268,7585],{},[902,53270,7585],{"encoding":904},[883,53272,53274],{"className":53273},[886],[888,53275,53276],{"xmlns":890},[892,53277,53278,53282],{},[895,53279,53280],{},[1716,53281,6607],{},[902,53283,53284],{"encoding":904},"0{,}1",[883,53286,53288],{"className":53287},[886],[888,53289,53290],{"xmlns":890},[892,53291,53292,53296],{},[895,53293,53294],{},[898,53295,2468],{},[902,53297,2468],{"encoding":904},[883,53299,53301],{"className":53300},[886],[888,53302,53303],{"xmlns":890},[892,53304,53305,53311],{},[895,53306,53307,53309],{},[1712,53308,2219],{},[1716,53310,1718],{},[902,53312,24330],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,53315,53317],{"className":53316},[886],[888,53318,53319],{"xmlns":890},[892,53320,53321,53331],{},[895,53322,53323],{},[6989,53324,53325,53327,53329],{},[898,53326,1734],{},[1716,53328,3068],{},[898,53330,2041],{},[902,53332,53333],{"encoding":904},"Q_5^E",[724,53335,53336,52559,53339,52596,53362,1659],{},[38,53337,53338],{},"2.15",[883,53340,53342],{"className":53341},[886],[888,53343,53344],{"xmlns":890},[892,53345,53346,53360],{},[895,53347,53348,53350,53352,53354,53356,53358],{},[898,53349,1710],{},[1712,53351,1714],{},[898,53353,207],{},[898,53355,1734],{},[1712,53357,3145],{},[898,53359,7544],{},[902,53361,41935],{"encoding":904},[883,53363,53365],{"className":53364},[886],[888,53366,53367],{"xmlns":890},[892,53368,53369,53383],{},[895,53370,53371,53373,53375,53377,53379,53381],{},[898,53372,1710],{},[1712,53374,1714],{},[898,53376,7585],{},[898,53378,1734],{},[1712,53380,3145],{},[898,53382,2468],{},[902,53384,45117],{"encoding":904},[120,53386,53387,53462,53479,53588,53641,53695],{},[123,53388,53389,53390,53403,53404,53429,53430,53461],{},"(a) Odvoďte redukovaný tvar pro ",[883,53391,53393],{"className":53392},[886],[888,53394,53395],{"xmlns":890},[892,53396,53397,53401],{},[895,53398,53399],{},[898,53400,1710],{},[902,53402,1710],{"encoding":904},". Stanovte podmínky pro ",[883,53405,53407],{"className":53406},[886],[888,53408,53409],{"xmlns":890},[892,53410,53411,53427],{},[895,53412,53413,53415,53417,53419,53421,53423,53425],{},[898,53414,207],{},[1712,53416,3138],{"separator":2565},[898,53418,7544],{},[1712,53420,3138],{"separator":2565},[898,53422,7585],{},[1712,53424,3138],{"separator":2565},[898,53426,2468],{},[902,53428,48160],{"encoding":904}," tak, aby rovnovážný bod ",[883,53431,53433],{"className":53432},[886],[888,53434,53435],{"xmlns":890},[892,53436,53437,53459],{},[895,53438,53439,53441,53443,53449,53451,53457],{},[898,53440,2041],{},[1712,53442,7910],{"stretchy":1903},[2037,53444,53445,53447],{},[898,53446,1734],{},[898,53448,2041],{},[1712,53450,3138],{"separator":2565},[2037,53452,53453,53455],{},[898,53454,1710],{},[898,53456,2041],{},[1712,53458,7925],{"stretchy":1903},[902,53460,46242],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,53463,53464,53465,53478],{},"(b) Vypočtěte multiplikátory pro ",[883,53466,53468],{"className":53467},[886],[888,53469,53470],{"xmlns":890},[892,53471,53472,53476],{},[895,53473,53474],{},[898,53475,1710],{},[902,53477,1710],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,53480,53481,53482,1343,53502,1343,53520,1343,53538,53556,53557,53574,53575,1659],{},"(c) Pro hodnoty parametrů ",[883,53483,53485],{"className":53484},[886],[888,53486,53487],{"xmlns":890},[892,53488,53489,53499],{},[895,53490,53491,53493,53495,53497],{},[898,53492,207],{},[1712,53494,1714],{},[1712,53496,2219],{},[1716,53498,2787],{},[902,53500,53501],{"encoding":904},"a = -2",[883,53503,53505],{"className":53504},[886],[888,53506,53507],{"xmlns":890},[892,53508,53509,53517],{},[895,53510,53511,53513,53515],{},[898,53512,7544],{},[1712,53514,1714],{},[1716,53516,3018],{},[902,53518,53519],{"encoding":904},"b = 40",[883,53521,53523],{"className":53522},[886],[888,53524,53525],{"xmlns":890},[892,53526,53527,53535],{},[895,53528,53529,53531,53533],{},[898,53530,7585],{},[1712,53532,1714],{},[1716,53534,2814],{},[902,53536,53537],{"encoding":904},"c = 0{,}5",[883,53539,53541],{"className":53540},[886],[888,53542,53543],{"xmlns":890},[892,53544,53545,53553],{},[895,53546,53547,53549,53551],{},[898,53548,2468],{},[1712,53550,1714],{},[1716,53552,1718],{},[902,53554,53555],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,53558,53560],{"className":53559},[886],[888,53561,53562],{"xmlns":890},[892,53563,53564,53572],{},[895,53565,53566],{},[2037,53567,53568,53570],{},[898,53569,1710],{},[898,53571,2041],{},[902,53573,46341],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,53576,53578],{"className":53577},[886],[888,53579,53580],{"xmlns":890},[892,53581,53582,53586],{},[895,53583,53584],{},[898,53585,1710],{},[902,53587,1710],{"encoding":904},[123,53589,53590,53591,52942,53608,53621,53622,1659],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,53592,53594],{"className":53593},[886],[888,53595,53596],{"xmlns":890},[892,53597,53598,53606],{},[895,53599,53600],{},[2037,53601,53602,53604],{},[898,53603,1710],{},[898,53605,2041],{},[902,53607,46341],{"encoding":904},[883,53609,53611],{"className":53610},[886],[888,53612,53613],{"xmlns":890},[892,53614,53615,53619],{},[895,53616,53617],{},[898,53618,207],{},[902,53620,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,53623,53625],{"className":53624},[886],[888,53626,53627],{"xmlns":890},[892,53628,53629,53639],{},[895,53630,53631],{},[6989,53632,53633,53635,53637],{},[898,53634,1710],{},[1716,53636,2222],{},[898,53638,2041],{},[902,53640,52732],{"encoding":904},[123,53642,53643,53644,53661,53662,53675,53676,1659],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,53645,53647],{"className":53646},[886],[888,53648,53649],{"xmlns":890},[892,53650,53651,53659],{},[895,53652,53653],{},[2037,53654,53655,53657],{},[898,53656,1710],{},[898,53658,2041],{},[902,53660,46341],{"encoding":904}," odpovídající poklesu ",[883,53663,53665],{"className":53664},[886],[888,53666,53667],{"xmlns":890},[892,53668,53669,53673],{},[895,53670,53671],{},[898,53672,207],{},[902,53674,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,53677,53679],{"className":53678},[886],[888,53680,53681],{"xmlns":890},[892,53682,53683,53693],{},[895,53684,53685],{},[6989,53686,53687,53689,53691],{},[898,53688,1710],{},[1716,53690,2787],{},[898,53692,2041],{},[902,53694,52793],{"encoding":904},[123,53696,53697,53698,53215,53715,53728,53729,3072,53742,1655,53757,53770,53771,1659],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,53699,53701],{"className":53700},[886],[888,53702,53703],{"xmlns":890},[892,53704,53705,53713],{},[895,53706,53707],{},[2037,53708,53709,53711],{},[898,53710,1710],{},[898,53712,2041],{},[902,53714,46341],{"encoding":904},[883,53716,53718],{"className":53717},[886],[888,53719,53720],{"xmlns":890},[892,53721,53722,53726],{},[895,53723,53724],{},[898,53725,207],{},[902,53727,207],{"encoding":904}," na 35, ",[883,53730,53732],{"className":53731},[886],[888,53733,53734],{"xmlns":890},[892,53735,53736,53740],{},[895,53737,53738],{},[898,53739,7585],{},[902,53741,7585],{"encoding":904},[883,53743,53745],{"className":53744},[886],[888,53746,53747],{"xmlns":890},[892,53748,53749,53754],{},[895,53750,53751],{},[1716,53752,53753],{},"0,7",[902,53755,53756],{"encoding":904},"0{,}7",[883,53758,53760],{"className":53759},[886],[888,53761,53762],{"xmlns":890},[892,53763,53764,53768],{},[895,53765,53766],{},[898,53767,2468],{},[902,53769,2468],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,53772,53774],{"className":53773},[886],[888,53775,53776],{"xmlns":890},[892,53777,53778,53788],{},[895,53779,53780],{},[6989,53781,53782,53784,53786],{},[898,53783,1710],{},[1716,53785,6198],{},[898,53787,2041],{},[902,53789,53790],{"encoding":904},"P_3^E",[724,53792,53793,52559,53796,52596,53824,26469,53852,1655,53878,1659],{},[38,53794,53795],{},"2.16",[883,53797,53799],{"className":53798},[886],[888,53800,53801],{"xmlns":890},[892,53802,53803,53821],{},[895,53804,53805,53807,53809,53811,53813,53815],{},[898,53806,1710],{},[1712,53808,1714],{},[898,53810,207],{},[1712,53812,3145],{},[898,53814,7544],{},[2037,53816,53817,53819],{},[898,53818,1734],{},[1716,53820,2787],{},[902,53822,53823],{"encoding":904},"P = a + bQ^2",[883,53825,53827],{"className":53826},[886],[888,53828,53829],{"xmlns":890},[892,53830,53831,53849],{},[895,53832,53833,53835,53837,53839,53841,53843],{},[898,53834,1710],{},[1712,53836,1714],{},[898,53838,7585],{},[1712,53840,3145],{},[898,53842,2468],{},[2037,53844,53845,53847],{},[898,53846,1734],{},[1716,53848,2787],{},[902,53850,53851],{"encoding":904},"P = c + dQ^2",[883,53853,53855],{"className":53854},[886],[888,53856,53857],{"xmlns":890},[892,53858,53859,53875],{},[895,53860,53861,53863,53865,53867,53869,53871,53873],{},[898,53862,207],{},[1712,53864,3138],{"separator":2565},[898,53866,7585],{},[1712,53868,3138],{"separator":2565},[898,53870,2468],{},[1712,53872,2302],{},[1716,53874,2085],{},[902,53876,53877],{"encoding":904},"a, c, d > 0",[883,53879,53881],{"className":53880},[886],[888,53882,53883],{"xmlns":890},[892,53884,53885,53893],{},[895,53886,53887,53889,53891],{},[898,53888,7544],{},[1712,53890,2252],{},[1716,53892,2085],{},[902,53894,53895],{"encoding":904},"b \u003C 0",[120,53897,53898,53946,53962,54069,54121,54173,54282,54298,54397,54450],{},[123,53899,53389,53900,53913,53914,53945],{},[883,53901,53903],{"className":53902},[886],[888,53904,53905],{"xmlns":890},[892,53906,53907,53911],{},[895,53908,53909],{},[898,53910,1734],{},[902,53912,1734],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,53915,53917],{"className":53916},[886],[888,53918,53919],{"xmlns":890},[892,53920,53921,53943],{},[895,53922,53923,53925,53927,53933,53935,53941],{},[898,53924,2041],{},[1712,53926,7910],{"stretchy":1903},[2037,53928,53929,53931],{},[898,53930,1734],{},[898,53932,2041],{},[1712,53934,3138],{"separator":2565},[2037,53936,53937,53939],{},[898,53938,1710],{},[898,53940,2041],{},[1712,53942,7925],{"stretchy":1903},[902,53944,46242],{"encoding":904}," patřil do 1. kvadrantu.",[123,53947,53464,53948,53961],{},[883,53949,53951],{"className":53950},[886],[888,53952,53953],{"xmlns":890},[892,53954,53955,53959],{},[895,53956,53957],{},[898,53958,1734],{},[902,53960,1734],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,53963,53481,53964,1343,53982,1343,54002,1343,54020,54038,54039,53574,54056,1659],{},[883,53965,53967],{"className":53966},[886],[888,53968,53969],{"xmlns":890},[892,53970,53971,53979],{},[895,53972,53973,53975,53977],{},[898,53974,207],{},[1712,53976,1714],{},[1716,53978,1739],{},[902,53980,53981],{"encoding":904},"a = 100",[883,53983,53985],{"className":53984},[886],[888,53986,53987],{"xmlns":890},[892,53988,53989,53999],{},[895,53990,53991,53993,53995,53997],{},[898,53992,7544],{},[1712,53994,1714],{},[1712,53996,2219],{},[1716,53998,2222],{},[902,54000,54001],{"encoding":904},"b = -1",[883,54003,54005],{"className":54004},[886],[888,54006,54007],{"xmlns":890},[892,54008,54009,54017],{},[895,54010,54011,54013,54015],{},[898,54012,7585],{},[1712,54014,1714],{},[1716,54016,6857],{},[902,54018,54019],{"encoding":904},"c = 20",[883,54021,54023],{"className":54022},[886],[888,54024,54025],{"xmlns":890},[892,54026,54027,54035],{},[895,54028,54029,54031,54033],{},[898,54030,2468],{},[1712,54032,1714],{},[1716,54034,2222],{},[902,54036,54037],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,54040,54042],{"className":54041},[886],[888,54043,54044],{"xmlns":890},[892,54045,54046,54054],{},[895,54047,54048],{},[2037,54049,54050,54052],{},[898,54051,1734],{},[898,54053,2041],{},[902,54055,47278],{"encoding":904},[883,54057,54059],{"className":54058},[886],[888,54060,54061],{"xmlns":890},[892,54062,54063,54067],{},[895,54064,54065],{},[898,54066,1734],{},[902,54068,1734],{"encoding":904},[123,54070,53010,54071,52942,54088,54101,54102,1659],{},[883,54072,54074],{"className":54073},[886],[888,54075,54076],{"xmlns":890},[892,54077,54078,54086],{},[895,54079,54080],{},[2037,54081,54082,54084],{},[898,54083,1734],{},[898,54085,2041],{},[902,54087,47278],{"encoding":904},[883,54089,54091],{"className":54090},[886],[888,54092,54093],{"xmlns":890},[892,54094,54095,54099],{},[895,54096,54097],{},[898,54098,207],{},[902,54100,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,54103,54105],{"className":54104},[886],[888,54106,54107],{"xmlns":890},[892,54108,54109,54119],{},[895,54110,54111],{},[6989,54112,54113,54115,54117],{},[898,54114,1734],{},[1716,54116,2222],{},[898,54118,2041],{},[902,54120,52711],{"encoding":904},[123,54122,53063,54123,52942,54140,54153,54154,1659],{},[883,54124,54126],{"className":54125},[886],[888,54127,54128],{"xmlns":890},[892,54129,54130,54138],{},[895,54131,54132],{},[2037,54133,54134,54136],{},[898,54135,1734],{},[898,54137,2041],{},[902,54139,47278],{"encoding":904},[883,54141,54143],{"className":54142},[886],[888,54144,54145],{"xmlns":890},[892,54146,54147,54151],{},[895,54148,54149],{},[898,54150,7585],{},[902,54152,7585],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,54155,54157],{"className":54156},[886],[888,54158,54159],{"xmlns":890},[892,54160,54161,54171],{},[895,54162,54163],{},[6989,54164,54165,54167,54169],{},[898,54166,1734],{},[1716,54168,2787],{},[898,54170,2041],{},[902,54172,52773],{"encoding":904},[123,54174,53143,54175,53215,54192,54205,54206,3072,54219,54234,54235,54248,54249,54262,54263,1659],{},[883,54176,54178],{"className":54177},[886],[888,54179,54180],{"xmlns":890},[892,54181,54182,54190],{},[895,54183,54184],{},[2037,54185,54186,54188],{},[898,54187,1734],{},[898,54189,2041],{},[902,54191,47278],{"encoding":904},[883,54193,54195],{"className":54194},[886],[888,54196,54197],{"xmlns":890},[892,54198,54199,54203],{},[895,54200,54201],{},[898,54202,207],{},[902,54204,207],{"encoding":904}," na 110, poklesu ",[883,54207,54209],{"className":54208},[886],[888,54210,54211],{"xmlns":890},[892,54212,54213,54217],{},[895,54214,54215],{},[898,54216,7544],{},[902,54218,7544],{"encoding":904},[883,54220,54222],{"className":54221},[886],[888,54223,54224],{"xmlns":890},[892,54225,54226,54232],{},[895,54227,54228,54230],{},[1712,54229,2219],{},[1716,54231,2787],{},[902,54233,52971],{"encoding":904},", růstu ",[883,54236,54238],{"className":54237},[886],[888,54239,54240],{"xmlns":890},[892,54241,54242,54246],{},[895,54243,54244],{},[898,54245,7585],{},[902,54247,7585],{"encoding":904}," na 25 a růstu ",[883,54250,54252],{"className":54251},[886],[888,54253,54254],{"xmlns":890},[892,54255,54256,54260],{},[895,54257,54258],{},[898,54259,2468],{},[902,54261,2468],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,54264,54266],{"className":54265},[886],[888,54267,54268],{"xmlns":890},[892,54269,54270,54280],{},[895,54271,54272],{},[6989,54273,54274,54276,54278],{},[898,54275,1734],{},[1716,54277,6198],{},[898,54279,2041],{},[902,54281,53140],{"encoding":904},[123,54283,54284,54285,53961],{},"(i) Vypočtěte multiplikátory pro ",[883,54286,54288],{"className":54287},[886],[888,54289,54290],{"xmlns":890},[892,54291,54292,54296],{},[895,54293,54294],{},[898,54295,1710],{},[902,54297,1710],{"encoding":904},[123,54299,54300,54301,53574,54318,54331,54332,52942,54349,3072,54362,54377,54378,1659],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,54302,54304],{"className":54303},[886],[888,54305,54306],{"xmlns":890},[892,54307,54308,54316],{},[895,54309,54310],{},[2037,54311,54312,54314],{},[898,54313,1710],{},[898,54315,2041],{},[902,54317,46341],{"encoding":904},[883,54319,54321],{"className":54320},[886],[888,54322,54323],{"xmlns":890},[892,54324,54325,54329],{},[895,54326,54327],{},[898,54328,1710],{},[902,54330,1710],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,54333,54335],{"className":54334},[886],[888,54336,54337],{"xmlns":890},[892,54338,54339,54347],{},[895,54340,54341],{},[2037,54342,54343,54345],{},[898,54344,1710],{},[898,54346,2041],{},[902,54348,46341],{"encoding":904},[883,54350,54352],{"className":54351},[886],[888,54353,54354],{"xmlns":890},[892,54355,54356,54360],{},[895,54357,54358],{},[898,54359,207],{},[902,54361,207],{"encoding":904},[883,54363,54365],{"className":54364},[886],[888,54366,54367],{"xmlns":890},[892,54368,54369,54375],{},[895,54370,54371,54373],{},[1712,54372,2219],{},[1716,54374,6198],{},[902,54376,52987],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,54379,54381],{"className":54380},[886],[888,54382,54383],{"xmlns":890},[892,54384,54385,54395],{},[895,54386,54387],{},[6989,54388,54389,54391,54393],{},[898,54390,1710],{},[1716,54392,2222],{},[898,54394,2041],{},[902,54396,52732],{"encoding":904},[123,54398,54399,54400,52942,54417,54430,54431,1659],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,54401,54403],{"className":54402},[886],[888,54404,54405],{"xmlns":890},[892,54406,54407,54415],{},[895,54408,54409],{},[2037,54410,54411,54413],{},[898,54412,1710],{},[898,54414,2041],{},[902,54416,46341],{"encoding":904},[883,54418,54420],{"className":54419},[886],[888,54421,54422],{"xmlns":890},[892,54423,54424,54428],{},[895,54425,54426],{},[898,54427,207],{},[902,54429,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,54432,54434],{"className":54433},[886],[888,54435,54436],{"xmlns":890},[892,54437,54438,54448],{},[895,54439,54440],{},[6989,54441,54442,54444,54446],{},[898,54443,1710],{},[1716,54445,2787],{},[898,54447,2041],{},[902,54449,52793],{"encoding":904},[123,54451,54452,54453,53661,54470,54483,54484,3072,54497,54234,54512,54525,54526,54539,54540,1659],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,54454,54456],{"className":54455},[886],[888,54457,54458],{"xmlns":890},[892,54459,54460,54468],{},[895,54461,54462],{},[2037,54463,54464,54466],{},[898,54465,1710],{},[898,54467,2041],{},[902,54469,46341],{"encoding":904},[883,54471,54473],{"className":54472},[886],[888,54474,54475],{"xmlns":890},[892,54476,54477,54481],{},[895,54478,54479],{},[898,54480,207],{},[902,54482,207],{"encoding":904}," na 90, poklesu ",[883,54485,54487],{"className":54486},[886],[888,54488,54489],{"xmlns":890},[892,54490,54491,54495],{},[895,54492,54493],{},[898,54494,7544],{},[902,54496,7544],{"encoding":904},[883,54498,54500],{"className":54499},[886],[888,54501,54502],{"xmlns":890},[892,54503,54504,54510],{},[895,54505,54506,54508],{},[1712,54507,2219],{},[1716,54509,6198],{},[902,54511,52987],{"encoding":904},[883,54513,54515],{"className":54514},[886],[888,54516,54517],{"xmlns":890},[892,54518,54519,54523],{},[895,54520,54521],{},[898,54522,7585],{},[902,54524,7585],{"encoding":904}," na 30 a růstu ",[883,54527,54529],{"className":54528},[886],[888,54530,54531],{"xmlns":890},[892,54532,54533,54537],{},[895,54534,54535],{},[898,54536,2468],{},[902,54538,2468],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,54541,54543],{"className":54542},[886],[888,54544,54545],{"xmlns":890},[892,54546,54547,54557],{},[895,54548,54549],{},[6989,54550,54551,54553,54555],{},[898,54552,1710],{},[1716,54554,6198],{},[898,54556,2041],{},[902,54558,53790],{"encoding":904},[198,54560,820],{"id":54561},"přebytek-spotřebitele-a-výrobce-1",[724,54563,54564,52559,54567,52596,54603,1659],{},[38,54565,54566],{},"2.17",[883,54568,54570],{"className":54569},[886],[888,54571,54572],{"xmlns":890},[892,54573,54574,54600],{},[895,54575,54576,54578,54580,54582,54584,54586,54588,54590,54592,54594],{},[898,54577,1710],{},[1712,54579,1714],{},[898,54581,1969],{},[1712,54583,1904],{"stretchy":1903},[898,54585,1734],{},[1712,54587,1910],{"stretchy":1903},[1712,54589,1714],{},[1716,54591,19912],{},[1712,54593,2219],{},[2037,54595,54596,54598],{},[898,54597,1734],{},[1716,54599,2787],{},[902,54601,54602],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,54604,54606],{"className":54605},[886],[888,54607,54608],{"xmlns":890},[892,54609,54610,54636],{},[895,54611,54612,54614,54616,54618,54620,54622,54624,54626,54628,54630],{},[898,54613,1710],{},[1712,54615,1714],{},[898,54617,6493],{},[1712,54619,1904],{"stretchy":1903},[898,54621,1734],{},[1712,54623,1910],{"stretchy":1903},[1712,54625,1714],{},[1716,54627,6198],{},[1712,54629,3145],{},[2037,54631,54632,54634],{},[898,54633,1734],{},[1716,54635,2787],{},[902,54637,54638],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,54640,54641,54644],{},[123,54642,54643],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,54645,54646],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,54648,54649,52559,54652,52596,54686,1659],{},[38,54650,54651],{},"2.18",[883,54653,54655],{"className":54654},[886],[888,54656,54657],{"xmlns":890},[892,54658,54659,54683],{},[895,54660,54661,54663,54665,54667,54669,54671,54673,54675,54677,54679,54681],{},[898,54662,1710],{},[1712,54664,1714],{},[898,54666,1969],{},[1712,54668,1904],{"stretchy":1903},[898,54670,1734],{},[1712,54672,1910],{"stretchy":1903},[1712,54674,1714],{},[1716,54676,9110],{},[1712,54678,2219],{},[1716,54680,2787],{},[898,54682,1734],{},[902,54684,54685],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,54687,54689],{"className":54688},[886],[888,54690,54691],{"xmlns":890},[892,54692,54693,54719],{},[895,54694,54695,54697,54699,54701,54703,54705,54707,54709,54711,54713],{},[898,54696,1710],{},[1712,54698,1714],{},[898,54700,6493],{},[1712,54702,1904],{"stretchy":1903},[898,54704,1734],{},[1712,54706,1910],{"stretchy":1903},[1712,54708,1714],{},[1716,54710,6198],{},[1712,54712,3145],{},[2037,54714,54715,54717],{},[898,54716,1734],{},[1716,54718,2787],{},[902,54720,54638],{"encoding":904},[120,54722,54723,54743,54746,54749],{},[123,54724,54725,54726,1659],{},"(a) Vypočtěte rovnovážné množství ",[883,54727,54729],{"className":54728},[886],[888,54730,54731],{"xmlns":890},[892,54732,54733,54741],{},[895,54734,54735],{},[2037,54736,54737,54739],{},[898,54738,1734],{},[898,54740,2041],{},[902,54742,47278],{"encoding":904},[123,54744,54745],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,54747,54748],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,54750,54751],{},"(c) Graficky interpretujte.",[41845,54753],{},[115,54755,54757],{"id":54756},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,54759,54760,54763,54766,54769,54772,54775,54778,54781,54784,54787,54790,54793,54796,54799],{},[123,54761,54762],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,54764,54765],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,54767,54768],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,54770,54771],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,54773,54774],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,54776,54777],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,54779,54780],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,54782,54783],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,54785,54786],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,54788,54789],{},"K čemu slouží multiplikátory?",[123,54791,54792],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,54794,54795],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,54797,54798],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,54800,54801],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[41845,54803],{},[115,54805,20594],{"id":20593},[724,54807,54808],{},[38,54809,18035],{},[120,54811,54812,54847,54852,54882,54887,54950,54976,54981,55011,55020,55027,55033],{},[123,54813,54814,14897,54817,23523,54820,3245,54822,1343,54845],{},[38,54815,54816],{},"Poptávané množství",[614,54818,54819],{},"quantity demanded",[38,54821,32877],{},[883,54823,54825],{"className":54824},[886],[888,54826,54827],{"xmlns":890},[892,54828,54829,54843],{},[895,54830,54831,54833,54835,54837,54839,54841],{},[898,54832,1734],{},[1712,54834,1714],{},[898,54836,1969],{},[1712,54838,1904],{"stretchy":1903},[898,54840,1710],{},[1712,54842,1910],{"stretchy":1903},[902,54844,1978],{"encoding":904},[38,54846,42324],{},[123,54848,54849,54851],{},[38,54850,42331],{}," — substituční + důchodový efekt",[123,54853,54854,3245,54857],{},[38,54855,54856],{},"Reálné cenové rozpětí",[883,54858,54860],{"className":54859},[886],[888,54861,54862],{"xmlns":890},[892,54863,54864,54880],{},[895,54865,54866,54868,54870,54872,54878],{},[1712,54867,1904],{"stretchy":1903},[1716,54869,2085],{},[1712,54871,3138],{"separator":2565},[6927,54873,54874,54876],{},[898,54875,1710],{},[1716,54877,2085],{},[1712,54879,1910],{"stretchy":1903},[902,54881,42532],{"encoding":904},[123,54883,54884,15969],{},[38,54885,54886],{},"Homogenita poptávky",[123,54888,54889,3245,54892,1343,54915,1343,54932,54949],{},[38,54890,54891],{},"Lineární poptávka",[883,54893,54895],{"className":54894},[886],[888,54896,54897],{"xmlns":890},[892,54898,54899,54913],{},[895,54900,54901,54903,54905,54907,54909,54911],{},[898,54902,1710],{},[1712,54904,1714],{},[898,54906,207],{},[898,54908,1734],{},[1712,54910,3145],{},[898,54912,7544],{},[902,54914,41935],{"encoding":904},[883,54916,54918],{"className":54917},[886],[888,54919,54920],{"xmlns":890},[892,54921,54922,54930],{},[895,54923,54924,54926,54928],{},[898,54925,207],{},[1712,54927,2252],{},[1716,54929,2085],{},[902,54931,47960],{"encoding":904},[883,54933,54935],{"className":54934},[886],[888,54936,54937],{"xmlns":890},[892,54938,54939,54947],{},[895,54940,54941,54943,54945],{},[898,54942,7544],{},[1712,54944,2302],{},[1716,54946,2085],{},[902,54948,23689],{"encoding":904}," — nedokonalá konkurence",[123,54951,54952,4831,54955],{},[38,54953,54954],{},"Dokonalá konkurence",[883,54956,54958],{"className":54957},[886],[888,54959,54960],{"xmlns":890},[892,54961,54962,54974],{},[895,54963,54964,54966,54968],{},[898,54965,1710],{},[1712,54967,1714],{},[2037,54969,54970,54972],{},[898,54971,1710],{},[1712,54973,2145],{},[902,54975,2148],{"encoding":904},[123,54977,54978,54980],{},[38,54979,43101],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,54982,54983,3245,54985,1343,55009],{},[38,54984,36602],{},[883,54986,54988],{"className":54987},[886],[888,54989,54990],{"xmlns":890},[892,54991,54992,55006],{},[895,54993,54994,54996,54998,55000,55002,55004],{},[898,54995,1734],{},[1712,54997,1714],{},[898,54999,2041],{},[1712,55001,1904],{"stretchy":1903},[898,55003,6951],{},[1712,55005,1910],{"stretchy":1903},[902,55007,55008],{"encoding":904},"Q = E(Y)",[38,55010,43298],{},[123,55012,55013,55016,55017,55019],{},[38,55014,55015],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,55018,43744],{}," zboží",[123,55021,55022,1655,55024,55026],{},[38,55023,44750],{},[38,55025,44697],{}," — znaménka zkřížených koeficientů",[123,55028,55029,55032],{},[38,55030,55031],{},"Dvoukomoditní trh"," (2.6)",[123,55034,55035,14897,55038,1910],{},[38,55036,55037],{},"Posun poptávky",[614,55039,43802],{},[724,55041,55042],{},[38,55043,17999],{},[120,55045,55046,55079,55083,55128],{},[123,55047,55048,14897,55050,23523,55052,3245,55054,1343,55077],{},[38,55049,45144],{},[614,55051,45147],{},[38,55053,45318],{},[883,55055,55057],{"className":55056},[886],[888,55058,55059],{"xmlns":890},[892,55060,55061,55075],{},[895,55062,55063,55065,55067,55069,55071,55073],{},[898,55064,1734],{},[1712,55066,1714],{},[898,55068,6493],{},[1712,55070,1904],{"stretchy":1903},[898,55072,1710],{},[1712,55074,1910],{"stretchy":1903},[902,55076,6502],{"encoding":904},[38,55078,45396],{},[123,55080,55081],{},[38,55082,45403],{},[123,55084,55085,3245,55088,1343,55111],{},[38,55086,55087],{},"Lineární nabídka",[883,55089,55091],{"className":55090},[886],[888,55092,55093],{"xmlns":890},[892,55094,55095,55109],{},[895,55096,55097,55099,55101,55103,55105,55107],{},[898,55098,1710],{},[1712,55100,1714],{},[898,55102,7585],{},[898,55104,1734],{},[1712,55106,3145],{},[898,55108,2468],{},[902,55110,45117],{"encoding":904},[883,55112,55114],{"className":55113},[886],[888,55115,55116],{"xmlns":890},[892,55117,55118,55126],{},[895,55119,55120,55122,55124],{},[898,55121,7585],{},[1712,55123,2302],{},[1716,55125,2085],{},[902,55127,45135],{"encoding":904},[123,55129,55130,14897,55133,1910],{},[38,55131,55132],{},"Posun nabídky",[614,55134,45781],{},[724,55136,55137],{},[38,55138,55139],{},"Rovnováha a komparativní statika",[120,55141,55142,55221,55227],{},[123,55143,55144,14897,55146,23523,55148,3245,55151,1343,55168,3245,55171,1343,55188,3245,55190],{},[38,55145,46200],{},[614,55147,46319],{},[38,55149,55150],{},"rovnovážná cena",[883,55152,55154],{"className":55153},[886],[888,55155,55156],{"xmlns":890},[892,55157,55158,55166],{},[895,55159,55160],{},[2037,55161,55162,55164],{},[898,55163,1710],{},[898,55165,2041],{},[902,55167,46341],{"encoding":904},[38,55169,55170],{},"rovnovážné množství",[883,55172,55174],{"className":55173},[886],[888,55175,55176],{"xmlns":890},[892,55177,55178,55186],{},[895,55179,55180],{},[2037,55181,55182,55184],{},[898,55183,1734],{},[898,55185,2041],{},[902,55187,47278],{"encoding":904},[38,55189,46377],{},[883,55191,55193],{"className":55192},[886],[888,55194,55195],{"xmlns":890},[892,55196,55197,55219],{},[895,55198,55199,55201,55203,55209,55211,55217],{},[898,55200,2041],{},[1712,55202,7910],{"stretchy":1903},[2037,55204,55205,55207],{},[898,55206,1734],{},[898,55208,2041],{},[1712,55210,3138],{"separator":2565},[2037,55212,55213,55215],{},[898,55214,1710],{},[898,55216,2041],{},[1712,55218,7925],{"stretchy":1903},[902,55220,46242],{"encoding":904},[123,55222,55223,55226],{},[38,55224,55225],{},"Pravidla 1–4"," komparativní statiky",[123,55228,55229,14897,55232,1910],{},[38,55230,55231],{},"Teorém pavučiny",[614,55233,47224],{},[724,55235,55236],{},[38,55237,55238],{},"Zdanění",[120,55240,55241,55297,55345],{},[123,55242,55243,55245,55246,55271,55272,1910],{},[38,55244,55238],{}," — daň výrobci (",[883,55247,55249],{"className":55248},[886],[888,55250,55251],{"xmlns":890},[892,55252,55253,55269],{},[895,55254,55255,55261,55263,55265,55267],{},[6927,55256,55257,55259],{},[898,55258,6493],{},[1716,55260,2222],{},[1712,55262,1714],{},[898,55264,6493],{},[1712,55266,3145],{},[898,55268,1772],{},[902,55270,47629],{"encoding":904},") vs. daň spotřebiteli (",[883,55273,55275],{"className":55274},[886],[888,55276,55277],{"xmlns":890},[892,55278,55279,55295],{},[895,55280,55281,55287,55289,55291,55293],{},[6927,55282,55283,55285],{},[898,55284,1969],{},[1716,55286,2787],{},[1712,55288,1714],{},[898,55290,1969],{},[1712,55292,2219],{},[898,55294,1772],{},[902,55296,47660],{"encoding":904},[123,55298,55299,3245,55301,1343,55322],{},[38,55300,47533],{},[883,55302,55304],{"className":55303},[886],[888,55305,55306],{"xmlns":890},[892,55307,55308,55320],{},[895,55309,55310],{},[6927,55311,55312,55314],{},[898,55313,1772],{},[895,55315,55316,55318],{},[898,55317,47552],{},[898,55319,724],{},[902,55321,47557],{"encoding":904},[883,55323,55325],{"className":55324},[886],[888,55326,55327],{"xmlns":890},[892,55328,55329,55343],{},[895,55330,55331],{},[6927,55332,55333,55335],{},[898,55334,1772],{},[895,55336,55337,55339,55341],{},[898,55338,47575],{},[898,55340,7446],{},[898,55342,16915],{},[902,55344,47582],{"encoding":904},[123,55346,55347,3245,55350,1343,55379],{},[38,55348,55349],{},"Ekvivalence zdanění",[883,55351,55353],{"className":55352},[886],[888,55354,55355],{"xmlns":890},[892,55356,55357,55377],{},[895,55358,55359,55367,55369],{},[6989,55360,55361,55363,55365],{},[898,55362,1734],{},[1716,55364,2222],{},[898,55366,2041],{},[1712,55368,1714],{},[6989,55370,55371,55373,55375],{},[898,55372,1734],{},[1716,55374,2787],{},[898,55376,2041],{},[902,55378,47783],{"encoding":904},[883,55380,55382],{"className":55381},[886],[888,55383,55384],{"xmlns":890},[892,55385,55386,55410],{},[895,55387,55388,55396,55398,55400,55402],{},[6989,55389,55390,55392,55394],{},[898,55391,1710],{},[1716,55393,2222],{},[898,55395,2041],{},[1712,55397,2219],{},[898,55399,1772],{},[1712,55401,1714],{},[6989,55403,55404,55406,55408],{},[898,55405,1710],{},[1716,55407,2787],{},[898,55409,2041],{},[902,55411,47817],{"encoding":904},[724,55413,55414],{},[38,55415,31283],{},[120,55417,55418,55464,55495,55500,55506,55513],{},[123,55419,55420,3245,55422],{},[38,55421,47916],{},[883,55423,55425],{"className":55424},[886],[888,55426,55427],{"xmlns":890},[892,55428,55429,55461],{},[895,55430,55431,55437,55439,55441,55443,55445,55447,55449,55451,55453,55455,55457,55459],{},[2037,55432,55433,55435],{},[898,55434,1734],{},[898,55436,2041],{},[1712,55438,1714],{},[1712,55440,1904],{"stretchy":1903},[898,55442,7544],{},[1712,55444,2219],{},[898,55446,2468],{},[1712,55448,1910],{"stretchy":1903},[898,55450,2473],{"mathvariant":2003},[1712,55452,1904],{"stretchy":1903},[898,55454,7585],{},[1712,55456,2219],{},[898,55458,207],{},[1712,55460,1910],{"stretchy":1903},[902,55462,55463],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,55465,55466,3245,55469,55494],{},[38,55467,55468],{},"Parametry",[883,55470,55472],{"className":55471},[886],[888,55473,55474],{"xmlns":890},[892,55475,55476,55492],{},[895,55477,55478,55480,55482,55484,55486,55488,55490],{},[898,55479,207],{},[1712,55481,3138],{"separator":2565},[898,55483,7544],{},[1712,55485,3138],{"separator":2565},[898,55487,7585],{},[1712,55489,3138],{"separator":2565},[898,55491,2468],{},[902,55493,48160],{"encoding":904}," — exogenní proměnné",[123,55496,55497],{},[38,55498,55499],{},"Endogenní \u002F exogenní proměnná",[123,55501,55502,55505],{},[38,55503,55504],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,55507,55508,1343,55511],{},[38,55509,55510],{},"Komparativní statika",[38,55512,41835],{},[123,55514,55515,3245,55517,55533],{},[38,55516,8366],{},[883,55518,55520],{"className":55519},[886],[888,55521,55522],{"xmlns":890},[892,55523,55524,55530],{},[895,55525,55526,55528],{},[898,55527,2468],{},[898,55529,1734],{},[902,55531,55532],{"encoding":904},"dQ"," (2.11)",[724,55535,55536],{},[38,55537,55538],{},"Přebytky a ostatní",[120,55540,55541,55579],{},[123,55542,55543,3245,55545,55560,55561,3245,55563,55578],{},[38,55544,49809],{},[883,55546,55548],{"className":55547},[886],[888,55549,55550],{"xmlns":890},[892,55551,55552,55558],{},[895,55553,55554,55556],{},[898,55555,8195],{},[898,55557,6493],{},[902,55559,49825],{"encoding":904}," (2.14), ",[38,55562,49828],{},[883,55564,55566],{"className":55565},[886],[888,55567,55568],{"xmlns":890},[892,55569,55570,55576],{},[895,55571,55572,55574],{},[898,55573,1710],{},[898,55575,6493],{},[902,55577,49844],{"encoding":904}," (2.15)",[123,55580,55581,1343,55584,55587],{},[38,55582,55583],{},"Homo economicus",[38,55585,55586],{},"Marshallova formulace"," (1890)",[41845,55589],{},[115,55591,9193],{"id":9192},[120,55593,55594,55629,55638],{},[123,55595,55596,3245,55599,55602,55603,1343,55606,55609,55610,55613,55614,55617,55618,55621,55622,55625,55626],{},[38,55597,55598],{},"Související témata:",[207,55600,811],{"className":55601,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,55604,820],{"className":55605,"dataFsResolvedFilePath":818,"href":819},[210],[207,55607,1690],{"className":55608,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,55611,775],{"className":55612,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,55615,784],{"className":55616,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,55619,793],{"className":55620,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,55623,1646],{"className":55624,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,55627,4992],{"className":55628,"dataFsResolvedFilePath":827,"href":828},[210],[123,55630,55631,3245,55634],{},[38,55632,55633],{},"Shrnutí přednášek:",[207,55635,55637],{"className":55636,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,55639,55640,3245,55642],{},[38,55641,21078],{},[207,55643,21082],{"className":55644,"dataFsResolvedFilePath":7413,"href":7414},[210],{"title":641,"searchDepth":642,"depth":642,"links":55646},[55647,55648,55656,55662,55669,55670,55677,55678,55679,55686,55687,55688],{"id":41669,"depth":642,"text":41670},{"id":41650,"depth":642,"text":18035,"children":55649},[55650,55651,55652,55653,55655],{"id":41938,"depth":649,"text":41939},{"id":42220,"depth":649,"text":42221},{"id":43230,"depth":649,"text":43231},{"id":43798,"depth":649,"text":55654},"Posun poptávky (shift of demand)",{"id":44302,"depth":649,"text":44303},{"id":41654,"depth":642,"text":17999,"children":55657},[55658,55659,55660],{"id":45139,"depth":649,"text":41939},{"id":45325,"depth":649,"text":45326},{"id":45777,"depth":649,"text":55661},"Posun nabídky (shift of supply)",{"id":46199,"depth":642,"text":46200,"children":55663},[55664,55665,55666,55667,55668],{"id":46311,"depth":649,"text":46312},{"id":46524,"depth":649,"text":46525},{"id":46842,"depth":649,"text":46843},{"id":47196,"depth":649,"text":47197},{"id":47227,"depth":649,"text":47228},{"id":47496,"depth":642,"text":811},{"id":47897,"depth":642,"text":47898,"children":55671},[55672,55673,55674,55675],{"id":47915,"depth":649,"text":47916},{"id":48296,"depth":649,"text":48297},{"id":48680,"depth":649,"text":48681},{"id":49134,"depth":649,"text":55676},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":16657,"depth":642,"text":820},{"id":50059,"depth":642,"text":50060},{"id":50290,"depth":642,"text":50291,"children":55680},[55681,55682,55683,55684,55685],{"id":50294,"depth":649,"text":50295},{"id":51134,"depth":649,"text":51135},{"id":51510,"depth":649,"text":46200},{"id":52805,"depth":649,"text":47898},{"id":54561,"depth":649,"text":820},{"id":54756,"depth":642,"text":54757},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,55695,55696,55697,22758,55698,55699],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":55702,"title":820,"body":55703,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":59982,"navigation":664,"path":59983,"seo":59984,"sources":59985,"stem":59986,"tags":59987,"type":7391,"updated":677,"__hash__":59992},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":55704,"toc":59960},[55705,55707,55775,55825,55827,55830,56088,56164,56169,56171,56190,56194,56270,56355,56357,56671,56764,56766,56785,56789,56863,56948,56951,57127,57132,57134,57554,57556,57560,57564,57800,57844,57944,58010,58013,58046,58222,58284,58414,58492,58603,58637,58835,58854,58873,58938,58942,58945,58990,58993,59111,59157,59159,59163,59511,59513,59515,59793,59795,59799,59834,59841,59914,59916,59918],[12,55706,820],{"id":16657},[1636,55708,55709],{},[724,55710,55711,1643,55713,14897,55715,55730,55731,14897,55733,55748,55749,55771,55772,1659],{},[883,55712,1642],{},[38,55714,49809],{},[883,55716,55718],{"className":55717},[886],[888,55719,55720],{"xmlns":890},[892,55721,55722,55728],{},[895,55723,55724,55726],{},[898,55725,8195],{},[898,55727,6493],{},[902,55729,49825],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,55732,49956],{},[883,55734,55736],{"className":55735},[886],[888,55737,55738],{"xmlns":890},[892,55739,55740,55746],{},[895,55741,55742,55744],{},[898,55743,1710],{},[898,55745,6493],{},[902,55747,49844],{"encoding":904},") 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 ",[883,55750,55752],{"className":55751},[886],[888,55753,55754],{"xmlns":890},[892,55755,55756,55768],{},[895,55757,55758,55760,55762,55764,55766],{},[898,55759,8195],{},[898,55761,6493],{},[1712,55763,3145],{},[898,55765,1710],{},[898,55767,6493],{},[902,55769,55770],{"encoding":904},"CS + PS"," měří ",[38,55773,55774],{},"celkový blahobyt trhu",[724,55776,55777,14897,55779,1343,55781,17002,55796,14897,55798,1343,55800,55815,55816,55820,55821,1659],{},[38,55778,49809],{},[614,55780,49863],{},[883,55782,55784],{"className":55783},[886],[888,55785,55786],{"xmlns":890},[892,55787,55788,55794],{},[895,55789,55790,55792],{},[898,55791,8195],{},[898,55793,6493],{},[902,55795,49825],{"encoding":904},[38,55797,49828],{},[614,55799,49959],{},[883,55801,55803],{"className":55802},[886],[888,55804,55805],{"xmlns":890},[892,55806,55807,55813],{},[895,55808,55809,55811],{},[898,55810,1710],{},[898,55812,6493],{},[902,55814,49844],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,55817,55819],{"className":55818,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,55822,55824],{"className":55823,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[41845,55826],{},[115,55828,1241],{"id":55829},"úvod",[724,55831,55832,55833,55856,55857,55880,55881,55898,55899,1682,55931,55963,55964,55990,55991,55994,55995,55998,55999,18885,56033,26469,56054,1659],{},"Je dána funkce poptávky ",[883,55834,55836],{"className":55835},[886],[888,55837,55838],{"xmlns":890},[892,55839,55840,55854],{},[895,55841,55842,55844,55846,55848,55850,55852],{},[898,55843,1710],{},[1712,55845,1714],{},[898,55847,1969],{},[1712,55849,1904],{"stretchy":1903},[898,55851,1734],{},[1712,55853,1910],{"stretchy":1903},[902,55855,2438],{"encoding":904},", resp. funkce nabídky ",[883,55858,55860],{"className":55859},[886],[888,55861,55862],{"xmlns":890},[892,55863,55864,55878],{},[895,55865,55866,55868,55870,55872,55874,55876],{},[898,55867,1710],{},[1712,55869,1714],{},[898,55871,6493],{},[1712,55873,1904],{"stretchy":1903},[898,55875,1734],{},[1712,55877,1910],{"stretchy":1903},[902,55879,45946],{"encoding":904},". Pro pevně zadané množství ",[883,55882,55884],{"className":55883},[886],[888,55885,55886],{"xmlns":890},[892,55887,55888,55896],{},[895,55889,55890],{},[6927,55891,55892,55894],{},[898,55893,1734],{},[1716,55895,2085],{},[902,55897,43183],{"encoding":904}," je odpovídající cena ",[883,55900,55902],{"className":55901},[886],[888,55903,55904],{"xmlns":890},[892,55905,55906,55928],{},[895,55907,55908,55914,55916,55918,55920,55926],{},[6927,55909,55910,55912],{},[898,55911,1710],{},[1716,55913,2085],{},[1712,55915,1714],{},[898,55917,1969],{},[1712,55919,1904],{"stretchy":1903},[6927,55921,55922,55924],{},[898,55923,1734],{},[1716,55925,2085],{},[1712,55927,1910],{"stretchy":1903},[902,55929,55930],{"encoding":904},"P_0 = D(Q_0)",[883,55932,55934],{"className":55933},[886],[888,55935,55936],{"xmlns":890},[892,55937,55938,55960],{},[895,55939,55940,55946,55948,55950,55952,55958],{},[6927,55941,55942,55944],{},[898,55943,1710],{},[1716,55945,2085],{},[1712,55947,1714],{},[898,55949,6493],{},[1712,55951,1904],{"stretchy":1903},[6927,55953,55954,55956],{},[898,55955,1734],{},[1716,55957,2085],{},[1712,55959,1910],{"stretchy":1903},[902,55961,55962],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,55965,55967],{"className":55966},[886],[888,55968,55969],{"xmlns":890},[892,55970,55971,55987],{},[895,55972,55973,55979,55981],{},[6927,55974,55975,55977],{},[898,55976,1710],{},[1716,55978,2085],{},[1762,55980,2583],{},[6927,55982,55983,55985],{},[898,55984,1734],{},[1716,55986,2085],{},[902,55988,55989],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,55992,55993],{},"výdaje spotřebitele",", nebo ",[38,55996,55997],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,56000,56002],{"className":56001},[886],[888,56003,56004],{"xmlns":890},[892,56005,56006,56030],{},[895,56007,56008,56010,56012,56018,56020,56022,56024],{},[1716,56009,2085],{},[1762,56011,2583],{},[6927,56013,56014,56016],{},[898,56015,1734],{},[1716,56017,2085],{},[1762,56019,2583],{},[898,56021,2044],{},[1762,56023,2583],{},[6927,56025,56026,56028],{},[898,56027,1710],{},[1716,56029,2085],{},[902,56031,56032],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,56034,56036],{"className":56035},[886],[888,56037,56038],{"xmlns":890},[892,56039,56040,56052],{},[895,56041,56042,56044,56046,56048,56050],{},[1712,56043,1904],{"stretchy":1903},[898,56045,1734],{},[1712,56047,3138],{"separator":2565},[898,56049,1710],{},[1712,56051,1910],{"stretchy":1903},[902,56053,42566],{"encoding":904},[883,56055,56057],{"className":56056},[886],[888,56058,56059],{"xmlns":890},[892,56060,56061,56085],{},[895,56062,56063,56065,56067,56069,56075,56077,56083],{},[898,56064,2044],{},[1712,56066,1714],{},[1712,56068,7910],{"stretchy":1903},[6927,56070,56071,56073],{},[898,56072,1734],{},[1716,56074,2085],{},[1712,56076,3138],{"separator":2565},[6927,56078,56079,56081],{},[898,56080,1710],{},[1716,56082,2085],{},[1712,56084,7925],{"stretchy":1903},[902,56086,56087],{"encoding":904},"A = [Q_0, P_0]",[1636,56089,56090,56095,56153],{},[724,56091,56092,56094],{},[883,56093,1941],{}," Intuice",[120,56096,56097,56125],{},[123,56098,56099,56100,56103,56104,56106,56107,56124],{},"Za jednotky zboží nakoupené ",[38,56101,56102],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,56105,30145],{}," než ",[883,56108,56110],{"className":56109},[886],[888,56111,56112],{"xmlns":890},[892,56113,56114,56122],{},[895,56115,56116],{},[6927,56117,56118,56120],{},[898,56119,1710],{},[1716,56121,2085],{},[902,56123,43823],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,56126,56127,56128,56130,56131,56134,56135,56152],{},"Za jednotky zboží prodané ",[38,56129,56102],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,56132,56133],{},"nižší"," cenu než ",[883,56136,56138],{"className":56137},[886],[888,56139,56140],{"xmlns":890},[892,56141,56142,56150],{},[895,56143,56144],{},[6927,56145,56146,56148],{},[898,56147,1710],{},[1716,56149,2085],{},[902,56151,43823],{"encoding":904}," — rozdíl je jeho přebytek.",[724,56154,56155,56156,56159,56160,56163],{},"Přebytek je tedy rozdíl mezi ",[614,56157,56158],{},"ochotou"," (platit \u002F prodávat) a ",[614,56161,56162],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,56165,56166],{},[3817,56167],{"alt":49854,"className":56168,"src":49856},[210,3821],[41845,56170],{},[115,56172,56174,56175,1910],{"id":56173},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,56176,56178],{"className":56177},[886],[888,56179,56180],{"xmlns":890},[892,56181,56182,56188],{},[895,56183,56184,56186],{},[898,56185,8195],{},[898,56187,6493],{},[902,56189,49825],{"encoding":904},[198,56191,56193],{"id":56192},"definice-vzorec-214","Definice (vzorec 2.14)",[724,56195,56196,56197,56220,56221,56238,56239,2854],{},"Pro poptávku ",[883,56198,56200],{"className":56199},[886],[888,56201,56202],{"xmlns":890},[892,56203,56204,56218],{},[895,56205,56206,56208,56210,56212,56214,56216],{},[898,56207,1710],{},[1712,56209,1714],{},[898,56211,1969],{},[1712,56213,1904],{"stretchy":1903},[898,56215,1734],{},[1712,56217,1910],{"stretchy":1903},[902,56219,2438],{"encoding":904}," a pevně zadané ",[883,56222,56224],{"className":56223},[886],[888,56225,56226],{"xmlns":890},[892,56227,56228,56236],{},[895,56229,56230],{},[6927,56231,56232,56234],{},[898,56233,1734],{},[1716,56235,2085],{},[902,56237,43183],{"encoding":904}," s cenou ",[883,56240,56242],{"className":56241},[886],[888,56243,56244],{"xmlns":890},[892,56245,56246,56268],{},[895,56247,56248,56254,56256,56258,56260,56266],{},[6927,56249,56250,56252],{},[898,56251,1710],{},[1716,56253,2085],{},[1712,56255,1714],{},[898,56257,1969],{},[1712,56259,1904],{"stretchy":1903},[6927,56261,56262,56264],{},[898,56263,1734],{},[1716,56265,2085],{},[1712,56267,1910],{"stretchy":1903},[902,56269,55930],{"encoding":904},[883,56271,56273],{"className":56272},[886],[888,56274,56275],{"xmlns":890,"display":32941},[892,56276,56277,56353],{},[25629,56278,56279],{"width":32946},[25634,56280,56281,56283,56347,56349],{},[25637,56282],{"width":32951},[25637,56284,56285],{},[895,56286,56287,56289,56291,56293,56299,56301,56303,56315,56317,56319,56321,56323,56325,56327,56329,56331,56337,56339,56345],{},[898,56288,8195],{},[898,56290,6493],{},[1712,56292,1904],{"stretchy":1903},[6927,56294,56295,56297],{},[898,56296,1734],{},[1716,56298,2085],{},[1712,56300,1910],{"stretchy":1903},[1712,56302,1714],{},[6989,56304,56305,56307,56309],{},[1712,56306,16042],{},[1716,56308,2085],{},[6927,56310,56311,56313],{},[898,56312,1734],{},[1716,56314,2085],{},[898,56316,1969],{},[1712,56318,1904],{"stretchy":1903},[898,56320,1734],{},[1712,56322,1910],{"stretchy":1903},[1762,56324,2583],{},[898,56326,2468],{},[898,56328,1734],{},[1712,56330,2219],{},[6927,56332,56333,56335],{},[898,56334,1710],{},[1716,56336,2085],{},[1762,56338,2583],{},[6927,56340,56341,56343],{},[898,56342,1734],{},[1716,56344,2085],{},[898,56346,1659],{"mathvariant":2003},[25637,56348],{"width":32951},[25637,56350,56351],{},[1762,56352,49948],{},[902,56354,49951],{"encoding":904},[198,56356,7868],{"id":7867},[120,56358,56359,56451,56513],{},[123,56360,56361,56401,56402,56428,56429,56432,56433,56450],{},[883,56362,56364],{"className":56363},[886],[888,56365,56366],{"xmlns":890},[892,56367,56368,56398],{},[895,56369,56370],{},[2563,56371,56372,56384,56386,56388,56390,56392,56394,56396],{"scriptlevel":2085,"displaystyle":2565},[6989,56373,56374,56376,56378],{},[1712,56375,16042],{},[1716,56377,2085],{},[6927,56379,56380,56382],{},[898,56381,1734],{},[1716,56383,2085],{},[898,56385,1969],{},[1712,56387,1904],{"stretchy":1903},[898,56389,1734],{},[1712,56391,1910],{"stretchy":1903},[1762,56393,2583],{},[898,56395,2468],{},[898,56397,1734],{},[902,56399,56400],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,56403,56405],{"className":56404},[886],[888,56406,56407],{"xmlns":890},[892,56408,56409,56425],{},[895,56410,56411,56413,56415,56417,56423],{},[1712,56412,7910],{"stretchy":1903},[1716,56414,2085],{},[1712,56416,3138],{"separator":2565},[6927,56418,56419,56421],{},[898,56420,1734],{},[1716,56422,2085],{},[1712,56424,7925],{"stretchy":1903},[902,56426,56427],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,56430,56431],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,56434,56436],{"className":56435},[886],[888,56437,56438],{"xmlns":890},[892,56439,56440,56448],{},[895,56441,56442],{},[6927,56443,56444,56446],{},[898,56445,1734],{},[1716,56447,2085],{},[902,56449,43183],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,56452,56453,56479,56480,1691],{},[883,56454,56456],{"className":56455},[886],[888,56457,56458],{"xmlns":890},[892,56459,56460,56476],{},[895,56461,56462,56468,56470],{},[6927,56463,56464,56466],{},[898,56465,1710],{},[1716,56467,2085],{},[1762,56469,2583],{},[6927,56471,56472,56474],{},[898,56473,1734],{},[1716,56475,2085],{},[902,56477,56478],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,56481,56483],{"className":56482},[886],[888,56484,56485],{"xmlns":890},[892,56486,56487,56511],{},[895,56488,56489,56491,56493,56499,56501,56503,56505],{},[1716,56490,2085],{},[1762,56492,2583],{},[6927,56494,56495,56497],{},[898,56496,1734],{},[1716,56498,2085],{},[1762,56500,2583],{},[898,56502,2044],{},[1762,56504,2583],{},[6927,56506,56507,56509],{},[898,56508,1710],{},[1716,56510,2085],{},[902,56512,56032],{"encoding":904},[123,56514,56515,56530,56531,56553,56554,56579,56580,26469,56606,1655,56638,1659],{},[883,56516,56518],{"className":56517},[886],[888,56519,56520],{"xmlns":890},[892,56521,56522,56528],{},[895,56523,56524,56526],{},[898,56525,8195],{},[898,56527,6493],{},[902,56529,49825],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,56532,56534],{"className":56533},[886],[888,56535,56536],{"xmlns":890},[892,56537,56538,56550],{},[895,56539,56540,56542,56544],{},[898,56541,1710],{},[1712,56543,1714],{},[6927,56545,56546,56548],{},[898,56547,1710],{},[1716,56549,2085],{},[902,56551,56552],{"encoding":904},"P = P_0"," v pásu ",[883,56555,56557],{"className":56556},[886],[888,56558,56559],{"xmlns":890},[892,56560,56561,56577],{},[895,56562,56563,56565,56567,56569,56575],{},[1712,56564,7910],{"stretchy":1903},[1716,56566,2085],{},[1712,56568,3138],{"separator":2565},[6927,56570,56571,56573],{},[898,56572,1734],{},[1716,56574,2085],{},[1712,56576,7925],{"stretchy":1903},[902,56578,56427],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,56581,56583],{"className":56582},[886],[888,56584,56585],{"xmlns":890},[892,56586,56587,56603],{},[895,56588,56589,56595,56597,56599,56601],{},[6927,56590,56591,56593],{},[898,56592,1710],{},[1716,56594,2085],{},[1762,56596,2583],{},[898,56598,28128],{},[1762,56600,2583],{},[898,56602,2044],{},[902,56604,56605],{"encoding":904},"P_0\\,B\\,A",[883,56607,56609],{"className":56608},[886],[888,56610,56611],{"xmlns":890},[892,56612,56613,56635],{},[895,56614,56615,56617,56619,56621,56623,56625,56627,56629,56631,56633],{},[898,56616,28128],{},[1712,56618,1714],{},[1712,56620,7910],{"stretchy":1903},[1716,56622,2085],{},[1712,56624,3138],{"separator":2565},[898,56626,1969],{},[1712,56628,1904],{"stretchy":1903},[1716,56630,2085],{},[1712,56632,1910],{"stretchy":1903},[1712,56634,7925],{"stretchy":1903},[902,56636,56637],{"encoding":904},"B = [0, D(0)]",[883,56639,56641],{"className":56640},[886],[888,56642,56643],{"xmlns":890},[892,56644,56645,56669],{},[895,56646,56647,56649,56651,56653,56659,56661,56667],{},[898,56648,2044],{},[1712,56650,1714],{},[1712,56652,7910],{"stretchy":1903},[6927,56654,56655,56657],{},[898,56656,1734],{},[1716,56658,2085],{},[1712,56660,3138],{"separator":2565},[6927,56662,56663,56665],{},[898,56664,1710],{},[1716,56666,2085],{},[1712,56668,7925],{"stretchy":1903},[902,56670,56087],{"encoding":904},[724,56672,56673],{},[614,56674,56675,56676,56689,56690,56723,56724,34017,56749,1659],{},"Obrázek 2.24: Křivka poptávky ",[883,56677,56679],{"className":56678},[886],[888,56680,56681],{"xmlns":890},[892,56682,56683,56687],{},[895,56684,56685],{},[898,56686,1969],{},[902,56688,1969],{"encoding":904},", bod ",[883,56691,56693],{"className":56692},[886],[888,56694,56695],{"xmlns":890},[892,56696,56697,56721],{},[895,56698,56699,56701,56703,56705,56711,56713,56719],{},[898,56700,2044],{},[1712,56702,1714],{},[1712,56704,7910],{"stretchy":1903},[6927,56706,56707,56709],{},[898,56708,1734],{},[1716,56710,2085],{},[1712,56712,3138],{"separator":2565},[6927,56714,56715,56717],{},[898,56716,1710],{},[1716,56718,2085],{},[1712,56720,7925],{"stretchy":1903},[902,56722,56087],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,56725,56727],{"className":56726},[886],[888,56728,56729],{"xmlns":890},[892,56730,56731,56747],{},[895,56732,56733,56739,56741,56743,56745],{},[6927,56734,56735,56737],{},[898,56736,1710],{},[1716,56738,2085],{},[1762,56740,2583],{},[898,56742,28128],{},[1762,56744,2583],{},[898,56746,2044],{},[902,56748,56605],{"encoding":904},[883,56750,56752],{"className":56751},[886],[888,56753,56754],{"xmlns":890},[892,56755,56756,56762],{},[895,56757,56758,56760],{},[898,56759,8195],{},[898,56761,6493],{},[902,56763,49825],{"encoding":904},[41845,56765],{},[115,56767,56769,56770,1910],{"id":56768},"přebytek-výrobce-psps","Přebytek výrobce (",[883,56771,56773],{"className":56772},[886],[888,56774,56775],{"xmlns":890},[892,56776,56777,56783],{},[895,56778,56779,56781],{},[898,56780,1710],{},[898,56782,6493],{},[902,56784,49844],{"encoding":904},[198,56786,56788],{"id":56787},"definice-vzorec-215","Definice (vzorec 2.15)",[724,56790,56791,56792,56220,56815,56238,56832,2854],{},"Analogicky — pro nabídku ",[883,56793,56795],{"className":56794},[886],[888,56796,56797],{"xmlns":890},[892,56798,56799,56813],{},[895,56800,56801,56803,56805,56807,56809,56811],{},[898,56802,1710],{},[1712,56804,1714],{},[898,56806,6493],{},[1712,56808,1904],{"stretchy":1903},[898,56810,1734],{},[1712,56812,1910],{"stretchy":1903},[902,56814,45946],{"encoding":904},[883,56816,56818],{"className":56817},[886],[888,56819,56820],{"xmlns":890},[892,56821,56822,56830],{},[895,56823,56824],{},[6927,56825,56826,56828],{},[898,56827,1734],{},[1716,56829,2085],{},[902,56831,43183],{"encoding":904},[883,56833,56835],{"className":56834},[886],[888,56836,56837],{"xmlns":890},[892,56838,56839,56861],{},[895,56840,56841,56847,56849,56851,56853,56859],{},[6927,56842,56843,56845],{},[898,56844,1710],{},[1716,56846,2085],{},[1712,56848,1714],{},[898,56850,6493],{},[1712,56852,1904],{"stretchy":1903},[6927,56854,56855,56857],{},[898,56856,1734],{},[1716,56858,2085],{},[1712,56860,1910],{"stretchy":1903},[902,56862,55962],{"encoding":904},[883,56864,56866],{"className":56865},[886],[888,56867,56868],{"xmlns":890,"display":32941},[892,56869,56870,56946],{},[25629,56871,56872],{"width":32946},[25634,56873,56874,56876,56940,56942],{},[25637,56875],{"width":32951},[25637,56877,56878],{},[895,56879,56880,56882,56884,56886,56892,56894,56896,56902,56904,56910,56912,56924,56926,56928,56930,56932,56934,56936,56938],{},[898,56881,1710],{},[898,56883,6493],{},[1712,56885,1904],{"stretchy":1903},[6927,56887,56888,56890],{},[898,56889,1734],{},[1716,56891,2085],{},[1712,56893,1910],{"stretchy":1903},[1712,56895,1714],{},[6927,56897,56898,56900],{},[898,56899,1710],{},[1716,56901,2085],{},[1762,56903,2583],{},[6927,56905,56906,56908],{},[898,56907,1734],{},[1716,56909,2085],{},[1712,56911,2219],{},[6989,56913,56914,56916,56918],{},[1712,56915,16042],{},[1716,56917,2085],{},[6927,56919,56920,56922],{},[898,56921,1734],{},[1716,56923,2085],{},[898,56925,6493],{},[1712,56927,1904],{"stretchy":1903},[898,56929,1734],{},[1712,56931,1910],{"stretchy":1903},[1762,56933,2583],{},[898,56935,2468],{},[898,56937,1734],{},[898,56939,1659],{"mathvariant":2003},[25637,56941],{"width":32951},[25637,56943,56944],{},[1762,56945,50044],{},[902,56947,50047],{"encoding":904},[198,56949,7868],{"id":56950},"geometrická-interpretace-1",[120,56952,56953,57001,57062],{},[123,56954,56955,4831,56980,56983,56984,1659],{},[883,56956,56958],{"className":56957},[886],[888,56959,56960],{"xmlns":890},[892,56961,56962,56978],{},[895,56963,56964,56970,56972],{},[6927,56965,56966,56968],{},[898,56967,1710],{},[1716,56969,2085],{},[1762,56971,2583],{},[6927,56973,56974,56976],{},[898,56975,1734],{},[1716,56977,2085],{},[902,56979,56478],{"encoding":904},[38,56981,56982],{},"tržba"," výrobce za prodané množství ",[883,56985,56987],{"className":56986},[886],[888,56988,56989],{"xmlns":890},[892,56990,56991,56999],{},[895,56992,56993],{},[6927,56994,56995,56997],{},[898,56996,1734],{},[1716,56998,2085],{},[902,57000,43183],{"encoding":904},[123,57002,57003,57043,57044,57061],{},[883,57004,57006],{"className":57005},[886],[888,57007,57008],{"xmlns":890},[892,57009,57010,57040],{},[895,57011,57012],{},[2563,57013,57014,57026,57028,57030,57032,57034,57036,57038],{"scriptlevel":2085,"displaystyle":2565},[6989,57015,57016,57018,57020],{},[1712,57017,16042],{},[1716,57019,2085],{},[6927,57021,57022,57024],{},[898,57023,1734],{},[1716,57025,2085],{},[898,57027,6493],{},[1712,57029,1904],{"stretchy":1903},[898,57031,1734],{},[1712,57033,1910],{"stretchy":1903},[1762,57035,2583],{},[898,57037,2468],{},[898,57039,1734],{},[902,57041,57042],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,57045,57047],{"className":57046},[886],[888,57048,57049],{"xmlns":890},[892,57050,57051,57059],{},[895,57052,57053],{},[6927,57054,57055,57057],{},[898,57056,1734],{},[1716,57058,2085],{},[902,57060,43183],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,57063,57064,57079,57080,57101,57102,1659],{},[883,57065,57067],{"className":57066},[886],[888,57068,57069],{"xmlns":890},[892,57070,57071,57077],{},[895,57072,57073,57075],{},[898,57074,1710],{},[898,57076,6493],{},[902,57078,49844],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,57081,57083],{"className":57082},[886],[888,57084,57085],{"xmlns":890},[892,57086,57087,57099],{},[895,57088,57089,57091,57093],{},[898,57090,1710],{},[1712,57092,1714],{},[6927,57094,57095,57097],{},[898,57096,1710],{},[1716,57098,2085],{},[902,57100,56552],{"encoding":904}," a křivkou nabídky v pásu ",[883,57103,57105],{"className":57104},[886],[888,57106,57107],{"xmlns":890},[892,57108,57109,57125],{},[895,57110,57111,57113,57115,57117,57123],{},[1712,57112,7910],{"stretchy":1903},[1716,57114,2085],{},[1712,57116,3138],{"separator":2565},[6927,57118,57119,57121],{},[898,57120,1734],{},[1716,57122,2085],{},[1712,57124,7925],{"stretchy":1903},[902,57126,56427],{"encoding":904},[724,57128,57129],{},[614,57130,57131],{},"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.",[41845,57133],{},[1636,57135,57136,57141],{},[724,57137,57138,57140],{},[883,57139,2370],{}," Postup výpočtu CS a PS",[152,57142,57143,57274,57384,57413,57547],{},[123,57144,57145,57146,57163,57164,57195,57196,57227,57228,1659],{},"Zjisti (nebo si zvol) množství ",[883,57147,57149],{"className":57148},[886],[888,57150,57151],{"xmlns":890},[892,57152,57153,57161],{},[895,57154,57155],{},[6927,57156,57157,57159],{},[898,57158,1734],{},[1716,57160,2085],{},[902,57162,43183],{"encoding":904}," a odpovídající cenu ",[883,57165,57167],{"className":57166},[886],[888,57168,57169],{"xmlns":890},[892,57170,57171,57193],{},[895,57172,57173,57179,57181,57183,57185,57191],{},[6927,57174,57175,57177],{},[898,57176,1710],{},[1716,57178,2085],{},[1712,57180,1714],{},[898,57182,1969],{},[1712,57184,1904],{"stretchy":1903},[6927,57186,57187,57189],{},[898,57188,1734],{},[1716,57190,2085],{},[1712,57192,1910],{"stretchy":1903},[902,57194,55930],{"encoding":904}," resp. ",[883,57197,57199],{"className":57198},[886],[888,57200,57201],{"xmlns":890},[892,57202,57203,57225],{},[895,57204,57205,57211,57213,57215,57217,57223],{},[6927,57206,57207,57209],{},[898,57208,1710],{},[1716,57210,2085],{},[1712,57212,1714],{},[898,57214,6493],{},[1712,57216,1904],{"stretchy":1903},[6927,57218,57219,57221],{},[898,57220,1734],{},[1716,57222,2085],{},[1712,57224,1910],{"stretchy":1903},[902,57226,55962],{"encoding":904},". V rovnováze platí ",[883,57229,57231],{"className":57230},[886],[888,57232,57233],{"xmlns":890},[892,57234,57235,57271],{},[895,57236,57237,57239,57241,57247,57249,57251,57253,57255,57261,57263,57265],{},[898,57238,1969],{},[1712,57240,1904],{"stretchy":1903},[2037,57242,57243,57245],{},[898,57244,1734],{},[898,57246,2041],{},[1712,57248,1910],{"stretchy":1903},[1712,57250,1714],{},[898,57252,6493],{},[1712,57254,1904],{"stretchy":1903},[2037,57256,57257,57259],{},[898,57258,1734],{},[898,57260,2041],{},[1712,57262,1910],{"stretchy":1903},[1712,57264,1714],{},[2037,57266,57267,57269],{},[898,57268,1710],{},[898,57270,2041],{},[902,57272,57273],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,57275,57276,57277,25001,57315,57330,57331,25001,57369,1691],{},"Spočti určitý integrál ",[883,57278,57280],{"className":57279},[886],[888,57281,57282],{"xmlns":890},[892,57283,57284,57312],{},[895,57285,57286,57298,57300,57302,57304,57306,57308,57310],{},[6989,57287,57288,57290,57292],{},[1712,57289,16042],{},[1716,57291,2085],{},[6927,57293,57294,57296],{},[898,57295,1734],{},[1716,57297,2085],{},[898,57299,1969],{},[1712,57301,1904],{"stretchy":1903},[898,57303,1734],{},[1712,57305,1910],{"stretchy":1903},[1762,57307,2583],{},[898,57309,2468],{},[898,57311,1734],{},[902,57313,57314],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,57316,57318],{"className":57317},[886],[888,57319,57320],{"xmlns":890},[892,57321,57322,57328],{},[895,57323,57324,57326],{},[898,57325,8195],{},[898,57327,6493],{},[902,57329,49825],{"encoding":904},") nebo ",[883,57332,57334],{"className":57333},[886],[888,57335,57336],{"xmlns":890},[892,57337,57338,57366],{},[895,57339,57340,57352,57354,57356,57358,57360,57362,57364],{},[6989,57341,57342,57344,57346],{},[1712,57343,16042],{},[1716,57345,2085],{},[6927,57347,57348,57350],{},[898,57349,1734],{},[1716,57351,2085],{},[898,57353,6493],{},[1712,57355,1904],{"stretchy":1903},[898,57357,1734],{},[1712,57359,1910],{"stretchy":1903},[1762,57361,2583],{},[898,57363,2468],{},[898,57365,1734],{},[902,57367,57368],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,57370,57372],{"className":57371},[886],[888,57373,57374],{"xmlns":890},[892,57375,57376,57382],{},[895,57377,57378,57380],{},[898,57379,1710],{},[898,57381,6493],{},[902,57383,49844],{"encoding":904},[123,57385,57386,57387,1659],{},"Sestav obdélník ",[883,57388,57390],{"className":57389},[886],[888,57391,57392],{"xmlns":890},[892,57393,57394,57410],{},[895,57395,57396,57402,57404],{},[6927,57397,57398,57400],{},[898,57399,1710],{},[1716,57401,2085],{},[1712,57403,1783],{},[6927,57405,57406,57408],{},[898,57407,1734],{},[1716,57409,2085],{},[902,57411,57412],{"encoding":904},"P_0 \\cdot Q_0",[123,57414,57415,57416],{},"Dosaď:\n",[120,57417,57418,57483],{},[123,57419,57420,57478,57479,57482],{},[883,57421,57423],{"className":57422},[886],[888,57424,57425],{"xmlns":890},[892,57426,57427,57475],{},[895,57428,57429,57431,57433,57435,57447,57449,57451,57453,57455,57457,57459,57461,57463,57469],{},[898,57430,8195],{},[898,57432,6493],{},[1712,57434,1714],{},[6989,57436,57437,57439,57441],{},[1712,57438,16042],{},[1716,57440,2085],{},[6927,57442,57443,57445],{},[898,57444,1734],{},[1716,57446,2085],{},[898,57448,1969],{},[1712,57450,1904],{"stretchy":1903},[898,57452,1734],{},[1712,57454,1910],{"stretchy":1903},[1762,57456,2583],{},[898,57458,2468],{},[898,57460,1734],{},[1712,57462,2219],{},[6927,57464,57465,57467],{},[898,57466,1710],{},[1716,57468,2085],{},[6927,57470,57471,57473],{},[898,57472,1734],{},[1716,57474,2085],{},[902,57476,57477],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,57480,57481],{},"mínus"," obdélník)",[123,57484,57485,57543,57544,57546],{},[883,57486,57488],{"className":57487},[886],[888,57489,57490],{"xmlns":890},[892,57491,57492,57540],{},[895,57493,57494,57496,57498,57500,57506,57512,57514,57526,57528,57530,57532,57534,57536,57538],{},[898,57495,1710],{},[898,57497,6493],{},[1712,57499,1714],{},[6927,57501,57502,57504],{},[898,57503,1710],{},[1716,57505,2085],{},[6927,57507,57508,57510],{},[898,57509,1734],{},[1716,57511,2085],{},[1712,57513,2219],{},[6989,57515,57516,57518,57520],{},[1712,57517,16042],{},[1716,57519,2085],{},[6927,57521,57522,57524],{},[898,57523,1734],{},[1716,57525,2085],{},[898,57527,6493],{},[1712,57529,1904],{"stretchy":1903},[898,57531,1734],{},[1712,57533,1910],{"stretchy":1903},[1762,57535,2583],{},[898,57537,2468],{},[898,57539,1734],{},[902,57541,57542],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,57545,57481],{}," integrál)",[123,57548,57549,57550,57553],{},"Kontrola znaménka: obě hodnoty musí být ",[38,57551,57552],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[41845,57555],{},[115,57557,57559],{"id":57558},"příklady","Příklady",[198,57561,57563],{"id":57562},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1636,57565,57566],{},[724,57567,57568,57571,57572,52596,57595,57618,57619,1343,57639,1343,57656,1343,57673,57690,57691,57767,57768,57785,57786,57799],{},[883,57569,57570],{},"!example"," Zadání\nJsou dány poptávka ",[883,57573,57575],{"className":57574},[886],[888,57576,57577],{"xmlns":890},[892,57578,57579,57593],{},[895,57580,57581,57583,57585,57587,57589,57591],{},[898,57582,1710],{},[1712,57584,1714],{},[898,57586,207],{},[898,57588,1734],{},[1712,57590,3145],{},[898,57592,7544],{},[902,57594,41935],{"encoding":904},[883,57596,57598],{"className":57597},[886],[888,57599,57600],{"xmlns":890},[892,57601,57602,57616],{},[895,57603,57604,57606,57608,57610,57612,57614],{},[898,57605,1710],{},[1712,57607,1714],{},[898,57609,7585],{},[898,57611,1734],{},[1712,57613,3145],{},[898,57615,2468],{},[902,57617,45117],{"encoding":904}," s hodnotami ",[883,57620,57622],{"className":57621},[886],[888,57623,57624],{"xmlns":890},[892,57625,57626,57636],{},[895,57627,57628,57630,57632,57634],{},[898,57629,207],{},[1712,57631,1714],{},[1712,57633,2219],{},[1716,57635,6198],{},[902,57637,57638],{"encoding":904},"a = -3",[883,57640,57642],{"className":57641},[886],[888,57643,57644],{"xmlns":890},[892,57645,57646,57654],{},[895,57647,57648,57650,57652],{},[898,57649,7544],{},[1712,57651,1714],{},[1716,57653,3018],{},[902,57655,53519],{"encoding":904},[883,57657,57659],{"className":57658},[886],[888,57660,57661],{"xmlns":890},[892,57662,57663,57671],{},[895,57664,57665,57667,57669],{},[898,57666,7585],{},[1712,57668,1714],{},[1716,57670,2814],{},[902,57672,53537],{"encoding":904},[883,57674,57676],{"className":57675},[886],[888,57677,57678],{"xmlns":890},[892,57679,57680,57688],{},[895,57681,57682,57684,57686],{},[898,57683,2468],{},[1712,57685,1714],{},[1716,57687,1718],{},[902,57689,53555],{"encoding":904},".\nRovnovážné množství:\n",[883,57692,57694],{"className":57693},[886],[888,57695,57696],{"xmlns":890},[892,57697,57698,57764],{},[895,57699,57700,57706,57708,57726,57728,57752,57754,57760,57762],{},[2037,57701,57702,57704],{},[898,57703,1734],{},[898,57705,2041],{},[1712,57707,1714],{},[2567,57709,57710,57718],{},[895,57711,57712,57714,57716],{},[898,57713,7544],{},[1712,57715,2219],{},[898,57717,2468],{},[895,57719,57720,57722,57724],{},[898,57721,7585],{},[1712,57723,2219],{},[898,57725,207],{},[1712,57727,1714],{},[2567,57729,57730,57738],{},[895,57731,57732,57734,57736],{},[1716,57733,3018],{},[1712,57735,2219],{},[1716,57737,1718],{},[895,57739,57740,57742,57744,57746,57748,57750],{},[1716,57741,2814],{},[1712,57743,2219],{},[1712,57745,1904],{"stretchy":1903},[1712,57747,2219],{},[1716,57749,6198],{},[1712,57751,1910],{"stretchy":1903},[1712,57753,1714],{},[2567,57755,57756,57758],{},[1716,57757,42894],{},[1716,57759,49281],{},[1712,57761,3712],{},[1716,57763,49286],{},[902,57765,57766],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,57769,57771],{"className":57770},[886],[888,57772,57773],{"xmlns":890},[892,57774,57775,57783],{},[895,57776,57777],{},[2037,57778,57779,57781],{},[898,57780,1734],{},[898,57782,2041],{},[902,57784,47278],{"encoding":904}," (a) při změně samotného parametru ",[883,57787,57789],{"className":57788},[886],[888,57790,57791],{"xmlns":890},[892,57792,57793,57797],{},[895,57794,57795],{},[898,57796,7585],{},[902,57798,7585],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,57801,57802],{},[38,57803,57804,57805,8093,57818,3072,57831,7119],{},"Řešení (a) — změna ",[883,57806,57808],{"className":57807},[886],[888,57809,57810],{"xmlns":890},[892,57811,57812,57816],{},[895,57813,57814],{},[898,57815,7585],{},[902,57817,7585],{"encoding":904},[883,57819,57821],{"className":57820},[886],[888,57822,57823],{"xmlns":890},[892,57824,57825,57829],{},[895,57826,57827],{},[1716,57828,2814],{},[902,57830,49321],{"encoding":904},[883,57832,57834],{"className":57833},[886],[888,57835,57836],{"xmlns":890},[892,57837,57838,57842],{},[895,57839,57840],{},[1716,57841,24196],{},[902,57843,49335],{"encoding":904},[724,57845,57846,57847,57911,57912,2854],{},"Pomocí vzorce (2.13) pro ",[883,57848,57850],{"className":57849},[886],[888,57851,57852],{"xmlns":890},[892,57853,57854,57908],{},[895,57855,57856,57876,57878,57880],{},[2563,57857,57858],{"scriptlevel":2085,"displaystyle":2565},[2567,57859,57860,57870],{},[895,57861,57862,57864],{},[898,57863,14744],{"mathvariant":2003},[2037,57865,57866,57868],{},[898,57867,1734],{},[898,57869,2041],{},[895,57871,57872,57874],{},[898,57873,14744],{"mathvariant":2003},[898,57875,7585],{},[1712,57877,1714],{},[1712,57879,2219],{},[2563,57881,57882],{"scriptlevel":2085,"displaystyle":2565},[2567,57883,57884,57892],{},[895,57885,57886,57888,57890],{},[898,57887,7544],{},[1712,57889,2219],{},[898,57891,2468],{},[895,57893,57894,57896,57898,57900,57902],{},[1712,57895,1904],{"stretchy":1903},[898,57897,7585],{},[1712,57899,2219],{},[898,57901,207],{},[2037,57903,57904,57906],{},[1712,57905,1910],{"stretchy":1903},[1716,57907,2787],{},[902,57909,57910],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,57913,57915],{"className":57914},[886],[888,57916,57917],{"xmlns":890},[892,57918,57919,57941],{},[895,57920,57921,57923],{},[1712,57922,2219],{},[2563,57924,57925],{"scriptlevel":2085,"displaystyle":2565},[2567,57926,57927,57933],{},[2037,57928,57929,57931],{},[898,57930,1734],{},[898,57932,2041],{},[895,57934,57935,57937,57939],{},[898,57936,7585],{},[1712,57938,2219],{},[898,57940,207],{},[902,57942,57943],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,57945,57947],{"className":57946},[886],[888,57948,57949],{"xmlns":890,"display":32941},[892,57950,57951,58007],{},[895,57952,57953,57955,57961,57963,57965,57981,57983,57985,57987,57989,57991,57997,57999,58001,58003,58005],{},[898,57954,2468],{},[2037,57956,57957,57959],{},[898,57958,1734],{},[898,57960,2041],{},[1712,57962,1714],{},[1712,57964,2219],{},[2567,57966,57967,57973],{},[2037,57968,57969,57971],{},[898,57970,1734],{},[898,57972,2041],{},[895,57974,57975,57977,57979],{},[898,57976,7585],{},[1712,57978,2219],{},[898,57980,207],{},[1762,57982,2583],{},[898,57984,2468],{},[898,57986,7585],{},[1712,57988,1714],{},[1712,57990,2219],{},[2567,57992,57993,57995],{},[1716,57994,49449],{},[1716,57996,49281],{},[1712,57998,1783],{},[1716,58000,6607],{},[1712,58002,3712],{},[1712,58004,2219],{},[1716,58006,49421],{},[902,58008,58009],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,58011,58012],{},"Nové rovnovážné množství:",[883,58014,58016],{"className":58015},[886],[888,58017,58018],{"xmlns":890,"display":32941},[892,58019,58020,58043],{},[895,58021,58022,58030,58032,58034,58036,58038,58040],{},[6989,58023,58024,58026,58028],{},[898,58025,1734],{},[1716,58027,2222],{},[898,58029,2041],{},[1712,58031,3740],{},[1716,58033,49449],{},[1712,58035,2219],{},[1716,58037,49454],{},[1712,58039,1714],{},[1716,58041,58042],{},"8,326.",[902,58044,58045],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,58047,58048,3245,58051,1343,58078,1343,58100,1343,58122,3401,58144,1343,58163,1343,58184,1343,58203,1659],{},[38,58049,58050],{},"Řešení (b) — současná změna všech parametrů:",[883,58052,58054],{"className":58053},[886],[888,58055,58056],{"xmlns":890},[892,58057,58058,58075],{},[895,58059,58060,58062,58064,58066,58068,58070,58072],{},[898,58061,207],{},[1712,58063,2854],{},[1712,58065,2219],{},[1716,58067,6198],{},[1712,58069,2082],{},[1712,58071,2219],{},[1716,58073,58074],{},"2,5",[902,58076,58077],{"encoding":904},"a: -3 \\to -2{,}5",[883,58079,58081],{"className":58080},[886],[888,58082,58083],{"xmlns":890},[892,58084,58085,58097],{},[895,58086,58087,58089,58091,58093,58095],{},[898,58088,7544],{},[1712,58090,2854],{},[1716,58092,3018],{},[1712,58094,2082],{},[1716,58096,19912],{},[902,58098,58099],{"encoding":904},"b: 40 \\to 35",[883,58101,58103],{"className":58102},[886],[888,58104,58105],{"xmlns":890},[892,58106,58107,58119],{},[895,58108,58109,58111,58113,58115,58117],{},[898,58110,7585],{},[1712,58112,2854],{},[1716,58114,2814],{},[1712,58116,2082],{},[1716,58118,24196],{},[902,58120,58121],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,58123,58125],{"className":58124},[886],[888,58126,58127],{"xmlns":890},[892,58128,58129,58141],{},[895,58130,58131,58133,58135,58137,58139],{},[898,58132,2468],{},[1712,58134,2854],{},[1716,58136,1718],{},[1712,58138,2082],{},[1716,58140,8316],{},[902,58142,58143],{"encoding":904},"d: 10 \\to 11",[883,58145,58147],{"className":58146},[886],[888,58148,58149],{"xmlns":890},[892,58150,58151,58161],{},[895,58152,58153,58155,58157,58159],{},[898,58154,2468],{},[898,58156,207],{},[1712,58158,1714],{},[1716,58160,2814],{},[902,58162,49487],{"encoding":904},[883,58164,58166],{"className":58165},[886],[888,58167,58168],{"xmlns":890},[892,58169,58170,58182],{},[895,58171,58172,58174,58176,58178,58180],{},[898,58173,2468],{},[898,58175,7544],{},[1712,58177,1714],{},[1712,58179,2219],{},[1716,58181,3068],{},[902,58183,49509],{"encoding":904},[883,58185,58187],{"className":58186},[886],[888,58188,58189],{"xmlns":890},[892,58190,58191,58201],{},[895,58192,58193,58195,58197,58199],{},[898,58194,2468],{},[898,58196,7585],{},[1712,58198,1714],{},[1716,58200,6607],{},[902,58202,49529],{"encoding":904},[883,58204,58206],{"className":58205},[886],[888,58207,58208],{"xmlns":890},[892,58209,58210,58220],{},[895,58211,58212,58214,58216,58218],{},[898,58213,2468],{},[898,58215,2468],{},[1712,58217,1714],{},[1716,58219,2222],{},[902,58221,49549],{"encoding":904},[724,58223,58224,58225,58283],{},"Totální diferenciál ",[883,58226,58228],{"className":58227},[886],[888,58229,58230],{"xmlns":890},[892,58231,58232,58280],{},[895,58233,58234,58240,58242,58244,58246,58248,58250,58252,58254,58256,58258,58260],{},[2037,58235,58236,58238],{},[898,58237,1734],{},[898,58239,2041],{},[1712,58241,1904],{"stretchy":1903},[898,58243,207],{},[1712,58245,3138],{"separator":2565},[898,58247,7544],{},[1712,58249,3138],{"separator":2565},[898,58251,7585],{},[1712,58253,3138],{"separator":2565},[898,58255,2468],{},[1712,58257,1910],{"stretchy":1903},[1712,58259,1714],{},[2563,58261,58262],{"scriptlevel":2085,"displaystyle":2565},[2567,58263,58264,58272],{},[895,58265,58266,58268,58270],{},[898,58267,7544],{},[1712,58269,2219],{},[898,58271,2468],{},[895,58273,58274,58276,58278],{},[898,58275,7585],{},[1712,58277,2219],{},[898,58279,207],{},[902,58281,58282],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,58285,58287],{"className":58286},[886],[888,58288,58289],{"xmlns":890,"display":32941},[892,58290,58291,58411],{},[895,58292,58293,58295,58301,58303,58329,58331,58333,58335,58337,58349,58351,58353,58355,58357,58383,58385,58387,58389,58391,58403,58405,58407,58409],{},[898,58294,2468],{},[2037,58296,58297,58299],{},[898,58298,1734],{},[898,58300,2041],{},[1712,58302,1714],{},[2567,58304,58305,58313],{},[895,58306,58307,58309,58311],{},[898,58308,7544],{},[1712,58310,2219],{},[898,58312,2468],{},[895,58314,58315,58317,58319,58321,58323],{},[1712,58316,1904],{"stretchy":1903},[898,58318,7585],{},[1712,58320,2219],{},[898,58322,207],{},[2037,58324,58325,58327],{},[1712,58326,1910],{"stretchy":1903},[1716,58328,2787],{},[1762,58330,2583],{},[898,58332,2468],{},[898,58334,207],{},[1712,58336,3145],{},[2567,58338,58339,58341],{},[1716,58340,2222],{},[895,58342,58343,58345,58347],{},[898,58344,7585],{},[1712,58346,2219],{},[898,58348,207],{},[1762,58350,2583],{},[898,58352,2468],{},[898,58354,7544],{},[1712,58356,2219],{},[2567,58358,58359,58367],{},[895,58360,58361,58363,58365],{},[898,58362,7544],{},[1712,58364,2219],{},[898,58366,2468],{},[895,58368,58369,58371,58373,58375,58377],{},[1712,58370,1904],{"stretchy":1903},[898,58372,7585],{},[1712,58374,2219],{},[898,58376,207],{},[2037,58378,58379,58381],{},[1712,58380,1910],{"stretchy":1903},[1716,58382,2787],{},[1762,58384,2583],{},[898,58386,2468],{},[898,58388,7585],{},[1712,58390,2219],{},[2567,58392,58393,58395],{},[1716,58394,2222],{},[895,58396,58397,58399,58401],{},[898,58398,7585],{},[1712,58400,2219],{},[898,58402,207],{},[1762,58404,2583],{},[898,58406,2468],{},[898,58408,2468],{},[898,58410,1659],{"mathvariant":2003},[902,58412,58413],{"encoding":904},"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.",[724,58415,58416,58417,1343,58439,1343,58470,8558],{},"Dosazením číselných hodnot (",[883,58418,58420],{"className":58419},[886],[888,58421,58422],{"xmlns":890},[892,58423,58424,58436],{},[895,58425,58426,58428,58430,58432,58434],{},[898,58427,7585],{},[1712,58429,2219],{},[898,58431,207],{},[1712,58433,1714],{},[1716,58435,49281],{},[902,58437,58438],{"encoding":904},"c - a = 3{,}5",[883,58440,58442],{"className":58441},[886],[888,58443,58444],{"xmlns":890},[892,58445,58446,58467],{},[895,58447,58448,58450,58452,58454,58456,58462,58464],{},[1712,58449,1904],{"stretchy":1903},[898,58451,7585],{},[1712,58453,2219],{},[898,58455,207],{},[2037,58457,58458,58460],{},[1712,58459,1910],{"stretchy":1903},[1716,58461,2787],{},[1712,58463,1714],{},[1716,58465,58466],{},"12,25",[902,58468,58469],{"encoding":904},"(c-a)^2 = 12{,}25",[883,58471,58473],{"className":58472},[886],[888,58474,58475],{"xmlns":890},[892,58476,58477,58489],{},[895,58478,58479,58481,58483,58485,58487],{},[898,58480,7544],{},[1712,58482,2219],{},[898,58484,2468],{},[1712,58486,1714],{},[1716,58488,42894],{},[902,58490,58491],{"encoding":904},"b - d = 30",[883,58493,58495],{"className":58494},[886],[888,58496,58497],{"xmlns":890,"display":32941},[892,58498,58499,58600],{},[895,58500,58501,58503,58509,58511,58519,58521,58523,58525,58527,58535,58537,58539,58541,58543,58545,58553,58555,58557,58559,58561,58569,58571,58573,58575,58577,58580,58582,58585,58587,58589,58591,58594,58596,58598],{},[898,58502,2468],{},[2037,58504,58505,58507],{},[898,58506,1734],{},[898,58508,2041],{},[1712,58510,3740],{},[2563,58512,58513],{"scriptlevel":2085,"displaystyle":1903},[2567,58514,58515,58517],{},[1716,58516,42894],{},[1716,58518,58466],{},[1712,58520,1904],{"stretchy":1903},[1716,58522,2814],{},[1712,58524,1910],{"stretchy":1903},[1712,58526,3145],{},[2563,58528,58529],{"scriptlevel":2085,"displaystyle":1903},[2567,58530,58531,58533],{},[1716,58532,2222],{},[1716,58534,49281],{},[1712,58536,1904],{"stretchy":1903},[1712,58538,2219],{},[1716,58540,3068],{},[1712,58542,1910],{"stretchy":1903},[1712,58544,2219],{},[2563,58546,58547],{"scriptlevel":2085,"displaystyle":1903},[2567,58548,58549,58551],{},[1716,58550,42894],{},[1716,58552,58466],{},[1712,58554,1904],{"stretchy":1903},[1716,58556,6607],{},[1712,58558,1910],{"stretchy":1903},[1712,58560,2219],{},[2563,58562,58563],{"scriptlevel":2085,"displaystyle":1903},[2567,58564,58565,58567],{},[1716,58566,2222],{},[1716,58568,49281],{},[1712,58570,1904],{"stretchy":1903},[1716,58572,2222],{},[1712,58574,1910],{"stretchy":1903},[1712,58576,3712],{},[1716,58578,58579],{},"1,224",[1712,58581,2219],{},[1716,58583,58584],{},"1,429",[1712,58586,2219],{},[1716,58588,49454],{},[1712,58590,2219],{},[1716,58592,58593],{},"0,286",[1712,58595,3712],{},[1712,58597,2219],{},[1716,58599,49700],{},[902,58601,58602],{"encoding":904},"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.",[724,58604,34940,58605,1659],{},[883,58606,58608],{"className":58607},[886],[888,58609,58610],{"xmlns":890},[892,58611,58612,58634],{},[895,58613,58614,58622,58624,58626,58628,58630,58632],{},[6989,58615,58616,58618,58620],{},[898,58617,1734],{},[1716,58619,2222],{},[898,58621,2041],{},[1712,58623,3740],{},[1716,58625,49449],{},[1712,58627,2219],{},[1716,58629,49731],{},[1712,58631,3712],{},[1716,58633,49736],{},[902,58635,58636],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1636,58638,58639],{},[724,58640,58641,58643,58644,58665,58666,58692,58693,58696,58697,58793,58794,58817,58818,58834],{},[883,58642,2203],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,58645,58647],{"className":58646},[886],[888,58648,58649],{"xmlns":890},[892,58650,58651,58663],{},[895,58652,58653,58655,58657,58659,58661],{},[898,58654,2004],{"mathvariant":2003},[898,58656,1734],{},[1712,58658,3740],{},[1712,58660,2219],{},[1716,58662,49766],{},[902,58664,49769],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,58667,58669],{"className":58668},[886],[888,58670,58671],{"xmlns":890},[892,58672,58673,58689],{},[895,58674,58675,58677,58683,58685,58687],{},[898,58676,2468],{},[2037,58678,58679,58681],{},[898,58680,1734],{},[898,58682,2041],{},[1712,58684,3712],{},[1712,58686,2219],{},[1716,58688,49731],{},[902,58690,58691],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,58694,58695],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,58698,58700],{"className":58699},[886],[888,58701,58702],{"xmlns":890},[892,58703,58704,58790],{},[895,58705,58706,58714,58716,58750,58752,58776,58778,58785,58787],{},[6989,58707,58708,58710,58712],{},[898,58709,1734],{},[1716,58711,2222],{},[898,58713,2041],{},[1712,58715,1714],{},[2567,58717,58718,58734],{},[895,58719,58720,58726,58728],{},[2037,58721,58722,58724],{},[898,58723,7544],{},[1712,58725,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,58727,2219],{},[2037,58729,58730,58732],{},[898,58731,2468],{},[1712,58733,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[895,58735,58736,58742,58744],{},[2037,58737,58738,58740],{},[898,58739,7585],{},[1712,58741,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,58743,2219],{},[2037,58745,58746,58748],{},[898,58747,207],{},[1712,58749,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,58751,1714],{},[2567,58753,58754,58762],{},[895,58755,58756,58758,58760],{},[1716,58757,19912],{},[1712,58759,2219],{},[1716,58761,8316],{},[895,58763,58764,58766,58768,58770,58772,58774],{},[1716,58765,24196],{},[1712,58767,2219],{},[1712,58769,1904],{"stretchy":1903},[1712,58771,2219],{},[1716,58773,58074],{},[1712,58775,1910],{"stretchy":1903},[1712,58777,1714],{},[2567,58779,58780,58782],{},[1716,58781,46675],{},[1716,58783,58784],{},"3,1",[1712,58786,3712],{},[1716,58788,58789],{},"7,742",[902,58791,58792],{"encoding":904},"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 ",[883,58795,58797],{"className":58796},[886],[888,58798,58799],{"xmlns":890},[892,58800,58801,58814],{},[895,58802,58803,58805,58807,58809,58811],{},[898,58804,2004],{"mathvariant":2003},[898,58806,1734],{},[1712,58808,3712],{},[1712,58810,2219],{},[1716,58812,58813],{},"0,829",[902,58815,58816],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,58819,58821],{"className":58820},[886],[888,58822,58823],{"xmlns":890},[892,58824,58825,58831],{},[895,58826,58827,58829],{},[1712,58828,2219],{},[1716,58830,49766],{},[902,58832,58833],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,58836,58837],{},[614,58838,58839,58840,58853],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,58841,58843],{"className":58842},[886],[888,58844,58845],{"xmlns":890},[892,58846,58847,58851],{},[895,58848,58849],{},[898,58850,1734],{},[902,58852,1734],{"encoding":904},", 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.",[198,58855,58857,58858],{"id":58856},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,58859,58861],{"className":58860},[886],[888,58862,58863],{"xmlns":890},[892,58864,58865,58871],{},[895,58866,58867,58869],{},[898,58868,1710],{},[898,58870,6493],{},[902,58872,49844],{"encoding":904},[1636,58874,58875],{},[724,58876,58877,58879,58880,58914,58915,58937],{},[883,58878,57570],{}," Zadání\nPro nabídku ",[883,58881,58883],{"className":58882},[886],[888,58884,58885],{"xmlns":890},[892,58886,58887,58911],{},[895,58888,58889,58891,58893,58895,58897,58899,58901,58903,58905,58907,58909],{},[898,58890,1710],{},[1712,58892,1714],{},[898,58894,6493],{},[1712,58896,1904],{"stretchy":1903},[898,58898,1734],{},[1712,58900,1910],{"stretchy":1903},[1712,58902,1714],{},[1716,58904,1718],{},[1712,58906,3145],{},[1716,58908,2787],{},[898,58910,1734],{},[902,58912,58913],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,58916,58918],{"className":58917},[886],[888,58919,58920],{"xmlns":890},[892,58921,58922,58934],{},[895,58923,58924,58930,58932],{},[6927,58925,58926,58928],{},[898,58927,1734],{},[1716,58929,2085],{},[1712,58931,1714],{},[1716,58933,1718],{},[902,58935,58936],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,58939,58940],{},[38,58941,27645],{},[724,58943,58944],{},"Odpovídající cena:",[883,58946,58948],{"className":58947},[886],[888,58949,58950],{"xmlns":890,"display":32941},[892,58951,58952,58987],{},[895,58953,58954,58960,58962,58964,58966,58968,58970,58972,58974,58976,58978,58980,58982,58984],{},[6927,58955,58956,58958],{},[898,58957,1710],{},[1716,58959,2085],{},[1712,58961,1714],{},[898,58963,6493],{},[1712,58965,1904],{"stretchy":1903},[1716,58967,1718],{},[1712,58969,1910],{"stretchy":1903},[1712,58971,1714],{},[1716,58973,1718],{},[1712,58975,3145],{},[1716,58977,2787],{},[1712,58979,1783],{},[1716,58981,1718],{},[1712,58983,1714],{},[1716,58985,58986],{},"30.",[902,58988,58989],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,58991,58992],{},"Dle vzorce (2.15):",[883,58994,58996],{"className":58995},[886],[888,58997,58998],{"xmlns":890,"display":32941},[892,58999,59000,59108],{},[895,59001,59002,59004,59006,59008,59010,59012,59014,59020,59026,59028,59036,59038,59040,59042,59044,59046,59048,59050,59052,59054,59056,59058,59060,59062,59064,59067,59069,59071,59073,59079,59087,59089,59091,59093,59095,59097,59099,59101,59103,59105],{},[898,59003,1710],{},[898,59005,6493],{},[1712,59007,1904],{"stretchy":1903},[1716,59009,1718],{},[1712,59011,1910],{"stretchy":1903},[1712,59013,1714],{},[6927,59015,59016,59018],{},[898,59017,1710],{},[1716,59019,2085],{},[6927,59021,59022,59024],{},[898,59023,1734],{},[1716,59025,2085],{},[1712,59027,2219],{},[6989,59029,59030,59032,59034],{},[1712,59031,16042],{},[1716,59033,2085],{},[1716,59035,1718],{},[1712,59037,1904],{"stretchy":1903},[1716,59039,1718],{},[1712,59041,3145],{},[1716,59043,2787],{},[898,59045,1734],{},[1712,59047,1910],{"stretchy":1903},[1762,59049,2583],{},[898,59051,2468],{},[898,59053,1734],{},[1712,59055,1714],{},[1716,59057,1718],{},[1712,59059,1783],{},[1716,59061,42894],{},[1712,59063,2219],{},[1712,59065,7910],{"fence":1903,"stretchy":2565,"minsize":59066,"maxsize":59066},"1.8em",[1716,59068,1718],{},[898,59070,1734],{},[1712,59072,3145],{},[2037,59074,59075,59077],{},[898,59076,1734],{},[1716,59078,2787],{},[6989,59080,59081,59083,59085],{},[1712,59082,7925],{"fence":1903,"stretchy":2565,"minsize":59066,"maxsize":59066},[1716,59084,2085],{},[1716,59086,1718],{},[1712,59088,1714],{},[1716,59090,34956],{},[1712,59092,2219],{},[1712,59094,1904],{"stretchy":1903},[1716,59096,1739],{},[1712,59098,3145],{},[1716,59100,1739],{},[1712,59102,1910],{"stretchy":1903},[1712,59104,1714],{},[1716,59106,59107],{},"100.",[902,59109,59110],{"encoding":904},"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.",[724,59112,59113,59114,59135,59136,59156],{},"Přebytek výrobce při množství ",[883,59115,59117],{"className":59116},[886],[888,59118,59119],{"xmlns":890},[892,59120,59121,59133],{},[895,59122,59123,59129,59131],{},[6927,59124,59125,59127],{},[898,59126,1734],{},[1716,59128,2085],{},[1712,59130,1714],{},[1716,59132,1718],{},[902,59134,58936],{"encoding":904}," je tedy ",[883,59137,59139],{"className":59138},[886],[888,59140,59141],{"xmlns":890},[892,59142,59143,59153],{},[895,59144,59145,59147,59149,59151],{},[898,59146,1710],{},[898,59148,6493],{},[1712,59150,1714],{},[1716,59152,1739],{},[902,59154,59155],{"encoding":904},"PS = 100"," (peněžních jednotek).",[41845,59158],{},[115,59160,59162],{"id":59161},"cheat-sheet","Cheat sheet",[16,59164,59165,59178],{},[19,59166,59167],{},[22,59168,59169,59172,59175],{},[25,59170,59171],{},"Veličina",[25,59173,59174],{},"Vzorec",[25,59176,59177],{},"Geometrie",[30,59179,59180,59298,59412,59480],{},[22,59181,59182,59210,59266],{},[35,59183,59184],{},[883,59185,59187],{"className":59186},[886],[888,59188,59189],{"xmlns":890},[892,59190,59191,59207],{},[895,59192,59193,59195,59197,59199,59205],{},[898,59194,8195],{},[898,59196,6493],{},[1712,59198,1904],{"stretchy":1903},[6927,59200,59201,59203],{},[898,59202,1734],{},[1716,59204,2085],{},[1712,59206,1910],{"stretchy":1903},[902,59208,59209],{"encoding":904},"CS(Q_0)",[35,59211,59212],{},[883,59213,59215],{"className":59214},[886],[888,59216,59217],{"xmlns":890},[892,59218,59219,59263],{},[895,59220,59221],{},[2563,59222,59223,59235,59237,59239,59241,59243,59245,59247,59249,59251,59257],{"scriptlevel":2085,"displaystyle":2565},[6989,59224,59225,59227,59229],{},[1712,59226,16042],{},[1716,59228,2085],{},[6927,59230,59231,59233],{},[898,59232,1734],{},[1716,59234,2085],{},[898,59236,1969],{},[1712,59238,1904],{"stretchy":1903},[898,59240,1734],{},[1712,59242,1910],{"stretchy":1903},[1762,59244,2583],{},[898,59246,2468],{},[898,59248,1734],{},[1712,59250,2219],{},[6927,59252,59253,59255],{},[898,59254,1710],{},[1716,59256,2085],{},[6927,59258,59259,59261],{},[898,59260,1734],{},[1716,59262,2085],{},[902,59264,59265],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,59267,59268,59269,59272,59273,59276,59277],{},"plocha ",[38,59270,59271],{},"pod"," křivkou poptávky, ",[38,59274,59275],{},"nad"," čárou ",[883,59278,59280],{"className":59279},[886],[888,59281,59282],{"xmlns":890},[892,59283,59284,59296],{},[895,59285,59286,59288,59290],{},[898,59287,1710],{},[1712,59289,1714],{},[6927,59291,59292,59294],{},[898,59293,1710],{},[1716,59295,2085],{},[902,59297,56552],{"encoding":904},[22,59299,59300,59328,59384],{},[35,59301,59302],{},[883,59303,59305],{"className":59304},[886],[888,59306,59307],{"xmlns":890},[892,59308,59309,59325],{},[895,59310,59311,59313,59315,59317,59323],{},[898,59312,1710],{},[898,59314,6493],{},[1712,59316,1904],{"stretchy":1903},[6927,59318,59319,59321],{},[898,59320,1734],{},[1716,59322,2085],{},[1712,59324,1910],{"stretchy":1903},[902,59326,59327],{"encoding":904},"PS(Q_0)",[35,59329,59330],{},[883,59331,59333],{"className":59332},[886],[888,59334,59335],{"xmlns":890},[892,59336,59337,59381],{},[895,59338,59339],{},[2563,59340,59341,59347,59353,59355,59367,59369,59371,59373,59375,59377,59379],{"scriptlevel":2085,"displaystyle":2565},[6927,59342,59343,59345],{},[898,59344,1710],{},[1716,59346,2085],{},[6927,59348,59349,59351],{},[898,59350,1734],{},[1716,59352,2085],{},[1712,59354,2219],{},[6989,59356,59357,59359,59361],{},[1712,59358,16042],{},[1716,59360,2085],{},[6927,59362,59363,59365],{},[898,59364,1734],{},[1716,59366,2085],{},[898,59368,6493],{},[1712,59370,1904],{"stretchy":1903},[898,59372,1734],{},[1712,59374,1910],{"stretchy":1903},[1762,59376,2583],{},[898,59378,2468],{},[898,59380,1734],{},[902,59382,59383],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,59385,59268,59386,59388,59389,59276,59391],{},[38,59387,59275],{}," křivkou nabídky, ",[38,59390,59271],{},[883,59392,59394],{"className":59393},[886],[888,59395,59396],{"xmlns":890},[892,59397,59398,59410],{},[895,59399,59400,59402,59404],{},[898,59401,1710],{},[1712,59403,1714],{},[6927,59405,59406,59408],{},[898,59407,1710],{},[1716,59409,2085],{},[902,59411,56552],{"encoding":904},[22,59413,59414,59417,59444],{},[35,59415,59416],{},"Výdaje \u002F tržby",[35,59418,59419],{},[883,59420,59422],{"className":59421},[886],[888,59423,59424],{"xmlns":890},[892,59425,59426,59442],{},[895,59427,59428,59434,59436],{},[6927,59429,59430,59432],{},[898,59431,1710],{},[1716,59433,2085],{},[1712,59435,1783],{},[6927,59437,59438,59440],{},[898,59439,1734],{},[1716,59441,2085],{},[902,59443,57412],{"encoding":904},[35,59445,59446,59447],{},"obdélník ",[883,59448,59450],{"className":59449},[886],[888,59451,59452],{"xmlns":890},[892,59453,59454,59478],{},[895,59455,59456,59458,59460,59466,59468,59470,59472],{},[1716,59457,2085],{},[1762,59459,2583],{},[6927,59461,59462,59464],{},[898,59463,1734],{},[1716,59465,2085],{},[1762,59467,2583],{},[898,59469,2044],{},[1762,59471,2583],{},[6927,59473,59474,59476],{},[898,59475,1710],{},[1716,59477,2085],{},[902,59479,56032],{"encoding":904},[22,59481,59482,59485,59508],{},[35,59483,59484],{},"Celkový přebytek",[35,59486,59487],{},[883,59488,59490],{"className":59489},[886],[888,59491,59492],{"xmlns":890},[892,59493,59494,59506],{},[895,59495,59496,59498,59500,59502,59504],{},[898,59497,8195],{},[898,59499,6493],{},[1712,59501,3145],{},[898,59503,1710],{},[898,59505,6493],{},[902,59507,55770],{"encoding":904},[35,59509,59510],{},"součet obou ploch v rovnováze",[41845,59512],{},[115,59514,20594],{"id":20593},[120,59516,59517,59539,59561,59605,59649,59712,59740],{},[123,59518,59519,14897,59521,1343,59536,59538],{},[38,59520,49809],{},[883,59522,59524],{"className":59523},[886],[888,59525,59526],{"xmlns":890},[892,59527,59528,59534],{},[895,59529,59530,59532],{},[898,59531,8195],{},[898,59533,6493],{},[902,59535,49825],{"encoding":904},[614,59537,49863],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,59540,59541,14897,59543,1343,59558,59560],{},[38,59542,49956],{},[883,59544,59546],{"className":59545},[886],[888,59547,59548],{"xmlns":890},[892,59549,59550,59556],{},[895,59551,59552,59554],{},[898,59553,1710],{},[898,59555,6493],{},[902,59557,49844],{"encoding":904},[614,59559,49959],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,59562,59563,4831,59566,1659],{},[38,59564,59565],{},"Ochota platit",[883,59567,59569],{"className":59568},[886],[888,59570,59571],{"xmlns":890},[892,59572,59573,59603],{},[895,59574,59575],{},[2563,59576,59577,59589,59591,59593,59595,59597,59599,59601],{"scriptlevel":2085,"displaystyle":2565},[6989,59578,59579,59581,59583],{},[1712,59580,16042],{},[1716,59582,2085],{},[6927,59584,59585,59587],{},[898,59586,1734],{},[1716,59588,2085],{},[898,59590,1969],{},[1712,59592,1904],{"stretchy":1903},[898,59594,1734],{},[1712,59596,1910],{"stretchy":1903},[1762,59598,2583],{},[898,59600,2468],{},[898,59602,1734],{},[902,59604,56400],{"encoding":904},[123,59606,59607,4831,59610,1659],{},[38,59608,59609],{},"Minimální cena výrobce",[883,59611,59613],{"className":59612},[886],[888,59614,59615],{"xmlns":890},[892,59616,59617,59647],{},[895,59618,59619],{},[2563,59620,59621,59633,59635,59637,59639,59641,59643,59645],{"scriptlevel":2085,"displaystyle":2565},[6989,59622,59623,59625,59627],{},[1712,59624,16042],{},[1716,59626,2085],{},[6927,59628,59629,59631],{},[898,59630,1734],{},[1716,59632,2085],{},[898,59634,6493],{},[1712,59636,1904],{"stretchy":1903},[898,59638,1734],{},[1712,59640,1910],{"stretchy":1903},[1762,59642,2583],{},[898,59644,2468],{},[898,59646,1734],{},[902,59648,57042],{"encoding":904},[123,59650,59651,4831,59654,57543,59679,1691],{},[38,59652,59653],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,59655,59657],{"className":59656},[886],[888,59658,59659],{"xmlns":890},[892,59660,59661,59677],{},[895,59662,59663,59669,59671],{},[6927,59664,59665,59667],{},[898,59666,1710],{},[1716,59668,2085],{},[1762,59670,2583],{},[6927,59672,59673,59675],{},[898,59674,1734],{},[1716,59676,2085],{},[902,59678,56478],{"encoding":904},[883,59680,59682],{"className":59681},[886],[888,59683,59684],{"xmlns":890},[892,59685,59686,59710],{},[895,59687,59688,59690,59692,59698,59700,59702,59704],{},[1716,59689,2085],{},[1762,59691,2583],{},[6927,59693,59694,59696],{},[898,59695,1734],{},[1716,59697,2085],{},[1762,59699,2583],{},[898,59701,2044],{},[1762,59703,2583],{},[6927,59705,59706,59708],{},[898,59707,1710],{},[1716,59709,2085],{},[902,59711,56032],{"encoding":904},[123,59713,59714,59717,59718,59739],{},[38,59715,59716],{},"Celkový přebytek trhu"," — součet ",[883,59719,59721],{"className":59720},[886],[888,59722,59723],{"xmlns":890},[892,59724,59725,59737],{},[895,59726,59727,59729,59731,59733,59735],{},[898,59728,8195],{},[898,59730,6493],{},[1712,59732,3145],{},[898,59734,1710],{},[898,59736,6493],{},[902,59738,55770],{"encoding":904}," v rovnovážném bodě.",[123,59741,59742,59744,59745,1343,59758,59771,59772,1659],{},[38,59743,7868],{}," — plochy ohraničené křivkami ",[883,59746,59748],{"className":59747},[886],[888,59749,59750],{"xmlns":890},[892,59751,59752,59756],{},[895,59753,59754],{},[898,59755,1969],{},[902,59757,1969],{"encoding":904},[883,59759,59761],{"className":59760},[886],[888,59762,59763],{"xmlns":890},[892,59764,59765,59769],{},[895,59766,59767],{},[898,59768,6493],{},[902,59770,6493],{"encoding":904}," a přímkou ",[883,59773,59775],{"className":59774},[886],[888,59776,59777],{"xmlns":890},[892,59778,59779,59791],{},[895,59780,59781,59783,59785],{},[898,59782,1710],{},[1712,59784,1714],{},[6927,59786,59787,59789],{},[898,59788,1710],{},[1716,59790,2085],{},[902,59792,56552],{"encoding":904},[41845,59794],{},[115,59796,59798],{"id":59797},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,59800,59801,59802,59815,59816,59833],{},"Uvalení jednotkové daně ",[883,59803,59805],{"className":59804},[886],[888,59806,59807],{"xmlns":890},[892,59808,59809,59813],{},[895,59810,59811],{},[898,59812,1772],{},[902,59814,1772],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,59817,59819],{"className":59818},[886],[888,59820,59821],{"xmlns":890},[892,59822,59823,59831],{},[895,59824,59825],{},[2037,59826,59827,59829],{},[898,59828,1734],{},[898,59830,2041],{},[902,59832,47278],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,59835,59836],{},[3817,59837],{"alt":59838,"className":59839,"src":59840},"imek-prebytky-s-dani-deadweight",[210,3821],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,59842,59843,59844,59859,59860,59875,59876,57543,59879,59903,59904,14897,59907,59910,59911,1659],{},"Přebytek spotřebitele ",[883,59845,59847],{"className":59846},[886],[888,59848,59849],{"xmlns":890},[892,59850,59851,59857],{},[895,59852,59853,59855],{},[898,59854,8195],{},[898,59856,6493],{},[902,59858,49825],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,59861,59863],{"className":59862},[886],[888,59864,59865],{"xmlns":890},[892,59866,59867,59873],{},[895,59868,59869,59871],{},[898,59870,1710],{},[898,59872,6493],{},[902,59874,49844],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,59877,59878],{},"daňový příjem",[883,59880,59882],{"className":59881},[886],[888,59883,59884],{"xmlns":890},[892,59885,59886,59900],{},[895,59887,59888,59890,59892],{},[898,59889,1772],{},[1712,59891,1783],{},[6989,59893,59894,59896,59898],{},[898,59895,1734],{},[1716,59897,2222],{},[898,59899,2041],{},[902,59901,59902],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,59905,59906],{},"mrtvá ztráta",[614,59908,59909],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,59912,811],{"className":59913,"dataFsResolvedFilePath":809,"href":810},[210],[41845,59915],{},[115,59917,9193],{"id":9192},[120,59919,59920,59927,59939,59946,59953],{},[123,59921,59922,3245,59924],{},[38,59923,21096],{},[207,59925,802],{"className":59926,"dataFsResolvedFilePath":800,"href":801},[210],[123,59928,59929,3245,59931,59934,59935,59938],{},[38,59930,41549],{},[207,59932,775],{"className":59933,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,59936,1690],{"className":59937,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,59940,59941,3245,59943],{},[38,59942,21106],{},[207,59944,4992],{"className":59945,"dataFsResolvedFilePath":827,"href":828},[210],[123,59947,59948,3245,59950],{},[38,59949,55633],{},[207,59951,55637],{"className":59952,"dataFsResolvedFilePath":745,"href":746},[210],[123,59954,59955,3245,59957],{},[38,59956,21078],{},[207,59958,21082],{"className":59959,"dataFsResolvedFilePath":7413,"href":7414},[210],{"title":641,"searchDepth":642,"depth":642,"links":59961},[59962,59963,59968,59973,59978,59979,59980,59981],{"id":55829,"depth":642,"text":1241},{"id":56173,"depth":642,"text":59964,"children":59965},"Přebytek spotřebitele (CSCS)",[59966,59967],{"id":56192,"depth":649,"text":56193},{"id":7867,"depth":649,"text":7868},{"id":56768,"depth":642,"text":59969,"children":59970},"Přebytek výrobce (PSPS)",[59971,59972],{"id":56787,"depth":649,"text":56788},{"id":56950,"depth":649,"text":7868},{"id":57558,"depth":642,"text":57559,"children":59974},[59975,59976],{"id":57562,"depth":649,"text":57563},{"id":58856,"depth":649,"text":59977},"Příklad 2.13 — numerický výpočet PSPS",{"id":59161,"depth":642,"text":59162},{"id":20593,"depth":642,"text":20594},{"id":59797,"depth":642,"text":59798},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,55699,59988,59989,16862,21114,59990,59991],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":59994,"title":59995,"body":59996,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":79325,"navigation":664,"path":79326,"seo":79327,"sources":79328,"stem":79329,"tags":79330,"type":7391,"updated":677,"__hash__":79336},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":59997,"toc":79289},[59998,60001,60187,60189,60280,60285,60611,60615,60622,60626,60671,60738,60769,60819,60854,60858,60917,60922,60988,61106,61208,61212,61235,61313,61356,61360,61389,61456,61462,61576,61580,61660,61697,61749,61947,62011,62098,62102,62105,62184,62187,62305,62324,62389,62393,62485,62553,62594,62648,62716,62753,62757,62815,62845,63056,63128,63180,63346,63439,63474,63478,63482,63519,63584,63639,63643,63666,63755,63859,63928,63932,64029,64142,64198,64252,64310,64371,64374,64410,64475,64505,64734,64792,64826,64830,64857,64936,65050,65071,65150,65152,65260,65264,65402,65724,65728,65731,65735,65784,65788,66042,66194,66201,66274,66458,66463,66806,66810,66833,66835,66856,66915,66925,66974,67116,67190,67285,67400,67498,67616,67620,67689,67694,67806,67951,68002,68114,68156,68160,68180,68241,68268,68330,68334,68356,68425,68705,68712,68742,68749,68942,68946,69024,69029,69105,69108,69196,69272,69339,69388,69491,69564,69685,70036,70149,70251,70255,70258,70265,70268,70304,70363,70372,70521,70745,70749,70812,70991,71083,71138,71142,71198,71268,71320,71341,71422,71425,71500,71544,71548,71589,71632,71658,71662,71733,71829,71891,71943,72046,72124,72147,72176,72180,72346,72463,72535,72850,73010,73014,73065,73127,73162,73192,73292,73334,73503,73508,73604,73642,73646,73765,74066,74068,74103,74107,74111,74239,74371,74693,74881,74959,74963,75268,75381,75527,75712,75818,76050,76165,76247,76366,76464,76505,76509,76564,76708,76862,77022,77115,77309,77621,77752,77881,77885,77957,77999,78050,78052,79247,79249],[12,59999,59995],{"id":60000},"příjem-náklady-zisk-a-nabídka-firmy",[1636,60002,60003],{},[724,60004,60005,1643,60007,3245,60010,60025,60026,3245,60029,60044,60045,3245,60048,60076,60077,60099,60100,60124,60125,60147,60148,60151,60152,60168,60169,1659],{},[883,60006,1642],{},[38,60008,60009],{},"Příjem",[883,60011,60013],{"className":60012},[886],[888,60014,60015],{"xmlns":890},[892,60016,60017,60023],{},[895,60018,60019,60021],{},[898,60020,1772],{},[898,60022,1775],{},[902,60024,1877],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,60027,60028],{},"náklady",[883,60030,60032],{"className":60031},[886],[888,60033,60034],{"xmlns":890},[892,60035,60036,60042],{},[895,60037,60038,60040],{},[898,60039,1772],{},[898,60041,8195],{},[902,60043,8648],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,60046,60047],{},"zisk",[883,60049,60051],{"className":60050},[886],[888,60052,60053],{"xmlns":890},[892,60054,60055,60073],{},[895,60056,60057,60059,60061,60063,60065,60067,60069,60071],{},[898,60058,1710],{},[898,60060,1775],{},[1712,60062,1714],{},[898,60064,1772],{},[898,60066,1775],{},[1712,60068,2219],{},[898,60070,1772],{},[898,60072,8195],{},[902,60074,60075],{"encoding":904},"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: ",[883,60078,60080],{"className":60079},[886],[888,60081,60082],{"xmlns":890},[892,60083,60084,60096],{},[895,60085,60086,60088,60090,60092,60094],{},[898,60087,2044],{},[898,60089,8195],{},[1712,60091,1714],{},[898,60093,4445],{},[898,60095,8195],{},[902,60097,60098],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,60101,60103],{"className":60102},[886],[888,60104,60105],{"xmlns":890},[892,60106,60107,60121],{},[895,60108,60109,60111,60113,60115,60117,60119],{},[898,60110,2044],{},[898,60112,45214],{},[898,60114,8195],{},[1712,60116,1714],{},[898,60118,4445],{},[898,60120,8195],{},[902,60122,60123],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,60126,60128],{"className":60127},[886],[888,60129,60130],{"xmlns":890},[892,60131,60132,60144],{},[895,60133,60134,60136,60138,60140,60142],{},[898,60135,4445],{},[898,60137,1775],{},[1712,60139,1714],{},[898,60141,4445],{},[898,60143,8195],{},[902,60145,60146],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,60149,60150],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,60153,60155],{"className":60154},[886],[888,60156,60157],{"xmlns":890},[892,60158,60159,60165],{},[895,60160,60161,60163],{},[898,60162,4445],{},[898,60164,8195],{},[902,60166,60167],{"encoding":904},"MC"," nad bodem minima ",[883,60170,60172],{"className":60171},[886],[888,60173,60174],{"xmlns":890},[892,60175,60176,60184],{},[895,60177,60178,60180,60182],{},[898,60179,2044],{},[898,60181,45214],{},[898,60183,8195],{},[902,60185,60186],{"encoding":904},"AVC",[115,60188,1241],{"id":55829},[724,60190,60191,60192,60195,60196,60198,60199,1343,60202,1343,60205,60207,60208,60211,60212,60215,60216,60219,60220,8093,60235,1348,60250,8093,60265,1691],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,60193,60194],{},"příjmem"," (revenue) a ",[38,60197,60028],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,60200,60201],{},"zisku",[38,60203,60204],{},"bodů zvratu",[38,60206,7423],{}," a konstrukcí ",[38,60209,60210],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,60213,1145],{"className":60214,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,60217,16003],{"className":60218,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,60221,60223],{"className":60222},[886],[888,60224,60225],{"xmlns":890},[892,60226,60227,60233],{},[895,60228,60229,60231],{},[898,60230,1772],{},[898,60232,1775],{},[902,60234,1877],{"encoding":904},[883,60236,60238],{"className":60237},[886],[888,60239,60240],{"xmlns":890},[892,60241,60242,60248],{},[895,60243,60244,60246],{},[898,60245,4445],{},[898,60247,1775],{},[902,60249,4450],{"encoding":904},[883,60251,60253],{"className":60252},[886],[888,60254,60255],{"xmlns":890},[892,60256,60257,60263],{},[895,60258,60259,60261],{},[898,60260,1772],{},[898,60262,8195],{},[902,60264,8648],{"encoding":904},[883,60266,60268],{"className":60267},[886],[888,60269,60270],{"xmlns":890},[892,60271,60272,60278],{},[895,60273,60274,60276],{},[898,60275,4445],{},[898,60277,8195],{},[902,60279,60167],{"encoding":904},[724,60281,60282],{},[38,60283,60284],{},"Cílové znalosti:",[120,60286,60287,60451,60454,60457,60550,60597,60604],{},[123,60288,60289,60290,1343,60305,1343,60321,1655,60336,1343,60351,1343,60367,1343,60385,1343,60403,1343,60420,1343,60436,6245],{},"odvodit a interpretovat funkce ",[883,60291,60293],{"className":60292},[886],[888,60294,60295],{"xmlns":890},[892,60296,60297,60303],{},[895,60298,60299,60301],{},[898,60300,1772],{},[898,60302,1775],{},[902,60304,1877],{"encoding":904},[883,60306,60308],{"className":60307},[886],[888,60309,60310],{"xmlns":890},[892,60311,60312,60318],{},[895,60313,60314,60316],{},[898,60315,2044],{},[898,60317,1775],{},[902,60319,60320],{"encoding":904},"AR",[883,60322,60324],{"className":60323},[886],[888,60325,60326],{"xmlns":890},[892,60327,60328,60334],{},[895,60329,60330,60332],{},[898,60331,4445],{},[898,60333,1775],{},[902,60335,4450],{"encoding":904},[883,60337,60339],{"className":60338},[886],[888,60340,60341],{"xmlns":890},[892,60342,60343,60349],{},[895,60344,60345,60347],{},[898,60346,1772],{},[898,60348,8195],{},[902,60350,8648],{"encoding":904},[883,60352,60354],{"className":60353},[886],[888,60355,60356],{"xmlns":890},[892,60357,60358,60364],{},[895,60359,60360,60362],{},[898,60361,15308],{},[898,60363,8195],{},[902,60365,60366],{"encoding":904},"FC",[883,60368,60370],{"className":60369},[886],[888,60371,60372],{"xmlns":890},[892,60373,60374,60382],{},[895,60375,60376,60378,60380],{},[898,60377,1772],{},[898,60379,45214],{},[898,60381,8195],{},[902,60383,60384],{"encoding":904},"TVC",[883,60386,60388],{"className":60387},[886],[888,60389,60390],{"xmlns":890},[892,60391,60392,60400],{},[895,60393,60394,60396,60398],{},[898,60395,2044],{},[898,60397,15308],{},[898,60399,8195],{},[902,60401,60402],{"encoding":904},"AFC",[883,60404,60406],{"className":60405},[886],[888,60407,60408],{"xmlns":890},[892,60409,60410,60418],{},[895,60411,60412,60414,60416],{},[898,60413,2044],{},[898,60415,45214],{},[898,60417,8195],{},[902,60419,60186],{"encoding":904},[883,60421,60423],{"className":60422},[886],[888,60424,60425],{"xmlns":890},[892,60426,60427,60433],{},[895,60428,60429,60431],{},[898,60430,2044],{},[898,60432,8195],{},[902,60434,60435],{"encoding":904},"AC",[883,60437,60439],{"className":60438},[886],[888,60440,60441],{"xmlns":890},[892,60442,60443,60449],{},[895,60444,60445,60447],{},[898,60446,4445],{},[898,60448,8195],{},[902,60450,60167],{"encoding":904},[123,60452,60453],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,60455,60456],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,60458,60459,60460,60463,60464,46689,60506,6245],{},"osvojit si ",[38,60461,60462],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,60465,60467],{"className":60466},[886],[888,60468,60469],{"xmlns":890},[892,60470,60471,60503],{},[895,60472,60473,60475,60477,60479,60485,60487,60489,60491,60493,60495,60501],{},[898,60474,2044],{},[898,60476,8195],{},[1712,60478,1904],{"stretchy":1903},[6927,60480,60481,60483],{},[898,60482,1734],{},[1716,60484,2085],{},[1712,60486,1910],{"stretchy":1903},[1712,60488,1714],{},[898,60490,4445],{},[898,60492,8195],{},[1712,60494,1904],{"stretchy":1903},[6927,60496,60497,60499],{},[898,60498,1734],{},[1716,60500,2085],{},[1712,60502,1910],{"stretchy":1903},[902,60504,60505],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,60507,60509],{"className":60508},[886],[888,60510,60511],{"xmlns":890},[892,60512,60513,60547],{},[895,60514,60515,60517,60519,60521,60523,60529,60531,60533,60535,60537,60539,60545],{},[898,60516,2044],{},[898,60518,45214],{},[898,60520,8195],{},[1712,60522,1904],{"stretchy":1903},[6927,60524,60525,60527],{},[898,60526,1734],{},[1716,60528,2085],{},[1712,60530,1910],{"stretchy":1903},[1712,60532,1714],{},[898,60534,4445],{},[898,60536,8195],{},[1712,60538,1904],{"stretchy":1903},[6927,60540,60541,60543],{},[898,60542,1734],{},[1716,60544,2085],{},[1712,60546,1910],{"stretchy":1903},[902,60548,60549],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,60551,60459,60552,60463,60555,6245],{},[38,60553,60554],{},"princip maximalizace zisku",[883,60556,60558],{"className":60557},[886],[888,60559,60560],{"xmlns":890},[892,60561,60562,60594],{},[895,60563,60564,60566,60568,60570,60576,60578,60580,60582,60584,60586,60592],{},[898,60565,4445],{},[898,60567,1775],{},[1712,60569,1904],{"stretchy":1903},[6927,60571,60572,60574],{},[898,60573,1734],{},[1716,60575,2085],{},[1712,60577,1910],{"stretchy":1903},[1712,60579,1714],{},[898,60581,4445],{},[898,60583,8195],{},[1712,60585,1904],{"stretchy":1903},[6927,60587,60588,60590],{},[898,60589,1734],{},[1716,60591,2085],{},[1712,60593,1910],{"stretchy":1903},[902,60595,60596],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,60598,60599,60600,60603],{},"stanovit ",[38,60601,60602],{},"body zvratu"," a interval zisku;",[123,60605,60606,60607,60610],{},"zkonstruovat ",[38,60608,60609],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,60612,60614],{"id":60613},"příjem-firmy","Příjem firmy",[724,60616,60617],{},[3817,60618],{"alt":60619,"className":60620,"src":60621},"imek-ar-mr-dvojnasobny-sklon",[210,3821],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,60623,60625],{"id":60624},"celkový-příjem","Celkový příjem",[724,60627,60628,60629,14897,60644,60647,60648,34819],{},"Celkový příjem ",[883,60630,60632],{"className":60631},[886],[888,60633,60634],{"xmlns":890},[892,60635,60636,60642],{},[895,60637,60638,60640],{},[898,60639,1772],{},[898,60641,1775],{},[902,60643,1877],{"encoding":904},[38,60645,60646],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,60649,60651],{"className":60650},[886],[888,60652,60653],{"xmlns":890},[892,60654,60655,60669],{},[895,60656,60657,60659,60661,60663,60665,60667],{},[898,60658,1710],{},[1712,60660,1714],{},[898,60662,1969],{},[1712,60664,1904],{"stretchy":1903},[898,60666,1734],{},[1712,60668,1910],{"stretchy":1903},[902,60670,2438],{"encoding":904},[883,60672,60674],{"className":60673},[886],[888,60675,60676],{"xmlns":890,"display":32941},[892,60677,60678,60735],{},[25629,60679,60680],{"width":32946},[25634,60681,60682,60684,60728,60730],{},[25637,60683],{"width":32951},[25637,60685,60686],{},[895,60687,60688,60690,60692,60694,60696,60698,60700,60702,60704,60706,60708,60710,60712,60714,60716,60718,60720,60722,60724,60726],{},[898,60689,1772],{},[898,60691,1775],{},[1712,60693,1714],{},[898,60695,1772],{},[898,60697,1775],{},[1712,60699,1904],{"stretchy":1903},[898,60701,1734],{},[1712,60703,1910],{"stretchy":1903},[1712,60705,1714],{},[898,60707,1710],{},[1712,60709,1783],{},[898,60711,1734],{},[1712,60713,1714],{},[898,60715,1969],{},[1712,60717,1904],{"stretchy":1903},[898,60719,1734],{},[1712,60721,1910],{"stretchy":1903},[1712,60723,1783],{},[898,60725,1734],{},[898,60727,1659],{"mathvariant":2003},[25637,60729],{"width":32951},[25637,60731,60732],{},[1762,60733,60734],{},"(3.1)",[902,60736,60737],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,60739,60740,60741,60744,60745,60768],{},"Graf funkce se nazývá ",[38,60742,60743],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,60746,60748],{"className":60747},[886],[888,60749,60750],{"xmlns":890},[892,60751,60752,60766],{},[895,60753,60754,60756,60758,60760,60762,60764],{},[898,60755,1710],{},[1712,60757,1714],{},[898,60759,207],{},[898,60761,1734],{},[1712,60763,3145],{},[898,60765,7544],{},[902,60767,41935],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,60770,60772],{"className":60771},[886],[888,60773,60774],{"xmlns":890,"display":32941},[892,60775,60776,60816],{},[895,60777,60778,60780,60782,60784,60786,60788,60790,60792,60794,60796,60798,60800,60802,60808,60810,60812,60814],{},[898,60779,1772],{},[898,60781,1775],{},[1712,60783,1714],{},[898,60785,1734],{},[1712,60787,1904],{"stretchy":1903},[898,60789,207],{},[898,60791,1734],{},[1712,60793,3145],{},[898,60795,7544],{},[1712,60797,1910],{"stretchy":1903},[1712,60799,1714],{},[898,60801,207],{},[2037,60803,60804,60806],{},[898,60805,1734],{},[1716,60807,2787],{},[1712,60809,3145],{},[898,60811,7544],{},[898,60813,1734],{},[1712,60815,3138],{"separator":2565},[902,60817,60818],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,60820,60821,60822,60835,60836,60853],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,60823,60825],{"className":60824},[886],[888,60826,60827],{"xmlns":890},[892,60828,60829,60833],{},[895,60830,60831],{},[898,60832,900],{},[902,60834,900],{"encoding":904}," (jelikož ",[883,60837,60839],{"className":60838},[886],[888,60840,60841],{"xmlns":890},[892,60842,60843,60851],{},[895,60844,60845,60847,60849],{},[898,60846,207],{},[1712,60848,2252],{},[1716,60850,2085],{},[902,60852,47960],{"encoding":904},") procházející počátkem.",[42223,60855,60857],{"id":60856},"příklad-31","Příklad 3.1",[724,60859,60860,60863,60864,60900,60901,60916],{},[38,60861,60862],{},"Zadání."," Pro poptávku ",[883,60865,60867],{"className":60866},[886],[888,60868,60869],{"xmlns":890},[892,60870,60871,60897],{},[895,60872,60873,60875,60877,60879,60881,60883,60885,60887,60889,60891,60893,60895],{},[898,60874,1710],{},[1712,60876,1714],{},[898,60878,1969],{},[1712,60880,1904],{"stretchy":1903},[898,60882,1734],{},[1712,60884,1910],{"stretchy":1903},[1712,60886,1714],{},[1712,60888,2219],{},[1716,60890,2787],{},[898,60892,1734],{},[1712,60894,3145],{},[1716,60896,1739],{},[902,60898,60899],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,60902,60904],{"className":60903},[886],[888,60905,60906],{"xmlns":890},[892,60907,60908,60914],{},[895,60909,60910,60912],{},[898,60911,1772],{},[898,60913,1775],{},[902,60915,1877],{"encoding":904}," a charakterizujte jeho křivku.",[724,60918,60919,60921],{},[38,60920,27645],{}," Celkový příjem je",[883,60923,60925],{"className":60924},[886],[888,60926,60927],{"xmlns":890,"display":32941},[892,60928,60929,60985],{},[895,60930,60931,60933,60935,60937,60939,60941,60943,60945,60947,60949,60951,60953,60955,60957,60959,60961,60963,60965,60967,60969,60971,60977,60979,60981,60983],{},[898,60932,1772],{},[898,60934,1775],{},[1712,60936,1714],{},[898,60938,1772],{},[898,60940,1775],{},[1712,60942,1904],{"stretchy":1903},[898,60944,1734],{},[1712,60946,1910],{"stretchy":1903},[1712,60948,1714],{},[898,60950,1734],{},[1712,60952,1904],{"stretchy":1903},[1712,60954,2219],{},[1716,60956,2787],{},[898,60958,1734],{},[1712,60960,3145],{},[1716,60962,1739],{},[1712,60964,1910],{"stretchy":1903},[1712,60966,1714],{},[1712,60968,2219],{},[1716,60970,2787],{},[2037,60972,60973,60975],{},[898,60974,1734],{},[1716,60976,2787],{},[1712,60978,3145],{},[1716,60980,1739],{},[898,60982,1734],{},[898,60984,1659],{"mathvariant":2003},[902,60986,60987],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,60989,60990,60991,1655,61013,61035,61036,61054,61055,1659],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,60992,60994],{"className":60993},[886],[888,60995,60996],{"xmlns":890},[892,60997,60998,61010],{},[895,60999,61000,61006,61008],{},[6927,61001,61002,61004],{},[898,61003,1734],{},[1716,61005,2222],{},[1712,61007,1714],{},[1716,61009,2085],{},[902,61011,61012],{"encoding":904},"Q_1 = 0",[883,61014,61016],{"className":61015},[886],[888,61017,61018],{"xmlns":890},[892,61019,61020,61032],{},[895,61021,61022,61028,61030],{},[6927,61023,61024,61026],{},[898,61025,1734],{},[1716,61027,2787],{},[1712,61029,1714],{},[1716,61031,2782],{},[902,61033,61034],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,61037,61039],{"className":61038},[886],[888,61040,61041],{"xmlns":890},[892,61042,61043,61051],{},[895,61044,61045,61047,61049],{},[898,61046,1734],{},[1712,61048,1714],{},[1716,61050,2809],{},[902,61052,61053],{"encoding":904},"Q = 25"," ve výši ",[883,61056,61058],{"className":61057},[886],[888,61059,61060],{"xmlns":890},[892,61061,61062,61103],{},[895,61063,61064,61066,61076,61078,61080,61082,61084,61087,61089,61091,61093,61095,61097,61099,61101],{},[898,61065,1772],{},[6927,61067,61068,61070,61073],{},[898,61069,1775],{},[898,61071,61072],{},"max",[1712,61074,61075],{},"⁡",[1712,61077,1714],{},[1712,61079,2219],{},[1716,61081,2787],{},[1712,61083,1783],{},[1716,61085,61086],{},"625",[1712,61088,3145],{},[1716,61090,1739],{},[1712,61092,1783],{},[1716,61094,2809],{},[1712,61096,1714],{},[1716,61098,2222],{},[1762,61100,2583],{},[1716,61102,35618],{},[902,61104,61105],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,61107,61108],{},[614,61109,61110,61111,61145,61146,1655,61159,61172,61173,8046,61191,1659],{},"Obrázek 3.1: Parabola ",[883,61112,61114],{"className":61113},[886],[888,61115,61116],{"xmlns":890},[892,61117,61118,61142],{},[895,61119,61120,61122,61124,61126,61128,61130,61136,61138,61140],{},[898,61121,1772],{},[898,61123,1775],{},[1712,61125,1714],{},[1712,61127,2219],{},[1716,61129,2787],{},[2037,61131,61132,61134],{},[898,61133,1734],{},[1716,61135,2787],{},[1712,61137,3145],{},[1716,61139,1739],{},[898,61141,1734],{},[902,61143,61144],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,61147,61149],{"className":61148},[886],[888,61150,61151],{"xmlns":890},[892,61152,61153,61157],{},[895,61154,61155],{},[1716,61156,2085],{},[902,61158,2085],{"encoding":904},[883,61160,61162],{"className":61161},[886],[888,61163,61164],{"xmlns":890},[892,61165,61166,61170],{},[895,61167,61168],{},[1716,61169,2782],{},[902,61171,2782],{"encoding":904}," a maximem ",[883,61174,61176],{"className":61175},[886],[888,61177,61178],{"xmlns":890},[892,61179,61180,61188],{},[895,61181,61182,61184,61186],{},[1716,61183,2222],{},[1762,61185,2583],{},[1716,61187,35618],{},[902,61189,61190],{"encoding":904},"1\\,250",[883,61192,61194],{"className":61193},[886],[888,61195,61196],{"xmlns":890},[892,61197,61198,61206],{},[895,61199,61200,61202,61204],{},[898,61201,1734],{},[1712,61203,1714],{},[1716,61205,2809],{},[902,61207,61053],{"encoding":904},[198,61209,61211],{"id":61210},"průměrný-příjem","Průměrný příjem",[724,61213,61214,3245,61216,14897,61231,61234],{},[38,61215,61211],{},[883,61217,61219],{"className":61218},[886],[888,61220,61221],{"xmlns":890},[892,61222,61223,61229],{},[895,61224,61225,61227],{},[898,61226,2044],{},[898,61228,1775],{},[902,61230,60320],{"encoding":904},[38,61232,61233],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,61236,61238],{"className":61237},[886],[888,61239,61240],{"xmlns":890,"display":32941},[892,61241,61242,61310],{},[895,61243,61244,61246,61248,61250,61252,61254,61256,61258,61260,61262,61278,61280,61298,61300,61302,61304,61306,61308],{},[898,61245,2044],{},[898,61247,1775],{},[1712,61249,1714],{},[898,61251,2044],{},[898,61253,1775],{},[1712,61255,1904],{"stretchy":1903},[898,61257,1734],{},[1712,61259,1910],{"stretchy":1903},[1712,61261,1714],{},[2567,61263,61264,61276],{},[895,61265,61266,61268,61270,61272,61274],{},[898,61267,1772],{},[898,61269,1775],{},[1712,61271,1904],{"stretchy":1903},[898,61273,1734],{},[1712,61275,1910],{"stretchy":1903},[898,61277,1734],{},[1712,61279,1714],{},[2567,61281,61282,61296],{},[895,61283,61284,61286,61288,61290,61292,61294],{},[898,61285,1734],{},[1762,61287,2583],{},[898,61289,1969],{},[1712,61291,1904],{"stretchy":1903},[898,61293,1734],{},[1712,61295,1910],{"stretchy":1903},[898,61297,1734],{},[1712,61299,1714],{},[898,61301,1969],{},[1712,61303,1904],{"stretchy":1903},[898,61305,1734],{},[1712,61307,1910],{"stretchy":1903},[898,61309,1659],{"mathvariant":2003},[902,61311,61312],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1636,61314,61315],{},[724,61316,61317,61320,61321,1343,61324,1659],{},[883,61318,61319],{},"!note"," Klíčové pozorování\n",[38,61322,61323],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,61325,61327],{"className":61326},[886],[888,61328,61329],{"xmlns":890},[892,61330,61331,61353],{},[895,61332,61333,61335,61337,61339,61341,61343,61345,61347,61349,61351],{},[898,61334,2044],{},[898,61336,1775],{},[1712,61338,1904],{"stretchy":1903},[898,61340,1734],{},[1712,61342,1910],{"stretchy":1903},[1712,61344,1714],{},[898,61346,1969],{},[1712,61348,1904],{"stretchy":1903},[898,61350,1734],{},[1712,61352,1910],{"stretchy":1903},[902,61354,61355],{"encoding":904},"AR(Q) = D(Q)",[198,61357,61359],{"id":61358},"mezní-příjem","Mezní příjem",[724,61361,61362,61363,3245,61366,14897,61381,61384,61385,61388],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,61364,61365],{},"mezní příjem",[883,61367,61369],{"className":61368},[886],[888,61370,61371],{"xmlns":890},[892,61372,61373,61379],{},[895,61374,61375,61377],{},[898,61376,4445],{},[898,61378,1775],{},[902,61380,4450],{"encoding":904},[38,61382,61383],{},"marginal revenue","), definovaný jako ",[207,61386,1145],{"className":61387,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,61390,61392],{"className":61391},[886],[888,61393,61394],{"xmlns":890,"display":32941},[892,61395,61396,61453],{},[25629,61397,61398],{"width":32946},[25634,61399,61400,61402,61446,61448],{},[25637,61401],{"width":32951},[25637,61403,61404],{},[895,61405,61406,61408,61410,61412,61428,61430,61432,61438,61440,61442,61444],{},[898,61407,4445],{},[898,61409,1775],{},[1712,61411,1714],{},[2567,61413,61414,61422],{},[895,61415,61416,61418,61420],{},[898,61417,2468],{"mathvariant":2003},[898,61419,1772],{},[898,61421,1775],{},[895,61423,61424,61426],{},[898,61425,2468],{"mathvariant":2003},[898,61427,1734],{},[1712,61429,1714],{},[898,61431,1772],{},[2037,61433,61434,61436],{},[898,61435,1775],{},[1712,61437,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,61439,1904],{"stretchy":1903},[898,61441,1734],{},[1712,61443,1910],{"stretchy":1903},[898,61445,1659],{"mathvariant":2003},[25637,61447],{"width":32951},[25637,61449,61450],{},[1762,61451,61452],{},"(3.2)",[902,61454,61455],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,61457,61458,61459,61461],{},"Mezní příjem udává ",[38,61460,8018],{}," celkového příjmu vzhledem k množství.",[1636,61463,61464],{},[724,61465,61466,61468,61469,61495,61496,61513,61514,1659],{},[883,61467,1941],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,61470,61472],{"className":61471},[886],[888,61473,61474],{"xmlns":890},[892,61475,61476,61492],{},[895,61477,61478,61480,61482,61484,61490],{},[898,61479,4445],{},[898,61481,1775],{},[1712,61483,1904],{"stretchy":1903},[2037,61485,61486,61488],{},[898,61487,1734],{},[1712,61489,2145],{},[1712,61491,1910],{"stretchy":1903},[902,61493,61494],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,61497,61499],{"className":61498},[886],[888,61500,61501],{"xmlns":890},[892,61502,61503,61511],{},[895,61504,61505],{},[2037,61506,61507,61509],{},[898,61508,1734],{},[1712,61510,2145],{},[902,61512,34719],{"encoding":904},". Jinak řečeno: ",[883,61515,61517],{"className":61516},[886],[888,61518,61519],{"xmlns":890},[892,61520,61521,61573],{},[895,61522,61523,61525,61527,61529,61535,61537,61539,61541,61543,61545,61551,61553,61555,61557,61559,61561,61563,61565,61571],{},[898,61524,4445],{},[898,61526,1775],{},[1712,61528,1904],{"stretchy":1903},[2037,61530,61531,61533],{},[898,61532,1734],{},[1712,61534,2145],{},[1712,61536,1910],{"stretchy":1903},[1712,61538,3740],{},[898,61540,1772],{},[898,61542,1775],{},[1712,61544,1904],{"stretchy":1903},[2037,61546,61547,61549],{},[898,61548,1734],{},[1712,61550,2145],{},[1712,61552,3145],{},[1716,61554,2222],{},[1712,61556,1910],{"stretchy":1903},[1712,61558,2219],{},[898,61560,1772],{},[898,61562,1775],{},[1712,61564,1904],{"stretchy":1903},[2037,61566,61567,61569],{},[898,61568,1734],{},[1712,61570,2145],{},[1712,61572,1910],{"stretchy":1903},[902,61574,61575],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[42223,61577,61579],{"id":61578},"příklad-32","Příklad 3.2",[724,61581,61582,60863,61584,60900,61618,61633,61634,1659],{},[38,61583,60862],{},[883,61585,61587],{"className":61586},[886],[888,61588,61589],{"xmlns":890},[892,61590,61591,61615],{},[895,61592,61593,61595,61597,61599,61601,61603,61605,61607,61609,61611,61613],{},[898,61594,1710],{},[1712,61596,1714],{},[898,61598,1969],{},[1712,61600,1904],{"stretchy":1903},[898,61602,1734],{},[1712,61604,1910],{"stretchy":1903},[1712,61606,1714],{},[1716,61608,1739],{},[1712,61610,2219],{},[1716,61612,2787],{},[898,61614,1734],{},[902,61616,61617],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,61619,61621],{"className":61620},[886],[888,61622,61623],{"xmlns":890},[892,61624,61625,61631],{},[895,61626,61627,61629],{},[898,61628,4445],{},[898,61630,1775],{},[902,61632,4450],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,61635,61637],{"className":61636},[886],[888,61638,61639],{"xmlns":890},[892,61640,61641,61657],{},[895,61642,61643,61645,61647,61649,61651,61653,61655],{},[898,61644,1734],{},[1712,61646,1714],{},[1716,61648,41119],{},[1712,61650,3138],{"separator":2565},[1716,61652,46737],{},[1712,61654,3138],{"separator":2565},[1716,61656,6857],{},[902,61658,61659],{"encoding":904},"Q = 15, 16, 20",[724,61661,61662,3245,61664,61696],{},[38,61663,27645],{},[883,61665,61667],{"className":61666},[886],[888,61668,61669],{"xmlns":890},[892,61670,61671,61693],{},[895,61672,61673,61675,61677,61679,61681,61683,61685,61687],{},[898,61674,1772],{},[898,61676,1775],{},[1712,61678,1714],{},[1716,61680,1739],{},[898,61682,1734],{},[1712,61684,2219],{},[1716,61686,2787],{},[2037,61688,61689,61691],{},[898,61690,1734],{},[1716,61692,2787],{},[902,61694,61695],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,61698,61700],{"className":61699},[886],[888,61701,61702],{"xmlns":890,"display":32941},[892,61703,61704,61746],{},[895,61705,61706,61708,61710,61712,61714,61716,61718,61720,61722,61728,61734,61736,61738,61740,61742,61744],{},[898,61707,4445],{},[898,61709,1775],{},[1712,61711,1714],{},[1712,61713,1904],{"stretchy":1903},[1716,61715,1739],{},[898,61717,1734],{},[1712,61719,2219],{},[1716,61721,2787],{},[2037,61723,61724,61726],{},[898,61725,1734],{},[1716,61727,2787],{},[2037,61729,61730,61732],{},[1712,61731,1910],{"stretchy":1903},[1712,61733,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,61735,1714],{},[1716,61737,1739],{},[1712,61739,2219],{},[1716,61741,2975],{},[898,61743,1734],{},[898,61745,1659],{"mathvariant":2003},[902,61747,61748],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,61750,14535,61751,5920,61769,61795,61796,2149,61809,61824,61825,61838,61839,26295,61852,2149,61865,61880,61881,61894,61895,61926,61927,61946],{},[883,61752,61754],{"className":61753},[886],[888,61755,61756],{"xmlns":890},[892,61757,61758,61766],{},[895,61759,61760,61762,61764],{},[898,61761,1734],{},[1712,61763,1714],{},[1716,61765,41119],{},[902,61767,61768],{"encoding":904},"Q = 15",[883,61770,61772],{"className":61771},[886],[888,61773,61774],{"xmlns":890},[892,61775,61776,61792],{},[895,61777,61778,61780,61782,61784,61786,61788,61790],{},[898,61779,4445],{},[898,61781,1775],{},[1712,61783,1904],{"stretchy":1903},[1716,61785,41119],{},[1712,61787,1910],{"stretchy":1903},[1712,61789,1714],{},[1716,61791,3018],{},[902,61793,61794],{"encoding":904},"MR(15) = 40",": při množství ",[883,61797,61799],{"className":61798},[886],[888,61800,61801],{"xmlns":890},[892,61802,61803,61807],{},[895,61804,61805],{},[1716,61806,41119],{},[902,61808,41119],{"encoding":904},[883,61810,61812],{"className":61811},[886],[888,61813,61814],{"xmlns":890},[892,61815,61816,61822],{},[895,61817,61818,61820],{},[898,61819,1772],{},[898,61821,1775],{},[902,61823,1877],{"encoding":904}," mění asi ",[883,61826,61828],{"className":61827},[886],[888,61829,61830],{"xmlns":890},[892,61831,61832,61836],{},[895,61833,61834],{},[1716,61835,3018],{},[902,61837,3018],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,61840,61842],{"className":61841},[886],[888,61843,61844],{"xmlns":890},[892,61845,61846,61850],{},[895,61847,61848],{},[898,61849,1734],{},[902,61851,1734],{"encoding":904},[883,61853,61855],{"className":61854},[886],[888,61856,61857],{"xmlns":890},[892,61858,61859,61863],{},[895,61860,61861],{},[1716,61862,2222],{},[902,61864,2222],{"encoding":904},[883,61866,61868],{"className":61867},[886],[888,61869,61870],{"xmlns":890},[892,61871,61872,61878],{},[895,61873,61874,61876],{},[898,61875,1772],{},[898,61877,1775],{},[902,61879,1877],{"encoding":904}," zvýší přibližně o ",[883,61882,61884],{"className":61883},[886],[888,61885,61886],{"xmlns":890},[892,61887,61888,61892],{},[895,61889,61890],{},[1716,61891,3018],{},[902,61893,3018],{"encoding":904},", tj. ze skutečné hodnoty ",[883,61896,61898],{"className":61897},[886],[888,61899,61900],{"xmlns":890},[892,61901,61902,61923],{},[895,61903,61904,61906,61908,61910,61912,61914,61916,61918,61920],{},[898,61905,1772],{},[898,61907,1775],{},[1712,61909,1904],{"stretchy":1903},[1716,61911,41119],{},[1712,61913,1910],{"stretchy":1903},[1712,61915,1714],{},[1716,61917,2222],{},[1762,61919,2583],{},[1716,61921,61922],{},"050",[902,61924,61925],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,61928,61930],{"className":61929},[886],[888,61931,61932],{"xmlns":890},[892,61933,61934,61943],{},[895,61935,61936,61938,61940],{},[1716,61937,2222],{},[1762,61939,2583],{},[1716,61941,61942],{},"090",[902,61944,61945],{"encoding":904},"1\\,090",". Skutečná změna je",[883,61948,61950],{"className":61949},[886],[888,61951,61952],{"xmlns":890,"display":32941},[892,61953,61954,62008],{},[895,61955,61956,61958,61960,61962,61964,61966,61968,61970,61972,61974,61976,61978,61980,61982,61984,61986,61988,61990,61992,61995,61997,61999,62001,62003,62005],{},[898,61957,2004],{"mathvariant":2003},[898,61959,1772],{},[898,61961,1775],{},[1712,61963,1714],{},[898,61965,1772],{},[898,61967,1775],{},[1712,61969,1904],{"stretchy":1903},[1716,61971,46737],{},[1712,61973,1910],{"stretchy":1903},[1712,61975,2219],{},[898,61977,1772],{},[898,61979,1775],{},[1712,61981,1904],{"stretchy":1903},[1716,61983,41119],{},[1712,61985,1910],{"stretchy":1903},[1712,61987,1714],{},[1716,61989,2222],{},[1762,61991,2583],{},[1716,61993,61994],{},"088",[1712,61996,2219],{},[1716,61998,2222],{},[1762,62000,2583],{},[1716,62002,61922],{},[1712,62004,1714],{},[1716,62006,62007],{},"38.",[902,62009,62010],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,62012,62013,62014,1343,62040,7037,62066,62081,62082,62097],{},"Podobně ",[883,62015,62017],{"className":62016},[886],[888,62018,62019],{"xmlns":890},[892,62020,62021,62037],{},[895,62022,62023,62025,62027,62029,62031,62033,62035],{},[898,62024,4445],{},[898,62026,1775],{},[1712,62028,1904],{"stretchy":1903},[1716,62030,46737],{},[1712,62032,1910],{"stretchy":1903},[1712,62034,1714],{},[1716,62036,3377],{},[902,62038,62039],{"encoding":904},"MR(16) = 36",[883,62041,62043],{"className":62042},[886],[888,62044,62045],{"xmlns":890},[892,62046,62047,62063],{},[895,62048,62049,62051,62053,62055,62057,62059,62061],{},[898,62050,4445],{},[898,62052,1775],{},[1712,62054,1904],{"stretchy":1903},[1716,62056,6857],{},[1712,62058,1910],{"stretchy":1903},[1712,62060,1714],{},[1716,62062,6857],{},[902,62064,62065],{"encoding":904},"MR(20) = 20",[883,62067,62069],{"className":62068},[886],[888,62070,62071],{"xmlns":890},[892,62072,62073,62079],{},[895,62074,62075,62077],{},[898,62076,4445],{},[898,62078,1775],{},[902,62080,4450],{"encoding":904}," je klesající funkce — rychlost změny ",[883,62083,62085],{"className":62084},[886],[888,62086,62087],{"xmlns":890},[892,62088,62089,62095],{},[895,62090,62091,62093],{},[898,62092,1772],{},[898,62094,1775],{},[902,62096,1877],{"encoding":904}," s růstem množství klesá.",[198,62099,62101],{"id":62100},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,62103,62104],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,62106,62108],{"className":62107},[886],[888,62109,62110],{"xmlns":890,"display":32941},[892,62111,62112,62181],{},[25629,62113,62114],{"width":32946},[25634,62115,62116,62118,62174,62176],{},[25637,62117],{"width":32951},[25637,62119,62120],{},[895,62121,62122,62124,62126,62128,62130,62132,62134,62136,62138,62140,62142,62144,62146,62148,62154,62156,62158,62160,62162,62164,62166,62168,62170,62172],{},[898,62123,2004],{"mathvariant":2003},[898,62125,1772],{},[898,62127,1775],{},[1762,62129,1764],{},[1712,62131,3740],{},[1762,62133,1764],{},[898,62135,2468],{"mathvariant":2003},[898,62137,1772],{},[898,62139,1775],{},[1712,62141,1714],{},[1712,62143,1904],{"stretchy":1903},[898,62145,1772],{},[898,62147,1775],{},[2037,62149,62150,62152],{},[1712,62151,1910],{"stretchy":1903},[1712,62153,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,62155,2583],{},[898,62157,2468],{"mathvariant":2003},[898,62159,1734],{},[1712,62161,1714],{},[898,62163,4445],{},[898,62165,1775],{},[1762,62167,2583],{},[898,62169,2468],{"mathvariant":2003},[898,62171,1734],{},[1712,62173,3138],{"separator":2565},[25637,62175],{"width":32951},[25637,62177,62178],{},[1762,62179,62180],{},"(3.3)",[902,62182,62183],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,62185,62186],{},"schematicky:",[883,62188,62190],{"className":62189},[886],[888,62191,62192],{"xmlns":890,"display":32941},[892,62193,62194,62302],{},[895,62195,62196,62234,62236,62238,62240,62269,62272,62300],{},[895,62197,62198,62201,62207,62210,62216,62219,62225,62231],{},[1762,62199,62200],{},"zm",[6205,62202,62203,62205],{"accent":2565},[1762,62204,50607],{},[1712,62206,29933],{},[1762,62208,62209],{},"na celkov",[6205,62211,62212,62214],{"accent":2565},[1762,62213,50607],{},[1712,62215,29852],{},[1762,62217,62218],{},"ho p",[6205,62220,62221,62223],{"accent":2565},[1762,62222,16915],{},[1712,62224,29933],{},[6205,62226,62227,62229],{"accent":2565},[1762,62228,29921],{},[1712,62230,29852],{},[1762,62232,62233],{},"jmu",[1762,62235,1764],{},[1712,62237,3740],{},[1762,62239,1764],{},[895,62241,62242,62245,62251,62254,62260,62266],{},[1762,62243,62244],{},"mezn",[6205,62246,62247,62249],{"accent":2565},[1762,62248,29921],{},[1712,62250,29852],{},[1762,62252,62253],{}," p",[6205,62255,62256,62258],{"accent":2565},[1762,62257,16915],{},[1712,62259,29933],{},[6205,62261,62262,62264],{"accent":2565},[1762,62263,29921],{},[1712,62265,29852],{},[1762,62267,62268],{},"jem",[1712,62270,62271],{},"×",[895,62273,62274,62276,62282,62285,62291,62294],{},[1762,62275,62200],{},[6205,62277,62278,62280],{"accent":2565},[1762,62279,50607],{},[1712,62281,29933],{},[1762,62283,62284],{},"na mno",[6205,62286,62287,62289],{"accent":2565},[1762,62288,14466],{},[1712,62290,29933],{},[1762,62292,62293],{},"stv",[6205,62295,62296,62298],{"accent":2565},[1762,62297,29921],{},[1712,62299,29852],{},[898,62301,1659],{"mathvariant":2003},[902,62303,62304],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,62306,62307,62308,62323],{},"Pro porovnání skutečná změna ",[883,62309,62311],{"className":62310},[886],[888,62312,62313],{"xmlns":890},[892,62314,62315,62321],{},[895,62316,62317,62319],{},[898,62318,1772],{},[898,62320,1775],{},[902,62322,1877],{"encoding":904}," je",[883,62325,62327],{"className":62326},[886],[888,62328,62329],{"xmlns":890,"display":32941},[892,62330,62331,62386],{},[25629,62332,62333],{"width":32946},[25634,62334,62335,62337,62379,62381],{},[25637,62336],{"width":32951},[25637,62338,62339],{},[895,62340,62341,62343,62345,62347,62349,62351,62353,62355,62357,62359,62361,62363,62365,62367,62369,62371,62373,62375,62377],{},[898,62342,2004],{"mathvariant":2003},[898,62344,1772],{},[898,62346,1775],{},[1712,62348,1714],{},[898,62350,1772],{},[898,62352,1775],{},[1712,62354,1904],{"stretchy":1903},[898,62356,1734],{},[1712,62358,3145],{},[898,62360,2468],{"mathvariant":2003},[898,62362,1734],{},[1712,62364,1910],{"stretchy":1903},[1712,62366,2219],{},[898,62368,1772],{},[898,62370,1775],{},[1712,62372,1904],{"stretchy":1903},[898,62374,1734],{},[1712,62376,1910],{"stretchy":1903},[898,62378,1659],{"mathvariant":2003},[25637,62380],{"width":32951},[25637,62382,62383],{},[1762,62384,62385],{},"(3.4)",[902,62387,62388],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[42223,62390,62392],{"id":62391},"příklad-33","Příklad 3.3",[724,62394,62395,62397,62398,62428,62429,8079,62444,8093,62457,3072,62470,62484],{},[38,62396,60862],{}," Pro ",[883,62399,62401],{"className":62400},[886],[888,62402,62403],{"xmlns":890},[892,62404,62405,62425],{},[895,62406,62407,62409,62411,62413,62415,62417,62419],{},[898,62408,1772],{},[898,62410,1775],{},[1712,62412,1714],{},[1716,62414,1739],{},[898,62416,1734],{},[1712,62418,2219],{},[2037,62420,62421,62423],{},[898,62422,1734],{},[1716,62424,2787],{},[902,62426,62427],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,62430,62432],{"className":62431},[886],[888,62433,62434],{"xmlns":890},[892,62435,62436,62442],{},[895,62437,62438,62440],{},[898,62439,1772],{},[898,62441,1775],{},[902,62443,1877],{"encoding":904},[883,62445,62447],{"className":62446},[886],[888,62448,62449],{"xmlns":890},[892,62450,62451,62455],{},[895,62452,62453],{},[898,62454,1734],{},[902,62456,1734],{"encoding":904},[883,62458,62460],{"className":62459},[886],[888,62461,62462],{"xmlns":890},[892,62463,62464,62468],{},[895,62465,62466],{},[1716,62467,8533],{},[902,62469,8533],{"encoding":904},[883,62471,62473],{"className":62472},[886],[888,62474,62475],{"xmlns":890},[892,62476,62477,62482],{},[895,62478,62479],{},[1716,62480,62481],{},"63",[902,62483,62481],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,62486,62487,3245,62489,62514,62515,1343,62533,2854],{},[38,62488,27645],{},[883,62490,62492],{"className":62491},[886],[888,62493,62494],{"xmlns":890},[892,62495,62496,62512],{},[895,62497,62498,62500,62502,62504,62506,62508,62510],{},[898,62499,4445],{},[898,62501,1775],{},[1712,62503,1714],{},[1716,62505,1739],{},[1712,62507,2219],{},[1716,62509,2787],{},[898,62511,1734],{},[902,62513,16309],{"encoding":904},", tedy při ",[883,62516,62518],{"className":62517},[886],[888,62519,62520],{"xmlns":890},[892,62521,62522,62530],{},[895,62523,62524,62526,62528],{},[898,62525,1734],{},[1712,62527,1714],{},[1716,62529,8533],{},[902,62531,62532],{"encoding":904},"Q = 60",[883,62534,62536],{"className":62535},[886],[888,62537,62538],{"xmlns":890},[892,62539,62540,62550],{},[895,62541,62542,62544,62546,62548],{},[898,62543,2468],{"mathvariant":2003},[898,62545,1734],{},[1712,62547,1714],{},[1716,62549,6198],{},[902,62551,62552],{"encoding":904},"\\mathrm{d}Q = 3",[883,62554,62556],{"className":62555},[886],[888,62557,62558],{"xmlns":890,"display":32941},[892,62559,62560,62591],{},[895,62561,62562,62564,62566,62568,62570,62572,62574,62576,62578,62580,62582,62584,62586,62588],{},[898,62563,2468],{"mathvariant":2003},[898,62565,1772],{},[898,62567,1775],{},[1712,62569,1714],{},[1712,62571,1904],{"stretchy":1903},[1716,62573,1739],{},[1712,62575,2219],{},[1716,62577,1829],{},[1712,62579,1910],{"stretchy":1903},[1712,62581,1783],{},[1716,62583,6198],{},[1712,62585,1714],{},[1712,62587,2219],{},[1716,62589,62590],{},"60.",[902,62592,62593],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,62595,62596,62597,62627,62628,62647],{},"Celkový příjem klesne z ",[883,62598,62600],{"className":62599},[886],[888,62601,62602],{"xmlns":890},[892,62603,62604,62624],{},[895,62605,62606,62608,62610,62612,62614,62616,62618,62620,62622],{},[898,62607,1772],{},[898,62609,1775],{},[1712,62611,1904],{"stretchy":1903},[1716,62613,8533],{},[1712,62615,1910],{"stretchy":1903},[1712,62617,1714],{},[1716,62619,2787],{},[1762,62621,2583],{},[1716,62623,25017],{},[902,62625,62626],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,62629,62631],{"className":62630},[886],[888,62632,62633],{"xmlns":890},[892,62634,62635,62644],{},[895,62636,62637,62639,62641],{},[1716,62638,2787],{},[1762,62640,2583],{},[1716,62642,62643],{},"340",[902,62645,62646],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,62649,62651],{"className":62650},[886],[888,62652,62653],{"xmlns":890,"display":32941},[892,62654,62655,62713],{},[895,62656,62657,62659,62661,62663,62665,62667,62669,62671,62673,62675,62677,62679,62681,62683,62685,62687,62689,62691,62693,62696,62698,62700,62702,62704,62706,62708,62711],{},[898,62658,2004],{"mathvariant":2003},[898,62660,1772],{},[898,62662,1775],{},[1712,62664,1714],{},[898,62666,1772],{},[898,62668,1775],{},[1712,62670,1904],{"stretchy":1903},[1716,62672,62481],{},[1712,62674,1910],{"stretchy":1903},[1712,62676,2219],{},[898,62678,1772],{},[898,62680,1775],{},[1712,62682,1904],{"stretchy":1903},[1716,62684,8533],{},[1712,62686,1910],{"stretchy":1903},[1712,62688,1714],{},[1716,62690,2787],{},[1762,62692,2583],{},[1716,62694,62695],{},"331",[1712,62697,2219],{},[1716,62699,2787],{},[1762,62701,2583],{},[1716,62703,25017],{},[1712,62705,1714],{},[1712,62707,2219],{},[1716,62709,62710],{},"69",[1712,62712,3138],{"separator":2565},[902,62714,62715],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,62717,62718,62719,62734,62735,1659],{},"tj. ",[883,62720,62722],{"className":62721},[886],[888,62723,62724],{"xmlns":890},[892,62725,62726,62732],{},[895,62727,62728,62730],{},[898,62729,1772],{},[898,62731,1775],{},[902,62733,1877],{"encoding":904}," klesne na ",[883,62736,62738],{"className":62737},[886],[888,62739,62740],{"xmlns":890},[892,62741,62742,62750],{},[895,62743,62744,62746,62748],{},[1716,62745,2787],{},[1762,62747,2583],{},[1716,62749,62695],{},[902,62751,62752],{"encoding":904},"2\\,331",[198,62754,62756],{"id":62755},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,62758,62759,62760,15266,62783,36455],{},"Obecně pro lineární poptávku ",[883,62761,62763],{"className":62762},[886],[888,62764,62765],{"xmlns":890},[892,62766,62767,62781],{},[895,62768,62769,62771,62773,62775,62777,62779],{},[898,62770,1710],{},[1712,62772,1714],{},[898,62774,207],{},[898,62776,1734],{},[1712,62778,3145],{},[898,62780,7544],{},[902,62782,41935],{"encoding":904},[883,62784,62786],{"className":62785},[886],[888,62787,62788],{"xmlns":890},[892,62789,62790,62812],{},[895,62791,62792,62794,62796,62798,62800,62806,62808,62810],{},[898,62793,1772],{},[898,62795,1775],{},[1712,62797,1714],{},[898,62799,207],{},[2037,62801,62802,62804],{},[898,62803,1734],{},[1716,62805,2787],{},[1712,62807,3145],{},[898,62809,7544],{},[898,62811,1734],{},[902,62813,62814],{"encoding":904},"TR = aQ^2 + bQ",[883,62816,62818],{"className":62817},[886],[888,62819,62820],{"xmlns":890,"display":32941},[892,62821,62822,62842],{},[895,62823,62824,62826,62828,62830,62832,62834,62836,62838,62840],{},[898,62825,4445],{},[898,62827,1775],{},[1712,62829,1714],{},[1716,62831,2787],{},[898,62833,207],{},[898,62835,1734],{},[1712,62837,3145],{},[898,62839,7544],{},[898,62841,1659],{"mathvariant":2003},[902,62843,62844],{"encoding":904},"MR = 2aQ + b.",[724,62846,62847,62848,62863,62864,62879,62880,62893,62894,14897,62897,62913,62914,62927,62928,62943,62944,62959,62960,62975,62976,8046,62989,63019,63020,63039,63040,63055],{},"Křivky ",[883,62849,62851],{"className":62850},[886],[888,62852,62853],{"xmlns":890},[892,62854,62855,62861],{},[895,62856,62857,62859],{},[898,62858,4445],{},[898,62860,1775],{},[902,62862,4450],{"encoding":904}," a poptávky (resp. ",[883,62865,62867],{"className":62866},[886],[888,62868,62869],{"xmlns":890},[892,62870,62871,62877],{},[895,62872,62873,62875],{},[898,62874,2044],{},[898,62876,1775],{},[902,62878,60320],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,62881,62883],{"className":62882},[886],[888,62884,62885],{"xmlns":890},[892,62886,62887,62891],{},[895,62888,62889],{},[898,62890,7544],{},[902,62892,7544],{"encoding":904},", přičemž ",[38,62895,62896],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,62898,62900],{"className":62899},[886],[888,62901,62902],{"xmlns":890},[892,62903,62904,62910],{},[895,62905,62906,62908],{},[1716,62907,2787],{},[898,62909,207],{},[902,62911,62912],{"encoding":904},"2a"," vs. ",[883,62915,62917],{"className":62916},[886],[888,62918,62919],{"xmlns":890},[892,62920,62921,62925],{},[895,62922,62923],{},[898,62924,207],{},[902,62926,207],{"encoding":904},", obrázek 3.2). ",[883,62929,62931],{"className":62930},[886],[888,62932,62933],{"xmlns":890},[892,62934,62935,62941],{},[895,62936,62937,62939],{},[898,62938,4445],{},[898,62940,1775],{},[902,62942,4450],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,62945,62947],{"className":62946},[886],[888,62948,62949],{"xmlns":890},[892,62950,62951,62957],{},[895,62952,62953,62955],{},[898,62954,1772],{},[898,62956,1775],{},[902,62958,1877],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,62961,62963],{"className":62962},[886],[888,62964,62965],{"xmlns":890},[892,62966,62967,62973],{},[895,62968,62969,62971],{},[898,62970,4445],{},[898,62972,1775],{},[902,62974,4450],{"encoding":904}," osu ",[883,62977,62979],{"className":62978},[886],[888,62980,62981],{"xmlns":890},[892,62982,62983,62987],{},[895,62984,62985],{},[898,62986,1734],{},[902,62988,1734],{"encoding":904},[883,62990,62992],{"className":62991},[886],[888,62993,62994],{"xmlns":890},[892,62995,62996,63016],{},[895,62997,62998,63000,63002,63004],{},[898,62999,1734],{},[1712,63001,1714],{},[1712,63003,2219],{},[2563,63005,63006],{"scriptlevel":2085,"displaystyle":1903},[2567,63007,63008,63010],{},[898,63009,7544],{},[895,63011,63012,63014],{},[1716,63013,2787],{},[898,63015,207],{},[902,63017,63018],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,63021,63023],{"className":63022},[886],[888,63024,63025],{"xmlns":890},[892,63026,63027,63037],{},[895,63028,63029,63031,63033,63035],{},[898,63030,4445],{},[898,63032,1775],{},[1712,63034,1714],{},[1716,63036,2085],{},[902,63038,4900],{"encoding":904},", a dále ",[883,63041,63043],{"className":63042},[886],[888,63044,63045],{"xmlns":890},[892,63046,63047,63053],{},[895,63048,63049,63051],{},[898,63050,1772],{},[898,63052,1775],{},[902,63054,1877],{"encoding":904}," klesá.",[724,63057,63058,63059,63065,63066,63098,63099,63127],{},"V případě ",[38,63060,63061],{},[207,63062,63064],{"className":63063,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,63067,63069],{"className":63068},[886],[888,63070,63071],{"xmlns":890},[892,63072,63073,63095],{},[895,63074,63075,63077,63079,63081,63083,63085,63087,63089],{},[898,63076,1710],{},[1712,63078,1714],{},[898,63080,1969],{},[1712,63082,1904],{"stretchy":1903},[898,63084,1734],{},[1712,63086,1910],{"stretchy":1903},[1712,63088,1714],{},[2037,63090,63091,63093],{},[898,63092,1710],{},[1712,63094,2145],{},[902,63096,63097],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,63100,63102],{"className":63101},[886],[888,63103,63104],{"xmlns":890},[892,63105,63106,63124],{},[895,63107,63108,63110,63112,63114,63116,63118],{},[898,63109,1772],{},[898,63111,1775],{},[1712,63113,1714],{},[898,63115,1734],{},[1712,63117,1783],{},[2037,63119,63120,63122],{},[898,63121,1710],{},[1712,63123,2145],{},[902,63125,63126],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,63129,63131],{"className":63130},[886],[888,63132,63133],{"xmlns":890,"display":32941},[892,63134,63135,63177],{},[895,63136,63137,63139,63141,63143,63145,63147,63149,63155,63157,63159,63173,63175],{},[898,63138,4445],{},[898,63140,1775],{},[1712,63142,1714],{},[898,63144,2044],{},[898,63146,1775],{},[1712,63148,1714],{},[2037,63150,63151,63153],{},[898,63152,1710],{},[1712,63154,2145],{},[3690,63156],{"width":20158},[1712,63158,1904],{"stretchy":1903},[895,63160,63161,63164,63170],{},[1762,63162,63163],{},"obr",[6205,63165,63166,63168],{"accent":2565},[1762,63167,207],{},[1712,63169,29852],{},[1762,63171,63172],{},"zek 3.4",[1712,63174,1910],{"stretchy":1903},[898,63176,1659],{"mathvariant":2003},[902,63178,63179],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,63181,63182],{},[614,63183,63184,63185,1655,63211,63239,63240,63253,63254,63269,63270,9120,63283,1343,63309,9120,63324,1659],{},"Obrázek 3.2: Přímky ",[883,63186,63188],{"className":63187},[886],[888,63189,63190],{"xmlns":890},[892,63191,63192,63208],{},[895,63193,63194,63196,63198,63200,63202,63204,63206],{},[898,63195,2044],{},[898,63197,1775],{},[1712,63199,1714],{},[898,63201,207],{},[898,63203,1734],{},[1712,63205,3145],{},[898,63207,7544],{},[902,63209,63210],{"encoding":904},"AR = aQ + b",[883,63212,63214],{"className":63213},[886],[888,63215,63216],{"xmlns":890},[892,63217,63218,63236],{},[895,63219,63220,63222,63224,63226,63228,63230,63232,63234],{},[898,63221,4445],{},[898,63223,1775],{},[1712,63225,1714],{},[1716,63227,2787],{},[898,63229,207],{},[898,63231,1734],{},[1712,63233,3145],{},[898,63235,7544],{},[902,63237,63238],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,63241,63243],{"className":63242},[886],[888,63244,63245],{"xmlns":890},[892,63246,63247,63251],{},[895,63248,63249],{},[898,63250,7544],{},[902,63252,7544],{"encoding":904}," se svislou osou, ",[883,63255,63257],{"className":63256},[886],[888,63258,63259],{"xmlns":890},[892,63260,63261,63267],{},[895,63262,63263,63265],{},[898,63264,4445],{},[898,63266,1775],{},[902,63268,4450],{"encoding":904}," protíná osu ",[883,63271,63273],{"className":63272},[886],[888,63274,63275],{"xmlns":890},[892,63276,63277,63281],{},[895,63278,63279],{},[898,63280,1734],{},[902,63282,1734],{"encoding":904},[883,63284,63286],{"className":63285},[886],[888,63287,63288],{"xmlns":890},[892,63289,63290,63306],{},[895,63291,63292,63294],{},[1712,63293,2219],{},[2563,63295,63296],{"scriptlevel":2085,"displaystyle":1903},[2567,63297,63298,63300],{},[898,63299,7544],{},[895,63301,63302,63304],{},[1716,63303,2787],{},[898,63305,207],{},[902,63307,63308],{"encoding":904},"-\\tfrac{b}{2a}",[883,63310,63312],{"className":63311},[886],[888,63313,63314],{"xmlns":890},[892,63315,63316,63322],{},[895,63317,63318,63320],{},[898,63319,2044],{},[898,63321,1775],{},[902,63323,60320],{"encoding":904},[883,63325,63327],{"className":63326},[886],[888,63328,63329],{"xmlns":890},[892,63330,63331,63343],{},[895,63332,63333,63335],{},[1712,63334,2219],{},[2563,63336,63337],{"scriptlevel":2085,"displaystyle":1903},[2567,63338,63339,63341],{},[898,63340,7544],{},[898,63342,207],{},[902,63344,63345],{"encoding":904},"-\\tfrac{b}{a}",[724,63347,63348],{},[614,63349,63350,63351,63382,63383,63412,63413,1659],{},"Obrázek 3.3: Parabola ",[883,63352,63354],{"className":63353},[886],[888,63355,63356],{"xmlns":890},[892,63357,63358,63380],{},[895,63359,63360,63362,63364,63366,63368,63374,63376,63378],{},[898,63361,1772],{},[898,63363,1775],{},[1712,63365,1714],{},[898,63367,207],{},[2037,63369,63370,63372],{},[898,63371,1734],{},[1716,63373,2787],{},[1712,63375,3145],{},[898,63377,7544],{},[898,63379,1734],{},[902,63381,62814],{"encoding":904}," s maximem v ",[883,63384,63386],{"className":63385},[886],[888,63387,63388],{"xmlns":890},[892,63389,63390,63410],{},[895,63391,63392,63394,63396,63398],{},[898,63393,1734],{},[1712,63395,1714],{},[1712,63397,2219],{},[2563,63399,63400],{"scriptlevel":2085,"displaystyle":1903},[2567,63401,63402,63404],{},[898,63403,7544],{},[895,63405,63406,63408],{},[1716,63407,2787],{},[898,63409,207],{},[902,63411,63018],{"encoding":904}," a nulou v ",[883,63414,63416],{"className":63415},[886],[888,63417,63418],{"xmlns":890},[892,63419,63420,63436],{},[895,63421,63422,63424,63426,63428],{},[898,63423,1734],{},[1712,63425,1714],{},[1712,63427,2219],{},[2563,63429,63430],{"scriptlevel":2085,"displaystyle":1903},[2567,63431,63432,63434],{},[898,63433,7544],{},[898,63435,207],{},[902,63437,63438],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,63440,63441],{},[614,63442,63443,63444,1659],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,63445,63447],{"className":63446},[886],[888,63448,63449],{"xmlns":890},[892,63450,63451,63471],{},[895,63452,63453,63455,63457,63459,63461,63463,63465],{},[898,63454,2044],{},[898,63456,1775],{},[1712,63458,1714],{},[898,63460,4445],{},[898,63462,1775],{},[1712,63464,1714],{},[2037,63466,63467,63469],{},[898,63468,1710],{},[1712,63470,2145],{},[902,63472,63473],{"encoding":904},"AR = MR = P^*",[115,63475,63477],{"id":63476},"náklady-firmy","Náklady firmy",[198,63479,63481],{"id":63480},"celkové-náklady","Celkové náklady",[724,63483,63484,3245,63486,14897,63501,63504,63505,63518],{},[38,63485,63481],{},[883,63487,63489],{"className":63488},[886],[888,63490,63491],{"xmlns":890},[892,63492,63493,63499],{},[895,63494,63495,63497],{},[898,63496,1772],{},[898,63498,8195],{},[902,63500,8648],{"encoding":904},[38,63502,63503],{},"total cost",") jsou veškeré náklady na realizaci ",[883,63506,63508],{"className":63507},[886],[888,63509,63510],{"xmlns":890},[892,63511,63512,63516],{},[895,63513,63514],{},[898,63515,1734],{},[902,63517,1734],{"encoding":904}," jednotek produkce:",[883,63520,63522],{"className":63521},[886],[888,63523,63524],{"xmlns":890,"display":32941},[892,63525,63526,63581],{},[25629,63527,63528],{"width":32946},[25634,63529,63530,63532,63574,63576],{},[25637,63531],{"width":32951},[25637,63533,63534],{},[895,63535,63536,63538,63540,63542,63544,63546,63548,63550,63552,63554,63556,63558,63560,63562,63564,63566,63568,63570,63572],{},[898,63537,1772],{},[898,63539,8195],{},[1712,63541,1714],{},[898,63543,1772],{},[898,63545,8195],{},[1712,63547,1904],{"stretchy":1903},[898,63549,1734],{},[1712,63551,1910],{"stretchy":1903},[1712,63553,1714],{},[898,63555,15308],{},[898,63557,8195],{},[1712,63559,3145],{},[898,63561,1772],{},[898,63563,45214],{},[898,63565,8195],{},[1712,63567,1904],{"stretchy":1903},[898,63569,1734],{},[1712,63571,1910],{"stretchy":1903},[1712,63573,3138],{"separator":2565},[25637,63575],{"width":32951},[25637,63577,63578],{},[1762,63579,63580],{},"(3.5)",[902,63582,63583],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,63585,2101,63586,63601,63602,14897,63605,17002,63608,63601,63632,14897,63635,63638],{},[883,63587,63589],{"className":63588},[886],[888,63590,63591],{"xmlns":890},[892,63592,63593,63599],{},[895,63594,63595,63597],{},[898,63596,15308],{},[898,63598,8195],{},[902,63600,60366],{"encoding":904}," jsou ",[38,63603,63604],{},"fixní náklady",[38,63606,63607],{},"fixed cost",[883,63609,63611],{"className":63610},[886],[888,63612,63613],{"xmlns":890},[892,63614,63615,63629],{},[895,63616,63617,63619,63621,63623,63625,63627],{},[898,63618,1772],{},[898,63620,45214],{},[898,63622,8195],{},[1712,63624,1904],{"stretchy":1903},[898,63626,1734],{},[1712,63628,1910],{"stretchy":1903},[902,63630,63631],{"encoding":904},"TVC(Q)",[38,63633,63634],{},"celkové variabilní náklady",[38,63636,63637],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,63640,63642],{"id":63641},"průměrné-náklady","Průměrné náklady",[724,63644,63645,3245,63647,14897,63662,63665],{},[38,63646,63642],{},[883,63648,63650],{"className":63649},[886],[888,63651,63652],{"xmlns":890},[892,63653,63654,63660],{},[895,63655,63656,63658],{},[898,63657,2044],{},[898,63659,8195],{},[902,63661,60435],{"encoding":904},[38,63663,63664],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,63667,63669],{"className":63668},[886],[888,63670,63671],{"xmlns":890,"display":32941},[892,63672,63673,63752],{},[25629,63674,63675],{"width":32946},[25634,63676,63677,63679,63745,63747],{},[25637,63678],{"width":32951},[25637,63680,63681],{},[895,63682,63683,63685,63687,63689,63691,63693,63695,63697,63699,63701,63711,63713,63723,63725,63743],{},[898,63684,2044],{},[898,63686,8195],{},[1712,63688,1714],{},[898,63690,2044],{},[898,63692,8195],{},[1712,63694,1904],{"stretchy":1903},[898,63696,1734],{},[1712,63698,1910],{"stretchy":1903},[1712,63700,1714],{},[2567,63702,63703,63709],{},[895,63704,63705,63707],{},[898,63706,1772],{},[898,63708,8195],{},[898,63710,1734],{},[1712,63712,1714],{},[2567,63714,63715,63721],{},[895,63716,63717,63719],{},[898,63718,15308],{},[898,63720,8195],{},[898,63722,1734],{},[1712,63724,3145],{},[2567,63726,63727,63741],{},[895,63728,63729,63731,63733,63735,63737,63739],{},[898,63730,1772],{},[898,63732,45214],{},[898,63734,8195],{},[1712,63736,1904],{"stretchy":1903},[898,63738,1734],{},[1712,63740,1910],{"stretchy":1903},[898,63742,1734],{},[1712,63744,3138],{"separator":2565},[25637,63746],{"width":32951},[25637,63748,63749],{},[1762,63750,63751],{},"(3.6)",[902,63753,63754],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,63756,2101,63757,63601,63781,3245,63784,14897,63801,17002,63804,63601,63836,3245,63839,14897,63856,8558],{},[883,63758,63760],{"className":63759},[886],[888,63761,63762],{"xmlns":890},[892,63763,63764,63778],{},[895,63765,63766],{},[2563,63767,63768],{"scriptlevel":2085,"displaystyle":1903},[2567,63769,63770,63776],{},[895,63771,63772,63774],{},[898,63773,15308],{},[898,63775,8195],{},[898,63777,1734],{},[902,63779,63780],{"encoding":904},"\\tfrac{FC}{Q}",[38,63782,63783],{},"průměrné fixní náklady",[883,63785,63787],{"className":63786},[886],[888,63788,63789],{"xmlns":890},[892,63790,63791,63799],{},[895,63792,63793,63795,63797],{},[898,63794,2044],{},[898,63796,15308],{},[898,63798,8195],{},[902,63800,60402],{"encoding":904},[38,63802,63803],{},"average fixed cost",[883,63805,63807],{"className":63806},[886],[888,63808,63809],{"xmlns":890},[892,63810,63811,63833],{},[895,63812,63813],{},[2563,63814,63815],{"scriptlevel":2085,"displaystyle":1903},[2567,63816,63817,63831],{},[895,63818,63819,63821,63823,63825,63827,63829],{},[898,63820,1772],{},[898,63822,45214],{},[898,63824,8195],{},[1712,63826,1904],{"stretchy":1903},[898,63828,1734],{},[1712,63830,1910],{"stretchy":1903},[898,63832,1734],{},[902,63834,63835],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,63837,63838],{},"průměrné variabilní náklady",[883,63840,63842],{"className":63841},[886],[888,63843,63844],{"xmlns":890},[892,63845,63846,63854],{},[895,63847,63848,63850,63852],{},[898,63849,2044],{},[898,63851,45214],{},[898,63853,8195],{},[902,63855,60186],{"encoding":904},[38,63857,63858],{},"average variable cost",[883,63860,63862],{"className":63861},[886],[888,63863,63864],{"xmlns":890,"display":32941},[892,63865,63866,63925],{},[25629,63867,63868],{"width":32946},[25634,63869,63870,63872,63918,63920],{},[25637,63871],{"width":32951},[25637,63873,63874],{},[895,63875,63876,63878,63880,63882,63884,63886,63888,63890,63892,63894,63896,63898,63916],{},[898,63877,2044],{},[898,63879,45214],{},[898,63881,8195],{},[1712,63883,1714],{},[898,63885,2044],{},[898,63887,45214],{},[898,63889,8195],{},[1712,63891,1904],{"stretchy":1903},[898,63893,1734],{},[1712,63895,1910],{"stretchy":1903},[1712,63897,1714],{},[2567,63899,63900,63914],{},[895,63901,63902,63904,63906,63908,63910,63912],{},[898,63903,1772],{},[898,63905,45214],{},[898,63907,8195],{},[1712,63909,1904],{"stretchy":1903},[898,63911,1734],{},[1712,63913,1910],{"stretchy":1903},[898,63915,1734],{},[898,63917,1659],{"mathvariant":2003},[25637,63919],{"width":32951},[25637,63921,63922],{},[1762,63923,63924],{},"(3.7)",[902,63926,63927],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[42223,63929,63931],{"id":63930},"příklad-34","Příklad 3.4",[724,63933,63934,62397,63936,1655,63961,60900,63985,1655,64000,64015,64016,1659],{},[38,63935,60862],{},[883,63937,63939],{"className":63938},[886],[888,63940,63941],{"xmlns":890},[892,63942,63943,63958],{},[895,63944,63945,63947,63949,63951,63953,63955],{},[898,63946,15308],{},[898,63948,8195],{},[1712,63950,1714],{},[1716,63952,2222],{},[1762,63954,2583],{},[1716,63956,63957],{},"000",[902,63959,63960],{"encoding":904},"FC = 1\\,000",[883,63962,63964],{"className":63963},[886],[888,63965,63966],{"xmlns":890},[892,63967,63968,63982],{},[895,63969,63970,63972,63974,63976,63978,63980],{},[898,63971,1772],{},[898,63973,45214],{},[898,63975,8195],{},[1712,63977,1714],{},[1716,63979,2975],{},[898,63981,1734],{},[902,63983,63984],{"encoding":904},"TVC = 4Q",[883,63986,63988],{"className":63987},[886],[888,63989,63990],{"xmlns":890},[892,63991,63992,63998],{},[895,63993,63994,63996],{},[898,63995,1772],{},[898,63997,8195],{},[902,63999,8648],{"encoding":904},[883,64001,64003],{"className":64002},[886],[888,64004,64005],{"xmlns":890},[892,64006,64007,64013],{},[895,64008,64009,64011],{},[898,64010,2044],{},[898,64012,8195],{},[902,64014,60435],{"encoding":904}," a jejich chování s rostoucím ",[883,64017,64019],{"className":64018},[886],[888,64020,64021],{"xmlns":890},[892,64022,64023,64027],{},[895,64024,64025],{},[898,64026,1734],{},[902,64028,1734],{"encoding":904},[724,64030,64031,3245,64033,1655,64063,64099,64100,2149,64113,64128,64129,2854],{},[38,64032,27645],{},[883,64034,64036],{"className":64035},[886],[888,64037,64038],{"xmlns":890},[892,64039,64040,64060],{},[895,64041,64042,64044,64046,64048,64050,64052,64054,64056,64058],{},[898,64043,1772],{},[898,64045,8195],{},[1712,64047,1714],{},[1716,64049,2222],{},[1762,64051,2583],{},[1716,64053,63957],{},[1712,64055,3145],{},[1716,64057,2975],{},[898,64059,1734],{},[902,64061,64062],{"encoding":904},"TC = 1\\,000 + 4Q",[883,64064,64066],{"className":64065},[886],[888,64067,64068],{"xmlns":890},[892,64069,64070,64096],{},[895,64071,64072,64074,64076,64078,64092,64094],{},[898,64073,2044],{},[898,64075,8195],{},[1712,64077,1714],{},[2563,64079,64080],{"scriptlevel":2085,"displaystyle":1903},[2567,64081,64082,64090],{},[895,64083,64084,64086,64088],{},[1716,64085,2222],{},[1762,64087,2583],{},[1716,64089,63957],{},[898,64091,1734],{},[1712,64093,3145],{},[1716,64095,2975],{},[902,64097,64098],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,64101,64103],{"className":64102},[886],[888,64104,64105],{"xmlns":890},[892,64106,64107,64111],{},[895,64108,64109],{},[898,64110,1734],{},[902,64112,1734],{"encoding":904},[883,64114,64116],{"className":64115},[886],[888,64117,64118],{"xmlns":890},[892,64119,64120,64126],{},[895,64121,64122,64124],{},[898,64123,2044],{},[898,64125,8195],{},[902,64127,60435],{"encoding":904}," blíží ",[883,64130,64132],{"className":64131},[886],[888,64133,64134],{"xmlns":890},[892,64135,64136,64140],{},[895,64137,64138],{},[1716,64139,2975],{},[902,64141,2975],{"encoding":904},[883,64143,64145],{"className":64144},[886],[888,64146,64147],{"xmlns":890,"display":32941},[892,64148,64149,64195],{},[895,64150,64151,64168,64190,64192],{},[44771,64152,64153,64160],{},[895,64154,64155,64158],{},[898,64156,64157],{},"lim",[1712,64159,61075],{},[895,64161,64162,64164,64166],{},[898,64163,1734],{},[1712,64165,2082],{},[898,64167,4112],{"mathvariant":2003},[895,64169,64170,64172,64184,64186,64188],{},[1712,64171,1904],{"fence":2565},[2567,64173,64174,64182],{},[895,64175,64176,64178,64180],{},[1716,64177,2222],{},[1762,64179,2583],{},[1716,64181,63957],{},[898,64183,1734],{},[1712,64185,3145],{},[1716,64187,2975],{},[1712,64189,1910],{"fence":2565},[1712,64191,1714],{},[1716,64193,64194],{},"4.",[902,64196,64197],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,64199,64200,64238,64239,1659],{},[883,64201,64203],{"className":64202},[886],[888,64204,64205],{"xmlns":890},[892,64206,64207,64235],{},[895,64208,64209,64211,64213,64215,64217,64231,64233],{},[898,64210,2044],{},[898,64212,15308],{},[898,64214,8195],{},[1712,64216,1714],{},[2563,64218,64219],{"scriptlevel":2085,"displaystyle":1903},[2567,64220,64221,64229],{},[895,64222,64223,64225,64227],{},[1716,64224,2222],{},[1762,64226,2583],{},[1716,64228,63957],{},[898,64230,1734],{},[1712,64232,2082],{},[1716,64234,2085],{},[902,64236,64237],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,64240,64242],{"className":64241},[886],[888,64243,64244],{"xmlns":890},[892,64245,64246,64250],{},[895,64247,64248],{},[898,64249,1734],{},[902,64251,1734],{"encoding":904},[724,64253,64254],{},[614,64255,64256,64257,64286,64287,1659],{},"Obrázek 3.5: Přímka ",[883,64258,64260],{"className":64259},[886],[888,64261,64262],{"xmlns":890},[892,64263,64264,64284],{},[895,64265,64266,64268,64270,64272,64274,64276,64278,64280,64282],{},[898,64267,1772],{},[898,64269,8195],{},[1712,64271,1714],{},[1716,64273,2222],{},[1762,64275,2583],{},[1716,64277,63957],{},[1712,64279,3145],{},[1716,64281,2975],{},[898,64283,1734],{},[902,64285,64062],{"encoding":904}," protínající svislou osu ve výši ",[883,64288,64290],{"className":64289},[886],[888,64291,64292],{"xmlns":890},[892,64293,64294,64308],{},[895,64295,64296,64298,64300,64302,64304,64306],{},[898,64297,15308],{},[898,64299,8195],{},[1712,64301,1714],{},[1716,64303,2222],{},[1762,64305,2583],{},[1716,64307,63957],{},[902,64309,63960],{"encoding":904},[724,64311,64312],{},[614,64313,64314,64315,64350,64351,1659],{},"Obrázek 3.6: Hyperbola ",[883,64316,64318],{"className":64317},[886],[888,64319,64320],{"xmlns":890},[892,64321,64322,64348],{},[895,64323,64324,64326,64328,64330,64344,64346],{},[898,64325,2044],{},[898,64327,8195],{},[1712,64329,1714],{},[2563,64331,64332],{"scriptlevel":2085,"displaystyle":1903},[2567,64333,64334,64342],{},[895,64335,64336,64338,64340],{},[1716,64337,2222],{},[1762,64339,2583],{},[1716,64341,63957],{},[898,64343,1734],{},[1712,64345,3145],{},[1716,64347,2975],{},[902,64349,64098],{"encoding":904}," s vodorovnou asymptotou ",[883,64352,64354],{"className":64353},[886],[888,64355,64356],{"xmlns":890},[892,64357,64358,64368],{},[895,64359,64360,64362,64364,64366],{},[898,64361,2044],{},[898,64363,8195],{},[1712,64365,1714],{},[1716,64367,2975],{},[902,64369,64370],{"encoding":904},"AC = 4",[724,64372,64373],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,64375,64377],{"className":64376},[886],[888,64378,64379],{"xmlns":890,"display":32941},[892,64380,64381,64407],{},[895,64382,64383,64385,64387,64389,64391,64393,64395,64397,64399,64401,64403,64405],{},[898,64384,1772],{},[898,64386,45214],{},[898,64388,8195],{},[1712,64390,1714],{},[898,64392,1734],{},[1712,64394,1783],{},[898,64396,45214],{},[898,64398,8195],{},[1712,64400,1904],{"stretchy":1903},[898,64402,1734],{},[1712,64404,1910],{"stretchy":1903},[1712,64406,3138],{"separator":2565},[902,64408,64409],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,64411,2101,64412,63601,64440,64443,64444,64474],{},[883,64413,64415],{"className":64414},[886],[888,64416,64417],{"xmlns":890},[892,64418,64419,64437],{},[895,64420,64421,64423,64425,64427,64429,64431,64433,64435],{},[898,64422,45214],{},[898,64424,8195],{},[1712,64426,1714],{},[898,64428,45214],{},[898,64430,8195],{},[1712,64432,1904],{"stretchy":1903},[898,64434,1734],{},[1712,64436,1910],{"stretchy":1903},[902,64438,64439],{"encoding":904},"VC = VC(Q)",[38,64441,64442],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,64445,64447],{"className":64446},[886],[888,64448,64449],{"xmlns":890},[892,64450,64451,64471],{},[895,64452,64453,64455,64457,64459,64461,64463,64465,64467,64469],{},[898,64454,1772],{},[898,64456,45214],{},[898,64458,8195],{},[1712,64460,1904],{"stretchy":1903},[898,64462,1734],{},[1712,64464,1910],{"stretchy":1903},[1712,64466,1714],{},[898,64468,207],{},[898,64470,1734],{},[902,64472,64473],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,64476,64478],{"className":64477},[886],[888,64479,64480],{"xmlns":890,"display":32941},[892,64481,64482,64502],{},[895,64483,64484,64486,64488,64490,64492,64494,64496,64498,64500],{},[898,64485,1772],{},[898,64487,8195],{},[1712,64489,1714],{},[898,64491,15308],{},[898,64493,8195],{},[1712,64495,3145],{},[898,64497,207],{},[898,64499,1734],{},[898,64501,1659],{"mathvariant":2003},[902,64503,64504],{"encoding":904},"TC = FC + aQ.",[724,64506,64507,64508,64523,64524,64539,64540,64563,64564,64598,64599,64350,64612,64625,64626,1655,64674,64718,64719,1659],{},"Křivkou ",[883,64509,64511],{"className":64510},[886],[888,64512,64513],{"xmlns":890},[892,64514,64515,64521],{},[895,64516,64517,64519],{},[898,64518,1772],{},[898,64520,8195],{},[902,64522,8648],{"encoding":904}," je přímka se svislým průsečíkem ",[883,64525,64527],{"className":64526},[886],[888,64528,64529],{"xmlns":890},[892,64530,64531,64537],{},[895,64532,64533,64535],{},[898,64534,15308],{},[898,64536,8195],{},[902,64538,60366],{"encoding":904}," a sklonem ",[883,64541,64543],{"className":64542},[886],[888,64544,64545],{"xmlns":890},[892,64546,64547,64560],{},[895,64548,64549,64552,64554,64556,64558],{},[898,64550,64551],{},"tan",[1712,64553,61075],{},[898,64555,23737],{},[1712,64557,1714],{},[898,64559,207],{},[902,64561,64562],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,64565,64567],{"className":64566},[886],[888,64568,64569],{"xmlns":890},[892,64570,64571,64595],{},[895,64572,64573,64575,64577,64579,64591,64593],{},[898,64574,2044],{},[898,64576,8195],{},[1712,64578,1714],{},[2563,64580,64581],{"scriptlevel":2085,"displaystyle":1903},[2567,64582,64583,64589],{},[895,64584,64585,64587],{},[898,64586,15308],{},[898,64588,8195],{},[898,64590,1734],{},[1712,64592,3145],{},[898,64594,207],{},[902,64596,64597],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,64600,64602],{"className":64601},[886],[888,64603,64604],{"xmlns":890},[892,64605,64606,64610],{},[895,64607,64608],{},[898,64609,14667],{},[902,64611,14667],{"encoding":904},[883,64613,64615],{"className":64614},[886],[888,64616,64617],{"xmlns":890},[892,64618,64619,64623],{},[895,64620,64621],{},[898,64622,207],{},[902,64624,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,64627,64629],{"className":64628},[886],[888,64630,64631],{"xmlns":890},[892,64632,64633,64671],{},[895,64634,64635,64655,64667,64669],{},[6927,64636,64637,64643],{},[895,64638,64639,64641],{},[898,64640,64157],{},[1712,64642,61075],{},[895,64644,64645,64647,64649],{},[898,64646,1734],{},[1712,64648,2082],{},[2037,64650,64651,64653],{},[1716,64652,2085],{},[1712,64654,3145],{},[2563,64656,64657],{"scriptlevel":2085,"displaystyle":1903},[2567,64658,64659,64665],{},[895,64660,64661,64663],{},[898,64662,15308],{},[898,64664,8195],{},[898,64666,1734],{},[1712,64668,1714],{},[898,64670,4112],{"mathvariant":2003},[902,64672,64673],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,64675,64677],{"className":64676},[886],[888,64678,64679],{"xmlns":890},[892,64680,64681,64715],{},[895,64682,64683,64699,64711,64713],{},[6927,64684,64685,64691],{},[895,64686,64687,64689],{},[898,64688,64157],{},[1712,64690,61075],{},[895,64692,64693,64695,64697],{},[898,64694,1734],{},[1712,64696,2082],{},[898,64698,4112],{"mathvariant":2003},[2563,64700,64701],{"scriptlevel":2085,"displaystyle":1903},[2567,64702,64703,64709],{},[895,64704,64705,64707],{},[898,64706,15308],{},[898,64708,8195],{},[898,64710,1734],{},[1712,64712,1714],{},[1716,64714,2085],{},[902,64716,64717],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,64720,64722],{"className":64721},[886],[888,64723,64724],{"xmlns":890},[892,64725,64726,64732],{},[895,64727,64728,64730],{},[898,64729,2044],{},[898,64731,8195],{},[902,64733,60435],{"encoding":904},[724,64735,64736],{},[614,64737,64738,64739,64754,64755,64770,64771,1659],{},"Obrázek 3.7: Přímka ",[883,64740,64742],{"className":64741},[886],[888,64743,64744],{"xmlns":890},[892,64745,64746,64752],{},[895,64747,64748,64750],{},[898,64749,1772],{},[898,64751,8195],{},[902,64753,8648],{"encoding":904}," s osovým průsečíkem ve výši ",[883,64756,64758],{"className":64757},[886],[888,64759,64760],{"xmlns":890},[892,64761,64762,64768],{},[895,64763,64764,64766],{},[898,64765,15308],{},[898,64767,8195],{},[902,64769,60366],{"encoding":904}," a se sklonem ",[883,64772,64774],{"className":64773},[886],[888,64775,64776],{"xmlns":890},[892,64777,64778,64790],{},[895,64779,64780,64782,64784,64786,64788],{},[898,64781,64551],{},[1712,64783,61075],{},[898,64785,23737],{},[1712,64787,1714],{},[898,64789,207],{},[902,64791,64562],{"encoding":904},[724,64793,64794],{},[614,64795,64796,64797,64812,64813,1659],{},"Obrázek 3.8: Klesající hyperbola ",[883,64798,64800],{"className":64799},[886],[888,64801,64802],{"xmlns":890},[892,64803,64804,64810],{},[895,64805,64806,64808],{},[898,64807,2044],{},[898,64809,8195],{},[902,64811,60435],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,64814,64816],{"className":64815},[886],[888,64817,64818],{"xmlns":890},[892,64819,64820,64824],{},[895,64821,64822],{},[898,64823,207],{},[902,64825,207],{"encoding":904},[198,64827,64829],{"id":64828},"mezní-náklady","Mezní náklady",[724,64831,64832,3245,64834,14897,64849,64852,64853,64856],{},[38,64833,64829],{},[883,64835,64837],{"className":64836},[886],[888,64838,64839],{"xmlns":890},[892,64840,64841,64847],{},[895,64842,64843,64845],{},[898,64844,4445],{},[898,64846,8195],{},[902,64848,60167],{"encoding":904},[38,64850,64851],{},"marginal cost",") jsou ",[207,64854,1145],{"className":64855,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,64858,64860],{"className":64859},[886],[888,64861,64862],{"xmlns":890,"display":32941},[892,64863,64864,64933],{},[25629,64865,64866],{"width":32946},[25634,64867,64868,64870,64926,64928],{},[25637,64869],{"width":32951},[25637,64871,64872],{},[895,64873,64874,64876,64878,64880,64882,64884,64886,64888,64890,64892,64908,64910,64912,64918,64920,64922,64924],{},[898,64875,4445],{},[898,64877,8195],{},[1712,64879,1714],{},[898,64881,4445],{},[898,64883,8195],{},[1712,64885,1904],{"stretchy":1903},[898,64887,1734],{},[1712,64889,1910],{"stretchy":1903},[1712,64891,1714],{},[2567,64893,64894,64902],{},[895,64895,64896,64898,64900],{},[898,64897,2468],{"mathvariant":2003},[898,64899,1772],{},[898,64901,8195],{},[895,64903,64904,64906],{},[898,64905,2468],{"mathvariant":2003},[898,64907,1734],{},[1712,64909,1714],{},[898,64911,1772],{},[2037,64913,64914,64916],{},[898,64915,8195],{},[1712,64917,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,64919,1904],{"stretchy":1903},[898,64921,1734],{},[1712,64923,1910],{"stretchy":1903},[898,64925,1659],{"mathvariant":2003},[25637,64927],{"width":32951},[25637,64929,64930],{},[1762,64931,64932],{},"(3.8)",[902,64934,64935],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1636,64937,64938],{},[724,64939,64940,64942,64943,64969,64970,64987,64988,1659],{},[883,64941,1941],{}," Intuice — „kolik stojí další kus\"\n",[883,64944,64946],{"className":64945},[886],[888,64947,64948],{"xmlns":890},[892,64949,64950,64966],{},[895,64951,64952,64954,64956,64958,64964],{},[898,64953,4445],{},[898,64955,8195],{},[1712,64957,1904],{"stretchy":1903},[2037,64959,64960,64962],{},[898,64961,1734],{},[1712,64963,2145],{},[1712,64965,1910],{"stretchy":1903},[902,64967,64968],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,64971,64973],{"className":64972},[886],[888,64974,64975],{"xmlns":890},[892,64976,64977,64985],{},[895,64978,64979],{},[2037,64980,64981,64983],{},[898,64982,1734],{},[1712,64984,2145],{},[902,64986,34719],{"encoding":904},". Formálně ",[883,64989,64991],{"className":64990},[886],[888,64992,64993],{"xmlns":890},[892,64994,64995,65047],{},[895,64996,64997,64999,65001,65003,65009,65011,65013,65015,65017,65019,65025,65027,65029,65031,65033,65035,65037,65039,65045],{},[898,64998,4445],{},[898,65000,8195],{},[1712,65002,1904],{"stretchy":1903},[2037,65004,65005,65007],{},[898,65006,1734],{},[1712,65008,2145],{},[1712,65010,1910],{"stretchy":1903},[1712,65012,3740],{},[898,65014,1772],{},[898,65016,8195],{},[1712,65018,1904],{"stretchy":1903},[2037,65020,65021,65023],{},[898,65022,1734],{},[1712,65024,2145],{},[1712,65026,3145],{},[1716,65028,2222],{},[1712,65030,1910],{"stretchy":1903},[1712,65032,2219],{},[898,65034,1772],{},[898,65036,8195],{},[1712,65038,1904],{"stretchy":1903},[2037,65040,65041,65043],{},[898,65042,1734],{},[1712,65044,2145],{},[1712,65046,1910],{"stretchy":1903},[902,65048,65049],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,65051,65052,65053,2854],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,65054,65056],{"className":65055},[886],[888,65057,65058],{"xmlns":890},[892,65059,65060,65068],{},[895,65061,65062,65064,65066],{},[898,65063,2004],{"mathvariant":2003},[898,65065,1772],{},[898,65067,8195],{},[902,65069,65070],{"encoding":904},"\\Delta TC",[883,65072,65074],{"className":65073},[886],[888,65075,65076],{"xmlns":890,"display":32941},[892,65077,65078,65147],{},[25629,65079,65080],{"width":32946},[25634,65081,65082,65084,65140,65142],{},[25637,65083],{"width":32951},[25637,65085,65086],{},[895,65087,65088,65090,65092,65094,65096,65098,65100,65102,65104,65106,65108,65110,65112,65114,65120,65122,65124,65126,65128,65130,65132,65134,65136,65138],{},[898,65089,2004],{"mathvariant":2003},[898,65091,1772],{},[898,65093,8195],{},[1762,65095,1764],{},[1712,65097,3740],{},[1762,65099,1764],{},[898,65101,2468],{"mathvariant":2003},[898,65103,1772],{},[898,65105,8195],{},[1712,65107,1714],{},[1712,65109,1904],{"stretchy":1903},[898,65111,1772],{},[898,65113,8195],{},[2037,65115,65116,65118],{},[1712,65117,1910],{"stretchy":1903},[1712,65119,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,65121,2583],{},[898,65123,2468],{"mathvariant":2003},[898,65125,1734],{},[1712,65127,1714],{},[898,65129,4445],{},[898,65131,8195],{},[1762,65133,2583],{},[898,65135,2468],{"mathvariant":2003},[898,65137,1734],{},[1712,65139,3138],{"separator":2565},[25637,65141],{"width":32951},[25637,65143,65144],{},[1762,65145,65146],{},"(3.9)",[902,65148,65149],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,65151,62186],{},[883,65153,65155],{"className":65154},[886],[888,65156,65157],{"xmlns":890,"display":32941},[892,65158,65159,65257],{},[895,65160,65161,65199,65201,65203,65205,65227,65229,65255],{},[895,65162,65163,65165,65171,65173,65179,65182,65188,65191],{},[1762,65164,62200],{},[6205,65166,65167,65169],{"accent":2565},[1762,65168,50607],{},[1712,65170,29933],{},[1762,65172,62209],{},[6205,65174,65175,65177],{"accent":2565},[1762,65176,7446],{},[1712,65178,29852],{},[1762,65180,65181],{},"ch n",[6205,65183,65184,65186],{"accent":2565},[1762,65185,207],{},[1712,65187,29852],{},[1762,65189,65190],{},"klad",[6205,65192,65193,65196],{"accent":2565},[1762,65194,65195],{},"u",[1712,65197,65198],{},"˚",[1762,65200,1764],{},[1712,65202,3740],{},[1762,65204,1764],{},[895,65206,65207,65209,65215,65218,65224],{},[1762,65208,62244],{},[6205,65210,65211,65213],{"accent":2565},[1762,65212,29921],{},[1712,65214,29852],{},[1762,65216,65217],{}," n",[6205,65219,65220,65222],{"accent":2565},[1762,65221,207],{},[1712,65223,29852],{},[1762,65225,65226],{},"klady",[1712,65228,62271],{},[895,65230,65231,65233,65239,65241,65247,65249],{},[1762,65232,62200],{},[6205,65234,65235,65237],{"accent":2565},[1762,65236,50607],{},[1712,65238,29933],{},[1762,65240,62284],{},[6205,65242,65243,65245],{"accent":2565},[1762,65244,14466],{},[1712,65246,29933],{},[1762,65248,62293],{},[6205,65250,65251,65253],{"accent":2565},[1762,65252,29921],{},[1712,65254,29852],{},[898,65256,1659],{"mathvariant":2003},[902,65258,65259],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[42223,65261,65263],{"id":65262},"příklad-35","Příklad 3.5",[724,65265,65266,62397,65268,60900,65304,65319,65320,65335,65336,8093,65349,3072,65362,65375,65376,3072,65389,1659],{},[38,65267,60862],{},[883,65269,65271],{"className":65270},[886],[888,65272,65273],{"xmlns":890},[892,65274,65275,65301],{},[895,65276,65277,65279,65281,65283,65285,65287,65289,65291,65293,65295],{},[898,65278,1772],{},[898,65280,8195],{},[1712,65282,1714],{},[1716,65284,6195],{},[1712,65286,3145],{},[1716,65288,6209],{},[898,65290,1734],{},[1712,65292,3145],{},[1716,65294,2787],{},[2037,65296,65297,65299],{},[898,65298,1734],{},[1716,65300,2787],{},[902,65302,65303],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,65305,65307],{"className":65306},[886],[888,65308,65309],{"xmlns":890},[892,65310,65311,65317],{},[895,65312,65313,65315],{},[898,65314,4445],{},[898,65316,8195],{},[902,65318,60167],{"encoding":904}," a odhadněte změny ",[883,65321,65323],{"className":65322},[886],[888,65324,65325],{"xmlns":890},[892,65326,65327,65333],{},[895,65328,65329,65331],{},[898,65330,1772],{},[898,65332,8195],{},[902,65334,8648],{"encoding":904}," při změnách ",[883,65337,65339],{"className":65338},[886],[888,65340,65341],{"xmlns":890},[892,65342,65343,65347],{},[895,65344,65345],{},[898,65346,1734],{},[902,65348,1734],{"encoding":904},[883,65350,65352],{"className":65351},[886],[888,65353,65354],{"xmlns":890},[892,65355,65356,65360],{},[895,65357,65358],{},[1716,65359,41119],{},[902,65361,41119],{"encoding":904},[883,65363,65365],{"className":65364},[886],[888,65366,65367],{"xmlns":890},[892,65368,65369,65373],{},[895,65370,65371],{},[1716,65372,46737],{},[902,65374,46737],{"encoding":904}," a z ",[883,65377,65379],{"className":65378},[886],[888,65380,65381],{"xmlns":890},[892,65382,65383,65387],{},[895,65384,65385],{},[1716,65386,41119],{},[902,65388,41119],{"encoding":904},[883,65390,65392],{"className":65391},[886],[888,65393,65394],{"xmlns":890},[892,65395,65396,65400],{},[895,65397,65398],{},[1716,65399,8912],{},[902,65401,8912],{"encoding":904},[724,65403,65404,3245,65406,7037,65432,1343,65459,65486,65487,65502,65503,65518,65519,65546,65547,65567,65568,25406,65589,65645,65646,8093,65659,3072,65672,5920,65685,1659],{},[38,65405,27645],{},[883,65407,65409],{"className":65408},[886],[888,65410,65411],{"xmlns":890},[892,65412,65413,65429],{},[895,65414,65415,65417,65419,65421,65423,65425,65427],{},[898,65416,4445],{},[898,65418,8195],{},[1712,65420,1714],{},[1716,65422,6209],{},[1712,65424,3145],{},[1716,65426,2975],{},[898,65428,1734],{},[902,65430,65431],{"encoding":904},"MC = 6 + 4Q",[883,65433,65435],{"className":65434},[886],[888,65436,65437],{"xmlns":890},[892,65438,65439,65456],{},[895,65440,65441,65443,65445,65447,65449,65451,65453],{},[898,65442,4445],{},[898,65444,8195],{},[1712,65446,1904],{"stretchy":1903},[1716,65448,41119],{},[1712,65450,1910],{"stretchy":1903},[1712,65452,1714],{},[1716,65454,65455],{},"66",[902,65457,65458],{"encoding":904},"MC(15) = 66",[883,65460,65462],{"className":65461},[886],[888,65463,65464],{"xmlns":890},[892,65465,65466,65483],{},[895,65467,65468,65470,65472,65474,65476,65478,65480],{},[898,65469,4445],{},[898,65471,8195],{},[1712,65473,1904],{"stretchy":1903},[1716,65475,6857],{},[1712,65477,1910],{"stretchy":1903},[1712,65479,1714],{},[1716,65481,65482],{},"86",[902,65484,65485],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,65488,65490],{"className":65489},[886],[888,65491,65492],{"xmlns":890},[892,65493,65494,65500],{},[895,65495,65496,65498],{},[898,65497,1772],{},[898,65499,8195],{},[902,65501,8648],{"encoding":904}," zvyšuje (",[883,65504,65506],{"className":65505},[886],[888,65507,65508],{"xmlns":890},[892,65509,65510,65516],{},[895,65511,65512,65514],{},[898,65513,4445],{},[898,65515,8195],{},[902,65517,60167],{"encoding":904}," je rostoucí). Z ",[883,65520,65522],{"className":65521},[886],[888,65523,65524],{"xmlns":890},[892,65525,65526,65543],{},[895,65527,65528,65530,65532,65534,65536,65538,65540],{},[898,65529,1772],{},[898,65531,8195],{},[1712,65533,1904],{"stretchy":1903},[1716,65535,41119],{},[1712,65537,1910],{"stretchy":1903},[1712,65539,1714],{},[1716,65541,65542],{},"740",[902,65544,65545],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,65548,65550],{"className":65549},[886],[888,65551,65552],{"xmlns":890},[892,65553,65554,65564],{},[895,65555,65556,65558,65560,65562],{},[898,65557,2468],{"mathvariant":2003},[898,65559,1734],{},[1712,65561,1714],{},[1716,65563,2222],{},[902,65565,65566],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,65569,65571],{"className":65570},[886],[888,65572,65573],{"xmlns":890},[892,65574,65575,65586],{},[895,65576,65577,65579,65581,65583],{},[898,65578,1772],{},[898,65580,8195],{},[1712,65582,3740],{},[1716,65584,65585],{},"806",[902,65587,65588],{"encoding":904},"TC \\approx 806",[883,65590,65592],{"className":65591},[886],[888,65593,65594],{"xmlns":890},[892,65595,65596,65642],{},[895,65597,65598,65600,65602,65604,65606,65608,65610,65612,65614,65616,65618,65620,65622,65624,65626,65628,65630,65633,65635,65637,65639],{},[898,65599,2004],{"mathvariant":2003},[898,65601,1772],{},[898,65603,8195],{},[1712,65605,1714],{},[898,65607,1772],{},[898,65609,8195],{},[1712,65611,1904],{"stretchy":1903},[1716,65613,46737],{},[1712,65615,1910],{"stretchy":1903},[1712,65617,2219],{},[898,65619,1772],{},[898,65621,8195],{},[1712,65623,1904],{"stretchy":1903},[1716,65625,41119],{},[1712,65627,1910],{"stretchy":1903},[1712,65629,1714],{},[1716,65631,65632],{},"808",[1712,65634,2219],{},[1716,65636,65542],{},[1712,65638,1714],{},[1716,65640,65641],{},"68",[902,65643,65644],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,65647,65649],{"className":65648},[886],[888,65650,65651],{"xmlns":890},[892,65652,65653,65657],{},[895,65654,65655],{},[898,65656,1734],{},[902,65658,1734],{"encoding":904},[883,65660,65662],{"className":65661},[886],[888,65663,65664],{"xmlns":890},[892,65665,65666,65670],{},[895,65667,65668],{},[1716,65669,41119],{},[902,65671,41119],{"encoding":904},[883,65673,65675],{"className":65674},[886],[888,65676,65677],{"xmlns":890},[892,65678,65679,65683],{},[895,65680,65681],{},[1716,65682,8912],{},[902,65684,8912],{"encoding":904},[883,65686,65688],{"className":65687},[886],[888,65689,65690],{"xmlns":890},[892,65691,65692,65721],{},[895,65693,65694,65696,65698,65700,65702,65704,65706,65708,65710,65712,65714,65716,65718],{},[898,65695,2004],{"mathvariant":2003},[898,65697,1772],{},[898,65699,8195],{},[1712,65701,3740],{},[1716,65703,65455],{},[1712,65705,1783],{},[1712,65707,1904],{"stretchy":1903},[1712,65709,2219],{},[1716,65711,6198],{},[1712,65713,1910],{"stretchy":1903},[1712,65715,1714],{},[1712,65717,2219],{},[1716,65719,65720],{},"198",[902,65722,65723],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,65725,65727],{"id":65726},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,65729,65730],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[42223,65732,65734],{"id":65733},"příklad-36","Příklad 3.6",[724,65736,65737,62397,65739,65783],{},[38,65738,60862],{},[883,65740,65742],{"className":65741},[886],[888,65743,65744],{"xmlns":890},[892,65745,65746,65780],{},[895,65747,65748,65750,65752,65754,65756,65758,65760,65762,65764,65766,65772,65774],{},[898,65749,1772],{},[898,65751,8195],{},[1712,65753,1714],{},[1716,65755,1739],{},[1712,65757,3145],{},[1716,65759,2809],{},[898,65761,1734],{},[1712,65763,2219],{},[1716,65765,3068],{},[2037,65767,65768,65770],{},[898,65769,1734],{},[1716,65771,2787],{},[1712,65773,3145],{},[2037,65775,65776,65778],{},[898,65777,1734],{},[1716,65779,6198],{},[902,65781,65782],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,65785,65786],{},[38,65787,27645],{},[883,65789,65791],{"className":65790},[886],[888,65792,65793],{"xmlns":890,"display":32941},[892,65794,65795,66039],{},[25629,65796,65797,65823,65871,65905,65947,65997],{"rowspacing":25631,"columnalign":25632,"columnspacing":2242},[25634,65798,65799,65809],{},[25637,65800,65801],{},[2563,65802,65803],{"scriptlevel":2085,"displaystyle":2565},[895,65804,65805,65807],{},[898,65806,15308],{},[898,65808,8195],{},[25637,65810,65811],{},[2563,65812,65813],{"scriptlevel":2085,"displaystyle":2565},[895,65814,65815,65817,65819,65821],{},[895,65816],{},[1712,65818,1714],{},[1716,65820,1739],{},[1712,65822,3138],{"separator":2565},[25634,65824,65825,65837],{},[25637,65826,65827],{},[2563,65828,65829],{"scriptlevel":2085,"displaystyle":2565},[895,65830,65831,65833,65835],{},[898,65832,1772],{},[898,65834,45214],{},[898,65836,8195],{},[25637,65838,65839],{},[2563,65840,65841],{"scriptlevel":2085,"displaystyle":2565},[895,65842,65843,65845,65847,65849,65851,65853,65855,65861,65863,65869],{},[895,65844],{},[1712,65846,1714],{},[1716,65848,2809],{},[898,65850,1734],{},[1712,65852,2219],{},[1716,65854,3068],{},[2037,65856,65857,65859],{},[898,65858,1734],{},[1716,65860,2787],{},[1712,65862,3145],{},[2037,65864,65865,65867],{},[898,65866,1734],{},[1716,65868,6198],{},[1712,65870,3138],{"separator":2565},[25634,65872,65873,65885],{},[25637,65874,65875],{},[2563,65876,65877],{"scriptlevel":2085,"displaystyle":2565},[895,65878,65879,65881,65883],{},[898,65880,2044],{},[898,65882,15308],{},[898,65884,8195],{},[25637,65886,65887],{},[2563,65888,65889],{"scriptlevel":2085,"displaystyle":2565},[895,65890,65891,65893,65895,65903],{},[895,65892],{},[1712,65894,1714],{},[2563,65896,65897],{"scriptlevel":2085,"displaystyle":1903},[2567,65898,65899,65901],{},[1716,65900,1739],{},[898,65902,1734],{},[1712,65904,3138],{"separator":2565},[25634,65906,65907,65919],{},[25637,65908,65909],{},[2563,65910,65911],{"scriptlevel":2085,"displaystyle":2565},[895,65912,65913,65915,65917],{},[898,65914,2044],{},[898,65916,45214],{},[898,65918,8195],{},[25637,65920,65921],{},[2563,65922,65923],{"scriptlevel":2085,"displaystyle":2565},[895,65924,65925,65927,65929,65931,65933,65935,65937,65939,65945],{},[895,65926],{},[1712,65928,1714],{},[1716,65930,2809],{},[1712,65932,2219],{},[1716,65934,3068],{},[898,65936,1734],{},[1712,65938,3145],{},[2037,65940,65941,65943],{},[898,65942,1734],{},[1716,65944,2787],{},[1712,65946,3138],{"separator":2565},[25634,65948,65949,65959],{},[25637,65950,65951],{},[2563,65952,65953],{"scriptlevel":2085,"displaystyle":2565},[895,65954,65955,65957],{},[898,65956,2044],{},[898,65958,8195],{},[25637,65960,65961],{},[2563,65962,65963],{"scriptlevel":2085,"displaystyle":2565},[895,65964,65965,65967,65969,65977,65979,65981,65983,65985,65987,65989,65995],{},[895,65966],{},[1712,65968,1714],{},[2563,65970,65971],{"scriptlevel":2085,"displaystyle":1903},[2567,65972,65973,65975],{},[1716,65974,1739],{},[898,65976,1734],{},[1712,65978,3145],{},[1716,65980,2809],{},[1712,65982,2219],{},[1716,65984,3068],{},[898,65986,1734],{},[1712,65988,3145],{},[2037,65990,65991,65993],{},[898,65992,1734],{},[1716,65994,2787],{},[1712,65996,3138],{"separator":2565},[25634,65998,65999,66009],{},[25637,66000,66001],{},[2563,66002,66003],{"scriptlevel":2085,"displaystyle":2565},[895,66004,66005,66007],{},[898,66006,4445],{},[898,66008,8195],{},[25637,66010,66011],{},[2563,66012,66013],{"scriptlevel":2085,"displaystyle":2565},[895,66014,66015,66017,66019,66021,66023,66025,66027,66029,66031,66037],{},[895,66016],{},[1712,66018,1714],{},[1716,66020,2809],{},[1712,66022,2219],{},[1716,66024,1718],{},[898,66026,1734],{},[1712,66028,3145],{},[1716,66030,6198],{},[2037,66032,66033,66035],{},[898,66034,1734],{},[1716,66036,2787],{},[898,66038,1659],{"mathvariant":2003},[902,66040,66041],{"encoding":904},"\\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}",[724,66043,66044,66045,20666,66060,20666,66075,66090,66091,66106,66107,1343,66125,66106,66142,1343,66160,66106,66175,66193],{},"Význačné body ",[883,66046,66048],{"className":66047},[886],[888,66049,66050],{"xmlns":890},[892,66051,66052,66057],{},[895,66053,66054],{},[1716,66055,66056],{},"1,67",[902,66058,66059],{"encoding":904},"1{,}67",[883,66061,66063],{"className":66062},[886],[888,66064,66065],{"xmlns":890},[892,66066,66067,66072],{},[895,66068,66069],{},[1716,66070,66071],{},"2,50",[902,66073,66074],{"encoding":904},"2{,}50",[883,66076,66078],{"className":66077},[886],[888,66079,66080],{"xmlns":890},[892,66081,66082,66087],{},[895,66083,66084],{},[1716,66085,66086],{},"4,73",[902,66088,66089],{"encoding":904},"4{,}73"," odpovídají: ",[883,66092,66094],{"className":66093},[886],[888,66095,66096],{"xmlns":890},[892,66097,66098,66104],{},[895,66099,66100,66102],{},[898,66101,4445],{},[898,66103,8195],{},[902,66105,60167],{"encoding":904}," minimum v ",[883,66108,66110],{"className":66109},[886],[888,66111,66112],{"xmlns":890},[892,66113,66114,66122],{},[895,66115,66116,66118,66120],{},[898,66117,1734],{},[1712,66119,3712],{},[1716,66121,66056],{},[902,66123,66124],{"encoding":904},"Q \\doteq 1{,}67",[883,66126,66128],{"className":66127},[886],[888,66129,66130],{"xmlns":890},[892,66131,66132,66140],{},[895,66133,66134,66136,66138],{},[898,66135,2044],{},[898,66137,45214],{},[898,66139,8195],{},[902,66141,60186],{"encoding":904},[883,66143,66145],{"className":66144},[886],[888,66146,66147],{"xmlns":890},[892,66148,66149,66157],{},[895,66150,66151,66153,66155],{},[898,66152,1734],{},[1712,66154,1714],{},[1716,66156,66071],{},[902,66158,66159],{"encoding":904},"Q = 2{,}50",[883,66161,66163],{"className":66162},[886],[888,66164,66165],{"xmlns":890},[892,66166,66167,66173],{},[895,66168,66169,66171],{},[898,66170,2044],{},[898,66172,8195],{},[902,66174,60435],{"encoding":904},[883,66176,66178],{"className":66177},[886],[888,66179,66180],{"xmlns":890},[892,66181,66182,66190],{},[895,66183,66184,66186,66188],{},[898,66185,1734],{},[1712,66187,3712],{},[1716,66189,66086],{},[902,66191,66192],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,66195,66196],{},[3817,66197],{"alt":66198,"className":66199,"src":66200},"imek-ac-avc-mc",[210,3821],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,66202,66203],{},[614,66204,66205,66206,1655,66221,66238,66239,20666,66258,66273],{},"Obrázek 3.9: Kubické křivky ",[883,66207,66209],{"className":66208},[886],[888,66210,66211],{"xmlns":890},[892,66212,66213,66219],{},[895,66214,66215,66217],{},[898,66216,1772],{},[898,66218,8195],{},[902,66220,8648],{"encoding":904},[883,66222,66224],{"className":66223},[886],[888,66225,66226],{"xmlns":890},[892,66227,66228,66236],{},[895,66229,66230,66232,66234],{},[898,66231,1772],{},[898,66233,45214],{},[898,66235,8195],{},[902,66237,60384],{"encoding":904}," rostoucí od bodu ",[883,66240,66242],{"className":66241},[886],[888,66243,66244],{"xmlns":890},[892,66245,66246,66256],{},[895,66247,66248,66250,66252,66254],{},[898,66249,15308],{},[898,66251,8195],{},[1712,66253,1714],{},[1716,66255,1739],{},[902,66257,16506],{"encoding":904},[883,66259,66261],{"className":66260},[886],[888,66262,66263],{"xmlns":890},[892,66264,66265,66271],{},[895,66266,66267,66269],{},[898,66268,15308],{},[898,66270,8195],{},[902,66272,60366],{"encoding":904}," je vodorovná přímka.",[724,66275,66276],{},[614,66277,66278,66279,1343,66294,1343,66311,34076,66326,66339,66340,7037,66357,66372,66373,4005,66390,66405,66406,31064,66419,1343,66432,1343,66445,1659],{},"Obrázek 3.10: Křivky ",[883,66280,66282],{"className":66281},[886],[888,66283,66284],{"xmlns":890},[892,66285,66286,66292],{},[895,66287,66288,66290],{},[898,66289,2044],{},[898,66291,8195],{},[902,66293,60435],{"encoding":904},[883,66295,66297],{"className":66296},[886],[888,66298,66299],{"xmlns":890},[892,66300,66301,66309],{},[895,66302,66303,66305,66307],{},[898,66304,2044],{},[898,66306,45214],{},[898,66308,8195],{},[902,66310,60186],{"encoding":904},[883,66312,66314],{"className":66313},[886],[888,66315,66316],{"xmlns":890},[892,66317,66318,66324],{},[895,66319,66320,66322],{},[898,66321,4445],{},[898,66323,8195],{},[902,66325,60167],{"encoding":904},[883,66327,66329],{"className":66328},[886],[888,66330,66331],{"xmlns":890},[892,66332,66333,66337],{},[895,66334,66335],{},[898,66336,900],{},[902,66338,900],{"encoding":904}," a klesající hyperbola ",[883,66341,66343],{"className":66342},[886],[888,66344,66345],{"xmlns":890},[892,66346,66347,66355],{},[895,66348,66349,66351,66353],{},[898,66350,2044],{},[898,66352,15308],{},[898,66354,8195],{},[902,66356,60402],{"encoding":904},[883,66358,66360],{"className":66359},[886],[888,66361,66362],{"xmlns":890},[892,66363,66364,66370],{},[895,66365,66366,66368],{},[898,66367,4445],{},[898,66369,8195],{},[902,66371,60167],{"encoding":904}," protíná ",[883,66374,66376],{"className":66375},[886],[888,66377,66378],{"xmlns":890},[892,66379,66380,66388],{},[895,66381,66382,66384,66386],{},[898,66383,2044],{},[898,66385,45214],{},[898,66387,8195],{},[902,66389,60186],{"encoding":904},[883,66391,66393],{"className":66392},[886],[888,66394,66395],{"xmlns":890},[892,66396,66397,66403],{},[895,66398,66399,66401],{},[898,66400,2044],{},[898,66402,8195],{},[902,66404,60435],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,66407,66409],{"className":66408},[886],[888,66410,66411],{"xmlns":890},[892,66412,66413,66417],{},[895,66414,66415],{},[898,66416,1734],{},[902,66418,1734],{"encoding":904},[883,66420,66422],{"className":66421},[886],[888,66423,66424],{"xmlns":890},[892,66425,66426,66430],{},[895,66427,66428],{},[1716,66429,66056],{},[902,66431,66059],{"encoding":904},[883,66433,66435],{"className":66434},[886],[888,66436,66437],{"xmlns":890},[892,66438,66439,66443],{},[895,66440,66441],{},[1716,66442,66071],{},[902,66444,66074],{"encoding":904},[883,66446,66448],{"className":66447},[886],[888,66449,66450],{"xmlns":890},[892,66451,66452,66456],{},[895,66453,66454],{},[1716,66455,66086],{},[902,66457,66089],{"encoding":904},[724,66459,66460],{},[38,66461,66462],{},"Standardní vlastnosti:",[120,66464,66465,66500,66564,66632,66682,66702],{},[123,66466,66467,1655,66482,66499],{},[883,66468,66470],{"className":66469},[886],[888,66471,66472],{"xmlns":890},[892,66473,66474,66480],{},[895,66475,66476,66478],{},[898,66477,1772],{},[898,66479,8195],{},[902,66481,8648],{"encoding":904},[883,66483,66485],{"className":66484},[886],[888,66486,66487],{"xmlns":890},[892,66488,66489,66497],{},[895,66490,66491,66493,66495],{},[898,66492,1772],{},[898,66494,45214],{},[898,66496,8195],{},[902,66498,60384],{"encoding":904}," jsou kubické funkce;",[123,66501,66502,1343,66517,1343,66534,66549,66550,66563],{},[883,66503,66505],{"className":66504},[886],[888,66506,66507],{"xmlns":890},[892,66508,66509,66515],{},[895,66510,66511,66513],{},[898,66512,2044],{},[898,66514,8195],{},[902,66516,60435],{"encoding":904},[883,66518,66520],{"className":66519},[886],[888,66521,66522],{"xmlns":890},[892,66523,66524,66532],{},[895,66525,66526,66528,66530],{},[898,66527,2044],{},[898,66529,45214],{},[898,66531,8195],{},[902,66533,60186],{"encoding":904},[883,66535,66537],{"className":66536},[886],[888,66538,66539],{"xmlns":890},[892,66540,66541,66547],{},[895,66542,66543,66545],{},[898,66544,4445],{},[898,66546,8195],{},[902,66548,60167],{"encoding":904}," jsou křivky tvaru ",[883,66551,66553],{"className":66552},[886],[888,66554,66555],{"xmlns":890},[892,66556,66557,66561],{},[895,66558,66559],{},[898,66560,900],{},[902,66562,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,66565,66566,66581,66582,1343,66599,66616,66617,6245],{},[883,66567,66569],{"className":66568},[886],[888,66570,66571],{"xmlns":890},[892,66572,66573,66579],{},[895,66574,66575,66577],{},[898,66576,4445],{},[898,66578,8195],{},[902,66580,60167],{"encoding":904}," nabývá minima před ",[883,66583,66585],{"className":66584},[886],[888,66586,66587],{"xmlns":890},[892,66588,66589,66597],{},[895,66590,66591,66593,66595],{},[898,66592,2044],{},[898,66594,45214],{},[898,66596,8195],{},[902,66598,60186],{"encoding":904},[883,66600,66602],{"className":66601},[886],[888,66603,66604],{"xmlns":890},[892,66605,66606,66614],{},[895,66607,66608,66610,66612],{},[898,66609,2044],{},[898,66611,45214],{},[898,66613,8195],{},[902,66615,60186],{"encoding":904}," před ",[883,66618,66620],{"className":66619},[886],[888,66621,66622],{"xmlns":890},[892,66623,66624,66630],{},[895,66625,66626,66628],{},[898,66627,2044],{},[898,66629,8195],{},[902,66631,60435],{"encoding":904},[123,66633,66634,66372,66649,1655,66664,66681],{},[883,66635,66637],{"className":66636},[886],[888,66638,66639],{"xmlns":890},[892,66640,66641,66647],{},[895,66642,66643,66645],{},[898,66644,4445],{},[898,66646,8195],{},[902,66648,60167],{"encoding":904},[883,66650,66652],{"className":66651},[886],[888,66653,66654],{"xmlns":890},[892,66655,66656,66662],{},[895,66657,66658,66660],{},[898,66659,2044],{},[898,66661,8195],{},[902,66663,60435],{"encoding":904},[883,66665,66667],{"className":66666},[886],[888,66668,66669],{"xmlns":890},[892,66670,66671,66679],{},[895,66672,66673,66675,66677],{},[898,66674,2044],{},[898,66676,45214],{},[898,66678,8195],{},[902,66680,60186],{"encoding":904}," zdola právě v jejich minimech;",[123,66683,66684,66701],{},[883,66685,66687],{"className":66686},[886],[888,66688,66689],{"xmlns":890},[892,66690,66691,66699],{},[895,66692,66693,66695,66697],{},[898,66694,2044],{},[898,66696,15308],{},[898,66698,8195],{},[902,66700,60402],{"encoding":904}," je hyperbola, stále klesající;",[123,66703,66704,66736,66737,1655,66752,66769,66770,66783,66784,1691],{},[883,66705,66707],{"className":66706},[886],[888,66708,66709],{"xmlns":890},[892,66710,66711,66733],{},[895,66712,66713,66715,66717,66719,66721,66723,66725,66727,66729,66731],{},[898,66714,2044],{},[898,66716,8195],{},[1712,66718,1714],{},[898,66720,2044],{},[898,66722,15308],{},[898,66724,8195],{},[1712,66726,3145],{},[898,66728,2044],{},[898,66730,45214],{},[898,66732,8195],{},[902,66734,66735],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,66738,66740],{"className":66739},[886],[888,66741,66742],{"xmlns":890},[892,66743,66744,66750],{},[895,66745,66746,66748],{},[898,66747,2044],{},[898,66749,8195],{},[902,66751,60435],{"encoding":904},[883,66753,66755],{"className":66754},[886],[888,66756,66757],{"xmlns":890},[892,66758,66759,66767],{},[895,66760,66761,66763,66765],{},[898,66762,2044],{},[898,66764,45214],{},[898,66766,8195],{},[902,66768,60186],{"encoding":904}," klesá s rostoucím ",[883,66771,66773],{"className":66772},[886],[888,66774,66775],{"xmlns":890},[892,66776,66777,66781],{},[895,66778,66779],{},[898,66780,1734],{},[902,66782,1734],{"encoding":904}," (protože ",[883,66785,66787],{"className":66786},[886],[888,66788,66789],{"xmlns":890},[892,66790,66791,66803],{},[895,66792,66793,66795,66797,66799,66801],{},[898,66794,2044],{},[898,66796,15308],{},[898,66798,8195],{},[1712,66800,2082],{},[1716,66802,2085],{},[902,66804,66805],{"encoding":904},"AFC \\to 0",[115,66807,66809],{"id":66808},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,66811,66812,66813,66816,66817,66832],{},"Častou optimalizační úlohou je ",[38,66814,66815],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,66818,66820],{"className":66819},[886],[888,66821,66822],{"xmlns":890},[892,66823,66824,66830],{},[895,66825,66826,66828],{},[898,66827,2044],{},[898,66829,8195],{},[902,66831,60435],{"encoding":904}," minimální.",[198,66834,21287],{"id":21286},[724,66836,66837,66838,66855],{},"Mají-li průměrné náklady minimum v bodě ",[883,66839,66841],{"className":66840},[886],[888,66842,66843],{"xmlns":890},[892,66844,66845,66853],{},[895,66846,66847],{},[6927,66848,66849,66851],{},[898,66850,1734],{},[1716,66852,2085],{},[902,66854,43183],{"encoding":904},", pak platí",[883,66857,66859],{"className":66858},[886],[888,66860,66861],{"xmlns":890,"display":32941},[892,66862,66863,66912],{},[25629,66864,66865],{"width":32946},[25634,66866,66867,66869,66905,66907],{},[25637,66868],{"width":32951},[25637,66870,66871],{},[895,66872,66873,66875,66877,66879,66885,66887,66889,66891,66893,66895,66901,66903],{},[898,66874,2044],{},[898,66876,8195],{},[1712,66878,1904],{"stretchy":1903},[6927,66880,66881,66883],{},[898,66882,1734],{},[1716,66884,2085],{},[1712,66886,1910],{"stretchy":1903},[1712,66888,1714],{},[898,66890,4445],{},[898,66892,8195],{},[1712,66894,1904],{"stretchy":1903},[6927,66896,66897,66899],{},[898,66898,1734],{},[1716,66900,2085],{},[1712,66902,1910],{"stretchy":1903},[898,66904,1659],{"mathvariant":2003},[25637,66906],{"width":32951},[25637,66908,66909],{},[1762,66910,66911],{},"(3.10)",[902,66913,66914],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1636,66916,66917],{},[724,66918,66919,66921,66922],{},[883,66920,61319],{}," Princip\n",[38,66923,66924],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,66926,66927,66930,66931,66973],{},[38,66928,66929],{},"Odvození."," Z ",[883,66932,66934],{"className":66933},[886],[888,66935,66936],{"xmlns":890},[892,66937,66938,66970],{},[895,66939,66940,66942,66944,66946,66948,66950,66952],{},[898,66941,2044],{},[898,66943,8195],{},[1712,66945,1904],{"stretchy":1903},[898,66947,1734],{},[1712,66949,1910],{"stretchy":1903},[1712,66951,1714],{},[2563,66953,66954],{"scriptlevel":2085,"displaystyle":1903},[2567,66955,66956,66968],{},[895,66957,66958,66960,66962,66964,66966],{},[898,66959,1772],{},[898,66961,8195],{},[1712,66963,1904],{"stretchy":1903},[898,66965,1734],{},[1712,66967,1910],{"stretchy":1903},[898,66969,1734],{},[902,66971,66972],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,66975,66977],{"className":66976},[886],[888,66978,66979],{"xmlns":890,"display":32941},[892,66980,66981,67113],{},[895,66982,66983,66985,66991,66993,66995,66997,66999,67039,67041,67081,67083,67111],{},[898,66984,2044],{},[2037,66986,66987,66989],{},[898,66988,8195],{},[1712,66990,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,66992,1904],{"stretchy":1903},[898,66994,1734],{},[1712,66996,1910],{"stretchy":1903},[1712,66998,1714],{},[2567,67000,67001,67033],{},[895,67002,67003,67005,67011,67013,67015,67017,67019,67021,67023,67025,67027,67029,67031],{},[898,67004,1772],{},[2037,67006,67007,67009],{},[898,67008,8195],{},[1712,67010,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,67012,1904],{"stretchy":1903},[898,67014,1734],{},[1712,67016,1910],{"stretchy":1903},[1712,67018,1783],{},[898,67020,1734],{},[1712,67022,2219],{},[898,67024,1772],{},[898,67026,8195],{},[1712,67028,1904],{"stretchy":1903},[898,67030,1734],{},[1712,67032,1910],{"stretchy":1903},[2037,67034,67035,67037],{},[898,67036,1734],{},[1716,67038,2787],{},[1712,67040,1714],{},[2567,67042,67043,67075],{},[895,67044,67045,67047,67049,67051,67053,67055,67057,67059,67061,67063,67065,67067,67069,67071,67073],{},[898,67046,4445],{},[898,67048,8195],{},[1712,67050,1904],{"stretchy":1903},[898,67052,1734],{},[1712,67054,1910],{"stretchy":1903},[1712,67056,1783],{},[898,67058,1734],{},[1712,67060,2219],{},[898,67062,2044],{},[898,67064,8195],{},[1712,67066,1904],{"stretchy":1903},[898,67068,1734],{},[1712,67070,1910],{"stretchy":1903},[1712,67072,1783],{},[898,67074,1734],{},[2037,67076,67077,67079],{},[898,67078,1734],{},[1716,67080,2787],{},[1712,67082,1714],{},[2567,67084,67085,67109],{},[895,67086,67087,67089,67091,67093,67095,67097,67099,67101,67103,67105,67107],{},[898,67088,4445],{},[898,67090,8195],{},[1712,67092,1904],{"stretchy":1903},[898,67094,1734],{},[1712,67096,1910],{"stretchy":1903},[1712,67098,2219],{},[898,67100,2044],{},[898,67102,8195],{},[1712,67104,1904],{"stretchy":1903},[898,67106,1734],{},[1712,67108,1910],{"stretchy":1903},[898,67110,1734],{},[898,67112,1659],{"mathvariant":2003},[902,67114,67115],{"encoding":904},"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}.",[724,67117,67118,67119,8046,67134,5920,67156,61696],{},"Nutnou podmínkou minima ",[883,67120,67122],{"className":67121},[886],[888,67123,67124],{"xmlns":890},[892,67125,67126,67132],{},[895,67127,67128,67130],{},[898,67129,2044],{},[898,67131,8195],{},[902,67133,60435],{"encoding":904},[883,67135,67137],{"className":67136},[886],[888,67138,67139],{"xmlns":890},[892,67140,67141,67153],{},[895,67142,67143,67149,67151],{},[6927,67144,67145,67147],{},[898,67146,1734],{},[1716,67148,2085],{},[1712,67150,2302],{},[1716,67152,2085],{},[902,67154,67155],{"encoding":904},"Q_0 > 0",[883,67157,67159],{"className":67158},[886],[888,67160,67161],{"xmlns":890},[892,67162,67163,67187],{},[895,67164,67165,67167,67173,67175,67181,67183,67185],{},[898,67166,2044],{},[2037,67168,67169,67171],{},[898,67170,8195],{},[1712,67172,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,67174,1904],{"stretchy":1903},[6927,67176,67177,67179],{},[898,67178,1734],{},[1716,67180,2085],{},[1712,67182,1910],{"stretchy":1903},[1712,67184,1714],{},[1716,67186,2085],{},[902,67188,67189],{"encoding":904},"AC'(Q_0) = 0",[883,67191,67193],{"className":67192},[886],[888,67194,67195],{"xmlns":890,"display":32941},[892,67196,67197,67282],{},[895,67198,67199,67239,67241,67243,67245,67248,67250,67252,67254,67256,67262,67264,67266,67268,67270,67272,67278,67280],{},[2567,67200,67201,67233],{},[895,67202,67203,67205,67207,67209,67215,67217,67219,67221,67223,67225,67231],{},[898,67204,4445],{},[898,67206,8195],{},[1712,67208,1904],{"stretchy":1903},[6927,67210,67211,67213],{},[898,67212,1734],{},[1716,67214,2085],{},[1712,67216,1910],{"stretchy":1903},[1712,67218,2219],{},[898,67220,2044],{},[898,67222,8195],{},[1712,67224,1904],{"stretchy":1903},[6927,67226,67227,67229],{},[898,67228,1734],{},[1716,67230,2085],{},[1712,67232,1910],{"stretchy":1903},[6927,67234,67235,67237],{},[898,67236,1734],{},[1716,67238,2085],{},[1712,67240,1714],{},[1716,67242,2085],{},[3690,67244],{"width":20158},[1712,67246,67247],{},"⟺",[3690,67249],{"width":20158},[898,67251,4445],{},[898,67253,8195],{},[1712,67255,1904],{"stretchy":1903},[6927,67257,67258,67260],{},[898,67259,1734],{},[1716,67261,2085],{},[1712,67263,1910],{"stretchy":1903},[1712,67265,1714],{},[898,67267,2044],{},[898,67269,8195],{},[1712,67271,1904],{"stretchy":1903},[6927,67273,67274,67276],{},[898,67275,1734],{},[1716,67277,2085],{},[1712,67279,1910],{"stretchy":1903},[898,67281,1659],{"mathvariant":2003},[902,67283,67284],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,67286,67287,3245,67290,66372,67305,67320,67321,67336,67337,5920,67354,67376,67377,67399],{},[38,67288,67289],{},"Geometrická interpretace.",[883,67291,67293],{"className":67292},[886],[888,67294,67295],{"xmlns":890},[892,67296,67297,67303],{},[895,67298,67299,67301],{},[898,67300,4445],{},[898,67302,8195],{},[902,67304,60167],{"encoding":904},[883,67306,67308],{"className":67307},[886],[888,67309,67310],{"xmlns":890},[892,67311,67312,67318],{},[895,67313,67314,67316],{},[898,67315,2044],{},[898,67317,8195],{},[902,67319,60435],{"encoding":904}," právě v bodě minima ",[883,67322,67324],{"className":67323},[886],[888,67325,67326],{"xmlns":890},[892,67327,67328,67334],{},[895,67329,67330,67332],{},[898,67331,2044],{},[898,67333,8195],{},[902,67335,60435],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,67338,67340],{"className":67339},[886],[888,67341,67342],{"xmlns":890},[892,67343,67344,67352],{},[895,67345,67346],{},[6927,67347,67348,67350],{},[898,67349,1734],{},[1716,67351,2085],{},[902,67353,43183],{"encoding":904},[883,67355,67357],{"className":67356},[886],[888,67358,67359],{"xmlns":890},[892,67360,67361,67373],{},[895,67362,67363,67365,67367,67369,67371],{},[898,67364,4445],{},[898,67366,8195],{},[1712,67368,2252],{},[898,67370,2044],{},[898,67372,8195],{},[902,67374,67375],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,67378,67380],{"className":67379},[886],[888,67381,67382],{"xmlns":890},[892,67383,67384,67396],{},[895,67385,67386,67388,67390,67392,67394],{},[898,67387,4445],{},[898,67389,8195],{},[1712,67391,2302],{},[898,67393,2044],{},[898,67395,8195],{},[902,67397,67398],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,67401,67402,67403,67445,67446,67463,67464,1659],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,67404,67406],{"className":67405},[886],[888,67407,67408],{"xmlns":890},[892,67409,67410,67442],{},[895,67411,67412,67414,67416,67418,67424,67426,67428,67430,67432,67434,67440],{},[898,67413,2044],{},[898,67415,8195],{},[1712,67417,1904],{"stretchy":1903},[6927,67419,67420,67422],{},[898,67421,1734],{},[1716,67423,2085],{},[1712,67425,1910],{"stretchy":1903},[1712,67427,1714],{},[898,67429,4445],{},[898,67431,8195],{},[1712,67433,1904],{"stretchy":1903},[6927,67435,67436,67438],{},[898,67437,1734],{},[1716,67439,2085],{},[1712,67441,1910],{"stretchy":1903},[902,67443,67444],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,67447,67449],{"className":67448},[886],[888,67450,67451],{"xmlns":890},[892,67452,67453,67461],{},[895,67454,67455],{},[6927,67456,67457,67459],{},[898,67458,1734],{},[1716,67460,2085],{},[902,67462,43183],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,67465,67467],{"className":67466},[886],[888,67468,67469],{"xmlns":890},[892,67470,67471,67495],{},[895,67472,67473,67475,67477,67479,67481,67483,67485,67487,67489,67491,67493],{},[898,67474,2044],{},[898,67476,8195],{},[1712,67478,1904],{"stretchy":1903},[898,67480,1734],{},[1712,67482,1910],{"stretchy":1903},[1712,67484,1714],{},[898,67486,4445],{},[898,67488,8195],{},[1712,67490,1904],{"stretchy":1903},[898,67492,1734],{},[1712,67494,1910],{"stretchy":1903},[902,67496,67497],{"encoding":904},"AC(Q) = MC(Q)",[1636,67499,67500],{},[724,67501,67502,67504,67505,15266,67523,67544,67545,15266,67548,67569,67570,67585,67586,62913,67601,1691],{},[883,67503,2203],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,67506,67507,67508],{},"minimum ",[883,67509,67511],{"className":67510},[886],[888,67512,67513],{"xmlns":890},[892,67514,67515,67521],{},[895,67516,67517,67519],{},[898,67518,2044],{},[898,67520,8195],{},[902,67522,60435],{"encoding":904},[883,67524,67526],{"className":67525},[886],[888,67527,67528],{"xmlns":890},[892,67529,67530,67542],{},[895,67531,67532,67534,67536,67538,67540],{},[898,67533,2044],{},[898,67535,8195],{},[1712,67537,1714],{},[898,67539,4445],{},[898,67541,8195],{},[902,67543,60098],{"encoding":904},", pro ",[38,67546,67547],{},"maximum zisku",[883,67549,67551],{"className":67550},[886],[888,67552,67553],{"xmlns":890},[892,67554,67555,67567],{},[895,67556,67557,67559,67561,67563,67565],{},[898,67558,4445],{},[898,67560,1775],{},[1712,67562,1714],{},[898,67564,4445],{},[898,67566,8195],{},[902,67568,60146],{"encoding":904},". Obě podmínky využívají ",[883,67571,67573],{"className":67572},[886],[888,67574,67575],{"xmlns":890},[892,67576,67577,67583],{},[895,67578,67579,67581],{},[898,67580,4445],{},[898,67582,8195],{},[902,67584,60167],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,67587,67589],{"className":67588},[886],[888,67590,67591],{"xmlns":890},[892,67592,67593,67599],{},[895,67594,67595,67597],{},[898,67596,2044],{},[898,67598,8195],{},[902,67600,60435],{"encoding":904},[883,67602,67604],{"className":67603},[886],[888,67605,67606],{"xmlns":890},[892,67607,67608,67614],{},[895,67609,67610,67612],{},[898,67611,4445],{},[898,67613,1775],{},[902,67615,4450],{"encoding":904},[42223,67617,67619],{"id":67618},"příklad-37","Příklad 3.7",[724,67621,67622,62397,67624,67658,67659,67672,67673,67688],{},[38,67623,60862],{},[883,67625,67627],{"className":67626},[886],[888,67628,67629],{"xmlns":890},[892,67630,67631,67655],{},[895,67632,67633,67635,67637,67639,67645,67647,67649,67651,67653],{},[898,67634,1772],{},[898,67636,8195],{},[1712,67638,1714],{},[2037,67640,67641,67643],{},[898,67642,1734],{},[1716,67644,2787],{},[1712,67646,3145],{},[1716,67648,6198],{},[898,67650,1734],{},[1712,67652,3145],{},[1716,67654,3377],{},[902,67656,67657],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,67660,67662],{"className":67661},[886],[888,67663,67664],{"xmlns":890},[892,67665,67666,67670],{},[895,67667,67668],{},[898,67669,1734],{},[902,67671,1734],{"encoding":904}," minimalizující ",[883,67674,67676],{"className":67675},[886],[888,67677,67678],{"xmlns":890},[892,67679,67680,67686],{},[895,67681,67682,67684],{},[898,67683,2044],{},[898,67685,8195],{},[902,67687,60435],{"encoding":904}," a ověřte princip (3.10).",[724,67690,67691,67693],{},[38,67692,27645],{}," Přímý výpočet:",[883,67695,67697],{"className":67696},[886],[888,67698,67699],{"xmlns":890,"display":32941},[892,67700,67701,67803],{},[895,67702,67703,67705,67707,67709,67731,67733,67735,67737,67739,67741,67747,67749,67751,67753,67755,67757,67763,67765,67767,67769,67779,67781,67801],{},[898,67704,2044],{},[898,67706,8195],{},[1712,67708,1714],{},[2567,67710,67711,67729],{},[895,67712,67713,67719,67721,67723,67725,67727],{},[2037,67714,67715,67717],{},[898,67716,1734],{},[1716,67718,2787],{},[1712,67720,3145],{},[1716,67722,6198],{},[898,67724,1734],{},[1712,67726,3145],{},[1716,67728,3377],{},[898,67730,1734],{},[1712,67732,1714],{},[898,67734,1734],{},[1712,67736,3145],{},[1716,67738,6198],{},[1712,67740,3145],{},[2567,67742,67743,67745],{},[1716,67744,3377],{},[898,67746,1734],{},[1712,67748,3138],{"separator":2565},[3690,67750],{"width":3692},[1712,67752,1904],{"stretchy":1903},[898,67754,2044],{},[898,67756,8195],{},[2037,67758,67759,67761],{},[1712,67760,1910],{"stretchy":1903},[1712,67762,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,67764,1714],{},[1716,67766,2222],{},[1712,67768,2219],{},[2567,67770,67771,67773],{},[1716,67772,3377],{},[2037,67774,67775,67777],{},[898,67776,1734],{},[1716,67778,2787],{},[1712,67780,1714],{},[2567,67782,67783,67795],{},[895,67784,67785,67791,67793],{},[2037,67786,67787,67789],{},[898,67788,1734],{},[1716,67790,2787],{},[1712,67792,2219],{},[1716,67794,3377],{},[2037,67796,67797,67799],{},[898,67798,1734],{},[1716,67800,2787],{},[898,67802,1659],{"mathvariant":2003},[902,67804,67805],{"encoding":904},"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}.",[724,67807,67808,67848,67849,67873,67874,67924,67925,1659],{},[883,67809,67811],{"className":67810},[886],[888,67812,67813],{"xmlns":890},[892,67814,67815,67845],{},[895,67816,67817,67819,67821,67823,67829,67831,67833,67835,67841,67843],{},[1712,67818,1904],{"stretchy":1903},[898,67820,2044],{},[898,67822,8195],{},[2037,67824,67825,67827],{},[1712,67826,1910],{"stretchy":1903},[1712,67828,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,67830,1714],{},[1716,67832,2085],{},[1712,67834,1767],{},[6927,67836,67837,67839],{},[898,67838,1734],{},[1716,67840,2222],{},[1712,67842,1714],{},[1716,67844,6209],{},[902,67846,67847],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,67850,67852],{"className":67851},[886],[888,67853,67854],{"xmlns":890},[892,67855,67856,67870],{},[895,67857,67858,67864,67866,67868],{},[6927,67859,67860,67862],{},[898,67861,1734],{},[1716,67863,2787],{},[1712,67865,1714],{},[1712,67867,2219],{},[1716,67869,6209],{},[902,67871,67872],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,67875,67877],{"className":67876},[886],[888,67878,67879],{"xmlns":890},[892,67880,67881,67921],{},[895,67882,67883,67885,67887,67889,67899,67901,67903,67905,67907,67915,67917,67919],{},[1712,67884,1904],{"stretchy":1903},[898,67886,2044],{},[898,67888,8195],{},[2037,67890,67891,67893],{},[1712,67892,1910],{"stretchy":1903},[895,67894,67895,67897],{},[1712,67896,2243],{"mathvariant":2003},[1712,67898,2243],{"mathvariant":2003},[1712,67900,1904],{"stretchy":1903},[1716,67902,6209],{},[1712,67904,1910],{"stretchy":1903},[1712,67906,1714],{},[2563,67908,67909],{"scriptlevel":2085,"displaystyle":1903},[2567,67910,67911,67913],{},[1716,67912,2222],{},[1716,67914,6198],{},[1712,67916,2302],{},[1716,67918,2085],{},[1712,67920,1767],{},[902,67922,67923],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,67926,67928],{"className":67927},[886],[888,67929,67930],{"xmlns":890},[892,67931,67932,67948],{},[895,67933,67934,67936,67938,67940,67942,67944,67946],{},[898,67935,2044],{},[898,67937,8195],{},[1712,67939,1904],{"stretchy":1903},[1716,67941,6209],{},[1712,67943,1910],{"stretchy":1903},[1712,67945,1714],{},[1716,67947,41119],{},[902,67949,67950],{"encoding":904},"AC(6) = 15",[724,67952,67953,67954,67980,67981,2854],{},"Pomocí principu: ",[883,67955,67957],{"className":67956},[886],[888,67958,67959],{"xmlns":890},[892,67960,67961,67977],{},[895,67962,67963,67965,67967,67969,67971,67973,67975],{},[898,67964,4445],{},[898,67966,8195],{},[1712,67968,1714],{},[1716,67970,2787],{},[898,67972,1734],{},[1712,67974,3145],{},[1716,67976,6198],{},[902,67978,67979],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,67982,67984],{"className":67983},[886],[888,67985,67986],{"xmlns":890},[892,67987,67988,68000],{},[895,67989,67990,67992,67994,67996,67998],{},[898,67991,2044],{},[898,67993,8195],{},[1712,67995,1714],{},[898,67997,4445],{},[898,67999,8195],{},[902,68001,60098],{"encoding":904},[883,68003,68005],{"className":68004},[886],[888,68006,68007],{"xmlns":890,"display":32941},[892,68008,68009,68111],{},[895,68010,68011,68033,68035,68037,68039,68041,68043,68045,68047,68049,68055,68057,68059,68061,68063,68065,68067,68069,68075,68077,68079,68081,68083,68085,68087,68093,68095,68097,68099,68101,68103,68105,68107,68109],{},[2567,68012,68013,68031],{},[895,68014,68015,68021,68023,68025,68027,68029],{},[2037,68016,68017,68019],{},[898,68018,1734],{},[1716,68020,2787],{},[1712,68022,3145],{},[1716,68024,6198],{},[898,68026,1734],{},[1712,68028,3145],{},[1716,68030,3377],{},[898,68032,1734],{},[1712,68034,1714],{},[1716,68036,2787],{},[898,68038,1734],{},[1712,68040,3145],{},[1716,68042,6198],{},[1762,68044,1764],{},[1712,68046,1767],{},[1762,68048,1764],{},[2037,68050,68051,68053],{},[898,68052,1734],{},[1716,68054,2787],{},[1712,68056,3145],{},[1716,68058,6198],{},[898,68060,1734],{},[1712,68062,3145],{},[1716,68064,3377],{},[1712,68066,1714],{},[1716,68068,2787],{},[2037,68070,68071,68073],{},[898,68072,1734],{},[1716,68074,2787],{},[1712,68076,3145],{},[1716,68078,6198],{},[898,68080,1734],{},[1762,68082,1764],{},[1712,68084,1767],{},[1762,68086,1764],{},[2037,68088,68089,68091],{},[898,68090,1734],{},[1716,68092,2787],{},[1712,68094,1714],{},[1716,68096,3377],{},[1762,68098,1764],{},[1712,68100,1767],{},[1762,68102,1764],{},[898,68104,1734],{},[1712,68106,1714],{},[1716,68108,6209],{},[1712,68110,3138],{"separator":2565},[902,68112,68113],{"encoding":904},"\\frac{Q^2 + 3Q + 36}{Q} = 2Q + 3 \\;\\Rightarrow\\; Q^2 + 3Q + 36 = 2Q^2 + 3Q \\;\\Rightarrow\\; Q^2 = 36 \\;\\Rightarrow\\; Q = 6,",[724,68115,68116,68117,68155],{},"a ",[883,68118,68120],{"className":68119},[886],[888,68121,68122],{"xmlns":890},[892,68123,68124,68152],{},[895,68125,68126,68128,68130,68132,68134,68136,68138,68140,68142,68144,68146,68148,68150],{},[898,68127,2044],{},[898,68129,8195],{},[1712,68131,1904],{"stretchy":1903},[1716,68133,6209],{},[1712,68135,1910],{"stretchy":1903},[1712,68137,1714],{},[898,68139,4445],{},[898,68141,8195],{},[1712,68143,1904],{"stretchy":1903},[1716,68145,6209],{},[1712,68147,1910],{"stretchy":1903},[1712,68149,1714],{},[1716,68151,41119],{},[902,68153,68154],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,68157,68159],{"id":68158},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,68161,68162,68163,2854],{},"Analogicky pro ",[883,68164,68166],{"className":68165},[886],[888,68167,68168],{"xmlns":890},[892,68169,68170,68178],{},[895,68171,68172,68174,68176],{},[898,68173,2044],{},[898,68175,45214],{},[898,68177,8195],{},[902,68179,60186],{"encoding":904},[883,68181,68183],{"className":68182},[886],[888,68184,68185],{"xmlns":890,"display":32941},[892,68186,68187,68238],{},[25629,68188,68189],{"width":32946},[25634,68190,68191,68193,68231,68233],{},[25637,68192],{"width":32951},[25637,68194,68195],{},[895,68196,68197,68199,68201,68203,68205,68211,68213,68215,68217,68219,68221,68227,68229],{},[898,68198,2044],{},[898,68200,45214],{},[898,68202,8195],{},[1712,68204,1904],{"stretchy":1903},[6927,68206,68207,68209],{},[898,68208,1734],{},[1716,68210,2085],{},[1712,68212,1910],{"stretchy":1903},[1712,68214,1714],{},[898,68216,4445],{},[898,68218,8195],{},[1712,68220,1904],{"stretchy":1903},[6927,68222,68223,68225],{},[898,68224,1734],{},[1716,68226,2085],{},[1712,68228,1910],{"stretchy":1903},[898,68230,1659],{"mathvariant":2003},[25637,68232],{"width":32951},[25637,68234,68235],{},[1762,68236,68237],{},"(3.11)",[902,68239,68240],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1636,68242,68243],{},[724,68244,68245,66921,68247],{},[883,68246,61319],{},[38,68248,68249,68250,68267],{},"V bodě minima průměrných variabilních nákladů se ",[883,68251,68253],{"className":68252},[886],[888,68254,68255],{"xmlns":890},[892,68256,68257,68265],{},[895,68258,68259,68261,68263],{},[898,68260,2044],{},[898,68262,45214],{},[898,68264,8195],{},[902,68266,60186],{"encoding":904}," rovnají mezním nákladům.",[724,68269,68270,68271,68293,68294,1659],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,68272,68274],{"className":68273},[886],[888,68275,68276],{"xmlns":890},[892,68277,68278,68290],{},[895,68279,68280,68286,68288],{},[6927,68281,68282,68284],{},[898,68283,1734],{},[1716,68285,2085],{},[1712,68287,1714],{},[1716,68289,58074],{},[902,68291,68292],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,68295,68297],{"className":68296},[886],[888,68298,68299],{"xmlns":890},[892,68300,68301,68327],{},[895,68302,68303,68305,68307,68309,68311,68313,68315,68317,68319,68321,68323,68325],{},[898,68304,2044],{},[898,68306,45214],{},[898,68308,8195],{},[1712,68310,1904],{"stretchy":1903},[898,68312,1734],{},[1712,68314,1910],{"stretchy":1903},[1712,68316,1714],{},[898,68318,4445],{},[898,68320,8195],{},[1712,68322,1904],{"stretchy":1903},[898,68324,1734],{},[1712,68326,1910],{"stretchy":1903},[902,68328,68329],{"encoding":904},"AVC(Q) = MC(Q)",[115,68331,68333],{"id":68332},"zisk-a-body-zvratu","Zisk a body zvratu",[724,68335,68336,3245,68339,68355],{},[38,68337,68338],{},"Zisk",[883,68340,68342],{"className":68341},[886],[888,68343,68344],{"xmlns":890},[892,68345,68346,68352],{},[895,68347,68348,68350],{},[898,68349,1710],{},[898,68351,1775],{},[902,68353,68354],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,68357,68359],{"className":68358},[886],[888,68360,68361],{"xmlns":890,"display":32941},[892,68362,68363,68422],{},[25629,68364,68365],{"width":32946},[25634,68366,68367,68369,68415,68417],{},[25637,68368],{"width":32951},[25637,68370,68371],{},[895,68372,68373,68375,68377,68379,68381,68383,68385,68387,68389,68391,68393,68395,68397,68399,68401,68403,68405,68407,68409,68411,68413],{},[898,68374,1710],{},[898,68376,1775],{},[1712,68378,1714],{},[898,68380,1710],{},[898,68382,1775],{},[1712,68384,1904],{"stretchy":1903},[898,68386,1734],{},[1712,68388,1910],{"stretchy":1903},[1712,68390,1714],{},[898,68392,1772],{},[898,68394,1775],{},[1712,68396,1904],{"stretchy":1903},[898,68398,1734],{},[1712,68400,1910],{"stretchy":1903},[1712,68402,2219],{},[898,68404,1772],{},[898,68406,8195],{},[1712,68408,1904],{"stretchy":1903},[898,68410,1734],{},[1712,68412,1910],{"stretchy":1903},[898,68414,1659],{"mathvariant":2003},[25637,68416],{"width":32951},[25637,68418,68419],{},[1762,68420,68421],{},"(3.12)",[902,68423,68424],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,68426,68427,68428,1655,68443,48511,68458,68460,68461,68464,68465,68481,68482,68497,68498,68513,68514,1343,68527,68540,68541,1343,68559,68577,68578,14897,68581,68584,68585,1348,68607,5920,68629,68651,68652,5920,68682,68704],{},"Body rovnosti ",[883,68429,68431],{"className":68430},[886],[888,68432,68433],{"xmlns":890},[892,68434,68435,68441],{},[895,68436,68437,68439],{},[898,68438,1772],{},[898,68440,1775],{},[902,68442,1877],{"encoding":904},[883,68444,68446],{"className":68445},[886],[888,68447,68448],{"xmlns":890},[892,68449,68450,68456],{},[895,68451,68452,68454],{},[898,68453,1772],{},[898,68455,8195],{},[902,68457,8648],{"encoding":904},[38,68459,60602],{}," (též vyrovnání, ",[614,68462,68463],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,68466,68468],{"className":68467},[886],[888,68469,68470],{"xmlns":890},[892,68471,68472,68478],{},[895,68473,68474,68476],{},[898,68475,45214],{},[898,68477,8195],{},[902,68479,68480],{"encoding":904},"VC",") je ",[883,68483,68485],{"className":68484},[886],[888,68486,68487],{"xmlns":890},[892,68488,68489,68495],{},[895,68490,68491,68493],{},[898,68492,1772],{},[898,68494,1775],{},[902,68496,1877],{"encoding":904}," kvadratická a ",[883,68499,68501],{"className":68500},[886],[888,68502,68503],{"xmlns":890},[892,68504,68505,68511],{},[895,68506,68507,68509],{},[898,68508,1772],{},[898,68510,8195],{},[902,68512,8648],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,68515,68517],{"className":68516},[886],[888,68518,68519],{"xmlns":890},[892,68520,68521,68525],{},[895,68522,68523],{},[898,68524,2044],{},[902,68526,2044],{"encoding":904},[883,68528,68530],{"className":68529},[886],[888,68531,68532],{"xmlns":890},[892,68533,68534,68538],{},[895,68535,68536],{},[898,68537,28128],{},[902,68539,28128],{"encoding":904}," odpovídajících množstvím ",[883,68542,68544],{"className":68543},[886],[888,68545,68546],{"xmlns":890},[892,68547,68548,68556],{},[895,68549,68550],{},[6927,68551,68552,68554],{},[898,68553,1734],{},[898,68555,2044],{},[902,68557,68558],{"encoding":904},"Q_A",[883,68560,68562],{"className":68561},[886],[888,68563,68564],{"xmlns":890},[892,68565,68566,68574],{},[895,68567,68568],{},[6927,68569,68570,68572],{},[898,68571,1734],{},[898,68573,28128],{},[902,68575,68576],{"encoding":904},"Q_B"," — firma je na ",[38,68579,68580],{},"prahu rentability",[614,68582,68583],{},"break even","). Pro ",[883,68586,68588],{"className":68587},[886],[888,68589,68590],{"xmlns":890},[892,68591,68592,68604],{},[895,68593,68594,68596,68598],{},[898,68595,1734],{},[1712,68597,2252],{},[6927,68599,68600,68602],{},[898,68601,1734],{},[898,68603,2044],{},[902,68605,68606],{"encoding":904},"Q \u003C Q_A",[883,68608,68610],{"className":68609},[886],[888,68611,68612],{"xmlns":890},[892,68613,68614,68626],{},[895,68615,68616,68618,68620],{},[898,68617,1734],{},[1712,68619,2302],{},[6927,68621,68622,68624],{},[898,68623,1734],{},[898,68625,28128],{},[902,68627,68628],{"encoding":904},"Q > Q_B",[883,68630,68632],{"className":68631},[886],[888,68633,68634],{"xmlns":890},[892,68635,68636,68648],{},[895,68637,68638,68640,68642,68644,68646],{},[898,68639,1772],{},[898,68641,8195],{},[1712,68643,2302],{},[898,68645,1772],{},[898,68647,1775],{},[902,68649,68650],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,68653,68655],{"className":68654},[886],[888,68656,68657],{"xmlns":890},[892,68658,68659,68679],{},[895,68660,68661,68667,68669,68671,68673],{},[6927,68662,68663,68665],{},[898,68664,1734],{},[898,68666,2044],{},[1712,68668,2252],{},[898,68670,1734],{},[1712,68672,2252],{},[6927,68674,68675,68677],{},[898,68676,1734],{},[898,68678,28128],{},[902,68680,68681],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,68683,68685],{"className":68684},[886],[888,68686,68687],{"xmlns":890},[892,68688,68689,68701],{},[895,68690,68691,68693,68695,68697,68699],{},[898,68692,1772],{},[898,68694,1775],{},[1712,68696,2302],{},[898,68698,1772],{},[898,68700,8195],{},[902,68702,68703],{"encoding":904},"TR > TC"," (zisk).",[1636,68706,68707],{},[724,68708,68709,68711],{},[883,68710,1941],{}," 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.",[724,68713,68714,68715,68741],{},"Body zvratu jsou řešení rovnice ",[883,68716,68718],{"className":68717},[886],[888,68719,68720],{"xmlns":890},[892,68721,68722,68738],{},[895,68723,68724,68726,68728,68730,68732,68734,68736],{},[898,68725,1710],{},[898,68727,1775],{},[1712,68729,1904],{"stretchy":1903},[898,68731,1734],{},[1712,68733,1910],{"stretchy":1903},[1712,68735,1714],{},[1716,68737,2085],{},[902,68739,68740],{"encoding":904},"PR(Q) = 0",". Pro vyšší stupně polynomu může být nutné použít software či numerický odhad. Maximum zisku se stanoví jako extrém funkce zisku.",[724,68743,68744],{},[3817,68745],{"alt":68746,"className":68747,"src":68748},"imek-tr-tc-body-zvratu",[210,3821],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,68750,68751],{},[614,68752,68753,68754,68769,68770,68785,68786,1655,68799,48235,68812,68825,68826,1655,68843,68860,68861,68881,68882,1655,68897,4288,68912,68941],{},"Obrázek 3.11: Body zvratu — křivky ",[883,68755,68757],{"className":68756},[886],[888,68758,68759],{"xmlns":890},[892,68760,68761,68767],{},[895,68762,68763,68765],{},[898,68764,1772],{},[898,68766,1775],{},[902,68768,1877],{"encoding":904}," (obrácená parabola) a ",[883,68771,68773],{"className":68772},[886],[888,68774,68775],{"xmlns":890},[892,68776,68777,68783],{},[895,68778,68779,68781],{},[898,68780,1772],{},[898,68782,8195],{},[902,68784,8648],{"encoding":904}," (přímka) se protínají v bodech ",[883,68787,68789],{"className":68788},[886],[888,68790,68791],{"xmlns":890},[892,68792,68793,68797],{},[895,68794,68795],{},[898,68796,2044],{},[902,68798,2044],{"encoding":904},[883,68800,68802],{"className":68801},[886],[888,68803,68804],{"xmlns":890},[892,68805,68806,68810],{},[895,68807,68808],{},[898,68809,28128],{},[902,68811,28128],{"encoding":904},[883,68813,68815],{"className":68814},[886],[888,68816,68817],{"xmlns":890},[892,68818,68819,68823],{},[895,68820,68821],{},[898,68822,1734],{},[902,68824,1734],{"encoding":904}," v hodnotách ",[883,68827,68829],{"className":68828},[886],[888,68830,68831],{"xmlns":890},[892,68832,68833,68841],{},[895,68834,68835],{},[6927,68836,68837,68839],{},[898,68838,1734],{},[898,68840,2044],{},[902,68842,68558],{"encoding":904},[883,68844,68846],{"className":68845},[886],[888,68847,68848],{"xmlns":890},[892,68849,68850,68858],{},[895,68851,68852],{},[6927,68853,68854,68856],{},[898,68855,1734],{},[898,68857,28128],{},[902,68859,68576],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,68862,68864],{"className":68863},[886],[888,68865,68866],{"xmlns":890},[892,68867,68868,68878],{},[895,68869,68870],{},[6927,68871,68872,68874,68876],{},[898,68873,1734],{},[898,68875,61072],{},[1712,68877,61075],{},[902,68879,68880],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,68883,68885],{"className":68884},[886],[888,68886,68887],{"xmlns":890},[892,68888,68889,68895],{},[895,68890,68891,68893],{},[898,68892,1772],{},[898,68894,1775],{},[902,68896,1877],{"encoding":904},[883,68898,68900],{"className":68899},[886],[888,68901,68902],{"xmlns":890},[892,68903,68904,68910],{},[895,68905,68906,68908],{},[898,68907,1772],{},[898,68909,8195],{},[902,68911,8648],{"encoding":904},[883,68913,68915],{"className":68914},[886],[888,68916,68917],{"xmlns":890},[892,68918,68919,68939],{},[895,68920,68921,68927,68929,68931,68933],{},[6927,68922,68923,68925],{},[898,68924,1734],{},[898,68926,2044],{},[1712,68928,2252],{},[898,68930,1734],{},[1712,68932,2252],{},[6927,68934,68935,68937],{},[898,68936,1734],{},[898,68938,28128],{},[902,68940,68681],{"encoding":904}," vyznačuje zisk.",[42223,68943,68945],{"id":68944},"příklad-38","Příklad 3.8",[724,68947,68948,68950,68951,1343,68971,1343,68997,69023],{},[38,68949,60862],{}," Dáno ",[883,68952,68954],{"className":68953},[886],[888,68955,68956],{"xmlns":890},[892,68957,68958,68968],{},[895,68959,68960,68962,68964,68966],{},[898,68961,15308],{},[898,68963,8195],{},[1712,68965,1714],{},[1716,68967,2975],{},[902,68969,68970],{"encoding":904},"FC = 4",[883,68972,68974],{"className":68973},[886],[888,68975,68976],{"xmlns":890},[892,68977,68978,68994],{},[895,68979,68980,68982,68984,68986,68988],{},[898,68981,1772],{},[898,68983,45214],{},[898,68985,8195],{},[1712,68987,1714],{},[2037,68989,68990,68992],{},[898,68991,1734],{},[1716,68993,2787],{},[902,68995,68996],{"encoding":904},"TVC = Q^2",[883,68998,69000],{"className":68999},[886],[888,69001,69002],{"xmlns":890},[892,69003,69004,69020],{},[895,69005,69006,69008,69010,69012,69014,69016,69018],{},[898,69007,1710],{},[1712,69009,1714],{},[1712,69011,2219],{},[1716,69013,2787],{},[898,69015,1734],{},[1712,69017,3145],{},[1716,69019,1780],{},[902,69021,69022],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,69025,69026,69028],{},[38,69027,27645],{}," Celkové náklady a příjem:",[883,69030,69032],{"className":69031},[886],[888,69033,69034],{"xmlns":890,"display":32941},[892,69035,69036,69102],{},[895,69037,69038,69040,69042,69044,69046,69048,69054,69056,69058,69060,69062,69064,69066,69068,69070,69072,69074,69076,69078,69080,69082,69084,69086,69088,69094,69096,69098,69100],{},[898,69039,1772],{},[898,69041,8195],{},[1712,69043,1714],{},[1716,69045,2975],{},[1712,69047,3145],{},[2037,69049,69050,69052],{},[898,69051,1734],{},[1716,69053,2787],{},[1712,69055,3138],{"separator":2565},[3690,69057],{"width":3692},[898,69059,1772],{},[898,69061,1775],{},[1712,69063,1714],{},[898,69065,1734],{},[1712,69067,1783],{},[1712,69069,1904],{"stretchy":1903},[1712,69071,2219],{},[1716,69073,2787],{},[898,69075,1734],{},[1712,69077,3145],{},[1716,69079,1780],{},[1712,69081,1910],{"stretchy":1903},[1712,69083,1714],{},[1712,69085,2219],{},[1716,69087,2787],{},[2037,69089,69090,69092],{},[898,69091,1734],{},[1716,69093,2787],{},[1712,69095,3145],{},[1716,69097,1780],{},[898,69099,1734],{},[898,69101,1659],{"mathvariant":2003},[902,69103,69104],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,69106,69107],{},"Zisk dle (3.12):",[883,69109,69111],{"className":69110},[886],[888,69112,69113],{"xmlns":890,"display":32941},[892,69114,69115,69193],{},[895,69116,69117,69119,69121,69123,69125,69127,69129,69131,69133,69135,69137,69139,69141,69147,69149,69151,69153,69155,69157,69159,69161,69163,69169,69171,69173,69175,69177,69183,69185,69187,69189,69191],{},[898,69118,1710],{},[898,69120,1775],{},[1712,69122,1714],{},[898,69124,1772],{},[898,69126,1775],{},[1712,69128,2219],{},[898,69130,1772],{},[898,69132,8195],{},[1712,69134,1714],{},[1712,69136,1904],{"stretchy":1903},[1712,69138,2219],{},[1716,69140,2787],{},[2037,69142,69143,69145],{},[898,69144,1734],{},[1716,69146,2787],{},[1712,69148,3145],{},[1716,69150,1780],{},[898,69152,1734],{},[1712,69154,1910],{"stretchy":1903},[1712,69156,2219],{},[1712,69158,1904],{"stretchy":1903},[1716,69160,2975],{},[1712,69162,3145],{},[2037,69164,69165,69167],{},[898,69166,1734],{},[1716,69168,2787],{},[1712,69170,1910],{"stretchy":1903},[1712,69172,1714],{},[1712,69174,2219],{},[1716,69176,6198],{},[2037,69178,69179,69181],{},[898,69180,1734],{},[1716,69182,2787],{},[1712,69184,3145],{},[1716,69186,1780],{},[898,69188,1734],{},[1712,69190,2219],{},[1716,69192,64194],{},[902,69194,69195],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,69197,69198,69201,69202,22451,69238,2854],{},[38,69199,69200],{},"Body zvratu"," jsou kořeny rovnice ",[883,69203,69205],{"className":69204},[886],[888,69206,69207],{"xmlns":890},[892,69208,69209,69235],{},[895,69210,69211,69213,69215,69221,69223,69225,69227,69229,69231,69233],{},[1712,69212,2219],{},[1716,69214,6198],{},[2037,69216,69217,69219],{},[898,69218,1734],{},[1716,69220,2787],{},[1712,69222,3145],{},[1716,69224,1780],{},[898,69226,1734],{},[1712,69228,2219],{},[1716,69230,2975],{},[1712,69232,1714],{},[1716,69234,2085],{},[902,69236,69237],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,69239,69241],{"className":69240},[886],[888,69242,69243],{"xmlns":890},[892,69244,69245,69269],{},[895,69246,69247,69249,69255,69257,69259,69261,69263,69265,69267],{},[1716,69248,6198],{},[2037,69250,69251,69253],{},[898,69252,1734],{},[1716,69254,2787],{},[1712,69256,2219],{},[1716,69258,1780],{},[898,69260,1734],{},[1712,69262,3145],{},[1716,69264,2975],{},[1712,69266,1714],{},[1716,69268,2085],{},[902,69270,69271],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,69273,69275],{"className":69274},[886],[888,69276,69277],{"xmlns":890,"display":32941},[892,69278,69279,69336],{},[895,69280,69281,69293,69295,69318,69320,69334],{},[6927,69282,69283,69285],{},[898,69284,1734],{},[895,69286,69287,69289,69291],{},[1716,69288,2222],{},[1712,69290,3138],{"separator":2565},[1716,69292,2787],{},[1712,69294,1714],{},[2567,69296,69297,69316],{},[895,69298,69299,69301,69304],{},[1716,69300,1780],{},[1712,69302,69303],{},"±",[5935,69305,69306],{},[895,69307,69308,69311,69313],{},[1716,69309,69310],{},"81",[1712,69312,2219],{},[1716,69314,69315],{},"48",[1716,69317,6209],{},[1712,69319,1714],{},[2567,69321,69322,69332],{},[895,69323,69324,69326,69328],{},[1716,69325,1780],{},[1712,69327,69303],{},[5935,69329,69330],{},[1716,69331,6773],{},[1716,69333,6209],{},[1712,69335,3138],{"separator":2565},[902,69337,69338],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,69340,69341,69342,1655,69365,1659],{},"numericky ",[883,69343,69345],{"className":69344},[886],[888,69346,69347],{"xmlns":890},[892,69348,69349,69362],{},[895,69350,69351,69357,69359],{},[6927,69352,69353,69355],{},[898,69354,1734],{},[1716,69356,2222],{},[1712,69358,3712],{},[1716,69360,69361],{},"0,543",[902,69363,69364],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,69366,69368],{"className":69367},[886],[888,69369,69370],{"xmlns":890},[892,69371,69372,69385],{},[895,69373,69374,69380,69382],{},[6927,69375,69376,69378],{},[898,69377,1734],{},[1716,69379,2787],{},[1712,69381,3712],{},[1716,69383,69384],{},"2,457",[902,69386,69387],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,69389,69390,3245,69393,5369,69438,22451,69472,69490],{},[38,69391,69392],{},"Maximum zisku.",[883,69394,69396],{"className":69395},[886],[888,69397,69398],{"xmlns":890},[892,69399,69400,69435],{},[895,69401,69402,69404,69410,69412,69414,69416,69418,69420,69422,69424,69426,69428,69430,69432],{},[898,69403,1710],{},[2037,69405,69406,69408],{},[898,69407,1775],{},[1712,69409,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,69411,1714],{},[1712,69413,2219],{},[1716,69415,6209],{},[898,69417,1734],{},[1712,69419,3145],{},[1716,69421,1780],{},[1712,69423,1714],{},[1716,69425,2085],{},[1712,69427,1767],{},[898,69429,1734],{},[1712,69431,1714],{},[1716,69433,69434],{},"1,5",[902,69436,69437],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,69439,69441],{"className":69440},[886],[888,69442,69443],{"xmlns":890},[892,69444,69445,69469],{},[895,69446,69447,69449,69459,69461,69463,69465,69467],{},[898,69448,1710],{},[2037,69450,69451,69453],{},[898,69452,1775],{},[895,69454,69455,69457],{},[1712,69456,2243],{"mathvariant":2003},[1712,69458,2243],{"mathvariant":2003},[1712,69460,1714],{},[1712,69462,2219],{},[1716,69464,6209],{},[1712,69466,2252],{},[1716,69468,2085],{},[902,69470,69471],{"encoding":904},"PR'' = -6 \u003C 0",[883,69473,69475],{"className":69474},[886],[888,69476,69477],{"xmlns":890},[892,69478,69479,69487],{},[895,69480,69481,69483,69485],{},[898,69482,1734],{},[1712,69484,1714],{},[1716,69486,69434],{},[902,69488,69489],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,69492,69494],{"className":69493},[886],[888,69495,69496],{"xmlns":890,"display":32941},[892,69497,69498,69561],{},[895,69499,69500,69502,69504,69506,69508,69510,69512,69514,69516,69518,69520,69522,69528,69530,69532,69534,69536,69538,69540,69542,69544,69547,69549,69552,69554,69556,69558],{},[898,69501,1710],{},[898,69503,1775],{},[1712,69505,1904],{"stretchy":1903},[1716,69507,69434],{},[1712,69509,1910],{"stretchy":1903},[1712,69511,1714],{},[1712,69513,2219],{},[1716,69515,6198],{},[1712,69517,1783],{},[1712,69519,1904],{"stretchy":1903},[1716,69521,69434],{},[2037,69523,69524,69526],{},[1712,69525,1910],{"stretchy":1903},[1716,69527,2787],{},[1712,69529,3145],{},[1716,69531,1780],{},[1712,69533,1783],{},[1716,69535,69434],{},[1712,69537,2219],{},[1716,69539,2975],{},[1712,69541,1714],{},[1712,69543,2219],{},[1716,69545,69546],{},"6,75",[1712,69548,3145],{},[1716,69550,69551],{},"13,5",[1712,69553,2219],{},[1716,69555,2975],{},[1712,69557,1714],{},[1716,69559,69560],{},"2,75.",[902,69562,69563],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,69565,69566,69567,1343,69612,69665,69666,69684],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,69568,69570],{"className":69569},[886],[888,69571,69572],{"xmlns":890},[892,69573,69574,69609],{},[895,69575,69576,69578,69584,69586,69588,69590,69592,69594,69596,69598,69600,69602,69604,69606],{},[898,69577,1772],{},[2037,69579,69580,69582],{},[898,69581,1775],{},[1712,69583,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,69585,1714],{},[1712,69587,2219],{},[1716,69589,2975],{},[898,69591,1734],{},[1712,69593,3145],{},[1716,69595,1780],{},[1712,69597,1714],{},[1716,69599,2085],{},[1712,69601,1767],{},[898,69603,1734],{},[1712,69605,1714],{},[1716,69607,69608],{},"2,25",[902,69610,69611],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,69613,69615],{"className":69614},[886],[888,69616,69617],{"xmlns":890},[892,69618,69619,69662],{},[895,69620,69621,69623,69631,69633,69635,69637,69639,69641,69643,69649,69651,69653,69655,69657,69659],{},[898,69622,1772],{},[6927,69624,69625,69627,69629],{},[898,69626,1775],{},[898,69628,61072],{},[1712,69630,61075],{},[1712,69632,1714],{},[1712,69634,2219],{},[1716,69636,2787],{},[1712,69638,1783],{},[1712,69640,1904],{"stretchy":1903},[1716,69642,69608],{},[2037,69644,69645,69647],{},[1712,69646,1910],{"stretchy":1903},[1716,69648,2787],{},[1712,69650,3145],{},[1716,69652,1780],{},[1712,69654,1783],{},[1716,69656,69608],{},[1712,69658,1714],{},[1716,69660,69661],{},"10,125",[902,69663,69664],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,69667,69669],{"className":69668},[886],[888,69670,69671],{"xmlns":890},[892,69672,69673,69681],{},[895,69674,69675,69677,69679],{},[898,69676,1734],{},[1712,69678,1714],{},[1716,69680,69608],{},[902,69682,69683],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1636,69686,69687],{},[724,69688,69689,69691,69692,1343,69714,69736,69737,1343,69754,69775,69776,69808,69809,69847,69848,8093,69866,69883,69884,1655,69912,69946,69947,5502,69985,1655,70009,1659],{},[883,69690,2203],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,69693,69695],{"className":69694},[886],[888,69696,69697],{"xmlns":890},[892,69698,69699,69711],{},[895,69700,69701,69707,69709],{},[6927,69702,69703,69705],{},[898,69704,1734],{},[1716,69706,2222],{},[1712,69708,1714],{},[1716,69710,2814],{},[902,69712,69713],{"encoding":904},"Q_1 = 0{,}5",[883,69715,69717],{"className":69716},[886],[888,69718,69719],{"xmlns":890},[892,69720,69721,69733],{},[895,69722,69723,69729,69731],{},[6927,69724,69725,69727],{},[898,69726,1734],{},[1716,69728,2787],{},[1712,69730,1714],{},[1716,69732,2975],{},[902,69734,69735],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,69738,69740],{"className":69739},[886],[888,69741,69742],{"xmlns":890},[892,69743,69744,69752],{},[895,69745,69746,69748,69750],{},[898,69747,1734],{},[1712,69749,1714],{},[1716,69751,69608],{},[902,69753,69683],{"encoding":904},[883,69755,69757],{"className":69756},[886],[888,69758,69759],{"xmlns":890},[892,69760,69761,69772],{},[895,69762,69763,69765,69767,69769],{},[898,69764,1710],{},[898,69766,1775],{},[1712,69768,1714],{},[1716,69770,69771],{},"6,125",[902,69773,69774],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,69777,69779],{"className":69778},[886],[888,69780,69781],{"xmlns":890},[892,69782,69783,69805],{},[895,69784,69785,69787,69793,69795,69797,69799,69801,69803],{},[898,69786,1710],{},[2037,69788,69789,69791],{},[898,69790,1775],{},[1712,69792,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,69794,1714],{},[1712,69796,2219],{},[1716,69798,2975],{},[898,69800,1734],{},[1712,69802,3145],{},[1716,69804,1780],{},[902,69806,69807],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,69810,69812],{"className":69811},[886],[888,69813,69814],{"xmlns":890},[892,69815,69816,69844],{},[895,69817,69818,69820,69822,69824,69826,69828,69834,69836,69838,69840,69842],{},[898,69819,1710],{},[898,69821,1775],{},[1712,69823,1714],{},[1712,69825,2219],{},[1716,69827,2787],{},[2037,69829,69830,69832],{},[898,69831,1734],{},[1716,69833,2787],{},[1712,69835,3145],{},[1716,69837,1780],{},[898,69839,1734],{},[1712,69841,2219],{},[1716,69843,2975],{},[902,69845,69846],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,69849,69851],{"className":69850},[886],[888,69852,69853],{"xmlns":890},[892,69854,69855,69863],{},[895,69856,69857],{},[2037,69858,69859,69861],{},[898,69860,1734],{},[1716,69862,2787],{},[902,69864,69865],{"encoding":904},"Q^2",[883,69867,69869],{"className":69868},[886],[888,69870,69871],{"xmlns":890},[892,69872,69873,69881],{},[895,69874,69875,69877,69879],{},[898,69876,1772],{},[898,69878,45214],{},[898,69880,8195],{},[902,69882,60384],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,69885,69887],{"className":69886},[886],[888,69888,69889],{"xmlns":890},[892,69890,69891,69909],{},[895,69892,69893,69895,69897,69899,69901,69903],{},[898,69894,1772],{},[898,69896,8195],{},[1712,69898,1714],{},[1716,69900,2975],{},[1712,69902,3145],{},[2037,69904,69905,69907],{},[898,69906,1734],{},[1716,69908,2787],{},[902,69910,69911],{"encoding":904},"TC = 4 + Q^2",[883,69913,69915],{"className":69914},[886],[888,69916,69917],{"xmlns":890},[892,69918,69919,69943],{},[895,69920,69921,69923,69925,69927,69929,69931,69937,69939,69941],{},[898,69922,1772],{},[898,69924,1775],{},[1712,69926,1714],{},[1712,69928,2219],{},[1716,69930,2787],{},[2037,69932,69933,69935],{},[898,69934,1734],{},[1716,69936,2787],{},[1712,69938,3145],{},[1716,69940,1780],{},[898,69942,1734],{},[902,69944,69945],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,69948,69950],{"className":69949},[886],[888,69951,69952],{"xmlns":890},[892,69953,69954,69982],{},[895,69955,69956,69958,69960,69962,69964,69966,69972,69974,69976,69978,69980],{},[898,69957,1710],{},[898,69959,1775],{},[1712,69961,1714],{},[1712,69963,2219],{},[1716,69965,6198],{},[2037,69967,69968,69970],{},[898,69969,1734],{},[1716,69971,2787],{},[1712,69973,3145],{},[1716,69975,1780],{},[898,69977,1734],{},[1712,69979,2219],{},[1716,69981,2975],{},[902,69983,69984],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,69986,69988],{"className":69987},[886],[888,69989,69990],{"xmlns":890},[892,69991,69992,70006],{},[895,69993,69994,70002,70004],{},[6927,69995,69996,69998,70000],{},[898,69997,1734],{},[898,69999,61072],{},[1712,70001,61075],{},[1712,70003,1714],{},[1716,70005,69434],{},[902,70007,70008],{"encoding":904},"Q_{\\max} = 1{,}5",[883,70010,70012],{"className":70011},[886],[888,70013,70014],{"xmlns":890},[892,70015,70016,70033],{},[895,70017,70018,70020,70028,70030],{},[898,70019,1710],{},[6927,70021,70022,70024,70026],{},[898,70023,1775],{},[898,70025,61072],{},[1712,70027,61075],{},[1712,70029,1714],{},[1716,70031,70032],{},"2,75",[902,70034,70035],{"encoding":904},"PR_{\\max} = 2{,}75",[724,70037,70038],{},[614,70039,70040,70041,70068,70069,70102,70103,1343,70126,1659],{},"Obrázek 3.12: Graf ",[883,70042,70044],{"className":70043},[886],[888,70045,70046],{"xmlns":890},[892,70047,70048,70066],{},[895,70049,70050,70052,70054,70056,70058,70060],{},[898,70051,1772],{},[898,70053,8195],{},[1712,70055,1714],{},[1716,70057,2975],{},[1712,70059,3145],{},[2037,70061,70062,70064],{},[898,70063,1734],{},[1716,70065,2787],{},[902,70067,69911],{"encoding":904}," (parabola) a ",[883,70070,70072],{"className":70071},[886],[888,70073,70074],{"xmlns":890},[892,70075,70076,70100],{},[895,70077,70078,70080,70082,70084,70086,70088,70094,70096,70098],{},[898,70079,1772],{},[898,70081,1775],{},[1712,70083,1714],{},[1712,70085,2219],{},[1716,70087,2787],{},[2037,70089,70090,70092],{},[898,70091,1734],{},[1716,70093,2787],{},[1712,70095,3145],{},[1716,70097,1780],{},[898,70099,1734],{},[902,70101,69945],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,70104,70106],{"className":70105},[886],[888,70107,70108],{"xmlns":890},[892,70109,70110,70123],{},[895,70111,70112,70118,70120],{},[6927,70113,70114,70116],{},[898,70115,1734],{},[1716,70117,2222],{},[1712,70119,3712],{},[1716,70121,70122],{},"0,54",[902,70124,70125],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,70127,70129],{"className":70128},[886],[888,70130,70131],{"xmlns":890},[892,70132,70133,70146],{},[895,70134,70135,70141,70143],{},[6927,70136,70137,70139],{},[898,70138,1734],{},[1716,70140,2787],{},[1712,70142,3712],{},[1716,70144,70145],{},"2,46",[902,70147,70148],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,70150,70151],{},[614,70152,70153,70154,63382,70191,70208,70209,1343,70230,1659],{},"Obrázek 3.13: Graf zisku ",[883,70155,70157],{"className":70156},[886],[888,70158,70159],{"xmlns":890},[892,70160,70161,70189],{},[895,70162,70163,70165,70167,70169,70171,70173,70179,70181,70183,70185,70187],{},[898,70164,1710],{},[898,70166,1775],{},[1712,70168,1714],{},[1712,70170,2219],{},[1716,70172,6198],{},[2037,70174,70175,70177],{},[898,70176,1734],{},[1716,70178,2787],{},[1712,70180,3145],{},[1716,70182,1780],{},[898,70184,1734],{},[1712,70186,2219],{},[1716,70188,2975],{},[902,70190,69984],{"encoding":904},[883,70192,70194],{"className":70193},[886],[888,70195,70196],{"xmlns":890},[892,70197,70198,70206],{},[895,70199,70200,70202,70204],{},[898,70201,1734],{},[1712,70203,1714],{},[1716,70205,69434],{},[902,70207,69489],{"encoding":904}," a nulami ",[883,70210,70212],{"className":70211},[886],[888,70213,70214],{"xmlns":890},[892,70215,70216,70228],{},[895,70217,70218,70224,70226],{},[6927,70219,70220,70222],{},[898,70221,1734],{},[1716,70223,2222],{},[1712,70225,3712],{},[1716,70227,70122],{},[902,70229,70125],{"encoding":904},[883,70231,70233],{"className":70232},[886],[888,70234,70235],{"xmlns":890},[892,70236,70237,70249],{},[895,70238,70239,70245,70247],{},[6927,70240,70241,70243],{},[898,70242,1734],{},[1716,70244,2787],{},[1712,70246,3712],{},[1716,70248,70145],{},[902,70250,70148],{"encoding":904},[115,70252,70254],{"id":70253},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,70256,70257],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,70259,70260],{},[3817,70261],{"alt":70262,"className":70263,"src":70264},"imek-max-zisku-dva-pohledy",[210,3821],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,70266,21287],{"id":70267},"princip-1",[724,70269,70270,70271,8046,70286,70303],{},"Má-li zisk ",[883,70272,70274],{"className":70273},[886],[888,70275,70276],{"xmlns":890},[892,70277,70278,70284],{},[895,70279,70280,70282],{},[898,70281,1710],{},[898,70283,1775],{},[902,70285,68354],{"encoding":904},[883,70287,70289],{"className":70288},[886],[888,70290,70291],{"xmlns":890},[892,70292,70293,70301],{},[895,70294,70295],{},[6927,70296,70297,70299],{},[898,70298,1734],{},[1716,70300,2085],{},[902,70302,43183],{"encoding":904}," maximum, pak platí",[883,70305,70307],{"className":70306},[886],[888,70308,70309],{"xmlns":890,"display":32941},[892,70310,70311,70360],{},[25629,70312,70313],{"width":32946},[25634,70314,70315,70317,70353,70355],{},[25637,70316],{"width":32951},[25637,70318,70319],{},[895,70320,70321,70323,70325,70327,70333,70335,70337,70339,70341,70343,70349,70351],{},[898,70322,4445],{},[898,70324,1775],{},[1712,70326,1904],{"stretchy":1903},[6927,70328,70329,70331],{},[898,70330,1734],{},[1716,70332,2085],{},[1712,70334,1910],{"stretchy":1903},[1712,70336,1714],{},[898,70338,4445],{},[898,70340,8195],{},[1712,70342,1904],{"stretchy":1903},[6927,70344,70345,70347],{},[898,70346,1734],{},[1716,70348,2085],{},[1712,70350,1910],{"stretchy":1903},[898,70352,1659],{"mathvariant":2003},[25637,70354],{"width":32951},[25637,70356,70357],{},[1762,70358,70359],{},"(3.13)",[902,70361,70362],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1636,70364,70365],{},[724,70366,70367,66921,70369],{},[883,70368,61319],{},[38,70370,70371],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,70373,70374,70377,70378,5920,70405,22451,70479,1659],{},[38,70375,70376],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,70379,70381],{"className":70380},[886],[888,70382,70383],{"xmlns":890},[892,70384,70385,70403],{},[895,70386,70387,70389,70391,70393,70395,70397,70399,70401],{},[898,70388,1710],{},[898,70390,1775],{},[1712,70392,1714],{},[898,70394,1772],{},[898,70396,1775],{},[1712,70398,2219],{},[898,70400,1772],{},[898,70402,8195],{},[902,70404,60075],{"encoding":904},[883,70406,70408],{"className":70407},[886],[888,70409,70410],{"xmlns":890},[892,70411,70412,70476],{},[895,70413,70414,70416,70422,70424,70430,70432,70434,70436,70442,70444,70450,70452,70454,70456,70462,70464,70470,70472,70474],{},[898,70415,1710],{},[2037,70417,70418,70420],{},[898,70419,1775],{},[1712,70421,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,70423,1904],{"stretchy":1903},[6927,70425,70426,70428],{},[898,70427,1734],{},[1716,70429,2085],{},[1712,70431,1910],{"stretchy":1903},[1712,70433,1714],{},[898,70435,1772],{},[2037,70437,70438,70440],{},[898,70439,1775],{},[1712,70441,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,70443,1904],{"stretchy":1903},[6927,70445,70446,70448],{},[898,70447,1734],{},[1716,70449,2085],{},[1712,70451,1910],{"stretchy":1903},[1712,70453,2219],{},[898,70455,1772],{},[2037,70457,70458,70460],{},[898,70459,8195],{},[1712,70461,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,70463,1904],{"stretchy":1903},[6927,70465,70466,70468],{},[898,70467,1734],{},[1716,70469,2085],{},[1712,70471,1910],{"stretchy":1903},[1712,70473,1714],{},[1716,70475,2085],{},[902,70477,70478],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,70480,70482],{"className":70481},[886],[888,70483,70484],{"xmlns":890},[892,70485,70486,70518],{},[895,70487,70488,70490,70492,70494,70500,70502,70504,70506,70508,70510,70516],{},[898,70489,4445],{},[898,70491,1775],{},[1712,70493,1904],{"stretchy":1903},[6927,70495,70496,70498],{},[898,70497,1734],{},[1716,70499,2085],{},[1712,70501,1910],{"stretchy":1903},[1712,70503,1714],{},[898,70505,4445],{},[898,70507,8195],{},[1712,70509,1904],{"stretchy":1903},[6927,70511,70512,70514],{},[898,70513,1734],{},[1716,70515,2085],{},[1712,70517,1910],{"stretchy":1903},[902,70519,70520],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1636,70522,70523,70528],{},[724,70524,70525,70527],{},[883,70526,2370],{}," Postup — jak najít maximum zisku",[152,70529,70530,70594,70649,70686,70714],{},[123,70531,70532,70533,1655,70548,70563,70564,1691],{},"Sestavte ",[883,70534,70536],{"className":70535},[886],[888,70537,70538],{"xmlns":890},[892,70539,70540,70546],{},[895,70541,70542,70544],{},[898,70543,1772],{},[898,70545,1775],{},[902,70547,1877],{"encoding":904},[883,70549,70551],{"className":70550},[886],[888,70552,70553],{"xmlns":890},[892,70554,70555,70561],{},[895,70556,70557,70559],{},[898,70558,1772],{},[898,70560,8195],{},[902,70562,8648],{"encoding":904}," ze zadání (typicky ",[883,70565,70567],{"className":70566},[886],[888,70568,70569],{"xmlns":890},[892,70570,70571,70591],{},[895,70572,70573,70575,70577,70579,70581,70583,70585,70587,70589],{},[898,70574,1772],{},[898,70576,1775],{},[1712,70578,1714],{},[898,70580,1710],{},[1712,70582,1904],{"stretchy":1903},[898,70584,1734],{},[1712,70586,1910],{"stretchy":1903},[1712,70588,1783],{},[898,70590,1734],{},[902,70592,70593],{"encoding":904},"TR = P(Q) \\cdot Q",[123,70595,70596,70597,1655,70623,1659],{},"Vypočtěte ",[883,70598,70600],{"className":70599},[886],[888,70601,70602],{"xmlns":890},[892,70603,70604,70620],{},[895,70605,70606,70608,70610,70612,70614],{},[898,70607,4445],{},[898,70609,1775],{},[1712,70611,1714],{},[898,70613,1772],{},[2037,70615,70616,70618],{},[898,70617,1775],{},[1712,70619,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,70621,70622],{"encoding":904},"MR = TR'",[883,70624,70626],{"className":70625},[886],[888,70627,70628],{"xmlns":890},[892,70629,70630,70646],{},[895,70631,70632,70634,70636,70638,70640],{},[898,70633,4445],{},[898,70635,8195],{},[1712,70637,1714],{},[898,70639,1772],{},[2037,70641,70642,70644],{},[898,70643,8195],{},[1712,70645,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,70647,70648],{"encoding":904},"MC = TC'",[123,70650,70651,70652,1659],{},"Řešte rovnici ",[883,70653,70655],{"className":70654},[886],[888,70656,70657],{"xmlns":890},[892,70658,70659,70683],{},[895,70660,70661,70663,70665,70667,70669,70671,70673,70675,70677,70679,70681],{},[898,70662,4445],{},[898,70664,1775],{},[1712,70666,1904],{"stretchy":1903},[898,70668,1734],{},[1712,70670,1910],{"stretchy":1903},[1712,70672,1714],{},[898,70674,4445],{},[898,70676,8195],{},[1712,70678,1904],{"stretchy":1903},[898,70680,1734],{},[1712,70682,1910],{"stretchy":1903},[902,70684,70685],{"encoding":904},"MR(Q) = MC(Q)",[123,70687,70688,70689,70713],{},"Ověřte druhou derivaci ",[883,70690,70692],{"className":70691},[886],[888,70693,70694],{"xmlns":890},[892,70695,70696,70710],{},[895,70697,70698,70700],{},[898,70699,1710],{},[2037,70701,70702,70704],{},[898,70703,1775],{},[895,70705,70706,70708],{},[1712,70707,2243],{"mathvariant":2003},[1712,70709,2243],{"mathvariant":2003},[902,70711,70712],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,70715,70716,70717,70744],{},"Dosaďte do ",[883,70718,70720],{"className":70719},[886],[888,70721,70722],{"xmlns":890},[892,70723,70724,70742],{},[895,70725,70726,70728,70730,70732,70734,70736,70738,70740],{},[898,70727,1710],{},[898,70729,1775],{},[1712,70731,1714],{},[898,70733,1772],{},[898,70735,1775],{},[1712,70737,2219],{},[898,70739,1772],{},[898,70741,8195],{},[902,70743,60075],{"encoding":904}," pro hodnotu maxima.",[42223,70746,70748],{"id":70747},"příklad-39","Příklad 3.9",[724,70750,70751,60863,70753,1655,70775,70811],{},[38,70752,60862],{},[883,70754,70756],{"className":70755},[886],[888,70757,70758],{"xmlns":890},[892,70759,70760,70772],{},[895,70761,70762,70764,70766,70768,70770],{},[898,70763,1710],{},[1712,70765,1714],{},[1716,70767,42894],{},[1712,70769,2219],{},[898,70771,1734],{},[902,70773,70774],{"encoding":904},"P = 30 - Q",[883,70776,70778],{"className":70777},[886],[888,70779,70780],{"xmlns":890},[892,70781,70782,70808],{},[895,70783,70784,70786,70788,70790,70792,70798,70800,70802,70804,70806],{},[898,70785,1772],{},[898,70787,8195],{},[1712,70789,1714],{},[1716,70791,2814],{},[2037,70793,70794,70796],{},[898,70795,1734],{},[1716,70797,2787],{},[1712,70799,3145],{},[1716,70801,6209],{},[898,70803,1734],{},[1712,70805,3145],{},[1716,70807,29076],{},[902,70809,70810],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,70813,70814,3245,70816,1343,70846,70884,70885,20666,70929,70963,70964,1659],{},[38,70815,27645],{},[883,70817,70819],{"className":70818},[886],[888,70820,70821],{"xmlns":890},[892,70822,70823,70843],{},[895,70824,70825,70827,70829,70831,70833,70835,70837],{},[898,70826,1772],{},[898,70828,1775],{},[1712,70830,1714],{},[1716,70832,42894],{},[898,70834,1734],{},[1712,70836,2219],{},[2037,70838,70839,70841],{},[898,70840,1734],{},[1716,70842,2787],{},[902,70844,70845],{"encoding":904},"TR = 30Q - Q^2",[883,70847,70849],{"className":70848},[886],[888,70850,70851],{"xmlns":890},[892,70852,70853,70881],{},[895,70854,70855,70857,70859,70861,70863,70865,70871,70873,70875,70877,70879],{},[898,70856,1710],{},[898,70858,1775],{},[1712,70860,1714],{},[1712,70862,2219],{},[1716,70864,69434],{},[2037,70866,70867,70869],{},[898,70868,1734],{},[1716,70870,2787],{},[1712,70872,3145],{},[1716,70874,46675],{},[898,70876,1734],{},[1712,70878,2219],{},[1716,70880,29076],{},[902,70882,70883],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,70886,70888],{"className":70887},[886],[888,70889,70890],{"xmlns":890},[892,70891,70892,70926],{},[895,70893,70894,70896,70902,70904,70906,70908,70910,70912,70914,70916,70918,70920,70922,70924],{},[898,70895,1710],{},[2037,70897,70898,70900],{},[898,70899,1775],{},[1712,70901,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,70903,1714],{},[1712,70905,2219],{},[1716,70907,6198],{},[898,70909,1734],{},[1712,70911,3145],{},[1716,70913,46675],{},[1712,70915,1714],{},[1716,70917,2085],{},[1712,70919,1767],{},[898,70921,1734],{},[1712,70923,1714],{},[1716,70925,3397],{},[902,70927,70928],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,70930,70932],{"className":70931},[886],[888,70933,70934],{"xmlns":890},[892,70935,70936,70960],{},[895,70937,70938,70940,70950,70952,70954,70956,70958],{},[898,70939,1710],{},[2037,70941,70942,70944],{},[898,70943,1775],{},[895,70945,70946,70948],{},[1712,70947,2243],{"mathvariant":2003},[1712,70949,2243],{"mathvariant":2003},[1712,70951,1714],{},[1712,70953,2219],{},[1716,70955,6198],{},[1712,70957,2252],{},[1716,70959,2085],{},[902,70961,70962],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,70965,70967],{"className":70966},[886],[888,70968,70969],{"xmlns":890},[892,70970,70971,70988],{},[895,70972,70973,70975,70977,70979,70981,70983,70985],{},[898,70974,1710],{},[898,70976,1775],{},[1712,70978,1904],{"stretchy":1903},[1716,70980,3397],{},[1712,70982,1910],{"stretchy":1903},[1712,70984,1714],{},[1716,70986,70987],{},"89",[902,70989,70990],{"encoding":904},"PR(8) = 89",[724,70992,70993,70994,1343,71020,20666,71044,71082],{},"Ověření principu: ",[883,70995,70997],{"className":70996},[886],[888,70998,70999],{"xmlns":890},[892,71000,71001,71017],{},[895,71002,71003,71005,71007,71009,71011,71013,71015],{},[898,71004,4445],{},[898,71006,1775],{},[1712,71008,1714],{},[1716,71010,42894],{},[1712,71012,2219],{},[1716,71014,2787],{},[898,71016,1734],{},[902,71018,71019],{"encoding":904},"MR = 30 - 2Q",[883,71021,71023],{"className":71022},[886],[888,71024,71025],{"xmlns":890},[892,71026,71027,71041],{},[895,71028,71029,71031,71033,71035,71037,71039],{},[898,71030,4445],{},[898,71032,8195],{},[1712,71034,1714],{},[898,71036,1734],{},[1712,71038,3145],{},[1716,71040,6209],{},[902,71042,71043],{"encoding":904},"MC = Q + 6",[883,71045,71047],{"className":71046},[886],[888,71048,71049],{"xmlns":890},[892,71050,71051,71079],{},[895,71052,71053,71055,71057,71059,71061,71063,71065,71067,71069,71071,71073,71075,71077],{},[898,71054,4445],{},[898,71056,1775],{},[1712,71058,1904],{"stretchy":1903},[1716,71060,3397],{},[1712,71062,1910],{"stretchy":1903},[1712,71064,1714],{},[1716,71066,27821],{},[1712,71068,1714],{},[898,71070,4445],{},[898,71072,8195],{},[1712,71074,1904],{"stretchy":1903},[1716,71076,3397],{},[1712,71078,1910],{"stretchy":1903},[902,71080,71081],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,71084,71085,71086,71119,71120,71137],{},"V řadě případů — má-li rovnice ",[883,71087,71089],{"className":71088},[886],[888,71090,71091],{"xmlns":890},[892,71092,71093,71117],{},[895,71094,71095,71097,71099,71101,71103,71105,71107,71109,71111,71113,71115],{},[898,71096,4445],{},[898,71098,1775],{},[1712,71100,1904],{"stretchy":1903},[898,71102,1734],{},[1712,71104,1910],{"stretchy":1903},[1712,71106,1714],{},[898,71108,4445],{},[898,71110,8195],{},[1712,71112,1904],{"stretchy":1903},[898,71114,1734],{},[1712,71116,1910],{"stretchy":1903},[902,71118,70685],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,71121,71123],{"className":71122},[886],[888,71124,71125],{"xmlns":890},[892,71126,71127,71135],{},[895,71128,71129],{},[6927,71130,71131,71133],{},[898,71132,1734],{},[1716,71134,2085],{},[902,71136,43183],{"encoding":904}," — není třeba provádět test druhé derivace.",[42223,71139,71141],{"id":71140},"příklad-310","Příklad 3.10",[724,71143,71144,71146,71147,71151,71152,71165,71166,71197],{},[38,71145,60862],{}," Firma vyrábí minipočítače v ",[207,71148,71150],{"className":71149,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,71153,71155],{"className":71154},[886],[888,71156,71157],{"xmlns":890},[892,71158,71159,71163],{},[895,71160,71161],{},[1716,71162,20065],{},[902,71164,20065],{"encoding":904}," EUR\u002Fks. ",[883,71167,71169],{"className":71168},[886],[888,71170,71171],{"xmlns":890},[892,71172,71173,71194],{},[895,71174,71175,71177,71179,71181,71183,71185,71188],{},[898,71176,1772],{},[898,71178,8195],{},[1712,71180,1714],{},[1716,71182,2782],{},[1712,71184,3145],{},[1716,71186,71187],{},"28",[2037,71189,71190,71192],{},[898,71191,1734],{},[1716,71193,2787],{},[902,71195,71196],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,71199,71200,3245,71202,1343,71224,1343,71244,71267],{},[38,71201,27645],{},[883,71203,71205],{"className":71204},[886],[888,71206,71207],{"xmlns":890},[892,71208,71209,71221],{},[895,71210,71211,71213,71215,71217,71219],{},[898,71212,1772],{},[898,71214,1775],{},[1712,71216,1714],{},[1716,71218,20065],{},[898,71220,1734],{},[902,71222,71223],{"encoding":904},"TR = 900Q",[883,71225,71227],{"className":71226},[886],[888,71228,71229],{"xmlns":890},[892,71230,71231,71241],{},[895,71232,71233,71235,71237,71239],{},[898,71234,4445],{},[898,71236,1775],{},[1712,71238,1714],{},[1716,71240,20065],{},[902,71242,71243],{"encoding":904},"MR = 900",[883,71245,71247],{"className":71246},[886],[888,71248,71249],{"xmlns":890},[892,71250,71251,71264],{},[895,71252,71253,71255,71257,71259,71262],{},[898,71254,4445],{},[898,71256,8195],{},[1712,71258,1714],{},[1716,71260,71261],{},"56",[898,71263,1734],{},[902,71265,71266],{"encoding":904},"MC = 56Q",". Z principu:",[883,71269,71271],{"className":71270},[886],[888,71272,71273],{"xmlns":890,"display":32941},[892,71274,71275,71317],{},[895,71276,71277,71279,71281,71283,71285,71287,71289,71291,71293,71295,71303,71305,71308,71310,71312,71314],{},[1716,71278,20065],{},[1712,71280,1714],{},[1716,71282,71261],{},[898,71284,1734],{},[1762,71286,1764],{},[1712,71288,1767],{},[1762,71290,1764],{},[898,71292,1734],{},[1712,71294,1714],{},[2563,71296,71297],{"scriptlevel":2085,"displaystyle":1903},[2567,71298,71299,71301],{},[1716,71300,20065],{},[1716,71302,71261],{},[1712,71304,3712],{},[1716,71306,71307],{},"16,07",[1762,71309,1764],{},[1712,71311,3740],{},[1762,71313,1764],{},[1716,71315,71316],{},"16.",[902,71318,71319],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,71321,71322,71323,2854],{},"Zisk při ",[883,71324,71326],{"className":71325},[886],[888,71327,71328],{"xmlns":890},[892,71329,71330,71338],{},[895,71331,71332,71334,71336],{},[898,71333,1734],{},[1712,71335,1714],{},[1716,71337,46737],{},[902,71339,71340],{"encoding":904},"Q = 16",[883,71342,71344],{"className":71343},[886],[888,71345,71346],{"xmlns":890,"display":32941},[892,71347,71348,71419],{},[895,71349,71350,71352,71354,71356,71358,71360,71362,71364,71366,71368,71370,71372,71374,71376,71378,71380,71386,71388,71390,71392,71394,71396,71398,71400,71402,71405,71407,71409,71411,71414,71417],{},[898,71351,1710],{},[898,71353,1775],{},[1712,71355,1904],{"stretchy":1903},[1716,71357,46737],{},[1712,71359,1910],{"stretchy":1903},[1712,71361,1714],{},[1716,71363,20065],{},[1712,71365,1783],{},[1716,71367,46737],{},[1712,71369,2219],{},[1712,71371,1904],{"stretchy":1903},[1716,71373,2782],{},[1712,71375,3145],{},[1716,71377,71187],{},[1712,71379,1783],{},[2037,71381,71382,71384],{},[1716,71383,46737],{},[1716,71385,2787],{},[1712,71387,1910],{"stretchy":1903},[1712,71389,1714],{},[1716,71391,27821],{},[1762,71393,2583],{},[1716,71395,25017],{},[1712,71397,2219],{},[1716,71399,29076],{},[1762,71401,2583],{},[1716,71403,71404],{},"218",[1712,71406,1714],{},[1716,71408,29076],{},[1762,71410,2583],{},[1716,71412,71413],{},"182",[1762,71415,71416],{}," EUR",[898,71418,1659],{"mathvariant":2003},[902,71420,71421],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,71423,71424],{},"Pro srovnání při původních 30 ks:",[883,71426,71428],{"className":71427},[886],[888,71429,71430],{"xmlns":890,"display":32941},[892,71431,71432,71497],{},[895,71433,71434,71436,71438,71440,71442,71444,71446,71448,71450,71452,71454,71456,71458,71460,71462,71464,71466,71468,71470,71473,71475,71477,71479,71481,71483,71485,71487,71489,71491,71493,71495],{},[898,71435,1710],{},[898,71437,1775],{},[1712,71439,1904],{"stretchy":1903},[1716,71441,42894],{},[1712,71443,1910],{"stretchy":1903},[1712,71445,1714],{},[1716,71447,20065],{},[1712,71449,1783],{},[1716,71451,42894],{},[1712,71453,2219],{},[1712,71455,1904],{"stretchy":1903},[1716,71457,2782],{},[1712,71459,3145],{},[1716,71461,71187],{},[1712,71463,1783],{},[1716,71465,20065],{},[1712,71467,1910],{"stretchy":1903},[1712,71469,1714],{},[1716,71471,71472],{},"27",[1762,71474,2583],{},[1716,71476,63957],{},[1712,71478,2219],{},[1716,71480,2809],{},[1762,71482,2583],{},[1716,71484,35618],{},[1712,71486,1714],{},[1716,71488,2222],{},[1762,71490,2583],{},[1716,71492,28618],{},[1762,71494,71416],{},[898,71496,1659],{"mathvariant":2003},[902,71498,71499],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,71501,71502,71505,71506,71524,71525,71543],{},[38,71503,71504],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,71507,71509],{"className":71508},[886],[888,71510,71511],{"xmlns":890},[892,71512,71513,71521],{},[895,71514,71515,71517,71519],{},[1716,71516,29076],{},[1762,71518,2583],{},[1716,71520,71413],{},[902,71522,71523],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,71526,71528],{"className":71527},[886],[888,71529,71530],{"xmlns":890},[892,71531,71532,71540],{},[895,71533,71534,71536,71538],{},[1716,71535,2222],{},[1762,71537,2583],{},[1716,71539,28618],{},[902,71541,71542],{"encoding":904},"1\\,750"," EUR.",[198,71545,71547],{"id":71546},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,71549,71550,71551,67445,71564,71588],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,71552,71554],{"className":71553},[886],[888,71555,71556],{"xmlns":890},[892,71557,71558,71562],{},[895,71559,71560],{},[898,71561,1710],{},[902,71563,1710],{"encoding":904},[883,71565,71567],{"className":71566},[886],[888,71568,71569],{"xmlns":890},[892,71570,71571,71585],{},[895,71572,71573,71575,71577,71579,71581,71583],{},[898,71574,1772],{},[898,71576,1775],{},[1712,71578,1714],{},[898,71580,1710],{},[1712,71582,1783],{},[898,71584,1734],{},[902,71586,71587],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,71590,71592],{"className":71591},[886],[888,71593,71594],{"xmlns":890,"display":32941},[892,71595,71596,71629],{},[25629,71597,71598],{"width":32946},[25634,71599,71600,71602,71622,71624],{},[25637,71601],{"width":32951},[25637,71603,71604],{},[895,71605,71606,71608,71610,71612,71614,71616,71618,71620],{},[898,71607,1710],{},[1712,71609,1714],{},[898,71611,4445],{},[898,71613,8195],{},[1712,71615,1904],{"stretchy":1903},[898,71617,1734],{},[1712,71619,1910],{"stretchy":1903},[898,71621,1659],{"mathvariant":2003},[25637,71623],{"width":32951},[25637,71625,71626],{},[1762,71627,71628],{},"(3.14)",[902,71630,71631],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,71633,71634,71635,1659],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,71636,71638],{"className":71637},[886],[888,71639,71640],{"xmlns":890},[892,71641,71642,71656],{},[895,71643,71644,71646],{},[898,71645,1710],{},[2037,71647,71648,71650],{},[898,71649,1775],{},[895,71651,71652,71654],{},[1712,71653,2243],{"mathvariant":2003},[1712,71655,2243],{"mathvariant":2003},[902,71657,70712],{"encoding":904},[42223,71659,71661],{"id":71660},"příklad-311","Příklad 3.11",[724,71663,71664,62397,71666,71713,71714,71732],{},[38,71665,60862],{},[883,71667,71669],{"className":71668},[886],[888,71670,71671],{"xmlns":890},[892,71672,71673,71710],{},[895,71674,71675,71677,71679,71681,71684,71690,71692,71694,71700,71702,71704,71706,71708],{},[898,71676,1772],{},[898,71678,8195],{},[1712,71680,1714],{},[1716,71682,71683],{},"0,04",[2037,71685,71686,71688],{},[898,71687,1734],{},[1716,71689,6198],{},[1712,71691,2219],{},[1716,71693,27420],{},[2037,71695,71696,71698],{},[898,71697,1734],{},[1716,71699,2787],{},[1712,71701,3145],{},[1716,71703,1718],{},[898,71705,1734],{},[1712,71707,3145],{},[1716,71709,3068],{},[902,71711,71712],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,71715,71717],{"className":71716},[886],[888,71718,71719],{"xmlns":890},[892,71720,71721,71729],{},[895,71722,71723,71725,71727],{},[898,71724,1710],{},[1712,71726,1714],{},[1716,71728,2975],{},[902,71730,71731],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,71734,71735,71737,71738,22451,71780,71814,71815,2854],{},[38,71736,27645],{}," Z (3.14): ",[883,71739,71741],{"className":71740},[886],[888,71742,71743],{"xmlns":890},[892,71744,71745,71777],{},[895,71746,71747,71749,71751,71753,71756,71762,71764,71767,71769,71771,71773,71775],{},[898,71748,4445],{},[898,71750,8195],{},[1712,71752,1714],{},[1716,71754,71755],{},"0,12",[2037,71757,71758,71760],{},[898,71759,1734],{},[1716,71761,2787],{},[1712,71763,2219],{},[1716,71765,71766],{},"1,8",[898,71768,1734],{},[1712,71770,3145],{},[1716,71772,1718],{},[1712,71774,1714],{},[1716,71776,2975],{},[902,71778,71779],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,71781,71783],{"className":71782},[886],[888,71784,71785],{"xmlns":890},[892,71786,71787,71811],{},[895,71788,71789,71791,71797,71799,71801,71803,71805,71807,71809],{},[1716,71790,71755],{},[2037,71792,71793,71795],{},[898,71794,1734],{},[1716,71796,2787],{},[1712,71798,2219],{},[1716,71800,71766],{},[898,71802,1734],{},[1712,71804,3145],{},[1716,71806,6209],{},[1712,71808,1714],{},[1716,71810,2085],{},[902,71812,71813],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,71816,71818],{"className":71817},[886],[888,71819,71820],{"xmlns":890},[892,71821,71822,71826],{},[895,71823,71824],{},[1716,71825,71755],{},[902,71827,71828],{"encoding":904},"0{,}12",[883,71830,71832],{"className":71831},[886],[888,71833,71834],{"xmlns":890,"display":32941},[892,71835,71836,71888],{},[895,71837,71838,71844,71846,71848,71850,71852,71854,71856,71858,71860,71862,71864,71870,71872,71874,71876,71878,71884,71886],{},[2037,71839,71840,71842],{},[898,71841,1734],{},[1716,71843,2787],{},[1712,71845,2219],{},[1716,71847,41119],{},[898,71849,1734],{},[1712,71851,3145],{},[1716,71853,2782],{},[1712,71855,1714],{},[1716,71857,2085],{},[1762,71859,1764],{},[1712,71861,1767],{},[1762,71863,1764],{},[6927,71865,71866,71868],{},[898,71867,1734],{},[1716,71869,2222],{},[1712,71871,1714],{},[1716,71873,3068],{},[1712,71875,3138],{"separator":2565},[1762,71877,1764],{},[6927,71879,71880,71882],{},[898,71881,1734],{},[1716,71883,2787],{},[1712,71885,1714],{},[1716,71887,24203],{},[902,71889,71890],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,71892,71893,71894,2854],{},"Dále ",[883,71895,71897],{"className":71896},[886],[888,71898,71899],{"xmlns":890},[892,71900,71901,71940],{},[895,71902,71903,71905,71915,71917,71919,71921,71927,71929,71931,71934,71936,71938],{},[898,71904,1710],{},[2037,71906,71907,71909],{},[898,71908,1775],{},[895,71910,71911,71913],{},[1712,71912,2243],{"mathvariant":2003},[1712,71914,2243],{"mathvariant":2003},[1712,71916,1714],{},[1712,71918,2219],{},[898,71920,4445],{},[2037,71922,71923,71925],{},[898,71924,8195],{},[1712,71926,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,71928,1714],{},[1712,71930,2219],{},[1716,71932,71933],{},"0,24",[898,71935,1734],{},[1712,71937,3145],{},[1716,71939,71766],{},[902,71941,71942],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,71944,71945,71995],{},[123,71946,71947,71991,71992,71994],{},[883,71948,71950],{"className":71949},[886],[888,71951,71952],{"xmlns":890},[892,71953,71954,71988],{},[895,71955,71956,71958,71968,71970,71972,71974,71976,71978,71980,71982,71984,71986],{},[898,71957,1710],{},[2037,71959,71960,71962],{},[898,71961,1775],{},[895,71963,71964,71966],{},[1712,71965,2243],{"mathvariant":2003},[1712,71967,2243],{"mathvariant":2003},[1712,71969,1904],{"stretchy":1903},[1716,71971,3068],{},[1712,71973,1910],{"stretchy":1903},[1712,71975,1714],{},[1716,71977,24196],{},[1712,71979,2302],{},[1716,71981,2085],{},[1762,71983,1764],{},[1712,71985,1767],{},[1762,71987,1764],{},[902,71989,71990],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,71993,9176],{}," zisku (minimalizace ztráty);",[123,71996,71997,71991,72043,72045],{},[883,71998,72000],{"className":71999},[886],[888,72001,72002],{"xmlns":890},[892,72003,72004,72040],{},[895,72005,72006,72008,72018,72020,72022,72024,72026,72028,72030,72032,72034,72036,72038],{},[898,72007,1710],{},[2037,72009,72010,72012],{},[898,72011,1775],{},[895,72013,72014,72016],{},[1712,72015,2243],{"mathvariant":2003},[1712,72017,2243],{"mathvariant":2003},[1712,72019,1904],{"stretchy":1903},[1716,72021,1718],{},[1712,72023,1910],{"stretchy":1903},[1712,72025,1714],{},[1712,72027,2219],{},[1716,72029,24196],{},[1712,72031,2252],{},[1716,72033,2085],{},[1762,72035,1764],{},[1712,72037,1767],{},[1762,72039,1764],{},[902,72041,72042],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,72044,5766],{}," zisku, avšak",[883,72047,72049],{"className":72048},[886],[888,72050,72051],{"xmlns":890,"display":32941},[892,72052,72053,72121],{},[895,72054,72055,72057,72059,72061,72063,72065,72067,72069,72071,72073,72075,72077,72079,72081,72083,72085,72087,72089,72091,72093,72095,72097,72099,72101,72103,72105,72107,72109,72111,72113,72115,72117,72119],{},[898,72056,1710],{},[898,72058,1775],{},[1712,72060,1904],{"stretchy":1903},[1716,72062,1718],{},[1712,72064,1910],{"stretchy":1903},[1712,72066,1714],{},[1716,72068,2975],{},[1712,72070,1783],{},[1716,72072,1718],{},[1712,72074,2219],{},[1712,72076,1904],{"stretchy":1903},[1716,72078,71683],{},[1712,72080,1783],{},[1716,72082,2222],{},[1762,72084,2583],{},[1716,72086,63957],{},[1712,72088,2219],{},[1716,72090,27420],{},[1712,72092,1783],{},[1716,72094,1739],{},[1712,72096,3145],{},[1716,72098,1739],{},[1712,72100,3145],{},[1716,72102,3068],{},[1712,72104,1910],{"stretchy":1903},[1712,72106,1714],{},[1716,72108,3018],{},[1712,72110,2219],{},[1716,72112,26055],{},[1712,72114,1714],{},[1712,72116,2219],{},[1716,72118,41119],{},[1712,72120,3138],{"separator":2565},[902,72122,72123],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,72125,72126,72127,1659],{},"tj. ztráta větší než ",[883,72128,72130],{"className":72129},[886],[888,72131,72132],{"xmlns":890},[892,72133,72134,72144],{},[895,72135,72136,72138,72140,72142],{},[898,72137,15308],{},[898,72139,8195],{},[1712,72141,1714],{},[1716,72143,3068],{},[902,72145,72146],{"encoding":904},"FC = 5",[724,72148,72149,72152,72153,72156,72157,1659],{},[38,72150,72151],{},"Závěr:"," firma by měla ",[38,72154,72155],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,72158,72160],{"className":72159},[886],[888,72161,72162],{"xmlns":890},[892,72163,72164,72174],{},[895,72165,72166,72168,72170,72172],{},[898,72167,15308],{},[898,72169,8195],{},[1712,72171,1714],{},[1716,72173,3068],{},[902,72175,72146],{"encoding":904},[115,72177,72179],{"id":72178},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,72181,72182,72183,72185,72186,72201,72202,72215,72216,72242,72243,72256,72257,72274,72275,8046,72292,72295,72296,72316,72317,72332,72333,2854],{},"Důležitým završením analýzy je konstrukce ",[38,72184,60150],{},". S nabízeným množstvím rostou mezní náklady ",[883,72187,72189],{"className":72188},[886],[888,72190,72191],{"xmlns":890},[892,72192,72193,72199],{},[895,72194,72195,72197],{},[898,72196,4445],{},[898,72198,8195],{},[902,72200,60167],{"encoding":904}," a tyto určují cenu ",[883,72203,72205],{"className":72204},[886],[888,72206,72207],{"xmlns":890},[892,72208,72209,72213],{},[895,72210,72211],{},[898,72212,1710],{},[902,72214,1710],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,72217,72219],{"className":72218},[886],[888,72220,72221],{"xmlns":890},[892,72222,72223,72239],{},[895,72224,72225,72227,72229,72231,72233,72235,72237],{},[898,72226,1710],{},[1712,72228,1714],{},[898,72230,4445],{},[898,72232,8195],{},[1712,72234,1904],{"stretchy":1903},[898,72236,1734],{},[1712,72238,1910],{"stretchy":1903},[902,72240,72241],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,72244,72246],{"className":72245},[886],[888,72247,72248],{"xmlns":890},[892,72249,72250,72254],{},[895,72251,72252],{},[898,72253,1710],{},[902,72255,1710],{"encoding":904}," však nemůže být nižší než ",[883,72258,72260],{"className":72259},[886],[888,72261,72262],{"xmlns":890},[892,72263,72264,72272],{},[895,72265,72266],{},[2037,72267,72268,72270],{},[898,72269,1710],{},[1712,72271,2145],{},[902,72273,2195],{"encoding":904}," odpovídající množství ",[883,72276,72278],{"className":72277},[886],[888,72279,72280],{"xmlns":890},[892,72281,72282,72290],{},[895,72283,72284],{},[2037,72285,72286,72288],{},[898,72287,1734],{},[1712,72289,2145],{},[902,72291,34719],{"encoding":904},[38,72293,72294],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,72297,72299],{"className":72298},[886],[888,72300,72301],{"xmlns":890},[892,72302,72303,72313],{},[895,72304,72305,72307],{},[1716,72306,2085],{},[2037,72308,72309,72311],{},[898,72310,1734],{},[1712,72312,2145],{},[902,72314,72315],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,72318,72320],{"className":72319},[886],[888,72321,72322],{"xmlns":890},[892,72323,72324,72330],{},[895,72325,72326,72328],{},[898,72327,4445],{},[898,72329,8195],{},[902,72331,60167],{"encoding":904}," nad bodem ",[883,72334,72336],{"className":72335},[886],[888,72337,72338],{"xmlns":890},[892,72339,72340,72344],{},[895,72341,72342],{},[898,72343,2044],{},[902,72345,2044],{"encoding":904},[883,72347,72349],{"className":72348},[886],[888,72350,72351],{"xmlns":890,"display":32941},[892,72352,72353,72460],{},[25629,72354,72355],{"width":32946},[25634,72356,72357,72359,72453,72455],{},[25637,72358],{"width":32951},[25637,72360,72361],{},[895,72362,72363,72365,72367,72369,72371,72373,72375,72377],{},[898,72364,1710],{},[1712,72366,1714],{},[898,72368,6493],{},[1712,72370,1904],{"stretchy":1903},[898,72372,1734],{},[1712,72374,1910],{"stretchy":1903},[1712,72376,1714],{},[895,72378,72379,72382],{},[1712,72380,72381],{"fence":2565},"{",[25629,72383,72386,72425],{"rowspacing":72384,"columnalign":72385,"columnspacing":20158},"0.36em","left left",[25634,72387,72388,72404],{},[25637,72389,72390],{},[2563,72391,72392],{"scriptlevel":2085,"displaystyle":1903},[895,72393,72394,72396,72398,72400,72402],{},[898,72395,4445],{},[898,72397,8195],{},[1712,72399,1904],{"stretchy":1903},[898,72401,1734],{},[1712,72403,1910],{"stretchy":1903},[25637,72405,72406],{},[2563,72407,72408],{"scriptlevel":2085,"displaystyle":1903},[895,72409,72410,72413,72415,72417,72423],{},[1762,72411,72412],{},"pro ",[898,72414,1734],{},[1712,72416,2282],{},[2037,72418,72419,72421],{},[898,72420,1734],{},[1712,72422,2145],{},[1712,72424,3138],{"separator":2565},[25634,72426,72427,72433],{},[25637,72428,72429],{},[2563,72430,72431],{"scriptlevel":2085,"displaystyle":1903},[1716,72432,2085],{},[25637,72434,72435],{},[2563,72436,72437],{"scriptlevel":2085,"displaystyle":1903},[895,72438,72439,72441,72443,72445,72451],{},[1762,72440,72412],{},[898,72442,1734],{},[1712,72444,2252],{},[2037,72446,72447,72449],{},[898,72448,1734],{},[1712,72450,2145],{},[1712,72452,3138],{"separator":2565},[25637,72454],{"width":32951},[25637,72456,72457],{},[1762,72458,72459],{},"(3.15)",[902,72461,72462],{"encoding":904},"P = S(Q) = \\begin{cases} MC(Q) & \\text{pro } Q \\geq Q^*, \\\\ 0 & \\text{pro } Q \u003C Q^*, \\end{cases}\n\\tag{3.15}",[724,72464,2101,72465,72482,72483,72500,72501,46374,72531,72534],{},[883,72466,72468],{"className":72467},[886],[888,72469,72470],{"xmlns":890},[892,72471,72472,72480],{},[895,72473,72474],{},[2037,72475,72476,72478],{},[898,72477,1734],{},[1712,72479,2145],{},[902,72481,34719],{"encoding":904}," je bod minima ",[883,72484,72486],{"className":72485},[886],[888,72487,72488],{"xmlns":890},[892,72489,72490,72498],{},[895,72491,72492,72494,72496],{},[898,72493,2044],{},[898,72495,45214],{},[898,72497,8195],{},[902,72499,60186],{"encoding":904},". Bod ",[883,72502,72504],{"className":72503},[886],[888,72505,72506],{"xmlns":890},[892,72507,72508,72528],{},[895,72509,72510,72512,72518,72520,72526],{},[1712,72511,1904],{"stretchy":1903},[2037,72513,72514,72516],{},[898,72515,1734],{},[1712,72517,2145],{},[1712,72519,3138],{"separator":2565},[2037,72521,72522,72524],{},[898,72523,1710],{},[1712,72525,2145],{},[1712,72527,1910],{"stretchy":1903},[902,72529,72530],{"encoding":904},"(Q^*, P^*)",[38,72532,72533],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1636,72536,72537,72542],{},[724,72538,72539,72541],{},[883,72540,2370],{}," Postup — jak odvodit nabídku firmy",[152,72543,72544,72593,72688,72743,72814],{},[123,72545,72546,72547,1655,72569,1659],{},"Ze zadaných nákladů určete ",[883,72548,72550],{"className":72549},[886],[888,72551,72552],{"xmlns":890},[892,72553,72554,72566],{},[895,72555,72556,72558,72560,72562,72564],{},[898,72557,4445],{},[898,72559,8195],{},[1712,72561,1904],{"stretchy":1903},[898,72563,1734],{},[1712,72565,1910],{"stretchy":1903},[902,72567,72568],{"encoding":904},"MC(Q)",[883,72570,72572],{"className":72571},[886],[888,72573,72574],{"xmlns":890},[892,72575,72576,72590],{},[895,72577,72578,72580,72582,72584,72586,72588],{},[898,72579,2044],{},[898,72581,45214],{},[898,72583,8195],{},[1712,72585,1904],{"stretchy":1903},[898,72587,1734],{},[1712,72589,1910],{"stretchy":1903},[902,72591,72592],{"encoding":904},"AVC(Q)",[123,72594,72595,72596,72613,72614,72631,72632,72664,72665,1691],{},"Najděte ",[883,72597,72599],{"className":72598},[886],[888,72600,72601],{"xmlns":890},[892,72602,72603,72611],{},[895,72604,72605],{},[2037,72606,72607,72609],{},[898,72608,1734],{},[1712,72610,2145],{},[902,72612,34719],{"encoding":904}," jako bod minima ",[883,72615,72617],{"className":72616},[886],[888,72618,72619],{"xmlns":890},[892,72620,72621,72629],{},[895,72622,72623,72625,72627],{},[898,72624,2044],{},[898,72626,45214],{},[898,72628,8195],{},[902,72630,60186],{"encoding":904}," (řešením ",[883,72633,72635],{"className":72634},[886],[888,72636,72637],{"xmlns":890},[892,72638,72639,72661],{},[895,72640,72641,72643,72645,72651,72653,72655,72657,72659],{},[898,72642,2044],{},[898,72644,45214],{},[2037,72646,72647,72649],{},[898,72648,8195],{},[1712,72650,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,72652,1904],{"stretchy":1903},[898,72654,1734],{},[1712,72656,1910],{"stretchy":1903},[1712,72658,1714],{},[1716,72660,2085],{},[902,72662,72663],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,72666,72668],{"className":72667},[886],[888,72669,72670],{"xmlns":890},[892,72671,72672,72686],{},[895,72673,72674,72676,72678,72680,72682,72684],{},[898,72675,2044],{},[898,72677,45214],{},[898,72679,8195],{},[1712,72681,1714],{},[898,72683,4445],{},[898,72685,8195],{},[902,72687,60123],{"encoding":904},[123,72689,70596,72690,72742],{},[883,72691,72693],{"className":72692},[886],[888,72694,72695],{"xmlns":890},[892,72696,72697,72739],{},[895,72698,72699,72705,72707,72709,72711,72713,72719,72721,72723,72725,72727,72729,72731,72737],{},[2037,72700,72701,72703],{},[898,72702,1710],{},[1712,72704,2145],{},[1712,72706,1714],{},[898,72708,4445],{},[898,72710,8195],{},[1712,72712,1904],{"stretchy":1903},[2037,72714,72715,72717],{},[898,72716,1734],{},[1712,72718,2145],{},[1712,72720,1910],{"stretchy":1903},[1712,72722,1714],{},[898,72724,2044],{},[898,72726,45214],{},[898,72728,8195],{},[1712,72730,1904],{"stretchy":1903},[2037,72732,72733,72735],{},[898,72734,1734],{},[1712,72736,2145],{},[1712,72738,1910],{"stretchy":1903},[902,72740,72741],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,72744,72745,72746,4288,72778,72800,72801,1659],{},"Zapište nabídku: ",[883,72747,72749],{"className":72748},[886],[888,72750,72751],{"xmlns":890},[892,72752,72753,72775],{},[895,72754,72755,72757,72759,72761,72763,72765,72767,72769,72771,72773],{},[898,72756,6493],{},[1712,72758,1904],{"stretchy":1903},[898,72760,1734],{},[1712,72762,1910],{"stretchy":1903},[1712,72764,1714],{},[898,72766,4445],{},[898,72768,8195],{},[1712,72770,1904],{"stretchy":1903},[898,72772,1734],{},[1712,72774,1910],{"stretchy":1903},[902,72776,72777],{"encoding":904},"S(Q) = MC(Q)",[883,72779,72781],{"className":72780},[886],[888,72782,72783],{"xmlns":890},[892,72784,72785,72797],{},[895,72786,72787,72789,72791],{},[898,72788,1734],{},[1712,72790,2282],{},[2037,72792,72793,72795],{},[898,72794,1734],{},[1712,72796,2145],{},[902,72798,72799],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,72802,72804],{"className":72803},[886],[888,72805,72806],{"xmlns":890},[892,72807,72808,72812],{},[895,72809,72810],{},[1716,72811,2085],{},[902,72813,2085],{"encoding":904},[123,72815,72816,72817,72849],{},"V případě potřeby vyjádřete inverzi ",[883,72818,72820],{"className":72819},[886],[888,72821,72822],{"xmlns":890},[892,72823,72824,72846],{},[895,72825,72826,72828,72830,72840,72842,72844],{},[898,72827,1734],{},[1712,72829,1714],{},[2037,72831,72832,72834],{},[898,72833,6493],{},[895,72835,72836,72838],{},[1712,72837,2219],{},[1716,72839,2222],{},[1712,72841,1904],{"stretchy":1903},[898,72843,1710],{},[1712,72845,1910],{"stretchy":1903},[902,72847,72848],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,72851,72852],{},[614,72853,72854,72855,1343,72870,1655,72887,34076,72902,72915,72916,72941,72942,72955,72956,72973,72974,72991,72992,73009],{},"Obrázek 3.14: Křivky ",[883,72856,72858],{"className":72857},[886],[888,72859,72860],{"xmlns":890},[892,72861,72862,72868],{},[895,72863,72864,72866],{},[898,72865,2044],{},[898,72867,8195],{},[902,72869,60435],{"encoding":904},[883,72871,72873],{"className":72872},[886],[888,72874,72875],{"xmlns":890},[892,72876,72877,72885],{},[895,72878,72879,72881,72883],{},[898,72880,2044],{},[898,72882,45214],{},[898,72884,8195],{},[902,72886,60186],{"encoding":904},[883,72888,72890],{"className":72889},[886],[888,72891,72892],{"xmlns":890},[892,72893,72894,72900],{},[895,72895,72896,72898],{},[898,72897,4445],{},[898,72899,8195],{},[902,72901,60167],{"encoding":904},[883,72903,72905],{"className":72904},[886],[888,72906,72907],{"xmlns":890},[892,72908,72909,72913],{},[895,72910,72911],{},[898,72912,900],{},[902,72914,900],{"encoding":904},"; křivka nabídky ",[883,72917,72919],{"className":72918},[886],[888,72920,72921],{"xmlns":890},[892,72922,72923,72939],{},[895,72924,72925,72927,72929,72931,72933,72935,72937],{},[898,72926,1710],{},[1712,72928,1714],{},[898,72930,4445],{},[898,72932,8195],{},[1712,72934,1904],{"stretchy":1903},[898,72936,1734],{},[1712,72938,1910],{"stretchy":1903},[902,72940,72241],{"encoding":904}," začíná v bodě ",[883,72943,72945],{"className":72944},[886],[888,72946,72947],{"xmlns":890},[892,72948,72949,72953],{},[895,72950,72951],{},[898,72952,2044],{},[902,72954,2044],{"encoding":904}," odpovídajícím minimu ",[883,72957,72959],{"className":72958},[886],[888,72960,72961],{"xmlns":890},[892,72962,72963,72971],{},[895,72964,72965,72967,72969],{},[898,72966,2044],{},[898,72968,45214],{},[898,72970,8195],{},[902,72972,60186],{"encoding":904}," při ceně ",[883,72975,72977],{"className":72976},[886],[888,72978,72979],{"xmlns":890},[892,72980,72981,72989],{},[895,72982,72983],{},[2037,72984,72985,72987],{},[898,72986,1710],{},[1712,72988,2145],{},[902,72990,2195],{"encoding":904}," (minimální cena nabídky); pod ",[883,72993,72995],{"className":72994},[886],[888,72996,72997],{"xmlns":890},[892,72998,72999,73007],{},[895,73000,73001],{},[2037,73002,73003,73005],{},[898,73004,1734],{},[1712,73006,2145],{},[902,73008,34719],{"encoding":904}," je nabídka nulová.",[42223,73011,73013],{"id":73012},"příklad-312","Příklad 3.12",[724,73015,73016,62397,73018,73064],{},[38,73017,60862],{},[883,73019,73021],{"className":73020},[886],[888,73022,73023],{"xmlns":890},[892,73024,73025,73061],{},[895,73026,73027,73029,73031,73033,73035,73041,73043,73045,73051,73053,73055,73057,73059],{},[898,73028,1772],{},[898,73030,8195],{},[1712,73032,1714],{},[1716,73034,6607],{},[2037,73036,73037,73039],{},[898,73038,1734],{},[1716,73040,6198],{},[1712,73042,2219],{},[1716,73044,2787],{},[2037,73046,73047,73049],{},[898,73048,1734],{},[1716,73050,2787],{},[1712,73052,3145],{},[1716,73054,41119],{},[898,73056,1734],{},[1712,73058,3145],{},[1716,73060,1718],{},[902,73062,73063],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,73066,73067,3245,73069,73106,73107,2854],{},[38,73068,27645],{},[883,73070,73072],{"className":73071},[886],[888,73073,73074],{"xmlns":890},[892,73075,73076,73103],{},[895,73077,73078,73080,73082,73084,73087,73093,73095,73097,73099,73101],{},[898,73079,4445],{},[898,73081,8195],{},[1712,73083,1714],{},[1716,73085,73086],{},"0,3",[2037,73088,73089,73091],{},[898,73090,1734],{},[1716,73092,2787],{},[1712,73094,2219],{},[1716,73096,2975],{},[898,73098,1734],{},[1712,73100,3145],{},[1716,73102,41119],{},[902,73104,73105],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,73108,73110],{"className":73109},[886],[888,73111,73112],{"xmlns":890},[892,73113,73114,73124],{},[895,73115,73116,73118,73120,73122],{},[898,73117,1710],{},[1712,73119,1714],{},[898,73121,4445],{},[898,73123,8195],{},[902,73125,73126],{"encoding":904},"P = MC",[883,73128,73130],{"className":73129},[886],[888,73131,73132],{"xmlns":890,"display":32941},[892,73133,73134,73159],{},[895,73135,73136,73138,73140,73142,73148,73150,73152,73154,73156],{},[898,73137,1710],{},[1712,73139,1714],{},[1716,73141,73086],{},[2037,73143,73144,73146],{},[898,73145,1734],{},[1716,73147,2787],{},[1712,73149,2219],{},[1716,73151,2975],{},[898,73153,1734],{},[1712,73155,3145],{},[1716,73157,73158],{},"15.",[902,73160,73161],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,73163,73164,73165,3193,73178,73191],{},"Vyjádření ",[883,73166,73168],{"className":73167},[886],[888,73169,73170],{"xmlns":890},[892,73171,73172,73176],{},[895,73173,73174],{},[898,73175,1734],{},[902,73177,1734],{"encoding":904},[883,73179,73181],{"className":73180},[886],[888,73182,73183],{"xmlns":890},[892,73184,73185,73189],{},[895,73186,73187],{},[898,73188,1710],{},[902,73190,1710],{"encoding":904}," doplněním na čtverec:",[883,73193,73195],{"className":73194},[886],[888,73196,73197],{"xmlns":890,"display":32941},[892,73198,73199,73289],{},[895,73200,73201,73203,73205,73207,73245,73247,73249,73271,73273,73287],{},[898,73202,1710],{},[1712,73204,1714],{},[1716,73206,73086],{},[895,73208,73209,73211,73233,73235,73243],{},[1712,73210,1904],{"fence":2565},[2037,73212,73213,73231],{},[895,73214,73215,73217,73219,73221,73229],{},[1712,73216,1904],{"fence":2565},[898,73218,1734],{},[1712,73220,2219],{},[2563,73222,73223],{"scriptlevel":2085,"displaystyle":1903},[2567,73224,73225,73227],{},[1716,73226,6857],{},[1716,73228,6198],{},[1712,73230,1910],{"fence":2565},[1716,73232,2787],{},[1712,73234,3145],{},[2563,73236,73237],{"scriptlevel":2085,"displaystyle":1903},[2567,73238,73239,73241],{},[1716,73240,2782],{},[1716,73242,1780],{},[1712,73244,1910],{"fence":2565},[1712,73246,3138],{"separator":2565},[3690,73248],{"width":3692},[2037,73250,73251,73269],{},[895,73252,73253,73255,73257,73259,73267],{},[1712,73254,1904],{"fence":2565},[898,73256,1734],{},[1712,73258,2219],{},[2563,73260,73261],{"scriptlevel":2085,"displaystyle":1903},[2567,73262,73263,73265],{},[1716,73264,6857],{},[1716,73266,6198],{},[1712,73268,1910],{"fence":2565},[1716,73270,2787],{},[1712,73272,1714],{},[2567,73274,73275,73285],{},[895,73276,73277,73279,73281,73283],{},[1716,73278,42894],{},[898,73280,1710],{},[1712,73282,2219],{},[1716,73284,2782],{},[1716,73286,1780],{},[1712,73288,3138],{"separator":2565},[902,73290,73291],{"encoding":904},"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},",[883,73293,73295],{"className":73294},[886],[888,73296,73297],{"xmlns":890,"display":32941},[892,73298,73299,73331],{},[895,73300,73301,73303,73305,73311,73313,73329],{},[898,73302,1734],{},[1712,73304,1714],{},[2567,73306,73307,73309],{},[1716,73308,6857],{},[1716,73310,6198],{},[1712,73312,3145],{},[2567,73314,73315,73327],{},[5935,73316,73317],{},[895,73318,73319,73321,73323,73325],{},[1716,73320,42894],{},[898,73322,1710],{},[1712,73324,2219],{},[1716,73326,2782],{},[1716,73328,6198],{},[898,73330,1659],{"mathvariant":2003},[902,73332,73333],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,73335,71893,73336,1343,73374,1343,73422,73456,73457,1659],{},[883,73337,73339],{"className":73338},[886],[888,73340,73341],{"xmlns":890},[892,73342,73343,73371],{},[895,73344,73345,73347,73349,73351,73353,73355,73361,73363,73365,73367,73369],{},[898,73346,2044],{},[898,73348,45214],{},[898,73350,8195],{},[1712,73352,1714],{},[1716,73354,6607],{},[2037,73356,73357,73359],{},[898,73358,1734],{},[1716,73360,2787],{},[1712,73362,2219],{},[1716,73364,2787],{},[898,73366,1734],{},[1712,73368,3145],{},[1716,73370,41119],{},[902,73372,73373],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,73375,73377],{"className":73376},[886],[888,73378,73379],{"xmlns":890},[892,73380,73381,73419],{},[895,73382,73383,73385,73387,73393,73395,73397,73399,73401,73403,73405,73407,73409,73415,73417],{},[898,73384,2044],{},[898,73386,45214],{},[2037,73388,73389,73391],{},[898,73390,8195],{},[1712,73392,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,73394,1714],{},[1716,73396,6673],{},[898,73398,1734],{},[1712,73400,2219],{},[1716,73402,2787],{},[1712,73404,1714],{},[1716,73406,2085],{},[1712,73408,1767],{},[2037,73410,73411,73413],{},[898,73412,1734],{},[1712,73414,2145],{},[1712,73416,1714],{},[1716,73418,1718],{},[902,73420,73421],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,73423,73425],{"className":73424},[886],[888,73426,73427],{"xmlns":890},[892,73428,73429,73453],{},[895,73430,73431,73433,73435,73445,73447,73449,73451],{},[898,73432,2044],{},[898,73434,45214],{},[2037,73436,73437,73439],{},[898,73438,8195],{},[895,73440,73441,73443],{},[1712,73442,2243],{"mathvariant":2003},[1712,73444,2243],{"mathvariant":2003},[1712,73446,1714],{},[1716,73448,6673],{},[1712,73450,2302],{},[1716,73452,2085],{},[902,73454,73455],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,73458,73460],{"className":73459},[886],[888,73461,73462],{"xmlns":890},[892,73463,73464,73500],{},[895,73465,73466,73472,73474,73476,73478,73480,73482,73484,73486,73488,73490,73492,73494,73496,73498],{},[2037,73467,73468,73470],{},[898,73469,1710],{},[1712,73471,2145],{},[1712,73473,1714],{},[898,73475,4445],{},[898,73477,8195],{},[1712,73479,1904],{"stretchy":1903},[1716,73481,1718],{},[1712,73483,1910],{"stretchy":1903},[1712,73485,1714],{},[1716,73487,42894],{},[1712,73489,2219],{},[1716,73491,3018],{},[1712,73493,3145],{},[1716,73495,41119],{},[1712,73497,1714],{},[1716,73499,3068],{},[902,73501,73502],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,73504,73505],{},[38,73506,73507],{},"Závěr.",[883,73509,73511],{"className":73510},[886],[888,73512,73513],{"xmlns":890,"display":32941},[892,73514,73515,73601],{},[895,73516,73517,73519,73521,73523,73525,73527,73529,73531],{},[898,73518,1710],{},[1712,73520,1714],{},[898,73522,6493],{},[1712,73524,1904],{"stretchy":1903},[898,73526,1734],{},[1712,73528,1910],{"stretchy":1903},[1712,73530,1714],{},[895,73532,73533,73535],{},[1712,73534,72381],{"fence":2565},[25629,73536,73537,73579],{"rowspacing":72384,"columnalign":72385,"columnspacing":20158},[25634,73538,73539,73563],{},[25637,73540,73541],{},[2563,73542,73543],{"scriptlevel":2085,"displaystyle":1903},[895,73544,73545,73547,73553,73555,73557,73559,73561],{},[1716,73546,73086],{},[2037,73548,73549,73551],{},[898,73550,1734],{},[1716,73552,2787],{},[1712,73554,2219],{},[1716,73556,2975],{},[898,73558,1734],{},[1712,73560,3145],{},[1716,73562,41119],{},[25637,73564,73565],{},[2563,73566,73567],{"scriptlevel":2085,"displaystyle":1903},[895,73568,73569,73571,73573,73575,73577],{},[1762,73570,72412],{},[898,73572,1734],{},[1712,73574,2282],{},[1716,73576,1718],{},[1712,73578,3138],{"separator":2565},[25634,73580,73581,73587],{},[25637,73582,73583],{},[2563,73584,73585],{"scriptlevel":2085,"displaystyle":1903},[1716,73586,2085],{},[25637,73588,73589],{},[2563,73590,73591],{"scriptlevel":2085,"displaystyle":1903},[895,73592,73593,73595,73597,73599],{},[1762,73594,72412],{},[898,73596,1734],{},[1712,73598,2252],{},[1716,73600,24203],{},[902,73602,73603],{"encoding":904},"P = S(Q) = \\begin{cases} 0{,}3Q^2 - 4Q + 15 & \\text{pro } Q \\geq 10, \\\\ 0 & \\text{pro } Q \u003C 10. \\end{cases}",[724,73605,73606],{},[614,73607,73608,73609,73624,73625,1659],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,73610,73612],{"className":73611},[886],[888,73613,73614],{"xmlns":890},[892,73615,73616,73622],{},[895,73617,73618,73620],{},[898,73619,4445],{},[898,73621,8195],{},[902,73623,60167],{"encoding":904}," ležící nad minimem ",[883,73626,73628],{"className":73627},[886],[888,73629,73630],{"xmlns":890},[892,73631,73632,73640],{},[895,73633,73634,73636,73638],{},[898,73635,2044],{},[898,73637,45214],{},[898,73639,8195],{},[902,73641,60186],{"encoding":904},[115,73643,73645],{"id":73644},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,73647,73648,73649,73653,73654,73669,73670,73690,73691,1655,73694,73697,73698,73700,73701,24820,73723,73725,73726,1655,73728,63601,73731,3245,73734,46689,73749,73764],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,73650,73652],{"className":73651,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,73655,73657],{"className":73656},[886],[888,73658,73659],{"xmlns":890},[892,73660,73661,73667],{},[895,73662,73663,73665],{},[898,73664,1772],{},[898,73666,1775],{},[902,73668,1877],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,73671,73673],{"className":73672},[886],[888,73674,73675],{"xmlns":890},[892,73676,73677,73687],{},[895,73678,73679,73681,73683,73685],{},[898,73680,1772],{},[898,73682,1775],{},[898,73684,2473],{"mathvariant":2003},[898,73686,1734],{},[902,73688,73689],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,73692,73693],{},"fixních",[38,73695,73696],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,73699,69200],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,73702,73704],{"className":73703},[886],[888,73705,73706],{"xmlns":890},[892,73707,73708,73720],{},[895,73709,73710,73712,73714,73716,73718],{},[898,73711,1772],{},[898,73713,1775],{},[1712,73715,2219],{},[898,73717,1772],{},[898,73719,8195],{},[902,73721,73722],{"encoding":904},"TR - TC",[38,73724,60047],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,73727,61359],{},[38,73729,73730],{},"mezní náklady",[207,73732,1145],{"className":73733,"dataFsResolvedFilePath":764,"href":765},[210],[883,73735,73737],{"className":73736},[886],[888,73738,73739],{"xmlns":890},[892,73740,73741,73747],{},[895,73742,73743,73745],{},[898,73744,1772],{},[898,73746,1775],{},[902,73748,1877],{"encoding":904},[883,73750,73752],{"className":73751},[886],[888,73753,73754],{"xmlns":890},[892,73755,73756,73762],{},[895,73757,73758,73760],{},[898,73759,1772],{},[898,73761,8195],{},[902,73763,8648],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,73766,73767,73829,73895,73957],{},[123,73768,73769,73772,73773,15266,73788,1659],{},[38,73770,73771],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,73774,73776],{"className":73775},[886],[888,73777,73778],{"xmlns":890},[892,73779,73780,73786],{},[895,73781,73782,73784],{},[898,73783,2044],{},[898,73785,8195],{},[902,73787,60435],{"encoding":904},[883,73789,73791],{"className":73790},[886],[888,73792,73793],{"xmlns":890},[892,73794,73795,73827],{},[895,73796,73797,73799,73801,73803,73809,73811,73813,73815,73817,73819,73825],{},[898,73798,2044],{},[898,73800,8195],{},[1712,73802,1904],{"stretchy":1903},[6927,73804,73805,73807],{},[898,73806,1734],{},[1716,73808,2085],{},[1712,73810,1910],{"stretchy":1903},[1712,73812,1714],{},[898,73814,4445],{},[898,73816,8195],{},[1712,73818,1904],{"stretchy":1903},[6927,73820,73821,73823],{},[898,73822,1734],{},[1716,73824,2085],{},[1712,73826,1910],{"stretchy":1903},[902,73828,67444],{"encoding":904},[123,73830,73831,73772,73834,15266,73851,1659],{},[38,73832,73833],{},"Princip minimalizace průměrných variabilních nákladů:",[883,73835,73837],{"className":73836},[886],[888,73838,73839],{"xmlns":890},[892,73840,73841,73849],{},[895,73842,73843,73845,73847],{},[898,73844,2044],{},[898,73846,45214],{},[898,73848,8195],{},[902,73850,60186],{"encoding":904},[883,73852,73854],{"className":73853},[886],[888,73855,73856],{"xmlns":890},[892,73857,73858,73892],{},[895,73859,73860,73862,73864,73866,73868,73874,73876,73878,73880,73882,73884,73890],{},[898,73861,2044],{},[898,73863,45214],{},[898,73865,8195],{},[1712,73867,1904],{"stretchy":1903},[6927,73869,73870,73872],{},[898,73871,1734],{},[1716,73873,2085],{},[1712,73875,1910],{"stretchy":1903},[1712,73877,1714],{},[898,73879,4445],{},[898,73881,8195],{},[1712,73883,1904],{"stretchy":1903},[6927,73885,73886,73888],{},[898,73887,1734],{},[1716,73889,2085],{},[1712,73891,1910],{"stretchy":1903},[902,73893,73894],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,73896,73897,73900,73901,15266,73916,1659],{},[38,73898,73899],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,73902,73904],{"className":73903},[886],[888,73905,73906],{"xmlns":890},[892,73907,73908,73914],{},[895,73909,73910,73912],{},[898,73911,1710],{},[898,73913,1775],{},[902,73915,68354],{"encoding":904},[883,73917,73919],{"className":73918},[886],[888,73920,73921],{"xmlns":890},[892,73922,73923,73955],{},[895,73924,73925,73927,73929,73931,73937,73939,73941,73943,73945,73947,73953],{},[898,73926,4445],{},[898,73928,1775],{},[1712,73930,1904],{"stretchy":1903},[6927,73932,73933,73935],{},[898,73934,1734],{},[1716,73936,2085],{},[1712,73938,1910],{"stretchy":1903},[1712,73940,1714],{},[898,73942,4445],{},[898,73944,8195],{},[1712,73946,1904],{"stretchy":1903},[6927,73948,73949,73951],{},[898,73950,1734],{},[1716,73952,2085],{},[1712,73954,1910],{"stretchy":1903},[902,73956,70520],{"encoding":904},[123,73958,73959,3245,73962,4288,73998,72800,74019,26469,74032,72482,74049,1659],{},[38,73960,73961],{},"Funkce nabídky firmy:",[883,73963,73965],{"className":73964},[886],[888,73966,73967],{"xmlns":890},[892,73968,73969,73995],{},[895,73970,73971,73973,73975,73977,73979,73981,73983,73985,73987,73989,73991,73993],{},[898,73972,1710],{},[1712,73974,1714],{},[898,73976,6493],{},[1712,73978,1904],{"stretchy":1903},[898,73980,1734],{},[1712,73982,1910],{"stretchy":1903},[1712,73984,1714],{},[898,73986,4445],{},[898,73988,8195],{},[1712,73990,1904],{"stretchy":1903},[898,73992,1734],{},[1712,73994,1910],{"stretchy":1903},[902,73996,73997],{"encoding":904},"P = S(Q) = MC(Q)",[883,73999,74001],{"className":74000},[886],[888,74002,74003],{"xmlns":890},[892,74004,74005,74017],{},[895,74006,74007,74009,74011],{},[898,74008,1734],{},[1712,74010,2282],{},[2037,74012,74013,74015],{},[898,74014,1734],{},[1712,74016,2145],{},[902,74018,72799],{"encoding":904},[883,74020,74022],{"className":74021},[886],[888,74023,74024],{"xmlns":890},[892,74025,74026,74030],{},[895,74027,74028],{},[1716,74029,2085],{},[902,74031,2085],{"encoding":904},[883,74033,74035],{"className":74034},[886],[888,74036,74037],{"xmlns":890},[892,74038,74039,74047],{},[895,74040,74041],{},[2037,74042,74043,74045],{},[898,74044,1734],{},[1712,74046,2145],{},[902,74048,34719],{"encoding":904},[883,74050,74052],{"className":74051},[886],[888,74053,74054],{"xmlns":890},[892,74055,74056,74064],{},[895,74057,74058,74060,74062],{},[898,74059,2044],{},[898,74061,45214],{},[898,74063,8195],{},[902,74065,60186],{"encoding":904},[115,74067,54757],{"id":54756},[152,74069,74070,74073,74076,74079,74082,74085,74088,74091,74094,74097,74100],{},[123,74071,74072],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,74074,74075],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,74077,74078],{},"Jak se vypočte mezní příjem a co udává?",[123,74080,74081],{},"Z jakých složek se skládají celkové náklady?",[123,74083,74084],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,74086,74087],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,74089,74090],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,74092,74093],{},"Jak se vypočte zisk?",[123,74095,74096],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,74098,74099],{},"Co jsou body zvratu? Jak se najdou?",[123,74101,74102],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,74104,74106],{"id":74105},"úlohy-31328","Úlohy 3.1–3.28",[198,74108,74110],{"id":74109},"příjem-3135","Příjem (3.1–3.5)",[724,74112,74113,50301,74116,74144,74145,74160,74161,74176,74177,74192,74193,1343,74208,1343,74223,74238],{},[38,74114,74115],{},"3.1",[883,74117,74119],{"className":74118},[886],[888,74120,74121],{"xmlns":890},[892,74122,74123,74141],{},[895,74124,74125,74127,74129,74131,74133,74135,74137,74139],{},[898,74126,1710],{},[1712,74128,1714],{},[898,74130,1969],{},[1712,74132,1904],{"stretchy":1903},[898,74134,1734],{},[1712,74136,1910],{"stretchy":1903},[1712,74138,1714],{},[1716,74140,1739],{},[902,74142,74143],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,74146,74148],{"className":74147},[886],[888,74149,74150],{"xmlns":890},[892,74151,74152,74158],{},[895,74153,74154,74156],{},[898,74155,1772],{},[898,74157,1775],{},[902,74159,1877],{"encoding":904},", průměrný příjem ",[883,74162,74164],{"className":74163},[886],[888,74165,74166],{"xmlns":890},[892,74167,74168,74174],{},[895,74169,74170,74172],{},[898,74171,2044],{},[898,74173,1775],{},[902,74175,60320],{"encoding":904}," a mezní příjem ",[883,74178,74180],{"className":74179},[886],[888,74181,74182],{"xmlns":890},[892,74183,74184,74190],{},[895,74185,74186,74188],{},[898,74187,4445],{},[898,74189,1775],{},[902,74191,4450],{"encoding":904},". (c) Vypočtěte ",[883,74194,74196],{"className":74195},[886],[888,74197,74198],{"xmlns":890},[892,74199,74200,74206],{},[895,74201,74202,74204],{},[898,74203,1772],{},[898,74205,1775],{},[902,74207,1877],{"encoding":904},[883,74209,74211],{"className":74210},[886],[888,74212,74213],{"xmlns":890},[892,74214,74215,74221],{},[895,74216,74217,74219],{},[898,74218,2044],{},[898,74220,1775],{},[902,74222,60320],{"encoding":904},[883,74224,74226],{"className":74225},[886],[888,74227,74228],{"xmlns":890},[892,74229,74230,74236],{},[895,74231,74232,74234],{},[898,74233,4445],{},[898,74235,1775],{},[902,74237,4450],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,74240,74241,50301,74244,74144,74280,74160,74295,74176,74310,74192,74325,1343,74340,1343,74355,74370],{},[38,74242,74243],{},"3.2",[883,74245,74247],{"className":74246},[886],[888,74248,74249],{"xmlns":890},[892,74250,74251,74277],{},[895,74252,74253,74255,74257,74259,74261,74263,74265,74267,74269,74271,74273,74275],{},[898,74254,1710],{},[1712,74256,1714],{},[898,74258,1969],{},[1712,74260,1904],{"stretchy":1903},[898,74262,1734],{},[1712,74264,1910],{"stretchy":1903},[1712,74266,1714],{},[1712,74268,2219],{},[1716,74270,2814],{},[898,74272,1734],{},[1712,74274,3145],{},[1716,74276,6857],{},[902,74278,74279],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,74281,74283],{"className":74282},[886],[888,74284,74285],{"xmlns":890},[892,74286,74287,74293],{},[895,74288,74289,74291],{},[898,74290,1772],{},[898,74292,1775],{},[902,74294,1877],{"encoding":904},[883,74296,74298],{"className":74297},[886],[888,74299,74300],{"xmlns":890},[892,74301,74302,74308],{},[895,74303,74304,74306],{},[898,74305,2044],{},[898,74307,1775],{},[902,74309,60320],{"encoding":904},[883,74311,74313],{"className":74312},[886],[888,74314,74315],{"xmlns":890},[892,74316,74317,74323],{},[895,74318,74319,74321],{},[898,74320,4445],{},[898,74322,1775],{},[902,74324,4450],{"encoding":904},[883,74326,74328],{"className":74327},[886],[888,74329,74330],{"xmlns":890},[892,74331,74332,74338],{},[895,74333,74334,74336],{},[898,74335,1772],{},[898,74337,1775],{},[902,74339,1877],{"encoding":904},[883,74341,74343],{"className":74342},[886],[888,74344,74345],{"xmlns":890},[892,74346,74347,74353],{},[895,74348,74349,74351],{},[898,74350,2044],{},[898,74352,1775],{},[902,74354,60320],{"encoding":904},[883,74356,74358],{"className":74357},[886],[888,74359,74360],{"xmlns":890},[892,74361,74362,74368],{},[895,74363,74364,74366],{},[898,74365,4445],{},[898,74367,1775],{},[902,74369,4450],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,74372,74373,50301,74376,74413,74414,74160,74429,74176,74444,74459,74460,4288,74475,74501,74502,74517,74518,1343,74533,4288,74548,74501,74573,74588,74589,74602,74603,74618,74619,74634,74635,1343,74648,1343,74663,1343,74678,1659],{},[38,74374,74375],{},"3.3",[883,74377,74379],{"className":74378},[886],[888,74380,74381],{"xmlns":890},[892,74382,74383,74410],{},[895,74384,74385,74387,74389,74391,74393,74395,74397,74399,74402,74404],{},[898,74386,1710],{},[1712,74388,1714],{},[898,74390,1969],{},[1712,74392,1904],{"stretchy":1903},[898,74394,1734],{},[1712,74396,1910],{"stretchy":1903},[1712,74398,1714],{},[1716,74400,74401],{},"1200",[1712,74403,2219],{},[2037,74405,74406,74408],{},[898,74407,1734],{},[1716,74409,2787],{},[902,74411,74412],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,74415,74417],{"className":74416},[886],[888,74418,74419],{"xmlns":890},[892,74420,74421,74427],{},[895,74422,74423,74425],{},[898,74424,1772],{},[898,74426,1775],{},[902,74428,1877],{"encoding":904},[883,74430,74432],{"className":74431},[886],[888,74433,74434],{"xmlns":890},[892,74435,74436,74442],{},[895,74437,74438,74440],{},[898,74439,2044],{},[898,74441,1775],{},[902,74443,60320],{"encoding":904},[883,74445,74447],{"className":74446},[886],[888,74448,74449],{"xmlns":890},[892,74450,74451,74457],{},[895,74452,74453,74455],{},[898,74454,4445],{},[898,74456,1775],{},[902,74458,4450],{"encoding":904},". (b) Vypočtěte ",[883,74461,74463],{"className":74462},[886],[888,74464,74465],{"xmlns":890},[892,74466,74467,74473],{},[895,74468,74469,74471],{},[898,74470,1772],{},[898,74472,1775],{},[902,74474,1877],{"encoding":904},[883,74476,74478],{"className":74477},[886],[888,74479,74480],{"xmlns":890},[892,74481,74482,74498],{},[895,74483,74484,74486,74488,74490,74492,74494,74496],{},[898,74485,1734],{},[1712,74487,1714],{},[1716,74489,1718],{},[1712,74491,3138],{"separator":2565},[1716,74493,6857],{},[1712,74495,3138],{"separator":2565},[1716,74497,42894],{},[902,74499,74500],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,74503,74505],{"className":74504},[886],[888,74506,74507],{"xmlns":890},[892,74508,74509,74515],{},[895,74510,74511,74513],{},[898,74512,1772],{},[898,74514,1775],{},[902,74516,1877],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,74519,74521],{"className":74520},[886],[888,74522,74523],{"xmlns":890},[892,74524,74525,74531],{},[895,74526,74527,74529],{},[898,74528,2044],{},[898,74530,1775],{},[902,74532,60320],{"encoding":904},[883,74534,74536],{"className":74535},[886],[888,74537,74538],{"xmlns":890},[892,74539,74540,74546],{},[895,74541,74542,74544],{},[898,74543,4445],{},[898,74545,1775],{},[902,74547,4450],{"encoding":904},[883,74549,74551],{"className":74550},[886],[888,74552,74553],{"xmlns":890},[892,74554,74555,74571],{},[895,74556,74557,74559,74561,74563,74565,74567,74569],{},[898,74558,1734],{},[1712,74560,1714],{},[1716,74562,1718],{},[1712,74564,3138],{"separator":2565},[1716,74566,6857],{},[1712,74568,3138],{"separator":2565},[1716,74570,42894],{},[902,74572,74500],{"encoding":904},[883,74574,74576],{"className":74575},[886],[888,74577,74578],{"xmlns":890},[892,74579,74580,74586],{},[895,74581,74582,74584],{},[898,74583,4445],{},[898,74585,1775],{},[902,74587,4450],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,74590,74592],{"className":74591},[886],[888,74593,74594],{"xmlns":890},[892,74595,74596,74600],{},[895,74597,74598],{},[898,74599,1734],{},[902,74601,1734],{"encoding":904},", které maximalizuje ",[883,74604,74606],{"className":74605},[886],[888,74607,74608],{"xmlns":890},[892,74609,74610,74616],{},[895,74611,74612,74614],{},[898,74613,1772],{},[898,74615,1775],{},[902,74617,1877],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,74620,74622],{"className":74621},[886],[888,74623,74624],{"xmlns":890},[892,74625,74626,74632],{},[895,74627,74628,74630],{},[898,74629,1772],{},[898,74631,1775],{},[902,74633,1877],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,74636,74638],{"className":74637},[886],[888,74639,74640],{"xmlns":890},[892,74641,74642,74646],{},[895,74643,74644],{},[898,74645,1969],{},[902,74647,1969],{"encoding":904},[883,74649,74651],{"className":74650},[886],[888,74652,74653],{"xmlns":890},[892,74654,74655,74661],{},[895,74656,74657,74659],{},[898,74658,1772],{},[898,74660,1775],{},[902,74662,1877],{"encoding":904},[883,74664,74666],{"className":74665},[886],[888,74667,74668],{"xmlns":890},[892,74669,74670,74676],{},[895,74671,74672,74674],{},[898,74673,2044],{},[898,74675,1775],{},[902,74677,60320],{"encoding":904},[883,74679,74681],{"className":74680},[886],[888,74682,74683],{"xmlns":890},[892,74684,74685,74691],{},[895,74686,74687,74689],{},[898,74688,4445],{},[898,74690,1775],{},[902,74692,4450],{"encoding":904},[724,74694,74695,74698,74699,74729,74730,74745,74746,15029,74759,1343,74777,1343,74794,74812,74813,74835,74836,74851,74852,74865,74866,1659],{},[38,74696,74697],{},"3.4"," Je dán celkový příjem ",[883,74700,74702],{"className":74701},[886],[888,74703,74704],{"xmlns":890},[892,74705,74706,74726],{},[895,74707,74708,74710,74712,74714,74716,74718,74720],{},[898,74709,1772],{},[898,74711,1775],{},[1712,74713,1714],{},[1716,74715,74401],{},[898,74717,1734],{},[1712,74719,2219],{},[2037,74721,74722,74724],{},[898,74723,1734],{},[1716,74725,6198],{},[902,74727,74728],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,74731,74733],{"className":74732},[886],[888,74734,74735],{"xmlns":890},[892,74736,74737,74743],{},[895,74738,74739,74741],{},[898,74740,1772],{},[898,74742,1775],{},[902,74744,1877],{"encoding":904}," vzhledem ke ",[883,74747,74749],{"className":74748},[886],[888,74750,74751],{"xmlns":890},[892,74752,74753,74757],{},[895,74754,74755],{},[898,74756,1734],{},[902,74758,1734],{"encoding":904},[883,74760,74762],{"className":74761},[886],[888,74763,74764],{"xmlns":890},[892,74765,74766,74774],{},[895,74767,74768,74770,74772],{},[898,74769,1734],{},[1712,74771,1714],{},[1716,74773,3068],{},[902,74775,74776],{"encoding":904},"Q = 5",[883,74778,74780],{"className":74779},[886],[888,74781,74782],{"xmlns":890},[892,74783,74784,74792],{},[895,74785,74786,74788,74790],{},[898,74787,1734],{},[1712,74789,1714],{},[1716,74791,3397],{},[902,74793,3400],{"encoding":904},[883,74795,74797],{"className":74796},[886],[888,74798,74799],{"xmlns":890},[892,74800,74801,74809],{},[895,74802,74803,74805,74807],{},[898,74804,1734],{},[1712,74806,1714],{},[1716,74808,8912],{},[902,74810,74811],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,74814,74816],{"className":74815},[886],[888,74817,74818],{"xmlns":890},[892,74819,74820,74832],{},[895,74821,74822,74824,74826,74828,74830],{},[898,74823,4445],{},[898,74825,1775],{},[1712,74827,1904],{"stretchy":1903},[1716,74829,1718],{},[1712,74831,1910],{"stretchy":1903},[902,74833,74834],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,74837,74839],{"className":74838},[886],[888,74840,74841],{"xmlns":890},[892,74842,74843,74849],{},[895,74844,74845,74847],{},[898,74846,1772],{},[898,74848,1775],{},[902,74850,1877],{"encoding":904},", jestliže se ",[883,74853,74855],{"className":74854},[886],[888,74856,74857],{"xmlns":890},[892,74858,74859,74863],{},[895,74860,74861],{},[898,74862,1734],{},[902,74864,1734],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,74867,74869],{"className":74868},[886],[888,74870,74871],{"xmlns":890},[892,74872,74873,74879],{},[895,74874,74875,74877],{},[898,74876,1772],{},[898,74878,1775],{},[902,74880,1877],{"encoding":904},[724,74882,74883,74886,74887,74913,74914,74929,74930,74851,74945,74958],{},[38,74884,74885],{},"3.5"," Je dán mezní příjem ",[883,74888,74890],{"className":74889},[886],[888,74891,74892],{"xmlns":890},[892,74893,74894,74910],{},[895,74895,74896,74898,74900,74902,74904,74906,74908],{},[898,74897,4445],{},[898,74899,1775],{},[1712,74901,1714],{},[1712,74903,2219],{},[898,74905,1734],{},[1712,74907,3145],{},[1716,74909,6857],{},[902,74911,74912],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,74915,74917],{"className":74916},[886],[888,74918,74919],{"xmlns":890},[892,74920,74921,74927],{},[895,74922,74923,74925],{},[898,74924,1772],{},[898,74926,1775],{},[902,74928,1877],{"encoding":904},". (b) Vypočtěte změnu ",[883,74931,74933],{"className":74932},[886],[888,74934,74935],{"xmlns":890},[892,74936,74937,74943],{},[895,74938,74939,74941],{},[898,74940,1772],{},[898,74942,1775],{},[902,74944,1877],{"encoding":904},[883,74946,74948],{"className":74947},[886],[888,74949,74950],{"xmlns":890},[892,74951,74952,74956],{},[895,74953,74954],{},[898,74955,1734],{},[902,74957,1734],{"encoding":904}," změní z 8 na 12.",[198,74960,74962],{"id":74961},"náklady-36316","Náklady (3.6–3.16)",[724,74964,74965,74968,74969,75009,75010,75025,75026,75043,75044,75061,75062,75077,75078,75093,75094,74459,75109,1343,75124,1343,75141,1343,75158,1343,75173,1343,75188,4288,75203,75221,75222,1343,75237,1343,75252,75267],{},[38,74966,74967],{},"3.6"," Jsou dány celkové náklady ",[883,74970,74972],{"className":74971},[886],[888,74973,74974],{"xmlns":890},[892,74975,74976,75006],{},[895,74977,74978,74980,74982,74984,74986,74988,74990,74992,74994],{},[898,74979,1772],{},[898,74981,8195],{},[1712,74983,1714],{},[1716,74985,1739],{},[1712,74987,3145],{},[1716,74989,2787],{},[898,74991,1734],{},[1712,74993,3145],{},[2563,74995,74996],{"scriptlevel":2085,"displaystyle":1903},[2567,74997,74998,75004],{},[2037,74999,75000,75002],{},[898,75001,1734],{},[1716,75003,2787],{},[1716,75005,1718],{},[902,75007,75008],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,75011,75013],{"className":75012},[886],[888,75014,75015],{"xmlns":890},[892,75016,75017,75023],{},[895,75018,75019,75021],{},[898,75020,15308],{},[898,75022,8195],{},[902,75024,60366],{"encoding":904},", celkové variabilní náklady ",[883,75027,75029],{"className":75028},[886],[888,75030,75031],{"xmlns":890},[892,75032,75033,75041],{},[895,75034,75035,75037,75039],{},[898,75036,1772],{},[898,75038,45214],{},[898,75040,8195],{},[902,75042,60384],{"encoding":904},", průměrné variabilní náklady ",[883,75045,75047],{"className":75046},[886],[888,75048,75049],{"xmlns":890},[892,75050,75051,75059],{},[895,75052,75053,75055,75057],{},[898,75054,2044],{},[898,75056,45214],{},[898,75058,8195],{},[902,75060,60186],{"encoding":904},", variabilní náklady na jednotku ",[883,75063,75065],{"className":75064},[886],[888,75066,75067],{"xmlns":890},[892,75068,75069,75075],{},[895,75070,75071,75073],{},[898,75072,45214],{},[898,75074,8195],{},[902,75076,68480],{"encoding":904},", průměrné náklady ",[883,75079,75081],{"className":75080},[886],[888,75082,75083],{"xmlns":890},[892,75084,75085,75091],{},[895,75086,75087,75089],{},[898,75088,2044],{},[898,75090,8195],{},[902,75092,60435],{"encoding":904}," a mezní náklady ",[883,75095,75097],{"className":75096},[886],[888,75098,75099],{"xmlns":890},[892,75100,75101,75107],{},[895,75102,75103,75105],{},[898,75104,4445],{},[898,75106,8195],{},[902,75108,60167],{"encoding":904},[883,75110,75112],{"className":75111},[886],[888,75113,75114],{"xmlns":890},[892,75115,75116,75122],{},[895,75117,75118,75120],{},[898,75119,1772],{},[898,75121,8195],{},[902,75123,8648],{"encoding":904},[883,75125,75127],{"className":75126},[886],[888,75128,75129],{"xmlns":890},[892,75130,75131,75139],{},[895,75132,75133,75135,75137],{},[898,75134,1772],{},[898,75136,45214],{},[898,75138,8195],{},[902,75140,60384],{"encoding":904},[883,75142,75144],{"className":75143},[886],[888,75145,75146],{"xmlns":890},[892,75147,75148,75156],{},[895,75149,75150,75152,75154],{},[898,75151,2044],{},[898,75153,45214],{},[898,75155,8195],{},[902,75157,60186],{"encoding":904},[883,75159,75161],{"className":75160},[886],[888,75162,75163],{"xmlns":890},[892,75164,75165,75171],{},[895,75166,75167,75169],{},[898,75168,45214],{},[898,75170,8195],{},[902,75172,68480],{"encoding":904},[883,75174,75176],{"className":75175},[886],[888,75177,75178],{"xmlns":890},[892,75179,75180,75186],{},[895,75181,75182,75184],{},[898,75183,2044],{},[898,75185,8195],{},[902,75187,60435],{"encoding":904},[883,75189,75191],{"className":75190},[886],[888,75192,75193],{"xmlns":890},[892,75194,75195,75201],{},[895,75196,75197,75199],{},[898,75198,4445],{},[898,75200,8195],{},[902,75202,60167],{"encoding":904},[883,75204,75206],{"className":75205},[886],[888,75207,75208],{"xmlns":890},[892,75209,75210,75218],{},[895,75211,75212,75214,75216],{},[898,75213,1734],{},[1712,75215,1714],{},[1716,75217,2782],{},[902,75219,75220],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,75223,75225],{"className":75224},[886],[888,75226,75227],{"xmlns":890},[892,75228,75229,75235],{},[895,75230,75231,75233],{},[898,75232,1772],{},[898,75234,8195],{},[902,75236,8648],{"encoding":904},[883,75238,75240],{"className":75239},[886],[888,75241,75242],{"xmlns":890},[892,75243,75244,75250],{},[895,75245,75246,75248],{},[898,75247,2044],{},[898,75249,8195],{},[902,75251,60435],{"encoding":904},[883,75253,75255],{"className":75254},[886],[888,75256,75257],{"xmlns":890},[892,75258,75259,75265],{},[895,75260,75261,75263],{},[898,75262,4445],{},[898,75264,8195],{},[902,75266,60167],{"encoding":904}," rostou, resp. klesají.",[724,75269,75270,75273,75274,75093,75304,75319,75320,75335,75336,1343,75351,1343,75366,1659],{},[38,75271,75272],{},"3.7"," Jsou dány průměrné náklady ",[883,75275,75277],{"className":75276},[886],[888,75278,75279],{"xmlns":890},[892,75280,75281,75301],{},[895,75282,75283,75285,75287,75289,75297,75299],{},[898,75284,2044],{},[898,75286,8195],{},[1712,75288,1714],{},[2563,75290,75291],{"scriptlevel":2085,"displaystyle":1903},[2567,75292,75293,75295],{},[1716,75294,1739],{},[898,75296,1734],{},[1712,75298,3145],{},[1716,75300,6857],{},[902,75302,75303],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,75305,75307],{"className":75306},[886],[888,75308,75309],{"xmlns":890},[892,75310,75311,75317],{},[895,75312,75313,75315],{},[898,75314,4445],{},[898,75316,8195],{},[902,75318,60167],{"encoding":904},". (a) Určete celkové náklady ",[883,75321,75323],{"className":75322},[886],[888,75324,75325],{"xmlns":890},[892,75326,75327,75333],{},[895,75328,75329,75331],{},[898,75330,1772],{},[898,75332,8195],{},[902,75334,8648],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,75337,75339],{"className":75338},[886],[888,75340,75341],{"xmlns":890},[892,75342,75343,75349],{},[895,75344,75345,75347],{},[898,75346,2044],{},[898,75348,8195],{},[902,75350,60435],{"encoding":904},[883,75352,75354],{"className":75353},[886],[888,75355,75356],{"xmlns":890},[892,75357,75358,75364],{},[895,75359,75360,75362],{},[898,75361,1772],{},[898,75363,8195],{},[902,75365,8648],{"encoding":904},[883,75367,75369],{"className":75368},[886],[888,75370,75371],{"xmlns":890},[892,75372,75373,75379],{},[895,75374,75375,75377],{},[898,75376,4445],{},[898,75378,8195],{},[902,75380,60167],{"encoding":904},[724,75382,75383,74968,75386,75430,75431,1343,75448,1343,75463,1343,75480,1343,75495,1343,75512,1659],{},[38,75384,75385],{},"3.8",[883,75387,75389],{"className":75388},[886],[888,75390,75391],{"xmlns":890},[892,75392,75393,75427],{},[895,75394,75395,75397,75399,75401,75403,75405,75407,75409,75411,75413,75419,75421],{},[898,75396,1772],{},[898,75398,8195],{},[1712,75400,1714],{},[1716,75402,51578],{},[1712,75404,3145],{},[1716,75406,42894],{},[898,75408,1734],{},[1712,75410,2219],{},[1716,75412,6209],{},[2037,75414,75415,75417],{},[898,75416,1734],{},[1716,75418,2787],{},[1712,75420,3145],{},[2037,75422,75423,75425],{},[898,75424,1734],{},[1716,75426,6198],{},[902,75428,75429],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,75432,75434],{"className":75433},[886],[888,75435,75436],{"xmlns":890},[892,75437,75438,75446],{},[895,75439,75440,75442,75444],{},[898,75441,1772],{},[898,75443,45214],{},[898,75445,8195],{},[902,75447,60384],{"encoding":904},[883,75449,75451],{"className":75450},[886],[888,75452,75453],{"xmlns":890},[892,75454,75455,75461],{},[895,75456,75457,75459],{},[898,75458,15308],{},[898,75460,8195],{},[902,75462,60366],{"encoding":904},[883,75464,75466],{"className":75465},[886],[888,75467,75468],{"xmlns":890},[892,75469,75470,75478],{},[895,75471,75472,75474,75476],{},[898,75473,2044],{},[898,75475,45214],{},[898,75477,8195],{},[902,75479,60186],{"encoding":904},[883,75481,75483],{"className":75482},[886],[888,75484,75485],{"xmlns":890},[892,75486,75487,75493],{},[895,75488,75489,75491],{},[898,75490,2044],{},[898,75492,8195],{},[902,75494,60435],{"encoding":904},[883,75496,75498],{"className":75497},[886],[888,75499,75500],{"xmlns":890},[892,75501,75502,75510],{},[895,75503,75504,75506,75508],{},[898,75505,2044],{},[898,75507,15308],{},[898,75509,8195],{},[902,75511,60402],{"encoding":904},[883,75513,75515],{"className":75514},[886],[888,75516,75517],{"xmlns":890},[892,75518,75519,75525],{},[895,75520,75521,75523],{},[898,75522,4445],{},[898,75524,8195],{},[902,75526,60167],{"encoding":904},[724,75528,75529,74968,75532,75562,75563,74745,75578,4288,75591,1343,75609,1343,75627,74812,75645,74835,75667,75682,75683,75696,75697,1659],{},[38,75530,75531],{},"3.9",[883,75533,75535],{"className":75534},[886],[888,75536,75537],{"xmlns":890},[892,75538,75539,75559],{},[895,75540,75541,75543,75545,75547,75549,75551,75553],{},[898,75542,1772],{},[898,75544,8195],{},[1712,75546,1714],{},[1716,75548,19984],{},[1712,75550,3145],{},[1716,75552,24196],{},[2037,75554,75555,75557],{},[898,75556,1734],{},[1716,75558,2787],{},[902,75560,75561],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,75564,75566],{"className":75565},[886],[888,75567,75568],{"xmlns":890},[892,75569,75570,75576],{},[895,75571,75572,75574],{},[898,75573,1772],{},[898,75575,8195],{},[902,75577,8648],{"encoding":904},[883,75579,75581],{"className":75580},[886],[888,75582,75583],{"xmlns":890},[892,75584,75585,75589],{},[895,75586,75587],{},[898,75588,1734],{},[902,75590,1734],{"encoding":904},[883,75592,75594],{"className":75593},[886],[888,75595,75596],{"xmlns":890},[892,75597,75598,75606],{},[895,75599,75600,75602,75604],{},[898,75601,1734],{},[1712,75603,1714],{},[1716,75605,1718],{},[902,75607,75608],{"encoding":904},"Q = 10",[883,75610,75612],{"className":75611},[886],[888,75613,75614],{"xmlns":890},[892,75615,75616,75624],{},[895,75617,75618,75620,75622],{},[898,75619,1734],{},[1712,75621,1714],{},[1716,75623,6857],{},[902,75625,75626],{"encoding":904},"Q = 20",[883,75628,75630],{"className":75629},[886],[888,75631,75632],{"xmlns":890},[892,75633,75634,75642],{},[895,75635,75636,75638,75640],{},[898,75637,1734],{},[1712,75639,1714],{},[1716,75641,42894],{},[902,75643,75644],{"encoding":904},"Q = 30",[883,75646,75648],{"className":75647},[886],[888,75649,75650],{"xmlns":890},[892,75651,75652,75664],{},[895,75653,75654,75656,75658,75660,75662],{},[898,75655,4445],{},[898,75657,8195],{},[1712,75659,1904],{"stretchy":1903},[1716,75661,41119],{},[1712,75663,1910],{"stretchy":1903},[902,75665,75666],{"encoding":904},"MC(15)",[883,75668,75670],{"className":75669},[886],[888,75671,75672],{"xmlns":890},[892,75673,75674,75680],{},[895,75675,75676,75678],{},[898,75677,1772],{},[898,75679,8195],{},[902,75681,8648],{"encoding":904}," v důsledku změny ",[883,75684,75686],{"className":75685},[886],[888,75687,75688],{"xmlns":890},[892,75689,75690,75694],{},[895,75691,75692],{},[898,75693,1734],{},[902,75695,1734],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,75698,75700],{"className":75699},[886],[888,75701,75702],{"xmlns":890},[892,75703,75704,75710],{},[895,75705,75706,75708],{},[898,75707,1772],{},[898,75709,8195],{},[902,75711,8648],{"encoding":904},[724,75713,75714,75717,75718,75319,75754,75769,75770,74929,75789,75682,75804,75817],{},[38,75715,75716],{},"3.10"," Jsou dány mezní náklady ",[883,75719,75721],{"className":75720},[886],[888,75722,75723],{"xmlns":890},[892,75724,75725,75751],{},[895,75726,75727,75729,75731,75733,75735,75737,75739,75741,75743,75745],{},[898,75728,4445],{},[898,75730,8195],{},[1712,75732,1714],{},[1716,75734,8533],{},[1712,75736,2219],{},[1716,75738,46737],{},[898,75740,1734],{},[1712,75742,3145],{},[1716,75744,69434],{},[2037,75746,75747,75749],{},[898,75748,1734],{},[1716,75750,2787],{},[902,75752,75753],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,75755,75757],{"className":75756},[886],[888,75758,75759],{"xmlns":890},[892,75760,75761,75767],{},[895,75762,75763,75765],{},[898,75764,1772],{},[898,75766,8195],{},[902,75768,8648],{"encoding":904},", jestliže fixní náklady ",[883,75771,75773],{"className":75772},[886],[888,75774,75775],{"xmlns":890},[892,75776,75777,75787],{},[895,75778,75779,75781,75783,75785],{},[898,75780,15308],{},[898,75782,8195],{},[1712,75784,1714],{},[1716,75786,1739],{},[902,75788,16506],{"encoding":904},[883,75790,75792],{"className":75791},[886],[888,75793,75794],{"xmlns":890},[892,75795,75796,75802],{},[895,75797,75798,75800],{},[898,75799,1772],{},[898,75801,8195],{},[902,75803,8648],{"encoding":904},[883,75805,75807],{"className":75806},[886],[888,75808,75809],{"xmlns":890},[892,75810,75811,75815],{},[895,75812,75813],{},[898,75814,1734],{},[902,75816,1734],{"encoding":904}," z 15 na 20.",[724,75819,75820,74968,75823,75866,75867,75880,75881,75896,75897,75912,75913,75880,75926,75896,75943,75960,75961,75880,75974,75896,75989,76004,76005,76025,76026,76049],{},[38,75821,75822],{},"3.11",[883,75824,75826],{"className":75825},[886],[888,75827,75828],{"xmlns":890},[892,75829,75830,75864],{},[895,75831,75832,75834,75836,75838,75840,75842,75844,75846,75848,75850,75856,75858],{},[898,75833,1772],{},[898,75835,8195],{},[1712,75837,1714],{},[1716,75839,1739],{},[1712,75841,3145],{},[1716,75843,2809],{},[898,75845,1734],{},[1712,75847,2219],{},[1716,75849,3068],{},[2037,75851,75852,75854],{},[898,75853,1734],{},[1716,75855,2787],{},[1712,75857,3145],{},[2037,75859,75860,75862],{},[898,75861,1734],{},[1716,75863,6198],{},[902,75865,65782],{"encoding":904},". (a) Určete ",[883,75868,75870],{"className":75869},[886],[888,75871,75872],{"xmlns":890},[892,75873,75874,75878],{},[895,75875,75876],{},[898,75877,1734],{},[902,75879,1734],{"encoding":904},", které minimalizuje ",[883,75882,75884],{"className":75883},[886],[888,75885,75886],{"xmlns":890},[892,75887,75888,75894],{},[895,75889,75890,75892],{},[898,75891,4445],{},[898,75893,8195],{},[902,75895,60167],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,75898,75900],{"className":75899},[886],[888,75901,75902],{"xmlns":890},[892,75903,75904,75910],{},[895,75905,75906,75908],{},[898,75907,4445],{},[898,75909,8195],{},[902,75911,60167],{"encoding":904},". (b) Určete ",[883,75914,75916],{"className":75915},[886],[888,75917,75918],{"xmlns":890},[892,75919,75920,75924],{},[895,75921,75922],{},[898,75923,1734],{},[902,75925,1734],{"encoding":904},[883,75927,75929],{"className":75928},[886],[888,75930,75931],{"xmlns":890},[892,75932,75933,75941],{},[895,75934,75935,75937,75939],{},[898,75936,2044],{},[898,75938,45214],{},[898,75940,8195],{},[902,75942,60186],{"encoding":904},[883,75944,75946],{"className":75945},[886],[888,75947,75948],{"xmlns":890},[892,75949,75950,75958],{},[895,75951,75952,75954,75956],{},[898,75953,2044],{},[898,75955,45214],{},[898,75957,8195],{},[902,75959,60186],{"encoding":904},". (c) Určete ",[883,75962,75964],{"className":75963},[886],[888,75965,75966],{"xmlns":890},[892,75967,75968,75972],{},[895,75969,75970],{},[898,75971,1734],{},[902,75973,1734],{"encoding":904},[883,75975,75977],{"className":75976},[886],[888,75978,75979],{"xmlns":890},[892,75980,75981,75987],{},[895,75982,75983,75985],{},[898,75984,2044],{},[898,75986,8195],{},[902,75988,60435],{"encoding":904},[883,75990,75992],{"className":75991},[886],[888,75993,75994],{"xmlns":890},[892,75995,75996,76002],{},[895,75997,75998,76000],{},[898,75999,2044],{},[898,76001,8195],{},[902,76003,60435],{"encoding":904}," (rada: hledaný kořen ",[883,76006,76008],{"className":76007},[886],[888,76009,76010],{"xmlns":890},[892,76011,76012,76022],{},[895,76013,76014,76016],{},[898,76015,2044],{},[2037,76017,76018,76020],{},[898,76019,8195],{},[1712,76021,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,76023,76024],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,76027,76029],{"className":76028},[886],[888,76030,76031],{"xmlns":890},[892,76032,76033,76046],{},[895,76034,76035,76037,76040,76042,76044],{},[1712,76036,1904],{"stretchy":1903},[1716,76038,76039],{},"4,7",[1712,76041,6245],{"separator":2565},[1716,76043,3088],{},[1712,76045,1910],{"stretchy":1903},[902,76047,76048],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,76051,76052,76055,76056,8046,76084,76101,76102,26469,76143,76164],{},[38,76053,76054],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,76057,76059],{"className":76058},[886],[888,76060,76061],{"xmlns":890},[892,76062,76063,76081],{},[895,76064,76065,76067,76069,76071,76073,76075,76077,76079],{},[898,76066,2044],{},[898,76068,8195],{},[1712,76070,1714],{},[898,76072,2044],{},[898,76074,8195],{},[1712,76076,1904],{"stretchy":1903},[898,76078,1734],{},[1712,76080,1910],{"stretchy":1903},[902,76082,76083],{"encoding":904},"AC = AC(Q)",[883,76085,76087],{"className":76086},[886],[888,76088,76089],{"xmlns":890},[892,76090,76091,76099],{},[895,76092,76093],{},[6927,76094,76095,76097],{},[898,76096,1734],{},[1716,76098,2085],{},[902,76100,43183],{"encoding":904}," minimum, pak platí ",[883,76103,76105],{"className":76104},[886],[888,76106,76107],{"xmlns":890},[892,76108,76109,76141],{},[895,76110,76111,76113,76115,76117,76123,76125,76127,76129,76131,76133,76139],{},[898,76112,2044],{},[898,76114,8195],{},[1712,76116,1904],{"stretchy":1903},[6927,76118,76119,76121],{},[898,76120,1734],{},[1716,76122,2085],{},[1712,76124,1910],{"stretchy":1903},[1712,76126,1714],{},[898,76128,4445],{},[898,76130,8195],{},[1712,76132,1904],{"stretchy":1903},[6927,76134,76135,76137],{},[898,76136,1734],{},[1716,76138,2085],{},[1712,76140,1910],{"stretchy":1903},[902,76142,67444],{"encoding":904},[883,76144,76146],{"className":76145},[886],[888,76147,76148],{"xmlns":890},[892,76149,76150,76162],{},[895,76151,76152,76154,76156,76158,76160],{},[898,76153,4445],{},[898,76155,8195],{},[1712,76157,1904],{"stretchy":1903},[898,76159,1734],{},[1712,76161,1910],{"stretchy":1903},[902,76163,72568],{"encoding":904}," jsou mezní náklady.",[724,76166,76167,74968,76170,75430,76204,75880,76217,75896,76232,1659],{},[38,76168,76169],{},"3.13",[883,76171,76173],{"className":76172},[886],[888,76174,76175],{"xmlns":890},[892,76176,76177,76201],{},[895,76178,76179,76181,76183,76185,76191,76193,76195,76197,76199],{},[898,76180,1772],{},[898,76182,8195],{},[1712,76184,1714],{},[2037,76186,76187,76189],{},[898,76188,1734],{},[1716,76190,2787],{},[1712,76192,3145],{},[1716,76194,2787],{},[898,76196,1734],{},[1712,76198,3145],{},[1716,76200,2809],{},[902,76202,76203],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,76205,76207],{"className":76206},[886],[888,76208,76209],{"xmlns":890},[892,76210,76211,76215],{},[895,76212,76213],{},[898,76214,1734],{},[902,76216,1734],{"encoding":904},[883,76218,76220],{"className":76219},[886],[888,76221,76222],{"xmlns":890},[892,76223,76224,76230],{},[895,76225,76226,76228],{},[898,76227,2044],{},[898,76229,8195],{},[902,76231,60435],{"encoding":904},[883,76233,76235],{"className":76234},[886],[888,76236,76237],{"xmlns":890},[892,76238,76239,76245],{},[895,76240,76241,76243],{},[898,76242,2044],{},[898,76244,8195],{},[902,76246,60435],{"encoding":904},[724,76248,76249,76252,76253,8046,76285,76101,76302,26469,76345,76164],{},[38,76250,76251],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,76254,76256],{"className":76255},[886],[888,76257,76258],{"xmlns":890},[892,76259,76260,76282],{},[895,76261,76262,76264,76266,76268,76270,76272,76274,76276,76278,76280],{},[898,76263,2044],{},[898,76265,45214],{},[898,76267,8195],{},[1712,76269,1714],{},[898,76271,2044],{},[898,76273,45214],{},[898,76275,8195],{},[1712,76277,1904],{"stretchy":1903},[898,76279,1734],{},[1712,76281,1910],{"stretchy":1903},[902,76283,76284],{"encoding":904},"AVC = AVC(Q)",[883,76286,76288],{"className":76287},[886],[888,76289,76290],{"xmlns":890},[892,76291,76292,76300],{},[895,76293,76294],{},[6927,76295,76296,76298],{},[898,76297,1734],{},[1716,76299,2085],{},[902,76301,43183],{"encoding":904},[883,76303,76305],{"className":76304},[886],[888,76306,76307],{"xmlns":890},[892,76308,76309,76343],{},[895,76310,76311,76313,76315,76317,76319,76325,76327,76329,76331,76333,76335,76341],{},[898,76312,2044],{},[898,76314,45214],{},[898,76316,8195],{},[1712,76318,1904],{"stretchy":1903},[6927,76320,76321,76323],{},[898,76322,1734],{},[1716,76324,2085],{},[1712,76326,1910],{"stretchy":1903},[1712,76328,1714],{},[898,76330,4445],{},[898,76332,8195],{},[1712,76334,1904],{"stretchy":1903},[6927,76336,76337,76339],{},[898,76338,1734],{},[1716,76340,2085],{},[1712,76342,1910],{"stretchy":1903},[902,76344,73894],{"encoding":904},[883,76346,76348],{"className":76347},[886],[888,76349,76350],{"xmlns":890},[892,76351,76352,76364],{},[895,76353,76354,76356,76358,76360,76362],{},[898,76355,4445],{},[898,76357,8195],{},[1712,76359,1904],{"stretchy":1903},[898,76361,1734],{},[1712,76363,1910],{"stretchy":1903},[902,76365,72568],{"encoding":904},[724,76367,76368,74968,76371,75430,76417,75880,76430,75896,76447,1659],{},[38,76369,76370],{},"3.15",[883,76372,76374],{"className":76373},[886],[888,76375,76376],{"xmlns":890},[892,76377,76378,76414],{},[895,76379,76380,76382,76384,76386,76388,76390,76392,76394,76396,76398,76404,76406,76408],{},[898,76381,1772],{},[898,76383,8195],{},[1712,76385,1714],{},[1716,76387,2782],{},[1712,76389,3145],{},[1716,76391,41119],{},[898,76393,1734],{},[1712,76395,2219],{},[1716,76397,2787],{},[2037,76399,76400,76402],{},[898,76401,1734],{},[1716,76403,2787],{},[1712,76405,3145],{},[1716,76407,6673],{},[2037,76409,76410,76412],{},[898,76411,1734],{},[1716,76413,6198],{},[902,76415,76416],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,76418,76420],{"className":76419},[886],[888,76421,76422],{"xmlns":890},[892,76423,76424,76428],{},[895,76425,76426],{},[898,76427,1734],{},[902,76429,1734],{"encoding":904},[883,76431,76433],{"className":76432},[886],[888,76434,76435],{"xmlns":890},[892,76436,76437,76445],{},[895,76438,76439,76441,76443],{},[898,76440,2044],{},[898,76442,45214],{},[898,76444,8195],{},[902,76446,60186],{"encoding":904},[883,76448,76450],{"className":76449},[886],[888,76451,76452],{"xmlns":890},[892,76453,76454,76462],{},[895,76455,76456,76458,76460],{},[898,76457,2044],{},[898,76459,45214],{},[898,76461,8195],{},[902,76463,60186],{"encoding":904},[724,76465,76466,76469,76470,76483,76484,76504],{},[38,76467,76468],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,76471,76473],{"className":76472},[886],[888,76474,76475],{"xmlns":890},[892,76476,76477,76481],{},[895,76478,76479],{},[898,76480,7456],{},[902,76482,7456],{"encoding":904}," 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 ",[883,76485,76487],{"className":76486},[886],[888,76488,76489],{"xmlns":890},[892,76490,76491,76501],{},[895,76492,76493,76495,76497,76499],{},[1716,76494,1718],{},[1762,76496,2583],{},[1716,76498,63957],{},[898,76500,7456],{},[902,76502,76503],{"encoding":904},"10\\,000 x"," Kč za podlaží. Určete počet podlaží, které minimalizuje průměrné náklady na jedno podlaží a stanovte příslušnou hodnotu minima průměrných nákladů.",[198,76506,76508],{"id":76507},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,76510,76511,76514,76515,1655,76537,76563],{},[38,76512,76513],{},"3.17"," Jsou dány ",[883,76516,76518],{"className":76517},[886],[888,76519,76520],{"xmlns":890},[892,76521,76522,76534],{},[895,76523,76524,76526,76528,76530,76532],{},[898,76525,1772],{},[898,76527,1775],{},[1712,76529,1714],{},[1716,76531,1718],{},[898,76533,1734],{},[902,76535,76536],{"encoding":904},"TR = 10Q",[883,76538,76540],{"className":76539},[886],[888,76541,76542],{"xmlns":890},[892,76543,76544,76560],{},[895,76545,76546,76548,76550,76552,76554,76556,76558],{},[898,76547,1772],{},[898,76549,8195],{},[1712,76551,1714],{},[1716,76553,1739],{},[1712,76555,3145],{},[1716,76557,3068],{},[898,76559,1734],{},[902,76561,76562],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,76565,76566,76569,76570,4005,76585,76600,76601,1343,76623,26469,76650,76672,76673,76707],{},[38,76567,76568],{},"3.18"," Odvoďte, že jestliže ",[883,76571,76573],{"className":76572},[886],[888,76574,76575],{"xmlns":890},[892,76576,76577,76583],{},[895,76578,76579,76581],{},[898,76580,1772],{},[898,76582,1775],{},[902,76584,1877],{"encoding":904},[883,76586,76588],{"className":76587},[886],[888,76589,76590],{"xmlns":890},[892,76591,76592,76598],{},[895,76593,76594,76596],{},[898,76595,1772],{},[898,76597,8195],{},[902,76599,8648],{"encoding":904}," jsou lineární tvaru ",[883,76602,76604],{"className":76603},[886],[888,76605,76606],{"xmlns":890},[892,76607,76608,76620],{},[895,76609,76610,76612,76614,76616,76618],{},[898,76611,1772],{},[898,76613,1775],{},[1712,76615,1714],{},[898,76617,724],{},[898,76619,1734],{},[902,76621,76622],{"encoding":904},"TR = pQ",[883,76624,76626],{"className":76625},[886],[888,76627,76628],{"xmlns":890},[892,76629,76630,76647],{},[895,76631,76632,76634,76636,76638,76641,76643,76645],{},[898,76633,1772],{},[898,76635,8195],{},[1712,76637,1714],{},[898,76639,76640],{},"m",[1712,76642,3145],{},[898,76644,41735],{},[898,76646,1734],{},[902,76648,76649],{"encoding":904},"TC = m + nQ",[883,76651,76653],{"className":76652},[886],[888,76654,76655],{"xmlns":890},[892,76656,76657,76669],{},[895,76658,76659,76661,76663,76665,76667],{},[898,76660,76640],{},[1712,76662,3138],{"separator":2565},[898,76664,41735],{},[1712,76666,3138],{"separator":2565},[898,76668,724],{},[902,76670,76671],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,76674,76676],{"className":76675},[886],[888,76677,76678],{"xmlns":890},[892,76679,76680,76704],{},[895,76681,76682,76688,76690],{},[2037,76683,76684,76686],{},[898,76685,1734],{},[1712,76687,2145],{},[1712,76689,1714],{},[2563,76691,76692],{"scriptlevel":2085,"displaystyle":1903},[2567,76693,76694,76696],{},[898,76695,76640],{},[895,76697,76698,76700,76702],{},[898,76699,724],{},[1712,76701,2219],{},[898,76703,41735],{},[902,76705,76706],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,76709,76710,76514,76713,1655,76747,75866,76773,76786,76787,74618,76802,76817,76818,74602,76831,74618,76846,76861],{},[38,76711,76712],{},"3.19",[883,76714,76716],{"className":76715},[886],[888,76717,76718],{"xmlns":890},[892,76719,76720,76744],{},[895,76721,76722,76724,76726,76728,76730,76732,76738,76740,76742],{},[898,76723,1772],{},[898,76725,1775],{},[1712,76727,1714],{},[1712,76729,2219],{},[1716,76731,2787],{},[2037,76733,76734,76736],{},[898,76735,1734],{},[1716,76737,2787],{},[1712,76739,3145],{},[1716,76741,27821],{},[898,76743,1734],{},[902,76745,76746],{"encoding":904},"TR = -2Q^2 + 14Q",[883,76748,76750],{"className":76749},[886],[888,76751,76752],{"xmlns":890},[892,76753,76754,76770],{},[895,76755,76756,76758,76760,76762,76764,76766,76768],{},[898,76757,1772],{},[898,76759,8195],{},[1712,76761,1714],{},[1716,76763,2787],{},[898,76765,1734],{},[1712,76767,3145],{},[1716,76769,1718],{},[902,76771,76772],{"encoding":904},"TC = 2Q + 10",[883,76774,76776],{"className":76775},[886],[888,76777,76778],{"xmlns":890},[892,76779,76780,76784],{},[895,76781,76782],{},[898,76783,1734],{},[902,76785,1734],{"encoding":904},", které maximalizuje zisk ",[883,76788,76790],{"className":76789},[886],[888,76791,76792],{"xmlns":890},[892,76793,76794,76800],{},[895,76795,76796,76798],{},[898,76797,1710],{},[898,76799,1775],{},[902,76801,68354],{"encoding":904},[883,76803,76805],{"className":76804},[886],[888,76806,76807],{"xmlns":890},[892,76808,76809,76815],{},[895,76810,76811,76813],{},[898,76812,1710],{},[898,76814,1775],{},[902,76816,68354],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,76819,76821],{"className":76820},[886],[888,76822,76823],{"xmlns":890},[892,76824,76825,76829],{},[895,76826,76827],{},[898,76828,1734],{},[902,76830,1734],{"encoding":904},[883,76832,76834],{"className":76833},[886],[888,76835,76836],{"xmlns":890},[892,76837,76838,76844],{},[895,76839,76840,76842],{},[898,76841,1772],{},[898,76843,1775],{},[902,76845,1877],{"encoding":904},[883,76847,76849],{"className":76848},[886],[888,76850,76851],{"xmlns":890},[892,76852,76853,76859],{},[895,76854,76855,76857],{},[898,76856,1772],{},[898,76858,1775],{},[902,76860,1877],{"encoding":904},". (d) Graficky interpretujte.",[724,76863,76864,52559,76867,1343,76893,1343,76912,75866,76932,76786,76945,74618,76960,76975,76976,76998,76999,76049],{},[38,76865,76866],{},"3.20",[883,76868,76870],{"className":76869},[886],[888,76871,76872],{"xmlns":890},[892,76873,76874,76890],{},[895,76875,76876,76878,76880,76882,76884],{},[898,76877,1710],{},[1712,76879,1714],{},[1716,76881,25017],{},[1712,76883,2219],{},[2037,76885,76886,76888],{},[898,76887,1734],{},[1716,76889,2787],{},[902,76891,76892],{"encoding":904},"P = 400 - Q^2",[883,76894,76896],{"className":76895},[886],[888,76897,76898],{"xmlns":890},[892,76899,76900,76910],{},[895,76901,76902,76904,76906,76908],{},[898,76903,15308],{},[898,76905,8195],{},[1712,76907,1714],{},[1716,76909,1739],{},[902,76911,16506],{"encoding":904},[883,76913,76915],{"className":76914},[886],[888,76916,76917],{"xmlns":890},[892,76918,76919,76929],{},[895,76920,76921,76923,76925,76927],{},[898,76922,4445],{},[898,76924,8195],{},[1712,76926,1714],{},[1716,76928,6857],{},[902,76930,76931],{"encoding":904},"MC = 20",[883,76933,76935],{"className":76934},[886],[888,76936,76937],{"xmlns":890},[892,76938,76939,76943],{},[895,76940,76941],{},[898,76942,1734],{},[902,76944,1734],{"encoding":904},[883,76946,76948],{"className":76947},[886],[888,76949,76950],{"xmlns":890},[892,76951,76952,76958],{},[895,76953,76954,76956],{},[898,76955,1710],{},[898,76957,1775],{},[902,76959,68354],{"encoding":904},[883,76961,76963],{"className":76962},[886],[888,76964,76965],{"xmlns":890},[892,76966,76967,76973],{},[895,76968,76969,76971],{},[898,76970,1710],{},[898,76972,1775],{},[902,76974,68354],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,76977,76979],{"className":76978},[886],[888,76980,76981],{"xmlns":890},[892,76982,76983,76995],{},[895,76984,76985,76987,76989,76991,76993],{},[1712,76986,1904],{"stretchy":1903},[1716,76988,2085],{},[1712,76990,3138],{"separator":2565},[1716,76992,2222],{},[1712,76994,1910],{"stretchy":1903},[902,76996,76997],{"encoding":904},"(0, 1)",", druhý do ",[883,77000,77002],{"className":77001},[886],[888,77003,77004],{"xmlns":890},[892,77005,77006,77019],{},[895,77007,77008,77010,77013,77015,77017],{},[1712,77009,1904],{"stretchy":1903},[1716,77011,77012],{},"19",[1712,77014,3138],{"separator":2565},[1716,77016,6857],{},[1712,77018,1910],{"stretchy":1903},[902,77020,77021],{"encoding":904},"(19, 20)",[724,77023,77024,77027,77028,8046,77056,77073,77074,1659],{},[38,77025,77026],{},"3.21"," Dokažte, že má-li zisk ",[883,77029,77031],{"className":77030},[886],[888,77032,77033],{"xmlns":890},[892,77034,77035,77053],{},[895,77036,77037,77039,77041,77043,77045,77047,77049,77051],{},[898,77038,1710],{},[898,77040,1775],{},[1712,77042,1714],{},[898,77044,1710],{},[898,77046,1775],{},[1712,77048,1904],{"stretchy":1903},[898,77050,1734],{},[1712,77052,1910],{"stretchy":1903},[902,77054,77055],{"encoding":904},"PR = PR(Q)",[883,77057,77059],{"className":77058},[886],[888,77060,77061],{"xmlns":890},[892,77062,77063,77071],{},[895,77064,77065],{},[6927,77066,77067,77069],{},[898,77068,1734],{},[1716,77070,2085],{},[902,77072,43183],{"encoding":904}," maximum, pak platí ",[883,77075,77077],{"className":77076},[886],[888,77078,77079],{"xmlns":890},[892,77080,77081,77113],{},[895,77082,77083,77085,77087,77089,77095,77097,77099,77101,77103,77105,77111],{},[898,77084,4445],{},[898,77086,1775],{},[1712,77088,1904],{"stretchy":1903},[6927,77090,77091,77093],{},[898,77092,1734],{},[1716,77094,2085],{},[1712,77096,1910],{"stretchy":1903},[1712,77098,1714],{},[898,77100,4445],{},[898,77102,8195],{},[1712,77104,1904],{"stretchy":1903},[6927,77106,77107,77109],{},[898,77108,1734],{},[1716,77110,2085],{},[1712,77112,1910],{"stretchy":1903},[902,77114,70520],{"encoding":904},[724,77116,77117,77120,77121,1655,77136,60900,77151,76786,77164,77179,77180,1343,77207,77244,77245,1343,77272,1659],{},[38,77118,77119],{},"3.22"," Pro zadané ",[883,77122,77124],{"className":77123},[886],[888,77125,77126],{"xmlns":890},[892,77127,77128,77134],{},[895,77129,77130,77132],{},[898,77131,4445],{},[898,77133,1775],{},[902,77135,4450],{"encoding":904},[883,77137,77139],{"className":77138},[886],[888,77140,77141],{"xmlns":890},[892,77142,77143,77149],{},[895,77144,77145,77147],{},[898,77146,4445],{},[898,77148,8195],{},[902,77150,60167],{"encoding":904},[883,77152,77154],{"className":77153},[886],[888,77155,77156],{"xmlns":890},[892,77157,77158,77162],{},[895,77159,77160],{},[898,77161,1734],{},[902,77163,1734],{"encoding":904},[883,77165,77167],{"className":77166},[886],[888,77168,77169],{"xmlns":890},[892,77170,77171,77177],{},[895,77172,77173,77175],{},[898,77174,1710],{},[898,77176,1775],{},[902,77178,68354],{"encoding":904},". (a) ",[883,77181,77183],{"className":77182},[886],[888,77184,77185],{"xmlns":890},[892,77186,77187,77204],{},[895,77188,77189,77191,77193,77195,77198,77200,77202],{},[898,77190,4445],{},[898,77192,1775],{},[1712,77194,1714],{},[1716,77196,77197],{},"236",[1712,77199,2219],{},[1716,77201,46737],{},[898,77203,1734],{},[902,77205,77206],{"encoding":904},"MR = 236 - 16Q",[883,77208,77210],{"className":77209},[886],[888,77211,77212],{"xmlns":890},[892,77213,77214,77241],{},[895,77215,77216,77218,77220,77222,77224,77230,77232,77235,77237,77239],{},[898,77217,4445],{},[898,77219,8195],{},[1712,77221,1714],{},[1716,77223,6198],{},[2037,77225,77226,77228],{},[898,77227,1734],{},[1716,77229,2787],{},[1712,77231,2219],{},[1716,77233,77234],{},"32",[898,77236,1734],{},[1712,77238,3145],{},[1716,77240,3556],{},[902,77242,77243],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,77246,77248],{"className":77247},[886],[888,77249,77250],{"xmlns":890},[892,77251,77252,77269],{},[895,77253,77254,77256,77258,77260,77263,77265,77267],{},[898,77255,4445],{},[898,77257,1775],{},[1712,77259,1714],{},[1716,77261,77262],{},"280",[1712,77264,2219],{},[1716,77266,6857],{},[898,77268,1734],{},[902,77270,77271],{"encoding":904},"MR = 280 - 20Q",[883,77273,77275],{"className":77274},[886],[888,77276,77277],{"xmlns":890},[892,77278,77279,77306],{},[895,77280,77281,77283,77285,77287,77290,77296,77298,77300,77302,77304],{},[898,77282,4445],{},[898,77284,8195],{},[1712,77286,1714],{},[1716,77288,77289],{},"1,6",[2037,77291,77292,77294],{},[898,77293,1734],{},[1716,77295,2787],{},[1712,77297,2219],{},[1716,77299,41119],{},[898,77301,1734],{},[1712,77303,3145],{},[1716,77305,8533],{},[902,77307,77308],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,77310,77311,77120,77314,1655,77329,60900,77344,74602,77357,74618,77372,77179,77387,1343,77418,77244,77454,1343,77486,77530,77531,1343,77563,1659],{},[38,77312,77313],{},"3.23",[883,77315,77317],{"className":77316},[886],[888,77318,77319],{"xmlns":890},[892,77320,77321,77327],{},[895,77322,77323,77325],{},[898,77324,1772],{},[898,77326,1775],{},[902,77328,1877],{"encoding":904},[883,77330,77332],{"className":77331},[886],[888,77333,77334],{"xmlns":890},[892,77335,77336,77342],{},[895,77337,77338,77340],{},[898,77339,1772],{},[898,77341,8195],{},[902,77343,8648],{"encoding":904},[883,77345,77347],{"className":77346},[886],[888,77348,77349],{"xmlns":890},[892,77350,77351,77355],{},[895,77352,77353],{},[898,77354,1734],{},[902,77356,1734],{"encoding":904},[883,77358,77360],{"className":77359},[886],[888,77361,77362],{"xmlns":890},[892,77363,77364,77370],{},[895,77365,77366,77368],{},[898,77367,1710],{},[898,77369,1775],{},[902,77371,68354],{"encoding":904},[883,77373,77375],{"className":77374},[886],[888,77376,77377],{"xmlns":890},[892,77378,77379,77385],{},[895,77380,77381,77383],{},[898,77382,1710],{},[898,77384,1775],{},[902,77386,68354],{"encoding":904},[883,77388,77390],{"className":77389},[886],[888,77391,77392],{"xmlns":890},[892,77393,77394,77415],{},[895,77395,77396,77398,77400,77402,77405,77407,77409],{},[898,77397,1772],{},[898,77399,1775],{},[1712,77401,1714],{},[1716,77403,77404],{},"125",[898,77406,1734],{},[1712,77408,2219],{},[2037,77410,77411,77413],{},[898,77412,1734],{},[1716,77414,2787],{},[902,77416,77417],{"encoding":904},"TR = 125Q - Q^2",[883,77419,77421],{"className":77420},[886],[888,77422,77423],{"xmlns":890},[892,77424,77425,77451],{},[895,77426,77427,77429,77431,77433,77435,77437,77439,77441,77443,77445],{},[898,77428,1772],{},[898,77430,8195],{},[1712,77432,1714],{},[1716,77434,19984],{},[1712,77436,3145],{},[1716,77438,3068],{},[898,77440,1734],{},[1712,77442,3145],{},[1716,77444,2814],{},[2037,77446,77447,77449],{},[898,77448,1734],{},[1716,77450,2787],{},[902,77452,77453],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,77455,77457],{"className":77456},[886],[888,77458,77459],{"xmlns":890},[892,77460,77461,77483],{},[895,77462,77463,77465,77467,77469,77471,77473,77475,77477],{},[898,77464,1772],{},[898,77466,1775],{},[1712,77468,1714],{},[1716,77470,6857],{},[898,77472,1734],{},[1712,77474,2219],{},[1716,77476,2787],{},[2037,77478,77479,77481],{},[898,77480,1734],{},[1716,77482,2787],{},[902,77484,77485],{"encoding":904},"TR = 20Q - 2Q^2",[883,77487,77489],{"className":77488},[886],[888,77490,77491],{"xmlns":890},[892,77492,77493,77527],{},[895,77494,77495,77497,77499,77501,77503,77505,77507,77509,77511,77513,77519,77521],{},[898,77496,1772],{},[898,77498,8195],{},[1712,77500,1714],{},[1716,77502,2787],{},[1712,77504,3145],{},[1716,77506,6857],{},[898,77508,1734],{},[1712,77510,2219],{},[1716,77512,3397],{},[2037,77514,77515,77517],{},[898,77516,1734],{},[1716,77518,2787],{},[1712,77520,3145],{},[2037,77522,77523,77525],{},[898,77524,1734],{},[1716,77526,6198],{},[902,77528,77529],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,77532,77534],{"className":77533},[886],[888,77535,77536],{"xmlns":890},[892,77537,77538,77560],{},[895,77539,77540,77542,77544,77546,77548,77550,77552,77554],{},[898,77541,1772],{},[898,77543,1775],{},[1712,77545,1714],{},[1716,77547,2975],{},[898,77549,1734],{},[1712,77551,2219],{},[1716,77553,28664],{},[2037,77555,77556,77558],{},[898,77557,1734],{},[1716,77559,2787],{},[902,77561,77562],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,77564,77566],{"className":77565},[886],[888,77567,77568],{"xmlns":890},[892,77569,77570,77618],{},[895,77571,77572,77574,77576,77578,77580,77582,77584,77586,77588,77604,77606],{},[898,77573,1772],{},[898,77575,8195],{},[1712,77577,1714],{},[1716,77579,2975],{},[1712,77581,3145],{},[1716,77583,2787],{},[898,77585,1734],{},[1712,77587,2219],{},[2563,77589,77590],{"scriptlevel":2085,"displaystyle":1903},[2567,77591,77592,77602],{},[895,77593,77594,77596],{},[1716,77595,6198],{},[2037,77597,77598,77600],{},[898,77599,1734],{},[1716,77601,2787],{},[1716,77603,1718],{},[1712,77605,3145],{},[2563,77607,77608],{"scriptlevel":2085,"displaystyle":1903},[2567,77609,77610,77616],{},[2037,77611,77612,77614],{},[898,77613,1734],{},[1716,77615,6198],{},[1716,77617,6857],{},[902,77619,77620],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,77622,77623,77626,77627,77657,77658,77690,77691,26469,77721,77751],{},[38,77624,77625],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,77628,77630],{"className":77629},[886],[888,77631,77632],{"xmlns":890},[892,77633,77634,77654],{},[895,77635,77636,77642,77644,77646,77648],{},[6927,77637,77638,77640],{},[898,77639,1710],{},[1716,77641,2222],{},[1712,77643,1714],{},[1716,77645,19984],{},[1712,77647,2219],{},[6927,77649,77650,77652],{},[898,77651,1734],{},[1716,77653,2222],{},[902,77655,77656],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,77659,77661],{"className":77660},[886],[888,77662,77663],{"xmlns":890},[892,77664,77665,77687],{},[895,77666,77667,77673,77675,77677,77679,77681],{},[6927,77668,77669,77671],{},[898,77670,1710],{},[1716,77672,2787],{},[1712,77674,1714],{},[1716,77676,34956],{},[1712,77678,2219],{},[1716,77680,69434],{},[6927,77682,77683,77685],{},[898,77684,1734],{},[1716,77686,2787],{},[902,77688,77689],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,77692,77694],{"className":77693},[886],[888,77695,77696],{"xmlns":890},[892,77697,77698,77718],{},[895,77699,77700,77702,77704,77706,77708,77710,77712,77714,77716],{},[898,77701,1772],{},[898,77703,8195],{},[1712,77705,1714],{},[1716,77707,2782],{},[1762,77709,2583],{},[1716,77711,63957],{},[1712,77713,3145],{},[1716,77715,6857],{},[898,77717,1734],{},[902,77719,77720],{"encoding":904},"TC = 50\\,000 + 20Q",[883,77722,77724],{"className":77723},[886],[888,77725,77726],{"xmlns":890},[892,77727,77728,77748],{},[895,77729,77730,77732,77734,77740,77742],{},[898,77731,1734],{},[1712,77733,1714],{},[6927,77735,77736,77738],{},[898,77737,1734],{},[1716,77739,2222],{},[1712,77741,3145],{},[6927,77743,77744,77746],{},[898,77745,1734],{},[1716,77747,2787],{},[902,77749,77750],{"encoding":904},"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.",[724,77753,77754,77757,77758,77788,77789,77690,77821,26469,77851,77880],{},[38,77755,77756],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,77759,77761],{"className":77760},[886],[888,77762,77763],{"xmlns":890},[892,77764,77765,77785],{},[895,77766,77767,77773,77775,77777,77779],{},[6927,77768,77769,77771],{},[898,77770,1710],{},[1716,77772,2222],{},[1712,77774,1714],{},[1716,77776,34956],{},[1712,77778,2219],{},[6927,77780,77781,77783],{},[898,77782,1734],{},[1716,77784,2222],{},[902,77786,77787],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,77790,77792],{"className":77791},[886],[888,77793,77794],{"xmlns":890},[892,77795,77796,77818],{},[895,77797,77798,77804,77806,77808,77810,77812],{},[6927,77799,77800,77802],{},[898,77801,1710],{},[1716,77803,2787],{},[1712,77805,1714],{},[1716,77807,6195],{},[1712,77809,2219],{},[1716,77811,2814],{},[6927,77813,77814,77816],{},[898,77815,1734],{},[1716,77817,2787],{},[902,77819,77820],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,77822,77824],{"className":77823},[886],[888,77825,77826],{"xmlns":890},[892,77827,77828,77848],{},[895,77829,77830,77832,77834,77836,77838,77840,77842,77844,77846],{},[898,77831,1772],{},[898,77833,8195],{},[1712,77835,1714],{},[1716,77837,3068],{},[1762,77839,2583],{},[1716,77841,63957],{},[1712,77843,3145],{},[1716,77845,1739],{},[898,77847,1734],{},[902,77849,77850],{"encoding":904},"TC = 5\\,000 + 100Q",[883,77852,77854],{"className":77853},[886],[888,77855,77856],{"xmlns":890},[892,77857,77858,77878],{},[895,77859,77860,77862,77864,77870,77872],{},[898,77861,1734],{},[1712,77863,1714],{},[6927,77865,77866,77868],{},[898,77867,1734],{},[1716,77869,2222],{},[1712,77871,3145],{},[6927,77873,77874,77876],{},[898,77875,1734],{},[1716,77877,2787],{},[902,77879,77750],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,77882,77884],{"id":77883},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,77886,77887,77890,77891,77938,77939,77956],{},[38,77888,77889],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,77892,77894],{"className":77893},[886],[888,77895,77896],{"xmlns":890},[892,77897,77898,77935],{},[895,77899,77900,77902,77904,77906,77908,77911,77917,77919,77922,77928,77930,77933],{},[898,77901,1772],{},[898,77903,45214],{},[898,77905,8195],{},[1712,77907,1714],{},[1716,77909,77910],{},"0,85",[2037,77912,77913,77915],{},[898,77914,1734],{},[1716,77916,6198],{},[1712,77918,2219],{},[1716,77920,77921],{},"11,9",[2037,77923,77924,77926],{},[898,77925,1734],{},[1716,77927,2787],{},[1712,77929,3145],{},[1716,77931,77932],{},"102",[898,77934,1734],{},[902,77936,77937],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,77940,77942],{"className":77941},[886],[888,77943,77944],{"xmlns":890},[892,77945,77946,77954],{},[895,77947,77948],{},[2037,77949,77950,77952],{},[898,77951,1710],{},[1712,77953,2145],{},[902,77955,2195],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,77958,77959,75717,77962,77998],{},[38,77960,77961],{},"3.27",[883,77963,77965],{"className":77964},[886],[888,77966,77967],{"xmlns":890},[892,77968,77969,77995],{},[895,77970,77971,77973,77975,77977,77979,77985,77987,77989,77991,77993],{},[898,77972,4445],{},[898,77974,8195],{},[1712,77976,1714],{},[1716,77978,8335],{},[2037,77980,77981,77983],{},[898,77982,1734],{},[1716,77984,2787],{},[1712,77986,2219],{},[1716,77988,69315],{},[898,77990,1734],{},[1712,77992,3145],{},[1716,77994,35618],{},[902,77996,77997],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,78000,78001,74968,78004,77998],{},[38,78002,78003],{},"3.28",[883,78005,78007],{"className":78006},[886],[888,78008,78009],{"xmlns":890},[892,78010,78011,78047],{},[895,78012,78013,78015,78017,78019,78021,78027,78029,78031,78037,78039,78041,78043,78045],{},[898,78014,1772],{},[898,78016,8195],{},[1712,78018,1714],{},[1716,78020,2814],{},[2037,78022,78023,78025],{},[898,78024,1734],{},[1716,78026,6198],{},[1712,78028,2219],{},[1716,78030,29076],{},[2037,78032,78033,78035],{},[898,78034,1734],{},[1716,78036,2787],{},[1712,78038,3145],{},[1716,78040,8533],{},[898,78042,1734],{},[1712,78044,3145],{},[1716,78046,19984],{},[902,78048,78049],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,78051,20594],{"id":20593},[120,78053,78054,78082,78127,78199,78264,78304,78396,78502,78542,78656,78749,78813,78845,78905,78911,78975,79024,79078,79186,79241],{},[123,78055,78056,3245,78058,78081],{},[38,78057,60625],{},[883,78059,78061],{"className":78060},[886],[888,78062,78063],{"xmlns":890},[892,78064,78065,78079],{},[895,78066,78067,78069,78071,78073,78075,78077],{},[898,78068,1772],{},[898,78070,1775],{},[1712,78072,1714],{},[898,78074,1710],{},[1712,78076,1783],{},[898,78078,1734],{},[902,78080,71587],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,78083,78084,3245,78086,78126],{},[38,78085,61211],{},[883,78087,78089],{"className":78088},[886],[888,78090,78091],{"xmlns":890},[892,78092,78093,78123],{},[895,78094,78095,78097,78099,78101,78113,78115,78117,78119,78121],{},[898,78096,2044],{},[898,78098,1775],{},[1712,78100,1714],{},[2563,78102,78103],{"scriptlevel":2085,"displaystyle":1903},[2567,78104,78105,78111],{},[895,78106,78107,78109],{},[898,78108,1772],{},[898,78110,1775],{},[898,78112,1734],{},[1712,78114,1714],{},[898,78116,1969],{},[1712,78118,1904],{"stretchy":1903},[898,78120,1734],{},[1712,78122,1910],{"stretchy":1903},[902,78124,78125],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,78128,78129,3245,78131,78167,78168,78183,78184,1659],{},[38,78130,61359],{},[883,78132,78134],{"className":78133},[886],[888,78135,78136],{"xmlns":890},[892,78137,78138,78164],{},[895,78139,78140,78142,78144,78146],{},[898,78141,4445],{},[898,78143,1775],{},[1712,78145,1714],{},[2563,78147,78148],{"scriptlevel":2085,"displaystyle":1903},[2567,78149,78150,78158],{},[895,78151,78152,78154,78156],{},[898,78153,2468],{"mathvariant":2003},[898,78155,1772],{},[898,78157,1775],{},[895,78159,78160,78162],{},[898,78161,2468],{"mathvariant":2003},[898,78163,1734],{},[902,78165,78166],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,78169,78171],{"className":78170},[886],[888,78172,78173],{"xmlns":890},[892,78174,78175,78181],{},[895,78176,78177,78179],{},[898,78178,1772],{},[898,78180,1775],{},[902,78182,1877],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,78185,78187],{"className":78186},[886],[888,78188,78189],{"xmlns":890},[892,78190,78191,78197],{},[895,78192,78193,78195],{},[898,78194,2044],{},[898,78196,1775],{},[902,78198,60320],{"encoding":904},[123,78200,78201,3245,78204,1343,78234,1659],{},[38,78202,78203],{},"Diferenciál příjmu\u002Fnákladů",[883,78205,78207],{"className":78206},[886],[888,78208,78209],{"xmlns":890},[892,78210,78211,78231],{},[895,78212,78213,78215,78217,78219,78221,78223,78225,78227,78229],{},[898,78214,2004],{"mathvariant":2003},[898,78216,1772],{},[898,78218,1775],{},[1712,78220,3740],{},[898,78222,4445],{},[898,78224,1775],{},[1762,78226,2583],{},[898,78228,2468],{"mathvariant":2003},[898,78230,1734],{},[902,78232,78233],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,78235,78237],{"className":78236},[886],[888,78238,78239],{"xmlns":890},[892,78240,78241,78261],{},[895,78242,78243,78245,78247,78249,78251,78253,78255,78257,78259],{},[898,78244,2004],{"mathvariant":2003},[898,78246,1772],{},[898,78248,8195],{},[1712,78250,3740],{},[898,78252,4445],{},[898,78254,8195],{},[1762,78256,2583],{},[898,78258,2468],{"mathvariant":2003},[898,78260,1734],{},[902,78262,78263],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,78265,78266,3245,78268,1659],{},[38,78267,63481],{},[883,78269,78271],{"className":78270},[886],[888,78272,78273],{"xmlns":890},[892,78274,78275,78301],{},[895,78276,78277,78279,78281,78283,78285,78287,78289,78291,78293,78295,78297,78299],{},[898,78278,1772],{},[898,78280,8195],{},[1712,78282,1714],{},[898,78284,15308],{},[898,78286,8195],{},[1712,78288,3145],{},[898,78290,1772],{},[898,78292,45214],{},[898,78294,8195],{},[1712,78296,1904],{"stretchy":1903},[898,78298,1734],{},[1712,78300,1910],{"stretchy":1903},[902,78302,78303],{"encoding":904},"TC = FC + TVC(Q)",[123,78305,78306,3245,78309,1343,78324,3245,78326,1343,78349,3245,78352,1659],{},[38,78307,78308],{},"Fixní náklady",[883,78310,78312],{"className":78311},[886],[888,78313,78314],{"xmlns":890},[892,78315,78316,78322],{},[895,78317,78318,78320],{},[898,78319,15308],{},[898,78321,8195],{},[902,78323,60366],{"encoding":904},[38,78325,63634],{},[883,78327,78329],{"className":78328},[886],[888,78330,78331],{"xmlns":890},[892,78332,78333,78347],{},[895,78334,78335,78337,78339,78341,78343,78345],{},[898,78336,1772],{},[898,78338,45214],{},[898,78340,8195],{},[1712,78342,1904],{"stretchy":1903},[898,78344,1734],{},[1712,78346,1910],{"stretchy":1903},[902,78348,63631],{"encoding":904},[38,78350,78351],{},"variabilní náklady na jednotku",[883,78353,78355],{"className":78354},[886],[888,78356,78357],{"xmlns":890},[892,78358,78359,78393],{},[895,78360,78361,78363,78365,78367,78369,78371,78373],{},[898,78362,45214],{},[898,78364,8195],{},[1712,78366,1904],{"stretchy":1903},[898,78368,1734],{},[1712,78370,1910],{"stretchy":1903},[1712,78372,1714],{},[2563,78374,78375],{"scriptlevel":2085,"displaystyle":1903},[2567,78376,78377,78391],{},[895,78378,78379,78381,78383,78385,78387,78389],{},[898,78380,1772],{},[898,78382,45214],{},[898,78384,8195],{},[1712,78386,1904],{"stretchy":1903},[898,78388,1734],{},[1712,78390,1910],{"stretchy":1903},[898,78392,1734],{},[902,78394,78395],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,78397,78398,3245,78400,1343,78430,3245,78433,1343,78465,3245,78468,1659],{},[38,78399,63642],{},[883,78401,78403],{"className":78402},[886],[888,78404,78405],{"xmlns":890},[892,78406,78407,78427],{},[895,78408,78409,78411,78413,78415],{},[898,78410,2044],{},[898,78412,8195],{},[1712,78414,1714],{},[2563,78416,78417],{"scriptlevel":2085,"displaystyle":1903},[2567,78418,78419,78425],{},[895,78420,78421,78423],{},[898,78422,1772],{},[898,78424,8195],{},[898,78426,1734],{},[902,78428,78429],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,78431,78432],{},"průměrné fixní",[883,78434,78436],{"className":78435},[886],[888,78437,78438],{"xmlns":890},[892,78439,78440,78462],{},[895,78441,78442,78444,78446,78448,78450],{},[898,78443,2044],{},[898,78445,15308],{},[898,78447,8195],{},[1712,78449,1714],{},[2563,78451,78452],{"scriptlevel":2085,"displaystyle":1903},[2567,78453,78454,78460],{},[895,78455,78456,78458],{},[898,78457,15308],{},[898,78459,8195],{},[898,78461,1734],{},[902,78463,78464],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,78466,78467],{},"průměrné variabilní",[883,78469,78471],{"className":78470},[886],[888,78472,78473],{"xmlns":890},[892,78474,78475,78499],{},[895,78476,78477,78479,78481,78483,78485],{},[898,78478,2044],{},[898,78480,45214],{},[898,78482,8195],{},[1712,78484,1714],{},[2563,78486,78487],{"scriptlevel":2085,"displaystyle":1903},[2567,78488,78489,78497],{},[895,78490,78491,78493,78495],{},[898,78492,1772],{},[898,78494,45214],{},[898,78496,8195],{},[898,78498,1734],{},[902,78500,78501],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,78503,78504,3245,78506,1659],{},[38,78505,64829],{},[883,78507,78509],{"className":78508},[886],[888,78510,78511],{"xmlns":890},[892,78512,78513,78539],{},[895,78514,78515,78517,78519,78521],{},[898,78516,4445],{},[898,78518,8195],{},[1712,78520,1714],{},[2563,78522,78523],{"scriptlevel":2085,"displaystyle":1903},[2567,78524,78525,78533],{},[895,78526,78527,78529,78531],{},[898,78528,2468],{"mathvariant":2003},[898,78530,1772],{},[898,78532,8195],{},[895,78534,78535,78537],{},[898,78536,2468],{"mathvariant":2003},[898,78538,1734],{},[902,78540,78541],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,78543,78544,3245,78546,78594,78595,78608,78609,1343,78624,1343,78641,1659],{},[38,78545,65727],{},[883,78547,78549],{"className":78548},[886],[888,78550,78551],{"xmlns":890},[892,78552,78553,78591],{},[895,78554,78555,78557,78559,78561,78563,78565,78567,78569,78571,78573,78575,78581,78583,78585],{},[898,78556,1772],{},[898,78558,8195],{},[1712,78560,1714],{},[898,78562,15308],{},[898,78564,8195],{},[1712,78566,3145],{},[898,78568,207],{},[898,78570,1734],{},[1712,78572,3145],{},[898,78574,7544],{},[2037,78576,78577,78579],{},[898,78578,1734],{},[1716,78580,2787],{},[1712,78582,3145],{},[898,78584,7585],{},[2037,78586,78587,78589],{},[898,78588,1734],{},[1716,78590,6198],{},[902,78592,78593],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,78596,78598],{"className":78597},[886],[888,78599,78600],{"xmlns":890},[892,78601,78602,78606],{},[895,78603,78604],{},[898,78605,900],{},[902,78607,900],{"encoding":904},"-průběhem ",[883,78610,78612],{"className":78611},[886],[888,78613,78614],{"xmlns":890},[892,78615,78616,78622],{},[895,78617,78618,78620],{},[898,78619,2044],{},[898,78621,8195],{},[902,78623,60435],{"encoding":904},[883,78625,78627],{"className":78626},[886],[888,78628,78629],{"xmlns":890},[892,78630,78631,78639],{},[895,78632,78633,78635,78637],{},[898,78634,2044],{},[898,78636,45214],{},[898,78638,8195],{},[902,78640,60186],{"encoding":904},[883,78642,78644],{"className":78643},[886],[888,78645,78646],{"xmlns":890},[892,78647,78648,78654],{},[895,78649,78650,78652],{},[898,78651,4445],{},[898,78653,8195],{},[902,78655,60167],{"encoding":904},[123,78657,78658,78660,78661,15266,78676,78717,78718,66372,78733,78748],{},[38,78659,66809],{},": v bodě minima ",[883,78662,78664],{"className":78663},[886],[888,78665,78666],{"xmlns":890},[892,78667,78668,78674],{},[895,78669,78670,78672],{},[898,78671,2044],{},[898,78673,8195],{},[902,78675,60435],{"encoding":904},[883,78677,78679],{"className":78678},[886],[888,78680,78681],{"xmlns":890},[892,78682,78683,78715],{},[895,78684,78685,78687,78689,78691,78697,78699,78701,78703,78705,78707,78713],{},[898,78686,2044],{},[898,78688,8195],{},[1712,78690,1904],{"stretchy":1903},[6927,78692,78693,78695],{},[898,78694,1734],{},[1716,78696,2085],{},[1712,78698,1910],{"stretchy":1903},[1712,78700,1714],{},[898,78702,4445],{},[898,78704,8195],{},[1712,78706,1904],{"stretchy":1903},[6927,78708,78709,78711],{},[898,78710,1734],{},[1716,78712,2085],{},[1712,78714,1910],{"stretchy":1903},[902,78716,67444],{"encoding":904},"; geometricky ",[883,78719,78721],{"className":78720},[886],[888,78722,78723],{"xmlns":890},[892,78724,78725,78731],{},[895,78726,78727,78729],{},[898,78728,4445],{},[898,78730,8195],{},[902,78732,60167],{"encoding":904},[883,78734,78736],{"className":78735},[886],[888,78737,78738],{"xmlns":890},[892,78739,78740,78746],{},[895,78741,78742,78744],{},[898,78743,2044],{},[898,78745,8195],{},[902,78747,60435],{"encoding":904}," v jejím minimu.",[123,78750,78751,78660,78753,15266,78770,1659],{},[38,78752,68159],{},[883,78754,78756],{"className":78755},[886],[888,78757,78758],{"xmlns":890},[892,78759,78760,78768],{},[895,78761,78762,78764,78766],{},[898,78763,2044],{},[898,78765,45214],{},[898,78767,8195],{},[902,78769,60186],{"encoding":904},[883,78771,78773],{"className":78772},[886],[888,78774,78775],{"xmlns":890},[892,78776,78777,78811],{},[895,78778,78779,78781,78783,78785,78787,78793,78795,78797,78799,78801,78803,78809],{},[898,78780,2044],{},[898,78782,45214],{},[898,78784,8195],{},[1712,78786,1904],{"stretchy":1903},[6927,78788,78789,78791],{},[898,78790,1734],{},[1716,78792,2085],{},[1712,78794,1910],{"stretchy":1903},[1712,78796,1714],{},[898,78798,4445],{},[898,78800,8195],{},[1712,78802,1904],{"stretchy":1903},[6927,78804,78805,78807],{},[898,78806,1734],{},[1716,78808,2085],{},[1712,78810,1910],{"stretchy":1903},[902,78812,73894],{"encoding":904},[123,78814,78815,3245,78817,78844],{},[38,78816,68338],{},[883,78818,78820],{"className":78819},[886],[888,78821,78822],{"xmlns":890},[892,78823,78824,78842],{},[895,78825,78826,78828,78830,78832,78834,78836,78838,78840],{},[898,78827,1710],{},[898,78829,1775],{},[1712,78831,1714],{},[898,78833,1772],{},[898,78835,1775],{},[1712,78837,2219],{},[898,78839,1772],{},[898,78841,8195],{},[902,78843,60075],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,78846,78847,14897,78849,78851,78852,78878,78879,78904],{},[38,78848,69200],{},[614,78850,68463],{},") — hodnoty ",[883,78853,78855],{"className":78854},[886],[888,78856,78857],{"xmlns":890},[892,78858,78859,78875],{},[895,78860,78861,78867,78869],{},[6927,78862,78863,78865],{},[898,78864,1734],{},[898,78866,2044],{},[1712,78868,3138],{"separator":2565},[6927,78870,78871,78873],{},[898,78872,1734],{},[898,78874,28128],{},[902,78876,78877],{"encoding":904},"Q_A, Q_B"," splňující ",[883,78880,78882],{"className":78881},[886],[888,78883,78884],{"xmlns":890},[892,78885,78886,78902],{},[895,78887,78888,78890,78892,78894,78896,78898,78900],{},[898,78889,1710],{},[898,78891,1775],{},[1712,78893,1904],{"stretchy":1903},[898,78895,1734],{},[1712,78897,1910],{"stretchy":1903},[1712,78899,1714],{},[1716,78901,2085],{},[902,78903,68740],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,78906,78907,78910],{},[38,78908,78909],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,78912,78913,78915,78916,15266,78933,78974],{},[38,78914,70254],{}," — v bodě maxima zisku ",[883,78917,78919],{"className":78918},[886],[888,78920,78921],{"xmlns":890},[892,78922,78923,78931],{},[895,78924,78925],{},[6927,78926,78927,78929],{},[898,78928,1734],{},[1716,78930,2085],{},[902,78932,43183],{"encoding":904},[883,78934,78936],{"className":78935},[886],[888,78937,78938],{"xmlns":890},[892,78939,78940,78972],{},[895,78941,78942,78944,78946,78948,78954,78956,78958,78960,78962,78964,78970],{},[898,78943,4445],{},[898,78945,1775],{},[1712,78947,1904],{"stretchy":1903},[6927,78949,78950,78952],{},[898,78951,1734],{},[1716,78953,2085],{},[1712,78955,1910],{"stretchy":1903},[1712,78957,1714],{},[898,78959,4445],{},[898,78961,8195],{},[1712,78963,1904],{"stretchy":1903},[6927,78965,78966,78968],{},[898,78967,1734],{},[1716,78969,2085],{},[1712,78971,1910],{"stretchy":1903},[902,78973,70520],{"encoding":904}," (3.13).",[123,78976,78977,25176,78979,15266,78998,79023],{},[38,78978,71547],{},[883,78980,78982],{"className":78981},[886],[888,78983,78984],{"xmlns":890},[892,78985,78986,78995],{},[895,78987,78988,78990,78992],{},[898,78989,1710],{},[1712,78991,1714],{},[1762,78993,78994],{},"konst",[902,78996,78997],{"encoding":904},"P = \\text{konst}",[883,78999,79001],{"className":79000},[886],[888,79002,79003],{"xmlns":890},[892,79004,79005,79021],{},[895,79006,79007,79009,79011,79013,79015,79017,79019],{},[898,79008,1710],{},[1712,79010,1714],{},[898,79012,4445],{},[898,79014,8195],{},[1712,79016,1904],{"stretchy":1903},[898,79018,1734],{},[1712,79020,1910],{"stretchy":1903},[902,79022,72241],{"encoding":904}," (3.14).",[123,79025,79026,79029,79030,79059,79060,79077],{},[38,79027,79028],{},"Shutdown point"," — bod ",[883,79031,79033],{"className":79032},[886],[888,79034,79035],{"xmlns":890},[892,79036,79037,79057],{},[895,79038,79039,79041,79047,79049,79055],{},[1712,79040,1904],{"stretchy":1903},[2037,79042,79043,79045],{},[898,79044,1734],{},[1712,79046,2145],{},[1712,79048,3138],{"separator":2565},[2037,79050,79051,79053],{},[898,79052,1710],{},[1712,79054,2145],{},[1712,79056,1910],{"stretchy":1903},[902,79058,72530],{"encoding":904}," v minimu ",[883,79061,79063],{"className":79062},[886],[888,79064,79065],{"xmlns":890},[892,79066,79067,79075],{},[895,79068,79069,79071,79073],{},[898,79070,2044],{},[898,79072,45214],{},[898,79074,8195],{},[902,79076,60186],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,79079,79080,3245,79083,4288,79118,72800,79139,79152,79153,79168,79169,1659],{},[38,79081,79082],{},"Funkce nabídky firmy",[883,79084,79086],{"className":79085},[886],[888,79087,79088],{"xmlns":890},[892,79089,79090,79116],{},[895,79091,79092,79094,79096,79098,79100,79102,79104,79106,79108,79110,79112,79114],{},[898,79093,1710],{},[1712,79095,1714],{},[898,79097,6493],{},[1712,79099,1904],{"stretchy":1903},[898,79101,1734],{},[1712,79103,1910],{"stretchy":1903},[1712,79105,1714],{},[898,79107,4445],{},[898,79109,8195],{},[1712,79111,1904],{"stretchy":1903},[898,79113,1734],{},[1712,79115,1910],{"stretchy":1903},[902,79117,73997],{"encoding":904},[883,79119,79121],{"className":79120},[886],[888,79122,79123],{"xmlns":890},[892,79124,79125,79137],{},[895,79126,79127,79129,79131],{},[898,79128,1734],{},[1712,79130,2282],{},[2037,79132,79133,79135],{},[898,79134,1734],{},[1712,79136,2145],{},[902,79138,72799],{"encoding":904},[883,79140,79142],{"className":79141},[886],[888,79143,79144],{"xmlns":890},[892,79145,79146,79150],{},[895,79147,79148],{},[1716,79149,2085],{},[902,79151,2085],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,79154,79156],{"className":79155},[886],[888,79157,79158],{"xmlns":890},[892,79159,79160,79166],{},[895,79161,79162,79164],{},[898,79163,4445],{},[898,79165,8195],{},[902,79167,60167],{"encoding":904}," nad minimem ",[883,79170,79172],{"className":79171},[886],[888,79173,79174],{"xmlns":890},[892,79175,79176,79184],{},[895,79177,79178,79180,79182],{},[898,79179,2044],{},[898,79181,45214],{},[898,79183,8195],{},[902,79185,60186],{"encoding":904},[123,79187,79188,4831,79190,79211,79212,1659],{},[38,79189,54954],{},[883,79191,79193],{"className":79192},[886],[888,79194,79195],{"xmlns":890},[892,79196,79197,79209],{},[895,79198,79199,79201,79203],{},[898,79200,1710],{},[1712,79202,1714],{},[2037,79204,79205,79207],{},[898,79206,1710],{},[1712,79208,2145],{},[902,79210,2148],{"encoding":904}," konstantní ⇒ ",[883,79213,79215],{"className":79214},[886],[888,79216,79217],{"xmlns":890},[892,79218,79219,79239],{},[895,79220,79221,79223,79225,79227,79229,79231,79233],{},[898,79222,2044],{},[898,79224,1775],{},[1712,79226,1714],{},[898,79228,4445],{},[898,79230,1775],{},[1712,79232,1714],{},[2037,79234,79235,79237],{},[898,79236,1710],{},[1712,79238,2145],{},[902,79240,63473],{"encoding":904},[123,79242,79243,79246],{},[38,79244,79245],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,79248,9193],{"id":9192},[120,79250,79251,79270,79282],{},[123,79252,79253,3245,79255,1343,79258,1343,79261,1343,79264,1343,79267],{},[38,79254,55598],{},[207,79256,16814],{"className":79257,"dataFsResolvedFilePath":800,"href":801},[210],[207,79259,1646],{"className":79260,"dataFsResolvedFilePath":848,"href":849},[210],[207,79262,1690],{"className":79263,"dataFsResolvedFilePath":764,"href":765},[210],[207,79265,775],{"className":79266,"dataFsResolvedFilePath":773,"href":774},[210],[207,79268,859],{"className":79269,"dataFsResolvedFilePath":857,"href":858},[210],[123,79271,79272,3245,79274,1343,79278],{},[38,79273,41578],{},[207,79275,79277],{"className":79276,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,79279,79281],{"className":79280,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,79283,79284,3245,79286],{},[38,79285,21078],{},[207,79287,21082],{"className":79288,"dataFsResolvedFilePath":7413,"href":7414},[210],{"title":641,"searchDepth":642,"depth":642,"links":79290},[79291,79292,79299,79305,79309,79310,79314,79315,79316,79317,79323,79324],{"id":55829,"depth":642,"text":1241},{"id":60613,"depth":642,"text":60614,"children":79293},[79294,79295,79296,79297,79298],{"id":60624,"depth":649,"text":60625},{"id":61210,"depth":649,"text":61211},{"id":61358,"depth":649,"text":61359},{"id":62100,"depth":649,"text":62101},{"id":62755,"depth":649,"text":62756},{"id":63476,"depth":642,"text":63477,"children":79300},[79301,79302,79303,79304],{"id":63480,"depth":649,"text":63481},{"id":63641,"depth":649,"text":63642},{"id":64828,"depth":649,"text":64829},{"id":65726,"depth":649,"text":65727},{"id":66808,"depth":642,"text":66809,"children":79306},[79307,79308],{"id":21286,"depth":649,"text":21287},{"id":68158,"depth":649,"text":68159},{"id":68332,"depth":642,"text":68333},{"id":70253,"depth":642,"text":70254,"children":79311},[79312,79313],{"id":70267,"depth":649,"text":21287},{"id":71546,"depth":649,"text":71547},{"id":72178,"depth":642,"text":72179},{"id":73644,"depth":642,"text":73645},{"id":54756,"depth":642,"text":54757},{"id":74105,"depth":642,"text":74106,"children":79318},[79319,79320,79321,79322],{"id":74109,"depth":649,"text":74110},{"id":74961,"depth":649,"text":74962},{"id":76507,"depth":649,"text":76508},{"id":77883,"depth":649,"text":77884},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":59995,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,79331,79332,60047,79333,79334,79335],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":79338,"title":79339,"body":79340,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":91437,"navigation":664,"path":91438,"seo":91439,"sources":91440,"stem":91441,"tags":91442,"type":7391,"updated":677,"__hash__":91448},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":79341,"toc":91394},[79342,79345,79701,79705,79708,79776,79828,79838,79842,79876,79917,79941,79964,79993,80060,80167,80210,80267,80342,80387,80391,80399,80407,80410,80675,80726,80806,80876,80899,80927,80972,80994,80998,81005,81054,81080,81231,81234,81271,81434,81542,81546,81583,81658,81727,81846,81968,82049,82055,82096,82169,82262,82266,82302,82390,82504,82609,82694,82834,82838,82886,82931,82937,82941,82944,82995,83045,83052,83118,83251,83296,83300,83321,83700,83795,83812,83866,83870,83952,84036,84206,84209,84252,84319,84393,84397,84402,84471,84479,84488,84566,84632,84637,84732,84775,84780,84828,84833,84881,84999,85082,85120,85223,85282,85423,85427,85470,85543,85567,85621,85628,85630,85675,85720,85731,85736,85772,85834,85857,85866,85967,86034,86107,86114,86205,86267,86303,86360,86419,86604,86700,86704,86708,86787,86792,86916,87002,87008,87118,87155,87246,87344,87347,87351,87417,87454,87576,87628,87632,87660,87712,87786,87891,87915,87974,87978,87996,88139,88287,88289,88324,88328,88330,88420,88550,88676,88768,88843,88847,88963,89067,89257,89293,89387,89393,89506,89809,89815,89933,90032,90108,90110,91272,91274],[12,79343,79339],{"id":79344},"produkce-produkční-funkce-cobb-douglas-mrts",[1636,79346,79347],{},[724,79348,79349,1643,79351,79353,79354,41771,79367,79380,79381,21251,79394,14897,79396,79420,79421,3245,79423,1655,79457,3245,79460,79488,79489,15266,79509,79539,79540,14897,79543,79571,79572,79575,79576,79606,79607,79637,79638,3245,79641,79681,79682,79700],{},[883,79350,1642],{},[38,79352,859],{}," popisuje vztah mezi vstupy (práce ",[883,79355,79357],{"className":79356},[886],[888,79358,79359],{"xmlns":890},[892,79360,79361,79365],{},[895,79362,79363],{},[898,79364,14667],{},[902,79366,14667],{"encoding":904},[883,79368,79370],{"className":79369},[886],[888,79371,79372],{"xmlns":890},[892,79373,79374,79378],{},[895,79375,79376],{},[898,79377,14672],{},[902,79379,14672],{"encoding":904},") a výstupem ",[883,79382,79384],{"className":79383},[886],[888,79385,79386],{"xmlns":890},[892,79387,79388,79392],{},[895,79389,79390],{},[898,79391,1734],{},[902,79393,1734],{"encoding":904},[38,79395,41839],{},[883,79397,79399],{"className":79398},[886],[888,79400,79401],{"xmlns":890},[892,79402,79403,79417],{},[895,79404,79405,79407,79409,79411,79413,79415],{},[898,79406,1734],{},[1712,79408,1714],{},[898,79410,1734],{},[1712,79412,1904],{"stretchy":1903},[898,79414,14667],{},[1712,79416,1910],{"stretchy":1903},[902,79418,79419],{"encoding":904},"Q = Q(L)",") studujeme ",[614,79422,14896],{},[883,79424,79426],{"className":79425},[886],[888,79427,79428],{"xmlns":890},[892,79429,79430,79454],{},[895,79431,79432,79434,79440,79442,79448,79450,79452],{},[898,79433,4445],{},[6927,79435,79436,79438],{},[898,79437,1710],{},[898,79439,14667],{},[1712,79441,1714],{},[2037,79443,79444,79446],{},[898,79445,1734],{},[1712,79447,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,79449,1904],{"stretchy":1903},[898,79451,14667],{},[1712,79453,1910],{"stretchy":1903},[902,79455,79456],{"encoding":904},"MP_L = Q'(L)",[614,79458,79459],{},"průměrný produkt",[883,79461,79463],{"className":79462},[886],[888,79464,79465],{"xmlns":890},[892,79466,79467,79485],{},[895,79468,79469,79471,79477,79479,79481,79483],{},[898,79470,2044],{},[6927,79472,79473,79475],{},[898,79474,1710],{},[898,79476,14667],{},[1712,79478,1714],{},[898,79480,1734],{},[898,79482,2473],{"mathvariant":2003},[898,79484,14667],{},[902,79486,79487],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,79490,79492],{"className":79491},[886],[888,79493,79494],{"xmlns":890},[892,79495,79496,79506],{},[895,79497,79498,79500],{},[898,79499,2044],{},[6927,79501,79502,79504],{},[898,79503,1710],{},[898,79505,14667],{},[902,79507,79508],{"encoding":904},"AP_L",[883,79510,79512],{"className":79511},[886],[888,79513,79514],{"xmlns":890},[892,79515,79516,79536],{},[895,79517,79518,79520,79526,79528,79530],{},[898,79519,4445],{},[6927,79521,79522,79524],{},[898,79523,1710],{},[898,79525,14667],{},[1712,79527,1714],{},[898,79529,2044],{},[6927,79531,79532,79534],{},[898,79533,1710],{},[898,79535,14667],{},[902,79537,79538],{"encoding":904},"MP_L = AP_L",". Ve ",[38,79541,79542],{},"dvoufaktorovém modelu",[883,79544,79546],{"className":79545},[886],[888,79547,79548],{"xmlns":890},[892,79549,79550,79568],{},[895,79551,79552,79554,79556,79558,79560,79562,79564,79566],{},[898,79553,1734],{},[1712,79555,1714],{},[898,79557,1734],{},[1712,79559,1904],{"stretchy":1903},[898,79561,14667],{},[1712,79563,3138],{"separator":2565},[898,79565,14672],{},[1712,79567,1910],{"stretchy":1903},[902,79569,79570],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,79573,79574],{},"Cobb-Douglasovy"," funkce ",[883,79577,79579],{"className":79578},[886],[888,79580,79581],{"xmlns":890},[892,79582,79583,79603],{},[895,79584,79585,79587,79589,79591,79597],{},[898,79586,1734],{},[1712,79588,1714],{},[898,79590,2044],{},[2037,79592,79593,79595],{},[898,79594,14667],{},[898,79596,207],{},[2037,79598,79599,79601],{},[898,79600,14672],{},[898,79602,7544],{},[902,79604,79605],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,79608,79610],{"className":79609},[886],[888,79611,79612],{"xmlns":890},[892,79613,79614,79634],{},[895,79615,79616,79618,79624,79626,79628],{},[898,79617,4445],{},[6927,79619,79620,79622],{},[898,79621,1710],{},[898,79623,14667],{},[1712,79625,3138],{"separator":2565},[898,79627,4445],{},[6927,79629,79630,79632],{},[898,79631,1710],{},[898,79633,14672],{},[902,79635,79636],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,79639,79640],{},"mezní míru technické substituce",[883,79642,79644],{"className":79643},[886],[888,79645,79646],{"xmlns":890},[892,79647,79648,79678],{},[895,79649,79650,79652,79654,79656,79658,79660,79662,79668,79670,79672],{},[898,79651,4445],{},[898,79653,1775],{},[898,79655,1772],{},[898,79657,6493],{},[1712,79659,1714],{},[898,79661,4445],{},[6927,79663,79664,79666],{},[898,79665,1710],{},[898,79667,14667],{},[898,79669,2473],{"mathvariant":2003},[898,79671,4445],{},[6927,79673,79674,79676],{},[898,79675,1710],{},[898,79677,14672],{},[902,79679,79680],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,79683,79685],{"className":79684},[886],[888,79686,79687],{"xmlns":890},[892,79688,79689,79697],{},[895,79690,79691,79693,79695],{},[898,79692,207],{},[1712,79694,3145],{},[898,79696,7544],{},[902,79698,79699],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,79702,79704],{"id":79703},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,79706,79707],{},"Po prostudování kapitoly 5 student umí:",[120,79709,79710,79716,79726,79732,79738,79743,79749,79759,79764,79770],{},[123,79711,79712,79713,3138],{},"popsat ",[38,79714,79715],{},"jednofaktorový model produkce",[123,79717,79718,79719,1655,79722,79725],{},"vypočítat ",[38,79720,79721],{},"mezní",[38,79723,79724],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,79727,79728,79729,3138],{},"charakterizovat průběh ",[38,79730,79731],{},"křivky produkce",[123,79733,79734,79735,3138],{},"formulovat ",[38,79736,79737],{},"princip maximalizace průměrného produktu práce",[123,79739,79712,79740,3138],{},[38,79741,79742],{},"dvoufaktorový model produkce",[123,79744,79745,79746,3138],{},"uvést tvar ",[38,79747,79748],{},"Cobb–Douglasových produkčních funkcí",[123,79750,79751,79752,1343,79754,1343,79756,3138],{},"vyložit, co jsou ",[38,79753,29488],{},[38,79755,18531],{},[38,79757,79758],{},"klesající výnosy z rozsahu",[123,79760,79718,79761,79725],{},[38,79762,79763],{},"mezní produkty práce a kapitálu",[123,79765,79766,79767,3138],{},"najít ",[38,79768,79769],{},"izokvanty",[123,79771,79718,79772,79775],{},[38,79773,79774],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,79777,79778,79779,79782,79783,79786,79787,3245,79790,1343,79803,3245,79806,1655,79819,79822,79823,79825,79826,1659],{},"Každý proces produkce je určován ",[38,79780,79781],{},"faktory"," (též ",[38,79784,79785],{},"vstupy",") produkce. K hlavním patří ",[38,79788,79789],{},"práce",[883,79791,79793],{"className":79792},[886],[888,79794,79795],{"xmlns":890},[892,79796,79797,79801],{},[895,79798,79799],{},[898,79800,14667],{},[902,79802,14667],{"encoding":904},[38,79804,79805],{},"kapitál",[883,79807,79809],{"className":79808},[886],[888,79810,79811],{"xmlns":890},[892,79812,79813,79817],{},[895,79814,79815],{},[898,79816,14672],{},[902,79818,14672],{"encoding":904},[38,79820,79821],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,79824,41839],{}," (produkce závisí jen na práci); v opačném případě o ",[38,79827,79542],{},[724,79829,79830,79831,1343,79834,79837],{},"Související matematický aparát: ",[207,79832,1690],{"className":79833,"dataFsResolvedFilePath":764,"href":765},[210],[207,79835,784],{"className":79836,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,79839,79841],{"id":79840},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,79843,79844,79845,79858,79859,79872,79873],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,79846,79848],{"className":79847},[886],[888,79849,79850],{"xmlns":890},[892,79851,79852,79856],{},[895,79853,79854],{},[898,79855,1734],{},[902,79857,1734],{"encoding":904}," na práci ",[883,79860,79862],{"className":79861},[886],[888,79863,79864],{"xmlns":890},[892,79865,79866,79870],{},[895,79867,79868],{},[898,79869,14667],{},[902,79871,14667],{"encoding":904}," vyjadřuje ",[38,79874,79875],{},"produkční funkce",[883,79877,79879],{"className":79878},[886],[888,79880,79881],{"xmlns":890,"display":32941},[892,79882,79883,79914],{},[25629,79884,79885],{"width":32946},[25634,79886,79887,79889,79907,79909],{},[25637,79888],{"width":32951},[25637,79890,79891],{},[895,79892,79893,79895,79897,79899,79901,79903,79905],{},[898,79894,1734],{},[1712,79896,1714],{},[898,79898,1734],{},[1712,79900,1904],{"stretchy":1903},[898,79902,14667],{},[1712,79904,1910],{"stretchy":1903},[1712,79906,3138],{"separator":2565},[25637,79908],{"width":32951},[25637,79910,79911],{},[1762,79912,79913],{},"(5.1)",[902,79915,79916],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,79918,79919,79920,14897,79923,79926,79927,79940],{},"jejíž graf se nazývá ",[38,79921,79922],{},"křivka produkce",[614,79924,79925],{},"production curve","). Práce ",[883,79928,79930],{"className":79929},[886],[888,79931,79932],{"xmlns":890},[892,79933,79934,79938],{},[895,79935,79936],{},[898,79937,14667],{},[902,79939,14667],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,79942,79944,79945,1910],{"id":79943},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,79946,79948],{"className":79947},[886],[888,79949,79950],{"xmlns":890},[892,79951,79952,79962],{},[895,79953,79954,79956],{},[898,79955,4445],{},[6927,79957,79958,79960],{},[898,79959,1710],{},[898,79961,14667],{},[902,79963,14917],{"encoding":904},[724,79965,79966,14897,79969,79972,79973,79992],{},[38,79967,79968],{},"Mezní produkt práce",[614,79970,79971],{},"marginal product of labour",") ",[883,79974,79976],{"className":79975},[886],[888,79977,79978],{"xmlns":890},[892,79979,79980,79990],{},[895,79981,79982,79984],{},[898,79983,4445],{},[6927,79985,79986,79988],{},[898,79987,1710],{},[898,79989,14667],{},[902,79991,14917],{"encoding":904}," je derivace produkce podle práce:",[883,79994,79996],{"className":79995},[886],[888,79997,79998],{"xmlns":890,"display":32941},[892,79999,80000,80057],{},[25629,80001,80002],{"width":32946},[25634,80003,80004,80006,80050,80052],{},[25637,80005],{"width":32951},[25637,80007,80008],{},[895,80009,80010,80012,80018,80020,80034,80036,80042,80044,80046,80048],{},[898,80011,4445],{},[6927,80013,80014,80016],{},[898,80015,1710],{},[898,80017,14667],{},[1712,80019,1714],{},[2567,80021,80022,80028],{},[895,80023,80024,80026],{},[898,80025,2468],{},[898,80027,1734],{},[895,80029,80030,80032],{},[898,80031,2468],{},[898,80033,14667],{},[1712,80035,1714],{},[2037,80037,80038,80040],{},[898,80039,1734],{},[1712,80041,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,80043,1904],{"stretchy":1903},[898,80045,14667],{},[1712,80047,1910],{"stretchy":1903},[898,80049,1659],{"mathvariant":2003},[25637,80051],{"width":32951},[25637,80053,80054],{},[1762,80055,80056],{},"(5.2)",[902,80058,80059],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,80061,80062,80063,24820,80081,80109,80110,80127,80128,3072,80145,1691],{},"Pro pevnou hodnotu ",[883,80064,80066],{"className":80065},[886],[888,80067,80068],{"xmlns":890},[892,80069,80070,80078],{},[895,80071,80072],{},[2037,80073,80074,80076],{},[898,80075,14667],{},[1712,80077,2145],{},[902,80079,80080],{"encoding":904},"L^*",[883,80082,80084],{"className":80083},[886],[888,80085,80086],{"xmlns":890},[892,80087,80088,80106],{},[895,80089,80090,80096,80098,80104],{},[2037,80091,80092,80094],{},[898,80093,1734],{},[1712,80095,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,80097,1904],{"stretchy":1903},[2037,80099,80100,80102],{},[898,80101,14667],{},[1712,80103,2145],{},[1712,80105,1910],{"stretchy":1903},[902,80107,80108],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,80111,80113],{"className":80112},[886],[888,80114,80115],{"xmlns":890},[892,80116,80117,80125],{},[895,80118,80119],{},[2037,80120,80121,80123],{},[898,80122,14667],{},[1712,80124,2145],{},[902,80126,80080],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,80129,80131],{"className":80130},[886],[888,80132,80133],{"xmlns":890},[892,80134,80135,80143],{},[895,80136,80137],{},[2037,80138,80139,80141],{},[898,80140,14667],{},[1712,80142,2145],{},[902,80144,80080],{"encoding":904},[883,80146,80148],{"className":80147},[886],[888,80149,80150],{"xmlns":890},[892,80151,80152,80164],{},[895,80153,80154,80160,80162],{},[2037,80155,80156,80158],{},[898,80157,14667],{},[1712,80159,2145],{},[1712,80161,3145],{},[1716,80163,2222],{},[902,80165,80166],{"encoding":904},"L^*+1",[1636,80168,80169],{},[724,80170,80171,22898,80173,80192,80193,80196,80197,1659],{},[883,80172,1941],{},[883,80174,80176],{"className":80175},[886],[888,80177,80178],{"xmlns":890},[892,80179,80180,80190],{},[895,80181,80182,80184],{},[898,80183,4445],{},[6927,80185,80186,80188],{},[898,80187,1710],{},[898,80189,14667],{},[902,80191,14917],{"encoding":904}," odpovídá na otázku „",[38,80194,80195],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,80198,80200],{"className":80199},[886],[888,80201,80202],{"xmlns":890},[892,80203,80204,80208],{},[895,80205,80206],{},[898,80207,14667],{},[902,80209,14667],{"encoding":904},[724,80211,80212,80215,80216,80232,80233,3072,80246,80266],{},[38,80213,80214],{},"Přibližná změna produkce"," pro změnu práce o ",[883,80217,80219],{"className":80218},[886],[888,80220,80221],{"xmlns":890},[892,80222,80223,80229],{},[895,80224,80225,80227],{},[898,80226,2468],{},[898,80228,14667],{},[902,80230,80231],{"encoding":904},"dL"," (z ",[883,80234,80236],{"className":80235},[886],[888,80237,80238],{"xmlns":890},[892,80239,80240,80244],{},[895,80241,80242],{},[898,80243,14667],{},[902,80245,14667],{"encoding":904},[883,80247,80249],{"className":80248},[886],[888,80250,80251],{"xmlns":890},[892,80252,80253,80263],{},[895,80254,80255,80257,80259,80261],{},[898,80256,14667],{},[1712,80258,3145],{},[898,80260,2468],{},[898,80262,14667],{},[902,80264,80265],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,80268,80270],{"className":80269},[886],[888,80271,80272],{"xmlns":890,"display":32941},[892,80273,80274,80339],{},[25629,80275,80276],{"width":32946},[25634,80277,80278,80280,80332,80334],{},[25637,80279],{"width":32951},[25637,80281,80282],{},[895,80283,80284,80286,80288,80290,80292,80294,80296,80302,80304,80306,80308,80310,80312,80314,80316,80318,80324,80326,80328,80330],{},[898,80285,2004],{"mathvariant":2003},[898,80287,1734],{},[1712,80289,3740],{},[898,80291,2468],{},[898,80293,1734],{},[1712,80295,1714],{},[2037,80297,80298,80300],{},[898,80299,1734],{},[1712,80301,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,80303,1904],{"stretchy":1903},[898,80305,14667],{},[1712,80307,1910],{"stretchy":1903},[1762,80309,2583],{},[898,80311,2468],{},[898,80313,14667],{},[1712,80315,1714],{},[898,80317,4445],{},[6927,80319,80320,80322],{},[898,80321,1710],{},[898,80323,14667],{},[1762,80325,2583],{},[898,80327,2468],{},[898,80329,14667],{},[898,80331,1659],{"mathvariant":2003},[25637,80333],{"width":32951},[25637,80335,80336],{},[1762,80337,80338],{},"(5.3)",[902,80340,80341],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,80343,80344,80345,1659],{},"Skutečná změna je ",[883,80346,80348],{"className":80347},[886],[888,80349,80350],{"xmlns":890},[892,80351,80352,80384],{},[895,80353,80354,80356,80358,80360,80362,80364,80366,80368,80370,80372,80374,80376,80378,80380,80382],{},[898,80355,2004],{"mathvariant":2003},[898,80357,1734],{},[1712,80359,1714],{},[898,80361,1734],{},[1712,80363,1904],{"stretchy":1903},[898,80365,14667],{},[1712,80367,3145],{},[898,80369,2468],{},[898,80371,14667],{},[1712,80373,1910],{"stretchy":1903},[1712,80375,2219],{},[898,80377,1734],{},[1712,80379,1904],{"stretchy":1903},[898,80381,14667],{},[1712,80383,1910],{"stretchy":1903},[902,80385,80386],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,80388,80390],{"id":80389},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,80392,80393,14897,80396,8558],{},[38,80394,80395],{},"Zákon klesajících výnosů",[614,80397,80398],{},"law of diminishing marginal productivity",[1636,80400,80401],{},[724,80402,80403,80404,80406],{},"Roste-li postupně některý ze vstupů (",[614,80405,41835],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,80408,80409],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,80411,80412,80413,3245,80434,80453,80454,80504,80505,80507,80508,3245,80528,80547,80548,80504,80580,7037,80582,80601,80602,26469,80619,80653,80654,5920,80671,80674],{},"1° ",[38,80414,80415,80416,2854],{},"Do bodu ",[883,80417,80419],{"className":80418},[886],[888,80420,80421],{"xmlns":890},[892,80422,80423,80431],{},[895,80424,80425],{},[6927,80426,80427,80429],{},[898,80428,14667],{},[1716,80430,2085],{},[902,80432,80433],{"encoding":904},"L_0",[883,80435,80437],{"className":80436},[886],[888,80438,80439],{"xmlns":890},[892,80440,80441,80451],{},[895,80442,80443,80445],{},[898,80444,4445],{},[6927,80446,80447,80449],{},[898,80448,1710],{},[898,80450,14667],{},[902,80452,14917],{"encoding":904}," roste, tj. ",[883,80455,80457],{"className":80456},[886],[888,80458,80459],{"xmlns":890},[892,80460,80461,80501],{},[895,80462,80463,80465,80467,80473,80479,80481,80491,80493,80495,80497,80499],{},[1712,80464,1904],{"stretchy":1903},[898,80466,4445],{},[6927,80468,80469,80471],{},[898,80470,1710],{},[898,80472,14667],{},[2037,80474,80475,80477],{},[1712,80476,1910],{"stretchy":1903},[1712,80478,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,80480,1714],{},[2037,80482,80483,80485],{},[898,80484,1734],{},[895,80486,80487,80489],{},[1712,80488,2243],{"mathvariant":2003},[1712,80490,2243],{"mathvariant":2003},[1712,80492,1904],{"stretchy":1903},[898,80494,14667],{},[1712,80496,1910],{"stretchy":1903},[1712,80498,2302],{},[1716,80500,2085],{},[902,80502,80503],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,80506,42539],{},".\n2° ",[38,80509,80510,80511,2854],{},"Od bodu ",[883,80512,80514],{"className":80513},[886],[888,80515,80516],{"xmlns":890},[892,80517,80518,80526],{},[895,80519,80520],{},[6927,80521,80522,80524],{},[898,80523,14667],{},[1716,80525,2085],{},[902,80527,80433],{"encoding":904},[883,80529,80531],{"className":80530},[886],[888,80532,80533],{"xmlns":890},[892,80534,80535,80545],{},[895,80536,80537,80539],{},[898,80538,4445],{},[6927,80540,80541,80543],{},[898,80542,1710],{},[898,80544,14667],{},[902,80546,14917],{"encoding":904}," klesá, ",[883,80549,80551],{"className":80550},[886],[888,80552,80553],{"xmlns":890},[892,80554,80555,80577],{},[895,80556,80557,80567,80569,80571,80573,80575],{},[2037,80558,80559,80561],{},[898,80560,1734],{},[895,80562,80563,80565],{},[1712,80564,2243],{"mathvariant":2003},[1712,80566,2243],{"mathvariant":2003},[1712,80568,1904],{"stretchy":1903},[898,80570,14667],{},[1712,80572,1910],{"stretchy":1903},[1712,80574,2252],{},[1716,80576,2085],{},[902,80578,80579],{"encoding":904},"Q''(L) \u003C 0",[38,80581,43363],{},[883,80583,80585],{"className":80584},[886],[888,80586,80587],{"xmlns":890},[892,80588,80589,80599],{},[895,80590,80591,80593],{},[898,80592,4445],{},[6927,80594,80595,80597],{},[898,80596,1710],{},[898,80598,14667],{},[902,80600,14917],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,80603,80605],{"className":80604},[886],[888,80606,80607],{"xmlns":890},[892,80608,80609,80617],{},[895,80610,80611],{},[6927,80612,80613,80615],{},[898,80614,14667],{},[1716,80616,2222],{},[902,80618,18086],{"encoding":904},[883,80620,80622],{"className":80621},[886],[888,80623,80624],{"xmlns":890},[892,80625,80626,80650],{},[895,80627,80628,80630,80636,80638,80644,80646,80648],{},[898,80629,4445],{},[6927,80631,80632,80634],{},[898,80633,1710],{},[898,80635,14667],{},[1712,80637,1904],{"stretchy":1903},[6927,80639,80640,80642],{},[898,80641,14667],{},[1716,80643,2222],{},[1712,80645,1910],{"stretchy":1903},[1712,80647,1714],{},[1716,80649,2085],{},[902,80651,80652],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,80655,80657],{"className":80656},[886],[888,80658,80659],{"xmlns":890},[892,80660,80661,80669],{},[895,80662,80663],{},[6927,80664,80665,80667],{},[898,80666,14667],{},[1716,80668,2085],{},[902,80670,80433],{"encoding":904},[38,80672,80673],{},"inflexním bodem"," produkční funkce.",[724,80676,80677,80678,15266,80695,1659],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,80679,80681],{"className":80680},[886],[888,80682,80683],{"xmlns":890},[892,80684,80685,80693],{},[895,80686,80687],{},[6927,80688,80689,80691],{},[898,80690,14667],{},[1716,80692,2085],{},[902,80694,80433],{"encoding":904},[883,80696,80698],{"className":80697},[886],[888,80699,80700],{"xmlns":890},[892,80701,80702,80724],{},[895,80703,80704,80714,80716,80718,80720,80722],{},[2037,80705,80706,80708],{},[898,80707,1734],{},[895,80709,80710,80712],{},[1712,80711,2243],{"mathvariant":2003},[1712,80713,2243],{"mathvariant":2003},[1712,80715,1904],{"stretchy":1903},[898,80717,14667],{},[1712,80719,1910],{"stretchy":1903},[1712,80721,2252],{},[1716,80723,2085],{},[902,80725,80579],{"encoding":904},[724,80727,80728,3245,80731,3481,80771,1343,80788,80805],{},[38,80729,80730],{},"Typický polynom třetího stupně:",[883,80732,80734],{"className":80733},[886],[888,80735,80736],{"xmlns":890},[892,80737,80738,80768],{},[895,80739,80740,80742,80744,80746,80748,80750,80752,80758,80760,80762],{},[898,80741,1734],{},[1712,80743,1904],{"stretchy":1903},[898,80745,14667],{},[1712,80747,1910],{"stretchy":1903},[1712,80749,1714],{},[898,80751,207],{},[2037,80753,80754,80756],{},[898,80755,14667],{},[1716,80757,6198],{},[1712,80759,3145],{},[898,80761,7544],{},[2037,80763,80764,80766],{},[898,80765,14667],{},[1716,80767,2787],{},[902,80769,80770],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,80772,80774],{"className":80773},[886],[888,80775,80776],{"xmlns":890},[892,80777,80778,80786],{},[895,80779,80780,80782,80784],{},[898,80781,207],{},[1712,80783,2252],{},[1716,80785,2085],{},[902,80787,47960],{"encoding":904},[883,80789,80791],{"className":80790},[886],[888,80792,80793],{"xmlns":890},[892,80794,80795,80803],{},[895,80796,80797,80799,80801],{},[898,80798,7544],{},[1712,80800,2302],{},[1716,80802,2085],{},[902,80804,23689],{"encoding":904},". Pak",[883,80807,80809],{"className":80808},[886],[888,80810,80811],{"xmlns":890,"display":32941},[892,80812,80813,80873],{},[895,80814,80815,80821,80823,80825,80833,80841,80843,80845,80851,80853,80855,80863,80871],{},[6927,80816,80817,80819],{},[898,80818,14667],{},[1716,80820,2085],{},[1712,80822,1714],{},[1712,80824,2219],{},[2563,80826,80827],{"scriptlevel":2085,"displaystyle":1903},[2567,80828,80829,80831],{},[1716,80830,2222],{},[1716,80832,6198],{},[2563,80834,80835],{"scriptlevel":2085,"displaystyle":1903},[2567,80836,80837,80839],{},[898,80838,7544],{},[898,80840,207],{},[1712,80842,3138],{"separator":2565},[3690,80844],{"width":3692},[6927,80846,80847,80849],{},[898,80848,14667],{},[1716,80850,2222],{},[1712,80852,1714],{},[1712,80854,2219],{},[2563,80856,80857],{"scriptlevel":2085,"displaystyle":1903},[2567,80858,80859,80861],{},[1716,80860,2787],{},[1716,80862,6198],{},[2563,80864,80865],{"scriptlevel":2085,"displaystyle":1903},[2567,80866,80867,80869],{},[898,80868,7544],{},[898,80870,207],{},[898,80872,1659],{"mathvariant":2003},[902,80874,80875],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,80877,80879,80880,1910],{"id":80878},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,80881,80883],{"className":80882},[886],[888,80884,80885],{"xmlns":890},[892,80886,80887,80897],{},[895,80888,80889,80891],{},[898,80890,2044],{},[6927,80892,80893,80895],{},[898,80894,1710],{},[898,80896,14667],{},[902,80898,79508],{"encoding":904},[724,80900,80901,14897,80904,79972,80907,80926],{},[38,80902,80903],{},"Průměrný produkt práce",[614,80905,80906],{},"average product of labour",[883,80908,80910],{"className":80909},[886],[888,80911,80912],{"xmlns":890},[892,80913,80914,80924],{},[895,80915,80916,80918],{},[898,80917,2044],{},[6927,80919,80920,80922],{},[898,80921,1710],{},[898,80923,14667],{},[902,80925,79508],{"encoding":904}," je podíl produkce a práce:",[883,80928,80930],{"className":80929},[886],[888,80931,80932],{"xmlns":890,"display":32941},[892,80933,80934,80969],{},[25629,80935,80936],{"width":32946},[25634,80937,80938,80940,80962,80964],{},[25637,80939],{"width":32951},[25637,80941,80942],{},[895,80943,80944,80946,80952,80954,80960],{},[898,80945,2044],{},[6927,80947,80948,80950],{},[898,80949,1710],{},[898,80951,14667],{},[1712,80953,1714],{},[2567,80955,80956,80958],{},[898,80957,1734],{},[898,80959,14667],{},[898,80961,1659],{"mathvariant":2003},[25637,80963],{"width":32951},[25637,80965,80966],{},[1762,80967,80968],{},"(5.4)",[902,80970,80971],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,80973,80974,80975,1659],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,80976,80978],{"className":80977},[886],[888,80979,80980],{"xmlns":890},[892,80981,80982,80992],{},[895,80983,80984,80986],{},[898,80985,2044],{},[6927,80987,80988,80990],{},[898,80989,1710],{},[898,80991,14667],{},[902,80993,79508],{"encoding":904},[115,80995,80997],{"id":80996},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,80999,81000],{},[3817,81001],{"alt":81002,"className":81003,"src":81004},"imek-q-mpl-apl-tripanel",[210,3821],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1636,81006,81007],{},[724,81008,81009,81012,81013,8046,81032,81049,81050],{},[38,81010,81011],{},"Princip:"," Má-li ",[883,81014,81016],{"className":81015},[886],[888,81017,81018],{"xmlns":890},[892,81019,81020,81030],{},[895,81021,81022,81024],{},[898,81023,2044],{},[6927,81025,81026,81028],{},[898,81027,1710],{},[898,81029,14667],{},[902,81031,79508],{"encoding":904},[883,81033,81035],{"className":81034},[886],[888,81036,81037],{"xmlns":890},[892,81038,81039,81047],{},[895,81040,81041],{},[6927,81042,81043,81045],{},[898,81044,14667],{},[1716,81046,2085],{},[902,81048,80433],{"encoding":904}," maximum, pak platí\n",[883,81051,81053],{"className":81052,"title":1986,"style":1987},[1985],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,81055,81056,81057,81060,81061,3245,81065,1659],{},"Slovně: ",[38,81058,81059],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,81062,81064],{"className":81063,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,81066,81068],{"className":81067},[886],[888,81069,81070],{"xmlns":890},[892,81071,81072,81078],{},[895,81073,81074,81076],{},[898,81075,2044],{},[898,81077,8195],{},[902,81079,60435],{"encoding":904},[1636,81081,81082,81106],{},[724,81083,81084,81086,81087],{},[883,81085,2370],{}," Postup — jak najít max ",[883,81088,81090],{"className":81089},[886],[888,81091,81092],{"xmlns":890},[892,81093,81094,81104],{},[895,81095,81096,81098],{},[898,81097,2044],{},[6927,81099,81100,81102],{},[898,81101,1710],{},[898,81103,14667],{},[902,81105,79508],{"encoding":904},[152,81107,81108,81146,81228],{},[123,81109,81110,81111,81145],{},"Napište ",[883,81112,81114],{"className":81113},[886],[888,81115,81116],{"xmlns":890},[892,81117,81118,81142],{},[895,81119,81120,81122,81128,81130,81132,81134,81136,81138,81140],{},[898,81121,2044],{},[6927,81123,81124,81126],{},[898,81125,1710],{},[898,81127,14667],{},[1712,81129,1714],{},[898,81131,1734],{},[1712,81133,1904],{"stretchy":1903},[898,81135,14667],{},[1712,81137,1910],{"stretchy":1903},[898,81139,2473],{"mathvariant":2003},[898,81141,14667],{},[902,81143,81144],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,81147,81148,81149,81181,81182,81185,81186,1659],{},"Položte ",[883,81150,81152],{"className":81151},[886],[888,81153,81154],{"xmlns":890},[892,81155,81156,81178],{},[895,81157,81158,81160,81162,81168,81174,81176],{},[1712,81159,1904],{"stretchy":1903},[898,81161,2044],{},[6927,81163,81164,81166],{},[898,81165,1710],{},[898,81167,14667],{},[2037,81169,81170,81172],{},[1712,81171,1910],{"stretchy":1903},[1712,81173,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,81175,1714],{},[1716,81177,2085],{},[902,81179,81180],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,81183,81184],{},"Zkratka:"," můžete rovnou řešit ",[883,81187,81189],{"className":81188},[886],[888,81190,81191],{"xmlns":890},[892,81192,81193,81225],{},[895,81194,81195,81197,81203,81205,81207,81209,81211,81213,81219,81221,81223],{},[898,81196,4445],{},[6927,81198,81199,81201],{},[898,81200,1710],{},[898,81202,14667],{},[1712,81204,1904],{"stretchy":1903},[898,81206,14667],{},[1712,81208,1910],{"stretchy":1903},[1712,81210,1714],{},[898,81212,2044],{},[6927,81214,81215,81217],{},[898,81216,1710],{},[898,81218,14667],{},[1712,81220,1904],{"stretchy":1903},[898,81222,14667],{},[1712,81224,1910],{"stretchy":1903},[902,81226,81227],{"encoding":904},"MP_L(L) = AP_L(L)",[123,81229,81230],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,81232,70376],{"id":81233},"odvození",[724,81235,81236,81237,81270],{},"Z ",[883,81238,81240],{"className":81239},[886],[888,81241,81242],{"xmlns":890},[892,81243,81244,81268],{},[895,81245,81246,81248,81254,81256,81258,81260,81262,81264,81266],{},[898,81247,2044],{},[6927,81249,81250,81252],{},[898,81251,1710],{},[898,81253,14667],{},[1712,81255,1714],{},[898,81257,1734],{},[1712,81259,1904],{"stretchy":1903},[898,81261,14667],{},[1712,81263,1910],{"stretchy":1903},[898,81265,2473],{"mathvariant":2003},[898,81267,14667],{},[902,81269,81144],{"encoding":904}," a derivace podílu:",[883,81272,81274],{"className":81273},[886],[888,81275,81276],{"xmlns":890,"display":32941},[892,81277,81278,81431],{},[895,81279,81280,81282,81284,81290,81296,81298,81300,81302,81304,81344,81346,81352,81386,81388,81394,81397,81399,81405,81407,81409,81411,81413,81415,81421,81423,81425,81427,81429],{},[1712,81281,1904],{"stretchy":1903},[898,81283,2044],{},[6927,81285,81286,81288],{},[898,81287,1710],{},[898,81289,14667],{},[2037,81291,81292,81294],{},[1712,81293,1910],{"stretchy":1903},[1712,81295,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,81297,1904],{"stretchy":1903},[898,81299,14667],{},[1712,81301,1910],{"stretchy":1903},[1712,81303,1714],{},[2567,81305,81306,81338],{},[895,81307,81308,81314,81316,81318,81320,81322,81324,81326,81328,81330,81332,81334,81336],{},[2037,81309,81310,81312],{},[898,81311,1734],{},[1712,81313,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,81315,1904],{"stretchy":1903},[898,81317,14667],{},[1712,81319,1910],{"stretchy":1903},[1712,81321,1783],{},[898,81323,14667],{},[1712,81325,2219],{},[898,81327,1734],{},[1712,81329,1904],{"stretchy":1903},[898,81331,14667],{},[1712,81333,1910],{"stretchy":1903},[1712,81335,1783],{},[1716,81337,2222],{},[2037,81339,81340,81342],{},[898,81341,14667],{},[1716,81343,2787],{},[1712,81345,1714],{},[2567,81347,81348,81350],{},[1716,81349,2222],{},[898,81351,14667],{},[895,81353,81354,81356,81362,81364,81366,81368,81370,81384],{},[1712,81355,1904],{"fence":2565},[2037,81357,81358,81360],{},[898,81359,1734],{},[1712,81361,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,81363,1904],{"stretchy":1903},[898,81365,14667],{},[1712,81367,1910],{"stretchy":1903},[1712,81369,2219],{},[2567,81371,81372,81382],{},[895,81373,81374,81376,81378,81380],{},[898,81375,1734],{},[1712,81377,1904],{"stretchy":1903},[898,81379,14667],{},[1712,81381,1910],{"stretchy":1903},[898,81383,14667],{},[1712,81385,1910],{"fence":2565},[1712,81387,1714],{},[2567,81389,81390,81392],{},[1716,81391,2222],{},[898,81393,14667],{},[1712,81395,1904],{"fence":2565,"stretchy":2565,"minsize":81396,"maxsize":81396},"1.2em",[898,81398,4445],{},[6927,81400,81401,81403],{},[898,81402,1710],{},[898,81404,14667],{},[1712,81406,1904],{"stretchy":1903},[898,81408,14667],{},[1712,81410,1910],{"stretchy":1903},[1712,81412,2219],{},[898,81414,2044],{},[6927,81416,81417,81419],{},[898,81418,1710],{},[898,81420,14667],{},[1712,81422,1904],{"stretchy":1903},[898,81424,14667],{},[1712,81426,1910],{"stretchy":1903},[1712,81428,1910],{"fence":2565,"stretchy":2565,"minsize":81396,"maxsize":81396},[898,81430,1659],{"mathvariant":2003},[902,81432,81433],{"encoding":904},"(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).",[724,81435,14535,81436,5920,81458,81541],{},[883,81437,81439],{"className":81438},[886],[888,81440,81441],{"xmlns":890},[892,81442,81443,81455],{},[895,81444,81445,81451,81453],{},[6927,81446,81447,81449],{},[898,81448,14667],{},[1716,81450,2085],{},[1712,81452,2302],{},[1716,81454,2085],{},[902,81456,81457],{"encoding":904},"L_0 > 0",[883,81459,81461],{"className":81460},[886],[888,81462,81463],{"xmlns":890},[892,81464,81465,81538],{},[895,81466,81467,81469,81471,81477,81483,81485,81491,81493,81495,81497,81500,81502,81508,81510,81516,81518,81520,81522,81528,81530,81536],{},[1712,81468,1904],{"stretchy":1903},[898,81470,2044],{},[6927,81472,81473,81475],{},[898,81474,1710],{},[898,81476,14667],{},[2037,81478,81479,81481],{},[1712,81480,1910],{"stretchy":1903},[1712,81482,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,81484,1904],{"stretchy":1903},[6927,81486,81487,81489],{},[898,81488,14667],{},[1716,81490,2085],{},[1712,81492,1910],{"stretchy":1903},[1712,81494,1714],{},[1716,81496,2085],{},[1712,81498,81499],{},"⇔",[898,81501,4445],{},[6927,81503,81504,81506],{},[898,81505,1710],{},[898,81507,14667],{},[1712,81509,1904],{"stretchy":1903},[6927,81511,81512,81514],{},[898,81513,14667],{},[1716,81515,2085],{},[1712,81517,1910],{"stretchy":1903},[1712,81519,1714],{},[898,81521,2044],{},[6927,81523,81524,81526],{},[898,81525,1710],{},[898,81527,14667],{},[1712,81529,1904],{"stretchy":1903},[6927,81531,81532,81534],{},[898,81533,14667],{},[1716,81535,2085],{},[1712,81537,1910],{"stretchy":1903},[902,81539,81540],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,81543,81545],{"id":81544},"příklad-51","Příklad 5.1",[724,81547,81548,81549,1659],{},"Je dána produkce ",[883,81550,81552],{"className":81551},[886],[888,81553,81554],{"xmlns":890},[892,81555,81556,81580],{},[895,81557,81558,81560,81562,81564,81570,81572,81574],{},[898,81559,1734],{},[1712,81561,1714],{},[1716,81563,6209],{},[2037,81565,81566,81568],{},[898,81567,14667],{},[1716,81569,2787],{},[1712,81571,2219],{},[1716,81573,6673],{},[2037,81575,81576,81578],{},[898,81577,14667],{},[1716,81579,6198],{},[902,81581,81582],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,81584,81585,62397,81588,81638,81639,1659],{},[38,81586,81587],{},"(a)",[883,81589,81591],{"className":81590},[886],[888,81592,81593],{"xmlns":890},[892,81594,81595,81635],{},[895,81596,81597,81599,81601,81603,81605,81607,81609,81611,81613,81615,81617,81619,81621,81623,81625,81627,81629,81631,81633],{},[898,81598,14667],{},[1712,81600,1714],{},[1716,81602,2787],{},[1712,81604,3138],{"separator":2565},[1716,81606,3068],{},[1712,81608,3138],{"separator":2565},[1716,81610,3397],{},[1712,81612,3138],{"separator":2565},[1716,81614,1718],{},[1712,81616,3138],{"separator":2565},[1716,81618,27821],{},[1712,81620,3138],{"separator":2565},[1716,81622,9110],{},[1712,81624,3138],{"separator":2565},[1716,81626,6857],{},[1712,81628,3138],{"separator":2565},[1716,81630,43221],{},[1712,81632,3138],{"separator":2565},[1716,81634,2809],{},[902,81636,81637],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,81640,81642],{"className":81641},[886],[888,81643,81644],{"xmlns":890},[892,81645,81646,81656],{},[895,81647,81648,81650],{},[898,81649,4445],{},[6927,81651,81652,81654],{},[898,81653,1710],{},[898,81655,14667],{},[902,81657,14917],{"encoding":904},[724,81659,81660,81661,39843],{},"Podle (5.2): ",[883,81662,81664],{"className":81663},[886],[888,81665,81666],{"xmlns":890},[892,81667,81668,81724],{},[895,81669,81670,81672,81678,81680,81686,81688,81690,81692,81694,81696,81698,81700,81702,81708,81710,81712,81714,81716,81718,81720,81722],{},[898,81671,4445],{},[6927,81673,81674,81676],{},[898,81675,1710],{},[898,81677,14667],{},[1712,81679,1714],{},[2037,81681,81682,81684],{},[898,81683,1734],{},[1712,81685,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,81687,1904],{"stretchy":1903},[898,81689,14667],{},[1712,81691,1910],{"stretchy":1903},[1712,81693,1714],{},[1716,81695,8912],{},[898,81697,14667],{},[1712,81699,2219],{},[1716,81701,24196],{},[2037,81703,81704,81706],{},[898,81705,14667],{},[1716,81707,2787],{},[1712,81709,1714],{},[898,81711,14667],{},[1712,81713,1904],{"stretchy":1903},[1716,81715,8912],{},[1712,81717,2219],{},[1716,81719,24196],{},[898,81721,14667],{},[1712,81723,1910],{"stretchy":1903},[902,81725,81726],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,81728,81729,81766],{},[19,81730,81731],{},[22,81732,81733,81748,81750,81752,81754,81756,81758,81760,81762,81764],{},[25,81734,81735],{},[883,81736,81738],{"className":81737},[886],[888,81739,81740],{"xmlns":890},[892,81741,81742,81746],{},[895,81743,81744],{},[898,81745,14667],{},[902,81747,14667],{"encoding":904},[25,81749,2787],{},[25,81751,3068],{},[25,81753,3397],{},[25,81755,1718],{},[25,81757,27821],{},[25,81759,9110],{},[25,81761,6857],{},[25,81763,43221],{},[25,81765,2809],{},[30,81767,81768],{},[22,81769,81770,81791,81794,81797,81800,81802,81805,81807,81809,81828],{},[35,81771,81772],{},[883,81773,81775],{"className":81774},[886],[888,81776,81777],{"xmlns":890},[892,81778,81779,81789],{},[895,81780,81781,81783],{},[898,81782,4445],{},[6927,81784,81785,81787],{},[898,81786,1710],{},[898,81788,14667],{},[902,81790,14917],{"encoding":904},[35,81792,81793],{},"21,6",[35,81795,81796],{},"45",[35,81798,81799],{},"57,6",[35,81801,8533],{},[35,81803,81804],{},"50,4",[35,81806,81793],{},[35,81808,2085],{},[35,81810,81811],{},[883,81812,81814],{"className":81813},[886],[888,81815,81816],{"xmlns":890},[892,81817,81818,81825],{},[895,81819,81820,81822],{},[1712,81821,2219],{},[1716,81823,81824],{},"12,6",[902,81826,81827],{"encoding":904},"-12{,}6",[35,81829,81830],{},[883,81831,81833],{"className":81832},[886],[888,81834,81835],{"xmlns":890},[892,81836,81837,81843],{},[895,81838,81839,81841],{},[1712,81840,2219],{},[1716,81842,50327],{},[902,81844,81845],{"encoding":904},"-75",[724,81847,81848,81867,81868,81886,81887,81904,81905,81923,81924,81948,81949,81967],{},[883,81849,81851],{"className":81850},[886],[888,81852,81853],{"xmlns":890},[892,81854,81855,81865],{},[895,81856,81857,81859],{},[898,81858,4445],{},[6927,81860,81861,81863],{},[898,81862,1710],{},[898,81864,14667],{},[902,81866,14917],{"encoding":904}," nabývá maxima pro ",[883,81869,81871],{"className":81870},[886],[888,81872,81873],{"xmlns":890},[892,81874,81875,81883],{},[895,81876,81877,81879,81881],{},[898,81878,14667],{},[1712,81880,1714],{},[1716,81882,1718],{},[902,81884,81885],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,81888,81890],{"className":81889},[886],[888,81891,81892],{"xmlns":890},[892,81893,81894,81902],{},[895,81895,81896,81898,81900],{},[898,81897,14667],{},[1712,81899,1714],{},[1716,81901,1718],{},[902,81903,81885],{"encoding":904}," přírůstky klesají, v ",[883,81906,81908],{"className":81907},[886],[888,81909,81910],{"xmlns":890},[892,81911,81912,81920],{},[895,81913,81914,81916,81918],{},[898,81915,14667],{},[1712,81917,1714],{},[1716,81919,6857],{},[902,81921,81922],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,81925,81927],{"className":81926},[886],[888,81928,81929],{"xmlns":890},[892,81930,81931,81945],{},[895,81932,81933,81935,81937,81939,81941,81943],{},[898,81934,1734],{},[1712,81936,1904],{"stretchy":1903},[1716,81938,6857],{},[1712,81940,1910],{"stretchy":1903},[1712,81942,1714],{},[1716,81944,28733],{},[902,81946,81947],{"encoding":904},"Q(20) = 800","), od ",[883,81950,81952],{"className":81951},[886],[888,81953,81954],{"xmlns":890},[892,81955,81956,81964],{},[895,81957,81958,81960,81962],{},[898,81959,14667],{},[1712,81961,2302],{},[1716,81963,6857],{},[902,81965,81966],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,81969,81970],{},[614,81971,81972,81973,82013,82014,8046,82032,1659],{},"Obrázek 5.1 — graf produkce ",[883,81974,81976],{"className":81975},[886],[888,81977,81978],{"xmlns":890},[892,81979,81980,82010],{},[895,81981,81982,81984,81986,81988,81990,81992,81994,82000,82002,82004],{},[898,81983,1734],{},[1712,81985,1904],{"stretchy":1903},[898,81987,14667],{},[1712,81989,1910],{"stretchy":1903},[1712,81991,1714],{},[1716,81993,6209],{},[2037,81995,81996,81998],{},[898,81997,14667],{},[1716,81999,2787],{},[1712,82001,2219],{},[1716,82003,6673],{},[2037,82005,82006,82008],{},[898,82007,14667],{},[1716,82009,6198],{},[902,82011,82012],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,82015,82017],{"className":82016},[886],[888,82018,82019],{"xmlns":890},[892,82020,82021,82029],{},[895,82022,82023,82025,82027],{},[898,82024,1734],{},[1712,82026,1714],{},[1716,82028,28733],{},[902,82030,82031],{"encoding":904},"Q = 800",[883,82033,82035],{"className":82034},[886],[888,82036,82037],{"xmlns":890},[892,82038,82039,82047],{},[895,82040,82041,82043,82045],{},[898,82042,14667],{},[1712,82044,1714],{},[1716,82046,6857],{},[902,82048,81922],{"encoding":904},[724,82050,82051,82054],{},[38,82052,82053],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,82056,82057,82058,1343,82076,2854],{},"Podle (5.3) s ",[883,82059,82061],{"className":82060},[886],[888,82062,82063],{"xmlns":890},[892,82064,82065,82073],{},[895,82066,82067,82069,82071],{},[898,82068,14667],{},[1712,82070,1714],{},[1716,82072,6209],{},[902,82074,82075],{"encoding":904},"L = 6",[883,82077,82079],{"className":82078},[886],[888,82080,82081],{"xmlns":890},[892,82082,82083,82093],{},[895,82084,82085,82087,82089,82091],{},[898,82086,2468],{},[898,82088,14667],{},[1712,82090,1714],{},[1716,82092,6198],{},[902,82094,82095],{"encoding":904},"dL = 3",[883,82097,82099],{"className":82098},[886],[888,82100,82101],{"xmlns":890,"display":32941},[892,82102,82103,82166],{},[895,82104,82105,82107,82109,82111,82113,82119,82121,82123,82125,82127,82129,82131,82133,82135,82137,82139,82141,82143,82145,82147,82149,82151,82153,82155,82157,82159,82161,82163],{},[898,82106,2468],{},[898,82108,1734],{},[1712,82110,1714],{},[898,82112,4445],{},[6927,82114,82115,82117],{},[898,82116,1710],{},[898,82118,14667],{},[1712,82120,1904],{"stretchy":1903},[1716,82122,6209],{},[1712,82124,1910],{"stretchy":1903},[1712,82126,1783],{},[1716,82128,6198],{},[1712,82130,1714],{},[1712,82132,1904],{"stretchy":1903},[1716,82134,8912],{},[1712,82136,1783],{},[1716,82138,6209],{},[1712,82140,2219],{},[1716,82142,24196],{},[1712,82144,1783],{},[1716,82146,3377],{},[1712,82148,1910],{"stretchy":1903},[1712,82150,1783],{},[1716,82152,6198],{},[1712,82154,1714],{},[1716,82156,81804],{},[1712,82158,1783],{},[1716,82160,6198],{},[1712,82162,1714],{},[1716,82164,82165],{},"151,2.",[902,82167,82168],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,82170,82171,82172,62627,82197,82211,82212,1659],{},"Produkce vzroste z ",[883,82173,82175],{"className":82174},[886],[888,82176,82177],{"xmlns":890},[892,82178,82179,82194],{},[895,82180,82181,82183,82185,82187,82189,82191],{},[898,82182,1734],{},[1712,82184,1904],{"stretchy":1903},[1716,82186,6209],{},[1712,82188,1910],{"stretchy":1903},[1712,82190,1714],{},[1716,82192,82193],{},"172,8",[902,82195,82196],{"encoding":904},"Q(6) = 172{,}8",[883,82198,82200],{"className":82199},[886],[888,82201,82202],{"xmlns":890},[892,82203,82204,82209],{},[895,82205,82206],{},[1716,82207,82208],{},"324",[902,82210,82208],{"encoding":904},". Skutečná hodnota: ",[883,82213,82215],{"className":82214},[886],[888,82216,82217],{"xmlns":890},[892,82218,82219,82259],{},[895,82220,82221,82223,82225,82227,82229,82231,82233,82235,82237,82239,82241,82243,82245,82247,82250,82252,82254,82256],{},[898,82222,2004],{"mathvariant":2003},[898,82224,1734],{},[1712,82226,1714],{},[898,82228,1734],{},[1712,82230,1904],{"stretchy":1903},[1716,82232,1780],{},[1712,82234,1910],{"stretchy":1903},[1712,82236,2219],{},[898,82238,1734],{},[1712,82240,1904],{"stretchy":1903},[1716,82242,6209],{},[1712,82244,1910],{"stretchy":1903},[1712,82246,1714],{},[1716,82248,82249],{},"340,2",[1712,82251,2219],{},[1716,82253,82193],{},[1712,82255,1714],{},[1716,82257,82258],{},"167,4",[902,82260,82261],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,82263,82265],{"id":82264},"příklad-52","Příklad 5.2",[724,82267,82268,82269,1659],{},"Ověříme princip (5.5) pro ",[883,82270,82272],{"className":82271},[886],[888,82273,82274],{"xmlns":890},[892,82275,82276,82300],{},[895,82277,82278,82280,82282,82284,82290,82292,82294],{},[898,82279,1734],{},[1712,82281,1714],{},[1716,82283,6209],{},[2037,82285,82286,82288],{},[898,82287,14667],{},[1716,82289,2787],{},[1712,82291,2219],{},[1716,82293,6673],{},[2037,82295,82296,82298],{},[898,82297,14667],{},[1716,82299,6198],{},[902,82301,81582],{"encoding":904},[883,82303,82305],{"className":82304},[886],[888,82306,82307],{"xmlns":890,"display":32941},[892,82308,82309,82387],{},[895,82310,82311,82313,82319,82321,82327,82329,82331,82333,82335,82337,82343,82345,82347,82349,82357,82359,82361,82363,82365,82367,82369,82371,82373,82375,82377,82383,82385],{},[898,82312,2044],{},[6927,82314,82315,82317],{},[898,82316,1710],{},[898,82318,14667],{},[1712,82320,1714],{},[2567,82322,82323,82325],{},[898,82324,1734],{},[898,82326,14667],{},[1712,82328,1714],{},[1716,82330,6209],{},[898,82332,14667],{},[1712,82334,2219],{},[1716,82336,6673],{},[2037,82338,82339,82341],{},[898,82340,14667],{},[1716,82342,2787],{},[1712,82344,3138],{"separator":2565},[3690,82346],{"width":20158},[898,82348,2044],{},[6989,82350,82351,82353,82355],{},[898,82352,1710],{},[898,82354,14667],{},[1712,82356,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,82358,1714],{},[1716,82360,6209],{},[1712,82362,2219],{},[1716,82364,24146],{},[898,82366,14667],{},[1712,82368,1714],{},[1716,82370,2085],{},[1762,82372,1764],{},[1712,82374,1767],{},[1762,82376,1764],{},[6927,82378,82379,82381],{},[898,82380,14667],{},[1716,82382,2085],{},[1712,82384,1714],{},[1716,82386,73158],{},[902,82388,82389],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,82391,82392,82428,82429,82447,82448,1659],{},[883,82393,82395],{"className":82394},[886],[888,82396,82397],{"xmlns":890},[892,82398,82399,82425],{},[895,82400,82401,82403,82415,82417,82419,82421,82423],{},[898,82402,2044],{},[6989,82404,82405,82407,82409],{},[898,82406,1710],{},[898,82408,14667],{},[895,82410,82411,82413],{},[1712,82412,2243],{"mathvariant":2003},[1712,82414,2243],{"mathvariant":2003},[1712,82416,1714],{},[1712,82418,2219],{},[1716,82420,24146],{},[1712,82422,2252],{},[1716,82424,2085],{},[902,82426,82427],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,82430,82432],{"className":82431},[886],[888,82433,82434],{"xmlns":890},[892,82435,82436,82444],{},[895,82437,82438,82440,82442],{},[898,82439,14667],{},[1712,82441,1714],{},[1716,82443,41119],{},[902,82445,82446],{"encoding":904},"L = 15"," je maximum, ",[883,82449,82451],{"className":82450},[886],[888,82452,82453],{"xmlns":890},[892,82454,82455,82501],{},[895,82456,82457,82459,82465,82467,82469,82471,82473,82475,82477,82479,82481,82483,82485,82488,82490,82493,82495,82497,82499],{},[898,82458,2044],{},[6927,82460,82461,82463],{},[898,82462,1710],{},[898,82464,14667],{},[1712,82466,1904],{"stretchy":1903},[1716,82468,41119],{},[1712,82470,1910],{"stretchy":1903},[1712,82472,1714],{},[1716,82474,6209],{},[1712,82476,1783],{},[1716,82478,41119],{},[1712,82480,2219],{},[1716,82482,6673],{},[1712,82484,1783],{},[1716,82486,82487],{},"225",[1712,82489,1714],{},[1716,82491,82492],{},"90",[1712,82494,2219],{},[1716,82496,81796],{},[1712,82498,1714],{},[1716,82500,81796],{},[902,82502,82503],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,82505,82506,46755,82562,82608],{},[883,82507,82509],{"className":82508},[886],[888,82510,82511],{"xmlns":890},[892,82512,82513,82559],{},[895,82514,82515,82517,82523,82525,82527,82529,82531,82533,82535,82537,82539,82541,82543,82545,82547,82550,82552,82555,82557],{},[898,82516,4445],{},[6927,82518,82519,82521],{},[898,82520,1710],{},[898,82522,14667],{},[1712,82524,1904],{"stretchy":1903},[1716,82526,41119],{},[1712,82528,1910],{"stretchy":1903},[1712,82530,1714],{},[1716,82532,8912],{},[1712,82534,1783],{},[1716,82536,41119],{},[1712,82538,2219],{},[1716,82540,24196],{},[1712,82542,1783],{},[1716,82544,82487],{},[1712,82546,1714],{},[1716,82548,82549],{},"180",[1712,82551,2219],{},[1716,82553,82554],{},"135",[1712,82556,1714],{},[1716,82558,81796],{},[902,82560,82561],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,82563,82565],{"className":82564},[886],[888,82566,82567],{"xmlns":890},[892,82568,82569,82605],{},[895,82570,82571,82573,82579,82581,82583,82585,82587,82589,82595,82597,82599,82601,82603],{},[898,82572,4445],{},[6927,82574,82575,82577],{},[898,82576,1710],{},[898,82578,14667],{},[1712,82580,1904],{"stretchy":1903},[1716,82582,41119],{},[1712,82584,1910],{"stretchy":1903},[1712,82586,1714],{},[898,82588,2044],{},[6927,82590,82591,82593],{},[898,82592,1710],{},[898,82594,14667],{},[1712,82596,1904],{"stretchy":1903},[1716,82598,41119],{},[1712,82600,1910],{"stretchy":1903},[1712,82602,1714],{},[1716,82604,81796],{},[902,82606,82607],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,82610,82611,82614,82615,22451,82644,1659],{},[38,82612,82613],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,82616,82618],{"className":82617},[886],[888,82619,82620],{"xmlns":890},[892,82621,82622,82642],{},[895,82623,82624,82626,82632,82634,82636],{},[898,82625,4445],{},[6927,82627,82628,82630],{},[898,82629,1710],{},[898,82631,14667],{},[1712,82633,1714],{},[898,82635,2044],{},[6927,82637,82638,82640],{},[898,82639,1710],{},[898,82641,14667],{},[902,82643,79538],{"encoding":904},[883,82645,82647],{"className":82646},[886],[888,82648,82649],{"xmlns":890},[892,82650,82651,82691],{},[895,82652,82653,82655,82657,82659,82661,82667,82669,82671,82673,82675,82677,82683,82685,82687,82689],{},[1716,82654,8912],{},[898,82656,14667],{},[1712,82658,2219],{},[1716,82660,24196],{},[2037,82662,82663,82665],{},[898,82664,14667],{},[1716,82666,2787],{},[1712,82668,1714],{},[1716,82670,6209],{},[898,82672,14667],{},[1712,82674,2219],{},[1716,82676,6673],{},[2037,82678,82679,82681],{},[898,82680,14667],{},[1716,82682,2787],{},[1712,82684,1767],{},[898,82686,14667],{},[1712,82688,1714],{},[1716,82690,41119],{},[902,82692,82693],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,82695,82696],{},[614,82697,82698,82699,82718,82719,17002,82737,82756,82757,82775,82776,82793,82794,82813,82814,82833],{},"Obrázek 5.3 — křivky ",[883,82700,82702],{"className":82701},[886],[888,82703,82704],{"xmlns":890},[892,82705,82706,82716],{},[895,82707,82708,82710],{},[898,82709,4445],{},[6927,82711,82712,82714],{},[898,82713,1710],{},[898,82715,14667],{},[902,82717,14917],{"encoding":904}," (max 60 při ",[883,82720,82722],{"className":82721},[886],[888,82723,82724],{"xmlns":890},[892,82725,82726,82734],{},[895,82727,82728,82730,82732],{},[898,82729,14667],{},[1712,82731,1714],{},[1716,82733,1718],{},[902,82735,82736],{"encoding":904},"L=10",[883,82738,82740],{"className":82739},[886],[888,82741,82742],{"xmlns":890},[892,82743,82744,82754],{},[895,82745,82746,82748],{},[898,82747,2044],{},[6927,82749,82750,82752],{},[898,82751,1710],{},[898,82753,14667],{},[902,82755,79508],{"encoding":904}," (max 45 při ",[883,82758,82760],{"className":82759},[886],[888,82761,82762],{"xmlns":890},[892,82763,82764,82772],{},[895,82765,82766,82768,82770],{},[898,82767,14667],{},[1712,82769,1714],{},[1716,82771,41119],{},[902,82773,82774],{"encoding":904},"L=15","), průsečík v ",[883,82777,82779],{"className":82778},[886],[888,82780,82781],{"xmlns":890},[892,82782,82783,82791],{},[895,82784,82785,82787,82789],{},[898,82786,14667],{},[1712,82788,1714],{},[1716,82790,41119],{},[902,82792,82446],{"encoding":904},". Nalevo od 15 leží ",[883,82795,82797],{"className":82796},[886],[888,82798,82799],{"xmlns":890},[892,82800,82801,82811],{},[895,82802,82803,82805],{},[898,82804,4445],{},[6927,82806,82807,82809],{},[898,82808,1710],{},[898,82810,14667],{},[902,82812,14917],{"encoding":904}," nad ",[883,82815,82817],{"className":82816},[886],[888,82818,82819],{"xmlns":890},[892,82820,82821,82831],{},[895,82822,82823,82825],{},[898,82824,2044],{},[6927,82826,82827,82829],{},[898,82828,1710],{},[898,82830,14667],{},[902,82832,79508],{"encoding":904},", napravo pod ní.",[115,82835,82837],{"id":82836},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,82839,82840,82841,3072,82854,3245,82857,4005,82870,3245,82873,2854],{},"V dvoufaktorovém modelu závisí produkce ",[883,82842,82844],{"className":82843},[886],[888,82845,82846],{"xmlns":890},[892,82847,82848,82852],{},[895,82849,82850],{},[898,82851,1734],{},[902,82853,1734],{"encoding":904},[38,82855,82856],{},"práci",[883,82858,82860],{"className":82859},[886],[888,82861,82862],{"xmlns":890},[892,82863,82864,82868],{},[895,82865,82866],{},[898,82867,14667],{},[902,82869,14667],{"encoding":904},[38,82871,82872],{},"kapitálu",[883,82874,82876],{"className":82875},[886],[888,82877,82878],{"xmlns":890},[892,82879,82880,82884],{},[895,82881,82882],{},[898,82883,14672],{},[902,82885,14672],{"encoding":904},[883,82887,82889],{"className":82888},[886],[888,82890,82891],{"xmlns":890,"display":32941},[892,82892,82893,82928],{},[25629,82894,82895],{"width":32946},[25634,82896,82897,82899,82921,82923],{},[25637,82898],{"width":32951},[25637,82900,82901],{},[895,82902,82903,82905,82907,82909,82911,82913,82915,82917,82919],{},[898,82904,1734],{},[1712,82906,1714],{},[898,82908,1734],{},[1712,82910,1904],{"stretchy":1903},[898,82912,14667],{},[1712,82914,3138],{"separator":2565},[898,82916,14672],{},[1712,82918,1910],{"stretchy":1903},[898,82920,1659],{"mathvariant":2003},[25637,82922],{"width":32951},[25637,82924,82925],{},[1762,82926,82927],{},"(5.6)",[902,82929,82930],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,82932,82933,82934,82936],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,82935,79875],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,82938,82940],{"id":82939},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,82942,82943],{},"Široce používané produkční funkce mají tvar",[883,82945,82947],{"className":82946},[886],[888,82948,82949],{"xmlns":890,"display":32941},[892,82950,82951,82992],{},[25629,82952,82953],{"width":32946},[25634,82954,82955,82957,82985,82987],{},[25637,82956],{"width":32951},[25637,82958,82959],{},[895,82960,82961,82963,82965,82967,82969,82975,82977,82983],{},[898,82962,1734],{},[1712,82964,1714],{},[898,82966,2044],{},[1762,82968,2583],{},[2037,82970,82971,82973],{},[898,82972,14667],{},[898,82974,207],{},[1762,82976,2583],{},[2037,82978,82979,82981],{},[898,82980,14672],{},[898,82982,7544],{},[1712,82984,3138],{"separator":2565},[25637,82986],{"width":32951},[25637,82988,82989],{},[1762,82990,82991],{},"(5.7)",[902,82993,82994],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,82996,2101,82997,83019,83020,83022,83023,1659],{},[883,82998,83000],{"className":82999},[886],[888,83001,83002],{"xmlns":890},[892,83003,83004,83016],{},[895,83005,83006,83008,83010,83012,83014],{},[898,83007,2044],{},[1712,83009,3138],{"separator":2565},[898,83011,207],{},[1712,83013,3138],{"separator":2565},[898,83015,7544],{},[902,83017,83018],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,83021,79574],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,83024,83026],{"className":83025},[886],[888,83027,83028],{"xmlns":890},[892,83029,83030,83042],{},[895,83031,83032,83034,83036,83038,83040],{},[898,83033,207],{},[1712,83035,3138],{"separator":2565},[898,83037,7544],{},[1712,83039,2252],{},[1716,83041,2222],{},[902,83043,83044],{"encoding":904},"a, b \u003C 1",[724,83046,83047],{},[3817,83048],{"alt":83049,"className":83050,"src":83051},"imek-vynosy-z-rozsahu-3typy",[210,3821],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,83053,83054,83055,83058,83059,3072,83072,83088,83089,3072,83102,2854],{},"Reflektují ekonomickou zákonitost, že ",[38,83056,83057],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,83060,83062],{"className":83061},[886],[888,83063,83064],{"xmlns":890},[892,83065,83066,83070],{},[895,83067,83068],{},[898,83069,14667],{},[902,83071,14667],{"encoding":904},[883,83073,83075],{"className":83074},[886],[888,83076,83077],{"xmlns":890},[892,83078,83079,83085],{},[895,83080,83081,83083],{},[898,83082,16915],{},[898,83084,14667],{},[902,83086,83087],{"encoding":904},"rL"," a kapitál z ",[883,83090,83092],{"className":83091},[886],[888,83093,83094],{"xmlns":890},[892,83095,83096,83100],{},[895,83097,83098],{},[898,83099,14672],{},[902,83101,14672],{"encoding":904},[883,83103,83105],{"className":83104},[886],[888,83106,83107],{"xmlns":890},[892,83108,83109,83115],{},[895,83110,83111,83113],{},[898,83112,16915],{},[898,83114,14672],{},[902,83116,83117],{"encoding":904},"rK",[883,83119,83121],{"className":83120},[886],[888,83122,83123],{"xmlns":890,"display":32941},[892,83124,83125,83248],{},[25629,83126,83127],{"width":32946},[25634,83128,83129,83131,83241,83243],{},[25637,83130],{"width":32951},[25637,83132,83133],{},[895,83134,83135,83137,83139,83141,83143,83145,83147,83149,83151,83153,83155,83157,83159,83161,83167,83169,83171,83173,83179,83181,83183,83185,83197,83199,83205,83211,83213,83225,83227,83229,83231,83233,83235,83237,83239],{},[898,83136,1734],{},[1712,83138,1904],{"stretchy":1903},[898,83140,16915],{},[898,83142,14667],{},[1712,83144,3138],{"separator":2565},[898,83146,16915],{},[898,83148,14672],{},[1712,83150,1910],{"stretchy":1903},[1712,83152,1714],{},[898,83154,2044],{},[1712,83156,1904],{"stretchy":1903},[898,83158,16915],{},[898,83160,14667],{},[2037,83162,83163,83165],{},[1712,83164,1910],{"stretchy":1903},[898,83166,207],{},[1712,83168,1904],{"stretchy":1903},[898,83170,16915],{},[898,83172,14672],{},[2037,83174,83175,83177],{},[1712,83176,1910],{"stretchy":1903},[898,83178,7544],{},[1712,83180,1714],{},[898,83182,2044],{},[1762,83184,2583],{},[2037,83186,83187,83189],{},[898,83188,16915],{},[895,83190,83191,83193,83195],{},[898,83192,207],{},[1712,83194,3145],{},[898,83196,7544],{},[1762,83198,2583],{},[2037,83200,83201,83203],{},[898,83202,14667],{},[898,83204,207],{},[2037,83206,83207,83209],{},[898,83208,14672],{},[898,83210,7544],{},[1712,83212,1714],{},[2037,83214,83215,83217],{},[898,83216,16915],{},[895,83218,83219,83221,83223],{},[898,83220,207],{},[1712,83222,3145],{},[898,83224,7544],{},[1762,83226,2583],{},[898,83228,1734],{},[1712,83230,1904],{"stretchy":1903},[898,83232,14667],{},[1712,83234,3138],{"separator":2565},[898,83236,14672],{},[1712,83238,1910],{"stretchy":1903},[898,83240,1659],{"mathvariant":2003},[25637,83242],{"width":32951},[25637,83244,83245],{},[1762,83246,83247],{},"(5.8)",[902,83249,83250],{"encoding":904},"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}",[724,83252,83253,83254],{},"Volně: ",[38,83255,83256,83257,83270,83271,83295],{},"změní-li se vstupy ",[883,83258,83260],{"className":83259},[886],[888,83261,83262],{"xmlns":890},[892,83263,83264,83268],{},[895,83265,83266],{},[898,83267,16915],{},[902,83269,16915],{"encoding":904},"-krát, změní se výstup ",[883,83272,83274],{"className":83273},[886],[888,83275,83276],{"xmlns":890},[892,83277,83278,83292],{},[895,83279,83280],{},[2037,83281,83282,83284],{},[898,83283,16915],{},[895,83285,83286,83288,83290],{},[898,83287,207],{},[1712,83289,3145],{},[898,83291,7544],{},[902,83293,83294],{"encoding":904},"r^{a+b}","-krát.",[198,83297,83299],{"id":83298},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,83301,83302,83303,83320],{},"Součet exponentů ",[883,83304,83306],{"className":83305},[886],[888,83307,83308],{"xmlns":890},[892,83309,83310,83318],{},[895,83311,83312,83314,83316],{},[898,83313,207],{},[1712,83315,3145],{},[898,83317,7544],{},[902,83319,79699],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,83322,83323,83352],{},[19,83324,83325],{},[22,83326,83327,83330,83333,83350],{},[25,83328,83329],{},"Typ",[25,83331,83332],{},"Podmínka",[25,83334,83335,83336,83349],{},"Chování produkce při ",[883,83337,83339],{"className":83338},[886],[888,83340,83341],{"xmlns":890},[892,83342,83343,83347],{},[895,83344,83345],{},[898,83346,16915],{},[902,83348,16915],{"encoding":904},"-násobném zvýšení vstupů",[25,83351,8480],{},[30,83353,83354,83465,83580],{},[22,83355,83356,83364,83388,83421],{},[35,83357,80412,83358,14897,83361,1910],{},[38,83359,83360],{},"Konstantní",[614,83362,83363],{},"constant returns",[35,83365,83366],{},[883,83367,83369],{"className":83368},[886],[888,83370,83371],{"xmlns":890},[892,83372,83373,83385],{},[895,83374,83375,83377,83379,83381,83383],{},[898,83376,207],{},[1712,83378,3145],{},[898,83380,7544],{},[1712,83382,1714],{},[1716,83384,2222],{},[902,83386,83387],{"encoding":904},"a+b = 1",[35,83389,83390,83403,83404,3245,83407,83420],{},[883,83391,83393],{"className":83392},[886],[888,83394,83395],{"xmlns":890},[892,83396,83397,83401],{},[895,83398,83399],{},[898,83400,1734],{},[902,83402,1734],{"encoding":904}," vzroste ",[38,83405,83406],{},"přesně",[883,83408,83410],{"className":83409},[886],[888,83411,83412],{"xmlns":890},[892,83413,83414,83418],{},[895,83415,83416],{},[898,83417,16915],{},[902,83419,16915],{"encoding":904},"-krát",[35,83422,83423],{},[883,83424,83426],{"className":83425},[886],[888,83427,83428],{"xmlns":890},[892,83429,83430,83462],{},[895,83431,83432,83434,83436,83438,83450],{},[898,83433,1734],{},[1712,83435,1714],{},[1716,83437,2787],{},[2037,83439,83440,83442],{},[898,83441,14667],{},[895,83443,83444,83446,83448],{},[1716,83445,2222],{},[898,83447,2473],{"mathvariant":2003},[1716,83449,2975],{},[2037,83451,83452,83454],{},[898,83453,14672],{},[895,83455,83456,83458,83460],{},[1716,83457,6198],{},[898,83459,2473],{"mathvariant":2003},[1716,83461,2975],{},[902,83463,83464],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,83466,83467,83476,83500,83530],{},[35,83468,83469,83470,14897,83473,1910],{},"2° ",[38,83471,83472],{},"Rostoucí",[614,83474,83475],{},"increasing returns",[35,83477,83478],{},[883,83479,83481],{"className":83480},[886],[888,83482,83483],{"xmlns":890},[892,83484,83485,83497],{},[895,83486,83487,83489,83491,83493,83495],{},[898,83488,207],{},[1712,83490,3145],{},[898,83492,7544],{},[1712,83494,2302],{},[1716,83496,2222],{},[902,83498,83499],{"encoding":904},"a+b > 1",[35,83501,83502,83403,83515,56106,83517,83420],{},[883,83503,83505],{"className":83504},[886],[888,83506,83507],{"xmlns":890},[892,83508,83509,83513],{},[895,83510,83511],{},[898,83512,1734],{},[902,83514,1734],{"encoding":904},[38,83516,30145],{},[883,83518,83520],{"className":83519},[886],[888,83521,83522],{"xmlns":890},[892,83523,83524,83528],{},[895,83525,83526],{},[898,83527,16915],{},[902,83529,16915],{"encoding":904},[35,83531,83532,14897,83558,1910],{},[883,83533,83535],{"className":83534},[886],[888,83536,83537],{"xmlns":890},[892,83538,83539,83555],{},[895,83540,83541,83543,83545,83547,83549],{},[898,83542,1734],{},[1712,83544,1714],{},[1716,83546,29076],{},[898,83548,14667],{},[2037,83550,83551,83553],{},[898,83552,14672],{},[1716,83554,2787],{},[902,83556,83557],{"encoding":904},"Q = 7LK^2",[883,83559,83561],{"className":83560},[886],[888,83562,83563],{"xmlns":890},[892,83564,83565,83577],{},[895,83566,83567,83569,83571,83573,83575],{},[898,83568,207],{},[1712,83570,3145],{},[898,83572,7544],{},[1712,83574,1714],{},[1716,83576,6198],{},[902,83578,83579],{"encoding":904},"a+b = 3",[22,83581,83582,83591,83615,83646],{},[35,83583,83584,83585,14897,83588,1910],{},"3° ",[38,83586,83587],{},"Klesající",[614,83589,83590],{},"decreasing returns",[35,83592,83593],{},[883,83594,83596],{"className":83595},[886],[888,83597,83598],{"xmlns":890},[892,83599,83600,83612],{},[895,83601,83602,83604,83606,83608,83610],{},[898,83603,207],{},[1712,83605,3145],{},[898,83607,7544],{},[1712,83609,2252],{},[1716,83611,2222],{},[902,83613,83614],{"encoding":904},"a+b \u003C 1",[35,83616,83617,83403,83630,56106,83633,83420],{},[883,83618,83620],{"className":83619},[886],[888,83621,83622],{"xmlns":890},[892,83623,83624,83628],{},[895,83625,83626],{},[898,83627,1734],{},[902,83629,1734],{"encoding":904},[38,83631,83632],{},"méně",[883,83634,83636],{"className":83635},[886],[888,83637,83638],{"xmlns":890},[892,83639,83640,83644],{},[895,83641,83642],{},[898,83643,16915],{},[902,83645,16915],{"encoding":904},[35,83647,83648,14897,83678,1910],{},[883,83649,83651],{"className":83650},[886],[888,83652,83653],{"xmlns":890},[892,83654,83655,83675],{},[895,83656,83657,83659,83661,83663,83669],{},[898,83658,1734],{},[1712,83660,1714],{},[1716,83662,1718],{},[2037,83664,83665,83667],{},[898,83666,14667],{},[1716,83668,73086],{},[2037,83670,83671,83673],{},[898,83672,14672],{},[1716,83674,2814],{},[902,83676,83677],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,83679,83681],{"className":83680},[886],[888,83682,83683],{"xmlns":890},[892,83684,83685,83697],{},[895,83686,83687,83689,83691,83693,83695],{},[898,83688,207],{},[1712,83690,3145],{},[898,83692,7544],{},[1712,83694,1714],{},[1716,83696,19463],{},[902,83698,83699],{"encoding":904},"a+b = 0{,}8",[1636,83701,83702],{},[724,83703,83704,83706,83707,83724,83725,83728,83729,3245,83732,83768,83769,83791,83792,1659],{},[883,83705,2203],{}," Pozor\nSoučet ",[883,83708,83710],{"className":83709},[886],[888,83711,83712],{"xmlns":890},[892,83713,83714,83722],{},[895,83715,83716,83718,83720],{},[898,83717,207],{},[1712,83719,3145],{},[898,83721,7544],{},[902,83723,79699],{"encoding":904}," neudává velikost produkce, ale ",[38,83726,83727],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,83730,83731],{},"ryzí Cobb-Douglas",[883,83733,83735],{"className":83734},[886],[888,83736,83737],{"xmlns":890},[892,83738,83739,83765],{},[895,83740,83741,83743,83745,83747,83753],{},[898,83742,1734],{},[1712,83744,1714],{},[898,83746,2044],{},[2037,83748,83749,83751],{},[898,83750,14667],{},[898,83752,207],{},[2037,83754,83755,83757],{},[898,83756,14672],{},[895,83758,83759,83761,83763],{},[1716,83760,2222],{},[1712,83762,2219],{},[898,83764,207],{},[902,83766,83767],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,83770,83772],{"className":83771},[886],[888,83773,83774],{"xmlns":890},[892,83775,83776,83788],{},[895,83777,83778,83780,83782,83784,83786],{},[898,83779,7544],{},[1712,83781,1714],{},[1716,83783,2222],{},[1712,83785,2219],{},[898,83787,207],{},[902,83789,83790],{"encoding":904},"b = 1-a",", tedy vždy ",[38,83793,83794],{},"konstantní výnosy z rozsahu",[198,83796,83798,83799],{"id":83797},"parametr-efektivity-aa","Parametr efektivity ",[883,83800,83802],{"className":83801},[886],[888,83803,83804],{"xmlns":890},[892,83805,83806,83810],{},[895,83807,83808],{},[898,83809,2044],{},[902,83811,2044],{"encoding":904},[724,83813,83814,83815,83828,83829,83842,83843,83861,83862,83865],{},"Konstanta ",[883,83816,83818],{"className":83817},[886],[888,83819,83820],{"xmlns":890},[892,83821,83822,83826],{},[895,83823,83824],{},[898,83825,2044],{},[902,83827,2044],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,83830,83832],{"className":83831},[886],[888,83833,83834],{"xmlns":890},[892,83835,83836,83840],{},[895,83837,83838],{},[898,83839,1734],{},[902,83841,1734],{"encoding":904}," při pevně zadaných ",[883,83844,83846],{"className":83845},[886],[888,83847,83848],{"xmlns":890},[892,83849,83850,83858],{},[895,83851,83852,83854,83856],{},[898,83853,14667],{},[1712,83855,3138],{"separator":2565},[898,83857,14672],{},[902,83859,83860],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,83863,83864],{},"parametr efektivity"," — indikátor stavu technologie.",[198,83867,83869],{"id":83868},"příklad-53","Příklad 5.3",[724,83871,83872,83873,83768,83915,83917,83918,1659],{},"Produkční funkce ",[883,83874,83876],{"className":83875},[886],[888,83877,83878],{"xmlns":890},[892,83879,83880,83912],{},[895,83881,83882,83884,83886,83888,83900],{},[898,83883,1734],{},[1712,83885,1714],{},[1716,83887,2787],{},[2037,83889,83890,83892],{},[898,83891,14667],{},[895,83893,83894,83896,83898],{},[1716,83895,2222],{},[898,83897,2473],{"mathvariant":2003},[1716,83899,2975],{},[2037,83901,83902,83904],{},[898,83903,14672],{},[895,83905,83906,83908,83910],{},[1716,83907,6198],{},[898,83909,2473],{"mathvariant":2003},[1716,83911,2975],{},[902,83913,83914],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,83916,29488],{}," výnosy z rozsahu, neboť ",[883,83919,83921],{"className":83920},[886],[888,83922,83923],{"xmlns":890},[892,83924,83925,83949],{},[895,83926,83927,83935,83937,83945,83947],{},[2563,83928,83929],{"scriptlevel":2085,"displaystyle":1903},[2567,83930,83931,83933],{},[1716,83932,2222],{},[1716,83934,2975],{},[1712,83936,3145],{},[2563,83938,83939],{"scriptlevel":2085,"displaystyle":1903},[2567,83940,83941,83943],{},[1716,83942,6198],{},[1716,83944,2975],{},[1712,83946,1714],{},[1716,83948,2222],{},[902,83950,83951],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,83953,83954,83955,4005,83968,83981,83982,3245,83995,84035],{},"Změní-li se ",[883,83956,83958],{"className":83957},[886],[888,83959,83960],{"xmlns":890},[892,83961,83962,83966],{},[895,83963,83964],{},[898,83965,14667],{},[902,83967,14667],{"encoding":904},[883,83969,83971],{"className":83970},[886],[888,83972,83973],{"xmlns":890},[892,83974,83975,83979],{},[895,83976,83977],{},[898,83978,14672],{},[902,83980,14672],{"encoding":904}," čtyřnásobně, změní se ",[883,83983,83985],{"className":83984},[886],[888,83986,83987],{"xmlns":890},[892,83988,83989,83993],{},[895,83990,83991],{},[898,83992,1734],{},[902,83994,1734],{"encoding":904},[883,83996,83998],{"className":83997},[886],[888,83999,84000],{"xmlns":890},[892,84001,84002,84032],{},[895,84003,84004,84024,84026],{},[2037,84005,84006,84008],{},[1716,84007,2975],{},[895,84009,84010,84012,84014,84016,84018,84020,84022],{},[1716,84011,2222],{},[898,84013,2473],{"mathvariant":2003},[1716,84015,2975],{},[1712,84017,3145],{},[1716,84019,6198],{},[898,84021,2473],{"mathvariant":2003},[1716,84023,2975],{},[1712,84025,1714],{},[2037,84027,84028,84030],{},[1716,84029,2975],{},[1716,84031,2222],{},[902,84033,84034],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,84037,84039],{"className":84038},[886],[888,84040,84041],{"xmlns":890,"display":32941},[892,84042,84043,84203],{},[895,84044,84045,84047,84049,84051,84053,84055,84057,84059,84061,84063,84065,84067,84069,84071,84083,84085,84087,84089,84101,84103,84105,84107,84127,84139,84151,84153,84155,84157,84159,84171,84183,84185,84187,84189,84191,84193,84195,84197,84199,84201],{},[898,84046,1734],{},[1712,84048,1904],{"stretchy":1903},[1716,84050,2975],{},[898,84052,14667],{},[1712,84054,3138],{"separator":2565},[1716,84056,2975],{},[898,84058,14672],{},[1712,84060,1910],{"stretchy":1903},[1712,84062,1714],{},[1716,84064,2787],{},[1712,84066,1904],{"stretchy":1903},[1716,84068,2975],{},[898,84070,14667],{},[2037,84072,84073,84075],{},[1712,84074,1910],{"stretchy":1903},[895,84076,84077,84079,84081],{},[1716,84078,2222],{},[898,84080,2473],{"mathvariant":2003},[1716,84082,2975],{},[1712,84084,1904],{"stretchy":1903},[1716,84086,2975],{},[898,84088,14672],{},[2037,84090,84091,84093],{},[1712,84092,1910],{"stretchy":1903},[895,84094,84095,84097,84099],{},[1716,84096,6198],{},[898,84098,2473],{"mathvariant":2003},[1716,84100,2975],{},[1712,84102,1714],{},[1716,84104,2787],{},[1712,84106,1783],{},[2037,84108,84109,84111],{},[1716,84110,2975],{},[895,84112,84113,84115,84117,84119,84121,84123,84125],{},[1716,84114,2222],{},[898,84116,2473],{"mathvariant":2003},[1716,84118,2975],{},[1712,84120,3145],{},[1716,84122,6198],{},[898,84124,2473],{"mathvariant":2003},[1716,84126,2975],{},[2037,84128,84129,84131],{},[898,84130,14667],{},[895,84132,84133,84135,84137],{},[1716,84134,2222],{},[898,84136,2473],{"mathvariant":2003},[1716,84138,2975],{},[2037,84140,84141,84143],{},[898,84142,14672],{},[895,84144,84145,84147,84149],{},[1716,84146,6198],{},[898,84148,2473],{"mathvariant":2003},[1716,84150,2975],{},[1712,84152,1714],{},[1716,84154,2975],{},[1712,84156,1783],{},[1716,84158,2787],{},[2037,84160,84161,84163],{},[898,84162,14667],{},[895,84164,84165,84167,84169],{},[1716,84166,2222],{},[898,84168,2473],{"mathvariant":2003},[1716,84170,2975],{},[2037,84172,84173,84175],{},[898,84174,14672],{},[895,84176,84177,84179,84181],{},[1716,84178,6198],{},[898,84180,2473],{"mathvariant":2003},[1716,84182,2975],{},[1712,84184,1714],{},[1716,84186,2975],{},[1762,84188,2583],{},[898,84190,1734],{},[1712,84192,1904],{"stretchy":1903},[898,84194,14667],{},[1712,84196,3138],{"separator":2565},[898,84198,14672],{},[1712,84200,1910],{"stretchy":1903},[898,84202,1659],{"mathvariant":2003},[902,84204,84205],{"encoding":904},"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).",[198,84207,84208],{"id":42054},"Homogenita",[724,84210,84211,84212,5920,84235,84251],{},"Funkce ",[883,84213,84215],{"className":84214},[886],[888,84216,84217],{"xmlns":890},[892,84218,84219,84233],{},[895,84220,84221,84223,84225,84227,84229,84231],{},[898,84222,1734],{},[1712,84224,1904],{"stretchy":1903},[898,84226,14667],{},[1712,84228,3138],{"separator":2565},[898,84230,14672],{},[1712,84232,1910],{"stretchy":1903},[902,84234,14869],{"encoding":904},[38,84236,84237,84238],{},"homogenní stupně ",[883,84239,84241],{"className":84240},[886],[888,84242,84243],{"xmlns":890},[892,84244,84245,84249],{},[895,84246,84247],{},[898,84248,41735],{},[902,84250,41735],{"encoding":904},", jestliže",[883,84253,84255],{"className":84254},[886],[888,84256,84257],{"xmlns":890,"display":32941},[892,84258,84259,84316],{},[25629,84260,84261],{"width":32946},[25634,84262,84263,84265,84309,84311],{},[25637,84264],{"width":32951},[25637,84266,84267],{},[895,84268,84269,84271,84273,84275,84277,84279,84281,84283,84285,84287,84293,84295,84297,84299,84301,84303,84305,84307],{},[898,84270,1734],{},[1712,84272,1904],{"stretchy":1903},[898,84274,16915],{},[898,84276,14667],{},[1712,84278,3138],{"separator":2565},[898,84280,16915],{},[898,84282,14672],{},[1712,84284,1910],{"stretchy":1903},[1712,84286,1714],{},[2037,84288,84289,84291],{},[898,84290,16915],{},[898,84292,41735],{},[1762,84294,2583],{},[898,84296,1734],{},[1712,84298,1904],{"stretchy":1903},[898,84300,14667],{},[1712,84302,3138],{"separator":2565},[898,84304,14672],{},[1712,84306,1910],{"stretchy":1903},[1712,84308,3138],{"separator":2565},[25637,84310],{"width":32951},[25637,84312,84313],{},[1762,84314,84315],{},"(5.10)",[902,84317,84318],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,84320,2101,84321,84339,84340,84358,84359,48511,84372,84375,84376,1659],{},[883,84322,84324],{"className":84323},[886],[888,84325,84326],{"xmlns":890},[892,84327,84328,84336],{},[895,84329,84330,84332,84334],{},[898,84331,41735],{},[1712,84333,2282],{},[1716,84335,2085],{},[902,84337,84338],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,84341,84343],{"className":84342},[886],[888,84344,84345],{"xmlns":890},[892,84346,84347,84355],{},[895,84348,84349,84351,84353],{},[898,84350,16915],{},[1712,84352,2302],{},[1716,84354,2085],{},[902,84356,84357],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,84360,84362],{"className":84361},[886],[888,84363,84364],{"xmlns":890},[892,84365,84366,84370],{},[895,84367,84368],{},[1716,84369,2222],{},[902,84371,2222],{"encoding":904},[38,84373,84374],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,84377,84379],{"className":84378},[886],[888,84380,84381],{"xmlns":890},[892,84382,84383,84391],{},[895,84384,84385,84387,84389],{},[898,84386,207],{},[1712,84388,3145],{},[898,84390,7544],{},[902,84392,79699],{"encoding":904},[115,84394,84396],{"id":84395},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,84398,84399],{},[38,84400,84401],{},"Ryzí Cobb-Douglasovy funkce:",[883,84403,84405],{"className":84404},[886],[888,84406,84407],{"xmlns":890,"display":32941},[892,84408,84409,84468],{},[25629,84410,84411],{"width":32946},[25634,84412,84413,84415,84461,84463],{},[25637,84414],{"width":32951},[25637,84416,84417],{},[895,84418,84419,84421,84423,84425,84427,84433,84435,84447,84449,84451,84453,84455,84457,84459],{},[898,84420,1734],{},[1712,84422,1714],{},[898,84424,2044],{},[1762,84426,2583],{},[2037,84428,84429,84431],{},[898,84430,14667],{},[898,84432,207],{},[1762,84434,2583],{},[2037,84436,84437,84439],{},[898,84438,14672],{},[895,84440,84441,84443,84445],{},[1716,84442,2222],{},[1712,84444,2219],{},[898,84446,207],{},[1712,84448,3138],{"separator":2565},[3690,84450],{"width":20158},[1716,84452,2085],{},[1712,84454,2252],{},[898,84456,207],{},[1712,84458,2252],{},[1716,84460,18134],{},[25637,84462],{"width":32951},[25637,84464,84465],{},[1762,84466,84467],{},"(5.9)",[902,84469,84470],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,84472,84473,84474,84476,84477,1659],{},"Mají vždy ",[38,84475,83794],{}," a jsou ",[38,84478,84374],{},[724,84480,84481,14897,84484,84487],{},[38,84482,84483],{},"CES produkční funkce",[614,84485,84486],{},"Constant Elasticity of Substitution",", 1961):",[883,84489,84491],{"className":84490},[886],[888,84492,84493],{"xmlns":890,"display":32941},[892,84494,84495,84563],{},[895,84496,84497,84499,84501,84503,84561],{},[898,84498,1734],{},[1712,84500,1714],{},[898,84502,2044],{},[2037,84504,84505,84549],{},[895,84506,84507,84509,84511,84513,84515,84517,84519,84521,84531,84533,84535,84537,84547],{},[1712,84508,7910],{"fence":2565},[1712,84510,1904],{"stretchy":1903},[1716,84512,2222],{},[1712,84514,2219],{},[898,84516,207],{},[1712,84518,1910],{"stretchy":1903},[1762,84520,2583],{},[2037,84522,84523,84525],{},[898,84524,14667],{},[895,84526,84527,84529],{},[1712,84528,2219],{},[898,84530,7544],{},[1712,84532,3145],{},[898,84534,207],{},[1762,84536,2583],{},[2037,84538,84539,84541],{},[898,84540,14672],{},[895,84542,84543,84545],{},[1712,84544,2219],{},[898,84546,7544],{},[1712,84548,7925],{"fence":2565},[895,84550,84551,84553],{},[1712,84552,2219],{},[2563,84554,84555],{"scriptlevel":2085,"displaystyle":1903},[2567,84556,84557,84559],{},[1716,84558,2222],{},[898,84560,7544],{},[1712,84562,3138],{"separator":2565},[902,84564,84565],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,84567,2101,84568,1343,84586,1343,84607,84631],{},[883,84569,84571],{"className":84570},[886],[888,84572,84573],{"xmlns":890},[892,84574,84575,84583],{},[895,84576,84577,84579,84581],{},[898,84578,2044],{},[1712,84580,2302],{},[1716,84582,2085],{},[902,84584,84585],{"encoding":904},"A > 0",[883,84587,84589],{"className":84588},[886],[888,84590,84591],{"xmlns":890},[892,84592,84593,84605],{},[895,84594,84595,84597,84599,84601,84603],{},[1716,84596,2085],{},[1712,84598,2252],{},[898,84600,207],{},[1712,84602,2252],{},[1716,84604,2222],{},[902,84606,23711],{"encoding":904},[883,84608,84610],{"className":84609},[886],[888,84611,84612],{"xmlns":890},[892,84613,84614,84628],{},[895,84615,84616,84618,84620,84622,84624,84626],{},[1712,84617,2219],{},[1716,84619,2222],{},[1712,84621,2252],{},[898,84623,7544],{},[1712,84625,8776],{"mathvariant":2003},[1716,84627,2085],{},[902,84629,84630],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,84633,84634],{},[38,84635,84636],{},"Další typy:",[120,84638,84639,84681],{},[123,84640,84641,3245,84644,84680],{},[38,84642,84643],{},"Lineární:",[883,84645,84647],{"className":84646},[886],[888,84648,84649],{"xmlns":890},[892,84650,84651,84677],{},[895,84652,84653,84655,84657,84659,84661,84663,84665,84667,84669,84671,84673,84675],{},[898,84654,1734],{},[1712,84656,1904],{"stretchy":1903},[898,84658,14667],{},[1712,84660,3138],{"separator":2565},[898,84662,14672],{},[1712,84664,1910],{"stretchy":1903},[1712,84666,1714],{},[898,84668,207],{},[898,84670,14667],{},[1712,84672,3145],{},[898,84674,7544],{},[898,84676,14672],{},[902,84678,84679],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,84682,84683,3245,84686,84731],{},[38,84684,84685],{},"Leontiefova:",[883,84687,84689],{"className":84688},[886],[888,84690,84691],{"xmlns":890},[892,84692,84693,84728],{},[895,84694,84695,84697,84699,84701,84703,84705,84707,84709,84712,84714,84716,84718,84720,84722,84724,84726],{},[898,84696,1734],{},[1712,84698,1904],{"stretchy":1903},[898,84700,14667],{},[1712,84702,3138],{"separator":2565},[898,84704,14672],{},[1712,84706,1910],{"stretchy":1903},[1712,84708,1714],{},[898,84710,84711],{},"min",[1712,84713,61075],{},[1712,84715,1904],{"stretchy":1903},[898,84717,207],{},[898,84719,14667],{},[1712,84721,3138],{"separator":2565},[898,84723,7544],{},[898,84725,14672],{},[1712,84727,1910],{"stretchy":1903},[902,84729,84730],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,84733,84735,84736,1343,84755,84774],{"id":84734},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,84737,84739],{"className":84738},[886],[888,84740,84741],{"xmlns":890},[892,84742,84743,84753],{},[895,84744,84745,84747],{},[898,84746,4445],{},[6927,84748,84749,84751],{},[898,84750,1710],{},[898,84752,14667],{},[902,84754,14917],{"encoding":904},[883,84756,84758],{"className":84757},[886],[888,84759,84760],{"xmlns":890},[892,84761,84762,84772],{},[895,84763,84764,84766],{},[898,84765,4445],{},[6927,84767,84768,84770],{},[898,84769,1710],{},[898,84771,14672],{},[902,84773,14962],{"encoding":904}," a totální diferenciál",[724,84776,84777],{},[38,84778,84779],{},"Mezní produkt práce:",[883,84781,84783],{"className":84782},[886],[888,84784,84785],{"xmlns":890,"display":32941},[892,84786,84787,84825],{},[895,84788,84789,84791,84797,84799,84807,84809,84823],{},[898,84790,4445],{},[6927,84792,84793,84795],{},[898,84794,1710],{},[898,84796,14667],{},[1712,84798,1714],{},[6989,84800,84801,84803,84805],{},[898,84802,1734],{},[898,84804,14667],{},[1712,84806,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,84808,1714],{},[2567,84810,84811,84817],{},[895,84812,84813,84815],{},[898,84814,14744],{"mathvariant":2003},[898,84816,1734],{},[895,84818,84819,84821],{},[898,84820,14744],{"mathvariant":2003},[898,84822,14667],{},[898,84824,1659],{"mathvariant":2003},[902,84826,84827],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,84829,84830],{},[38,84831,84832],{},"Mezní produkt kapitálu:",[883,84834,84836],{"className":84835},[886],[888,84837,84838],{"xmlns":890,"display":32941},[892,84839,84840,84878],{},[895,84841,84842,84844,84850,84852,84860,84862,84876],{},[898,84843,4445],{},[6927,84845,84846,84848],{},[898,84847,1710],{},[898,84849,14672],{},[1712,84851,1714],{},[6989,84853,84854,84856,84858],{},[898,84855,1734],{},[898,84857,14672],{},[1712,84859,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,84861,1714],{},[2567,84863,84864,84870],{},[895,84865,84866,84868],{},[898,84867,14744],{"mathvariant":2003},[898,84869,1734],{},[895,84871,84872,84874],{},[898,84873,14744],{"mathvariant":2003},[898,84875,14672],{},[898,84877,1659],{"mathvariant":2003},[902,84879,84880],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,84882,84883,84913,84914,84935,84936,84954,84955,84968,84969,1659],{},[883,84884,84886],{"className":84885},[886],[888,84887,84888],{"xmlns":890},[892,84889,84890,84910],{},[895,84891,84892,84894,84900,84902,84904,84906,84908],{},[898,84893,4445],{},[6927,84895,84896,84898],{},[898,84897,1710],{},[898,84899,14667],{},[1712,84901,1904],{"stretchy":1903},[898,84903,207],{},[1712,84905,3138],{"separator":2565},[898,84907,7544],{},[1712,84909,1910],{"stretchy":1903},[902,84911,84912],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,84915,84917],{"className":84916},[886],[888,84918,84919],{"xmlns":890},[892,84920,84921,84933],{},[895,84922,84923,84925,84927,84929,84931],{},[1712,84924,7910],{"stretchy":1903},[898,84926,207],{},[1712,84928,3138],{"separator":2565},[898,84930,7544],{},[1712,84932,7925],{"stretchy":1903},[902,84934,15696],{"encoding":904}," (na hladině ",[883,84937,84939],{"className":84938},[886],[888,84940,84941],{"xmlns":890},[892,84942,84943,84951],{},[895,84944,84945,84947,84949],{},[898,84946,14672],{},[1712,84948,1714],{},[898,84950,7544],{},[902,84952,84953],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,84956,84958],{"className":84957},[886],[888,84959,84960],{"xmlns":890},[892,84961,84962,84966],{},[895,84963,84964],{},[898,84965,14667],{},[902,84967,14667],{"encoding":904},". Analogicky ",[883,84970,84972],{"className":84971},[886],[888,84973,84974],{"xmlns":890},[892,84975,84976,84996],{},[895,84977,84978,84980,84986,84988,84990,84992,84994],{},[898,84979,4445],{},[6927,84981,84982,84984],{},[898,84983,1710],{},[898,84985,14672],{},[1712,84987,1904],{"stretchy":1903},[898,84989,207],{},[1712,84991,3138],{"separator":2565},[898,84993,7544],{},[1712,84995,1910],{"stretchy":1903},[902,84997,84998],{"encoding":904},"MP_K(a, b)",[1636,85000,85001,85005],{},[724,85002,85003,56094],{},[883,85004,1941],{},[120,85006,85007,85045],{},[123,85008,85009,31064,85028],{},[883,85010,85012],{"className":85011},[886],[888,85013,85014],{"xmlns":890},[892,85015,85016,85026],{},[895,85017,85018,85020],{},[898,85019,4445],{},[6927,85021,85022,85024],{},[898,85023,1710],{},[898,85025,14667],{},[902,85027,14917],{"encoding":904},[614,85029,85030,85031,85044],{},"„o kolik vzroste ",[883,85032,85034],{"className":85033},[886],[888,85035,85036],{"xmlns":890},[892,85037,85038,85042],{},[895,85039,85040],{},[898,85041,1734],{},[902,85043,1734],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,85046,85047,31064,85066],{},[883,85048,85050],{"className":85049},[886],[888,85051,85052],{"xmlns":890},[892,85053,85054,85064],{},[895,85055,85056,85058],{},[898,85057,4445],{},[6927,85059,85060,85062],{},[898,85061,1710],{},[898,85063,14672],{},[902,85065,14962],{"encoding":904},[614,85067,85030,85068,85081],{},[883,85069,85071],{"className":85070},[886],[888,85072,85073],{"xmlns":890},[892,85074,85075,85079],{},[895,85076,85077],{},[898,85078,1734],{},[902,85080,1734],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,85083,85084,85087,85088,85103,85104,2854],{},[38,85085,85086],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,85089,85091],{"className":85090},[886],[888,85092,85093],{"xmlns":890},[892,85094,85095,85101],{},[895,85096,85097,85099],{},[898,85098,2468],{},[898,85100,14667],{},[902,85102,80231],{"encoding":904}," a kapitálu o ",[883,85105,85107],{"className":85106},[886],[888,85108,85109],{"xmlns":890},[892,85110,85111,85117],{},[895,85112,85113,85115],{},[898,85114,2468],{},[898,85116,14672],{},[902,85118,85119],{"encoding":904},"dK",[883,85121,85123],{"className":85122},[886],[888,85124,85125],{"xmlns":890,"display":32941},[892,85126,85127,85220],{},[25629,85128,85129],{"width":32946},[25634,85130,85131,85133,85213,85215],{},[25637,85132],{"width":32951},[25637,85134,85135],{},[895,85136,85137,85139,85141,85143,85145,85147,85149,85157,85159,85161,85163,85165,85173,85175,85177,85179,85181,85183,85189,85191,85193,85195,85197,85199,85205,85207,85209,85211],{},[898,85138,2004],{"mathvariant":2003},[898,85140,1734],{},[1712,85142,3740],{},[898,85144,2468],{},[898,85146,1734],{},[1712,85148,1714],{},[6989,85150,85151,85153,85155],{},[898,85152,1734],{},[898,85154,14667],{},[1712,85156,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,85158,2583],{},[898,85160,2468],{},[898,85162,14667],{},[1712,85164,3145],{},[6989,85166,85167,85169,85171],{},[898,85168,1734],{},[898,85170,14672],{},[1712,85172,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1762,85174,2583],{},[898,85176,2468],{},[898,85178,14672],{},[1712,85180,1714],{},[898,85182,4445],{},[6927,85184,85185,85187],{},[898,85186,1710],{},[898,85188,14667],{},[1762,85190,2583],{},[898,85192,2468],{},[898,85194,14667],{},[1712,85196,3145],{},[898,85198,4445],{},[6927,85200,85201,85203],{},[898,85202,1710],{},[898,85204,14672],{},[1762,85206,2583],{},[898,85208,2468],{},[898,85210,14672],{},[898,85212,1659],{"mathvariant":2003},[25637,85214],{"width":32951},[25637,85216,85217],{},[1762,85218,85219],{},"(5.11)",[902,85221,85222],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,85224,85225,85226,1659],{},"Skutečná změna: ",[883,85227,85229],{"className":85228},[886],[888,85230,85231],{"xmlns":890},[892,85232,85233,85279],{},[895,85234,85235,85237,85239,85241,85243,85245,85247,85249,85251,85253,85255,85257,85259,85261,85263,85265,85267,85269,85271,85273,85275,85277],{},[898,85236,2004],{"mathvariant":2003},[898,85238,1734],{},[1712,85240,1714],{},[898,85242,1734],{},[1712,85244,1904],{"stretchy":1903},[898,85246,14667],{},[1712,85248,3145],{},[898,85250,2468],{},[898,85252,14667],{},[1712,85254,3138],{"separator":2565},[898,85256,14672],{},[1712,85258,3145],{},[898,85260,2468],{},[898,85262,14672],{},[1712,85264,1910],{"stretchy":1903},[1712,85266,2219],{},[898,85268,1734],{},[1712,85270,1904],{"stretchy":1903},[898,85272,14667],{},[1712,85274,3138],{"separator":2565},[898,85276,14672],{},[1712,85278,1910],{"stretchy":1903},[902,85280,85281],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,85283,85284,85286,85287,85305,85306,85319,85320,85339,85340,85372,85373,85405,85406,1659],{},[38,85285,80395],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,85288,85290],{"className":85289},[886],[888,85291,85292],{"xmlns":890},[892,85293,85294,85302],{},[895,85295,85296],{},[6927,85297,85298,85300],{},[898,85299,14672],{},[1716,85301,2085],{},[902,85303,85304],{"encoding":904},"K_0"," se od jistého ",[883,85307,85309],{"className":85308},[886],[888,85310,85311],{"xmlns":890},[892,85312,85313,85317],{},[895,85314,85315],{},[898,85316,14667],{},[902,85318,14667],{"encoding":904}," stane ",[883,85321,85323],{"className":85322},[886],[888,85324,85325],{"xmlns":890},[892,85326,85327,85337],{},[895,85328,85329,85331],{},[898,85330,4445],{},[6927,85332,85333,85335],{},[898,85334,1710],{},[898,85336,14667],{},[902,85338,14917],{"encoding":904}," klesající (",[883,85341,85343],{"className":85342},[886],[888,85344,85345],{"xmlns":890},[892,85346,85347,85369],{},[895,85348,85349,85365,85367],{},[6989,85350,85351,85353,85359],{},[898,85352,1734],{},[895,85354,85355,85357],{},[898,85356,14667],{},[898,85358,14667],{},[895,85360,85361,85363],{},[1712,85362,2243],{"mathvariant":2003},[1712,85364,2243],{"mathvariant":2003},[1712,85366,2252],{},[1716,85368,2085],{},[902,85370,85371],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,85374,85376],{"className":85375},[886],[888,85377,85378],{"xmlns":890},[892,85379,85380,85402],{},[895,85381,85382,85398,85400],{},[6989,85383,85384,85386,85392],{},[898,85385,1734],{},[895,85387,85388,85390],{},[898,85389,14672],{},[898,85391,14672],{},[895,85393,85394,85396],{},[1712,85395,2243],{"mathvariant":2003},[1712,85397,2243],{"mathvariant":2003},[1712,85399,2252],{},[1716,85401,2085],{},[902,85403,85404],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,85407,85409],{"className":85408},[886],[888,85410,85411],{"xmlns":890},[892,85412,85413,85421],{},[895,85414,85415],{},[6927,85416,85417,85419],{},[898,85418,14667],{},[1716,85420,2085],{},[902,85422,80433],{"encoding":904},[115,85424,85426],{"id":85425},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,85428,85429,85432,85433,85456,85457,34819],{},[38,85430,85431],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,85434,85436],{"className":85435},[886],[888,85437,85438],{"xmlns":890},[892,85439,85440,85454],{},[895,85441,85442,85444,85446,85448,85450,85452],{},[898,85443,1734],{},[1712,85445,1904],{"stretchy":1903},[898,85447,14667],{},[1712,85449,3138],{"separator":2565},[898,85451,14672],{},[1712,85453,1910],{"stretchy":1903},[902,85455,14869],{"encoding":904}," stupně ",[883,85458,85460],{"className":85459},[886],[888,85461,85462],{"xmlns":890},[892,85463,85464,85468],{},[895,85465,85466],{},[898,85467,41735],{},[902,85469,41735],{"encoding":904},[883,85471,85473],{"className":85472},[886],[888,85474,85475],{"xmlns":890,"display":32941},[892,85476,85477,85540],{},[25629,85478,85479],{"width":32946},[25634,85480,85481,85483,85533,85535],{},[25637,85482],{"width":32951},[25637,85484,85485],{},[895,85486,85487,85489,85491,85499,85501,85503,85505,85513,85515,85517,85519,85521,85523,85525,85527,85529,85531],{},[898,85488,14667],{},[1762,85490,2583],{},[6989,85492,85493,85495,85497],{},[898,85494,1734],{},[898,85496,14667],{},[1712,85498,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,85500,3145],{},[898,85502,14672],{},[1762,85504,2583],{},[6989,85506,85507,85509,85511],{},[898,85508,1734],{},[898,85510,14672],{},[1712,85512,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,85514,1714],{},[898,85516,41735],{},[1762,85518,2583],{},[898,85520,1734],{},[1712,85522,1904],{"stretchy":1903},[898,85524,14667],{},[1712,85526,3138],{"separator":2565},[898,85528,14672],{},[1712,85530,1910],{"stretchy":1903},[898,85532,1659],{"mathvariant":2003},[25637,85534],{"width":32951},[25637,85536,85537],{},[1762,85538,85539],{},"(5.12)",[902,85541,85542],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,85544,85545,85566],{},[38,85546,85547,85548],{},"Speciální případ ",[883,85549,85551],{"className":85550},[886],[888,85552,85553],{"xmlns":890},[892,85554,85555,85563],{},[895,85556,85557,85559,85561],{},[898,85558,41735],{},[1712,85560,1714],{},[1716,85562,2222],{},[902,85564,85565],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,85568,85570],{"className":85569},[886],[888,85571,85572],{"xmlns":890,"display":32941},[892,85573,85574,85618],{},[895,85575,85576,85578,85580,85582,85588,85590,85592,85594,85596,85602,85604,85606,85608,85610,85612,85614,85616],{},[898,85577,14667],{},[1712,85579,1783],{},[898,85581,4445],{},[6927,85583,85584,85586],{},[898,85585,1710],{},[898,85587,14667],{},[1712,85589,3145],{},[898,85591,14672],{},[1712,85593,1783],{},[898,85595,4445],{},[6927,85597,85598,85600],{},[898,85599,1710],{},[898,85601,14672],{},[1712,85603,1714],{},[898,85605,1734],{},[1712,85607,1904],{"stretchy":1903},[898,85609,14667],{},[1712,85611,3138],{"separator":2565},[898,85613,14672],{},[1712,85615,1910],{"stretchy":1903},[898,85617,1659],{"mathvariant":2003},[902,85619,85620],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,85622,85623,85624,85627],{},"Slovně — ",[38,85625,85626],{},"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).",[115,85629,14650],{"id":79769},[724,85631,85632,14897,85634,85637,85638,85660,85661,2854],{},[38,85633,14650],{},[614,85635,85636],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,85639,85641],{"className":85640},[886],[888,85642,85643],{"xmlns":890},[892,85644,85645,85657],{},[895,85646,85647,85649,85651,85653,85655],{},[1712,85648,7910],{"stretchy":1903},[898,85650,14667],{},[1712,85652,3138],{"separator":2565},[898,85654,14672],{},[1712,85656,7925],{"stretchy":1903},[902,85658,85659],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,85662,85664],{"className":85663},[886],[888,85665,85666],{"xmlns":890},[892,85667,85668,85673],{},[895,85669,85670],{},[898,85671,85672],{},"q",[902,85674,85672],{"encoding":904},[883,85676,85678],{"className":85677},[886],[888,85679,85680],{"xmlns":890,"display":32941},[892,85681,85682,85717],{},[25629,85683,85684],{"width":32946},[25634,85685,85686,85688,85710,85712],{},[25637,85687],{"width":32951},[25637,85689,85690],{},[895,85691,85692,85694,85696,85698,85700,85702,85704,85706,85708],{},[898,85693,1734],{},[1712,85695,1904],{"stretchy":1903},[898,85697,14667],{},[1712,85699,3138],{"separator":2565},[898,85701,14672],{},[1712,85703,1910],{"stretchy":1903},[1712,85705,1714],{},[898,85707,85672],{},[898,85709,1659],{"mathvariant":2003},[25637,85711],{"width":32951},[25637,85713,85714],{},[1762,85715,85716],{},"(5.13)",[902,85718,85719],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,85721,85722,85723,85726,85727,1691],{},"Jsou to ",[38,85724,85725],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,85728,85730],{"className":85729,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,85732,85733],{},[38,85734,85735],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,85737,85738,85743,85748,85753],{},[123,85739,85740,85742],{},[38,85741,17393],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,85744,85745,85747],{},[38,85746,42539],{}," (úloha 5.14);",[123,85749,85750,6245],{},[38,85751,85752],{},"neprotínají se",[123,85754,85755,85756,2149,85769,1659],{},"s rostoucím ",[883,85757,85759],{"className":85758},[886],[888,85760,85761],{"xmlns":890},[892,85762,85763,85767],{},[895,85764,85765],{},[898,85766,85672],{},[902,85768,85672],{"encoding":904},[38,85770,85771],{},"vzdalují od počátku",[724,85773,85774],{},[614,85775,85776,85777,85799,85800,1659],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,85778,85780],{"className":85779},[886],[888,85781,85782],{"xmlns":890},[892,85783,85784,85796],{},[895,85785,85786,85788,85790,85792,85794],{},[1712,85787,1904],{"stretchy":1903},[898,85789,14667],{},[1712,85791,3138],{"separator":2565},[898,85793,14672],{},[1712,85795,1910],{"stretchy":1903},[902,85797,85798],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,85801,85803],{"className":85802},[886],[888,85804,85805],{"xmlns":890},[892,85806,85807,85831],{},[895,85808,85809,85815,85817,85823,85825],{},[6927,85810,85811,85813],{},[898,85812,85672],{},[1716,85814,2222],{},[1712,85816,2252],{},[6927,85818,85819,85821],{},[898,85820,85672],{},[1716,85822,2085],{},[1712,85824,2252],{},[6927,85826,85827,85829],{},[898,85828,85672],{},[1716,85830,2787],{},[902,85832,85833],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,85835,85837,85838,1910],{"id":85836},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,85839,85841],{"className":85840},[886],[888,85842,85843],{"xmlns":890},[892,85844,85845,85855],{},[895,85846,85847,85849,85851,85853],{},[898,85848,4445],{},[898,85850,1775],{},[898,85852,1772],{},[898,85854,6493],{},[902,85856,15471],{"encoding":904},[724,85858,85859,14897,85862,85865],{},[38,85860,85861],{},"Mezní míra technické substituce",[614,85863,85864],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,85867,85869],{"className":85868},[886],[888,85870,85871],{"xmlns":890,"display":32941},[892,85872,85873,85964],{},[25629,85874,85875],{"width":32946},[25634,85876,85877,85879,85957,85959],{},[25637,85878],{"width":32951},[25637,85880,85881],{},[895,85882,85883,85885,85887,85889,85891,85893,85895,85897,85899,85901,85903,85905,85907,85909,85911,85913,85935,85937,85955],{},[898,85884,4445],{},[898,85886,1775],{},[898,85888,1772],{},[898,85890,6493],{},[1712,85892,1714],{},[898,85894,4445],{},[898,85896,1775],{},[898,85898,1772],{},[898,85900,6493],{},[1712,85902,1904],{"stretchy":1903},[898,85904,14667],{},[1712,85906,3138],{"separator":2565},[898,85908,14672],{},[1712,85910,1910],{"stretchy":1903},[1712,85912,1714],{},[2567,85914,85915,85925],{},[895,85916,85917,85919],{},[898,85918,4445],{},[6927,85920,85921,85923],{},[898,85922,1710],{},[898,85924,14667],{},[895,85926,85927,85929],{},[898,85928,4445],{},[6927,85930,85931,85933],{},[898,85932,1710],{},[898,85934,14672],{},[1712,85936,1714],{},[2567,85938,85939,85947],{},[6989,85940,85941,85943,85945],{},[898,85942,1734],{},[898,85944,14667],{},[1712,85946,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,85948,85949,85951,85953],{},[898,85950,1734],{},[898,85952,14672],{},[1712,85954,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[898,85956,1659],{"mathvariant":2003},[25637,85958],{"width":32951},[25637,85960,85961],{},[1762,85962,85963],{},"(5.14)",[902,85965,85966],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,85968,85969,3245,85971,86001,86002,86033],{},[38,85970,7040],{},[883,85972,85974],{"className":85973},[886],[888,85975,85976],{"xmlns":890},[892,85977,85978,85998],{},[895,85979,85980,85982,85984,85986,85988,85990,85992,85994,85996],{},[898,85981,4445],{},[898,85983,1775],{},[898,85985,1772],{},[898,85987,6493],{},[1712,85989,1904],{"stretchy":1903},[898,85991,14667],{},[1712,85993,3138],{"separator":2565},[898,85995,14672],{},[1712,85997,1910],{"stretchy":1903},[902,85999,86000],{"encoding":904},"MRTS(L, K)"," udává, ",[38,86003,86004,86005,86018,86019,86032],{},"o kolik se musí přibližně změnit kapitál ",[883,86006,86008],{"className":86007},[886],[888,86009,86010],{"xmlns":890},[892,86011,86012,86016],{},[895,86013,86014],{},[898,86015,14672],{},[902,86017,14672],{"encoding":904},", jestliže se práce ",[883,86020,86022],{"className":86021},[886],[888,86023,86024],{"xmlns":890},[892,86025,86026,86030],{},[895,86027,86028],{},[898,86029,14667],{},[902,86031,14667],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1636,86035,86036],{},[724,86037,86038,22898,86040,86059,86060,86097,86098,86101,86102,86106],{},[883,86039,1941],{},[883,86041,86043],{"className":86042},[886],[888,86044,86045],{"xmlns":890},[892,86046,86047,86057],{},[895,86048,86049,86051,86053,86055],{},[898,86050,4445],{},[898,86052,1775],{},[898,86054,1772],{},[898,86056,6493],{},[902,86058,15471],{"encoding":904}," říká: ",[614,86061,86062,86063,86082,86083,86096],{},"„jednu jednotku práce musím nahradit přibližně ",[883,86064,86066],{"className":86065},[886],[888,86067,86068],{"xmlns":890},[892,86069,86070,86080],{},[895,86071,86072,86074,86076,86078],{},[898,86073,4445],{},[898,86075,1775],{},[898,86077,1772],{},[898,86079,6493],{},[902,86081,15471],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,86084,86086],{"className":86085},[886],[888,86087,86088],{"xmlns":890},[892,86089,86090,86094],{},[895,86091,86092],{},[898,86093,1734],{},[902,86095,1734],{"encoding":904}," zůstala stejná.\""," Je to ",[38,86099,86100],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,86103,86105],{"className":86104,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,86108,86109],{},[3817,86110],{"alt":86111,"className":86112,"src":86113},"imek-izokvanty-mrts",[210,3821],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,86115,86116,86119,86120,5920,86150,86172,86173,8558],{},[38,86117,86118],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,86121,86123],{"className":86122},[886],[888,86124,86125],{"xmlns":890},[892,86126,86127,86147],{},[895,86128,86129,86131,86137,86139,86145],{},[1712,86130,7910],{"stretchy":1903},[6927,86132,86133,86135],{},[898,86134,14667],{},[1716,86136,2085],{},[1712,86138,3138],{"separator":2565},[6927,86140,86141,86143],{},[898,86142,14672],{},[1716,86144,2085],{},[1712,86146,7925],{"stretchy":1903},[902,86148,86149],{"encoding":904},"[L_0, K_0]",[883,86151,86153],{"className":86152},[886],[888,86154,86155],{"xmlns":890},[892,86156,86157,86169],{},[895,86158,86159,86161,86163,86165,86167],{},[1712,86160,2219],{},[898,86162,4445],{},[898,86164,1775],{},[898,86166,1772],{},[898,86168,6493],{},[902,86170,86171],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,86174,86176],{"className":86175},[886],[888,86177,86178],{"xmlns":890},[892,86179,86180,86202],{},[895,86181,86182,86184,86186,86188,86190,86192,86194,86196],{},[898,86183,1734],{},[1712,86185,1904],{"stretchy":1903},[898,86187,14667],{},[1712,86189,3138],{"separator":2565},[898,86191,14672],{},[1712,86193,1910],{"stretchy":1903},[1712,86195,1714],{},[6927,86197,86198,86200],{},[898,86199,85672],{},[1716,86201,2085],{},[902,86203,86204],{"encoding":904},"Q(L,K) = q_0",[883,86206,86208],{"className":86207},[886],[888,86209,86210],{"xmlns":890,"display":32941},[892,86211,86212,86264],{},[895,86213,86214,86228,86230,86232,86250,86252,86254,86256,86258,86260,86262],{},[2567,86215,86216,86222],{},[895,86217,86218,86220],{},[898,86219,2468],{},[898,86221,14672],{},[895,86223,86224,86226],{},[898,86225,2468],{},[898,86227,14667],{},[1712,86229,1714],{},[1712,86231,2219],{},[2567,86233,86234,86242],{},[6989,86235,86236,86238,86240],{},[898,86237,1734],{},[898,86239,14667],{},[1712,86241,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,86243,86244,86246,86248],{},[898,86245,1734],{},[898,86247,14672],{},[1712,86249,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,86251,1714],{},[1712,86253,2219],{},[898,86255,4445],{},[898,86257,1775],{},[898,86259,1772],{},[898,86261,6493],{},[898,86263,1659],{"mathvariant":2003},[902,86265,86266],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,86268,86269,86270,86285,86286,86302],{},"Změní-li se práce o ",[883,86271,86273],{"className":86272},[886],[888,86274,86275],{"xmlns":890},[892,86276,86277,86283],{},[895,86278,86279,86281],{},[898,86280,2468],{},[898,86282,14667],{},[902,86284,80231],{"encoding":904},", lze pro odhad změny kapitálu ",[883,86287,86289],{"className":86288},[886],[888,86290,86291],{"xmlns":890},[892,86292,86293,86299],{},[895,86294,86295,86297],{},[898,86296,2004],{"mathvariant":2003},[898,86298,14672],{},[902,86300,86301],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,86304,86306],{"className":86305},[886],[888,86307,86308],{"xmlns":890,"display":32941},[892,86309,86310,86357],{},[25629,86311,86312],{"width":32946},[25634,86313,86314,86316,86350,86352],{},[25637,86315],{"width":32951},[25637,86317,86318],{},[895,86319,86320,86322,86324,86326,86328,86330,86332,86334,86336,86338,86340,86342,86344,86346,86348],{},[898,86321,2004],{"mathvariant":2003},[898,86323,14672],{},[1712,86325,3740],{},[898,86327,2468],{},[898,86329,14672],{},[1712,86331,1714],{},[1712,86333,2219],{},[898,86335,4445],{},[898,86337,1775],{},[898,86339,1772],{},[898,86341,6493],{},[1762,86343,2583],{},[898,86345,2468],{},[898,86347,14667],{},[1712,86349,3138],{"separator":2565},[25637,86351],{"width":32951},[25637,86353,86354],{},[1762,86355,86356],{},"(5.15)",[902,86358,86359],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,86361,86363],{"className":86362},[886],[888,86364,86365],{"xmlns":890,"display":32941},[892,86366,86367,86416],{},[25629,86368,86369],{"width":32946},[25634,86370,86371,86373,86409,86411],{},[25637,86372],{"width":32951},[25637,86374,86375],{},[895,86376,86377,86379,86381,86383,86401,86403,86405,86407],{},[898,86378,2468],{},[898,86380,14667],{},[1712,86382,1714],{},[2567,86384,86385,86391],{},[895,86386,86387,86389],{},[1712,86388,2219],{},[1716,86390,2222],{},[895,86392,86393,86395,86397,86399],{},[898,86394,4445],{},[898,86396,1775],{},[898,86398,1772],{},[898,86400,6493],{},[1762,86402,2583],{},[898,86404,2468],{},[898,86406,14672],{},[898,86408,1659],{"mathvariant":2003},[25637,86410],{"width":32951},[25637,86412,86413],{},[1762,86414,86415],{},"(5.16)",[902,86417,86418],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1636,86420,86421,86445],{},[724,86422,86423,86425,86426],{},[883,86424,2370],{}," Postup — jak spočítat ",[883,86427,86429],{"className":86428},[886],[888,86430,86431],{"xmlns":890},[892,86432,86433,86443],{},[895,86434,86435,86437,86439,86441],{},[898,86436,4445],{},[898,86438,1775],{},[898,86440,1772],{},[898,86442,6493],{},[902,86444,15471],{"encoding":904},[152,86446,86447,86488,86531,86563],{},[123,86448,86449,86450,1655,86469,1659],{},"Vypočtěte parciální derivace ",[883,86451,86453],{"className":86452},[886],[888,86454,86455],{"xmlns":890},[892,86456,86457,86467],{},[895,86458,86459],{},[6989,86460,86461,86463,86465],{},[898,86462,1734],{},[898,86464,14667],{},[1712,86466,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,86468,14893],{"encoding":904},[883,86470,86472],{"className":86471},[886],[888,86473,86474],{"xmlns":890},[892,86475,86476,86486],{},[895,86477,86478],{},[6989,86479,86480,86482,86484],{},[898,86481,1734],{},[898,86483,14672],{},[1712,86485,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,86487,14939],{"encoding":904},[123,86489,70716,86490,86530],{},[883,86491,86493],{"className":86492},[886],[888,86494,86495],{"xmlns":890},[892,86496,86497,86527],{},[895,86498,86499,86501,86503,86505,86507,86509,86517,86519],{},[898,86500,4445],{},[898,86502,1775],{},[898,86504,1772],{},[898,86506,6493],{},[1712,86508,1714],{},[6989,86510,86511,86513,86515],{},[898,86512,1734],{},[898,86514,14667],{},[1712,86516,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[898,86518,2473],{"mathvariant":2003},[6989,86520,86521,86523,86525],{},[898,86522,1734],{},[898,86524,14672],{},[1712,86526,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,86528,86529],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,86532,86533,86534,1659],{},"Případně dosaďte konkrétní ",[883,86535,86537],{"className":86536},[886],[888,86538,86539],{"xmlns":890},[892,86540,86541,86561],{},[895,86542,86543,86545,86551,86553,86559],{},[1712,86544,7910],{"stretchy":1903},[6927,86546,86547,86549],{},[898,86548,14667],{},[1716,86550,2085],{},[1712,86552,3138],{"separator":2565},[6927,86554,86555,86557],{},[898,86556,14672],{},[1716,86558,2085],{},[1712,86560,7925],{"stretchy":1903},[902,86562,86149],{"encoding":904},[123,86564,86565,86566,86600,86601,86603],{},"Pro odhad substituce použijte ",[883,86567,86569],{"className":86568},[886],[888,86570,86571],{"xmlns":890},[892,86572,86573,86597],{},[895,86574,86575,86577,86579,86581,86583,86585,86587,86589,86591,86593,86595],{},[898,86576,2004],{"mathvariant":2003},[898,86578,14672],{},[1712,86580,3740],{},[1712,86582,2219],{},[898,86584,4445],{},[898,86586,1775],{},[898,86588,1772],{},[898,86590,6493],{},[1712,86592,1783],{},[898,86594,2004],{"mathvariant":2003},[898,86596,14667],{},[902,86598,86599],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,86602,57481],{}," — substituce, ne doplnění).",[724,86605,86606],{},[614,86607,86608,86609,86641,86642,8046,86655,20666,86684,86699],{},"Obrázek 5.7 — izokvanta ",[883,86610,86612],{"className":86611},[886],[888,86613,86614],{"xmlns":890},[892,86615,86616,86638],{},[895,86617,86618,86624,86626,86628,86630,86632,86634,86636],{},[6927,86619,86620,86622],{},[898,86621,85672],{},[1716,86623,2085],{},[1712,86625,1714],{},[898,86627,1734],{},[1712,86629,1904],{"stretchy":1903},[898,86631,14667],{},[1712,86633,3138],{"separator":2565},[898,86635,14672],{},[1712,86637,1910],{"stretchy":1903},[902,86639,86640],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,86643,86645],{"className":86644},[886],[888,86646,86647],{"xmlns":890},[892,86648,86649,86653],{},[895,86650,86651],{},[898,86652,23730],{},[902,86654,23730],{"encoding":904},[883,86656,86658],{"className":86657},[886],[888,86659,86660],{"xmlns":890},[892,86661,86662,86682],{},[895,86663,86664,86666,86672,86674,86680],{},[1712,86665,7910],{"stretchy":1903},[6927,86667,86668,86670],{},[898,86669,14667],{},[1716,86671,2085],{},[1712,86673,3138],{"separator":2565},[6927,86675,86676,86678],{},[898,86677,14672],{},[1716,86679,2085],{},[1712,86681,7925],{"stretchy":1903},[902,86683,86149],{"encoding":904},[883,86685,86687],{"className":86686},[886],[888,86688,86689],{"xmlns":890},[892,86690,86691,86697],{},[895,86692,86693,86695],{},[898,86694,2004],{"mathvariant":2003},[898,86696,14672],{},[902,86698,86301],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,86701,86703],{"id":86702},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,86705,86707],{"id":86706},"příklad-54","Příklad 5.4",[724,86709,81548,86710,1343,86752,1343,86769,1659],{},[883,86711,86713],{"className":86712},[886],[888,86714,86715],{"xmlns":890},[892,86716,86717,86749],{},[895,86718,86719,86721,86723,86725,86737],{},[898,86720,1734],{},[1712,86722,1714],{},[1716,86724,41119],{},[2037,86726,86727,86729],{},[898,86728,14667],{},[895,86730,86731,86733,86735],{},[1716,86732,2222],{},[898,86734,2473],{"mathvariant":2003},[1716,86736,2787],{},[2037,86738,86739,86741],{},[898,86740,14672],{},[895,86742,86743,86745,86747],{},[1716,86744,2222],{},[898,86746,2473],{"mathvariant":2003},[1716,86748,6198],{},[902,86750,86751],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,86753,86755],{"className":86754},[886],[888,86756,86757],{"xmlns":890},[892,86758,86759,86767],{},[895,86760,86761,86763,86765],{},[898,86762,14667],{},[1712,86764,1714],{},[1716,86766,6857],{},[902,86768,81922],{"encoding":904},[883,86770,86772],{"className":86771},[886],[888,86773,86774],{"xmlns":890},[892,86775,86776,86784],{},[895,86777,86778,86780,86782],{},[898,86779,14672],{},[1712,86781,1714],{},[1716,86783,1739],{},[902,86785,86786],{"encoding":904},"K = 100",[724,86788,86789],{},[38,86790,86791],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,86793,86795],{"className":86794},[886],[888,86796,86797],{"xmlns":890,"display":32941},[892,86798,86799,86913],{},[895,86800,86801,86803,86809,86811,86819,86821,86829,86843,86855,86857,86859,86861,86867,86869,86871,86873,86875,86877,86879,86887,86889,86899,86901,86908,86910],{},[898,86802,4445],{},[6927,86804,86805,86807],{},[898,86806,1710],{},[898,86808,14667],{},[1712,86810,1714],{},[6989,86812,86813,86815,86817],{},[898,86814,1734],{},[898,86816,14667],{},[1712,86818,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,86820,1714],{},[2563,86822,86823],{"scriptlevel":2085,"displaystyle":1903},[2567,86824,86825,86827],{},[1716,86826,41119],{},[1716,86828,2787],{},[2037,86830,86831,86833],{},[898,86832,14667],{},[895,86834,86835,86837,86839,86841],{},[1712,86836,2219],{},[1716,86838,2222],{},[898,86840,2473],{"mathvariant":2003},[1716,86842,2787],{},[2037,86844,86845,86847],{},[898,86846,14672],{},[895,86848,86849,86851,86853],{},[1716,86850,2222],{},[898,86852,2473],{"mathvariant":2003},[1716,86854,6198],{},[1712,86856,3138],{"separator":2565},[3690,86858],{"width":20158},[898,86860,4445],{},[6927,86862,86863,86865],{},[898,86864,1710],{},[898,86866,14667],{},[1712,86868,1904],{"stretchy":1903},[1716,86870,6857],{},[1712,86872,3138],{"separator":2565},[1716,86874,1739],{},[1712,86876,1910],{"stretchy":1903},[1712,86878,1714],{},[2563,86880,86881],{"scriptlevel":2085,"displaystyle":1903},[2567,86882,86883,86885],{},[1716,86884,41119],{},[1716,86886,2787],{},[1712,86888,1783],{},[2563,86890,86891],{"scriptlevel":2085,"displaystyle":1903},[2567,86892,86893,86895],{},[1716,86894,2222],{},[5935,86896,86897],{},[1716,86898,6857],{},[1712,86900,1783],{},[86902,86903,86904,86906],"mroot",{},[1716,86905,1739],{},[1716,86907,6198],{},[1712,86909,3740],{},[1716,86911,86912],{},"7,153.",[902,86914,86915],{"encoding":904},"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.",[724,86917,86918,86919,49035,86941,15105,86958,86979,86980,87001],{},"Přibližná změna při ",[883,86920,86922],{"className":86921},[886],[888,86923,86924],{"xmlns":890},[892,86925,86926,86938],{},[895,86927,86928,86930,86932,86934,86936],{},[898,86929,14667],{},[1712,86931,2854],{},[1716,86933,6857],{},[1712,86935,2082],{},[1716,86937,43221],{},[902,86939,86940],{"encoding":904},"L: 20 \\to 21",[883,86942,86944],{"className":86943},[886],[888,86945,86946],{"xmlns":890},[892,86947,86948,86956],{},[895,86949,86950,86952,86954],{},[898,86951,14672],{},[1712,86953,1714],{},[1716,86955,1739],{},[902,86957,86786],{"encoding":904},[883,86959,86961],{"className":86960},[886],[888,86962,86963],{"xmlns":890},[892,86964,86965,86976],{},[895,86966,86967,86969,86971,86973],{},[898,86968,2004],{"mathvariant":2003},[898,86970,1734],{},[1712,86972,3740],{},[1716,86974,86975],{},"7,153",[902,86977,86978],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,86981,86983],{"className":86982},[886],[888,86984,86985],{"xmlns":890},[892,86986,86987,86998],{},[895,86988,86989,86991,86993,86995],{},[898,86990,2004],{"mathvariant":2003},[898,86992,1734],{},[1712,86994,3740],{},[1716,86996,86997],{},"26,888",[902,86999,87000],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,87003,87004,87007],{},[38,87005,87006],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,87009,87011],{"className":87010},[886],[888,87012,87013],{"xmlns":890,"display":32941},[892,87014,87015,87115],{},[895,87016,87017,87019,87025,87027,87035,87037,87039,87051,87065,87067,87069,87071,87077,87079,87081,87083,87085,87087,87089,87091,87095,87097,87110,87112],{},[898,87018,4445],{},[6927,87020,87021,87023],{},[898,87022,1710],{},[898,87024,14672],{},[1712,87026,1714],{},[6989,87028,87029,87031,87033],{},[898,87030,1734],{},[898,87032,14672],{},[1712,87034,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,87036,1714],{},[1716,87038,3068],{},[2037,87040,87041,87043],{},[898,87042,14667],{},[895,87044,87045,87047,87049],{},[1716,87046,2222],{},[898,87048,2473],{"mathvariant":2003},[1716,87050,2787],{},[2037,87052,87053,87055],{},[898,87054,14672],{},[895,87056,87057,87059,87061,87063],{},[1712,87058,2219],{},[1716,87060,2787],{},[898,87062,2473],{"mathvariant":2003},[1716,87064,6198],{},[1712,87066,3138],{"separator":2565},[3690,87068],{"width":20158},[898,87070,4445],{},[6927,87072,87073,87075],{},[898,87074,1710],{},[898,87076,14672],{},[1712,87078,1904],{"stretchy":1903},[1716,87080,6857],{},[1712,87082,3138],{"separator":2565},[1716,87084,1739],{},[1712,87086,1910],{"stretchy":1903},[1712,87088,1714],{},[1716,87090,3068],{},[5935,87092,87093],{},[1716,87094,6857],{},[1712,87096,1783],{},[2563,87098,87099],{"scriptlevel":2085,"displaystyle":1903},[2567,87100,87101,87103],{},[1716,87102,2222],{},[86902,87104,87105,87108],{},[1716,87106,87107],{},"10000",[1716,87109,6198],{},[1712,87111,3740],{},[1716,87113,87114],{},"4,525.",[902,87116,87117],{"encoding":904},"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.",[724,87119,87120,87121,3072,87138,1691],{},"Produkce poklesne přibližně o 4,525 (z ",[883,87122,87124],{"className":87123},[886],[888,87125,87126],{"xmlns":890},[892,87127,87128,87135],{},[895,87129,87130,87132],{},[1712,87131,3740],{},[1716,87133,87134],{},"905,126",[902,87136,87137],{"encoding":904},"\\approx 905{,}126",[883,87139,87141],{"className":87140},[886],[888,87142,87143],{"xmlns":890},[892,87144,87145,87152],{},[895,87146,87147,87149],{},[1712,87148,3740],{},[1716,87150,87151],{},"900,601",[902,87153,87154],{"encoding":904},"\\approx 900{,}601",[724,87156,87157,8537,87204,1343,87226,1691],{},[38,87158,87159,87160,1655,87182],{},"(c) Změna ",[883,87161,87163],{"className":87162},[886],[888,87164,87165],{"xmlns":890},[892,87166,87167,87179],{},[895,87168,87169,87171,87173,87175,87177],{},[898,87170,14667],{},[1712,87172,2854],{},[1716,87174,6857],{},[1712,87176,2082],{},[1716,87178,41119],{},[902,87180,87181],{"encoding":904},"L: 20 \\to 15",[883,87183,87185],{"className":87184},[886],[888,87186,87187],{"xmlns":890},[892,87188,87189,87201],{},[895,87190,87191,87193,87195,87197,87199],{},[898,87192,14672],{},[1712,87194,2854],{},[1716,87196,1739],{},[1712,87198,2082],{},[1716,87200,6624],{},[902,87202,87203],{"encoding":904},"K: 100 \\to 150",[883,87205,87207],{"className":87206},[886],[888,87208,87209],{"xmlns":890},[892,87210,87211,87223],{},[895,87212,87213,87215,87217,87219,87221],{},[898,87214,2468],{},[898,87216,14667],{},[1712,87218,1714],{},[1712,87220,2219],{},[1716,87222,3068],{},[902,87224,87225],{"encoding":904},"dL = -5",[883,87227,87229],{"className":87228},[886],[888,87230,87231],{"xmlns":890},[892,87232,87233,87243],{},[895,87234,87235,87237,87239,87241],{},[898,87236,2468],{},[898,87238,14672],{},[1712,87240,1714],{},[1716,87242,2782],{},[902,87244,87245],{"encoding":904},"dK = 50",[883,87247,87249],{"className":87248},[886],[888,87250,87251],{"xmlns":890,"display":32941},[892,87252,87253,87341],{},[895,87254,87255,87257,87259,87261,87263,87269,87271,87273,87275,87277,87279,87281,87283,87285,87287,87289,87291,87293,87299,87301,87303,87305,87307,87309,87311,87313,87315,87317,87319,87321,87323,87325,87327,87329,87332,87334,87336,87338],{},[898,87256,2468],{},[898,87258,1734],{},[1712,87260,1714],{},[898,87262,4445],{},[6927,87264,87265,87267],{},[898,87266,1710],{},[898,87268,14667],{},[1712,87270,1904],{"stretchy":1903},[1716,87272,6857],{},[1712,87274,3138],{"separator":2565},[1716,87276,1739],{},[1712,87278,1910],{"stretchy":1903},[1712,87280,1783],{},[1712,87282,1904],{"stretchy":1903},[1712,87284,2219],{},[1716,87286,3068],{},[1712,87288,1910],{"stretchy":1903},[1712,87290,3145],{},[898,87292,4445],{},[6927,87294,87295,87297],{},[898,87296,1710],{},[898,87298,14672],{},[1712,87300,1904],{"stretchy":1903},[1716,87302,6857],{},[1712,87304,3138],{"separator":2565},[1716,87306,1739],{},[1712,87308,1910],{"stretchy":1903},[1712,87310,1783],{},[1716,87312,2782],{},[1712,87314,1714],{},[1716,87316,86975],{},[1712,87318,1783],{},[1712,87320,1904],{"stretchy":1903},[1712,87322,2219],{},[1716,87324,3068],{},[1712,87326,1910],{"stretchy":1903},[1712,87328,3145],{},[1716,87330,87331],{},"4,525",[1712,87333,1783],{},[1716,87335,2782],{},[1712,87337,3740],{},[1716,87339,87340],{},"190,485.",[902,87342,87343],{"encoding":904},"dQ = MP_L(20,100)\\cdot(-5) + MP_K(20,100)\\cdot 50 = 7{,}153\\cdot(-5) + 4{,}525\\cdot 50 \\approx 190{,}485.",[724,87345,87346],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,87348,87350],{"id":87349},"příklad-55","Příklad 5.5",[724,87352,87353,87354,87390,87391,1659],{},"Pro produkci ",[883,87355,87357],{"className":87356},[886],[888,87358,87359],{"xmlns":890},[892,87360,87361,87387],{},[895,87362,87363,87365,87367,87369,87371,87373,87375,87377,87383],{},[898,87364,1734],{},[1712,87366,1904],{"stretchy":1903},[898,87368,14667],{},[1712,87370,3138],{"separator":2565},[898,87372,14672],{},[1712,87374,1910],{"stretchy":1903},[1712,87376,1714],{},[86902,87378,87379,87381],{},[898,87380,14667],{},[1716,87382,6198],{},[5935,87384,87385],{},[898,87386,14672],{},[902,87388,87389],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,87392,87394],{"className":87393},[886],[888,87395,87396],{"xmlns":890},[892,87397,87398,87414],{},[895,87399,87400,87406,87410,87412],{},[86902,87401,87402,87404],{},[898,87403,14667],{},[1716,87405,6198],{},[5935,87407,87408],{},[898,87409,14672],{},[1712,87411,1714],{},[898,87413,85672],{},[902,87415,87416],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,87418,87419,87420,1659],{},"Umocněním na druhou: ",[883,87421,87423],{"className":87422},[886],[888,87424,87425],{"xmlns":890},[892,87426,87427,87451],{},[895,87428,87429,87431,87433,87439,87441],{},[898,87430,14672],{},[1712,87432,1714],{},[2037,87434,87435,87437],{},[898,87436,85672],{},[1716,87438,2787],{},[898,87440,2473],{"mathvariant":2003},[86902,87442,87443,87449],{},[2037,87444,87445,87447],{},[898,87446,14667],{},[1716,87448,2787],{},[1716,87450,6198],{},[902,87452,87453],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,87455,87456,87496,87536],{},[123,87457,87458],{},[883,87459,87461],{"className":87460},[886],[888,87462,87463],{"xmlns":890},[892,87464,87465,87493],{},[895,87466,87467,87469,87471,87473,87475,87477,87479,87481,87483],{},[898,87468,85672],{},[1712,87470,1714],{},[1716,87472,2222],{},[1712,87474,1767],{},[898,87476,14672],{},[1712,87478,1714],{},[1716,87480,2222],{},[898,87482,2473],{"mathvariant":2003},[86902,87484,87485,87491],{},[2037,87486,87487,87489],{},[898,87488,14667],{},[1716,87490,2787],{},[1716,87492,6198],{},[902,87494,87495],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,87497,87498],{},[883,87499,87501],{"className":87500},[886],[888,87502,87503],{"xmlns":890},[892,87504,87505,87533],{},[895,87506,87507,87509,87511,87513,87515,87517,87519,87521,87523],{},[898,87508,85672],{},[1712,87510,1714],{},[1716,87512,2787],{},[1712,87514,1767],{},[898,87516,14672],{},[1712,87518,1714],{},[1716,87520,2975],{},[898,87522,2473],{"mathvariant":2003},[86902,87524,87525,87531],{},[2037,87526,87527,87529],{},[898,87528,14667],{},[1716,87530,2787],{},[1716,87532,6198],{},[902,87534,87535],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,87537,87538],{},[883,87539,87541],{"className":87540},[886],[888,87542,87543],{"xmlns":890},[892,87544,87545,87573],{},[895,87546,87547,87549,87551,87553,87555,87557,87559,87561,87563],{},[898,87548,85672],{},[1712,87550,1714],{},[1716,87552,6198],{},[1712,87554,1767],{},[898,87556,14672],{},[1712,87558,1714],{},[1716,87560,1780],{},[898,87562,2473],{"mathvariant":2003},[86902,87564,87565,87571],{},[2037,87566,87567,87569],{},[898,87568,14667],{},[1716,87570,2787],{},[1716,87572,6198],{},[902,87574,87575],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,87577,87578],{},[614,87579,87580,87581,4288,87602,1659],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,87582,87584],{"className":87583},[886],[888,87585,87586],{"xmlns":890},[892,87587,87588,87600],{},[895,87589,87590,87592,87594,87596,87598],{},[1712,87591,1904],{"stretchy":1903},[898,87593,14667],{},[1712,87595,3138],{"separator":2565},[898,87597,14672],{},[1712,87599,1910],{"stretchy":1903},[902,87601,85798],{"encoding":904},[883,87603,87605],{"className":87604},[886],[888,87606,87607],{"xmlns":890},[892,87608,87609,87625],{},[895,87610,87611,87613,87615,87617,87619,87621,87623],{},[898,87612,85672],{},[1712,87614,1714],{},[1716,87616,2222],{},[1712,87618,3138],{"separator":2565},[1716,87620,2787],{},[1712,87622,3138],{"separator":2565},[1716,87624,6198],{},[902,87626,87627],{"encoding":904},"q = 1, 2, 3",[198,87629,87631],{"id":87630},"příklad-56","Příklad 5.6",[724,87633,81548,87634,1659],{},[883,87635,87637],{"className":87636},[886],[888,87638,87639],{"xmlns":890},[892,87640,87641,87657],{},[895,87642,87643,87645,87647,87649,87651,87653],{},[898,87644,1734],{},[1712,87646,1714],{},[1716,87648,2787],{},[898,87650,14667],{},[1712,87652,3145],{},[5935,87654,87655],{},[898,87656,14672],{},[902,87658,87659],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,87661,87663],{"className":87662},[886],[888,87664,87665],{"xmlns":890,"display":32941},[892,87666,87667,87709],{},[895,87668,87669,87671,87677,87679,87681,87683,87685,87687,87693,87695,87707],{},[898,87670,4445],{},[6927,87672,87673,87675],{},[898,87674,1710],{},[898,87676,14667],{},[1712,87678,1714],{},[1716,87680,2787],{},[1712,87682,3138],{"separator":2565},[3690,87684],{"width":3692},[898,87686,4445],{},[6927,87688,87689,87691],{},[898,87690,1710],{},[898,87692,14672],{},[1712,87694,1714],{},[2567,87696,87697,87699],{},[1716,87698,2222],{},[895,87700,87701,87703],{},[1716,87702,2787],{},[5935,87704,87705],{},[898,87706,14672],{},[898,87708,1659],{"mathvariant":2003},[902,87710,87711],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,87713,87715],{"className":87714},[886],[888,87716,87717],{"xmlns":890,"display":32941},[892,87718,87719,87783],{},[895,87720,87721,87723,87725,87727,87729,87731,87753,87755,87773,87775,87777,87781],{},[898,87722,4445],{},[898,87724,1775],{},[898,87726,1772],{},[898,87728,6493],{},[1712,87730,1714],{},[2567,87732,87733,87743],{},[895,87734,87735,87737],{},[898,87736,4445],{},[6927,87738,87739,87741],{},[898,87740,1710],{},[898,87742,14667],{},[895,87744,87745,87747],{},[898,87746,4445],{},[6927,87748,87749,87751],{},[898,87750,1710],{},[898,87752,14672],{},[1712,87754,1714],{},[2567,87756,87757,87759],{},[1716,87758,2787],{},[2563,87760,87761],{"scriptlevel":2085,"displaystyle":1903},[2567,87762,87763,87765],{},[1716,87764,2222],{},[895,87766,87767,87769],{},[1716,87768,2787],{},[5935,87770,87771],{},[898,87772,14672],{},[1712,87774,1714],{},[1716,87776,2975],{},[5935,87778,87779],{},[898,87780,14672],{},[898,87782,1659],{"mathvariant":2003},[902,87784,87785],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,87787,87788,87789,87832,87833,87872,87873,1659],{},"Například ",[883,87790,87792],{"className":87791},[886],[888,87793,87794],{"xmlns":890},[892,87795,87796,87829],{},[895,87797,87798,87800,87802,87804,87806,87808,87810,87812,87814,87816,87818,87820,87824,87826],{},[898,87799,4445],{},[898,87801,1775],{},[898,87803,1772],{},[898,87805,6493],{},[1712,87807,1904],{"stretchy":1903},[1716,87809,2975],{},[1712,87811,3138],{"separator":2565},[1716,87813,29076],{},[1712,87815,1910],{"stretchy":1903},[1712,87817,1714],{},[1716,87819,2975],{},[5935,87821,87822],{},[1716,87823,29076],{},[1712,87825,3740],{},[1716,87827,87828],{},"10,58",[902,87830,87831],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,87834,87836],{"className":87835},[886],[888,87837,87838],{"xmlns":890},[892,87839,87840,87869],{},[895,87841,87842,87844,87846,87848,87850,87852,87854,87856,87858,87860,87864,87866],{},[898,87843,1734],{},[1712,87845,1904],{"stretchy":1903},[1716,87847,2975],{},[1712,87849,3138],{"separator":2565},[1716,87851,29076],{},[1712,87853,1910],{"stretchy":1903},[1712,87855,1714],{},[1716,87857,3397],{},[1712,87859,3145],{},[5935,87861,87862],{},[1716,87863,29076],{},[1712,87865,3740],{},[1716,87867,87868],{},"10,646",[902,87870,87871],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,87874,87876],{"className":87875},[886],[888,87877,87878],{"xmlns":890},[892,87879,87880,87888],{},[895,87881,87882,87884],{},[1716,87883,2975],{},[5935,87885,87886],{},[1716,87887,29076],{},[902,87889,87890],{"encoding":904},"4\\sqrt{7}",[724,87892,87893,87894,87914],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,87895,87897],{"className":87896},[886],[888,87898,87899],{"xmlns":890},[892,87900,87901,87911],{},[895,87902,87903,87905,87907,87909],{},[898,87904,2468],{},[898,87906,14667],{},[1712,87908,1714],{},[1716,87910,2787],{},[902,87912,87913],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,87916,87918],{"className":87917},[886],[888,87919,87920],{"xmlns":890,"display":32941},[892,87921,87922,87971],{},[895,87923,87924,87926,87928,87930,87932,87934,87936,87938,87940,87942,87944,87946,87948,87950,87952,87954,87956,87958,87960,87964,87966,87968],{},[898,87925,2468],{},[898,87927,14672],{},[1712,87929,1714],{},[1712,87931,2219],{},[898,87933,4445],{},[898,87935,1775],{},[898,87937,1772],{},[898,87939,6493],{},[1712,87941,1904],{"stretchy":1903},[1716,87943,2975],{},[1712,87945,3138],{"separator":2565},[1716,87947,29076],{},[1712,87949,1910],{"stretchy":1903},[1712,87951,1783],{},[1716,87953,2787],{},[1712,87955,1714],{},[1712,87957,2219],{},[1716,87959,3397],{},[5935,87961,87962],{},[1716,87963,29076],{},[1712,87965,3740],{},[1712,87967,2219],{},[1716,87969,87970],{},"21,17.",[902,87972,87973],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,87975,87977],{"id":87976},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,87979,87980,87981,1343,87983,1655,87985,87987,87988,87991,87992,87995],{},"Hlavními faktory produkce jsou ",[38,87982,79789],{},[38,87984,79805],{},[38,87986,79821],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,87989,87990],{},"jednofaktorový"," (pouze práce) a ",[38,87993,87994],{},"dvoufaktorový"," (práce + kapitál) model.",[724,87997,87998,87999,88002,88003,88005,88006,88008,88009,31064,88012,88031,88032,88049,88050,88067,88068,88090,88091,2149,88110,1659],{},"V ",[38,88000,88001],{},"1F modelu"," se definuje ",[38,88004,14896],{}," (derivace produkce podle práce) a ",[38,88007,79724],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,88010,88011],{},"zákonu klesajících výnosů",[883,88013,88015],{"className":88014},[886],[888,88016,88017],{"xmlns":890},[892,88018,88019,88029],{},[895,88020,88021,88023],{},[898,88022,4445],{},[6927,88024,88025,88027],{},[898,88026,1710],{},[898,88028,14667],{},[902,88030,14917],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,88033,88035],{"className":88034},[886],[888,88036,88037],{"xmlns":890},[892,88038,88039,88047],{},[895,88040,88041],{},[6927,88042,88043,88045],{},[898,88044,14667],{},[1716,88046,2085],{},[902,88048,80433],{"encoding":904}," klesá a v bodě ",[883,88051,88053],{"className":88052},[886],[888,88054,88055],{"xmlns":890},[892,88056,88057,88065],{},[895,88058,88059],{},[6927,88060,88061,88063],{},[898,88062,14667],{},[1716,88064,2222],{},[902,88066,18086],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,88069,88070,88071],{},"princip maximalizace ",[883,88072,88074],{"className":88073},[886],[888,88075,88076],{"xmlns":890},[892,88077,88078,88088],{},[895,88079,88080,88082],{},[898,88081,2044],{},[6927,88083,88084,88086],{},[898,88085,1710],{},[898,88087,14667],{},[902,88089,79508],{"encoding":904},": v bodě maxima ",[883,88092,88094],{"className":88093},[886],[888,88095,88096],{"xmlns":890},[892,88097,88098,88108],{},[895,88099,88100,88102],{},[898,88101,2044],{},[6927,88103,88104,88106],{},[898,88105,1710],{},[898,88107,14667],{},[902,88109,79508],{"encoding":904},[883,88111,88113],{"className":88112},[886],[888,88114,88115],{"xmlns":890},[892,88116,88117,88137],{},[895,88118,88119,88121,88127,88129,88131],{},[898,88120,4445],{},[6927,88122,88123,88125],{},[898,88124,1710],{},[898,88126,14667],{},[1712,88128,1714],{},[898,88130,2044],{},[6927,88132,88133,88135],{},[898,88134,1710],{},[898,88136,14667],{},[902,88138,79538],{"encoding":904},[724,88140,88141,88142,88145,88146,3245,88149,88178,88179,88196,88197,88200,88201,88230,88231,88233,88234,5920,88264,88286],{},"Ve ",[38,88143,88144],{},"2F modelu"," se obvykle používají ",[38,88147,88148],{},"Cobb-Douglasovy funkce",[883,88150,88152],{"className":88151},[886],[888,88153,88154],{"xmlns":890},[892,88155,88156,88176],{},[895,88157,88158,88160,88162,88164,88170],{},[898,88159,1734],{},[1712,88161,1714],{},[898,88163,2044],{},[2037,88165,88166,88168],{},[898,88167,14667],{},[898,88169,207],{},[2037,88171,88172,88174],{},[898,88173,14672],{},[898,88175,7544],{},[902,88177,79605],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,88180,88182],{"className":88181},[886],[888,88183,88184],{"xmlns":890},[892,88185,88186,88194],{},[895,88187,88188,88190,88192],{},[898,88189,207],{},[1712,88191,3145],{},[898,88193,7544],{},[902,88195,79699],{"encoding":904}," rozlišujeme ",[38,88198,88199],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,88202,88204],{"className":88203},[886],[888,88205,88206],{"xmlns":890},[892,88207,88208,88228],{},[895,88209,88210,88212,88218,88220,88222],{},[898,88211,4445],{},[6927,88213,88214,88216],{},[898,88215,1710],{},[898,88217,14667],{},[1712,88219,3138],{"separator":2565},[898,88221,4445],{},[6927,88223,88224,88226],{},[898,88225,1710],{},[898,88227,14672],{},[902,88229,79636],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,88232,14650],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,88235,88237],{"className":88236},[886],[888,88238,88239],{"xmlns":890},[892,88240,88241,88261],{},[895,88242,88243,88245,88251,88253,88255],{},[898,88244,4445],{},[6927,88246,88247,88249],{},[898,88248,1710],{},[898,88250,14667],{},[898,88252,2473],{"mathvariant":2003},[898,88254,4445],{},[6927,88256,88257,88259],{},[898,88258,1710],{},[898,88260,14672],{},[902,88262,88263],{"encoding":904},"MP_L\u002FMP_K",[38,88265,88266,88267,1910],{},"mezní míra technické substituce (",[883,88268,88270],{"className":88269},[886],[888,88271,88272],{"xmlns":890},[892,88273,88274,88284],{},[895,88275,88276,88278,88280,88282],{},[898,88277,4445],{},[898,88279,1775],{},[898,88281,1772],{},[898,88283,6493],{},[902,88285,15471],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,88288,54757],{"id":54756},[152,88290,88291,88294,88297,88300,88303,88306,88309,88312,88315,88318,88321],{},[123,88292,88293],{},"Jaké jsou faktory produkce?",[123,88295,88296],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,88298,88299],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,88301,88302],{},"Co udává mezní produkt práce?",[123,88304,88305],{},"Co musí respektovat průběh křivky produkce?",[123,88307,88308],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,88310,88311],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,88313,88314],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,88316,88317],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,88319,88320],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,88322,88323],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,88325,88327],{"id":88326},"úlohy-51517","Úlohy 5.1–5.17",[198,88329,45326],{"id":45325},[724,88331,88332,88335,88336,88358,88359,1343,88379,1343,88399,88419],{},[38,88333,88334],{},"5.1"," Je dána produkce ",[883,88337,88339],{"className":88338},[886],[888,88340,88341],{"xmlns":890},[892,88342,88343,88355],{},[895,88344,88345,88347,88349,88351],{},[898,88346,1734],{},[1712,88348,1714],{},[1716,88350,1718],{},[5935,88352,88353],{},[898,88354,14667],{},[902,88356,88357],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,88360,88362],{"className":88361},[886],[888,88363,88364],{"xmlns":890},[892,88365,88366,88376],{},[895,88367,88368,88370,88372,88374],{},[898,88369,1734],{},[1712,88371,1904],{"stretchy":1903},[1716,88373,2222],{},[1712,88375,1910],{"stretchy":1903},[902,88377,88378],{"encoding":904},"Q(1)",[883,88380,88382],{"className":88381},[886],[888,88383,88384],{"xmlns":890},[892,88385,88386,88396],{},[895,88387,88388,88390,88392,88394],{},[898,88389,1734],{},[1712,88391,1904],{"stretchy":1903},[1716,88393,2975],{},[1712,88395,1910],{"stretchy":1903},[902,88397,88398],{"encoding":904},"Q(4)",[883,88400,88402],{"className":88401},[886],[888,88403,88404],{"xmlns":890},[892,88405,88406,88416],{},[895,88407,88408,88410,88412,88414],{},[898,88409,1734],{},[1712,88411,1904],{"stretchy":1903},[1716,88413,1780],{},[1712,88415,1910],{"stretchy":1903},[902,88417,88418],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,88421,88422,88335,88425,88461,88462,88475,88476,88495,88496,88522,88523,3072,88536,88549],{},[38,88423,88424],{},"5.2",[883,88426,88428],{"className":88427},[886],[888,88429,88430],{"xmlns":890},[892,88431,88432,88458],{},[895,88433,88434,88436,88438,88440,88442,88448,88450,88452],{},[898,88435,1734],{},[1712,88437,1714],{},[1712,88439,2219],{},[1716,88441,6607],{},[2037,88443,88444,88446],{},[898,88445,14667],{},[1716,88447,6198],{},[1712,88449,3145],{},[1716,88451,1780],{},[2037,88453,88454,88456],{},[898,88455,14667],{},[1716,88457,2787],{},[902,88459,88460],{"encoding":904},"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 ",[883,88463,88465],{"className":88464},[886],[888,88466,88467],{"xmlns":890},[892,88468,88469,88473],{},[895,88470,88471],{},[898,88472,14667],{},[902,88474,14667],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,88477,88479],{"className":88478},[886],[888,88480,88481],{"xmlns":890},[892,88482,88483,88493],{},[895,88484,88485,88487],{},[898,88486,4445],{},[6927,88488,88489,88491],{},[898,88490,1710],{},[898,88492,14667],{},[902,88494,14917],{"encoding":904},". (f) Vypočtěte ",[883,88497,88499],{"className":88498},[886],[888,88500,88501],{"xmlns":890},[892,88502,88503,88519],{},[895,88504,88505,88507,88513,88515,88517],{},[898,88506,4445],{},[6927,88508,88509,88511],{},[898,88510,1710],{},[898,88512,14667],{},[1712,88514,1904],{"stretchy":1903},[1716,88516,1718],{},[1712,88518,1910],{"stretchy":1903},[902,88520,88521],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,88524,88526],{"className":88525},[886],[888,88527,88528],{"xmlns":890},[892,88529,88530,88534],{},[895,88531,88532],{},[1716,88533,1718],{},[902,88535,1718],{"encoding":904},[883,88537,88539],{"className":88538},[886],[888,88540,88541],{"xmlns":890},[892,88542,88543,88547],{},[895,88544,88545],{},[1716,88546,47162],{},[902,88548,47162],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,88551,88552,88555,88556,88578,88579,88607,88608,88639,88640,1659],{},[38,88553,88554],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,88557,88559],{"className":88558},[886],[888,88560,88561],{"xmlns":890},[892,88562,88563,88575],{},[895,88564,88565,88567,88569,88571],{},[898,88566,1734],{},[1712,88568,1714],{},[1716,88570,19984],{},[5935,88572,88573],{},[898,88574,14667],{},[902,88576,88577],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,88580,88582],{"className":88581},[886],[888,88583,88584],{"xmlns":890},[892,88585,88586,88604],{},[895,88587,88588,88590,88592,88594,88598,88600,88602],{},[898,88589,1734],{},[1712,88591,1714],{},[1716,88593,34956],{},[5935,88595,88596],{},[898,88597,14667],{},[1712,88599,2219],{},[1716,88601,2975],{},[898,88603,14667],{},[902,88605,88606],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,88609,88611],{"className":88610},[886],[888,88612,88613],{"xmlns":890},[892,88614,88615,88636],{},[895,88616,88617,88619,88621,88623,88625,88627,88630],{},[898,88618,1734],{},[1712,88620,1714],{},[1716,88622,2782],{},[898,88624,14667],{},[1712,88626,2219],{},[1716,88628,88629],{},"0,01",[2037,88631,88632,88634],{},[898,88633,14667],{},[1716,88635,2787],{},[902,88637,88638],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,88641,88643],{"className":88642},[886],[888,88644,88645],{"xmlns":890},[892,88646,88647,88673],{},[895,88648,88649,88651,88653,88655,88657,88663,88665,88667],{},[898,88650,1734],{},[1712,88652,1714],{},[1712,88654,2219],{},[1716,88656,73086],{},[2037,88658,88659,88661],{},[898,88660,14667],{},[1716,88662,6198],{},[1712,88664,3145],{},[1716,88666,1780],{},[2037,88668,88669,88671],{},[898,88670,14667],{},[1716,88672,2787],{},[902,88674,88675],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,88677,88678,88681,88682,8046,88701,77073,88718,1659],{},[38,88679,88680],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,88683,88685],{"className":88684},[886],[888,88686,88687],{"xmlns":890},[892,88688,88689,88699],{},[895,88690,88691,88693],{},[898,88692,2044],{},[6927,88694,88695,88697],{},[898,88696,1710],{},[898,88698,14667],{},[902,88700,79508],{"encoding":904},[883,88702,88704],{"className":88703},[886],[888,88705,88706],{"xmlns":890},[892,88707,88708,88716],{},[895,88709,88710],{},[6927,88711,88712,88714],{},[898,88713,14667],{},[1716,88715,2085],{},[902,88717,80433],{"encoding":904},[883,88719,88721],{"className":88720},[886],[888,88722,88723],{"xmlns":890},[892,88724,88725,88765],{},[895,88726,88727,88729,88735,88737,88743,88745,88747,88749,88755,88757,88763],{},[898,88728,2044],{},[6927,88730,88731,88733],{},[898,88732,1710],{},[898,88734,14667],{},[1712,88736,1904],{"stretchy":1903},[6927,88738,88739,88741],{},[898,88740,14667],{},[1716,88742,2085],{},[1712,88744,1910],{"stretchy":1903},[1712,88746,1714],{},[898,88748,4445],{},[6927,88750,88751,88753],{},[898,88752,1710],{},[898,88754,14667],{},[1712,88756,1904],{"stretchy":1903},[6927,88758,88759,88761],{},[898,88760,14667],{},[1716,88762,2085],{},[1712,88764,1910],{"stretchy":1903},[902,88766,88767],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,88769,88770,88335,88773,26469,88809,88822,88823,88842],{},[38,88771,88772],{},"5.5",[883,88774,88776],{"className":88775},[886],[888,88777,88778],{"xmlns":890},[892,88779,88780,88806],{},[895,88781,88782,88784,88786,88788,88790,88796,88798,88800],{},[898,88783,1734],{},[1712,88785,1714],{},[1712,88787,2219],{},[1716,88789,6673],{},[2037,88791,88792,88794],{},[898,88793,14667],{},[1716,88795,6198],{},[1712,88797,3145],{},[1716,88799,8912],{},[2037,88801,88802,88804],{},[898,88803,14667],{},[1716,88805,2787],{},[902,88807,88808],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,88810,88812],{"className":88811},[886],[888,88813,88814],{"xmlns":890},[892,88815,88816,88820],{},[895,88817,88818],{},[898,88819,14667],{},[902,88821,14667],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,88824,88826],{"className":88825},[886],[888,88827,88828],{"xmlns":890},[892,88829,88830,88840],{},[895,88831,88832,88834],{},[898,88833,2044],{},[6927,88835,88836,88838],{},[898,88837,1710],{},[898,88839,14667],{},[902,88841,79508],{"encoding":904},") 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.",[198,88844,88846],{"id":88845},"dvoufaktorový-model","Dvoufaktorový model",[724,88848,88849,88852,88853,88578,88879,88607,88921,1659],{},[38,88850,88851],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,88854,88856],{"className":88855},[886],[888,88857,88858],{"xmlns":890},[892,88859,88860,88876],{},[895,88861,88862,88864,88866,88868,88870],{},[898,88863,1734],{},[1712,88865,1714],{},[1716,88867,29076],{},[898,88869,14667],{},[2037,88871,88872,88874],{},[898,88873,14672],{},[1716,88875,2787],{},[902,88877,88878],{"encoding":904},"Q = 7 L K^{2}",[883,88880,88882],{"className":88881},[886],[888,88883,88884],{"xmlns":890},[892,88885,88886,88918],{},[895,88887,88888,88890,88892,88894,88906],{},[898,88889,1734],{},[1712,88891,1714],{},[1716,88893,2782],{},[2037,88895,88896,88898],{},[898,88897,14667],{},[895,88899,88900,88902,88904],{},[1716,88901,2787],{},[898,88903,2473],{"mathvariant":2003},[1716,88905,6198],{},[2037,88907,88908,88910],{},[898,88909,14672],{},[895,88911,88912,88914,88916],{},[1716,88913,2222],{},[898,88915,2473],{"mathvariant":2003},[1716,88917,6198],{},[902,88919,88920],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,88922,88924],{"className":88923},[886],[888,88925,88926],{"xmlns":890},[892,88927,88928,88960],{},[895,88929,88930,88932,88934,88936,88948],{},[898,88931,1734],{},[1712,88933,1714],{},[1716,88935,9110],{},[2037,88937,88938,88940],{},[898,88939,14667],{},[895,88941,88942,88944,88946],{},[1716,88943,6198],{},[898,88945,2473],{"mathvariant":2003},[1716,88947,3068],{},[2037,88949,88950,88952],{},[898,88951,14672],{},[895,88953,88954,88956,88958],{},[1716,88955,2787],{},[898,88957,2473],{"mathvariant":2003},[1716,88959,3068],{},[902,88961,88962],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,88964,88965,88335,88968,89010,89011,1343,89029,89048,89049,89066],{},[38,88966,88967],{},"5.7",[883,88969,88971],{"className":88970},[886],[888,88972,88973],{"xmlns":890},[892,88974,88975,89007],{},[895,88976,88977,88979,88981,88983,88995],{},[898,88978,1734],{},[1712,88980,1714],{},[1716,88982,1718],{},[2037,88984,88985,88987],{},[898,88986,14667],{},[895,88988,88989,88991,88993],{},[1716,88990,2222],{},[898,88992,2473],{"mathvariant":2003},[1716,88994,2787],{},[2037,88996,88997,88999],{},[898,88998,14672],{},[895,89000,89001,89003,89005],{},[1716,89002,2222],{},[898,89004,2473],{"mathvariant":2003},[1716,89006,2787],{},[902,89008,89009],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,89012,89014],{"className":89013},[886],[888,89015,89016],{"xmlns":890},[892,89017,89018,89026],{},[895,89019,89020,89022,89024],{},[898,89021,14667],{},[1712,89023,1714],{},[1716,89025,25017],{},[902,89027,89028],{"encoding":904},"L = 400",[883,89030,89032],{"className":89031},[886],[888,89033,89034],{"xmlns":890},[892,89035,89036,89045],{},[895,89037,89038,89040,89042],{},[898,89039,14672],{},[1712,89041,1714],{},[1716,89043,89044],{},"17576",[902,89046,89047],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,89050,89052],{"className":89051},[886],[888,89053,89054],{"xmlns":890},[892,89055,89056,89064],{},[895,89057,89058,89060,89062],{},[898,89059,14667],{},[1712,89061,3138],{"separator":2565},[898,89063,14672],{},[902,89065,83860],{"encoding":904}," zdvojnásobí.",[724,89068,89069,89072,89073,89010,89104,1343,89122,74459,89140,89170,89171,89201,89202,3072,89215,89229,89230,3072,89243,89256],{},[38,89070,89071],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,89074,89076],{"className":89075},[886],[888,89077,89078],{"xmlns":890},[892,89079,89080,89101],{},[895,89081,89082,89084,89086,89089,89095],{},[898,89083,1734],{},[1712,89085,1714],{},[1716,89087,89088],{},"1,01",[2037,89090,89091,89093],{},[898,89092,14667],{},[1716,89094,28605],{},[2037,89096,89097,89099],{},[898,89098,14672],{},[1716,89100,28664],{},[902,89102,89103],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,89105,89107],{"className":89106},[886],[888,89108,89109],{"xmlns":890},[892,89110,89111,89119],{},[895,89112,89113,89115,89117],{},[898,89114,14667],{},[1712,89116,1714],{},[1716,89118,35618],{},[902,89120,89121],{"encoding":904},"L = 250",[883,89123,89125],{"className":89124},[886],[888,89126,89127],{"xmlns":890},[892,89128,89129,89137],{},[895,89130,89131,89133,89135],{},[898,89132,14672],{},[1712,89134,1714],{},[1716,89136,8200],{},[902,89138,89139],{"encoding":904},"K = 1000",[883,89141,89143],{"className":89142},[886],[888,89144,89145],{"xmlns":890},[892,89146,89147,89167],{},[895,89148,89149,89151,89157,89159,89161,89163,89165],{},[898,89150,4445],{},[6927,89152,89153,89155],{},[898,89154,1710],{},[898,89156,14667],{},[1712,89158,1904],{"stretchy":1903},[1716,89160,35618],{},[1712,89162,3138],{"separator":2565},[1716,89164,8200],{},[1712,89166,1910],{"stretchy":1903},[902,89168,89169],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,89172,89174],{"className":89173},[886],[888,89175,89176],{"xmlns":890},[892,89177,89178,89198],{},[895,89179,89180,89182,89188,89190,89192,89194,89196],{},[898,89181,4445],{},[6927,89183,89184,89186],{},[898,89185,1710],{},[898,89187,14672],{},[1712,89189,1904],{"stretchy":1903},[1716,89191,35618],{},[1712,89193,3138],{"separator":2565},[1716,89195,8200],{},[1712,89197,1910],{"stretchy":1903},[902,89199,89200],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,89203,89205],{"className":89204},[886],[888,89206,89207],{"xmlns":890},[892,89208,89209,89213],{},[895,89210,89211],{},[898,89212,14667],{},[902,89214,14667],{"encoding":904},[883,89216,89218],{"className":89217},[886],[888,89219,89220],{"xmlns":890},[892,89221,89222,89227],{},[895,89223,89224],{},[1716,89225,89226],{},"260",[902,89228,89226],{"encoding":904}," a současném poklesu ",[883,89231,89233],{"className":89232},[886],[888,89234,89235],{"xmlns":890},[892,89236,89237,89241],{},[895,89238,89239],{},[898,89240,14672],{},[902,89242,14672],{"encoding":904},[883,89244,89246],{"className":89245},[886],[888,89247,89248],{"xmlns":890},[892,89249,89250,89254],{},[895,89251,89252],{},[1716,89253,20065],{},[902,89255,20065],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,89258,89259,89262,89263,1659],{},[38,89260,89261],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,89264,89266],{"className":89265},[886],[888,89267,89268],{"xmlns":890},[892,89269,89270,89290],{},[895,89271,89272,89274,89276,89278,89284],{},[898,89273,1734],{},[1712,89275,1714],{},[1716,89277,1718],{},[2037,89279,89280,89282],{},[898,89281,14667],{},[1716,89283,73086],{},[2037,89285,89286,89288],{},[898,89287,14672],{},[1716,89289,2814],{},[902,89291,89292],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,89294,89295,89298,89299,85456,89322,15266,89335,14897,89385,1691],{},[38,89296,89297],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,89300,89302],{"className":89301},[886],[888,89303,89304],{"xmlns":890},[892,89305,89306,89320],{},[895,89307,89308,89310,89312,89314,89316,89318],{},[898,89309,1734],{},[1712,89311,1904],{"stretchy":1903},[898,89313,14667],{},[1712,89315,3138],{"separator":2565},[898,89317,14672],{},[1712,89319,1910],{"stretchy":1903},[902,89321,14869],{"encoding":904},[883,89323,89325],{"className":89324},[886],[888,89326,89327],{"xmlns":890},[892,89328,89329,89333],{},[895,89330,89331],{},[898,89332,41735],{},[902,89334,41735],{"encoding":904},[883,89336,89338],{"className":89337},[886],[888,89339,89340],{"xmlns":890},[892,89341,89342,89382],{},[895,89343,89344,89346,89354,89356,89358,89366,89368,89370,89372,89374,89376,89378,89380],{},[898,89345,14667],{},[6989,89347,89348,89350,89352],{},[898,89349,1734],{},[898,89351,14667],{},[1712,89353,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,89355,3145],{},[898,89357,14672],{},[6989,89359,89360,89362,89364],{},[898,89361,1734],{},[898,89363,14672],{},[1712,89365,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,89367,1714],{},[898,89369,41735],{},[898,89371,1734],{},[1712,89373,1904],{"stretchy":1903},[898,89375,14667],{},[1712,89377,3138],{"separator":2565},[898,89379,14672],{},[1712,89381,1910],{"stretchy":1903},[902,89383,89384],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,89386,85431],{},[724,89388,89389,89392],{},[38,89390,89391],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,89394,89395,88335,89398,89438,89439,1343,89461,1343,89483,89505],{},[38,89396,89397],{},"5.12",[883,89399,89401],{"className":89400},[886],[888,89402,89403],{"xmlns":890},[892,89404,89405,89435],{},[895,89406,89407,89409,89411,89423],{},[898,89408,1734],{},[1712,89410,1714],{},[2037,89412,89413,89415],{},[898,89414,14667],{},[895,89416,89417,89419,89421],{},[1716,89418,2222],{},[898,89420,2473],{"mathvariant":2003},[1716,89422,6198],{},[2037,89424,89425,89427],{},[898,89426,14672],{},[895,89428,89429,89431,89433],{},[1716,89430,2222],{},[898,89432,2473],{"mathvariant":2003},[1716,89434,2975],{},[902,89436,89437],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,89440,89442],{"className":89441},[886],[888,89443,89444],{"xmlns":890},[892,89445,89446,89458],{},[895,89447,89448,89454,89456],{},[6927,89449,89450,89452],{},[898,89451,85672],{},[1716,89453,2085],{},[1712,89455,1714],{},[1716,89457,2222],{},[902,89459,89460],{"encoding":904},"q_0 = 1",[883,89462,89464],{"className":89463},[886],[888,89465,89466],{"xmlns":890},[892,89467,89468,89480],{},[895,89469,89470,89476,89478],{},[6927,89471,89472,89474],{},[898,89473,85672],{},[1716,89475,2222],{},[1712,89477,1714],{},[1716,89479,2787],{},[902,89481,89482],{"encoding":904},"q_1 = 2",[883,89484,89486],{"className":89485},[886],[888,89487,89488],{"xmlns":890},[892,89489,89490,89502],{},[895,89491,89492,89498,89500],{},[6927,89493,89494,89496],{},[898,89495,85672],{},[1716,89497,2787],{},[1712,89499,1714],{},[1716,89501,6198],{},[902,89503,89504],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,89507,89508,88335,89511,89551,89552,1343,89580,1343,89608,1343,89636,1343,89665,1343,89694,1343,89723,1343,89752,1343,89781,1659],{},[38,89509,89510],{},"5.13",[883,89512,89514],{"className":89513},[886],[888,89515,89516],{"xmlns":890},[892,89517,89518,89548],{},[895,89519,89520,89522,89524,89536],{},[898,89521,1734],{},[1712,89523,1714],{},[2037,89525,89526,89528],{},[898,89527,14667],{},[895,89529,89530,89532,89534],{},[1716,89531,2222],{},[898,89533,2473],{"mathvariant":2003},[1716,89535,6198],{},[2037,89537,89538,89540],{},[898,89539,14672],{},[895,89541,89542,89544,89546],{},[1716,89543,2222],{},[898,89545,2473],{"mathvariant":2003},[1716,89547,2787],{},[902,89549,89550],{"encoding":904},"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): ",[883,89553,89555],{"className":89554},[886],[888,89556,89557],{"xmlns":890},[892,89558,89559,89577],{},[895,89560,89561,89567,89569,89571,89573,89575],{},[6927,89562,89563,89565],{},[898,89564,2044],{},[1716,89566,2222],{},[1712,89568,7910],{"stretchy":1903},[1716,89570,2222],{},[1712,89572,6245],{"separator":2565},[1716,89574,2222],{},[1712,89576,7925],{"stretchy":1903},[902,89578,89579],{"encoding":904},"A_1[1; 1]",[883,89581,89583],{"className":89582},[886],[888,89584,89585],{"xmlns":890},[892,89586,89587,89605],{},[895,89588,89589,89595,89597,89599,89601,89603],{},[6927,89590,89591,89593],{},[898,89592,2044],{},[1716,89594,2787],{},[1712,89596,7910],{"stretchy":1903},[1716,89598,2222],{},[1712,89600,6245],{"separator":2565},[1716,89602,3397],{},[1712,89604,7925],{"stretchy":1903},[902,89606,89607],{"encoding":904},"A_2[1; 8]",[883,89609,89611],{"className":89610},[886],[888,89612,89613],{"xmlns":890},[892,89614,89615,89633],{},[895,89616,89617,89623,89625,89627,89629,89631],{},[6927,89618,89619,89621],{},[898,89620,2044],{},[1716,89622,6198],{},[1712,89624,7910],{"stretchy":1903},[1716,89626,2222],{},[1712,89628,6245],{"separator":2565},[1716,89630,71472],{},[1712,89632,7925],{"stretchy":1903},[902,89634,89635],{"encoding":904},"A_3[1; 27]",[883,89637,89639],{"className":89638},[886],[888,89640,89641],{"xmlns":890},[892,89642,89643,89662],{},[895,89644,89645,89651,89653,89655,89657,89660],{},[6927,89646,89647,89649],{},[898,89648,2044],{},[1716,89650,2975],{},[1712,89652,7910],{"stretchy":1903},[1716,89654,2787],{},[1712,89656,6245],{"separator":2565},[1716,89658,89659],{},"0,353",[1712,89661,7925],{"stretchy":1903},[902,89663,89664],{"encoding":904},"A_4[2; 0{,}353]",[883,89666,89668],{"className":89667},[886],[888,89669,89670],{"xmlns":890},[892,89671,89672,89691],{},[895,89673,89674,89680,89682,89684,89686,89689],{},[6927,89675,89676,89678],{},[898,89677,2044],{},[1716,89679,3068],{},[1712,89681,7910],{"stretchy":1903},[1716,89683,2787],{},[1712,89685,6245],{"separator":2565},[1716,89687,89688],{},"2,828",[1712,89690,7925],{"stretchy":1903},[902,89692,89693],{"encoding":904},"A_5[2; 2{,}828]",[883,89695,89697],{"className":89696},[886],[888,89698,89699],{"xmlns":890},[892,89700,89701,89720],{},[895,89702,89703,89709,89711,89713,89715,89718],{},[6927,89704,89705,89707],{},[898,89706,2044],{},[1716,89708,6209],{},[1712,89710,7910],{"stretchy":1903},[1716,89712,2787],{},[1712,89714,6245],{"separator":2565},[1716,89716,89717],{},"9,545",[1712,89719,7925],{"stretchy":1903},[902,89721,89722],{"encoding":904},"A_6[2; 9{,}545]",[883,89724,89726],{"className":89725},[886],[888,89727,89728],{"xmlns":890},[892,89729,89730,89749],{},[895,89731,89732,89738,89740,89742,89744,89747],{},[6927,89733,89734,89736],{},[898,89735,2044],{},[1716,89737,29076],{},[1712,89739,7910],{"stretchy":1903},[1716,89741,69434],{},[1712,89743,6245],{"separator":2565},[1716,89745,89746],{},"0,544",[1712,89748,7925],{"stretchy":1903},[902,89750,89751],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,89753,89755],{"className":89754},[886],[888,89756,89757],{"xmlns":890},[892,89758,89759,89778],{},[895,89760,89761,89767,89769,89771,89773,89776],{},[6927,89762,89763,89765],{},[898,89764,2044],{},[1716,89766,3397],{},[1712,89768,7910],{"stretchy":1903},[1716,89770,69434],{},[1712,89772,6245],{"separator":2565},[1716,89774,89775],{},"14,696",[1712,89777,7925],{"stretchy":1903},[902,89779,89780],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,89782,89784],{"className":89783},[886],[888,89785,89786],{"xmlns":890},[892,89787,89788,89806],{},[895,89789,89790,89796,89798,89800,89802,89804],{},[6927,89791,89792,89794],{},[898,89793,2044],{},[1716,89795,1780],{},[1712,89797,7910],{"stretchy":1903},[1716,89799,2787],{},[1712,89801,6245],{"separator":2565},[1716,89803,3068],{},[1712,89805,7925],{"stretchy":1903},[902,89807,89808],{"encoding":904},"A_9[2; 5]",[724,89810,89811,89814],{},[38,89812,89813],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,89816,89817,89820,89821,89851,89852,89865,89866,89879,89880,74192,89899,89918,89919,1659],{},[38,89818,89819],{},"5.15"," Produkce firmy je dána vztahem ",[883,89822,89824],{"className":89823},[886],[888,89825,89826],{"xmlns":890},[892,89827,89828,89848],{},[895,89829,89830,89832,89834,89836,89842],{},[898,89831,1734],{},[1712,89833,1714],{},[1716,89835,2787],{},[2037,89837,89838,89840],{},[898,89839,14667],{},[1716,89841,2814],{},[2037,89843,89844,89846],{},[898,89845,14672],{},[1716,89847,28664],{},[902,89849,89850],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,89853,89855],{"className":89854},[886],[888,89856,89857],{"xmlns":890},[892,89858,89859,89863],{},[895,89860,89861],{},[1716,89862,1739],{},[902,89864,1739],{"encoding":904}," pracovníků a disponuje-li ",[883,89867,89869],{"className":89868},[886],[888,89870,89871],{"xmlns":890},[892,89872,89873,89877],{},[895,89874,89875],{},[1716,89876,69310],{},[902,89878,69310],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,89881,89883],{"className":89882},[886],[888,89884,89885],{"xmlns":890},[892,89886,89887,89897],{},[895,89888,89889,89891,89893,89895],{},[898,89890,4445],{},[898,89892,1775],{},[898,89894,1772],{},[898,89896,6493],{},[902,89898,15471],{"encoding":904},[883,89900,89902],{"className":89901},[886],[888,89903,89904],{"xmlns":890},[892,89905,89906,89916],{},[895,89907,89908,89910,89912,89914],{},[898,89909,4445],{},[898,89911,1775],{},[898,89913,1772],{},[898,89915,6493],{},[902,89917,15471],{"encoding":904}," 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 ",[883,89920,89922],{"className":89921},[886],[888,89923,89924],{"xmlns":890},[892,89925,89926,89931],{},[895,89927,89928],{},[1716,89929,89930],{},"95",[902,89932,89930],{"encoding":904},[724,89934,89935,88335,89938,75866,89970,89989,89990,90003,90004,90017,90018,90031],{},[38,89936,89937],{},"5.16",[883,89939,89941],{"className":89940},[886],[888,89942,89943],{"xmlns":890},[892,89944,89945,89967],{},[895,89946,89947,89949,89951,89957,89959,89961],{},[898,89948,1734],{},[1712,89950,1714],{},[2037,89952,89953,89955],{},[898,89954,14672],{},[1716,89956,2787],{},[1712,89958,3145],{},[1716,89960,2787],{},[2037,89962,89963,89965],{},[898,89964,14667],{},[1716,89966,2787],{},[902,89968,89969],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,89971,89973],{"className":89972},[886],[888,89974,89975],{"xmlns":890},[892,89976,89977,89987],{},[895,89978,89979,89981,89983,89985],{},[898,89980,4445],{},[898,89982,1775],{},[898,89984,1772],{},[898,89986,6493],{},[902,89988,15471],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,89991,89993],{"className":89992},[886],[888,89994,89995],{"xmlns":890},[892,89996,89997,90001],{},[895,89998,89999],{},[1716,90000,2782],{},[902,90002,2782],{"encoding":904}," pracovníky a ",[883,90005,90007],{"className":90006},[886],[888,90008,90009],{"xmlns":890},[892,90010,90011,90015],{},[895,90012,90013],{},[1716,90014,82492],{},[902,90016,82492],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,90019,90021],{"className":90020},[886],[888,90022,90023],{"xmlns":890},[892,90024,90025,90029],{},[895,90026,90027],{},[1716,90028,51578],{},[902,90030,51578],{"encoding":904}," jednotek.",[724,90033,90034,90037,90038,15266,90068,1659],{},[38,90035,90036],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,90039,90041],{"className":90040},[886],[888,90042,90043],{"xmlns":890},[892,90044,90045,90065],{},[895,90046,90047,90049,90051,90053,90059],{},[898,90048,1734],{},[1712,90050,1714],{},[898,90052,2044],{},[2037,90054,90055,90057],{},[898,90056,14667],{},[898,90058,207],{},[2037,90060,90061,90063],{},[898,90062,14672],{},[898,90064,7544],{},[902,90066,90067],{"encoding":904},"Q = A L^{a} K^{b}",[883,90069,90071],{"className":90070},[886],[888,90072,90073],{"xmlns":890},[892,90074,90075,90105],{},[895,90076,90077,90079,90081,90083,90085,90087,90095,90097],{},[898,90078,4445],{},[898,90080,1775],{},[898,90082,1772],{},[898,90084,6493],{},[1712,90086,1714],{},[2563,90088,90089],{"scriptlevel":2085,"displaystyle":1903},[2567,90090,90091,90093],{},[898,90092,207],{},[898,90094,7544],{},[1712,90096,1783],{},[2563,90098,90099],{"scriptlevel":2085,"displaystyle":1903},[2567,90100,90101,90103],{},[898,90102,14672],{},[898,90104,14667],{},[902,90106,90107],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,90109,20594],{"id":20593},[120,90111,90112,90145,90172,90181,90231,90262,90315,90338,90393,90466,90544,90587,90619,90652,90693,90765,90826,90892,90909,90982,91048,91100,91156,91190,91233],{},[123,90113,90114,90117,90118,41771,90131,90144],{},[38,90115,90116],{},"Faktory (vstupy) produkce:"," práce ",[883,90119,90121],{"className":90120},[886],[888,90122,90123],{"xmlns":890},[892,90124,90125,90129],{},[895,90126,90127],{},[898,90128,14667],{},[902,90130,14667],{"encoding":904},[883,90132,90134],{"className":90133},[886],[888,90135,90136],{"xmlns":890},[892,90137,90138,90142],{},[895,90139,90140],{},[898,90141,14672],{},[902,90143,14672],{"encoding":904},", půda.",[123,90146,90147,4831,90149,1659],{},[38,90148,45326],{},[883,90150,90152],{"className":90151},[886],[888,90153,90154],{"xmlns":890},[892,90155,90156,90170],{},[895,90157,90158,90160,90162,90164,90166,90168],{},[898,90159,1734],{},[1712,90161,1714],{},[898,90163,1734],{},[1712,90165,1904],{"stretchy":1903},[898,90167,14667],{},[1712,90169,1910],{"stretchy":1903},[902,90171,79419],{"encoding":904},[123,90173,90174,14897,90176,17002,90179,1659],{},[38,90175,859],{},[614,90177,90178],{},"production function",[38,90180,79922],{},[123,90182,90183,3245,90185,1659],{},[38,90184,79968],{},[883,90186,90188],{"className":90187},[886],[888,90189,90190],{"xmlns":890},[892,90191,90192,90228],{},[895,90193,90194,90196,90202,90204,90206,90208,90210,90212,90214,90216,90222,90224,90226],{},[898,90195,4445],{},[6927,90197,90198,90200],{},[898,90199,1710],{},[898,90201,14667],{},[1712,90203,1714],{},[898,90205,2468],{},[898,90207,1734],{},[898,90209,2473],{"mathvariant":2003},[898,90211,2468],{},[898,90213,14667],{},[1712,90215,1714],{},[2037,90217,90218,90220],{},[898,90219,1734],{},[1712,90221,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,90223,1904],{"stretchy":1903},[898,90225,14667],{},[1712,90227,1910],{"stretchy":1903},[902,90229,90230],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,90232,90233,3245,90235,1659],{},[38,90234,80903],{},[883,90236,90238],{"className":90237},[886],[888,90239,90240],{"xmlns":890},[892,90241,90242,90260],{},[895,90243,90244,90246,90252,90254,90256,90258],{},[898,90245,2044],{},[6927,90247,90248,90250],{},[898,90249,1710],{},[898,90251,14667],{},[1712,90253,1714],{},[898,90255,1734],{},[898,90257,2473],{"mathvariant":2003},[898,90259,14667],{},[902,90261,79487],{"encoding":904},[123,90263,90264,90266,90267,15266,90284,1659],{},[38,90265,80390],{}," — od určitého ",[883,90268,90270],{"className":90269},[886],[888,90271,90272],{"xmlns":890},[892,90273,90274,90282],{},[895,90275,90276],{},[6927,90277,90278,90280],{},[898,90279,14667],{},[1716,90281,2085],{},[902,90283,80433],{"encoding":904},[883,90285,90287],{"className":90286},[886],[888,90288,90289],{"xmlns":890},[892,90290,90291,90313],{},[895,90292,90293,90303,90305,90307,90309,90311],{},[2037,90294,90295,90297],{},[898,90296,1734],{},[895,90298,90299,90301],{},[1712,90300,2243],{"mathvariant":2003},[1712,90302,2243],{"mathvariant":2003},[1712,90304,1904],{"stretchy":1903},[898,90306,14667],{},[1712,90308,1910],{"stretchy":1903},[1712,90310,2252],{},[1716,90312,2085],{},[902,90314,80579],{"encoding":904},[123,90316,90317,3245,90320,90337],{},[38,90318,90319],{},"Inflexní bod",[883,90321,90323],{"className":90322},[886],[888,90324,90325],{"xmlns":890},[892,90326,90327,90335],{},[895,90328,90329],{},[6927,90330,90331,90333],{},[898,90332,14667],{},[1716,90334,2085],{},[902,90336,80433],{"encoding":904}," — přechod z konvexity do konkavity.",[123,90339,90340,3245,90343,4831,90360,1659],{},[38,90341,90342],{},"Bod maxima produkce",[883,90344,90346],{"className":90345},[886],[888,90347,90348],{"xmlns":890},[892,90349,90350,90358],{},[895,90351,90352],{},[6927,90353,90354,90356],{},[898,90355,14667],{},[1716,90357,2222],{},[902,90359,18086],{"encoding":904},[883,90361,90363],{"className":90362},[886],[888,90364,90365],{"xmlns":890},[892,90366,90367,90391],{},[895,90368,90369,90371,90377,90379,90385,90387,90389],{},[898,90370,4445],{},[6927,90372,90373,90375],{},[898,90374,1710],{},[898,90376,14667],{},[1712,90378,1904],{"stretchy":1903},[6927,90380,90381,90383],{},[898,90382,14667],{},[1716,90384,2222],{},[1712,90386,1910],{"stretchy":1903},[1712,90388,1714],{},[1716,90390,2085],{},[902,90392,80652],{"encoding":904},[123,90394,90395,90417,90418,15266,90437,1659],{},[38,90396,90397,90398],{},"Princip maximalizace ",[883,90399,90401],{"className":90400},[886],[888,90402,90403],{"xmlns":890},[892,90404,90405,90415],{},[895,90406,90407,90409],{},[898,90408,2044],{},[6927,90410,90411,90413],{},[898,90412,1710],{},[898,90414,14667],{},[902,90416,79508],{"encoding":904}," — v bodě maxima ",[883,90419,90421],{"className":90420},[886],[888,90422,90423],{"xmlns":890},[892,90424,90425,90435],{},[895,90426,90427,90429],{},[898,90428,2044],{},[6927,90430,90431,90433],{},[898,90432,1710],{},[898,90434,14667],{},[902,90436,79508],{"encoding":904},[883,90438,90440],{"className":90439},[886],[888,90441,90442],{"xmlns":890},[892,90443,90444,90464],{},[895,90445,90446,90448,90454,90456,90458],{},[898,90447,4445],{},[6927,90449,90450,90452],{},[898,90451,1710],{},[898,90453,14667],{},[1712,90455,1714],{},[898,90457,2044],{},[6927,90459,90460,90462],{},[898,90461,1710],{},[898,90463,14667],{},[902,90465,79538],{"encoding":904},[123,90467,90468,3245,90471,1343,90510,1343,90527,1659],{},[38,90469,90470],{},"Polynomiální produkční funkce",[883,90472,90474],{"className":90473},[886],[888,90475,90476],{"xmlns":890},[892,90477,90478,90508],{},[895,90479,90480,90482,90484,90486,90488,90490,90492,90498,90500,90502],{},[898,90481,1734],{},[1712,90483,1904],{"stretchy":1903},[898,90485,14667],{},[1712,90487,1910],{"stretchy":1903},[1712,90489,1714],{},[898,90491,207],{},[2037,90493,90494,90496],{},[898,90495,14667],{},[1716,90497,6198],{},[1712,90499,3145],{},[898,90501,7544],{},[2037,90503,90504,90506],{},[898,90505,14667],{},[1716,90507,2787],{},[902,90509,80770],{"encoding":904},[883,90511,90513],{"className":90512},[886],[888,90514,90515],{"xmlns":890},[892,90516,90517,90525],{},[895,90518,90519,90521,90523],{},[898,90520,207],{},[1712,90522,2252],{},[1716,90524,2085],{},[902,90526,47960],{"encoding":904},[883,90528,90530],{"className":90529},[886],[888,90531,90532],{"xmlns":890},[892,90533,90534,90542],{},[895,90535,90536,90538,90540],{},[898,90537,7544],{},[1712,90539,2302],{},[1716,90541,2085],{},[902,90543,23689],{"encoding":904},[123,90545,90546,3245,90549,1659],{},[38,90547,90548],{},"Diferenciál produkce",[883,90550,90552],{"className":90551},[886],[888,90553,90554],{"xmlns":890},[892,90555,90556,90584],{},[895,90557,90558,90560,90562,90564,90566,90568,90570,90572,90578,90580,90582],{},[898,90559,2004],{"mathvariant":2003},[898,90561,1734],{},[1712,90563,3740],{},[898,90565,2468],{},[898,90567,1734],{},[1712,90569,1714],{},[898,90571,4445],{},[6927,90573,90574,90576],{},[898,90575,1710],{},[898,90577,14667],{},[1762,90579,2583],{},[898,90581,2468],{},[898,90583,14667],{},[902,90585,90586],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,90588,90589,4831,90591,1659],{},[38,90590,88846],{},[883,90592,90594],{"className":90593},[886],[888,90595,90596],{"xmlns":890},[892,90597,90598,90616],{},[895,90599,90600,90602,90604,90606,90608,90610,90612,90614],{},[898,90601,1734],{},[1712,90603,1714],{},[898,90605,1734],{},[1712,90607,1904],{"stretchy":1903},[898,90609,14667],{},[1712,90611,3138],{"separator":2565},[898,90613,14672],{},[1712,90615,1910],{"stretchy":1903},[902,90617,90618],{"encoding":904},"Q = Q(L, K)",[123,90620,90621,4831,90623,1659],{},[38,90622,82940],{},[883,90624,90626],{"className":90625},[886],[888,90627,90628],{"xmlns":890},[892,90629,90630,90650],{},[895,90631,90632,90634,90636,90638,90644],{},[898,90633,1734],{},[1712,90635,1714],{},[898,90637,2044],{},[2037,90639,90640,90642],{},[898,90641,14667],{},[898,90643,207],{},[2037,90645,90646,90648],{},[898,90647,14672],{},[898,90649,7544],{},[902,90651,79605],{"encoding":904},[123,90653,90654,4831,90657,90692],{},[38,90655,90656],{},"Ryzí Cobb-Douglas",[883,90658,90660],{"className":90659},[886],[888,90661,90662],{"xmlns":890},[892,90663,90664,90690],{},[895,90665,90666,90668,90670,90672,90678],{},[898,90667,1734],{},[1712,90669,1714],{},[898,90671,2044],{},[2037,90673,90674,90676],{},[898,90675,14667],{},[898,90677,207],{},[2037,90679,90680,90682],{},[898,90681,14672],{},[895,90683,90684,90686,90688],{},[1716,90685,2222],{},[1712,90687,2219],{},[898,90689,207],{},[902,90691,83767],{"encoding":904}," (konstantní výnosy).",[123,90694,90695,4831,90697,1659],{},[38,90696,84483],{},[883,90698,90700],{"className":90699},[886],[888,90701,90702],{"xmlns":890},[892,90703,90704,90762],{},[895,90705,90706,90708,90710,90712,90714,90716,90718,90720,90722,90724,90734,90736,90738,90748],{},[898,90707,1734],{},[1712,90709,1714],{},[898,90711,2044],{},[1712,90713,7910],{"stretchy":1903},[1712,90715,1904],{"stretchy":1903},[1716,90717,2222],{},[1712,90719,2219],{},[898,90721,207],{},[1712,90723,1910],{"stretchy":1903},[2037,90725,90726,90728],{},[898,90727,14667],{},[895,90729,90730,90732],{},[1712,90731,2219],{},[898,90733,7544],{},[1712,90735,3145],{},[898,90737,207],{},[2037,90739,90740,90742],{},[898,90741,14672],{},[895,90743,90744,90746],{},[1712,90745,2219],{},[898,90747,7544],{},[2037,90749,90750,90752],{},[1712,90751,7925],{"stretchy":1903},[895,90753,90754,90756,90758,90760],{},[1712,90755,2219],{},[1716,90757,2222],{},[898,90759,2473],{"mathvariant":2003},[898,90761,7544],{},[902,90763,90764],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,90766,90767,14897,90770,17002,90792,14897,90795,90825],{},[38,90768,90769],{},"Lineární",[883,90771,90773],{"className":90772},[886],[888,90774,90775],{"xmlns":890},[892,90776,90777,90789],{},[895,90778,90779,90781,90783,90785,90787],{},[898,90780,207],{},[898,90782,14667],{},[1712,90784,3145],{},[898,90786,7544],{},[898,90788,14672],{},[902,90790,90791],{"encoding":904},"aL + bK",[38,90793,90794],{},"Leontiefova",[883,90796,90798],{"className":90797},[886],[888,90799,90800],{"xmlns":890},[892,90801,90802,90822],{},[895,90803,90804,90806,90808,90810,90812,90814,90816,90818,90820],{},[898,90805,84711],{},[1712,90807,61075],{},[1712,90809,1904],{"stretchy":1903},[898,90811,207],{},[898,90813,14667],{},[1712,90815,3138],{"separator":2565},[898,90817,7544],{},[898,90819,14672],{},[1712,90821,1910],{"stretchy":1903},[902,90823,90824],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,90827,90828,4831,90844,1659],{},[38,90829,90830,90831],{},"Homogenita stupně ",[883,90832,90834],{"className":90833},[886],[888,90835,90836],{"xmlns":890},[892,90837,90838,90842],{},[895,90839,90840],{},[898,90841,41735],{},[902,90843,41735],{"encoding":904},[883,90845,90847],{"className":90846},[886],[888,90848,90849],{"xmlns":890},[892,90850,90851,90889],{},[895,90852,90853,90855,90857,90859,90861,90863,90865,90867,90869,90871,90877,90879,90881,90883,90885,90887],{},[898,90854,1734],{},[1712,90856,1904],{"stretchy":1903},[898,90858,16915],{},[898,90860,14667],{},[1712,90862,3138],{"separator":2565},[898,90864,16915],{},[898,90866,14672],{},[1712,90868,1910],{"stretchy":1903},[1712,90870,1714],{},[2037,90872,90873,90875],{},[898,90874,16915],{},[898,90876,41735],{},[898,90878,1734],{},[1712,90880,1904],{"stretchy":1903},[898,90882,14667],{},[1712,90884,3138],{"separator":2565},[898,90886,14672],{},[1712,90888,1910],{"stretchy":1903},[902,90890,90891],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,90893,90894,83865],{},[38,90895,83798,90896],{},[883,90897,90899],{"className":90898},[886],[888,90900,90901],{"xmlns":890},[892,90902,90903,90907],{},[895,90904,90905],{},[898,90906,2044],{},[902,90908,2044],{"encoding":904},[123,90910,90911,90913,90914,90936,90937,90959,90960,1691],{},[38,90912,83299],{}," — konstantní (",[883,90915,90917],{"className":90916},[886],[888,90918,90919],{"xmlns":890},[892,90920,90921,90933],{},[895,90922,90923,90925,90927,90929,90931],{},[898,90924,207],{},[1712,90926,3145],{},[898,90928,7544],{},[1712,90930,1714],{},[1716,90932,2222],{},[902,90934,90935],{"encoding":904},"a+b=1","), rostoucí (",[883,90938,90940],{"className":90939},[886],[888,90941,90942],{"xmlns":890},[892,90943,90944,90956],{},[895,90945,90946,90948,90950,90952,90954],{},[898,90947,207],{},[1712,90949,3145],{},[898,90951,7544],{},[1712,90953,2302],{},[1716,90955,2222],{},[902,90957,90958],{"encoding":904},"a+b>1","), klesající (",[883,90961,90963],{"className":90962},[886],[888,90964,90965],{"xmlns":890},[892,90966,90967,90979],{},[895,90968,90969,90971,90973,90975,90977],{},[898,90970,207],{},[1712,90972,3145],{},[898,90974,7544],{},[1712,90976,2252],{},[1716,90978,2222],{},[902,90980,90981],{"encoding":904},"a+b\u003C1",[123,90983,90984,3245,90986,1343,91016,3245,91018,1659],{},[38,90985,79968],{},[883,90987,90989],{"className":90988},[886],[888,90990,90991],{"xmlns":890},[892,90992,90993,91013],{},[895,90994,90995,90997,91003,91005],{},[898,90996,4445],{},[6927,90998,90999,91001],{},[898,91000,1710],{},[898,91002,14667],{},[1712,91004,1714],{},[6989,91006,91007,91009,91011],{},[898,91008,1734],{},[898,91010,14667],{},[1712,91012,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,91014,91015],{"encoding":904},"MP_L = Q'_L",[38,91017,82872],{},[883,91019,91021],{"className":91020},[886],[888,91022,91023],{"xmlns":890},[892,91024,91025,91045],{},[895,91026,91027,91029,91035,91037],{},[898,91028,4445],{},[6927,91030,91031,91033],{},[898,91032,1710],{},[898,91034,14672],{},[1712,91036,1714],{},[6989,91038,91039,91041,91043],{},[898,91040,1734],{},[898,91042,14672],{},[1712,91044,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,91046,91047],{"encoding":904},"MP_K = Q'_K",[123,91049,91050,3245,91052,1659],{},[38,91051,85086],{},[883,91053,91055],{"className":91054},[886],[888,91056,91057],{"xmlns":890},[892,91058,91059,91097],{},[895,91060,91061,91063,91065,91067,91069,91075,91077,91079,91081,91083,91085,91091,91093,91095],{},[898,91062,2468],{},[898,91064,1734],{},[1712,91066,1714],{},[898,91068,4445],{},[6927,91070,91071,91073],{},[898,91072,1710],{},[898,91074,14667],{},[1762,91076,2583],{},[898,91078,2468],{},[898,91080,14667],{},[1712,91082,3145],{},[898,91084,4445],{},[6927,91086,91087,91089],{},[898,91088,1710],{},[898,91090,14672],{},[1762,91092,2583],{},[898,91094,2468],{},[898,91096,14672],{},[902,91098,91099],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,91101,91102,4831,91104,1659],{},[38,91103,85431],{},[883,91105,91107],{"className":91106},[886],[888,91108,91109],{"xmlns":890},[892,91110,91111,91153],{},[895,91112,91113,91115,91123,91125,91127,91135,91137,91139,91141,91143,91145,91147,91149,91151],{},[898,91114,14667],{},[6989,91116,91117,91119,91121],{},[898,91118,1734],{},[898,91120,14667],{},[1712,91122,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,91124,3145],{},[898,91126,14672],{},[6989,91128,91129,91131,91133],{},[898,91130,1734],{},[898,91132,14672],{},[1712,91134,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,91136,1714],{},[898,91138,41735],{},[1762,91140,2583],{},[898,91142,1734],{},[1712,91144,1904],{"stretchy":1903},[898,91146,14667],{},[1712,91148,3138],{"separator":2565},[898,91150,14672],{},[1712,91152,1910],{"stretchy":1903},[902,91154,91155],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,91157,91158,91161,91162,1659],{},[38,91159,91160],{},"Izokvanta"," — křivka ",[883,91163,91165],{"className":91164},[886],[888,91166,91167],{"xmlns":890},[892,91168,91169,91187],{},[895,91170,91171,91173,91175,91177,91179,91181,91183,91185],{},[898,91172,1734],{},[1712,91174,1904],{"stretchy":1903},[898,91176,14667],{},[1712,91178,3138],{"separator":2565},[898,91180,14672],{},[1712,91182,1910],{"stretchy":1903},[1712,91184,1714],{},[898,91186,85672],{},[902,91188,91189],{"encoding":904},"Q(L, K) = q",[123,91191,91192,3245,91194,1659],{},[38,91193,85861],{},[883,91195,91197],{"className":91196},[886],[888,91198,91199],{"xmlns":890},[892,91200,91201,91231],{},[895,91202,91203,91205,91207,91209,91211,91213,91215,91221,91223,91225],{},[898,91204,4445],{},[898,91206,1775],{},[898,91208,1772],{},[898,91210,6493],{},[1712,91212,1714],{},[898,91214,4445],{},[6927,91216,91217,91219],{},[898,91218,1710],{},[898,91220,14667],{},[898,91222,2473],{"mathvariant":2003},[898,91224,4445],{},[6927,91226,91227,91229],{},[898,91228,1710],{},[898,91230,14672],{},[902,91232,79680],{"encoding":904},[123,91234,91235,3245,91238,1659],{},[38,91236,91237],{},"Substituční vztah",[883,91239,91241],{"className":91240},[886],[888,91242,91243],{"xmlns":890},[892,91244,91245,91269],{},[895,91246,91247,91249,91251,91253,91255,91257,91259,91261,91263,91265,91267],{},[898,91248,2004],{"mathvariant":2003},[898,91250,14672],{},[1712,91252,3740],{},[1712,91254,2219],{},[898,91256,4445],{},[898,91258,1775],{},[898,91260,1772],{},[898,91262,6493],{},[1762,91264,2583],{},[898,91266,2468],{},[898,91268,14667],{},[902,91270,91271],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,91273,9193],{"id":9192},[120,91275,91276,91373,91380,91387],{},[123,91277,91278,3245,91280,91283,91284,1343,91287,91290,91291,91294,91295,91314,91315,23523,91334,91337,91338,91357,91358,1691],{},[38,91279,55598],{},[207,91281,784],{"className":91282,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,91285,1690],{"className":91286,"dataFsResolvedFilePath":764,"href":765},[210],[207,91288,793],{"className":91289,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,91292,880],{"className":91293,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,91296,91298],{"className":91297},[886],[888,91299,91300],{"xmlns":890},[892,91301,91302,91312],{},[895,91303,91304,91306,91308,91310],{},[898,91305,4445],{},[898,91307,1775],{},[898,91309,1772],{},[898,91311,6493],{},[902,91313,15471],{"encoding":904}," ↔ ",[883,91316,91318],{"className":91317},[886],[888,91319,91320],{"xmlns":890},[892,91321,91322,91332],{},[895,91323,91324,91326,91328,91330],{},[898,91325,4445],{},[898,91327,1775],{},[898,91329,8195],{},[898,91331,6493],{},[902,91333,15475],{"encoding":904},[207,91335,4992],{"className":91336,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,91339,91341],{"className":91340},[886],[888,91342,91343],{"xmlns":890},[892,91344,91345,91355],{},[895,91346,91347,91349],{},[898,91348,2044],{},[6927,91350,91351,91353],{},[898,91352,1710],{},[898,91354,14667],{},[902,91356,79508],{"encoding":904}," ↔ min ",[883,91359,91361],{"className":91360},[886],[888,91362,91363],{"xmlns":890},[892,91364,91365,91371],{},[895,91366,91367,91369],{},[898,91368,2044],{},[898,91370,8195],{},[902,91372,60435],{"encoding":904},[123,91374,91375,3245,91377,1659],{},[38,91376,9200],{},[207,91378,1646],{"className":91379,"dataFsResolvedFilePath":848,"href":849},[210],[123,91381,91382,3245,91384,1659],{},[38,91383,21087],{},[207,91385,1094],{"className":91386,"dataFsResolvedFilePath":838,"href":839},[210],[123,91388,91389,3245,91391,1659],{},[38,91390,21078],{},[207,91392,21082],{"className":91393,"dataFsResolvedFilePath":7413,"href":7414},[210],{"title":641,"searchDepth":642,"depth":642,"links":91395},[91396,91397,91398,91402,91404,91409,91410,91417,91418,91420,91421,91422,91424,91429,91430,91431,91435,91436],{"id":79703,"depth":642,"text":79704},{"id":79840,"depth":642,"text":79841},{"id":79943,"depth":642,"text":91399,"children":91400},"Mezní produkt práce (MPLMP_L)",[91401],{"id":80389,"depth":649,"text":80390},{"id":80878,"depth":642,"text":91403},"Průměrný produkt práce (APLAP_L)",{"id":80996,"depth":642,"text":80997,"children":91405},[91406,91407,91408],{"id":81233,"depth":649,"text":70376},{"id":81544,"depth":649,"text":81545},{"id":82264,"depth":649,"text":82265},{"id":82836,"depth":642,"text":82837},{"id":82939,"depth":642,"text":82940,"children":91411},[91412,91413,91415,91416],{"id":83298,"depth":649,"text":83299},{"id":83797,"depth":649,"text":91414},"Parametr efektivity AA",{"id":83868,"depth":649,"text":83869},{"id":42054,"depth":649,"text":84208},{"id":84395,"depth":642,"text":84396},{"id":84734,"depth":642,"text":91419},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":85425,"depth":642,"text":85426},{"id":79769,"depth":642,"text":14650},{"id":85836,"depth":642,"text":91423},"Mezní míra technické substituce (MRTSMRTS)",{"id":86702,"depth":642,"text":86703,"children":91425},[91426,91427,91428],{"id":86706,"depth":649,"text":86707},{"id":87349,"depth":649,"text":87350},{"id":87630,"depth":649,"text":87631},{"id":87976,"depth":642,"text":87977},{"id":54756,"depth":642,"text":54757},{"id":88326,"depth":642,"text":88327,"children":91432},[91433,91434],{"id":45325,"depth":649,"text":45326},{"id":88845,"depth":649,"text":88846},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fprodukce",{"title":79339,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,14685,91443,91444,91445,79769,91446,91447],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":91450,"title":91451,"body":91452,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":100399,"navigation":664,"path":100400,"seo":100401,"sources":100402,"stem":100403,"tags":100404,"type":7391,"updated":677,"__hash__":100407},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":91453,"toc":100373},[91454,91457,91459,91656,91665,91669,91672,91725,91729,91741,91745,91748,91765,91888,91894,92038,92048,92052,92087,92125,92173,92230,92290,92332,92908,92912,92995,93104,93197,93455,93458,93511,93622,93704,93708,93719,93952,94007,94013,94053,94116,94127,94318,94424,94577,94625,94630,94744,94782,94908,94954,94981,95058,95133,95213,95343,95404,95492,95496,95499,95568,95651,95658,95718,96028,96032,96038,96091,96107,96158,96296,96372,96485,96802,96806,96813,96973,97032,97036,97058,97155,97276,97390,97413,97476,97533,97785,97793,97797,97804,98058,98108,98164,98167,98331,98335,98433,98435,98467,98471,98604,98846,99030,99198,99505,99638,99825,99837,99839,100274,100276],[12,91455,91451],{"id":91456},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,91458,16880],{"id":16879},[724,91460,91461,3245,91463,91494,91495,91498,91499,91529,91530,91548,91549,91589,91590,91593,91594,91607,91608,33128,91611,91624,91625,91638,91639,91652,91653,1659],{},[38,91462,880],{},[883,91464,91466],{"className":91465},[886],[888,91467,91468],{"xmlns":890},[892,91469,91470,91492],{},[895,91471,91472,91474,91476,91482,91484,91490],{},[898,91473,900],{},[1712,91475,1904],{"stretchy":1903},[6927,91477,91478,91480],{},[898,91479,1734],{},[1716,91481,2222],{},[1712,91483,3138],{"separator":2565},[6927,91485,91486,91488],{},[898,91487,1734],{},[1716,91489,2787],{},[1712,91491,1910],{"stretchy":1903},[902,91493,21218],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,91496,91497],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,91500,91502],{"className":91501},[886],[888,91503,91504],{"xmlns":890},[892,91505,91506,91526],{},[895,91507,91508,91510,91516,91518],{},[898,91509,4445],{},[6927,91511,91512,91514],{},[898,91513,900],{},[898,91515,22665],{},[1712,91517,1714],{},[6989,91519,91520,91522,91524],{},[898,91521,900],{},[898,91523,22665],{},[1712,91525,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,91527,91528],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,91531,91533],{"className":91532},[886],[888,91534,91535],{"xmlns":890},[892,91536,91537,91545],{},[895,91538,91539,91541,91543],{},[898,91540,900],{},[1712,91542,1714],{},[898,91544,7585],{},[902,91546,91547],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,91550,91552],{"className":91551},[886],[888,91553,91554],{"xmlns":890},[892,91555,91556,91586],{},[895,91557,91558,91560,91562,91564,91566,91568,91570,91576,91578,91580],{},[898,91559,4445],{},[898,91561,1775],{},[898,91563,8195],{},[898,91565,6493],{},[1712,91567,1714],{},[898,91569,4445],{},[6927,91571,91572,91574],{},[898,91573,900],{},[1716,91575,2222],{},[898,91577,2473],{"mathvariant":2003},[898,91579,4445],{},[6927,91581,91582,91584],{},[898,91583,900],{},[1716,91585,2787],{},[902,91587,91588],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,91591,91592],{},"teorii užitečnosti"," — funkce ",[883,91595,91597],{"className":91596},[886],[888,91598,91599],{"xmlns":890},[892,91600,91601,91605],{},[895,91602,91603],{},[898,91604,900],{},[902,91606,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,91609,91610],{},"Optimalizaci spotřebitele",[883,91612,91614],{"className":91613},[886],[888,91615,91616],{"xmlns":890},[892,91617,91618,91622],{},[895,91619,91620],{},[898,91621,900],{},[902,91623,900],{"encoding":904}," při rozpočtu, min ",[883,91626,91628],{"className":91627},[886],[888,91629,91630],{"xmlns":890},[892,91631,91632,91636],{},[895,91633,91634],{},[898,91635,2041],{},[902,91637,2041],{"encoding":904}," při dané ",[883,91640,91642],{"className":91641},[886],[888,91643,91644],{"xmlns":890},[892,91645,91646,91650],{},[895,91647,91648],{},[898,91649,900],{},[902,91651,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,91654,913],{"className":91655,"dataFsResolvedFilePath":911,"href":912},[210],[724,91657,91658,91659,91661,91662,1659],{},"Kapitola 6 knihy ",[614,91660,21082],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,91663,41629],{"className":91664,"dataFsResolvedFilePath":911,"href":912},[210],[115,91666,91668],{"id":91667},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,91670,91671],{},"Po prostudování této kapitoly byste měli umět:",[120,91673,91674,91680,91689,91694,91697,91703,91709,91712,91718],{},[123,91675,91676,91677,3138],{},"vyložit, co se rozumí termínem ",[38,91678,91679],{},"užitečnost",[123,91681,91682,91683,1655,91686,3138],{},"definovat pojmy ",[38,91684,91685],{},"svazek zboží",[38,91687,91688],{},"funkce užitečnosti",[123,91690,79718,91691,79725],{},[38,91692,91693],{},"mezní užitečnosti",[123,91695,91696],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,91698,79745,91699,91702],{},[38,91700,91701],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,91704,79766,91705,91708],{},[38,91706,91707],{},"křivky užitečnosti"," (indiferenční křivky),",[123,91710,91711],{},"vyjmenovat jejich základní vlastnosti,",[123,91713,79718,91714,91717],{},[38,91715,91716],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,91719,91720,91721,91724],{},"řešit ",[38,91722,91723],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,91726,91728],{"id":91727},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,91730,91731,91732,91736,91737,91740],{},"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 ",[207,91733,91735],{"className":91734,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,91738,91739],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,91742,91744],{"id":91743},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,91746,91747],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,91749,91750,91756],{},[123,91751,91752,91755],{},[38,91753,91754],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,91757,91758,91761,91762,91764],{},[38,91759,91760],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,91763,91497],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1636,91766,91767],{},[724,91768,91769,91771,91772,91775,91776,3245,91789,91792,91793,1655,91806,91825,91826,1343,91852,91879,91880,91883,91884,91887],{},[883,91770,2203],{}," Pozor — ordinalisté užitečnost ",[38,91773,91774],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,91777,91779],{"className":91778},[886],[888,91780,91781],{"xmlns":890},[892,91782,91783,91787],{},[895,91784,91785],{},[898,91786,900],{},[902,91788,900],{"encoding":904},[38,91790,91791],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,91794,91796],{"className":91795},[886],[888,91797,91798],{"xmlns":890},[892,91799,91800,91804],{},[895,91801,91802],{},[898,91803,900],{},[902,91805,900],{"encoding":904},[883,91807,91809],{"className":91808},[886],[888,91810,91811],{"xmlns":890},[892,91812,91813,91822],{},[895,91814,91815],{},[6205,91816,91817,91819],{"accent":2565},[898,91818,900],{},[1712,91820,91821],{},"~",[902,91823,91824],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,91827,91829],{"className":91828},[886],[888,91830,91831],{"xmlns":890},[892,91832,91833,91849],{},[895,91834,91835,91841,91843],{},[6205,91836,91837,91839],{"accent":2565},[898,91838,900],{},[1712,91840,91821],{},[1712,91842,1714],{},[2037,91844,91845,91847],{},[898,91846,900],{},[1716,91848,2787],{},[902,91850,91851],{"encoding":904},"\\tilde U = U^2",[883,91853,91855],{"className":91854},[886],[888,91856,91857],{"xmlns":890},[892,91858,91859,91876],{},[895,91860,91861,91867,91869,91872,91874],{},[6205,91862,91863,91865],{"accent":2565},[898,91864,900],{},[1712,91866,91821],{},[1712,91868,1714],{},[898,91870,91871],{},"ln",[1712,91873,61075],{},[898,91875,900],{},[902,91877,91878],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,91881,91882],{},"porovnání"," mezi svazky a ",[38,91885,91886],{},"poměry"," mezních veličin.",[724,91889,91890,91891,2854],{},"Ordinalistický přístup vychází z ",[38,91892,91893],{},"pěti hlavních předpokladů",[152,91895,91896,91902,91908,92026,92032],{},[123,91897,91898,91901],{},[38,91899,91900],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,91903,91904,91907],{},[38,91905,91906],{},"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.",[123,91909,91910,91913,91914,66616,91927,91940,91941,66616,91954,7037,91967,91970,91971,1655,91990,67445,92008,1659],{},[38,91911,91912],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,91915,91917],{"className":91916},[886],[888,91918,91919],{"xmlns":890},[892,91920,91921,91925],{},[895,91922,91923],{},[898,91924,2044],{},[902,91926,2044],{"encoding":904},[883,91928,91930],{"className":91929},[886],[888,91931,91932],{"xmlns":890},[892,91933,91934,91938],{},[895,91935,91936],{},[898,91937,28128],{},[902,91939,28128],{"encoding":904},", nebude jindy preferovat ",[883,91942,91944],{"className":91943},[886],[888,91945,91946],{"xmlns":890},[892,91947,91948,91952],{},[895,91949,91950],{},[898,91951,28128],{},[902,91953,28128],{"encoding":904},[883,91955,91957],{"className":91956},[886],[888,91958,91959],{"xmlns":890},[892,91960,91961,91965],{},[895,91962,91963],{},[898,91964,2044],{},[902,91966,2044],{"encoding":904},[38,91968,91969],{},"Tranzitivita",": pokud ",[883,91972,91974],{"className":91973},[886],[888,91975,91976],{"xmlns":890},[892,91977,91978,91987],{},[895,91979,91980,91982,91985],{},[898,91981,2044],{},[1712,91983,91984],{},"≻",[898,91986,28128],{},[902,91988,91989],{"encoding":904},"A \\succ B",[883,91991,91993],{"className":91992},[886],[888,91994,91995],{"xmlns":890},[892,91996,91997,92005],{},[895,91998,91999,92001,92003],{},[898,92000,28128],{},[1712,92002,91984],{},[898,92004,8195],{},[902,92006,92007],{"encoding":904},"B \\succ C",[883,92009,92011],{"className":92010},[886],[888,92012,92013],{"xmlns":890},[892,92014,92015,92023],{},[895,92016,92017,92019,92021],{},[898,92018,2044],{},[1712,92020,91984],{},[898,92022,8195],{},[902,92024,92025],{"encoding":904},"A \\succ C",[123,92027,92028,92031],{},[38,92029,92030],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,92033,92034,92037],{},[38,92035,92036],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,92039,92040,92041,92044,92045,1659],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,92042,92043],{},"preference"," a na příbuzné ",[614,92046,92047],{},"funkci užitečnosti",[115,92049,92051],{"id":92050},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,92053,92054,92055,92068,92069,92072,92073,92086],{},"Uvažujme ",[883,92056,92058],{"className":92057},[886],[888,92059,92060],{"xmlns":890},[892,92061,92062,92066],{},[895,92063,92064],{},[898,92065,41735],{},[902,92067,41735],{"encoding":904}," různých zboží. ",[38,92070,92071],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,92074,92076],{"className":92075},[886],[888,92077,92078],{"xmlns":890},[892,92079,92080,92084],{},[895,92081,92082],{},[898,92083,41735],{},[902,92085,41735],{"encoding":904},"-tice",[724,92088,92089],{},[883,92090,92092],{"className":92091},[886],[888,92093,92094],{"xmlns":890},[892,92095,92096,92122],{},[895,92097,92098,92100,92106,92108,92110,92112,92118,92120],{},[1712,92099,1904],{"stretchy":1903},[6927,92101,92102,92104],{},[898,92103,1734],{},[1716,92105,2222],{},[1712,92107,3138],{"separator":2565},[1712,92109,14518],{},[1712,92111,3138],{"separator":2565},[6927,92113,92114,92116],{},[898,92115,1734],{},[898,92117,41735],{},[1712,92119,1910],{"stretchy":1903},[1712,92121,3138],{"separator":2565},[902,92123,92124],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,92126,2101,92127,92144,92145,92158,92159,92162,92163,92166,92167,92170,92171,2854],{},[883,92128,92130],{"className":92129},[886],[888,92131,92132],{"xmlns":890},[892,92133,92134,92142],{},[895,92135,92136],{},[6927,92137,92138,92140],{},[898,92139,1734],{},[898,92141,22665],{},[902,92143,52413],{"encoding":904}," značí množství ",[883,92146,92148],{"className":92147},[886],[888,92149,92150],{"xmlns":890},[892,92151,92152,92156],{},[895,92153,92154],{},[898,92155,22665],{},[902,92157,22665],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,92160,92161],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,92164,92165],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,92168,92169],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,92172,92047],{},[883,92174,92176],{"className":92175},[886],[888,92177,92178],{"xmlns":890,"display":32941},[892,92179,92180,92227],{},[25629,92181,92182],{"width":32946},[25634,92183,92184,92186,92220,92222],{},[25637,92185],{"width":32951},[25637,92187,92188],{},[895,92189,92190,92192,92194,92196,92198,92204,92206,92208,92210,92216,92218],{},[898,92191,900],{},[1712,92193,1714],{},[898,92195,900],{},[1712,92197,1904],{"stretchy":1903},[6927,92199,92200,92202],{},[898,92201,1734],{},[1716,92203,2222],{},[1712,92205,3138],{"separator":2565},[1712,92207,14518],{},[1712,92209,3138],{"separator":2565},[6927,92211,92212,92214],{},[898,92213,1734],{},[898,92215,41735],{},[1712,92217,1910],{"stretchy":1903},[1712,92219,3138],{"separator":2565},[25637,92221],{"width":32951},[25637,92223,92224],{},[1762,92225,92226],{},"(6.1)",[902,92228,92229],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,92231,2101,92232,92262,92263,92285,92286,92289],{},[883,92233,92235],{"className":92234},[886],[888,92236,92237],{"xmlns":890},[892,92238,92239,92259],{},[895,92240,92241,92247,92249,92251,92253],{},[6927,92242,92243,92245],{},[898,92244,1734],{},[1716,92246,2222],{},[1712,92248,3138],{"separator":2565},[1712,92250,14518],{},[1712,92252,3138],{"separator":2565},[6927,92254,92255,92257],{},[898,92256,1734],{},[898,92258,41735],{},[902,92260,92261],{"encoding":904},"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 ",[883,92264,92266],{"className":92265},[886],[888,92267,92268],{"xmlns":890},[892,92269,92270,92282],{},[895,92271,92272,92274,92276],{},[898,92273,900],{},[1712,92275,3138],{"separator":2565},[6205,92277,92278,92280],{"accent":2565},[898,92279,900],{},[1712,92281,91821],{},[902,92283,92284],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,92287,92288],{},"monotónní transformace"," zachovávající pořadí.",[724,92291,92292,92293,4831,92296,1659],{},"Dále se omezíme na funkce pro ",[38,92294,92295],{},"dvě zboží",[883,92297,92299],{"className":92298},[886],[888,92300,92301],{"xmlns":890},[892,92302,92303,92329],{},[895,92304,92305,92307,92309,92311,92313,92319,92321,92327],{},[898,92306,900],{},[1712,92308,1714],{},[898,92310,900],{},[1712,92312,1904],{"stretchy":1903},[6927,92314,92315,92317],{},[898,92316,1734],{},[1716,92318,2222],{},[1712,92320,3138],{"separator":2565},[6927,92322,92323,92325],{},[898,92324,1734],{},[1716,92326,2787],{},[1712,92328,1910],{"stretchy":1903},[902,92330,92331],{"encoding":904},"U = U(Q_1, Q_2)",[1636,92333,92334,92409],{},[724,92335,92336,92338,92339,2854],{},[883,92337,57570],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,92340,92342],{"className":92341},[886],[888,92343,92344],{"xmlns":890},[892,92345,92346,92406],{},[895,92347,92348,92350,92352,92354,92356,92362,92364,92370,92372,92378,92380,92382,92384],{},[898,92349,900],{},[1712,92351,1714],{},[898,92353,900],{},[1712,92355,1904],{"stretchy":1903},[6927,92357,92358,92360],{},[898,92359,1734],{},[1716,92361,2222],{},[1712,92363,3138],{"separator":2565},[6927,92365,92366,92368],{},[898,92367,1734],{},[1716,92369,2787],{},[1712,92371,3138],{"separator":2565},[6927,92373,92374,92376],{},[898,92375,1734],{},[1716,92377,6198],{},[1712,92379,1910],{"stretchy":1903},[1712,92381,1714],{},[1716,92383,2787],{},[5935,92385,92386],{},[895,92387,92388,92394,92400],{},[6927,92389,92390,92392],{},[898,92391,1734],{},[1716,92393,2222],{},[6927,92395,92396,92398],{},[898,92397,1734],{},[1716,92399,2787],{},[6927,92401,92402,92404],{},[898,92403,1734],{},[1716,92405,6198],{},[902,92407,92408],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,92410,92411,92604],{},[123,92412,92413,92414,92440,92441,17812,92467,1655,92526,3401,92586,6245],{},"svazek ",[883,92415,92417],{"className":92416},[886],[888,92418,92419],{"xmlns":890},[892,92420,92421,92437],{},[895,92422,92423,92425,92427,92429,92431,92433,92435],{},[1712,92424,1904],{"stretchy":1903},[1716,92426,46737],{},[1712,92428,3138],{"separator":2565},[1716,92430,2975],{},[1712,92432,3138],{"separator":2565},[1716,92434,46715],{},[1712,92436,1910],{"stretchy":1903},[902,92438,92439],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,92442,92444],{"className":92443},[886],[888,92445,92446],{"xmlns":890},[892,92447,92448,92464],{},[895,92449,92450,92452,92454,92456,92458,92460,92462],{},[1712,92451,1904],{"stretchy":1903},[1716,92453,1780],{},[1712,92455,3138],{"separator":2565},[1716,92457,1780],{},[1712,92459,3138],{"separator":2565},[1716,92461,71472],{},[1712,92463,1910],{"stretchy":1903},[902,92465,92466],{"encoding":904},"(9, 9, 27)",[883,92468,92470],{"className":92469},[886],[888,92471,92472],{"xmlns":890},[892,92473,92474,92523],{},[895,92475,92476,92478,92480,92482,92484,92486,92488,92490,92492,92494,92496,92510,92512,92514,92519,92521],{},[898,92477,900],{},[1712,92479,1904],{"stretchy":1903},[1716,92481,46737],{},[1712,92483,3138],{"separator":2565},[1716,92485,2975],{},[1712,92487,3138],{"separator":2565},[1716,92489,46715],{},[1712,92491,1910],{"stretchy":1903},[1712,92493,1714],{},[1716,92495,2787],{},[5935,92497,92498],{},[895,92499,92500,92502,92504,92506,92508],{},[1716,92501,46737],{},[1712,92503,1783],{},[1716,92505,2975],{},[1712,92507,1783],{},[1716,92509,46715],{},[1712,92511,1714],{},[1716,92513,2787],{},[5935,92515,92516],{},[1716,92517,92518],{},"4096",[1712,92520,1714],{},[1716,92522,3429],{},[902,92524,92525],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,92527,92529],{"className":92528},[886],[888,92530,92531],{"xmlns":890},[892,92532,92533,92583],{},[895,92534,92535,92537,92539,92541,92543,92545,92547,92549,92551,92553,92555,92569,92571,92573,92578,92580],{},[898,92536,900],{},[1712,92538,1904],{"stretchy":1903},[1716,92540,1780],{},[1712,92542,3138],{"separator":2565},[1716,92544,1780],{},[1712,92546,3138],{"separator":2565},[1716,92548,71472],{},[1712,92550,1910],{"stretchy":1903},[1712,92552,1714],{},[1716,92554,2787],{},[5935,92556,92557],{},[895,92558,92559,92561,92563,92565,92567],{},[1716,92560,1780],{},[1712,92562,1783],{},[1716,92564,1780],{},[1712,92566,1783],{},[1716,92568,71472],{},[1712,92570,1714],{},[1716,92572,2787],{},[5935,92574,92575],{},[1716,92576,92577],{},"2187",[1712,92579,3712],{},[1716,92581,92582],{},"93,53",[902,92584,92585],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,92587,92589],{"className":92588},[886],[888,92590,92591],{"xmlns":890},[892,92592,92593,92601],{},[895,92594,92595,92597,92599],{},[1716,92596,3429],{},[1712,92598,2302],{},[1716,92600,92582],{},[902,92602,92603],{"encoding":904},"128 > 93{,}53",[123,92605,92606,92607,1655,92633,92659,92660,1655,92700,92741,92742,92788,92789,1655,92815,8259,92841,1655,92859,92877,92878,1659],{},"svazky ",[883,92608,92610],{"className":92609},[886],[888,92611,92612],{"xmlns":890},[892,92613,92614,92630],{},[895,92615,92616,92618,92620,92622,92624,92626,92628],{},[1712,92617,1904],{"stretchy":1903},[1716,92619,2975],{},[1712,92621,3138],{"separator":2565},[1716,92623,3397],{},[1712,92625,3138],{"separator":2565},[1716,92627,2787],{},[1712,92629,1910],{"stretchy":1903},[902,92631,92632],{"encoding":904},"(4, 8, 2)",[883,92634,92636],{"className":92635},[886],[888,92637,92638],{"xmlns":890},[892,92639,92640,92656],{},[895,92641,92642,92644,92646,92648,92650,92652,92654],{},[1712,92643,1904],{"stretchy":1903},[1716,92645,46715],{},[1712,92647,3138],{"separator":2565},[1716,92649,2222],{},[1712,92651,3138],{"separator":2565},[1716,92653,2975],{},[1712,92655,1910],{"stretchy":1903},[902,92657,92658],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,92661,92663],{"className":92662},[886],[888,92664,92665],{"xmlns":890},[892,92666,92667,92697],{},[895,92668,92669,92671,92673,92675,92677,92679,92681,92683,92685,92687,92689,92693,92695],{},[898,92670,900],{},[1712,92672,1904],{"stretchy":1903},[1716,92674,2975],{},[1712,92676,3138],{"separator":2565},[1716,92678,3397],{},[1712,92680,3138],{"separator":2565},[1716,92682,2787],{},[1712,92684,1910],{"stretchy":1903},[1712,92686,1714],{},[1716,92688,2787],{},[5935,92690,92691],{},[1716,92692,46715],{},[1712,92694,1714],{},[1716,92696,46737],{},[902,92698,92699],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,92701,92703],{"className":92702},[886],[888,92704,92705],{"xmlns":890},[892,92706,92707,92738],{},[895,92708,92709,92711,92713,92715,92717,92719,92721,92723,92725,92727,92729,92734,92736],{},[898,92710,900],{},[1712,92712,1904],{"stretchy":1903},[1716,92714,46715],{},[1712,92716,3138],{"separator":2565},[1716,92718,2222],{},[1712,92720,3138],{"separator":2565},[1716,92722,2975],{},[1712,92724,1910],{"stretchy":1903},[1712,92726,1714],{},[1716,92728,2787],{},[5935,92730,92731],{},[1716,92732,92733],{},"256",[1712,92735,1714],{},[1716,92737,77234],{},[902,92739,92740],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,92743,92745],{"className":92744},[886],[888,92746,92747],{"xmlns":890},[892,92748,92749,92785],{},[895,92750,92751,92753,92755,92757,92759,92761,92763,92765,92767,92769,92771,92773,92775,92777,92779,92781,92783],{},[898,92752,900],{},[1712,92754,1904],{"stretchy":1903},[1716,92756,2975],{},[1712,92758,3138],{"separator":2565},[1716,92760,3397],{},[1712,92762,3138],{"separator":2565},[1716,92764,2787],{},[1712,92766,1910],{"stretchy":1903},[1712,92768,1714],{},[898,92770,900],{},[1712,92772,1904],{"stretchy":1903},[1716,92774,46715],{},[1712,92776,3138],{"separator":2565},[1716,92778,2222],{},[1712,92780,3138],{"separator":2565},[1716,92782,2975],{},[1712,92784,1910],{"stretchy":1903},[902,92786,92787],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,92790,92792],{"className":92791},[886],[888,92793,92794],{"xmlns":890},[892,92795,92796,92812],{},[895,92797,92798,92800,92802,92804,92806,92808,92810],{},[1716,92799,2975],{},[1712,92801,1783],{},[1716,92803,3397],{},[1712,92805,1783],{},[1716,92807,2787],{},[1712,92809,1714],{},[1716,92811,46715],{},[902,92813,92814],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,92816,92818],{"className":92817},[886],[888,92819,92820],{"xmlns":890},[892,92821,92822,92838],{},[895,92823,92824,92826,92828,92830,92832,92834,92836],{},[1716,92825,46715],{},[1712,92827,1783],{},[1716,92829,2222],{},[1712,92831,1783],{},[1716,92833,2975],{},[1712,92835,1714],{},[1716,92837,92733],{},[902,92839,92840],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,92842,92844],{"className":92843},[886],[888,92845,92846],{"xmlns":890},[892,92847,92848,92856],{},[895,92849,92850,92852,92854],{},[898,92851,900],{},[1712,92853,1714],{},[1716,92855,46737],{},[902,92857,92858],{"encoding":904},"U = 16",[883,92860,92862],{"className":92861},[886],[888,92863,92864],{"xmlns":890},[892,92865,92866,92874],{},[895,92867,92868,92870,92872],{},[898,92869,900],{},[1712,92871,1714],{},[1716,92873,77234],{},[902,92875,92876],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,92879,92881],{"className":92880},[886],[888,92882,92883],{"xmlns":890},[892,92884,92885,92905],{},[895,92886,92887,92893,92899],{},[6927,92888,92889,92891],{},[898,92890,1734],{},[1716,92892,2222],{},[6927,92894,92895,92897],{},[898,92896,1734],{},[1716,92898,2787],{},[6927,92900,92901,92903],{},[898,92902,1734],{},[1716,92904,6198],{},[902,92906,92907],{"encoding":904},"Q_1 Q_2 Q_3",[115,92909,92911],{"id":92910},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,92913,92914,92915,5920,92950,3245,92953,46689,92970,14897,92987,92990,92991,92994],{},"Pro funkci užitečnosti ",[883,92916,92918],{"className":92917},[886],[888,92919,92920],{"xmlns":890},[892,92921,92922,92948],{},[895,92923,92924,92926,92928,92930,92932,92938,92940,92946],{},[898,92925,900],{},[1712,92927,1714],{},[898,92929,900],{},[1712,92931,1904],{"stretchy":1903},[6927,92933,92934,92936],{},[898,92935,1734],{},[1716,92937,2222],{},[1712,92939,3138],{"separator":2565},[6927,92941,92942,92944],{},[898,92943,1734],{},[1716,92945,2787],{},[1712,92947,1910],{"stretchy":1903},[902,92949,92331],{"encoding":904},[38,92951,92952],{},"mezní užitečnost",[883,92954,92956],{"className":92955},[886],[888,92957,92958],{"xmlns":890},[892,92959,92960,92968],{},[895,92961,92962],{},[6927,92963,92964,92966],{},[898,92965,1734],{},[1716,92967,2222],{},[902,92969,33877],{"encoding":904},[883,92971,92973],{"className":92972},[886],[888,92974,92975],{"xmlns":890},[892,92976,92977,92985],{},[895,92978,92979],{},[6927,92980,92981,92983],{},[898,92982,1734],{},[1716,92984,2787],{},[902,92986,33896],{"encoding":904},[38,92988,92989],{},"marginal utility",") parciální ",[207,92992,1145],{"className":92993,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,92996,92998],{"className":92997},[886],[888,92999,93000],{"xmlns":890,"display":32941},[892,93001,93002,93101],{},[25629,93003,93004],{"width":32946},[25634,93005,93006,93008,93094,93096],{},[25637,93007],{"width":32951},[25637,93009,93010],{},[895,93011,93012,93014,93020,93022,93030,93032,93050,93052,93054,93056,93062,93064,93072,93074,93092],{},[898,93013,4445],{},[6927,93015,93016,93018],{},[898,93017,900],{},[1716,93019,2222],{},[1712,93021,1714],{},[6989,93023,93024,93026,93028],{},[898,93025,900],{},[1716,93027,2222],{},[1712,93029,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,93031,1714],{},[2567,93033,93034,93040],{},[895,93035,93036,93038],{},[898,93037,14744],{"mathvariant":2003},[898,93039,900],{},[895,93041,93042,93044],{},[898,93043,14744],{"mathvariant":2003},[6927,93045,93046,93048],{},[898,93047,1734],{},[1716,93049,2222],{},[1712,93051,3138],{"separator":2565},[3690,93053],{"width":20158},[898,93055,4445],{},[6927,93057,93058,93060],{},[898,93059,900],{},[1716,93061,2787],{},[1712,93063,1714],{},[6989,93065,93066,93068,93070],{},[898,93067,900],{},[1716,93069,2787],{},[1712,93071,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,93073,1714],{},[2567,93075,93076,93082],{},[895,93077,93078,93080],{},[898,93079,14744],{"mathvariant":2003},[898,93081,900],{},[895,93083,93084,93086],{},[898,93085,14744],{"mathvariant":2003},[6927,93087,93088,93090],{},[898,93089,1734],{},[1716,93091,2787],{},[898,93093,1659],{"mathvariant":2003},[25637,93095],{"width":32951},[25637,93097,93098],{},[1762,93099,93100],{},"(6.2)",[902,93102,93103],{"encoding":904},"MU_1 = U'_1 = \\frac{\\partial U}{\\partial Q_1}, \\quad MU_2 = U'_2 = \\frac{\\partial U}{\\partial Q_2}. \\tag{6.2}",[724,93105,93106,93107,93141,93142,93172,93173,3245,93176,1659],{},"Pro pevné ",[883,93108,93110],{"className":93109},[886],[888,93111,93112],{"xmlns":890},[892,93113,93114,93138],{},[895,93115,93116,93122,93124,93126,93128,93134,93136],{},[6927,93117,93118,93120],{},[898,93119,1734],{},[1716,93121,2222],{},[1712,93123,1714],{},[898,93125,207],{},[1712,93127,3138],{"separator":2565},[6927,93129,93130,93132],{},[898,93131,1734],{},[1716,93133,2787],{},[1712,93135,1714],{},[898,93137,7544],{},[902,93139,93140],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,93143,93145],{"className":93144},[886],[888,93146,93147],{"xmlns":890},[892,93148,93149,93169],{},[895,93150,93151,93153,93159,93161,93163,93165,93167],{},[898,93152,4445],{},[6927,93154,93155,93157],{},[898,93156,900],{},[1716,93158,2222],{},[1712,93160,1904],{"stretchy":1903},[898,93162,207],{},[1712,93164,3138],{"separator":2565},[898,93166,7544],{},[1712,93168,1910],{"stretchy":1903},[902,93170,93171],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,93174,93175],{},"v bodě (na hladině)",[883,93177,93179],{"className":93178},[886],[888,93180,93181],{"xmlns":890},[892,93182,93183,93195],{},[895,93184,93185,93187,93189,93191,93193],{},[1712,93186,7910],{"stretchy":1903},[898,93188,207],{},[1712,93190,3138],{"separator":2565},[898,93192,7544],{},[1712,93194,7925],{"stretchy":1903},[902,93196,15696],{"encoding":904},[1636,93198,93199],{},[724,93200,93201,93203,93204,93234,93263,93264,8032,93277,8046,93294,93315,93316,8093,93333,3072,93346,93363,93364,93386,93387,93416,93417,4288,93437,93454],{},[883,93202,1941],{}," Intuice — co říká ",[883,93205,93207],{"className":93206},[886],[888,93208,93209],{"xmlns":890},[892,93210,93211,93231],{},[895,93212,93213,93215,93221,93223,93225,93227,93229],{},[898,93214,4445],{},[6927,93216,93217,93219],{},[898,93218,900],{},[1716,93220,2222],{},[1712,93222,1904],{"stretchy":1903},[898,93224,207],{},[1712,93226,3138],{"separator":2565},[898,93228,7544],{},[1712,93230,1910],{"stretchy":1903},[902,93232,93233],{"encoding":904},"MU_1(a,b)",[883,93235,93237],{"className":93236},[886],[888,93238,93239],{"xmlns":890},[892,93240,93241,93261],{},[895,93242,93243,93245,93251,93253,93255,93257,93259],{},[898,93244,4445],{},[6927,93246,93247,93249],{},[898,93248,900],{},[1716,93250,2222],{},[1712,93252,1904],{"stretchy":1903},[898,93254,207],{},[1712,93256,3138],{"separator":2565},[898,93258,7544],{},[1712,93260,1910],{"stretchy":1903},[902,93262,93171],{"encoding":904}," je rychlost změny ",[883,93265,93267],{"className":93266},[886],[888,93268,93269],{"xmlns":890},[892,93270,93271,93275],{},[895,93272,93273],{},[898,93274,900],{},[902,93276,900],{"encoding":904},[883,93278,93280],{"className":93279},[886],[888,93281,93282],{"xmlns":890},[892,93283,93284,93292],{},[895,93285,93286],{},[6927,93287,93288,93290],{},[898,93289,1734],{},[1716,93291,2222],{},[902,93293,33877],{"encoding":904},[883,93295,93297],{"className":93296},[886],[888,93298,93299],{"xmlns":890},[892,93300,93301,93313],{},[895,93302,93303,93305,93307,93309,93311],{},[1712,93304,7910],{"stretchy":1903},[898,93306,207],{},[1712,93308,3138],{"separator":2565},[898,93310,7544],{},[1712,93312,7925],{"stretchy":1903},[902,93314,15696],{"encoding":904},". Přibližně: změní-li se ",[883,93317,93319],{"className":93318},[886],[888,93320,93321],{"xmlns":890},[892,93322,93323,93331],{},[895,93324,93325],{},[6927,93326,93327,93329],{},[898,93328,1734],{},[1716,93330,2222],{},[902,93332,33877],{"encoding":904},[883,93334,93336],{"className":93335},[886],[888,93337,93338],{"xmlns":890},[892,93339,93340,93344],{},[895,93341,93342],{},[898,93343,207],{},[902,93345,207],{"encoding":904},[883,93347,93349],{"className":93348},[886],[888,93350,93351],{"xmlns":890},[892,93352,93353,93361],{},[895,93354,93355,93357,93359],{},[898,93356,207],{},[1712,93358,3145],{},[1716,93360,2222],{},[902,93362,8124],{"encoding":904}," při pevném ",[883,93365,93367],{"className":93366},[886],[888,93368,93369],{"xmlns":890},[892,93370,93371,93383],{},[895,93372,93373,93379,93381],{},[6927,93374,93375,93377],{},[898,93376,1734],{},[1716,93378,2787],{},[1712,93380,1714],{},[898,93382,7544],{},[902,93384,93385],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,93388,93390],{"className":93389},[886],[888,93391,93392],{"xmlns":890},[892,93393,93394,93414],{},[895,93395,93396,93398,93404,93406,93408,93410,93412],{},[898,93397,4445],{},[6927,93399,93400,93402],{},[898,93401,900],{},[1716,93403,2222],{},[1712,93405,1904],{"stretchy":1903},[898,93407,207],{},[1712,93409,3138],{"separator":2565},[898,93411,7544],{},[1712,93413,1910],{"stretchy":1903},[902,93415,93171],{"encoding":904},". Stejně tak ",[883,93418,93420],{"className":93419},[886],[888,93421,93422],{"xmlns":890},[892,93423,93424,93434],{},[895,93425,93426,93428],{},[898,93427,4445],{},[6927,93429,93430,93432],{},[898,93431,900],{},[1716,93433,2787],{},[902,93435,93436],{"encoding":904},"MU_2",[883,93438,93440],{"className":93439},[886],[888,93441,93442],{"xmlns":890},[892,93443,93444,93452],{},[895,93445,93446],{},[6927,93447,93448,93450],{},[898,93449,1734],{},[1716,93451,2787],{},[902,93453,33896],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,93456,85086],{"id":93457},"totální-diferenciál",[724,93459,93460,93461,53215,93477,93507,93508,2854],{},"Přibližnou změnu užitečnosti ",[883,93462,93464],{"className":93463},[886],[888,93465,93466],{"xmlns":890},[892,93467,93468,93474],{},[895,93469,93470,93472],{},[898,93471,2004],{"mathvariant":2003},[898,93473,900],{},[902,93475,93476],{"encoding":904},"\\Delta U",[883,93478,93480],{"className":93479},[886],[888,93481,93482],{"xmlns":890},[892,93483,93484,93504],{},[895,93485,93486,93488,93494,93496,93498],{},[898,93487,2468],{"mathvariant":2003},[6927,93489,93490,93492],{},[898,93491,1734],{},[1716,93493,2222],{},[1712,93495,3138],{"separator":2565},[898,93497,2468],{"mathvariant":2003},[6927,93499,93500,93502],{},[898,93501,1734],{},[1716,93503,2787],{},[902,93505,93506],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,93509,93510],{},"totálního diferenciálu",[883,93512,93514],{"className":93513},[886],[888,93515,93516],{"xmlns":890,"display":32941},[892,93517,93518,93619],{},[25629,93519,93520],{"width":32946},[25634,93521,93522,93524,93612,93614],{},[25637,93523],{"width":32951},[25637,93525,93526],{},[895,93527,93528,93530,93532,93534,93536,93538,93540,93548,93550,93556,93558,93566,93568,93574,93576,93578,93584,93586,93592,93594,93596,93602,93604,93610],{},[898,93529,2004],{"mathvariant":2003},[898,93531,900],{},[1712,93533,3740],{},[898,93535,2468],{"mathvariant":2003},[898,93537,900],{},[1712,93539,1714],{},[6989,93541,93542,93544,93546],{},[898,93543,900],{},[1716,93545,2222],{},[1712,93547,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[898,93549,2468],{"mathvariant":2003},[6927,93551,93552,93554],{},[898,93553,1734],{},[1716,93555,2222],{},[1712,93557,3145],{},[6989,93559,93560,93562,93564],{},[898,93561,900],{},[1716,93563,2787],{},[1712,93565,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[898,93567,2468],{"mathvariant":2003},[6927,93569,93570,93572],{},[898,93571,1734],{},[1716,93573,2787],{},[1712,93575,1714],{},[898,93577,4445],{},[6927,93579,93580,93582],{},[898,93581,900],{},[1716,93583,2222],{},[898,93585,2468],{"mathvariant":2003},[6927,93587,93588,93590],{},[898,93589,1734],{},[1716,93591,2222],{},[1712,93593,3145],{},[898,93595,4445],{},[6927,93597,93598,93600],{},[898,93599,900],{},[1716,93601,2787],{},[898,93603,2468],{"mathvariant":2003},[6927,93605,93606,93608],{},[898,93607,1734],{},[1716,93609,2787],{},[898,93611,1659],{"mathvariant":2003},[25637,93613],{"width":32951},[25637,93615,93616],{},[1762,93617,93618],{},"(6.3)",[902,93620,93621],{"encoding":904},"\\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}",[724,93623,80344,93624,1659],{},[883,93625,93627],{"className":93626},[886],[888,93628,93629],{"xmlns":890},[892,93630,93631,93701],{},[895,93632,93633,93635,93637,93639,93641,93643,93649,93651,93653,93659,93661,93667,93669,93671,93677,93679,93681,93683,93685,93691,93693,93699],{},[898,93634,2004],{"mathvariant":2003},[898,93636,900],{},[1712,93638,1714],{},[898,93640,900],{},[1712,93642,1904],{"stretchy":1903},[6927,93644,93645,93647],{},[898,93646,1734],{},[1716,93648,2222],{},[1712,93650,3145],{},[898,93652,2468],{"mathvariant":2003},[6927,93654,93655,93657],{},[898,93656,1734],{},[1716,93658,2222],{},[1712,93660,3138],{"separator":2565},[6927,93662,93663,93665],{},[898,93664,1734],{},[1716,93666,2787],{},[1712,93668,3145],{},[898,93670,2468],{"mathvariant":2003},[6927,93672,93673,93675],{},[898,93674,1734],{},[1716,93676,2787],{},[1712,93678,1910],{"stretchy":1903},[1712,93680,2219],{},[898,93682,900],{},[1712,93684,1904],{"stretchy":1903},[6927,93686,93687,93689],{},[898,93688,1734],{},[1716,93690,2222],{},[1712,93692,3138],{"separator":2565},[6927,93694,93695,93697],{},[898,93696,1734],{},[1716,93698,2787],{},[1712,93700,1910],{"stretchy":1903},[902,93702,93703],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,93705,93707],{"id":93706},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,93709,93710,93711,93714,93715,93718],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,93712,93713],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,93716,93717],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,93720,93721,93724,93725,46689,93751,93777,93778,1343,93810,93842,93843,1655,93897,93951],{},[38,93722,93723],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,93726,93728],{"className":93727},[886],[888,93729,93730],{"xmlns":890},[892,93731,93732,93748],{},[895,93733,93734,93740,93742],{},[6927,93735,93736,93738],{},[898,93737,1734],{},[1716,93739,2787],{},[1712,93741,1714],{},[6927,93743,93744,93746],{},[898,93745,207],{},[1716,93747,2085],{},[902,93749,93750],{"encoding":904},"Q_2 = a_0",[883,93752,93754],{"className":93753},[886],[888,93755,93756],{"xmlns":890},[892,93757,93758,93774],{},[895,93759,93760,93766,93768],{},[6927,93761,93762,93764],{},[898,93763,1734],{},[1716,93765,2222],{},[1712,93767,1714],{},[6927,93769,93770,93772],{},[898,93771,7544],{},[1716,93773,2085],{},[902,93775,93776],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,93779,93781],{"className":93780},[886],[888,93782,93783],{"xmlns":890},[892,93784,93785,93807],{},[895,93786,93787,93789,93791,93797,93799,93805],{},[898,93788,900],{},[1712,93790,1904],{"stretchy":1903},[6927,93792,93793,93795],{},[898,93794,1734],{},[1716,93796,2222],{},[1712,93798,3138],{"separator":2565},[6927,93800,93801,93803],{},[898,93802,207],{},[1716,93804,2085],{},[1712,93806,1910],{"stretchy":1903},[902,93808,93809],{"encoding":904},"U(Q_1, a_0)",[883,93811,93813],{"className":93812},[886],[888,93814,93815],{"xmlns":890},[892,93816,93817,93839],{},[895,93818,93819,93821,93823,93829,93831,93837],{},[898,93820,900],{},[1712,93822,1904],{"stretchy":1903},[6927,93824,93825,93827],{},[898,93826,7544],{},[1716,93828,2085],{},[1712,93830,3138],{"separator":2565},[6927,93832,93833,93835],{},[898,93834,1734],{},[1716,93836,2787],{},[1712,93838,1910],{"stretchy":1903},[902,93840,93841],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,93844,93846],{"className":93845},[886],[888,93847,93848],{"xmlns":890},[892,93849,93850,93894],{},[895,93851,93852,93890,93892],{},[2563,93853,93854],{"scriptlevel":2085,"displaystyle":2565},[2567,93855,93856,93880],{},[895,93857,93858,93860,93862,93864,93870,93872,93878],{},[898,93859,2468],{"mathvariant":2003},[898,93861,900],{},[1712,93863,1904],{"stretchy":1903},[6927,93865,93866,93868],{},[898,93867,1734],{},[1716,93869,2222],{},[1712,93871,3138],{"separator":2565},[6927,93873,93874,93876],{},[898,93875,207],{},[1716,93877,2085],{},[1712,93879,1910],{"stretchy":1903},[895,93881,93882,93884],{},[898,93883,2468],{"mathvariant":2003},[6927,93885,93886,93888],{},[898,93887,1734],{},[1716,93889,2222],{},[1712,93891,2302],{},[1716,93893,2085],{},[902,93895,93896],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,93898,93900],{"className":93899},[886],[888,93901,93902],{"xmlns":890},[892,93903,93904,93948],{},[895,93905,93906,93944,93946],{},[2563,93907,93908],{"scriptlevel":2085,"displaystyle":2565},[2567,93909,93910,93934],{},[895,93911,93912,93914,93916,93918,93924,93926,93932],{},[898,93913,2468],{"mathvariant":2003},[898,93915,900],{},[1712,93917,1904],{"stretchy":1903},[6927,93919,93920,93922],{},[898,93921,7544],{},[1716,93923,2085],{},[1712,93925,3138],{"separator":2565},[6927,93927,93928,93930],{},[898,93929,1734],{},[1716,93931,2787],{},[1712,93933,1910],{"stretchy":1903},[895,93935,93936,93938],{},[898,93937,2468],{"mathvariant":2003},[6927,93939,93940,93942],{},[898,93941,1734],{},[1716,93943,2787],{},[1712,93945,2302],{},[1716,93947,2085],{},[902,93949,93950],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,93953,93955],{"className":93954},[886],[888,93956,93957],{"xmlns":890,"display":32941},[892,93958,93959,94004],{},[25629,93960,93961],{"width":32946},[25634,93962,93963,93965,93997,93999],{},[25637,93964],{"width":32951},[25637,93966,93967],{},[895,93968,93969,93977,93979,93981,93983,93985,93993,93995],{},[6989,93970,93971,93973,93975],{},[898,93972,900],{},[1716,93974,2222],{},[1712,93976,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,93978,2302],{},[1716,93980,2085],{},[1712,93982,3138],{"separator":2565},[3690,93984],{"width":20158},[6989,93986,93987,93989,93991],{},[898,93988,900],{},[1716,93990,2787],{},[1712,93992,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,93994,2302],{},[1716,93996,17334],{},[25637,93998],{"width":32951},[25637,94000,94001],{},[1762,94002,94003],{},"(6.4)",[902,94005,94006],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,94008,94009,94010,94012],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,94011,57552],{}," — užitečnost roste s množstvím každého zboží.",[724,94014,94015,94018,94019,94049,94050,2854],{},[38,94016,94017],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,94020,94022],{"className":94021},[886],[888,94023,94024],{"xmlns":890},[892,94025,94026,94046],{},[895,94027,94028,94036,94038],{},[6989,94029,94030,94032,94034],{},[898,94031,900],{},[1716,94033,2222],{},[1712,94035,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,94037,3138],{"separator":2565},[6989,94039,94040,94042,94044],{},[898,94041,900],{},[1716,94043,2787],{},[1712,94045,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,94047,94048],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,94051,94052],{},"záporné",[883,94054,94056],{"className":94055},[886],[888,94057,94058],{"xmlns":890,"display":32941},[892,94059,94060,94113],{},[25629,94061,94062],{"width":32946},[25634,94063,94064,94066,94106,94108],{},[25637,94065],{"width":32951},[25637,94067,94068],{},[895,94069,94070,94082,94084,94086,94088,94090,94102,94104],{},[6989,94071,94072,94074,94076],{},[898,94073,900],{},[1716,94075,8316],{},[895,94077,94078,94080],{},[1712,94079,2243],{"mathvariant":2003},[1712,94081,2243],{"mathvariant":2003},[1712,94083,2252],{},[1716,94085,2085],{},[1712,94087,3138],{"separator":2565},[3690,94089],{"width":20158},[6989,94091,94092,94094,94096],{},[898,94093,900],{},[1716,94095,37421],{},[895,94097,94098,94100],{},[1712,94099,2243],{"mathvariant":2003},[1712,94101,2243],{"mathvariant":2003},[1712,94103,2252],{},[1716,94105,17334],{},[25637,94107],{"width":32951},[25637,94109,94110],{},[1762,94111,94112],{},"(6.5)",[902,94114,94115],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,94117,94118,94119,94122,94123,1659],{},"Podmínka (6.5) je známa jako ",[38,94120,94121],{},"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 ",[207,94124,94126],{"className":94125,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,94128,94129,94130,1655,94162,94194,94195,1655,94221,94247,94248,94276,94277,1655,94279,94281,94282,94317],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,94131,94133],{"className":94132},[886],[888,94134,94135],{"xmlns":890},[892,94136,94137,94159],{},[895,94138,94139,94141,94143,94149,94151,94157],{},[898,94140,900],{},[1712,94142,1904],{"stretchy":1903},[6927,94144,94145,94147],{},[898,94146,1734],{},[1716,94148,2222],{},[1712,94150,3138],{"separator":2565},[6927,94152,94153,94155],{},[898,94154,7544],{},[1716,94156,2085],{},[1712,94158,1910],{"stretchy":1903},[902,94160,94161],{"encoding":904},"U(Q_1, b_0)",[883,94163,94165],{"className":94164},[886],[888,94166,94167],{"xmlns":890},[892,94168,94169,94191],{},[895,94170,94171,94173,94175,94181,94183,94189],{},[898,94172,900],{},[1712,94174,1904],{"stretchy":1903},[6927,94176,94177,94179],{},[898,94178,207],{},[1716,94180,2085],{},[1712,94182,3138],{"separator":2565},[6927,94184,94185,94187],{},[898,94186,1734],{},[1716,94188,2787],{},[1712,94190,1910],{"stretchy":1903},[902,94192,94193],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,94196,94198],{"className":94197},[886],[888,94199,94200],{"xmlns":890},[892,94201,94202,94218],{},[895,94203,94204,94206,94208,94210,94216],{},[1712,94205,1904],{"stretchy":1903},[898,94207,900],{},[1712,94209,3138],{"separator":2565},[6927,94211,94212,94214],{},[898,94213,1734],{},[1716,94215,2222],{},[1712,94217,1910],{"stretchy":1903},[902,94219,94220],{"encoding":904},"(U, Q_1)",[883,94222,94224],{"className":94223},[886],[888,94225,94226],{"xmlns":890},[892,94227,94228,94244],{},[895,94229,94230,94232,94234,94236,94242],{},[1712,94231,1904],{"stretchy":1903},[898,94233,900],{},[1712,94235,3138],{"separator":2565},[6927,94237,94238,94240],{},[898,94239,1734],{},[1716,94241,2787],{},[1712,94243,1910],{"stretchy":1903},[902,94245,94246],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,94249,94251],{"className":94250},[886],[888,94252,94253],{"xmlns":890},[892,94254,94255,94273],{},[895,94256,94257,94259,94261,94263,94265,94267,94269,94271],{},[898,94258,900],{},[1712,94260,1904],{"stretchy":1903},[1716,94262,2085],{},[1712,94264,3138],{"separator":2565},[1716,94266,2085],{},[1712,94268,1910],{"stretchy":1903},[1712,94270,1714],{},[1716,94272,2085],{},[902,94274,94275],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,94278,18531],{},[38,94280,43363],{},". Typický tvar grafu ",[883,94283,94285],{"className":94284},[886],[888,94286,94287],{"xmlns":890},[892,94288,94289,94315],{},[895,94290,94291,94293,94295,94297,94299,94305,94307,94313],{},[898,94292,900],{},[1712,94294,1714],{},[898,94296,900],{},[1712,94298,1904],{"stretchy":1903},[6927,94300,94301,94303],{},[898,94302,1734],{},[1716,94304,2222],{},[1712,94306,3138],{"separator":2565},[6927,94308,94309,94311],{},[898,94310,1734],{},[1716,94312,2787],{},[1712,94314,1910],{"stretchy":1903},[902,94316,92331],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,94319,94320],{},[614,94321,94322,94323,93363,94351,94372,94373,93363,94401,94423],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,94324,94326],{"className":94325},[886],[888,94327,94328],{"xmlns":890},[892,94329,94330,94348],{},[895,94331,94332,94334,94336,94342,94344,94346],{},[898,94333,900],{},[1712,94335,1904],{"stretchy":1903},[6927,94337,94338,94340],{},[898,94339,1734],{},[1716,94341,2222],{},[1712,94343,3138],{"separator":2565},[898,94345,7544],{},[1712,94347,1910],{"stretchy":1903},[902,94349,94350],{"encoding":904},"U(Q_1, b)",[883,94352,94354],{"className":94353},[886],[888,94355,94356],{"xmlns":890},[892,94357,94358,94370],{},[895,94359,94360,94366,94368],{},[6927,94361,94362,94364],{},[898,94363,1734],{},[1716,94365,2787],{},[1712,94367,1714],{},[898,94369,7544],{},[902,94371,93385],{"encoding":904}," (vlevo) a ",[883,94374,94376],{"className":94375},[886],[888,94377,94378],{"xmlns":890},[892,94379,94380,94398],{},[895,94381,94382,94384,94386,94388,94390,94396],{},[898,94383,900],{},[1712,94385,1904],{"stretchy":1903},[898,94387,207],{},[1712,94389,3138],{"separator":2565},[6927,94391,94392,94394],{},[898,94393,1734],{},[1716,94395,2787],{},[1712,94397,1910],{"stretchy":1903},[902,94399,94400],{"encoding":904},"U(a, Q_2)",[883,94402,94404],{"className":94403},[886],[888,94405,94406],{"xmlns":890},[892,94407,94408,94420],{},[895,94409,94410,94416,94418],{},[6927,94411,94412,94414],{},[898,94413,1734],{},[1716,94415,2222],{},[1712,94417,1714],{},[898,94419,207],{},[902,94421,94422],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,94425,94426],{},[614,94427,94428,94429,94464,94465,94495,94496,1655,94519,94541,94542,1659],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,94430,94432],{"className":94431},[886],[888,94433,94434],{"xmlns":890},[892,94435,94436,94462],{},[895,94437,94438,94440,94442,94444,94446,94452,94454,94460],{},[898,94439,900],{},[1712,94441,1714],{},[898,94443,900],{},[1712,94445,1904],{"stretchy":1903},[6927,94447,94448,94450],{},[898,94449,1734],{},[1716,94451,2222],{},[1712,94453,3138],{"separator":2565},[6927,94455,94456,94458],{},[898,94457,1734],{},[1716,94459,2787],{},[1712,94461,1910],{"stretchy":1903},[902,94463,92331],{"encoding":904}," nad rovinou ",[883,94466,94468],{"className":94467},[886],[888,94469,94470],{"xmlns":890},[892,94471,94472,94492],{},[895,94473,94474,94476,94482,94484,94490],{},[1712,94475,1904],{"stretchy":1903},[6927,94477,94478,94480],{},[898,94479,1734],{},[1716,94481,2222],{},[1712,94483,3138],{"separator":2565},[6927,94485,94486,94488],{},[898,94487,1734],{},[1716,94489,2787],{},[1712,94491,1910],{"stretchy":1903},[902,94493,94494],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,94497,94499],{"className":94498},[886],[888,94500,94501],{"xmlns":890},[892,94502,94503,94516],{},[895,94504,94505,94511,94513],{},[6927,94506,94507,94509],{},[898,94508,1734],{},[1716,94510,2222],{},[1712,94512,1714],{},[1762,94514,94515],{},"const",[902,94517,94518],{"encoding":904},"Q_1 = \\text{const}",[883,94520,94522],{"className":94521},[886],[888,94523,94524],{"xmlns":890},[892,94525,94526,94538],{},[895,94527,94528,94534,94536],{},[6927,94529,94530,94532],{},[898,94531,1734],{},[1716,94533,2787],{},[1712,94535,1714],{},[1762,94537,94515],{},[902,94539,94540],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,94543,94545],{"className":94544},[886],[888,94546,94547],{"xmlns":890},[892,94548,94549,94575],{},[895,94550,94551,94553,94555,94561,94563,94569,94571,94573],{},[898,94552,900],{},[1712,94554,1904],{"stretchy":1903},[6927,94556,94557,94559],{},[898,94558,1734],{},[1716,94560,2222],{},[1712,94562,3138],{"separator":2565},[6927,94564,94565,94567],{},[898,94566,1734],{},[1716,94568,2787],{},[1712,94570,1910],{"stretchy":1903},[1712,94572,1714],{},[898,94574,7585],{},[902,94576,14640],{"encoding":904},[198,94578,94580,94581],{"id":94579},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,94582,94584],{"className":94583},[886],[888,94585,94586],{"xmlns":890},[892,94587,94588,94622],{},[895,94589,94590,94592,94594,94608],{},[898,94591,900],{},[1712,94593,1714],{},[6989,94595,94596,94598,94600],{},[898,94597,1734],{},[1716,94599,2222],{},[895,94601,94602,94604,94606],{},[1716,94603,2222],{},[898,94605,2473],{"mathvariant":2003},[1716,94607,2787],{},[6989,94609,94610,94612,94614],{},[898,94611,1734],{},[1716,94613,2787],{},[895,94615,94616,94618,94620],{},[1716,94617,2222],{},[898,94619,2473],{"mathvariant":2003},[1716,94621,6198],{},[902,94623,94624],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,94626,94627],{},[38,94628,94629],{},"Ověření (6.4) a (6.5).",[883,94631,94633],{"className":94632},[886],[888,94634,94635],{"xmlns":890,"display":32941},[892,94636,94637,94741],{},[895,94638,94639,94647,94649,94657,94673,94687,94689,94691,94699,94701,94709,94723,94739],{},[6989,94640,94641,94643,94645],{},[898,94642,900],{},[1716,94644,2222],{},[1712,94646,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,94648,1714],{},[2563,94650,94651],{"scriptlevel":2085,"displaystyle":1903},[2567,94652,94653,94655],{},[1716,94654,2222],{},[1716,94656,2787],{},[6989,94658,94659,94661,94663],{},[898,94660,1734],{},[1716,94662,2222],{},[895,94664,94665,94667,94669,94671],{},[1712,94666,2219],{},[1716,94668,2222],{},[898,94670,2473],{"mathvariant":2003},[1716,94672,2787],{},[6989,94674,94675,94677,94679],{},[898,94676,1734],{},[1716,94678,2787],{},[895,94680,94681,94683,94685],{},[1716,94682,2222],{},[898,94684,2473],{"mathvariant":2003},[1716,94686,6198],{},[1712,94688,3138],{"separator":2565},[3690,94690],{"width":20158},[6989,94692,94693,94695,94697],{},[898,94694,900],{},[1716,94696,2787],{},[1712,94698,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,94700,1714],{},[2563,94702,94703],{"scriptlevel":2085,"displaystyle":1903},[2567,94704,94705,94707],{},[1716,94706,2222],{},[1716,94708,6198],{},[6989,94710,94711,94713,94715],{},[898,94712,1734],{},[1716,94714,2222],{},[895,94716,94717,94719,94721],{},[1716,94718,2222],{},[898,94720,2473],{"mathvariant":2003},[1716,94722,2787],{},[6989,94724,94725,94727,94729],{},[898,94726,1734],{},[1716,94728,2787],{},[895,94730,94731,94733,94735,94737],{},[1712,94732,2219],{},[1716,94734,2787],{},[898,94736,2473],{"mathvariant":2003},[1716,94738,6198],{},[1712,94740,3138],{"separator":2565},[902,94742,94743],{"encoding":904},"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},",[724,94745,94746,94747,94781],{},"zřejmě ",[883,94748,94750],{"className":94749},[886],[888,94751,94752],{"xmlns":890},[892,94753,94754,94778],{},[895,94755,94756,94764,94766,94774,94776],{},[6989,94757,94758,94760,94762],{},[898,94759,900],{},[1716,94761,2222],{},[1712,94763,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,94765,3138],{"separator":2565},[6989,94767,94768,94770,94772],{},[898,94769,900],{},[1716,94771,2787],{},[1712,94773,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,94775,2302],{},[1716,94777,2085],{},[902,94779,94780],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,94783,94785],{"className":94784},[886],[888,94786,94787],{"xmlns":890,"display":32941},[892,94788,94789,94905],{},[895,94790,94791,94803,94805,94807,94815,94831,94845,94847,94849,94861,94863,94865,94873,94887,94903],{},[6989,94792,94793,94795,94797],{},[898,94794,900],{},[1716,94796,8316],{},[895,94798,94799,94801],{},[1712,94800,2243],{"mathvariant":2003},[1712,94802,2243],{"mathvariant":2003},[1712,94804,1714],{},[1712,94806,2219],{},[2563,94808,94809],{"scriptlevel":2085,"displaystyle":1903},[2567,94810,94811,94813],{},[1716,94812,2222],{},[1716,94814,2975],{},[6989,94816,94817,94819,94821],{},[898,94818,1734],{},[1716,94820,2222],{},[895,94822,94823,94825,94827,94829],{},[1712,94824,2219],{},[1716,94826,6198],{},[898,94828,2473],{"mathvariant":2003},[1716,94830,2787],{},[6989,94832,94833,94835,94837],{},[898,94834,1734],{},[1716,94836,2787],{},[895,94838,94839,94841,94843],{},[1716,94840,2222],{},[898,94842,2473],{"mathvariant":2003},[1716,94844,6198],{},[1712,94846,3138],{"separator":2565},[3690,94848],{"width":20158},[6989,94850,94851,94853,94855],{},[898,94852,900],{},[1716,94854,37421],{},[895,94856,94857,94859],{},[1712,94858,2243],{"mathvariant":2003},[1712,94860,2243],{"mathvariant":2003},[1712,94862,1714],{},[1712,94864,2219],{},[2563,94866,94867],{"scriptlevel":2085,"displaystyle":1903},[2567,94868,94869,94871],{},[1716,94870,2787],{},[1716,94872,1780],{},[6989,94874,94875,94877,94879],{},[898,94876,1734],{},[1716,94878,2222],{},[895,94880,94881,94883,94885],{},[1716,94882,2222],{},[898,94884,2473],{"mathvariant":2003},[1716,94886,2787],{},[6989,94888,94889,94891,94893],{},[898,94890,1734],{},[1716,94892,2787],{},[895,94894,94895,94897,94899,94901],{},[1712,94896,2219],{},[1716,94898,3068],{},[898,94900,2473],{"mathvariant":2003},[1716,94902,6198],{},[1712,94904,3138],{"separator":2565},[902,94906,94907],{"encoding":904},"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},",[724,94909,94910,94911,94953],{},"opět ",[883,94912,94914],{"className":94913},[886],[888,94915,94916],{"xmlns":890},[892,94917,94918,94950],{},[895,94919,94920,94932,94934,94946,94948],{},[6989,94921,94922,94924,94926],{},[898,94923,900],{},[1716,94925,8316],{},[895,94927,94928,94930],{},[1712,94929,2243],{"mathvariant":2003},[1712,94931,2243],{"mathvariant":2003},[1712,94933,3138],{"separator":2565},[6989,94935,94936,94938,94940],{},[898,94937,900],{},[1716,94939,37421],{},[895,94941,94942,94944],{},[1712,94943,2243],{"mathvariant":2003},[1712,94945,2243],{"mathvariant":2003},[1712,94947,2252],{},[1716,94949,2085],{},[902,94951,94952],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,94955,94956],{},[38,94957,94958,94959,1659],{},"(a) Mezní užitečnosti v bodě ",[883,94960,94962],{"className":94961},[886],[888,94963,94964],{"xmlns":890},[892,94965,94966,94978],{},[895,94967,94968,94970,94972,94974,94976],{},[1712,94969,7910],{"stretchy":1903},[1716,94971,1739],{},[1712,94973,3138],{"separator":2565},[1716,94975,6195],{},[1712,94977,7925],{"stretchy":1903},[902,94979,94980],{"encoding":904},"[100, 200]",[883,94982,94984],{"className":94983},[886],[888,94985,94986],{"xmlns":890,"display":32941},[892,94987,94988,95055],{},[895,94989,94990,94992,94998,95000,95002,95004,95006,95008,95010,95018,95020,95034,95036,95048,95050,95053],{},[898,94991,4445],{},[6927,94993,94994,94996],{},[898,94995,900],{},[1716,94997,2222],{},[1712,94999,1904],{"stretchy":1903},[1716,95001,1739],{},[1712,95003,3138],{"separator":2565},[1716,95005,6195],{},[1712,95007,1910],{"stretchy":1903},[1712,95009,1714],{},[2563,95011,95012],{"scriptlevel":2085,"displaystyle":1903},[2567,95013,95014,95016],{},[1716,95015,2222],{},[1716,95017,2787],{},[1712,95019,1783],{},[2037,95021,95022,95024],{},[1716,95023,1739],{},[895,95025,95026,95028,95030,95032],{},[1712,95027,2219],{},[1716,95029,2222],{},[898,95031,2473],{"mathvariant":2003},[1716,95033,2787],{},[1712,95035,1783],{},[2037,95037,95038,95040],{},[1716,95039,6195],{},[895,95041,95042,95044,95046],{},[1716,95043,2222],{},[898,95045,2473],{"mathvariant":2003},[1716,95047,6198],{},[1712,95049,3712],{},[1716,95051,95052],{},"0,4204",[1712,95054,3138],{"separator":2565},[902,95056,95057],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,95059,95061],{"className":95060},[886],[888,95062,95063],{"xmlns":890,"display":32941},[892,95064,95065,95130],{},[895,95066,95067,95069,95075,95077,95079,95081,95083,95085,95087,95095,95097,95109,95111,95125,95127],{},[898,95068,4445],{},[6927,95070,95071,95073],{},[898,95072,900],{},[1716,95074,2787],{},[1712,95076,1904],{"stretchy":1903},[1716,95078,1739],{},[1712,95080,3138],{"separator":2565},[1716,95082,6195],{},[1712,95084,1910],{"stretchy":1903},[1712,95086,1714],{},[2563,95088,95089],{"scriptlevel":2085,"displaystyle":1903},[2567,95090,95091,95093],{},[1716,95092,2222],{},[1716,95094,6198],{},[1712,95096,1783],{},[2037,95098,95099,95101],{},[1716,95100,1739],{},[895,95102,95103,95105,95107],{},[1716,95104,2222],{},[898,95106,2473],{"mathvariant":2003},[1716,95108,2787],{},[1712,95110,1783],{},[2037,95112,95113,95115],{},[1716,95114,6195],{},[895,95116,95117,95119,95121,95123],{},[1712,95118,2219],{},[1716,95120,2787],{},[898,95122,2473],{"mathvariant":2003},[1716,95124,6198],{},[1712,95126,3712],{},[1716,95128,95129],{},"0,63067.",[902,95131,95132],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,95134,95135,3245,95137,95172,95173,95194,95195,95212],{},[614,95136,7040],{},[883,95138,95140],{"className":95139},[886],[888,95141,95142],{"xmlns":890},[892,95143,95144,95169],{},[895,95145,95146,95148,95154,95156,95158,95160,95162,95164,95166],{},[898,95147,4445],{},[6927,95149,95150,95152],{},[898,95151,900],{},[1716,95153,2787],{},[1712,95155,1904],{"stretchy":1903},[1716,95157,1739],{},[1712,95159,3138],{"separator":2565},[1716,95161,6195],{},[1712,95163,1910],{"stretchy":1903},[1712,95165,3712],{},[1716,95167,95168],{},"0,63067",[902,95170,95171],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,95174,95176],{"className":95175},[886],[888,95177,95178],{"xmlns":890},[892,95179,95180,95192],{},[895,95181,95182,95184,95186,95188,95190],{},[1712,95183,7910],{"stretchy":1903},[1716,95185,1739],{},[1712,95187,3138],{"separator":2565},[1716,95189,6195],{},[1712,95191,7925],{"stretchy":1903},[902,95193,94980],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,95196,95198],{"className":95197},[886],[888,95199,95200],{"xmlns":890},[892,95201,95202,95210],{},[895,95203,95204],{},[6927,95205,95206,95208],{},[898,95207,1734],{},[1716,95209,2787],{},[902,95211,33896],{"encoding":904}," přibližně o 0,63067.",[724,95214,95215,95234,95235,44059,95256,95273,95274,95300,95301,95318,95319,8558],{},[38,95216,95217,95218,95233],{},"(b) Odhad změny ",[883,95219,95221],{"className":95220},[886],[888,95222,95223],{"xmlns":890},[892,95224,95225,95231],{},[895,95226,95227,95229],{},[898,95228,2004],{"mathvariant":2003},[898,95230,900],{},[902,95232,93476],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,95236,95238],{"className":95237},[886],[888,95239,95240],{"xmlns":890},[892,95241,95242,95254],{},[895,95243,95244,95246,95248,95250,95252],{},[1712,95245,7910],{"stretchy":1903},[1716,95247,1739],{},[1712,95249,3138],{"separator":2565},[1716,95251,6195],{},[1712,95253,7925],{"stretchy":1903},[902,95255,94980],{"encoding":904},[883,95257,95259],{"className":95258},[886],[888,95260,95261],{"xmlns":890},[892,95262,95263,95271],{},[895,95264,95265],{},[6927,95266,95267,95269],{},[898,95268,1734],{},[1716,95270,2222],{},[902,95272,33877],{"encoding":904}," na 98 (tj. ",[883,95275,95277],{"className":95276},[886],[888,95278,95279],{"xmlns":890},[892,95280,95281,95297],{},[895,95282,95283,95285,95291,95293,95295],{},[898,95284,2468],{"mathvariant":2003},[6927,95286,95287,95289],{},[898,95288,1734],{},[1716,95290,2222],{},[1712,95292,1714],{},[1712,95294,2219],{},[1716,95296,2787],{},[902,95298,95299],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,95302,95304],{"className":95303},[886],[888,95305,95306],{"xmlns":890},[892,95307,95308,95316],{},[895,95309,95310],{},[6927,95311,95312,95314],{},[898,95313,1734],{},[1716,95315,2787],{},[902,95317,33896],{"encoding":904}," o 3 (tj. ",[883,95320,95322],{"className":95321},[886],[888,95323,95324],{"xmlns":890},[892,95325,95326,95340],{},[895,95327,95328,95330,95336,95338],{},[898,95329,2468],{"mathvariant":2003},[6927,95331,95332,95334],{},[898,95333,1734],{},[1716,95335,2787],{},[1712,95337,1714],{},[1716,95339,6198],{},[902,95341,95342],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,95344,95346],{"className":95345},[886],[888,95347,95348],{"xmlns":890,"display":32941},[892,95349,95350,95401],{},[895,95351,95352,95354,95356,95358,95360,95362,95364,95366,95368,95370,95372,95374,95376,95378,95380,95382,95384,95386,95388,95391,95393,95396,95398],{},[898,95353,2004],{"mathvariant":2003},[898,95355,900],{},[1712,95357,3740],{},[898,95359,2468],{"mathvariant":2003},[898,95361,900],{},[1712,95363,1714],{},[1716,95365,95052],{},[1712,95367,1783],{},[1712,95369,1904],{"stretchy":1903},[1712,95371,2219],{},[1716,95373,2787],{},[1712,95375,1910],{"stretchy":1903},[1712,95377,3145],{},[1716,95379,95168],{},[1712,95381,1783],{},[1716,95383,6198],{},[1712,95385,1714],{},[1712,95387,2219],{},[1716,95389,95390],{},"0,8408",[1712,95392,3145],{},[1716,95394,95395],{},"1,89201",[1712,95397,3712],{},[1716,95399,95400],{},"1,05.",[902,95402,95403],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,95405,95406,95407,95410,95411,95462,95463,1659],{},"Užitečnost se tedy zvýší přibližně o ",[38,95408,95409],{},"1,05",". Skutečná změna je ",[883,95412,95414],{"className":95413},[886],[888,95415,95416],{"xmlns":890},[892,95417,95418,95459],{},[895,95419,95420,95422,95424,95426,95428,95430,95433,95435,95438,95440,95442,95444,95446,95448,95450,95452,95454,95456],{},[898,95421,2004],{"mathvariant":2003},[898,95423,900],{},[1712,95425,1714],{},[898,95427,900],{},[1712,95429,1904],{"stretchy":1903},[1716,95431,95432],{},"98",[1712,95434,3138],{"separator":2565},[1716,95436,95437],{},"203",[1712,95439,1910],{"stretchy":1903},[1712,95441,2219],{},[898,95443,900],{},[1712,95445,1904],{"stretchy":1903},[1716,95447,1739],{},[1712,95449,3138],{"separator":2565},[1716,95451,6195],{},[1712,95453,1910],{"stretchy":1903},[1712,95455,3712],{},[1716,95457,95458],{},"1,031",[902,95460,95461],{"encoding":904},"\\Delta U = U(98, 203) - U(100, 200) \\doteq 1{,}031"," — relativní chyba odhadu je zhruba 2 %. Aproximace totálním diferenciálem je uspokojivá pro malé ",[883,95464,95466],{"className":95465},[886],[888,95467,95468],{"xmlns":890},[892,95469,95470,95490],{},[895,95471,95472,95474,95480,95482,95484],{},[898,95473,2468],{"mathvariant":2003},[6927,95475,95476,95478],{},[898,95477,1734],{},[1716,95479,2222],{},[1712,95481,3138],{"separator":2565},[898,95483,2468],{"mathvariant":2003},[6927,95485,95486,95488],{},[898,95487,1734],{},[1716,95489,2787],{},[902,95491,93506],{"encoding":904},[115,95493,95495],{"id":95494},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,95497,95498],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,95500,95502],{"className":95501},[886],[888,95503,95504],{"xmlns":890,"display":32941},[892,95505,95506,95565],{},[25629,95507,95508],{"width":32946},[25634,95509,95510,95512,95558,95560],{},[25637,95511],{"width":32951},[25637,95513,95514],{},[895,95515,95516,95518,95520,95526,95528,95534,95536,95538,95546,95548,95556],{},[898,95517,900],{},[1712,95519,1904],{"stretchy":1903},[6927,95521,95522,95524],{},[898,95523,1734],{},[1716,95525,2222],{},[1712,95527,3138],{"separator":2565},[6927,95529,95530,95532],{},[898,95531,1734],{},[1716,95533,2787],{},[1712,95535,1910],{"stretchy":1903},[1712,95537,1714],{},[6989,95539,95540,95542,95544],{},[898,95541,1734],{},[1716,95543,2222],{},[898,95545,207],{},[1712,95547,1783],{},[6989,95549,95550,95552,95554],{},[898,95551,1734],{},[1716,95553,2787],{},[898,95555,7544],{},[1712,95557,3138],{"separator":2565},[25637,95559],{"width":32951},[25637,95561,95562],{},[1762,95563,95564],{},"(6.6)",[902,95566,95567],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,95569,2101,95570,95588,95589,95591,95592,95596,95597,95627,95628,95650],{},[883,95571,95573],{"className":95572},[886],[888,95574,95575],{"xmlns":890},[892,95576,95577,95585],{},[895,95578,95579,95581,95583],{},[898,95580,207],{},[1712,95582,3138],{"separator":2565},[898,95584,7544],{},[902,95586,95587],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,95590,79574],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,95593,95595],{"className":95594,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,95598,95600],{"className":95599},[886],[888,95601,95602],{"xmlns":890},[892,95603,95604,95624],{},[895,95605,95606,95608,95610,95612,95614,95616,95618,95620,95622],{},[898,95607,207],{},[1712,95609,3138],{"separator":2565},[898,95611,7544],{},[1712,95613,4321],{},[1712,95615,1904],{"stretchy":1903},[1716,95617,2085],{},[1712,95619,3138],{"separator":2565},[1716,95621,2222],{},[1712,95623,1910],{"stretchy":1903},[902,95625,95626],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,95629,95631],{"className":95630},[886],[888,95632,95633],{"xmlns":890},[892,95634,95635,95647],{},[895,95636,95637,95639,95641,95643,95645],{},[898,95638,7544],{},[1712,95640,1714],{},[1716,95642,2222],{},[1712,95644,2219],{},[898,95646,207],{},[902,95648,95649],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,95652,95653],{},[3817,95654],{"alt":95655,"className":95656,"src":95657},"imek-cobb-douglas-3d-plus-ic",[210,3821],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,95659,95661],{"className":95660},[886],[888,95662,95663],{"xmlns":890,"display":32941},[892,95664,95665,95715],{},[895,95666,95667,95669,95671,95677,95679,95685,95687,95689,95697,95699,95713],{},[898,95668,900],{},[1712,95670,1904],{"stretchy":1903},[6927,95672,95673,95675],{},[898,95674,1734],{},[1716,95676,2222],{},[1712,95678,3138],{"separator":2565},[6927,95680,95681,95683],{},[898,95682,1734],{},[1716,95684,2787],{},[1712,95686,1910],{"stretchy":1903},[1712,95688,1714],{},[6989,95690,95691,95693,95695],{},[898,95692,1734],{},[1716,95694,2222],{},[898,95696,207],{},[1712,95698,1783],{},[6989,95700,95701,95703,95705],{},[898,95702,1734],{},[1716,95704,2787],{},[895,95706,95707,95709,95711],{},[1716,95708,2222],{},[1712,95710,2219],{},[898,95712,207],{},[898,95714,1659],{"mathvariant":2003},[902,95716,95717],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1636,95719,95720,95769,95891,96025],{},[724,95721,95722,95724,95725],{},[883,95723,57570],{}," Příklad 6.3 — ověření vlastností pro ",[883,95726,95728],{"className":95727},[886],[888,95729,95730],{"xmlns":890},[892,95731,95732,95766],{},[895,95733,95734,95736,95738,95752],{},[898,95735,900],{},[1712,95737,1714],{},[6989,95739,95740,95742,95744],{},[898,95741,1734],{},[1716,95743,2222],{},[895,95745,95746,95748,95750],{},[1716,95747,2222],{},[898,95749,2473],{"mathvariant":2003},[1716,95751,2975],{},[6989,95753,95754,95756,95758],{},[898,95755,1734],{},[1716,95757,2787],{},[895,95759,95760,95762,95764],{},[1716,95761,6198],{},[898,95763,2473],{"mathvariant":2003},[1716,95765,2975],{},[902,95767,95768],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,95770,95772],{"className":95771},[886],[888,95773,95774],{"xmlns":890,"display":32941},[892,95775,95776,95888],{},[895,95777,95778,95786,95788,95796,95812,95826,95828,95830,95832,95834,95842,95844,95852,95866,95882,95884,95886],{},[6989,95779,95780,95782,95784],{},[898,95781,900],{},[1716,95783,2222],{},[1712,95785,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,95787,1714],{},[2563,95789,95790],{"scriptlevel":2085,"displaystyle":1903},[2567,95791,95792,95794],{},[1716,95793,2222],{},[1716,95795,2975],{},[6989,95797,95798,95800,95802],{},[898,95799,1734],{},[1716,95801,2222],{},[895,95803,95804,95806,95808,95810],{},[1712,95805,2219],{},[1716,95807,6198],{},[898,95809,2473],{"mathvariant":2003},[1716,95811,2975],{},[6989,95813,95814,95816,95818],{},[898,95815,1734],{},[1716,95817,2787],{},[895,95819,95820,95822,95824],{},[1716,95821,6198],{},[898,95823,2473],{"mathvariant":2003},[1716,95825,2975],{},[1712,95827,2302],{},[1716,95829,2085],{},[1712,95831,3138],{"separator":2565},[3690,95833],{"width":20158},[6989,95835,95836,95838,95840],{},[898,95837,900],{},[1716,95839,2787],{},[1712,95841,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,95843,1714],{},[2563,95845,95846],{"scriptlevel":2085,"displaystyle":1903},[2567,95847,95848,95850],{},[1716,95849,6198],{},[1716,95851,2975],{},[6989,95853,95854,95856,95858],{},[898,95855,1734],{},[1716,95857,2222],{},[895,95859,95860,95862,95864],{},[1716,95861,2222],{},[898,95863,2473],{"mathvariant":2003},[1716,95865,2975],{},[6989,95867,95868,95870,95872],{},[898,95869,1734],{},[1716,95871,2787],{},[895,95873,95874,95876,95878,95880],{},[1712,95875,2219],{},[1716,95877,2222],{},[898,95879,2473],{"mathvariant":2003},[1716,95881,2975],{},[1712,95883,2302],{},[1716,95885,2085],{},[1712,95887,3138],{"separator":2565},[902,95889,95890],{"encoding":904},"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,",[883,95892,95894],{"className":95893},[886],[888,95895,95896],{"xmlns":890,"display":32941},[892,95897,95898,96022],{},[895,95899,95900,95912,95914,95916,95924,95940,95954,95956,95958,95960,95962,95974,95976,95978,95986,96000,96016,96018,96020],{},[6989,95901,95902,95904,95906],{},[898,95903,900],{},[1716,95905,8316],{},[895,95907,95908,95910],{},[1712,95909,2243],{"mathvariant":2003},[1712,95911,2243],{"mathvariant":2003},[1712,95913,1714],{},[1712,95915,2219],{},[2563,95917,95918],{"scriptlevel":2085,"displaystyle":1903},[2567,95919,95920,95922],{},[1716,95921,6198],{},[1716,95923,46737],{},[6989,95925,95926,95928,95930],{},[898,95927,1734],{},[1716,95929,2222],{},[895,95931,95932,95934,95936,95938],{},[1712,95933,2219],{},[1716,95935,29076],{},[898,95937,2473],{"mathvariant":2003},[1716,95939,2975],{},[6989,95941,95942,95944,95946],{},[898,95943,1734],{},[1716,95945,2787],{},[895,95947,95948,95950,95952],{},[1716,95949,6198],{},[898,95951,2473],{"mathvariant":2003},[1716,95953,2975],{},[1712,95955,2252],{},[1716,95957,2085],{},[1712,95959,3138],{"separator":2565},[3690,95961],{"width":20158},[6989,95963,95964,95966,95968],{},[898,95965,900],{},[1716,95967,37421],{},[895,95969,95970,95972],{},[1712,95971,2243],{"mathvariant":2003},[1712,95973,2243],{"mathvariant":2003},[1712,95975,1714],{},[1712,95977,2219],{},[2563,95979,95980],{"scriptlevel":2085,"displaystyle":1903},[2567,95981,95982,95984],{},[1716,95983,6198],{},[1716,95985,46737],{},[6989,95987,95988,95990,95992],{},[898,95989,1734],{},[1716,95991,2222],{},[895,95993,95994,95996,95998],{},[1716,95995,2222],{},[898,95997,2473],{"mathvariant":2003},[1716,95999,2975],{},[6989,96001,96002,96004,96006],{},[898,96003,1734],{},[1716,96005,2787],{},[895,96007,96008,96010,96012,96014],{},[1712,96009,2219],{},[1716,96011,3068],{},[898,96013,2473],{"mathvariant":2003},[1716,96015,2975],{},[1712,96017,2252],{},[1716,96019,2085],{},[1712,96021,3138],{"separator":2565},[902,96023,96024],{"encoding":904},"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,",[724,96026,96027],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,96029,96031],{"id":96030},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,96033,96034,96037],{},[38,96035,96036],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,96039,96041],{"className":96040},[886],[888,96042,96043],{"xmlns":890,"display":32941},[892,96044,96045,96088],{},[25629,96046,96047],{"width":32946},[25634,96048,96049,96051,96081,96083],{},[25637,96050],{"width":32951},[25637,96052,96053],{},[895,96054,96055,96057,96059,96065,96067,96073,96075,96077,96079],{},[898,96056,900],{},[1712,96058,1904],{"stretchy":1903},[6927,96060,96061,96063],{},[898,96062,1734],{},[1716,96064,2222],{},[1712,96066,3138],{"separator":2565},[6927,96068,96069,96071],{},[898,96070,1734],{},[1716,96072,2787],{},[1712,96074,1910],{"stretchy":1903},[1712,96076,1714],{},[898,96078,7585],{},[1712,96080,3138],{"separator":2565},[25637,96082],{"width":32951},[25637,96084,96085],{},[1762,96086,96087],{},"(6.7)",[902,96089,96090],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,96092,2101,96093,96106],{},[883,96094,96096],{"className":96095},[886],[888,96097,96098],{"xmlns":890},[892,96099,96100,96104],{},[895,96101,96102],{},[898,96103,7585],{},[902,96105,7585],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,96108,96110],{"className":96109},[886],[888,96111,96112],{"xmlns":890,"display":32941},[892,96113,96114,96155],{},[25629,96115,96116],{"width":32946},[25634,96117,96118,96120,96148,96150],{},[25637,96119],{"width":32951},[25637,96121,96122],{},[895,96123,96124,96132,96134,96142,96144,96146],{},[6989,96125,96126,96128,96130],{},[898,96127,1734],{},[1716,96129,2222],{},[898,96131,207],{},[1712,96133,1783],{},[6989,96135,96136,96138,96140],{},[898,96137,1734],{},[1716,96139,2787],{},[898,96141,7544],{},[1712,96143,1714],{},[898,96145,7585],{},[898,96147,1659],{"mathvariant":2003},[25637,96149],{"width":32951},[25637,96151,96152],{},[1762,96153,96154],{},"(6.8)",[902,96156,96157],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,96159,96160,96161,2149,96191,3245,96194,96207,96208,96243,96244,96261,96262,96291,96292,96295],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,96162,96164],{"className":96163},[886],[888,96165,96166],{"xmlns":890},[892,96167,96168,96188],{},[895,96169,96170,96172,96178,96180,96186],{},[1712,96171,7910],{"stretchy":1903},[6927,96173,96174,96176],{},[898,96175,1734],{},[1716,96177,2222],{},[1712,96179,3138],{"separator":2565},[6927,96181,96182,96184],{},[898,96183,1734],{},[1716,96185,2787],{},[1712,96187,7925],{"stretchy":1903},[902,96189,96190],{"encoding":904},"[Q_1, Q_2]",[38,96192,96193],{},"stejnou úrovní uspokojení",[883,96195,96197],{"className":96196},[886],[888,96198,96199],{"xmlns":890},[892,96200,96201,96205],{},[895,96202,96203],{},[898,96204,7585],{},[902,96206,7585],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,96209,96211],{"className":96210},[886],[888,96212,96213],{"xmlns":890},[892,96214,96215,96241],{},[895,96216,96217,96219,96221,96223,96225,96231,96233,96239],{},[898,96218,900],{},[1712,96220,1714],{},[898,96222,900],{},[1712,96224,1904],{"stretchy":1903},[6927,96226,96227,96229],{},[898,96228,1734],{},[1716,96230,2222],{},[1712,96232,3138],{"separator":2565},[6927,96234,96235,96237],{},[898,96236,1734],{},[1716,96238,2787],{},[1712,96240,1910],{"stretchy":1903},[902,96242,92331],{"encoding":904}," s rovinami ",[883,96245,96247],{"className":96246},[886],[888,96248,96249],{"xmlns":890},[892,96250,96251,96259],{},[895,96252,96253,96255,96257],{},[898,96254,900],{},[1712,96256,1714],{},[898,96258,7585],{},[902,96260,91547],{"encoding":904}," rovnoběžnými s rovinou ",[883,96263,96265],{"className":96264},[886],[888,96266,96267],{"xmlns":890},[892,96268,96269,96289],{},[895,96270,96271,96273,96279,96281,96287],{},[1712,96272,1904],{"stretchy":1903},[6927,96274,96275,96277],{},[898,96276,1734],{},[1716,96278,2222],{},[1712,96280,3138],{"separator":2565},[6927,96282,96283,96285],{},[898,96284,1734],{},[1716,96286,2787],{},[1712,96288,1910],{"stretchy":1903},[902,96290,94494],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,96293,96294],{},"izokvantami"," produkčních funkcí.",[724,96297,96298],{},[614,96299,96300,96301,94372,96319,96337,96338,1659],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,96302,96304],{"className":96303},[886],[888,96305,96306],{"xmlns":890},[892,96307,96308,96316],{},[895,96309,96310,96312,96314],{},[898,96311,207],{},[1712,96313,2252],{},[898,96315,7544],{},[902,96317,96318],{"encoding":904},"a \u003C b",[883,96320,96322],{"className":96321},[886],[888,96323,96324],{"xmlns":890},[892,96325,96326,96334],{},[895,96327,96328,96330,96332],{},[898,96329,207],{},[1712,96331,2302],{},[898,96333,7544],{},[902,96335,96336],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,96339,96341],{"className":96340},[886],[888,96342,96343],{"xmlns":890},[892,96344,96345,96369],{},[895,96346,96347,96353,96355,96361,96363],{},[6927,96348,96349,96351],{},[898,96350,7585],{},[1716,96352,2085],{},[1712,96354,2252],{},[6927,96356,96357,96359],{},[898,96358,7585],{},[1716,96360,2222],{},[1712,96362,2252],{},[6927,96364,96365,96367],{},[898,96366,7585],{},[1716,96368,2787],{},[902,96370,96371],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,96373,96374],{},[614,96375,96376,96377,96406,96407,96465,96466,96484],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,96378,96380],{"className":96379},[886],[888,96381,96382],{"xmlns":890},[892,96383,96384,96404],{},[895,96385,96386,96388,96394,96396,96402],{},[1712,96387,1904],{"stretchy":1903},[6927,96389,96390,96392],{},[898,96391,1734],{},[1716,96393,2222],{},[1712,96395,3138],{"separator":2565},[6927,96397,96398,96400],{},[898,96399,1734],{},[1716,96401,2787],{},[1712,96403,1910],{"stretchy":1903},[902,96405,94494],{"encoding":904},"; body ",[883,96408,96410],{"className":96409},[886],[888,96411,96412],{"xmlns":890},[892,96413,96414,96462],{},[895,96415,96416,96418,96420,96422,96428,96430,96436,96438,96440,96442,96444,96446,96452,96454,96460],{},[898,96417,2044],{},[1712,96419,1714],{},[1712,96421,7910],{"stretchy":1903},[6927,96423,96424,96426],{},[898,96425,207],{},[1716,96427,2222],{},[1712,96429,3138],{"separator":2565},[6927,96431,96432,96434],{},[898,96433,207],{},[1716,96435,2787],{},[1712,96437,7925],{"stretchy":1903},[1712,96439,3138],{"separator":2565},[898,96441,28128],{},[1712,96443,1714],{},[1712,96445,7910],{"stretchy":1903},[6927,96447,96448,96450],{},[898,96449,7544],{},[1716,96451,2222],{},[1712,96453,3138],{"separator":2565},[6927,96455,96456,96458],{},[898,96457,7544],{},[1716,96459,2787],{},[1712,96461,7925],{"stretchy":1903},[902,96463,96464],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,96467,96469],{"className":96468},[886],[888,96470,96471],{"xmlns":890},[892,96472,96473,96481],{},[895,96474,96475,96477,96479],{},[898,96476,8195],{},[1712,96478,3138],{"separator":2565},[898,96480,1969],{},[902,96482,96483],{"encoding":904},"C, D"," na vyšší hladině.",[1636,96486,96487],{},[724,96488,96489,96491,96492,96554,96555,96599,96600,96634,96635,31064,96653,96634,96707,31064,96725,96801],{},[883,96490,57570],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,96493,96495],{"className":96494},[886],[888,96496,96497],{"xmlns":890},[892,96498,96499,96551],{},[895,96500,96501,96503,96505,96511,96513,96519,96521,96523,96537],{},[898,96502,900],{},[1712,96504,1904],{"stretchy":1903},[6927,96506,96507,96509],{},[898,96508,1734],{},[1716,96510,2222],{},[1712,96512,3138],{"separator":2565},[6927,96514,96515,96517],{},[898,96516,1734],{},[1716,96518,2787],{},[1712,96520,1910],{"stretchy":1903},[1712,96522,1714],{},[6989,96524,96525,96527,96529],{},[898,96526,1734],{},[1716,96528,2222],{},[895,96530,96531,96533,96535],{},[1716,96532,2222],{},[898,96534,2473],{"mathvariant":2003},[1716,96536,2975],{},[6989,96538,96539,96541,96543],{},[898,96540,1734],{},[1716,96542,2787],{},[895,96544,96545,96547,96549],{},[1716,96546,6198],{},[898,96548,2473],{"mathvariant":2003},[1716,96550,2975],{},[902,96552,96553],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,96556,96558],{"className":96557},[886],[888,96559,96560],{"xmlns":890},[892,96561,96562,96596],{},[895,96563,96564,96578,96592,96594],{},[6989,96565,96566,96568,96570],{},[898,96567,1734],{},[1716,96569,2222],{},[895,96571,96572,96574,96576],{},[1716,96573,2222],{},[898,96575,2473],{"mathvariant":2003},[1716,96577,2975],{},[6989,96579,96580,96582,96584],{},[898,96581,1734],{},[1716,96583,2787],{},[895,96585,96586,96588,96590],{},[1716,96587,6198],{},[898,96589,2473],{"mathvariant":2003},[1716,96591,2975],{},[1712,96593,1714],{},[898,96595,7585],{},[902,96597,96598],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,96601,96603],{"className":96602},[886],[888,96604,96605],{"xmlns":890},[892,96606,96607,96631],{},[895,96608,96609,96615,96623,96625],{},[6927,96610,96611,96613],{},[898,96612,1734],{},[1716,96614,2222],{},[6989,96616,96617,96619,96621],{},[898,96618,1734],{},[1716,96620,2787],{},[1716,96622,6198],{},[1712,96624,1714],{},[2037,96626,96627,96629],{},[898,96628,7585],{},[1716,96630,2975],{},[902,96632,96633],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,96636,96638],{"className":96637},[886],[888,96639,96640],{"xmlns":890},[892,96641,96642,96650],{},[895,96643,96644,96646,96648],{},[898,96645,7585],{},[1712,96647,1714],{},[1716,96649,2222],{},[902,96651,96652],{"encoding":904},"c = 1",[883,96654,96656],{"className":96655},[886],[888,96657,96658],{"xmlns":890},[892,96659,96660,96704],{},[895,96661,96662,96668,96670,96686,96688],{},[6927,96663,96664,96666],{},[898,96665,1734],{},[1716,96667,2787],{},[1712,96669,1714],{},[6989,96671,96672,96674,96676],{},[898,96673,1734],{},[1716,96675,2222],{},[895,96677,96678,96680,96682,96684],{},[1712,96679,2219],{},[1716,96681,2222],{},[898,96683,2473],{"mathvariant":2003},[1716,96685,6198],{},[1712,96687,1714],{},[2563,96689,96690],{"scriptlevel":2085,"displaystyle":2565},[2567,96691,96692,96694],{},[1716,96693,2222],{},[86902,96695,96696,96702],{},[6927,96697,96698,96700],{},[898,96699,1734],{},[1716,96701,2222],{},[1716,96703,6198],{},[902,96705,96706],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,96708,96710],{"className":96709},[886],[888,96711,96712],{"xmlns":890},[892,96713,96714,96722],{},[895,96715,96716,96718,96720],{},[898,96717,7585],{},[1712,96719,1714],{},[1716,96721,2787],{},[902,96723,96724],{"encoding":904},"c = 2",[883,96726,96728],{"className":96727},[886],[888,96729,96730],{"xmlns":890},[892,96731,96732,96798],{},[895,96733,96734,96740,96742,96754,96756,96772,96774],{},[6927,96735,96736,96738],{},[898,96737,1734],{},[1716,96739,2787],{},[1712,96741,1714],{},[2037,96743,96744,96746],{},[1716,96745,2787],{},[895,96747,96748,96750,96752],{},[1716,96749,2975],{},[898,96751,2473],{"mathvariant":2003},[1716,96753,6198],{},[1712,96755,1783],{},[6989,96757,96758,96760,96762],{},[898,96759,1734],{},[1716,96761,2222],{},[895,96763,96764,96766,96768,96770],{},[1712,96765,2219],{},[1716,96767,2222],{},[898,96769,2473],{"mathvariant":2003},[1716,96771,6198],{},[1712,96773,1714],{},[2563,96775,96776],{"scriptlevel":2085,"displaystyle":2565},[2567,96777,96778,96788],{},[895,96779,96780,96782],{},[1716,96781,2787],{},[86902,96783,96784,96786],{},[1716,96785,2787],{},[1716,96787,6198],{},[86902,96789,96790,96796],{},[6927,96791,96792,96794],{},[898,96793,1734],{},[1716,96795,2222],{},[1716,96797,6198],{},[902,96799,96800],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,96803,96805],{"id":96804},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,96807,96808],{},[3817,96809],{"alt":96810,"className":96811,"src":96812},"imek-ic-4vlastnosti-anotovane",[210,3821],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1636,96814,96815,96824,96871,96915,96921,96927],{},[724,96816,96817,96819,96820,96823],{},[883,96818,2203],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,96821,96822],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,96825,96826],{},[883,96827,96829],{"className":96828},[886],[888,96830,96831],{"xmlns":890},[892,96832,96833,96868],{},[895,96834,96835,96838,96840,96842,96844,96846,96864,96866],{},[898,96836,96837],{"mathvariant":2003},"tg",[1712,96839,61075],{},[898,96841,23737],{},[1712,96843,1714],{},[1712,96845,2219],{},[2567,96847,96848,96856],{},[6989,96849,96850,96852,96854],{},[898,96851,900],{},[1716,96853,2222],{},[1712,96855,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,96857,96858,96860,96862],{},[898,96859,900],{},[1716,96861,2787],{},[1712,96863,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,96865,2252],{},[1716,96867,2085],{},[902,96869,96870],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,96872,96873,96874,96914],{},"(derivace implicitně zadané funkce ",[883,96875,96877],{"className":96876},[886],[888,96878,96879],{"xmlns":890},[892,96880,96881,96911],{},[895,96882,96883,96885,96887,96893,96895,96901,96903,96905,96907,96909],{},[898,96884,900],{},[1712,96886,1904],{"stretchy":1903},[6927,96888,96889,96891],{},[898,96890,1734],{},[1716,96892,2222],{},[1712,96894,3138],{"separator":2565},[6927,96896,96897,96899],{},[898,96898,1734],{},[1716,96900,2787],{},[1712,96902,1910],{"stretchy":1903},[1712,96904,2219],{},[898,96906,7585],{},[1712,96908,1714],{},[1716,96910,2085],{},[902,96912,96913],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,96916,96917,96920],{},[38,96918,96919],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,96922,96923,96926],{},[38,96924,96925],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,96928,96929,96932,96933,96951,96952,96968,96969,96972],{},[38,96930,96931],{},"4° Konvexní."," Pro každé dva body ",[883,96934,96936],{"className":96935},[886],[888,96937,96938],{"xmlns":890},[892,96939,96940,96948],{},[895,96941,96942,96944,96946],{},[898,96943,2044],{},[1712,96945,3138],{"separator":2565},[898,96947,28128],{},[902,96949,96950],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,96953,96955],{"className":96954},[886],[888,96956,96957],{"xmlns":890},[892,96958,96959,96965],{},[895,96960,96961,96963],{},[898,96962,2044],{},[898,96964,28128],{},[902,96966,96967],{"encoding":904},"AB"," ve ",[38,96970,96971],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,96974,96975],{},[614,96976,96977,96978,97013,97014,1659],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,96979,96981],{"className":96980},[886],[888,96982,96983],{"xmlns":890},[892,96984,96985,97011],{},[895,96986,96987,96989,96991,96997,96999,97005,97007,97009],{},[898,96988,900],{},[1712,96990,1904],{"stretchy":1903},[6927,96992,96993,96995],{},[898,96994,1734],{},[1716,96996,2222],{},[1712,96998,3138],{"separator":2565},[6927,97000,97001,97003],{},[898,97002,1734],{},[1716,97004,2787],{},[1712,97006,1910],{"stretchy":1903},[1712,97008,1714],{},[898,97010,7585],{},[902,97012,14640],{"encoding":904}," s tečnou se sklonem ",[883,97015,97017],{"className":97016},[886],[888,97018,97019],{"xmlns":890},[892,97020,97021,97029],{},[895,97022,97023,97025,97027],{},[898,97024,96837],{"mathvariant":2003},[1712,97026,61075],{},[898,97028,23737],{},[902,97030,97031],{"encoding":904},"\\operatorname{tg}\\alpha",[115,97033,97035],{"id":97034},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,97037,97038,3245,97041,14897,97054,97057],{},[38,97039,97040],{},"Mezní míra komoditní substituce",[883,97042,97044],{"className":97043},[886],[888,97045,97046],{"xmlns":890},[892,97047,97048,97052],{},[895,97049,97050],{},[1762,97051,15475],{},[902,97053,33113],{"encoding":904},[38,97055,97056],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,97059,97061],{"className":97060},[886],[888,97062,97063],{"xmlns":890,"display":32941},[892,97064,97065,97152],{},[25629,97066,97067],{"width":32946},[25634,97068,97069,97071,97145,97147],{},[25637,97070],{"width":32951},[25637,97072,97073],{},[895,97074,97075,97077,97079,97081,97083,97089,97091,97097,97099,97101,97123,97125,97143],{},[1762,97076,15475],{},[1712,97078,1714],{},[1762,97080,15475],{},[1712,97082,1904],{"stretchy":1903},[6927,97084,97085,97087],{},[898,97086,1734],{},[1716,97088,2222],{},[1712,97090,3138],{"separator":2565},[6927,97092,97093,97095],{},[898,97094,1734],{},[1716,97096,2787],{},[1712,97098,1910],{"stretchy":1903},[1712,97100,1714],{},[2567,97102,97103,97113],{},[895,97104,97105,97107],{},[898,97106,4445],{},[6927,97108,97109,97111],{},[898,97110,900],{},[1716,97112,2222],{},[895,97114,97115,97117],{},[898,97116,4445],{},[6927,97118,97119,97121],{},[898,97120,900],{},[1716,97122,2787],{},[1712,97124,1714],{},[2567,97126,97127,97135],{},[6989,97128,97129,97131,97133],{},[898,97130,900],{},[1716,97132,2222],{},[1712,97134,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,97136,97137,97139,97141],{},[898,97138,900],{},[1716,97140,2787],{},[1712,97142,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[898,97144,1659],{"mathvariant":2003},[25637,97146],{"width":32951},[25637,97148,97149],{},[1762,97150,97151],{},"(6.9)",[902,97153,97154],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,97156,97157,97158,97192,97193,97225,97226,97261,97262,97275],{},"Geometricky: ",[883,97159,97161],{"className":97160},[886],[888,97162,97163],{"xmlns":890},[892,97164,97165,97189],{},[895,97166,97167,97169],{},[1712,97168,2219],{},[2563,97170,97171],{"scriptlevel":2085,"displaystyle":1903},[2567,97172,97173,97181],{},[6989,97174,97175,97177,97179],{},[898,97176,900],{},[1716,97178,2222],{},[1712,97180,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,97182,97183,97185,97187],{},[898,97184,900],{},[1716,97186,2787],{},[1712,97188,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,97190,97191],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,97194,97196],{"className":97195},[886],[888,97197,97198],{"xmlns":890},[892,97199,97200,97222],{},[895,97201,97202,97208,97210,97212,97214,97220],{},[6927,97203,97204,97206],{},[898,97205,1734],{},[1716,97207,2787],{},[1712,97209,1714],{},[898,97211,7451],{},[1712,97213,1904],{"stretchy":1903},[6927,97215,97216,97218],{},[898,97217,1734],{},[1716,97219,2222],{},[1712,97221,1910],{"stretchy":1903},[902,97223,97224],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,97227,97229],{"className":97228},[886],[888,97230,97231],{"xmlns":890},[892,97232,97233,97259],{},[895,97234,97235,97237,97239,97245,97247,97253,97255,97257],{},[898,97236,900],{},[1712,97238,1904],{"stretchy":1903},[6927,97240,97241,97243],{},[898,97242,1734],{},[1716,97244,2222],{},[1712,97246,3138],{"separator":2565},[6927,97248,97249,97251],{},[898,97250,1734],{},[1716,97252,2787],{},[1712,97254,1910],{"stretchy":1903},[1712,97256,1714],{},[898,97258,7585],{},[902,97260,14640],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,97263,97265],{"className":97264},[886],[888,97266,97267],{"xmlns":890},[892,97268,97269,97273],{},[895,97270,97271],{},[1762,97272,15475],{},[902,97274,33113],{"encoding":904}," chápeme jako velikost kompenzace.",[1636,97277,97278],{},[724,97279,97280,97282,97283,5920,97315,97353,97354,97371,97372,97389],{},[883,97281,1941],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,97284,97286],{"className":97285},[886],[888,97287,97288],{"xmlns":890},[892,97289,97290,97312],{},[895,97291,97292,97294,97296,97302,97304,97310],{},[1762,97293,15475],{},[1712,97295,1904],{"stretchy":1903},[6927,97297,97298,97300],{},[898,97299,1734],{},[1716,97301,2222],{},[1712,97303,3138],{"separator":2565},[6927,97305,97306,97308],{},[898,97307,1734],{},[1716,97309,2787],{},[1712,97311,1910],{"stretchy":1903},[902,97313,97314],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,97316,97317,97318,33878,97335,97352],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,97319,97321],{"className":97320},[886],[888,97322,97323],{"xmlns":890},[892,97324,97325,97333],{},[895,97326,97327],{},[6927,97328,97329,97331],{},[898,97330,1734],{},[1716,97332,2222],{},[902,97334,33877],{"encoding":904},[883,97336,97338],{"className":97337},[886],[888,97339,97340],{"xmlns":890},[892,97341,97342,97350],{},[895,97343,97344],{},[6927,97345,97346,97348],{},[898,97347,1734],{},[1716,97349,2787],{},[902,97351,33896],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,97355,97357],{"className":97356},[886],[888,97358,97359],{"xmlns":890},[892,97360,97361,97369],{},[895,97362,97363],{},[6927,97364,97365,97367],{},[898,97366,1734],{},[1716,97368,2787],{},[902,97370,33896],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,97373,97375],{"className":97374},[886],[888,97376,97377],{"xmlns":890},[892,97378,97379,97387],{},[895,97380,97381],{},[6927,97382,97383,97385],{},[898,97384,1734],{},[1716,97386,2222],{},[902,97388,33877],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,97391,97392,97393,34819],{},"Pro obecnou změnu ",[883,97394,97396],{"className":97395},[886],[888,97397,97398],{"xmlns":890},[892,97399,97400,97410],{},[895,97401,97402,97404],{},[898,97403,2468],{"mathvariant":2003},[6927,97405,97406,97408],{},[898,97407,1734],{},[1716,97409,2222],{},[902,97411,97412],{"encoding":904},"\\mathrm{d} Q_1",[883,97414,97416],{"className":97415},[886],[888,97417,97418],{"xmlns":890,"display":32941},[892,97419,97420,97473],{},[25629,97421,97422],{"width":32946},[25634,97423,97424,97426,97466,97468],{},[25637,97425],{"width":32951},[25637,97427,97428],{},[895,97429,97430,97432,97438,97440,97442,97448,97450,97452,97454,97456,97458,97464],{},[898,97431,2004],{"mathvariant":2003},[6927,97433,97434,97436],{},[898,97435,1734],{},[1716,97437,2787],{},[1712,97439,3740],{},[898,97441,2468],{"mathvariant":2003},[6927,97443,97444,97446],{},[898,97445,1734],{},[1716,97447,2787],{},[1712,97449,1714],{},[1712,97451,2219],{},[1762,97453,15475],{},[1712,97455,1783],{},[898,97457,2468],{"mathvariant":2003},[6927,97459,97460,97462],{},[898,97461,1734],{},[1716,97463,2222],{},[1712,97465,3138],{"separator":2565},[25637,97467],{"width":32951},[25637,97469,97470],{},[1762,97471,97472],{},"(6.10)",[902,97474,97475],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,97477,97479],{"className":97478},[886],[888,97480,97481],{"xmlns":890,"display":32941},[892,97482,97483,97530],{},[25629,97484,97485],{"width":32946},[25634,97486,97487,97489,97523,97525],{},[25637,97488],{"width":32951},[25637,97490,97491],{},[895,97492,97493,97495,97501,97503,97505,97511,97513,97515,97521],{},[898,97494,2468],{"mathvariant":2003},[6927,97496,97497,97499],{},[898,97498,1734],{},[1716,97500,2222],{},[1712,97502,1714],{},[1712,97504,2219],{},[2567,97506,97507,97509],{},[1716,97508,2222],{},[1762,97510,15475],{},[1762,97512,2583],{},[898,97514,2468],{"mathvariant":2003},[6927,97516,97517,97519],{},[898,97518,1734],{},[1716,97520,2787],{},[898,97522,1659],{"mathvariant":2003},[25637,97524],{"width":32951},[25637,97526,97527],{},[1762,97528,97529],{},"(6.11)",[902,97531,97532],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1636,97534,97535,97601,97718],{},[724,97536,97537,97539,97540,34819],{},[883,97538,57570],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,97541,97543],{"className":97542},[886],[888,97544,97545],{"xmlns":890},[892,97546,97547,97599],{},[895,97548,97549,97551,97553,97559,97561,97567,97569,97571,97585],{},[898,97550,900],{},[1712,97552,1904],{"stretchy":1903},[6927,97554,97555,97557],{},[898,97556,1734],{},[1716,97558,2222],{},[1712,97560,3138],{"separator":2565},[6927,97562,97563,97565],{},[898,97564,1734],{},[1716,97566,2787],{},[1712,97568,1910],{"stretchy":1903},[1712,97570,1714],{},[6989,97572,97573,97575,97577],{},[898,97574,1734],{},[1716,97576,2222],{},[895,97578,97579,97581,97583],{},[1716,97580,2222],{},[898,97582,2473],{"mathvariant":2003},[1716,97584,2787],{},[6989,97586,97587,97589,97591],{},[898,97588,1734],{},[1716,97590,2787],{},[895,97592,97593,97595,97597],{},[1716,97594,2222],{},[898,97596,2473],{"mathvariant":2003},[1716,97598,2787],{},[902,97600,34818],{"encoding":904},[724,97602,97603],{},[883,97604,97606],{"className":97605},[886],[888,97607,97608],{"xmlns":890},[892,97609,97610,97716],{},[895,97611,97612,97614,97616,97698,97700,97714],{},[1762,97613,15475],{},[1712,97615,1714],{},[2567,97617,97618,97658],{},[895,97619,97620,97628,97644],{},[2563,97621,97622],{"scriptlevel":2085,"displaystyle":1903},[2567,97623,97624,97626],{},[1716,97625,2222],{},[1716,97627,2787],{},[6989,97629,97630,97632,97634],{},[898,97631,1734],{},[1716,97633,2222],{},[895,97635,97636,97638,97640,97642],{},[1712,97637,2219],{},[1716,97639,2222],{},[898,97641,2473],{"mathvariant":2003},[1716,97643,2787],{},[6989,97645,97646,97648,97650],{},[898,97647,1734],{},[1716,97649,2787],{},[895,97651,97652,97654,97656],{},[1716,97653,2222],{},[898,97655,2473],{"mathvariant":2003},[1716,97657,2787],{},[895,97659,97660,97668,97682],{},[2563,97661,97662],{"scriptlevel":2085,"displaystyle":1903},[2567,97663,97664,97666],{},[1716,97665,2222],{},[1716,97667,2787],{},[6989,97669,97670,97672,97674],{},[898,97671,1734],{},[1716,97673,2222],{},[895,97675,97676,97678,97680],{},[1716,97677,2222],{},[898,97679,2473],{"mathvariant":2003},[1716,97681,2787],{},[6989,97683,97684,97686,97688],{},[898,97685,1734],{},[1716,97687,2787],{},[895,97689,97690,97692,97694,97696],{},[1712,97691,2219],{},[1716,97693,2222],{},[898,97695,2473],{"mathvariant":2003},[1716,97697,2787],{},[1712,97699,1714],{},[2567,97701,97702,97708],{},[6927,97703,97704,97706],{},[898,97705,1734],{},[1716,97707,2787],{},[6927,97709,97710,97712],{},[898,97711,1734],{},[1716,97713,2222],{},[898,97715,1659],{"mathvariant":2003},[902,97717,34937],{"encoding":904},[724,97719,34940,97720,7037,97763,34988,97765,97784],{},[883,97721,97723],{"className":97722},[886],[888,97724,97725],{"xmlns":890},[892,97726,97727,97761],{},[895,97728,97729,97731,97733,97735,97737,97739,97741,97743,97751,97753],{},[1762,97730,15475],{},[1712,97732,1904],{"stretchy":1903},[1716,97734,34956],{},[1712,97736,3138],{"separator":2565},[1716,97738,19984],{},[1712,97740,1910],{"stretchy":1903},[1712,97742,1714],{},[2563,97744,97745],{"scriptlevel":2085,"displaystyle":1903},[2567,97746,97747,97749],{},[1716,97748,19984],{},[1716,97750,34956],{},[1712,97752,1714],{},[2563,97754,97755],{"scriptlevel":2085,"displaystyle":1903},[2567,97756,97757,97759],{},[1716,97758,3068],{},[1716,97760,6198],{},[902,97762,34985],{"encoding":904},[614,97764,7040],{},[883,97766,97768],{"className":97767},[886],[888,97769,97770],{"xmlns":890},[892,97771,97772,97782],{},[895,97773,97774],{},[2563,97775,97776],{"scriptlevel":2085,"displaystyle":1903},[2567,97777,97778,97780],{},[1716,97779,3068],{},[1716,97781,6198],{},[902,97783,35008],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,97786,97787,97788,97792],{},"(Paralelou je ",[207,97789,97791],{"className":97790,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,97794,97796],{"id":97795},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,97798,97799,97800,97803],{},"Rámcově se v kapitole 6 studují ",[38,97801,97802],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,97805,97806,97942],{},[123,97807,97808,97810,97811,15029,97842,3245,97845,97894,97895,1659],{},[38,97809,33127],{}," — maximalizace ",[883,97812,97814],{"className":97813},[886],[888,97815,97816],{"xmlns":890},[892,97817,97818,97840],{},[895,97819,97820,97822,97824,97830,97832,97838],{},[898,97821,900],{},[1712,97823,1904],{"stretchy":1903},[6927,97825,97826,97828],{},[898,97827,1734],{},[1716,97829,2222],{},[1712,97831,3138],{"separator":2565},[6927,97833,97834,97836],{},[898,97835,1734],{},[1716,97837,2787],{},[1712,97839,1910],{"stretchy":1903},[902,97841,21218],{"encoding":904},[38,97843,97844],{},"rozpočtovém omezení",[883,97846,97848],{"className":97847},[886],[888,97849,97850],{"xmlns":890},[892,97851,97852,97892],{},[895,97853,97854,97860,97862,97870,97876,97878,97886],{},[2037,97855,97856,97858],{},[898,97857,6951],{},[1712,97859,2145],{},[1712,97861,1714],{},[6989,97863,97864,97866,97868],{},[898,97865,1710],{},[1716,97867,2222],{},[1712,97869,2145],{},[6927,97871,97872,97874],{},[898,97873,1734],{},[1716,97875,2222],{},[1712,97877,3145],{},[6989,97879,97880,97882,97884],{},[898,97881,1710],{},[1716,97883,2787],{},[1712,97885,2145],{},[6927,97887,97888,97890],{},[898,97889,1734],{},[1716,97891,2787],{},[902,97893,22173],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,97896,97898],{"className":97897},[886],[888,97899,97900],{"xmlns":890},[892,97901,97902,97940],{},[895,97903,97904,97910,97912,97918,97920,97926,97928,97934,97936,97938],{},[6927,97905,97906,97908],{},[898,97907,1734],{},[898,97909,22665],{},[1712,97911,1714],{},[6927,97913,97914,97916],{},[898,97915,1969],{},[898,97917,22665],{},[1712,97919,1904],{"stretchy":1903},[6927,97921,97922,97924],{},[898,97923,1710],{},[1716,97925,2222],{},[1712,97927,3138],{"separator":2565},[6927,97929,97930,97932],{},[898,97931,1710],{},[1716,97933,2787],{},[1712,97935,3138],{"separator":2565},[898,97937,6951],{},[1712,97939,1910],{"stretchy":1903},[902,97941,41330],{"encoding":904},[123,97943,97944,32776,97947,32819,97993,98010,98011,1659],{},[38,97945,97946],{},"Duální úloha",[883,97948,97950],{"className":97949},[886],[888,97951,97952],{"xmlns":890},[892,97953,97954,97990],{},[895,97955,97956,97958,97960,97968,97974,97976,97984],{},[898,97957,2041],{},[1712,97959,1714],{},[6989,97961,97962,97964,97966],{},[898,97963,1710],{},[1716,97965,2222],{},[1712,97967,2145],{},[6927,97969,97970,97972],{},[898,97971,1734],{},[1716,97973,2222],{},[1712,97975,3145],{},[6989,97977,97978,97980,97982],{},[898,97979,1710],{},[1716,97981,2787],{},[1712,97983,2145],{},[6927,97985,97986,97988],{},[898,97987,1734],{},[1716,97989,2787],{},[902,97991,97992],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,97994,97996],{"className":97995},[886],[888,97997,97998],{"xmlns":890},[892,97999,98000,98008],{},[895,98001,98002],{},[2037,98003,98004,98006],{},[898,98005,900],{},[1712,98007,2145],{},[902,98009,32837],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,98012,98014],{"className":98013},[886],[888,98015,98016],{"xmlns":890},[892,98017,98018,98056],{},[895,98019,98020,98026,98028,98034,98036,98042,98044,98050,98052,98054],{},[6927,98021,98022,98024],{},[898,98023,1734],{},[898,98025,22665],{},[1712,98027,1714],{},[6927,98029,98030,98032],{},[898,98031,1969],{},[898,98033,22665],{},[1712,98035,1904],{"stretchy":1903},[6927,98037,98038,98040],{},[898,98039,1710],{},[1716,98041,2222],{},[1712,98043,3138],{"separator":2565},[6927,98045,98046,98048],{},[898,98047,1710],{},[1716,98049,2787],{},[1712,98051,3138],{"separator":2565},[898,98053,900],{},[1712,98055,1910],{"stretchy":1903},[902,98057,22698],{"encoding":904},[724,98059,98060,98061,98064,98065,3245,98068,98107],{},"Obě úlohy se řeší ",[207,98062,32842],{"className":98063,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,98066,98067],{},"tentýž bod dotyku",[883,98069,98071],{"className":98070},[886],[888,98072,98073],{"xmlns":890},[892,98074,98075,98105],{},[895,98076,98077,98083,98085,98093,98095,98103],{},[2037,98078,98079,98081],{},[898,98080,1734],{},[1712,98082,2145],{},[1712,98084,7910],{"stretchy":1903},[6989,98086,98087,98089,98091],{},[898,98088,1734],{},[1716,98090,2222],{},[1712,98092,2145],{},[1712,98094,3138],{"separator":2565},[6989,98096,98097,98099,98101],{},[898,98098,1734],{},[1716,98100,2787],{},[1712,98102,2145],{},[1712,98104,7925],{"stretchy":1903},[902,98106,33202],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,98109,98111],{"className":98110},[886],[888,98112,98113],{"xmlns":890,"display":32941},[892,98114,98115,98161],{},[895,98116,98117,98119,98121,98139,98141,98159],{},[1762,98118,15475],{},[1712,98120,1714],{},[2567,98122,98123,98131],{},[6989,98124,98125,98127,98129],{},[898,98126,900],{},[1716,98128,2222],{},[1712,98130,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[6989,98132,98133,98135,98137],{},[898,98134,900],{},[1716,98136,2787],{},[1712,98138,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,98140,1714],{},[2567,98142,98143,98151],{},[6989,98144,98145,98147,98149],{},[898,98146,1710],{},[1716,98148,2222],{},[1712,98150,2145],{},[6989,98152,98153,98155,98157],{},[898,98154,1710],{},[1716,98156,2787],{},[1712,98158,2145],{},[898,98160,1659],{"mathvariant":2003},[902,98162,98163],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,98165,98166],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1636,98168,98169],{},[724,98170,98171,98173,98174,98177,98178,98181,98182,98209,98210,98244,98245,98279,98280,98323,98324,98327,98328,1659],{},[883,98172,1941],{}," Pro detailní postup viz ",[207,98175,41629],{"className":98176,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,98179,98180],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,98183,98185],{"className":98184},[886],[888,98186,98187],{"xmlns":890},[892,98188,98189,98207],{},[895,98190,98191,98193,98195,98201],{},[898,98192,900],{},[1712,98194,1714],{},[6927,98196,98197,98199],{},[898,98198,1734],{},[1716,98200,2222],{},[6927,98202,98203,98205],{},[898,98204,1734],{},[1716,98206,2787],{},[902,98208,35101],{"encoding":904}," s výsledkem ",[883,98211,98213],{"className":98212},[886],[888,98214,98215],{"xmlns":890},[892,98216,98217,98241],{},[895,98218,98219,98225,98227,98229,98231,98237,98239],{},[6927,98220,98221,98223],{},[898,98222,1734],{},[1716,98224,2222],{},[1712,98226,1714],{},[1716,98228,2809],{},[1712,98230,3138],{"separator":2565},[6927,98232,98233,98235],{},[898,98234,1734],{},[1716,98236,2787],{},[1712,98238,1714],{},[1716,98240,1718],{},[902,98242,98243],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,98246,98248],{"className":98247},[886],[888,98249,98250],{"xmlns":890},[892,98251,98252,98276],{},[895,98253,98254,98260,98262,98264,98266,98272,98274],{},[6927,98255,98256,98258],{},[898,98257,1734],{},[1716,98259,2222],{},[1712,98261,1714],{},[1716,98263,2975],{},[1712,98265,3138],{"separator":2565},[6927,98267,98268,98270],{},[898,98269,1734],{},[1716,98271,2787],{},[1712,98273,1714],{},[1716,98275,2222],{},[902,98277,98278],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,98281,98283],{"className":98282},[886],[888,98284,98285],{"xmlns":890},[892,98286,98287,98321],{},[895,98288,98289,98291,98293,98307],{},[898,98290,900],{},[1712,98292,1714],{},[6989,98294,98295,98297,98299],{},[898,98296,1734],{},[1716,98298,2222],{},[895,98300,98301,98303,98305],{},[1716,98302,2222],{},[898,98304,2473],{"mathvariant":2003},[1716,98306,2787],{},[6989,98308,98309,98311,98313],{},[898,98310,1734],{},[1716,98312,2787],{},[895,98314,98315,98317,98319],{},[1716,98316,2222],{},[898,98318,2473],{"mathvariant":2003},[1716,98320,2787],{},[902,98322,38034],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,98325,98326],{},"6.8–6.13"," jsou na stránce ",[207,98329,32642],{"className":98330,"dataFsResolvedFilePath":911,"href":912},[210],[115,98332,98334],{"id":98333},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,98336,98337,98338,98351,98352,98354,98355,98357,98358,98360,98361,98363,98364,98366,98367,98369,98370,3245,98372,98407,98408,98421,98422,98425,98426,98429,98430,1659],{},"Každá ",[883,98339,98341],{"className":98340},[886],[888,98342,98343],{"xmlns":890},[892,98344,98345,98349],{},[895,98346,98347],{},[898,98348,41735],{},[902,98350,41735],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,98353,91685],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,98356,92169],{}," a současně ",[38,98359,91688],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,98362,91693],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,98365,57552],{}," (6.4) a druhé parciální derivace ",[38,98368,94052],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,98371,14603],{},[883,98373,98375],{"className":98374},[886],[888,98376,98377],{"xmlns":890},[892,98378,98379,98405],{},[895,98380,98381,98383,98385,98391,98393,98399,98401,98403],{},[898,98382,900],{},[1712,98384,1904],{"stretchy":1903},[6927,98386,98387,98389],{},[898,98388,1734],{},[1716,98390,2222],{},[1712,98392,3138],{"separator":2565},[6927,98394,98395,98397],{},[898,98396,1734],{},[1716,98398,2787],{},[1712,98400,1910],{"stretchy":1903},[1712,98402,1714],{},[898,98404,7585],{},[902,98406,14640],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,98409,98411],{"className":98410},[886],[888,98412,98413],{"xmlns":890},[892,98414,98415,98419],{},[895,98416,98417],{},[1762,98418,15475],{},[902,98420,33113],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,98423,98424],{},"maximalizace užitečnosti"," a duální ",[38,98427,98428],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,98431,41629],{"className":98432,"dataFsResolvedFilePath":911,"href":912},[210],[115,98434,54757],{"id":54756},[152,98436,98437,98440,98443,98446,98449,98452,98455,98458,98461,98464],{},[123,98438,98439],{},"Co se zahrnuje pod termín užitečnost?",[123,98441,98442],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,98444,98445],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,98447,98448],{},"Jak se vypočítá mezní užitečnost?",[123,98450,98451],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,98453,98454],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,98456,98457],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,98459,98460],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,98462,98463],{},"Proč mají křivky užitečnosti záporný sklon?",[123,98465,98466],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,98468,98470],{"id":98469},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,98472,98473,98476,98477,88358,98519,1343,98547,1343,98575,98603],{},[38,98474,98475],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,98478,98480],{"className":98479},[886],[888,98481,98482],{"xmlns":890},[892,98483,98484,98516],{},[895,98485,98486,98488,98490,98496,98498,98500,98506,98508,98510],{},[898,98487,900],{},[1712,98489,1714],{},[6927,98491,98492,98494],{},[898,98493,1734],{},[1716,98495,2222],{},[1712,98497,3145],{},[1716,98499,69434],{},[6927,98501,98502,98504],{},[898,98503,1734],{},[1716,98505,2787],{},[1712,98507,3145],{},[1716,98509,2787],{},[6927,98511,98512,98514],{},[898,98513,1734],{},[1716,98515,6198],{},[902,98517,98518],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,98520,98522],{"className":98521},[886],[888,98523,98524],{"xmlns":890},[892,98525,98526,98544],{},[895,98527,98528,98530,98532,98534,98536,98538,98540,98542],{},[898,98529,900],{},[1712,98531,1904],{"stretchy":1903},[1716,98533,2975],{},[1712,98535,3138],{"separator":2565},[1716,98537,2787],{},[1712,98539,3138],{"separator":2565},[1716,98541,2787],{},[1712,98543,1910],{"stretchy":1903},[902,98545,98546],{"encoding":904},"U(4, 2, 2)",[883,98548,98550],{"className":98549},[886],[888,98551,98552],{"xmlns":890},[892,98553,98554,98572],{},[895,98555,98556,98558,98560,98562,98564,98566,98568,98570],{},[898,98557,900],{},[1712,98559,1904],{"stretchy":1903},[1716,98561,2222],{},[1712,98563,3138],{"separator":2565},[1716,98565,2975],{},[1712,98567,3138],{"separator":2565},[1716,98569,2787],{},[1712,98571,1910],{"stretchy":1903},[902,98573,98574],{"encoding":904},"U(1, 4, 2)",[883,98576,98578],{"className":98577},[886],[888,98579,98580],{"xmlns":890},[892,98581,98582,98600],{},[895,98583,98584,98586,98588,98590,98592,98594,98596,98598],{},[898,98585,900],{},[1712,98587,1904],{"stretchy":1903},[1716,98589,2787],{},[1712,98591,3138],{"separator":2565},[1716,98593,6198],{},[1712,98595,3138],{"separator":2565},[1716,98597,2222],{},[1712,98599,1910],{"stretchy":1903},[902,98601,98602],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,98605,98606,98609,98610,98662,98663,1343,98689,1343,98715,1343,98741,1343,98767,1343,98793,1343,98819,98845],{},[38,98607,98608],{},"6.2"," Je dána užitečnost ",[883,98611,98613],{"className":98612},[886],[888,98614,98615],{"xmlns":890},[892,98616,98617,98659],{},[895,98618,98619,98621,98623,98625,98639,98653],{},[898,98620,900],{},[1712,98622,1714],{},[1716,98624,2787],{},[6989,98626,98627,98629,98631],{},[898,98628,1734],{},[1716,98630,2222],{},[895,98632,98633,98635,98637],{},[1716,98634,2222],{},[898,98636,2473],{"mathvariant":2003},[1716,98638,6198],{},[6989,98640,98641,98643,98645],{},[898,98642,1734],{},[1716,98644,2787],{},[895,98646,98647,98649,98651],{},[1716,98648,2222],{},[898,98650,2473],{"mathvariant":2003},[1716,98652,2787],{},[6927,98654,98655,98657],{},[898,98656,1734],{},[1716,98658,6198],{},[902,98660,98661],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,98664,98666],{"className":98665},[886],[888,98667,98668],{"xmlns":890},[892,98669,98670,98686],{},[895,98671,98672,98674,98676,98678,98680,98682,98684],{},[1712,98673,1904],{"stretchy":1903},[1716,98675,3377],{},[1712,98677,3138],{"separator":2565},[1716,98679,71472],{},[1712,98681,3138],{"separator":2565},[1716,98683,1718],{},[1712,98685,1910],{"stretchy":1903},[902,98687,98688],{"encoding":904},"(36, 27, 10)",[883,98690,98692],{"className":98691},[886],[888,98693,98694],{"xmlns":890},[892,98695,98696,98712],{},[895,98697,98698,98700,98702,98704,98706,98708,98710],{},[1712,98699,1904],{"stretchy":1903},[1716,98701,46715],{},[1712,98703,3138],{"separator":2565},[1716,98705,3397],{},[1712,98707,3138],{"separator":2565},[1716,98709,6857],{},[1712,98711,1910],{"stretchy":1903},[902,98713,98714],{"encoding":904},"(64, 8, 20)",[883,98716,98718],{"className":98717},[886],[888,98719,98720],{"xmlns":890},[892,98721,98722,98738],{},[895,98723,98724,98726,98728,98730,98732,98734,98736],{},[1712,98725,1904],{"stretchy":1903},[1716,98727,2809],{},[1712,98729,3138],{"separator":2565},[1716,98731,46715],{},[1712,98733,3138],{"separator":2565},[1716,98735,3397],{},[1712,98737,1910],{"stretchy":1903},[902,98739,98740],{"encoding":904},"(25, 64, 8)",[883,98742,98744],{"className":98743},[886],[888,98745,98746],{"xmlns":890},[892,98747,98748,98764],{},[895,98749,98750,98752,98754,98756,98758,98760,98762],{},[1712,98751,1904],{"stretchy":1903},[1716,98753,2975],{},[1712,98755,3138],{"separator":2565},[1716,98757,77404],{},[1712,98759,3138],{"separator":2565},[1716,98761,6209],{},[1712,98763,1910],{"stretchy":1903},[902,98765,98766],{"encoding":904},"(4, 125, 6)",[883,98768,98770],{"className":98769},[886],[888,98771,98772],{"xmlns":890},[892,98773,98774,98790],{},[895,98775,98776,98778,98780,98782,98784,98786,98788],{},[1712,98777,1904],{"stretchy":1903},[1716,98779,1780],{},[1712,98781,3138],{"separator":2565},[1716,98783,3018],{},[1712,98785,3138],{"separator":2565},[1716,98787,8912],{},[1712,98789,1910],{"stretchy":1903},[902,98791,98792],{"encoding":904},"(9, 40, 12)",[883,98794,98796],{"className":98795},[886],[888,98797,98798],{"xmlns":890},[892,98799,98800,98816],{},[895,98801,98802,98804,98806,98808,98810,98812,98814],{},[1712,98803,1904],{"stretchy":1903},[1716,98805,1780],{},[1712,98807,3138],{"separator":2565},[1716,98809,46715],{},[1712,98811,3138],{"separator":2565},[1716,98813,3068],{},[1712,98815,1910],{"stretchy":1903},[902,98817,98818],{"encoding":904},"(9, 64, 5)",[883,98820,98822],{"className":98821},[886],[888,98823,98824],{"xmlns":890},[892,98825,98826,98842],{},[895,98827,98828,98830,98832,98834,98836,98838,98840],{},[1712,98829,1904],{"stretchy":1903},[1716,98831,46715],{},[1712,98833,3138],{"separator":2565},[1716,98835,3397],{},[1712,98837,3138],{"separator":2565},[1716,98839,1718],{},[1712,98841,1910],{"stretchy":1903},[902,98843,98844],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,98847,98848,98609,98851,98894,98895,98929,98930,4288,98960,98993,98994,99011,99012,99029],{},[38,98849,98850],{},"6.3",[883,98852,98854],{"className":98853},[886],[888,98855,98856],{"xmlns":890},[892,98857,98858,98892],{},[895,98859,98860,98862,98864,98878],{},[898,98861,900],{},[1712,98863,1714],{},[6989,98865,98866,98868,98870],{},[898,98867,1734],{},[1716,98869,2222],{},[895,98871,98872,98874,98876],{},[1716,98873,2222],{},[898,98875,2473],{"mathvariant":2003},[1716,98877,2787],{},[6989,98879,98880,98882,98884],{},[898,98881,1734],{},[1716,98883,2787],{},[895,98885,98886,98888,98890],{},[1716,98887,2222],{},[898,98889,2473],{"mathvariant":2003},[1716,98891,2787],{},[902,98893,38034],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,98896,98898],{"className":98897},[886],[888,98899,98900],{"xmlns":890},[892,98901,98902,98926],{},[895,98903,98904,98910,98912,98914,98916,98922,98924],{},[6927,98905,98906,98908],{},[898,98907,1734],{},[1716,98909,2222],{},[1712,98911,1714],{},[1716,98913,2782],{},[1712,98915,3138],{"separator":2565},[6927,98917,98918,98920],{},[898,98919,1734],{},[1716,98921,2787],{},[1712,98923,1714],{},[1716,98925,51578],{},[902,98927,98928],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,98931,98933],{"className":98932},[886],[888,98934,98935],{"xmlns":890},[892,98936,98937,98957],{},[895,98938,98939,98941,98947,98949,98951],{},[898,98940,4445],{},[6927,98942,98943,98945],{},[898,98944,900],{},[1716,98946,2222],{},[1712,98948,3138],{"separator":2565},[898,98950,4445],{},[6927,98952,98953,98955],{},[898,98954,900],{},[1716,98956,2787],{},[902,98958,98959],{"encoding":904},"MU_1, MU_2",[883,98961,98963],{"className":98962},[886],[888,98964,98965],{"xmlns":890},[892,98966,98967,98991],{},[895,98968,98969,98975,98977,98979,98981,98987,98989],{},[6927,98970,98971,98973],{},[898,98972,1734],{},[1716,98974,2222],{},[1712,98976,1714],{},[1716,98978,2782],{},[1712,98980,3138],{"separator":2565},[6927,98982,98983,98985],{},[898,98984,1734],{},[1716,98986,2787],{},[1712,98988,1714],{},[1716,98990,51578],{},[902,98992,98928],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,98995,98997],{"className":98996},[886],[888,98998,98999],{"xmlns":890},[892,99000,99001,99009],{},[895,99002,99003],{},[6927,99004,99005,99007],{},[898,99006,1734],{},[1716,99008,2222],{},[902,99010,33877],{"encoding":904}," na 60 a poklesu ",[883,99013,99015],{"className":99014},[886],[888,99016,99017],{"xmlns":890},[892,99018,99019,99027],{},[895,99020,99021],{},[6927,99022,99023,99025],{},[898,99024,1734],{},[1716,99026,2787],{},[902,99028,33896],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,99031,99032,99035,99036,99097,99098,1659],{},[38,99033,99034],{},"6.4"," Je dána funkce ",[883,99037,99039],{"className":99038},[886],[888,99040,99041],{"xmlns":890},[892,99042,99043,99095],{},[895,99044,99045,99047,99049,99055,99057,99063,99065,99067,99081],{},[898,99046,900],{},[1712,99048,1904],{"stretchy":1903},[6927,99050,99051,99053],{},[898,99052,1734],{},[1716,99054,2222],{},[1712,99056,3138],{"separator":2565},[6927,99058,99059,99061],{},[898,99060,1734],{},[1716,99062,2787],{},[1712,99064,1910],{"stretchy":1903},[1712,99066,1714],{},[6989,99068,99069,99071,99073],{},[898,99070,1734],{},[1716,99072,2222],{},[895,99074,99075,99077,99079],{},[1716,99076,2222],{},[898,99078,2473],{"mathvariant":2003},[1716,99080,2787],{},[6989,99082,99083,99085,99087],{},[898,99084,1734],{},[1716,99086,2787],{},[895,99088,99089,99091,99093],{},[1716,99090,2222],{},[898,99092,2473],{"mathvariant":2003},[1716,99094,2787],{},[902,99096,34818],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,99099,99101],{"className":99100},[886],[888,99102,99103],{"xmlns":890},[892,99104,99105,99195],{},[895,99106,99107,99109,99111,99117,99119,99121,99123,99125,99127,99129,99135,99137,99139,99141,99143,99145,99147,99149,99151,99157,99159,99161,99163,99165,99167,99169,99175,99177,99179,99181,99183,99185,99187,99193],{},[898,99108,900],{},[1712,99110,1904],{"stretchy":1903},[6927,99112,99113,99115],{},[898,99114,1734],{},[1716,99116,2222],{},[1712,99118,3138],{"separator":2565},[1716,99120,2222],{},[1712,99122,1910],{"stretchy":1903},[1712,99124,3138],{"separator":2565},[898,99126,900],{},[1712,99128,1904],{"stretchy":1903},[6927,99130,99131,99133],{},[898,99132,1734],{},[1716,99134,2222],{},[1712,99136,3138],{"separator":2565},[1716,99138,2787],{},[1712,99140,1910],{"stretchy":1903},[1712,99142,3138],{"separator":2565},[898,99144,900],{},[1712,99146,1904],{"stretchy":1903},[1716,99148,2222],{},[1712,99150,3138],{"separator":2565},[6927,99152,99153,99155],{},[898,99154,1734],{},[1716,99156,2787],{},[1712,99158,1910],{"stretchy":1903},[1712,99160,3138],{"separator":2565},[898,99162,900],{},[1712,99164,1904],{"stretchy":1903},[1716,99166,2787],{},[1712,99168,3138],{"separator":2565},[6927,99170,99171,99173],{},[898,99172,1734],{},[1716,99174,2787],{},[1712,99176,1910],{"stretchy":1903},[1712,99178,3138],{"separator":2565},[898,99180,900],{},[1712,99182,1904],{"stretchy":1903},[1716,99184,6198],{},[1712,99186,3138],{"separator":2565},[6927,99188,99189,99191],{},[898,99190,1734],{},[1716,99192,2787],{},[1712,99194,1910],{"stretchy":1903},[902,99196,99197],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,99199,99200,98609,99203,99247,99248,99356,99357,1343,99382,1343,99407,99449,99450,1343,99479,99504],{},[38,99201,99202],{},"6.5",[883,99204,99206],{"className":99205},[886],[888,99207,99208],{"xmlns":890},[892,99209,99210,99244],{},[895,99211,99212,99214,99216,99230],{},[898,99213,900],{},[1712,99215,1714],{},[6989,99217,99218,99220,99222],{},[898,99219,1734],{},[1716,99221,2222],{},[895,99223,99224,99226,99228],{},[1716,99225,2787],{},[898,99227,2473],{"mathvariant":2003},[1716,99229,6198],{},[6989,99231,99232,99234,99236],{},[898,99233,1734],{},[1716,99235,2787],{},[895,99237,99238,99240,99242],{},[1716,99239,2222],{},[898,99241,2473],{"mathvariant":2003},[1716,99243,6198],{},[902,99245,99246],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,99249,99251],{"className":99250},[886],[888,99252,99253],{"xmlns":890},[892,99254,99255,99353],{},[895,99256,99257,99259,99261,99267,99269,99275,99277,99279,99281,99283,99285,99287,99293,99295,99297,99299,99301,99303,99305,99311,99313,99315,99317,99319,99321,99323,99325,99327,99333,99335,99337,99339,99341,99343,99345,99351],{},[898,99258,900],{},[1712,99260,1904],{"stretchy":1903},[6927,99262,99263,99265],{},[898,99264,1734],{},[1716,99266,2222],{},[1712,99268,3138],{"separator":2565},[6927,99270,99271,99273],{},[898,99272,1734],{},[1716,99274,2787],{},[1712,99276,1910],{"stretchy":1903},[1712,99278,1714],{},[1716,99280,2787],{},[1712,99282,3138],{"separator":2565},[898,99284,900],{},[1712,99286,1904],{"stretchy":1903},[6927,99288,99289,99291],{},[898,99290,1734],{},[1716,99292,2222],{},[1712,99294,3138],{"separator":2565},[1716,99296,6198],{},[1712,99298,1910],{"stretchy":1903},[1712,99300,3138],{"separator":2565},[898,99302,900],{},[1712,99304,1904],{"stretchy":1903},[6927,99306,99307,99309],{},[898,99308,1734],{},[1716,99310,2222],{},[1712,99312,3138],{"separator":2565},[1716,99314,2787],{},[1712,99316,1910],{"stretchy":1903},[1712,99318,3138],{"separator":2565},[898,99320,900],{},[1712,99322,1904],{"stretchy":1903},[1716,99324,2787],{},[1712,99326,3138],{"separator":2565},[6927,99328,99329,99331],{},[898,99330,1734],{},[1716,99332,2787],{},[1712,99334,1910],{"stretchy":1903},[1712,99336,3138],{"separator":2565},[898,99338,900],{},[1712,99340,1904],{"stretchy":1903},[1716,99342,6198],{},[1712,99344,3138],{"separator":2565},[6927,99346,99347,99349],{},[898,99348,1734],{},[1716,99350,2787],{},[1712,99352,1910],{"stretchy":1903},[902,99354,99355],{"encoding":904},"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 ",[883,99358,99360],{"className":99359},[886],[888,99361,99362],{"xmlns":890},[892,99363,99364,99379],{},[895,99365,99366,99368,99370,99372,99374,99377],{},[898,99367,2044],{},[1712,99369,7910],{"stretchy":1903},[1716,99371,69434],{},[1712,99373,6245],{"separator":2565},[1716,99375,99376],{},"3,555",[1712,99378,7925],{"stretchy":1903},[902,99380,99381],{"encoding":904},"A[1{,}5; 3{,}555]",[883,99383,99385],{"className":99384},[886],[888,99386,99387],{"xmlns":890},[892,99388,99389,99404],{},[895,99390,99391,99393,99395,99397,99399,99402],{},[898,99392,28128],{},[1712,99394,7910],{"stretchy":1903},[1716,99396,58074],{},[1712,99398,6245],{"separator":2565},[1716,99400,99401],{},"1,28",[1712,99403,7925],{"stretchy":1903},[902,99405,99406],{"encoding":904},"B[2{,}5; 1{,}28]",[883,99408,99410],{"className":99409},[886],[888,99411,99412],{"xmlns":890},[892,99413,99414,99446],{},[895,99415,99416,99418,99420,99422,99424,99426,99428,99434,99436,99438,99440,99442,99444],{},[898,99417,8195],{},[1712,99419,7910],{"stretchy":1903},[1716,99421,2787],{},[1712,99423,6245],{"separator":2565},[898,99425,900],{},[1712,99427,1904],{"stretchy":1903},[6927,99429,99430,99432],{},[898,99431,1734],{},[1716,99433,2222],{},[1712,99435,3138],{"separator":2565},[1716,99437,6198],{},[1712,99439,1910],{"stretchy":1903},[1712,99441,1714],{},[1716,99443,6198],{},[1712,99445,7925],{"stretchy":1903},[902,99447,99448],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,99451,99453],{"className":99452},[886],[888,99454,99455],{"xmlns":890},[892,99456,99457,99476],{},[895,99458,99459,99461,99463,99465,99467,99469,99471,99474],{},[898,99460,1969],{},[1712,99462,7910],{"stretchy":1903},[1716,99464,6198],{},[1712,99466,6245],{"separator":2565},[1716,99468,2222],{},[1712,99470,6245],{"separator":2565},[1716,99472,99473],{},"0,832",[1712,99475,7925],{"stretchy":1903},[902,99477,99478],{"encoding":904},"D[3; 1; 0{,}832]",[883,99480,99482],{"className":99481},[886],[888,99483,99484],{"xmlns":890},[892,99485,99486,99501],{},[895,99487,99488,99490,99492,99494,99496,99499],{},[898,99489,2041],{},[1712,99491,7910],{"stretchy":1903},[1716,99493,58074],{},[1712,99495,6245],{"separator":2565},[1716,99497,99498],{},"4,32",[1712,99500,7925],{"stretchy":1903},[902,99502,99503],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,99506,99507,98609,99510,99553,99554,4288,99567,99601,99602,99619,99620,99637],{},[38,99508,99509],{},"6.6",[883,99511,99513],{"className":99512},[886],[888,99514,99515],{"xmlns":890},[892,99516,99517,99551],{},[895,99518,99519,99521,99523,99537],{},[898,99520,900],{},[1712,99522,1714],{},[6989,99524,99525,99527,99529],{},[898,99526,1734],{},[1716,99528,2222],{},[895,99530,99531,99533,99535],{},[1716,99532,2787],{},[898,99534,2473],{"mathvariant":2003},[1716,99536,6198],{},[6989,99538,99539,99541,99543],{},[898,99540,1734],{},[1716,99542,2787],{},[895,99544,99545,99547,99549],{},[1716,99546,2222],{},[898,99548,2473],{"mathvariant":2003},[1716,99550,6198],{},[902,99552,99246],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,99555,99557],{"className":99556},[886],[888,99558,99559],{"xmlns":890},[892,99560,99561,99565],{},[895,99562,99563],{},[1762,99564,15475],{},[902,99566,33113],{"encoding":904},[883,99568,99570],{"className":99569},[886],[888,99571,99572],{"xmlns":890},[892,99573,99574,99598],{},[895,99575,99576,99582,99584,99586,99588,99594,99596],{},[6927,99577,99578,99580],{},[898,99579,1734],{},[1716,99581,2222],{},[1712,99583,1714],{},[1716,99585,1739],{},[1712,99587,3138],{"separator":2565},[6927,99589,99590,99592],{},[898,99591,1734],{},[1716,99593,2787],{},[1712,99595,1714],{},[1716,99597,6195],{},[902,99599,99600],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,99603,99605],{"className":99604},[886],[888,99606,99607],{"xmlns":890},[892,99608,99609,99617],{},[895,99610,99611],{},[6927,99612,99613,99615],{},[898,99614,1734],{},[1716,99616,2222],{},[902,99618,33877],{"encoding":904},", poklesne-li ",[883,99621,99623],{"className":99622},[886],[888,99624,99625],{"xmlns":890},[892,99626,99627,99635],{},[895,99628,99629],{},[6927,99630,99631,99633],{},[898,99632,1734],{},[1716,99634,2787],{},[902,99636,33896],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,99639,99640,99643,99644,99661,99662,99679,99680,99712,99713,99738,99739,99752,99753,1343,99777,1343,99801,1659],{},[38,99641,99642],{},"6.7"," Míra uspokojení z nákupu množství ",[883,99645,99647],{"className":99646},[886],[888,99648,99649],{"xmlns":890},[892,99650,99651,99659],{},[895,99652,99653],{},[6927,99654,99655,99657],{},[898,99656,1734],{},[1716,99658,2222],{},[902,99660,33877],{"encoding":904}," nealko nápojů a množství ",[883,99663,99665],{"className":99664},[886],[888,99666,99667],{"xmlns":890},[892,99668,99669,99677],{},[895,99670,99671],{},[6927,99672,99673,99675],{},[898,99674,1734],{},[1716,99676,2787],{},[902,99678,33896],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,99681,99683],{"className":99682},[886],[888,99684,99685],{"xmlns":890},[892,99686,99687,99709],{},[895,99688,99689,99691,99693],{},[898,99690,900],{},[1712,99692,1714],{},[5935,99694,99695],{},[895,99696,99697,99703],{},[6927,99698,99699,99701],{},[898,99700,1734],{},[1716,99702,2222],{},[6927,99704,99705,99707],{},[898,99706,1734],{},[1716,99708,2787],{},[902,99710,99711],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,99714,99716],{"className":99715},[886],[888,99717,99718],{"xmlns":890},[892,99719,99720,99736],{},[895,99721,99722,99728,99730],{},[6927,99723,99724,99726],{},[898,99725,1734],{},[1716,99727,2222],{},[1712,99729,3138],{"separator":2565},[6927,99731,99732,99734],{},[898,99733,1734],{},[1716,99735,2787],{},[902,99737,40497],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,99740,99742],{"className":99741},[886],[888,99743,99744],{"xmlns":890},[892,99745,99746,99750],{},[895,99747,99748],{},[1762,99749,15475],{},[902,99751,33113],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,99754,99756],{"className":99755},[886],[888,99757,99758],{"xmlns":890},[892,99759,99760,99774],{},[895,99761,99762,99764,99766,99768,99770,99772],{},[1762,99763,15475],{},[1712,99765,1904],{"stretchy":1903},[1716,99767,3068],{},[1712,99769,3138],{"separator":2565},[1716,99771,6857],{},[1712,99773,1910],{"stretchy":1903},[902,99775,99776],{"encoding":904},"\\text{MRCS}(5, 20)",[883,99778,99780],{"className":99779},[886],[888,99781,99782],{"xmlns":890},[892,99783,99784,99798],{},[895,99785,99786,99788,99790,99792,99794,99796],{},[1762,99787,15475],{},[1712,99789,1904],{"stretchy":1903},[1716,99791,6857],{},[1712,99793,3138],{"separator":2565},[1716,99795,3068],{},[1712,99797,1910],{"stretchy":1903},[902,99799,99800],{"encoding":904},"\\text{MRCS}(20, 5)",[883,99802,99804],{"className":99803},[886],[888,99805,99806],{"xmlns":890},[892,99807,99808,99822],{},[895,99809,99810,99812,99814,99816,99818,99820],{},[1762,99811,15475],{},[1712,99813,1904],{"stretchy":1903},[1716,99815,2787],{},[1712,99817,3138],{"separator":2565},[1716,99819,2782],{},[1712,99821,1910],{"stretchy":1903},[902,99823,99824],{"encoding":904},"\\text{MRCS}(2, 50)",[1636,99826,99827],{},[724,99828,99829,99831,99832,1659],{},[883,99830,2370],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,99833,99836],{"className":99834,"dataFsResolvedFilePath":911,"href":99835},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,99838,20594],{"id":20593},[120,99840,99841,99847,99852,99858,99911,99921,99967,100022,100085,100142,100197,100236],{},[123,99842,99843,99846],{},[38,99844,99845],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,99848,99849,99851],{},[38,99850,91744],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,99853,99854,99857],{},[38,99855,99856],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,99859,99860,99862,99863,99876,99877,1659],{},[38,99861,92071],{}," — uspořádaná ",[883,99864,99866],{"className":99865},[886],[888,99867,99868],{"xmlns":890},[892,99869,99870,99874],{},[895,99871,99872],{},[898,99873,41735],{},[902,99875,41735],{"encoding":904},"-tice ",[883,99878,99880],{"className":99879},[886],[888,99881,99882],{"xmlns":890},[892,99883,99884,99908],{},[895,99885,99886,99888,99894,99896,99898,99900,99906],{},[1712,99887,1904],{"stretchy":1903},[6927,99889,99890,99892],{},[898,99891,1734],{},[1716,99893,2222],{},[1712,99895,3138],{"separator":2565},[1712,99897,14518],{},[1712,99899,3138],{"separator":2565},[6927,99901,99902,99904],{},[898,99903,1734],{},[898,99905,41735],{},[1712,99907,1910],{"stretchy":1903},[902,99909,99910],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,99912,99913,99916,99917,99920],{},[38,99914,99915],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,99918,99919],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,99922,99923,3245,99926,99966],{},[38,99924,99925],{},"Funkce užitečnosti",[883,99927,99929],{"className":99928},[886],[888,99930,99931],{"xmlns":890},[892,99932,99933,99963],{},[895,99934,99935,99937,99939,99941,99943,99949,99951,99953,99955,99961],{},[898,99936,900],{},[1712,99938,1714],{},[898,99940,900],{},[1712,99942,1904],{"stretchy":1903},[6927,99944,99945,99947],{},[898,99946,1734],{},[1716,99948,2222],{},[1712,99950,3138],{"separator":2565},[1712,99952,14518],{},[1712,99954,3138],{"separator":2565},[6927,99956,99957,99959],{},[898,99958,1734],{},[898,99960,41735],{},[1712,99962,1910],{"stretchy":1903},[902,99964,99965],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,99968,99969,3245,99972,100001,100002,3245,100005,100021],{},[38,99970,99971],{},"Mezní užitečnost",[883,99973,99975],{"className":99974},[886],[888,99976,99977],{"xmlns":890},[892,99978,99979,99999],{},[895,99980,99981,99983,99989,99991],{},[898,99982,4445],{},[6927,99984,99985,99987],{},[898,99986,900],{},[898,99988,22665],{},[1712,99990,1714],{},[6989,99992,99993,99995,99997],{},[898,99994,900],{},[898,99996,22665],{},[1712,99998,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[902,100000,91528],{"encoding":904}," — vzorec (6.2); ",[38,100003,100004],{},"totální diferenciál",[883,100006,100008],{"className":100007},[886],[888,100009,100010],{"xmlns":890},[892,100011,100012,100018],{},[895,100013,100014,100016],{},[898,100015,2468],{"mathvariant":2003},[898,100017,900],{},[902,100019,100020],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,100023,100024,100026,100027,100051,100052,100084],{},[38,100025,93707],{}," — (6.4) ",[883,100028,100030],{"className":100029},[886],[888,100031,100032],{"xmlns":890},[892,100033,100034,100048],{},[895,100035,100036,100044,100046],{},[6989,100037,100038,100040,100042],{},[898,100039,900],{},[898,100041,22665],{},[1712,100043,2243],{"mathvariant":2003,"lspace":2242,"rspace":2242},[1712,100045,2302],{},[1716,100047,2085],{},[902,100049,100050],{"encoding":904},"U'_i > 0",", (6.5) ",[883,100053,100055],{"className":100054},[886],[888,100056,100057],{"xmlns":890},[892,100058,100059,100081],{},[895,100060,100061,100077,100079],{},[6989,100062,100063,100065,100071],{},[898,100064,900],{},[895,100066,100067,100069],{},[898,100068,22665],{},[898,100070,22665],{},[895,100072,100073,100075],{},[1712,100074,2243],{"mathvariant":2003},[1712,100076,2243],{"mathvariant":2003},[1712,100078,2252],{},[1716,100080,2085],{},[902,100082,100083],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,100086,100087,3245,100089,100120,100121,1659],{},[38,100088,95495],{},[883,100090,100092],{"className":100091},[886],[888,100093,100094],{"xmlns":890},[892,100095,100096,100118],{},[895,100097,100098,100100,100102,100110],{},[898,100099,900],{},[1712,100101,1714],{},[6989,100103,100104,100106,100108],{},[898,100105,1734],{},[1716,100107,2222],{},[898,100109,207],{},[6989,100111,100112,100114,100116],{},[898,100113,1734],{},[1716,100115,2787],{},[898,100117,7544],{},[902,100119,40678],{"encoding":904}," — (6.6), speciálně ",[883,100122,100124],{"className":100123},[886],[888,100125,100126],{"xmlns":890},[892,100127,100128,100140],{},[895,100129,100130,100132,100134,100136,100138],{},[898,100131,7544],{},[1712,100133,1714],{},[1716,100135,2222],{},[1712,100137,2219],{},[898,100139,207],{},[902,100141,95649],{"encoding":904},[123,100143,100144,3245,100147,100182,100183,100196],{},[38,100145,100146],{},"Křivky užitečnosti (indiferenční)",[883,100148,100150],{"className":100149},[886],[888,100151,100152],{"xmlns":890},[892,100153,100154,100180],{},[895,100155,100156,100158,100160,100166,100168,100174,100176,100178],{},[898,100157,900],{},[1712,100159,1904],{"stretchy":1903},[6927,100161,100162,100164],{},[898,100163,1734],{},[1716,100165,2222],{},[1712,100167,3138],{"separator":2565},[6927,100169,100170,100172],{},[898,100171,1734],{},[1716,100173,2787],{},[1712,100175,1910],{"stretchy":1903},[1712,100177,1714],{},[898,100179,7585],{},[902,100181,14640],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,100184,100186],{"className":100185},[886],[888,100187,100188],{"xmlns":890},[892,100189,100190,100194],{},[895,100191,100192],{},[898,100193,900],{},[902,100195,900],{"encoding":904},", konvexní.",[123,100198,100199,3245,100201,100235],{},[38,100200,97040],{},[883,100202,100204],{"className":100203},[886],[888,100205,100206],{"xmlns":890},[892,100207,100208,100232],{},[895,100209,100210,100212,100214,100216,100222,100224,100226],{},[1762,100211,15475],{},[1712,100213,1714],{},[898,100215,4445],{},[6927,100217,100218,100220],{},[898,100219,900],{},[1716,100221,2222],{},[898,100223,2473],{"mathvariant":2003},[898,100225,4445],{},[6927,100227,100228,100230],{},[898,100229,900],{},[1716,100231,2787],{},[902,100233,100234],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,100237,100238,3245,100241,14641,100270,100273],{},[38,100239,100240],{},"Podmínka optimality",[883,100242,100244],{"className":100243},[886],[888,100245,100246],{"xmlns":890},[892,100247,100248,100268],{},[895,100249,100250,100252,100254,100260,100262],{},[1762,100251,15475],{},[1712,100253,1714],{},[6927,100255,100256,100258],{},[898,100257,1710],{},[1716,100259,2222],{},[898,100261,2473],{"mathvariant":2003},[6927,100263,100264,100266],{},[898,100265,1710],{},[1716,100267,2787],{},[902,100269,32873],{"encoding":904},[207,100271,41629],{"className":100272,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,100275,9193],{"id":9192},[120,100277,100278,100315,100356,100366],{},[123,100279,100280,3245,100283,100286,100287,100300,100301,100314],{},[38,100281,100282],{},"Navazující téma:",[207,100284,913],{"className":100285,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,100288,100290],{"className":100289},[886],[888,100291,100292],{"xmlns":890},[892,100293,100294,100298],{},[895,100295,100296],{},[898,100297,900],{},[902,100299,900],{"encoding":904},", min ",[883,100302,100304],{"className":100303},[886],[888,100305,100306],{"xmlns":890},[892,100307,100308,100312],{},[895,100309,100310],{},[898,100311,2041],{},[902,100313,2041],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,100316,100317,3245,100320,15965,100323,91283,100326,100329,100330,100333,100334,23523,100352,100355],{},[38,100318,100319],{},"Související pojmy:",[207,100321,784],{"className":100322,"dataFsResolvedFilePath":782,"href":783},[210],[207,100324,1690],{"className":100325,"dataFsResolvedFilePath":764,"href":765},[210],[207,100327,15960],{"className":100328,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,100331,16814],{"className":100332,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,100335,100337],{"className":100336},[886],[888,100338,100339],{"xmlns":890},[892,100340,100341,100349],{},[895,100342,100343],{},[6927,100344,100345,100347],{},[898,100346,1969],{},[898,100348,22665],{},[902,100350,100351],{"encoding":904},"D_i",[207,100353,793],{"className":100354,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,100357,100358,3245,100360,1343,100363],{},[38,100359,41578],{},[207,100361,1094],{"className":100362,"dataFsResolvedFilePath":838,"href":839},[210],[207,100364,1101],{"className":100365,"dataFsResolvedFilePath":868,"href":869},[210],[123,100367,100368,3245,100370],{},[38,100369,21078],{},[207,100371,21082],{"className":100372,"dataFsResolvedFilePath":7413,"href":7414},[210],{"title":641,"searchDepth":642,"depth":642,"links":100374},[100375,100376,100377,100380,100381,100384,100388,100389,100392,100393,100394,100395,100396,100397,100398],{"id":16879,"depth":642,"text":16880},{"id":91667,"depth":642,"text":91668},{"id":91727,"depth":642,"text":91728,"children":100378},[100379],{"id":91743,"depth":649,"text":91744},{"id":92050,"depth":642,"text":92051},{"id":92910,"depth":642,"text":92911,"children":100382},[100383],{"id":93457,"depth":649,"text":85086},{"id":93706,"depth":642,"text":93707,"children":100385},[100386],{"id":94579,"depth":649,"text":100387},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":95494,"depth":642,"text":95495},{"id":96030,"depth":642,"text":96031,"children":100390},[100391],{"id":96804,"depth":649,"text":96805},{"id":97034,"depth":642,"text":97035},{"id":97795,"depth":642,"text":97796},{"id":98333,"depth":642,"text":98334},{"id":54756,"depth":642,"text":54757},{"id":98469,"depth":642,"text":98470},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fuzitecnost",{"title":91451,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,14645,100405,91445,15995,100406],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":100409,"title":757,"body":100410,"course":1128,"courses":659,"created":1129,"description":100683,"extension":661,"meta":100684,"navigation":664,"path":100685,"seo":100686,"sources":100687,"stem":100688,"tags":100689,"type":7391,"updated":677,"__hash__":100695},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":100411,"toc":100675},[100412,100415,100422,100429,100433,100443,100445,100479,100483,100526,100529,100587,100591,100621,100625,100646,100648],[12,100413,757],{"id":100414},"základy-matematické-ekonomie",[724,100416,100417,100418,100421],{},"Úvodní pojmy a princip modelování v ",[207,100419,21255],{"className":100420,"dataFsResolvedFilePath":7413,"href":7414},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,100423,100424],{},[3817,100425],{"alt":100426,"className":100427,"src":100428},"imek-model-promenne",[210,3821],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,100430,100432],{"id":100431},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,100434,100435,100438,100439,100442],{},[38,100436,100437],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,100440,100441],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,100444,20594],{"id":20593},[120,100446,100447,100453,100459,100465,100474],{},[123,100448,100449,100452],{},[38,100450,100451],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,100454,100455,100458],{},[38,100456,100457],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,100460,100461,100464],{},[38,100462,100463],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,100466,100467,4831,100470,100473],{},[38,100468,100469],{},"Ceteris paribus",[614,100471,100472],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,100475,100476,100478],{},[38,100477,55510],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,100480,100482],{"id":100481},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,100484,100485,100525],{},[883,100486,100488],{"className":100487},[886],[888,100489,100490],{"xmlns":890},[892,100491,100492,100522],{},[895,100493,100494,100496,100498,100500,100502,100504,100506,100508,100510,100512,100514,100516,100518,100520],{},[898,100495,1734],{},[1712,100497,1714],{},[898,100499,1969],{},[1712,100501,1904],{"stretchy":1903},[898,100503,1710],{},[1712,100505,3138],{"separator":2565},[898,100507,6951],{},[1712,100509,3138],{"separator":2565},[898,100511,23169],{},[1712,100513,3138],{"separator":2565},[898,100515,900],{},[1712,100517,3138],{"separator":2565},[1712,100519,14518],{},[1712,100521,1910],{"stretchy":1903},[902,100523,100524],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,100527,100528],{},"Zjednodušení:",[120,100530,100531,100559],{},[123,100532,100533,3245,100536],{},[38,100534,100535],{},"Jednofaktorový model:",[883,100537,100539],{"className":100538},[886],[888,100540,100541],{"xmlns":890},[892,100542,100543,100557],{},[895,100544,100545,100547,100549,100551,100553,100555],{},[898,100546,1734],{},[1712,100548,1714],{},[898,100550,1969],{},[1712,100552,1904],{"stretchy":1903},[898,100554,1710],{},[1712,100556,1910],{"stretchy":1903},[902,100558,1978],{"encoding":904},[123,100560,100561,3245,100564],{},[38,100562,100563],{},"Inverzní zápis:",[883,100565,100567],{"className":100566},[886],[888,100568,100569],{"xmlns":890},[892,100570,100571,100585],{},[895,100572,100573,100575,100577,100579,100581,100583],{},[898,100574,1710],{},[1712,100576,1714],{},[898,100578,1969],{},[1712,100580,1904],{"stretchy":1903},[898,100582,1734],{},[1712,100584,1910],{"stretchy":1903},[902,100586,2438],{"encoding":904},[115,100588,100590],{"id":100589},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,100592,100593,100602],{},[123,100594,100595,100598,100599,1691],{},[38,100596,100597],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,100600,21114],{"className":100601,"dataFsResolvedFilePath":800,"href":801},[210],[123,100603,100604,100607,100608,100611,100612,100615,100616,100620],{},[38,100605,100606],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,100609,1145],{"className":100610,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,100613,21127],{"className":100614,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,100617,100619],{"className":100618,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,100622,100624],{"id":100623},"konvence-z-přednášek","Konvence z přednášek",[120,100626,100627,100634,100640],{},[123,100628,100629,100630,100633],{},"Symbol ",[100631,100632,3740],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,100635,100636,100637,1659],{},"Numerické výsledky ",[38,100638,100639],{},"na 3 desetinná místa",[123,100641,1666,100642,100645],{},[614,100643,100644],{},"jednotková změna"," má standardní význam (změna o 1).",[115,100647,9193],{"id":9192},[120,100649,100650,100655,100663],{},[123,100651,100652,100654],{},[38,100653,9200],{}," —",[123,100656,100657,3245,100659],{},[38,100658,9208],{},[207,100660,100662],{"className":100661,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,100664,100665,3245,100667,1343,100671],{},[38,100666,9216],{},[207,100668,100670],{"className":100669,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,100672,100674],{"className":100673,"dataFsResolvedFilePath":7413,"href":7414},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":100676},[100677,100678,100679,100680,100681,100682],{"id":100431,"depth":642,"text":100432},{"id":20593,"depth":642,"text":20594},{"id":100481,"depth":642,"text":100482},{"id":100589,"depth":642,"text":100590},{"id":100623,"depth":642,"text":100624},{"id":9192,"depth":642,"text":9193},"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":757,"description":100683},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,100690,100691,100692,100693,100694],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":100697,"title":100698,"body":100699,"course":1128,"courses":659,"created":7380,"description":641,"extension":661,"meta":104971,"navigation":664,"path":104972,"seo":104973,"sources":104974,"stem":104975,"tags":104976,"type":7391,"updated":677,"__hash__":104980},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":100700,"toc":104954},[100701,100704,100798,100802,100824,100838,100890,100892,100896,100959,101002,101021,101184,101283,101286,101353,101357,101486,101525,101555,101667,101712,101778,101831,101907,101963,101965,101969,102033,102077,102097,102258,102261,102345,102442,102445,102511,102515,102564,102590,102695,102759,102764,102860,102907,102909,102912,102934,102976,102983,103016,103018,103089,103143,103252,103256,103345,103421,103685,103723,103725,103729,103732,103739,104050,104053,104111,104291,104320,104322,104326,104332,104470,104479,104481,104483,104908,104910,104912],[12,100702,100698],{"id":100703},"zdanění-trhu-dopady-daně-na-rovnováhu",[1636,100705,100706],{},[724,100707,100708,47503,100710,100723,100724,100727,100728,100730,100731,100734,100735,100756,100757,100780,100781,100784,100785,1659],{},[883,100709,1941],{},[883,100711,100713],{"className":100712},[886],[888,100714,100715],{"xmlns":890},[892,100716,100717,100721],{},[895,100718,100719],{},[898,100720,1772],{},[902,100722,1772],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,100725,100726],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,100729,91735],{}," (je-li uložena spotřebiteli). Výsledné ",[38,100732,100733],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,100736,100738],{"className":100737},[886],[888,100739,100740],{"xmlns":890},[892,100741,100742,100754],{},[895,100743,100744],{},[6927,100745,100746,100748],{},[898,100747,1772],{},[895,100749,100750,100752],{},[898,100751,47552],{},[898,100753,724],{},[902,100755,47557],{"encoding":904}," (spotřebitel) a ",[883,100758,100760],{"className":100759},[886],[888,100761,100762],{"xmlns":890},[892,100763,100764,100778],{},[895,100765,100766],{},[6927,100767,100768,100770],{},[898,100769,1772],{},[895,100771,100772,100774,100776],{},[898,100773,47575],{},[898,100775,7446],{},[898,100777,16915],{},[902,100779,47582],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,100782,100783],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,100786,100788],{"className":100787},[886],[888,100789,100790],{"xmlns":890},[892,100791,100792,100796],{},[895,100793,100794],{},[898,100795,1772],{},[902,100797,1772],{"encoding":904},[115,100799,100801],{"id":100800},"dvě-formy-zdanění","Dvě formy zdanění",[724,100803,100804,100805,100823],{},"Uvažujme jednotkovou daň ",[883,100806,100808],{"className":100807},[886],[888,100809,100810],{"xmlns":890},[892,100811,100812,100820],{},[895,100813,100814,100816,100818],{},[898,100815,1772],{},[1712,100817,2302],{},[1716,100819,2085],{},[902,100821,100822],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,100825,100826,100832],{},[123,100827,100828,100831],{},[38,100829,100830],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,100833,100834,100837],{},[38,100835,100836],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,100839,100840,100841,100854,100855,100858,100859,1659],{},"V obou případech dochází k posunu jedné z křivek o ",[883,100842,100844],{"className":100843},[886],[888,100845,100846],{"xmlns":890},[892,100847,100848,100852],{},[895,100849,100850],{},[898,100851,1772],{},[902,100853,1772],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,100856,100857],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,100860,100862],{"className":100861},[886],[888,100863,100864],{"xmlns":890},[892,100865,100866,100888],{},[895,100867,100868,100870,100872,100878,100880,100886],{},[898,100869,2041],{},[1712,100871,7910],{"stretchy":1903},[2037,100873,100874,100876],{},[898,100875,1734],{},[898,100877,2041],{},[1712,100879,3138],{"separator":2565},[2037,100881,100882,100884],{},[898,100883,1710],{},[898,100885,2041],{},[1712,100887,7925],{"stretchy":1903},[902,100889,46242],{"encoding":904},[41845,100891],{},[115,100893,100895],{"id":100894},"daň-uložená-výrobci","Daň uložená výrobci",[724,100897,100898,100899,100912,100913,100930,100931,100958],{},"Je-li daň ",[883,100900,100902],{"className":100901},[886],[888,100903,100904],{"xmlns":890},[892,100905,100906,100910],{},[895,100907,100908],{},[898,100909,1772],{},[902,100911,1772],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,100914,100916],{"className":100915},[886],[888,100917,100918],{"xmlns":890},[892,100919,100920,100928],{},[895,100921,100922,100924,100926],{},[898,100923,1710],{},[1712,100925,2219],{},[898,100927,1772],{},[902,100929,45997],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,100932,100934],{"className":100933},[886],[888,100935,100936],{"xmlns":890},[892,100937,100938,100956],{},[895,100939,100940,100942,100944,100946,100948,100950,100952,100954],{},[898,100941,1710],{},[1712,100943,2219],{},[898,100945,1772],{},[1712,100947,1714],{},[898,100949,6493],{},[1712,100951,1904],{"stretchy":1903},[898,100953,1734],{},[1712,100955,1910],{"stretchy":1903},[902,100957,46026],{"encoding":904}," nová funkce nabídky:",[883,100960,100962],{"className":100961},[886],[888,100963,100964],{"xmlns":890,"display":32941},[892,100965,100966,101000],{},[895,100967,100968,100970,100972,100978,100980,100982,100984,100986,100988,100990,100992,100994,100996,100998],{},[898,100969,1710],{},[1712,100971,1714],{},[6927,100973,100974,100976],{},[898,100975,6493],{},[1716,100977,2222],{},[1712,100979,1904],{"stretchy":1903},[898,100981,1734],{},[1712,100983,1910],{"stretchy":1903},[1712,100985,1714],{},[898,100987,6493],{},[1712,100989,1904],{"stretchy":1903},[898,100991,1734],{},[1712,100993,1910],{"stretchy":1903},[1712,100995,3145],{},[898,100997,1772],{},[898,100999,1659],{"mathvariant":2003},[902,101001,46071],{"encoding":904},[724,101003,101004,101005,3245,101018,101020],{},"Nabídka se tedy posouvá o ",[883,101006,101008],{"className":101007},[886],[888,101009,101010],{"xmlns":890},[892,101011,101012,101016],{},[895,101013,101014],{},[898,101015,1772],{},[902,101017,1772],{"encoding":904},[38,101019,46104],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,101022,101023,101024,101064,101065,1655,101093,101121,101122,101141,101142,101166,101167,1691],{},"Nový rovnovážný bod ",[883,101025,101027],{"className":101026},[886],[888,101028,101029],{"xmlns":890},[892,101030,101031,101061],{},[895,101032,101033,101039,101041,101049,101051,101059],{},[6927,101034,101035,101037],{},[898,101036,2041],{},[1716,101038,2222],{},[1712,101040,7910],{"stretchy":1903},[6989,101042,101043,101045,101047],{},[898,101044,1734],{},[1716,101046,2222],{},[898,101048,2041],{},[1712,101050,3138],{"separator":2565},[6989,101052,101053,101055,101057],{},[898,101054,1710],{},[1716,101056,2222],{},[898,101058,2041],{},[1712,101060,7925],{"stretchy":1903},[902,101062,101063],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,101066,101068],{"className":101067},[886],[888,101069,101070],{"xmlns":890},[892,101071,101072,101090],{},[895,101073,101074,101082,101084],{},[6989,101075,101076,101078,101080],{},[898,101077,1734],{},[1716,101079,2222],{},[898,101081,2041],{},[1712,101083,2252],{},[2037,101085,101086,101088],{},[898,101087,1734],{},[898,101089,2041],{},[902,101091,101092],{"encoding":904},"Q_1^E \u003C Q^E",[883,101094,101096],{"className":101095},[886],[888,101097,101098],{"xmlns":890},[892,101099,101100,101118],{},[895,101101,101102,101110,101112],{},[6989,101103,101104,101106,101108],{},[898,101105,1710],{},[1716,101107,2222],{},[898,101109,2041],{},[1712,101111,2302],{},[2037,101113,101114,101116],{},[898,101115,1710],{},[898,101117,2041],{},[902,101119,101120],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,101123,101125],{"className":101124},[886],[888,101126,101127],{"xmlns":890},[892,101128,101129,101139],{},[895,101130,101131],{},[6989,101132,101133,101135,101137],{},[898,101134,1710],{},[1716,101136,2222],{},[898,101138,2041],{},[902,101140,52732],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,101143,101145],{"className":101144},[886],[888,101146,101147],{"xmlns":890},[892,101148,101149,101163],{},[895,101150,101151,101159,101161],{},[6989,101152,101153,101155,101157],{},[898,101154,1710],{},[1716,101156,2222],{},[898,101158,2041],{},[1712,101160,2219],{},[898,101162,1772],{},[902,101164,101165],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,101168,101170],{"className":101169},[886],[888,101171,101172],{"xmlns":890},[892,101173,101174,101182],{},[895,101175,101176],{},[2037,101177,101178,101180],{},[898,101179,1710],{},[898,101181,2041],{},[902,101183,46341],{"encoding":904},[724,101185,101186],{},[614,101187,101188,101189,101219,101220,101233,101234,3481,101251,101264,101265,1659],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,101190,101192],{"className":101191},[886],[888,101193,101194],{"xmlns":890},[892,101195,101196,101216],{},[895,101197,101198,101200,101202,101208,101210,101212,101214],{},[898,101199,6493],{},[1712,101201,2082],{},[6927,101203,101204,101206],{},[898,101205,6493],{},[1716,101207,2222],{},[1712,101209,1714],{},[898,101211,6493],{},[1712,101213,3145],{},[898,101215,1772],{},[902,101217,101218],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,101221,101223],{"className":101222},[886],[888,101224,101225],{"xmlns":890},[892,101226,101227,101231],{},[895,101228,101229],{},[898,101230,1772],{},[902,101232,1772],{"encoding":904},". Průsečík ",[883,101235,101237],{"className":101236},[886],[888,101238,101239],{"xmlns":890},[892,101240,101241,101249],{},[895,101242,101243],{},[6927,101244,101245,101247],{},[898,101246,6493],{},[1716,101248,2222],{},[902,101250,45872],{"encoding":904},[883,101252,101254],{"className":101253},[886],[888,101255,101256],{"xmlns":890},[892,101257,101258,101262],{},[895,101259,101260],{},[898,101261,1969],{},[902,101263,1969],{"encoding":904}," je nový rovnovážný bod ",[883,101266,101268],{"className":101267},[886],[888,101269,101270],{"xmlns":890},[892,101271,101272,101280],{},[895,101273,101274],{},[6927,101275,101276,101278],{},[898,101277,2041],{},[1716,101279,2222],{},[902,101281,101282],{"encoding":904},"E_1",[198,101284,50178],{"id":101285},"příklad-29",[724,101287,101288,46530,101290,46565,101314,101334,101335,101352],{},[38,101289,42808],{},[883,101291,101293],{"className":101292},[886],[888,101294,101295],{"xmlns":890},[892,101296,101297,101311],{},[895,101298,101299,101301,101303,101305,101307,101309],{},[898,101300,1710],{},[1712,101302,1714],{},[1716,101304,8912],{},[1712,101306,2219],{},[1716,101308,2787],{},[898,101310,1734],{},[902,101312,101313],{"encoding":904},"P = 12 - 2Q",[883,101315,101317],{"className":101316},[886],[888,101318,101319],{"xmlns":890},[892,101320,101321,101331],{},[895,101322,101323,101325,101327,101329],{},[898,101324,1710],{},[1712,101326,1714],{},[1716,101328,2975],{},[898,101330,1734],{},[902,101332,101333],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,101336,101338],{"className":101337},[886],[888,101339,101340],{"xmlns":890},[892,101341,101342,101350],{},[895,101343,101344,101346,101348],{},[898,101345,1772],{},[1712,101347,1714],{},[1716,101349,6209],{},[902,101351,46143],{"encoding":904}," Kč.",[724,101354,101355],{},[38,101356,42840],{},[724,101358,101359,101362,101363,3381,101389,3401,101409,1343,101431,101461,101462,1659],{},[614,101360,101361],{},"Bez daně."," Z rovnosti ",[883,101364,101366],{"className":101365},[886],[888,101367,101368],{"xmlns":890},[892,101369,101370,101386],{},[895,101371,101372,101374,101376,101378,101380,101382,101384],{},[1716,101373,8912],{},[1712,101375,2219],{},[1716,101377,2787],{},[898,101379,1734],{},[1712,101381,1714],{},[1716,101383,2975],{},[898,101385,1734],{},[902,101387,101388],{"encoding":904},"12 - 2Q = 4Q",[883,101390,101392],{"className":101391},[886],[888,101393,101394],{"xmlns":890},[892,101395,101396,101406],{},[895,101397,101398,101400,101402,101404],{},[1716,101399,6209],{},[898,101401,1734],{},[1712,101403,1714],{},[1716,101405,8912],{},[902,101407,101408],{"encoding":904},"6Q = 12",[883,101410,101412],{"className":101411},[886],[888,101413,101414],{"xmlns":890},[892,101415,101416,101428],{},[895,101417,101418,101424,101426],{},[2037,101419,101420,101422],{},[898,101421,1734],{},[898,101423,2041],{},[1712,101425,1714],{},[1716,101427,2787],{},[902,101429,101430],{"encoding":904},"Q^E = 2",[883,101432,101434],{"className":101433},[886],[888,101435,101436],{"xmlns":890},[892,101437,101438,101458],{},[895,101439,101440,101446,101448,101450,101452,101454,101456],{},[2037,101441,101442,101444],{},[898,101443,1710],{},[898,101445,2041],{},[1712,101447,1714],{},[1716,101449,2975],{},[1712,101451,1783],{},[1716,101453,2787],{},[1712,101455,1714],{},[1716,101457,3397],{},[902,101459,101460],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,101463,101465],{"className":101464},[886],[888,101466,101467],{"xmlns":890},[892,101468,101469,101483],{},[895,101470,101471,101473,101475,101477,101479,101481],{},[898,101472,2041],{},[1712,101474,7910],{"stretchy":1903},[1716,101476,2787],{},[1712,101478,3138],{"separator":2565},[1716,101480,3397],{},[1712,101482,7925],{"stretchy":1903},[902,101484,101485],{"encoding":904},"E[2, 8]",[724,101487,101488,101491,101492,101524],{},[614,101489,101490],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,101493,101495],{"className":101494},[886],[888,101496,101497],{"xmlns":890},[892,101498,101499,101521],{},[895,101500,101501,101507,101509,101511,101513,101515,101517,101519],{},[6927,101502,101503,101505],{},[898,101504,6493],{},[1716,101506,2222],{},[1712,101508,2854],{},[898,101510,1710],{},[1712,101512,1714],{},[1716,101514,2975],{},[898,101516,1734],{},[1712,101518,3145],{},[1716,101520,6209],{},[902,101522,101523],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,101526,101528],{"className":101527},[886],[888,101529,101530],{"xmlns":890,"display":32941},[892,101531,101532,101552],{},[895,101533,101534,101536,101538,101540,101542,101544,101546,101548,101550],{},[1716,101535,8912],{},[1712,101537,2219],{},[1716,101539,2787],{},[898,101541,1734],{},[1712,101543,1714],{},[1716,101545,2975],{},[898,101547,1734],{},[1712,101549,3145],{},[1716,101551,6209],{},[902,101553,101554],{"encoding":904},"12 - 2Q = 4Q + 6",[724,101556,101557,101558,3401,101578,1343,101602,101638,101639,1659],{},"plyne ",[883,101559,101561],{"className":101560},[886],[888,101562,101563],{"xmlns":890},[892,101564,101565,101575],{},[895,101566,101567,101569,101571,101573],{},[1716,101568,6209],{},[898,101570,1734],{},[1712,101572,1714],{},[1716,101574,6209],{},[902,101576,101577],{"encoding":904},"6Q = 6",[883,101579,101581],{"className":101580},[886],[888,101582,101583],{"xmlns":890},[892,101584,101585,101599],{},[895,101586,101587,101595,101597],{},[6989,101588,101589,101591,101593],{},[898,101590,1734],{},[1716,101592,2222],{},[898,101594,2041],{},[1712,101596,1714],{},[1716,101598,2222],{},[902,101600,101601],{"encoding":904},"Q_1^E = 1",[883,101603,101605],{"className":101604},[886],[888,101606,101607],{"xmlns":890},[892,101608,101609,101635],{},[895,101610,101611,101619,101621,101623,101625,101627,101629,101631,101633],{},[6989,101612,101613,101615,101617],{},[898,101614,1710],{},[1716,101616,2222],{},[898,101618,2041],{},[1712,101620,1714],{},[1716,101622,2975],{},[1712,101624,1783],{},[1716,101626,2222],{},[1712,101628,3145],{},[1716,101630,6209],{},[1712,101632,1714],{},[1716,101634,1718],{},[902,101636,101637],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,101640,101642],{"className":101641},[886],[888,101643,101644],{"xmlns":890},[892,101645,101646,101664],{},[895,101647,101648,101654,101656,101658,101660,101662],{},[6927,101649,101650,101652],{},[898,101651,2041],{},[1716,101653,2222],{},[1712,101655,7910],{"stretchy":1903},[1716,101657,2222],{},[1712,101659,3138],{"separator":2565},[1716,101661,1718],{},[1712,101663,7925],{"stretchy":1903},[902,101665,101666],{"encoding":904},"E_1[1, 10]",[724,101668,101669,101672,101673,101697,101698,101711],{},[614,101670,101671],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,101674,101676],{"className":101675},[886],[888,101677,101678],{"xmlns":890},[892,101679,101680,101694],{},[895,101681,101682,101690,101692],{},[6989,101683,101684,101686,101688],{},[898,101685,1710],{},[1716,101687,2222],{},[898,101689,2041],{},[1712,101691,1714],{},[1716,101693,1718],{},[902,101695,101696],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,101699,101701],{"className":101700},[886],[888,101702,101703],{"xmlns":890},[892,101704,101705,101709],{},[895,101706,101707],{},[1716,101708,3397],{},[902,101710,3397],{"encoding":904},", navýšení je",[883,101713,101715],{"className":101714},[886],[888,101716,101717],{"xmlns":890,"display":32941},[892,101718,101719,101775],{},[895,101720,101721,101731,101733,101741,101743,101749,101751,101753,101755,101757,101759,101761,101763,101773],{},[6927,101722,101723,101725],{},[898,101724,1772],{},[895,101726,101727,101729],{},[898,101728,47552],{},[898,101730,724],{},[1712,101732,1714],{},[6989,101734,101735,101737,101739],{},[898,101736,1710],{},[1716,101738,2222],{},[898,101740,2041],{},[1712,101742,2219],{},[2037,101744,101745,101747],{},[898,101746,1710],{},[898,101748,2041],{},[1712,101750,1714],{},[1716,101752,1718],{},[1712,101754,2219],{},[1716,101756,3397],{},[1712,101758,1714],{},[1716,101760,2787],{},[1762,101762,7722],{},[895,101764,101765,101767],{},[1762,101766,14672],{},[6205,101768,101769,101771],{"accent":2565},[1762,101770,7585],{},[1712,101772,29933],{},[898,101774,1659],{"mathvariant":2003},[902,101776,101777],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,101779,101780,101781,101697,101817,101830],{},"Výrobci zůstává čistá cena ",[883,101782,101784],{"className":101783},[886],[888,101785,101786],{"xmlns":890},[892,101787,101788,101814],{},[895,101789,101790,101798,101800,101802,101804,101806,101808,101810,101812],{},[6989,101791,101792,101794,101796],{},[898,101793,1710],{},[1716,101795,2222],{},[898,101797,2041],{},[1712,101799,2219],{},[898,101801,1772],{},[1712,101803,1714],{},[1716,101805,1718],{},[1712,101807,2219],{},[1716,101809,6209],{},[1712,101811,1714],{},[1716,101813,2975],{},[902,101815,101816],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,101818,101820],{"className":101819},[886],[888,101821,101822],{"xmlns":890},[892,101823,101824,101828],{},[895,101825,101826],{},[1716,101827,3397],{},[902,101829,3397],{"encoding":904},", pokles je",[883,101832,101834],{"className":101833},[886],[888,101835,101836],{"xmlns":890,"display":32941},[892,101837,101838,101904],{},[895,101839,101840,101852,101854,101860,101862,101864,101872,101874,101876,101878,101880,101882,101884,101886,101888,101890,101892,101902],{},[6927,101841,101842,101844],{},[898,101843,1772],{},[895,101845,101846,101848,101850],{},[898,101847,47575],{},[898,101849,7446],{},[898,101851,16915],{},[1712,101853,1714],{},[2037,101855,101856,101858],{},[898,101857,1710],{},[898,101859,2041],{},[1712,101861,2219],{},[1712,101863,1904],{"stretchy":1903},[6989,101865,101866,101868,101870],{},[898,101867,1710],{},[1716,101869,2222],{},[898,101871,2041],{},[1712,101873,2219],{},[898,101875,1772],{},[1712,101877,1910],{"stretchy":1903},[1712,101879,1714],{},[1716,101881,3397],{},[1712,101883,2219],{},[1716,101885,2975],{},[1712,101887,1714],{},[1716,101889,2975],{},[1762,101891,7722],{},[895,101893,101894,101896],{},[1762,101895,14672],{},[6205,101897,101898,101900],{"accent":2565},[1762,101899,7585],{},[1712,101901,29933],{},[898,101903,1659],{"mathvariant":2003},[902,101905,101906],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,101908,101909,101910,101962],{},"Kontrola: ",[883,101911,101913],{"className":101912},[886],[888,101914,101915],{"xmlns":890},[892,101916,101917,101959],{},[895,101918,101919,101929,101931,101943,101945,101947,101949,101951,101953,101955,101957],{},[6927,101920,101921,101923],{},[898,101922,1772],{},[895,101924,101925,101927],{},[898,101926,47552],{},[898,101928,724],{},[1712,101930,3145],{},[6927,101932,101933,101935],{},[898,101934,1772],{},[895,101936,101937,101939,101941],{},[898,101938,47575],{},[898,101940,7446],{},[898,101942,16915],{},[1712,101944,1714],{},[1716,101946,2787],{},[1712,101948,3145],{},[1716,101950,2975],{},[1712,101952,1714],{},[1716,101954,6209],{},[1712,101956,1714],{},[898,101958,1772],{},[902,101960,101961],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[41845,101964],{},[115,101966,101968],{"id":101967},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,101970,100898,101971,101984,101985,102003,102004,102032],{},[883,101972,101974],{"className":101973},[886],[888,101975,101976],{"xmlns":890},[892,101977,101978,101982],{},[895,101979,101980],{},[898,101981,1772],{},[902,101983,1772],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,101986,101988],{"className":101987},[886],[888,101989,101990],{"xmlns":890},[892,101991,101992,102000],{},[895,101993,101994,101996,101998],{},[898,101995,1710],{},[1712,101997,3145],{},[898,101999,1772],{},[902,102001,102002],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,102005,102007],{"className":102006},[886],[888,102008,102009],{"xmlns":890},[892,102010,102011,102029],{},[895,102012,102013,102015,102017,102019,102021,102023,102025,102027],{},[898,102014,1710],{},[1712,102016,3145],{},[898,102018,1772],{},[1712,102020,1714],{},[898,102022,1969],{},[1712,102024,1904],{"stretchy":1903},[898,102026,1734],{},[1712,102028,1910],{"stretchy":1903},[902,102030,102031],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,102034,102036],{"className":102035},[886],[888,102037,102038],{"xmlns":890,"display":32941},[892,102039,102040,102074],{},[895,102041,102042,102044,102046,102052,102054,102056,102058,102060,102062,102064,102066,102068,102070,102072],{},[898,102043,1710],{},[1712,102045,1714],{},[6927,102047,102048,102050],{},[898,102049,1969],{},[1716,102051,2787],{},[1712,102053,1904],{"stretchy":1903},[898,102055,1734],{},[1712,102057,1910],{"stretchy":1903},[1712,102059,1714],{},[898,102061,1969],{},[1712,102063,1904],{"stretchy":1903},[898,102065,1734],{},[1712,102067,1910],{"stretchy":1903},[1712,102069,2219],{},[898,102071,1772],{},[898,102073,1659],{"mathvariant":2003},[902,102075,102076],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,102078,102079,102080,3245,102093,102096],{},"Poptávka se tedy posouvá o ",[883,102081,102083],{"className":102082},[886],[888,102084,102085],{"xmlns":890},[892,102086,102087,102091],{},[895,102088,102089],{},[898,102090,1772],{},[902,102092,1772],{"encoding":904},[38,102094,102095],{},"svisle dolů",". Nabídka se nemění.",[724,102098,101023,102099,101064,102139,1655,102167,102195,102196,102215,102216,102240,102241,1691],{},[883,102100,102102],{"className":102101},[886],[888,102103,102104],{"xmlns":890},[892,102105,102106,102136],{},[895,102107,102108,102114,102116,102124,102126,102134],{},[6927,102109,102110,102112],{},[898,102111,2041],{},[1716,102113,2787],{},[1712,102115,7910],{"stretchy":1903},[6989,102117,102118,102120,102122],{},[898,102119,1734],{},[1716,102121,2787],{},[898,102123,2041],{},[1712,102125,3138],{"separator":2565},[6989,102127,102128,102130,102132],{},[898,102129,1710],{},[1716,102131,2787],{},[898,102133,2041],{},[1712,102135,7925],{"stretchy":1903},[902,102137,102138],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,102140,102142],{"className":102141},[886],[888,102143,102144],{"xmlns":890},[892,102145,102146,102164],{},[895,102147,102148,102156,102158],{},[6989,102149,102150,102152,102154],{},[898,102151,1734],{},[1716,102153,2787],{},[898,102155,2041],{},[1712,102157,2252],{},[2037,102159,102160,102162],{},[898,102161,1734],{},[898,102163,2041],{},[902,102165,102166],{"encoding":904},"Q_2^E \u003C Q^E",[883,102168,102170],{"className":102169},[886],[888,102171,102172],{"xmlns":890},[892,102173,102174,102192],{},[895,102175,102176,102184,102186],{},[6989,102177,102178,102180,102182],{},[898,102179,1710],{},[1716,102181,2787],{},[898,102183,2041],{},[1712,102185,2252],{},[2037,102187,102188,102190],{},[898,102189,1710],{},[898,102191,2041],{},[902,102193,102194],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,102197,102199],{"className":102198},[886],[888,102200,102201],{"xmlns":890},[892,102202,102203,102213],{},[895,102204,102205],{},[6989,102206,102207,102209,102211],{},[898,102208,1710],{},[1716,102210,2787],{},[898,102212,2041],{},[902,102214,52793],{"encoding":904},", spotřebitel platí celkem ",[883,102217,102219],{"className":102218},[886],[888,102220,102221],{"xmlns":890},[892,102222,102223,102237],{},[895,102224,102225,102233,102235],{},[6989,102226,102227,102229,102231],{},[898,102228,1710],{},[1716,102230,2787],{},[898,102232,2041],{},[1712,102234,3145],{},[898,102236,1772],{},[902,102238,102239],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,102242,102244],{"className":102243},[886],[888,102245,102246],{"xmlns":890},[892,102247,102248,102256],{},[895,102249,102250],{},[2037,102251,102252,102254],{},[898,102253,1710],{},[898,102255,2041],{},[902,102257,46341],{"encoding":904},[724,102259,102260],{},"Daňové břemeno:",[883,102262,102264],{"className":102263},[886],[888,102265,102266],{"xmlns":890,"display":32941},[892,102267,102268,102342],{},[895,102269,102270,102280,102282,102284,102292,102294,102296,102298,102300,102306,102308,102310,102322,102324,102330,102332,102340],{},[6927,102271,102272,102274],{},[898,102273,1772],{},[895,102275,102276,102278],{},[898,102277,47552],{},[898,102279,724],{},[1712,102281,1714],{},[1712,102283,1904],{"stretchy":1903},[6989,102285,102286,102288,102290],{},[898,102287,1710],{},[1716,102289,2787],{},[898,102291,2041],{},[1712,102293,3145],{},[898,102295,1772],{},[1712,102297,1910],{"stretchy":1903},[1712,102299,2219],{},[2037,102301,102302,102304],{},[898,102303,1710],{},[898,102305,2041],{},[1712,102307,3138],{"separator":2565},[3690,102309],{"width":3692},[6927,102311,102312,102314],{},[898,102313,1772],{},[895,102315,102316,102318,102320],{},[898,102317,47575],{},[898,102319,7446],{},[898,102321,16915],{},[1712,102323,1714],{},[2037,102325,102326,102328],{},[898,102327,1710],{},[898,102329,2041],{},[1712,102331,2219],{},[6989,102333,102334,102336,102338],{},[898,102335,1710],{},[1716,102337,2787],{},[898,102339,2041],{},[898,102341,1659],{"mathvariant":2003},[902,102343,102344],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,102346,102347],{},[614,102348,102349,102350,102380,102381,101233,102394,3481,102411,101264,102424,1659],{},"Obrázek 2.19: Posun ",[883,102351,102353],{"className":102352},[886],[888,102354,102355],{"xmlns":890},[892,102356,102357,102377],{},[895,102358,102359,102361,102363,102369,102371,102373,102375],{},[898,102360,1969],{},[1712,102362,2082],{},[6927,102364,102365,102367],{},[898,102366,1969],{},[1716,102368,2787],{},[1712,102370,1714],{},[898,102372,1969],{},[1712,102374,2219],{},[898,102376,1772],{},[902,102378,102379],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,102382,102384],{"className":102383},[886],[888,102385,102386],{"xmlns":890},[892,102387,102388,102392],{},[895,102389,102390],{},[898,102391,1772],{},[902,102393,1772],{"encoding":904},[883,102395,102397],{"className":102396},[886],[888,102398,102399],{"xmlns":890},[892,102400,102401,102409],{},[895,102402,102403],{},[6927,102404,102405,102407],{},[898,102406,1969],{},[1716,102408,2787],{},[902,102410,43202],{"encoding":904},[883,102412,102414],{"className":102413},[886],[888,102415,102416],{"xmlns":890},[892,102417,102418,102422],{},[895,102419,102420],{},[898,102421,6493],{},[902,102423,6493],{"encoding":904},[883,102425,102427],{"className":102426},[886],[888,102428,102429],{"xmlns":890},[892,102430,102431,102439],{},[895,102432,102433],{},[6927,102434,102435,102437],{},[898,102436,2041],{},[1716,102438,2787],{},[902,102440,102441],{"encoding":904},"E_2",[198,102443,50258],{"id":102444},"příklad-210",[724,102446,102447,102449,102450,46565,102473,102492,102493,102510],{},[38,102448,42808],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,102451,102453],{"className":102452},[886],[888,102454,102455],{"xmlns":890},[892,102456,102457,102471],{},[895,102458,102459,102461,102463,102465,102467,102469],{},[898,102460,1710],{},[1712,102462,1714],{},[1716,102464,8912],{},[1712,102466,2219],{},[1716,102468,2787],{},[898,102470,1734],{},[902,102472,101313],{"encoding":904},[883,102474,102476],{"className":102475},[886],[888,102477,102478],{"xmlns":890},[892,102479,102480,102490],{},[895,102481,102482,102484,102486,102488],{},[898,102483,1710],{},[1712,102485,1714],{},[1716,102487,2975],{},[898,102489,1734],{},[902,102491,101333],{"encoding":904},". Daň ",[883,102494,102496],{"className":102495},[886],[888,102497,102498],{"xmlns":890},[892,102499,102500,102508],{},[895,102501,102502,102504,102506],{},[898,102503,1772],{},[1712,102505,1714],{},[1716,102507,6209],{},[902,102509,46143],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,102512,102513],{},[38,102514,42840],{},[724,102516,102517,102518,101524],{},"Nová poptávka je ",[883,102519,102521],{"className":102520},[886],[888,102522,102523],{"xmlns":890},[892,102524,102525,102561],{},[895,102526,102527,102533,102535,102537,102539,102541,102543,102545,102547,102549,102551,102553,102555,102557,102559],{},[6927,102528,102529,102531],{},[898,102530,1969],{},[1716,102532,2787],{},[1712,102534,2854],{},[898,102536,1710],{},[1712,102538,1714],{},[1716,102540,8912],{},[1712,102542,2219],{},[1716,102544,2787],{},[898,102546,1734],{},[1712,102548,2219],{},[1716,102550,6209],{},[1712,102552,1714],{},[1716,102554,6209],{},[1712,102556,2219],{},[1716,102558,2787],{},[898,102560,1734],{},[902,102562,102563],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,102565,102567],{"className":102566},[886],[888,102568,102569],{"xmlns":890,"display":32941},[892,102570,102571,102587],{},[895,102572,102573,102575,102577,102579,102581,102583,102585],{},[1716,102574,6209],{},[1712,102576,2219],{},[1716,102578,2787],{},[898,102580,1734],{},[1712,102582,1714],{},[1716,102584,2975],{},[898,102586,1734],{},[902,102588,102589],{"encoding":904},"6 - 2Q = 4Q",[724,102591,101557,102592,3401,102611,1343,102635,101638,102667,1659],{},[883,102593,102595],{"className":102594},[886],[888,102596,102597],{"xmlns":890},[892,102598,102599,102609],{},[895,102600,102601,102603,102605,102607],{},[1716,102602,6209],{},[898,102604,1734],{},[1712,102606,1714],{},[1716,102608,6209],{},[902,102610,101577],{"encoding":904},[883,102612,102614],{"className":102613},[886],[888,102615,102616],{"xmlns":890},[892,102617,102618,102632],{},[895,102619,102620,102628,102630],{},[6989,102621,102622,102624,102626],{},[898,102623,1734],{},[1716,102625,2787],{},[898,102627,2041],{},[1712,102629,1714],{},[1716,102631,2222],{},[902,102633,102634],{"encoding":904},"Q_2^E = 1",[883,102636,102638],{"className":102637},[886],[888,102639,102640],{"xmlns":890},[892,102641,102642,102664],{},[895,102643,102644,102652,102654,102656,102658,102660,102662],{},[6989,102645,102646,102648,102650],{},[898,102647,1710],{},[1716,102649,2787],{},[898,102651,2041],{},[1712,102653,1714],{},[1716,102655,2975],{},[1712,102657,1783],{},[1716,102659,2222],{},[1712,102661,1714],{},[1716,102663,2975],{},[902,102665,102666],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,102668,102670],{"className":102669},[886],[888,102671,102672],{"xmlns":890},[892,102673,102674,102692],{},[895,102675,102676,102682,102684,102686,102688,102690],{},[6927,102677,102678,102680],{},[898,102679,2041],{},[1716,102681,2787],{},[1712,102683,7910],{"stretchy":1903},[1716,102685,2222],{},[1712,102687,3138],{"separator":2565},[1716,102689,2975],{},[1712,102691,7925],{"stretchy":1903},[902,102693,102694],{"encoding":904},"E_2[1, 4]",[724,102696,102697,102698,102734,102735,101352],{},"Spotřebitel platí celkem ",[883,102699,102701],{"className":102700},[886],[888,102702,102703],{"xmlns":890},[892,102704,102705,102731],{},[895,102706,102707,102715,102717,102719,102721,102723,102725,102727,102729],{},[6989,102708,102709,102711,102713],{},[898,102710,1710],{},[1716,102712,2787],{},[898,102714,2041],{},[1712,102716,3145],{},[898,102718,1772],{},[1712,102720,1714],{},[1716,102722,2975],{},[1712,102724,3145],{},[1716,102726,6209],{},[1712,102728,1714],{},[1716,102730,1718],{},[902,102732,102733],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,102736,102738],{"className":102737},[886],[888,102739,102740],{"xmlns":890},[892,102741,102742,102756],{},[895,102743,102744,102752,102754],{},[6989,102745,102746,102748,102750],{},[898,102747,1710],{},[1716,102749,2787],{},[898,102751,2041],{},[1712,102753,1714],{},[1716,102755,2975],{},[902,102757,102758],{"encoding":904},"P_2^E = 4",[724,102760,102761],{},[614,102762,102763],{},"Rozklad daňového břemene:",[883,102765,102767],{"className":102766},[886],[888,102768,102769],{"xmlns":890,"display":32941},[892,102770,102771,102857],{},[895,102772,102773,102783,102785,102787,102789,102791,102793,102795,102797,102799,102801,102803,102805,102815,102817,102819,102831,102833,102835,102837,102839,102841,102843,102845,102855],{},[6927,102774,102775,102777],{},[898,102776,1772],{},[895,102778,102779,102781],{},[898,102780,47552],{},[898,102782,724],{},[1712,102784,1714],{},[1712,102786,1904],{"stretchy":1903},[1716,102788,2975],{},[1712,102790,3145],{},[1716,102792,6209],{},[1712,102794,1910],{"stretchy":1903},[1712,102796,2219],{},[1716,102798,3397],{},[1712,102800,1714],{},[1716,102802,2787],{},[1762,102804,7722],{},[895,102806,102807,102809],{},[1762,102808,14672],{},[6205,102810,102811,102813],{"accent":2565},[1762,102812,7585],{},[1712,102814,29933],{},[1712,102816,3138],{"separator":2565},[3690,102818],{"width":3692},[6927,102820,102821,102823],{},[898,102822,1772],{},[895,102824,102825,102827,102829],{},[898,102826,47575],{},[898,102828,7446],{},[898,102830,16915],{},[1712,102832,1714],{},[1716,102834,3397],{},[1712,102836,2219],{},[1716,102838,2975],{},[1712,102840,1714],{},[1716,102842,2975],{},[1762,102844,7722],{},[895,102846,102847,102849],{},[1762,102848,14672],{},[6205,102850,102851,102853],{"accent":2565},[1762,102852,7585],{},[1712,102854,29933],{},[898,102856,1659],{"mathvariant":2003},[902,102858,102859],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,102861,102862,102863,1659],{},"Opět ",[883,102864,102866],{"className":102865},[886],[888,102867,102868],{"xmlns":890},[892,102869,102870,102904],{},[895,102871,102872,102882,102884,102896,102898,102900,102902],{},[6927,102873,102874,102876],{},[898,102875,1772],{},[895,102877,102878,102880],{},[898,102879,47552],{},[898,102881,724],{},[1712,102883,3145],{},[6927,102885,102886,102888],{},[898,102887,1772],{},[895,102889,102890,102892,102894],{},[898,102891,47575],{},[898,102893,7446],{},[898,102895,16915],{},[1712,102897,1714],{},[1716,102899,6209],{},[1712,102901,1714],{},[898,102903,1772],{},[902,102905,102906],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[41845,102908],{},[115,102910,47533],{"id":102911},"daňové-břemeno",[724,102913,102914,14897,102916,102919,102920,102933],{},[38,102915,47533],{},[614,102917,102918],{},"tax burden",") je rozdělení zaplacené daně ",[883,102921,102923],{"className":102922},[886],[888,102924,102925],{"xmlns":890},[892,102926,102927,102931],{},[895,102928,102929],{},[898,102930,1772],{},[902,102932,1772],{"encoding":904}," mezi spotřebitele a výrobce:",[883,102935,102937],{"className":102936},[886],[888,102938,102939],{"xmlns":890,"display":32941},[892,102940,102941,102973],{},[895,102942,102943,102945,102947,102957,102959,102971],{},[898,102944,1772],{},[1712,102946,1714],{},[6927,102948,102949,102951],{},[898,102950,1772],{},[895,102952,102953,102955],{},[898,102954,47552],{},[898,102956,724],{},[1712,102958,3145],{},[6927,102960,102961,102963],{},[898,102962,1772],{},[895,102964,102965,102967,102969],{},[898,102966,47575],{},[898,102968,7446],{},[898,102970,16915],{},[898,102972,1659],{"mathvariant":2003},[902,102974,102975],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,102977,102978],{},[3817,102979],{"alt":102980,"className":102981,"src":102982},"imek-dan-rozklad-bremene-sklony",[210,3821],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1636,102984,102985],{},[724,102986,102987,102989,102990,1655,103003,1659],{},[883,102988,1941],{}," 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 ",[883,102991,102993],{"className":102992},[886],[888,102994,102995],{"xmlns":890},[892,102996,102997,103001],{},[895,102998,102999],{},[898,103000,1969],{},[902,103002,1969],{"encoding":904},[883,103004,103006],{"className":103005},[886],[888,103007,103008],{"xmlns":890},[892,103009,103010,103014],{},[895,103011,103012],{},[898,103013,6493],{},[902,103015,6493],{"encoding":904},[198,103017,7868],{"id":7867},[724,103019,103020,103021,103042,103043,103056,103057,103074,103075,103088],{},"V grafu ",[883,103022,103024],{"className":103023},[886],[888,103025,103026],{"xmlns":890},[892,103027,103028,103040],{},[895,103029,103030,103032,103034,103036,103038],{},[1712,103031,1904],{"stretchy":1903},[898,103033,1734],{},[1712,103035,3138],{"separator":2565},[898,103037,1710],{},[1712,103039,1910],{"stretchy":1903},[902,103041,42566],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,103044,103046],{"className":103045},[886],[888,103047,103048],{"xmlns":890},[892,103049,103050,103054],{},[895,103051,103052],{},[898,103053,1772],{},[902,103055,1772],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,103058,103060],{"className":103059},[886],[888,103061,103062],{"xmlns":890},[892,103063,103064,103072],{},[895,103065,103066],{},[2037,103067,103068,103070],{},[898,103069,1710],{},[898,103071,2041],{},[902,103073,46341],{"encoding":904},", rozdělí se úsečka ",[883,103076,103078],{"className":103077},[886],[888,103079,103080],{"xmlns":890},[892,103081,103082,103086],{},[895,103083,103084],{},[898,103085,1772],{},[902,103087,1772],{"encoding":904}," na dvě části:",[120,103090,103091,103116],{},[123,103092,103093,103094,103115],{},"horní část odpovídá ",[883,103095,103097],{"className":103096},[886],[888,103098,103099],{"xmlns":890},[892,103100,103101,103113],{},[895,103102,103103],{},[6927,103104,103105,103107],{},[898,103106,1772],{},[895,103108,103109,103111],{},[898,103110,47552],{},[898,103112,724],{},[902,103114,47557],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,103117,103118,103119,103142],{},"dolní část odpovídá ",[883,103120,103122],{"className":103121},[886],[888,103123,103124],{"xmlns":890},[892,103125,103126,103140],{},[895,103127,103128],{},[6927,103129,103130,103132],{},[898,103131,1772],{},[895,103133,103134,103136,103138],{},[898,103135,47575],{},[898,103137,7446],{},[898,103139,16915],{},[902,103141,47582],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,103144,103145],{},[614,103146,103147,103148,3072,103161,103182,103183,103206,103207,1655,103228,103251],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,103149,103151],{"className":103150},[886],[888,103152,103153],{"xmlns":890},[892,103154,103155,103159],{},[895,103156,103157],{},[898,103158,1772],{},[902,103160,1772],{"encoding":904},[883,103162,103164],{"className":103163},[886],[888,103165,103166],{"xmlns":890},[892,103167,103168,103180],{},[895,103169,103170],{},[6927,103171,103172,103174],{},[898,103173,1772],{},[895,103175,103176,103178],{},[898,103177,47552],{},[898,103179,724],{},[902,103181,47557],{"encoding":904}," (nahoře) a ",[883,103184,103186],{"className":103185},[886],[888,103187,103188],{"xmlns":890},[892,103189,103190,103204],{},[895,103191,103192],{},[6927,103193,103194,103196],{},[898,103195,1772],{},[895,103197,103198,103200,103202],{},[898,103199,47575],{},[898,103201,7446],{},[898,103203,16915],{},[902,103205,47582],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,103208,103210],{"className":103209},[886],[888,103211,103212],{"xmlns":890},[892,103213,103214,103226],{},[895,103215,103216],{},[6927,103217,103218,103220],{},[898,103219,1772],{},[895,103221,103222,103224],{},[898,103223,47552],{},[898,103225,724],{},[902,103227,47557],{"encoding":904},[883,103229,103231],{"className":103230},[886],[888,103232,103233],{"xmlns":890},[892,103234,103235,103249],{},[895,103236,103237],{},[6927,103238,103239,103241],{},[898,103240,1772],{},[895,103242,103243,103245,103247],{},[898,103244,47575],{},[898,103246,7446],{},[898,103248,16915],{},[902,103250,47582],{"encoding":904}," je v obou případech stejná.",[198,103253,103255],{"id":103254},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,103257,103258,103259,103262,103263,14897,103286,103303,103304,14897,103327,103344],{},"Platí obecně: ",[38,103260,103261],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,103264,103266],{"className":103265},[886],[888,103267,103268],{"xmlns":890},[892,103269,103270,103284],{},[895,103271,103272,103274,103276,103278,103280,103282],{},[898,103273,1710],{},[1712,103275,1714],{},[898,103277,207],{},[898,103279,1734],{},[1712,103281,3145],{},[898,103283,7544],{},[902,103285,41935],{"encoding":904},[883,103287,103289],{"className":103288},[886],[888,103290,103291],{"xmlns":890},[892,103292,103293,103301],{},[895,103294,103295,103297,103299],{},[898,103296,207],{},[1712,103298,2252],{},[1716,103300,2085],{},[902,103302,47960],{"encoding":904},") a lineární nabídku ",[883,103305,103307],{"className":103306},[886],[888,103308,103309],{"xmlns":890},[892,103310,103311,103325],{},[895,103312,103313,103315,103317,103319,103321,103323],{},[898,103314,1710],{},[1712,103316,1714],{},[898,103318,7585],{},[898,103320,1734],{},[1712,103322,3145],{},[898,103324,2468],{},[902,103326,45117],{"encoding":904},[883,103328,103330],{"className":103329},[886],[888,103331,103332],{"xmlns":890},[892,103333,103334,103342],{},[895,103335,103336,103338,103340],{},[898,103337,7585],{},[1712,103339,2302],{},[1716,103341,2085],{},[902,103343,45135],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,103346,103348],{"className":103347},[886],[888,103349,103350],{"xmlns":890,"display":32941},[892,103351,103352,103418],{},[895,103353,103354,103378,103380,103390,103392,103416],{},[2567,103355,103356,103366],{},[6927,103357,103358,103360],{},[898,103359,1772],{},[895,103361,103362,103364],{},[898,103363,47552],{},[898,103365,724],{},[6927,103367,103368,103370],{},[898,103369,1772],{},[895,103371,103372,103374,103376],{},[898,103373,47575],{},[898,103375,7446],{},[898,103377,16915],{},[1712,103379,1714],{},[2567,103381,103382,103384],{},[898,103383,7585],{},[895,103385,103386,103388],{},[1712,103387,2219],{},[898,103389,207],{},[1712,103391,1714],{},[2567,103393,103394,103406],{},[895,103395,103396,103399,103402,103404],{},[898,103397,103398],{"mathvariant":2003},"∣",[1762,103400,103401],{},"sklon ",[898,103403,6493],{},[898,103405,103398],{"mathvariant":2003},[895,103407,103408,103410,103412,103414],{},[898,103409,103398],{"mathvariant":2003},[1762,103411,103401],{},[898,103413,1969],{},[898,103415,103398],{"mathvariant":2003},[898,103417,1659],{"mathvariant":2003},[902,103419,103420],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1636,103422,103423,103428],{},[724,103424,103425,103427],{},[883,103426,2370],{}," Postup výpočtu rozkladu",[152,103429,103430,103465,103518,103597],{},[123,103431,103432,103433,103464],{},"Spočti rovnovážný bod ",[883,103434,103436],{"className":103435},[886],[888,103437,103438],{"xmlns":890},[892,103439,103440,103462],{},[895,103441,103442,103444,103446,103452,103454,103460],{},[898,103443,2041],{},[1712,103445,7910],{"stretchy":1903},[2037,103447,103448,103450],{},[898,103449,1734],{},[898,103451,2041],{},[1712,103453,3138],{"separator":2565},[2037,103455,103456,103458],{},[898,103457,1710],{},[898,103459,2041],{},[1712,103461,7925],{"stretchy":1903},[902,103463,46242],{"encoding":904}," bez daně.",[123,103466,103467,103468,1348,103493,1691],{},"Urči posunutou křivku (",[883,103469,103471],{"className":103470},[886],[888,103472,103473],{"xmlns":890},[892,103474,103475,103491],{},[895,103476,103477,103483,103485,103487,103489],{},[6927,103478,103479,103481],{},[898,103480,6493],{},[1716,103482,2222],{},[1712,103484,1714],{},[898,103486,6493],{},[1712,103488,3145],{},[898,103490,1772],{},[902,103492,47629],{"encoding":904},[883,103494,103496],{"className":103495},[886],[888,103497,103498],{"xmlns":890},[892,103499,103500,103516],{},[895,103501,103502,103508,103510,103512,103514],{},[6927,103503,103504,103506],{},[898,103505,1969],{},[1716,103507,2787],{},[1712,103509,1714],{},[898,103511,1969],{},[1712,103513,2219],{},[898,103515,1772],{},[902,103517,47660],{"encoding":904},[123,103519,103520,103521,1682,103540,17002,103559,1682,103578,1691],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,103522,103524],{"className":103523},[886],[888,103525,103526],{"xmlns":890},[892,103527,103528,103538],{},[895,103529,103530],{},[6989,103531,103532,103534,103536],{},[898,103533,1734],{},[1716,103535,2222],{},[898,103537,2041],{},[902,103539,52711],{"encoding":904},[883,103541,103543],{"className":103542},[886],[888,103544,103545],{"xmlns":890},[892,103546,103547,103557],{},[895,103548,103549],{},[6989,103550,103551,103553,103555],{},[898,103552,1734],{},[1716,103554,2787],{},[898,103556,2041],{},[902,103558,52773],{"encoding":904},[883,103560,103562],{"className":103561},[886],[888,103563,103564],{"xmlns":890},[892,103565,103566,103576],{},[895,103567,103568],{},[6989,103569,103570,103572,103574],{},[898,103571,1710],{},[1716,103573,2222],{},[898,103575,2041],{},[902,103577,52732],{"encoding":904},[883,103579,103581],{"className":103580},[886],[888,103582,103583],{"xmlns":890},[892,103584,103585,103595],{},[895,103586,103587],{},[6989,103588,103589,103591,103593],{},[898,103590,1710],{},[1716,103592,2787],{},[898,103594,2041],{},[902,103596,52793],{"encoding":904},[123,103598,103599,103600,1655,103621,103644,103645,1659],{},"Dopočítej ",[883,103601,103603],{"className":103602},[886],[888,103604,103605],{"xmlns":890},[892,103606,103607,103619],{},[895,103608,103609],{},[6927,103610,103611,103613],{},[898,103612,1772],{},[895,103614,103615,103617],{},[898,103616,47552],{},[898,103618,724],{},[902,103620,47557],{"encoding":904},[883,103622,103624],{"className":103623},[886],[888,103625,103626],{"xmlns":890},[892,103627,103628,103642],{},[895,103629,103630],{},[6927,103631,103632,103634],{},[898,103633,1772],{},[895,103635,103636,103638,103640],{},[898,103637,47575],{},[898,103639,7446],{},[898,103641,16915],{},[902,103643,47582],{"encoding":904}," z definice, vždy ověř ",[883,103646,103648],{"className":103647},[886],[888,103649,103650],{"xmlns":890},[892,103651,103652,103682],{},[895,103653,103654,103664,103666,103678,103680],{},[6927,103655,103656,103658],{},[898,103657,1772],{},[895,103659,103660,103662],{},[898,103661,47552],{},[898,103663,724],{},[1712,103665,3145],{},[6927,103667,103668,103670],{},[898,103669,1772],{},[895,103671,103672,103674,103676],{},[898,103673,47575],{},[898,103675,7446],{},[898,103677,16915],{},[1712,103679,1714],{},[898,103681,1772],{},[902,103683,103684],{"encoding":904},"T_{sp} + T_{vyr} = T",[1636,103686,103687],{},[724,103688,103689,103691,103692,103695,103696,1655,103709,103722],{},[883,103690,2203],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,103693,103694],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,103697,103699],{"className":103698},[886],[888,103700,103701],{"xmlns":890},[892,103702,103703,103707],{},[895,103704,103705],{},[898,103706,1969],{},[902,103708,1969],{"encoding":904},[883,103710,103712],{"className":103711},[886],[888,103713,103714],{"xmlns":890},[892,103715,103716,103720],{},[895,103717,103718],{},[898,103719,6493],{},[902,103721,6493],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[41845,103724],{},[115,103726,103728],{"id":103727},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,103730,103731],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,103733,103734],{},[3817,103735],{"alt":103736,"className":103737,"src":103738},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,3821],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,103740,103741,103753],{},[19,103742,103743],{},[22,103744,103745,103747,103750],{},[25,103746,59171],{},[25,103748,103749],{},"(a) daň výrobci",[25,103751,103752],{},"(b) daň spotřebiteli",[30,103754,103755,103810,103877,103937],{},[22,103756,103757,103760,103785],{},[35,103758,103759],{},"Rovnovážné množství",[35,103761,103762],{},[883,103763,103765],{"className":103764},[886],[888,103766,103767],{"xmlns":890},[892,103768,103769,103783],{},[895,103770,103771,103779,103781],{},[6989,103772,103773,103775,103777],{},[898,103774,1734],{},[1716,103776,2222],{},[898,103778,2041],{},[1712,103780,1714],{},[1716,103782,2222],{},[902,103784,101601],{"encoding":904},[35,103786,103787],{},[883,103788,103790],{"className":103789},[886],[888,103791,103792],{"xmlns":890},[892,103793,103794,103808],{},[895,103795,103796,103804,103806],{},[6989,103797,103798,103800,103802],{},[898,103799,1734],{},[1716,103801,2787],{},[898,103803,2041],{},[1712,103805,1714],{},[1716,103807,2222],{},[902,103809,102634],{"encoding":904},[22,103811,103812,103815,103840],{},[35,103813,103814],{},"Cena placená spotřebitelem",[35,103816,103817],{},[883,103818,103820],{"className":103819},[886],[888,103821,103822],{"xmlns":890},[892,103823,103824,103838],{},[895,103825,103826,103834,103836],{},[6989,103827,103828,103830,103832],{},[898,103829,1710],{},[1716,103831,2222],{},[898,103833,2041],{},[1712,103835,1714],{},[1716,103837,1718],{},[902,103839,101696],{"encoding":904},[35,103841,103842],{},[883,103843,103845],{"className":103844},[886],[888,103846,103847],{"xmlns":890},[892,103848,103849,103875],{},[895,103850,103851,103859,103861,103863,103865,103867,103869,103871,103873],{},[6989,103852,103853,103855,103857],{},[898,103854,1710],{},[1716,103856,2787],{},[898,103858,2041],{},[1712,103860,3145],{},[898,103862,1772],{},[1712,103864,1714],{},[1716,103866,2975],{},[1712,103868,3145],{},[1716,103870,6209],{},[1712,103872,1714],{},[1716,103874,1718],{},[902,103876,102733],{"encoding":904},[22,103878,103879,103882,103912],{},[35,103880,103881],{},"Cena přijímaná výrobcem",[35,103883,103884],{},[883,103885,103887],{"className":103886},[886],[888,103888,103889],{"xmlns":890},[892,103890,103891,103909],{},[895,103892,103893,103901,103903,103905,103907],{},[6989,103894,103895,103897,103899],{},[898,103896,1710],{},[1716,103898,2222],{},[898,103900,2041],{},[1712,103902,2219],{},[898,103904,1772],{},[1712,103906,1714],{},[1716,103908,2975],{},[902,103910,103911],{"encoding":904},"P_1^E - T = 4",[35,103913,103914],{},[883,103915,103917],{"className":103916},[886],[888,103918,103919],{"xmlns":890},[892,103920,103921,103935],{},[895,103922,103923,103931,103933],{},[6989,103924,103925,103927,103929],{},[898,103926,1710],{},[1716,103928,2787],{},[898,103930,2041],{},[1712,103932,1714],{},[1716,103934,2975],{},[902,103936,102758],{"encoding":904},[22,103938,103939,103942,103996],{},[35,103940,103941],{},"Rozklad břemene",[35,103943,103944,1343,103969],{},[883,103945,103947],{"className":103946},[886],[888,103948,103949],{"xmlns":890},[892,103950,103951,103967],{},[895,103952,103953,103963,103965],{},[6927,103954,103955,103957],{},[898,103956,1772],{},[895,103958,103959,103961],{},[898,103960,47552],{},[898,103962,724],{},[1712,103964,1714],{},[1716,103966,2787],{},[902,103968,47851],{"encoding":904},[883,103970,103972],{"className":103971},[886],[888,103973,103974],{"xmlns":890},[892,103975,103976,103994],{},[895,103977,103978,103990,103992],{},[6927,103979,103980,103982],{},[898,103981,1772],{},[895,103983,103984,103986,103988],{},[898,103985,47575],{},[898,103987,7446],{},[898,103989,16915],{},[1712,103991,1714],{},[1716,103993,2975],{},[902,103995,47880],{"encoding":904},[35,103997,103998,1343,104023],{},[883,103999,104001],{"className":104000},[886],[888,104002,104003],{"xmlns":890},[892,104004,104005,104021],{},[895,104006,104007,104017,104019],{},[6927,104008,104009,104011],{},[898,104010,1772],{},[895,104012,104013,104015],{},[898,104014,47552],{},[898,104016,724],{},[1712,104018,1714],{},[1716,104020,2787],{},[902,104022,47851],{"encoding":904},[883,104024,104026],{"className":104025},[886],[888,104027,104028],{"xmlns":890},[892,104029,104030,104048],{},[895,104031,104032,104044,104046],{},[6927,104033,104034,104036],{},[898,104035,1772],{},[895,104037,104038,104040,104042],{},[898,104039,47575],{},[898,104041,7446],{},[898,104043,16915],{},[1712,104045,1714],{},[1716,104047,2975],{},[902,104049,47880],{"encoding":904},[724,104051,104052],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,104054,104056],{"className":104055},[886],[888,104057,104058],{"xmlns":890,"display":32941},[892,104059,104060,104108],{},[895,104061,104062,104070,104072,104080,104082,104084,104092,104094,104096,104098,104106],{},[6989,104063,104064,104066,104068],{},[898,104065,1734],{},[1716,104067,2222],{},[898,104069,2041],{},[1712,104071,1714],{},[6989,104073,104074,104076,104078],{},[898,104075,1734],{},[1716,104077,2787],{},[898,104079,2041],{},[1712,104081,3138],{"separator":2565},[3690,104083],{"width":3692},[6989,104085,104086,104088,104090],{},[898,104087,1710],{},[1716,104089,2222],{},[898,104091,2041],{},[1712,104093,2219],{},[898,104095,1772],{},[1712,104097,1714],{},[6989,104099,104100,104102,104104],{},[898,104101,1710],{},[1716,104103,2787],{},[898,104105,2041],{},[898,104107,1659],{"mathvariant":2003},[902,104109,104110],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1636,104112,104113,104132,104286],{},[724,104114,104115,104117,104118,104131],{},[883,104116,2370],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,104119,104121],{"className":104120},[886],[888,104122,104123],{"xmlns":890},[892,104124,104125,104129],{},[895,104126,104127],{},[898,104128,1772],{},[902,104130,1772],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,104133,104134,104166,104202,104239],{},[123,104135,104136,104137,3138],{},"rovnovážná množství obou režimů, ",[883,104138,104140],{"className":104139},[886],[888,104141,104142],{"xmlns":890},[892,104143,104144,104164],{},[895,104145,104146,104154,104156],{},[6989,104147,104148,104150,104152],{},[898,104149,1734],{},[1716,104151,2222],{},[898,104153,2041],{},[1712,104155,1714],{},[6989,104157,104158,104160,104162],{},[898,104159,1734],{},[1716,104161,2787],{},[898,104163,2041],{},[902,104165,47783],{"encoding":904},[123,104167,104168,104169,3138],{},"čistá cena přijímaná výrobcem, ",[883,104170,104172],{"className":104171},[886],[888,104173,104174],{"xmlns":890},[892,104175,104176,104200],{},[895,104177,104178,104186,104188,104190,104192],{},[6989,104179,104180,104182,104184],{},[898,104181,1710],{},[1716,104183,2222],{},[898,104185,2041],{},[1712,104187,2219],{},[898,104189,1772],{},[1712,104191,1714],{},[6989,104193,104194,104196,104198],{},[898,104195,1710],{},[1716,104197,2787],{},[898,104199,2041],{},[902,104201,47817],{"encoding":904},[123,104203,104204,104205,3138],{},"celková cena placená spotřebitelem, ",[883,104206,104208],{"className":104207},[886],[888,104209,104210],{"xmlns":890},[892,104211,104212,104236],{},[895,104213,104214,104222,104224,104232,104234],{},[6989,104215,104216,104218,104220],{},[898,104217,1710],{},[1716,104219,2222],{},[898,104221,2041],{},[1712,104223,1714],{},[6989,104225,104226,104228,104230],{},[898,104227,1710],{},[1716,104229,2787],{},[898,104231,2041],{},[1712,104233,3145],{},[898,104235,1772],{},[902,104237,104238],{"encoding":904},"P_1^E = P_2^E + T",[123,104240,104241,104242,1655,104263,1659],{},"rozklad daňového břemene ",[883,104243,104245],{"className":104244},[886],[888,104246,104247],{"xmlns":890},[892,104248,104249,104261],{},[895,104250,104251],{},[6927,104252,104253,104255],{},[898,104254,1772],{},[895,104256,104257,104259],{},[898,104258,47552],{},[898,104260,724],{},[902,104262,47557],{"encoding":904},[883,104264,104266],{"className":104265},[886],[888,104267,104268],{"xmlns":890},[892,104269,104270,104284],{},[895,104271,104272],{},[6927,104273,104274,104276],{},[898,104275,1772],{},[895,104277,104278,104280,104282],{},[898,104279,47575],{},[898,104281,7446],{},[898,104283,16915],{},[902,104285,47582],{"encoding":904},[724,104287,104288,104289,1659],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,104290,40072],{},[724,104292,104293,104294,1655,104307,1691],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,104295,104297],{"className":104296},[886],[888,104298,104299],{"xmlns":890},[892,104300,104301,104305],{},[895,104302,104303],{},[898,104304,1969],{},[902,104306,1969],{"encoding":904},[883,104308,104310],{"className":104309},[886],[888,104311,104312],{"xmlns":890},[892,104313,104314,104318],{},[895,104315,104316],{},[898,104317,6493],{},[902,104319,6493],{"encoding":904},[41845,104321],{},[115,104323,104325],{"id":104324},"úlohy","Úlohy",[724,104327,104328,104329,8558],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,104330,21114],{"className":104331,"dataFsResolvedFilePath":800,"href":801},[210],[120,104333,104334,104364,104395],{},[123,104335,104336,104339,104340,104363],{},[38,104337,104338],{},"Úloha 2.4"," — Poptávka ",[883,104341,104343],{"className":104342},[886],[888,104344,104345],{"xmlns":890},[892,104346,104347,104361],{},[895,104348,104349,104351,104353,104355,104357,104359],{},[898,104350,1710],{},[1712,104352,1714],{},[1716,104354,8912],{},[1712,104356,2219],{},[1716,104358,2787],{},[898,104360,1734],{},[902,104362,101313],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,104365,104366,104369,104370,104394],{},[38,104367,104368],{},"Úloha 2.9"," — Nabídka ",[883,104371,104373],{"className":104372},[886],[888,104374,104375],{"xmlns":890},[892,104376,104377,104391],{},[895,104378,104379,104381,104383,104385,104387,104389],{},[898,104380,1710],{},[1712,104382,1714],{},[1716,104384,2814],{},[898,104386,1734],{},[1712,104388,3145],{},[1716,104390,41119],{},[902,104392,104393],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,104396,104397,104400,104401,1655,104427,104451,104452,104469],{},[38,104398,104399],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,104402,104404],{"className":104403},[886],[888,104405,104406],{"xmlns":890},[892,104407,104408,104424],{},[895,104409,104410,104412,104414,104416,104418,104420,104422],{},[898,104411,1710],{},[1712,104413,1714],{},[1712,104415,2219],{},[1716,104417,2975],{},[898,104419,1734],{},[1712,104421,3145],{},[1716,104423,51578],{},[902,104425,104426],{"encoding":904},"P = -4Q + 80",[883,104428,104430],{"className":104429},[886],[888,104431,104432],{"xmlns":890},[892,104433,104434,104448],{},[895,104435,104436,104438,104440,104442,104444,104446],{},[898,104437,1710],{},[1712,104439,1714],{},[1716,104441,6198],{},[898,104443,1734],{},[1712,104445,3145],{},[1716,104447,1718],{},[902,104449,104450],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,104453,104455],{"className":104454},[886],[888,104456,104457],{"xmlns":890},[892,104458,104459,104467],{},[895,104460,104461,104463,104465],{},[898,104462,1772],{},[1712,104464,1714],{},[1716,104466,29076],{},[902,104468,52690],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,104471,104472,104473,104475,104476,104478],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,104474,50103],{}," (posun poptávky při zdanění kupujícího) a ",[38,104477,50137],{}," (posun nabídky při zdanění výrobce).",[41845,104480],{},[115,104482,20594],{"id":20593},[120,104484,104485,104504,104562,104619,104702,104748,104791,104836,104902],{},[123,104486,104487,3245,104490,104503],{},[38,104488,104489],{},"Jednotková daň",[883,104491,104493],{"className":104492},[886],[888,104494,104495],{"xmlns":890},[892,104496,104497,104501],{},[895,104498,104499],{},[898,104500,1772],{},[902,104502,1772],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,104505,104506,104508,104509,104547,104548,104561],{},[38,104507,100895],{}," — posun nabídky ",[883,104510,104512],{"className":104511},[886],[888,104513,104514],{"xmlns":890},[892,104515,104516,104544],{},[895,104517,104518,104524,104526,104528,104530,104532,104534,104536,104538,104540,104542],{},[6927,104519,104520,104522],{},[898,104521,6493],{},[1716,104523,2222],{},[1712,104525,1904],{"stretchy":1903},[898,104527,1734],{},[1712,104529,1910],{"stretchy":1903},[1712,104531,1714],{},[898,104533,6493],{},[1712,104535,1904],{"stretchy":1903},[898,104537,1734],{},[1712,104539,1910],{"stretchy":1903},[1712,104541,3145],{},[898,104543,1772],{},[902,104545,104546],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,104549,104551],{"className":104550},[886],[888,104552,104553],{"xmlns":890},[892,104554,104555,104559],{},[895,104556,104557],{},[898,104558,1772],{},[902,104560,1772],{"encoding":904}," svisle nahoru)",[123,104563,104564,104566,104567,104547,104605,104618],{},[38,104565,101968],{}," — posun poptávky ",[883,104568,104570],{"className":104569},[886],[888,104571,104572],{"xmlns":890},[892,104573,104574,104602],{},[895,104575,104576,104582,104584,104586,104588,104590,104592,104594,104596,104598,104600],{},[6927,104577,104578,104580],{},[898,104579,1969],{},[1716,104581,2787],{},[1712,104583,1904],{"stretchy":1903},[898,104585,1734],{},[1712,104587,1910],{"stretchy":1903},[1712,104589,1714],{},[898,104591,1969],{},[1712,104593,1904],{"stretchy":1903},[898,104595,1734],{},[1712,104597,1910],{"stretchy":1903},[1712,104599,2219],{},[898,104601,1772],{},[902,104603,104604],{"encoding":904},"D_2(Q) = D(Q) - T",[883,104606,104608],{"className":104607},[886],[888,104609,104610],{"xmlns":890},[892,104611,104612,104616],{},[895,104613,104614],{},[898,104615,1772],{},[902,104617,1772],{"encoding":904}," svisle dolů)",[123,104620,104621,4831,104624,46689,104663],{},[38,104622,104623],{},"Rovnovážný bod s daní",[883,104625,104627],{"className":104626},[886],[888,104628,104629],{"xmlns":890},[892,104630,104631,104661],{},[895,104632,104633,104639,104641,104649,104651,104659],{},[6927,104634,104635,104637],{},[898,104636,2041],{},[1716,104638,2222],{},[1712,104640,7910],{"stretchy":1903},[6989,104642,104643,104645,104647],{},[898,104644,1734],{},[1716,104646,2222],{},[898,104648,2041],{},[1712,104650,3138],{"separator":2565},[6989,104652,104653,104655,104657],{},[898,104654,1710],{},[1716,104656,2222],{},[898,104658,2041],{},[1712,104660,7925],{"stretchy":1903},[902,104662,101063],{"encoding":904},[883,104664,104666],{"className":104665},[886],[888,104667,104668],{"xmlns":890},[892,104669,104670,104700],{},[895,104671,104672,104678,104680,104688,104690,104698],{},[6927,104673,104674,104676],{},[898,104675,2041],{},[1716,104677,2787],{},[1712,104679,7910],{"stretchy":1903},[6989,104681,104682,104684,104686],{},[898,104683,1734],{},[1716,104685,2787],{},[898,104687,2041],{},[1712,104689,3138],{"separator":2565},[6989,104691,104692,104694,104696],{},[898,104693,1710],{},[1716,104695,2787],{},[898,104697,2041],{},[1712,104699,7925],{"stretchy":1903},[902,104701,102138],{"encoding":904},[123,104703,104704,14897,104706,104708,104709],{},[38,104705,47533],{},[614,104707,102918],{},") — rozklad ",[883,104710,104712],{"className":104711},[886],[888,104713,104714],{"xmlns":890},[892,104715,104716,104746],{},[895,104717,104718,104720,104722,104732,104734],{},[898,104719,1772],{},[1712,104721,1714],{},[6927,104723,104724,104726],{},[898,104725,1772],{},[895,104727,104728,104730],{},[898,104729,47552],{},[898,104731,724],{},[1712,104733,3145],{},[6927,104735,104736,104738],{},[898,104737,1772],{},[895,104739,104740,104742,104744],{},[898,104741,47575],{},[898,104743,7446],{},[898,104745,16915],{},[902,104747,47719],{"encoding":904},[123,104749,104750,104773,104774,1910],{},[38,104751,104752],{},[883,104753,104755],{"className":104754},[886],[888,104756,104757],{"xmlns":890},[892,104758,104759,104771],{},[895,104760,104761],{},[6927,104762,104763,104765],{},[898,104764,1772],{},[895,104766,104767,104769],{},[898,104768,47552],{},[898,104770,724],{},[902,104772,47557],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,104775,104777],{"className":104776},[886],[888,104778,104779],{"xmlns":890},[892,104780,104781,104789],{},[895,104782,104783],{},[2037,104784,104785,104787],{},[898,104786,1710],{},[898,104788,2041],{},[902,104790,46341],{"encoding":904},[123,104792,104793,104818,104819,1910],{},[38,104794,104795],{},[883,104796,104798],{"className":104797},[886],[888,104799,104800],{"xmlns":890},[892,104801,104802,104816],{},[895,104803,104804],{},[6927,104805,104806,104808],{},[898,104807,1772],{},[895,104809,104810,104812,104814],{},[898,104811,47575],{},[898,104813,7446],{},[898,104815,16915],{},[902,104817,47582],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,104820,104822],{"className":104821},[886],[888,104823,104824],{"xmlns":890},[892,104825,104826,104834],{},[895,104827,104828],{},[2037,104829,104830,104832],{},[898,104831,1710],{},[898,104833,2041],{},[902,104835,46341],{"encoding":904},[123,104837,104838,4831,104840,1343,104869],{},[38,104839,55349],{},[883,104841,104843],{"className":104842},[886],[888,104844,104845],{"xmlns":890},[892,104846,104847,104867],{},[895,104848,104849,104857,104859],{},[6989,104850,104851,104853,104855],{},[898,104852,1734],{},[1716,104854,2222],{},[898,104856,2041],{},[1712,104858,1714],{},[6989,104860,104861,104863,104865],{},[898,104862,1734],{},[1716,104864,2787],{},[898,104866,2041],{},[902,104868,47783],{"encoding":904},[883,104870,104872],{"className":104871},[886],[888,104873,104874],{"xmlns":890},[892,104875,104876,104900],{},[895,104877,104878,104886,104888,104890,104892],{},[6989,104879,104880,104882,104884],{},[898,104881,1710],{},[1716,104883,2222],{},[898,104885,2041],{},[1712,104887,2219],{},[898,104889,1772],{},[1712,104891,1714],{},[6989,104893,104894,104896,104898],{},[898,104895,1710],{},[1716,104897,2787],{},[898,104899,2041],{},[902,104901,47817],{"encoding":904},[123,104903,104904,104907],{},[38,104905,104906],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[41845,104909],{},[115,104911,9193],{"id":9192},[120,104913,104914,104922,104940,104947],{},[123,104915,104916,3245,104919],{},[38,104917,104918],{},"Kontext (hub):",[207,104920,802],{"className":104921,"dataFsResolvedFilePath":800,"href":801},[210],[123,104923,104924,3245,104926,104929,104930,23523,104932,104935,104936,104939],{},[38,104925,55598],{},[207,104927,820],{"className":104928,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,104931,59909],{},[207,104933,1690],{"className":104934,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,104937,1646],{"className":104938,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,104941,104942,3245,104944],{},[38,104943,55633],{},[207,104945,55637],{"className":104946,"dataFsResolvedFilePath":745,"href":746},[210],[123,104948,104949,3245,104951],{},[38,104950,21078],{},[207,104952,21082],{"className":104953,"dataFsResolvedFilePath":7413,"href":7414},[210],{"title":641,"searchDepth":642,"depth":642,"links":104955},[104956,104957,104960,104963,104967,104968,104969,104970],{"id":100800,"depth":642,"text":100801},{"id":100894,"depth":642,"text":100895,"children":104958},[104959],{"id":101285,"depth":649,"text":50178},{"id":101967,"depth":642,"text":101968,"children":104961},[104962],{"id":102444,"depth":649,"text":50258},{"id":102911,"depth":642,"text":47533,"children":104964},[104965,104966],{"id":7867,"depth":649,"text":7868},{"id":103254,"depth":649,"text":103255},{"id":103727,"depth":642,"text":103728},{"id":104324,"depth":642,"text":104325},{"id":20593,"depth":642,"text":20594},{"id":9192,"depth":642,"text":9193},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":100698,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,55698,104977,104978,104979,21114],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[104982,104984,104986,104988,104992,104996,105000,105004],{"slug":1145,"path":765,"title":7401,"snippet":104983},"… zšíření na 2D), Příjem, náklady, zisk (aplikace mezních veličin), \u003C\u003Celasticita>> (procentní citlivost přes derivaci)",{"slug":21127,"path":783,"title":14442,"snippet":104985},"… ace = mezní produkty), Užitečnost (parciální derivace = mezní užitečnost), \u003C\u003Celasticita>> (vícefaktorový model)",{"slug":1128,"path":7414,"title":681,"snippet":104987},"… y zvratu, konstrukce nabídky firmy ### Blok 2 — Elasticita a produkce - \u003C\u003Celasticita>> (jedno- i vícefaktorový model) - Produkční funkce — Cobb-Douglasova, CES, li …",{"slug":104989,"path":746,"title":104990,"snippet":104991},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… , body zvratu, maximalizace zisku, konstrukce nabídky firmy ## Vazby do dalších bloků - \u003C\u003Celasticita>> (Blok 2) — navazuje na příjem (vliv elasticity na TR) a využívá derivace. - [[produkce|Pr …",{"slug":104993,"path":839,"title":104994,"snippet":104995},"imek-blok-02","KS 2. blok — Elasticita a produkce","… vě hlavní témata, každé se samostatnou stránkou. ## Témata bloku — doporučené pořadí 1. \u003C\u003Celasticita>> — motivační hypotéza (procentní růst $Q$ ≥ procentní pokles $P$), cenová\u002Fkřížová\u002Fdůchodov …",{"slug":104997,"path":1109,"title":104998,"snippet":104999},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… = 1$), křížová a důchodová elasticita. **Příklady 4.1–4.8**, **Úlohy 4.1–4.21**. Topic: \u003C\u003Celasticita>>. ### Kapitola 5 — Produkce *(str. 97–111)* Jednofaktorový model $Q(L)$ s mezním produkt …",{"slug":105001,"path":959,"title":105002,"snippet":105003},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… áta z pokračování výroby pod náklady. --- ## 7. Elasticita poptávky **Základní téma:** \u003C\u003Celasticita>> ### Cenová elasticita poptávky (definiční tvar) $$E = -\\frac{P}{Q} \\cdot \\frac{dQ}{dP}$ …",{"slug":21114,"path":801,"title":802,"snippet":105005},"… y $Y_0$ množství s růstem důchodu klesá. Mírou citlivosti je *důchodová elasticita* (viz \u003C\u003Celasticita>>). *Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné z …",[105007],{"slug":104993,"title":104994,"path":839,"sharedTags":642},1777154952679]