[{"data":1,"prerenderedAt":111164},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-produkce":1626,"course-stats-imek":13954,"course-topics-imek":13958,"backlinks-produkce":111136,"related-produkce":111161},{"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":13953},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":13939,"navigation":664,"path":13940,"seo":13941,"sources":13942,"stem":13943,"tags":13944,"type":13951,"updated":677,"__hash__":13952},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":1631,"toc":13895},[1632,1635,2026,2030,2033,2103,2156,2167,2171,2205,2253,2277,2301,2330,2399,2512,2557,2614,2692,2738,2742,2751,2760,2763,3038,3089,3174,3247,3270,3298,3343,3365,3369,3378,3431,3459,3611,3615,3652,3816,3925,3929,3968,4052,4124,4245,4368,4449,4455,4496,4570,4665,4669,4705,4799,4914,5020,5106,5247,5251,5300,5345,5351,5355,5358,5409,5460,5467,5534,5667,5712,5716,5737,6124,6220,6237,6291,6295,6377,6461,6631,6635,6680,6747,6823,6827,6832,6902,6910,6919,6999,7067,7072,7168,7212,7217,7266,7271,7319,7438,7523,7561,7664,7723,7864,7868,7912,7985,8009,8063,8070,8073,8118,8163,8174,8179,8218,8280,8304,8313,8414,8482,8555,8562,8653,8715,8751,8808,8867,9056,9154,9158,9162,9242,9247,9372,9461,9467,9577,9614,9708,9806,9809,9813,9879,9916,10038,10091,10095,10123,10175,10249,10354,10378,10437,10441,10459,10602,10750,10754,10789,10793,10797,10887,11019,11147,11240,11315,11319,11435,11540,11736,11772,11866,11872,11985,12290,12296,12416,12517,12593,12597,13760,13764],[12,1633,1629],{"id":1634},"produkce-produkční-funkce-cobb-douglas-mrts",[1636,1637,1638],"blockquote",{},[724,1639,1640,1643,1644,1646,1647,1661,1662,1676,1677,1691,1692,1695,1696,1725,1726,1729,1730,1771,1772,1729,1775,1805,1806,1826,1827,1857,1858,1695,1861,1891,1892,1895,1896,1927,1928,1958,1959,1729,1962,2005,2006,2025],{},[883,1641,1642],{},"!abstract"," TL;DR\n",[38,1645,859],{}," popisuje vztah mezi vstupy (práce ",[883,1648,1650],{"className":1649},[886],[888,1651,1652],{"xmlns":890},[892,1653,1654,1659],{},[895,1655,1656],{},[898,1657,1658],{},"L",[902,1660,1658],{"encoding":904},", kapitál ",[883,1663,1665],{"className":1664},[886],[888,1666,1667],{"xmlns":890},[892,1668,1669,1674],{},[895,1670,1671],{},[898,1672,1673],{},"K",[902,1675,1673],{"encoding":904},") a výstupem ",[883,1678,1680],{"className":1679},[886],[888,1681,1682],{"xmlns":890},[892,1683,1684,1689],{},[895,1685,1686],{},[898,1687,1688],{},"Q",[902,1690,1688],{"encoding":904},". V ",[38,1693,1694],{},"jednofaktorovém modelu"," (",[883,1697,1699],{"className":1698},[886],[888,1700,1701],{"xmlns":890},[892,1702,1703,1722],{},[895,1704,1705,1707,1711,1713,1717,1719],{},[898,1706,1688],{},[1708,1709,1710],"mo",{},"=",[898,1712,1688],{},[1708,1714,1716],{"stretchy":1715},"false","(",[898,1718,1658],{},[1708,1720,1721],{"stretchy":1715},")",[902,1723,1724],{"encoding":904},"Q = Q(L)",") studujeme ",[614,1727,1728],{},"mezní produkt práce"," ",[883,1731,1733],{"className":1732},[886],[888,1734,1735],{"xmlns":890},[892,1736,1737,1768],{},[895,1738,1739,1742,1750,1752,1762,1764,1766],{},[898,1740,1741],{},"M",[1743,1744,1745,1748],"msub",{},[898,1746,1747],{},"P",[898,1749,1658],{},[1708,1751,1710],{},[1753,1754,1755,1757],"msup",{},[898,1756,1688],{},[1708,1758,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},"normal","0em","′",[1708,1763,1716],{"stretchy":1715},[898,1765,1658],{},[1708,1767,1721],{"stretchy":1715},[902,1769,1770],{"encoding":904},"MP_L = Q'(L)"," a ",[614,1773,1774],{},"průměrný produkt",[883,1776,1778],{"className":1777},[886],[888,1779,1780],{"xmlns":890},[892,1781,1782,1802],{},[895,1783,1784,1787,1793,1795,1797,1800],{},[898,1785,1786],{},"A",[1743,1788,1789,1791],{},[898,1790,1747],{},[898,1792,1658],{},[1708,1794,1710],{},[898,1796,1688],{},[898,1798,1799],{"mathvariant":1759},"\u002F",[898,1801,1658],{},[902,1803,1804],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,1807,1809],{"className":1808},[886],[888,1810,1811],{"xmlns":890},[892,1812,1813,1823],{},[895,1814,1815,1817],{},[898,1816,1786],{},[1743,1818,1819,1821],{},[898,1820,1747],{},[898,1822,1658],{},[902,1824,1825],{"encoding":904},"AP_L"," platí ",[883,1828,1830],{"className":1829},[886],[888,1831,1832],{"xmlns":890},[892,1833,1834,1854],{},[895,1835,1836,1838,1844,1846,1848],{},[898,1837,1741],{},[1743,1839,1840,1842],{},[898,1841,1747],{},[898,1843,1658],{},[1708,1845,1710],{},[898,1847,1786],{},[1743,1849,1850,1852],{},[898,1851,1747],{},[898,1853,1658],{},[902,1855,1856],{"encoding":904},"MP_L = AP_L",". Ve ",[38,1859,1860],{},"dvoufaktorovém modelu",[883,1862,1864],{"className":1863},[886],[888,1865,1866],{"xmlns":890},[892,1867,1868,1888],{},[895,1869,1870,1872,1874,1876,1878,1880,1884,1886],{},[898,1871,1688],{},[1708,1873,1710],{},[898,1875,1688],{},[1708,1877,1716],{"stretchy":1715},[898,1879,1658],{},[1708,1881,1883],{"separator":1882},"true",",",[898,1885,1673],{},[1708,1887,1721],{"stretchy":1715},[902,1889,1890],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,1893,1894],{},"Cobb-Douglasovy"," funkce ",[883,1897,1899],{"className":1898},[886],[888,1900,1901],{"xmlns":890},[892,1902,1903,1924],{},[895,1904,1905,1907,1909,1911,1917],{},[898,1906,1688],{},[1708,1908,1710],{},[898,1910,1786],{},[1753,1912,1913,1915],{},[898,1914,1658],{},[898,1916,207],{},[1753,1918,1919,1921],{},[898,1920,1673],{},[898,1922,1923],{},"b",[902,1925,1926],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,1929,1931],{"className":1930},[886],[888,1932,1933],{"xmlns":890},[892,1934,1935,1955],{},[895,1936,1937,1939,1945,1947,1949],{},[898,1938,1741],{},[1743,1940,1941,1943],{},[898,1942,1747],{},[898,1944,1658],{},[1708,1946,1883],{"separator":1882},[898,1948,1741],{},[1743,1950,1951,1953],{},[898,1952,1747],{},[898,1954,1673],{},[902,1956,1957],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,1960,1961],{},"mezní míru technické substituce",[883,1963,1965],{"className":1964},[886],[888,1966,1967],{"xmlns":890},[892,1968,1969,2002],{},[895,1970,1971,1973,1976,1979,1982,1984,1986,1992,1994,1996],{},[898,1972,1741],{},[898,1974,1975],{},"R",[898,1977,1978],{},"T",[898,1980,1981],{},"S",[1708,1983,1710],{},[898,1985,1741],{},[1743,1987,1988,1990],{},[898,1989,1747],{},[898,1991,1658],{},[898,1993,1799],{"mathvariant":1759},[898,1995,1741],{},[1743,1997,1998,2000],{},[898,1999,1747],{},[898,2001,1673],{},[902,2003,2004],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,2007,2009],{"className":2008},[886],[888,2010,2011],{"xmlns":890},[892,2012,2013,2022],{},[895,2014,2015,2017,2020],{},[898,2016,207],{},[1708,2018,2019],{},"+",[898,2021,1923],{},[902,2023,2024],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,2027,2029],{"id":2028},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,2031,2032],{},"Po prostudování kapitoly 5 student umí:",[120,2034,2035,2041,2051,2057,2063,2068,2074,2086,2091,2097],{},[123,2036,2037,2038,1883],{},"popsat ",[38,2039,2040],{},"jednofaktorový model produkce",[123,2042,2043,2044,1771,2047,2050],{},"vypočítat ",[38,2045,2046],{},"mezní",[38,2048,2049],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,2052,2053,2054,1883],{},"charakterizovat průběh ",[38,2055,2056],{},"křivky produkce",[123,2058,2059,2060,1883],{},"formulovat ",[38,2061,2062],{},"princip maximalizace průměrného produktu práce",[123,2064,2037,2065,1883],{},[38,2066,2067],{},"dvoufaktorový model produkce",[123,2069,2070,2071,1883],{},"uvést tvar ",[38,2072,2073],{},"Cobb–Douglasových produkčních funkcí",[123,2075,2076,2077,1343,2080,1343,2083,1883],{},"vyložit, co jsou ",[38,2078,2079],{},"konstantní",[38,2081,2082],{},"rostoucí",[38,2084,2085],{},"klesající výnosy z rozsahu",[123,2087,2043,2088,2050],{},[38,2089,2090],{},"mezní produkty práce a kapitálu",[123,2092,2093,2094,1883],{},"najít ",[38,2095,2096],{},"izokvanty",[123,2098,2043,2099,2102],{},[38,2100,2101],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,2104,2105,2106,2109,2110,2113,2114,1729,2117,1343,2130,1729,2133,1771,2146,2149,2150,2152,2153,2155],{},"Každý proces produkce je určován ",[38,2107,2108],{},"faktory"," (též ",[38,2111,2112],{},"vstupy",") produkce. K hlavním patří ",[38,2115,2116],{},"práce",[883,2118,2120],{"className":2119},[886],[888,2121,2122],{"xmlns":890},[892,2123,2124,2128],{},[895,2125,2126],{},[898,2127,1658],{},[902,2129,1658],{"encoding":904},[38,2131,2132],{},"kapitál",[883,2134,2136],{"className":2135},[886],[888,2137,2138],{"xmlns":890},[892,2139,2140,2144],{},[895,2141,2142],{},[898,2143,1673],{},[902,2145,1673],{"encoding":904},[38,2147,2148],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,2151,1694],{}," (produkce závisí jen na práci); v opačném případě o ",[38,2154,1860],{},".",[724,2157,2158,2159,1343,2163,2166],{},"Související matematický aparát: ",[207,2160,2162],{"className":2161,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace",[207,2164,784],{"className":2165,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,2168,2170],{"id":2169},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,2172,2173,2174,2187,2188,2201,2202],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,2175,2177],{"className":2176},[886],[888,2178,2179],{"xmlns":890},[892,2180,2181,2185],{},[895,2182,2183],{},[898,2184,1688],{},[902,2186,1688],{"encoding":904}," na práci ",[883,2189,2191],{"className":2190},[886],[888,2192,2193],{"xmlns":890},[892,2194,2195,2199],{},[895,2196,2197],{},[898,2198,1658],{},[902,2200,1658],{"encoding":904}," vyjadřuje ",[38,2203,2204],{},"produkční funkce",[883,2206,2208],{"className":2207},[886],[888,2209,2211],{"xmlns":890,"display":2210},"block",[892,2212,2213,2250],{},[2214,2215,2217],"mtable",{"width":2216},"100%",[2218,2219,2220,2224,2242,2244],"mtr",{},[2221,2222],"mtd",{"width":2223},"50%",[2221,2225,2226],{},[895,2227,2228,2230,2232,2234,2236,2238,2240],{},[898,2229,1688],{},[1708,2231,1710],{},[898,2233,1688],{},[1708,2235,1716],{"stretchy":1715},[898,2237,1658],{},[1708,2239,1721],{"stretchy":1715},[1708,2241,1883],{"separator":1882},[2221,2243],{"width":2223},[2221,2245,2246],{},[2247,2248,2249],"mtext",{},"(5.1)",[902,2251,2252],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,2254,2255,2256,1695,2259,2262,2263,2276],{},"jejíž graf se nazývá ",[38,2257,2258],{},"křivka produkce",[614,2260,2261],{},"production curve","). Práce ",[883,2264,2266],{"className":2265},[886],[888,2267,2268],{"xmlns":890},[892,2269,2270,2274],{},[895,2271,2272],{},[898,2273,1658],{},[902,2275,1658],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,2278,2280,2281,1721],{"id":2279},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,2282,2284],{"className":2283},[886],[888,2285,2286],{"xmlns":890},[892,2287,2288,2298],{},[895,2289,2290,2292],{},[898,2291,1741],{},[1743,2293,2294,2296],{},[898,2295,1747],{},[898,2297,1658],{},[902,2299,2300],{"encoding":904},"MP_L",[724,2302,2303,1695,2306,2309,2310,2329],{},[38,2304,2305],{},"Mezní produkt práce",[614,2307,2308],{},"marginal product of labour",") ",[883,2311,2313],{"className":2312},[886],[888,2314,2315],{"xmlns":890},[892,2316,2317,2327],{},[895,2318,2319,2321],{},[898,2320,1741],{},[1743,2322,2323,2325],{},[898,2324,1747],{},[898,2326,1658],{},[902,2328,2300],{"encoding":904}," je derivace produkce podle práce:",[883,2331,2333],{"className":2332},[886],[888,2334,2335],{"xmlns":890,"display":2210},[892,2336,2337,2396],{},[2214,2338,2339],{"width":2216},[2218,2340,2341,2343,2389,2391],{},[2221,2342],{"width":2223},[2221,2344,2345],{},[895,2346,2347,2349,2355,2357,2373,2375,2381,2383,2385,2387],{},[898,2348,1741],{},[1743,2350,2351,2353],{},[898,2352,1747],{},[898,2354,1658],{},[1708,2356,1710],{},[2358,2359,2360,2367],"mfrac",{},[895,2361,2362,2365],{},[898,2363,2364],{},"d",[898,2366,1688],{},[895,2368,2369,2371],{},[898,2370,2364],{},[898,2372,1658],{},[1708,2374,1710],{},[1753,2376,2377,2379],{},[898,2378,1688],{},[1708,2380,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,2382,1716],{"stretchy":1715},[898,2384,1658],{},[1708,2386,1721],{"stretchy":1715},[898,2388,2155],{"mathvariant":1759},[2221,2390],{"width":2223},[2221,2392,2393],{},[2247,2394,2395],{},"(5.2)",[902,2397,2398],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,2400,2401,2402,2421,2422,2450,2451,2468,2469,2486,2487,2511],{},"Pro pevnou hodnotu ",[883,2403,2405],{"className":2404},[886],[888,2406,2407],{"xmlns":890},[892,2408,2409,2418],{},[895,2410,2411],{},[1753,2412,2413,2415],{},[898,2414,1658],{},[1708,2416,2417],{},"∗",[902,2419,2420],{"encoding":904},"L^*"," udává ",[883,2423,2425],{"className":2424},[886],[888,2426,2427],{"xmlns":890},[892,2428,2429,2447],{},[895,2430,2431,2437,2439,2445],{},[1753,2432,2433,2435],{},[898,2434,1688],{},[1708,2436,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,2438,1716],{"stretchy":1715},[1753,2440,2441,2443],{},[898,2442,1658],{},[1708,2444,2417],{},[1708,2446,1721],{"stretchy":1715},[902,2448,2449],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,2452,2454],{"className":2453},[886],[888,2455,2456],{"xmlns":890},[892,2457,2458,2466],{},[895,2459,2460],{},[1753,2461,2462,2464],{},[898,2463,1658],{},[1708,2465,2417],{},[902,2467,2420],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,2470,2472],{"className":2471},[886],[888,2473,2474],{"xmlns":890},[892,2475,2476,2484],{},[895,2477,2478],{},[1753,2479,2480,2482],{},[898,2481,1658],{},[1708,2483,2417],{},[902,2485,2420],{"encoding":904}," na ",[883,2488,2490],{"className":2489},[886],[888,2491,2492],{"xmlns":890},[892,2493,2494,2508],{},[895,2495,2496,2502,2504],{},[1753,2497,2498,2500],{},[898,2499,1658],{},[1708,2501,2417],{},[1708,2503,2019],{},[2505,2506,2507],"mn",{},"1",[902,2509,2510],{"encoding":904},"L^*+1",").",[1636,2513,2514],{},[724,2515,2516,2519,2520,2539,2540,2543,2544,2155],{},[883,2517,2518],{},"!info"," Intuice\n",[883,2521,2523],{"className":2522},[886],[888,2524,2525],{"xmlns":890},[892,2526,2527,2537],{},[895,2528,2529,2531],{},[898,2530,1741],{},[1743,2532,2533,2535],{},[898,2534,1747],{},[898,2536,1658],{},[902,2538,2300],{"encoding":904}," odpovídá na otázku „",[38,2541,2542],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,2545,2547],{"className":2546},[886],[888,2548,2549],{"xmlns":890},[892,2550,2551,2555],{},[895,2552,2553],{},[898,2554,1658],{},[902,2556,1658],{"encoding":904},[724,2558,2559,2562,2563,2579,2580,2486,2593,2613],{},[38,2560,2561],{},"Přibližná změna produkce"," pro změnu práce o ",[883,2564,2566],{"className":2565},[886],[888,2567,2568],{"xmlns":890},[892,2569,2570,2576],{},[895,2571,2572,2574],{},[898,2573,2364],{},[898,2575,1658],{},[902,2577,2578],{"encoding":904},"dL"," (z ",[883,2581,2583],{"className":2582},[886],[888,2584,2585],{"xmlns":890},[892,2586,2587,2591],{},[895,2588,2589],{},[898,2590,1658],{},[902,2592,1658],{"encoding":904},[883,2594,2596],{"className":2595},[886],[888,2597,2598],{"xmlns":890},[892,2599,2600,2610],{},[895,2601,2602,2604,2606,2608],{},[898,2603,1658],{},[1708,2605,2019],{},[898,2607,2364],{},[898,2609,1658],{},[902,2611,2612],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,2615,2617],{"className":2616},[886],[888,2618,2619],{"xmlns":890,"display":2210},[892,2620,2621,2689],{},[2214,2622,2623],{"width":2216},[2218,2624,2625,2627,2682,2684],{},[2221,2626],{"width":2223},[2221,2628,2629],{},[895,2630,2631,2634,2636,2639,2641,2643,2645,2651,2653,2655,2657,2660,2662,2664,2666,2668,2674,2676,2678,2680],{},[898,2632,2633],{"mathvariant":1759},"Δ",[898,2635,1688],{},[1708,2637,2638],{},"≈",[898,2640,2364],{},[898,2642,1688],{},[1708,2644,1710],{},[1753,2646,2647,2649],{},[898,2648,1688],{},[1708,2650,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,2652,1716],{"stretchy":1715},[898,2654,1658],{},[1708,2656,1721],{"stretchy":1715},[2247,2658,2659],{}," ",[898,2661,2364],{},[898,2663,1658],{},[1708,2665,1710],{},[898,2667,1741],{},[1743,2669,2670,2672],{},[898,2671,1747],{},[898,2673,1658],{},[2247,2675,2659],{},[898,2677,2364],{},[898,2679,1658],{},[898,2681,2155],{"mathvariant":1759},[2221,2683],{"width":2223},[2221,2685,2686],{},[2247,2687,2688],{},"(5.3)",[902,2690,2691],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,2693,2694,2695,2155],{},"Skutečná změna je ",[883,2696,2698],{"className":2697},[886],[888,2699,2700],{"xmlns":890},[892,2701,2702,2735],{},[895,2703,2704,2706,2708,2710,2712,2714,2716,2718,2720,2722,2724,2727,2729,2731,2733],{},[898,2705,2633],{"mathvariant":1759},[898,2707,1688],{},[1708,2709,1710],{},[898,2711,1688],{},[1708,2713,1716],{"stretchy":1715},[898,2715,1658],{},[1708,2717,2019],{},[898,2719,2364],{},[898,2721,1658],{},[1708,2723,1721],{"stretchy":1715},[1708,2725,2726],{},"−",[898,2728,1688],{},[1708,2730,1716],{"stretchy":1715},[898,2732,1658],{},[1708,2734,1721],{"stretchy":1715},[902,2736,2737],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,2739,2741],{"id":2740},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,2743,2744,1695,2747,2750],{},[38,2745,2746],{},"Zákon klesajících výnosů",[614,2748,2749],{},"law of diminishing marginal productivity","):",[1636,2752,2753],{},[724,2754,2755,2756,2759],{},"Roste-li postupně některý ze vstupů (",[614,2757,2758],{},"ceteris paribus","), budou přírůstky výstupu od jistého bodu klesat.",[724,2761,2762],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,2764,2765,2766,1729,2789,2808,2809,2860,2861,2864,2865,1729,2885,2904,2905,2860,2938,2941,2942,2961,2962,2980,2981,3015,3016,3033,3034,3037],{},"1° ",[38,2767,2768,2769,2788],{},"Do bodu ",[883,2770,2772],{"className":2771},[886],[888,2773,2774],{"xmlns":890},[892,2775,2776,2785],{},[895,2777,2778],{},[1743,2779,2780,2782],{},[898,2781,1658],{},[2505,2783,2784],{},"0",[902,2786,2787],{"encoding":904},"L_0",":",[883,2790,2792],{"className":2791},[886],[888,2793,2794],{"xmlns":890},[892,2795,2796,2806],{},[895,2797,2798,2800],{},[898,2799,1741],{},[1743,2801,2802,2804],{},[898,2803,1747],{},[898,2805,1658],{},[902,2807,2300],{"encoding":904}," roste, tj. ",[883,2810,2812],{"className":2811},[886],[888,2813,2814],{"xmlns":890},[892,2815,2816,2857],{},[895,2817,2818,2820,2822,2828,2834,2836,2846,2848,2850,2852,2855],{},[1708,2819,1716],{"stretchy":1715},[898,2821,1741],{},[1743,2823,2824,2826],{},[898,2825,1747],{},[898,2827,1658],{},[1753,2829,2830,2832],{},[1708,2831,1721],{"stretchy":1715},[1708,2833,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,2835,1710],{},[1753,2837,2838,2840],{},[898,2839,1688],{},[895,2841,2842,2844],{},[1708,2843,1761],{"mathvariant":1759},[1708,2845,1761],{"mathvariant":1759},[1708,2847,1716],{"stretchy":1715},[898,2849,1658],{},[1708,2851,1721],{"stretchy":1715},[1708,2853,2854],{},">",[2505,2856,2784],{},[902,2858,2859],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,2862,2863],{},"konvexní",".\n2° ",[38,2866,2867,2868,2788],{},"Od bodu ",[883,2869,2871],{"className":2870},[886],[888,2872,2873],{"xmlns":890},[892,2874,2875,2883],{},[895,2876,2877],{},[1743,2878,2879,2881],{},[898,2880,1658],{},[2505,2882,2784],{},[902,2884,2787],{"encoding":904},[883,2886,2888],{"className":2887},[886],[888,2889,2890],{"xmlns":890},[892,2891,2892,2902],{},[895,2893,2894,2896],{},[898,2895,1741],{},[1743,2897,2898,2900],{},[898,2899,1747],{},[898,2901,1658],{},[902,2903,2300],{"encoding":904}," klesá, ",[883,2906,2908],{"className":2907},[886],[888,2909,2910],{"xmlns":890},[892,2911,2912,2935],{},[895,2913,2914,2924,2926,2928,2930,2933],{},[1753,2915,2916,2918],{},[898,2917,1688],{},[895,2919,2920,2922],{},[1708,2921,1761],{"mathvariant":1759},[1708,2923,1761],{"mathvariant":1759},[1708,2925,1716],{"stretchy":1715},[898,2927,1658],{},[1708,2929,1721],{"stretchy":1715},[1708,2931,2932],{},"\u003C",[2505,2934,2784],{},[902,2936,2937],{"encoding":904},"Q''(L) \u003C 0",[38,2939,2940],{},"konkávní",". ",[883,2943,2945],{"className":2944},[886],[888,2946,2947],{"xmlns":890},[892,2948,2949,2959],{},[895,2950,2951,2953],{},[898,2952,1741],{},[1743,2954,2955,2957],{},[898,2956,1747],{},[898,2958,1658],{},[902,2960,2300],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,2963,2965],{"className":2964},[886],[888,2966,2967],{"xmlns":890},[892,2968,2969,2977],{},[895,2970,2971],{},[1743,2972,2973,2975],{},[898,2974,1658],{},[2505,2976,2507],{},[902,2978,2979],{"encoding":904},"L_1",", kde ",[883,2982,2984],{"className":2983},[886],[888,2985,2986],{"xmlns":890},[892,2987,2988,3012],{},[895,2989,2990,2992,2998,3000,3006,3008,3010],{},[898,2991,1741],{},[1743,2993,2994,2996],{},[898,2995,1747],{},[898,2997,1658],{},[1708,2999,1716],{"stretchy":1715},[1743,3001,3002,3004],{},[898,3003,1658],{},[2505,3005,2507],{},[1708,3007,1721],{"stretchy":1715},[1708,3009,1710],{},[2505,3011,2784],{},[902,3013,3014],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,3017,3019],{"className":3018},[886],[888,3020,3021],{"xmlns":890},[892,3022,3023,3031],{},[895,3024,3025],{},[1743,3026,3027,3029],{},[898,3028,1658],{},[2505,3030,2784],{},[902,3032,2787],{"encoding":904}," je ",[38,3035,3036],{},"inflexním bodem"," produkční funkce.",[724,3039,3040,3041,1826,3058,2155],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,3042,3044],{"className":3043},[886],[888,3045,3046],{"xmlns":890},[892,3047,3048,3056],{},[895,3049,3050],{},[1743,3051,3052,3054],{},[898,3053,1658],{},[2505,3055,2784],{},[902,3057,2787],{"encoding":904},[883,3059,3061],{"className":3060},[886],[888,3062,3063],{"xmlns":890},[892,3064,3065,3087],{},[895,3066,3067,3077,3079,3081,3083,3085],{},[1753,3068,3069,3071],{},[898,3070,1688],{},[895,3072,3073,3075],{},[1708,3074,1761],{"mathvariant":1759},[1708,3076,1761],{"mathvariant":1759},[1708,3078,1716],{"stretchy":1715},[898,3080,1658],{},[1708,3082,1721],{"stretchy":1715},[1708,3084,2932],{},[2505,3086,2784],{},[902,3088,2937],{"encoding":904},[724,3090,3091,1729,3094,3136,3137,1343,3155,3173],{},[38,3092,3093],{},"Typický polynom třetího stupně:",[883,3095,3097],{"className":3096},[886],[888,3098,3099],{"xmlns":890},[892,3100,3101,3133],{},[895,3102,3103,3105,3107,3109,3111,3113,3115,3122,3124,3126],{},[898,3104,1688],{},[1708,3106,1716],{"stretchy":1715},[898,3108,1658],{},[1708,3110,1721],{"stretchy":1715},[1708,3112,1710],{},[898,3114,207],{},[1753,3116,3117,3119],{},[898,3118,1658],{},[2505,3120,3121],{},"3",[1708,3123,2019],{},[898,3125,1923],{},[1753,3127,3128,3130],{},[898,3129,1658],{},[2505,3131,3132],{},"2",[902,3134,3135],{"encoding":904},"Q(L) = aL^3 + bL^2"," s ",[883,3138,3140],{"className":3139},[886],[888,3141,3142],{"xmlns":890},[892,3143,3144,3152],{},[895,3145,3146,3148,3150],{},[898,3147,207],{},[1708,3149,2932],{},[2505,3151,2784],{},[902,3153,3154],{"encoding":904},"a \u003C 0",[883,3156,3158],{"className":3157},[886],[888,3159,3160],{"xmlns":890},[892,3161,3162,3170],{},[895,3163,3164,3166,3168],{},[898,3165,1923],{},[1708,3167,2854],{},[2505,3169,2784],{},[902,3171,3172],{"encoding":904},"b > 0",". Pak",[883,3175,3177],{"className":3176},[886],[888,3178,3179],{"xmlns":890,"display":2210},[892,3180,3181,3244],{},[895,3182,3183,3189,3191,3193,3202,3210,3212,3216,3222,3224,3226,3234,3242],{},[1743,3184,3185,3187],{},[898,3186,1658],{},[2505,3188,2784],{},[1708,3190,1710],{},[1708,3192,2726],{},[3194,3195,3196],"mstyle",{"scriptlevel":2784,"displaystyle":1715},[2358,3197,3198,3200],{},[2505,3199,2507],{},[2505,3201,3121],{},[3194,3203,3204],{"scriptlevel":2784,"displaystyle":1715},[2358,3205,3206,3208],{},[898,3207,1923],{},[898,3209,207],{},[1708,3211,1883],{"separator":1882},[3213,3214],"mspace",{"width":3215},"2em",[1743,3217,3218,3220],{},[898,3219,1658],{},[2505,3221,2507],{},[1708,3223,1710],{},[1708,3225,2726],{},[3194,3227,3228],{"scriptlevel":2784,"displaystyle":1715},[2358,3229,3230,3232],{},[2505,3231,3132],{},[2505,3233,3121],{},[3194,3235,3236],{"scriptlevel":2784,"displaystyle":1715},[2358,3237,3238,3240],{},[898,3239,1923],{},[898,3241,207],{},[898,3243,2155],{"mathvariant":1759},[902,3245,3246],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,3248,3250,3251,1721],{"id":3249},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,3252,3254],{"className":3253},[886],[888,3255,3256],{"xmlns":890},[892,3257,3258,3268],{},[895,3259,3260,3262],{},[898,3261,1786],{},[1743,3263,3264,3266],{},[898,3265,1747],{},[898,3267,1658],{},[902,3269,1825],{"encoding":904},[724,3271,3272,1695,3275,2309,3278,3297],{},[38,3273,3274],{},"Průměrný produkt práce",[614,3276,3277],{},"average product of labour",[883,3279,3281],{"className":3280},[886],[888,3282,3283],{"xmlns":890},[892,3284,3285,3295],{},[895,3286,3287,3289],{},[898,3288,1786],{},[1743,3290,3291,3293],{},[898,3292,1747],{},[898,3294,1658],{},[902,3296,1825],{"encoding":904}," je podíl produkce a práce:",[883,3299,3301],{"className":3300},[886],[888,3302,3303],{"xmlns":890,"display":2210},[892,3304,3305,3340],{},[2214,3306,3307],{"width":2216},[2218,3308,3309,3311,3333,3335],{},[2221,3310],{"width":2223},[2221,3312,3313],{},[895,3314,3315,3317,3323,3325,3331],{},[898,3316,1786],{},[1743,3318,3319,3321],{},[898,3320,1747],{},[898,3322,1658],{},[1708,3324,1710],{},[2358,3326,3327,3329],{},[898,3328,1688],{},[898,3330,1658],{},[898,3332,2155],{"mathvariant":1759},[2221,3334],{"width":2223},[2221,3336,3337],{},[2247,3338,3339],{},"(5.4)",[902,3341,3342],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,3344,3345,3346,2155],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,3347,3349],{"className":3348},[886],[888,3350,3351],{"xmlns":890},[892,3352,3353,3363],{},[895,3354,3355,3357],{},[898,3356,1786],{},[1743,3358,3359,3361],{},[898,3360,1747],{},[898,3362,1658],{},[902,3364,1825],{"encoding":904},[115,3366,3368],{"id":3367},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,3370,3371],{},[3372,3373],"img",{"alt":3374,"className":3375,"src":3377},"imek-q-mpl-apl-tripanel",[210,3376],"wikilink-broken","\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1636,3379,3380],{},[724,3381,3382,3385,3386,3405,3406,3423,3424],{},[38,3383,3384],{},"Princip:"," Má-li ",[883,3387,3389],{"className":3388},[886],[888,3390,3391],{"xmlns":890},[892,3392,3393,3403],{},[895,3394,3395,3397],{},[898,3396,1786],{},[1743,3398,3399,3401],{},[898,3400,1747],{},[898,3402,1658],{},[902,3404,1825],{"encoding":904}," v bodě ",[883,3407,3409],{"className":3408},[886],[888,3410,3411],{"xmlns":890},[892,3412,3413,3421],{},[895,3414,3415],{},[1743,3416,3417,3419],{},[898,3418,1658],{},[2505,3420,2784],{},[902,3422,2787],{"encoding":904}," maximum, pak platí\n",[883,3425,3430],{"className":3426,"title":3428,"style":3429},[3427],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,3432,3433,3434,3437,3438,1729,3442,2155],{},"Slovně: ",[38,3435,3436],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,3439,3441],{"className":3440,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,3443,3445],{"className":3444},[886],[888,3446,3447],{"xmlns":890},[892,3448,3449,3456],{},[895,3450,3451,3453],{},[898,3452,1786],{},[898,3454,3455],{},"C",[902,3457,3458],{"encoding":904},"AC",[1636,3460,3461,3486],{},[724,3462,3463,3466,3467],{},[883,3464,3465],{},"!tip"," Postup — jak najít max ",[883,3468,3470],{"className":3469},[886],[888,3471,3472],{"xmlns":890},[892,3473,3474,3484],{},[895,3475,3476,3478],{},[898,3477,1786],{},[1743,3479,3480,3482],{},[898,3481,1747],{},[898,3483,1658],{},[902,3485,1825],{"encoding":904},[152,3487,3488,3526,3608],{},[123,3489,3490,3491,3525],{},"Napište ",[883,3492,3494],{"className":3493},[886],[888,3495,3496],{"xmlns":890},[892,3497,3498,3522],{},[895,3499,3500,3502,3508,3510,3512,3514,3516,3518,3520],{},[898,3501,1786],{},[1743,3503,3504,3506],{},[898,3505,1747],{},[898,3507,1658],{},[1708,3509,1710],{},[898,3511,1688],{},[1708,3513,1716],{"stretchy":1715},[898,3515,1658],{},[1708,3517,1721],{"stretchy":1715},[898,3519,1799],{"mathvariant":1759},[898,3521,1658],{},[902,3523,3524],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,3527,3528,3529,3561,3562,3565,3566,2155],{},"Položte ",[883,3530,3532],{"className":3531},[886],[888,3533,3534],{"xmlns":890},[892,3535,3536,3558],{},[895,3537,3538,3540,3542,3548,3554,3556],{},[1708,3539,1716],{"stretchy":1715},[898,3541,1786],{},[1743,3543,3544,3546],{},[898,3545,1747],{},[898,3547,1658],{},[1753,3549,3550,3552],{},[1708,3551,1721],{"stretchy":1715},[1708,3553,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,3555,1710],{},[2505,3557,2784],{},[902,3559,3560],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,3563,3564],{},"Zkratka:"," můžete rovnou řešit ",[883,3567,3569],{"className":3568},[886],[888,3570,3571],{"xmlns":890},[892,3572,3573,3605],{},[895,3574,3575,3577,3583,3585,3587,3589,3591,3593,3599,3601,3603],{},[898,3576,1741],{},[1743,3578,3579,3581],{},[898,3580,1747],{},[898,3582,1658],{},[1708,3584,1716],{"stretchy":1715},[898,3586,1658],{},[1708,3588,1721],{"stretchy":1715},[1708,3590,1710],{},[898,3592,1786],{},[1743,3594,3595,3597],{},[898,3596,1747],{},[898,3598,1658],{},[1708,3600,1716],{"stretchy":1715},[898,3602,1658],{},[1708,3604,1721],{"stretchy":1715},[902,3606,3607],{"encoding":904},"MP_L(L) = AP_L(L)",[123,3609,3610],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,3612,3614],{"id":3613},"odvození","Odvození",[724,3616,3617,3618,3651],{},"Z ",[883,3619,3621],{"className":3620},[886],[888,3622,3623],{"xmlns":890},[892,3624,3625,3649],{},[895,3626,3627,3629,3635,3637,3639,3641,3643,3645,3647],{},[898,3628,1786],{},[1743,3630,3631,3633],{},[898,3632,1747],{},[898,3634,1658],{},[1708,3636,1710],{},[898,3638,1688],{},[1708,3640,1716],{"stretchy":1715},[898,3642,1658],{},[1708,3644,1721],{"stretchy":1715},[898,3646,1799],{"mathvariant":1759},[898,3648,1658],{},[902,3650,3524],{"encoding":904}," a derivace podílu:",[883,3653,3655],{"className":3654},[886],[888,3656,3657],{"xmlns":890,"display":2210},[892,3658,3659,3813],{},[895,3660,3661,3663,3665,3671,3677,3679,3681,3683,3685,3726,3728,3734,3768,3770,3776,3779,3781,3787,3789,3791,3793,3795,3797,3803,3805,3807,3809,3811],{},[1708,3662,1716],{"stretchy":1715},[898,3664,1786],{},[1743,3666,3667,3669],{},[898,3668,1747],{},[898,3670,1658],{},[1753,3672,3673,3675],{},[1708,3674,1721],{"stretchy":1715},[1708,3676,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,3678,1716],{"stretchy":1715},[898,3680,1658],{},[1708,3682,1721],{"stretchy":1715},[1708,3684,1710],{},[2358,3686,3687,3720],{},[895,3688,3689,3695,3697,3699,3701,3704,3706,3708,3710,3712,3714,3716,3718],{},[1753,3690,3691,3693],{},[898,3692,1688],{},[1708,3694,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,3696,1716],{"stretchy":1715},[898,3698,1658],{},[1708,3700,1721],{"stretchy":1715},[1708,3702,3703],{},"⋅",[898,3705,1658],{},[1708,3707,2726],{},[898,3709,1688],{},[1708,3711,1716],{"stretchy":1715},[898,3713,1658],{},[1708,3715,1721],{"stretchy":1715},[1708,3717,3703],{},[2505,3719,2507],{},[1753,3721,3722,3724],{},[898,3723,1658],{},[2505,3725,3132],{},[1708,3727,1710],{},[2358,3729,3730,3732],{},[2505,3731,2507],{},[898,3733,1658],{},[895,3735,3736,3738,3744,3746,3748,3750,3752,3766],{},[1708,3737,1716],{"fence":1882},[1753,3739,3740,3742],{},[898,3741,1688],{},[1708,3743,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,3745,1716],{"stretchy":1715},[898,3747,1658],{},[1708,3749,1721],{"stretchy":1715},[1708,3751,2726],{},[2358,3753,3754,3764],{},[895,3755,3756,3758,3760,3762],{},[898,3757,1688],{},[1708,3759,1716],{"stretchy":1715},[898,3761,1658],{},[1708,3763,1721],{"stretchy":1715},[898,3765,1658],{},[1708,3767,1721],{"fence":1882},[1708,3769,1710],{},[2358,3771,3772,3774],{},[2505,3773,2507],{},[898,3775,1658],{},[1708,3777,1716],{"fence":1882,"stretchy":1882,"minsize":3778,"maxsize":3778},"1.2em",[898,3780,1741],{},[1743,3782,3783,3785],{},[898,3784,1747],{},[898,3786,1658],{},[1708,3788,1716],{"stretchy":1715},[898,3790,1658],{},[1708,3792,1721],{"stretchy":1715},[1708,3794,2726],{},[898,3796,1786],{},[1743,3798,3799,3801],{},[898,3800,1747],{},[898,3802,1658],{},[1708,3804,1716],{"stretchy":1715},[898,3806,1658],{},[1708,3808,1721],{"stretchy":1715},[1708,3810,1721],{"fence":1882,"stretchy":1882,"minsize":3778,"maxsize":3778},[898,3812,2155],{"mathvariant":1759},[902,3814,3815],{"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).",[724,3817,3818,3819,3033,3841,3924],{},"Pro ",[883,3820,3822],{"className":3821},[886],[888,3823,3824],{"xmlns":890},[892,3825,3826,3838],{},[895,3827,3828,3834,3836],{},[1743,3829,3830,3832],{},[898,3831,1658],{},[2505,3833,2784],{},[1708,3835,2854],{},[2505,3837,2784],{},[902,3839,3840],{"encoding":904},"L_0 > 0",[883,3842,3844],{"className":3843},[886],[888,3845,3846],{"xmlns":890},[892,3847,3848,3921],{},[895,3849,3850,3852,3854,3860,3866,3868,3874,3876,3878,3880,3883,3885,3891,3893,3899,3901,3903,3905,3911,3913,3919],{},[1708,3851,1716],{"stretchy":1715},[898,3853,1786],{},[1743,3855,3856,3858],{},[898,3857,1747],{},[898,3859,1658],{},[1753,3861,3862,3864],{},[1708,3863,1721],{"stretchy":1715},[1708,3865,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,3867,1716],{"stretchy":1715},[1743,3869,3870,3872],{},[898,3871,1658],{},[2505,3873,2784],{},[1708,3875,1721],{"stretchy":1715},[1708,3877,1710],{},[2505,3879,2784],{},[1708,3881,3882],{},"⇔",[898,3884,1741],{},[1743,3886,3887,3889],{},[898,3888,1747],{},[898,3890,1658],{},[1708,3892,1716],{"stretchy":1715},[1743,3894,3895,3897],{},[898,3896,1658],{},[2505,3898,2784],{},[1708,3900,1721],{"stretchy":1715},[1708,3902,1710],{},[898,3904,1786],{},[1743,3906,3907,3909],{},[898,3908,1747],{},[898,3910,1658],{},[1708,3912,1716],{"stretchy":1715},[1743,3914,3915,3917],{},[898,3916,1658],{},[2505,3918,2784],{},[1708,3920,1721],{"stretchy":1715},[902,3922,3923],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,3926,3928],{"id":3927},"příklad-51","Příklad 5.1",[724,3930,3931,3932,2155],{},"Je dána produkce ",[883,3933,3935],{"className":3934},[886],[888,3936,3937],{"xmlns":890},[892,3938,3939,3965],{},[895,3940,3941,3943,3945,3948,3954,3956,3959],{},[898,3942,1688],{},[1708,3944,1710],{},[2505,3946,3947],{},"6",[1753,3949,3950,3952],{},[898,3951,1658],{},[2505,3953,3132],{},[1708,3955,2726],{},[2505,3957,3958],{},"0,2",[1753,3960,3961,3963],{},[898,3962,1658],{},[2505,3964,3121],{},[902,3966,3967],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,3969,3970,3973,3974,4032,4033,2155],{},[38,3971,3972],{},"(a)"," Pro ",[883,3975,3977],{"className":3976},[886],[888,3978,3979],{"xmlns":890},[892,3980,3981,4029],{},[895,3982,3983,3985,3987,3989,3991,3994,3996,3999,4001,4004,4006,4009,4011,4014,4016,4019,4021,4024,4026],{},[898,3984,1658],{},[1708,3986,1710],{},[2505,3988,3132],{},[1708,3990,1883],{"separator":1882},[2505,3992,3993],{},"5",[1708,3995,1883],{"separator":1882},[2505,3997,3998],{},"8",[1708,4000,1883],{"separator":1882},[2505,4002,4003],{},"10",[1708,4005,1883],{"separator":1882},[2505,4007,4008],{},"14",[1708,4010,1883],{"separator":1882},[2505,4012,4013],{},"18",[1708,4015,1883],{"separator":1882},[2505,4017,4018],{},"20",[1708,4020,1883],{"separator":1882},[2505,4022,4023],{},"21",[1708,4025,1883],{"separator":1882},[2505,4027,4028],{},"25",[902,4030,4031],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,4034,4036],{"className":4035},[886],[888,4037,4038],{"xmlns":890},[892,4039,4040,4050],{},[895,4041,4042,4044],{},[898,4043,1741],{},[1743,4045,4046,4048],{},[898,4047,1747],{},[898,4049,1658],{},[902,4051,2300],{"encoding":904},[724,4053,4054,4055,4123],{},"Podle (5.2): ",[883,4056,4058],{"className":4057},[886],[888,4059,4060],{"xmlns":890},[892,4061,4062,4120],{},[895,4063,4064,4066,4072,4074,4080,4082,4084,4086,4088,4091,4093,4095,4098,4104,4106,4108,4110,4112,4114,4116,4118],{},[898,4065,1741],{},[1743,4067,4068,4070],{},[898,4069,1747],{},[898,4071,1658],{},[1708,4073,1710],{},[1753,4075,4076,4078],{},[898,4077,1688],{},[1708,4079,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,4081,1716],{"stretchy":1715},[898,4083,1658],{},[1708,4085,1721],{"stretchy":1715},[1708,4087,1710],{},[2505,4089,4090],{},"12",[898,4092,1658],{},[1708,4094,2726],{},[2505,4096,4097],{},"0,6",[1753,4099,4100,4102],{},[898,4101,1658],{},[2505,4103,3132],{},[1708,4105,1710],{},[898,4107,1658],{},[1708,4109,1716],{"stretchy":1715},[2505,4111,4090],{},[1708,4113,2726],{},[2505,4115,4097],{},[898,4117,1658],{},[1708,4119,1721],{"stretchy":1715},[902,4121,4122],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",". Dosazením:",[16,4125,4126,4163],{},[19,4127,4128],{},[22,4129,4130,4145,4147,4149,4151,4153,4155,4157,4159,4161],{},[25,4131,4132],{},[883,4133,4135],{"className":4134},[886],[888,4136,4137],{"xmlns":890},[892,4138,4139,4143],{},[895,4140,4141],{},[898,4142,1658],{},[902,4144,1658],{"encoding":904},[25,4146,3132],{},[25,4148,3993],{},[25,4150,3998],{},[25,4152,4003],{},[25,4154,4008],{},[25,4156,4013],{},[25,4158,4018],{},[25,4160,4023],{},[25,4162,4028],{},[30,4164,4165],{},[22,4166,4167,4188,4191,4194,4197,4200,4203,4205,4207,4226],{},[35,4168,4169],{},[883,4170,4172],{"className":4171},[886],[888,4173,4174],{"xmlns":890},[892,4175,4176,4186],{},[895,4177,4178,4180],{},[898,4179,1741],{},[1743,4181,4182,4184],{},[898,4183,1747],{},[898,4185,1658],{},[902,4187,2300],{"encoding":904},[35,4189,4190],{},"21,6",[35,4192,4193],{},"45",[35,4195,4196],{},"57,6",[35,4198,4199],{},"60",[35,4201,4202],{},"50,4",[35,4204,4190],{},[35,4206,2784],{},[35,4208,4209],{},[883,4210,4212],{"className":4211},[886],[888,4213,4214],{"xmlns":890},[892,4215,4216,4223],{},[895,4217,4218,4220],{},[1708,4219,2726],{},[2505,4221,4222],{},"12,6",[902,4224,4225],{"encoding":904},"-12{,}6",[35,4227,4228],{},[883,4229,4231],{"className":4230},[886],[888,4232,4233],{"xmlns":890},[892,4234,4235,4242],{},[895,4236,4237,4239],{},[1708,4238,2726],{},[2505,4240,4241],{},"75",[902,4243,4244],{"encoding":904},"-75",[724,4246,4247,4266,4267,4285,4286,4303,4304,4322,4323,4348,4349,4367],{},[883,4248,4250],{"className":4249},[886],[888,4251,4252],{"xmlns":890},[892,4253,4254,4264],{},[895,4255,4256,4258],{},[898,4257,1741],{},[1743,4259,4260,4262],{},[898,4261,1747],{},[898,4263,1658],{},[902,4265,2300],{"encoding":904}," nabývá maxima pro ",[883,4268,4270],{"className":4269},[886],[888,4271,4272],{"xmlns":890},[892,4273,4274,4282],{},[895,4275,4276,4278,4280],{},[898,4277,1658],{},[1708,4279,1710],{},[2505,4281,4003],{},[902,4283,4284],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,4287,4289],{"className":4288},[886],[888,4290,4291],{"xmlns":890},[892,4292,4293,4301],{},[895,4294,4295,4297,4299],{},[898,4296,1658],{},[1708,4298,1710],{},[2505,4300,4003],{},[902,4302,4284],{"encoding":904}," přírůstky klesají, v ",[883,4305,4307],{"className":4306},[886],[888,4308,4309],{"xmlns":890},[892,4310,4311,4319],{},[895,4312,4313,4315,4317],{},[898,4314,1658],{},[1708,4316,1710],{},[2505,4318,4018],{},[902,4320,4321],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,4324,4326],{"className":4325},[886],[888,4327,4328],{"xmlns":890},[892,4329,4330,4345],{},[895,4331,4332,4334,4336,4338,4340,4342],{},[898,4333,1688],{},[1708,4335,1716],{"stretchy":1715},[2505,4337,4018],{},[1708,4339,1721],{"stretchy":1715},[1708,4341,1710],{},[2505,4343,4344],{},"800",[902,4346,4347],{"encoding":904},"Q(20) = 800","), od ",[883,4350,4352],{"className":4351},[886],[888,4353,4354],{"xmlns":890},[892,4355,4356,4364],{},[895,4357,4358,4360,4362],{},[898,4359,1658],{},[1708,4361,2854],{},[2505,4363,4018],{},[902,4365,4366],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,4369,4370],{},[614,4371,4372,4373,4413,4414,3405,4432,2155],{},"Obrázek 5.1 — graf produkce ",[883,4374,4376],{"className":4375},[886],[888,4377,4378],{"xmlns":890},[892,4379,4380,4410],{},[895,4381,4382,4384,4386,4388,4390,4392,4394,4400,4402,4404],{},[898,4383,1688],{},[1708,4385,1716],{"stretchy":1715},[898,4387,1658],{},[1708,4389,1721],{"stretchy":1715},[1708,4391,1710],{},[2505,4393,3947],{},[1753,4395,4396,4398],{},[898,4397,1658],{},[2505,4399,3132],{},[1708,4401,2726],{},[2505,4403,3958],{},[1753,4405,4406,4408],{},[898,4407,1658],{},[2505,4409,3121],{},[902,4411,4412],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,4415,4417],{"className":4416},[886],[888,4418,4419],{"xmlns":890},[892,4420,4421,4429],{},[895,4422,4423,4425,4427],{},[898,4424,1688],{},[1708,4426,1710],{},[2505,4428,4344],{},[902,4430,4431],{"encoding":904},"Q = 800",[883,4433,4435],{"className":4434},[886],[888,4436,4437],{"xmlns":890},[892,4438,4439,4447],{},[895,4440,4441,4443,4445],{},[898,4442,1658],{},[1708,4444,1710],{},[2505,4446,4018],{},[902,4448,4321],{"encoding":904},[724,4450,4451,4454],{},[38,4452,4453],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,4456,4457,4458,1343,4476,2788],{},"Podle (5.3) s ",[883,4459,4461],{"className":4460},[886],[888,4462,4463],{"xmlns":890},[892,4464,4465,4473],{},[895,4466,4467,4469,4471],{},[898,4468,1658],{},[1708,4470,1710],{},[2505,4472,3947],{},[902,4474,4475],{"encoding":904},"L = 6",[883,4477,4479],{"className":4478},[886],[888,4480,4481],{"xmlns":890},[892,4482,4483,4493],{},[895,4484,4485,4487,4489,4491],{},[898,4486,2364],{},[898,4488,1658],{},[1708,4490,1710],{},[2505,4492,3121],{},[902,4494,4495],{"encoding":904},"dL = 3",[883,4497,4499],{"className":4498},[886],[888,4500,4501],{"xmlns":890,"display":2210},[892,4502,4503,4567],{},[895,4504,4505,4507,4509,4511,4513,4519,4521,4523,4525,4527,4529,4531,4533,4535,4537,4539,4541,4543,4545,4548,4550,4552,4554,4556,4558,4560,4562,4564],{},[898,4506,2364],{},[898,4508,1688],{},[1708,4510,1710],{},[898,4512,1741],{},[1743,4514,4515,4517],{},[898,4516,1747],{},[898,4518,1658],{},[1708,4520,1716],{"stretchy":1715},[2505,4522,3947],{},[1708,4524,1721],{"stretchy":1715},[1708,4526,3703],{},[2505,4528,3121],{},[1708,4530,1710],{},[1708,4532,1716],{"stretchy":1715},[2505,4534,4090],{},[1708,4536,3703],{},[2505,4538,3947],{},[1708,4540,2726],{},[2505,4542,4097],{},[1708,4544,3703],{},[2505,4546,4547],{},"36",[1708,4549,1721],{"stretchy":1715},[1708,4551,3703],{},[2505,4553,3121],{},[1708,4555,1710],{},[2505,4557,4202],{},[1708,4559,3703],{},[2505,4561,3121],{},[1708,4563,1710],{},[2505,4565,4566],{},"151,2.",[902,4568,4569],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,4571,4572,4573,4598,4599,4613,4614,2155],{},"Produkce vzroste z ",[883,4574,4576],{"className":4575},[886],[888,4577,4578],{"xmlns":890},[892,4579,4580,4595],{},[895,4581,4582,4584,4586,4588,4590,4592],{},[898,4583,1688],{},[1708,4585,1716],{"stretchy":1715},[2505,4587,3947],{},[1708,4589,1721],{"stretchy":1715},[1708,4591,1710],{},[2505,4593,4594],{},"172,8",[902,4596,4597],{"encoding":904},"Q(6) = 172{,}8"," přibližně na ",[883,4600,4602],{"className":4601},[886],[888,4603,4604],{"xmlns":890},[892,4605,4606,4611],{},[895,4607,4608],{},[2505,4609,4610],{},"324",[902,4612,4610],{"encoding":904},". Skutečná hodnota: ",[883,4615,4617],{"className":4616},[886],[888,4618,4619],{"xmlns":890},[892,4620,4621,4662],{},[895,4622,4623,4625,4627,4629,4631,4633,4636,4638,4640,4642,4644,4646,4648,4650,4653,4655,4657,4659],{},[898,4624,2633],{"mathvariant":1759},[898,4626,1688],{},[1708,4628,1710],{},[898,4630,1688],{},[1708,4632,1716],{"stretchy":1715},[2505,4634,4635],{},"9",[1708,4637,1721],{"stretchy":1715},[1708,4639,2726],{},[898,4641,1688],{},[1708,4643,1716],{"stretchy":1715},[2505,4645,3947],{},[1708,4647,1721],{"stretchy":1715},[1708,4649,1710],{},[2505,4651,4652],{},"340,2",[1708,4654,2726],{},[2505,4656,4594],{},[1708,4658,1710],{},[2505,4660,4661],{},"167,4",[902,4663,4664],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,4666,4668],{"id":4667},"příklad-52","Příklad 5.2",[724,4670,4671,4672,2155],{},"Ověříme princip (5.5) pro ",[883,4673,4675],{"className":4674},[886],[888,4676,4677],{"xmlns":890},[892,4678,4679,4703],{},[895,4680,4681,4683,4685,4687,4693,4695,4697],{},[898,4682,1688],{},[1708,4684,1710],{},[2505,4686,3947],{},[1753,4688,4689,4691],{},[898,4690,1658],{},[2505,4692,3132],{},[1708,4694,2726],{},[2505,4696,3958],{},[1753,4698,4699,4701],{},[898,4700,1658],{},[2505,4702,3121],{},[902,4704,3967],{"encoding":904},[883,4706,4708],{"className":4707},[886],[888,4709,4710],{"xmlns":890,"display":2210},[892,4711,4712,4796],{},[895,4713,4714,4716,4722,4724,4730,4732,4734,4736,4738,4740,4746,4748,4751,4753,4762,4764,4766,4768,4771,4773,4775,4777,4780,4783,4785,4791,4793],{},[898,4715,1786],{},[1743,4717,4718,4720],{},[898,4719,1747],{},[898,4721,1658],{},[1708,4723,1710],{},[2358,4725,4726,4728],{},[898,4727,1688],{},[898,4729,1658],{},[1708,4731,1710],{},[2505,4733,3947],{},[898,4735,1658],{},[1708,4737,2726],{},[2505,4739,3958],{},[1753,4741,4742,4744],{},[898,4743,1658],{},[2505,4745,3132],{},[1708,4747,1883],{"separator":1882},[3213,4749],{"width":4750},"1em",[898,4752,1786],{},[4754,4755,4756,4758,4760],"msubsup",{},[898,4757,1747],{},[898,4759,1658],{},[1708,4761,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,4763,1710],{},[2505,4765,3947],{},[1708,4767,2726],{},[2505,4769,4770],{},"0,4",[898,4772,1658],{},[1708,4774,1710],{},[2505,4776,2784],{},[2247,4778,4779],{},"  ",[1708,4781,4782],{},"⇒",[2247,4784,4779],{},[1743,4786,4787,4789],{},[898,4788,1658],{},[2505,4790,2784],{},[1708,4792,1710],{},[2505,4794,4795],{},"15.",[902,4797,4798],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,4800,4801,4837,4838,4857,4858,2155],{},[883,4802,4804],{"className":4803},[886],[888,4805,4806],{"xmlns":890},[892,4807,4808,4834],{},[895,4809,4810,4812,4824,4826,4828,4830,4832],{},[898,4811,1786],{},[4754,4813,4814,4816,4818],{},[898,4815,1747],{},[898,4817,1658],{},[895,4819,4820,4822],{},[1708,4821,1761],{"mathvariant":1759},[1708,4823,1761],{"mathvariant":1759},[1708,4825,1710],{},[1708,4827,2726],{},[2505,4829,4770],{},[1708,4831,2932],{},[2505,4833,2784],{},[902,4835,4836],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,4839,4841],{"className":4840},[886],[888,4842,4843],{"xmlns":890},[892,4844,4845,4854],{},[895,4846,4847,4849,4851],{},[898,4848,1658],{},[1708,4850,1710],{},[2505,4852,4853],{},"15",[902,4855,4856],{"encoding":904},"L = 15"," je maximum, ",[883,4859,4861],{"className":4860},[886],[888,4862,4863],{"xmlns":890},[892,4864,4865,4911],{},[895,4866,4867,4869,4875,4877,4879,4881,4883,4885,4887,4889,4891,4893,4895,4898,4900,4903,4905,4907,4909],{},[898,4868,1786],{},[1743,4870,4871,4873],{},[898,4872,1747],{},[898,4874,1658],{},[1708,4876,1716],{"stretchy":1715},[2505,4878,4853],{},[1708,4880,1721],{"stretchy":1715},[1708,4882,1710],{},[2505,4884,3947],{},[1708,4886,3703],{},[2505,4888,4853],{},[1708,4890,2726],{},[2505,4892,3958],{},[1708,4894,3703],{},[2505,4896,4897],{},"225",[1708,4899,1710],{},[2505,4901,4902],{},"90",[1708,4904,2726],{},[2505,4906,4193],{},[1708,4908,1710],{},[2505,4910,4193],{},[902,4912,4913],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,4915,4916,4972,4973,5019],{},[883,4917,4919],{"className":4918},[886],[888,4920,4921],{"xmlns":890},[892,4922,4923,4969],{},[895,4924,4925,4927,4933,4935,4937,4939,4941,4943,4945,4947,4949,4951,4953,4955,4957,4960,4962,4965,4967],{},[898,4926,1741],{},[1743,4928,4929,4931],{},[898,4930,1747],{},[898,4932,1658],{},[1708,4934,1716],{"stretchy":1715},[2505,4936,4853],{},[1708,4938,1721],{"stretchy":1715},[1708,4940,1710],{},[2505,4942,4090],{},[1708,4944,3703],{},[2505,4946,4853],{},[1708,4948,2726],{},[2505,4950,4097],{},[1708,4952,3703],{},[2505,4954,4897],{},[1708,4956,1710],{},[2505,4958,4959],{},"180",[1708,4961,2726],{},[2505,4963,4964],{},"135",[1708,4966,1710],{},[2505,4968,4193],{},[902,4970,4971],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",". Tedy ",[883,4974,4976],{"className":4975},[886],[888,4977,4978],{"xmlns":890},[892,4979,4980,5016],{},[895,4981,4982,4984,4990,4992,4994,4996,4998,5000,5006,5008,5010,5012,5014],{},[898,4983,1741],{},[1743,4985,4986,4988],{},[898,4987,1747],{},[898,4989,1658],{},[1708,4991,1716],{"stretchy":1715},[2505,4993,4853],{},[1708,4995,1721],{"stretchy":1715},[1708,4997,1710],{},[898,4999,1786],{},[1743,5001,5002,5004],{},[898,5003,1747],{},[898,5005,1658],{},[1708,5007,1716],{"stretchy":1715},[2505,5009,4853],{},[1708,5011,1721],{"stretchy":1715},[1708,5013,1710],{},[2505,5015,4193],{},[902,5017,5018],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,5021,5022,5025,5026,5055,5056,2155],{},[38,5023,5024],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,5027,5029],{"className":5028},[886],[888,5030,5031],{"xmlns":890},[892,5032,5033,5053],{},[895,5034,5035,5037,5043,5045,5047],{},[898,5036,1741],{},[1743,5038,5039,5041],{},[898,5040,1747],{},[898,5042,1658],{},[1708,5044,1710],{},[898,5046,1786],{},[1743,5048,5049,5051],{},[898,5050,1747],{},[898,5052,1658],{},[902,5054,1856],{"encoding":904},", tj. ",[883,5057,5059],{"className":5058},[886],[888,5060,5061],{"xmlns":890},[892,5062,5063,5103],{},[895,5064,5065,5067,5069,5071,5073,5079,5081,5083,5085,5087,5089,5095,5097,5099,5101],{},[2505,5066,4090],{},[898,5068,1658],{},[1708,5070,2726],{},[2505,5072,4097],{},[1753,5074,5075,5077],{},[898,5076,1658],{},[2505,5078,3132],{},[1708,5080,1710],{},[2505,5082,3947],{},[898,5084,1658],{},[1708,5086,2726],{},[2505,5088,3958],{},[1753,5090,5091,5093],{},[898,5092,1658],{},[2505,5094,3132],{},[1708,5096,4782],{},[898,5098,1658],{},[1708,5100,1710],{},[2505,5102,4853],{},[902,5104,5105],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,5107,5108],{},[614,5109,5110,5111,5130,5131,5149,5150,5169,5170,5188,5189,5206,5207,5226,5227,5246],{},"Obrázek 5.3 — křivky ",[883,5112,5114],{"className":5113},[886],[888,5115,5116],{"xmlns":890},[892,5117,5118,5128],{},[895,5119,5120,5122],{},[898,5121,1741],{},[1743,5123,5124,5126],{},[898,5125,1747],{},[898,5127,1658],{},[902,5129,2300],{"encoding":904}," (max 60 při ",[883,5132,5134],{"className":5133},[886],[888,5135,5136],{"xmlns":890},[892,5137,5138,5146],{},[895,5139,5140,5142,5144],{},[898,5141,1658],{},[1708,5143,1710],{},[2505,5145,4003],{},[902,5147,5148],{"encoding":904},"L=10",") a ",[883,5151,5153],{"className":5152},[886],[888,5154,5155],{"xmlns":890},[892,5156,5157,5167],{},[895,5158,5159,5161],{},[898,5160,1786],{},[1743,5162,5163,5165],{},[898,5164,1747],{},[898,5166,1658],{},[902,5168,1825],{"encoding":904}," (max 45 při ",[883,5171,5173],{"className":5172},[886],[888,5174,5175],{"xmlns":890},[892,5176,5177,5185],{},[895,5178,5179,5181,5183],{},[898,5180,1658],{},[1708,5182,1710],{},[2505,5184,4853],{},[902,5186,5187],{"encoding":904},"L=15","), průsečík v ",[883,5190,5192],{"className":5191},[886],[888,5193,5194],{"xmlns":890},[892,5195,5196,5204],{},[895,5197,5198,5200,5202],{},[898,5199,1658],{},[1708,5201,1710],{},[2505,5203,4853],{},[902,5205,4856],{"encoding":904},". Nalevo od 15 leží ",[883,5208,5210],{"className":5209},[886],[888,5211,5212],{"xmlns":890},[892,5213,5214,5224],{},[895,5215,5216,5218],{},[898,5217,1741],{},[1743,5219,5220,5222],{},[898,5221,1747],{},[898,5223,1658],{},[902,5225,2300],{"encoding":904}," nad ",[883,5228,5230],{"className":5229},[886],[888,5231,5232],{"xmlns":890},[892,5233,5234,5244],{},[895,5235,5236,5238],{},[898,5237,1786],{},[1743,5239,5240,5242],{},[898,5241,1747],{},[898,5243,1658],{},[902,5245,1825],{"encoding":904},", napravo pod ní.",[115,5248,5250],{"id":5249},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,5252,5253,5254,2486,5267,1729,5270,5283,5284,1729,5287,2788],{},"V dvoufaktorovém modelu závisí produkce ",[883,5255,5257],{"className":5256},[886],[888,5258,5259],{"xmlns":890},[892,5260,5261,5265],{},[895,5262,5263],{},[898,5264,1688],{},[902,5266,1688],{"encoding":904},[38,5268,5269],{},"práci",[883,5271,5273],{"className":5272},[886],[888,5274,5275],{"xmlns":890},[892,5276,5277,5281],{},[895,5278,5279],{},[898,5280,1658],{},[902,5282,1658],{"encoding":904}," i ",[38,5285,5286],{},"kapitálu",[883,5288,5290],{"className":5289},[886],[888,5291,5292],{"xmlns":890},[892,5293,5294,5298],{},[895,5295,5296],{},[898,5297,1673],{},[902,5299,1673],{"encoding":904},[883,5301,5303],{"className":5302},[886],[888,5304,5305],{"xmlns":890,"display":2210},[892,5306,5307,5342],{},[2214,5308,5309],{"width":2216},[2218,5310,5311,5313,5335,5337],{},[2221,5312],{"width":2223},[2221,5314,5315],{},[895,5316,5317,5319,5321,5323,5325,5327,5329,5331,5333],{},[898,5318,1688],{},[1708,5320,1710],{},[898,5322,1688],{},[1708,5324,1716],{"stretchy":1715},[898,5326,1658],{},[1708,5328,1883],{"separator":1882},[898,5330,1673],{},[1708,5332,1721],{"stretchy":1715},[898,5334,2155],{"mathvariant":1759},[2221,5336],{"width":2223},[2221,5338,5339],{},[2247,5340,5341],{},"(5.6)",[902,5343,5344],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,5346,5347,5348,5350],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,5349,2204],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,5352,5354],{"id":5353},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,5356,5357],{},"Široce používané produkční funkce mají tvar",[883,5359,5361],{"className":5360},[886],[888,5362,5363],{"xmlns":890,"display":2210},[892,5364,5365,5406],{},[2214,5366,5367],{"width":2216},[2218,5368,5369,5371,5399,5401],{},[2221,5370],{"width":2223},[2221,5372,5373],{},[895,5374,5375,5377,5379,5381,5383,5389,5391,5397],{},[898,5376,1688],{},[1708,5378,1710],{},[898,5380,1786],{},[2247,5382,2659],{},[1753,5384,5385,5387],{},[898,5386,1658],{},[898,5388,207],{},[2247,5390,2659],{},[1753,5392,5393,5395],{},[898,5394,1673],{},[898,5396,1923],{},[1708,5398,1883],{"separator":1882},[2221,5400],{"width":2223},[2221,5402,5403],{},[2247,5404,5405],{},"(5.7)",[902,5407,5408],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,5410,5411,5412,5434,5435,5437,5438,2155],{},"kde ",[883,5413,5415],{"className":5414},[886],[888,5416,5417],{"xmlns":890},[892,5418,5419,5431],{},[895,5420,5421,5423,5425,5427,5429],{},[898,5422,1786],{},[1708,5424,1883],{"separator":1882},[898,5426,207],{},[1708,5428,1883],{"separator":1882},[898,5430,1923],{},[902,5432,5433],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,5436,1894],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,5439,5441],{"className":5440},[886],[888,5442,5443],{"xmlns":890},[892,5444,5445,5457],{},[895,5446,5447,5449,5451,5453,5455],{},[898,5448,207],{},[1708,5450,1883],{"separator":1882},[898,5452,1923],{},[1708,5454,2932],{},[2505,5456,2507],{},[902,5458,5459],{"encoding":904},"a, b \u003C 1",[724,5461,5462],{},[3372,5463],{"alt":5464,"className":5465,"src":5466},"imek-vynosy-z-rozsahu-3typy",[210,3376],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,5468,5469,5470,5473,5474,2486,5487,5504,5505,2486,5518,2788],{},"Reflektují ekonomickou zákonitost, že ",[38,5471,5472],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,5475,5477],{"className":5476},[886],[888,5478,5479],{"xmlns":890},[892,5480,5481,5485],{},[895,5482,5483],{},[898,5484,1658],{},[902,5486,1658],{"encoding":904},[883,5488,5490],{"className":5489},[886],[888,5491,5492],{"xmlns":890},[892,5493,5494,5501],{},[895,5495,5496,5499],{},[898,5497,5498],{},"r",[898,5500,1658],{},[902,5502,5503],{"encoding":904},"rL"," a kapitál z ",[883,5506,5508],{"className":5507},[886],[888,5509,5510],{"xmlns":890},[892,5511,5512,5516],{},[895,5513,5514],{},[898,5515,1673],{},[902,5517,1673],{"encoding":904},[883,5519,5521],{"className":5520},[886],[888,5522,5523],{"xmlns":890},[892,5524,5525,5531],{},[895,5526,5527,5529],{},[898,5528,5498],{},[898,5530,1673],{},[902,5532,5533],{"encoding":904},"rK",[883,5535,5537],{"className":5536},[886],[888,5538,5539],{"xmlns":890,"display":2210},[892,5540,5541,5664],{},[2214,5542,5543],{"width":2216},[2218,5544,5545,5547,5657,5659],{},[2221,5546],{"width":2223},[2221,5548,5549],{},[895,5550,5551,5553,5555,5557,5559,5561,5563,5565,5567,5569,5571,5573,5575,5577,5583,5585,5587,5589,5595,5597,5599,5601,5613,5615,5621,5627,5629,5641,5643,5645,5647,5649,5651,5653,5655],{},[898,5552,1688],{},[1708,5554,1716],{"stretchy":1715},[898,5556,5498],{},[898,5558,1658],{},[1708,5560,1883],{"separator":1882},[898,5562,5498],{},[898,5564,1673],{},[1708,5566,1721],{"stretchy":1715},[1708,5568,1710],{},[898,5570,1786],{},[1708,5572,1716],{"stretchy":1715},[898,5574,5498],{},[898,5576,1658],{},[1753,5578,5579,5581],{},[1708,5580,1721],{"stretchy":1715},[898,5582,207],{},[1708,5584,1716],{"stretchy":1715},[898,5586,5498],{},[898,5588,1673],{},[1753,5590,5591,5593],{},[1708,5592,1721],{"stretchy":1715},[898,5594,1923],{},[1708,5596,1710],{},[898,5598,1786],{},[2247,5600,2659],{},[1753,5602,5603,5605],{},[898,5604,5498],{},[895,5606,5607,5609,5611],{},[898,5608,207],{},[1708,5610,2019],{},[898,5612,1923],{},[2247,5614,2659],{},[1753,5616,5617,5619],{},[898,5618,1658],{},[898,5620,207],{},[1753,5622,5623,5625],{},[898,5624,1673],{},[898,5626,1923],{},[1708,5628,1710],{},[1753,5630,5631,5633],{},[898,5632,5498],{},[895,5634,5635,5637,5639],{},[898,5636,207],{},[1708,5638,2019],{},[898,5640,1923],{},[2247,5642,2659],{},[898,5644,1688],{},[1708,5646,1716],{"stretchy":1715},[898,5648,1658],{},[1708,5650,1883],{"separator":1882},[898,5652,1673],{},[1708,5654,1721],{"stretchy":1715},[898,5656,2155],{"mathvariant":1759},[2221,5658],{"width":2223},[2221,5660,5661],{},[2247,5662,5663],{},"(5.8)",[902,5665,5666],{"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}",[724,5668,5669,5670],{},"Volně: ",[38,5671,5672,5673,5686,5687,5711],{},"změní-li se vstupy ",[883,5674,5676],{"className":5675},[886],[888,5677,5678],{"xmlns":890},[892,5679,5680,5684],{},[895,5681,5682],{},[898,5683,5498],{},[902,5685,5498],{"encoding":904},"-krát, změní se výstup ",[883,5688,5690],{"className":5689},[886],[888,5691,5692],{"xmlns":890},[892,5693,5694,5708],{},[895,5695,5696],{},[1753,5697,5698,5700],{},[898,5699,5498],{},[895,5701,5702,5704,5706],{},[898,5703,207],{},[1708,5705,2019],{},[898,5707,1923],{},[902,5709,5710],{"encoding":904},"r^{a+b}","-krát.",[198,5713,5715],{"id":5714},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,5717,5718,5719,5736],{},"Součet exponentů ",[883,5720,5722],{"className":5721},[886],[888,5723,5724],{"xmlns":890},[892,5725,5726,5734],{},[895,5727,5728,5730,5732],{},[898,5729,207],{},[1708,5731,2019],{},[898,5733,1923],{},[902,5735,2024],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,5738,5739,5769],{},[19,5740,5741],{},[22,5742,5743,5746,5749,5766],{},[25,5744,5745],{},"Typ",[25,5747,5748],{},"Podmínka",[25,5750,5751,5752,5765],{},"Chování produkce při ",[883,5753,5755],{"className":5754},[886],[888,5756,5757],{"xmlns":890},[892,5758,5759,5763],{},[895,5760,5761],{},[898,5762,5498],{},[902,5764,5498],{"encoding":904},"-násobném zvýšení vstupů",[25,5767,5768],{},"Příklad",[30,5770,5771,5883,6001],{},[22,5772,5773,5781,5805,5838],{},[35,5774,2765,5775,1695,5778,1721],{},[38,5776,5777],{},"Konstantní",[614,5779,5780],{},"constant returns",[35,5782,5783],{},[883,5784,5786],{"className":5785},[886],[888,5787,5788],{"xmlns":890},[892,5789,5790,5802],{},[895,5791,5792,5794,5796,5798,5800],{},[898,5793,207],{},[1708,5795,2019],{},[898,5797,1923],{},[1708,5799,1710],{},[2505,5801,2507],{},[902,5803,5804],{"encoding":904},"a+b = 1",[35,5806,5807,5820,5821,1729,5824,5837],{},[883,5808,5810],{"className":5809},[886],[888,5811,5812],{"xmlns":890},[892,5813,5814,5818],{},[895,5815,5816],{},[898,5817,1688],{},[902,5819,1688],{"encoding":904}," vzroste ",[38,5822,5823],{},"přesně",[883,5825,5827],{"className":5826},[886],[888,5828,5829],{"xmlns":890},[892,5830,5831,5835],{},[895,5832,5833],{},[898,5834,5498],{},[902,5836,5498],{"encoding":904},"-krát",[35,5839,5840],{},[883,5841,5843],{"className":5842},[886],[888,5844,5845],{"xmlns":890},[892,5846,5847,5880],{},[895,5848,5849,5851,5853,5855,5868],{},[898,5850,1688],{},[1708,5852,1710],{},[2505,5854,3132],{},[1753,5856,5857,5859],{},[898,5858,1658],{},[895,5860,5861,5863,5865],{},[2505,5862,2507],{},[898,5864,1799],{"mathvariant":1759},[2505,5866,5867],{},"4",[1753,5869,5870,5872],{},[898,5871,1673],{},[895,5873,5874,5876,5878],{},[2505,5875,3121],{},[898,5877,1799],{"mathvariant":1759},[2505,5879,5867],{},[902,5881,5882],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,5884,5885,5894,5918,5950],{},[35,5886,5887,5888,1695,5891,1721],{},"2° ",[38,5889,5890],{},"Rostoucí",[614,5892,5893],{},"increasing returns",[35,5895,5896],{},[883,5897,5899],{"className":5898},[886],[888,5900,5901],{"xmlns":890},[892,5902,5903,5915],{},[895,5904,5905,5907,5909,5911,5913],{},[898,5906,207],{},[1708,5908,2019],{},[898,5910,1923],{},[1708,5912,2854],{},[2505,5914,2507],{},[902,5916,5917],{"encoding":904},"a+b > 1",[35,5919,5920,5820,5933,5936,5937,5837],{},[883,5921,5923],{"className":5922},[886],[888,5924,5925],{"xmlns":890},[892,5926,5927,5931],{},[895,5928,5929],{},[898,5930,1688],{},[902,5932,1688],{"encoding":904},[38,5934,5935],{},"více"," než ",[883,5938,5940],{"className":5939},[886],[888,5941,5942],{"xmlns":890},[892,5943,5944,5948],{},[895,5945,5946],{},[898,5947,5498],{},[902,5949,5498],{"encoding":904},[35,5951,5952,1695,5979,1721],{},[883,5953,5955],{"className":5954},[886],[888,5956,5957],{"xmlns":890},[892,5958,5959,5976],{},[895,5960,5961,5963,5965,5968,5970],{},[898,5962,1688],{},[1708,5964,1710],{},[2505,5966,5967],{},"7",[898,5969,1658],{},[1753,5971,5972,5974],{},[898,5973,1673],{},[2505,5975,3132],{},[902,5977,5978],{"encoding":904},"Q = 7LK^2",[883,5980,5982],{"className":5981},[886],[888,5983,5984],{"xmlns":890},[892,5985,5986,5998],{},[895,5987,5988,5990,5992,5994,5996],{},[898,5989,207],{},[1708,5991,2019],{},[898,5993,1923],{},[1708,5995,1710],{},[2505,5997,3121],{},[902,5999,6000],{"encoding":904},"a+b = 3",[22,6002,6003,6012,6036,6067],{},[35,6004,6005,6006,1695,6009,1721],{},"3° ",[38,6007,6008],{},"Klesající",[614,6010,6011],{},"decreasing returns",[35,6013,6014],{},[883,6015,6017],{"className":6016},[886],[888,6018,6019],{"xmlns":890},[892,6020,6021,6033],{},[895,6022,6023,6025,6027,6029,6031],{},[898,6024,207],{},[1708,6026,2019],{},[898,6028,1923],{},[1708,6030,2932],{},[2505,6032,2507],{},[902,6034,6035],{"encoding":904},"a+b \u003C 1",[35,6037,6038,5820,6051,5936,6054,5837],{},[883,6039,6041],{"className":6040},[886],[888,6042,6043],{"xmlns":890},[892,6044,6045,6049],{},[895,6046,6047],{},[898,6048,1688],{},[902,6050,1688],{"encoding":904},[38,6052,6053],{},"méně",[883,6055,6057],{"className":6056},[886],[888,6058,6059],{"xmlns":890},[892,6060,6061,6065],{},[895,6062,6063],{},[898,6064,5498],{},[902,6066,5498],{"encoding":904},[35,6068,6069,1695,6101,1721],{},[883,6070,6072],{"className":6071},[886],[888,6073,6074],{"xmlns":890},[892,6075,6076,6098],{},[895,6077,6078,6080,6082,6084,6091],{},[898,6079,1688],{},[1708,6081,1710],{},[2505,6083,4003],{},[1753,6085,6086,6088],{},[898,6087,1658],{},[2505,6089,6090],{},"0,3",[1753,6092,6093,6095],{},[898,6094,1673],{},[2505,6096,6097],{},"0,5",[902,6099,6100],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,6102,6104],{"className":6103},[886],[888,6105,6106],{"xmlns":890},[892,6107,6108,6121],{},[895,6109,6110,6112,6114,6116,6118],{},[898,6111,207],{},[1708,6113,2019],{},[898,6115,1923],{},[1708,6117,1710],{},[2505,6119,6120],{},"0,8",[902,6122,6123],{"encoding":904},"a+b = 0{,}8",[1636,6125,6126],{},[724,6127,6128,6131,6132,6149,6150,6153,6154,1729,6157,6193,6194,6216,6217,2155],{},[883,6129,6130],{},"!warning"," Pozor\nSoučet ",[883,6133,6135],{"className":6134},[886],[888,6136,6137],{"xmlns":890},[892,6138,6139,6147],{},[895,6140,6141,6143,6145],{},[898,6142,207],{},[1708,6144,2019],{},[898,6146,1923],{},[902,6148,2024],{"encoding":904}," neudává velikost produkce, ale ",[38,6151,6152],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,6155,6156],{},"ryzí Cobb-Douglas",[883,6158,6160],{"className":6159},[886],[888,6161,6162],{"xmlns":890},[892,6163,6164,6190],{},[895,6165,6166,6168,6170,6172,6178],{},[898,6167,1688],{},[1708,6169,1710],{},[898,6171,1786],{},[1753,6173,6174,6176],{},[898,6175,1658],{},[898,6177,207],{},[1753,6179,6180,6182],{},[898,6181,1673],{},[895,6183,6184,6186,6188],{},[2505,6185,2507],{},[1708,6187,2726],{},[898,6189,207],{},[902,6191,6192],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,6195,6197],{"className":6196},[886],[888,6198,6199],{"xmlns":890},[892,6200,6201,6213],{},[895,6202,6203,6205,6207,6209,6211],{},[898,6204,1923],{},[1708,6206,1710],{},[2505,6208,2507],{},[1708,6210,2726],{},[898,6212,207],{},[902,6214,6215],{"encoding":904},"b = 1-a",", tedy vždy ",[38,6218,6219],{},"konstantní výnosy z rozsahu",[198,6221,6223,6224],{"id":6222},"parametr-efektivity-aa","Parametr efektivity ",[883,6225,6227],{"className":6226},[886],[888,6228,6229],{"xmlns":890},[892,6230,6231,6235],{},[895,6232,6233],{},[898,6234,1786],{},[902,6236,1786],{"encoding":904},[724,6238,6239,6240,6253,6254,6267,6268,6286,6287,6290],{},"Konstanta ",[883,6241,6243],{"className":6242},[886],[888,6244,6245],{"xmlns":890},[892,6246,6247,6251],{},[895,6248,6249],{},[898,6250,1786],{},[902,6252,1786],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,6255,6257],{"className":6256},[886],[888,6258,6259],{"xmlns":890},[892,6260,6261,6265],{},[895,6262,6263],{},[898,6264,1688],{},[902,6266,1688],{"encoding":904}," při pevně zadaných ",[883,6269,6271],{"className":6270},[886],[888,6272,6273],{"xmlns":890},[892,6274,6275,6283],{},[895,6276,6277,6279,6281],{},[898,6278,1658],{},[1708,6280,1883],{"separator":1882},[898,6282,1673],{},[902,6284,6285],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,6288,6289],{},"parametr efektivity"," — indikátor stavu technologie.",[198,6292,6294],{"id":6293},"příklad-53","Příklad 5.3",[724,6296,6297,6298,6193,6340,6342,6343,2155],{},"Produkční funkce ",[883,6299,6301],{"className":6300},[886],[888,6302,6303],{"xmlns":890},[892,6304,6305,6337],{},[895,6306,6307,6309,6311,6313,6325],{},[898,6308,1688],{},[1708,6310,1710],{},[2505,6312,3132],{},[1753,6314,6315,6317],{},[898,6316,1658],{},[895,6318,6319,6321,6323],{},[2505,6320,2507],{},[898,6322,1799],{"mathvariant":1759},[2505,6324,5867],{},[1753,6326,6327,6329],{},[898,6328,1673],{},[895,6330,6331,6333,6335],{},[2505,6332,3121],{},[898,6334,1799],{"mathvariant":1759},[2505,6336,5867],{},[902,6338,6339],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,6341,2079],{}," výnosy z rozsahu, neboť ",[883,6344,6346],{"className":6345},[886],[888,6347,6348],{"xmlns":890},[892,6349,6350,6374],{},[895,6351,6352,6360,6362,6370,6372],{},[3194,6353,6354],{"scriptlevel":2784,"displaystyle":1715},[2358,6355,6356,6358],{},[2505,6357,2507],{},[2505,6359,5867],{},[1708,6361,2019],{},[3194,6363,6364],{"scriptlevel":2784,"displaystyle":1715},[2358,6365,6366,6368],{},[2505,6367,3121],{},[2505,6369,5867],{},[1708,6371,1710],{},[2505,6373,2507],{},[902,6375,6376],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,6378,6379,6380,5283,6393,6406,6407,1729,6420,6460],{},"Změní-li se ",[883,6381,6383],{"className":6382},[886],[888,6384,6385],{"xmlns":890},[892,6386,6387,6391],{},[895,6388,6389],{},[898,6390,1658],{},[902,6392,1658],{"encoding":904},[883,6394,6396],{"className":6395},[886],[888,6397,6398],{"xmlns":890},[892,6399,6400,6404],{},[895,6401,6402],{},[898,6403,1673],{},[902,6405,1673],{"encoding":904}," čtyřnásobně, změní se ",[883,6408,6410],{"className":6409},[886],[888,6411,6412],{"xmlns":890},[892,6413,6414,6418],{},[895,6415,6416],{},[898,6417,1688],{},[902,6419,1688],{"encoding":904},[883,6421,6423],{"className":6422},[886],[888,6424,6425],{"xmlns":890},[892,6426,6427,6457],{},[895,6428,6429,6449,6451],{},[1753,6430,6431,6433],{},[2505,6432,5867],{},[895,6434,6435,6437,6439,6441,6443,6445,6447],{},[2505,6436,2507],{},[898,6438,1799],{"mathvariant":1759},[2505,6440,5867],{},[1708,6442,2019],{},[2505,6444,3121],{},[898,6446,1799],{"mathvariant":1759},[2505,6448,5867],{},[1708,6450,1710],{},[1753,6452,6453,6455],{},[2505,6454,5867],{},[2505,6456,2507],{},[902,6458,6459],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,6462,6464],{"className":6463},[886],[888,6465,6466],{"xmlns":890,"display":2210},[892,6467,6468,6628],{},[895,6469,6470,6472,6474,6476,6478,6480,6482,6484,6486,6488,6490,6492,6494,6496,6508,6510,6512,6514,6526,6528,6530,6532,6552,6564,6576,6578,6580,6582,6584,6596,6608,6610,6612,6614,6616,6618,6620,6622,6624,6626],{},[898,6471,1688],{},[1708,6473,1716],{"stretchy":1715},[2505,6475,5867],{},[898,6477,1658],{},[1708,6479,1883],{"separator":1882},[2505,6481,5867],{},[898,6483,1673],{},[1708,6485,1721],{"stretchy":1715},[1708,6487,1710],{},[2505,6489,3132],{},[1708,6491,1716],{"stretchy":1715},[2505,6493,5867],{},[898,6495,1658],{},[1753,6497,6498,6500],{},[1708,6499,1721],{"stretchy":1715},[895,6501,6502,6504,6506],{},[2505,6503,2507],{},[898,6505,1799],{"mathvariant":1759},[2505,6507,5867],{},[1708,6509,1716],{"stretchy":1715},[2505,6511,5867],{},[898,6513,1673],{},[1753,6515,6516,6518],{},[1708,6517,1721],{"stretchy":1715},[895,6519,6520,6522,6524],{},[2505,6521,3121],{},[898,6523,1799],{"mathvariant":1759},[2505,6525,5867],{},[1708,6527,1710],{},[2505,6529,3132],{},[1708,6531,3703],{},[1753,6533,6534,6536],{},[2505,6535,5867],{},[895,6537,6538,6540,6542,6544,6546,6548,6550],{},[2505,6539,2507],{},[898,6541,1799],{"mathvariant":1759},[2505,6543,5867],{},[1708,6545,2019],{},[2505,6547,3121],{},[898,6549,1799],{"mathvariant":1759},[2505,6551,5867],{},[1753,6553,6554,6556],{},[898,6555,1658],{},[895,6557,6558,6560,6562],{},[2505,6559,2507],{},[898,6561,1799],{"mathvariant":1759},[2505,6563,5867],{},[1753,6565,6566,6568],{},[898,6567,1673],{},[895,6569,6570,6572,6574],{},[2505,6571,3121],{},[898,6573,1799],{"mathvariant":1759},[2505,6575,5867],{},[1708,6577,1710],{},[2505,6579,5867],{},[1708,6581,3703],{},[2505,6583,3132],{},[1753,6585,6586,6588],{},[898,6587,1658],{},[895,6589,6590,6592,6594],{},[2505,6591,2507],{},[898,6593,1799],{"mathvariant":1759},[2505,6595,5867],{},[1753,6597,6598,6600],{},[898,6599,1673],{},[895,6601,6602,6604,6606],{},[2505,6603,3121],{},[898,6605,1799],{"mathvariant":1759},[2505,6607,5867],{},[1708,6609,1710],{},[2505,6611,5867],{},[2247,6613,2659],{},[898,6615,1688],{},[1708,6617,1716],{"stretchy":1715},[898,6619,1658],{},[1708,6621,1883],{"separator":1882},[898,6623,1673],{},[1708,6625,1721],{"stretchy":1715},[898,6627,2155],{"mathvariant":1759},[902,6629,6630],{"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).",[198,6632,6634],{"id":6633},"homogenita","Homogenita",[724,6636,6637,6638,3033,6662,6679],{},"Funkce ",[883,6639,6641],{"className":6640},[886],[888,6642,6643],{"xmlns":890},[892,6644,6645,6659],{},[895,6646,6647,6649,6651,6653,6655,6657],{},[898,6648,1688],{},[1708,6650,1716],{"stretchy":1715},[898,6652,1658],{},[1708,6654,1883],{"separator":1882},[898,6656,1673],{},[1708,6658,1721],{"stretchy":1715},[902,6660,6661],{"encoding":904},"Q(L, K)",[38,6663,6664,6665],{},"homogenní stupně ",[883,6666,6668],{"className":6667},[886],[888,6669,6670],{"xmlns":890},[892,6671,6672,6677],{},[895,6673,6674],{},[898,6675,6676],{},"n",[902,6678,6676],{"encoding":904},", jestliže",[883,6681,6683],{"className":6682},[886],[888,6684,6685],{"xmlns":890,"display":2210},[892,6686,6687,6744],{},[2214,6688,6689],{"width":2216},[2218,6690,6691,6693,6737,6739],{},[2221,6692],{"width":2223},[2221,6694,6695],{},[895,6696,6697,6699,6701,6703,6705,6707,6709,6711,6713,6715,6721,6723,6725,6727,6729,6731,6733,6735],{},[898,6698,1688],{},[1708,6700,1716],{"stretchy":1715},[898,6702,5498],{},[898,6704,1658],{},[1708,6706,1883],{"separator":1882},[898,6708,5498],{},[898,6710,1673],{},[1708,6712,1721],{"stretchy":1715},[1708,6714,1710],{},[1753,6716,6717,6719],{},[898,6718,5498],{},[898,6720,6676],{},[2247,6722,2659],{},[898,6724,1688],{},[1708,6726,1716],{"stretchy":1715},[898,6728,1658],{},[1708,6730,1883],{"separator":1882},[898,6732,1673],{},[1708,6734,1721],{"stretchy":1715},[1708,6736,1883],{"separator":1882},[2221,6738],{"width":2223},[2221,6740,6741],{},[2247,6742,6743],{},"(5.10)",[902,6745,6746],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,6748,5411,6749,6768,6769,6787,6788,6801,6802,6805,6806,2155],{},[883,6750,6752],{"className":6751},[886],[888,6753,6754],{"xmlns":890},[892,6755,6756,6765],{},[895,6757,6758,6760,6763],{},[898,6759,6676],{},[1708,6761,6762],{},"≥",[2505,6764,2784],{},[902,6766,6767],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,6770,6772],{"className":6771},[886],[888,6773,6774],{"xmlns":890},[892,6775,6776,6784],{},[895,6777,6778,6780,6782],{},[898,6779,5498],{},[1708,6781,2854],{},[2505,6783,2784],{},[902,6785,6786],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,6789,6791],{"className":6790},[886],[888,6792,6793],{"xmlns":890},[892,6794,6795,6799],{},[895,6796,6797],{},[2505,6798,2507],{},[902,6800,2507],{"encoding":904}," se nazývají ",[38,6803,6804],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,6807,6809],{"className":6808},[886],[888,6810,6811],{"xmlns":890},[892,6812,6813,6821],{},[895,6814,6815,6817,6819],{},[898,6816,207],{},[1708,6818,2019],{},[898,6820,1923],{},[902,6822,2024],{"encoding":904},[115,6824,6826],{"id":6825},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,6828,6829],{},[38,6830,6831],{},"Ryzí Cobb-Douglasovy funkce:",[883,6833,6835],{"className":6834},[886],[888,6836,6837],{"xmlns":890,"display":2210},[892,6838,6839,6899],{},[2214,6840,6841],{"width":2216},[2218,6842,6843,6845,6892,6894],{},[2221,6844],{"width":2223},[2221,6846,6847],{},[895,6848,6849,6851,6853,6855,6857,6863,6865,6877,6879,6881,6883,6885,6887,6889],{},[898,6850,1688],{},[1708,6852,1710],{},[898,6854,1786],{},[2247,6856,2659],{},[1753,6858,6859,6861],{},[898,6860,1658],{},[898,6862,207],{},[2247,6864,2659],{},[1753,6866,6867,6869],{},[898,6868,1673],{},[895,6870,6871,6873,6875],{},[2505,6872,2507],{},[1708,6874,2726],{},[898,6876,207],{},[1708,6878,1883],{"separator":1882},[3213,6880],{"width":4750},[2505,6882,2784],{},[1708,6884,2932],{},[898,6886,207],{},[1708,6888,2932],{},[2505,6890,6891],{},"1.",[2221,6893],{"width":2223},[2221,6895,6896],{},[2247,6897,6898],{},"(5.9)",[902,6900,6901],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,6903,6904,6905,6907,6908,2155],{},"Mají vždy ",[38,6906,6219],{}," a jsou ",[38,6909,6804],{},[724,6911,6912,1695,6915,6918],{},[38,6913,6914],{},"CES produkční funkce",[614,6916,6917],{},"Constant Elasticity of Substitution",", 1961):",[883,6920,6922],{"className":6921},[886],[888,6923,6924],{"xmlns":890,"display":2210},[892,6925,6926,6996],{},[895,6927,6928,6930,6932,6934,6994],{},[898,6929,1688],{},[1708,6931,1710],{},[898,6933,1786],{},[1753,6935,6936,6982],{},[895,6937,6938,6941,6943,6945,6947,6949,6951,6953,6963,6965,6967,6969,6979],{},[1708,6939,6940],{"fence":1882},"[",[1708,6942,1716],{"stretchy":1715},[2505,6944,2507],{},[1708,6946,2726],{},[898,6948,207],{},[1708,6950,1721],{"stretchy":1715},[2247,6952,2659],{},[1753,6954,6955,6957],{},[898,6956,1658],{},[895,6958,6959,6961],{},[1708,6960,2726],{},[898,6962,1923],{},[1708,6964,2019],{},[898,6966,207],{},[2247,6968,2659],{},[1753,6970,6971,6973],{},[898,6972,1673],{},[895,6974,6975,6977],{},[1708,6976,2726],{},[898,6978,1923],{},[1708,6980,6981],{"fence":1882},"]",[895,6983,6984,6986],{},[1708,6985,2726],{},[3194,6987,6988],{"scriptlevel":2784,"displaystyle":1715},[2358,6989,6990,6992],{},[2505,6991,2507],{},[898,6993,1923],{},[1708,6995,1883],{"separator":1882},[902,6997,6998],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,7000,5411,7001,1343,7019,1343,7041,7066],{},[883,7002,7004],{"className":7003},[886],[888,7005,7006],{"xmlns":890},[892,7007,7008,7016],{},[895,7009,7010,7012,7014],{},[898,7011,1786],{},[1708,7013,2854],{},[2505,7015,2784],{},[902,7017,7018],{"encoding":904},"A > 0",[883,7020,7022],{"className":7021},[886],[888,7023,7024],{"xmlns":890},[892,7025,7026,7038],{},[895,7027,7028,7030,7032,7034,7036],{},[2505,7029,2784],{},[1708,7031,2932],{},[898,7033,207],{},[1708,7035,2932],{},[2505,7037,2507],{},[902,7039,7040],{"encoding":904},"0 \u003C a \u003C 1",[883,7042,7044],{"className":7043},[886],[888,7045,7046],{"xmlns":890},[892,7047,7048,7063],{},[895,7049,7050,7052,7054,7056,7058,7061],{},[1708,7051,2726],{},[2505,7053,2507],{},[1708,7055,2932],{},[898,7057,1923],{},[1708,7059,7060],{"mathvariant":1759},"≠",[2505,7062,2784],{},[902,7064,7065],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,7068,7069],{},[38,7070,7071],{},"Další typy:",[120,7073,7074,7116],{},[123,7075,7076,1729,7079,7115],{},[38,7077,7078],{},"Lineární:",[883,7080,7082],{"className":7081},[886],[888,7083,7084],{"xmlns":890},[892,7085,7086,7112],{},[895,7087,7088,7090,7092,7094,7096,7098,7100,7102,7104,7106,7108,7110],{},[898,7089,1688],{},[1708,7091,1716],{"stretchy":1715},[898,7093,1658],{},[1708,7095,1883],{"separator":1882},[898,7097,1673],{},[1708,7099,1721],{"stretchy":1715},[1708,7101,1710],{},[898,7103,207],{},[898,7105,1658],{},[1708,7107,2019],{},[898,7109,1923],{},[898,7111,1673],{},[902,7113,7114],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,7117,7118,1729,7121,7167],{},[38,7119,7120],{},"Leontiefova:",[883,7122,7124],{"className":7123},[886],[888,7125,7126],{"xmlns":890},[892,7127,7128,7164],{},[895,7129,7130,7132,7134,7136,7138,7140,7142,7144,7147,7150,7152,7154,7156,7158,7160,7162],{},[898,7131,1688],{},[1708,7133,1716],{"stretchy":1715},[898,7135,1658],{},[1708,7137,1883],{"separator":1882},[898,7139,1673],{},[1708,7141,1721],{"stretchy":1715},[1708,7143,1710],{},[898,7145,7146],{},"min",[1708,7148,7149],{},"⁡",[1708,7151,1716],{"stretchy":1715},[898,7153,207],{},[898,7155,1658],{},[1708,7157,1883],{"separator":1882},[898,7159,1923],{},[898,7161,1673],{},[1708,7163,1721],{"stretchy":1715},[902,7165,7166],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,7169,7171,7172,1343,7191,7211],{"id":7170},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,7173,7175],{"className":7174},[886],[888,7176,7177],{"xmlns":890},[892,7178,7179,7189],{},[895,7180,7181,7183],{},[898,7182,1741],{},[1743,7184,7185,7187],{},[898,7186,1747],{},[898,7188,1658],{},[902,7190,2300],{"encoding":904},[883,7192,7194],{"className":7193},[886],[888,7195,7196],{"xmlns":890},[892,7197,7198,7208],{},[895,7199,7200,7202],{},[898,7201,1741],{},[1743,7203,7204,7206],{},[898,7205,1747],{},[898,7207,1673],{},[902,7209,7210],{"encoding":904},"MP_K"," a totální diferenciál",[724,7213,7214],{},[38,7215,7216],{},"Mezní produkt práce:",[883,7218,7220],{"className":7219},[886],[888,7221,7222],{"xmlns":890,"display":2210},[892,7223,7224,7263],{},[895,7225,7226,7228,7234,7236,7244,7246,7261],{},[898,7227,1741],{},[1743,7229,7230,7232],{},[898,7231,1747],{},[898,7233,1658],{},[1708,7235,1710],{},[4754,7237,7238,7240,7242],{},[898,7239,1688],{},[898,7241,1658],{},[1708,7243,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,7245,1710],{},[2358,7247,7248,7255],{},[895,7249,7250,7253],{},[898,7251,7252],{"mathvariant":1759},"∂",[898,7254,1688],{},[895,7256,7257,7259],{},[898,7258,7252],{"mathvariant":1759},[898,7260,1658],{},[898,7262,2155],{"mathvariant":1759},[902,7264,7265],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,7267,7268],{},[38,7269,7270],{},"Mezní produkt kapitálu:",[883,7272,7274],{"className":7273},[886],[888,7275,7276],{"xmlns":890,"display":2210},[892,7277,7278,7316],{},[895,7279,7280,7282,7288,7290,7298,7300,7314],{},[898,7281,1741],{},[1743,7283,7284,7286],{},[898,7285,1747],{},[898,7287,1673],{},[1708,7289,1710],{},[4754,7291,7292,7294,7296],{},[898,7293,1688],{},[898,7295,1673],{},[1708,7297,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,7299,1710],{},[2358,7301,7302,7308],{},[895,7303,7304,7306],{},[898,7305,7252],{"mathvariant":1759},[898,7307,1688],{},[895,7309,7310,7312],{},[898,7311,7252],{"mathvariant":1759},[898,7313,1673],{},[898,7315,2155],{"mathvariant":1759},[902,7317,7318],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,7320,7321,7351,7352,7374,7375,7393,7394,7407,7408,2155],{},[883,7322,7324],{"className":7323},[886],[888,7325,7326],{"xmlns":890},[892,7327,7328,7348],{},[895,7329,7330,7332,7338,7340,7342,7344,7346],{},[898,7331,1741],{},[1743,7333,7334,7336],{},[898,7335,1747],{},[898,7337,1658],{},[1708,7339,1716],{"stretchy":1715},[898,7341,207],{},[1708,7343,1883],{"separator":1882},[898,7345,1923],{},[1708,7347,1721],{"stretchy":1715},[902,7349,7350],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,7353,7355],{"className":7354},[886],[888,7356,7357],{"xmlns":890},[892,7358,7359,7371],{},[895,7360,7361,7363,7365,7367,7369],{},[1708,7362,6940],{"stretchy":1715},[898,7364,207],{},[1708,7366,1883],{"separator":1882},[898,7368,1923],{},[1708,7370,6981],{"stretchy":1715},[902,7372,7373],{"encoding":904},"[a, b]"," (na hladině ",[883,7376,7378],{"className":7377},[886],[888,7379,7380],{"xmlns":890},[892,7381,7382,7390],{},[895,7383,7384,7386,7388],{},[898,7385,1673],{},[1708,7387,1710],{},[898,7389,1923],{},[902,7391,7392],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,7395,7397],{"className":7396},[886],[888,7398,7399],{"xmlns":890},[892,7400,7401,7405],{},[895,7402,7403],{},[898,7404,1658],{},[902,7406,1658],{"encoding":904},". Analogicky ",[883,7409,7411],{"className":7410},[886],[888,7412,7413],{"xmlns":890},[892,7414,7415,7435],{},[895,7416,7417,7419,7425,7427,7429,7431,7433],{},[898,7418,1741],{},[1743,7420,7421,7423],{},[898,7422,1747],{},[898,7424,1673],{},[1708,7426,1716],{"stretchy":1715},[898,7428,207],{},[1708,7430,1883],{"separator":1882},[898,7432,1923],{},[1708,7434,1721],{"stretchy":1715},[902,7436,7437],{"encoding":904},"MP_K(a, b)",[1636,7439,7440,7445],{},[724,7441,7442,7444],{},[883,7443,2518],{}," Intuice",[120,7446,7447,7486],{},[123,7448,7449,7468,7469],{},[883,7450,7452],{"className":7451},[886],[888,7453,7454],{"xmlns":890},[892,7455,7456,7466],{},[895,7457,7458,7460],{},[898,7459,1741],{},[1743,7461,7462,7464],{},[898,7463,1747],{},[898,7465,1658],{},[902,7467,2300],{"encoding":904},": ",[614,7470,7471,7472,7485],{},"„o kolik vzroste ",[883,7473,7475],{"className":7474},[886],[888,7476,7477],{"xmlns":890},[892,7478,7479,7483],{},[895,7480,7481],{},[898,7482,1688],{},[902,7484,1688],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,7487,7488,7468,7507],{},[883,7489,7491],{"className":7490},[886],[888,7492,7493],{"xmlns":890},[892,7494,7495,7505],{},[895,7496,7497,7499],{},[898,7498,1741],{},[1743,7500,7501,7503],{},[898,7502,1747],{},[898,7504,1673],{},[902,7506,7210],{"encoding":904},[614,7508,7471,7509,7522],{},[883,7510,7512],{"className":7511},[886],[888,7513,7514],{"xmlns":890},[892,7515,7516,7520],{},[895,7517,7518],{},[898,7519,1688],{},[902,7521,1688],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,7524,7525,7528,7529,7544,7545,2788],{},[38,7526,7527],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,7530,7532],{"className":7531},[886],[888,7533,7534],{"xmlns":890},[892,7535,7536,7542],{},[895,7537,7538,7540],{},[898,7539,2364],{},[898,7541,1658],{},[902,7543,2578],{"encoding":904}," a kapitálu o ",[883,7546,7548],{"className":7547},[886],[888,7549,7550],{"xmlns":890},[892,7551,7552,7558],{},[895,7553,7554,7556],{},[898,7555,2364],{},[898,7557,1673],{},[902,7559,7560],{"encoding":904},"dK",[883,7562,7564],{"className":7563},[886],[888,7565,7566],{"xmlns":890,"display":2210},[892,7567,7568,7661],{},[2214,7569,7570],{"width":2216},[2218,7571,7572,7574,7654,7656],{},[2221,7573],{"width":2223},[2221,7575,7576],{},[895,7577,7578,7580,7582,7584,7586,7588,7590,7598,7600,7602,7604,7606,7614,7616,7618,7620,7622,7624,7630,7632,7634,7636,7638,7640,7646,7648,7650,7652],{},[898,7579,2633],{"mathvariant":1759},[898,7581,1688],{},[1708,7583,2638],{},[898,7585,2364],{},[898,7587,1688],{},[1708,7589,1710],{},[4754,7591,7592,7594,7596],{},[898,7593,1688],{},[898,7595,1658],{},[1708,7597,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,7599,2659],{},[898,7601,2364],{},[898,7603,1658],{},[1708,7605,2019],{},[4754,7607,7608,7610,7612],{},[898,7609,1688],{},[898,7611,1673],{},[1708,7613,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,7615,2659],{},[898,7617,2364],{},[898,7619,1673],{},[1708,7621,1710],{},[898,7623,1741],{},[1743,7625,7626,7628],{},[898,7627,1747],{},[898,7629,1658],{},[2247,7631,2659],{},[898,7633,2364],{},[898,7635,1658],{},[1708,7637,2019],{},[898,7639,1741],{},[1743,7641,7642,7644],{},[898,7643,1747],{},[898,7645,1673],{},[2247,7647,2659],{},[898,7649,2364],{},[898,7651,1673],{},[898,7653,2155],{"mathvariant":1759},[2221,7655],{"width":2223},[2221,7657,7658],{},[2247,7659,7660],{},"(5.11)",[902,7662,7663],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,7665,7666,7667,2155],{},"Skutečná změna: ",[883,7668,7670],{"className":7669},[886],[888,7671,7672],{"xmlns":890},[892,7673,7674,7720],{},[895,7675,7676,7678,7680,7682,7684,7686,7688,7690,7692,7694,7696,7698,7700,7702,7704,7706,7708,7710,7712,7714,7716,7718],{},[898,7677,2633],{"mathvariant":1759},[898,7679,1688],{},[1708,7681,1710],{},[898,7683,1688],{},[1708,7685,1716],{"stretchy":1715},[898,7687,1658],{},[1708,7689,2019],{},[898,7691,2364],{},[898,7693,1658],{},[1708,7695,1883],{"separator":1882},[898,7697,1673],{},[1708,7699,2019],{},[898,7701,2364],{},[898,7703,1673],{},[1708,7705,1721],{"stretchy":1715},[1708,7707,2726],{},[898,7709,1688],{},[1708,7711,1716],{"stretchy":1715},[898,7713,1658],{},[1708,7715,1883],{"separator":1882},[898,7717,1673],{},[1708,7719,1721],{"stretchy":1715},[902,7721,7722],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,7724,7725,7727,7728,7746,7747,7760,7761,7780,7781,7813,7814,7846,7847,2155],{},[38,7726,2746],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,7729,7731],{"className":7730},[886],[888,7732,7733],{"xmlns":890},[892,7734,7735,7743],{},[895,7736,7737],{},[1743,7738,7739,7741],{},[898,7740,1673],{},[2505,7742,2784],{},[902,7744,7745],{"encoding":904},"K_0"," se od jistého ",[883,7748,7750],{"className":7749},[886],[888,7751,7752],{"xmlns":890},[892,7753,7754,7758],{},[895,7755,7756],{},[898,7757,1658],{},[902,7759,1658],{"encoding":904}," stane ",[883,7762,7764],{"className":7763},[886],[888,7765,7766],{"xmlns":890},[892,7767,7768,7778],{},[895,7769,7770,7772],{},[898,7771,1741],{},[1743,7773,7774,7776],{},[898,7775,1747],{},[898,7777,1658],{},[902,7779,2300],{"encoding":904}," klesající (",[883,7782,7784],{"className":7783},[886],[888,7785,7786],{"xmlns":890},[892,7787,7788,7810],{},[895,7789,7790,7806,7808],{},[4754,7791,7792,7794,7800],{},[898,7793,1688],{},[895,7795,7796,7798],{},[898,7797,1658],{},[898,7799,1658],{},[895,7801,7802,7804],{},[1708,7803,1761],{"mathvariant":1759},[1708,7805,1761],{"mathvariant":1759},[1708,7807,2932],{},[2505,7809,2784],{},[902,7811,7812],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,7815,7817],{"className":7816},[886],[888,7818,7819],{"xmlns":890},[892,7820,7821,7843],{},[895,7822,7823,7839,7841],{},[4754,7824,7825,7827,7833],{},[898,7826,1688],{},[895,7828,7829,7831],{},[898,7830,1673],{},[898,7832,1673],{},[895,7834,7835,7837],{},[1708,7836,1761],{"mathvariant":1759},[1708,7838,1761],{"mathvariant":1759},[1708,7840,2932],{},[2505,7842,2784],{},[902,7844,7845],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,7848,7850],{"className":7849},[886],[888,7851,7852],{"xmlns":890},[892,7853,7854,7862],{},[895,7855,7856],{},[1743,7857,7858,7860],{},[898,7859,1658],{},[2505,7861,2784],{},[902,7863,2787],{"encoding":904},[115,7865,7867],{"id":7866},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,7869,7870,7873,7874,7897,7898,7911],{},[38,7871,7872],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,7875,7877],{"className":7876},[886],[888,7878,7879],{"xmlns":890},[892,7880,7881,7895],{},[895,7882,7883,7885,7887,7889,7891,7893],{},[898,7884,1688],{},[1708,7886,1716],{"stretchy":1715},[898,7888,1658],{},[1708,7890,1883],{"separator":1882},[898,7892,1673],{},[1708,7894,1721],{"stretchy":1715},[902,7896,6661],{"encoding":904}," stupně ",[883,7899,7901],{"className":7900},[886],[888,7902,7903],{"xmlns":890},[892,7904,7905,7909],{},[895,7906,7907],{},[898,7908,6676],{},[902,7910,6676],{"encoding":904}," platí",[883,7913,7915],{"className":7914},[886],[888,7916,7917],{"xmlns":890,"display":2210},[892,7918,7919,7982],{},[2214,7920,7921],{"width":2216},[2218,7922,7923,7925,7975,7977],{},[2221,7924],{"width":2223},[2221,7926,7927],{},[895,7928,7929,7931,7933,7941,7943,7945,7947,7955,7957,7959,7961,7963,7965,7967,7969,7971,7973],{},[898,7930,1658],{},[2247,7932,2659],{},[4754,7934,7935,7937,7939],{},[898,7936,1688],{},[898,7938,1658],{},[1708,7940,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,7942,2019],{},[898,7944,1673],{},[2247,7946,2659],{},[4754,7948,7949,7951,7953],{},[898,7950,1688],{},[898,7952,1673],{},[1708,7954,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,7956,1710],{},[898,7958,6676],{},[2247,7960,2659],{},[898,7962,1688],{},[1708,7964,1716],{"stretchy":1715},[898,7966,1658],{},[1708,7968,1883],{"separator":1882},[898,7970,1673],{},[1708,7972,1721],{"stretchy":1715},[898,7974,2155],{"mathvariant":1759},[2221,7976],{"width":2223},[2221,7978,7979],{},[2247,7980,7981],{},"(5.12)",[902,7983,7984],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,7986,7987,8008],{},[38,7988,7989,7990],{},"Speciální případ ",[883,7991,7993],{"className":7992},[886],[888,7994,7995],{"xmlns":890},[892,7996,7997,8005],{},[895,7998,7999,8001,8003],{},[898,8000,6676],{},[1708,8002,1710],{},[2505,8004,2507],{},[902,8006,8007],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,8010,8012],{"className":8011},[886],[888,8013,8014],{"xmlns":890,"display":2210},[892,8015,8016,8060],{},[895,8017,8018,8020,8022,8024,8030,8032,8034,8036,8038,8044,8046,8048,8050,8052,8054,8056,8058],{},[898,8019,1658],{},[1708,8021,3703],{},[898,8023,1741],{},[1743,8025,8026,8028],{},[898,8027,1747],{},[898,8029,1658],{},[1708,8031,2019],{},[898,8033,1673],{},[1708,8035,3703],{},[898,8037,1741],{},[1743,8039,8040,8042],{},[898,8041,1747],{},[898,8043,1673],{},[1708,8045,1710],{},[898,8047,1688],{},[1708,8049,1716],{"stretchy":1715},[898,8051,1658],{},[1708,8053,1883],{"separator":1882},[898,8055,1673],{},[1708,8057,1721],{"stretchy":1715},[898,8059,2155],{"mathvariant":1759},[902,8061,8062],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,8064,8065,8066,8069],{},"Slovně — ",[38,8067,8068],{},"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).",[115,8071,8072],{"id":2096},"Izokvanty",[724,8074,8075,1695,8077,8080,8081,8103,8104,2788],{},[38,8076,8072],{},[614,8078,8079],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,8082,8084],{"className":8083},[886],[888,8085,8086],{"xmlns":890},[892,8087,8088,8100],{},[895,8089,8090,8092,8094,8096,8098],{},[1708,8091,6940],{"stretchy":1715},[898,8093,1658],{},[1708,8095,1883],{"separator":1882},[898,8097,1673],{},[1708,8099,6981],{"stretchy":1715},[902,8101,8102],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,8105,8107],{"className":8106},[886],[888,8108,8109],{"xmlns":890},[892,8110,8111,8116],{},[895,8112,8113],{},[898,8114,8115],{},"q",[902,8117,8115],{"encoding":904},[883,8119,8121],{"className":8120},[886],[888,8122,8123],{"xmlns":890,"display":2210},[892,8124,8125,8160],{},[2214,8126,8127],{"width":2216},[2218,8128,8129,8131,8153,8155],{},[2221,8130],{"width":2223},[2221,8132,8133],{},[895,8134,8135,8137,8139,8141,8143,8145,8147,8149,8151],{},[898,8136,1688],{},[1708,8138,1716],{"stretchy":1715},[898,8140,1658],{},[1708,8142,1883],{"separator":1882},[898,8144,1673],{},[1708,8146,1721],{"stretchy":1715},[1708,8148,1710],{},[898,8150,8115],{},[898,8152,2155],{"mathvariant":1759},[2221,8154],{"width":2223},[2221,8156,8157],{},[2247,8158,8159],{},"(5.13)",[902,8161,8162],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,8164,8165,8166,8169,8170,2511],{},"Jsou to ",[38,8167,8168],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,8171,8173],{"className":8172,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,8175,8176],{},[38,8177,8178],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,8180,8181,8187,8192,8198],{},[123,8182,8183,8186],{},[38,8184,8185],{},"klesající"," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,8188,8189,8191],{},[38,8190,2863],{}," (úloha 5.14);",[123,8193,8194,8197],{},[38,8195,8196],{},"neprotínají se",";",[123,8199,8200,8201,8214,8215,2155],{},"s rostoucím ",[883,8202,8204],{"className":8203},[886],[888,8205,8206],{"xmlns":890},[892,8207,8208,8212],{},[895,8209,8210],{},[898,8211,8115],{},[902,8213,8115],{"encoding":904}," se ",[38,8216,8217],{},"vzdalují od počátku",[724,8219,8220],{},[614,8221,8222,8223,8245,8246,2155],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,8224,8226],{"className":8225},[886],[888,8227,8228],{"xmlns":890},[892,8229,8230,8242],{},[895,8231,8232,8234,8236,8238,8240],{},[1708,8233,1716],{"stretchy":1715},[898,8235,1658],{},[1708,8237,1883],{"separator":1882},[898,8239,1673],{},[1708,8241,1721],{"stretchy":1715},[902,8243,8244],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,8247,8249],{"className":8248},[886],[888,8250,8251],{"xmlns":890},[892,8252,8253,8277],{},[895,8254,8255,8261,8263,8269,8271],{},[1743,8256,8257,8259],{},[898,8258,8115],{},[2505,8260,2507],{},[1708,8262,2932],{},[1743,8264,8265,8267],{},[898,8266,8115],{},[2505,8268,2784],{},[1708,8270,2932],{},[1743,8272,8273,8275],{},[898,8274,8115],{},[2505,8276,3132],{},[902,8278,8279],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,8281,8283,8284,1721],{"id":8282},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,8285,8287],{"className":8286},[886],[888,8288,8289],{"xmlns":890},[892,8290,8291,8301],{},[895,8292,8293,8295,8297,8299],{},[898,8294,1741],{},[898,8296,1975],{},[898,8298,1978],{},[898,8300,1981],{},[902,8302,8303],{"encoding":904},"MRTS",[724,8305,8306,1695,8309,8312],{},[38,8307,8308],{},"Mezní míra technické substituce",[614,8310,8311],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,8314,8316],{"className":8315},[886],[888,8317,8318],{"xmlns":890,"display":2210},[892,8319,8320,8411],{},[2214,8321,8322],{"width":2216},[2218,8323,8324,8326,8404,8406],{},[2221,8325],{"width":2223},[2221,8327,8328],{},[895,8329,8330,8332,8334,8336,8338,8340,8342,8344,8346,8348,8350,8352,8354,8356,8358,8360,8382,8384,8402],{},[898,8331,1741],{},[898,8333,1975],{},[898,8335,1978],{},[898,8337,1981],{},[1708,8339,1710],{},[898,8341,1741],{},[898,8343,1975],{},[898,8345,1978],{},[898,8347,1981],{},[1708,8349,1716],{"stretchy":1715},[898,8351,1658],{},[1708,8353,1883],{"separator":1882},[898,8355,1673],{},[1708,8357,1721],{"stretchy":1715},[1708,8359,1710],{},[2358,8361,8362,8372],{},[895,8363,8364,8366],{},[898,8365,1741],{},[1743,8367,8368,8370],{},[898,8369,1747],{},[898,8371,1658],{},[895,8373,8374,8376],{},[898,8375,1741],{},[1743,8377,8378,8380],{},[898,8379,1747],{},[898,8381,1673],{},[1708,8383,1710],{},[2358,8385,8386,8394],{},[4754,8387,8388,8390,8392],{},[898,8389,1688],{},[898,8391,1658],{},[1708,8393,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,8395,8396,8398,8400],{},[898,8397,1688],{},[898,8399,1673],{},[1708,8401,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[898,8403,2155],{"mathvariant":1759},[2221,8405],{"width":2223},[2221,8407,8408],{},[2247,8409,8410],{},"(5.14)",[902,8412,8413],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,8415,8416,1729,8419,8449,8450,8481],{},[38,8417,8418],{},"Interpretace:",[883,8420,8422],{"className":8421},[886],[888,8423,8424],{"xmlns":890},[892,8425,8426,8446],{},[895,8427,8428,8430,8432,8434,8436,8438,8440,8442,8444],{},[898,8429,1741],{},[898,8431,1975],{},[898,8433,1978],{},[898,8435,1981],{},[1708,8437,1716],{"stretchy":1715},[898,8439,1658],{},[1708,8441,1883],{"separator":1882},[898,8443,1673],{},[1708,8445,1721],{"stretchy":1715},[902,8447,8448],{"encoding":904},"MRTS(L, K)"," udává, ",[38,8451,8452,8453,8466,8467,8480],{},"o kolik se musí přibližně změnit kapitál ",[883,8454,8456],{"className":8455},[886],[888,8457,8458],{"xmlns":890},[892,8459,8460,8464],{},[895,8461,8462],{},[898,8463,1673],{},[902,8465,1673],{"encoding":904},", jestliže se práce ",[883,8468,8470],{"className":8469},[886],[888,8471,8472],{"xmlns":890},[892,8473,8474,8478],{},[895,8475,8476],{},[898,8477,1658],{},[902,8479,1658],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1636,8483,8484],{},[724,8485,8486,2519,8488,8507,8508,8545,8546,8549,8550,8554],{},[883,8487,2518],{},[883,8489,8491],{"className":8490},[886],[888,8492,8493],{"xmlns":890},[892,8494,8495,8505],{},[895,8496,8497,8499,8501,8503],{},[898,8498,1741],{},[898,8500,1975],{},[898,8502,1978],{},[898,8504,1981],{},[902,8506,8303],{"encoding":904}," říká: ",[614,8509,8510,8511,8530,8531,8544],{},"„jednu jednotku práce musím nahradit přibližně ",[883,8512,8514],{"className":8513},[886],[888,8515,8516],{"xmlns":890},[892,8517,8518,8528],{},[895,8519,8520,8522,8524,8526],{},[898,8521,1741],{},[898,8523,1975],{},[898,8525,1978],{},[898,8527,1981],{},[902,8529,8303],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,8532,8534],{"className":8533},[886],[888,8535,8536],{"xmlns":890},[892,8537,8538,8542],{},[895,8539,8540],{},[898,8541,1688],{},[902,8543,1688],{"encoding":904}," zůstala stejná.\""," Je to ",[38,8547,8548],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,8551,8553],{"className":8552,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,8556,8557],{},[3372,8558],{"alt":8559,"className":8560,"src":8561},"imek-izokvanty-mrts",[210,3376],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,8563,8564,8567,8568,3033,8598,8620,8621,2750],{},[38,8565,8566],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,8569,8571],{"className":8570},[886],[888,8572,8573],{"xmlns":890},[892,8574,8575,8595],{},[895,8576,8577,8579,8585,8587,8593],{},[1708,8578,6940],{"stretchy":1715},[1743,8580,8581,8583],{},[898,8582,1658],{},[2505,8584,2784],{},[1708,8586,1883],{"separator":1882},[1743,8588,8589,8591],{},[898,8590,1673],{},[2505,8592,2784],{},[1708,8594,6981],{"stretchy":1715},[902,8596,8597],{"encoding":904},"[L_0, K_0]",[883,8599,8601],{"className":8600},[886],[888,8602,8603],{"xmlns":890},[892,8604,8605,8617],{},[895,8606,8607,8609,8611,8613,8615],{},[1708,8608,2726],{},[898,8610,1741],{},[898,8612,1975],{},[898,8614,1978],{},[898,8616,1981],{},[902,8618,8619],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,8622,8624],{"className":8623},[886],[888,8625,8626],{"xmlns":890},[892,8627,8628,8650],{},[895,8629,8630,8632,8634,8636,8638,8640,8642,8644],{},[898,8631,1688],{},[1708,8633,1716],{"stretchy":1715},[898,8635,1658],{},[1708,8637,1883],{"separator":1882},[898,8639,1673],{},[1708,8641,1721],{"stretchy":1715},[1708,8643,1710],{},[1743,8645,8646,8648],{},[898,8647,8115],{},[2505,8649,2784],{},[902,8651,8652],{"encoding":904},"Q(L,K) = q_0",[883,8654,8656],{"className":8655},[886],[888,8657,8658],{"xmlns":890,"display":2210},[892,8659,8660,8712],{},[895,8661,8662,8676,8678,8680,8698,8700,8702,8704,8706,8708,8710],{},[2358,8663,8664,8670],{},[895,8665,8666,8668],{},[898,8667,2364],{},[898,8669,1673],{},[895,8671,8672,8674],{},[898,8673,2364],{},[898,8675,1658],{},[1708,8677,1710],{},[1708,8679,2726],{},[2358,8681,8682,8690],{},[4754,8683,8684,8686,8688],{},[898,8685,1688],{},[898,8687,1658],{},[1708,8689,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,8691,8692,8694,8696],{},[898,8693,1688],{},[898,8695,1673],{},[1708,8697,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,8699,1710],{},[1708,8701,2726],{},[898,8703,1741],{},[898,8705,1975],{},[898,8707,1978],{},[898,8709,1981],{},[898,8711,2155],{"mathvariant":1759},[902,8713,8714],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,8716,8717,8718,8733,8734,8750],{},"Změní-li se práce o ",[883,8719,8721],{"className":8720},[886],[888,8722,8723],{"xmlns":890},[892,8724,8725,8731],{},[895,8726,8727,8729],{},[898,8728,2364],{},[898,8730,1658],{},[902,8732,2578],{"encoding":904},", lze pro odhad změny kapitálu ",[883,8735,8737],{"className":8736},[886],[888,8738,8739],{"xmlns":890},[892,8740,8741,8747],{},[895,8742,8743,8745],{},[898,8744,2633],{"mathvariant":1759},[898,8746,1673],{},[902,8748,8749],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,8752,8754],{"className":8753},[886],[888,8755,8756],{"xmlns":890,"display":2210},[892,8757,8758,8805],{},[2214,8759,8760],{"width":2216},[2218,8761,8762,8764,8798,8800],{},[2221,8763],{"width":2223},[2221,8765,8766],{},[895,8767,8768,8770,8772,8774,8776,8778,8780,8782,8784,8786,8788,8790,8792,8794,8796],{},[898,8769,2633],{"mathvariant":1759},[898,8771,1673],{},[1708,8773,2638],{},[898,8775,2364],{},[898,8777,1673],{},[1708,8779,1710],{},[1708,8781,2726],{},[898,8783,1741],{},[898,8785,1975],{},[898,8787,1978],{},[898,8789,1981],{},[2247,8791,2659],{},[898,8793,2364],{},[898,8795,1658],{},[1708,8797,1883],{"separator":1882},[2221,8799],{"width":2223},[2221,8801,8802],{},[2247,8803,8804],{},"(5.15)",[902,8806,8807],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,8809,8811],{"className":8810},[886],[888,8812,8813],{"xmlns":890,"display":2210},[892,8814,8815,8864],{},[2214,8816,8817],{"width":2216},[2218,8818,8819,8821,8857,8859],{},[2221,8820],{"width":2223},[2221,8822,8823],{},[895,8824,8825,8827,8829,8831,8849,8851,8853,8855],{},[898,8826,2364],{},[898,8828,1658],{},[1708,8830,1710],{},[2358,8832,8833,8839],{},[895,8834,8835,8837],{},[1708,8836,2726],{},[2505,8838,2507],{},[895,8840,8841,8843,8845,8847],{},[898,8842,1741],{},[898,8844,1975],{},[898,8846,1978],{},[898,8848,1981],{},[2247,8850,2659],{},[898,8852,2364],{},[898,8854,1673],{},[898,8856,2155],{"mathvariant":1759},[2221,8858],{"width":2223},[2221,8860,8861],{},[2247,8862,8863],{},"(5.16)",[902,8865,8866],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1636,8868,8869,8893],{},[724,8870,8871,8873,8874],{},[883,8872,3465],{}," Postup — jak spočítat ",[883,8875,8877],{"className":8876},[886],[888,8878,8879],{"xmlns":890},[892,8880,8881,8891],{},[895,8882,8883,8885,8887,8889],{},[898,8884,1741],{},[898,8886,1975],{},[898,8888,1978],{},[898,8890,1981],{},[902,8892,8303],{"encoding":904},[152,8894,8895,8938,8982,9014],{},[123,8896,8897,8898,1771,8918,2155],{},"Vypočtěte parciální derivace ",[883,8899,8901],{"className":8900},[886],[888,8902,8903],{"xmlns":890},[892,8904,8905,8915],{},[895,8906,8907],{},[4754,8908,8909,8911,8913],{},[898,8910,1688],{},[898,8912,1658],{},[1708,8914,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,8916,8917],{"encoding":904},"Q'_L",[883,8919,8921],{"className":8920},[886],[888,8922,8923],{"xmlns":890},[892,8924,8925,8935],{},[895,8926,8927],{},[4754,8928,8929,8931,8933],{},[898,8930,1688],{},[898,8932,1673],{},[1708,8934,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,8936,8937],{"encoding":904},"Q'_K",[123,8939,8940,8941,8981],{},"Dosaďte do ",[883,8942,8944],{"className":8943},[886],[888,8945,8946],{"xmlns":890},[892,8947,8948,8978],{},[895,8949,8950,8952,8954,8956,8958,8960,8968,8970],{},[898,8951,1741],{},[898,8953,1975],{},[898,8955,1978],{},[898,8957,1981],{},[1708,8959,1710],{},[4754,8961,8962,8964,8966],{},[898,8963,1688],{},[898,8965,1658],{},[1708,8967,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[898,8969,1799],{"mathvariant":1759},[4754,8971,8972,8974,8976],{},[898,8973,1688],{},[898,8975,1673],{},[1708,8977,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,8979,8980],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,8983,8984,8985,2155],{},"Případně dosaďte konkrétní ",[883,8986,8988],{"className":8987},[886],[888,8989,8990],{"xmlns":890},[892,8991,8992,9012],{},[895,8993,8994,8996,9002,9004,9010],{},[1708,8995,6940],{"stretchy":1715},[1743,8997,8998,9000],{},[898,8999,1658],{},[2505,9001,2784],{},[1708,9003,1883],{"separator":1882},[1743,9005,9006,9008],{},[898,9007,1673],{},[2505,9009,2784],{},[1708,9011,6981],{"stretchy":1715},[902,9013,8597],{"encoding":904},[123,9015,9016,9017,9051,9052,9055],{},"Pro odhad substituce použijte ",[883,9018,9020],{"className":9019},[886],[888,9021,9022],{"xmlns":890},[892,9023,9024,9048],{},[895,9025,9026,9028,9030,9032,9034,9036,9038,9040,9042,9044,9046],{},[898,9027,2633],{"mathvariant":1759},[898,9029,1673],{},[1708,9031,2638],{},[1708,9033,2726],{},[898,9035,1741],{},[898,9037,1975],{},[898,9039,1978],{},[898,9041,1981],{},[1708,9043,3703],{},[898,9045,2633],{"mathvariant":1759},[898,9047,1658],{},[902,9049,9050],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,9053,9054],{},"mínus"," — substituce, ne doplnění).",[724,9057,9058],{},[614,9059,9060,9061,9093,9094,3405,9108,9137,9138,9153],{},"Obrázek 5.7 — izokvanta ",[883,9062,9064],{"className":9063},[886],[888,9065,9066],{"xmlns":890},[892,9067,9068,9090],{},[895,9069,9070,9076,9078,9080,9082,9084,9086,9088],{},[1743,9071,9072,9074],{},[898,9073,8115],{},[2505,9075,2784],{},[1708,9077,1710],{},[898,9079,1688],{},[1708,9081,1716],{"stretchy":1715},[898,9083,1658],{},[1708,9085,1883],{"separator":1882},[898,9087,1673],{},[1708,9089,1721],{"stretchy":1715},[902,9091,9092],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,9095,9097],{"className":9096},[886],[888,9098,9099],{"xmlns":890},[892,9100,9101,9106],{},[895,9102,9103],{},[898,9104,9105],{},"t",[902,9107,9105],{"encoding":904},[883,9109,9111],{"className":9110},[886],[888,9112,9113],{"xmlns":890},[892,9114,9115,9135],{},[895,9116,9117,9119,9125,9127,9133],{},[1708,9118,6940],{"stretchy":1715},[1743,9120,9121,9123],{},[898,9122,1658],{},[2505,9124,2784],{},[1708,9126,1883],{"separator":1882},[1743,9128,9129,9131],{},[898,9130,1673],{},[2505,9132,2784],{},[1708,9134,6981],{"stretchy":1715},[902,9136,8597],{"encoding":904},"; ",[883,9139,9141],{"className":9140},[886],[888,9142,9143],{"xmlns":890},[892,9144,9145,9151],{},[895,9146,9147,9149],{},[898,9148,2633],{"mathvariant":1759},[898,9150,1673],{},[902,9152,8749],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,9155,9157],{"id":9156},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,9159,9161],{"id":9160},"příklad-54","Příklad 5.4",[724,9163,3931,9164,1343,9206,1343,9223,2155],{},[883,9165,9167],{"className":9166},[886],[888,9168,9169],{"xmlns":890},[892,9170,9171,9203],{},[895,9172,9173,9175,9177,9179,9191],{},[898,9174,1688],{},[1708,9176,1710],{},[2505,9178,4853],{},[1753,9180,9181,9183],{},[898,9182,1658],{},[895,9184,9185,9187,9189],{},[2505,9186,2507],{},[898,9188,1799],{"mathvariant":1759},[2505,9190,3132],{},[1753,9192,9193,9195],{},[898,9194,1673],{},[895,9196,9197,9199,9201],{},[2505,9198,2507],{},[898,9200,1799],{"mathvariant":1759},[2505,9202,3121],{},[902,9204,9205],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,9207,9209],{"className":9208},[886],[888,9210,9211],{"xmlns":890},[892,9212,9213,9221],{},[895,9214,9215,9217,9219],{},[898,9216,1658],{},[1708,9218,1710],{},[2505,9220,4018],{},[902,9222,4321],{"encoding":904},[883,9224,9226],{"className":9225},[886],[888,9227,9228],{"xmlns":890},[892,9229,9230,9239],{},[895,9231,9232,9234,9236],{},[898,9233,1673],{},[1708,9235,1710],{},[2505,9237,9238],{},"100",[902,9240,9241],{"encoding":904},"K = 100",[724,9243,9244],{},[38,9245,9246],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,9248,9250],{"className":9249},[886],[888,9251,9252],{"xmlns":890,"display":2210},[892,9253,9254,9369],{},[895,9255,9256,9258,9264,9266,9274,9276,9284,9298,9310,9312,9314,9316,9322,9324,9326,9328,9330,9332,9334,9342,9344,9355,9357,9364,9366],{},[898,9257,1741],{},[1743,9259,9260,9262],{},[898,9261,1747],{},[898,9263,1658],{},[1708,9265,1710],{},[4754,9267,9268,9270,9272],{},[898,9269,1688],{},[898,9271,1658],{},[1708,9273,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,9275,1710],{},[3194,9277,9278],{"scriptlevel":2784,"displaystyle":1715},[2358,9279,9280,9282],{},[2505,9281,4853],{},[2505,9283,3132],{},[1753,9285,9286,9288],{},[898,9287,1658],{},[895,9289,9290,9292,9294,9296],{},[1708,9291,2726],{},[2505,9293,2507],{},[898,9295,1799],{"mathvariant":1759},[2505,9297,3132],{},[1753,9299,9300,9302],{},[898,9301,1673],{},[895,9303,9304,9306,9308],{},[2505,9305,2507],{},[898,9307,1799],{"mathvariant":1759},[2505,9309,3121],{},[1708,9311,1883],{"separator":1882},[3213,9313],{"width":4750},[898,9315,1741],{},[1743,9317,9318,9320],{},[898,9319,1747],{},[898,9321,1658],{},[1708,9323,1716],{"stretchy":1715},[2505,9325,4018],{},[1708,9327,1883],{"separator":1882},[2505,9329,9238],{},[1708,9331,1721],{"stretchy":1715},[1708,9333,1710],{},[3194,9335,9336],{"scriptlevel":2784,"displaystyle":1715},[2358,9337,9338,9340],{},[2505,9339,4853],{},[2505,9341,3132],{},[1708,9343,3703],{},[3194,9345,9346],{"scriptlevel":2784,"displaystyle":1715},[2358,9347,9348,9350],{},[2505,9349,2507],{},[9351,9352,9353],"msqrt",{},[2505,9354,4018],{},[1708,9356,3703],{},[9358,9359,9360,9362],"mroot",{},[2505,9361,9238],{},[2505,9363,3121],{},[1708,9365,2638],{},[2505,9367,9368],{},"7,153.",[902,9370,9371],{"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.",[724,9373,9374,9375,9398,9399,9416,9417,9438,9439,9460],{},"Přibližná změna při ",[883,9376,9378],{"className":9377},[886],[888,9379,9380],{"xmlns":890},[892,9381,9382,9395],{},[895,9383,9384,9386,9388,9390,9393],{},[898,9385,1658],{},[1708,9387,2788],{},[2505,9389,4018],{},[1708,9391,9392],{},"→",[2505,9394,4023],{},[902,9396,9397],{"encoding":904},"L: 20 \\to 21"," (při ",[883,9400,9402],{"className":9401},[886],[888,9403,9404],{"xmlns":890},[892,9405,9406,9414],{},[895,9407,9408,9410,9412],{},[898,9409,1673],{},[1708,9411,1710],{},[2505,9413,9238],{},[902,9415,9241],{"encoding":904},"): ",[883,9418,9420],{"className":9419},[886],[888,9421,9422],{"xmlns":890},[892,9423,9424,9435],{},[895,9425,9426,9428,9430,9432],{},[898,9427,2633],{"mathvariant":1759},[898,9429,1688],{},[1708,9431,2638],{},[2505,9433,9434],{},"7,153",[902,9436,9437],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,9440,9442],{"className":9441},[886],[888,9443,9444],{"xmlns":890},[892,9445,9446,9457],{},[895,9447,9448,9450,9452,9454],{},[898,9449,2633],{"mathvariant":1759},[898,9451,1688],{},[1708,9453,2638],{},[2505,9455,9456],{},"26,888",[902,9458,9459],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,9462,9463,9466],{},[38,9464,9465],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,9468,9470],{"className":9469},[886],[888,9471,9472],{"xmlns":890,"display":2210},[892,9473,9474,9574],{},[895,9475,9476,9478,9484,9486,9494,9496,9498,9510,9524,9526,9528,9530,9536,9538,9540,9542,9544,9546,9548,9550,9554,9556,9569,9571],{},[898,9477,1741],{},[1743,9479,9480,9482],{},[898,9481,1747],{},[898,9483,1673],{},[1708,9485,1710],{},[4754,9487,9488,9490,9492],{},[898,9489,1688],{},[898,9491,1673],{},[1708,9493,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,9495,1710],{},[2505,9497,3993],{},[1753,9499,9500,9502],{},[898,9501,1658],{},[895,9503,9504,9506,9508],{},[2505,9505,2507],{},[898,9507,1799],{"mathvariant":1759},[2505,9509,3132],{},[1753,9511,9512,9514],{},[898,9513,1673],{},[895,9515,9516,9518,9520,9522],{},[1708,9517,2726],{},[2505,9519,3132],{},[898,9521,1799],{"mathvariant":1759},[2505,9523,3121],{},[1708,9525,1883],{"separator":1882},[3213,9527],{"width":4750},[898,9529,1741],{},[1743,9531,9532,9534],{},[898,9533,1747],{},[898,9535,1673],{},[1708,9537,1716],{"stretchy":1715},[2505,9539,4018],{},[1708,9541,1883],{"separator":1882},[2505,9543,9238],{},[1708,9545,1721],{"stretchy":1715},[1708,9547,1710],{},[2505,9549,3993],{},[9351,9551,9552],{},[2505,9553,4018],{},[1708,9555,3703],{},[3194,9557,9558],{"scriptlevel":2784,"displaystyle":1715},[2358,9559,9560,9562],{},[2505,9561,2507],{},[9358,9563,9564,9567],{},[2505,9565,9566],{},"10000",[2505,9568,3121],{},[1708,9570,2638],{},[2505,9572,9573],{},"4,525.",[902,9575,9576],{"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.",[724,9578,9579,9580,2486,9597,2511],{},"Produkce poklesne přibližně o 4,525 (z ",[883,9581,9583],{"className":9582},[886],[888,9584,9585],{"xmlns":890},[892,9586,9587,9594],{},[895,9588,9589,9591],{},[1708,9590,2638],{},[2505,9592,9593],{},"905,126",[902,9595,9596],{"encoding":904},"\\approx 905{,}126",[883,9598,9600],{"className":9599},[886],[888,9601,9602],{"xmlns":890},[892,9603,9604,9611],{},[895,9605,9606,9608],{},[1708,9607,2638],{},[2505,9609,9610],{},"900,601",[902,9612,9613],{"encoding":904},"\\approx 900{,}601",[724,9615,9616,9664,9665,1343,9687,2511],{},[38,9617,9618,9619,1771,9641],{},"(c) Změna ",[883,9620,9622],{"className":9621},[886],[888,9623,9624],{"xmlns":890},[892,9625,9626,9638],{},[895,9627,9628,9630,9632,9634,9636],{},[898,9629,1658],{},[1708,9631,2788],{},[2505,9633,4018],{},[1708,9635,9392],{},[2505,9637,4853],{},[902,9639,9640],{"encoding":904},"L: 20 \\to 15",[883,9642,9644],{"className":9643},[886],[888,9645,9646],{"xmlns":890},[892,9647,9648,9661],{},[895,9649,9650,9652,9654,9656,9658],{},[898,9651,1673],{},[1708,9653,2788],{},[2505,9655,9238],{},[1708,9657,9392],{},[2505,9659,9660],{},"150",[902,9662,9663],{"encoding":904},"K: 100 \\to 150"," (tj. ",[883,9666,9668],{"className":9667},[886],[888,9669,9670],{"xmlns":890},[892,9671,9672,9684],{},[895,9673,9674,9676,9678,9680,9682],{},[898,9675,2364],{},[898,9677,1658],{},[1708,9679,1710],{},[1708,9681,2726],{},[2505,9683,3993],{},[902,9685,9686],{"encoding":904},"dL = -5",[883,9688,9690],{"className":9689},[886],[888,9691,9692],{"xmlns":890},[892,9693,9694,9705],{},[895,9695,9696,9698,9700,9702],{},[898,9697,2364],{},[898,9699,1673],{},[1708,9701,1710],{},[2505,9703,9704],{},"50",[902,9706,9707],{"encoding":904},"dK = 50",[883,9709,9711],{"className":9710},[886],[888,9712,9713],{"xmlns":890,"display":2210},[892,9714,9715,9803],{},[895,9716,9717,9719,9721,9723,9725,9731,9733,9735,9737,9739,9741,9743,9745,9747,9749,9751,9753,9755,9761,9763,9765,9767,9769,9771,9773,9775,9777,9779,9781,9783,9785,9787,9789,9791,9794,9796,9798,9800],{},[898,9718,2364],{},[898,9720,1688],{},[1708,9722,1710],{},[898,9724,1741],{},[1743,9726,9727,9729],{},[898,9728,1747],{},[898,9730,1658],{},[1708,9732,1716],{"stretchy":1715},[2505,9734,4018],{},[1708,9736,1883],{"separator":1882},[2505,9738,9238],{},[1708,9740,1721],{"stretchy":1715},[1708,9742,3703],{},[1708,9744,1716],{"stretchy":1715},[1708,9746,2726],{},[2505,9748,3993],{},[1708,9750,1721],{"stretchy":1715},[1708,9752,2019],{},[898,9754,1741],{},[1743,9756,9757,9759],{},[898,9758,1747],{},[898,9760,1673],{},[1708,9762,1716],{"stretchy":1715},[2505,9764,4018],{},[1708,9766,1883],{"separator":1882},[2505,9768,9238],{},[1708,9770,1721],{"stretchy":1715},[1708,9772,3703],{},[2505,9774,9704],{},[1708,9776,1710],{},[2505,9778,9434],{},[1708,9780,3703],{},[1708,9782,1716],{"stretchy":1715},[1708,9784,2726],{},[2505,9786,3993],{},[1708,9788,1721],{"stretchy":1715},[1708,9790,2019],{},[2505,9792,9793],{},"4,525",[1708,9795,3703],{},[2505,9797,9704],{},[1708,9799,2638],{},[2505,9801,9802],{},"190,485.",[902,9804,9805],{"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.",[724,9807,9808],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,9810,9812],{"id":9811},"příklad-55","Příklad 5.5",[724,9814,9815,9816,9852,9853,2155],{},"Pro produkci ",[883,9817,9819],{"className":9818},[886],[888,9820,9821],{"xmlns":890},[892,9822,9823,9849],{},[895,9824,9825,9827,9829,9831,9833,9835,9837,9839,9845],{},[898,9826,1688],{},[1708,9828,1716],{"stretchy":1715},[898,9830,1658],{},[1708,9832,1883],{"separator":1882},[898,9834,1673],{},[1708,9836,1721],{"stretchy":1715},[1708,9838,1710],{},[9358,9840,9841,9843],{},[898,9842,1658],{},[2505,9844,3121],{},[9351,9846,9847],{},[898,9848,1673],{},[902,9850,9851],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,9854,9856],{"className":9855},[886],[888,9857,9858],{"xmlns":890},[892,9859,9860,9876],{},[895,9861,9862,9868,9872,9874],{},[9358,9863,9864,9866],{},[898,9865,1658],{},[2505,9867,3121],{},[9351,9869,9870],{},[898,9871,1673],{},[1708,9873,1710],{},[898,9875,8115],{},[902,9877,9878],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,9880,9881,9882,2155],{},"Umocněním na druhou: ",[883,9883,9885],{"className":9884},[886],[888,9886,9887],{"xmlns":890},[892,9888,9889,9913],{},[895,9890,9891,9893,9895,9901,9903],{},[898,9892,1673],{},[1708,9894,1710],{},[1753,9896,9897,9899],{},[898,9898,8115],{},[2505,9900,3132],{},[898,9902,1799],{"mathvariant":1759},[9358,9904,9905,9911],{},[1753,9906,9907,9909],{},[898,9908,1658],{},[2505,9910,3132],{},[2505,9912,3121],{},[902,9914,9915],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,9917,9918,9958,9998],{},[123,9919,9920],{},[883,9921,9923],{"className":9922},[886],[888,9924,9925],{"xmlns":890},[892,9926,9927,9955],{},[895,9928,9929,9931,9933,9935,9937,9939,9941,9943,9945],{},[898,9930,8115],{},[1708,9932,1710],{},[2505,9934,2507],{},[1708,9936,4782],{},[898,9938,1673],{},[1708,9940,1710],{},[2505,9942,2507],{},[898,9944,1799],{"mathvariant":1759},[9358,9946,9947,9953],{},[1753,9948,9949,9951],{},[898,9950,1658],{},[2505,9952,3132],{},[2505,9954,3121],{},[902,9956,9957],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,9959,9960],{},[883,9961,9963],{"className":9962},[886],[888,9964,9965],{"xmlns":890},[892,9966,9967,9995],{},[895,9968,9969,9971,9973,9975,9977,9979,9981,9983,9985],{},[898,9970,8115],{},[1708,9972,1710],{},[2505,9974,3132],{},[1708,9976,4782],{},[898,9978,1673],{},[1708,9980,1710],{},[2505,9982,5867],{},[898,9984,1799],{"mathvariant":1759},[9358,9986,9987,9993],{},[1753,9988,9989,9991],{},[898,9990,1658],{},[2505,9992,3132],{},[2505,9994,3121],{},[902,9996,9997],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,9999,10000],{},[883,10001,10003],{"className":10002},[886],[888,10004,10005],{"xmlns":890},[892,10006,10007,10035],{},[895,10008,10009,10011,10013,10015,10017,10019,10021,10023,10025],{},[898,10010,8115],{},[1708,10012,1710],{},[2505,10014,3121],{},[1708,10016,4782],{},[898,10018,1673],{},[1708,10020,1710],{},[2505,10022,4635],{},[898,10024,1799],{"mathvariant":1759},[9358,10026,10027,10033],{},[1753,10028,10029,10031],{},[898,10030,1658],{},[2505,10032,3132],{},[2505,10034,3121],{},[902,10036,10037],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,10039,10040],{},[614,10041,10042,10043,10064,10065,2155],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,10044,10046],{"className":10045},[886],[888,10047,10048],{"xmlns":890},[892,10049,10050,10062],{},[895,10051,10052,10054,10056,10058,10060],{},[1708,10053,1716],{"stretchy":1715},[898,10055,1658],{},[1708,10057,1883],{"separator":1882},[898,10059,1673],{},[1708,10061,1721],{"stretchy":1715},[902,10063,8244],{"encoding":904}," pro ",[883,10066,10068],{"className":10067},[886],[888,10069,10070],{"xmlns":890},[892,10071,10072,10088],{},[895,10073,10074,10076,10078,10080,10082,10084,10086],{},[898,10075,8115],{},[1708,10077,1710],{},[2505,10079,2507],{},[1708,10081,1883],{"separator":1882},[2505,10083,3132],{},[1708,10085,1883],{"separator":1882},[2505,10087,3121],{},[902,10089,10090],{"encoding":904},"q = 1, 2, 3",[198,10092,10094],{"id":10093},"příklad-56","Příklad 5.6",[724,10096,3931,10097,2155],{},[883,10098,10100],{"className":10099},[886],[888,10101,10102],{"xmlns":890},[892,10103,10104,10120],{},[895,10105,10106,10108,10110,10112,10114,10116],{},[898,10107,1688],{},[1708,10109,1710],{},[2505,10111,3132],{},[898,10113,1658],{},[1708,10115,2019],{},[9351,10117,10118],{},[898,10119,1673],{},[902,10121,10122],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,10124,10126],{"className":10125},[886],[888,10127,10128],{"xmlns":890,"display":2210},[892,10129,10130,10172],{},[895,10131,10132,10134,10140,10142,10144,10146,10148,10150,10156,10158,10170],{},[898,10133,1741],{},[1743,10135,10136,10138],{},[898,10137,1747],{},[898,10139,1658],{},[1708,10141,1710],{},[2505,10143,3132],{},[1708,10145,1883],{"separator":1882},[3213,10147],{"width":3215},[898,10149,1741],{},[1743,10151,10152,10154],{},[898,10153,1747],{},[898,10155,1673],{},[1708,10157,1710],{},[2358,10159,10160,10162],{},[2505,10161,2507],{},[895,10163,10164,10166],{},[2505,10165,3132],{},[9351,10167,10168],{},[898,10169,1673],{},[898,10171,2155],{"mathvariant":1759},[902,10173,10174],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,10176,10178],{"className":10177},[886],[888,10179,10180],{"xmlns":890,"display":2210},[892,10181,10182,10246],{},[895,10183,10184,10186,10188,10190,10192,10194,10216,10218,10236,10238,10240,10244],{},[898,10185,1741],{},[898,10187,1975],{},[898,10189,1978],{},[898,10191,1981],{},[1708,10193,1710],{},[2358,10195,10196,10206],{},[895,10197,10198,10200],{},[898,10199,1741],{},[1743,10201,10202,10204],{},[898,10203,1747],{},[898,10205,1658],{},[895,10207,10208,10210],{},[898,10209,1741],{},[1743,10211,10212,10214],{},[898,10213,1747],{},[898,10215,1673],{},[1708,10217,1710],{},[2358,10219,10220,10222],{},[2505,10221,3132],{},[3194,10223,10224],{"scriptlevel":2784,"displaystyle":1715},[2358,10225,10226,10228],{},[2505,10227,2507],{},[895,10229,10230,10232],{},[2505,10231,3132],{},[9351,10233,10234],{},[898,10235,1673],{},[1708,10237,1710],{},[2505,10239,5867],{},[9351,10241,10242],{},[898,10243,1673],{},[898,10245,2155],{"mathvariant":1759},[902,10247,10248],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,10250,10251,10252,10295,10296,10335,10336,2155],{},"Například ",[883,10253,10255],{"className":10254},[886],[888,10256,10257],{"xmlns":890},[892,10258,10259,10292],{},[895,10260,10261,10263,10265,10267,10269,10271,10273,10275,10277,10279,10281,10283,10287,10289],{},[898,10262,1741],{},[898,10264,1975],{},[898,10266,1978],{},[898,10268,1981],{},[1708,10270,1716],{"stretchy":1715},[2505,10272,5867],{},[1708,10274,1883],{"separator":1882},[2505,10276,5967],{},[1708,10278,1721],{"stretchy":1715},[1708,10280,1710],{},[2505,10282,5867],{},[9351,10284,10285],{},[2505,10286,5967],{},[1708,10288,2638],{},[2505,10290,10291],{},"10,58",[902,10293,10294],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,10297,10299],{"className":10298},[886],[888,10300,10301],{"xmlns":890},[892,10302,10303,10332],{},[895,10304,10305,10307,10309,10311,10313,10315,10317,10319,10321,10323,10327,10329],{},[898,10306,1688],{},[1708,10308,1716],{"stretchy":1715},[2505,10310,5867],{},[1708,10312,1883],{"separator":1882},[2505,10314,5967],{},[1708,10316,1721],{"stretchy":1715},[1708,10318,1710],{},[2505,10320,3998],{},[1708,10322,2019],{},[9351,10324,10325],{},[2505,10326,5967],{},[1708,10328,2638],{},[2505,10330,10331],{},"10,646",[902,10333,10334],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,10337,10339],{"className":10338},[886],[888,10340,10341],{"xmlns":890},[892,10342,10343,10351],{},[895,10344,10345,10347],{},[2505,10346,5867],{},[9351,10348,10349],{},[2505,10350,5967],{},[902,10352,10353],{"encoding":904},"4\\sqrt{7}",[724,10355,10356,10357,10377],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,10358,10360],{"className":10359},[886],[888,10361,10362],{"xmlns":890},[892,10363,10364,10374],{},[895,10365,10366,10368,10370,10372],{},[898,10367,2364],{},[898,10369,1658],{},[1708,10371,1710],{},[2505,10373,3132],{},[902,10375,10376],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,10379,10381],{"className":10380},[886],[888,10382,10383],{"xmlns":890,"display":2210},[892,10384,10385,10434],{},[895,10386,10387,10389,10391,10393,10395,10397,10399,10401,10403,10405,10407,10409,10411,10413,10415,10417,10419,10421,10423,10427,10429,10431],{},[898,10388,2364],{},[898,10390,1673],{},[1708,10392,1710],{},[1708,10394,2726],{},[898,10396,1741],{},[898,10398,1975],{},[898,10400,1978],{},[898,10402,1981],{},[1708,10404,1716],{"stretchy":1715},[2505,10406,5867],{},[1708,10408,1883],{"separator":1882},[2505,10410,5967],{},[1708,10412,1721],{"stretchy":1715},[1708,10414,3703],{},[2505,10416,3132],{},[1708,10418,1710],{},[1708,10420,2726],{},[2505,10422,3998],{},[9351,10424,10425],{},[2505,10426,5967],{},[1708,10428,2638],{},[1708,10430,2726],{},[2505,10432,10433],{},"21,17.",[902,10435,10436],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,10438,10440],{"id":10439},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,10442,10443,10444,1343,10446,1771,10448,10450,10451,10454,10455,10458],{},"Hlavními faktory produkce jsou ",[38,10445,2116],{},[38,10447,2132],{},[38,10449,2148],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,10452,10453],{},"jednofaktorový"," (pouze práce) a ",[38,10456,10457],{},"dvoufaktorový"," (práce + kapitál) model.",[724,10460,10461,10462,10465,10466,10468,10469,10471,10472,7468,10475,10494,10495,10512,10513,10530,10531,10553,10554,8214,10573,2155],{},"V ",[38,10463,10464],{},"1F modelu"," se definuje ",[38,10467,1728],{}," (derivace produkce podle práce) a ",[38,10470,2049],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,10473,10474],{},"zákonu klesajících výnosů",[883,10476,10478],{"className":10477},[886],[888,10479,10480],{"xmlns":890},[892,10481,10482,10492],{},[895,10483,10484,10486],{},[898,10485,1741],{},[1743,10487,10488,10490],{},[898,10489,1747],{},[898,10491,1658],{},[902,10493,2300],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,10496,10498],{"className":10497},[886],[888,10499,10500],{"xmlns":890},[892,10501,10502,10510],{},[895,10503,10504],{},[1743,10505,10506,10508],{},[898,10507,1658],{},[2505,10509,2784],{},[902,10511,2787],{"encoding":904}," klesá a v bodě ",[883,10514,10516],{"className":10515},[886],[888,10517,10518],{"xmlns":890},[892,10519,10520,10528],{},[895,10521,10522],{},[1743,10523,10524,10526],{},[898,10525,1658],{},[2505,10527,2507],{},[902,10529,2979],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,10532,10533,10534],{},"princip maximalizace ",[883,10535,10537],{"className":10536},[886],[888,10538,10539],{"xmlns":890},[892,10540,10541,10551],{},[895,10542,10543,10545],{},[898,10544,1786],{},[1743,10546,10547,10549],{},[898,10548,1747],{},[898,10550,1658],{},[902,10552,1825],{"encoding":904},": v bodě maxima ",[883,10555,10557],{"className":10556},[886],[888,10558,10559],{"xmlns":890},[892,10560,10561,10571],{},[895,10562,10563,10565],{},[898,10564,1786],{},[1743,10566,10567,10569],{},[898,10568,1747],{},[898,10570,1658],{},[902,10572,1825],{"encoding":904},[883,10574,10576],{"className":10575},[886],[888,10577,10578],{"xmlns":890},[892,10579,10580,10600],{},[895,10581,10582,10584,10590,10592,10594],{},[898,10583,1741],{},[1743,10585,10586,10588],{},[898,10587,1747],{},[898,10589,1658],{},[1708,10591,1710],{},[898,10593,1786],{},[1743,10595,10596,10598],{},[898,10597,1747],{},[898,10599,1658],{},[902,10601,1856],{"encoding":904},[724,10603,10604,10605,10608,10609,1729,10612,10641,10642,10659,10660,10663,10664,10693,10694,10696,10697,3033,10727,10749],{},"Ve ",[38,10606,10607],{},"2F modelu"," se obvykle používají ",[38,10610,10611],{},"Cobb-Douglasovy funkce",[883,10613,10615],{"className":10614},[886],[888,10616,10617],{"xmlns":890},[892,10618,10619,10639],{},[895,10620,10621,10623,10625,10627,10633],{},[898,10622,1688],{},[1708,10624,1710],{},[898,10626,1786],{},[1753,10628,10629,10631],{},[898,10630,1658],{},[898,10632,207],{},[1753,10634,10635,10637],{},[898,10636,1673],{},[898,10638,1923],{},[902,10640,1926],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,10643,10645],{"className":10644},[886],[888,10646,10647],{"xmlns":890},[892,10648,10649,10657],{},[895,10650,10651,10653,10655],{},[898,10652,207],{},[1708,10654,2019],{},[898,10656,1923],{},[902,10658,2024],{"encoding":904}," rozlišujeme ",[38,10661,10662],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,10665,10667],{"className":10666},[886],[888,10668,10669],{"xmlns":890},[892,10670,10671,10691],{},[895,10672,10673,10675,10681,10683,10685],{},[898,10674,1741],{},[1743,10676,10677,10679],{},[898,10678,1747],{},[898,10680,1658],{},[1708,10682,1883],{"separator":1882},[898,10684,1741],{},[1743,10686,10687,10689],{},[898,10688,1747],{},[898,10690,1673],{},[902,10692,1957],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,10695,8072],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,10698,10700],{"className":10699},[886],[888,10701,10702],{"xmlns":890},[892,10703,10704,10724],{},[895,10705,10706,10708,10714,10716,10718],{},[898,10707,1741],{},[1743,10709,10710,10712],{},[898,10711,1747],{},[898,10713,1658],{},[898,10715,1799],{"mathvariant":1759},[898,10717,1741],{},[1743,10719,10720,10722],{},[898,10721,1747],{},[898,10723,1673],{},[902,10725,10726],{"encoding":904},"MP_L\u002FMP_K",[38,10728,10729,10730,1721],{},"mezní míra technické substituce (",[883,10731,10733],{"className":10732},[886],[888,10734,10735],{"xmlns":890},[892,10736,10737,10747],{},[895,10738,10739,10741,10743,10745],{},[898,10740,1741],{},[898,10742,1975],{},[898,10744,1978],{},[898,10746,1981],{},[902,10748,8303],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,10751,10753],{"id":10752},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,10755,10756,10759,10762,10765,10768,10771,10774,10777,10780,10783,10786],{},[123,10757,10758],{},"Jaké jsou faktory produkce?",[123,10760,10761],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,10763,10764],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,10766,10767],{},"Co udává mezní produkt práce?",[123,10769,10770],{},"Co musí respektovat průběh křivky produkce?",[123,10772,10773],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,10775,10776],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,10778,10779],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,10781,10782],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,10784,10785],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,10787,10788],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,10790,10792],{"id":10791},"úlohy-51517","Úlohy 5.1–5.17",[198,10794,10796],{"id":10795},"jednofaktorový-model","Jednofaktorový model",[724,10798,10799,10802,10803,10825,10826,1343,10846,1343,10866,10886],{},[38,10800,10801],{},"5.1"," Je dána produkce ",[883,10804,10806],{"className":10805},[886],[888,10807,10808],{"xmlns":890},[892,10809,10810,10822],{},[895,10811,10812,10814,10816,10818],{},[898,10813,1688],{},[1708,10815,1710],{},[2505,10817,4003],{},[9351,10819,10820],{},[898,10821,1658],{},[902,10823,10824],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,10827,10829],{"className":10828},[886],[888,10830,10831],{"xmlns":890},[892,10832,10833,10843],{},[895,10834,10835,10837,10839,10841],{},[898,10836,1688],{},[1708,10838,1716],{"stretchy":1715},[2505,10840,2507],{},[1708,10842,1721],{"stretchy":1715},[902,10844,10845],{"encoding":904},"Q(1)",[883,10847,10849],{"className":10848},[886],[888,10850,10851],{"xmlns":890},[892,10852,10853,10863],{},[895,10854,10855,10857,10859,10861],{},[898,10856,1688],{},[1708,10858,1716],{"stretchy":1715},[2505,10860,5867],{},[1708,10862,1721],{"stretchy":1715},[902,10864,10865],{"encoding":904},"Q(4)",[883,10867,10869],{"className":10868},[886],[888,10870,10871],{"xmlns":890},[892,10872,10873,10883],{},[895,10874,10875,10877,10879,10881],{},[898,10876,1688],{},[1708,10878,1716],{"stretchy":1715},[2505,10880,4635],{},[1708,10882,1721],{"stretchy":1715},[902,10884,10885],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,10888,10889,10802,10892,10929,10930,10943,10944,10963,10964,10990,10991,2486,11004,11018],{},[38,10890,10891],{},"5.2",[883,10893,10895],{"className":10894},[886],[888,10896,10897],{"xmlns":890},[892,10898,10899,10926],{},[895,10900,10901,10903,10905,10907,10910,10916,10918,10920],{},[898,10902,1688],{},[1708,10904,1710],{},[1708,10906,2726],{},[2505,10908,10909],{},"0,1",[1753,10911,10912,10914],{},[898,10913,1658],{},[2505,10915,3121],{},[1708,10917,2019],{},[2505,10919,4635],{},[1753,10921,10922,10924],{},[898,10923,1658],{},[2505,10925,3132],{},[902,10927,10928],{"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 ",[883,10931,10933],{"className":10932},[886],[888,10934,10935],{"xmlns":890},[892,10936,10937,10941],{},[895,10938,10939],{},[898,10940,1658],{},[902,10942,1658],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,10945,10947],{"className":10946},[886],[888,10948,10949],{"xmlns":890},[892,10950,10951,10961],{},[895,10952,10953,10955],{},[898,10954,1741],{},[1743,10956,10957,10959],{},[898,10958,1747],{},[898,10960,1658],{},[902,10962,2300],{"encoding":904},". (f) Vypočtěte ",[883,10965,10967],{"className":10966},[886],[888,10968,10969],{"xmlns":890},[892,10970,10971,10987],{},[895,10972,10973,10975,10981,10983,10985],{},[898,10974,1741],{},[1743,10976,10977,10979],{},[898,10978,1747],{},[898,10980,1658],{},[1708,10982,1716],{"stretchy":1715},[2505,10984,4003],{},[1708,10986,1721],{"stretchy":1715},[902,10988,10989],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,10992,10994],{"className":10993},[886],[888,10995,10996],{"xmlns":890},[892,10997,10998,11002],{},[895,10999,11000],{},[2505,11001,4003],{},[902,11003,4003],{"encoding":904},[883,11005,11007],{"className":11006},[886],[888,11008,11009],{"xmlns":890},[892,11010,11011,11016],{},[895,11012,11013],{},[2505,11014,11015],{},"13",[902,11017,11015],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,11020,11021,11024,11025,11048,11049,11078,11079,11110,11111,2155],{},[38,11022,11023],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,11026,11028],{"className":11027},[886],[888,11029,11030],{"xmlns":890},[892,11031,11032,11045],{},[895,11033,11034,11036,11038,11041],{},[898,11035,1688],{},[1708,11037,1710],{},[2505,11039,11040],{},"500",[9351,11042,11043],{},[898,11044,1658],{},[902,11046,11047],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,11050,11052],{"className":11051},[886],[888,11053,11054],{"xmlns":890},[892,11055,11056,11075],{},[895,11057,11058,11060,11062,11065,11069,11071,11073],{},[898,11059,1688],{},[1708,11061,1710],{},[2505,11063,11064],{},"300",[9351,11066,11067],{},[898,11068,1658],{},[1708,11070,2726],{},[2505,11072,5867],{},[898,11074,1658],{},[902,11076,11077],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,11080,11082],{"className":11081},[886],[888,11083,11084],{"xmlns":890},[892,11085,11086,11107],{},[895,11087,11088,11090,11092,11094,11096,11098,11101],{},[898,11089,1688],{},[1708,11091,1710],{},[2505,11093,9704],{},[898,11095,1658],{},[1708,11097,2726],{},[2505,11099,11100],{},"0,01",[1753,11102,11103,11105],{},[898,11104,1658],{},[2505,11106,3132],{},[902,11108,11109],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,11112,11114],{"className":11113},[886],[888,11115,11116],{"xmlns":890},[892,11117,11118,11144],{},[895,11119,11120,11122,11124,11126,11128,11134,11136,11138],{},[898,11121,1688],{},[1708,11123,1710],{},[1708,11125,2726],{},[2505,11127,6090],{},[1753,11129,11130,11132],{},[898,11131,1658],{},[2505,11133,3121],{},[1708,11135,2019],{},[2505,11137,4635],{},[1753,11139,11140,11142],{},[898,11141,1658],{},[2505,11143,3132],{},[902,11145,11146],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,11148,11149,11152,11153,3405,11172,11189,11190,2155],{},[38,11150,11151],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,11154,11156],{"className":11155},[886],[888,11157,11158],{"xmlns":890},[892,11159,11160,11170],{},[895,11161,11162,11164],{},[898,11163,1786],{},[1743,11165,11166,11168],{},[898,11167,1747],{},[898,11169,1658],{},[902,11171,1825],{"encoding":904},[883,11173,11175],{"className":11174},[886],[888,11176,11177],{"xmlns":890},[892,11178,11179,11187],{},[895,11180,11181],{},[1743,11182,11183,11185],{},[898,11184,1658],{},[2505,11186,2784],{},[902,11188,2787],{"encoding":904}," maximum, pak platí ",[883,11191,11193],{"className":11192},[886],[888,11194,11195],{"xmlns":890},[892,11196,11197,11237],{},[895,11198,11199,11201,11207,11209,11215,11217,11219,11221,11227,11229,11235],{},[898,11200,1786],{},[1743,11202,11203,11205],{},[898,11204,1747],{},[898,11206,1658],{},[1708,11208,1716],{"stretchy":1715},[1743,11210,11211,11213],{},[898,11212,1658],{},[2505,11214,2784],{},[1708,11216,1721],{"stretchy":1715},[1708,11218,1710],{},[898,11220,1741],{},[1743,11222,11223,11225],{},[898,11224,1747],{},[898,11226,1658],{},[1708,11228,1716],{"stretchy":1715},[1743,11230,11231,11233],{},[898,11232,1658],{},[2505,11234,2784],{},[1708,11236,1721],{"stretchy":1715},[902,11238,11239],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,11241,11242,10802,11245,2980,11281,11294,11295,11314],{},[38,11243,11244],{},"5.5",[883,11246,11248],{"className":11247},[886],[888,11249,11250],{"xmlns":890},[892,11251,11252,11278],{},[895,11253,11254,11256,11258,11260,11262,11268,11270,11272],{},[898,11255,1688],{},[1708,11257,1710],{},[1708,11259,2726],{},[2505,11261,3958],{},[1753,11263,11264,11266],{},[898,11265,1658],{},[2505,11267,3121],{},[1708,11269,2019],{},[2505,11271,4090],{},[1753,11273,11274,11276],{},[898,11275,1658],{},[2505,11277,3132],{},[902,11279,11280],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,11282,11284],{"className":11283},[886],[888,11285,11286],{"xmlns":890},[892,11287,11288,11292],{},[895,11289,11290],{},[898,11291,1658],{},[902,11293,1658],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,11296,11298],{"className":11297},[886],[888,11299,11300],{"xmlns":890},[892,11301,11302,11312],{},[895,11303,11304,11306],{},[898,11305,1786],{},[1743,11307,11308,11310],{},[898,11309,1747],{},[898,11311,1658],{},[902,11313,1825],{"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.",[198,11316,11318],{"id":11317},"dvoufaktorový-model","Dvoufaktorový model",[724,11320,11321,11324,11325,11048,11351,11078,11393,2155],{},[38,11322,11323],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,11326,11328],{"className":11327},[886],[888,11329,11330],{"xmlns":890},[892,11331,11332,11348],{},[895,11333,11334,11336,11338,11340,11342],{},[898,11335,1688],{},[1708,11337,1710],{},[2505,11339,5967],{},[898,11341,1658],{},[1753,11343,11344,11346],{},[898,11345,1673],{},[2505,11347,3132],{},[902,11349,11350],{"encoding":904},"Q = 7 L K^{2}",[883,11352,11354],{"className":11353},[886],[888,11355,11356],{"xmlns":890},[892,11357,11358,11390],{},[895,11359,11360,11362,11364,11366,11378],{},[898,11361,1688],{},[1708,11363,1710],{},[2505,11365,9704],{},[1753,11367,11368,11370],{},[898,11369,1658],{},[895,11371,11372,11374,11376],{},[2505,11373,3132],{},[898,11375,1799],{"mathvariant":1759},[2505,11377,3121],{},[1753,11379,11380,11382],{},[898,11381,1673],{},[895,11383,11384,11386,11388],{},[2505,11385,2507],{},[898,11387,1799],{"mathvariant":1759},[2505,11389,3121],{},[902,11391,11392],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,11394,11396],{"className":11395},[886],[888,11397,11398],{"xmlns":890},[892,11399,11400,11432],{},[895,11401,11402,11404,11406,11408,11420],{},[898,11403,1688],{},[1708,11405,1710],{},[2505,11407,4013],{},[1753,11409,11410,11412],{},[898,11411,1658],{},[895,11413,11414,11416,11418],{},[2505,11415,3121],{},[898,11417,1799],{"mathvariant":1759},[2505,11419,3993],{},[1753,11421,11422,11424],{},[898,11423,1673],{},[895,11425,11426,11428,11430],{},[2505,11427,3132],{},[898,11429,1799],{"mathvariant":1759},[2505,11431,3993],{},[902,11433,11434],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,11436,11437,10802,11440,11482,11483,1343,11502,11521,11522,11539],{},[38,11438,11439],{},"5.7",[883,11441,11443],{"className":11442},[886],[888,11444,11445],{"xmlns":890},[892,11446,11447,11479],{},[895,11448,11449,11451,11453,11455,11467],{},[898,11450,1688],{},[1708,11452,1710],{},[2505,11454,4003],{},[1753,11456,11457,11459],{},[898,11458,1658],{},[895,11460,11461,11463,11465],{},[2505,11462,2507],{},[898,11464,1799],{"mathvariant":1759},[2505,11466,3132],{},[1753,11468,11469,11471],{},[898,11470,1673],{},[895,11472,11473,11475,11477],{},[2505,11474,2507],{},[898,11476,1799],{"mathvariant":1759},[2505,11478,3132],{},[902,11480,11481],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,11484,11486],{"className":11485},[886],[888,11487,11488],{"xmlns":890},[892,11489,11490,11499],{},[895,11491,11492,11494,11496],{},[898,11493,1658],{},[1708,11495,1710],{},[2505,11497,11498],{},"400",[902,11500,11501],{"encoding":904},"L = 400",[883,11503,11505],{"className":11504},[886],[888,11506,11507],{"xmlns":890},[892,11508,11509,11518],{},[895,11510,11511,11513,11515],{},[898,11512,1673],{},[1708,11514,1710],{},[2505,11516,11517],{},"17576",[902,11519,11520],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,11523,11525],{"className":11524},[886],[888,11526,11527],{"xmlns":890},[892,11528,11529,11537],{},[895,11530,11531,11533,11535],{},[898,11532,1658],{},[1708,11534,1883],{"separator":1882},[898,11536,1673],{},[902,11538,6285],{"encoding":904}," zdvojnásobí.",[724,11541,11542,11545,11546,11482,11579,1343,11598,11617,11618,11648,11649,11679,11680,2486,11693,11707,11708,2486,11721,11735],{},[38,11543,11544],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,11547,11549],{"className":11548},[886],[888,11550,11551],{"xmlns":890},[892,11552,11553,11576],{},[895,11554,11555,11557,11559,11562,11569],{},[898,11556,1688],{},[1708,11558,1710],{},[2505,11560,11561],{},"1,01",[1753,11563,11564,11566],{},[898,11565,1658],{},[2505,11567,11568],{},"0,75",[1753,11570,11571,11573],{},[898,11572,1673],{},[2505,11574,11575],{},"0,25",[902,11577,11578],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,11580,11582],{"className":11581},[886],[888,11583,11584],{"xmlns":890},[892,11585,11586,11595],{},[895,11587,11588,11590,11592],{},[898,11589,1658],{},[1708,11591,1710],{},[2505,11593,11594],{},"250",[902,11596,11597],{"encoding":904},"L = 250",[883,11599,11601],{"className":11600},[886],[888,11602,11603],{"xmlns":890},[892,11604,11605,11614],{},[895,11606,11607,11609,11611],{},[898,11608,1673],{},[1708,11610,1710],{},[2505,11612,11613],{},"1000",[902,11615,11616],{"encoding":904},"K = 1000",". (b) Vypočtěte ",[883,11619,11621],{"className":11620},[886],[888,11622,11623],{"xmlns":890},[892,11624,11625,11645],{},[895,11626,11627,11629,11635,11637,11639,11641,11643],{},[898,11628,1741],{},[1743,11630,11631,11633],{},[898,11632,1747],{},[898,11634,1658],{},[1708,11636,1716],{"stretchy":1715},[2505,11638,11594],{},[1708,11640,1883],{"separator":1882},[2505,11642,11613],{},[1708,11644,1721],{"stretchy":1715},[902,11646,11647],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,11650,11652],{"className":11651},[886],[888,11653,11654],{"xmlns":890},[892,11655,11656,11676],{},[895,11657,11658,11660,11666,11668,11670,11672,11674],{},[898,11659,1741],{},[1743,11661,11662,11664],{},[898,11663,1747],{},[898,11665,1673],{},[1708,11667,1716],{"stretchy":1715},[2505,11669,11594],{},[1708,11671,1883],{"separator":1882},[2505,11673,11613],{},[1708,11675,1721],{"stretchy":1715},[902,11677,11678],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,11681,11683],{"className":11682},[886],[888,11684,11685],{"xmlns":890},[892,11686,11687,11691],{},[895,11688,11689],{},[898,11690,1658],{},[902,11692,1658],{"encoding":904},[883,11694,11696],{"className":11695},[886],[888,11697,11698],{"xmlns":890},[892,11699,11700,11705],{},[895,11701,11702],{},[2505,11703,11704],{},"260",[902,11706,11704],{"encoding":904}," a současném poklesu ",[883,11709,11711],{"className":11710},[886],[888,11712,11713],{"xmlns":890},[892,11714,11715,11719],{},[895,11716,11717],{},[898,11718,1673],{},[902,11720,1673],{"encoding":904},[883,11722,11724],{"className":11723},[886],[888,11725,11726],{"xmlns":890},[892,11727,11728,11733],{},[895,11729,11730],{},[2505,11731,11732],{},"900",[902,11734,11732],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,11737,11738,11741,11742,2155],{},[38,11739,11740],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,11743,11745],{"className":11744},[886],[888,11746,11747],{"xmlns":890},[892,11748,11749,11769],{},[895,11750,11751,11753,11755,11757,11763],{},[898,11752,1688],{},[1708,11754,1710],{},[2505,11756,4003],{},[1753,11758,11759,11761],{},[898,11760,1658],{},[2505,11762,6090],{},[1753,11764,11765,11767],{},[898,11766,1673],{},[2505,11768,6097],{},[902,11770,11771],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,11773,11774,11777,11778,7897,11801,1826,11814,1695,11864,2511],{},[38,11775,11776],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,11779,11781],{"className":11780},[886],[888,11782,11783],{"xmlns":890},[892,11784,11785,11799],{},[895,11786,11787,11789,11791,11793,11795,11797],{},[898,11788,1688],{},[1708,11790,1716],{"stretchy":1715},[898,11792,1658],{},[1708,11794,1883],{"separator":1882},[898,11796,1673],{},[1708,11798,1721],{"stretchy":1715},[902,11800,6661],{"encoding":904},[883,11802,11804],{"className":11803},[886],[888,11805,11806],{"xmlns":890},[892,11807,11808,11812],{},[895,11809,11810],{},[898,11811,6676],{},[902,11813,6676],{"encoding":904},[883,11815,11817],{"className":11816},[886],[888,11818,11819],{"xmlns":890},[892,11820,11821,11861],{},[895,11822,11823,11825,11833,11835,11837,11845,11847,11849,11851,11853,11855,11857,11859],{},[898,11824,1658],{},[4754,11826,11827,11829,11831],{},[898,11828,1688],{},[898,11830,1658],{},[1708,11832,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,11834,2019],{},[898,11836,1673],{},[4754,11838,11839,11841,11843],{},[898,11840,1688],{},[898,11842,1673],{},[1708,11844,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,11846,1710],{},[898,11848,6676],{},[898,11850,1688],{},[1708,11852,1716],{"stretchy":1715},[898,11854,1658],{},[1708,11856,1883],{"separator":1882},[898,11858,1673],{},[1708,11860,1721],{"stretchy":1715},[902,11862,11863],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,11865,7872],{},[724,11867,11868,11871],{},[38,11869,11870],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,11873,11874,10802,11877,11917,11918,1343,11940,1343,11962,11984],{},[38,11875,11876],{},"5.12",[883,11878,11880],{"className":11879},[886],[888,11881,11882],{"xmlns":890},[892,11883,11884,11914],{},[895,11885,11886,11888,11890,11902],{},[898,11887,1688],{},[1708,11889,1710],{},[1753,11891,11892,11894],{},[898,11893,1658],{},[895,11895,11896,11898,11900],{},[2505,11897,2507],{},[898,11899,1799],{"mathvariant":1759},[2505,11901,3121],{},[1753,11903,11904,11906],{},[898,11905,1673],{},[895,11907,11908,11910,11912],{},[2505,11909,2507],{},[898,11911,1799],{"mathvariant":1759},[2505,11913,5867],{},[902,11915,11916],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,11919,11921],{"className":11920},[886],[888,11922,11923],{"xmlns":890},[892,11924,11925,11937],{},[895,11926,11927,11933,11935],{},[1743,11928,11929,11931],{},[898,11930,8115],{},[2505,11932,2784],{},[1708,11934,1710],{},[2505,11936,2507],{},[902,11938,11939],{"encoding":904},"q_0 = 1",[883,11941,11943],{"className":11942},[886],[888,11944,11945],{"xmlns":890},[892,11946,11947,11959],{},[895,11948,11949,11955,11957],{},[1743,11950,11951,11953],{},[898,11952,8115],{},[2505,11954,2507],{},[1708,11956,1710],{},[2505,11958,3132],{},[902,11960,11961],{"encoding":904},"q_1 = 2",[883,11963,11965],{"className":11964},[886],[888,11966,11967],{"xmlns":890},[892,11968,11969,11981],{},[895,11970,11971,11977,11979],{},[1743,11972,11973,11975],{},[898,11974,8115],{},[2505,11976,3132],{},[1708,11978,1710],{},[2505,11980,3121],{},[902,11982,11983],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,11986,11987,10802,11990,12030,12031,1343,12059,1343,12087,1343,12116,1343,12145,1343,12174,1343,12203,1343,12233,1343,12262,2155],{},[38,11988,11989],{},"5.13",[883,11991,11993],{"className":11992},[886],[888,11994,11995],{"xmlns":890},[892,11996,11997,12027],{},[895,11998,11999,12001,12003,12015],{},[898,12000,1688],{},[1708,12002,1710],{},[1753,12004,12005,12007],{},[898,12006,1658],{},[895,12008,12009,12011,12013],{},[2505,12010,2507],{},[898,12012,1799],{"mathvariant":1759},[2505,12014,3121],{},[1753,12016,12017,12019],{},[898,12018,1673],{},[895,12020,12021,12023,12025],{},[2505,12022,2507],{},[898,12024,1799],{"mathvariant":1759},[2505,12026,3132],{},[902,12028,12029],{"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): ",[883,12032,12034],{"className":12033},[886],[888,12035,12036],{"xmlns":890},[892,12037,12038,12056],{},[895,12039,12040,12046,12048,12050,12052,12054],{},[1743,12041,12042,12044],{},[898,12043,1786],{},[2505,12045,2507],{},[1708,12047,6940],{"stretchy":1715},[2505,12049,2507],{},[1708,12051,8197],{"separator":1882},[2505,12053,2507],{},[1708,12055,6981],{"stretchy":1715},[902,12057,12058],{"encoding":904},"A_1[1; 1]",[883,12060,12062],{"className":12061},[886],[888,12063,12064],{"xmlns":890},[892,12065,12066,12084],{},[895,12067,12068,12074,12076,12078,12080,12082],{},[1743,12069,12070,12072],{},[898,12071,1786],{},[2505,12073,3132],{},[1708,12075,6940],{"stretchy":1715},[2505,12077,2507],{},[1708,12079,8197],{"separator":1882},[2505,12081,3998],{},[1708,12083,6981],{"stretchy":1715},[902,12085,12086],{"encoding":904},"A_2[1; 8]",[883,12088,12090],{"className":12089},[886],[888,12091,12092],{"xmlns":890},[892,12093,12094,12113],{},[895,12095,12096,12102,12104,12106,12108,12111],{},[1743,12097,12098,12100],{},[898,12099,1786],{},[2505,12101,3121],{},[1708,12103,6940],{"stretchy":1715},[2505,12105,2507],{},[1708,12107,8197],{"separator":1882},[2505,12109,12110],{},"27",[1708,12112,6981],{"stretchy":1715},[902,12114,12115],{"encoding":904},"A_3[1; 27]",[883,12117,12119],{"className":12118},[886],[888,12120,12121],{"xmlns":890},[892,12122,12123,12142],{},[895,12124,12125,12131,12133,12135,12137,12140],{},[1743,12126,12127,12129],{},[898,12128,1786],{},[2505,12130,5867],{},[1708,12132,6940],{"stretchy":1715},[2505,12134,3132],{},[1708,12136,8197],{"separator":1882},[2505,12138,12139],{},"0,353",[1708,12141,6981],{"stretchy":1715},[902,12143,12144],{"encoding":904},"A_4[2; 0{,}353]",[883,12146,12148],{"className":12147},[886],[888,12149,12150],{"xmlns":890},[892,12151,12152,12171],{},[895,12153,12154,12160,12162,12164,12166,12169],{},[1743,12155,12156,12158],{},[898,12157,1786],{},[2505,12159,3993],{},[1708,12161,6940],{"stretchy":1715},[2505,12163,3132],{},[1708,12165,8197],{"separator":1882},[2505,12167,12168],{},"2,828",[1708,12170,6981],{"stretchy":1715},[902,12172,12173],{"encoding":904},"A_5[2; 2{,}828]",[883,12175,12177],{"className":12176},[886],[888,12178,12179],{"xmlns":890},[892,12180,12181,12200],{},[895,12182,12183,12189,12191,12193,12195,12198],{},[1743,12184,12185,12187],{},[898,12186,1786],{},[2505,12188,3947],{},[1708,12190,6940],{"stretchy":1715},[2505,12192,3132],{},[1708,12194,8197],{"separator":1882},[2505,12196,12197],{},"9,545",[1708,12199,6981],{"stretchy":1715},[902,12201,12202],{"encoding":904},"A_6[2; 9{,}545]",[883,12204,12206],{"className":12205},[886],[888,12207,12208],{"xmlns":890},[892,12209,12210,12230],{},[895,12211,12212,12218,12220,12223,12225,12228],{},[1743,12213,12214,12216],{},[898,12215,1786],{},[2505,12217,5967],{},[1708,12219,6940],{"stretchy":1715},[2505,12221,12222],{},"1,5",[1708,12224,8197],{"separator":1882},[2505,12226,12227],{},"0,544",[1708,12229,6981],{"stretchy":1715},[902,12231,12232],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,12234,12236],{"className":12235},[886],[888,12237,12238],{"xmlns":890},[892,12239,12240,12259],{},[895,12241,12242,12248,12250,12252,12254,12257],{},[1743,12243,12244,12246],{},[898,12245,1786],{},[2505,12247,3998],{},[1708,12249,6940],{"stretchy":1715},[2505,12251,12222],{},[1708,12253,8197],{"separator":1882},[2505,12255,12256],{},"14,696",[1708,12258,6981],{"stretchy":1715},[902,12260,12261],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,12263,12265],{"className":12264},[886],[888,12266,12267],{"xmlns":890},[892,12268,12269,12287],{},[895,12270,12271,12277,12279,12281,12283,12285],{},[1743,12272,12273,12275],{},[898,12274,1786],{},[2505,12276,4635],{},[1708,12278,6940],{"stretchy":1715},[2505,12280,3132],{},[1708,12282,8197],{"separator":1882},[2505,12284,3993],{},[1708,12286,6981],{"stretchy":1715},[902,12288,12289],{"encoding":904},"A_9[2; 5]",[724,12291,12292,12295],{},[38,12293,12294],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,12297,12298,12301,12302,12332,12333,12346,12347,12361,12362,12381,12382,12401,12402,2155],{},[38,12299,12300],{},"5.15"," Produkce firmy je dána vztahem ",[883,12303,12305],{"className":12304},[886],[888,12306,12307],{"xmlns":890},[892,12308,12309,12329],{},[895,12310,12311,12313,12315,12317,12323],{},[898,12312,1688],{},[1708,12314,1710],{},[2505,12316,3132],{},[1753,12318,12319,12321],{},[898,12320,1658],{},[2505,12322,6097],{},[1753,12324,12325,12327],{},[898,12326,1673],{},[2505,12328,11575],{},[902,12330,12331],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,12334,12336],{"className":12335},[886],[888,12337,12338],{"xmlns":890},[892,12339,12340,12344],{},[895,12341,12342],{},[2505,12343,9238],{},[902,12345,9238],{"encoding":904}," pracovníků a disponuje-li ",[883,12348,12350],{"className":12349},[886],[888,12351,12352],{"xmlns":890},[892,12353,12354,12359],{},[895,12355,12356],{},[2505,12357,12358],{},"81",[902,12360,12358],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,12363,12365],{"className":12364},[886],[888,12366,12367],{"xmlns":890},[892,12368,12369,12379],{},[895,12370,12371,12373,12375,12377],{},[898,12372,1741],{},[898,12374,1975],{},[898,12376,1978],{},[898,12378,1981],{},[902,12380,8303],{"encoding":904},". (c) Vypočtěte ",[883,12383,12385],{"className":12384},[886],[888,12386,12387],{"xmlns":890},[892,12388,12389,12399],{},[895,12390,12391,12393,12395,12397],{},[898,12392,1741],{},[898,12394,1975],{},[898,12396,1978],{},[898,12398,1981],{},[902,12400,8303],{"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 ",[883,12403,12405],{"className":12404},[886],[888,12406,12407],{"xmlns":890},[892,12408,12409,12414],{},[895,12410,12411],{},[2505,12412,12413],{},"95",[902,12415,12413],{"encoding":904},[724,12417,12418,10802,12421,12453,12454,12473,12474,12487,12488,12501,12502,12516],{},[38,12419,12420],{},"5.16",[883,12422,12424],{"className":12423},[886],[888,12425,12426],{"xmlns":890},[892,12427,12428,12450],{},[895,12429,12430,12432,12434,12440,12442,12444],{},[898,12431,1688],{},[1708,12433,1710],{},[1753,12435,12436,12438],{},[898,12437,1673],{},[2505,12439,3132],{},[1708,12441,2019],{},[2505,12443,3132],{},[1753,12445,12446,12448],{},[898,12447,1658],{},[2505,12449,3132],{},[902,12451,12452],{"encoding":904},"Q = K^{2} + 2 L^{2}",". (a) Určete ",[883,12455,12457],{"className":12456},[886],[888,12458,12459],{"xmlns":890},[892,12460,12461,12471],{},[895,12462,12463,12465,12467,12469],{},[898,12464,1741],{},[898,12466,1975],{},[898,12468,1978],{},[898,12470,1981],{},[902,12472,8303],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,12475,12477],{"className":12476},[886],[888,12478,12479],{"xmlns":890},[892,12480,12481,12485],{},[895,12482,12483],{},[2505,12484,9704],{},[902,12486,9704],{"encoding":904}," pracovníky a ",[883,12489,12491],{"className":12490},[886],[888,12492,12493],{"xmlns":890},[892,12494,12495,12499],{},[895,12496,12497],{},[2505,12498,4902],{},[902,12500,4902],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,12503,12505],{"className":12504},[886],[888,12506,12507],{"xmlns":890},[892,12508,12509,12514],{},[895,12510,12511],{},[2505,12512,12513],{},"80",[902,12515,12513],{"encoding":904}," jednotek.",[724,12518,12519,12522,12523,1826,12553,2155],{},[38,12520,12521],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,12524,12526],{"className":12525},[886],[888,12527,12528],{"xmlns":890},[892,12529,12530,12550],{},[895,12531,12532,12534,12536,12538,12544],{},[898,12533,1688],{},[1708,12535,1710],{},[898,12537,1786],{},[1753,12539,12540,12542],{},[898,12541,1658],{},[898,12543,207],{},[1753,12545,12546,12548],{},[898,12547,1673],{},[898,12549,1923],{},[902,12551,12552],{"encoding":904},"Q = A L^{a} K^{b}",[883,12554,12556],{"className":12555},[886],[888,12557,12558],{"xmlns":890},[892,12559,12560,12590],{},[895,12561,12562,12564,12566,12568,12570,12572,12580,12582],{},[898,12563,1741],{},[898,12565,1975],{},[898,12567,1978],{},[898,12569,1981],{},[1708,12571,1710],{},[3194,12573,12574],{"scriptlevel":2784,"displaystyle":1715},[2358,12575,12576,12578],{},[898,12577,207],{},[898,12579,1923],{},[1708,12581,3703],{},[3194,12583,12584],{"scriptlevel":2784,"displaystyle":1715},[2358,12585,12586,12588],{},[898,12587,1673],{},[898,12589,1658],{},[902,12591,12592],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,12594,12596],{"id":12595},"klíčové-pojmy","Klíčové pojmy",[120,12598,12599,12632,12660,12669,12719,12750,12803,12826,12881,12954,13032,13075,13107,13140,13181,13253,13314,13380,13397,13470,13536,13588,13644,13678,13721],{},[123,12600,12601,12604,12605,1661,12618,12631],{},[38,12602,12603],{},"Faktory (vstupy) produkce:"," práce ",[883,12606,12608],{"className":12607},[886],[888,12609,12610],{"xmlns":890},[892,12611,12612,12616],{},[895,12613,12614],{},[898,12615,1658],{},[902,12617,1658],{"encoding":904},[883,12619,12621],{"className":12620},[886],[888,12622,12623],{"xmlns":890},[892,12624,12625,12629],{},[895,12626,12627],{},[898,12628,1673],{},[902,12630,1673],{"encoding":904},", půda.",[123,12633,12634,12636,12637,2155],{},[38,12635,10796],{}," — ",[883,12638,12640],{"className":12639},[886],[888,12641,12642],{"xmlns":890},[892,12643,12644,12658],{},[895,12645,12646,12648,12650,12652,12654,12656],{},[898,12647,1688],{},[1708,12649,1710],{},[898,12651,1688],{},[1708,12653,1716],{"stretchy":1715},[898,12655,1658],{},[1708,12657,1721],{"stretchy":1715},[902,12659,1724],{"encoding":904},[123,12661,12662,1695,12664,5149,12667,2155],{},[38,12663,859],{},[614,12665,12666],{},"production function",[38,12668,2258],{},[123,12670,12671,1729,12673,2155],{},[38,12672,2305],{},[883,12674,12676],{"className":12675},[886],[888,12677,12678],{"xmlns":890},[892,12679,12680,12716],{},[895,12681,12682,12684,12690,12692,12694,12696,12698,12700,12702,12704,12710,12712,12714],{},[898,12683,1741],{},[1743,12685,12686,12688],{},[898,12687,1747],{},[898,12689,1658],{},[1708,12691,1710],{},[898,12693,2364],{},[898,12695,1688],{},[898,12697,1799],{"mathvariant":1759},[898,12699,2364],{},[898,12701,1658],{},[1708,12703,1710],{},[1753,12705,12706,12708],{},[898,12707,1688],{},[1708,12709,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,12711,1716],{"stretchy":1715},[898,12713,1658],{},[1708,12715,1721],{"stretchy":1715},[902,12717,12718],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,12720,12721,1729,12723,2155],{},[38,12722,3274],{},[883,12724,12726],{"className":12725},[886],[888,12727,12728],{"xmlns":890},[892,12729,12730,12748],{},[895,12731,12732,12734,12740,12742,12744,12746],{},[898,12733,1786],{},[1743,12735,12736,12738],{},[898,12737,1747],{},[898,12739,1658],{},[1708,12741,1710],{},[898,12743,1688],{},[898,12745,1799],{"mathvariant":1759},[898,12747,1658],{},[902,12749,1804],{"encoding":904},[123,12751,12752,12754,12755,1826,12772,2155],{},[38,12753,2741],{}," — od určitého ",[883,12756,12758],{"className":12757},[886],[888,12759,12760],{"xmlns":890},[892,12761,12762,12770],{},[895,12763,12764],{},[1743,12765,12766,12768],{},[898,12767,1658],{},[2505,12769,2784],{},[902,12771,2787],{"encoding":904},[883,12773,12775],{"className":12774},[886],[888,12776,12777],{"xmlns":890},[892,12778,12779,12801],{},[895,12780,12781,12791,12793,12795,12797,12799],{},[1753,12782,12783,12785],{},[898,12784,1688],{},[895,12786,12787,12789],{},[1708,12788,1761],{"mathvariant":1759},[1708,12790,1761],{"mathvariant":1759},[1708,12792,1716],{"stretchy":1715},[898,12794,1658],{},[1708,12796,1721],{"stretchy":1715},[1708,12798,2932],{},[2505,12800,2784],{},[902,12802,2937],{"encoding":904},[123,12804,12805,1729,12808,12825],{},[38,12806,12807],{},"Inflexní bod",[883,12809,12811],{"className":12810},[886],[888,12812,12813],{"xmlns":890},[892,12814,12815,12823],{},[895,12816,12817],{},[1743,12818,12819,12821],{},[898,12820,1658],{},[2505,12822,2784],{},[902,12824,2787],{"encoding":904}," — přechod z konvexity do konkavity.",[123,12827,12828,1729,12831,12636,12848,2155],{},[38,12829,12830],{},"Bod maxima produkce",[883,12832,12834],{"className":12833},[886],[888,12835,12836],{"xmlns":890},[892,12837,12838,12846],{},[895,12839,12840],{},[1743,12841,12842,12844],{},[898,12843,1658],{},[2505,12845,2507],{},[902,12847,2979],{"encoding":904},[883,12849,12851],{"className":12850},[886],[888,12852,12853],{"xmlns":890},[892,12854,12855,12879],{},[895,12856,12857,12859,12865,12867,12873,12875,12877],{},[898,12858,1741],{},[1743,12860,12861,12863],{},[898,12862,1747],{},[898,12864,1658],{},[1708,12866,1716],{"stretchy":1715},[1743,12868,12869,12871],{},[898,12870,1658],{},[2505,12872,2507],{},[1708,12874,1721],{"stretchy":1715},[1708,12876,1710],{},[2505,12878,2784],{},[902,12880,3014],{"encoding":904},[123,12882,12883,12905,12906,1826,12925,2155],{},[38,12884,12885,12886],{},"Princip maximalizace ",[883,12887,12889],{"className":12888},[886],[888,12890,12891],{"xmlns":890},[892,12892,12893,12903],{},[895,12894,12895,12897],{},[898,12896,1786],{},[1743,12898,12899,12901],{},[898,12900,1747],{},[898,12902,1658],{},[902,12904,1825],{"encoding":904}," — v bodě maxima ",[883,12907,12909],{"className":12908},[886],[888,12910,12911],{"xmlns":890},[892,12912,12913,12923],{},[895,12914,12915,12917],{},[898,12916,1786],{},[1743,12918,12919,12921],{},[898,12920,1747],{},[898,12922,1658],{},[902,12924,1825],{"encoding":904},[883,12926,12928],{"className":12927},[886],[888,12929,12930],{"xmlns":890},[892,12931,12932,12952],{},[895,12933,12934,12936,12942,12944,12946],{},[898,12935,1741],{},[1743,12937,12938,12940],{},[898,12939,1747],{},[898,12941,1658],{},[1708,12943,1710],{},[898,12945,1786],{},[1743,12947,12948,12950],{},[898,12949,1747],{},[898,12951,1658],{},[902,12953,1856],{"encoding":904},[123,12955,12956,1729,12959,1343,12998,1343,13015,2155],{},[38,12957,12958],{},"Polynomiální produkční funkce",[883,12960,12962],{"className":12961},[886],[888,12963,12964],{"xmlns":890},[892,12965,12966,12996],{},[895,12967,12968,12970,12972,12974,12976,12978,12980,12986,12988,12990],{},[898,12969,1688],{},[1708,12971,1716],{"stretchy":1715},[898,12973,1658],{},[1708,12975,1721],{"stretchy":1715},[1708,12977,1710],{},[898,12979,207],{},[1753,12981,12982,12984],{},[898,12983,1658],{},[2505,12985,3121],{},[1708,12987,2019],{},[898,12989,1923],{},[1753,12991,12992,12994],{},[898,12993,1658],{},[2505,12995,3132],{},[902,12997,3135],{"encoding":904},[883,12999,13001],{"className":13000},[886],[888,13002,13003],{"xmlns":890},[892,13004,13005,13013],{},[895,13006,13007,13009,13011],{},[898,13008,207],{},[1708,13010,2932],{},[2505,13012,2784],{},[902,13014,3154],{"encoding":904},[883,13016,13018],{"className":13017},[886],[888,13019,13020],{"xmlns":890},[892,13021,13022,13030],{},[895,13023,13024,13026,13028],{},[898,13025,1923],{},[1708,13027,2854],{},[2505,13029,2784],{},[902,13031,3172],{"encoding":904},[123,13033,13034,1729,13037,2155],{},[38,13035,13036],{},"Diferenciál produkce",[883,13038,13040],{"className":13039},[886],[888,13041,13042],{"xmlns":890},[892,13043,13044,13072],{},[895,13045,13046,13048,13050,13052,13054,13056,13058,13060,13066,13068,13070],{},[898,13047,2633],{"mathvariant":1759},[898,13049,1688],{},[1708,13051,2638],{},[898,13053,2364],{},[898,13055,1688],{},[1708,13057,1710],{},[898,13059,1741],{},[1743,13061,13062,13064],{},[898,13063,1747],{},[898,13065,1658],{},[2247,13067,2659],{},[898,13069,2364],{},[898,13071,1658],{},[902,13073,13074],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,13076,13077,12636,13079,2155],{},[38,13078,11318],{},[883,13080,13082],{"className":13081},[886],[888,13083,13084],{"xmlns":890},[892,13085,13086,13104],{},[895,13087,13088,13090,13092,13094,13096,13098,13100,13102],{},[898,13089,1688],{},[1708,13091,1710],{},[898,13093,1688],{},[1708,13095,1716],{"stretchy":1715},[898,13097,1658],{},[1708,13099,1883],{"separator":1882},[898,13101,1673],{},[1708,13103,1721],{"stretchy":1715},[902,13105,13106],{"encoding":904},"Q = Q(L, K)",[123,13108,13109,12636,13111,2155],{},[38,13110,5354],{},[883,13112,13114],{"className":13113},[886],[888,13115,13116],{"xmlns":890},[892,13117,13118,13138],{},[895,13119,13120,13122,13124,13126,13132],{},[898,13121,1688],{},[1708,13123,1710],{},[898,13125,1786],{},[1753,13127,13128,13130],{},[898,13129,1658],{},[898,13131,207],{},[1753,13133,13134,13136],{},[898,13135,1673],{},[898,13137,1923],{},[902,13139,1926],{"encoding":904},[123,13141,13142,12636,13145,13180],{},[38,13143,13144],{},"Ryzí Cobb-Douglas",[883,13146,13148],{"className":13147},[886],[888,13149,13150],{"xmlns":890},[892,13151,13152,13178],{},[895,13153,13154,13156,13158,13160,13166],{},[898,13155,1688],{},[1708,13157,1710],{},[898,13159,1786],{},[1753,13161,13162,13164],{},[898,13163,1658],{},[898,13165,207],{},[1753,13167,13168,13170],{},[898,13169,1673],{},[895,13171,13172,13174,13176],{},[2505,13173,2507],{},[1708,13175,2726],{},[898,13177,207],{},[902,13179,6192],{"encoding":904}," (konstantní výnosy).",[123,13182,13183,12636,13185,2155],{},[38,13184,6914],{},[883,13186,13188],{"className":13187},[886],[888,13189,13190],{"xmlns":890},[892,13191,13192,13250],{},[895,13193,13194,13196,13198,13200,13202,13204,13206,13208,13210,13212,13222,13224,13226,13236],{},[898,13195,1688],{},[1708,13197,1710],{},[898,13199,1786],{},[1708,13201,6940],{"stretchy":1715},[1708,13203,1716],{"stretchy":1715},[2505,13205,2507],{},[1708,13207,2726],{},[898,13209,207],{},[1708,13211,1721],{"stretchy":1715},[1753,13213,13214,13216],{},[898,13215,1658],{},[895,13217,13218,13220],{},[1708,13219,2726],{},[898,13221,1923],{},[1708,13223,2019],{},[898,13225,207],{},[1753,13227,13228,13230],{},[898,13229,1673],{},[895,13231,13232,13234],{},[1708,13233,2726],{},[898,13235,1923],{},[1753,13237,13238,13240],{},[1708,13239,6981],{"stretchy":1715},[895,13241,13242,13244,13246,13248],{},[1708,13243,2726],{},[2505,13245,2507],{},[898,13247,1799],{"mathvariant":1759},[898,13249,1923],{},[902,13251,13252],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,13254,13255,1695,13258,5149,13280,1695,13283,13313],{},[38,13256,13257],{},"Lineární",[883,13259,13261],{"className":13260},[886],[888,13262,13263],{"xmlns":890},[892,13264,13265,13277],{},[895,13266,13267,13269,13271,13273,13275],{},[898,13268,207],{},[898,13270,1658],{},[1708,13272,2019],{},[898,13274,1923],{},[898,13276,1673],{},[902,13278,13279],{"encoding":904},"aL + bK",[38,13281,13282],{},"Leontiefova",[883,13284,13286],{"className":13285},[886],[888,13287,13288],{"xmlns":890},[892,13289,13290,13310],{},[895,13291,13292,13294,13296,13298,13300,13302,13304,13306,13308],{},[898,13293,7146],{},[1708,13295,7149],{},[1708,13297,1716],{"stretchy":1715},[898,13299,207],{},[898,13301,1658],{},[1708,13303,1883],{"separator":1882},[898,13305,1923],{},[898,13307,1673],{},[1708,13309,1721],{"stretchy":1715},[902,13311,13312],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,13315,13316,12636,13332,2155],{},[38,13317,13318,13319],{},"Homogenita stupně ",[883,13320,13322],{"className":13321},[886],[888,13323,13324],{"xmlns":890},[892,13325,13326,13330],{},[895,13327,13328],{},[898,13329,6676],{},[902,13331,6676],{"encoding":904},[883,13333,13335],{"className":13334},[886],[888,13336,13337],{"xmlns":890},[892,13338,13339,13377],{},[895,13340,13341,13343,13345,13347,13349,13351,13353,13355,13357,13359,13365,13367,13369,13371,13373,13375],{},[898,13342,1688],{},[1708,13344,1716],{"stretchy":1715},[898,13346,5498],{},[898,13348,1658],{},[1708,13350,1883],{"separator":1882},[898,13352,5498],{},[898,13354,1673],{},[1708,13356,1721],{"stretchy":1715},[1708,13358,1710],{},[1753,13360,13361,13363],{},[898,13362,5498],{},[898,13364,6676],{},[898,13366,1688],{},[1708,13368,1716],{"stretchy":1715},[898,13370,1658],{},[1708,13372,1883],{"separator":1882},[898,13374,1673],{},[1708,13376,1721],{"stretchy":1715},[902,13378,13379],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,13381,13382,6290],{},[38,13383,6223,13384],{},[883,13385,13387],{"className":13386},[886],[888,13388,13389],{"xmlns":890},[892,13390,13391,13395],{},[895,13392,13393],{},[898,13394,1786],{},[902,13396,1786],{"encoding":904},[123,13398,13399,13401,13402,13424,13425,13447,13448,2511],{},[38,13400,5715],{}," — konstantní (",[883,13403,13405],{"className":13404},[886],[888,13406,13407],{"xmlns":890},[892,13408,13409,13421],{},[895,13410,13411,13413,13415,13417,13419],{},[898,13412,207],{},[1708,13414,2019],{},[898,13416,1923],{},[1708,13418,1710],{},[2505,13420,2507],{},[902,13422,13423],{"encoding":904},"a+b=1","), rostoucí (",[883,13426,13428],{"className":13427},[886],[888,13429,13430],{"xmlns":890},[892,13431,13432,13444],{},[895,13433,13434,13436,13438,13440,13442],{},[898,13435,207],{},[1708,13437,2019],{},[898,13439,1923],{},[1708,13441,2854],{},[2505,13443,2507],{},[902,13445,13446],{"encoding":904},"a+b>1","), klesající (",[883,13449,13451],{"className":13450},[886],[888,13452,13453],{"xmlns":890},[892,13454,13455,13467],{},[895,13456,13457,13459,13461,13463,13465],{},[898,13458,207],{},[1708,13460,2019],{},[898,13462,1923],{},[1708,13464,2932],{},[2505,13466,2507],{},[902,13468,13469],{"encoding":904},"a+b\u003C1",[123,13471,13472,1729,13474,1343,13504,1729,13506,2155],{},[38,13473,2305],{},[883,13475,13477],{"className":13476},[886],[888,13478,13479],{"xmlns":890},[892,13480,13481,13501],{},[895,13482,13483,13485,13491,13493],{},[898,13484,1741],{},[1743,13486,13487,13489],{},[898,13488,1747],{},[898,13490,1658],{},[1708,13492,1710],{},[4754,13494,13495,13497,13499],{},[898,13496,1688],{},[898,13498,1658],{},[1708,13500,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,13502,13503],{"encoding":904},"MP_L = Q'_L",[38,13505,5286],{},[883,13507,13509],{"className":13508},[886],[888,13510,13511],{"xmlns":890},[892,13512,13513,13533],{},[895,13514,13515,13517,13523,13525],{},[898,13516,1741],{},[1743,13518,13519,13521],{},[898,13520,1747],{},[898,13522,1673],{},[1708,13524,1710],{},[4754,13526,13527,13529,13531],{},[898,13528,1688],{},[898,13530,1673],{},[1708,13532,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,13534,13535],{"encoding":904},"MP_K = Q'_K",[123,13537,13538,1729,13540,2155],{},[38,13539,7527],{},[883,13541,13543],{"className":13542},[886],[888,13544,13545],{"xmlns":890},[892,13546,13547,13585],{},[895,13548,13549,13551,13553,13555,13557,13563,13565,13567,13569,13571,13573,13579,13581,13583],{},[898,13550,2364],{},[898,13552,1688],{},[1708,13554,1710],{},[898,13556,1741],{},[1743,13558,13559,13561],{},[898,13560,1747],{},[898,13562,1658],{},[2247,13564,2659],{},[898,13566,2364],{},[898,13568,1658],{},[1708,13570,2019],{},[898,13572,1741],{},[1743,13574,13575,13577],{},[898,13576,1747],{},[898,13578,1673],{},[2247,13580,2659],{},[898,13582,2364],{},[898,13584,1673],{},[902,13586,13587],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,13589,13590,12636,13592,2155],{},[38,13591,7872],{},[883,13593,13595],{"className":13594},[886],[888,13596,13597],{"xmlns":890},[892,13598,13599,13641],{},[895,13600,13601,13603,13611,13613,13615,13623,13625,13627,13629,13631,13633,13635,13637,13639],{},[898,13602,1658],{},[4754,13604,13605,13607,13609],{},[898,13606,1688],{},[898,13608,1658],{},[1708,13610,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,13612,2019],{},[898,13614,1673],{},[4754,13616,13617,13619,13621],{},[898,13618,1688],{},[898,13620,1673],{},[1708,13622,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,13624,1710],{},[898,13626,6676],{},[2247,13628,2659],{},[898,13630,1688],{},[1708,13632,1716],{"stretchy":1715},[898,13634,1658],{},[1708,13636,1883],{"separator":1882},[898,13638,1673],{},[1708,13640,1721],{"stretchy":1715},[902,13642,13643],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,13645,13646,13649,13650,2155],{},[38,13647,13648],{},"Izokvanta"," — křivka ",[883,13651,13653],{"className":13652},[886],[888,13654,13655],{"xmlns":890},[892,13656,13657,13675],{},[895,13658,13659,13661,13663,13665,13667,13669,13671,13673],{},[898,13660,1688],{},[1708,13662,1716],{"stretchy":1715},[898,13664,1658],{},[1708,13666,1883],{"separator":1882},[898,13668,1673],{},[1708,13670,1721],{"stretchy":1715},[1708,13672,1710],{},[898,13674,8115],{},[902,13676,13677],{"encoding":904},"Q(L, K) = q",[123,13679,13680,1729,13682,2155],{},[38,13681,8308],{},[883,13683,13685],{"className":13684},[886],[888,13686,13687],{"xmlns":890},[892,13688,13689,13719],{},[895,13690,13691,13693,13695,13697,13699,13701,13703,13709,13711,13713],{},[898,13692,1741],{},[898,13694,1975],{},[898,13696,1978],{},[898,13698,1981],{},[1708,13700,1710],{},[898,13702,1741],{},[1743,13704,13705,13707],{},[898,13706,1747],{},[898,13708,1658],{},[898,13710,1799],{"mathvariant":1759},[898,13712,1741],{},[1743,13714,13715,13717],{},[898,13716,1747],{},[898,13718,1673],{},[902,13720,2004],{"encoding":904},[123,13722,13723,1729,13726,2155],{},[38,13724,13725],{},"Substituční vztah",[883,13727,13729],{"className":13728},[886],[888,13730,13731],{"xmlns":890},[892,13732,13733,13757],{},[895,13734,13735,13737,13739,13741,13743,13745,13747,13749,13751,13753,13755],{},[898,13736,2633],{"mathvariant":1759},[898,13738,1673],{},[1708,13740,2638],{},[1708,13742,2726],{},[898,13744,1741],{},[898,13746,1975],{},[898,13748,1978],{},[898,13750,1981],{},[2247,13752,2659],{},[898,13754,2364],{},[898,13756,1658],{},[902,13758,13759],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,13761,13763],{"id":13762},"navigace","Navigace",[120,13765,13766,13867,13876,13884],{},[123,13767,13768,1729,13771,13774,13775,1343,13778,13781,13782,13785,13786,13805,13806,13826,13827,13831,13832,13851,13852,2511],{},[38,13769,13770],{},"Související témata:",[207,13772,784],{"className":13773,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,13776,2162],{"className":13777,"dataFsResolvedFilePath":764,"href":765},[210],[207,13779,793],{"className":13780,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,13783,880],{"className":13784,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,13787,13789],{"className":13788},[886],[888,13790,13791],{"xmlns":890},[892,13792,13793,13803],{},[895,13794,13795,13797,13799,13801],{},[898,13796,1741],{},[898,13798,1975],{},[898,13800,1978],{},[898,13802,1981],{},[902,13804,8303],{"encoding":904}," ↔ ",[883,13807,13809],{"className":13808},[886],[888,13810,13811],{"xmlns":890},[892,13812,13813,13823],{},[895,13814,13815,13817,13819,13821],{},[898,13816,1741],{},[898,13818,1975],{},[898,13820,3455],{},[898,13822,1981],{},[902,13824,13825],{"encoding":904},"MRCS","), ",[207,13828,13830],{"className":13829,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (analogie principu max ",[883,13833,13835],{"className":13834},[886],[888,13836,13837],{"xmlns":890},[892,13838,13839,13849],{},[895,13840,13841,13843],{},[898,13842,1786],{},[1743,13844,13845,13847],{},[898,13846,1747],{},[898,13848,1658],{},[902,13850,1825],{"encoding":904}," ↔ min ",[883,13853,13855],{"className":13854},[886],[888,13856,13857],{"xmlns":890},[892,13858,13859,13865],{},[895,13860,13861,13863],{},[898,13862,1786],{},[898,13864,3455],{},[902,13866,3458],{"encoding":904},[123,13868,13869,1729,13872,2155],{},[38,13870,13871],{},"Předchozí:",[207,13873,13875],{"className":13874,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita",[123,13877,13878,1729,13881,2155],{},[38,13879,13880],{},"Přednáška:",[207,13882,1094],{"className":13883,"dataFsResolvedFilePath":838,"href":839},[210],[123,13885,13886,1729,13889,2155],{},[38,13887,13888],{},"Kurz:",[207,13890,13894],{"className":13891,"dataFsResolvedFilePath":13892,"href":13893},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",{"title":641,"searchDepth":642,"depth":642,"links":13896},[13897,13898,13899,13903,13905,13910,13911,13918,13919,13921,13922,13923,13925,13930,13931,13932,13936,13937],{"id":2028,"depth":642,"text":2029},{"id":2169,"depth":642,"text":2170},{"id":2279,"depth":642,"text":13900,"children":13901},"Mezní produkt práce (MPLMP_L)",[13902],{"id":2740,"depth":649,"text":2741},{"id":3249,"depth":642,"text":13904},"Průměrný produkt práce (APLAP_L)",{"id":3367,"depth":642,"text":3368,"children":13906},[13907,13908,13909],{"id":3613,"depth":649,"text":3614},{"id":3927,"depth":649,"text":3928},{"id":4667,"depth":649,"text":4668},{"id":5249,"depth":642,"text":5250},{"id":5353,"depth":642,"text":5354,"children":13912},[13913,13914,13916,13917],{"id":5714,"depth":649,"text":5715},{"id":6222,"depth":649,"text":13915},"Parametr efektivity AA",{"id":6293,"depth":649,"text":6294},{"id":6633,"depth":649,"text":6634},{"id":6825,"depth":642,"text":6826},{"id":7170,"depth":642,"text":13920},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":7866,"depth":642,"text":7867},{"id":2096,"depth":642,"text":8072},{"id":8282,"depth":642,"text":13924},"Mezní míra technické substituce (MRTSMRTS)",{"id":9156,"depth":642,"text":9157,"children":13926},[13927,13928,13929],{"id":9160,"depth":649,"text":9161},{"id":9811,"depth":649,"text":9812},{"id":10093,"depth":649,"text":10094},{"id":10439,"depth":642,"text":10440},{"id":10752,"depth":642,"text":10753},{"id":10791,"depth":642,"text":10792,"children":13933},[13934,13935],{"id":10795,"depth":649,"text":10796},{"id":11317,"depth":649,"text":11318},{"id":12595,"depth":642,"text":12596},{"id":13762,"depth":642,"text":13763},"2026-04-22",{},"\u002Ftopics\u002Fprodukce",{"title":1629,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,13945,13946,13947,13948,2096,13949,13950],"produkce","produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","topic","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y","topics",{"zapisku":1625,"topics":13955,"summaries":13956,"outputs":13957},15,5,1,[13959,15802,21472,23011,23883,28151,29756,39615,48601,62648,66937,86266,97604,106563,106851],{"id":13960,"title":13961,"body":13962,"course":1128,"courses":659,"created":1129,"description":15791,"extension":661,"meta":15792,"navigation":664,"path":15793,"seo":15794,"sources":15795,"stem":15796,"tags":15797,"type":13951,"updated":677,"__hash__":15801},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":13963,"toc":15774},[13964,13967,13986,13990,14069,14072,14196,14340,14342,14422,14426,14485,14535,14542,14546,14679,14729,14733,14772,14838,14907,14915,14919,14957,15029,15032,15107,15155,15199,15203,15207,15277,15281,15330,15407,15414,15417,15469,15738,15740],[12,13965,13961],{"id":13966},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,13968,13969,13970,13974,13975,13978,13979,13982,13983,2155],{},"Matematický aparát kurzu ",[207,13971,13973],{"className":13972,"dataFsResolvedFilePath":13892,"href":13893},[210],"ImeK",". Bez derivace se neobejdou ",[38,13976,13977],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,13980,13981],{},"maximalizace zisku"," ani ",[38,13984,13985],{},"minimalizace nákladů",[115,13987,13989],{"id":13988},"funkce-a-polynomy","Funkce a polynomy",[724,13991,13992,13993,14020,14021,14034,14035,14048,14049,2155],{},"Funkce jedné proměnné ",[883,13994,13996],{"className":13995},[886],[888,13997,13998],{"xmlns":890},[892,13999,14000,14017],{},[895,14001,14002,14005,14007,14010,14012,14015],{},[898,14003,14004],{},"y",[1708,14006,1710],{},[898,14008,14009],{},"f",[1708,14011,1716],{"stretchy":1715},[898,14013,14014],{},"x",[1708,14016,1721],{"stretchy":1715},[902,14018,14019],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,14022,14024],{"className":14023},[886],[888,14025,14026],{"xmlns":890},[892,14027,14028,14032],{},[895,14029,14030],{},[898,14031,14014],{},[902,14033,14014],{"encoding":904}," (nezávislá) → ",[883,14036,14038],{"className":14037},[886],[888,14039,14040],{"xmlns":890},[892,14041,14042,14046],{},[895,14043,14044],{},[898,14045,14004],{},[902,14047,14004],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,14050,14052],{"className":14051},[886],[888,14053,14054],{"xmlns":890},[892,14055,14056,14066],{},[895,14057,14058,14060,14062,14064],{},[898,14059,14009],{},[1708,14061,1716],{"stretchy":1715},[898,14063,207],{},[1708,14065,1721],{"stretchy":1715},[902,14067,14068],{"encoding":904},"f(a)",[724,14070,14071],{},"Polynomy:",[120,14073,14074,14105,14146],{},[123,14075,14076],{},[152,14077,14078],{},[123,14079,14080,14081],{},"stupně: ",[883,14082,14084],{"className":14083},[886],[888,14085,14086],{"xmlns":890},[892,14087,14088,14102],{},[895,14089,14090,14092,14094,14096,14098,14100],{},[898,14091,14004],{},[1708,14093,1710],{},[898,14095,207],{},[898,14097,14014],{},[1708,14099,2019],{},[898,14101,1923],{},[902,14103,14104],{"encoding":904},"y = ax + b",[123,14106,14107],{},[152,14108,14109],{"start":642},[123,14110,14080,14111],{},[883,14112,14114],{"className":14113},[886],[888,14115,14116],{"xmlns":890},[892,14117,14118,14143],{},[895,14119,14120,14122,14124,14126,14132,14134,14136,14138,14140],{},[898,14121,14004],{},[1708,14123,1710],{},[898,14125,207],{},[1753,14127,14128,14130],{},[898,14129,14014],{},[2505,14131,3132],{},[1708,14133,2019],{},[898,14135,1923],{},[898,14137,14014],{},[1708,14139,2019],{},[898,14141,14142],{},"c",[902,14144,14145],{"encoding":904},"y = ax^2 + bx + c",[123,14147,14148],{},[152,14149,14150],{"start":649},[123,14151,14080,14152],{},[883,14153,14155],{"className":14154},[886],[888,14156,14157],{"xmlns":890},[892,14158,14159,14193],{},[895,14160,14161,14163,14165,14167,14173,14175,14177,14183,14185,14187,14189,14191],{},[898,14162,14004],{},[1708,14164,1710],{},[898,14166,207],{},[1753,14168,14169,14171],{},[898,14170,14014],{},[2505,14172,3121],{},[1708,14174,2019],{},[898,14176,1923],{},[1753,14178,14179,14181],{},[898,14180,14014],{},[2505,14182,3132],{},[1708,14184,2019],{},[898,14186,14142],{},[898,14188,14014],{},[1708,14190,2019],{},[898,14192,2364],{},[902,14194,14195],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,14197,14198,1729,14201,14255,14256,14293,14294,2155],{},[38,14199,14200],{},"Příklad rozkladu:",[883,14202,14204],{"className":14203},[886],[888,14205,14206],{"xmlns":890},[892,14207,14208,14252],{},[895,14209,14210,14212,14214,14220,14222,14224,14226,14228,14230,14232,14234,14236,14238,14240,14242,14244,14246,14248,14250],{},[898,14211,14004],{},[1708,14213,1710],{},[1753,14215,14216,14218],{},[898,14217,14014],{},[2505,14219,3132],{},[1708,14221,2726],{},[2505,14223,3993],{},[898,14225,14014],{},[1708,14227,2019],{},[2505,14229,3947],{},[1708,14231,1710],{},[1708,14233,1716],{"stretchy":1715},[898,14235,14014],{},[1708,14237,2726],{},[2505,14239,3132],{},[1708,14241,1721],{"stretchy":1715},[1708,14243,1716],{"stretchy":1715},[898,14245,14014],{},[1708,14247,2726],{},[2505,14249,3121],{},[1708,14251,1721],{"stretchy":1715},[902,14253,14254],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,14257,14259],{"className":14258},[886],[888,14260,14261],{"xmlns":890},[892,14262,14263,14290],{},[895,14264,14265,14271,14273,14275,14277,14280,14286,14288],{},[1743,14266,14267,14269],{},[898,14268,14014],{},[2505,14270,2507],{},[1708,14272,1710],{},[2505,14274,3132],{},[1708,14276,1883],{"separator":1882},[2247,14278,14279],{}," ",[1743,14281,14282,14284],{},[898,14283,14014],{},[2505,14285,3132],{},[1708,14287,1710],{},[2505,14289,3121],{},[902,14291,14292],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,14295,14297],{"className":14296},[886],[888,14298,14299],{"xmlns":890},[892,14300,14301,14337],{},[895,14302,14303,14305,14307,14309,14311,14313,14321,14327,14329],{},[898,14304,14004],{},[1708,14306,1710],{},[1708,14308,1716],{"stretchy":1715},[898,14310,14014],{},[1708,14312,2726],{},[3194,14314,14315],{"scriptlevel":2784,"displaystyle":1715},[2358,14316,14317,14319],{},[2505,14318,3993],{},[2505,14320,3132],{},[1753,14322,14323,14325],{},[1708,14324,1721],{"stretchy":1715},[2505,14326,3132],{},[1708,14328,2726],{},[3194,14330,14331],{"scriptlevel":2784,"displaystyle":1715},[2358,14332,14333,14335],{},[2505,14334,2507],{},[2505,14336,5867],{},[902,14338,14339],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,14341,2162],{"id":1145},[724,14343,14344,14345,1348,14369,14397,14398,2155],{},"Označení ",[883,14346,14348],{"className":14347},[886],[888,14349,14350],{"xmlns":890},[892,14351,14352,14366],{},[895,14353,14354,14360,14362,14364],{},[1753,14355,14356,14358],{},[898,14357,14009],{},[1708,14359,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14361,1716],{"stretchy":1715},[898,14363,14014],{},[1708,14365,1721],{"stretchy":1715},[902,14367,14368],{"encoding":904},"f'(x)",[883,14370,14372],{"className":14371},[886],[888,14373,14374],{"xmlns":890},[892,14375,14376,14394],{},[895,14377,14378],{},[3194,14379,14380],{"scriptlevel":2784,"displaystyle":1882},[2358,14381,14382,14388],{},[895,14383,14384,14386],{},[898,14385,2364],{},[898,14387,14004],{},[895,14389,14390,14392],{},[898,14391,2364],{},[898,14393,14014],{},[902,14395,14396],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,14399,14401],{"className":14400},[886],[888,14402,14403],{"xmlns":890},[892,14404,14405,14419],{},[895,14406,14407,14413,14415,14417],{},[1753,14408,14409,14411],{},[898,14410,14009],{},[1708,14412,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14414,1716],{"stretchy":1715},[898,14416,207],{},[1708,14418,1721],{"stretchy":1715},[902,14420,14421],{"encoding":904},"f'(a)",[198,14423,14425],{"id":14424},"geometrická-interpretace","Geometrická interpretace",[724,14427,14428,14451,14452,14455,14456,14484],{},[883,14429,14431],{"className":14430},[886],[888,14432,14433],{"xmlns":890},[892,14434,14435,14449],{},[895,14436,14437,14443,14445,14447],{},[1753,14438,14439,14441],{},[898,14440,14009],{},[1708,14442,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14444,1716],{"stretchy":1715},[898,14446,207],{},[1708,14448,1721],{"stretchy":1715},[902,14450,14421],{"encoding":904}," = ",[38,14453,14454],{},"sklon tečny"," ke grafu funkce v bodě ",[883,14457,14459],{"className":14458},[886],[888,14460,14461],{"xmlns":890},[892,14462,14463,14481],{},[895,14464,14465,14467,14469,14471,14473,14475,14477,14479],{},[1708,14466,6940],{"stretchy":1715},[898,14468,207],{},[1708,14470,1883],{"separator":1882},[898,14472,14009],{},[1708,14474,1716],{"stretchy":1715},[898,14476,207],{},[1708,14478,1721],{"stretchy":1715},[1708,14480,6981],{"stretchy":1715},[902,14482,14483],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,14486,14487],{},[883,14488,14490],{"className":14489},[886],[888,14491,14492],{"xmlns":890},[892,14493,14494,14532],{},[895,14495,14496,14498,14500,14502,14504,14506,14508,14510,14516,14518,14520,14522,14524,14526,14528,14530],{},[898,14497,14004],{},[1708,14499,2726],{},[898,14501,14009],{},[1708,14503,1716],{"stretchy":1715},[898,14505,207],{},[1708,14507,1721],{"stretchy":1715},[1708,14509,1710],{},[1753,14511,14512,14514],{},[898,14513,14009],{},[1708,14515,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14517,1716],{"stretchy":1715},[898,14519,207],{},[1708,14521,1721],{"stretchy":1715},[1708,14523,1716],{"stretchy":1715},[898,14525,14014],{},[1708,14527,2726],{},[898,14529,207],{},[1708,14531,1721],{"stretchy":1715},[902,14533,14534],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,14536,14537],{},[3372,14538],{"alt":14539,"className":14540,"src":14541},"imek-derivace-tecna",[210,3376],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,14543,14545],{"id":14544},"inženýrská-interpretace","Inženýrská interpretace",[724,14547,14548,14451,14571,1729,14574,14587,14588,3405,14601,14619,14620,14633,14634,14647,14648,2486,14661,2788],{},[883,14549,14551],{"className":14550},[886],[888,14552,14553],{"xmlns":890},[892,14554,14555,14569],{},[895,14556,14557,14563,14565,14567],{},[1753,14558,14559,14561],{},[898,14560,14009],{},[1708,14562,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14564,1716],{"stretchy":1715},[898,14566,207],{},[1708,14568,1721],{"stretchy":1715},[902,14570,14421],{"encoding":904},[38,14572,14573],{},"rychlost změny",[883,14575,14577],{"className":14576},[886],[888,14578,14579],{"xmlns":890},[892,14580,14581,14585],{},[895,14582,14583],{},[898,14584,14004],{},[902,14586,14004],{"encoding":904}," vzhledem k ",[883,14589,14591],{"className":14590},[886],[888,14592,14593],{"xmlns":890},[892,14594,14595,14599],{},[895,14596,14597],{},[898,14598,14014],{},[902,14600,14014],{"encoding":904},[883,14602,14604],{"className":14603},[886],[888,14605,14606],{"xmlns":890},[892,14607,14608,14616],{},[895,14609,14610,14612,14614],{},[898,14611,14014],{},[1708,14613,1710],{},[898,14615,207],{},[902,14617,14618],{"encoding":904},"x = a","; přibližná změna ",[883,14621,14623],{"className":14622},[886],[888,14624,14625],{"xmlns":890},[892,14626,14627,14631],{},[895,14628,14629],{},[898,14630,14004],{},[902,14632,14004],{"encoding":904}," při změně ",[883,14635,14637],{"className":14636},[886],[888,14638,14639],{"xmlns":890},[892,14640,14641,14645],{},[895,14642,14643],{},[898,14644,14014],{},[902,14646,14014],{"encoding":904}," z ",[883,14649,14651],{"className":14650},[886],[888,14652,14653],{"xmlns":890},[892,14654,14655,14659],{},[895,14656,14657],{},[898,14658,207],{},[902,14660,207],{"encoding":904},[883,14662,14664],{"className":14663},[886],[888,14665,14666],{"xmlns":890},[892,14667,14668,14676],{},[895,14669,14670,14672,14674],{},[898,14671,207],{},[1708,14673,2019],{},[2505,14675,2507],{},[902,14677,14678],{"encoding":904},"a+1",[724,14680,14681],{},[883,14682,14684],{"className":14683},[886],[888,14685,14686],{"xmlns":890},[892,14687,14688,14726],{},[895,14689,14690,14692,14694,14696,14698,14700,14702,14704,14706,14708,14710,14712,14714,14720,14722,14724],{},[898,14691,14009],{},[1708,14693,1716],{"stretchy":1715},[898,14695,207],{},[1708,14697,2019],{},[2505,14699,2507],{},[1708,14701,1721],{"stretchy":1715},[1708,14703,2638],{},[898,14705,14009],{},[1708,14707,1716],{"stretchy":1715},[898,14709,207],{},[1708,14711,1721],{"stretchy":1715},[1708,14713,2019],{},[1753,14715,14716,14718],{},[898,14717,14009],{},[1708,14719,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14721,1716],{"stretchy":1715},[898,14723,207],{},[1708,14725,1721],{"stretchy":1715},[902,14727,14728],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,14730,14732],{"id":14731},"příklad-mezní-náklady","Příklad — mezní náklady",[724,14734,14735,14736,2155],{},"Celkové náklady ",[883,14737,14739],{"className":14738},[886],[888,14740,14741],{"xmlns":890},[892,14742,14743,14769],{},[895,14744,14745,14747,14749,14751,14753,14755,14757,14759,14761,14763],{},[898,14746,1978],{},[898,14748,3455],{},[1708,14750,1710],{},[2505,14752,11613],{},[1708,14754,2019],{},[2505,14756,3132],{},[898,14758,1688],{},[1708,14760,2019],{},[2505,14762,10909],{},[1753,14764,14765,14767],{},[898,14766,1688],{},[2505,14768,3132],{},[902,14770,14771],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,14773,14774,14775,14811,14812,2155],{},"Mezní náklady: ",[883,14776,14778],{"className":14777},[886],[888,14779,14780],{"xmlns":890},[892,14781,14782,14808],{},[895,14783,14784,14786,14788,14790,14792,14798,14800,14802,14804,14806],{},[898,14785,1741],{},[898,14787,3455],{},[1708,14789,1710],{},[898,14791,1978],{},[1753,14793,14794,14796],{},[898,14795,3455],{},[1708,14797,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14799,1710],{},[2505,14801,3132],{},[1708,14803,2019],{},[2505,14805,3958],{},[898,14807,1688],{},[902,14809,14810],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,14813,14815],{"className":14814},[886],[888,14816,14817],{"xmlns":890},[892,14818,14819,14835],{},[895,14820,14821,14823,14825,14827,14829,14831,14833],{},[898,14822,1741],{},[898,14824,3455],{},[1708,14826,1716],{"stretchy":1715},[2505,14828,4003],{},[1708,14830,1721],{"stretchy":1715},[1708,14832,1710],{},[2505,14834,5867],{},[902,14836,14837],{"encoding":904},"MC(10) = 4",[724,14839,14840,1729,14843,2941,14891,1729,14894,2155],{},[38,14841,14842],{},"Skutečný přírůstek:",[883,14844,14846],{"className":14845},[886],[888,14847,14848],{"xmlns":890},[892,14849,14850,14888],{},[895,14851,14852,14854,14856,14858,14860,14862,14864,14866,14869,14871,14873,14875,14877,14879,14881,14883,14885],{},[898,14853,2633],{"mathvariant":1759},[898,14855,1978],{},[898,14857,3455],{},[1708,14859,1710],{},[898,14861,1978],{},[898,14863,3455],{},[1708,14865,1716],{"stretchy":1715},[2505,14867,14868],{},"11",[1708,14870,1721],{"stretchy":1715},[1708,14872,2726],{},[898,14874,1978],{},[898,14876,3455],{},[1708,14878,1716],{"stretchy":1715},[2505,14880,4003],{},[1708,14882,1721],{"stretchy":1715},[1708,14884,1710],{},[2505,14886,14887],{},"4,2",[902,14889,14890],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,14892,14893],{},"Přibližný (lineární):",[883,14895,14897],{"className":14896},[886],[888,14898,14899],{"xmlns":890},[892,14900,14901,14905],{},[895,14902,14903],{},[2505,14904,5867],{},[902,14906,5867],{"encoding":904},[724,14908,14909,14910,14914],{},"(Viz aplikace v ",[207,14911,14913],{"className":14912,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,14916,14918],{"id":14917},"diferenciál","Diferenciál",[724,14920,14921],{},[883,14922,14924],{"className":14923},[886],[888,14925,14926],{"xmlns":890},[892,14927,14928,14954],{},[895,14929,14930,14932,14934,14936,14942,14944,14946,14948,14950,14952],{},[898,14931,2364],{},[898,14933,14009],{},[1708,14935,1710],{},[1753,14937,14938,14940],{},[898,14939,14009],{},[1708,14941,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,14943,1716],{"stretchy":1715},[898,14945,14014],{},[1708,14947,1721],{"stretchy":1715},[2247,14949,2659],{},[898,14951,2364],{},[898,14953,14014],{},[902,14955,14956],{"encoding":904},"df = f'(x)\\, dx",[724,14958,14959,14960,14976,14977,15025,15026,2155],{},"Pro malá ",[883,14961,14963],{"className":14962},[886],[888,14964,14965],{"xmlns":890},[892,14966,14967,14973],{},[895,14968,14969,14971],{},[898,14970,2364],{},[898,14972,14014],{},[902,14974,14975],{"encoding":904},"dx"," platí: ",[883,14978,14980],{"className":14979},[886],[888,14981,14982],{"xmlns":890},[892,14983,14984,15022],{},[895,14985,14986,14988,14990,14992,14994,14996,14998,15000,15002,15004,15006,15008,15010,15012,15014,15016,15018,15020],{},[898,14987,2633],{"mathvariant":1759},[898,14989,14009],{},[1708,14991,1710],{},[898,14993,14009],{},[1708,14995,1716],{"stretchy":1715},[898,14997,14014],{},[1708,14999,2019],{},[898,15001,2364],{},[898,15003,14014],{},[1708,15005,1721],{"stretchy":1715},[1708,15007,2726],{},[898,15009,14009],{},[1708,15011,1716],{"stretchy":1715},[898,15013,14014],{},[1708,15015,1721],{"stretchy":1715},[1708,15017,2638],{},[898,15019,2364],{},[898,15021,14009],{},[902,15023,15024],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,15027,15028],{},"lineární odhad přírůstku",[198,15030,5768],{"id":15031},"příklad",[724,15033,15034,15064,15065,9664,15087,2750],{},[883,15035,15037],{"className":15036},[886],[888,15038,15039],{"xmlns":890},[892,15040,15041,15061],{},[895,15042,15043,15045,15047,15049,15051,15053,15055],{},[898,15044,1978],{},[898,15046,3455],{},[1708,15048,1710],{},[2505,15050,9238],{},[1708,15052,2019],{},[2505,15054,10909],{},[1753,15056,15057,15059],{},[898,15058,1688],{},[2505,15060,3132],{},[902,15062,15063],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,15066,15068],{"className":15067},[886],[888,15069,15070],{"xmlns":890},[892,15071,15072,15084],{},[895,15073,15074,15076,15078,15080,15082],{},[898,15075,1688],{},[1708,15077,2788],{},[2505,15079,9704],{},[1708,15081,9392],{},[2505,15083,4199],{},[902,15085,15086],{"encoding":904},"Q: 50 \\to 60",[883,15088,15090],{"className":15089},[886],[888,15091,15092],{"xmlns":890},[892,15093,15094,15104],{},[895,15095,15096,15098,15100,15102],{},[898,15097,2364],{},[898,15099,1688],{},[1708,15101,1710],{},[2505,15103,4003],{},[902,15105,15106],{"encoding":904},"dQ = 10",[724,15108,15109],{},[883,15110,15112],{"className":15111},[886],[888,15113,15114],{"xmlns":890},[892,15115,15116,15152],{},[895,15117,15118,15120,15122,15124,15126,15128,15130,15132,15134,15136,15138,15140,15142,15144,15146,15148,15150],{},[898,15119,2364],{},[898,15121,1978],{},[898,15123,3455],{},[1708,15125,1710],{},[2505,15127,3958],{},[898,15129,1688],{},[1708,15131,3703],{},[898,15133,2364],{},[898,15135,1688],{},[1708,15137,1710],{},[2505,15139,3958],{},[1708,15141,3703],{},[2505,15143,9704],{},[1708,15145,3703],{},[2505,15147,4003],{},[1708,15149,1710],{},[2505,15151,9238],{},[902,15153,15154],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,15156,15157,15158,15181,15182,15198],{},"Přesná změna: ",[883,15159,15161],{"className":15160},[886],[888,15162,15163],{"xmlns":890},[892,15164,15165,15178],{},[895,15166,15167,15169,15171,15173,15175],{},[898,15168,2633],{"mathvariant":1759},[898,15170,1978],{},[898,15172,3455],{},[1708,15174,1710],{},[2505,15176,15177],{},"110",[902,15179,15180],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,15183,15185],{"className":15184},[886],[888,15186,15187],{"xmlns":890},[892,15188,15189,15195],{},[895,15190,15191,15193],{},[898,15192,1978],{},[898,15194,3455],{},[902,15196,15197],{"encoding":904},"TC"," je konvexní.",[115,15200,15202],{"id":15201},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,15204,15206],{"id":15205},"nutná-podmínka","Nutná podmínka",[724,15208,15209,15210,3405,15230,15243,15244,15272,15273,15276],{},"Má-li ",[883,15211,15213],{"className":15212},[886],[888,15214,15215],{"xmlns":890},[892,15216,15217,15227],{},[895,15218,15219,15221,15223,15225],{},[898,15220,14009],{},[1708,15222,1716],{"stretchy":1715},[898,15224,14014],{},[1708,15226,1721],{"stretchy":1715},[902,15228,15229],{"encoding":904},"f(x)",[883,15231,15233],{"className":15232},[886],[888,15234,15235],{"xmlns":890},[892,15236,15237,15241],{},[895,15238,15239],{},[898,15240,207],{},[902,15242,207],{"encoding":904}," extrém, pak ",[883,15245,15247],{"className":15246},[886],[888,15248,15249],{"xmlns":890},[892,15250,15251,15269],{},[895,15252,15253,15259,15261,15263,15265,15267],{},[1753,15254,15255,15257],{},[898,15256,14009],{},[1708,15258,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,15260,1716],{"stretchy":1715},[898,15262,207],{},[1708,15264,1721],{"stretchy":1715},[1708,15266,1710],{},[2505,15268,2784],{},[902,15270,15271],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,15274,15275],{},"stacionární"," (podezřelé) body.",[198,15278,15280],{"id":15279},"postačující-podmínka","Postačující podmínka",[724,15282,15283,15284,15297,15298,2788],{},"Pro stacionární bod ",[883,15285,15287],{"className":15286},[886],[888,15288,15289],{"xmlns":890},[892,15290,15291,15295],{},[895,15292,15293],{},[898,15294,207],{},[902,15296,207],{"encoding":904},", je-li ",[883,15299,15301],{"className":15300},[886],[888,15302,15303],{"xmlns":890},[892,15304,15305,15327],{},[895,15306,15307,15317,15319,15321,15323,15325],{},[1753,15308,15309,15311],{},[898,15310,14009],{},[895,15312,15313,15315],{},[1708,15314,1761],{"mathvariant":1759},[1708,15316,1761],{"mathvariant":1759},[1708,15318,1716],{"stretchy":1715},[898,15320,207],{},[1708,15322,1721],{"stretchy":1715},[1708,15324,7060],{"mathvariant":1759},[2505,15326,2784],{},[902,15328,15329],{"encoding":904},"f''(a) \\neq 0",[120,15331,15332,15370],{},[123,15333,15334,15366,15367],{},[883,15335,15337],{"className":15336},[886],[888,15338,15339],{"xmlns":890},[892,15340,15341,15363],{},[895,15342,15343,15353,15355,15357,15359,15361],{},[1753,15344,15345,15347],{},[898,15346,14009],{},[895,15348,15349,15351],{},[1708,15350,1761],{"mathvariant":1759},[1708,15352,1761],{"mathvariant":1759},[1708,15354,1716],{"stretchy":1715},[898,15356,207],{},[1708,15358,1721],{"stretchy":1715},[1708,15360,2854],{},[2505,15362,2784],{},[902,15364,15365],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,15368,15369],{},"lokální minimum",[123,15371,15372,15366,15404],{},[883,15373,15375],{"className":15374},[886],[888,15376,15377],{"xmlns":890},[892,15378,15379,15401],{},[895,15380,15381,15391,15393,15395,15397,15399],{},[1753,15382,15383,15385],{},[898,15384,14009],{},[895,15386,15387,15389],{},[1708,15388,1761],{"mathvariant":1759},[1708,15390,1761],{"mathvariant":1759},[1708,15392,1716],{"stretchy":1715},[898,15394,207],{},[1708,15396,1721],{"stretchy":1715},[1708,15398,2932],{},[2505,15400,2784],{},[902,15402,15403],{"encoding":904},"f''(a) \u003C 0",[38,15405,15406],{},"lokální maximum",[724,15408,15409],{},[3372,15410],{"alt":15411,"className":15412,"src":15413},"imek-extremy-1d",[210,3376],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,15415,5768],{"id":15416},"příklad-1",[724,15418,15419],{},[883,15420,15422],{"className":15421},[886],[888,15423,15424],{"xmlns":890},[892,15425,15426,15466],{},[895,15427,15428,15430,15432,15434,15436,15438,15440,15446,15448,15450,15456,15458,15460,15462,15464],{},[898,15429,14009],{},[1708,15431,1716],{"stretchy":1715},[898,15433,14014],{},[1708,15435,1721],{"stretchy":1715},[1708,15437,1710],{},[2505,15439,3132],{},[1753,15441,15442,15444],{},[898,15443,14014],{},[2505,15445,3121],{},[1708,15447,2726],{},[2505,15449,3121],{},[1753,15451,15452,15454],{},[898,15453,14014],{},[2505,15455,3132],{},[1708,15457,2726],{},[2505,15459,4090],{},[898,15461,14014],{},[1708,15463,2019],{},[2505,15465,3121],{},[902,15467,15468],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,15470,15471,15582,15622,15684],{},[123,15472,15473,15545,15546],{},[883,15474,15476],{"className":15475},[886],[888,15477,15478],{"xmlns":890},[892,15479,15480,15542],{},[895,15481,15482,15488,15490,15492,15494,15496,15498,15504,15506,15508,15510,15512,15514,15516,15518,15520,15522,15524,15526,15528,15530,15532,15534,15536,15538,15540],{},[1753,15483,15484,15486],{},[898,15485,14009],{},[1708,15487,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,15489,1716],{"stretchy":1715},[898,15491,14014],{},[1708,15493,1721],{"stretchy":1715},[1708,15495,1710],{},[2505,15497,3947],{},[1753,15499,15500,15502],{},[898,15501,14014],{},[2505,15503,3132],{},[1708,15505,2726],{},[2505,15507,3947],{},[898,15509,14014],{},[1708,15511,2726],{},[2505,15513,4090],{},[1708,15515,1710],{},[2505,15517,3947],{},[1708,15519,1716],{"stretchy":1715},[898,15521,14014],{},[1708,15523,2019],{},[2505,15525,2507],{},[1708,15527,1721],{"stretchy":1715},[1708,15529,1716],{"stretchy":1715},[898,15531,14014],{},[1708,15533,2726],{},[2505,15535,3132],{},[1708,15537,1721],{"stretchy":1715},[1708,15539,1710],{},[2505,15541,2784],{},[902,15543,15544],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,15547,15549],{"className":15548},[886],[888,15550,15551],{"xmlns":890},[892,15552,15553,15579],{},[895,15554,15555,15561,15563,15565,15567,15569,15575,15577],{},[1743,15556,15557,15559],{},[898,15558,14014],{},[2505,15560,2507],{},[1708,15562,1710],{},[1708,15564,2726],{},[2505,15566,2507],{},[1708,15568,1883],{"separator":1882},[1743,15570,15571,15573],{},[898,15572,14014],{},[2505,15574,3132],{},[1708,15576,1710],{},[2505,15578,3132],{},[902,15580,15581],{"encoding":904},"x_1 = -1, x_2 = 2",[123,15583,15584],{},[883,15585,15587],{"className":15586},[886],[888,15588,15589],{"xmlns":890},[892,15590,15591,15619],{},[895,15592,15593,15603,15605,15607,15609,15611,15613,15615,15617],{},[1753,15594,15595,15597],{},[898,15596,14009],{},[895,15598,15599,15601],{},[1708,15600,1761],{"mathvariant":1759},[1708,15602,1761],{"mathvariant":1759},[1708,15604,1716],{"stretchy":1715},[898,15606,14014],{},[1708,15608,1721],{"stretchy":1715},[1708,15610,1710],{},[2505,15612,4090],{},[898,15614,14014],{},[1708,15616,2726],{},[2505,15618,3947],{},[902,15620,15621],{"encoding":904},"f''(x) = 12x - 6",[123,15623,15624,15366,15664,15667,15668],{},[883,15625,15627],{"className":15626},[886],[888,15628,15629],{"xmlns":890},[892,15630,15631,15661],{},[895,15632,15633,15643,15645,15647,15649,15651,15653,15655,15657,15659],{},[1753,15634,15635,15637],{},[898,15636,14009],{},[895,15638,15639,15641],{},[1708,15640,1761],{"mathvariant":1759},[1708,15642,1761],{"mathvariant":1759},[1708,15644,1716],{"stretchy":1715},[1708,15646,2726],{},[2505,15648,2507],{},[1708,15650,1721],{"stretchy":1715},[1708,15652,1710],{},[1708,15654,2726],{},[2505,15656,4013],{},[1708,15658,2932],{},[2505,15660,2784],{},[902,15662,15663],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,15665,15666],{},"maximum"," v ",[883,15669,15671],{"className":15670},[886],[888,15672,15673],{"xmlns":890},[892,15674,15675,15681],{},[895,15676,15677,15679],{},[1708,15678,2726],{},[2505,15680,2507],{},[902,15682,15683],{"encoding":904},"-1",[123,15685,15686,15366,15722,15667,15725],{},[883,15687,15689],{"className":15688},[886],[888,15690,15691],{"xmlns":890},[892,15692,15693,15719],{},[895,15694,15695,15705,15707,15709,15711,15713,15715,15717],{},[1753,15696,15697,15699],{},[898,15698,14009],{},[895,15700,15701,15703],{},[1708,15702,1761],{"mathvariant":1759},[1708,15704,1761],{"mathvariant":1759},[1708,15706,1716],{"stretchy":1715},[2505,15708,3132],{},[1708,15710,1721],{"stretchy":1715},[1708,15712,1710],{},[2505,15714,4013],{},[1708,15716,2854],{},[2505,15718,2784],{},[902,15720,15721],{"encoding":904},"f''(2) = 18 > 0",[38,15723,15724],{},"minimum",[883,15726,15728],{"className":15727},[886],[888,15729,15730],{"xmlns":890},[892,15731,15732,15736],{},[895,15733,15734],{},[2505,15735,3132],{},[902,15737,3132],{"encoding":904},[115,15739,13763],{"id":13762},[120,15741,15742,15749,15757],{},[123,15743,15744,1729,15746],{},[38,15745,13871],{},[207,15747,757],{"className":15748,"dataFsResolvedFilePath":755,"href":756},[210],[123,15750,15751,1729,15754],{},[38,15752,15753],{},"Navazující:",[207,15755,775],{"className":15756,"dataFsResolvedFilePath":773,"href":774},[210],[123,15758,15759,1729,15762,15765,15766,15769,15770,15773],{},[38,15760,15761],{},"Souvislosti:",[207,15763,784],{"className":15764,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,15767,13830],{"className":15768,"dataFsResolvedFilePath":827,"href":828},[210]," (aplikace mezních veličin), ",[207,15771,13875],{"className":15772,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":15775},[15776,15777,15782,15785,15790],{"id":13988,"depth":642,"text":13989},{"id":1145,"depth":642,"text":2162,"children":15778},[15779,15780,15781],{"id":14424,"depth":649,"text":14425},{"id":14544,"depth":649,"text":14545},{"id":14731,"depth":649,"text":14732},{"id":14917,"depth":642,"text":14918,"children":15783},[15784],{"id":15031,"depth":649,"text":5768},{"id":15201,"depth":642,"text":15202,"children":15786},[15787,15788,15789],{"id":15205,"depth":649,"text":15206},{"id":15279,"depth":649,"text":15280},{"id":15416,"depth":649,"text":5768},{"id":13762,"depth":642,"text":13763},"Matematický aparát kurzu ImeK. Bez derivace se neobejdou mezní veličiny (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde maximalizace zisku ani minimalizace nákladů.",{},"\u002Ftopics\u002Fderivace",{"title":13961,"description":15791},[1135],"topics\u002Fderivace",[1128,1145,15798,15799,15800],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":15803,"title":15804,"body":15805,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":21461,"navigation":664,"path":21462,"seo":21463,"sources":21464,"stem":21465,"tags":21466,"type":13951,"updated":677,"__hash__":21471},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":15806,"toc":21434},[15807,15810,15829,15833,15859,15863,15904,15991,16035,16039,16063,16070,16074,16084,16095,16099,16128,16134,16190,16196,16199,16205,16232,16238,16333,16491,16780,16784,16864,16870,16874,16970,17036,17204,17208,17286,17317,17344,17350,17382,17460,17545,17549,17611,17617,17620,17626,17740,17823,17867,17871,17917,17924,18240,18245,18269,18298,18365,18461,18465,18472,18479,18550,18670,18754,18757,18763,19089,19093,19256,19264,19400,19408,19646,19654,19657,19662,19918,19922,20094,20228,20265,20309,20312,20441,20531,20549,20553,20560,20566,20626,20629,20653,20656,20662,20665,20671,20674,20678,20715,20773,20961,20965,21038,21044,21051,21055,21061,21201,21205,21211,21247,21252,21429],[12,15808,15804],{"id":15809},"elasticita-poptávky-a-nabídky",[1636,15811,15812],{},[724,15813,15814,1643,15816,15818,15819,15822,15823,1771,15826,2155],{},[883,15815,1642],{},[38,15817,13875],{}," 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: ",[38,15820,15821],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,15824,15825],{},"křížově-cenovou elasticitu",[38,15827,15828],{},"důchodovou elasticitu",[115,15830,15832],{"id":15831},"úvod-motivace","Úvod — motivace",[724,15834,15835,15836,15839,15840,15843,15844,15847,15848,15851,15852,15855,15856,2511],{},"Termín ",[614,15837,15838],{},"elasticita"," (alternativně ",[614,15841,15842],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,15845,15846],{},"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 ",[614,15849,15850],{},"cenové elasticity poptávky"," (resp. ",[614,15853,15854],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,15857,2162],{"className":15858,"dataFsResolvedFilePath":764,"href":765},[210],[198,15860,15862],{"id":15861},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,15864,15865,15866,15884,15885,15903],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,15867,15869],{"className":15868},[886],[888,15870,15871],{"xmlns":890},[892,15872,15873,15881],{},[895,15874,15875,15877,15879],{},[898,15876,1747],{},[1708,15878,1710],{},[2505,15880,4003],{},[902,15882,15883],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,15886,15888],{"className":15887},[886],[888,15889,15890],{"xmlns":890},[892,15891,15892,15900],{},[895,15893,15894,15896,15898],{},[898,15895,1688],{},[1708,15897,1710],{},[2505,15899,9238],{},[902,15901,15902],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,15905,15906,15948],{},[123,15907,15908,15911,15912,15947],{},[38,15909,15910],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,15913,15915],{"className":15914},[886],[888,15916,15917],{"xmlns":890},[892,15918,15919,15944],{},[895,15920,15921,15923,15925,15927,15929,15931,15933,15935,15937,15939,15941],{},[2247,15922,4779],{},[1708,15924,4782],{},[2247,15926,4779],{},[898,15928,1978],{},[898,15930,1975],{},[1708,15932,1710],{},[2505,15934,4635],{},[1708,15936,3703],{},[2505,15938,15177],{},[1708,15940,1710],{},[2505,15942,15943],{},"990",[902,15945,15946],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,15949,15950,15953,15954,15990],{},[38,15951,15952],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,15955,15957],{"className":15956},[886],[888,15958,15959],{"xmlns":890},[892,15960,15961,15987],{},[895,15962,15963,15965,15967,15969,15971,15973,15975,15977,15979,15982,15984],{},[2247,15964,4779],{},[1708,15966,4782],{},[2247,15968,4779],{},[898,15970,1978],{},[898,15972,1975],{},[1708,15974,1710],{},[2505,15976,4635],{},[1708,15978,3703],{},[2505,15980,15981],{},"120",[1708,15983,1710],{},[2505,15985,15986],{},"1080",[902,15988,15989],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,15992,15993,15994,15997,15998,16001,16002,16005,16006,16009,16010,16013,16014,16030,16031,16034],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,15995,15996],{},"nerozumné",", na Trhu 2 ",[38,15999,16000],{},"rozumné",". Trh 2 je ",[38,16003,16004],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,16007,16008],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,16011,16012],{},"neelastická"," a vyššího ",[883,16015,16017],{"className":16016},[886],[888,16018,16019],{"xmlns":890},[892,16020,16021,16027],{},[895,16022,16023,16025],{},[898,16024,1978],{},[898,16026,1975],{},[902,16028,16029],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,16032,16033],{},"zvýšením"," ceny.",[198,16036,16038],{"id":16037},"hypotéza-41","Hypotéza 4.1",[1636,16040,16041],{},[724,16042,16043,16044],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,16045,16047],{"className":16046},[886],[888,16048,16049],{"xmlns":890},[892,16050,16051,16060],{},[895,16052,16053,16055,16058],{},[1708,16054,1716],{"stretchy":1715},[2505,16056,16057],{},"4.1",[1708,16059,1721],{"stretchy":1715},[902,16061,16062],{"encoding":904},"(4.1)",[724,16064,16065,16066,16069],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,16067,16068],{},"procentní změny"," obou faktorů.",[115,16071,16073],{"id":16072},"pojem-elasticity","Pojem elasticity",[724,16075,16076,16077,16079,16080,16083],{},"Obecně ",[38,16078,15838],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,16081,16082],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1636,16085,16086],{},[724,16087,16088,16090,16091,16094],{},[883,16089,2518],{}," Intuice\nElasticitu lze číst jako ",[38,16092,16093],{},"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.",[115,16096,16098],{"id":16097},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,16100,16101,16102,16127],{},"Nechť ",[883,16103,16105],{"className":16104},[886],[888,16106,16107],{"xmlns":890},[892,16108,16109,16124],{},[895,16110,16111,16113,16115,16118,16120,16122],{},[898,16112,1688],{},[1708,16114,1710],{},[898,16116,16117],{},"D",[1708,16119,1716],{"stretchy":1715},[898,16121,1747],{},[1708,16123,1721],{"stretchy":1715},[902,16125,16126],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,16129,16130],{},[883,16131,16133],{"className":16132,"title":3428,"style":3429},[3427],"E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,16135,16136,16137,1771,16153,16169,16170,16189],{},"Znaménko minus je korekce: změny ",[883,16138,16140],{"className":16139},[886],[888,16141,16142],{"xmlns":890},[892,16143,16144,16150],{},[895,16145,16146,16148],{},[898,16147,2633],{"mathvariant":1759},[898,16149,1688],{},[902,16151,16152],{"encoding":904},"\\Delta Q",[883,16154,16156],{"className":16155},[886],[888,16157,16158],{"xmlns":890},[892,16159,16160,16166],{},[895,16161,16162,16164],{},[898,16163,2633],{"mathvariant":1759},[898,16165,1747],{},[902,16167,16168],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,16171,16173],{"className":16172},[886],[888,16174,16175],{"xmlns":890},[892,16176,16177,16186],{},[895,16178,16179],{},[1753,16180,16181,16184],{},[898,16182,16183],{},"E",[898,16185,1786],{},[902,16187,16188],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,16191,16192],{},[883,16193,16195],{"className":16194,"title":3428,"style":3429},[3427],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,16197,16198],{},"Po dosazení:",[724,16200,16201],{},[883,16202,16204],{"className":16203,"title":3428,"style":3429},[3427],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,16206,16207,16208,16228,16229,16231],{},"Limitním přechodem ",[883,16209,16211],{"className":16210},[886],[888,16212,16213],{"xmlns":890},[892,16214,16215,16225],{},[895,16216,16217,16219,16221,16223],{},[898,16218,2633],{"mathvariant":1759},[898,16220,1747],{},[1708,16222,9392],{},[2505,16224,2784],{},[902,16226,16227],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,16230,15850],{}," (price elasticity of demand):",[724,16233,16234],{},[883,16235,16237],{"className":16236,"title":3428,"style":3429},[3427],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,16239,5411,16240,16263,16264,8214,16286,16310,16311,16332],{},[883,16241,16243],{"className":16242},[886],[888,16244,16245],{"xmlns":890},[892,16246,16247,16261],{},[895,16248,16249,16251,16253,16255,16257,16259],{},[898,16250,1688],{},[1708,16252,1710],{},[898,16254,16117],{},[1708,16256,1716],{"stretchy":1715},[898,16258,1747],{},[1708,16260,1721],{"stretchy":1715},[902,16262,16126],{"encoding":904},". Pro pevnou cenu ",[883,16265,16267],{"className":16266},[886],[888,16268,16269],{"xmlns":890},[892,16270,16271,16283],{},[895,16272,16273,16275,16277],{},[898,16274,1747],{},[1708,16276,1710],{},[1753,16278,16279,16281],{},[898,16280,1747],{},[1708,16282,2417],{},[902,16284,16285],{"encoding":904},"P = P^*",[883,16287,16289],{"className":16288},[886],[888,16290,16291],{"xmlns":890},[892,16292,16293,16307],{},[895,16294,16295,16297,16299,16305],{},[898,16296,16183],{},[1708,16298,1716],{"stretchy":1715},[1753,16300,16301,16303],{},[898,16302,1747],{},[1708,16304,2417],{},[1708,16306,1721],{"stretchy":1715},[902,16308,16309],{"encoding":904},"E(P^*)"," nazývá ",[614,16312,16313,16314],{},"elasticita poptávky při ceně ",[883,16315,16317],{"className":16316},[886],[888,16318,16319],{"xmlns":890},[892,16320,16321,16329],{},[895,16322,16323],{},[1753,16324,16325,16327],{},[898,16326,1747],{},[1708,16328,2417],{},[902,16330,16331],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1636,16334,16335],{},[724,16336,16337,16339,16340,16358,16359,16387,16388,16416,16417,1343,16435,1343,16453,16471,16472,16487,16488,2155],{},[883,16338,6130],{}," Pozor na znaménko\nV (4.5) je ",[38,16341,16342,16343],{},"explicitní ",[883,16344,16346],{"className":16345},[886],[888,16347,16348],{"xmlns":890},[892,16349,16350,16356],{},[895,16351,16352,16354],{},[1708,16353,2726],{},[2505,16355,2507],{},[902,16357,15683],{"encoding":904}," právě proto, že ",[883,16360,16362],{"className":16361},[886],[888,16363,16364],{"xmlns":890},[892,16365,16366,16384],{},[895,16367,16368,16374,16376,16378,16380,16382],{},[1753,16369,16370,16372],{},[898,16371,1688],{},[1708,16373,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,16375,1716],{"stretchy":1715},[898,16377,1747],{},[1708,16379,1721],{"stretchy":1715},[1708,16381,2932],{},[2505,16383,2784],{},[902,16385,16386],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,16389,16391],{"className":16390},[886],[888,16392,16393],{"xmlns":890},[892,16394,16395,16413],{},[895,16396,16397,16399,16401,16407,16409,16411],{},[898,16398,16183],{},[1708,16400,1716],{"stretchy":1715},[1753,16402,16403,16405],{},[898,16404,1747],{},[1708,16406,2417],{},[1708,16408,1721],{"stretchy":1715},[1708,16410,6762],{},[2505,16412,2784],{},[902,16414,16415],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,16418,16420],{"className":16419},[886],[888,16421,16422],{"xmlns":890},[892,16423,16424,16432],{},[895,16425,16426,16428,16430],{},[898,16427,16183],{},[1708,16429,2854],{},[2505,16431,2507],{},[902,16433,16434],{"encoding":904},"E > 1",[883,16436,16438],{"className":16437},[886],[888,16439,16440],{"xmlns":890},[892,16441,16442,16450],{},[895,16443,16444,16446,16448],{},[898,16445,16183],{},[1708,16447,2932],{},[2505,16449,2507],{},[902,16451,16452],{"encoding":904},"E \u003C 1",[883,16454,16456],{"className":16455},[886],[888,16457,16458],{"xmlns":890},[892,16459,16460,16468],{},[895,16461,16462,16464,16466],{},[898,16463,16183],{},[1708,16465,1710],{},[2505,16467,2507],{},[902,16469,16470],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,16473,16475],{"className":16474},[886],[888,16476,16477],{"xmlns":890},[892,16478,16479,16485],{},[895,16480,16481,16483],{},[1708,16482,2726],{},[2505,16484,2507],{},[902,16486,15683],{"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 ",[38,16489,16490],{},"absolutní hodnotou",[1636,16492,16493,16512],{},[724,16494,16495,16497,16498,16511],{},[883,16496,3465],{}," Postup: jak spočítat ",[883,16499,16501],{"className":16500},[886],[888,16502,16503],{"xmlns":890},[892,16504,16505,16509],{},[895,16506,16507],{},[898,16508,16183],{},[902,16510,16183],{"encoding":904}," v bodě",[152,16513,16514,16566,16605,16658,16723],{},[123,16515,16516,16517,16540,16541,16565],{},"Zapište ",[883,16518,16520],{"className":16519},[886],[888,16521,16522],{"xmlns":890},[892,16523,16524,16538],{},[895,16525,16526,16528,16530,16532,16534,16536],{},[898,16527,1688],{},[1708,16529,1710],{},[898,16531,16117],{},[1708,16533,1716],{"stretchy":1715},[898,16535,1747],{},[1708,16537,1721],{"stretchy":1715},[902,16539,16126],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,16542,16544],{"className":16543},[886],[888,16545,16546],{"xmlns":890},[892,16547,16548,16562],{},[895,16549,16550,16552,16554,16556,16558,16560],{},[898,16551,1747],{},[1708,16553,1710],{},[898,16555,16117],{},[1708,16557,1716],{"stretchy":1715},[898,16559,1688],{},[1708,16561,1721],{"stretchy":1715},[902,16563,16564],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,16567,16568,16569,2155],{},"Spočítejte derivaci ",[883,16570,16572],{"className":16571},[886],[888,16573,16574],{"xmlns":890},[892,16575,16576,16602],{},[895,16577,16578,16584,16586,16588,16590,16592,16594,16596,16598,16600],{},[1753,16579,16580,16582],{},[898,16581,1688],{},[1708,16583,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,16585,1716],{"stretchy":1715},[898,16587,1747],{},[1708,16589,1721],{"stretchy":1715},[1708,16591,1710],{},[898,16593,2364],{"mathvariant":1759},[898,16595,1688],{},[898,16597,1799],{"mathvariant":1759},[898,16599,2364],{"mathvariant":1759},[898,16601,1747],{},[902,16603,16604],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,16606,16607,16608,16625,16626,2155],{},"Dosaďte zadanou cenu ",[883,16609,16611],{"className":16610},[886],[888,16612,16613],{"xmlns":890},[892,16614,16615,16623],{},[895,16616,16617],{},[1753,16618,16619,16621],{},[898,16620,1747],{},[1708,16622,2417],{},[902,16624,16331],{"encoding":904}," a dopočítejte odpovídající ",[883,16627,16629],{"className":16628},[886],[888,16630,16631],{"xmlns":890},[892,16632,16633,16655],{},[895,16634,16635,16641,16643,16645,16647,16653],{},[1753,16636,16637,16639],{},[898,16638,1688],{},[1708,16640,2417],{},[1708,16642,1710],{},[898,16644,16117],{},[1708,16646,1716],{"stretchy":1715},[1753,16648,16649,16651],{},[898,16650,1747],{},[1708,16652,2417],{},[1708,16654,1721],{"stretchy":1715},[902,16656,16657],{"encoding":904},"Q^* = D(P^*)",[123,16659,16660,16661,2155],{},"Dosaďte do (4.5): ",[883,16662,16664],{"className":16663},[886],[888,16665,16666],{"xmlns":890},[892,16667,16668,16720],{},[895,16669,16670,16672,16674,16680,16682,16684,16686,16702,16704,16710,16712,16718],{},[898,16671,16183],{},[1708,16673,1716],{"stretchy":1715},[1753,16675,16676,16678],{},[898,16677,1747],{},[1708,16679,2417],{},[1708,16681,1721],{"stretchy":1715},[1708,16683,1710],{},[1708,16685,2726],{},[3194,16687,16688],{"scriptlevel":2784,"displaystyle":1882},[2358,16689,16690,16696],{},[1753,16691,16692,16694],{},[898,16693,1747],{},[1708,16695,2417],{},[1753,16697,16698,16700],{},[898,16699,1688],{},[1708,16701,2417],{},[2247,16703,2659],{},[1753,16705,16706,16708],{},[898,16707,1688],{},[1708,16709,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,16711,1716],{"stretchy":1715},[1753,16713,16714,16716],{},[898,16715,1747],{},[1708,16717,2417],{},[1708,16719,1721],{"stretchy":1715},[902,16721,16722],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,16724,16725,16726,16743,16744,16761,16762,16779],{},"Klasifikujte: ",[883,16727,16729],{"className":16728},[886],[888,16730,16731],{"xmlns":890},[892,16732,16733,16741],{},[895,16734,16735,16737,16739],{},[898,16736,16183],{},[1708,16738,2854],{},[2505,16740,2507],{},[902,16742,16434],{"encoding":904}," elastická, ",[883,16745,16747],{"className":16746},[886],[888,16748,16749],{"xmlns":890},[892,16750,16751,16759],{},[895,16752,16753,16755,16757],{},[898,16754,16183],{},[1708,16756,1710],{},[2505,16758,2507],{},[902,16760,16470],{"encoding":904}," jednotková, ",[883,16763,16765],{"className":16764},[886],[888,16766,16767],{"xmlns":890},[892,16768,16769,16777],{},[895,16770,16771,16773,16775],{},[898,16772,16183],{},[1708,16774,2932],{},[2505,16776,2507],{},[902,16778,16452],{"encoding":904}," neelastická.",[198,16781,16783],{"id":16782},"interpretace-46","Interpretace (4.6)",[1636,16785,16786],{},[724,16787,16788,16789,16812,16813,16826,16827,16844,16845],{},"Číslo ",[883,16790,16792],{"className":16791},[886],[888,16793,16794],{"xmlns":890},[892,16795,16796,16810],{},[895,16797,16798,16800,16802,16808],{},[898,16799,16183],{},[1708,16801,1716],{"stretchy":1715},[1753,16803,16804,16806],{},[898,16805,1747],{},[1708,16807,2417],{},[1708,16809,1721],{"stretchy":1715},[902,16811,16309],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,16814,16816],{"className":16815},[886],[888,16817,16818],{"xmlns":890},[892,16819,16820,16824],{},[895,16821,16822],{},[898,16823,1688],{},[902,16825,1688],{"encoding":904},", jestliže se cena ",[883,16828,16830],{"className":16829},[886],[888,16831,16832],{"xmlns":890},[892,16833,16834,16842],{},[895,16835,16836],{},[1753,16837,16838,16840],{},[898,16839,1747],{},[1708,16841,2417],{},[902,16843,16331],{"encoding":904}," změní o 1 %. ",[883,16846,16848],{"className":16847},[886],[888,16849,16850],{"xmlns":890},[892,16851,16852,16861],{},[895,16853,16854,16856,16859],{},[1708,16855,1716],{"stretchy":1715},[2505,16857,16858],{},"4.6",[1708,16860,1721],{"stretchy":1715},[902,16862,16863],{"encoding":904},"(4.6)",[724,16865,16866,16869],{},[38,16867,16868],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,16871,16873],{"id":16872},"příklad-41","Příklad 4.1",[724,16875,16876,16877,16911,16912,1343,16936,2788],{},"Poptávka ",[883,16878,16880],{"className":16879},[886],[888,16881,16882],{"xmlns":890},[892,16883,16884,16908],{},[895,16885,16886,16888,16890,16892,16894,16896,16898,16900,16902,16904,16906],{},[898,16887,1747],{},[1708,16889,1710],{},[898,16891,16117],{},[1708,16893,1716],{"stretchy":1715},[898,16895,1688],{},[1708,16897,1721],{"stretchy":1715},[1708,16899,1710],{},[2505,16901,9704],{},[1708,16903,2726],{},[2505,16905,3132],{},[898,16907,1688],{},[902,16909,16910],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,16913,16915],{"className":16914},[886],[888,16916,16917],{"xmlns":890},[892,16918,16919,16933],{},[895,16920,16921,16923,16925,16927,16929,16931],{},[898,16922,1688],{},[1708,16924,1710],{},[2505,16926,4028],{},[1708,16928,2726],{},[2505,16930,6097],{},[898,16932,1747],{},[902,16934,16935],{"encoding":904},"Q = 25 - 0{,}5P",[883,16937,16939],{"className":16938},[886],[888,16940,16941],{"xmlns":890},[892,16942,16943,16967],{},[895,16944,16945,16961,16963,16965],{},[3194,16946,16947],{"scriptlevel":2784,"displaystyle":1882},[2358,16948,16949,16955],{},[895,16950,16951,16953],{},[898,16952,2364],{"mathvariant":1759},[898,16954,1688],{},[895,16956,16957,16959],{},[898,16958,2364],{"mathvariant":1759},[898,16960,1747],{},[1708,16962,1710],{},[1708,16964,2726],{},[2505,16966,6097],{},[902,16968,16969],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,16971,16972],{},[883,16973,16975],{"className":16974},[886],[888,16976,16977],{"xmlns":890},[892,16978,16979,17033],{},[895,16980,16981,16983,16985,16987,17001,17003,17005,17007,17009,17011,17013,17031],{},[898,16982,16183],{},[1708,16984,1710],{},[1708,16986,2726],{},[2358,16988,16989,16991],{},[898,16990,1747],{},[895,16992,16993,16995,16997,16999],{},[2505,16994,4028],{},[1708,16996,2726],{},[2505,16998,6097],{},[898,17000,1747],{},[1708,17002,3703],{},[1708,17004,1716],{"stretchy":1715},[1708,17006,2726],{},[2505,17008,6097],{},[1708,17010,1721],{"stretchy":1715},[1708,17012,1710],{},[2358,17014,17015,17021],{},[895,17016,17017,17019],{},[2505,17018,6097],{},[898,17020,1747],{},[895,17022,17023,17025,17027,17029],{},[2505,17024,4028],{},[1708,17026,2726],{},[2505,17028,6097],{},[898,17030,1747],{},[898,17032,2155],{"mathvariant":1759},[902,17034,17035],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,17037,17038,17039,1343,17063,1343,17093,1343,17117,17142,17143,17166,17167,2486,17185,2511],{},"Potom ",[883,17040,17042],{"className":17041},[886],[888,17043,17044],{"xmlns":890},[892,17045,17046,17060],{},[895,17047,17048,17050,17052,17054,17056,17058],{},[898,17049,16183],{},[1708,17051,1716],{"stretchy":1715},[2505,17053,2784],{},[1708,17055,1721],{"stretchy":1715},[1708,17057,1710],{},[2505,17059,2784],{},[902,17061,17062],{"encoding":904},"E(0)=0",[883,17064,17066],{"className":17065},[886],[888,17067,17068],{"xmlns":890},[892,17069,17070,17090],{},[895,17071,17072,17074,17076,17078,17080,17082],{},[898,17073,16183],{},[1708,17075,1716],{"stretchy":1715},[2505,17077,4003],{},[1708,17079,1721],{"stretchy":1715},[1708,17081,1710],{},[3194,17083,17084],{"scriptlevel":2784,"displaystyle":1715},[2358,17085,17086,17088],{},[2505,17087,2507],{},[2505,17089,5867],{},[902,17091,17092],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,17094,17096],{"className":17095},[886],[888,17097,17098],{"xmlns":890},[892,17099,17100,17114],{},[895,17101,17102,17104,17106,17108,17110,17112],{},[898,17103,16183],{},[1708,17105,1716],{"stretchy":1715},[2505,17107,4028],{},[1708,17109,1721],{"stretchy":1715},[1708,17111,1710],{},[2505,17113,2507],{},[902,17115,17116],{"encoding":904},"E(25)=1",[883,17118,17120],{"className":17119},[886],[888,17121,17122],{"xmlns":890},[892,17123,17124,17139],{},[895,17125,17126,17128,17130,17133,17135,17137],{},[898,17127,16183],{},[1708,17129,1716],{"stretchy":1715},[2505,17131,17132],{},"40",[1708,17134,1721],{"stretchy":1715},[1708,17136,1710],{},[2505,17138,5867],{},[902,17140,17141],{"encoding":904},"E(40)=4",". Např. ",[883,17144,17146],{"className":17145},[886],[888,17147,17148],{"xmlns":890},[892,17149,17150,17164],{},[895,17151,17152,17154,17156,17158,17160,17162],{},[898,17153,16183],{},[1708,17155,1716],{"stretchy":1715},[2505,17157,17132],{},[1708,17159,1721],{"stretchy":1715},[1708,17161,1710],{},[2505,17163,5867],{},[902,17165,17141],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,17168,17170],{"className":17169},[886],[888,17171,17172],{"xmlns":890},[892,17173,17174,17182],{},[895,17175,17176,17178,17180],{},[898,17177,1688],{},[1708,17179,1710],{},[2505,17181,3993],{},[902,17183,17184],{"encoding":904},"Q=5",[883,17186,17188],{"className":17187},[886],[888,17189,17190],{"xmlns":890},[892,17191,17192,17201],{},[895,17193,17194,17196,17198],{},[898,17195,1688],{},[1708,17197,1710],{},[2505,17199,17200],{},"4,8",[902,17202,17203],{"encoding":904},"Q=4{,}8",[198,17205,17207],{"id":17206},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,17209,17210,17266],{},[123,17211,17212,17215,17216,17233,17234,2155],{},[38,17213,17214],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,17217,17219],{"className":17218},[886],[888,17220,17221],{"xmlns":890},[892,17222,17223,17231],{},[895,17224,17225],{},[1753,17226,17227,17229],{},[898,17228,16183],{},[898,17230,1786],{},[902,17232,16188],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,17235,17237],{"className":17236},[886],[888,17238,17239],{"xmlns":890},[892,17240,17241,17263],{},[895,17242,17243,17246,17248,17250,17252,17254,17256,17258,17260],{},[1708,17244,17245],{"stretchy":1715},"⟨",[898,17247,1747],{},[1708,17249,1883],{"separator":1882},[2247,17251,2659],{},[898,17253,1747],{},[1708,17255,2019],{},[898,17257,2633],{"mathvariant":1759},[898,17259,1747],{},[1708,17261,17262],{"stretchy":1715},"⟩",[902,17264,17265],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,17267,17268,17271,17272,17285],{},[38,17269,17270],{},"Bodová"," (okamžitá) elasticita: ",[883,17273,17275],{"className":17274},[886],[888,17276,17277],{"xmlns":890},[892,17278,17279,17283],{},[895,17280,17281],{},[898,17282,16183],{},[902,17284,16183],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,17287,17289,17290,17303,17304],{"id":17288},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,17291,17293],{"className":17292},[886],[888,17294,17295],{"xmlns":890},[892,17296,17297,17301],{},[895,17298,17299],{},[898,17300,1747],{},[902,17302,1747],{"encoding":904}," jako funkce ",[883,17305,17307],{"className":17306},[886],[888,17308,17309],{"xmlns":890},[892,17310,17311,17315],{},[895,17312,17313],{},[898,17314,1688],{},[902,17316,1688],{"encoding":904},[724,17318,17319,17320,17343],{},"Pokud je poptávka zadaná ve tvaru ",[883,17321,17323],{"className":17322},[886],[888,17324,17325],{"xmlns":890},[892,17326,17327,17341],{},[895,17328,17329,17331,17333,17335,17337,17339],{},[898,17330,1747],{},[1708,17332,1710],{},[898,17334,16117],{},[1708,17336,1716],{"stretchy":1715},[898,17338,1688],{},[1708,17340,1721],{"stretchy":1715},[902,17342,16564],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,17345,17346],{},[883,17347,17349],{"className":17348,"title":3428,"style":3429},[3427],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,17351,17352,1729,17355,17381],{},[38,17353,17354],{},"Příklad 4.3.",[883,17356,17358],{"className":17357},[886],[888,17359,17360],{"xmlns":890},[892,17361,17362,17378],{},[895,17363,17364,17366,17368,17370,17372],{},[898,17365,1747],{},[1708,17367,1710],{},[2505,17369,9238],{},[1708,17371,2726],{},[1753,17373,17374,17376],{},[898,17375,1688],{},[2505,17377,3132],{},[902,17379,17380],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,17383,17384],{},[883,17385,17387],{"className":17386},[886],[888,17388,17389],{"xmlns":890},[892,17390,17391,17457],{},[895,17392,17393,17395,17397,17399,17415,17417,17429,17431,17455],{},[898,17394,16183],{},[1708,17396,1710],{},[1708,17398,2726],{},[2358,17400,17401,17413],{},[895,17402,17403,17405,17407],{},[2505,17404,9238],{},[1708,17406,2726],{},[1753,17408,17409,17411],{},[898,17410,1688],{},[2505,17412,3132],{},[898,17414,1688],{},[1708,17416,3703],{},[2358,17418,17419,17421],{},[2505,17420,2507],{},[895,17422,17423,17425,17427],{},[1708,17424,2726],{},[2505,17426,3132],{},[898,17428,1688],{},[1708,17430,1710],{},[2358,17432,17433,17445],{},[895,17434,17435,17437,17439],{},[2505,17436,9238],{},[1708,17438,2726],{},[1753,17440,17441,17443],{},[898,17442,1688],{},[2505,17444,3132],{},[895,17446,17447,17449],{},[2505,17448,3132],{},[1753,17450,17451,17453],{},[898,17452,1688],{},[2505,17454,3132],{},[898,17456,2155],{"mathvariant":1759},[902,17458,17459],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,17461,17462,17463,17489,17490,17508,17509,2155],{},"Z rovnice ",[883,17464,17466],{"className":17465},[886],[888,17467,17468],{"xmlns":890},[892,17469,17470,17486],{},[895,17471,17472,17474,17476,17482,17484],{},[2505,17473,9238],{},[1708,17475,2726],{},[1753,17477,17478,17480],{},[898,17479,1688],{},[2505,17481,3132],{},[1708,17483,1710],{},[2505,17485,4547],{},[902,17487,17488],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,17491,17493],{"className":17492},[886],[888,17494,17495],{"xmlns":890},[892,17496,17497,17505],{},[895,17498,17499,17501,17503],{},[898,17500,1688],{},[1708,17502,1710],{},[2505,17504,3998],{},[902,17506,17507],{"encoding":904},"Q = 8",", tedy ",[883,17510,17512],{"className":17511},[886],[888,17513,17514],{"xmlns":890},[892,17515,17516,17542],{},[895,17517,17518,17520,17522,17524,17526,17528,17537,17539],{},[898,17519,16183],{},[1708,17521,1716],{"stretchy":1715},[2505,17523,3998],{},[1708,17525,1721],{"stretchy":1715},[1708,17527,1710],{},[3194,17529,17530],{"scriptlevel":2784,"displaystyle":1715},[2358,17531,17532,17534],{},[2505,17533,4547],{},[2505,17535,17536],{},"128",[1708,17538,1710],{},[2505,17540,17541],{},"0,281",[902,17543,17544],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,17546,17548],{"id":17547},"přibližné-změny","Přibližné změny",[724,17550,17551,17552,3136,17588,17610],{},"Diferenciál ",[883,17553,17555],{"className":17554},[886],[888,17556,17557],{"xmlns":890},[892,17558,17559,17585],{},[895,17560,17561,17563,17565,17567,17573,17575,17577,17579,17581,17583],{},[898,17562,2364],{"mathvariant":1759},[898,17564,1688],{},[1708,17566,1710],{},[1753,17568,17569,17571],{},[898,17570,1688],{},[1708,17572,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,17574,1716],{"stretchy":1715},[898,17576,1747],{},[1708,17578,1721],{"stretchy":1715},[2247,17580,2659],{},[898,17582,2364],{"mathvariant":1759},[898,17584,1747],{},[902,17586,17587],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P",[883,17589,17591],{"className":17590},[886],[888,17592,17593],{"xmlns":890},[892,17594,17595,17607],{},[895,17596,17597,17599,17601,17603,17605],{},[898,17598,2364],{"mathvariant":1759},[898,17600,1747],{},[1708,17602,1710],{},[898,17604,2633],{"mathvariant":1759},[898,17606,1747],{},[902,17608,17609],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,17612,17613],{},[883,17614,17616],{"className":17615,"title":3428,"style":3429},[3427],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,17618,17619],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,17621,17622],{},[883,17623,17625],{"className":17624,"title":3428,"style":3429},[3427],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,17627,17628,1729,17631,17666,17667,17686,17687,17721,17722,17739],{},[38,17629,17630],{},"Příklad 4.5.",[883,17632,17634],{"className":17633},[886],[888,17635,17636],{"xmlns":890},[892,17637,17638,17663],{},[895,17639,17640,17642,17644,17646,17652,17654,17656,17658,17660],{},[898,17641,1747],{},[1708,17643,1710],{},[1708,17645,2726],{},[1753,17647,17648,17650],{},[898,17649,1688],{},[2505,17651,3132],{},[1708,17653,2726],{},[2505,17655,5867],{},[898,17657,1688],{},[1708,17659,2019],{},[2505,17661,17662],{},"96",[902,17664,17665],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,17668,17670],{"className":17669},[886],[888,17671,17672],{"xmlns":890},[892,17673,17674,17683],{},[895,17675,17676,17678,17680],{},[898,17677,1747],{},[1708,17679,1710],{},[2505,17681,17682],{},"51",[902,17684,17685],{"encoding":904},"P=51",". Z rovnice ",[883,17688,17690],{"className":17689},[886],[888,17691,17692],{"xmlns":890},[892,17693,17694,17718],{},[895,17695,17696,17698,17700,17702,17708,17710,17712,17714,17716],{},[2505,17697,17682],{},[1708,17699,1710],{},[1708,17701,2726],{},[1753,17703,17704,17706],{},[898,17705,1688],{},[2505,17707,3132],{},[1708,17709,2726],{},[2505,17711,5867],{},[898,17713,1688],{},[1708,17715,2019],{},[2505,17717,17662],{},[902,17719,17720],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,17723,17725],{"className":17724},[886],[888,17726,17727],{"xmlns":890},[892,17728,17729,17737],{},[895,17730,17731,17733,17735],{},[898,17732,1688],{},[1708,17734,1710],{},[2505,17736,3993],{},[902,17738,17184],{"encoding":904},". Elasticita:",[724,17741,17742],{},[883,17743,17745],{"className":17744},[886],[888,17746,17747],{"xmlns":890},[892,17748,17749,17820],{},[895,17750,17751,17753,17755,17793,17795,17797,17799,17801,17803,17805,17807,17814,17817],{},[898,17752,16183],{},[1708,17754,1710],{},[2358,17756,17757,17777],{},[895,17758,17759,17761,17767,17769,17771,17773,17775],{},[1708,17760,2726],{},[1753,17762,17763,17765],{},[898,17764,1688],{},[2505,17766,3132],{},[1708,17768,2726],{},[2505,17770,5867],{},[898,17772,1688],{},[1708,17774,2019],{},[2505,17776,17662],{},[895,17778,17779,17781,17783,17785,17787,17789,17791],{},[898,17780,1688],{},[1708,17782,1716],{"stretchy":1715},[2505,17784,3132],{},[898,17786,1688],{},[1708,17788,2019],{},[2505,17790,5867],{},[1708,17792,1721],{"stretchy":1715},[1708,17794,1883],{"separator":1882},[3213,17796],{"width":3215},[898,17798,16183],{},[1708,17800,1716],{"stretchy":1715},[2505,17802,3993],{},[1708,17804,1721],{"stretchy":1715},[1708,17806,1710],{},[2358,17808,17809,17811],{},[2505,17810,17682],{},[2505,17812,17813],{},"70",[1708,17815,17816],{},"≐",[2505,17818,17819],{},"0,728.",[902,17821,17822],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,17824,17825,17826,2155],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,17827,17829],{"className":17828},[886],[888,17830,17831],{"xmlns":890},[892,17832,17833,17864],{},[895,17834,17835,17837,17839,17842,17844,17846,17849,17851,17853,17855,17857,17860,17862],{},[898,17836,2633],{"mathvariant":1759},[898,17838,1688],{},[898,17840,17841],{"mathvariant":1759},"%",[1708,17843,2638],{},[1708,17845,2726],{},[2505,17847,17848],{},"0,728",[1708,17850,3703],{},[2505,17852,3132],{},[1708,17854,1710],{},[1708,17856,2726],{},[2505,17858,17859],{},"1,456",[2247,17861,2659],{},[898,17863,17841],{"mathvariant":1759},[902,17865,17866],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,17868,17870],{"id":17869},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,17872,17873,17874,17897,17898,2788],{},"V závislosti na hodnotě ",[883,17875,17877],{"className":17876},[886],[888,17878,17879],{"xmlns":890},[892,17880,17881,17895],{},[895,17882,17883,17885,17887,17893],{},[898,17884,16183],{},[1708,17886,1716],{"stretchy":1715},[1753,17888,17889,17891],{},[898,17890,1747],{},[1708,17892,2417],{},[1708,17894,1721],{"stretchy":1715},[902,17896,16309],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,17899,17901],{"className":17900},[886],[888,17902,17903],{"xmlns":890},[892,17904,17905,17914],{},[895,17906,17907,17909,17912],{},[1708,17908,1716],{"stretchy":1715},[2505,17910,17911],{},"4.7",[1708,17913,1721],{"stretchy":1715},[902,17915,17916],{"encoding":904},"(4.7)",[724,17918,17919],{},[3372,17920],{"alt":17921,"className":17922,"src":17923},"imek-typy-elasticity-5panelu",[210,3376],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,17925,17926,17965],{},[19,17927,17928],{},[22,17929,17930,17956,17959,17962],{},[25,17931,17932,17933],{},"Hodnota ",[883,17934,17936],{"className":17935},[886],[888,17937,17938],{"xmlns":890},[892,17939,17940,17954],{},[895,17941,17942,17944,17946,17952],{},[898,17943,16183],{},[1708,17945,1716],{"stretchy":1715},[1753,17947,17948,17950],{},[898,17949,1747],{},[1708,17951,2417],{},[1708,17953,1721],{"stretchy":1715},[902,17955,16309],{"encoding":904},[25,17957,17958],{},"Typ poptávky",[25,17960,17961],{},"Termín",[25,17963,17964],{},"Význam",[30,17966,17967,18000,18062,18136,18193],{},[22,17968,17969,17989,17994,17997],{},[35,17970,17971],{},[883,17972,17974],{"className":17973},[886],[888,17975,17976],{"xmlns":890},[892,17977,17978,17986],{},[895,17979,17980,17982,17984],{},[898,17981,16183],{},[1708,17983,1710],{},[2505,17985,2784],{},[902,17987,17988],{"encoding":904},"E = 0",[35,17990,17991],{},[38,17992,17993],{},"dokonale neelastická",[35,17995,17996],{},"perfectly inelastic",[35,17998,17999],{},"množství se nemění bez ohledu na cenu",[22,18001,18002,18026,18030,18033],{},[35,18003,18004],{},[883,18005,18007],{"className":18006},[886],[888,18008,18009],{"xmlns":890},[892,18010,18011,18023],{},[895,18012,18013,18015,18017,18019,18021],{},[2505,18014,2784],{},[1708,18016,2932],{},[898,18018,16183],{},[1708,18020,2932],{},[2505,18022,2507],{},[902,18024,18025],{"encoding":904},"0 \u003C E \u003C 1",[35,18027,18028],{},[38,18029,16012],{},[35,18031,18032],{},"inelastic",[35,18034,18035,18048,18049],{},[883,18036,18038],{"className":18037},[886],[888,18039,18040],{"xmlns":890},[892,18041,18042,18046],{},[895,18043,18044],{},[898,18045,1688],{},[902,18047,1688],{"encoding":904}," se mění pomaleji než ",[883,18050,18052],{"className":18051},[886],[888,18053,18054],{"xmlns":890},[892,18055,18056,18060],{},[895,18057,18058],{},[898,18059,1747],{},[902,18061,1747],{"encoding":904},[22,18063,18064,18083,18088,18091],{},[35,18065,18066],{},[883,18067,18069],{"className":18068},[886],[888,18070,18071],{"xmlns":890},[892,18072,18073,18081],{},[895,18074,18075,18077,18079],{},[898,18076,16183],{},[1708,18078,1710],{},[2505,18080,2507],{},[902,18082,16470],{"encoding":904},[35,18084,18085],{},[38,18086,18087],{},"jednotkově elastická",[35,18089,18090],{},"unit elastic",[35,18092,18093,5283,18106,18119,18120,18135],{},[883,18094,18096],{"className":18095},[886],[888,18097,18098],{"xmlns":890},[892,18099,18100,18104],{},[895,18101,18102],{},[898,18103,1688],{},[902,18105,1688],{"encoding":904},[883,18107,18109],{"className":18108},[886],[888,18110,18111],{"xmlns":890},[892,18112,18113,18117],{},[895,18114,18115],{},[898,18116,1747],{},[902,18118,1747],{"encoding":904}," se mění stejně rychle; ",[883,18121,18123],{"className":18122},[886],[888,18124,18125],{"xmlns":890},[892,18126,18127,18133],{},[895,18128,18129,18131],{},[898,18130,1978],{},[898,18132,1975],{},[902,18134,16029],{"encoding":904}," má maximum",[22,18137,18138,18157,18161,18164],{},[35,18139,18140],{},[883,18141,18143],{"className":18142},[886],[888,18144,18145],{"xmlns":890},[892,18146,18147,18155],{},[895,18148,18149,18151,18153],{},[898,18150,16183],{},[1708,18152,2854],{},[2505,18154,2507],{},[902,18156,16434],{"encoding":904},[35,18158,18159],{},[38,18160,16008],{},[35,18162,18163],{},"elastic",[35,18165,18166,18179,18180],{},[883,18167,18169],{"className":18168},[886],[888,18170,18171],{"xmlns":890},[892,18172,18173,18177],{},[895,18174,18175],{},[898,18176,1688],{},[902,18178,1688],{"encoding":904}," se mění rychleji než ",[883,18181,18183],{"className":18182},[886],[888,18184,18185],{"xmlns":890},[892,18186,18187,18191],{},[895,18188,18189],{},[898,18190,1747],{},[902,18192,1747],{"encoding":904},[22,18194,18195,18216,18221,18224],{},[35,18196,18197],{},[883,18198,18200],{"className":18199},[886],[888,18201,18202],{"xmlns":890},[892,18203,18204,18213],{},[895,18205,18206,18208,18210],{},[898,18207,16183],{},[1708,18209,9392],{},[898,18211,18212],{"mathvariant":1759},"∞",[902,18214,18215],{"encoding":904},"E \\to \\infty",[35,18217,18218],{},[38,18219,18220],{},"dokonale elastická",[35,18222,18223],{},"perfectly elastic",[35,18225,18226,18227],{},"sebemenší změna ceny úplně mění ",[883,18228,18230],{"className":18229},[886],[888,18231,18232],{"xmlns":890},[892,18233,18234,18238],{},[895,18235,18236],{},[898,18237,1688],{},[902,18239,1688],{"encoding":904},[724,18241,18242],{},[38,18243,18244],{},"Pravidlo růstu elasticity s cenou:",[1636,18246,18247],{},[724,18248,18249,18250],{},"S rostoucí cenou elasticita poptávky roste. ",[883,18251,18253],{"className":18252},[886],[888,18254,18255],{"xmlns":890},[892,18256,18257,18266],{},[895,18258,18259,18261,18264],{},[1708,18260,1716],{"stretchy":1715},[2505,18262,18263],{},"4.8",[1708,18265,1721],{"stretchy":1715},[902,18267,18268],{"encoding":904},"(4.8)",[724,18270,18271,18272,18275,18276,18279,18280,18297],{},"Z toho plyne, že při ",[614,18273,18274],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,18277,18278],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,18281,18283],{"className":18282},[886],[888,18284,18285],{"xmlns":890},[892,18286,18287,18295],{},[895,18288,18289],{},[1753,18290,18291,18293],{},[898,18292,1747],{},[1708,18294,2417],{},[902,18296,16331],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1636,18299,18300,18305],{},[724,18301,18302,18304],{},[883,18303,3465],{}," Postup: jak klasifikovat poptávku",[152,18306,18307,18334,18337],{},[123,18308,18309,18310,18333],{},"Spočítejte ",[883,18311,18313],{"className":18312},[886],[888,18314,18315],{"xmlns":890},[892,18316,18317,18331],{},[895,18318,18319,18321,18323,18329],{},[898,18320,16183],{},[1708,18322,1716],{"stretchy":1715},[1753,18324,18325,18327],{},[898,18326,1747],{},[1708,18328,2417],{},[1708,18330,1721],{"stretchy":1715},[902,18332,16309],{"encoding":904}," dle (4.5).",[123,18335,18336],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,18338,18339,18340,18364],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,18341,18343],{"className":18342},[886],[888,18344,18345],{"xmlns":890},[892,18346,18347,18361],{},[895,18348,18349,18351,18353,18355,18357,18359],{},[898,18350,16183],{},[1708,18352,1716],{"stretchy":1715},[898,18354,1747],{},[1708,18356,1721],{"stretchy":1715},[1708,18358,1710],{},[2505,18360,2507],{},[902,18362,18363],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,18366,18367,18370,18371,10064,18388,18406,18407,18434,18435,2155],{},[38,18368,18369],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,18372,18374],{"className":18373},[886],[888,18375,18376],{"xmlns":890},[892,18377,18378,18386],{},[895,18379,18380,18382,18384],{},[898,18381,16183],{},[1708,18383,1710],{},[2505,18385,2507],{},[902,18387,16470],{"encoding":904},[883,18389,18391],{"className":18390},[886],[888,18392,18393],{"xmlns":890},[892,18394,18395,18403],{},[895,18396,18397,18399,18401],{},[898,18398,1747],{},[1708,18400,1710],{},[2505,18402,4028],{},[902,18404,18405],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,18408,18410],{"className":18409},[886],[888,18411,18412],{"xmlns":890},[892,18413,18414,18431],{},[895,18415,18416,18418,18421,18423,18425,18427,18429],{},[898,18417,1747],{},[1708,18419,18420],{},"∈",[1708,18422,17245],{"stretchy":1715},[2505,18424,2784],{},[1708,18426,1883],{"separator":1882},[2505,18428,4028],{},[1708,18430,1721],{"stretchy":1715},[902,18432,18433],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,18436,18438],{"className":18437},[886],[888,18439,18440],{"xmlns":890},[892,18441,18442,18458],{},[895,18443,18444,18446,18448,18450,18452,18454,18456],{},[898,18445,1747],{},[1708,18447,18420],{},[1708,18449,1716],{"stretchy":1715},[2505,18451,4028],{},[1708,18453,1883],{"separator":1882},[2505,18455,9704],{},[1708,18457,17262],{"stretchy":1715},[902,18459,18460],{"encoding":904},"P \\in (25, 50\\rangle",[115,18462,18464],{"id":18463},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,18466,18467],{},[3372,18468],{"alt":18469,"className":18470,"src":18471},"imek-elasticita-tr",[210,3376],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,18473,18474],{},[3372,18475],{"alt":18476,"className":18477,"src":18478},"imek-elasticita-podel-linearni-poptavky",[210,3376],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,18480,18481,18482,18532,18533,18549],{},"Pro celkový příjem platí ",[883,18483,18485],{"className":18484},[886],[888,18486,18487],{"xmlns":890},[892,18488,18489,18529],{},[895,18490,18491,18493,18495,18497,18499,18501,18503,18505,18507,18509,18511,18513,18515,18517,18519,18521,18523,18525,18527],{},[898,18492,1978],{},[898,18494,1975],{},[1708,18496,1710],{},[898,18498,1978],{},[898,18500,1975],{},[1708,18502,1716],{"stretchy":1715},[898,18504,1688],{},[1708,18506,1721],{"stretchy":1715},[1708,18508,1710],{},[898,18510,1747],{},[1708,18512,3703],{},[898,18514,1688],{},[1708,18516,1710],{},[898,18518,1688],{},[1708,18520,3703],{},[898,18522,16117],{},[1708,18524,1716],{"stretchy":1715},[898,18526,1688],{},[1708,18528,1721],{"stretchy":1715},[902,18530,18531],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,18534,18536],{"className":18535},[886],[888,18537,18538],{"xmlns":890},[892,18539,18540,18546],{},[895,18541,18542,18544],{},[898,18543,1741],{},[898,18545,1975],{},[902,18547,18548],{"encoding":904},"MR"," odvodíme:",[724,18551,18552],{},[883,18553,18555],{"className":18554},[886],[888,18556,18557],{"xmlns":890},[892,18558,18559,18667],{},[895,18560,18561,18563,18565,18567,18569,18575,18577,18579,18581,18583,18585,18587,18589,18591,18593,18595,18597,18603,18605,18607,18609,18611,18613,18615,18617,18631,18633,18635],{},[898,18562,1741],{},[898,18564,1975],{},[1708,18566,1710],{},[898,18568,1978],{},[1753,18570,18571,18573],{},[898,18572,1975],{},[1708,18574,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,18576,1716],{"stretchy":1715},[898,18578,1688],{},[1708,18580,1721],{"stretchy":1715},[1708,18582,1710],{},[898,18584,16117],{},[1708,18586,1716],{"stretchy":1715},[898,18588,1688],{},[1708,18590,1721],{"stretchy":1715},[1708,18592,2019],{},[898,18594,1688],{},[2247,18596,2659],{},[1753,18598,18599,18601],{},[898,18600,16117],{},[1708,18602,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,18604,1716],{"stretchy":1715},[898,18606,1688],{},[1708,18608,1721],{"stretchy":1715},[1708,18610,1710],{},[898,18612,1747],{},[1708,18614,2019],{},[898,18616,1688],{},[2358,18618,18619,18625],{},[895,18620,18621,18623],{},[898,18622,2364],{"mathvariant":1759},[898,18624,1747],{},[895,18626,18627,18629],{},[898,18628,2364],{"mathvariant":1759},[898,18630,1688],{},[1708,18632,1710],{},[898,18634,1747],{},[895,18636,18637,18639,18641,18643,18649,18651,18665],{},[1708,18638,1716],{"fence":1882},[2505,18640,2507],{},[1708,18642,2019],{},[2358,18644,18645,18647],{},[898,18646,1688],{},[898,18648,1747],{},[1708,18650,3703],{},[2358,18652,18653,18659],{},[895,18654,18655,18657],{},[898,18656,2364],{"mathvariant":1759},[898,18658,1747],{},[895,18660,18661,18663],{},[898,18662,2364],{"mathvariant":1759},[898,18664,1688],{},[1708,18666,1721],{"fence":1882},[902,18668,18669],{"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)",[724,18671,18672],{},[883,18673,18675],{"className":18674},[886],[888,18676,18677],{"xmlns":890},[892,18678,18679,18751],{},[895,18680,18681,18683,18685,18727,18729,18731],{},[1708,18682,1710],{},[898,18684,1747],{},[895,18686,18687,18689,18691,18693,18725],{},[1708,18688,1716],{"fence":1882},[2505,18690,2507],{},[1708,18692,2019],{},[2358,18694,18695,18697],{},[2505,18696,2507],{},[895,18698,18699,18707,18709],{},[3194,18700,18701],{"scriptlevel":2784,"displaystyle":1715},[2358,18702,18703,18705],{},[898,18704,1747],{},[898,18706,1688],{},[1708,18708,3703],{},[3194,18710,18711],{"scriptlevel":2784,"displaystyle":1715},[2358,18712,18713,18719],{},[895,18714,18715,18717],{},[898,18716,2364],{"mathvariant":1759},[898,18718,1688],{},[895,18720,18721,18723],{},[898,18722,2364],{"mathvariant":1759},[898,18724,1747],{},[1708,18726,1721],{"fence":1882},[1708,18728,1710],{},[898,18730,1747],{},[895,18732,18733,18735,18737,18739,18749],{},[1708,18734,1716],{"fence":1882},[2505,18736,2507],{},[1708,18738,2019],{},[2358,18740,18741,18743],{},[2505,18742,2507],{},[895,18744,18745,18747],{},[1708,18746,2726],{},[898,18748,16183],{},[1708,18750,1721],{"fence":1882},[902,18752,18753],{"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)",[724,18755,18756],{},"a tedy",[724,18758,18759],{},[883,18760,18762],{"className":18761,"title":3428,"style":3429},[3427],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1636,18764,18765,18834,19083],{},[724,18766,18767,18769,18770,18804,18805,18820,18821,2788],{},[883,18768,2518],{}," Intuice: vztah ",[883,18771,18773],{"className":18772},[886],[888,18774,18775],{"xmlns":890},[892,18776,18777,18801],{},[895,18778,18779,18781,18783,18785,18787,18789,18791,18793,18795,18797,18799],{},[898,18780,1741],{},[898,18782,1975],{},[1708,18784,1710],{},[898,18786,1747],{},[1708,18788,1716],{"stretchy":1715},[2505,18790,2507],{},[1708,18792,2726],{},[2505,18794,2507],{},[898,18796,1799],{"mathvariant":1759},[898,18798,16183],{},[1708,18800,1721],{"stretchy":1715},[902,18802,18803],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,18806,18808],{"className":18807},[886],[888,18809,18810],{"xmlns":890},[892,18811,18812,18818],{},[895,18813,18814,18816],{},[898,18815,1741],{},[898,18817,1975],{},[902,18819,18548],{"encoding":904}," jednoznačně určuje hodnota ",[883,18822,18824],{"className":18823},[886],[888,18825,18826],{"xmlns":890},[892,18827,18828,18832],{},[895,18829,18830],{},[898,18831,16183],{},[902,18833,16183],{"encoding":904},[120,18835,18836,18945,19014],{},[123,18837,18838,18855,18856,1729,18870,1729,18896,1729,18909,12636,18929,18944],{},[883,18839,18841],{"className":18840},[886],[888,18842,18843],{"xmlns":890},[892,18844,18845,18853],{},[895,18846,18847,18849,18851],{},[898,18848,16183],{},[1708,18850,2854],{},[2505,18852,2507],{},[902,18854,16434],{"encoding":904}," (elastická) ",[883,18857,18859],{"className":18858},[886],[888,18860,18861],{"xmlns":890},[892,18862,18863,18867],{},[895,18864,18865],{},[1708,18866,4782],{},[902,18868,18869],{"encoding":904},"\\Rightarrow",[883,18871,18873],{"className":18872},[886],[888,18874,18875],{"xmlns":890},[892,18876,18877,18893],{},[895,18878,18879,18881,18883,18885,18887,18889,18891],{},[2505,18880,2507],{},[1708,18882,2726],{},[2505,18884,2507],{},[898,18886,1799],{"mathvariant":1759},[898,18888,16183],{},[1708,18890,2854],{},[2505,18892,2784],{},[902,18894,18895],{"encoding":904},"1 - 1\u002FE > 0",[883,18897,18899],{"className":18898},[886],[888,18900,18901],{"xmlns":890},[892,18902,18903,18907],{},[895,18904,18905],{},[1708,18906,4782],{},[902,18908,18869],{"encoding":904},[883,18910,18912],{"className":18911},[886],[888,18913,18914],{"xmlns":890},[892,18915,18916,18926],{},[895,18917,18918,18920,18922,18924],{},[898,18919,1741],{},[898,18921,1975],{},[1708,18923,2854],{},[2505,18925,2784],{},[902,18927,18928],{"encoding":904},"MR > 0",[883,18930,18932],{"className":18931},[886],[888,18933,18934],{"xmlns":890},[892,18935,18936,18942],{},[895,18937,18938,18940],{},[898,18939,1978],{},[898,18941,1975],{},[902,18943,16029],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,18946,18947,18964,18965,1729,18978,12636,18998,19013],{},[883,18948,18950],{"className":18949},[886],[888,18951,18952],{"xmlns":890},[892,18953,18954,18962],{},[895,18955,18956,18958,18960],{},[898,18957,16183],{},[1708,18959,1710],{},[2505,18961,2507],{},[902,18963,16470],{"encoding":904}," (jednotková) ",[883,18966,18968],{"className":18967},[886],[888,18969,18970],{"xmlns":890},[892,18971,18972,18976],{},[895,18973,18974],{},[1708,18975,4782],{},[902,18977,18869],{"encoding":904},[883,18979,18981],{"className":18980},[886],[888,18982,18983],{"xmlns":890},[892,18984,18985,18995],{},[895,18986,18987,18989,18991,18993],{},[898,18988,1741],{},[898,18990,1975],{},[1708,18992,1710],{},[2505,18994,2784],{},[902,18996,18997],{"encoding":904},"MR = 0",[883,18999,19001],{"className":19000},[886],[888,19002,19003],{"xmlns":890},[892,19004,19005,19011],{},[895,19006,19007,19009],{},[898,19008,1978],{},[898,19010,1975],{},[902,19012,16029],{"encoding":904}," je extrém (maximum).",[123,19015,19016,19033,19034,1729,19047,12636,19067,19082],{},[883,19017,19019],{"className":19018},[886],[888,19020,19021],{"xmlns":890},[892,19022,19023,19031],{},[895,19024,19025,19027,19029],{},[898,19026,16183],{},[1708,19028,2932],{},[2505,19030,2507],{},[902,19032,16452],{"encoding":904}," (neelastická) ",[883,19035,19037],{"className":19036},[886],[888,19038,19039],{"xmlns":890},[892,19040,19041,19045],{},[895,19042,19043],{},[1708,19044,4782],{},[902,19046,18869],{"encoding":904},[883,19048,19050],{"className":19049},[886],[888,19051,19052],{"xmlns":890},[892,19053,19054,19064],{},[895,19055,19056,19058,19060,19062],{},[898,19057,1741],{},[898,19059,1975],{},[1708,19061,2932],{},[2505,19063,2784],{},[902,19065,19066],{"encoding":904},"MR \u003C 0",[883,19068,19070],{"className":19069},[886],[888,19071,19072],{"xmlns":890},[892,19073,19074,19080],{},[895,19075,19076,19078],{},[898,19077,1978],{},[898,19079,1975],{},[902,19081,16029],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,19084,19085,19086,2155],{},"Viz také ",[207,19087,13830],{"className":19088,"dataFsResolvedFilePath":827,"href":828},[210],[198,19090,19092],{"id":19091},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,19094,19095,19115,19116,19142,19143,19158,19159,19172,19173,19186,19187,19200,19201,19217,19218,1729,19233,19236,19237,19217,19253,2155],{},[38,19096,19097,19098,2511],{},"(a) Poptávka elastická (",[883,19099,19101],{"className":19100},[886],[888,19102,19103],{"xmlns":890},[892,19104,19105,19113],{},[895,19106,19107,19109,19111],{},[898,19108,16183],{},[1708,19110,2854],{},[2505,19112,2507],{},[902,19114,16434],{"encoding":904}," Z (4.12) plyne ",[883,19117,19119],{"className":19118},[886],[888,19120,19121],{"xmlns":890},[892,19122,19123,19139],{},[895,19124,19125,19127,19129,19131,19133,19135,19137],{},[898,19126,1741],{},[898,19128,1975],{},[1708,19130,1716],{"stretchy":1715},[898,19132,1688],{},[1708,19134,1721],{"stretchy":1715},[1708,19136,2854],{},[2505,19138,2784],{},[902,19140,19141],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,19144,19146],{"className":19145},[886],[888,19147,19148],{"xmlns":890},[892,19149,19150,19156],{},[895,19151,19152,19154],{},[898,19153,1978],{},[898,19155,1975],{},[902,19157,16029],{"encoding":904}," je rostoucí funkcí ",[883,19160,19162],{"className":19161},[886],[888,19163,19164],{"xmlns":890},[892,19165,19166,19170],{},[895,19167,19168],{},[898,19169,1688],{},[902,19171,1688],{"encoding":904},". Avšak růst ",[883,19174,19176],{"className":19175},[886],[888,19177,19178],{"xmlns":890},[892,19179,19180,19184],{},[895,19181,19182],{},[898,19183,1688],{},[902,19185,1688],{"encoding":904}," je odezvou na pokles ceny ",[883,19188,19190],{"className":19189},[886],[888,19191,19192],{"xmlns":890},[892,19193,19194,19198],{},[895,19195,19196],{},[898,19197,1747],{},[902,19199,1747],{"encoding":904},". Tudíž s ",[614,19202,19203,19204],{},"poklesem ceny ",[883,19205,19207],{"className":19206},[886],[888,19208,19209],{"xmlns":890},[892,19210,19211,19215],{},[895,19212,19213],{},[898,19214,1747],{},[902,19216,1747],{"encoding":904}," celkový příjem ",[883,19219,19221],{"className":19220},[886],[888,19222,19223],{"xmlns":890},[892,19224,19225,19231],{},[895,19226,19227,19229],{},[898,19228,1978],{},[898,19230,1975],{},[902,19232,16029],{"encoding":904},[614,19234,19235],{},"roste"," a s ",[614,19238,19239,19240],{},"růstem ceny ",[883,19241,19243],{"className":19242},[886],[888,19244,19245],{"xmlns":890},[892,19246,19247,19251],{},[895,19248,19249],{},[898,19250,1747],{},[902,19252,1747],{"encoding":904},[614,19254,19255],{},"klesá",[1636,19257,19258],{},[724,19259,19260,19263],{},[38,19261,19262],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,19265,19266,19115,19286,1343,19312,19327,19328,19341,19342,19355,19356,19369,19370,19217,19383,1729,19398,2155],{},[38,19267,19268,19269,2511],{},"(b) Poptávka neelastická (",[883,19270,19272],{"className":19271},[886],[888,19273,19274],{"xmlns":890},[892,19275,19276,19284],{},[895,19277,19278,19280,19282],{},[898,19279,16183],{},[1708,19281,2932],{},[2505,19283,2507],{},[902,19285,16452],{"encoding":904},[883,19287,19289],{"className":19288},[886],[888,19290,19291],{"xmlns":890},[892,19292,19293,19309],{},[895,19294,19295,19297,19299,19301,19303,19305,19307],{},[898,19296,1741],{},[898,19298,1975],{},[1708,19300,1716],{"stretchy":1715},[898,19302,1688],{},[1708,19304,1721],{"stretchy":1715},[1708,19306,2932],{},[2505,19308,2784],{},[902,19310,19311],{"encoding":904},"MR(Q) \u003C 0",[883,19313,19315],{"className":19314},[886],[888,19316,19317],{"xmlns":890},[892,19318,19319,19325],{},[895,19320,19321,19323],{},[898,19322,1978],{},[898,19324,1975],{},[902,19326,16029],{"encoding":904}," je klesající funkce ",[883,19329,19331],{"className":19330},[886],[888,19332,19333],{"xmlns":890},[892,19334,19335,19339],{},[895,19336,19337],{},[898,19338,1688],{},[902,19340,1688],{"encoding":904},", tj. s růstem ",[883,19343,19345],{"className":19344},[886],[888,19346,19347],{"xmlns":890},[892,19348,19349,19353],{},[895,19350,19351],{},[898,19352,1688],{},[902,19354,1688],{"encoding":904}," (s poklesem ceny ",[883,19357,19359],{"className":19358},[886],[888,19360,19361],{"xmlns":890},[892,19362,19363,19367],{},[895,19364,19365],{},[898,19366,1747],{},[902,19368,1747],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,19371,19373],{"className":19372},[886],[888,19374,19375],{"xmlns":890},[892,19376,19377,19381],{},[895,19378,19379],{},[898,19380,1747],{},[902,19382,1747],{"encoding":904},[883,19384,19386],{"className":19385},[886],[888,19387,19388],{"xmlns":890},[892,19389,19390,19396],{},[895,19391,19392,19394],{},[898,19393,1978],{},[898,19395,1975],{},[902,19397,16029],{"encoding":904},[614,19399,19235],{},[1636,19401,19402],{},[724,19403,19404,19407],{},[38,19405,19406],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,19409,19410,19115,19430,19449,19450,19465,19466,19536,19537,1771,19565,19598,19599,17508,19627,19642,19643,2155],{},[38,19411,19412,19413,2511],{},"(c) Jednotková elasticita (",[883,19414,19416],{"className":19415},[886],[888,19417,19418],{"xmlns":890},[892,19419,19420,19428],{},[895,19421,19422,19424,19426],{},[898,19423,16183],{},[1708,19425,1710],{},[2505,19427,2507],{},[902,19429,16470],{"encoding":904},[883,19431,19433],{"className":19432},[886],[888,19434,19435],{"xmlns":890},[892,19436,19437,19447],{},[895,19438,19439,19441,19443,19445],{},[898,19440,1741],{},[898,19442,1975],{},[1708,19444,1710],{},[2505,19446,2784],{},[902,19448,18997],{"encoding":904}," — nutná podmínka extrému ",[883,19451,19453],{"className":19452},[886],[888,19454,19455],{"xmlns":890},[892,19456,19457,19463],{},[895,19458,19459,19461],{},[898,19460,1978],{},[898,19462,1975],{},[902,19464,16029],{"encoding":904},". Dále ",[883,19467,19469],{"className":19468},[886],[888,19470,19471],{"xmlns":890},[892,19472,19473,19533],{},[895,19474,19475,19477,19487,19489,19491,19497,19499,19505,19507,19509,19511,19513,19515,19517,19527,19529,19531],{},[898,19476,1978],{},[1753,19478,19479,19481],{},[898,19480,1975],{},[895,19482,19483,19485],{},[1708,19484,1761],{"mathvariant":1759},[1708,19486,1761],{"mathvariant":1759},[1708,19488,1710],{},[898,19490,1741],{},[1753,19492,19493,19495],{},[898,19494,1975],{},[1708,19496,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,19498,1710],{},[1753,19500,19501,19503],{},[898,19502,16117],{},[1708,19504,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,19506,1716],{"stretchy":1715},[898,19508,1688],{},[1708,19510,1721],{"stretchy":1715},[1708,19512,2019],{},[898,19514,1688],{},[2247,19516,2659],{},[1753,19518,19519,19521],{},[898,19520,16117],{},[895,19522,19523,19525],{},[1708,19524,1761],{"mathvariant":1759},[1708,19526,1761],{"mathvariant":1759},[1708,19528,1716],{"stretchy":1715},[898,19530,1688],{},[1708,19532,1721],{"stretchy":1715},[902,19534,19535],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,19538,19540],{"className":19539},[886],[888,19541,19542],{"xmlns":890},[892,19543,19544,19562],{},[895,19545,19546,19552,19554,19556,19558,19560],{},[1753,19547,19548,19550],{},[898,19549,16117],{},[1708,19551,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,19553,1716],{"stretchy":1715},[898,19555,1688],{},[1708,19557,1721],{"stretchy":1715},[1708,19559,2932],{},[2505,19561,2784],{},[902,19563,19564],{"encoding":904},"D'(Q) \u003C 0",[883,19566,19568],{"className":19567},[886],[888,19569,19570],{"xmlns":890},[892,19571,19572,19595],{},[895,19573,19574,19584,19586,19588,19590,19593],{},[1753,19575,19576,19578],{},[898,19577,16117],{},[895,19579,19580,19582],{},[1708,19581,1761],{"mathvariant":1759},[1708,19583,1761],{"mathvariant":1759},[1708,19585,1716],{"stretchy":1715},[898,19587,1688],{},[1708,19589,1721],{"stretchy":1715},[1708,19591,19592],{},"≤",[2505,19594,2784],{},[902,19596,19597],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,19600,19602],{"className":19601},[886],[888,19603,19604],{"xmlns":890},[892,19605,19606,19624],{},[895,19607,19608,19610,19620,19622],{},[898,19609,1978],{},[1753,19611,19612,19614],{},[898,19613,1975],{},[895,19615,19616,19618],{},[1708,19617,1761],{"mathvariant":1759},[1708,19619,1761],{"mathvariant":1759},[1708,19621,2932],{},[2505,19623,2784],{},[902,19625,19626],{"encoding":904},"TR'' \u003C 0",[883,19628,19630],{"className":19629},[886],[888,19631,19632],{"xmlns":890},[892,19633,19634,19640],{},[895,19635,19636,19638],{},[898,19637,1978],{},[898,19639,1975],{},[902,19641,16029],{"encoding":904}," nabývá ",[38,19644,19645],{},"maxima",[1636,19647,19648],{},[724,19649,19650,19653],{},[38,19651,19652],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,19655,19656],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,19658,19659],{},[38,19660,19661],{},"Souhrnná tabulka Pravidel 1–3:",[16,19663,19664,19768],{},[19,19665,19666],{},[22,19667,19668,19671,19686,19703,19734,19765],{},[25,19669,19670],{},"Charakter poptávky",[25,19672,19673],{},[883,19674,19676],{"className":19675},[886],[888,19677,19678],{"xmlns":890},[892,19679,19680,19684],{},[895,19681,19682],{},[898,19683,16183],{},[902,19685,16183],{"encoding":904},[25,19687,19688],{},[883,19689,19691],{"className":19690},[886],[888,19692,19693],{"xmlns":890},[892,19694,19695,19701],{},[895,19696,19697,19699],{},[898,19698,1741],{},[898,19700,1975],{},[902,19702,18548],{"encoding":904},[25,19704,19705,19706,1729,19719],{},"Pokles ceny ",[883,19707,19709],{"className":19708},[886],[888,19710,19711],{"xmlns":890},[892,19712,19713,19717],{},[895,19714,19715],{},[1708,19716,4782],{},[902,19718,18869],{"encoding":904},[883,19720,19722],{"className":19721},[886],[888,19723,19724],{"xmlns":890},[892,19725,19726,19732],{},[895,19727,19728,19730],{},[898,19729,1978],{},[898,19731,1975],{},[902,19733,16029],{"encoding":904},[25,19735,19736,19737,1729,19750],{},"Růst ceny ",[883,19738,19740],{"className":19739},[886],[888,19741,19742],{"xmlns":890},[892,19743,19744,19748],{},[895,19745,19746],{},[1708,19747,4782],{},[902,19749,18869],{"encoding":904},[883,19751,19753],{"className":19752},[886],[888,19754,19755],{"xmlns":890},[892,19756,19757,19763],{},[895,19758,19759,19761],{},[898,19760,1978],{},[898,19762,1975],{},[902,19764,16029],{"encoding":904},[25,19766,19767],{},"Doporučení",[30,19769,19770,19819,19869],{},[22,19771,19772,19774,19792,19810,19812,19814],{},[35,19773,16008],{},[35,19775,19776],{},[883,19777,19779],{"className":19778},[886],[888,19780,19781],{"xmlns":890},[892,19782,19783,19789],{},[895,19784,19785,19787],{},[1708,19786,2854],{},[2505,19788,2507],{},[902,19790,19791],{"encoding":904},"> 1",[35,19793,19794],{},[883,19795,19797],{"className":19796},[886],[888,19798,19799],{"xmlns":890},[892,19800,19801,19807],{},[895,19802,19803,19805],{},[1708,19804,2854],{},[2505,19806,2784],{},[902,19808,19809],{"encoding":904},"> 0",[35,19811,19235],{},[35,19813,19255],{},[35,19815,19816],{},[38,19817,19818],{},"snížit cenu",[22,19820,19821,19824,19842,19860,19862,19864],{},[35,19822,19823],{},"jednotková",[35,19825,19826],{},[883,19827,19829],{"className":19828},[886],[888,19830,19831],{"xmlns":890},[892,19832,19833,19839],{},[895,19834,19835,19837],{},[1708,19836,1710],{},[2505,19838,2507],{},[902,19840,19841],{"encoding":904},"= 1",[35,19843,19844],{},[883,19845,19847],{"className":19846},[886],[888,19848,19849],{"xmlns":890},[892,19850,19851,19857],{},[895,19852,19853,19855],{},[1708,19854,1710],{},[2505,19856,2784],{},[902,19858,19859],{"encoding":904},"= 0",[35,19861,15666],{},[35,19863,15666],{},[35,19865,19866],{},[38,19867,19868],{},"držet cenu",[22,19870,19871,19873,19891,19909,19911,19913],{},[35,19872,16012],{},[35,19874,19875],{},[883,19876,19878],{"className":19877},[886],[888,19879,19880],{"xmlns":890},[892,19881,19882,19888],{},[895,19883,19884,19886],{},[1708,19885,2932],{},[2505,19887,2507],{},[902,19889,19890],{"encoding":904},"\u003C 1",[35,19892,19893],{},[883,19894,19896],{"className":19895},[886],[888,19897,19898],{"xmlns":890},[892,19899,19900,19906],{},[895,19901,19902,19904],{},[1708,19903,2932],{},[2505,19905,2784],{},[902,19907,19908],{"encoding":904},"\u003C 0",[35,19910,19255],{},[35,19912,19235],{},[35,19914,19915],{},[38,19916,19917],{},"zvýšit cenu",[198,19919,19921],{"id":19920},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,19923,19924,19925,19950,19951,19973,19974,19987,19988,20001,20002,3033,20015,17508,20041,20093],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,19926,19928],{"className":19927},[886],[888,19929,19930],{"xmlns":890},[892,19931,19932,19948],{},[895,19933,19934,19936,19938,19940,19942],{},[898,19935,1747],{},[1708,19937,1710],{},[2505,19939,9238],{},[1708,19941,2726],{},[1753,19943,19944,19946],{},[898,19945,1688],{},[2505,19947,3132],{},[902,19949,17380],{"encoding":904},". Reálné cenové rozpětí je ",[883,19952,19954],{"className":19953},[886],[888,19955,19956],{"xmlns":890},[892,19957,19958,19970],{},[895,19959,19960,19962,19964,19966,19968],{},[1708,19961,17245],{"stretchy":1715},[2505,19963,2507],{},[1708,19965,1883],{"separator":1882},[2505,19967,9238],{},[1708,19969,17262],{"stretchy":1715},[902,19971,19972],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,19975,19977],{"className":19976},[886],[888,19978,19979],{"xmlns":890},[892,19980,19981,19985],{},[895,19982,19983],{},[898,19984,1688],{},[902,19986,1688],{"encoding":904}," jako funkci ",[883,19989,19991],{"className":19990},[886],[888,19992,19993],{"xmlns":890},[892,19994,19995,19999],{},[895,19996,19997],{},[898,19998,1747],{},[902,20000,1747],{"encoding":904},"; pro nezáporné ",[883,20003,20005],{"className":20004},[886],[888,20006,20007],{"xmlns":890},[892,20008,20009,20013],{},[895,20010,20011],{},[898,20012,1688],{},[902,20014,1688],{"encoding":904},[883,20016,20018],{"className":20017},[886],[888,20019,20020],{"xmlns":890},[892,20021,20022,20038],{},[895,20023,20024,20026,20028],{},[898,20025,1688],{},[1708,20027,1710],{},[9351,20029,20030],{},[895,20031,20032,20034,20036],{},[2505,20033,9238],{},[1708,20035,2726],{},[898,20037,1747],{},[902,20039,20040],{"encoding":904},"Q = \\sqrt{100 - P}",[883,20042,20044],{"className":20043},[886],[888,20045,20046],{"xmlns":890},[892,20047,20048,20090],{},[895,20049,20050,20066,20068,20070],{},[3194,20051,20052],{"scriptlevel":2784,"displaystyle":1882},[2358,20053,20054,20060],{},[895,20055,20056,20058],{},[898,20057,2364],{"mathvariant":1759},[898,20059,1688],{},[895,20061,20062,20064],{},[898,20063,2364],{"mathvariant":1759},[898,20065,1747],{},[1708,20067,1710],{},[1708,20069,2726],{},[3194,20071,20072],{"scriptlevel":2784,"displaystyle":1882},[2358,20073,20074,20076],{},[2505,20075,2507],{},[895,20077,20078,20080],{},[2505,20079,3132],{},[9351,20081,20082],{},[895,20083,20084,20086,20088],{},[2505,20085,9238],{},[1708,20087,2726],{},[898,20089,1747],{},[902,20091,20092],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,20095,20096],{},[883,20097,20099],{"className":20098},[886],[888,20100,20101],{"xmlns":890},[892,20102,20103,20225],{},[895,20104,20105,20107,20109,20111,20113,20115,20117,20123,20125,20139,20141,20143,20157,20159,20185,20187,20205,20207,20223],{},[898,20106,16183],{},[1708,20108,1716],{"stretchy":1715},[898,20110,1747],{},[1708,20112,1721],{"stretchy":1715},[1708,20114,1710],{},[1708,20116,2726],{},[2358,20118,20119,20121],{},[898,20120,1747],{},[898,20122,1688],{},[1708,20124,3703],{},[2358,20126,20127,20133],{},[895,20128,20129,20131],{},[898,20130,2364],{"mathvariant":1759},[898,20132,1688],{},[895,20134,20135,20137],{},[898,20136,2364],{"mathvariant":1759},[898,20138,1747],{},[1708,20140,1710],{},[1708,20142,2726],{},[2358,20144,20145,20147],{},[898,20146,1747],{},[9351,20148,20149],{},[895,20150,20151,20153,20155],{},[2505,20152,9238],{},[1708,20154,2726],{},[898,20156,1747],{},[1708,20158,3703],{},[895,20160,20161,20163,20165,20183],{},[1708,20162,1716],{"fence":1882},[1708,20164,2726],{},[2358,20166,20167,20169],{},[2505,20168,2507],{},[895,20170,20171,20173],{},[2505,20172,3132],{},[9351,20174,20175],{},[895,20176,20177,20179,20181],{},[2505,20178,9238],{},[1708,20180,2726],{},[898,20182,1747],{},[1708,20184,1721],{"fence":1882},[1708,20186,1710],{},[2358,20188,20189,20191],{},[898,20190,1747],{},[895,20192,20193,20195,20197,20199,20201,20203],{},[2505,20194,3132],{},[1708,20196,1716],{"stretchy":1715},[2505,20198,9238],{},[1708,20200,2726],{},[898,20202,1747],{},[1708,20204,1721],{"stretchy":1715},[1708,20206,1710],{},[2358,20208,20209,20215],{},[895,20210,20211,20213],{},[2505,20212,6097],{},[898,20214,1747],{},[895,20216,20217,20219,20221],{},[2505,20218,9238],{},[1708,20220,2726],{},[898,20222,1747],{},[898,20224,2155],{"mathvariant":1759},[902,20226,20227],{"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}.",[724,20229,20230,20231,2788],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,20232,20234],{"className":20233},[886],[888,20235,20236],{"xmlns":890},[892,20237,20238,20262],{},[895,20239,20240,20258,20260],{},[3194,20241,20242],{"scriptlevel":2784,"displaystyle":1882},[2358,20243,20244,20250],{},[895,20245,20246,20248],{},[2505,20247,6097],{},[898,20249,1747],{},[895,20251,20252,20254,20256],{},[2505,20253,9238],{},[1708,20255,2726],{},[898,20257,1747],{},[1708,20259,1710],{},[2505,20261,2507],{},[902,20263,20264],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,20266,20267],{},[883,20268,20270],{"className":20269},[886],[888,20271,20272],{"xmlns":890},[892,20273,20274,20306],{},[895,20275,20276,20282,20284,20291,20293,20296,20304],{},[1753,20277,20278,20280],{},[898,20279,1747],{},[1708,20281,2417],{},[1708,20283,1710],{},[2358,20285,20286,20289],{},[2505,20287,20288],{},"200",[2505,20290,3121],{},[1708,20292,17816],{},[2505,20294,20295],{},"66,",[20297,20298,20299,20301],"mover",{"accent":1882},[2505,20300,3947],{},[1708,20302,20303],{"stretchy":1882},"‾",[898,20305,2155],{"mathvariant":1759},[902,20307,20308],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,20310,20311],{},"S využitím vlastnosti (4.8):",[120,20313,20314,20359,20401],{},[123,20315,20316,20317,20351,20352,20354,20355,20358],{},"Při cenách ",[883,20318,20320],{"className":20319},[886],[888,20321,20322],{"xmlns":890},[892,20323,20324,20348],{},[895,20325,20326,20328,20330,20332,20334,20336,20338,20340,20346],{},[898,20327,1747],{},[1708,20329,18420],{},[1708,20331,17245],{"stretchy":1715},[2505,20333,2507],{},[1708,20335,8197],{"separator":1882},[2247,20337,2659],{},[2505,20339,20295],{},[20297,20341,20342,20344],{"accent":1882},[2505,20343,3947],{},[1708,20345,20303],{"stretchy":1882},[1708,20347,1721],{"stretchy":1715},[902,20349,20350],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,20353,16012],{}," — dle ",[614,20356,20357],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,20360,20316,20361,20351,20395,20354,20397,20400],{},[883,20362,20364],{"className":20363},[886],[888,20365,20366],{"xmlns":890},[892,20367,20368,20392],{},[895,20369,20370,20372,20374,20376,20378,20384,20386,20388,20390],{},[898,20371,1747],{},[1708,20373,18420],{},[1708,20375,1716],{"stretchy":1715},[2505,20377,20295],{},[20297,20379,20380,20382],{"accent":1882},[2505,20381,3947],{},[1708,20383,20303],{"stretchy":1882},[1708,20385,8197],{"separator":1882},[2247,20387,2659],{},[2505,20389,9238],{},[1708,20391,17262],{"stretchy":1715},[902,20393,20394],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,20396,16008],{},[614,20398,20399],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,20402,20403,20404,20407,20408,20436,20437,20440],{},"Dle ",[614,20405,20406],{},"Pravidla 3"," je při ceně ",[883,20409,20411],{"className":20410},[886],[888,20412,20413],{"xmlns":890},[892,20414,20415,20433],{},[895,20416,20417,20423,20425,20427],{},[1753,20418,20419,20421],{},[898,20420,1747],{},[1708,20422,2417],{},[1708,20424,1710],{},[2505,20426,20295],{},[20297,20428,20429,20431],{"accent":1882},[2505,20430,3947],{},[1708,20432,20303],{"stretchy":1882},[902,20434,20435],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,20438,20439],{},"maxima celkového příjmu"," ve výši",[724,20442,20443],{},[883,20444,20446],{"className":20445},[886],[888,20447,20448],{"xmlns":890},[892,20449,20450,20528],{},[895,20451,20452,20454,20456,20458,20464,20466,20468,20474,20476,20490,20492,20498,20500,20508,20510,20523,20525],{},[898,20453,1978],{},[898,20455,1975],{},[1708,20457,1716],{"stretchy":1715},[1753,20459,20460,20462],{},[898,20461,1747],{},[1708,20463,2417],{},[1708,20465,1721],{"stretchy":1715},[1708,20467,1710],{},[1753,20469,20470,20472],{},[898,20471,1747],{},[1708,20473,2417],{},[1708,20475,3703],{},[9351,20477,20478],{},[895,20479,20480,20482,20484],{},[2505,20481,9238],{},[1708,20483,2726],{},[1753,20485,20486,20488],{},[898,20487,1747],{},[1708,20489,2417],{},[1708,20491,1710],{},[2358,20493,20494,20496],{},[2505,20495,20288],{},[2505,20497,3121],{},[1708,20499,3703],{},[9351,20501,20502],{},[2358,20503,20504,20506],{},[2505,20505,9238],{},[2505,20507,3121],{},[1708,20509,1710],{},[2358,20511,20512,20515],{},[2505,20513,20514],{},"2000",[895,20516,20517,20519],{},[2505,20518,3121],{},[9351,20520,20521],{},[2505,20522,3121],{},[1708,20524,17816],{},[2505,20526,20527],{},"384,9.",[902,20529,20530],{"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.",[724,20532,20533,20534,2155],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,20535,20537],{"className":20536},[886],[888,20538,20539],{"xmlns":890},[892,20540,20541,20547],{},[895,20542,20543,20545],{},[898,20544,1978],{},[898,20546,1975],{},[902,20548,16029],{"encoding":904},[115,20550,20552],{"id":20551},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,20554,20555,20556,20559],{},"Analogicky se definuje ",[38,20557,20558],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,20561,20562],{},[883,20563,20565],{"className":20564,"title":3428,"style":3429},[3427],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,20567,5411,20568,20592,20593,20625],{},[883,20569,20571],{"className":20570},[886],[888,20572,20573],{"xmlns":890},[892,20574,20575,20589],{},[895,20576,20577,20579,20581,20583,20585,20587],{},[898,20578,1688],{},[1708,20580,1710],{},[898,20582,1981],{},[1708,20584,1716],{"stretchy":1715},[898,20586,1747],{},[1708,20588,1721],{"stretchy":1715},[902,20590,20591],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,20594,20596],{"className":20595},[886],[888,20597,20598],{"xmlns":890},[892,20599,20600,20622],{},[895,20601,20602,20618,20620],{},[3194,20603,20604],{"scriptlevel":2784,"displaystyle":1882},[2358,20605,20606,20612],{},[895,20607,20608,20610],{},[898,20609,2364],{"mathvariant":1759},[898,20611,1688],{},[895,20613,20614,20616],{},[898,20615,2364],{"mathvariant":1759},[898,20617,1747],{},[1708,20619,2854],{},[2505,20621,2784],{},[902,20623,20624],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,20627,20628],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1636,20630,20631],{},[724,20632,20633,20634],{},"S rostoucí cenou elasticita nabídky roste. ",[883,20635,20637],{"className":20636},[886],[888,20638,20639],{"xmlns":890},[892,20640,20641,20650],{},[895,20642,20643,20645,20648],{},[1708,20644,1716],{"stretchy":1715},[2505,20646,20647],{},"4.14",[1708,20649,1721],{"stretchy":1715},[902,20651,20652],{"encoding":904},"(4.14)",[724,20654,20655],{},"Pro nominální změny platí",[724,20657,20658],{},[883,20659,20661],{"className":20660,"title":3428,"style":3429},[3427],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,20663,20664],{},"a pro procentní změny",[724,20666,20667],{},[883,20668,20670],{"className":20669,"title":3428,"style":3429},[3427],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,20672,20673],{},"(bez znaménka minus).",[198,20675,20677],{"id":20676},"příklad-47","Příklad 4.7",[724,20679,20680,20681,2788],{},"Nabídka ",[883,20682,20684],{"className":20683},[886],[888,20685,20686],{"xmlns":890},[892,20687,20688,20712],{},[895,20689,20690,20692,20694,20696,20702,20704,20706,20708,20710],{},[898,20691,1688],{},[1708,20693,1710],{},[2505,20695,10909],{},[1753,20697,20698,20700],{},[898,20699,1747],{},[2505,20701,3132],{},[1708,20703,2019],{},[2505,20705,3993],{},[898,20707,1747],{},[1708,20709,2019],{},[2505,20711,9660],{},[902,20713,20714],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,20716,20717],{},[883,20718,20720],{"className":20719},[886],[888,20721,20722],{"xmlns":890},[892,20723,20724,20770],{},[895,20725,20726,20728,20730,20754,20756,20758,20760,20762,20764,20766,20768],{},[898,20727,16183],{},[1708,20729,1710],{},[2358,20731,20732,20734],{},[898,20733,1747],{},[895,20735,20736,20738,20744,20746,20748,20750,20752],{},[2505,20737,10909],{},[1753,20739,20740,20742],{},[898,20741,1747],{},[2505,20743,3132],{},[1708,20745,2019],{},[2505,20747,3993],{},[898,20749,1747],{},[1708,20751,2019],{},[2505,20753,9660],{},[2247,20755,2659],{},[1708,20757,1716],{"stretchy":1715},[2505,20759,3958],{},[898,20761,1747],{},[1708,20763,2019],{},[2505,20765,3993],{},[1708,20767,1721],{"stretchy":1715},[898,20769,2155],{"mathvariant":1759},[902,20771,20772],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,20774,17038,20775,1343,20805,1343,20832,20868,20869,20894,20895,20913,20914,2155],{},[883,20776,20778],{"className":20777},[886],[888,20779,20780],{"xmlns":890},[892,20781,20782,20802],{},[895,20783,20784,20786,20788,20790,20792,20794],{},[898,20785,16183],{},[1708,20787,1716],{"stretchy":1715},[2505,20789,4003],{},[1708,20791,1721],{"stretchy":1715},[1708,20793,1710],{},[3194,20795,20796],{"scriptlevel":2784,"displaystyle":1715},[2358,20797,20798,20800],{},[2505,20799,2507],{},[2505,20801,3121],{},[902,20803,20804],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,20806,20808],{"className":20807},[886],[888,20809,20810],{"xmlns":890},[892,20811,20812,20829],{},[895,20813,20814,20816,20818,20823,20825,20827],{},[898,20815,16183],{},[1708,20817,1716],{"stretchy":1715},[9351,20819,20820],{},[2505,20821,20822],{},"1500",[1708,20824,1721],{"stretchy":1715},[1708,20826,1710],{},[2505,20828,2507],{},[902,20830,20831],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,20833,20835],{"className":20834},[886],[888,20836,20837],{"xmlns":890},[892,20838,20839,20865],{},[895,20840,20841,20843,20845,20847,20849,20851,20860,20862],{},[898,20842,16183],{},[1708,20844,1716],{"stretchy":1715},[2505,20846,9238],{},[1708,20848,1721],{"stretchy":1715},[1708,20850,1710],{},[3194,20852,20853],{"scriptlevel":2784,"displaystyle":1715},[2358,20854,20855,20857],{},[2505,20856,9704],{},[2505,20858,20859],{},"33",[1708,20861,17816],{},[2505,20863,20864],{},"1,515",[902,20866,20867],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,20870,20872],{"className":20871},[886],[888,20873,20874],{"xmlns":890},[892,20875,20876,20891],{},[895,20877,20878,20880,20882,20886,20888],{},[898,20879,1747],{},[1708,20881,2854],{},[9351,20883,20884],{},[2505,20885,20822],{},[1708,20887,2638],{},[2505,20889,20890],{},"38,7",[902,20892,20893],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,20896,20898],{"className":20897},[886],[888,20899,20900],{"xmlns":890},[892,20901,20902,20910],{},[895,20903,20904,20906,20908],{},[898,20905,1747],{},[1708,20907,2932],{},[2505,20909,20890],{},[902,20911,20912],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,20915,20917],{"className":20916},[886],[888,20918,20919],{"xmlns":890},[892,20920,20921,20958],{},[895,20922,20923,20925,20927,20929,20931,20939,20941,20943,20945,20948,20954,20956],{},[898,20924,2633],{"mathvariant":1759},[898,20926,1688],{},[898,20928,17841],{"mathvariant":1759},[1708,20930,2638],{},[3194,20932,20933],{"scriptlevel":2784,"displaystyle":1715},[2358,20934,20935,20937],{},[2505,20936,2507],{},[2505,20938,3121],{},[1708,20940,3703],{},[2505,20942,4018],{},[1708,20944,1710],{},[2505,20946,20947],{},"6,",[20297,20949,20950,20952],{"accent":1882},[2505,20951,3947],{},[1708,20953,20303],{"stretchy":1882},[2247,20955,2659],{},[898,20957,17841],{"mathvariant":1759},[902,20959,20960],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,20962,20964],{"id":20963},"vícefaktorový-model","Vícefaktorový model",[724,20966,20967,20968,20981,20982,1729,20985,20998,20999,1729,21002,21020,21021,1729,21024,2788],{},"Předpokládejme, že poptávané množství ",[883,20969,20971],{"className":20970},[886],[888,20972,20973],{"xmlns":890},[892,20974,20975,20979],{},[895,20976,20977],{},[898,20978,1688],{},[902,20980,1688],{"encoding":904}," závisí na ",[38,20983,20984],{},"ceně základního zboží",[883,20986,20988],{"className":20987},[886],[888,20989,20990],{"xmlns":890},[892,20991,20992,20996],{},[895,20993,20994],{},[898,20995,1747],{},[902,20997,1747],{"encoding":904},", na ",[38,21000,21001],{},"ceně alternativního zboží",[883,21003,21005],{"className":21004},[886],[888,21006,21007],{"xmlns":890},[892,21008,21009,21017],{},[895,21010,21011],{},[1743,21012,21013,21015],{},[898,21014,1747],{},[898,21016,1786],{},[902,21018,21019],{"encoding":904},"P_A"," a na ",[38,21022,21023],{},"důchodu",[883,21025,21027],{"className":21026},[886],[888,21028,21029],{"xmlns":890},[892,21030,21031,21036],{},[895,21032,21033],{},[898,21034,21035],{},"Y",[902,21037,21035],{"encoding":904},[724,21039,21040],{},[883,21041,21043],{"className":21042,"title":3428,"style":3429},[3427],"Q = D(P, P_A, Y). \\tag{4.17}",[724,21045,21046,21047,21050],{},"V analogii jednofaktorového modelu pracujeme s ",[38,21048,21049],{},"parciálními derivacemi"," funkce poptávky.",[198,21052,21054],{"id":21053},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,21056,21057],{},[883,21058,21060],{"className":21059,"title":3428,"style":3429},[3427],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,21062,5411,21063,21083,21084,21097,21098,2941,21120,1729,21122,21168,21169,21182,21183,21200],{},[883,21064,21066],{"className":21065},[886],[888,21067,21068],{"xmlns":890},[892,21069,21070,21080],{},[895,21071,21072],{},[4754,21073,21074,21076,21078],{},[898,21075,1688],{},[898,21077,1747],{},[1708,21079,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,21081,21082],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,21085,21087],{"className":21086},[886],[888,21088,21089],{"xmlns":890},[892,21090,21091,21095],{},[895,21092,21093],{},[898,21094,1747],{},[902,21096,1747],{"encoding":904},". Vždy ",[883,21099,21101],{"className":21100},[886],[888,21102,21103],{"xmlns":890},[892,21104,21105,21117],{},[895,21106,21107,21113,21115],{},[1743,21108,21109,21111],{},[898,21110,16183],{},[898,21112,1747],{},[1708,21114,6762],{},[2505,21116,2784],{},[902,21118,21119],{"encoding":904},"E_P \\ge 0",[614,21121,8418],{},[883,21123,21125],{"className":21124},[886],[888,21126,21127],{"xmlns":890},[892,21128,21129,21165],{},[895,21130,21131,21137,21139,21145,21147,21155,21157,21163],{},[1743,21132,21133,21135],{},[898,21134,16183],{},[898,21136,1747],{},[1708,21138,1716],{"stretchy":1715},[1753,21140,21141,21143],{},[898,21142,1747],{},[1708,21144,2417],{},[1708,21146,1883],{"separator":1882},[4754,21148,21149,21151,21153],{},[898,21150,1747],{},[898,21152,1786],{},[1708,21154,2417],{},[1708,21156,1883],{"separator":1882},[1753,21158,21159,21161],{},[898,21160,21035],{},[1708,21162,2417],{},[1708,21164,1721],{"stretchy":1715},[902,21166,21167],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,21170,21172],{"className":21171},[886],[888,21173,21174],{"xmlns":890},[892,21175,21176,21180],{},[895,21177,21178],{},[898,21179,1688],{},[902,21181,1688],{"encoding":904}," při 1% změně ",[883,21184,21186],{"className":21185},[886],[888,21187,21188],{"xmlns":890},[892,21189,21190,21198],{},[895,21191,21192],{},[1753,21193,21194,21196],{},[898,21195,1747],{},[1708,21197,2417],{},[902,21199,16331],{"encoding":904},", ceteris paribus.",[198,21202,21204],{"id":21203},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,21206,21207],{},[883,21208,21210],{"className":21209,"title":3428,"style":3429},[3427],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,21212,21213,21168,21215,21228,21229,21246],{},[614,21214,8418],{},[883,21216,21218],{"className":21217},[886],[888,21219,21220],{"xmlns":890},[892,21221,21222,21226],{},[895,21223,21224],{},[898,21225,1688],{},[902,21227,1688],{"encoding":904}," základního zboží při 1% změně ceny ",[883,21230,21232],{"className":21231},[886],[888,21233,21234],{"xmlns":890},[892,21235,21236,21244],{},[895,21237,21238],{},[1743,21239,21240,21242],{},[898,21241,1747],{},[898,21243,1786],{},[902,21245,21019],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,21248,21249],{},[38,21250,21251],{},"Znaménko závisí na povaze alternativního zboží:",[120,21253,21254,21342],{},[123,21255,21256,21257,21260,21261,21278,21279,1729,21292,2155],{},"Je-li alternativní zboží ",[38,21258,21259],{},"komplement",", růst ",[883,21262,21264],{"className":21263},[886],[888,21265,21266],{"xmlns":890},[892,21267,21268,21276],{},[895,21269,21270],{},[1743,21271,21272,21274],{},[898,21273,1747],{},[898,21275,1786],{},[902,21277,21019],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,21280,21282],{"className":21281},[886],[888,21283,21284],{"xmlns":890},[892,21285,21286,21290],{},[895,21287,21288],{},[898,21289,1688],{},[902,21291,1688],{"encoding":904},[883,21293,21295],{"className":21294},[886],[888,21296,21297],{"xmlns":890},[892,21298,21299,21339],{},[895,21300,21301,21303,21305,21317,21319,21321,21323,21325,21335,21337],{},[1708,21302,4782],{},[2247,21304,4779],{},[4754,21306,21307,21309,21315],{},[898,21308,1688],{},[1743,21310,21311,21313],{},[898,21312,1747],{},[898,21314,1786],{},[1708,21316,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,21318,2932],{},[2505,21320,2784],{},[1708,21322,1883],{"separator":1882},[2247,21324,4779],{},[1743,21326,21327,21329],{},[898,21328,16183],{},[1743,21330,21331,21333],{},[898,21332,1747],{},[898,21334,1786],{},[1708,21336,2932],{},[2505,21338,2784],{},[902,21340,21341],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,21343,21256,21344,21260,21347,21364,21365,21378,21379,2155],{},[38,21345,21346],{},"substitut",[883,21348,21350],{"className":21349},[886],[888,21351,21352],{"xmlns":890},[892,21353,21354,21362],{},[895,21355,21356],{},[1743,21357,21358,21360],{},[898,21359,1747],{},[898,21361,1786],{},[902,21363,21019],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,21366,21368],{"className":21367},[886],[888,21369,21370],{"xmlns":890},[892,21371,21372,21376],{},[895,21373,21374],{},[898,21375,1688],{},[902,21377,1688],{"encoding":904}," roste ",[883,21380,21382],{"className":21381},[886],[888,21383,21384],{"xmlns":890},[892,21385,21386,21426],{},[895,21387,21388,21390,21392,21404,21406,21408,21410,21412,21422,21424],{},[1708,21389,4782],{},[2247,21391,4779],{},[4754,21393,21394,21396,21402],{},[898,21395,1688],{},[1743,21397,21398,21400],{},[898,21399,1747],{},[898,21401,1786],{},[1708,21403,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,21405,2854],{},[2505,21407,2784],{},[1708,21409,1883],{"separator":1882},[2247,21411,4779],{},[1743,21413,21414,21416],{},[898,21415,16183],{},[1743,21417,21418,21420],{},[898,21419,1747],{},[898,21421,1786],{},[1708,21423,2854],{},[2505,21425,2784],{},[902,21427,21428],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,21430,21433],{"className":21431,"title":21432,"style":3429},[3427],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":21435},[21436,21440,21441,21449,21450,21454,21457],{"id":15831,"depth":642,"text":15832,"children":21437},[21438,21439],{"id":15861,"depth":649,"text":15862},{"id":16037,"depth":649,"text":16038},{"id":16072,"depth":642,"text":16073},{"id":16097,"depth":642,"text":16098,"children":21442},[21443,21444,21445,21446,21448],{"id":16782,"depth":649,"text":16783},{"id":16872,"depth":649,"text":16873},{"id":17206,"depth":649,"text":17207},{"id":17288,"depth":649,"text":21447},"Výpočet, je-li dáno PP jako funkce QQ",{"id":17547,"depth":649,"text":17548},{"id":17869,"depth":642,"text":17870},{"id":18463,"depth":642,"text":18464,"children":21451},[21452,21453],{"id":19091,"depth":649,"text":19092},{"id":19920,"depth":649,"text":19921},{"id":20551,"depth":642,"text":20552,"children":21455},[21456],{"id":20676,"depth":649,"text":20677},{"id":20963,"depth":642,"text":20964,"children":21458},[21459,21460],{"id":21053,"depth":649,"text":21054},{"id":21203,"depth":649,"text":21204},{},"\u002Ftopics\u002Felasticita",{"title":15804,"description":641},[1138,1136],"topics\u002Felasticita",[1128,15838,21467,21468,21469,21470],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":21473,"title":21474,"body":21475,"course":1128,"courses":659,"created":1129,"description":22999,"extension":661,"meta":23000,"navigation":664,"path":23001,"seo":23002,"sources":23003,"stem":23004,"tags":23005,"type":13951,"updated":677,"__hash__":23010},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":21476,"toc":22984},[21477,21480,21554,21561,21565,21628,21713,21717,21744,21810,21865,21869,21895,21982,21984,22016,22186,22190,22260,22307,22311,22372,22478,22491,22495,22497,22525,22590,22592,22599,22687,22711,22909,22913,22949,22951],[12,21478,21474],{"id":21479},"kalkul-funkcí-více-proměnných",[724,21481,21482,21483,21486,21487,1343,21516,2155],{},"Většina ekonomických veličin závisí na ",[38,21484,21485],{},"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 ",[883,21488,21490],{"className":21489},[886],[888,21491,21492],{"xmlns":890},[892,21493,21494,21513],{},[895,21495,21496,21499,21501,21503,21505,21507,21509,21511],{},[898,21497,21498],{},"z",[1708,21500,1710],{},[898,21502,14009],{},[1708,21504,1716],{"stretchy":1715},[898,21506,14014],{},[1708,21508,1883],{"separator":1882},[898,21510,14004],{},[1708,21512,1721],{"stretchy":1715},[902,21514,21515],{"encoding":904},"z = f(x, y)",[883,21517,21519],{"className":21518},[886],[888,21520,21521],{"xmlns":890},[892,21522,21523,21551],{},[895,21524,21525,21528,21530,21532,21534,21536,21538,21540,21542,21544,21546,21548],{},[898,21526,21527],{},"w",[1708,21529,1710],{},[898,21531,14009],{},[1708,21533,1716],{"stretchy":1715},[898,21535,14014],{},[1708,21537,1883],{"separator":1882},[898,21539,14004],{},[1708,21541,1883],{"separator":1882},[898,21543,21498],{},[1708,21545,1721],{"stretchy":1715},[1708,21547,1883],{"separator":1882},[1708,21549,21550],{},"…",[902,21552,21553],{"encoding":904},"w = f(x, y, z), \\ldots",[724,21555,21556],{},[3372,21557],{"alt":21558,"className":21559,"src":21560},"imek-funkce-2d-vrstevnice",[210,3376],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,21562,21564],{"id":21563},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,21566,3818,21567,21594,21595,21623,21624,21627],{},[883,21568,21570],{"className":21569},[886],[888,21571,21572],{"xmlns":890},[892,21573,21574,21592],{},[895,21575,21576,21578,21580,21582,21584,21586,21588,21590],{},[898,21577,21498],{},[1708,21579,1710],{},[898,21581,14009],{},[1708,21583,1716],{"stretchy":1715},[898,21585,14014],{},[1708,21587,1883],{"separator":1882},[898,21589,14004],{},[1708,21591,1721],{"stretchy":1715},[902,21593,21515],{"encoding":904}," se křivkou s předpisem ",[883,21596,21598],{"className":21597},[886],[888,21599,21600],{"xmlns":890},[892,21601,21602,21620],{},[895,21603,21604,21606,21608,21610,21612,21614,21616,21618],{},[898,21605,14009],{},[1708,21607,1716],{"stretchy":1715},[898,21609,14014],{},[1708,21611,1883],{"separator":1882},[898,21613,14004],{},[1708,21615,1721],{"stretchy":1715},[1708,21617,1710],{},[898,21619,14142],{},[902,21621,21622],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,21625,21626],{},"vrstevnice"," funkce. V ekonomii:",[120,21629,21630,21677],{},[123,21631,21632,21635,21636,21672,21673,2155],{},[38,21633,21634],{},"Indiferenční křivky"," užitečnosti ",[883,21637,21639],{"className":21638},[886],[888,21640,21641],{"xmlns":890},[892,21642,21643,21669],{},[895,21644,21645,21647,21649,21655,21657,21663,21665,21667],{},[898,21646,900],{},[1708,21648,1716],{"stretchy":1715},[1743,21650,21651,21653],{},[898,21652,1688],{},[2505,21654,2507],{},[1708,21656,1883],{"separator":1882},[1743,21658,21659,21661],{},[898,21660,1688],{},[2505,21662,3132],{},[1708,21664,1721],{"stretchy":1715},[1708,21666,1710],{},[898,21668,14142],{},[902,21670,21671],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,21674,21676],{"className":21675,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,21678,21679,21681,21682,21672,21710,2155],{},[38,21680,8072],{}," produkce ",[883,21683,21685],{"className":21684},[886],[888,21686,21687],{"xmlns":890},[892,21688,21689,21707],{},[895,21690,21691,21693,21695,21697,21699,21701,21703,21705],{},[898,21692,1688],{},[1708,21694,1716],{"stretchy":1715},[898,21696,1658],{},[1708,21698,1883],{"separator":1882},[898,21700,1673],{},[1708,21702,1721],{"stretchy":1715},[1708,21704,1710],{},[898,21706,14142],{},[902,21708,21709],{"encoding":904},"Q(L, K) = c",[207,21711,13945],{"className":21712,"dataFsResolvedFilePath":857,"href":858},[210],[115,21714,21716],{"id":21715},"parciální-derivace","Parciální derivace",[724,21718,3818,21719,21743],{},[883,21720,21722],{"className":21721},[886],[888,21723,21724],{"xmlns":890},[892,21725,21726,21740],{},[895,21727,21728,21730,21732,21734,21736,21738],{},[898,21729,14009],{},[1708,21731,1716],{"stretchy":1715},[898,21733,14014],{},[1708,21735,1883],{"separator":1882},[898,21737,14004],{},[1708,21739,1721],{"stretchy":1715},[902,21741,21742],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,21745,21746],{},[883,21747,21749],{"className":21748},[886],[888,21750,21751],{"xmlns":890},[892,21752,21753,21807],{},[895,21754,21755,21763,21765,21779,21781,21783,21791,21793],{},[4754,21756,21757,21759,21761],{},[898,21758,14009],{},[898,21760,14014],{},[1708,21762,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,21764,1710],{},[2358,21766,21767,21773],{},[895,21768,21769,21771],{},[898,21770,7252],{"mathvariant":1759},[898,21772,14009],{},[895,21774,21775,21777],{},[898,21776,7252],{"mathvariant":1759},[898,21778,14014],{},[1708,21780,1883],{"separator":1882},[3213,21782],{"width":3215},[4754,21784,21785,21787,21789],{},[898,21786,14009],{},[898,21788,14004],{},[1708,21790,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,21792,1710],{},[2358,21794,21795,21801],{},[895,21796,21797,21799],{},[898,21798,7252],{"mathvariant":1759},[898,21800,14009],{},[895,21802,21803,21805],{},[898,21804,7252],{"mathvariant":1759},[898,21806,14004],{},[902,21808,21809],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,21811,21812,21813,2155],{},"Hodnoty v bodě: ",[883,21814,21816],{"className":21815},[886],[888,21817,21818],{"xmlns":890},[892,21819,21820,21862],{},[895,21821,21822,21830,21832,21834,21836,21838,21840,21842,21844,21852,21854,21856,21858,21860],{},[4754,21823,21824,21826,21828],{},[898,21825,14009],{},[898,21827,14014],{},[1708,21829,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,21831,1716],{"stretchy":1715},[898,21833,207],{},[1708,21835,1883],{"separator":1882},[898,21837,1923],{},[1708,21839,1721],{"stretchy":1715},[1708,21841,1883],{"separator":1882},[2247,21843,14279],{},[4754,21845,21846,21848,21850],{},[898,21847,14009],{},[898,21849,14004],{},[1708,21851,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,21853,1716],{"stretchy":1715},[898,21855,207],{},[1708,21857,1883],{"separator":1882},[898,21859,1923],{},[1708,21861,1721],{"stretchy":1715},[902,21863,21864],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,21866,21868],{"id":21867},"ekonomické-značení","Ekonomické značení",[724,21870,21871,21872,2788],{},"Pro produkční funkci ",[883,21873,21875],{"className":21874},[886],[888,21876,21877],{"xmlns":890},[892,21878,21879,21893],{},[895,21880,21881,21883,21885,21887,21889,21891],{},[898,21882,1688],{},[1708,21884,1716],{"stretchy":1715},[898,21886,1658],{},[1708,21888,1883],{"separator":1882},[898,21890,1673],{},[1708,21892,1721],{"stretchy":1715},[902,21894,6661],{"encoding":904},[120,21896,21897,21939],{},[123,21898,21899,14451,21918,1695,21920,1721],{},[883,21900,21902],{"className":21901},[886],[888,21903,21904],{"xmlns":890},[892,21905,21906,21916],{},[895,21907,21908],{},[4754,21909,21910,21912,21914],{},[898,21911,1688],{},[898,21913,1658],{},[1708,21915,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,21917,8917],{"encoding":904},[38,21919,1728],{},[883,21921,21923],{"className":21922},[886],[888,21924,21925],{"xmlns":890},[892,21926,21927,21937],{},[895,21928,21929,21931],{},[898,21930,1741],{},[1743,21932,21933,21935],{},[898,21934,1747],{},[898,21936,1658],{},[902,21938,2300],{"encoding":904},[123,21940,21941,14451,21960,1695,21963,1721],{},[883,21942,21944],{"className":21943},[886],[888,21945,21946],{"xmlns":890},[892,21947,21948,21958],{},[895,21949,21950],{},[4754,21951,21952,21954,21956],{},[898,21953,1688],{},[898,21955,1673],{},[1708,21957,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,21959,8937],{"encoding":904},[38,21961,21962],{},"mezní produkt kapitálu",[883,21964,21966],{"className":21965},[886],[888,21967,21968],{"xmlns":890},[892,21969,21970,21980],{},[895,21971,21972,21974],{},[898,21973,1741],{},[1743,21975,21976,21978],{},[898,21977,1747],{},[898,21979,1673],{},[902,21981,7210],{"encoding":904},[198,21983,14545],{"id":14544},[724,21985,21986,2788],{},[883,21987,21989],{"className":21988},[886],[888,21990,21991],{"xmlns":890},[892,21992,21993,22013],{},[895,21994,21995,22003,22005,22007,22009,22011],{},[4754,21996,21997,21999,22001],{},[898,21998,14009],{},[898,22000,14014],{},[1708,22002,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22004,1716],{"stretchy":1715},[898,22006,207],{},[1708,22008,1883],{"separator":1882},[898,22010,1923],{},[1708,22012,1721],{"stretchy":1715},[902,22014,22015],{"encoding":904},"f'_x(a, b)",[120,22017,22018,22076],{},[123,22019,22020,22021,22034,22035,22048,22049,22075],{},"rychlost změny ",[883,22022,22024],{"className":22023},[886],[888,22025,22026],{"xmlns":890},[892,22027,22028,22032],{},[895,22029,22030],{},[898,22031,14009],{},[902,22033,14009],{"encoding":904}," vůči ",[883,22036,22038],{"className":22037},[886],[888,22039,22040],{"xmlns":890},[892,22041,22042,22046],{},[895,22043,22044],{},[898,22045,14014],{},[902,22047,14014],{"encoding":904}," při ",[883,22050,22052],{"className":22051},[886],[888,22053,22054],{"xmlns":890},[892,22055,22056,22072],{},[895,22057,22058,22060,22062,22064,22066,22068,22070],{},[898,22059,14014],{},[1708,22061,1710],{},[898,22063,207],{},[1708,22065,1883],{"separator":1882},[898,22067,14004],{},[1708,22069,1710],{},[898,22071,1923],{},[902,22073,22074],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,22077,22078,22079,14633,22092,22105,22106,9416,22124,2155],{},"přibližná změna ",[883,22080,22082],{"className":22081},[886],[888,22083,22084],{"xmlns":890},[892,22085,22086,22090],{},[895,22087,22088],{},[898,22089,14009],{},[902,22091,14009],{"encoding":904},[883,22093,22095],{"className":22094},[886],[888,22096,22097],{"xmlns":890},[892,22098,22099,22103],{},[895,22100,22101],{},[898,22102,14014],{},[902,22104,14014],{"encoding":904}," o 1 (a pevném ",[883,22107,22109],{"className":22108},[886],[888,22110,22111],{"xmlns":890},[892,22112,22113,22121],{},[895,22114,22115,22117,22119],{},[898,22116,14004],{},[1708,22118,1710],{},[898,22120,1923],{},[902,22122,22123],{"encoding":904},"y = b",[883,22125,22127],{"className":22126},[886],[888,22128,22129],{"xmlns":890},[892,22130,22131,22183],{},[895,22132,22133,22135,22137,22139,22141,22143,22145,22147,22149,22151,22153,22155,22157,22159,22161,22163,22165,22173,22175,22177,22179,22181],{},[898,22134,14009],{},[1708,22136,1716],{"stretchy":1715},[898,22138,207],{},[1708,22140,2019],{},[2505,22142,2507],{},[1708,22144,1883],{"separator":1882},[898,22146,1923],{},[1708,22148,1721],{"stretchy":1715},[1708,22150,2638],{},[898,22152,14009],{},[1708,22154,1716],{"stretchy":1715},[898,22156,207],{},[1708,22158,1883],{"separator":1882},[898,22160,1923],{},[1708,22162,1721],{"stretchy":1715},[1708,22164,2019],{},[4754,22166,22167,22169,22171],{},[898,22168,14009],{},[898,22170,14014],{},[1708,22172,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22174,1716],{"stretchy":1715},[898,22176,207],{},[1708,22178,1883],{"separator":1882},[898,22180,1923],{},[1708,22182,1721],{"stretchy":1715},[902,22184,22185],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,22187,22189],{"id":22188},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,22191,22192],{},[883,22193,22195],{"className":22194},[886],[888,22196,22197],{"xmlns":890},[892,22198,22199,22257],{},[895,22200,22201,22203,22205,22207,22215,22217,22219,22221,22223,22225,22227,22229,22231,22233,22241,22243,22245,22247,22249,22251,22253,22255],{},[898,22202,2364],{},[898,22204,14009],{},[1708,22206,1710],{},[4754,22208,22209,22211,22213],{},[898,22210,14009],{},[898,22212,14014],{},[1708,22214,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22216,1716],{"stretchy":1715},[898,22218,14014],{},[1708,22220,1883],{"separator":1882},[898,22222,14004],{},[1708,22224,1721],{"stretchy":1715},[2247,22226,2659],{},[898,22228,2364],{},[898,22230,14014],{},[1708,22232,2019],{},[4754,22234,22235,22237,22239],{},[898,22236,14009],{},[898,22238,14004],{},[1708,22240,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22242,1716],{"stretchy":1715},[898,22244,14014],{},[1708,22246,1883],{"separator":1882},[898,22248,14004],{},[1708,22250,1721],{"stretchy":1715},[2247,22252,2659],{},[898,22254,2364],{},[898,22256,14004],{},[902,22258,22259],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,22261,14959,22262,1826,22284,22306],{},[883,22263,22265],{"className":22264},[886],[888,22266,22267],{"xmlns":890},[892,22268,22269,22281],{},[895,22270,22271,22273,22275,22277,22279],{},[898,22272,2364],{},[898,22274,14014],{},[1708,22276,1883],{"separator":1882},[898,22278,2364],{},[898,22280,14004],{},[902,22282,22283],{"encoding":904},"dx, dy",[883,22285,22287],{"className":22286},[886],[888,22288,22289],{"xmlns":890},[892,22290,22291,22303],{},[895,22292,22293,22295,22297,22299,22301],{},[898,22294,2633],{"mathvariant":1759},[898,22296,14009],{},[1708,22298,2638],{},[898,22300,2364],{},[898,22302,14009],{},[902,22304,22305],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,22308,22310],{"id":22309},"implicitní-funkce","Implicitní funkce",[724,22312,22313,22314,22343,22344,22357,22358,22371],{},"Je-li vztah dán rovnicí ",[883,22315,22317],{"className":22316},[886],[888,22318,22319],{"xmlns":890},[892,22320,22321,22340],{},[895,22322,22323,22326,22328,22330,22332,22334,22336,22338],{},[898,22324,22325],{},"F",[1708,22327,1716],{"stretchy":1715},[898,22329,14014],{},[1708,22331,1883],{"separator":1882},[898,22333,14004],{},[1708,22335,1721],{"stretchy":1715},[1708,22337,1710],{},[2505,22339,2784],{},[902,22341,22342],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,22345,22347],{"className":22346},[886],[888,22348,22349],{"xmlns":890},[892,22350,22351,22355],{},[895,22352,22353],{},[898,22354,14004],{},[902,22356,14004],{"encoding":904}," podle ",[883,22359,22361],{"className":22360},[886],[888,22362,22363],{"xmlns":890},[892,22364,22365,22369],{},[895,22366,22367],{},[898,22368,14014],{},[902,22370,14014],{"encoding":904}," (nebo naopak):",[724,22373,22374],{},[883,22375,22377],{"className":22376},[886],[888,22378,22379],{"xmlns":890},[892,22380,22381,22475],{},[895,22382,22383,22389,22391,22405,22407,22409,22427,22429,22431,22437,22439,22453,22455,22457],{},[1753,22384,22385,22387],{},[898,22386,14004],{},[1708,22388,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22390,1710],{},[2358,22392,22393,22399],{},[895,22394,22395,22397],{},[898,22396,2364],{},[898,22398,14004],{},[895,22400,22401,22403],{},[898,22402,2364],{},[898,22404,14014],{},[1708,22406,1710],{},[1708,22408,2726],{},[2358,22410,22411,22419],{},[4754,22412,22413,22415,22417],{},[898,22414,22325],{},[898,22416,14014],{},[1708,22418,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,22420,22421,22423,22425],{},[898,22422,22325],{},[898,22424,14004],{},[1708,22426,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22428,1883],{"separator":1882},[3213,22430],{"width":3215},[1753,22432,22433,22435],{},[898,22434,14014],{},[1708,22436,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22438,1710],{},[2358,22440,22441,22447],{},[895,22442,22443,22445],{},[898,22444,2364],{},[898,22446,14014],{},[895,22448,22449,22451],{},[898,22450,2364],{},[898,22452,14004],{},[1708,22454,1710],{},[1708,22456,2726],{},[2358,22458,22459,22467],{},[4754,22460,22461,22463,22465],{},[898,22462,22325],{},[898,22464,14004],{},[1708,22466,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,22468,22469,22471,22473],{},[898,22470,22325],{},[898,22472,14014],{},[1708,22474,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,22476,22477],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,22479,22480,22481,22484,22485,1771,22488,2155],{},"Tato vzorec dává ",[38,22482,22483],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,22486,8303],{"className":22487,"dataFsResolvedFilePath":857,"href":858},[210],[207,22489,13825],{"className":22490,"dataFsResolvedFilePath":878,"href":879},[210],[115,22492,22494],{"id":22493},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,22496,15206],{"id":15205},[724,22498,22499,22500,22524],{},"V bodě extrému ",[883,22501,22503],{"className":22502},[886],[888,22504,22505],{"xmlns":890},[892,22506,22507,22521],{},[895,22508,22509,22511,22513,22515,22517,22519],{},[898,22510,1786],{},[1708,22512,6940],{"stretchy":1715},[898,22514,207],{},[1708,22516,1883],{"separator":1882},[898,22518,1923],{},[1708,22520,6981],{"stretchy":1715},[902,22522,22523],{"encoding":904},"A[a, b]"," musí platit současně:",[724,22526,22527],{},[883,22528,22530],{"className":22529},[886],[888,22531,22532],{"xmlns":890},[892,22533,22534,22587],{},[895,22535,22536,22544,22546,22548,22550,22552,22554,22556,22558,22560,22563,22565,22573,22575,22577,22579,22581,22583,22585],{},[4754,22537,22538,22540,22542],{},[898,22539,14009],{},[898,22541,14014],{},[1708,22543,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22545,1716],{"stretchy":1715},[898,22547,207],{},[1708,22549,1883],{"separator":1882},[898,22551,1923],{},[1708,22553,1721],{"stretchy":1715},[1708,22555,1710],{},[2505,22557,2784],{},[2247,22559,4779],{},[1708,22561,22562],{},"∧",[2247,22564,4779],{},[4754,22566,22567,22569,22571],{},[898,22568,14009],{},[898,22570,14004],{},[1708,22572,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,22574,1716],{"stretchy":1715},[898,22576,207],{},[1708,22578,1883],{"separator":1882},[898,22580,1923],{},[1708,22582,1721],{"stretchy":1715},[1708,22584,1710],{},[2505,22586,2784],{},[902,22588,22589],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,22591,15280],{"id":15279},[724,22593,22594,22595,22598],{},"Definujeme ",[38,22596,22597],{},"diskriminant"," (Hessián zjednodušeně):",[724,22600,22601],{},[883,22602,22604],{"className":22603},[886],[888,22605,22606],{"xmlns":890},[892,22607,22608,22684],{},[895,22609,22610,22612,22614,22616,22618,22620,22622,22624,22640,22642,22658,22660,22662,22678],{},[898,22611,16117],{},[1708,22613,1716],{"stretchy":1715},[898,22615,14014],{},[1708,22617,1883],{"separator":1882},[898,22619,14004],{},[1708,22621,1721],{"stretchy":1715},[1708,22623,1710],{},[4754,22625,22626,22628,22634],{},[898,22627,14009],{},[895,22629,22630,22632],{},[898,22631,14014],{},[898,22633,14014],{},[895,22635,22636,22638],{},[1708,22637,1761],{"mathvariant":1759},[1708,22639,1761],{"mathvariant":1759},[1708,22641,3703],{},[4754,22643,22644,22646,22652],{},[898,22645,14009],{},[895,22647,22648,22650],{},[898,22649,14004],{},[898,22651,14004],{},[895,22653,22654,22656],{},[1708,22655,1761],{"mathvariant":1759},[1708,22657,1761],{"mathvariant":1759},[1708,22659,2726],{},[1708,22661,1716],{"stretchy":1715},[4754,22663,22664,22666,22672],{},[898,22665,14009],{},[895,22667,22668,22670],{},[898,22669,14014],{},[898,22671,14004],{},[895,22673,22674,22676],{},[1708,22675,1761],{"mathvariant":1759},[1708,22677,1761],{"mathvariant":1759},[1753,22679,22680,22682],{},[1708,22681,1721],{"stretchy":1715},[2505,22683,3132],{},[902,22685,22686],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,22688,22689,22690,2788],{},"V podezřelém bodě ",[883,22691,22693],{"className":22692},[886],[888,22694,22695],{"xmlns":890},[892,22696,22697,22709],{},[895,22698,22699,22701,22703,22705,22707],{},[1708,22700,6940],{"stretchy":1715},[898,22702,207],{},[1708,22704,1883],{"separator":1882},[898,22706,1923],{},[1708,22708,6981],{"stretchy":1715},[902,22710,7373],{"encoding":904},[152,22712,22713,22840,22876],{},[123,22714,22715,22745,22746],{},[38,22716,22717,2788],{},[883,22718,22720],{"className":22719},[886],[888,22721,22722],{"xmlns":890},[892,22723,22724,22742],{},[895,22725,22726,22728,22730,22732,22734,22736,22738,22740],{},[898,22727,16117],{},[1708,22729,1716],{"stretchy":1715},[898,22731,207],{},[1708,22733,1883],{"separator":1882},[898,22735,1923],{},[1708,22737,1721],{"stretchy":1715},[1708,22739,2854],{},[2505,22741,2784],{},[902,22743,22744],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,22747,22748,22794],{},[123,22749,22750,15366,22792],{},[883,22751,22753],{"className":22752},[886],[888,22754,22755],{"xmlns":890},[892,22756,22757,22789],{},[895,22758,22759,22775,22777,22779,22781,22783,22785,22787],{},[4754,22760,22761,22763,22769],{},[898,22762,14009],{},[895,22764,22765,22767],{},[898,22766,14014],{},[898,22768,14014],{},[895,22770,22771,22773],{},[1708,22772,1761],{"mathvariant":1759},[1708,22774,1761],{"mathvariant":1759},[1708,22776,1716],{"stretchy":1715},[898,22778,207],{},[1708,22780,1883],{"separator":1882},[898,22782,1923],{},[1708,22784,1721],{"stretchy":1715},[1708,22786,2854],{},[2505,22788,2784],{},[902,22790,22791],{"encoding":904},"f''_{xx}(a, b) > 0",[38,22793,15724],{},[123,22795,22796,15366,22838],{},[883,22797,22799],{"className":22798},[886],[888,22800,22801],{"xmlns":890},[892,22802,22803,22835],{},[895,22804,22805,22821,22823,22825,22827,22829,22831,22833],{},[4754,22806,22807,22809,22815],{},[898,22808,14009],{},[895,22810,22811,22813],{},[898,22812,14014],{},[898,22814,14014],{},[895,22816,22817,22819],{},[1708,22818,1761],{"mathvariant":1759},[1708,22820,1761],{"mathvariant":1759},[1708,22822,1716],{"stretchy":1715},[898,22824,207],{},[1708,22826,1883],{"separator":1882},[898,22828,1923],{},[1708,22830,1721],{"stretchy":1715},[1708,22832,2932],{},[2505,22834,2784],{},[902,22836,22837],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,22839,15666],{},[123,22841,22842,1729,22872,22875],{},[38,22843,22844,2788],{},[883,22845,22847],{"className":22846},[886],[888,22848,22849],{"xmlns":890},[892,22850,22851,22869],{},[895,22852,22853,22855,22857,22859,22861,22863,22865,22867],{},[898,22854,16117],{},[1708,22856,1716],{"stretchy":1715},[898,22858,207],{},[1708,22860,1883],{"separator":1882},[898,22862,1923],{},[1708,22864,1721],{"stretchy":1715},[1708,22866,2932],{},[2505,22868,2784],{},[902,22870,22871],{"encoding":904},"D(a, b) \u003C 0",[38,22873,22874],{},"sedlo"," (v daném bodě extrém není).",[123,22877,22878,22908],{},[38,22879,22880,2788],{},[883,22881,22883],{"className":22882},[886],[888,22884,22885],{"xmlns":890},[892,22886,22887,22905],{},[895,22888,22889,22891,22893,22895,22897,22899,22901,22903],{},[898,22890,16117],{},[1708,22892,1716],{"stretchy":1715},[898,22894,207],{},[1708,22896,1883],{"separator":1882},[898,22898,1923],{},[1708,22900,1721],{"stretchy":1715},[1708,22902,1710],{},[2505,22904,2784],{},[902,22906,22907],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,22910,22912],{"id":22911},"vázané-extrémy","Vázané extrémy",[724,22914,22915,22916,22945,22946,2155],{},"Pro extrémy s omezující podmínkou ",[883,22917,22919],{"className":22918},[886],[888,22920,22921],{"xmlns":890},[892,22922,22923,22942],{},[895,22924,22925,22928,22930,22932,22934,22936,22938,22940],{},[898,22926,22927],{},"g",[1708,22929,1716],{"stretchy":1715},[898,22931,14014],{},[1708,22933,1883],{"separator":1882},[898,22935,14004],{},[1708,22937,1721],{"stretchy":1715},[1708,22939,1710],{},[2505,22941,2784],{},[902,22943,22944],{"encoding":904},"g(x, y) = 0"," se používá ",[207,22947,793],{"className":22948,"dataFsResolvedFilePath":791,"href":792},[210],[115,22950,13763],{"id":13762},[120,22952,22953,22960,22967],{},[123,22954,22955,1729,22957],{},[38,22956,13871],{},[207,22958,775],{"className":22959,"dataFsResolvedFilePath":773,"href":774},[210],[123,22961,22962,1729,22964],{},[38,22963,15753],{},[207,22965,793],{"className":22966,"dataFsResolvedFilePath":791,"href":792},[210],[123,22968,22969,1729,22971,22975,22976,22979,22980,22983],{},[38,22970,15761],{},[207,22972,22974],{"className":22973,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,22977,880],{"className":22978,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,22981,13875],{"className":22982,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":22985},[22986,22987,22991,22992,22993,22997,22998],{"id":21563,"depth":642,"text":21564},{"id":21715,"depth":642,"text":21716,"children":22988},[22989,22990],{"id":21867,"depth":649,"text":21868},{"id":14544,"depth":649,"text":14545},{"id":22188,"depth":642,"text":22189},{"id":22309,"depth":642,"text":22310},{"id":22493,"depth":642,"text":22494,"children":22994},[22995,22996],{"id":15205,"depth":649,"text":15206},{"id":15279,"depth":649,"text":15280},{"id":22911,"depth":642,"text":22912},{"id":13762,"depth":642,"text":13763},"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":21474,"description":22999},[1135],"topics\u002Ffunkce-vice-promennych",[1128,23006,15798,23007,23008,23009],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":23012,"title":775,"body":23013,"course":1128,"courses":659,"created":1129,"description":23869,"extension":661,"meta":23870,"navigation":664,"path":23871,"seo":23872,"sources":23873,"stem":23874,"tags":23875,"type":13951,"updated":677,"__hash__":23882},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":23014,"toc":23859},[23015,23018,23029,23033,23078,23158,23162,23238,23280,23287,23291,23295,23324,23382,23429,23467,23471,23521,23573,23625,23669,23672,23675,23747,23750,23822,23829,23831],[12,23016,775],{"id":23017},"integrál",[724,23019,23020,23021,23024,23025,23028],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,23022,23023],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,23026,23027],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,23030,23032],{"id":23031},"neurčitý-integrál","Neurčitý integrál",[724,23034,23035],{},[883,23036,23038],{"className":23037},[886],[888,23039,23040],{"xmlns":890},[892,23041,23042,23075],{},[895,23043,23044,23046,23048,23050,23052,23054,23057,23059,23061,23063,23065,23067,23069,23071,23073],{},[898,23045,22325],{},[1708,23047,1716],{"stretchy":1715},[898,23049,14014],{},[1708,23051,1721],{"stretchy":1715},[1708,23053,1710],{},[1708,23055,23056],{},"∫",[898,23058,14009],{},[1708,23060,1716],{"stretchy":1715},[898,23062,14014],{},[1708,23064,1721],{"stretchy":1715},[2247,23066,2659],{},[898,23068,2364],{},[898,23070,14014],{},[1708,23072,2019],{},[898,23074,3455],{},[902,23076,23077],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,23079,5411,23080,2941,23114,3033,23127,23130,23131,1343,23144,23157],{},[883,23081,23083],{"className":23082},[886],[888,23084,23085],{"xmlns":890},[892,23086,23087,23111],{},[895,23088,23089,23095,23097,23099,23101,23103,23105,23107,23109],{},[1753,23090,23091,23093],{},[898,23092,22325],{},[1708,23094,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,23096,1716],{"stretchy":1715},[898,23098,14014],{},[1708,23100,1721],{"stretchy":1715},[1708,23102,1710],{},[898,23104,14009],{},[1708,23106,1716],{"stretchy":1715},[898,23108,14014],{},[1708,23110,1721],{"stretchy":1715},[902,23112,23113],{"encoding":904},"F'(x) = f(x)",[883,23115,23117],{"className":23116},[886],[888,23118,23119],{"xmlns":890},[892,23120,23121,23125],{},[895,23122,23123],{},[898,23124,22325],{},[902,23126,22325],{"encoding":904},[38,23128,23129],{},"primitivní funkce"," k ",[883,23132,23134],{"className":23133},[886],[888,23135,23136],{"xmlns":890},[892,23137,23138,23142],{},[895,23139,23140],{},[898,23141,14009],{},[902,23143,14009],{"encoding":904},[883,23145,23147],{"className":23146},[886],[888,23148,23149],{"xmlns":890},[892,23150,23151,23155],{},[895,23152,23153],{},[898,23154,3455],{},[902,23156,3455],{"encoding":904}," konstanta.",[115,23159,23161],{"id":23160},"určitý-integrál","Určitý integrál",[724,23163,23164],{},[883,23165,23167],{"className":23166},[886],[888,23168,23169],{"xmlns":890},[892,23170,23171,23235],{},[895,23172,23173,23181,23183,23185,23187,23189,23191,23193,23195,23197,23199,23201,23203,23205,23207,23215,23217,23219,23221,23223,23225,23227,23229,23231,23233],{},[4754,23174,23175,23177,23179],{},[1708,23176,23056],{},[898,23178,207],{},[898,23180,1923],{},[898,23182,14009],{},[1708,23184,1716],{"stretchy":1715},[898,23186,14014],{},[1708,23188,1721],{"stretchy":1715},[2247,23190,2659],{},[898,23192,2364],{},[898,23194,14014],{},[1708,23196,1710],{},[1708,23198,6940],{"stretchy":1715},[898,23200,22325],{},[1708,23202,1716],{"stretchy":1715},[898,23204,14014],{},[1708,23206,1721],{"stretchy":1715},[4754,23208,23209,23211,23213],{},[1708,23210,6981],{"stretchy":1715},[898,23212,207],{},[898,23214,1923],{},[1708,23216,1710],{},[898,23218,22325],{},[1708,23220,1716],{"stretchy":1715},[898,23222,1923],{},[1708,23224,1721],{"stretchy":1715},[1708,23226,2726],{},[898,23228,22325],{},[1708,23230,1716],{"stretchy":1715},[898,23232,207],{},[1708,23234,1721],{"stretchy":1715},[902,23236,23237],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,23239,23240,23241,1729,23244,23257,23258,23279],{},"Geometricky ",[38,23242,23243],{},"plocha pod grafem",[883,23245,23247],{"className":23246},[886],[888,23248,23249],{"xmlns":890},[892,23250,23251,23255],{},[895,23252,23253],{},[898,23254,14009],{},[902,23256,14009],{"encoding":904}," na intervalu ",[883,23259,23261],{"className":23260},[886],[888,23262,23263],{"xmlns":890},[892,23264,23265,23277],{},[895,23266,23267,23269,23271,23273,23275],{},[1708,23268,6940],{"stretchy":1715},[898,23270,207],{},[1708,23272,1883],{"separator":1882},[898,23274,1923],{},[1708,23276,6981],{"stretchy":1715},[902,23278,7373],{"encoding":904}," (orientovaná).",[724,23281,23282],{},[3372,23283],{"alt":23284,"className":23285,"src":23286},"imek-integral-plocha",[210,3376],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,23288,23290],{"id":23289},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,23292,23294],{"id":23293},"příklad-tr-z-mr","Příklad — TR z MR",[724,23296,23297,23298,2155],{},"Mezní příjem ",[883,23299,23301],{"className":23300},[886],[888,23302,23303],{"xmlns":890},[892,23304,23305,23321],{},[895,23306,23307,23309,23311,23313,23315,23317,23319],{},[898,23308,1741],{},[898,23310,1975],{},[1708,23312,1710],{},[2505,23314,9238],{},[1708,23316,2726],{},[2505,23318,3132],{},[898,23320,1688],{},[902,23322,23323],{"encoding":904},"MR = 100 - 2Q",[724,23325,23326],{},[883,23327,23329],{"className":23328},[886],[888,23330,23331],{"xmlns":890},[892,23332,23333,23379],{},[895,23334,23335,23337,23339,23341,23343,23345,23347,23349,23351,23353,23355,23357,23359,23361,23363,23365,23367,23369,23375,23377],{},[898,23336,1978],{},[898,23338,1975],{},[1708,23340,1710],{},[1708,23342,23056],{},[1708,23344,1716],{"stretchy":1715},[2505,23346,9238],{},[1708,23348,2726],{},[2505,23350,3132],{},[898,23352,1688],{},[1708,23354,1721],{"stretchy":1715},[2247,23356,2659],{},[898,23358,2364],{},[898,23360,1688],{},[1708,23362,1710],{},[2505,23364,9238],{},[898,23366,1688],{},[1708,23368,2726],{},[1753,23370,23371,23373],{},[898,23372,1688],{},[2505,23374,3132],{},[1708,23376,2019],{},[898,23378,14142],{},[902,23380,23381],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,23383,23384,23385,15366,23411,2788],{},"Okrajová podmínka ",[883,23386,23388],{"className":23387},[886],[888,23389,23390],{"xmlns":890},[892,23391,23392,23408],{},[895,23393,23394,23396,23398,23400,23402,23404,23406],{},[898,23395,1978],{},[898,23397,1975],{},[1708,23399,1716],{"stretchy":1715},[2505,23401,2784],{},[1708,23403,1721],{"stretchy":1715},[1708,23405,1710],{},[2505,23407,2784],{},[902,23409,23410],{"encoding":904},"TR(0) = 0",[883,23412,23414],{"className":23413},[886],[888,23415,23416],{"xmlns":890},[892,23417,23418,23426],{},[895,23419,23420,23422,23424],{},[898,23421,14142],{},[1708,23423,1710],{},[2505,23425,2784],{},[902,23427,23428],{"encoding":904},"c = 0",[724,23430,23431],{},[883,23432,23434],{"className":23433},[886],[888,23435,23436],{"xmlns":890},[892,23437,23438,23464],{},[895,23439,23440,23442,23444,23446,23448,23450,23452,23454,23456,23458],{},[898,23441,1978],{},[898,23443,1975],{},[1708,23445,1716],{"stretchy":1715},[898,23447,1688],{},[1708,23449,1721],{"stretchy":1715},[1708,23451,1710],{},[2505,23453,9238],{},[898,23455,1688],{},[1708,23457,2726],{},[1753,23459,23460,23462],{},[898,23461,1688],{},[2505,23463,3132],{},[902,23465,23466],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,23468,23470],{"id":23469},"příklad-tc-z-mc","Příklad — TC z MC",[724,23472,23473,23474,23500,23501,2155],{},"Mezní náklady ",[883,23475,23477],{"className":23476},[886],[888,23478,23479],{"xmlns":890},[892,23480,23481,23497],{},[895,23482,23483,23485,23487,23489,23491,23493,23495],{},[898,23484,1741],{},[898,23486,3455],{},[1708,23488,1710],{},[2505,23490,3132],{},[1708,23492,2019],{},[2505,23494,3958],{},[898,23496,1688],{},[902,23498,23499],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,23502,23504],{"className":23503},[886],[888,23505,23506],{"xmlns":890},[892,23507,23508,23518],{},[895,23509,23510,23512,23514,23516],{},[898,23511,22325],{},[898,23513,3455],{},[1708,23515,1710],{},[2505,23517,9238],{},[902,23519,23520],{"encoding":904},"FC = 100",[724,23522,23523],{},[883,23524,23526],{"className":23525},[886],[888,23527,23528],{"xmlns":890},[892,23529,23530,23570],{},[895,23531,23532,23534,23536,23538,23540,23542,23544,23546,23548,23550,23552,23554,23556,23558,23560,23566,23568],{},[898,23533,1978],{},[898,23535,3455],{},[1708,23537,1710],{},[1708,23539,23056],{},[898,23541,1741],{},[898,23543,3455],{},[2247,23545,2659],{},[898,23547,2364],{},[898,23549,1688],{},[1708,23551,1710],{},[2505,23553,3132],{},[898,23555,1688],{},[1708,23557,2019],{},[2505,23559,10909],{},[1753,23561,23562,23564],{},[898,23563,1688],{},[2505,23565,3132],{},[1708,23567,2019],{},[898,23569,14142],{},[902,23571,23572],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,23574,23384,23575,15366,23607,2788],{},[883,23576,23578],{"className":23577},[886],[888,23579,23580],{"xmlns":890},[892,23581,23582,23604],{},[895,23583,23584,23586,23588,23590,23592,23594,23596,23598,23600,23602],{},[898,23585,1978],{},[898,23587,3455],{},[1708,23589,1716],{"stretchy":1715},[2505,23591,2784],{},[1708,23593,1721],{"stretchy":1715},[1708,23595,1710],{},[898,23597,22325],{},[898,23599,3455],{},[1708,23601,1710],{},[2505,23603,9238],{},[902,23605,23606],{"encoding":904},"TC(0) = FC = 100",[883,23608,23610],{"className":23609},[886],[888,23611,23612],{"xmlns":890},[892,23613,23614,23622],{},[895,23615,23616,23618,23620],{},[898,23617,14142],{},[1708,23619,1710],{},[2505,23621,9238],{},[902,23623,23624],{"encoding":904},"c = 100",[724,23626,23627],{},[883,23628,23630],{"className":23629},[886],[888,23631,23632],{"xmlns":890},[892,23633,23634,23666],{},[895,23635,23636,23638,23640,23642,23644,23646,23648,23650,23652,23654,23656,23658,23660],{},[898,23637,1978],{},[898,23639,3455],{},[1708,23641,1716],{"stretchy":1715},[898,23643,1688],{},[1708,23645,1721],{"stretchy":1715},[1708,23647,1710],{},[2505,23649,9238],{},[1708,23651,2019],{},[2505,23653,3132],{},[898,23655,1688],{},[1708,23657,2019],{},[2505,23659,10909],{},[1753,23661,23662,23664],{},[898,23663,1688],{},[2505,23665,3132],{},[902,23667,23668],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,23670,820],{"id":23671},"přebytek-spotřebitele-a-výrobce",[724,23673,23674],{},"Přebytek spotřebitele:",[724,23676,23677],{},[883,23678,23680],{"className":23679},[886],[888,23681,23682],{"xmlns":890},[892,23683,23684,23744],{},[895,23685,23686,23688,23690,23692,23698,23700,23702,23714,23716,23718,23720,23722,23724,23726,23728,23730,23736,23738],{},[898,23687,3455],{},[898,23689,1981],{},[1708,23691,1716],{"stretchy":1715},[1743,23693,23694,23696],{},[898,23695,1688],{},[2505,23697,2784],{},[1708,23699,1721],{"stretchy":1715},[1708,23701,1710],{},[4754,23703,23704,23706,23708],{},[1708,23705,23056],{},[2505,23707,2784],{},[1743,23709,23710,23712],{},[898,23711,1688],{},[2505,23713,2784],{},[898,23715,16117],{},[1708,23717,1716],{"stretchy":1715},[898,23719,1688],{},[1708,23721,1721],{"stretchy":1715},[2247,23723,2659],{},[898,23725,2364],{},[898,23727,1688],{},[1708,23729,2726],{},[1743,23731,23732,23734],{},[898,23733,1747],{},[2505,23735,2784],{},[2247,23737,2659],{},[1743,23739,23740,23742],{},[898,23741,1688],{},[2505,23743,2784],{},[902,23745,23746],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,23748,23749],{},"Přebytek výrobce:",[724,23751,23752],{},[883,23753,23755],{"className":23754},[886],[888,23756,23757],{"xmlns":890},[892,23758,23759,23819],{},[895,23760,23761,23763,23765,23767,23773,23775,23777,23783,23785,23791,23793,23805,23807,23809,23811,23813,23815,23817],{},[898,23762,1747],{},[898,23764,1981],{},[1708,23766,1716],{"stretchy":1715},[1743,23768,23769,23771],{},[898,23770,1688],{},[2505,23772,2784],{},[1708,23774,1721],{"stretchy":1715},[1708,23776,1710],{},[1743,23778,23779,23781],{},[898,23780,1747],{},[2505,23782,2784],{},[2247,23784,2659],{},[1743,23786,23787,23789],{},[898,23788,1688],{},[2505,23790,2784],{},[1708,23792,2726],{},[4754,23794,23795,23797,23799],{},[1708,23796,23056],{},[2505,23798,2784],{},[1743,23800,23801,23803],{},[898,23802,1688],{},[2505,23804,2784],{},[898,23806,1981],{},[1708,23808,1716],{"stretchy":1715},[898,23810,1688],{},[1708,23812,1721],{"stretchy":1715},[2247,23814,2659],{},[898,23816,2364],{},[898,23818,1688],{},[902,23820,23821],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,23823,23824,23825,2155],{},"Detailně viz ",[207,23826,23828],{"className":23827,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,23830,13763],{"id":13762},[120,23832,23833,23840,23847],{},[123,23834,23835,1729,23837],{},[38,23836,13871],{},[207,23838,766],{"className":23839,"dataFsResolvedFilePath":764,"href":765},[210],[123,23841,23842,1729,23844],{},[38,23843,15753],{},[207,23845,784],{"className":23846,"dataFsResolvedFilePath":782,"href":783},[210],[123,23848,23849,1729,23851,23854,23855,23858],{},[38,23850,15761],{},[207,23852,13830],{"className":23853,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,23856,23828],{"className":23857,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":23860},[23861,23862,23863,23868],{"id":23031,"depth":642,"text":23032},{"id":23160,"depth":642,"text":23161},{"id":23289,"depth":642,"text":23290,"children":23864},[23865,23866,23867],{"id":23293,"depth":649,"text":23294},{"id":23469,"depth":649,"text":23470},{"id":23671,"depth":649,"text":820},{"id":13762,"depth":642,"text":13763},"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":23869},[1135],"topics\u002Fintegral",[1128,23876,23877,23878,23879,23880,23881],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":23884,"title":23885,"body":23886,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":28139,"navigation":664,"path":28140,"seo":28141,"sources":28142,"stem":28143,"tags":28144,"type":13951,"updated":677,"__hash__":28150},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":23887,"toc":28127},[23888,23891,23895,24037,24044,24048,24118,24156,24259,24263,24293,24359,24405,24408,24477,24480,24515,24551,24555,24603,24610,24656,24702,24705,24784,24881,24964,24968,25012,25042,25048,25077,25098,25147,25200,25266,25269,25335,25364,25423,25439,25526,25623,25754,25758,25915,26064,26444,26448,26451,26509,26512,26598,26626,26664,26667,26704,26744,26778,26780,26817,26849,26947,26952,27074,27126,27207,27346,27350,27470,27477,27588,27595,27597,28071,28073],[12,23889,23885],{"id":23890},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,23892,23894],{"id":23893},"tldr","TL;DR",[724,23896,23897,23900,23901,1695,23904,23917,23918,23931,23932,23935,23936,1343,23939,23942,23943,1343,23946,23949,23950,1729,23953,23983,23984,23987,23988,1343,24002,5149,24015,24018,24019,2511],{},[38,23898,23899],{},"IS-LM"," je makroekonomický model se ",[38,23902,23903],{},"dvěma neznámými",[883,23905,23907],{"className":23906},[886],[888,23908,23909],{"xmlns":890},[892,23910,23911,23915],{},[895,23912,23913],{},[898,23914,21035],{},[902,23916,21035],{"encoding":904}," — národní důchod a ",[883,23919,23921],{"className":23920},[886],[888,23922,23923],{"xmlns":890},[892,23924,23925,23929],{},[895,23926,23927],{},[898,23928,5498],{},[902,23930,5498],{"encoding":904}," — úroková míra) a ",[38,23933,23934],{},"dvěma trhy",": trhem zboží (křivka ",[38,23937,23938],{},"IS",[614,23940,23941],{},"Investment = Savings",") a trhem peněz (křivka ",[38,23944,23945],{},"LM",[614,23947,23948],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,23951,23952],{},"simultánní rovnováhu",[883,23954,23956],{"className":23955},[886],[888,23957,23958],{"xmlns":890},[892,23959,23960,23980],{},[895,23961,23962,23964,23970,23972,23978],{},[1708,23963,1716],{"stretchy":1715},[1753,23965,23966,23968],{},[898,23967,21035],{},[898,23969,16183],{},[1708,23971,1883],{"separator":1882},[1753,23973,23974,23976],{},[898,23975,5498],{},[898,23977,16183],{},[1708,23979,1721],{"stretchy":1715},[902,23981,23982],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,23985,23986],{},"fiskální politiky"," (posun IS změnou ",[883,23989,23991],{"className":23990},[886],[888,23992,23993],{"xmlns":890},[892,23994,23995,24000],{},[895,23996,23997],{},[898,23998,23999],{},"G",[902,24001,23999],{"encoding":904},[883,24003,24005],{"className":24004},[886],[888,24006,24007],{"xmlns":890},[892,24008,24009,24013],{},[895,24010,24011],{},[898,24012,1978],{},[902,24014,1978],{"encoding":904},[38,24016,24017],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,24020,24022],{"className":24021},[886],[888,24023,24024],{"xmlns":890},[892,24025,24026,24034],{},[895,24027,24028],{},[1753,24029,24030,24032],{},[898,24031,1741],{},[1708,24033,2417],{},[902,24035,24036],{"encoding":904},"M^*",[724,24038,24039],{},[3372,24040],{"alt":24041,"className":24042,"src":24043},"imek-is-lm-model",[210,3376],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,24045,24047],{"id":24046},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,24049,24050,24051,24055,24056,1695,24059,24082,24083,24086,24087,24103,24104,24117],{},"V modelech ",[207,24052,24054],{"className":24053,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,24057,24058],{},"investice pokládány za konstantní",[883,24060,24062],{"className":24061},[886],[888,24063,24064],{"xmlns":890},[892,24065,24066,24079],{},[895,24067,24068,24071,24073],{},[898,24069,24070],{},"I",[1708,24072,1710],{},[1753,24074,24075,24077],{},[898,24076,24070],{},[1708,24078,2417],{},[902,24080,24081],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,24084,24085],{},"ceně peněz",", tedy na ",[38,24088,24089,24090],{},"úrokové míře ",[883,24091,24093],{"className":24092},[886],[888,24094,24095],{"xmlns":890},[892,24096,24097,24101],{},[895,24098,24099],{},[898,24100,5498],{},[902,24102,5498],{"encoding":904},": čím vyšší ",[883,24105,24107],{"className":24106},[886],[888,24108,24109],{"xmlns":890},[892,24110,24111,24115],{},[895,24112,24113],{},[898,24114,5498],{},[902,24116,5498],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,24119,24120,24150],{},[123,24121,24122,1729,24125,24149],{},[38,24123,24124],{},"funkci investic",[883,24126,24128],{"className":24127},[886],[888,24129,24130],{"xmlns":890},[892,24131,24132,24146],{},[895,24133,24134,24136,24138,24140,24142,24144],{},[898,24135,24070],{},[1708,24137,1710],{},[898,24139,24070],{},[1708,24141,1716],{"stretchy":1715},[898,24143,5498],{},[1708,24145,1721],{"stretchy":1715},[902,24147,24148],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,24151,24152,24155],{},[38,24153,24154],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1636,24157,24158],{},[724,24159,24160,24162,24163,24182,24183,24210,24211,24224,24225,24254,24255,24258],{},[883,24161,6130],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,24164,24166],{"className":24165},[886],[888,24167,24168],{"xmlns":890},[892,24169,24170,24179],{},[895,24171,24172,24174,24177],{},[898,24173,3455],{},[2247,24175,24176],{},"-",[898,24178,24070],{},[902,24180,24181],{"encoding":904},"C\\text{-}I"," až ",[883,24184,24186],{"className":24185},[886],[888,24187,24188],{"xmlns":890},[892,24189,24190,24207],{},[895,24191,24192,24194,24196,24198,24200,24202,24204],{},[898,24193,3455],{},[2247,24195,24176],{},[898,24197,24070],{},[2247,24199,24176],{},[898,24201,23999],{},[2247,24203,24176],{},[898,24205,24206],{},"X",[902,24208,24209],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,24212,24214],{"className":24213},[886],[888,24215,24216],{"xmlns":890},[892,24217,24218,24222],{},[895,24219,24220],{},[898,24221,21035],{},[902,24223,21035],{"encoding":904},". V IS-LM jsou ",[38,24226,24227,24228,1771,24241],{},"dvě neznámé ",[883,24229,24231],{"className":24230},[886],[888,24232,24233],{"xmlns":890},[892,24234,24235,24239],{},[895,24236,24237],{},[898,24238,21035],{},[902,24240,21035],{"encoding":904},[883,24242,24244],{"className":24243},[886],[888,24245,24246],{"xmlns":890},[892,24247,24248,24252],{},[895,24249,24250],{},[898,24251,5498],{},[902,24253,5498],{"encoding":904},", a proto potřebujeme ",[38,24256,24257],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,24260,24262],{"id":24261},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,24264,24265,24266,24279,24280,2788],{},"Lineární závislost investic ",[883,24267,24269],{"className":24268},[886],[888,24270,24271],{"xmlns":890},[892,24272,24273,24277],{},[895,24274,24275],{},[898,24276,24070],{},[902,24278,24070],{"encoding":904}," na úrokové míře ",[883,24281,24283],{"className":24282},[886],[888,24284,24285],{"xmlns":890},[892,24286,24287,24291],{},[895,24288,24289],{},[898,24290,5498],{},[902,24292,5498],{"encoding":904},[724,24294,24295],{},[883,24296,24298],{"className":24297},[886],[888,24299,24300],{"xmlns":890},[892,24301,24302,24356],{},[895,24303,24304,24306,24308,24310,24312,24314,24316,24318,24320,24322,24324,24326,24328,24330,24332,24334,24336,24338,24340,24342,24344,24347,24349,24351,24354],{},[898,24305,24070],{},[1708,24307,1710],{},[898,24309,24070],{},[1708,24311,1716],{"stretchy":1715},[898,24313,5498],{},[1708,24315,1721],{"stretchy":1715},[1708,24317,1710],{},[898,24319,14142],{},[898,24321,5498],{},[1708,24323,2019],{},[898,24325,2364],{},[1708,24327,1883],{"separator":1882},[3213,24329],{"width":3215},[898,24331,14142],{},[1708,24333,2932],{},[2505,24335,2784],{},[1708,24337,1883],{"separator":1882},[2247,24339,14279],{},[898,24341,2364],{},[1708,24343,2854],{},[2505,24345,24346],{},"0.",[3213,24348],{"width":3215},[1708,24350,1716],{"stretchy":1715},[2505,24352,24353],{},"7.11",[1708,24355,1721],{"stretchy":1715},[902,24357,24358],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,24360,24361,24382],{},[123,24362,24363,24381],{},[883,24364,24366],{"className":24365},[886],[888,24367,24368],{"xmlns":890},[892,24369,24370,24378],{},[895,24371,24372,24374,24376],{},[898,24373,2364],{},[1708,24375,2854],{},[2505,24377,2784],{},[902,24379,24380],{"encoding":904},"d > 0"," zřejmé,",[123,24383,24384,24402,24403,2155],{},[883,24385,24387],{"className":24386},[886],[888,24388,24389],{"xmlns":890},[892,24390,24391,24399],{},[895,24392,24393,24395,24397],{},[898,24394,14142],{},[1708,24396,2932],{},[2505,24398,2784],{},[902,24400,24401],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,24404,8185],{},[724,24406,24407],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,24409,24410],{},[883,24411,24413],{"className":24412},[886],[888,24414,24415],{"xmlns":890},[892,24416,24417,24474],{},[895,24418,24419,24421,24423,24425,24427,24429,24431,24433,24435,24437,24439,24441,24443,24445,24447,24449,24451,24453,24455,24457,24459,24461,24463,24465,24467,24469,24472],{},[898,24420,3455],{},[1708,24422,1710],{},[898,24424,3455],{},[1708,24426,1716],{"stretchy":1715},[898,24428,21035],{},[1708,24430,1721],{"stretchy":1715},[1708,24432,1710],{},[898,24434,207],{},[898,24436,21035],{},[1708,24438,2019],{},[898,24440,1923],{},[1708,24442,1883],{"separator":1882},[3213,24444],{"width":3215},[2505,24446,2784],{},[1708,24448,2932],{},[898,24450,207],{},[1708,24452,2932],{},[2505,24454,2507],{},[1708,24456,1883],{"separator":1882},[2247,24458,14279],{},[898,24460,1923],{},[1708,24462,2854],{},[2505,24464,24346],{},[3213,24466],{"width":3215},[1708,24468,1716],{"stretchy":1715},[2505,24470,24471],{},"7.12",[1708,24473,1721],{"stretchy":1715},[902,24475,24476],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,24478,24479],{},"Podmínka rovnováhy na trhu zboží:",[724,24481,24482],{},[883,24483,24485],{"className":24484},[886],[888,24486,24487],{"xmlns":890},[892,24488,24489,24512],{},[895,24490,24491,24493,24495,24497,24499,24501,24503,24505,24507,24510],{},[898,24492,21035],{},[1708,24494,1710],{},[898,24496,3455],{},[1708,24498,2019],{},[898,24500,24070],{},[898,24502,2155],{"mathvariant":1759},[3213,24504],{"width":3215},[1708,24506,1716],{"stretchy":1715},[2505,24508,24509],{},"7.13",[1708,24511,1721],{"stretchy":1715},[902,24513,24514],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,24516,24517,24518,1729,24521,24547,24548,2155],{},"To dává ",[38,24519,24520],{},"tři rovnice o čtyřech neznámých",[883,24522,24524],{"className":24523},[886],[888,24525,24526],{"xmlns":890},[892,24527,24528,24544],{},[895,24529,24530,24532,24534,24536,24538,24540,24542],{},[898,24531,21035],{},[1708,24533,1883],{"separator":1882},[898,24535,3455],{},[1708,24537,1883],{"separator":1882},[898,24539,24070],{},[1708,24541,1883],{"separator":1882},[898,24543,5498],{},[902,24545,24546],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,24549,24550],{},"rovnováhy na trhu peněz",[115,24552,24554],{"id":24553},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,24556,24557,24558,17489,24580,24598,24599,24602],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,24559,24561],{"className":24560},[886],[888,24562,24563],{"xmlns":890},[892,24564,24565,24577],{},[895,24566,24567,24569,24571,24573,24575],{},[898,24568,21035],{},[1708,24570,1710],{},[898,24572,3455],{},[1708,24574,2019],{},[898,24576,1981],{},[902,24578,24579],{"encoding":904},"Y = C + S",[883,24581,24583],{"className":24582},[886],[888,24584,24585],{"xmlns":890},[892,24586,24587,24595],{},[895,24588,24589,24591,24593],{},[898,24590,24070],{},[1708,24592,1710],{},[898,24594,1981],{},[902,24596,24597],{"encoding":904},"I = S"," (plánované ",[38,24600,24601],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,24604,24605],{},[3372,24606],{"alt":24607,"className":24608,"src":24609},"imek-odvozeni-is-4panelu",[210,3376],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,24611,24612],{},[883,24613,24615],{"className":24614},[886],[888,24616,24617],{"xmlns":890},[892,24618,24619,24653],{},[895,24620,24621,24623,24625,24627,24629,24631,24633,24635,24637,24639,24641,24643,24645,24647,24649,24651],{},[898,24622,21035],{},[1708,24624,1710],{},[1708,24626,1716],{"stretchy":1715},[898,24628,207],{},[898,24630,21035],{},[1708,24632,2019],{},[898,24634,1923],{},[1708,24636,1721],{"stretchy":1715},[1708,24638,2019],{},[1708,24640,1716],{"stretchy":1715},[898,24642,14142],{},[898,24644,5498],{},[1708,24646,2019],{},[898,24648,2364],{},[1708,24650,1721],{"stretchy":1715},[1708,24652,1883],{"separator":1882},[902,24654,24655],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,24657,24658],{},[883,24659,24661],{"className":24660},[886],[888,24662,24663],{"xmlns":890},[892,24664,24665,24699],{},[895,24666,24667,24669,24671,24673,24675,24677,24679,24681,24683,24685,24687,24689,24691,24693,24695,24697],{},[1708,24668,1716],{"stretchy":1715},[2505,24670,2507],{},[1708,24672,2726],{},[898,24674,207],{},[1708,24676,1721],{"stretchy":1715},[898,24678,21035],{},[1708,24680,2726],{},[898,24682,14142],{},[898,24684,5498],{},[1708,24686,2726],{},[898,24688,1923],{},[1708,24690,2726],{},[898,24692,2364],{},[1708,24694,1710],{},[2505,24696,2784],{},[1708,24698,1883],{"separator":1882},[902,24700,24701],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,24703,24704],{},"odkud",[724,24706,24707],{},[883,24708,24710],{"className":24709},[886],[888,24711,24712],{"xmlns":890},[892,24713,24714,24781],{},[895,24715,24716,24772,24774,24776,24779],{},[24717,24718,24720],"menclose",{"notation":24719},"box",[3194,24721,24722],{"scriptlevel":2784,"displaystyle":1715},[3194,24723,24724],{"scriptlevel":2784,"displaystyle":1715},[3194,24725,24726],{"scriptlevel":2784,"displaystyle":1882},[895,24727,24728,24730,24732,24734,24746,24748,24750,24752,24770],{},[2247,24729,2659],{},[898,24731,21035],{},[1708,24733,1710],{},[2358,24735,24736,24738],{},[898,24737,14142],{},[895,24739,24740,24742,24744],{},[2505,24741,2507],{},[1708,24743,2726],{},[898,24745,207],{},[2247,24747,2659],{},[898,24749,5498],{},[1708,24751,2019],{},[2358,24753,24754,24762],{},[895,24755,24756,24758,24760],{},[898,24757,1923],{},[1708,24759,2019],{},[898,24761,2364],{},[895,24763,24764,24766,24768],{},[2505,24765,2507],{},[1708,24767,2726],{},[898,24769,207],{},[2247,24771,2659],{},[3213,24773],{"width":3215},[1708,24775,1716],{"stretchy":1715},[2505,24777,24778],{},"7.14",[1708,24780,1721],{"stretchy":1715},[902,24782,24783],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,24785,24786,24787,1695,24790,24793,24794,24797,24798,24800,24801,24823,24824,24852,24853,24874,24875,24877,24878,24880],{},"Tento vztah se nazývá ",[38,24788,24789],{},"funkce IS",[614,24791,24792],{},"IS schedule",") a její graf ",[38,24795,24796],{},"křivka IS",". Křivka je ",[38,24799,8185],{}," přímka v rovině ",[883,24802,24804],{"className":24803},[886],[888,24805,24806],{"xmlns":890},[892,24807,24808,24820],{},[895,24809,24810,24812,24814,24816,24818],{},[1708,24811,1716],{"stretchy":1715},[898,24813,5498],{},[1708,24815,1883],{"separator":1882},[898,24817,21035],{},[1708,24819,1721],{"stretchy":1715},[902,24821,24822],{"encoding":904},"(r, Y)",", neboť ",[883,24825,24827],{"className":24826},[886],[888,24828,24829],{"xmlns":890},[892,24830,24831,24849],{},[895,24832,24833,24845,24847],{},[2358,24834,24835,24837],{},[898,24836,14142],{},[895,24838,24839,24841,24843],{},[2505,24840,2507],{},[1708,24842,2726],{},[898,24844,207],{},[1708,24846,2932],{},[2505,24848,2784],{},[902,24850,24851],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,24854,24856],{"className":24855},[886],[888,24857,24858],{"xmlns":890},[892,24859,24860,24872],{},[895,24861,24862,24864,24866,24868,24870],{},[1708,24863,1716],{"stretchy":1715},[898,24865,5498],{},[1708,24867,1883],{"separator":1882},[898,24869,21035],{},[1708,24871,1721],{"stretchy":1715},[902,24873,24822],{"encoding":904},", pro které plánované ",[38,24876,24070],{},"nvestment = ",[38,24879,1981],{},"avings.",[1636,24882,24883],{},[724,24884,24885,24887,24888,24901,24902,1729,24905,24918,24919,24932,24933,1771,24946,24959,24960,24963],{},[883,24886,2518],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,24889,24891],{"className":24890},[886],[888,24892,24893],{"xmlns":890},[892,24894,24895,24899],{},[895,24896,24897],{},[898,24898,5498],{},[902,24900,5498],{"encoding":904}," → levnější úvěr → ",[38,24903,24904],{},"více investic",[883,24906,24908],{"className":24907},[886],[888,24909,24910],{"xmlns":890},[892,24911,24912,24916],{},[895,24913,24914],{},[898,24915,24070],{},[902,24917,24070],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,24920,24922],{"className":24921},[886],[888,24923,24924],{"xmlns":890},[892,24925,24926,24930],{},[895,24927,24928],{},[898,24929,21035],{},[902,24931,21035],{"encoding":904},". Vztah mezi ",[883,24934,24936],{"className":24935},[886],[888,24937,24938],{"xmlns":890},[892,24939,24940,24944],{},[895,24941,24942],{},[898,24943,5498],{},[902,24945,5498],{"encoding":904},[883,24947,24949],{"className":24948},[886],[888,24950,24951],{"xmlns":890},[892,24952,24953,24957],{},[895,24954,24955],{},[898,24956,21035],{},[902,24958,21035],{"encoding":904}," na trhu zboží je proto ",[38,24961,24962],{},"nepřímý"," (klesající křivka).",[115,24965,24967],{"id":24966},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,24969,24970,24971,24989,24990,2941,25008,25011],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,24972,24974],{"className":24973},[886],[888,24975,24976],{"xmlns":890},[892,24977,24978,24986],{},[895,24979,24980],{},[1753,24981,24982,24984],{},[898,24983,1741],{},[898,24985,16117],{},[902,24987,24988],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,24991,24993],{"className":24992},[886],[888,24994,24995],{"xmlns":890},[892,24996,24997,25005],{},[895,24998,24999],{},[1753,25000,25001,25003],{},[898,25002,1741],{},[898,25004,1981],{},[902,25006,25007],{"encoding":904},"M^S",[38,25009,25010],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,25013,25014],{},[883,25015,25017],{"className":25016},[886],[888,25018,25019],{"xmlns":890},[892,25020,25021,25039],{},[895,25022,25023,25029,25031,25037],{},[1753,25024,25025,25027],{},[898,25026,1741],{},[898,25028,1981],{},[1708,25030,1710],{},[1753,25032,25033,25035],{},[898,25034,1741],{},[1708,25036,2417],{},[898,25038,2155],{"mathvariant":1759},[902,25040,25041],{"encoding":904},"M^S = M^*.",[724,25043,25044,25047],{},[38,25045,25046],{},"Poptávka"," po penězích má tři zdroje:",[120,25049,25050,25059,25068],{},[123,25051,25052,1695,25055,25058],{},[38,25053,25054],{},"transakční poptávka",[614,25056,25057],{},"transactions demand",") — peníze pro nákup zboží,",[123,25060,25061,1695,25064,25067],{},[38,25062,25063],{},"opatrnostní poptávka",[614,25065,25066],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,25069,25070,1695,25073,25076],{},[38,25071,25072],{},"spekulační poptávka",[614,25074,25075],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,25078,25079,25080,25097],{},"Součet transakční a opatrnostní poptávky ",[883,25081,25083],{"className":25082},[886],[888,25084,25085],{"xmlns":890},[892,25086,25087,25095],{},[895,25088,25089],{},[1743,25090,25091,25093],{},[898,25092,1658],{},[2505,25094,2507],{},[902,25096,2979],{"encoding":904}," je úměrný důchodu:",[724,25099,25100],{},[883,25101,25103],{"className":25102},[886],[888,25104,25105],{"xmlns":890},[892,25106,25107,25144],{},[895,25108,25109,25115,25117,25124,25126,25128,25130,25132,25134,25140,25142],{},[1743,25110,25111,25113],{},[898,25112,1658],{},[2505,25114,2507],{},[1708,25116,1710],{},[1743,25118,25119,25122],{},[898,25120,25121],{},"k",[2505,25123,2507],{},[898,25125,21035],{},[1708,25127,1883],{"separator":1882},[3213,25129],{"width":3215},[2505,25131,2784],{},[1708,25133,2932],{},[1743,25135,25136,25138],{},[898,25137,25121],{},[2505,25139,2507],{},[1708,25141,2932],{},[2505,25143,6891],{},[902,25145,25146],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,25148,25149,25150,25168,25169,1343,25182,25199],{},"Spekulační poptávka ",[883,25151,25153],{"className":25152},[886],[888,25154,25155],{"xmlns":890},[892,25156,25157,25165],{},[895,25158,25159],{},[1743,25160,25161,25163],{},[898,25162,1658],{},[2505,25164,3132],{},[902,25166,25167],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,25170,25172],{"className":25171},[886],[888,25173,25174],{"xmlns":890},[892,25175,25176,25180],{},[895,25177,25178],{},[898,25179,5498],{},[902,25181,5498],{"encoding":904},[883,25183,25185],{"className":25184},[886],[888,25186,25187],{"xmlns":890},[892,25188,25189,25197],{},[895,25190,25191],{},[1743,25192,25193,25195],{},[898,25194,1658],{},[2505,25196,3132],{},[902,25198,25167],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,25201,25202],{},[883,25203,25205],{"className":25204},[886],[888,25206,25207],{"xmlns":890},[892,25208,25209,25263],{},[895,25210,25211,25217,25219,25225,25227,25229,25235,25237,25239,25245,25247,25249,25251,25253,25259,25261],{},[1743,25212,25213,25215],{},[898,25214,1658],{},[2505,25216,3132],{},[1708,25218,1710],{},[1743,25220,25221,25223],{},[898,25222,25121],{},[2505,25224,3132],{},[898,25226,5498],{},[1708,25228,2019],{},[1743,25230,25231,25233],{},[898,25232,25121],{},[2505,25234,3121],{},[1708,25236,1883],{"separator":1882},[3213,25238],{"width":3215},[1743,25240,25241,25243],{},[898,25242,25121],{},[2505,25244,3132],{},[1708,25246,2932],{},[2505,25248,2784],{},[1708,25250,1883],{"separator":1882},[2247,25252,14279],{},[1743,25254,25255,25257],{},[898,25256,25121],{},[2505,25258,3121],{},[1708,25260,2854],{},[2505,25262,24346],{},[902,25264,25265],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,25267,25268],{},"Celková poptávka po penězích:",[724,25270,25271],{},[883,25272,25274],{"className":25273},[886],[888,25275,25276],{"xmlns":890},[892,25277,25278,25332],{},[895,25279,25280,25286,25288,25294,25296,25302,25304,25310,25312,25314,25320,25322,25324,25330],{},[1753,25281,25282,25284],{},[898,25283,1741],{},[898,25285,16117],{},[1708,25287,1710],{},[1743,25289,25290,25292],{},[898,25291,1658],{},[2505,25293,2507],{},[1708,25295,2019],{},[1743,25297,25298,25300],{},[898,25299,1658],{},[2505,25301,3132],{},[1708,25303,1710],{},[1743,25305,25306,25308],{},[898,25307,25121],{},[2505,25309,2507],{},[898,25311,21035],{},[1708,25313,2019],{},[1743,25315,25316,25318],{},[898,25317,25121],{},[2505,25319,3132],{},[898,25321,5498],{},[1708,25323,2019],{},[1743,25325,25326,25328],{},[898,25327,25121],{},[2505,25329,3121],{},[898,25331,2155],{"mathvariant":1759},[902,25333,25334],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,25336,25337,25338,2788],{},"Podmínka rovnováhy na trhu peněz ",[883,25339,25341],{"className":25340},[886],[888,25342,25343],{"xmlns":890},[892,25344,25345,25361],{},[895,25346,25347,25353,25355],{},[1753,25348,25349,25351],{},[898,25350,1741],{},[898,25352,16117],{},[1708,25354,1710],{},[1753,25356,25357,25359],{},[898,25358,1741],{},[1708,25360,2417],{},[902,25362,25363],{"encoding":904},"M^D = M^*",[724,25365,25366],{},[883,25367,25369],{"className":25368},[886],[888,25370,25371],{"xmlns":890},[892,25372,25373,25420],{},[895,25374,25375,25381,25383,25389,25391,25393,25399,25401,25403,25409,25411,25413,25415,25418],{},[1753,25376,25377,25379],{},[898,25378,1741],{},[1708,25380,2417],{},[1708,25382,1710],{},[1743,25384,25385,25387],{},[898,25386,25121],{},[2505,25388,2507],{},[898,25390,21035],{},[1708,25392,2019],{},[1743,25394,25395,25397],{},[898,25396,25121],{},[2505,25398,3132],{},[898,25400,5498],{},[1708,25402,2019],{},[1743,25404,25405,25407],{},[898,25406,25121],{},[2505,25408,3121],{},[1708,25410,1883],{"separator":1882},[3213,25412],{"width":3215},[1708,25414,1716],{"stretchy":1715},[2505,25416,25417],{},"7.15",[1708,25419,1721],{"stretchy":1715},[902,25421,25422],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,25424,25425,25426,2750],{},"po úpravě (vyjádření ",[883,25427,25429],{"className":25428},[886],[888,25430,25431],{"xmlns":890},[892,25432,25433,25437],{},[895,25434,25435],{},[898,25436,21035],{},[902,25438,21035],{"encoding":904},[724,25440,25441],{},[883,25442,25444],{"className":25443},[886],[888,25445,25446],{"xmlns":890},[892,25447,25448,25523],{},[895,25449,25450,25514,25516,25518,25521],{},[24717,25451,25452],{"notation":24719},[3194,25453,25454],{"scriptlevel":2784,"displaystyle":1715},[3194,25455,25456],{"scriptlevel":2784,"displaystyle":1715},[3194,25457,25458],{"scriptlevel":2784,"displaystyle":1882},[895,25459,25460,25462,25464,25466,25468,25482,25484,25486,25488,25512],{},[2247,25461,2659],{},[898,25463,21035],{},[1708,25465,1710],{},[1708,25467,2726],{},[2358,25469,25470,25476],{},[1743,25471,25472,25474],{},[898,25473,25121],{},[2505,25475,3132],{},[1743,25477,25478,25480],{},[898,25479,25121],{},[2505,25481,2507],{},[2247,25483,2659],{},[898,25485,5498],{},[1708,25487,2019],{},[2358,25489,25490,25506],{},[895,25491,25492,25498,25500],{},[1753,25493,25494,25496],{},[898,25495,1741],{},[1708,25497,2417],{},[1708,25499,2726],{},[1743,25501,25502,25504],{},[898,25503,25121],{},[2505,25505,3121],{},[1743,25507,25508,25510],{},[898,25509,25121],{},[2505,25511,2507],{},[2247,25513,2659],{},[3213,25515],{"width":3215},[1708,25517,1716],{"stretchy":1715},[2505,25519,25520],{},"7.16",[1708,25522,1721],{"stretchy":1715},[902,25524,25525],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,25527,24786,25528,1695,25531,25534,25535,24797,25538,24800,25540,24823,25561,25593,25594,25616,25617,25619,25620,25622],{},[38,25529,25530],{},"funkce LM",[614,25532,25533],{},"LM schedule","), její graf ",[38,25536,25537],{},"křivka LM",[38,25539,2082],{},[883,25541,25543],{"className":25542},[886],[888,25544,25545],{"xmlns":890},[892,25546,25547,25559],{},[895,25548,25549,25551,25553,25555,25557],{},[1708,25550,1716],{"stretchy":1715},[898,25552,5498],{},[1708,25554,1883],{"separator":1882},[898,25556,21035],{},[1708,25558,1721],{"stretchy":1715},[902,25560,24822],{"encoding":904},[883,25562,25564],{"className":25563},[886],[888,25565,25566],{"xmlns":890},[892,25567,25568,25590],{},[895,25569,25570,25572,25586,25588],{},[1708,25571,2726],{},[2358,25573,25574,25580],{},[1743,25575,25576,25578],{},[898,25577,25121],{},[2505,25579,3132],{},[1743,25581,25582,25584],{},[898,25583,25121],{},[2505,25585,2507],{},[1708,25587,2854],{},[2505,25589,2784],{},[902,25591,25592],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,25595,25597],{"className":25596},[886],[888,25598,25599],{"xmlns":890},[892,25600,25601,25613],{},[895,25602,25603,25609,25611],{},[1743,25604,25605,25607],{},[898,25606,25121],{},[2505,25608,3132],{},[1708,25610,2932],{},[2505,25612,2784],{},[902,25614,25615],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,25618,1658],{},"iquidity of ",[38,25621,1741],{},"oney.",[1636,25624,25625],{},[724,25626,25627,25629,25630,25643,25644,25672,25673,25690,25691,25704,25705,25722,25723,1771,25736,25749,25750,25753],{},[883,25628,2518],{}," Intuice — proč LM roste\nVyšší důchod ",[883,25631,25633],{"className":25632},[886],[888,25634,25635],{"xmlns":890},[892,25636,25637,25641],{},[895,25638,25639],{},[898,25640,21035],{},[902,25642,21035],{"encoding":904}," → větší transakční poptávka po penězích ",[883,25645,25647],{"className":25646},[886],[888,25648,25649],{"xmlns":890},[892,25650,25651,25669],{},[895,25652,25653,25659,25661,25667],{},[1743,25654,25655,25657],{},[898,25656,1658],{},[2505,25658,2507],{},[1708,25660,1710],{},[1743,25662,25663,25665],{},[898,25664,25121],{},[2505,25666,2507],{},[898,25668,21035],{},[902,25670,25671],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,25674,25676],{"className":25675},[886],[888,25677,25678],{"xmlns":890},[892,25679,25680,25688],{},[895,25681,25682],{},[1753,25683,25684,25686],{},[898,25685,1741],{},[1708,25687,2417],{},[902,25689,24036],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,25692,25694],{"className":25693},[886],[888,25695,25696],{"xmlns":890},[892,25697,25698,25702],{},[895,25699,25700],{},[898,25701,5498],{},[902,25703,5498],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,25706,25708],{"className":25707},[886],[888,25709,25710],{"xmlns":890},[892,25711,25712,25720],{},[895,25713,25714],{},[1743,25715,25716,25718],{},[898,25717,1658],{},[2505,25719,3132],{},[902,25721,25167],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,25724,25726],{"className":25725},[886],[888,25727,25728],{"xmlns":890},[892,25729,25730,25734],{},[895,25731,25732],{},[898,25733,21035],{},[902,25735,21035],{"encoding":904},[883,25737,25739],{"className":25738},[886],[888,25740,25741],{"xmlns":890},[892,25742,25743,25747],{},[895,25744,25745],{},[898,25746,5498],{},[902,25748,5498],{"encoding":904}," na trhu peněz je proto ",[38,25751,25752],{},"přímý"," (rostoucí křivka).",[115,25755,25757],{"id":25756},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,25759,25760,25761,25764,25765,1729,25768,1771,25786,1729,25789,25807,25808,25826,25827,25845,25846,25862,25863,1771,25878,25893,25894,2155],{},"Řešením ",[38,25762,25763],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,25766,25767],{},"rovnovážný důchod",[883,25769,25771],{"className":25770},[886],[888,25772,25773],{"xmlns":890},[892,25774,25775,25783],{},[895,25776,25777],{},[1753,25778,25779,25781],{},[898,25780,21035],{},[898,25782,16183],{},[902,25784,25785],{"encoding":904},"Y^E",[38,25787,25788],{},"rovnovážnou úrokovou míru",[883,25790,25792],{"className":25791},[886],[888,25793,25794],{"xmlns":890},[892,25795,25796,25804],{},[895,25797,25798],{},[1753,25799,25800,25802],{},[898,25801,5498],{},[898,25803,16183],{},[902,25805,25806],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,25809,25811],{"className":25810},[886],[888,25812,25813],{"xmlns":890},[892,25814,25815,25823],{},[895,25816,25817],{},[1753,25818,25819,25821],{},[898,25820,24070],{},[898,25822,16183],{},[902,25824,25825],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,25828,25830],{"className":25829},[886],[888,25831,25832],{"xmlns":890},[892,25833,25834,25842],{},[895,25835,25836],{},[1753,25837,25838,25840],{},[898,25839,3455],{},[898,25841,16183],{},[902,25843,25844],{"encoding":904},"C^E",". Graficky jde o ",[38,25847,25848,25849],{},"průsečík ",[883,25850,25852],{"className":25851},[886],[888,25853,25854],{"xmlns":890},[892,25855,25856,25860],{},[895,25857,25858],{},[898,25859,16183],{},[902,25861,16183],{"encoding":904}," křivek ",[883,25864,25866],{"className":25865},[886],[888,25867,25868],{"xmlns":890},[892,25869,25870,25876],{},[895,25871,25872,25874],{},[898,25873,24070],{},[898,25875,1981],{},[902,25877,23938],{"encoding":904},[883,25879,25881],{"className":25880},[886],[888,25882,25883],{"xmlns":890},[892,25884,25885,25891],{},[895,25886,25887,25889],{},[898,25888,1658],{},[898,25890,1741],{},[902,25892,23945],{"encoding":904}," v rovině ",[883,25895,25897],{"className":25896},[886],[888,25898,25899],{"xmlns":890},[892,25900,25901,25913],{},[895,25902,25903,25905,25907,25909,25911],{},[1708,25904,1716],{"stretchy":1715},[898,25906,5498],{},[1708,25908,1883],{"separator":1882},[898,25910,21035],{},[1708,25912,1721],{"stretchy":1715},[902,25914,24822],{"encoding":904},[724,25916,25917],{},[614,25918,25919,25920,25941,25942,25957,25958,25973,25974,25987,25988,26005,26006,5149,26019,26005,26036,26049,26050,26063],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,25921,25923],{"className":25922},[886],[888,25924,25925],{"xmlns":890},[892,25926,25927,25939],{},[895,25928,25929,25931,25933,25935,25937],{},[1708,25930,1716],{"stretchy":1715},[898,25932,5498],{},[1708,25934,1883],{"separator":1882},[898,25936,21035],{},[1708,25938,1721],{"stretchy":1715},[902,25940,24822],{"encoding":904},". Rostoucí přímka ",[883,25943,25945],{"className":25944},[886],[888,25946,25947],{"xmlns":890},[892,25948,25949,25955],{},[895,25950,25951,25953],{},[898,25952,1658],{},[898,25954,1741],{},[902,25956,23945],{"encoding":904}," a klesající přímka ",[883,25959,25961],{"className":25960},[886],[888,25962,25963],{"xmlns":890},[892,25964,25965,25971],{},[895,25966,25967,25969],{},[898,25968,24070],{},[898,25970,1981],{},[902,25972,23938],{"encoding":904}," se protínají v bodě ",[883,25975,25977],{"className":25976},[886],[888,25978,25979],{"xmlns":890},[892,25980,25981,25985],{},[895,25982,25983],{},[898,25984,16183],{},[902,25986,16183],{"encoding":904}," se souřadnicemi ",[883,25989,25991],{"className":25990},[886],[888,25992,25993],{"xmlns":890},[892,25994,25995,26003],{},[895,25996,25997],{},[1753,25998,25999,26001],{},[898,26000,5498],{},[898,26002,16183],{},[902,26004,25806],{"encoding":904}," (na ose ",[883,26007,26009],{"className":26008},[886],[888,26010,26011],{"xmlns":890},[892,26012,26013,26017],{},[895,26014,26015],{},[898,26016,5498],{},[902,26018,5498],{"encoding":904},[883,26020,26022],{"className":26021},[886],[888,26023,26024],{"xmlns":890},[892,26025,26026,26034],{},[895,26027,26028],{},[1753,26029,26030,26032],{},[898,26031,21035],{},[898,26033,16183],{},[902,26035,25785],{"encoding":904},[883,26037,26039],{"className":26038},[886],[888,26040,26041],{"xmlns":890},[892,26042,26043,26047],{},[895,26044,26045],{},[898,26046,21035],{},[902,26048,21035],{"encoding":904},"); tečkované čáry z ",[883,26051,26053],{"className":26052},[886],[888,26054,26055],{"xmlns":890},[892,26056,26057,26061],{},[895,26058,26059],{},[898,26060,16183],{},[902,26062,16183],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1636,26065,26066,26071],{},[724,26067,26068,26070],{},[883,26069,3465],{}," Postup — jak najít IS-LM rovnováhu",[152,26072,26073,26149,26217,26275,26348],{},[123,26074,26075,26078,26079,1771,26099,26119,26120,1771,26133,26146,26147,2155],{},[38,26076,26077],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,26080,26082],{"className":26081},[886],[888,26083,26084],{"xmlns":890},[892,26085,26086,26096],{},[895,26087,26088,26090,26092,26094],{},[898,26089,3455],{},[1708,26091,1716],{"stretchy":1715},[898,26093,21035],{},[1708,26095,1721],{"stretchy":1715},[902,26097,26098],{"encoding":904},"C(Y)",[883,26100,26102],{"className":26101},[886],[888,26103,26104],{"xmlns":890},[892,26105,26106,26116],{},[895,26107,26108,26110,26112,26114],{},[898,26109,24070],{},[1708,26111,1716],{"stretchy":1715},[898,26113,5498],{},[1708,26115,1721],{"stretchy":1715},[902,26117,26118],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,26121,26123],{"className":26122},[886],[888,26124,26125],{"xmlns":890},[892,26126,26127,26131],{},[895,26128,26129],{},[898,26130,21035],{},[902,26132,21035],{"encoding":904},[883,26134,26136],{"className":26135},[886],[888,26137,26138],{"xmlns":890},[892,26139,26140,26144],{},[895,26141,26142],{},[898,26143,5498],{},[902,26145,5498],{"encoding":904}," — dostaneš rovnici ",[38,26148,23938],{},[123,26150,26151,26154,26155,1771,26172,26189,26190,26146,26215,2155],{},[38,26152,26153],{},"Z trhu peněz (7.15)"," dosaď ",[883,26156,26158],{"className":26157},[886],[888,26159,26160],{"xmlns":890},[892,26161,26162,26170],{},[895,26163,26164],{},[1743,26165,26166,26168],{},[898,26167,1658],{},[2505,26169,2507],{},[902,26171,2979],{"encoding":904},[883,26173,26175],{"className":26174},[886],[888,26176,26177],{"xmlns":890},[892,26178,26179,26187],{},[895,26180,26181],{},[1743,26182,26183,26185],{},[898,26184,1658],{},[2505,26186,3132],{},[902,26188,25167],{"encoding":904}," a vztah ",[883,26191,26193],{"className":26192},[886],[888,26194,26195],{"xmlns":890},[892,26196,26197,26213],{},[895,26198,26199,26205,26207],{},[1753,26200,26201,26203],{},[898,26202,1741],{},[898,26204,16117],{},[1708,26206,1710],{},[1753,26208,26209,26211],{},[898,26210,1741],{},[1708,26212,2417],{},[902,26214,25363],{"encoding":904},[38,26216,23945],{},[123,26218,26219,26222,26223,1771,26236,26249,26250,26274],{},[38,26220,26221],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,26224,26226],{"className":26225},[886],[888,26227,26228],{"xmlns":890},[892,26229,26230,26234],{},[895,26231,26232],{},[898,26233,21035],{},[902,26235,21035],{"encoding":904},[883,26237,26239],{"className":26238},[886],[888,26240,26241],{"xmlns":890},[892,26242,26243,26247],{},[895,26244,26245],{},[898,26246,5498],{},[902,26248,5498],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,26251,26253],{"className":26252},[886],[888,26254,26255],{"xmlns":890},[892,26256,26257,26271],{},[895,26258,26259,26261,26263,26265,26267,26269],{},[898,26260,21035],{},[1708,26262,1710],{},[898,26264,14009],{},[1708,26266,1716],{"stretchy":1715},[898,26268,5498],{},[1708,26270,1721],{"stretchy":1715},[902,26272,26273],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,26276,26277,1729,26280,1771,26314,2155],{},[38,26278,26279],{},"Zpětně dopočítej",[883,26281,26283],{"className":26282},[886],[888,26284,26285],{"xmlns":890},[892,26286,26287,26311],{},[895,26288,26289,26295,26297,26299,26301,26307,26309],{},[1753,26290,26291,26293],{},[898,26292,3455],{},[898,26294,16183],{},[1708,26296,1710],{},[898,26298,207],{},[2247,26300,2659],{},[1753,26302,26303,26305],{},[898,26304,21035],{},[898,26306,16183],{},[1708,26308,2019],{},[898,26310,1923],{},[902,26312,26313],{"encoding":904},"C^E = a\\,Y^E + b",[883,26315,26317],{"className":26316},[886],[888,26318,26319],{"xmlns":890},[892,26320,26321,26345],{},[895,26322,26323,26329,26331,26333,26335,26341,26343],{},[1753,26324,26325,26327],{},[898,26326,24070],{},[898,26328,16183],{},[1708,26330,1710],{},[898,26332,14142],{},[2247,26334,2659],{},[1753,26336,26337,26339],{},[898,26338,5498],{},[898,26340,16183],{},[1708,26342,2019],{},[898,26344,2364],{},[902,26346,26347],{"encoding":904},"I^E = c\\,r^E + d",[123,26349,26350,26353,26354,26388,26389,26443],{},[38,26351,26352],{},"Ověř:"," musí platit ",[883,26355,26357],{"className":26356},[886],[888,26358,26359],{"xmlns":890},[892,26360,26361,26385],{},[895,26362,26363,26369,26371,26377,26379],{},[1753,26364,26365,26367],{},[898,26366,21035],{},[898,26368,16183],{},[1708,26370,1710],{},[1753,26372,26373,26375],{},[898,26374,3455],{},[898,26376,16183],{},[1708,26378,2019],{},[1753,26380,26381,26383],{},[898,26382,24070],{},[898,26384,16183],{},[902,26386,26387],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,26390,26392],{"className":26391},[886],[888,26393,26394],{"xmlns":890},[892,26395,26396,26440],{},[895,26397,26398,26404,26406,26412,26418,26420,26426,26432,26434],{},[1753,26399,26400,26402],{},[898,26401,1741],{},[1708,26403,2417],{},[1708,26405,1710],{},[1743,26407,26408,26410],{},[898,26409,25121],{},[2505,26411,2507],{},[1753,26413,26414,26416],{},[898,26415,21035],{},[898,26417,16183],{},[1708,26419,2019],{},[1743,26421,26422,26424],{},[898,26423,25121],{},[2505,26425,3132],{},[1753,26427,26428,26430],{},[898,26429,5498],{},[898,26431,16183],{},[1708,26433,2019],{},[1743,26435,26436,26438],{},[898,26437,25121],{},[2505,26439,3121],{},[902,26441,26442],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,26445,26447],{"id":26446},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,26449,26450],{},"Pro trh zboží jsou dány:",[120,26452,26453,26480],{},[123,26454,26455,26456,1883],{},"spotřeba ",[883,26457,26459],{"className":26458},[886],[888,26460,26461],{"xmlns":890},[892,26462,26463,26477],{},[895,26464,26465,26467,26469,26471,26473,26475],{},[898,26466,3455],{},[1708,26468,1710],{},[2505,26470,6120],{},[898,26472,21035],{},[1708,26474,2019],{},[2505,26476,9238],{},[902,26478,26479],{"encoding":904},"C = 0{,}8Y + 100",[123,26481,26482,26483,2155],{},"investice ",[883,26484,26486],{"className":26485},[886],[888,26487,26488],{"xmlns":890},[892,26489,26490,26506],{},[895,26491,26492,26494,26496,26498,26500,26502,26504],{},[898,26493,24070],{},[1708,26495,1710],{},[1708,26497,2726],{},[2505,26499,4018],{},[898,26501,5498],{},[1708,26503,2019],{},[2505,26505,11613],{},[902,26507,26508],{"encoding":904},"I = -20r + 1000",[724,26510,26511],{},"Pro trh peněz:",[120,26513,26514,26540,26572],{},[123,26515,26516,1883],{},[883,26517,26519],{"className":26518},[886],[888,26520,26521],{"xmlns":890},[892,26522,26523,26537],{},[895,26524,26525,26531,26533,26535],{},[1743,26526,26527,26529],{},[898,26528,1658],{},[2505,26530,2507],{},[1708,26532,1710],{},[2505,26534,10909],{},[898,26536,21035],{},[902,26538,26539],{"encoding":904},"L_1 = 0{,}1Y",[123,26541,26542,1883],{},[883,26543,26545],{"className":26544},[886],[888,26546,26547],{"xmlns":890},[892,26548,26549,26569],{},[895,26550,26551,26557,26559,26561,26563,26565,26567],{},[1743,26552,26553,26555],{},[898,26554,1658],{},[2505,26556,3132],{},[1708,26558,1710],{},[1708,26560,2726],{},[2505,26562,4028],{},[898,26564,5498],{},[1708,26566,2019],{},[2505,26568,20514],{},[902,26570,26571],{"encoding":904},"L_2 = -25r + 2000",[123,26573,26574,26575,2155],{},"nabídka peněz ",[883,26576,26578],{"className":26577},[886],[888,26579,26580],{"xmlns":890},[892,26581,26582,26595],{},[895,26583,26584,26590,26592],{},[1753,26585,26586,26588],{},[898,26587,1741],{},[1708,26589,2417],{},[1708,26591,1710],{},[2505,26593,26594],{},"2375",[902,26596,26597],{"encoding":904},"M^* = 2375",[724,26599,26600,26603,26604,2788],{},[38,26601,26602],{},"Funkce IS"," — dosazením do (7.13) ",[883,26605,26607],{"className":26606},[886],[888,26608,26609],{"xmlns":890},[892,26610,26611,26623],{},[895,26612,26613,26615,26617,26619,26621],{},[898,26614,21035],{},[1708,26616,1710],{},[898,26618,3455],{},[1708,26620,2019],{},[898,26622,24070],{},[902,26624,26625],{"encoding":904},"Y = C + I",[724,26627,26628],{},[883,26629,26631],{"className":26630},[886],[888,26632,26633],{"xmlns":890},[892,26634,26635,26661],{},[895,26636,26637,26639,26641,26643,26645,26647,26649,26651,26653,26655,26657,26659],{},[898,26638,21035],{},[1708,26640,1710],{},[2505,26642,6120],{},[898,26644,21035],{},[1708,26646,2019],{},[2505,26648,9238],{},[1708,26650,2726],{},[2505,26652,4018],{},[898,26654,5498],{},[1708,26656,2019],{},[2505,26658,11613],{},[1708,26660,1883],{"separator":1882},[902,26662,26663],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,26665,26666],{},"tj.",[724,26668,26669],{},[883,26670,26672],{"className":26671},[886],[888,26673,26674],{"xmlns":890},[892,26675,26676,26701],{},[895,26677,26678,26680,26682,26684,26686,26688,26690,26693,26695,26697,26699],{},[2505,26679,3958],{},[898,26681,21035],{},[1708,26683,2019],{},[2505,26685,4018],{},[898,26687,5498],{},[1708,26689,1710],{},[2505,26691,26692],{},"1100.",[3213,26694],{"width":3215},[1708,26696,1716],{"stretchy":1715},[2247,26698,23938],{},[1708,26700,1721],{"stretchy":1715},[902,26702,26703],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,26705,26706,26709,26710,2788],{},[38,26707,26708],{},"Funkce LM"," — dosazením do (7.15) ",[883,26711,26713],{"className":26712},[886],[888,26714,26715],{"xmlns":890},[892,26716,26717,26741],{},[895,26718,26719,26725,26727,26733,26735],{},[1753,26720,26721,26723],{},[898,26722,1741],{},[1708,26724,2417],{},[1708,26726,1710],{},[1743,26728,26729,26731],{},[898,26730,1658],{},[2505,26732,2507],{},[1708,26734,2019],{},[1743,26736,26737,26739],{},[898,26738,1658],{},[2505,26740,3132],{},[902,26742,26743],{"encoding":904},"M^* = L_1 + L_2",[724,26745,26746],{},[883,26747,26749],{"className":26748},[886],[888,26750,26751],{"xmlns":890},[892,26752,26753,26775],{},[895,26754,26755,26757,26759,26761,26763,26765,26767,26769,26771,26773],{},[2505,26756,26594],{},[1708,26758,1710],{},[2505,26760,10909],{},[898,26762,21035],{},[1708,26764,2726],{},[2505,26766,4028],{},[898,26768,5498],{},[1708,26770,2019],{},[2505,26772,20514],{},[1708,26774,1883],{"separator":1882},[902,26776,26777],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,26779,26666],{},[724,26781,26782],{},[883,26783,26785],{"className":26784},[886],[888,26786,26787],{"xmlns":890},[892,26788,26789,26814],{},[895,26790,26791,26793,26795,26797,26799,26801,26803,26806,26808,26810,26812],{},[2505,26792,10909],{},[898,26794,21035],{},[1708,26796,2726],{},[2505,26798,4028],{},[898,26800,5498],{},[1708,26802,1710],{},[2505,26804,26805],{},"375.",[3213,26807],{"width":3215},[1708,26809,1716],{"stretchy":1715},[2247,26811,23945],{},[1708,26813,1721],{"stretchy":1715},[902,26815,26816],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,26818,26819,26822,26823,26848],{},[38,26820,26821],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,26824,26826],{"className":26825},[886],[888,26827,26828],{"xmlns":890},[892,26829,26830,26845],{},[895,26831,26832,26834,26836,26839,26841,26843],{},[898,26833,21035],{},[1708,26835,1710],{},[2505,26837,26838],{},"5500",[1708,26840,2726],{},[2505,26842,9238],{},[898,26844,5498],{},[902,26846,26847],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,26850,26851],{},[883,26852,26854],{"className":26853},[886],[888,26855,26856],{"xmlns":890},[892,26857,26858,26944],{},[895,26859,26860,26862,26864,26866,26868,26870,26872,26874,26876,26878,26880,26882,26885,26887,26890,26892,26895,26897,26899,26901,26903,26905,26907,26909,26911,26913,26915,26917,26920,26922,26924,26927,26929,26931,26933,26939,26941],{},[2505,26861,10909],{},[1708,26863,1716],{"stretchy":1715},[2505,26865,26838],{},[1708,26867,2726],{},[2505,26869,9238],{},[898,26871,5498],{},[1708,26873,1721],{"stretchy":1715},[1708,26875,2726],{},[2505,26877,4028],{},[898,26879,5498],{},[1708,26881,1710],{},[2505,26883,26884],{},"375",[2247,26886,4779],{},[1708,26888,26889],{},"⟹",[2247,26891,4779],{},[2505,26893,26894],{},"550",[1708,26896,2726],{},[2505,26898,4003],{},[898,26900,5498],{},[1708,26902,2726],{},[2505,26904,4028],{},[898,26906,5498],{},[1708,26908,1710],{},[2505,26910,26884],{},[2247,26912,4779],{},[1708,26914,26889],{},[2247,26916,4779],{},[2505,26918,26919],{},"35",[898,26921,5498],{},[1708,26923,1710],{},[2505,26925,26926],{},"175",[2247,26928,4779],{},[1708,26930,26889],{},[2247,26932,4779],{},[1753,26934,26935,26937],{},[898,26936,5498],{},[898,26938,16183],{},[1708,26940,1710],{},[2505,26942,26943],{},"5.",[902,26945,26946],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,26948,26949],{},[38,26950,26951],{},"Zpětné dosazení:",[120,26953,26954,26999,27036],{},[123,26955,26956,1883],{},[883,26957,26959],{"className":26958},[886],[888,26960,26961],{"xmlns":890},[892,26962,26963,26996],{},[895,26964,26965,26971,26973,26975,26977,26979,26981,26983,26985,26987,26989,26991,26993],{},[1753,26966,26967,26969],{},[898,26968,21035],{},[898,26970,16183],{},[1708,26972,1710],{},[2505,26974,26838],{},[1708,26976,2726],{},[2505,26978,9238],{},[1708,26980,3703],{},[2505,26982,3993],{},[1708,26984,1710],{},[2505,26986,26838],{},[1708,26988,2726],{},[2505,26990,11040],{},[1708,26992,1710],{},[2505,26994,26995],{},"5000",[902,26997,26998],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,27000,27001,1883],{},[883,27002,27004],{"className":27003},[886],[888,27005,27006],{"xmlns":890},[892,27007,27008,27033],{},[895,27009,27010,27016,27018,27020,27022,27024,27026,27028,27030],{},[1753,27011,27012,27014],{},[898,27013,3455],{},[898,27015,16183],{},[1708,27017,1710],{},[2505,27019,6120],{},[1708,27021,3703],{},[2505,27023,26995],{},[1708,27025,2019],{},[2505,27027,9238],{},[1708,27029,1710],{},[2505,27031,27032],{},"4100",[902,27034,27035],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,27037,27038,2155],{},[883,27039,27041],{"className":27040},[886],[888,27042,27043],{"xmlns":890},[892,27044,27045,27071],{},[895,27046,27047,27053,27055,27057,27059,27061,27063,27065,27067,27069],{},[1753,27048,27049,27051],{},[898,27050,24070],{},[898,27052,16183],{},[1708,27054,1710],{},[1708,27056,2726],{},[2505,27058,4018],{},[1708,27060,3703],{},[2505,27062,3993],{},[1708,27064,2019],{},[2505,27066,11613],{},[1708,27068,1710],{},[2505,27070,11732],{},[902,27072,27073],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,27075,27076,1729,27079,27125],{},[38,27077,27078],{},"Ověření:",[883,27080,27082],{"className":27081},[886],[888,27083,27084],{"xmlns":890},[892,27085,27086,27122],{},[895,27087,27088,27094,27096,27102,27104,27106,27108,27110,27112,27114,27116],{},[1753,27089,27090,27092],{},[898,27091,3455],{},[898,27093,16183],{},[1708,27095,2019],{},[1753,27097,27098,27100],{},[898,27099,24070],{},[898,27101,16183],{},[1708,27103,1710],{},[2505,27105,27032],{},[1708,27107,2019],{},[2505,27109,11732],{},[1708,27111,1710],{},[2505,27113,26995],{},[1708,27115,1710],{},[1753,27117,27118,27120],{},[898,27119,21035],{},[898,27121,16183],{},[902,27123,27124],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,27127,27128],{},[883,27129,27131],{"className":27130},[886],[888,27132,27133],{"xmlns":890},[892,27134,27135,27204],{},[895,27136,27137],{},[24717,27138,27139],{"notation":24719},[3194,27140,27141],{"scriptlevel":2784,"displaystyle":1715},[3194,27142,27143],{"scriptlevel":2784,"displaystyle":1715},[3194,27144,27145],{"scriptlevel":2784,"displaystyle":1882},[895,27146,27147,27149,27155,27157,27159,27161,27163,27169,27171,27173,27175,27177,27183,27185,27187,27189,27191,27197,27199,27202],{},[2247,27148,2659],{},[1753,27150,27151,27153],{},[898,27152,21035],{},[898,27154,16183],{},[1708,27156,1710],{},[2505,27158,26995],{},[1708,27160,1883],{"separator":1882},[3213,27162],{"width":4750},[1753,27164,27165,27167],{},[898,27166,5498],{},[898,27168,16183],{},[1708,27170,1710],{},[2505,27172,3993],{},[1708,27174,1883],{"separator":1882},[3213,27176],{"width":4750},[1753,27178,27179,27181],{},[898,27180,3455],{},[898,27182,16183],{},[1708,27184,1710],{},[2505,27186,27032],{},[1708,27188,1883],{"separator":1882},[3213,27190],{"width":4750},[1753,27192,27193,27195],{},[898,27194,24070],{},[898,27196,16183],{},[1708,27198,1710],{},[2505,27200,27201],{},"900.",[2247,27203,2659],{},[902,27205,27206],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,27208,27209],{},[614,27210,27211,27212,27225,27226,27239,27240,27255,27256,27269,27270,27285,27286,27299,27300,27313,27314,2155],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,27213,27215],{"className":27214},[886],[888,27216,27217],{"xmlns":890},[892,27218,27219,27223],{},[895,27220,27221],{},[898,27222,21035],{},[902,27224,21035],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,27227,27229],{"className":27228},[886],[888,27230,27231],{"xmlns":890},[892,27232,27233,27237],{},[895,27234,27235],{},[898,27236,5498],{},[902,27238,5498],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,27241,27243],{"className":27242},[886],[888,27244,27245],{"xmlns":890},[892,27246,27247,27253],{},[895,27248,27249,27251],{},[898,27250,1658],{},[898,27252,1741],{},[902,27254,23945],{"encoding":904}," stoupá z oblasti nízkých ",[883,27257,27259],{"className":27258},[886],[888,27260,27261],{"xmlns":890},[892,27262,27263,27267],{},[895,27264,27265],{},[898,27266,5498],{},[902,27268,5498],{"encoding":904},", přímka ",[883,27271,27273],{"className":27272},[886],[888,27274,27275],{"xmlns":890},[892,27276,27277,27283],{},[895,27278,27279,27281],{},[898,27280,24070],{},[898,27282,1981],{},[902,27284,23938],{"encoding":904}," klesá a protíná osu ",[883,27287,27289],{"className":27288},[886],[888,27290,27291],{"xmlns":890},[892,27292,27293,27297],{},[895,27294,27295],{},[898,27296,5498],{},[902,27298,5498],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,27301,27303],{"className":27302},[886],[888,27304,27305],{"xmlns":890},[892,27306,27307,27311],{},[895,27308,27309],{},[898,27310,16183],{},[902,27312,16183],{"encoding":904}," leží v bodě ",[883,27315,27317],{"className":27316},[886],[888,27318,27319],{"xmlns":890},[892,27320,27321,27343],{},[895,27322,27323,27325,27327,27329,27331,27333,27335,27337,27339,27341],{},[1708,27324,6940],{"stretchy":1715},[898,27326,5498],{},[1708,27328,1710],{},[2505,27330,3993],{},[1708,27332,1883],{"separator":1882},[2247,27334,14279],{},[898,27336,21035],{},[1708,27338,1710],{},[2505,27340,26995],{},[1708,27342,6981],{"stretchy":1715},[902,27344,27345],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,27347,27349],{"id":27348},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,27351,27352,27355,27356,27369,27370,12636,27383,27386,27387,27405,27406,27423,27424,27441,27442,27455,27456,27469],{},[38,27353,27354],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,27357,27359],{"className":27358},[886],[888,27360,27361],{"xmlns":890},[892,27362,27363,27367],{},[895,27364,27365],{},[898,27366,23999],{},[902,27368,23999],{"encoding":904}," nebo snížení daní ",[883,27371,27373],{"className":27372},[886],[888,27374,27375],{"xmlns":890},[892,27376,27377,27381],{},[895,27378,27379],{},[898,27380,1978],{},[902,27382,1978],{"encoding":904},[38,27384,27385],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,27388,27390],{"className":27389},[886],[888,27391,27392],{"xmlns":890},[892,27393,27394,27402],{},[895,27395,27396],{},[1753,27397,27398,27400],{},[898,27399,16183],{},[1708,27401,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,27403,27404],{"encoding":904},"E'"," má vyšší ",[883,27407,27409],{"className":27408},[886],[888,27410,27411],{"xmlns":890},[892,27412,27413,27421],{},[895,27414,27415],{},[1753,27416,27417,27419],{},[898,27418,21035],{},[898,27420,16183],{},[902,27422,25785],{"encoding":904}," i vyšší ",[883,27425,27427],{"className":27426},[886],[888,27428,27429],{"xmlns":890},[892,27430,27431,27439],{},[895,27432,27433],{},[1753,27434,27435,27437],{},[898,27436,5498],{},[898,27438,16183],{},[902,27440,25806],{"encoding":904}," (vyšší ",[883,27443,27445],{"className":27444},[886],[888,27446,27447],{"xmlns":890},[892,27448,27449,27453],{},[895,27450,27451],{},[898,27452,21035],{},[902,27454,21035],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,27457,27459],{"className":27458},[886],[888,27460,27461],{"xmlns":890},[892,27462,27463,27467],{},[895,27464,27465],{},[898,27466,5498],{},[902,27468,5498],{"encoding":904}," nahoru).",[724,27471,27472],{},[3372,27473],{"alt":27474,"className":27475,"src":27476},"imek-posun-is-lm-politiky",[210,3376],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,27478,27479,27482,27483,27500,27501,27504,27505,27522,27523,27540,27541,27554,27555,27574,27575,2511],{},[38,27480,27481],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,27484,27486],{"className":27485},[886],[888,27487,27488],{"xmlns":890},[892,27489,27490,27498],{},[895,27491,27492],{},[1753,27493,27494,27496],{},[898,27495,1741],{},[1708,27497,2417],{},[902,27499,24036],{"encoding":904}," národní bankou — ",[38,27502,27503],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,27506,27508],{"className":27507},[886],[888,27509,27510],{"xmlns":890},[892,27511,27512,27520],{},[895,27513,27514],{},[1753,27515,27516,27518],{},[898,27517,5498],{},[898,27519,16183],{},[902,27521,25806],{"encoding":904}," a vyšší ",[883,27524,27526],{"className":27525},[886],[888,27527,27528],{"xmlns":890},[892,27529,27530,27538],{},[895,27531,27532],{},[1753,27533,27534,27536],{},[898,27535,21035],{},[898,27537,16183],{},[902,27539,25785],{"encoding":904}," (nižší ",[883,27542,27544],{"className":27543},[886],[888,27545,27546],{"xmlns":890},[892,27547,27548,27552],{},[895,27549,27550],{},[898,27551,5498],{},[902,27553,5498],{"encoding":904}," povzbuzuje investice ",[883,27556,27558],{"className":27557},[886],[888,27559,27560],{"xmlns":890},[892,27561,27562,27572],{},[895,27563,27564,27566,27568,27570],{},[898,27565,24070],{},[1708,27567,1716],{"stretchy":1715},[898,27569,5498],{},[1708,27571,1721],{"stretchy":1715},[902,27573,26118],{"encoding":904},", ty zvedají ",[883,27576,27578],{"className":27577},[886],[888,27579,27580],{"xmlns":890},[892,27581,27582,27586],{},[895,27583,27584],{},[898,27585,21035],{},[902,27587,21035],{"encoding":904},[724,27589,27590,27591,27594],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,27592,27593],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,27596,12596],{"id":12595},[120,27598,27599,27671,27717,27799,27849,27916,27973,28014,28047],{},[123,27600,27601,12636,27634,1343,27651,9137,27668,27670],{},[38,27602,27603,27604],{},"Funkce investic ",[883,27605,27607],{"className":27606},[886],[888,27608,27609],{"xmlns":890},[892,27610,27611,27631],{},[895,27612,27613,27615,27617,27619,27621,27623,27625,27627,27629],{},[898,27614,24070],{},[1708,27616,1716],{"stretchy":1715},[898,27618,5498],{},[1708,27620,1721],{"stretchy":1715},[1708,27622,1710],{},[898,27624,14142],{},[898,27626,5498],{},[1708,27628,2019],{},[898,27630,2364],{},[902,27632,27633],{"encoding":904},"I(r) = cr + d",[883,27635,27637],{"className":27636},[886],[888,27638,27639],{"xmlns":890},[892,27640,27641,27649],{},[895,27642,27643,27645,27647],{},[898,27644,14142],{},[1708,27646,2932],{},[2505,27648,2784],{},[902,27650,24401],{"encoding":904},[883,27652,27654],{"className":27653},[886],[888,27655,27656],{"xmlns":890},[892,27657,27658,27666],{},[895,27659,27660,27662,27664],{},[898,27661,2364],{},[1708,27663,2854],{},[2505,27665,2784],{},[902,27667,24380],{"encoding":904},[38,27669,8185],{}," funkce úrokové míry.",[123,27672,27673,27676,27677,27698,27699,27716],{},[38,27674,27675],{},"Trh zboží"," — rovnováha ",[883,27678,27680],{"className":27679},[886],[888,27681,27682],{"xmlns":890},[892,27683,27684,27696],{},[895,27685,27686,27688,27690,27692,27694],{},[898,27687,21035],{},[1708,27689,1710],{},[898,27691,3455],{},[1708,27693,2019],{},[898,27695,24070],{},[902,27697,26625],{"encoding":904},", ekvivalentně ",[883,27700,27702],{"className":27701},[886],[888,27703,27704],{"xmlns":890},[892,27705,27706,27714],{},[895,27707,27708,27710,27712],{},[898,27709,24070],{},[1708,27711,1710],{},[898,27713,1981],{},[902,27715,24597],{"encoding":904}," (investice = úspory).",[123,27718,27719,1695,27722,27724,27725,27775,27776,24800,27778,2155],{},[38,27720,27721],{},"Křivka IS",[614,27723,23941],{},") — ",[883,27726,27728],{"className":27727},[886],[888,27729,27730],{"xmlns":890},[892,27731,27732,27772],{},[895,27733,27734,27736,27738,27750,27752,27754],{},[898,27735,21035],{},[1708,27737,1710],{},[2358,27739,27740,27742],{},[898,27741,14142],{},[895,27743,27744,27746,27748],{},[2505,27745,2507],{},[1708,27747,2726],{},[898,27749,207],{},[898,27751,5498],{},[1708,27753,2019],{},[2358,27755,27756,27764],{},[895,27757,27758,27760,27762],{},[898,27759,1923],{},[1708,27761,2019],{},[898,27763,2364],{},[895,27765,27766,27768,27770],{},[2505,27767,2507],{},[1708,27769,2726],{},[898,27771,207],{},[902,27773,27774],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,27777,8185],{},[883,27779,27781],{"className":27780},[886],[888,27782,27783],{"xmlns":890},[892,27784,27785,27797],{},[895,27786,27787,27789,27791,27793,27795],{},[1708,27788,1716],{"stretchy":1715},[898,27790,5498],{},[1708,27792,1883],{"separator":1882},[898,27794,21035],{},[1708,27796,1721],{"stretchy":1715},[902,27798,24822],{"encoding":904},[123,27800,27801,27676,27804,27830,27831,2155],{},[38,27802,27803],{},"Trh peněz",[883,27805,27807],{"className":27806},[886],[888,27808,27809],{"xmlns":890},[892,27810,27811,27827],{},[895,27812,27813,27819,27821],{},[1753,27814,27815,27817],{},[898,27816,1741],{},[898,27818,16117],{},[1708,27820,1710],{},[1753,27822,27823,27825],{},[898,27824,1741],{},[898,27826,1981],{},[902,27828,27829],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,27832,27834],{"className":27833},[886],[888,27835,27836],{"xmlns":890},[892,27837,27838,27846],{},[895,27839,27840],{},[1753,27841,27842,27844],{},[898,27843,1741],{},[1708,27845,2417],{},[902,27847,27848],{"encoding":904},"M^* ",[123,27850,27851,12636,27854,2155],{},[38,27852,27853],{},"Transakční, opatrnostní, spekulační poptávka",[883,27855,27857],{"className":27856},[886],[888,27858,27859],{"xmlns":890},[892,27860,27861,27913],{},[895,27862,27863,27869,27871,27877,27879,27885,27887,27893,27895,27897,27903,27905,27907],{},[1753,27864,27865,27867],{},[898,27866,1741],{},[898,27868,16117],{},[1708,27870,1710],{},[1743,27872,27873,27875],{},[898,27874,1658],{},[2505,27876,2507],{},[1708,27878,2019],{},[1743,27880,27881,27883],{},[898,27882,1658],{},[2505,27884,3132],{},[1708,27886,1710],{},[1743,27888,27889,27891],{},[898,27890,25121],{},[2505,27892,2507],{},[898,27894,21035],{},[1708,27896,2019],{},[1743,27898,27899,27901],{},[898,27900,25121],{},[2505,27902,3132],{},[898,27904,5498],{},[1708,27906,2019],{},[1743,27908,27909,27911],{},[898,27910,25121],{},[2505,27912,3121],{},[902,27914,27915],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,27917,27918,1695,27921,27724,27923,27969,27970,27972],{},[38,27919,27920],{},"Křivka LM",[614,27922,23948],{},[883,27924,27926],{"className":27925},[886],[888,27927,27928],{"xmlns":890},[892,27929,27930,27966],{},[895,27931,27932,27938,27940,27946,27948,27950,27956,27958,27960],{},[1753,27933,27934,27936],{},[898,27935,1741],{},[1708,27937,2417],{},[1708,27939,1710],{},[1743,27941,27942,27944],{},[898,27943,25121],{},[2505,27945,2507],{},[898,27947,21035],{},[1708,27949,2019],{},[1743,27951,27952,27954],{},[898,27953,25121],{},[2505,27955,3132],{},[898,27957,5498],{},[1708,27959,2019],{},[1743,27961,27962,27964],{},[898,27963,25121],{},[2505,27965,3121],{},[902,27967,27968],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,27971,2082],{}," přímka.",[123,27974,27975,27978,27979,28013],{},[38,27976,27977],{},"Simultánní rovnováha"," — průsečík ",[883,27980,27982],{"className":27981},[886],[888,27983,27984],{"xmlns":890},[892,27985,27986,28010],{},[895,27987,27988,27990,27992,27994,28000,28002,28008],{},[898,27989,16183],{},[1708,27991,1710],{},[1708,27993,1716],{"stretchy":1715},[1753,27995,27996,27998],{},[898,27997,5498],{},[898,27999,16183],{},[1708,28001,1883],{"separator":1882},[1753,28003,28004,28006],{},[898,28005,21035],{},[898,28007,16183],{},[1708,28009,1721],{"stretchy":1715},[902,28011,28012],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,28015,28016,28019,28020,1343,28033,28046],{},[38,28017,28018],{},"Fiskální politika"," — nástroje ",[883,28021,28023],{"className":28022},[886],[888,28024,28025],{"xmlns":890},[892,28026,28027,28031],{},[895,28028,28029],{},[898,28030,23999],{},[902,28032,23999],{"encoding":904},[883,28034,28036],{"className":28035},[886],[888,28037,28038],{"xmlns":890},[892,28039,28040,28044],{},[895,28041,28042],{},[898,28043,1978],{},[902,28045,1978],{"encoding":904}," posouvající křivku IS.",[123,28048,28049,28052,28053,28070],{},[38,28050,28051],{},"Monetární politika"," — nástroj ",[883,28054,28056],{"className":28055},[886],[888,28057,28058],{"xmlns":890},[892,28059,28060,28068],{},[895,28061,28062],{},[1753,28063,28064,28066],{},[898,28065,1741],{},[1708,28067,2417],{},[902,28069,24036],{"encoding":904}," posouvající křivku LM.",[115,28072,13763],{"id":13762},[120,28074,28075,28082,28090,28100],{},[123,28076,28077,1729,28079],{},[38,28078,13888],{},[207,28080,13894],{"className":28081,"dataFsResolvedFilePath":13892,"href":13893},[210],[123,28083,28084,1729,28086],{},[38,28085,13880],{},[207,28087,28089],{"className":28088,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,28091,28092,1729,28095,28099],{},[38,28093,28094],{},"Nadřazené téma:",[207,28096,28098],{"className":28097,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,28101,28102,28105],{},[38,28103,28104],{},"Související:",[120,28106,28107,28114,28120],{},[123,28108,28109,28113],{},[207,28110,28112],{"className":28111,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,28115,28116,28119],{},[207,28117,1145],{"className":28118,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,28121,28122,28126],{},[207,28123,28125],{"className":28124,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":28128},[28129,28130,28131,28132,28133,28134,28135,28136,28137,28138],{"id":23893,"depth":642,"text":23894},{"id":24046,"depth":642,"text":24047},{"id":24261,"depth":642,"text":24262},{"id":24553,"depth":642,"text":24554},{"id":24966,"depth":642,"text":24967},{"id":25756,"depth":642,"text":25757},{"id":26446,"depth":642,"text":26447},{"id":27348,"depth":642,"text":27349},{"id":12595,"depth":642,"text":12596},{"id":13762,"depth":642,"text":13763},{},"\u002Ftopics\u002Fis-lm",{"title":23885,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,28145,1143,28146,28147,28148,28149,28098],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":28152,"title":28153,"body":28154,"course":659,"courses":29745,"created":1129,"description":29746,"extension":661,"meta":29747,"navigation":664,"path":29748,"seo":29749,"sources":29750,"stem":29751,"tags":29752,"type":13951,"updated":677,"__hash__":29755},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":28155,"toc":29733},[28156,28159,28254,28261,28281,28285,28290,28353,28372,28374,28377,28513,28515,28725,28759,28896,28900,28964,28980,29008,29012,29110,29114,29118,29171,29277,29490,29494,29537,29643,29695,29697],[12,28157,28153],{"id":28158},"lagrangeova-metoda-vázané-extrémy",[724,28160,28161,28162,15851,28185,28217,28218,28221,28222,1691,28249,28253],{},"Hledáme extrém funkce ",[883,28163,28165],{"className":28164},[886],[888,28166,28167],{"xmlns":890},[892,28168,28169,28183],{},[895,28170,28171,28173,28175,28177,28179,28181],{},[898,28172,14009],{},[1708,28174,1716],{"stretchy":1715},[898,28176,14014],{},[1708,28178,1883],{"separator":1882},[898,28180,14004],{},[1708,28182,1721],{"stretchy":1715},[902,28184,21742],{"encoding":904},[883,28186,28188],{"className":28187},[886],[888,28189,28190],{"xmlns":890},[892,28191,28192,28214],{},[895,28193,28194,28196,28198,28204,28206,28212],{},[898,28195,900],{},[1708,28197,1716],{"stretchy":1715},[1743,28199,28200,28202],{},[898,28201,1688],{},[2505,28203,2507],{},[1708,28205,1883],{"separator":1882},[1743,28207,28208,28210],{},[898,28209,1688],{},[2505,28211,3132],{},[1708,28213,1721],{"stretchy":1715},[902,28215,28216],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,28219,28220],{},"podmíněný"," rovnicí ",[883,28223,28225],{"className":28224},[886],[888,28226,28227],{"xmlns":890},[892,28228,28229,28247],{},[895,28230,28231,28233,28235,28237,28239,28241,28243,28245],{},[898,28232,22927],{},[1708,28234,1716],{"stretchy":1715},[898,28236,14014],{},[1708,28238,1883],{"separator":1882},[898,28240,14004],{},[1708,28242,1721],{"stretchy":1715},[1708,28244,1710],{},[2505,28246,2784],{},[902,28248,22944],{"encoding":904},[207,28250,28252],{"className":28251,"dataFsResolvedFilePath":13892,"href":13893},[210],"matematické ekonomii"," se používá pro:",[724,28255,28256],{},[3372,28257],{"alt":28258,"className":28259,"src":28260},"imek-lagrange-tecnost",[210,3376],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,28262,28263,28272,28278],{},[123,28264,28265,28268,28269,1721],{},[38,28266,28267],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,28270,21676],{"className":28271,"dataFsResolvedFilePath":878,"href":879},[210],[123,28273,28274,28277],{},[38,28275,28276],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,28279,28280],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,28282,28284],{"id":28283},"princip","Princip",[724,28286,22594,28287,2788],{},[38,28288,28289],{},"Lagrangeovu funkci",[724,28291,28292],{},[883,28293,28295],{"className":28294},[886],[888,28296,28297],{"xmlns":890},[892,28298,28299,28350],{},[895,28300,28301,28303,28305,28307,28309,28311,28313,28316,28318,28320,28322,28324,28326,28328,28330,28332,28334,28336,28338,28340,28342,28344,28346,28348],{},[898,28302,1658],{},[1708,28304,1716],{"stretchy":1715},[898,28306,14014],{},[1708,28308,1883],{"separator":1882},[898,28310,14004],{},[1708,28312,1883],{"separator":1882},[898,28314,28315],{},"λ",[1708,28317,1721],{"stretchy":1715},[1708,28319,1710],{},[898,28321,14009],{},[1708,28323,1716],{"stretchy":1715},[898,28325,14014],{},[1708,28327,1883],{"separator":1882},[898,28329,14004],{},[1708,28331,1721],{"stretchy":1715},[1708,28333,2019],{},[898,28335,28315],{},[2247,28337,2659],{},[898,28339,22927],{},[1708,28341,1716],{"stretchy":1715},[898,28343,14014],{},[1708,28345,1883],{"separator":1882},[898,28347,14004],{},[1708,28349,1721],{"stretchy":1715},[902,28351,28352],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,28354,5411,28355,3033,28369,2155],{},[883,28356,28358],{"className":28357},[886],[888,28359,28360],{"xmlns":890},[892,28361,28362,28366],{},[895,28363,28364],{},[898,28365,28315],{},[902,28367,28368],{"encoding":904},"\\lambda",[38,28370,28371],{},"Lagrangeův multiplikátor",[115,28373,15206],{"id":15205},[724,28375,28376],{},"Řešíme soustavu:",[724,28378,28379,28427,28475],{},[883,28380,28382],{"className":28381},[886],[888,28383,28384],{"xmlns":890},[892,28385,28386,28424],{},[895,28387,28388,28396,28398,28406,28408,28410,28412,28420,28422],{},[4754,28389,28390,28392,28394],{},[898,28391,1658],{},[898,28393,14014],{},[1708,28395,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28397,1710],{},[4754,28399,28400,28402,28404],{},[898,28401,14009],{},[898,28403,14014],{},[1708,28405,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28407,2019],{},[898,28409,28315],{},[2247,28411,2659],{},[4754,28413,28414,28416,28418],{},[898,28415,22927],{},[898,28417,14014],{},[1708,28419,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28421,1710],{},[2505,28423,2784],{},[902,28425,28426],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,28428,28430],{"className":28429},[886],[888,28431,28432],{"xmlns":890},[892,28433,28434,28472],{},[895,28435,28436,28444,28446,28454,28456,28458,28460,28468,28470],{},[4754,28437,28438,28440,28442],{},[898,28439,1658],{},[898,28441,14004],{},[1708,28443,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28445,1710],{},[4754,28447,28448,28450,28452],{},[898,28449,14009],{},[898,28451,14004],{},[1708,28453,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28455,2019],{},[898,28457,28315],{},[2247,28459,2659],{},[4754,28461,28462,28464,28466],{},[898,28463,22927],{},[898,28465,14004],{},[1708,28467,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28469,1710],{},[2505,28471,2784],{},[902,28473,28474],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,28476,28478],{"className":28477},[886],[888,28479,28480],{"xmlns":890},[892,28481,28482,28510],{},[895,28483,28484,28492,28494,28496,28498,28500,28502,28504,28506,28508],{},[4754,28485,28486,28488,28490],{},[898,28487,1658],{},[898,28489,28315],{},[1708,28491,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28493,1710],{},[898,28495,22927],{},[1708,28497,1716],{"stretchy":1715},[898,28499,14014],{},[1708,28501,1883],{"separator":1882},[898,28503,14004],{},[1708,28505,1721],{"stretchy":1715},[1708,28507,1710],{},[2505,28509,2784],{},[902,28511,28512],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,28514,15280],{"id":15279},[724,28516,28517],{},[883,28518,28520],{"className":28519},[886],[888,28521,28522],{"xmlns":890},[892,28523,28524,28722],{},[895,28525,28526,28528,28530,28532,28534,28536,28538,28540,28542,28544,28546,28562,28564,28566,28582,28584,28586,28594,28600,28602,28604,28620,28622,28624,28640,28642,28644,28652,28658,28660,28662,28664,28680,28682,28684,28700,28702,28704,28712,28714],{},[898,28527,16117],{},[1708,28529,1716],{"stretchy":1715},[898,28531,14014],{},[1708,28533,1883],{"separator":1882},[898,28535,14004],{},[1708,28537,1883],{"separator":1882},[898,28539,28315],{},[1708,28541,1721],{"stretchy":1715},[1708,28543,1710],{},[1708,28545,1716],{"stretchy":1715},[4754,28547,28548,28550,28556],{},[898,28549,14009],{},[895,28551,28552,28554],{},[898,28553,14014],{},[898,28555,14014],{},[895,28557,28558,28560],{},[1708,28559,1761],{"mathvariant":1759},[1708,28561,1761],{"mathvariant":1759},[1708,28563,2019],{},[898,28565,28315],{},[4754,28567,28568,28570,28576],{},[898,28569,22927],{},[895,28571,28572,28574],{},[898,28573,14014],{},[898,28575,14014],{},[895,28577,28578,28580],{},[1708,28579,1761],{"mathvariant":1759},[1708,28581,1761],{"mathvariant":1759},[1708,28583,1721],{"stretchy":1715},[1708,28585,1716],{"stretchy":1715},[4754,28587,28588,28590,28592],{},[898,28589,22927],{},[898,28591,14004],{},[1708,28593,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1753,28595,28596,28598],{},[1708,28597,1721],{"stretchy":1715},[2505,28599,3132],{},[1708,28601,2019],{},[1708,28603,1716],{"stretchy":1715},[4754,28605,28606,28608,28614],{},[898,28607,14009],{},[895,28609,28610,28612],{},[898,28611,14004],{},[898,28613,14004],{},[895,28615,28616,28618],{},[1708,28617,1761],{"mathvariant":1759},[1708,28619,1761],{"mathvariant":1759},[1708,28621,2019],{},[898,28623,28315],{},[4754,28625,28626,28628,28634],{},[898,28627,22927],{},[895,28629,28630,28632],{},[898,28631,14004],{},[898,28633,14004],{},[895,28635,28636,28638],{},[1708,28637,1761],{"mathvariant":1759},[1708,28639,1761],{"mathvariant":1759},[1708,28641,1721],{"stretchy":1715},[1708,28643,1716],{"stretchy":1715},[4754,28645,28646,28648,28650],{},[898,28647,22927],{},[898,28649,14014],{},[1708,28651,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1753,28653,28654,28656],{},[1708,28655,1721],{"stretchy":1715},[2505,28657,3132],{},[1708,28659,2726],{},[2505,28661,3132],{},[1708,28663,1716],{"stretchy":1715},[4754,28665,28666,28668,28674],{},[898,28667,14009],{},[895,28669,28670,28672],{},[898,28671,14014],{},[898,28673,14004],{},[895,28675,28676,28678],{},[1708,28677,1761],{"mathvariant":1759},[1708,28679,1761],{"mathvariant":1759},[1708,28681,2019],{},[898,28683,28315],{},[4754,28685,28686,28688,28694],{},[898,28687,22927],{},[895,28689,28690,28692],{},[898,28691,14014],{},[898,28693,14004],{},[895,28695,28696,28698],{},[1708,28697,1761],{"mathvariant":1759},[1708,28699,1761],{"mathvariant":1759},[1708,28701,1721],{"stretchy":1715},[2247,28703,2659],{},[4754,28705,28706,28708,28710],{},[898,28707,22927],{},[898,28709,14014],{},[1708,28711,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,28713,2659],{},[4754,28715,28716,28718,28720],{},[898,28717,22927],{},[898,28719,14004],{},[1708,28721,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,28723,28724],{"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",[724,28726,28727,28728,28758],{},"Je-li ",[883,28729,28731],{"className":28730},[886],[888,28732,28733],{"xmlns":890},[892,28734,28735,28755],{},[895,28736,28737,28739,28741,28743,28745,28747,28753],{},[1708,28738,6940],{"stretchy":1715},[898,28740,207],{},[1708,28742,1883],{"separator":1882},[898,28744,1923],{},[1708,28746,1883],{"separator":1882},[1743,28748,28749,28751],{},[898,28750,28315],{},[2505,28752,2784],{},[1708,28754,6981],{"stretchy":1715},[902,28756,28757],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,28760,28761,28829],{},[123,28762,28763,15366,28799,28801,28802],{},[883,28764,28766],{"className":28765},[886],[888,28767,28768],{"xmlns":890},[892,28769,28770,28796],{},[895,28771,28772,28774,28776,28778,28780,28782,28784,28790,28792,28794],{},[898,28773,16117],{},[1708,28775,1716],{"stretchy":1715},[898,28777,207],{},[1708,28779,1883],{"separator":1882},[898,28781,1923],{},[1708,28783,1883],{"separator":1882},[1743,28785,28786,28788],{},[898,28787,28315],{},[2505,28789,2784],{},[1708,28791,1721],{"stretchy":1715},[1708,28793,2932],{},[2505,28795,2784],{},[902,28797,28798],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,28800,15666],{}," vázané podmínkou ",[883,28803,28805],{"className":28804},[886],[888,28806,28807],{"xmlns":890},[892,28808,28809,28827],{},[895,28810,28811,28813,28815,28817,28819,28821,28823,28825],{},[898,28812,22927],{},[1708,28814,1716],{"stretchy":1715},[898,28816,14014],{},[1708,28818,1883],{"separator":1882},[898,28820,14004],{},[1708,28822,1721],{"stretchy":1715},[1708,28824,1710],{},[2505,28826,2784],{},[902,28828,22944],{"encoding":904},[123,28830,28831,15366,28867,28801,28869],{},[883,28832,28834],{"className":28833},[886],[888,28835,28836],{"xmlns":890},[892,28837,28838,28864],{},[895,28839,28840,28842,28844,28846,28848,28850,28852,28858,28860,28862],{},[898,28841,16117],{},[1708,28843,1716],{"stretchy":1715},[898,28845,207],{},[1708,28847,1883],{"separator":1882},[898,28849,1923],{},[1708,28851,1883],{"separator":1882},[1743,28853,28854,28856],{},[898,28855,28315],{},[2505,28857,2784],{},[1708,28859,1721],{"stretchy":1715},[1708,28861,2854],{},[2505,28863,2784],{},[902,28865,28866],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,28868,15724],{},[883,28870,28872],{"className":28871},[886],[888,28873,28874],{"xmlns":890},[892,28875,28876,28894],{},[895,28877,28878,28880,28882,28884,28886,28888,28890,28892],{},[898,28879,22927],{},[1708,28881,1716],{"stretchy":1715},[898,28883,14014],{},[1708,28885,1883],{"separator":1882},[898,28887,14004],{},[1708,28889,1721],{"stretchy":1715},[1708,28891,1710],{},[2505,28893,2784],{},[902,28895,22944],{"encoding":904},[115,28897,28899],{"id":28898},"význam-multiplikátoru","Význam multiplikátoru",[724,28901,28902],{},[883,28903,28905],{"className":28904},[886],[888,28906,28907],{"xmlns":890},[892,28908,28909,28961],{},[895,28910,28911,28913,28915,28937,28939],{},[898,28912,28315],{},[1708,28914,1710],{},[2358,28916,28917,28925],{},[4754,28918,28919,28921,28923],{},[898,28920,14009],{},[898,28922,14014],{},[1708,28924,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[895,28926,28927,28929],{},[1708,28928,2726],{},[4754,28930,28931,28933,28935],{},[898,28932,22927],{},[898,28934,14014],{},[1708,28936,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,28938,1710],{},[2358,28940,28941,28949],{},[4754,28942,28943,28945,28947],{},[898,28944,14009],{},[898,28946,14004],{},[1708,28948,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[895,28950,28951,28953],{},[1708,28952,2726],{},[4754,28954,28955,28957,28959],{},[898,28956,22927],{},[898,28958,14004],{},[1708,28960,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,28962,28963],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,28965,28966,28979],{},[883,28967,28969],{"className":28968},[886],[888,28970,28971],{"xmlns":890},[892,28972,28973,28977],{},[895,28974,28975],{},[898,28976,28315],{},[902,28978,28368],{"encoding":904}," udává:",[120,28981,28982,28988],{},[123,28983,28984,28985],{},"konstantní ",[38,28986,28987],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,28989,28990,28993,28994,29007],{},[38,28991,28992],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,28995,28997],{"className":28996},[886],[888,28998,28999],{"xmlns":890},[892,29000,29001,29005],{},[895,29002,29003],{},[898,29004,14009],{},[902,29006,14009],{"encoding":904},", uvolní-li se omezení o jednotku",[115,29009,29011],{"id":29010},"alternativní-postup","Alternativní postup",[724,29013,29014,29015,29042,29043,29067,29068,29092,29093,29106,29107,2155],{},"Lze-li z ",[883,29016,29018],{"className":29017},[886],[888,29019,29020],{"xmlns":890},[892,29021,29022,29040],{},[895,29023,29024,29026,29028,29030,29032,29034,29036,29038],{},[898,29025,22927],{},[1708,29027,1716],{"stretchy":1715},[898,29029,14014],{},[1708,29031,1883],{"separator":1882},[898,29033,14004],{},[1708,29035,1721],{"stretchy":1715},[1708,29037,1710],{},[2505,29039,2784],{},[902,29041,22944],{"encoding":904}," vyjádřit ",[883,29044,29046],{"className":29045},[886],[888,29047,29048],{"xmlns":890},[892,29049,29050,29064],{},[895,29051,29052,29054,29056,29058,29060,29062],{},[898,29053,14004],{},[1708,29055,1710],{},[898,29057,14004],{},[1708,29059,1716],{"stretchy":1715},[898,29061,14014],{},[1708,29063,1721],{"stretchy":1715},[902,29065,29066],{"encoding":904},"y = y(x)"," (nebo ",[883,29069,29071],{"className":29070},[886],[888,29072,29073],{"xmlns":890},[892,29074,29075,29089],{},[895,29076,29077,29079,29081,29083,29085,29087],{},[898,29078,14014],{},[1708,29080,1710],{},[898,29082,14014],{},[1708,29084,1716],{"stretchy":1715},[898,29086,14004],{},[1708,29088,1721],{"stretchy":1715},[902,29090,29091],{"encoding":904},"x = x(y)","), dosadíme do ",[883,29094,29096],{"className":29095},[886],[888,29097,29098],{"xmlns":890},[892,29099,29100,29104],{},[895,29101,29102],{},[898,29103,14009],{},[902,29105,14009],{"encoding":904}," a převedeme na ",[38,29108,29109],{},"extrém funkce jedné proměnné",[115,29111,29113],{"id":29112},"použití-v-imek","Použití v ImeK",[198,29115,29117],{"id":29116},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,29119,29120,29121,2155],{},"Rozpočtové omezení: ",[883,29122,29124],{"className":29123},[886],[888,29125,29126],{"xmlns":890},[892,29127,29128,29168],{},[895,29129,29130,29136,29138,29146,29152,29154,29162],{},[1753,29131,29132,29134],{},[898,29133,21035],{},[1708,29135,2417],{},[1708,29137,1710],{},[4754,29139,29140,29142,29144],{},[898,29141,1747],{},[2505,29143,2507],{},[1708,29145,2417],{},[1743,29147,29148,29150],{},[898,29149,1688],{},[2505,29151,2507],{},[1708,29153,2019],{},[4754,29155,29156,29158,29160],{},[898,29157,1747],{},[2505,29159,3132],{},[1708,29161,2417],{},[1743,29163,29164,29166],{},[898,29165,1688],{},[2505,29167,3132],{},[902,29169,29170],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,29172,29173],{},[883,29174,29176],{"className":29175},[886],[888,29177,29178],{"xmlns":890},[892,29179,29180,29274],{},[895,29181,29182,29184,29186,29192,29194,29200,29202,29204,29206,29208,29210,29212,29218,29220,29226,29228,29230,29232,29234,29240,29242,29250,29256,29258,29266,29272],{},[898,29183,1658],{},[1708,29185,1716],{"stretchy":1715},[1743,29187,29188,29190],{},[898,29189,1688],{},[2505,29191,2507],{},[1708,29193,1883],{"separator":1882},[1743,29195,29196,29198],{},[898,29197,1688],{},[2505,29199,3132],{},[1708,29201,1883],{"separator":1882},[898,29203,28315],{},[1708,29205,1721],{"stretchy":1715},[1708,29207,1710],{},[898,29209,900],{},[1708,29211,1716],{"stretchy":1715},[1743,29213,29214,29216],{},[898,29215,1688],{},[2505,29217,2507],{},[1708,29219,1883],{"separator":1882},[1743,29221,29222,29224],{},[898,29223,1688],{},[2505,29225,3132],{},[1708,29227,1721],{"stretchy":1715},[1708,29229,2019],{},[898,29231,28315],{},[1708,29233,1716],{"stretchy":1715},[1753,29235,29236,29238],{},[898,29237,21035],{},[1708,29239,2417],{},[1708,29241,2726],{},[4754,29243,29244,29246,29248],{},[898,29245,1747],{},[2505,29247,2507],{},[1708,29249,2417],{},[1743,29251,29252,29254],{},[898,29253,1688],{},[2505,29255,2507],{},[1708,29257,2726],{},[4754,29259,29260,29262,29264],{},[898,29261,1747],{},[2505,29263,3132],{},[1708,29265,2417],{},[1743,29267,29268,29270],{},[898,29269,1688],{},[2505,29271,3132],{},[1708,29273,1721],{"stretchy":1715},[902,29275,29276],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,29278,29279,29280,1343,29312,1343,29344,29393,29394,5055,29448,2155],{},"Soustava: ",[883,29281,29283],{"className":29282},[886],[888,29284,29285],{"xmlns":890},[892,29286,29287,29309],{},[895,29288,29289,29297,29299,29301],{},[4754,29290,29291,29293,29295],{},[898,29292,900],{},[2505,29294,2507],{},[1708,29296,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,29298,1710],{},[898,29300,28315],{},[4754,29302,29303,29305,29307],{},[898,29304,1747],{},[2505,29306,2507],{},[1708,29308,2417],{},[902,29310,29311],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,29313,29315],{"className":29314},[886],[888,29316,29317],{"xmlns":890},[892,29318,29319,29341],{},[895,29320,29321,29329,29331,29333],{},[4754,29322,29323,29325,29327],{},[898,29324,900],{},[2505,29326,3132],{},[1708,29328,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,29330,1710],{},[898,29332,28315],{},[4754,29334,29335,29337,29339],{},[898,29336,1747],{},[2505,29338,3132],{},[1708,29340,2417],{},[902,29342,29343],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,29345,29347],{"className":29346},[886],[888,29348,29349],{"xmlns":890},[892,29350,29351,29391],{},[895,29352,29353,29359,29361,29369,29375,29377,29385],{},[1753,29354,29355,29357],{},[898,29356,21035],{},[1708,29358,2417],{},[1708,29360,1710],{},[4754,29362,29363,29365,29367],{},[898,29364,1747],{},[2505,29366,2507],{},[1708,29368,2417],{},[1743,29370,29371,29373],{},[898,29372,1688],{},[2505,29374,2507],{},[1708,29376,2019],{},[4754,29378,29379,29381,29383],{},[898,29380,1747],{},[2505,29382,3132],{},[1708,29384,2417],{},[1743,29386,29387,29389],{},[898,29388,1688],{},[2505,29390,3132],{},[902,29392,29170],{"encoding":904},". Z prvních dvou: ",[883,29395,29397],{"className":29396},[886],[888,29398,29399],{"xmlns":890},[892,29400,29401,29445],{},[895,29402,29403,29423,29425],{},[3194,29404,29405],{"scriptlevel":2784,"displaystyle":1715},[2358,29406,29407,29415],{},[4754,29408,29409,29411,29413],{},[898,29410,900],{},[2505,29412,2507],{},[1708,29414,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,29416,29417,29419,29421],{},[898,29418,900],{},[2505,29420,3132],{},[1708,29422,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,29424,1710],{},[3194,29426,29427],{"scriptlevel":2784,"displaystyle":1715},[2358,29428,29429,29437],{},[4754,29430,29431,29433,29435],{},[898,29432,1747],{},[2505,29434,2507],{},[1708,29436,2417],{},[4754,29438,29439,29441,29443],{},[898,29440,1747],{},[2505,29442,3132],{},[1708,29444,2417],{},[902,29446,29447],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",[883,29449,29451],{"className":29450},[886],[888,29452,29453],{"xmlns":890},[892,29454,29455,29487],{},[895,29456,29457,29459,29461,29463,29465,29467],{},[898,29458,1741],{},[898,29460,1975],{},[898,29462,3455],{},[898,29464,1981],{},[1708,29466,1710],{},[3194,29468,29469],{"scriptlevel":2784,"displaystyle":1715},[2358,29470,29471,29479],{},[4754,29472,29473,29475,29477],{},[898,29474,1747],{},[2505,29476,2507],{},[1708,29478,2417],{},[4754,29480,29481,29483,29485],{},[898,29482,1747],{},[2505,29484,3132],{},[1708,29486,2417],{},[902,29488,29489],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,29491,29493],{"id":29492},"minimalizace-výdajů","Minimalizace výdajů",[724,29495,29496,29497,2155],{},"Podmínka dané užitečnosti ",[883,29498,29500],{"className":29499},[886],[888,29501,29502],{"xmlns":890},[892,29503,29504,29534],{},[895,29505,29506,29512,29514,29516,29518,29524,29526,29532],{},[1753,29507,29508,29510],{},[898,29509,900],{},[1708,29511,2417],{},[1708,29513,1710],{},[898,29515,900],{},[1708,29517,1716],{"stretchy":1715},[1743,29519,29520,29522],{},[898,29521,1688],{},[2505,29523,2507],{},[1708,29525,1883],{"separator":1882},[1743,29527,29528,29530],{},[898,29529,1688],{},[2505,29531,3132],{},[1708,29533,1721],{"stretchy":1715},[902,29535,29536],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,29538,29539],{},[883,29540,29542],{"className":29541},[886],[888,29543,29544],{"xmlns":890},[892,29545,29546,29640],{},[895,29547,29548,29550,29552,29558,29560,29566,29568,29570,29572,29574,29582,29588,29590,29598,29604,29606,29608,29610,29616,29618,29620,29622,29628,29630,29636,29638],{},[898,29549,1658],{},[1708,29551,1716],{"stretchy":1715},[1743,29553,29554,29556],{},[898,29555,1688],{},[2505,29557,2507],{},[1708,29559,1883],{"separator":1882},[1743,29561,29562,29564],{},[898,29563,1688],{},[2505,29565,3132],{},[1708,29567,1883],{"separator":1882},[898,29569,28315],{},[1708,29571,1721],{"stretchy":1715},[1708,29573,1710],{},[4754,29575,29576,29578,29580],{},[898,29577,1747],{},[2505,29579,2507],{},[1708,29581,2417],{},[1743,29583,29584,29586],{},[898,29585,1688],{},[2505,29587,2507],{},[1708,29589,2019],{},[4754,29591,29592,29594,29596],{},[898,29593,1747],{},[2505,29595,3132],{},[1708,29597,2417],{},[1743,29599,29600,29602],{},[898,29601,1688],{},[2505,29603,3132],{},[1708,29605,2019],{},[898,29607,28315],{},[1708,29609,1716],{"stretchy":1715},[1753,29611,29612,29614],{},[898,29613,900],{},[1708,29615,2417],{},[1708,29617,2726],{},[898,29619,900],{},[1708,29621,1716],{"stretchy":1715},[1743,29623,29624,29626],{},[898,29625,1688],{},[2505,29627,2507],{},[1708,29629,1883],{"separator":1882},[1743,29631,29632,29634],{},[898,29633,1688],{},[2505,29635,3132],{},[1708,29637,1721],{"stretchy":1715},[1708,29639,1721],{"stretchy":1715},[902,29641,29642],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,29644,29645,29646,2155],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,29647,29649],{"className":29648},[886],[888,29650,29651],{"xmlns":890},[892,29652,29653,29692],{},[895,29654,29655,29662,29664,29670,29672,29678,29680,29686,29688,29690],{},[1743,29656,29657,29659],{},[898,29658,1688],{},[898,29660,29661],{},"i",[1708,29663,1710],{},[1743,29665,29666,29668],{},[898,29667,16117],{},[898,29669,29661],{},[1708,29671,1716],{"stretchy":1715},[1743,29673,29674,29676],{},[898,29675,1747],{},[2505,29677,2507],{},[1708,29679,1883],{"separator":1882},[1743,29681,29682,29684],{},[898,29683,1747],{},[2505,29685,3132],{},[1708,29687,1883],{"separator":1882},[898,29689,900],{},[1708,29691,1721],{"stretchy":1715},[902,29693,29694],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,29696,13763],{"id":13762},[120,29698,29699,29706,29713,29722],{},[123,29700,29701,1729,29703],{},[38,29702,13871],{},[207,29704,784],{"className":29705,"dataFsResolvedFilePath":782,"href":783},[210],[123,29707,29708,1729,29710],{},[38,29709,15753],{},[207,29711,23828],{"className":29712,"dataFsResolvedFilePath":800,"href":801},[210],[123,29714,29715,1729,29718,29721],{},[38,29716,29717],{},"Aplikace v kurzu:",[207,29719,880],{"className":29720,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,29723,29724,1729,29726,1343,29729,29732],{},[38,29725,15761],{},[207,29727,936],{"className":29728,"dataFsResolvedFilePath":934,"href":935},[210],[207,29730,1400],{"className":29731,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":29734},[29735,29736,29737,29738,29739,29740,29744],{"id":28283,"depth":642,"text":28284},{"id":15205,"depth":642,"text":15206},{"id":15279,"depth":642,"text":15280},{"id":28898,"depth":642,"text":28899},{"id":29010,"depth":642,"text":29011},{"id":29112,"depth":642,"text":29113,"children":29741},[29742,29743],{"id":29116,"depth":649,"text":29117},{"id":29492,"depth":649,"text":29493},{"id":13762,"depth":642,"text":13763},[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":28153,"description":29746},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,29753,29754],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":29757,"title":936,"body":29758,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":39605,"navigation":664,"path":39606,"seo":39607,"sources":39608,"stem":39609,"tags":39610,"type":13951,"updated":677,"__hash__":39614},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":29759,"toc":39567},[29760,29763,29765,29888,30022,30026,30029,30142,30146,30174,30221,30224,30290,30335,30338,30364,30395,30399,30403,30447,30491,30552,30607,30610,30614,30617,30664,30758,30864,30870,30947,30976,31115,31119,31147,31196,31343,31433,31437,31463,31501,31528,31566,31628,31703,31781,31838,31904,31948,31952,32009,32058,32103,32316,32436,32442,32446,32469,32473,32480,32484,32515,32550,32554,32604,32689,32731,32752,32814,32874,32878,32949,33017,33089,33204,33252,33256,33259,33300,33339,33362,33475,33639,33647,33674,33704,33707,33784,33937,34021,34360,34364,34488,34624,34760,34812,34815,35065,35146,35150,35153,35211,35243,35246,35295,35298,35369,35565,35569,35717,35947,35985,36038,36083,36086,36142,36191,36395,36484,36488,36504,36511,36680,36684,36755,36836,36917,36996,37141,37229,37233,37416,37547,37592,37689,37693,38431,38433,39484,39486],[12,29761,936],{"id":29762},"národní-důchod",[115,29764,23894],{"id":23893},[724,29766,29767,29768,1729,29772,29775,29776,1729,29779,29792,29793,29796,29797,29800,29801,29804,29805,29807,29808,1729,29810,29827,29828,29845,29846,29849,29850,2511],{},"Kapitola 7 ",[207,29769,29771],{"className":29770,"dataFsResolvedFilePath":13892,"href":13893},[210],"Matematické ekonomie",[38,29773,29774],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,29777,29778],{},"národním důchodem",[883,29780,29782],{"className":29781},[886],[888,29783,29784],{"xmlns":890},[892,29785,29786,29790],{},[895,29787,29788],{},[898,29789,21035],{},[902,29791,21035],{"encoding":904},". Budují se postupně bohatší modely — ",[38,29794,29795],{},"C-I"," (jen spotřeba a investice) → ",[38,29798,29799],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,29802,29803],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,29806,23899],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,29809,25767],{},[883,29811,29813],{"className":29812},[886],[888,29814,29815],{"xmlns":890},[892,29816,29817,29825],{},[895,29818,29819],{},[1753,29820,29821,29823],{},[898,29822,21035],{},[898,29824,16183],{},[902,29826,25785],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,29829,29831],{"className":29830},[886],[888,29832,29833],{"xmlns":890},[892,29834,29835,29843],{},[895,29836,29837],{},[1753,29838,29839,29841],{},[898,29840,21035],{},[898,29842,16183],{},[902,29844,25785],{"encoding":904}," na exogenní veličiny popisují ",[38,29847,29848],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,29851,29853],{"className":29852},[886],[888,29854,29855],{"xmlns":890},[892,29856,29857,29885],{},[895,29858,29859,29861,29863,29865,29867,29869,29871,29873,29875,29877,29879,29881,29883],{},[2505,29860,2507],{},[898,29862,1799],{"mathvariant":1759},[1708,29864,1716],{"stretchy":1715},[2505,29866,2507],{},[1708,29868,2726],{},[898,29870,207],{},[1708,29872,1721],{"stretchy":1715},[1708,29874,1710],{},[2505,29876,2507],{},[898,29878,1799],{"mathvariant":1759},[898,29880,1741],{},[898,29882,1747],{},[898,29884,1981],{},[902,29886,29887],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1636,29889,29890],{},[724,29891,29892,2519,29894,29897,29898,29916,29917,29947,29948,29995,29996,29998,29999,30021],{},[883,29893,2518],{},[38,29895,29896],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,29899,29901],{"className":29900},[886],[888,29902,29903],{"xmlns":890},[892,29904,29905,29913],{},[895,29906,29907,29909,29911],{},[898,29908,1741],{},[898,29910,1747],{},[898,29912,3455],{},[902,29914,29915],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,29918,29920],{"className":29919},[886],[888,29921,29922],{"xmlns":890},[892,29923,29924,29944],{},[895,29925,29926,29928,29930,29932,29934,29936,29938,29940,29942],{},[898,29927,1741],{},[898,29929,1747],{},[898,29931,1981],{},[1708,29933,1710],{},[2505,29935,2507],{},[1708,29937,2726],{},[898,29939,1741],{},[898,29941,1747],{},[898,29943,3455],{},[902,29945,29946],{"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 ",[883,29949,29951],{"className":29950},[886],[888,29952,29953],{"xmlns":890},[892,29954,29955,29992],{},[895,29956,29957,29959,29961,29963,29965,29971,29973,29976,29978,29980,29982,29984,29986,29988,29990],{},[2505,29958,2507],{},[1708,29960,2019],{},[898,29962,207],{},[1708,29964,2019],{},[1753,29966,29967,29969],{},[898,29968,207],{},[2505,29970,3132],{},[1708,29972,2019],{},[1708,29974,29975],{},"⋯",[1708,29977,1710],{},[2505,29979,2507],{},[898,29981,1799],{"mathvariant":1759},[1708,29983,1716],{"stretchy":1715},[2505,29985,2507],{},[1708,29987,2726],{},[898,29989,207],{},[1708,29991,1721],{"stretchy":1715},[902,29993,29994],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,29997,23899],{}," 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 ",[883,30000,30002],{"className":30001},[886],[888,30003,30004],{"xmlns":890},[892,30005,30006,30018],{},[895,30007,30008,30010,30012,30014,30016],{},[1708,30009,1716],{"stretchy":1715},[898,30011,21035],{},[1708,30013,1883],{"separator":1882},[898,30015,5498],{},[1708,30017,1721],{"stretchy":1715},[902,30019,30020],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,30023,30025],{"id":30024},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,30027,30028],{},"Po prostudování kapitoly by čtenář měl umět:",[120,30030,30031,30034,30037,30040,30043,30046,30049,30139],{},[123,30032,30033],{},"popsat zjednodušený model národní ekonomiky,",[123,30035,30036],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,30038,30039],{},"popsat lineární model spotřeby a úspor,",[123,30041,30042],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,30044,30045],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,30047,30048],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,30050,30051,30052,1343,30069,1343,30091,1771,30116,30138],{},"popsat modely ",[883,30053,30055],{"className":30054},[886],[888,30056,30057],{"xmlns":890},[892,30058,30059,30067],{},[895,30060,30061,30063,30065],{},[898,30062,3455],{},[2247,30064,24176],{},[898,30066,24070],{},[902,30068,24181],{"encoding":904},[883,30070,30072],{"className":30071},[886],[888,30073,30074],{"xmlns":890},[892,30075,30076,30088],{},[895,30077,30078,30080,30082,30084,30086],{},[898,30079,3455],{},[2247,30081,24176],{},[898,30083,24070],{},[2247,30085,24176],{},[898,30087,23999],{},[902,30089,30090],{"encoding":904},"C\\text{-}I\\text{-}G",[883,30092,30094],{"className":30093},[886],[888,30095,30096],{"xmlns":890},[892,30097,30098,30114],{},[895,30099,30100,30102,30104,30106,30108,30110,30112],{},[898,30101,3455],{},[2247,30103,24176],{},[898,30105,24070],{},[2247,30107,24176],{},[898,30109,23999],{},[2247,30111,24176],{},[898,30113,24206],{},[902,30115,24209],{"encoding":904},[883,30117,30119],{"className":30118},[886],[888,30120,30121],{"xmlns":890},[892,30122,30123,30135],{},[895,30124,30125,30127,30129,30131,30133],{},[898,30126,24070],{},[898,30128,1981],{},[2247,30130,24176],{},[898,30132,1658],{},[898,30134,1741],{},[902,30136,30137],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,30140,30141],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,30143,30145],{"id":30144},"gnp-a-národní-důchod","GNP a národní důchod",[724,30147,30148,1729,30151,1695,30170,30173],{},[38,30149,30150],{},"Hrubý národní produkt",[883,30152,30154],{"className":30153},[886],[888,30155,30156],{"xmlns":890},[892,30157,30158,30167],{},[895,30159,30160,30162,30165],{},[898,30161,23999],{},[898,30163,30164],{},"N",[898,30166,1747],{},[902,30168,30169],{"encoding":904},"GNP",[614,30171,30172],{},"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:",[724,30175,30176],{},[883,30177,30179],{"className":30178},[886],[888,30180,30181],{"xmlns":890},[892,30182,30183,30218],{},[895,30184,30185,30187,30189,30191,30193,30195,30197,30199,30201,30203,30205,30207,30209,30211,30213,30216],{},[898,30186,23999],{},[898,30188,30164],{},[898,30190,1747],{},[1708,30192,1710],{},[898,30194,3455],{},[1708,30196,2019],{},[898,30198,24070],{},[1708,30200,2019],{},[898,30202,23999],{},[1708,30204,2019],{},[898,30206,24206],{},[1708,30208,1883],{"separator":1882},[3213,30210],{"width":3215},[1708,30212,1716],{"stretchy":1715},[2505,30214,30215],{},"7.1",[1708,30217,1721],{"stretchy":1715},[902,30219,30220],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,30222,30223],{},"kde",[120,30225,30226,30242,30258,30274],{},[123,30227,30228,30241],{},[883,30229,30231],{"className":30230},[886],[888,30232,30233],{"xmlns":890},[892,30234,30235,30239],{},[895,30236,30237],{},[898,30238,3455],{},[902,30240,3455],{"encoding":904}," — výdaje domácností na spotřebu,",[123,30243,30244,30257],{},[883,30245,30247],{"className":30246},[886],[888,30248,30249],{"xmlns":890},[892,30250,30251,30255],{},[895,30252,30253],{},[898,30254,24070],{},[902,30256,24070],{"encoding":904}," — hrubé domácí investice,",[123,30259,30260,30273],{},[883,30261,30263],{"className":30262},[886],[888,30264,30265],{"xmlns":890},[892,30266,30267,30271],{},[895,30268,30269],{},[898,30270,23999],{},[902,30272,23999],{"encoding":904}," — vládní výdaje,",[123,30275,30276,30289],{},[883,30277,30279],{"className":30278},[886],[888,30280,30281],{"xmlns":890},[892,30282,30283,30287],{},[895,30284,30285],{},[898,30286,24206],{},[902,30288,24206],{"encoding":904}," — čistý export.",[724,30291,30292,30293,30310,30311,30314,30315,1729,30318,1695,30331,30334],{},"K měření ",[883,30294,30296],{"className":30295},[886],[888,30297,30298],{"xmlns":890},[892,30299,30300,30308],{},[895,30301,30302,30304,30306],{},[898,30303,23999],{},[898,30305,30164],{},[898,30307,1747],{},[902,30309,30169],{"encoding":904}," se užívá ",[38,30312,30313],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,30316,30317],{},"národní důchod",[883,30319,30321],{"className":30320},[886],[888,30322,30323],{"xmlns":890},[892,30324,30325,30329],{},[895,30326,30327],{},[898,30328,21035],{},[902,30330,21035],{"encoding":904},[614,30332,30333],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,30336,30337],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,30339,30340],{},[883,30341,30343],{"className":30342},[886],[888,30344,30345],{"xmlns":890},[892,30346,30347,30361],{},[895,30348,30349,30351,30353,30355,30357,30359],{},[898,30350,23999],{},[898,30352,30164],{},[898,30354,1747],{},[1708,30356,2638],{},[898,30358,21035],{},[1708,30360,1883],{"separator":1882},[902,30362,30363],{"encoding":904},"GNP \\approx Y,",[724,30365,30366,30367,1695,30370,30373,30374,30387,30388,30391,30392,2155],{},"a užívá se společného názvu ",[38,30368,30369],{},"důchod",[614,30371,30372],{},"income",") s označením ",[883,30375,30377],{"className":30376},[886],[888,30378,30379],{"xmlns":890},[892,30380,30381,30385],{},[895,30382,30383],{},[898,30384,21035],{},[902,30386,21035],{"encoding":904},". Domácnosti důchod použijí ke ",[38,30389,30390],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,30393,30394],{},"úspor",[115,30396,30398],{"id":30397},"spotřeba-a-úspory","Spotřeba a úspory",[198,30400,30402],{"id":30401},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,30404,30405,30406,30419,30420,30433,30434,2788],{},"Jak spotřeba ",[883,30407,30409],{"className":30408},[886],[888,30410,30411],{"xmlns":890},[892,30412,30413,30417],{},[895,30414,30415],{},[898,30416,3455],{},[902,30418,3455],{"encoding":904},", tak úspory ",[883,30421,30423],{"className":30422},[886],[888,30424,30425],{"xmlns":890},[892,30426,30427,30431],{},[895,30428,30429],{},[898,30430,1981],{},[902,30432,1981],{"encoding":904}," závisejí na důchodu ",[883,30435,30437],{"className":30436},[886],[888,30438,30439],{"xmlns":890},[892,30440,30441,30445],{},[895,30442,30443],{},[898,30444,21035],{},[902,30446,21035],{"encoding":904},[724,30448,30449],{},[883,30450,30452],{"className":30451},[886],[888,30453,30454],{"xmlns":890},[892,30455,30456,30488],{},[895,30457,30458,30460,30462,30464,30466,30468,30470,30472,30474,30476,30478,30480,30482,30484,30486],{},[898,30459,3455],{},[1708,30461,1710],{},[898,30463,3455],{},[1708,30465,1716],{"stretchy":1715},[898,30467,21035],{},[1708,30469,1721],{"stretchy":1715},[1708,30471,1883],{"separator":1882},[3213,30473],{"width":3215},[898,30475,1981],{},[1708,30477,1710],{},[898,30479,1981],{},[1708,30481,1716],{"stretchy":1715},[898,30483,21035],{},[1708,30485,1721],{"stretchy":1715},[898,30487,2155],{"mathvariant":1759},[902,30489,30490],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,30492,30493,3033,30512,1695,30515,13826,30518,3033,30538,1695,30541,30544,30545,1771,30548,30551],{},[883,30494,30496],{"className":30495},[886],[888,30497,30498],{"xmlns":890},[892,30499,30500,30510],{},[895,30501,30502,30504,30506,30508],{},[898,30503,3455],{},[1708,30505,1716],{"stretchy":1715},[898,30507,21035],{},[1708,30509,1721],{"stretchy":1715},[902,30511,26098],{"encoding":904},[38,30513,30514],{},"funkce spotřeby",[614,30516,30517],{},"consumption function",[883,30519,30521],{"className":30520},[886],[888,30522,30523],{"xmlns":890},[892,30524,30525,30535],{},[895,30526,30527,30529,30531,30533],{},[898,30528,1981],{},[1708,30530,1716],{"stretchy":1715},[898,30532,21035],{},[1708,30534,1721],{"stretchy":1715},[902,30536,30537],{"encoding":904},"S(Y)",[38,30539,30540],{},"funkce úspor",[614,30542,30543],{},"savings function","); jejich grafy se nazývají ",[38,30546,30547],{},"křivka spotřeby",[38,30549,30550],{},"křivka úspor",". Platí základní identita",[724,30553,30554],{},[883,30555,30557],{"className":30556},[886],[888,30558,30559],{"xmlns":890},[892,30560,30561,30604],{},[895,30562,30563,30565,30567,30569,30571,30573,30575,30577,30579,30581,30583,30585,30587,30589,30591,30593,30595,30597,30599,30602],{},[898,30564,21035],{},[1708,30566,1710],{},[898,30568,3455],{},[1708,30570,2019],{},[898,30572,1981],{},[1708,30574,1710],{},[898,30576,3455],{},[1708,30578,1716],{"stretchy":1715},[898,30580,21035],{},[1708,30582,1721],{"stretchy":1715},[1708,30584,2019],{},[898,30586,1981],{},[1708,30588,1716],{"stretchy":1715},[898,30590,21035],{},[1708,30592,1721],{"stretchy":1715},[898,30594,2155],{"mathvariant":1759},[3213,30596],{"width":3215},[1708,30598,1716],{"stretchy":1715},[2505,30600,30601],{},"7.2",[1708,30603,1721],{"stretchy":1715},[902,30605,30606],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,30608,30609],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,30611,30613],{"id":30612},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,30615,30616],{},"Nejjednodušší model předpokládá lineární tvar",[724,30618,30619],{},[883,30620,30622],{"className":30621},[886],[888,30623,30624],{"xmlns":890},[892,30625,30626,30661],{},[895,30627,30628,30630,30632,30634,30636,30638,30640,30642,30644,30646,30648,30650,30652,30654,30656,30659],{},[898,30629,3455],{},[1708,30631,1710],{},[898,30633,3455],{},[1708,30635,1716],{"stretchy":1715},[898,30637,21035],{},[1708,30639,1721],{"stretchy":1715},[1708,30641,1710],{},[898,30643,207],{},[898,30645,21035],{},[1708,30647,2019],{},[898,30649,1923],{},[1708,30651,1883],{"separator":1882},[3213,30653],{"width":3215},[1708,30655,1716],{"stretchy":1715},[2505,30657,30658],{},"7.3",[1708,30660,1721],{"stretchy":1715},[902,30662,30663],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,30665,5411,30666,1771,30683,30704,30705,30744,30745,2155],{},[883,30667,30669],{"className":30668},[886],[888,30670,30671],{"xmlns":890},[892,30672,30673,30681],{},[895,30674,30675,30677,30679],{},[898,30676,1923],{},[1708,30678,2854],{},[2505,30680,2784],{},[902,30682,3172],{"encoding":904},[883,30684,30686],{"className":30685},[886],[888,30687,30688],{"xmlns":890},[892,30689,30690,30702],{},[895,30691,30692,30694,30696,30698,30700],{},[2505,30693,2784],{},[1708,30695,2932],{},[898,30697,207],{},[1708,30699,2932],{},[2505,30701,2507],{},[902,30703,7040],{"encoding":904},". Směrnice ",[883,30706,30708],{"className":30707},[886],[888,30709,30710],{"xmlns":890},[892,30711,30712,30741],{},[895,30713,30714,30716,30718,30724,30726,30729,30731,30733,30735,30737,30739],{},[898,30715,207],{},[1708,30717,1710],{},[895,30719,30720,30722],{},[898,30721,9105],{"mathvariant":1759},[898,30723,22927],{"mathvariant":1759},[2247,30725,2659],{},[898,30727,30728],{},"α",[1708,30730,1710],{},[898,30732,2633],{"mathvariant":1759},[898,30734,3455],{},[898,30736,1799],{"mathvariant":1759},[898,30738,2633],{"mathvariant":1759},[898,30740,21035],{},[902,30742,30743],{"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 ",[883,30746,30748],{"className":30747},[886],[888,30749,30750],{"xmlns":890},[892,30751,30752,30756],{},[895,30753,30754],{},[898,30755,21035],{},[902,30757,21035],{"encoding":904},[724,30759,30760],{},[614,30761,30762,30763,30787,30788,30826,30827,30843,30844,2155],{},"Obrázek 7.1 — Přímka spotřeby ",[883,30764,30766],{"className":30765},[886],[888,30767,30768],{"xmlns":890},[892,30769,30770,30784],{},[895,30771,30772,30774,30776,30778,30780,30782],{},[898,30773,3455],{},[1708,30775,1710],{},[898,30777,207],{},[898,30779,21035],{},[1708,30781,2019],{},[898,30783,1923],{},[902,30785,30786],{"encoding":904},"C = aY + b"," se směrnicí ",[883,30789,30791],{"className":30790},[886],[888,30792,30793],{"xmlns":890},[892,30794,30795,30823],{},[895,30796,30797,30799,30801,30807,30809,30811,30813,30815,30817,30819,30821],{},[898,30798,207],{},[1708,30800,1710],{},[895,30802,30803,30805],{},[898,30804,9105],{"mathvariant":1759},[898,30806,22927],{"mathvariant":1759},[2247,30808,2659],{},[898,30810,30728],{},[1708,30812,1710],{},[898,30814,2633],{"mathvariant":1759},[898,30816,3455],{},[898,30818,1799],{"mathvariant":1759},[898,30820,2633],{"mathvariant":1759},[898,30822,21035],{},[902,30824,30825],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,30828,30830],{"className":30829},[886],[888,30831,30832],{"xmlns":890},[892,30833,30834,30840],{},[895,30835,30836,30838],{},[898,30837,2633],{"mathvariant":1759},[898,30839,3455],{},[902,30841,30842],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,30845,30847],{"className":30846},[886],[888,30848,30849],{"xmlns":890},[892,30850,30851,30861],{},[895,30852,30853,30855,30857,30859],{},[898,30854,2633],{"mathvariant":1759},[898,30856,21035],{},[1708,30858,1710],{},[2505,30860,2507],{},[902,30862,30863],{"encoding":904},"\\Delta Y = 1",[724,30865,30866,30867,2788],{},"Dosazením do (7.2) plyne ",[38,30868,30869],{},"lineární model úspor",[724,30871,30872],{},[883,30873,30875],{"className":30874},[886],[888,30876,30877],{"xmlns":890},[892,30878,30879,30944],{},[895,30880,30881,30883,30885,30887,30889,30891,30893,30895,30897,30899,30901,30903,30905,30907,30909,30911,30913,30915,30917,30919,30921,30923,30925,30927,30929,30931,30933,30935,30937,30939,30942],{},[898,30882,1981],{},[1708,30884,1710],{},[898,30886,21035],{},[1708,30888,2726],{},[898,30890,3455],{},[1708,30892,1716],{"stretchy":1715},[898,30894,21035],{},[1708,30896,1721],{"stretchy":1715},[1708,30898,1710],{},[898,30900,21035],{},[1708,30902,2726],{},[1708,30904,1716],{"stretchy":1715},[898,30906,207],{},[898,30908,21035],{},[1708,30910,2019],{},[898,30912,1923],{},[1708,30914,1721],{"stretchy":1715},[1708,30916,1710],{},[1708,30918,1716],{"stretchy":1715},[2505,30920,2507],{},[1708,30922,2726],{},[898,30924,207],{},[1708,30926,1721],{"stretchy":1715},[898,30928,21035],{},[1708,30930,2726],{},[898,30932,1923],{},[898,30934,2155],{"mathvariant":1759},[3213,30936],{"width":3215},[1708,30938,1716],{"stretchy":1715},[2505,30940,30941],{},"7.4",[1708,30943,1721],{"stretchy":1715},[902,30945,30946],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,30948,30949,30950,2511],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,30951,30953],{"className":30952},[886],[888,30954,30955],{"xmlns":890},[892,30956,30957,30973],{},[895,30958,30959,30961,30963,30965,30967,30969,30971],{},[2505,30960,2784],{},[1708,30962,2932],{},[2505,30964,2507],{},[1708,30966,2726],{},[898,30968,207],{},[1708,30970,2932],{},[2505,30972,2507],{},[902,30974,30975],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,30977,30978],{},[614,30979,30980,30981,1771,31004,31036,31037,3405,31050,31080,31081,3405,31099,2155],{},"Obrázek 7.2 — Přímky ",[883,30982,30984],{"className":30983},[886],[888,30985,30986],{"xmlns":890},[892,30987,30988,31002],{},[895,30989,30990,30992,30994,30996,30998,31000],{},[898,30991,3455],{},[1708,30993,1710],{},[898,30995,207],{},[898,30997,21035],{},[1708,30999,2019],{},[898,31001,1923],{},[902,31003,30786],{"encoding":904},[883,31005,31007],{"className":31006},[886],[888,31008,31009],{"xmlns":890},[892,31010,31011,31033],{},[895,31012,31013,31015,31017,31019,31021,31023,31025,31027,31029,31031],{},[898,31014,1981],{},[1708,31016,1710],{},[1708,31018,1716],{"stretchy":1715},[2505,31020,2507],{},[1708,31022,2726],{},[898,31024,207],{},[1708,31026,1721],{"stretchy":1715},[898,31028,21035],{},[1708,31030,2726],{},[898,31032,1923],{},[902,31034,31035],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,31038,31040],{"className":31039},[886],[888,31041,31042],{"xmlns":890},[892,31043,31044,31048],{},[895,31045,31046],{},[898,31047,21035],{},[902,31049,21035],{"encoding":904},[883,31051,31053],{"className":31052},[886],[888,31054,31055],{"xmlns":890},[892,31056,31057,31077],{},[895,31058,31059,31061,31063,31065,31067,31069,31071,31073,31075],{},[898,31060,21035],{},[1708,31062,1710],{},[898,31064,1923],{},[898,31066,1799],{"mathvariant":1759},[1708,31068,1716],{"stretchy":1715},[2505,31070,2507],{},[1708,31072,2726],{},[898,31074,207],{},[1708,31076,1721],{"stretchy":1715},[902,31078,31079],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,31082,31084],{"className":31083},[886],[888,31085,31086],{"xmlns":890},[892,31087,31088,31096],{},[895,31089,31090,31092,31094],{},[898,31091,3455],{},[1708,31093,1883],{"separator":1882},[898,31095,1981],{},[902,31097,31098],{"encoding":904},"C, S",[883,31100,31102],{"className":31101},[886],[888,31103,31104],{"xmlns":890},[892,31105,31106,31112],{},[895,31107,31108,31110],{},[1708,31109,2726],{},[898,31111,1923],{},[902,31113,31114],{"encoding":904},"-b",[198,31116,31118],{"id":31117},"příklad-71","Příklad 7.1",[724,31120,31121,31122,31146],{},"Pro spotřebu ",[883,31123,31125],{"className":31124},[886],[888,31126,31127],{"xmlns":890},[892,31128,31129,31143],{},[895,31130,31131,31133,31135,31137,31139,31141],{},[898,31132,3455],{},[1708,31134,1710],{},[2505,31136,4770],{},[898,31138,21035],{},[1708,31140,2019],{},[2505,31142,4003],{},[902,31144,31145],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,31148,31149],{},[883,31150,31152],{"className":31151},[886],[888,31153,31154],{"xmlns":890},[892,31155,31156,31193],{},[895,31157,31158,31160,31162,31164,31166,31168,31170,31172,31174,31176,31178,31180,31182,31184,31186,31188,31190],{},[898,31159,1981],{},[1708,31161,1710],{},[898,31163,21035],{},[1708,31165,2726],{},[898,31167,3455],{},[1708,31169,1710],{},[898,31171,21035],{},[1708,31173,2726],{},[2505,31175,4770],{},[898,31177,21035],{},[1708,31179,2726],{},[2505,31181,4003],{},[1708,31183,1710],{},[2505,31185,4097],{},[898,31187,21035],{},[1708,31189,2726],{},[2505,31191,31192],{},"10.",[902,31194,31195],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,31197,31198],{},[614,31199,31200,31201,1771,31224,31248,31249,3033,31262,31286,31287,3033,31304,31320,31321,2155],{},"Obrázek 7.3 — Přímky ",[883,31202,31204],{"className":31203},[886],[888,31205,31206],{"xmlns":890},[892,31207,31208,31222],{},[895,31209,31210,31212,31214,31216,31218,31220],{},[898,31211,3455],{},[1708,31213,1710],{},[2505,31215,4770],{},[898,31217,21035],{},[1708,31219,2019],{},[2505,31221,4003],{},[902,31223,31145],{"encoding":904},[883,31225,31227],{"className":31226},[886],[888,31228,31229],{"xmlns":890},[892,31230,31231,31245],{},[895,31232,31233,31235,31237,31239,31241,31243],{},[898,31234,1981],{},[1708,31236,1710],{},[2505,31238,4097],{},[898,31240,21035],{},[1708,31242,2726],{},[2505,31244,4003],{},[902,31246,31247],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,31250,31252],{"className":31251},[886],[888,31253,31254],{"xmlns":890},[892,31255,31256,31260],{},[895,31257,31258],{},[898,31259,21035],{},[902,31261,21035],{"encoding":904},[883,31263,31265],{"className":31264},[886],[888,31266,31267],{"xmlns":890},[892,31268,31269,31283],{},[895,31270,31271,31273,31276],{},[1708,31272,2638],{},[2505,31274,31275],{},"16,",[20297,31277,31278,31280],{"accent":1882},[2505,31279,3947],{},[1708,31281,31282],{},"ˉ",[902,31284,31285],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,31288,31290],{"className":31289},[886],[888,31291,31292],{"xmlns":890},[892,31293,31294,31302],{},[895,31295,31296,31298,31300],{},[898,31297,3455],{},[1708,31299,1883],{"separator":1882},[898,31301,1981],{},[902,31303,31098],{"encoding":904},[883,31305,31307],{"className":31306},[886],[888,31308,31309],{"xmlns":890},[892,31310,31311,31317],{},[895,31312,31313,31315],{},[1708,31314,2726],{},[2505,31316,4003],{},[902,31318,31319],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,31322,31324],{"className":31323},[886],[888,31325,31326],{"xmlns":890},[892,31327,31328,31340],{},[895,31329,31330,31332,31334,31336,31338],{},[1708,31331,1716],{"stretchy":1715},[2505,31333,2784],{},[1708,31335,1883],{"separator":1882},[2505,31337,4003],{},[1708,31339,1721],{"stretchy":1715},[902,31341,31342],{"encoding":904},"(0, 10)",[724,31344,31345,31346,3033,31364,31394,31395,1695,31398,31401,31402,3033,31426,1695,31429,31432],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,31347,31349],{"className":31348},[886],[888,31350,31351],{"xmlns":890},[892,31352,31353,31361],{},[895,31354,31355,31357,31359],{},[898,31356,21035],{},[1708,31358,1710],{},[2505,31360,2784],{},[902,31362,31363],{"encoding":904},"Y = 0",[883,31365,31367],{"className":31366},[886],[888,31368,31369],{"xmlns":890},[892,31370,31371,31391],{},[895,31372,31373,31375,31377,31379,31381,31383,31385,31387,31389],{},[898,31374,1981],{},[1708,31376,1716],{"stretchy":1715},[2505,31378,2784],{},[1708,31380,1721],{"stretchy":1715},[1708,31382,1710],{},[1708,31384,2726],{},[898,31386,1923],{},[1708,31388,2932],{},[2505,31390,2784],{},[902,31392,31393],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,31396,31397],{},"autonomních úsporách",[614,31399,31400],{},"autonomous savings","). Analogicky ",[883,31403,31405],{"className":31404},[886],[888,31406,31407],{"xmlns":890},[892,31408,31409,31423],{},[895,31410,31411,31413,31415,31417,31419,31421],{},[898,31412,3455],{},[1708,31414,1716],{"stretchy":1715},[2505,31416,2784],{},[1708,31418,1721],{"stretchy":1715},[1708,31420,1710],{},[898,31422,1923],{},[902,31424,31425],{"encoding":904},"C(0) = b",[38,31427,31428],{},"autonomní spotřeba",[614,31430,31431],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,31434,31436],{"id":31435},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,31438,31439,1729,31442,1695,31459,31462],{},[38,31440,31441],{},"Mezní sklon ke spotřebě",[883,31443,31445],{"className":31444},[886],[888,31446,31447],{"xmlns":890},[892,31448,31449,31457],{},[895,31450,31451,31453,31455],{},[898,31452,1741],{},[898,31454,1747],{},[898,31456,3455],{},[902,31458,29915],{"encoding":904},[614,31460,31461],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,31464,31465],{},[883,31466,31468],{"className":31467},[886],[888,31469,31470],{"xmlns":890},[892,31471,31472,31498],{},[895,31473,31474,31476,31478,31480,31482,31496],{},[898,31475,1741],{},[898,31477,1747],{},[898,31479,3455],{},[1708,31481,1710],{},[2358,31483,31484,31490],{},[895,31485,31486,31488],{},[898,31487,2364],{"mathvariant":1759},[898,31489,3455],{},[895,31491,31492,31494],{},[898,31493,2364],{"mathvariant":1759},[898,31495,21035],{},[898,31497,2155],{"mathvariant":1759},[902,31499,31500],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,31502,31503,1729,31506,1695,31524,31527],{},[38,31504,31505],{},"Mezní sklon k úsporám",[883,31507,31509],{"className":31508},[886],[888,31510,31511],{"xmlns":890},[892,31512,31513,31521],{},[895,31514,31515,31517,31519],{},[898,31516,1741],{},[898,31518,1747],{},[898,31520,1981],{},[902,31522,31523],{"encoding":904},"MPS",[614,31525,31526],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,31529,31530],{},[883,31531,31533],{"className":31532},[886],[888,31534,31535],{"xmlns":890},[892,31536,31537,31563],{},[895,31538,31539,31541,31543,31545,31547,31561],{},[898,31540,1741],{},[898,31542,1747],{},[898,31544,1981],{},[1708,31546,1710],{},[2358,31548,31549,31555],{},[895,31550,31551,31553],{},[898,31552,2364],{"mathvariant":1759},[898,31554,1981],{},[895,31556,31557,31559],{},[898,31558,2364],{"mathvariant":1759},[898,31560,21035],{},[898,31562,2155],{"mathvariant":1759},[902,31564,31565],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,31567,31568,31569,31627],{},"Z (7.2) plyne ",[883,31570,31572],{"className":31571},[886],[888,31573,31574],{"xmlns":890},[892,31575,31576,31624],{},[895,31577,31578,31592,31594,31608,31610],{},[2358,31579,31580,31586],{},[895,31581,31582,31584],{},[898,31583,2364],{"mathvariant":1759},[898,31585,21035],{},[895,31587,31588,31590],{},[898,31589,2364],{"mathvariant":1759},[898,31591,21035],{},[1708,31593,1710],{},[2358,31595,31596,31602],{},[895,31597,31598,31600],{},[898,31599,2364],{"mathvariant":1759},[898,31601,3455],{},[895,31603,31604,31606],{},[898,31605,2364],{"mathvariant":1759},[898,31607,21035],{},[1708,31609,2019],{},[2358,31611,31612,31618],{},[895,31613,31614,31616],{},[898,31615,2364],{"mathvariant":1759},[898,31617,1981],{},[895,31619,31620,31622],{},[898,31621,2364],{"mathvariant":1759},[898,31623,21035],{},[902,31625,31626],{"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",[724,31629,31630],{},[883,31631,31633],{"className":31632},[886],[888,31634,31635],{"xmlns":890},[892,31636,31637,31700],{},[895,31638,31639,31691,31693,31695,31698],{},[24717,31640,31641],{"notation":24719},[3194,31642,31643],{"scriptlevel":2784,"displaystyle":1715},[3194,31644,31645],{"scriptlevel":2784,"displaystyle":1715},[3194,31646,31647],{"scriptlevel":2784,"displaystyle":1882},[895,31648,31649,31651,31653,31655,31657,31659,31661,31663,31665,31667,31669,31671,31673,31675,31677,31679,31681,31683,31685,31687,31689],{},[898,31650,1741],{},[898,31652,1747],{},[898,31654,3455],{},[1708,31656,2019],{},[898,31658,1741],{},[898,31660,1747],{},[898,31662,1981],{},[1708,31664,1710],{},[2505,31666,2507],{},[1708,31668,1883],{"separator":1882},[3213,31670],{"width":3215},[898,31672,1741],{},[898,31674,1747],{},[898,31676,1981],{},[1708,31678,1710],{},[2505,31680,2507],{},[1708,31682,2726],{},[898,31684,1741],{},[898,31686,1747],{},[898,31688,3455],{},[898,31690,2155],{"mathvariant":1759},[3213,31692],{"width":3215},[1708,31694,1716],{"stretchy":1715},[2505,31696,31697],{},"7.5",[1708,31699,1721],{"stretchy":1715},[902,31701,31702],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,31704,31705,1729,31708,31731,31732,1771,31754,31780],{},[38,31706,31707],{},"Pro lineární model",[883,31709,31711],{"className":31710},[886],[888,31712,31713],{"xmlns":890},[892,31714,31715,31729],{},[895,31716,31717,31719,31721,31723,31725,31727],{},[898,31718,3455],{},[1708,31720,1710],{},[898,31722,207],{},[898,31724,21035],{},[1708,31726,2019],{},[898,31728,1923],{},[902,31730,30786],{"encoding":904}," vychází ",[883,31733,31735],{"className":31734},[886],[888,31736,31737],{"xmlns":890},[892,31738,31739,31751],{},[895,31740,31741,31743,31745,31747,31749],{},[898,31742,1741],{},[898,31744,1747],{},[898,31746,3455],{},[1708,31748,1710],{},[898,31750,207],{},[902,31752,31753],{"encoding":904},"MPC = a",[883,31755,31757],{"className":31756},[886],[888,31758,31759],{"xmlns":890},[892,31760,31761,31777],{},[895,31762,31763,31765,31767,31769,31771,31773,31775],{},[898,31764,1741],{},[898,31766,1747],{},[898,31768,1981],{},[1708,31770,1710],{},[2505,31772,2507],{},[1708,31774,2726],{},[898,31776,207],{},[902,31778,31779],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,31782,31783,31786,31787,2421,31809,31837],{},[38,31784,31785],{},"Interpretace diferenciálem."," Pro pevné ",[883,31788,31790],{"className":31789},[886],[888,31791,31792],{"xmlns":890},[892,31793,31794,31806],{},[895,31795,31796,31798,31800],{},[898,31797,21035],{},[1708,31799,1710],{},[1753,31801,31802,31804],{},[898,31803,21035],{},[1708,31805,2417],{},[902,31807,31808],{"encoding":904},"Y = Y^*",[883,31810,31812],{"className":31811},[886],[888,31813,31814],{"xmlns":890},[892,31815,31816,31834],{},[895,31817,31818,31820,31822,31824,31826,31832],{},[898,31819,1741],{},[898,31821,1747],{},[898,31823,3455],{},[1708,31825,1716],{"stretchy":1715},[1753,31827,31828,31830],{},[898,31829,21035],{},[1708,31831,2417],{},[1708,31833,1721],{"stretchy":1715},[902,31835,31836],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,31839,31840],{},[883,31841,31843],{"className":31842},[886],[888,31844,31845],{"xmlns":890},[892,31846,31847,31901],{},[895,31848,31849,31851,31853,31855,31857,31859,31861,31867,31869,31871,31873,31875,31877,31879,31881,31883,31885,31887,31889,31891,31893,31895,31897,31899],{},[898,31850,2633],{"mathvariant":1759},[898,31852,3455],{},[1708,31854,2638],{},[898,31856,2364],{"mathvariant":1759},[898,31858,3455],{},[1708,31860,1710],{},[1753,31862,31863,31865],{},[898,31864,3455],{},[1708,31866,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,31868,1716],{"stretchy":1715},[898,31870,21035],{},[1708,31872,1721],{"stretchy":1715},[2247,31874,2659],{},[898,31876,2364],{"mathvariant":1759},[898,31878,21035],{},[1708,31880,1710],{},[898,31882,1741],{},[898,31884,1747],{},[898,31886,3455],{},[1708,31888,1716],{"stretchy":1715},[898,31890,21035],{},[1708,31892,1721],{"stretchy":1715},[2247,31894,2659],{},[898,31896,2364],{"mathvariant":1759},[898,31898,21035],{},[898,31900,2155],{"mathvariant":1759},[902,31902,31903],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,31905,31906,31907,31943,31944,31947],{},"Analogicky ",[883,31908,31910],{"className":31909},[886],[888,31911,31912],{"xmlns":890},[892,31913,31914,31940],{},[895,31915,31916,31918,31920,31922,31924,31926,31928,31930,31932,31934,31936,31938],{},[898,31917,2633],{"mathvariant":1759},[898,31919,1981],{},[1708,31921,2638],{},[898,31923,1741],{},[898,31925,1747],{},[898,31927,1981],{},[1708,31929,1716],{"stretchy":1715},[898,31931,21035],{},[1708,31933,1721],{"stretchy":1715},[2247,31935,2659],{},[898,31937,2364],{"mathvariant":1759},[898,31939,21035],{},[902,31941,31942],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,31945,1145],{"className":31946,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,31949,31951],{"id":31950},"příklad-72","Příklad 7.2",[724,31953,31121,31954,31989,31990,32008],{},[883,31955,31957],{"className":31956},[886],[888,31958,31959],{"xmlns":890},[892,31960,31961,31986],{},[895,31962,31963,31965,31967,31970,31976,31978,31980,31982,31984],{},[898,31964,3455],{},[1708,31966,1710],{},[2505,31968,31969],{},"0,001",[1753,31971,31972,31974],{},[898,31973,21035],{},[2505,31975,3132],{},[1708,31977,2019],{},[2505,31979,3958],{},[898,31981,21035],{},[1708,31983,2019],{},[2505,31985,9704],{},[902,31987,31988],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,31991,31993],{"className":31992},[886],[888,31994,31995],{"xmlns":890},[892,31996,31997,32005],{},[895,31998,31999,32001,32003],{},[898,32000,21035],{},[1708,32002,2932],{},[2505,32004,11498],{},[902,32006,32007],{"encoding":904},"Y \u003C 400",") platí",[724,32010,32011],{},[883,32012,32014],{"className":32013},[886],[888,32015,32016],{"xmlns":890},[892,32017,32018,32055],{},[895,32019,32020,32022,32024,32026,32028,32042,32044,32047,32049,32051,32053],{},[898,32021,1741],{},[898,32023,1747],{},[898,32025,3455],{},[1708,32027,1710],{},[2358,32029,32030,32036],{},[895,32031,32032,32034],{},[898,32033,2364],{"mathvariant":1759},[898,32035,3455],{},[895,32037,32038,32040],{},[898,32039,2364],{"mathvariant":1759},[898,32041,21035],{},[1708,32043,1710],{},[2505,32045,32046],{},"0,002",[898,32048,21035],{},[1708,32050,2019],{},[2505,32052,3958],{},[1708,32054,1883],{"separator":1882},[902,32056,32057],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,32059,32060],{},[883,32061,32063],{"className":32062},[886],[888,32064,32065],{"xmlns":890},[892,32066,32067,32100],{},[895,32068,32069,32071,32073,32075,32077,32079,32081,32083,32085,32087,32089,32091,32093,32095,32097],{},[898,32070,1741],{},[898,32072,1747],{},[898,32074,1981],{},[1708,32076,1710],{},[2505,32078,2507],{},[1708,32080,2726],{},[898,32082,1741],{},[898,32084,1747],{},[898,32086,3455],{},[1708,32088,1710],{},[1708,32090,2726],{},[2505,32092,32046],{},[898,32094,21035],{},[1708,32096,2019],{},[2505,32098,32099],{},"0,8.",[902,32101,32102],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,32104,32105,32185,32264],{},[123,32106,32107,1343,32135,32163,32164,3033,32182,2155],{},[883,32108,32110],{"className":32109},[886],[888,32111,32112],{"xmlns":890},[892,32113,32114,32132],{},[895,32115,32116,32118,32120,32122,32124,32126,32128,32130],{},[898,32117,1741],{},[898,32119,1747],{},[898,32121,3455],{},[1708,32123,1716],{"stretchy":1715},[2505,32125,9238],{},[1708,32127,1721],{"stretchy":1715},[1708,32129,1710],{},[2505,32131,4770],{},[902,32133,32134],{"encoding":904},"MPC(100) = 0{,}4",[883,32136,32138],{"className":32137},[886],[888,32139,32140],{"xmlns":890},[892,32141,32142,32160],{},[895,32143,32144,32146,32148,32150,32152,32154,32156,32158],{},[898,32145,1741],{},[898,32147,1747],{},[898,32149,1981],{},[1708,32151,1716],{"stretchy":1715},[2505,32153,9238],{},[1708,32155,1721],{"stretchy":1715},[1708,32157,1710],{},[2505,32159,4097],{},[902,32161,32162],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,32165,32167],{"className":32166},[886],[888,32168,32169],{"xmlns":890},[892,32170,32171,32179],{},[895,32172,32173,32175,32177],{},[898,32174,21035],{},[1708,32176,1710],{},[2505,32178,9238],{},[902,32180,32181],{"encoding":904},"Y = 100",[38,32183,32184],{},"větší sklon k úsporám",[123,32186,32187,1343,32215,32163,32243,3033,32261,2155],{},[883,32188,32190],{"className":32189},[886],[888,32191,32192],{"xmlns":890},[892,32193,32194,32212],{},[895,32195,32196,32198,32200,32202,32204,32206,32208,32210],{},[898,32197,1741],{},[898,32199,1747],{},[898,32201,3455],{},[1708,32203,1716],{"stretchy":1715},[2505,32205,20288],{},[1708,32207,1721],{"stretchy":1715},[1708,32209,1710],{},[2505,32211,4097],{},[902,32213,32214],{"encoding":904},"MPC(200) = 0{,}6",[883,32216,32218],{"className":32217},[886],[888,32219,32220],{"xmlns":890},[892,32221,32222,32240],{},[895,32223,32224,32226,32228,32230,32232,32234,32236,32238],{},[898,32225,1741],{},[898,32227,1747],{},[898,32229,1981],{},[1708,32231,1716],{"stretchy":1715},[2505,32233,20288],{},[1708,32235,1721],{"stretchy":1715},[1708,32237,1710],{},[2505,32239,4770],{},[902,32241,32242],{"encoding":904},"MPS(200) = 0{,}4",[883,32244,32246],{"className":32245},[886],[888,32247,32248],{"xmlns":890},[892,32249,32250,32258],{},[895,32251,32252,32254,32256],{},[898,32253,21035],{},[1708,32255,1710],{},[2505,32257,20288],{},[902,32259,32260],{"encoding":904},"Y = 200",[38,32262,32263],{},"větší sklon ke spotřebě",[123,32265,32266,32267,32285,32286,2511],{},"Přesně při ",[883,32268,32270],{"className":32269},[886],[888,32271,32272],{"xmlns":890},[892,32273,32274,32282],{},[895,32275,32276,32278,32280],{},[898,32277,21035],{},[1708,32279,1710],{},[2505,32281,9660],{},[902,32283,32284],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,32287,32289],{"className":32288},[886],[888,32290,32291],{"xmlns":890},[892,32292,32293,32313],{},[895,32294,32295,32297,32299,32301,32303,32305,32307,32309,32311],{},[898,32296,1741],{},[898,32298,1747],{},[898,32300,3455],{},[1708,32302,1710],{},[898,32304,1741],{},[898,32306,1747],{},[898,32308,1981],{},[1708,32310,1710],{},[2505,32312,6097],{},[902,32314,32315],{"encoding":904},"MPC = MPS = 0{,}5",[724,32317,32318,32319,32336,32337,32351,32352,2486,32365,32379,32380,32393,32394,32435],{},"Interpretace: při ",[883,32320,32322],{"className":32321},[886],[888,32323,32324],{"xmlns":890},[892,32325,32326,32334],{},[895,32327,32328,32330,32332],{},[898,32329,21035],{},[1708,32331,1710],{},[2505,32333,9238],{},[902,32335,32181],{"encoding":904}," se spotřeba mění ",[883,32338,32340],{"className":32339},[886],[888,32341,32342],{"xmlns":890},[892,32343,32344,32348],{},[895,32345,32346],{},[2505,32347,4770],{},[902,32349,32350],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,32353,32355],{"className":32354},[886],[888,32356,32357],{"xmlns":890},[892,32358,32359,32363],{},[895,32360,32361],{},[2505,32362,9238],{},[902,32364,9238],{"encoding":904},[883,32366,32368],{"className":32367},[886],[888,32369,32370],{"xmlns":890},[892,32371,32372,32377],{},[895,32373,32374],{},[2505,32375,32376],{},"101",[902,32378,32376],{"encoding":904},", změní se spotřeba přibližně o ",[883,32381,32383],{"className":32382},[886],[888,32384,32385],{"xmlns":890},[892,32386,32387,32391],{},[895,32388,32389],{},[2505,32390,4770],{},[902,32392,32350],{"encoding":904},". Skutečná změna ",[883,32395,32397],{"className":32396},[886],[888,32398,32399],{"xmlns":890},[892,32400,32401,32432],{},[895,32402,32403,32405,32407,32409,32411,32413,32415,32417,32419,32421,32423,32425,32427,32429],{},[898,32404,2633],{"mathvariant":1759},[898,32406,3455],{},[1708,32408,1710],{},[898,32410,3455],{},[1708,32412,1716],{"stretchy":1715},[2505,32414,32376],{},[1708,32416,1721],{"stretchy":1715},[1708,32418,2726],{},[898,32420,3455],{},[1708,32422,1716],{"stretchy":1715},[2505,32424,9238],{},[1708,32426,1721],{"stretchy":1715},[1708,32428,1710],{},[2505,32430,32431],{},"0,401",[902,32433,32434],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,32437,32438,32439],{},"Obecný trend: ",[38,32440,32441],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,32443,32445],{"id":32444},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,32447,32448,32449,1695,32452,32455,32456,1695,32459,5149,32462,1695,32465,32468],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,32450,32451],{},"makroekonomická rovnováha",[614,32453,32454],{},"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 ",[38,32457,32458],{},"agregátní poptávky",[614,32460,32461],{},"aggregate demand",[38,32463,32464],{},"agregátní nabídky",[614,32466,32467],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,32470,32472],{"id":32471},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,32474,32475],{},[3372,32476],{"alt":32477,"className":32478,"src":32479},"imek-keynesian-kriz",[210,3376],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,32481,32483],{"id":32482},"zadání-modelu","Zadání modelu",[724,32485,32486,32487,32500,32501,32514],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,32488,32490],{"className":32489},[886],[888,32491,32492],{"xmlns":890},[892,32493,32494,32498],{},[895,32495,32496],{},[898,32497,3455],{},[902,32499,3455],{"encoding":904}," a investice ",[883,32502,32504],{"className":32503},[886],[888,32505,32506],{"xmlns":890},[892,32507,32508,32512],{},[895,32509,32510],{},[898,32511,24070],{},[902,32513,24070],{"encoding":904},". Podmínka rovnováhy:",[724,32516,32517],{},[883,32518,32520],{"className":32519},[886],[888,32521,32522],{"xmlns":890},[892,32523,32524,32547],{},[895,32525,32526,32528,32530,32532,32534,32536,32538,32540,32542,32545],{},[898,32527,21035],{},[1708,32529,1710],{},[898,32531,3455],{},[1708,32533,2019],{},[898,32535,24070],{},[898,32537,2155],{"mathvariant":1759},[3213,32539],{"width":3215},[1708,32541,1716],{"stretchy":1715},[2505,32543,32544],{},"7.6",[1708,32546,1721],{"stretchy":1715},[902,32548,32549],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,32551,32553],{"id":32552},"soustava-rovnic","Soustava rovnic",[724,32555,32556,32557,32578,32579,32603],{},"Pro pevně zadané (plánované) investice ",[883,32558,32560],{"className":32559},[886],[888,32561,32562],{"xmlns":890},[892,32563,32564,32576],{},[895,32565,32566,32568,32570],{},[898,32567,24070],{},[1708,32569,1710],{},[1753,32571,32572,32574],{},[898,32573,24070],{},[1708,32575,2417],{},[902,32577,24081],{"encoding":904}," a funkci spotřeby ",[883,32580,32582],{"className":32581},[886],[888,32583,32584],{"xmlns":890},[892,32585,32586,32600],{},[895,32587,32588,32590,32592,32594,32596,32598],{},[898,32589,3455],{},[1708,32591,1710],{},[898,32593,3455],{},[1708,32595,1716],{"stretchy":1715},[898,32597,21035],{},[1708,32599,1721],{"stretchy":1715},[902,32601,32602],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,32605,32606],{},[883,32607,32609],{"className":32608},[886],[888,32610,32611],{"xmlns":890},[892,32612,32613,32686],{},[895,32614,32615,32677,32679,32681,32684],{},[2214,32616,32619,32649],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},"0.25em","right left",[2218,32620,32621,32627],{},[2221,32622,32623],{},[3194,32624,32625],{"scriptlevel":2784,"displaystyle":1882},[898,32626,21035],{},[2221,32628,32629],{},[3194,32630,32631],{"scriptlevel":2784,"displaystyle":1882},[895,32632,32633,32635,32637,32639,32641,32647],{},[895,32634],{},[1708,32636,1710],{},[898,32638,3455],{},[1708,32640,2019],{},[1753,32642,32643,32645],{},[898,32644,24070],{},[1708,32646,2417],{},[1708,32648,1883],{"separator":1882},[2218,32650,32651,32657],{},[2221,32652,32653],{},[3194,32654,32655],{"scriptlevel":2784,"displaystyle":1882},[898,32656,3455],{},[2221,32658,32659],{},[3194,32660,32661],{"scriptlevel":2784,"displaystyle":1882},[895,32662,32663,32665,32667,32669,32671,32673,32675],{},[895,32664],{},[1708,32666,1710],{},[898,32668,3455],{},[1708,32670,1716],{"stretchy":1715},[898,32672,21035],{},[1708,32674,1721],{"stretchy":1715},[1708,32676,1883],{"separator":1882},[3213,32678],{"width":3215},[1708,32680,1716],{"stretchy":1715},[2505,32682,32683],{},"7.7",[1708,32685,1721],{"stretchy":1715},[902,32687,32688],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,32690,32691,32692,1729,32694,1771,32711,1729,32714,2155],{},"jejímž řešením jsou ",[38,32693,25767],{},[883,32695,32697],{"className":32696},[886],[888,32698,32699],{"xmlns":890},[892,32700,32701,32709],{},[895,32702,32703],{},[1753,32704,32705,32707],{},[898,32706,21035],{},[898,32708,16183],{},[902,32710,25785],{"encoding":904},[38,32712,32713],{},"rovnovážná spotřeba",[883,32715,32717],{"className":32716},[886],[888,32718,32719],{"xmlns":890},[892,32720,32721,32729],{},[895,32722,32723],{},[1753,32724,32725,32727],{},[898,32726,3455],{},[898,32728,16183],{},[902,32730,25844],{"encoding":904},[198,32732,32734,32735],{"id":32733},"výpočet-yeye","Výpočet ",[883,32736,32738],{"className":32737},[886],[888,32739,32740],{"xmlns":890},[892,32741,32742,32750],{},[895,32743,32744],{},[1753,32745,32746,32748],{},[898,32747,21035],{},[898,32749,16183],{},[902,32751,25785],{"encoding":904},[724,32753,32754,32755,32778,32779,19598,32811],{},"Pro lineární spotřebu ",[883,32756,32758],{"className":32757},[886],[888,32759,32760],{"xmlns":890},[892,32761,32762,32776],{},[895,32763,32764,32766,32768,32770,32772,32774],{},[898,32765,3455],{},[1708,32767,1710],{},[898,32769,207],{},[898,32771,21035],{},[1708,32773,2019],{},[898,32775,1923],{},[902,32777,30786],{"encoding":904}," plyne z (7.7) rovnice ",[883,32780,32782],{"className":32781},[886],[888,32783,32784],{"xmlns":890},[892,32785,32786,32808],{},[895,32787,32788,32790,32792,32794,32796,32798,32800,32802],{},[898,32789,21035],{},[1708,32791,1710],{},[898,32793,207],{},[898,32795,21035],{},[1708,32797,2019],{},[898,32799,1923],{},[1708,32801,2019],{},[1753,32803,32804,32806],{},[898,32805,24070],{},[1708,32807,2417],{},[902,32809,32810],{"encoding":904},"Y = aY + b + I^*",[38,32812,32813],{},"redukovaný tvar",[724,32815,32816],{},[883,32817,32819],{"className":32818},[886],[888,32820,32821],{"xmlns":890},[892,32822,32823,32871],{},[895,32824,32825],{},[24717,32826,32827],{"notation":24719},[3194,32828,32829],{"scriptlevel":2784,"displaystyle":1715},[3194,32830,32831],{"scriptlevel":2784,"displaystyle":1715},[3194,32832,32833],{"scriptlevel":2784,"displaystyle":1882},[895,32834,32835,32837,32843,32845,32867,32869],{},[2247,32836,2659],{},[1753,32838,32839,32841],{},[898,32840,21035],{},[898,32842,16183],{},[1708,32844,1710],{},[2358,32846,32847,32859],{},[895,32848,32849,32851,32853],{},[898,32850,1923],{},[1708,32852,2019],{},[1753,32854,32855,32857],{},[898,32856,24070],{},[1708,32858,2417],{},[895,32860,32861,32863,32865],{},[2505,32862,2507],{},[1708,32864,2726],{},[898,32866,207],{},[898,32868,2155],{"mathvariant":1759},[2247,32870,2659],{},[902,32872,32873],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,32875,32877],{"id":32876},"příklad-73","Příklad 7.3",[724,32879,32880,32881,3033,32898,1771,32922,32948],{},"V modelu ",[883,32882,32884],{"className":32883},[886],[888,32885,32886],{"xmlns":890},[892,32887,32888,32896],{},[895,32889,32890,32892,32894],{},[898,32891,3455],{},[2247,32893,24176],{},[898,32895,24070],{},[902,32897,24181],{"encoding":904},[883,32899,32901],{"className":32900},[886],[888,32902,32903],{"xmlns":890},[892,32904,32905,32919],{},[895,32906,32907,32909,32911,32913,32915,32917],{},[898,32908,3455],{},[1708,32910,1710],{},[2505,32912,4097],{},[898,32914,21035],{},[1708,32916,2019],{},[2505,32918,4003],{},[902,32920,32921],{"encoding":904},"C = 0{,}6Y + 10",[883,32923,32925],{"className":32924},[886],[888,32926,32927],{"xmlns":890},[892,32928,32929,32945],{},[895,32930,32931,32933,32935,32937,32939],{},[898,32932,24070],{},[1708,32934,1710],{},[2505,32936,4090],{},[1708,32938,1710],{},[1753,32940,32941,32943],{},[898,32942,24070],{},[1708,32944,2417],{},[902,32946,32947],{"encoding":904},"I = 12 = I^*",". Soustava",[724,32950,32951],{},[883,32952,32954],{"className":32953},[886],[888,32955,32956],{"xmlns":890},[892,32957,32958,33014],{},[2214,32959,32960,32986],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,32961,32962,32968],{},[2221,32963,32964],{},[3194,32965,32966],{"scriptlevel":2784,"displaystyle":1882},[898,32967,21035],{},[2221,32969,32970],{},[3194,32971,32972],{"scriptlevel":2784,"displaystyle":1882},[895,32973,32974,32976,32978,32980,32982,32984],{},[895,32975],{},[1708,32977,1710],{},[898,32979,3455],{},[1708,32981,2019],{},[2505,32983,4090],{},[1708,32985,1883],{"separator":1882},[2218,32987,32988,32994],{},[2221,32989,32990],{},[3194,32991,32992],{"scriptlevel":2784,"displaystyle":1882},[898,32993,3455],{},[2221,32995,32996],{},[3194,32997,32998],{"scriptlevel":2784,"displaystyle":1882},[895,32999,33000,33002,33004,33006,33008,33010,33012],{},[895,33001],{},[1708,33003,1710],{},[2505,33005,4097],{},[898,33007,21035],{},[1708,33009,2019],{},[2505,33011,4003],{},[1708,33013,1883],{"separator":1882},[902,33015,33016],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,33018,33019,33020,1343,33043,33066,33067,2511],{},"má řešení ",[883,33021,33023],{"className":33022},[886],[888,33024,33025],{"xmlns":890},[892,33026,33027,33040],{},[895,33028,33029,33035,33037],{},[1753,33030,33031,33033],{},[898,33032,21035],{},[898,33034,16183],{},[1708,33036,1710],{},[2505,33038,33039],{},"55",[902,33041,33042],{"encoding":904},"Y^E = 55",[883,33044,33046],{"className":33045},[886],[888,33047,33048],{"xmlns":890},[892,33049,33050,33063],{},[895,33051,33052,33058,33060],{},[1753,33053,33054,33056],{},[898,33055,3455],{},[898,33057,16183],{},[1708,33059,1710],{},[2505,33061,33062],{},"43",[902,33064,33065],{"encoding":904},"C^E = 43"," (a ",[883,33068,33070],{"className":33069},[886],[888,33071,33072],{"xmlns":890},[892,33073,33074,33086],{},[895,33075,33076,33082,33084],{},[1753,33077,33078,33080],{},[898,33079,1981],{},[898,33081,16183],{},[1708,33083,1710],{},[2505,33085,4090],{},[902,33087,33088],{"encoding":904},"S^E = 12",[724,33090,33091],{},[614,33092,33093,33094,33116,33117,5149,33138,33161,33162,2155],{},"Obrázek 7.5 — Přímky ",[883,33095,33097],{"className":33096},[886],[888,33098,33099],{"xmlns":890},[892,33100,33101,33113],{},[895,33102,33103,33105,33107,33109,33111],{},[898,33104,3455],{},[1708,33106,1710],{},[898,33108,21035],{},[1708,33110,2726],{},[2505,33112,4090],{},[902,33114,33115],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,33118,33120],{"className":33119},[886],[888,33121,33122],{"xmlns":890},[892,33123,33124,33136],{},[895,33125,33126,33128,33130,33132,33134],{},[898,33127,21035],{},[1708,33129,1710],{},[898,33131,3455],{},[1708,33133,2019],{},[898,33135,24070],{},[902,33137,26625],{"encoding":904},[883,33139,33141],{"className":33140},[886],[888,33142,33143],{"xmlns":890},[892,33144,33145,33159],{},[895,33146,33147,33149,33151,33153,33155,33157],{},[898,33148,3455],{},[1708,33150,1710],{},[2505,33152,4097],{},[898,33154,21035],{},[1708,33156,2019],{},[2505,33158,4003],{},[902,33160,32921],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,33163,33165],{"className":33164},[886],[888,33166,33167],{"xmlns":890},[892,33168,33169,33201],{},[895,33170,33171,33173,33179,33181,33187,33189,33191,33193,33195,33197,33199],{},[1708,33172,6940],{"stretchy":1715},[1753,33174,33175,33177],{},[898,33176,21035],{},[898,33178,16183],{},[1708,33180,1883],{"separator":1882},[1753,33182,33183,33185],{},[898,33184,3455],{},[898,33186,16183],{},[1708,33188,6981],{"stretchy":1715},[1708,33190,1710],{},[1708,33192,6940],{"stretchy":1715},[2505,33194,33039],{},[1708,33196,1883],{"separator":1882},[2505,33198,33062],{},[1708,33200,6981],{"stretchy":1715},[902,33202,33203],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,33205,33206,33209,33210,33227,33228,2155],{},[38,33207,33208],{},"Komentář k přechodu."," Model ",[883,33211,33213],{"className":33212},[886],[888,33214,33215],{"xmlns":890},[892,33216,33217,33225],{},[895,33218,33219,33221,33223],{},[898,33220,3455],{},[2247,33222,24176],{},[898,33224,24070],{},[902,33226,24181],{"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 ",[38,33229,33230,33231],{},"model ",[883,33232,33234],{"className":33233},[886],[888,33235,33236],{"xmlns":890},[892,33237,33238,33250],{},[895,33239,33240,33242,33244,33246,33248],{},[898,33241,3455],{},[2247,33243,24176],{},[898,33245,24070],{},[2247,33247,24176],{},[898,33249,23999],{},[902,33251,30090],{"encoding":904},[115,33253,33255],{"id":33254},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,33257,32483],{"id":33258},"zadání-modelu-1",[724,33260,33261,33262,33279,33280,1729,33283,1695,33296,33299],{},"Rozšíření modelu ",[883,33263,33265],{"className":33264},[886],[888,33266,33267],{"xmlns":890},[892,33268,33269,33277],{},[895,33270,33271,33273,33275],{},[898,33272,3455],{},[2247,33274,24176],{},[898,33276,24070],{},[902,33278,24181],{"encoding":904}," o ",[38,33281,33282],{},"vládní výdaje",[883,33284,33286],{"className":33285},[886],[888,33287,33288],{"xmlns":890},[892,33289,33290,33294],{},[895,33291,33292],{},[898,33293,23999],{},[902,33295,23999],{"encoding":904},[614,33297,33298],{},"government expenditure","). Podmínka rovnováhy:",[724,33301,33302],{},[883,33303,33305],{"className":33304},[886],[888,33306,33307],{"xmlns":890},[892,33308,33309,33336],{},[895,33310,33311,33313,33315,33317,33319,33321,33323,33325,33327,33329,33331,33334],{},[898,33312,21035],{},[1708,33314,1710],{},[898,33316,3455],{},[1708,33318,2019],{},[898,33320,24070],{},[1708,33322,2019],{},[898,33324,23999],{},[898,33326,2155],{"mathvariant":1759},[3213,33328],{"width":3215},[1708,33330,1716],{"stretchy":1715},[2505,33332,33333],{},"7.8",[1708,33335,1721],{"stretchy":1715},[902,33337,33338],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,33340,33341,33342,1729,33345,1695,33358,33361],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,33343,33344],{},"zdaněním domácností",[883,33346,33348],{"className":33347},[886],[888,33349,33350],{"xmlns":890},[892,33351,33352,33356],{},[895,33353,33354],{},[898,33355,1978],{},[902,33357,1978],{"encoding":904},[614,33359,33360],{},"taxation","). Zdanění bývá:",[120,33363,33364,33397,33422],{},[123,33365,33366,33367,1883],{},"úměrné důchodu: ",[883,33368,33370],{"className":33369},[886],[888,33371,33372],{"xmlns":890},[892,33373,33374,33394],{},[895,33375,33376,33378,33380,33382,33384,33386,33388,33390,33392],{},[898,33377,1978],{},[1708,33379,1710],{},[898,33381,1978],{},[1708,33383,1716],{"stretchy":1715},[898,33385,21035],{},[1708,33387,1721],{"stretchy":1715},[1708,33389,1710],{},[898,33391,9105],{},[898,33393,21035],{},[902,33395,33396],{"encoding":904},"T = T(Y) = tY",[123,33398,33399,33400,1883],{},"fixní: ",[883,33401,33403],{"className":33402},[886],[888,33404,33405],{"xmlns":890},[892,33406,33407,33419],{},[895,33408,33409,33411,33413],{},[898,33410,1978],{},[1708,33412,1710],{},[1753,33414,33415,33417],{},[898,33416,1978],{},[1708,33418,2417],{},[902,33420,33421],{"encoding":904},"T = T^*",[123,33423,33424,33425,2980,33453,2155],{},"kombinované: ",[883,33426,33428],{"className":33427},[886],[888,33429,33430],{"xmlns":890},[892,33431,33432,33450],{},[895,33433,33434,33436,33438,33444,33446,33448],{},[898,33435,1978],{},[1708,33437,1710],{},[1753,33439,33440,33442],{},[898,33441,1978],{},[1708,33443,2417],{},[1708,33445,2019],{},[898,33447,9105],{},[898,33449,21035],{},[902,33451,33452],{"encoding":904},"T = T^* + tY",[883,33454,33456],{"className":33455},[886],[888,33457,33458],{"xmlns":890},[892,33459,33460,33472],{},[895,33461,33462,33464,33466,33468,33470],{},[2505,33463,2784],{},[1708,33465,19592],{},[898,33467,9105],{},[1708,33469,2932],{},[2505,33471,2507],{},[902,33473,33474],{"encoding":904},"0 \\le t \u003C 1",[1636,33476,33477],{},[724,33478,33479,33481,33482,33503,33504,33507,33508,33521,33522,5149,33548,1729,33551,33577,33578,33606,33607,1771,33620,33638],{},[883,33480,6130],{}," Pozor na disponibilní důchod\nV modelu ",[883,33483,33485],{"className":33484},[886],[888,33486,33487],{"xmlns":890},[892,33488,33489,33501],{},[895,33490,33491,33493,33495,33497,33499],{},[898,33492,3455],{},[2247,33494,24176],{},[898,33496,24070],{},[2247,33498,24176],{},[898,33500,23999],{},[902,33502,30090],{"encoding":904}," je nutné ",[38,33505,33506],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,33509,33511],{"className":33510},[886],[888,33512,33513],{"xmlns":890},[892,33514,33515,33519],{},[895,33516,33517],{},[898,33518,21035],{},[902,33520,21035],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,33523,33525],{"className":33524},[886],[888,33526,33527],{"xmlns":890},[892,33528,33529,33545],{},[895,33530,33531,33533,33535,33537,33539,33541,33543],{},[898,33532,21035],{},[1708,33534,1710],{},[898,33536,3455],{},[1708,33538,2019],{},[898,33540,24070],{},[1708,33542,2019],{},[898,33544,23999],{},[902,33546,33547],{"encoding":904},"Y = C + I + G",[38,33549,33550],{},"disponibilní důchod",[883,33552,33554],{"className":33553},[886],[888,33555,33556],{"xmlns":890},[892,33557,33558,33574],{},[895,33559,33560,33566,33568,33570,33572],{},[1743,33561,33562,33564],{},[898,33563,21035],{},[898,33565,16117],{},[1708,33567,1710],{},[898,33569,21035],{},[1708,33571,2726],{},[898,33573,1978],{},[902,33575,33576],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,33579,33581],{"className":33580},[886],[888,33582,33583],{"xmlns":890},[892,33584,33585,33603],{},[895,33586,33587,33589,33591,33593,33595,33601],{},[898,33588,3455],{},[1708,33590,1710],{},[898,33592,3455],{},[1708,33594,1716],{"stretchy":1715},[1743,33596,33597,33599],{},[898,33598,21035],{},[898,33600,16117],{},[1708,33602,1721],{"stretchy":1715},[902,33604,33605],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,33608,33610],{"className":33609},[886],[888,33611,33612],{"xmlns":890},[892,33613,33614,33618],{},[895,33615,33616],{},[898,33617,21035],{},[902,33619,21035],{"encoding":904},[883,33621,33623],{"className":33622},[886],[888,33624,33625],{"xmlns":890},[892,33626,33627,33635],{},[895,33628,33629],{},[1743,33630,33631,33633],{},[898,33632,21035],{},[898,33634,16117],{},[902,33636,33637],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,33640,33641,1695,33644,1721],{},[38,33642,33643],{},"Disponibilní důchod",[614,33645,33646],{},"disposable income",[724,33648,33649],{},[883,33650,33652],{"className":33651},[886],[888,33653,33654],{"xmlns":890},[892,33655,33656,33672],{},[895,33657,33658,33664,33666,33668,33670],{},[1743,33659,33660,33662],{},[898,33661,21035],{},[898,33663,16117],{},[1708,33665,1710],{},[898,33667,21035],{},[1708,33669,2726],{},[898,33671,1978],{},[902,33673,33576],{"encoding":904},[724,33675,33676,33677,2155],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,33678,33680],{"className":33679},[886],[888,33681,33682],{"xmlns":890},[892,33683,33684,33702],{},[895,33685,33686,33688,33690,33692,33694,33700],{},[898,33687,3455],{},[1708,33689,1710],{},[898,33691,3455],{},[1708,33693,1716],{"stretchy":1715},[1743,33695,33696,33698],{},[898,33697,21035],{},[898,33699,16117],{},[1708,33701,1721],{"stretchy":1715},[902,33703,33605],{"encoding":904},[198,33705,32553],{"id":33706},"soustava-rovnic-1",[724,33708,33709,33710,1343,33731,33753,33754,2788],{},"Pro pevně zadané ",[883,33711,33713],{"className":33712},[886],[888,33714,33715],{"xmlns":890},[892,33716,33717,33729],{},[895,33718,33719,33721,33723],{},[898,33720,24070],{},[1708,33722,1710],{},[1753,33724,33725,33727],{},[898,33726,24070],{},[1708,33728,2417],{},[902,33730,24081],{"encoding":904},[883,33732,33734],{"className":33733},[886],[888,33735,33736],{"xmlns":890},[892,33737,33738,33750],{},[895,33739,33740,33742,33744],{},[898,33741,23999],{},[1708,33743,1710],{},[1753,33745,33746,33748],{},[898,33747,23999],{},[1708,33749,2417],{},[902,33751,33752],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,33755,33757],{"className":33756},[886],[888,33758,33759],{"xmlns":890},[892,33760,33761,33781],{},[895,33762,33763,33765,33767,33769,33771,33777,33779],{},[898,33764,21035],{},[1708,33766,1883],{"separator":1882},[898,33768,3455],{},[1708,33770,1883],{"separator":1882},[1743,33772,33773,33775],{},[898,33774,21035],{},[898,33776,16117],{},[1708,33778,1883],{"separator":1882},[898,33780,1978],{},[902,33782,33783],{"encoding":904},"Y, C, Y_D, T",[724,33785,33786],{},[883,33787,33789],{"className":33788},[886],[888,33790,33791],{"xmlns":890},[892,33792,33793,33934],{},[895,33794,33795,33925,33927,33929,33932],{},[2214,33796,33797,33835,33863,33895],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,33798,33799,33805],{},[2221,33800,33801],{},[3194,33802,33803],{"scriptlevel":2784,"displaystyle":1882},[898,33804,21035],{},[2221,33806,33807],{},[3194,33808,33809],{"scriptlevel":2784,"displaystyle":1882},[895,33810,33811,33813,33815,33817,33819,33825,33827,33833],{},[895,33812],{},[1708,33814,1710],{},[898,33816,3455],{},[1708,33818,2019],{},[1753,33820,33821,33823],{},[898,33822,24070],{},[1708,33824,2417],{},[1708,33826,2019],{},[1753,33828,33829,33831],{},[898,33830,23999],{},[1708,33832,2417],{},[1708,33834,1883],{"separator":1882},[2218,33836,33837,33843],{},[2221,33838,33839],{},[3194,33840,33841],{"scriptlevel":2784,"displaystyle":1882},[898,33842,1978],{},[2221,33844,33845],{},[3194,33846,33847],{"scriptlevel":2784,"displaystyle":1882},[895,33848,33849,33851,33853,33855,33857,33859,33861],{},[895,33850],{},[1708,33852,1710],{},[898,33854,1978],{},[1708,33856,1716],{"stretchy":1715},[898,33858,21035],{},[1708,33860,1721],{"stretchy":1715},[1708,33862,1883],{"separator":1882},[2218,33864,33865,33871],{},[2221,33866,33867],{},[3194,33868,33869],{"scriptlevel":2784,"displaystyle":1882},[898,33870,3455],{},[2221,33872,33873],{},[3194,33874,33875],{"scriptlevel":2784,"displaystyle":1882},[895,33876,33877,33879,33881,33883,33885,33891,33893],{},[895,33878],{},[1708,33880,1710],{},[898,33882,3455],{},[1708,33884,1716],{"stretchy":1715},[1743,33886,33887,33889],{},[898,33888,21035],{},[898,33890,16117],{},[1708,33892,1721],{"stretchy":1715},[1708,33894,1883],{"separator":1882},[2218,33896,33897,33907],{},[2221,33898,33899],{},[3194,33900,33901],{"scriptlevel":2784,"displaystyle":1882},[1743,33902,33903,33905],{},[898,33904,21035],{},[898,33906,16117],{},[2221,33908,33909],{},[3194,33910,33911],{"scriptlevel":2784,"displaystyle":1882},[895,33912,33913,33915,33917,33919,33921,33923],{},[895,33914],{},[1708,33916,1710],{},[898,33918,21035],{},[1708,33920,2726],{},[898,33922,1978],{},[1708,33924,1883],{"separator":1882},[3213,33926],{"width":3215},[1708,33928,1716],{"stretchy":1715},[2505,33930,33931],{},"7.9",[1708,33933,1721],{"stretchy":1715},[902,33935,33936],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,33938,33939,33940,33984,33985,2155],{},"s řešeními ",[883,33941,33943],{"className":33942},[886],[888,33944,33945],{"xmlns":890},[892,33946,33947,33981],{},[895,33948,33949,33955,33957,33963,33965,33971,33973],{},[1753,33950,33951,33953],{},[898,33952,21035],{},[898,33954,16183],{},[1708,33956,1883],{"separator":1882},[1753,33958,33959,33961],{},[898,33960,3455],{},[898,33962,16183],{},[1708,33964,1883],{"separator":1882},[1753,33966,33967,33969],{},[898,33968,1978],{},[898,33970,16183],{},[1708,33972,1883],{"separator":1882},[4754,33974,33975,33977,33979],{},[898,33976,21035],{},[898,33978,16117],{},[898,33980,16183],{},[902,33982,33983],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,33986,33988],{"className":33987},[886],[888,33989,33990],{"xmlns":890},[892,33991,33992,34018],{},[895,33993,33994,34000,34002,34010,34012],{},[1753,33995,33996,33998],{},[898,33997,1981],{},[898,33999,16183],{},[1708,34001,1710],{},[4754,34003,34004,34006,34008],{},[898,34005,21035],{},[898,34007,16117],{},[898,34009,16183],{},[1708,34011,2726],{},[1753,34013,34014,34016],{},[898,34015,3455],{},[898,34017,16183],{},[902,34019,34020],{"encoding":904},"S^E = Y_D^E - C^E",[1636,34022,34023,34028],{},[724,34024,34025,34027],{},[883,34026,3465],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,34029,34030,34053,34136,34191,34281],{},[123,34031,34032,34035,34036,2155],{},[38,34033,34034],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,34037,34039],{"className":34038},[886],[888,34040,34041],{"xmlns":890},[892,34042,34043,34051],{},[895,34044,34045],{},[1743,34046,34047,34049],{},[898,34048,21035],{},[898,34050,16117],{},[902,34052,33637],{"encoding":904},[123,34054,34055,34104,34105,34122,34123,2155],{},[38,34056,34057,34058,34078,34079],{},"Dosaď ",[883,34059,34061],{"className":34060},[886],[888,34062,34063],{"xmlns":890},[892,34064,34065,34075],{},[895,34066,34067,34069,34071,34073],{},[898,34068,1978],{},[1708,34070,1716],{"stretchy":1715},[898,34072,21035],{},[1708,34074,1721],{"stretchy":1715},[902,34076,34077],{"encoding":904},"T(Y)"," do ",[883,34080,34082],{"className":34081},[886],[888,34083,34084],{"xmlns":890},[892,34085,34086,34102],{},[895,34087,34088,34094,34096,34098,34100],{},[1743,34089,34090,34092],{},[898,34091,21035],{},[898,34093,16117],{},[1708,34095,1710],{},[898,34097,21035],{},[1708,34099,2726],{},[898,34101,1978],{},[902,34103,33576],{"encoding":904}," — dostaneš ",[883,34106,34108],{"className":34107},[886],[888,34109,34110],{"xmlns":890},[892,34111,34112,34120],{},[895,34113,34114],{},[1743,34115,34116,34118],{},[898,34117,21035],{},[898,34119,16117],{},[902,34121,33637],{"encoding":904}," jako lineární funkci ",[883,34124,34126],{"className":34125},[886],[888,34127,34128],{"xmlns":890},[892,34129,34130,34134],{},[895,34131,34132],{},[898,34133,21035],{},[902,34135,21035],{"encoding":904},[123,34137,34138,34104,34165,34122,34178,2155],{},[38,34139,34057,34140,34164],{},[883,34141,34143],{"className":34142},[886],[888,34144,34145],{"xmlns":890},[892,34146,34147,34161],{},[895,34148,34149,34155,34157,34159],{},[1743,34150,34151,34153],{},[898,34152,21035],{},[898,34154,16117],{},[1708,34156,1716],{"stretchy":1715},[898,34158,21035],{},[1708,34160,1721],{"stretchy":1715},[902,34162,34163],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,34166,34168],{"className":34167},[886],[888,34169,34170],{"xmlns":890},[892,34171,34172,34176],{},[895,34173,34174],{},[898,34175,3455],{},[902,34177,3455],{"encoding":904},[883,34179,34181],{"className":34180},[886],[888,34182,34183],{"xmlns":890},[892,34184,34185,34189],{},[895,34186,34187],{},[898,34188,21035],{},[902,34190,21035],{"encoding":904},[123,34192,34193,1729,34215,34249,34250,34263,34264,2155],{},[38,34194,34057,34195,34214],{},[883,34196,34198],{"className":34197},[886],[888,34199,34200],{"xmlns":890},[892,34201,34202,34212],{},[895,34203,34204,34206,34208,34210],{},[898,34205,3455],{},[1708,34207,1716],{"stretchy":1715},[898,34209,21035],{},[1708,34211,1721],{"stretchy":1715},[902,34213,26098],{"encoding":904}," do podmínky rovnováhy",[883,34216,34218],{"className":34217},[886],[888,34219,34220],{"xmlns":890},[892,34221,34222,34246],{},[895,34223,34224,34226,34228,34230,34232,34238,34240],{},[898,34225,21035],{},[1708,34227,1710],{},[898,34229,3455],{},[1708,34231,2019],{},[1753,34233,34234,34236],{},[898,34235,24070],{},[1708,34237,2417],{},[1708,34239,2019],{},[1753,34241,34242,34244],{},[898,34243,23999],{},[1708,34245,2417],{},[902,34247,34248],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,34251,34253],{"className":34252},[886],[888,34254,34255],{"xmlns":890},[892,34256,34257,34261],{},[895,34258,34259],{},[898,34260,21035],{},[902,34262,21035],{"encoding":904},", odtud ",[883,34265,34267],{"className":34266},[886],[888,34268,34269],{"xmlns":890},[892,34270,34271,34279],{},[895,34272,34273],{},[1753,34274,34275,34277],{},[898,34276,21035],{},[898,34278,16183],{},[902,34280,25785],{"encoding":904},[123,34282,34283,34286,34287,1343,34305,1343,34325,1343,34342,2155],{},[38,34284,34285],{},"Zpětným dosazením"," dopočítej ",[883,34288,34290],{"className":34289},[886],[888,34291,34292],{"xmlns":890},[892,34293,34294,34302],{},[895,34295,34296],{},[1753,34297,34298,34300],{},[898,34299,1978],{},[898,34301,16183],{},[902,34303,34304],{"encoding":904},"T^E",[883,34306,34308],{"className":34307},[886],[888,34309,34310],{"xmlns":890},[892,34311,34312,34322],{},[895,34313,34314],{},[4754,34315,34316,34318,34320],{},[898,34317,21035],{},[898,34319,16117],{},[898,34321,16183],{},[902,34323,34324],{"encoding":904},"Y_D^E",[883,34326,34328],{"className":34327},[886],[888,34329,34330],{"xmlns":890},[892,34331,34332,34340],{},[895,34333,34334],{},[1753,34335,34336,34338],{},[898,34337,3455],{},[898,34339,16183],{},[902,34341,25844],{"encoding":904},[883,34343,34345],{"className":34344},[886],[888,34346,34347],{"xmlns":890},[892,34348,34349,34357],{},[895,34350,34351],{},[1753,34352,34353,34355],{},[898,34354,1981],{},[898,34356,16183],{},[902,34358,34359],{"encoding":904},"S^E",[198,34361,34363],{"id":34362},"příklad-74","Příklad 7.4",[724,34365,32880,34366,34387,34388,1343,34419,1343,34443,1343,34465,34487],{},[883,34367,34369],{"className":34368},[886],[888,34370,34371],{"xmlns":890},[892,34372,34373,34385],{},[895,34374,34375,34377,34379,34381,34383],{},[898,34376,3455],{},[2247,34378,24176],{},[898,34380,24070],{},[2247,34382,24176],{},[898,34384,23999],{},[902,34386,30090],{"encoding":904}," jsou dány ",[883,34389,34391],{"className":34390},[886],[888,34392,34393],{"xmlns":890},[892,34394,34395,34416],{},[895,34396,34397,34399,34401,34404,34406,34412,34414],{},[898,34398,3455],{},[1708,34400,1710],{},[2505,34402,34403],{},"0,9",[2247,34405,2659],{},[1743,34407,34408,34410],{},[898,34409,21035],{},[898,34411,16117],{},[1708,34413,2019],{},[2505,34415,17813],{},[902,34417,34418],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,34420,34422],{"className":34421},[886],[888,34423,34424],{"xmlns":890},[892,34425,34426,34440],{},[895,34427,34428,34430,34432,34434,34436,34438],{},[898,34429,1978],{},[1708,34431,1710],{},[2505,34433,3958],{},[898,34435,21035],{},[1708,34437,2019],{},[2505,34439,4028],{},[902,34441,34442],{"encoding":904},"T = 0{,}2Y + 25",[883,34444,34446],{"className":34445},[886],[888,34447,34448],{"xmlns":890},[892,34449,34450,34462],{},[895,34451,34452,34458,34460],{},[1753,34453,34454,34456],{},[898,34455,24070],{},[1708,34457,2417],{},[1708,34459,1710],{},[2505,34461,26919],{},[902,34463,34464],{"encoding":904},"I^* = 35",[883,34466,34468],{"className":34467},[886],[888,34469,34470],{"xmlns":890},[892,34471,34472,34484],{},[895,34473,34474,34480,34482],{},[1753,34475,34476,34478],{},[898,34477,23999],{},[1708,34479,2417],{},[1708,34481,1710],{},[2505,34483,4018],{},[902,34485,34486],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,34489,34490],{},[883,34491,34493],{"className":34492},[886],[888,34494,34495],{"xmlns":890},[892,34496,34497,34621],{},[2214,34498,34499,34529,34557,34591],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,34500,34501,34507],{},[2221,34502,34503],{},[3194,34504,34505],{"scriptlevel":2784,"displaystyle":1882},[898,34506,21035],{},[2221,34508,34509],{},[3194,34510,34511],{"scriptlevel":2784,"displaystyle":1882},[895,34512,34513,34515,34517,34519,34521,34523,34525,34527],{},[895,34514],{},[1708,34516,1710],{},[898,34518,3455],{},[1708,34520,2019],{},[2505,34522,26919],{},[1708,34524,2019],{},[2505,34526,4018],{},[1708,34528,1883],{"separator":1882},[2218,34530,34531,34537],{},[2221,34532,34533],{},[3194,34534,34535],{"scriptlevel":2784,"displaystyle":1882},[898,34536,1978],{},[2221,34538,34539],{},[3194,34540,34541],{"scriptlevel":2784,"displaystyle":1882},[895,34542,34543,34545,34547,34549,34551,34553,34555],{},[895,34544],{},[1708,34546,1710],{},[2505,34548,3958],{},[898,34550,21035],{},[1708,34552,2019],{},[2505,34554,4028],{},[1708,34556,1883],{"separator":1882},[2218,34558,34559,34565],{},[2221,34560,34561],{},[3194,34562,34563],{"scriptlevel":2784,"displaystyle":1882},[898,34564,3455],{},[2221,34566,34567],{},[3194,34568,34569],{"scriptlevel":2784,"displaystyle":1882},[895,34570,34571,34573,34575,34577,34579,34585,34587,34589],{},[895,34572],{},[1708,34574,1710],{},[2505,34576,34403],{},[2247,34578,2659],{},[1743,34580,34581,34583],{},[898,34582,21035],{},[898,34584,16117],{},[1708,34586,2019],{},[2505,34588,17813],{},[1708,34590,1883],{"separator":1882},[2218,34592,34593,34603],{},[2221,34594,34595],{},[3194,34596,34597],{"scriptlevel":2784,"displaystyle":1882},[1743,34598,34599,34601],{},[898,34600,21035],{},[898,34602,16117],{},[2221,34604,34605],{},[3194,34606,34607],{"scriptlevel":2784,"displaystyle":1882},[895,34608,34609,34611,34613,34615,34617,34619],{},[895,34610],{},[1708,34612,1710],{},[898,34614,21035],{},[1708,34616,2726],{},[898,34618,1978],{},[898,34620,2155],{"mathvariant":1759},[902,34622,34623],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,34625,34626,34629,34630,34684,34685,34731,34732,2788],{},[38,34627,34628],{},"Řešení."," Z definice ",[883,34631,34633],{"className":34632},[886],[888,34634,34635],{"xmlns":890},[892,34636,34637,34681],{},[895,34638,34639,34645,34647,34649,34651,34653,34655,34657,34659,34661,34663,34665,34667,34669,34671,34673,34675,34677,34679],{},[1743,34640,34641,34643],{},[898,34642,21035],{},[898,34644,16117],{},[1708,34646,1710],{},[898,34648,21035],{},[1708,34650,2726],{},[898,34652,1978],{},[1708,34654,1710],{},[898,34656,21035],{},[1708,34658,2726],{},[1708,34660,1716],{"stretchy":1715},[2505,34662,3958],{},[898,34664,21035],{},[1708,34666,2019],{},[2505,34668,4028],{},[1708,34670,1721],{"stretchy":1715},[1708,34672,1710],{},[2505,34674,6120],{},[898,34676,21035],{},[1708,34678,2726],{},[2505,34680,4028],{},[902,34682,34683],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,34686,34688],{"className":34687},[886],[888,34689,34690],{"xmlns":890},[892,34691,34692,34728],{},[895,34693,34694,34696,34698,34700,34702,34704,34706,34708,34710,34712,34714,34716,34718,34721,34723,34725],{},[898,34695,3455],{},[1708,34697,1710],{},[2505,34699,34403],{},[1708,34701,1716],{"stretchy":1715},[2505,34703,6120],{},[898,34705,21035],{},[1708,34707,2726],{},[2505,34709,4028],{},[1708,34711,1721],{"stretchy":1715},[1708,34713,2019],{},[2505,34715,17813],{},[1708,34717,1710],{},[2505,34719,34720],{},"0,72",[898,34722,21035],{},[1708,34724,2019],{},[2505,34726,34727],{},"47,5",[902,34729,34730],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,34733,34735],{"className":34734},[886],[888,34736,34737],{"xmlns":890},[892,34738,34739,34757],{},[895,34740,34741,34743,34745,34747,34749,34751,34753,34755],{},[898,34742,21035],{},[1708,34744,1710],{},[2505,34746,34720],{},[898,34748,21035],{},[1708,34750,2019],{},[2505,34752,34727],{},[1708,34754,2019],{},[2505,34756,33039],{},[902,34758,34759],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,34761,34762],{},[883,34763,34765],{"className":34764},[886],[888,34766,34767],{"xmlns":890},[892,34768,34769,34809],{},[895,34770,34771,34774,34776,34778,34781,34783,34785,34787,34793,34795,34804,34806],{},[2505,34772,34773],{},"0,28",[898,34775,21035],{},[1708,34777,1710],{},[2505,34779,34780],{},"102,5",[2247,34782,4779],{},[1708,34784,26889],{},[2247,34786,4779],{},[1753,34788,34789,34791],{},[898,34790,21035],{},[898,34792,16183],{},[1708,34794,1710],{},[3194,34796,34797],{"scriptlevel":2784,"displaystyle":1715},[2358,34798,34799,34802],{},[2505,34800,34801],{},"5125",[2505,34803,4008],{},[1708,34805,17816],{},[2505,34807,34808],{},"366,071.",[902,34810,34811],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,34813,34814],{},"Rovnovážné veličiny:",[120,34816,34817,34852,34904,34958,35006],{},[123,34818,34819,1883],{},[883,34820,34822],{"className":34821},[886],[888,34823,34824],{"xmlns":890},[892,34825,34826,34849],{},[895,34827,34828,34834,34836,34844,34846],{},[1753,34829,34830,34832],{},[898,34831,21035],{},[898,34833,16183],{},[1708,34835,1710],{},[3194,34837,34838],{"scriptlevel":2784,"displaystyle":1715},[2358,34839,34840,34842],{},[2505,34841,34801],{},[2505,34843,4008],{},[1708,34845,17816],{},[2505,34847,34848],{},"366,071",[902,34850,34851],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,34853,34854,1883],{},[883,34855,34857],{"className":34856},[886],[888,34858,34859],{"xmlns":890},[892,34860,34861,34901],{},[895,34862,34863,34869,34871,34873,34875,34881,34883,34885,34887,34896,34898],{},[1753,34864,34865,34867],{},[898,34866,1978],{},[898,34868,16183],{},[1708,34870,1710],{},[2505,34872,3958],{},[2247,34874,2659],{},[1753,34876,34877,34879],{},[898,34878,21035],{},[898,34880,16183],{},[1708,34882,2019],{},[2505,34884,4028],{},[1708,34886,1710],{},[3194,34888,34889],{"scriptlevel":2784,"displaystyle":1715},[2358,34890,34891,34894],{},[2505,34892,34893],{},"1375",[2505,34895,4008],{},[1708,34897,17816],{},[2505,34899,34900],{},"98,214",[902,34902,34903],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,34905,34906,1883],{},[883,34907,34909],{"className":34908},[886],[888,34910,34911],{"xmlns":890},[892,34912,34913,34955],{},[895,34914,34915,34923,34925,34931,34933,34939,34941,34950,34952],{},[4754,34916,34917,34919,34921],{},[898,34918,21035],{},[898,34920,16117],{},[898,34922,16183],{},[1708,34924,1710],{},[1753,34926,34927,34929],{},[898,34928,21035],{},[898,34930,16183],{},[1708,34932,2726],{},[1753,34934,34935,34937],{},[898,34936,1978],{},[898,34938,16183],{},[1708,34940,1710],{},[3194,34942,34943],{"scriptlevel":2784,"displaystyle":1715},[2358,34944,34945,34948],{},[2505,34946,34947],{},"3750",[2505,34949,4008],{},[1708,34951,17816],{},[2505,34953,34954],{},"267,857",[902,34956,34957],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,34959,34960,1883],{},[883,34961,34963],{"className":34962},[886],[888,34964,34965],{"xmlns":890},[892,34966,34967,35003],{},[895,34968,34969,34975,34977,34983,34985,34987,34989,34998,35000],{},[1753,34970,34971,34973],{},[898,34972,3455],{},[898,34974,16183],{},[1708,34976,1710],{},[1753,34978,34979,34981],{},[898,34980,21035],{},[898,34982,16183],{},[1708,34984,2726],{},[2505,34986,33039],{},[1708,34988,1710],{},[3194,34990,34991],{"scriptlevel":2784,"displaystyle":1715},[2358,34992,34993,34996],{},[2505,34994,34995],{},"4355",[2505,34997,4008],{},[1708,34999,17816],{},[2505,35001,35002],{},"311,071",[902,35004,35005],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,35007,35008,35064],{},[883,35009,35011],{"className":35010},[886],[888,35012,35013],{"xmlns":890},[892,35014,35015,35061],{},[895,35016,35017,35023,35025,35033,35035,35041,35043,35045,35054,35056,35058],{},[1753,35018,35019,35021],{},[898,35020,1981],{},[898,35022,16183],{},[1708,35024,1710],{},[4754,35026,35027,35029,35031],{},[898,35028,21035],{},[898,35030,16117],{},[898,35032,16183],{},[1708,35034,2726],{},[1753,35036,35037,35039],{},[898,35038,3455],{},[898,35040,16183],{},[1708,35042,1710],{},[1708,35044,2726],{},[3194,35046,35047],{"scriptlevel":2784,"displaystyle":1715},[2358,35048,35049,35052],{},[2505,35050,35051],{},"605",[2505,35053,4008],{},[1708,35055,17816],{},[1708,35057,2726],{},[2505,35059,35060],{},"43,214",[902,35062,35063],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,35066,35067,33209,35069,35090,35091,35094,35095,35118,35119,2155],{},[38,35068,33208],{},[883,35070,35072],{"className":35071},[886],[888,35073,35074],{"xmlns":890},[892,35075,35076,35088],{},[895,35077,35078,35080,35082,35084,35086],{},[898,35079,3455],{},[2247,35081,24176],{},[898,35083,24070],{},[2247,35085,24176],{},[898,35087,23999],{},[902,35089,30090],{"encoding":904}," stále uvažuje ",[38,35092,35093],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,35096,35098],{"className":35097},[886],[888,35099,35100],{"xmlns":890},[892,35101,35102,35115],{},[895,35103,35104,35106,35108,35111,35113],{},[898,35105,24206],{},[1708,35107,1710],{},[898,35109,35110],{},"B",[1708,35112,2726],{},[898,35114,1741],{},[902,35116,35117],{"encoding":904},"X = B - M"," dává ",[38,35120,33230,35121],{},[883,35122,35124],{"className":35123},[886],[888,35125,35126],{"xmlns":890},[892,35127,35128,35144],{},[895,35129,35130,35132,35134,35136,35138,35140,35142],{},[898,35131,3455],{},[2247,35133,24176],{},[898,35135,24070],{},[2247,35137,24176],{},[898,35139,23999],{},[2247,35141,24176],{},[898,35143,24206],{},[902,35145,24209],{"encoding":904},[115,35147,35149],{"id":35148},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,35151,32483],{"id":35152},"zadání-modelu-2",[724,35154,35155,35156,1729,35159,2980,35180,35193,35194,5149,35197,35210],{},"Rozšíření o ",[38,35157,35158],{},"čistý export",[883,35160,35162],{"className":35161},[886],[888,35163,35164],{"xmlns":890},[892,35165,35166,35178],{},[895,35167,35168,35170,35172,35174,35176],{},[898,35169,24206],{},[1708,35171,1710],{},[898,35173,35110],{},[1708,35175,2726],{},[898,35177,1741],{},[902,35179,35117],{"encoding":904},[883,35181,35183],{"className":35182},[886],[888,35184,35185],{"xmlns":890},[892,35186,35187,35191],{},[895,35188,35189],{},[898,35190,35110],{},[902,35192,35110],{"encoding":904}," je hrubý export (",[614,35195,35196],{},"brutto export",[883,35198,35200],{"className":35199},[886],[888,35201,35202],{"xmlns":890},[892,35203,35204,35208],{},[895,35205,35206],{},[898,35207,1741],{},[902,35209,1741],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,35212,35213],{},[883,35214,35216],{"className":35215},[886],[888,35217,35218],{"xmlns":890},[892,35219,35220,35240],{},[895,35221,35222,35224,35226,35228,35230,35236,35238],{},[898,35223,1741],{},[1708,35225,1710],{},[898,35227,1741],{},[1708,35229,1716],{"stretchy":1715},[1743,35231,35232,35234],{},[898,35233,21035],{},[898,35235,16117],{},[1708,35237,1721],{"stretchy":1715},[898,35239,2155],{"mathvariant":1759},[902,35241,35242],{"encoding":904},"M = M(Y_D).",[724,35244,35245],{},"Podmínka rovnováhy:",[724,35247,35248],{},[883,35249,35251],{"className":35250},[886],[888,35252,35253],{"xmlns":890},[892,35254,35255,35292],{},[895,35256,35257,35259,35261,35263,35265,35267,35269,35271,35273,35275,35277,35279,35281,35283,35285,35288,35290],{},[898,35258,21035],{},[1708,35260,1710],{},[898,35262,3455],{},[1708,35264,2019],{},[898,35266,24070],{},[1708,35268,2019],{},[898,35270,23999],{},[1708,35272,2019],{},[898,35274,35110],{},[1708,35276,2726],{},[898,35278,1741],{},[898,35280,2155],{"mathvariant":1759},[3213,35282],{"width":3215},[1708,35284,1716],{"stretchy":1715},[2505,35286,35287],{},"7.10",[2247,35289,207],{},[1708,35291,1721],{"stretchy":1715},[902,35293,35294],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,35296,32553],{"id":35297},"soustava-rovnic-2",[724,35299,33709,35300,35334,35335,2788],{},[883,35301,35303],{"className":35302},[886],[888,35304,35305],{"xmlns":890},[892,35306,35307,35331],{},[895,35308,35309,35315,35317,35323,35325],{},[1753,35310,35311,35313],{},[898,35312,24070],{},[1708,35314,2417],{},[1708,35316,1883],{"separator":1882},[1753,35318,35319,35321],{},[898,35320,23999],{},[1708,35322,2417],{},[1708,35324,1883],{"separator":1882},[1753,35326,35327,35329],{},[898,35328,35110],{},[1708,35330,2417],{},[902,35332,35333],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,35336,35338],{"className":35337},[886],[888,35339,35340],{"xmlns":890},[892,35341,35342,35366],{},[895,35343,35344,35346,35348,35350,35352,35354,35356,35362,35364],{},[898,35345,21035],{},[1708,35347,1883],{"separator":1882},[898,35349,3455],{},[1708,35351,1883],{"separator":1882},[898,35353,1978],{},[1708,35355,1883],{"separator":1882},[1743,35357,35358,35360],{},[898,35359,21035],{},[898,35361,16117],{},[1708,35363,1883],{"separator":1882},[898,35365,1741],{},[902,35367,35368],{"encoding":904},"Y, C, T, Y_D, M",[724,35370,35371],{},[883,35372,35374],{"className":35373},[886],[888,35375,35376],{"xmlns":890},[892,35377,35378,35562],{},[895,35379,35380,35554,35556,35558,35560],{},[2214,35381,35382,35414,35444,35472,35504],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,35383,35384,35390],{},[2221,35385,35386],{},[3194,35387,35388],{"scriptlevel":2784,"displaystyle":1882},[898,35389,3455],{},[2221,35391,35392],{},[3194,35393,35394],{"scriptlevel":2784,"displaystyle":1882},[895,35395,35396,35398,35400,35402,35404,35410,35412],{},[895,35397],{},[1708,35399,1710],{},[898,35401,3455],{},[1708,35403,1716],{"stretchy":1715},[1743,35405,35406,35408],{},[898,35407,21035],{},[898,35409,16117],{},[1708,35411,1721],{"stretchy":1715},[1708,35413,1883],{"separator":1882},[2218,35415,35416,35426],{},[2221,35417,35418],{},[3194,35419,35420],{"scriptlevel":2784,"displaystyle":1882},[1743,35421,35422,35424],{},[898,35423,21035],{},[898,35425,16117],{},[2221,35427,35428],{},[3194,35429,35430],{"scriptlevel":2784,"displaystyle":1882},[895,35431,35432,35434,35436,35438,35440,35442],{},[895,35433],{},[1708,35435,1710],{},[898,35437,21035],{},[1708,35439,2726],{},[898,35441,1978],{},[1708,35443,1883],{"separator":1882},[2218,35445,35446,35452],{},[2221,35447,35448],{},[3194,35449,35450],{"scriptlevel":2784,"displaystyle":1882},[898,35451,1978],{},[2221,35453,35454],{},[3194,35455,35456],{"scriptlevel":2784,"displaystyle":1882},[895,35457,35458,35460,35462,35464,35466,35468,35470],{},[895,35459],{},[1708,35461,1710],{},[898,35463,1978],{},[1708,35465,1716],{"stretchy":1715},[898,35467,21035],{},[1708,35469,1721],{"stretchy":1715},[1708,35471,1883],{"separator":1882},[2218,35473,35474,35480],{},[2221,35475,35476],{},[3194,35477,35478],{"scriptlevel":2784,"displaystyle":1882},[898,35479,1741],{},[2221,35481,35482],{},[3194,35483,35484],{"scriptlevel":2784,"displaystyle":1882},[895,35485,35486,35488,35490,35492,35494,35500,35502],{},[895,35487],{},[1708,35489,1710],{},[898,35491,1741],{},[1708,35493,1716],{"stretchy":1715},[1743,35495,35496,35498],{},[898,35497,21035],{},[898,35499,16117],{},[1708,35501,1721],{"stretchy":1715},[1708,35503,1883],{"separator":1882},[2218,35505,35506,35512],{},[2221,35507,35508],{},[3194,35509,35510],{"scriptlevel":2784,"displaystyle":1882},[898,35511,21035],{},[2221,35513,35514],{},[3194,35515,35516],{"scriptlevel":2784,"displaystyle":1882},[895,35517,35518,35520,35522,35524,35526,35532,35534,35540,35542,35548,35550,35552],{},[895,35519],{},[1708,35521,1710],{},[898,35523,3455],{},[1708,35525,2019],{},[1753,35527,35528,35530],{},[898,35529,24070],{},[1708,35531,2417],{},[1708,35533,2019],{},[1753,35535,35536,35538],{},[898,35537,23999],{},[1708,35539,2417],{},[1708,35541,2019],{},[1753,35543,35544,35546],{},[898,35545,35110],{},[1708,35547,2417],{},[1708,35549,2726],{},[898,35551,1741],{},[898,35553,2155],{"mathvariant":1759},[3213,35555],{"width":3215},[1708,35557,1716],{"stretchy":1715},[2505,35559,35287],{},[1708,35561,1721],{"stretchy":1715},[902,35563,35564],{"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)",[198,35566,35568],{"id":35567},"příklad-75","Příklad 7.5",[724,35570,35571,35572,1343,35603,1343,35630,1343,35650,1343,35672,1343,35694,35716],{},"Dáno: ",[883,35573,35575],{"className":35574},[886],[888,35576,35577],{"xmlns":890},[892,35578,35579,35600],{},[895,35580,35581,35583,35585,35587,35589,35595,35597],{},[898,35582,3455],{},[1708,35584,1710],{},[2505,35586,11568],{},[2247,35588,2659],{},[1743,35590,35591,35593],{},[898,35592,21035],{},[898,35594,16117],{},[1708,35596,2019],{},[2505,35598,35599],{},"750",[902,35601,35602],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,35604,35606],{"className":35605},[886],[888,35607,35608],{"xmlns":890},[892,35609,35610,35627],{},[895,35611,35612,35614,35616,35619,35621],{},[898,35613,1741],{},[1708,35615,1710],{},[2505,35617,35618],{},"0,15",[2247,35620,2659],{},[1743,35622,35623,35625],{},[898,35624,21035],{},[898,35626,16117],{},[902,35628,35629],{"encoding":904},"M = 0{,}15\\,Y_D",[883,35631,35633],{"className":35632},[886],[888,35634,35635],{"xmlns":890},[892,35636,35637,35647],{},[895,35638,35639,35641,35643,35645],{},[898,35640,1978],{},[1708,35642,1710],{},[2505,35644,11575],{},[898,35646,21035],{},[902,35648,35649],{"encoding":904},"T = 0{,}25Y",[883,35651,35653],{"className":35652},[886],[888,35654,35655],{"xmlns":890},[892,35656,35657,35669],{},[895,35658,35659,35665,35667],{},[1753,35660,35661,35663],{},[898,35662,24070],{},[1708,35664,2417],{},[1708,35666,1710],{},[2505,35668,11040],{},[902,35670,35671],{"encoding":904},"I^* = 500",[883,35673,35675],{"className":35674},[886],[888,35676,35677],{"xmlns":890},[892,35678,35679,35691],{},[895,35680,35681,35687,35689],{},[1753,35682,35683,35685],{},[898,35684,23999],{},[1708,35686,2417],{},[1708,35688,1710],{},[2505,35690,9660],{},[902,35692,35693],{"encoding":904},"G^* = 150",[883,35695,35697],{"className":35696},[886],[888,35698,35699],{"xmlns":890},[892,35700,35701,35713],{},[895,35702,35703,35709,35711],{},[1753,35704,35705,35707],{},[898,35706,35110],{},[1708,35708,2417],{},[1708,35710,1710],{},[2505,35712,4344],{},[902,35714,35715],{"encoding":904},"B^* = 800",". Soustava:",[724,35718,35719],{},[883,35720,35722],{"className":35721},[886],[888,35723,35724],{"xmlns":890},[892,35725,35726,35944],{},[2214,35727,35728,35774,35816,35852,35894],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,35729,35730,35746],{},[2221,35731,35732],{},[3194,35733,35734],{"scriptlevel":2784,"displaystyle":1882},[895,35735,35736,35738,35740,35742,35744],{},[1708,35737,1716],{"stretchy":1715},[898,35739,5498],{},[2505,35741,2507],{},[1708,35743,1721],{"stretchy":1715},[2247,35745,14279],{},[2221,35747,35748],{},[3194,35749,35750],{"scriptlevel":2784,"displaystyle":1882},[895,35751,35752,35754,35756,35758,35760,35762,35768,35770,35772],{},[895,35753],{},[898,35755,3455],{},[1708,35757,1710],{},[2505,35759,11568],{},[2247,35761,2659],{},[1743,35763,35764,35766],{},[898,35765,21035],{},[898,35767,16117],{},[1708,35769,2019],{},[2505,35771,35599],{},[1708,35773,1883],{"separator":1882},[2218,35775,35776,35792],{},[2221,35777,35778],{},[3194,35779,35780],{"scriptlevel":2784,"displaystyle":1882},[895,35781,35782,35784,35786,35788,35790],{},[1708,35783,1716],{"stretchy":1715},[898,35785,5498],{},[2505,35787,3132],{},[1708,35789,1721],{"stretchy":1715},[2247,35791,14279],{},[2221,35793,35794],{},[3194,35795,35796],{"scriptlevel":2784,"displaystyle":1882},[895,35797,35798,35800,35806,35808,35810,35812,35814],{},[895,35799],{},[1743,35801,35802,35804],{},[898,35803,21035],{},[898,35805,16117],{},[1708,35807,1710],{},[898,35809,21035],{},[1708,35811,2726],{},[898,35813,1978],{},[1708,35815,1883],{"separator":1882},[2218,35817,35818,35834],{},[2221,35819,35820],{},[3194,35821,35822],{"scriptlevel":2784,"displaystyle":1882},[895,35823,35824,35826,35828,35830,35832],{},[1708,35825,1716],{"stretchy":1715},[898,35827,5498],{},[2505,35829,3121],{},[1708,35831,1721],{"stretchy":1715},[2247,35833,14279],{},[2221,35835,35836],{},[3194,35837,35838],{"scriptlevel":2784,"displaystyle":1882},[895,35839,35840,35842,35844,35846,35848,35850],{},[895,35841],{},[898,35843,1978],{},[1708,35845,1710],{},[2505,35847,11575],{},[898,35849,21035],{},[1708,35851,1883],{"separator":1882},[2218,35853,35854,35870],{},[2221,35855,35856],{},[3194,35857,35858],{"scriptlevel":2784,"displaystyle":1882},[895,35859,35860,35862,35864,35866,35868],{},[1708,35861,1716],{"stretchy":1715},[898,35863,5498],{},[2505,35865,5867],{},[1708,35867,1721],{"stretchy":1715},[2247,35869,14279],{},[2221,35871,35872],{},[3194,35873,35874],{"scriptlevel":2784,"displaystyle":1882},[895,35875,35876,35878,35880,35882,35884,35886,35892],{},[895,35877],{},[898,35879,1741],{},[1708,35881,1710],{},[2505,35883,35618],{},[2247,35885,2659],{},[1743,35887,35888,35890],{},[898,35889,21035],{},[898,35891,16117],{},[1708,35893,1883],{"separator":1882},[2218,35895,35896,35912],{},[2221,35897,35898],{},[3194,35899,35900],{"scriptlevel":2784,"displaystyle":1882},[895,35901,35902,35904,35906,35908,35910],{},[1708,35903,1716],{"stretchy":1715},[898,35905,5498],{},[2505,35907,3993],{},[1708,35909,1721],{"stretchy":1715},[2247,35911,14279],{},[2221,35913,35914],{},[3194,35915,35916],{"scriptlevel":2784,"displaystyle":1882},[895,35917,35918,35920,35922,35924,35926,35928,35930,35932,35934,35936,35938,35940,35942],{},[895,35919],{},[898,35921,21035],{},[1708,35923,1710],{},[898,35925,3455],{},[1708,35927,2019],{},[2505,35929,11040],{},[1708,35931,2019],{},[2505,35933,9660],{},[1708,35935,2019],{},[2505,35937,4344],{},[1708,35939,2726],{},[898,35941,1741],{},[898,35943,2155],{"mathvariant":1759},[902,35945,35946],{"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}",[724,35948,35949,35950,35984],{},"Postupná substituce — z (r3) do (r2): ",[883,35951,35953],{"className":35952},[886],[888,35954,35955],{"xmlns":890},[892,35956,35957,35981],{},[895,35958,35959,35965,35967,35969,35971,35973,35975,35977,35979],{},[1743,35960,35961,35963],{},[898,35962,21035],{},[898,35964,16117],{},[1708,35966,1710],{},[898,35968,21035],{},[1708,35970,2726],{},[2505,35972,11575],{},[898,35974,21035],{},[1708,35976,1710],{},[2505,35978,11568],{},[898,35980,21035],{},[902,35982,35983],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,35986,35987],{},[883,35988,35990],{"className":35989},[886],[888,35991,35992],{"xmlns":890},[892,35993,35994,36035],{},[895,35995,35996,35998,36000,36002,36004,36006,36008,36010,36012,36014,36016,36018,36020,36022,36024,36027,36029,36031,36033],{},[1708,35997,1716],{"stretchy":1715},[898,35999,5498],{},[2505,36001,3947],{},[1708,36003,1721],{"stretchy":1715},[2247,36005,14279],{},[898,36007,3455],{},[1708,36009,1710],{},[2505,36011,11568],{},[1708,36013,3703],{},[2505,36015,11568],{},[898,36017,21035],{},[1708,36019,2019],{},[2505,36021,35599],{},[1708,36023,1710],{},[2505,36025,36026],{},"0,5625",[898,36028,21035],{},[1708,36030,2019],{},[2505,36032,35599],{},[1708,36034,1883],{"separator":1882},[902,36036,36037],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,36039,36040],{},[883,36041,36043],{"className":36042},[886],[888,36044,36045],{"xmlns":890},[892,36046,36047,36080],{},[895,36048,36049,36051,36053,36055,36057,36059,36061,36063,36065,36067,36069,36071,36073,36076,36078],{},[1708,36050,1716],{"stretchy":1715},[898,36052,5498],{},[2505,36054,5967],{},[1708,36056,1721],{"stretchy":1715},[2247,36058,14279],{},[898,36060,1741],{},[1708,36062,1710],{},[2505,36064,35618],{},[1708,36066,3703],{},[2505,36068,11568],{},[898,36070,21035],{},[1708,36072,1710],{},[2505,36074,36075],{},"0,1125",[898,36077,21035],{},[898,36079,2155],{"mathvariant":1759},[902,36081,36082],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,36084,36085],{},"Dosazením do (r5):",[724,36087,36088],{},[883,36089,36091],{"className":36090},[886],[888,36092,36093],{"xmlns":890},[892,36094,36095,36139],{},[895,36096,36097,36099,36101,36103,36105,36107,36109,36111,36113,36115,36117,36119,36121,36123,36125,36127,36129,36132,36134,36136],{},[898,36098,21035],{},[1708,36100,1710],{},[2505,36102,36026],{},[898,36104,21035],{},[1708,36106,2019],{},[2505,36108,35599],{},[1708,36110,2019],{},[2505,36112,11040],{},[1708,36114,2019],{},[2505,36116,9660],{},[1708,36118,2019],{},[2505,36120,4344],{},[1708,36122,2726],{},[2505,36124,36075],{},[898,36126,21035],{},[1708,36128,1710],{},[2505,36130,36131],{},"0,45",[898,36133,21035],{},[1708,36135,2019],{},[2505,36137,36138],{},"2200.",[902,36140,36141],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,36143,36144,36145,17508,36167,36190],{},"Odtud ",[883,36146,36148],{"className":36147},[886],[888,36149,36150],{"xmlns":890},[892,36151,36152,36164],{},[895,36153,36154,36157,36159,36161],{},[2505,36155,36156],{},"0,55",[898,36158,21035],{},[1708,36160,1710],{},[2505,36162,36163],{},"2200",[902,36165,36166],{"encoding":904},"0{,}55Y = 2200",[883,36168,36170],{"className":36169},[886],[888,36171,36172],{"xmlns":890},[892,36173,36174,36187],{},[895,36175,36176,36182,36184],{},[1753,36177,36178,36180],{},[898,36179,21035],{},[898,36181,16183],{},[1708,36183,1710],{},[2505,36185,36186],{},"4000",[902,36188,36189],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,36192,36193,36216,36248,36283,36316,36352],{},[123,36194,36195,1883],{},[883,36196,36198],{"className":36197},[886],[888,36199,36200],{"xmlns":890},[892,36201,36202,36214],{},[895,36203,36204,36210,36212],{},[1753,36205,36206,36208],{},[898,36207,21035],{},[898,36209,16183],{},[1708,36211,1710],{},[2505,36213,36186],{},[902,36215,36189],{"encoding":904},[123,36217,36218,1883],{},[883,36219,36221],{"className":36220},[886],[888,36222,36223],{"xmlns":890},[892,36224,36225,36245],{},[895,36226,36227,36233,36235,36237,36239,36241,36243],{},[1753,36228,36229,36231],{},[898,36230,1978],{},[898,36232,16183],{},[1708,36234,1710],{},[2505,36236,11575],{},[1708,36238,3703],{},[2505,36240,36186],{},[1708,36242,1710],{},[2505,36244,11613],{},[902,36246,36247],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,36249,36250,1883],{},[883,36251,36253],{"className":36252},[886],[888,36254,36255],{"xmlns":890},[892,36256,36257,36280],{},[895,36258,36259,36267,36269,36271,36273,36275,36277],{},[4754,36260,36261,36263,36265],{},[898,36262,21035],{},[898,36264,16117],{},[898,36266,16183],{},[1708,36268,1710],{},[2505,36270,11568],{},[1708,36272,3703],{},[2505,36274,36186],{},[1708,36276,1710],{},[2505,36278,36279],{},"3000",[902,36281,36282],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,36284,36285,1883],{},[883,36286,36288],{"className":36287},[886],[888,36289,36290],{"xmlns":890},[892,36291,36292,36313],{},[895,36293,36294,36300,36302,36304,36306,36308,36310],{},[1753,36295,36296,36298],{},[898,36297,1741],{},[898,36299,16183],{},[1708,36301,1710],{},[2505,36303,35618],{},[1708,36305,3703],{},[2505,36307,36279],{},[1708,36309,1710],{},[2505,36311,36312],{},"450",[902,36314,36315],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,36317,36318,1883],{},[883,36319,36321],{"className":36320},[886],[888,36322,36323],{"xmlns":890},[892,36324,36325,36349],{},[895,36326,36327,36333,36335,36337,36339,36341,36343,36345,36347],{},[1753,36328,36329,36331],{},[898,36330,3455],{},[898,36332,16183],{},[1708,36334,1710],{},[2505,36336,11568],{},[1708,36338,3703],{},[2505,36340,36279],{},[1708,36342,2019],{},[2505,36344,35599],{},[1708,36346,1710],{},[2505,36348,36279],{},[902,36350,36351],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,36353,36354,36394],{},[883,36355,36357],{"className":36356},[886],[888,36358,36359],{"xmlns":890},[892,36360,36361,36391],{},[895,36362,36363,36369,36371,36379,36381,36387,36389],{},[1753,36364,36365,36367],{},[898,36366,1981],{},[898,36368,16183],{},[1708,36370,1710],{},[4754,36372,36373,36375,36377],{},[898,36374,21035],{},[898,36376,16117],{},[898,36378,16183],{},[1708,36380,2726],{},[1753,36382,36383,36385],{},[898,36384,3455],{},[898,36386,16183],{},[1708,36388,1710],{},[2505,36390,2784],{},[902,36392,36393],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,36396,36397,36399,36400,1343,36417,1771,36438,36463,36464,36466,36467,36480,36481,2155],{},[38,36398,33208],{}," Modely ",[883,36401,36403],{"className":36402},[886],[888,36404,36405],{"xmlns":890},[892,36406,36407,36415],{},[895,36408,36409,36411,36413],{},[898,36410,3455],{},[2247,36412,24176],{},[898,36414,24070],{},[902,36416,24181],{"encoding":904},[883,36418,36420],{"className":36419},[886],[888,36421,36422],{"xmlns":890},[892,36423,36424,36436],{},[895,36425,36426,36428,36430,36432,36434],{},[898,36427,3455],{},[2247,36429,24176],{},[898,36431,24070],{},[2247,36433,24176],{},[898,36435,23999],{},[902,36437,30090],{"encoding":904},[883,36439,36441],{"className":36440},[886],[888,36442,36443],{"xmlns":890},[892,36444,36445,36461],{},[895,36446,36447,36449,36451,36453,36455,36457,36459],{},[898,36448,3455],{},[2247,36450,24176],{},[898,36452,24070],{},[2247,36454,24176],{},[898,36456,23999],{},[2247,36458,24176],{},[898,36460,24206],{},[902,36462,24209],{"encoding":904}," pokládají investice za ",[38,36465,2079],{},". To není realistické — investice závisejí na úrokové míře ",[883,36468,36470],{"className":36469},[886],[888,36471,36472],{"xmlns":890},[892,36473,36474,36478],{},[895,36475,36476],{},[898,36477,5498],{},[902,36479,5498],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,36482,36483],{},"model IS-LM",[115,36485,36487],{"id":36486},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,36489,36490,36491,36495,36496,36499,36500,36503],{},"V článku ",[207,36492,36494],{"className":36493,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,36497,36498],{},"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 ",[38,36501,36502],{},"výraznější"," než v mikroekonomických modelech.",[724,36505,36506],{},[3372,36507],{"alt":36508,"className":36509,"src":36510},"imek-multiplikatorovy-efekt-chain",[210,3376],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,36512,24050,36513,1343,36530,1343,36551,36576,36577,36580,36581,36599,36600,36618,36619,36637,36638,36641,36642,1343,36659,36676,36677,36679],{},[883,36514,36516],{"className":36515},[886],[888,36517,36518],{"xmlns":890},[892,36519,36520,36528],{},[895,36521,36522,36524,36526],{},[898,36523,3455],{},[2247,36525,24176],{},[898,36527,24070],{},[902,36529,24181],{"encoding":904},[883,36531,36533],{"className":36532},[886],[888,36534,36535],{"xmlns":890},[892,36536,36537,36549],{},[895,36538,36539,36541,36543,36545,36547],{},[898,36540,3455],{},[2247,36542,24176],{},[898,36544,24070],{},[2247,36546,24176],{},[898,36548,23999],{},[902,36550,30090],{"encoding":904},[883,36552,36554],{"className":36553},[886],[888,36555,36556],{"xmlns":890},[892,36557,36558,36574],{},[895,36559,36560,36562,36564,36566,36568,36570,36572],{},[898,36561,3455],{},[2247,36563,24176],{},[898,36565,24070],{},[2247,36567,24176],{},[898,36569,23999],{},[2247,36571,24176],{},[898,36573,24206],{},[902,36575,24209],{"encoding":904}," se vyšetřuje vliv změn ",[38,36578,36579],{},"exogenních"," veličin (plánovaných investic ",[883,36582,36584],{"className":36583},[886],[888,36585,36586],{"xmlns":890},[892,36587,36588,36596],{},[895,36589,36590],{},[1753,36591,36592,36594],{},[898,36593,24070],{},[1708,36595,2417],{},[902,36597,36598],{"encoding":904},"I^*",", vládních výdajů ",[883,36601,36603],{"className":36602},[886],[888,36604,36605],{"xmlns":890},[892,36606,36607,36615],{},[895,36608,36609],{},[1753,36610,36611,36613],{},[898,36612,23999],{},[1708,36614,2417],{},[902,36616,36617],{"encoding":904},"G^*",", exportu ",[883,36620,36622],{"className":36621},[886],[888,36623,36624],{"xmlns":890},[892,36625,36626,36634],{},[895,36627,36628],{},[1753,36629,36630,36632],{},[898,36631,35110],{},[1708,36633,2417],{},[902,36635,36636],{"encoding":904},"B^*",") na změny ",[38,36639,36640],{},"endogenních"," rovnovážných veličin (",[883,36643,36645],{"className":36644},[886],[888,36646,36647],{"xmlns":890},[892,36648,36649,36657],{},[895,36650,36651],{},[1753,36652,36653,36655],{},[898,36654,21035],{},[898,36656,16183],{},[902,36658,25785],{"encoding":904},[883,36660,36662],{"className":36661},[886],[888,36663,36664],{"xmlns":890},[892,36665,36666,36674],{},[895,36667,36668],{},[1753,36669,36670,36672],{},[898,36671,3455],{},[898,36673,16183],{},[902,36675,25844],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,36678,29848],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,36681,36683],{"id":36682},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,36685,32754,36686,36709,36710,36754],{},[883,36687,36689],{"className":36688},[886],[888,36690,36691],{"xmlns":890},[892,36692,36693,36707],{},[895,36694,36695,36697,36699,36701,36703,36705],{},[898,36696,3455],{},[1708,36698,1710],{},[898,36700,207],{},[898,36702,21035],{},[1708,36704,2019],{},[898,36706,1923],{},[902,36708,30786],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,36711,36713],{"className":36712},[886],[888,36714,36715],{"xmlns":890},[892,36716,36717,36751],{},[895,36718,36719,36725,36727],{},[1753,36720,36721,36723],{},[898,36722,21035],{},[898,36724,16183],{},[1708,36726,1710],{},[3194,36728,36729],{"scriptlevel":2784,"displaystyle":1882},[2358,36730,36731,36743],{},[895,36732,36733,36735,36737],{},[898,36734,1923],{},[1708,36736,2019],{},[1753,36738,36739,36741],{},[898,36740,24070],{},[1708,36742,2417],{},[895,36744,36745,36747,36749],{},[2505,36746,2507],{},[1708,36748,2726],{},[898,36750,207],{},[902,36752,36753],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,36756,36757],{},[883,36758,36760],{"className":36759},[886],[888,36761,36762],{"xmlns":890},[892,36763,36764,36833],{},[895,36765,36766,36784,36786,36816,36818],{},[2358,36767,36768,36778],{},[895,36769,36770,36772],{},[898,36771,7252],{"mathvariant":1759},[1753,36773,36774,36776],{},[898,36775,21035],{},[898,36777,16183],{},[895,36779,36780,36782],{},[898,36781,7252],{"mathvariant":1759},[898,36783,207],{},[1708,36785,1710],{},[2358,36787,36788,36800],{},[895,36789,36790,36792,36794],{},[898,36791,1923],{},[1708,36793,2019],{},[1753,36795,36796,36798],{},[898,36797,24070],{},[1708,36799,2417],{},[895,36801,36802,36804,36806,36808,36810],{},[1708,36803,1716],{"stretchy":1715},[2505,36805,2507],{},[1708,36807,2726],{},[898,36809,207],{},[1753,36811,36812,36814],{},[1708,36813,1721],{"stretchy":1715},[2505,36815,3132],{},[3213,36817],{"width":3215},[895,36819,36820,36823,36830],{},[2247,36821,36822],{},"(multiplik",[20297,36824,36825,36827],{"accent":1882},[2247,36826,207],{},[1708,36828,36829],{},"ˊ",[2247,36831,36832],{},"tor MPC)",[902,36834,36835],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,36837,36838],{},[883,36839,36841],{"className":36840},[886],[888,36842,36843],{"xmlns":890},[892,36844,36845,36914],{},[895,36846,36847,36865,36867,36879,36881],{},[2358,36848,36849,36859],{},[895,36850,36851,36853],{},[898,36852,7252],{"mathvariant":1759},[1753,36854,36855,36857],{},[898,36856,21035],{},[898,36858,16183],{},[895,36860,36861,36863],{},[898,36862,7252],{"mathvariant":1759},[898,36864,1923],{},[1708,36866,1710],{},[2358,36868,36869,36871],{},[2505,36870,2507],{},[895,36872,36873,36875,36877],{},[2505,36874,2507],{},[1708,36876,2726],{},[898,36878,207],{},[3213,36880],{"width":3215},[895,36882,36883,36885,36891,36894,36901,36904,36911],{},[2247,36884,36822],{},[20297,36886,36887,36889],{"accent":1882},[2247,36888,207],{},[1708,36890,36829],{},[2247,36892,36893],{},"tor autonomn",[20297,36895,36896,36899],{"accent":1882},[2247,36897,36898],{},"ı",[1708,36900,36829],{},[2247,36902,36903],{}," spot",[20297,36905,36906,36908],{"accent":1882},[2247,36907,5498],{},[1708,36909,36910],{},"ˇ",[2247,36912,36913],{},"eby)",[902,36915,36916],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,36918,36919],{},[883,36920,36922],{"className":36921},[886],[888,36923,36924],{"xmlns":890},[892,36925,36926,36993],{},[895,36927,36928,36950,36952,36964,36966,36978,36980],{},[2358,36929,36930,36940],{},[895,36931,36932,36934],{},[898,36933,7252],{"mathvariant":1759},[1753,36935,36936,36938],{},[898,36937,21035],{},[898,36939,16183],{},[895,36941,36942,36944],{},[898,36943,7252],{"mathvariant":1759},[1753,36945,36946,36948],{},[898,36947,24070],{},[1708,36949,2417],{},[1708,36951,1710],{},[2358,36953,36954,36956],{},[2505,36955,2507],{},[895,36957,36958,36960,36962],{},[2505,36959,2507],{},[1708,36961,2726],{},[898,36963,207],{},[1708,36965,1710],{},[2358,36967,36968,36970],{},[2505,36969,2507],{},[895,36971,36972,36974,36976],{},[898,36973,1741],{},[898,36975,1747],{},[898,36977,1981],{},[3213,36979],{"width":3215},[895,36981,36982,36984,36990],{},[2247,36983,36822],{},[20297,36985,36986,36988],{"accent":1882},[2247,36987,207],{},[1708,36989,36829],{},[2247,36991,36992],{},"tor investic)",[902,36994,36995],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1636,36997,36998],{},[724,36999,37000,37002,37003,37006,37007,37020,37021,37038,37039,37057,37058,37102,37103,33279,37120,37122,37123,37140],{},[883,37001,2518],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,37004,37005],{},"důchodem","; z něj se utratí ",[883,37008,37010],{"className":37009},[886],[888,37011,37012],{"xmlns":890},[892,37013,37014,37018],{},[895,37015,37016],{},[898,37017,207],{},[902,37019,207],{"encoding":904}," Kč (= ",[883,37022,37024],{"className":37023},[886],[888,37025,37026],{"xmlns":890},[892,37027,37028,37036],{},[895,37029,37030,37032,37034],{},[898,37031,1741],{},[898,37033,1747],{},[898,37035,3455],{},[902,37037,29915],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,37040,37042],{"className":37041},[886],[888,37043,37044],{"xmlns":890},[892,37045,37046,37054],{},[895,37047,37048],{},[1753,37049,37050,37052],{},[898,37051,207],{},[2505,37053,3132],{},[902,37055,37056],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,37059,37061],{"className":37060},[886],[888,37062,37063],{"xmlns":890},[892,37064,37065,37099],{},[895,37066,37067,37069,37071,37073,37075,37081,37083,37085,37087],{},[2505,37068,2507],{},[1708,37070,2019],{},[898,37072,207],{},[1708,37074,2019],{},[1753,37076,37077,37079],{},[898,37078,207],{},[2505,37080,3132],{},[1708,37082,2019],{},[1708,37084,29975],{},[1708,37086,1710],{},[2358,37088,37089,37091],{},[2505,37090,2507],{},[895,37092,37093,37095,37097],{},[2505,37094,2507],{},[1708,37096,2726],{},[898,37098,207],{},[902,37100,37101],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,37104,37106],{"className":37105},[886],[888,37107,37108],{"xmlns":890},[892,37109,37110,37118],{},[895,37111,37112],{},[1753,37113,37114,37116],{},[898,37115,21035],{},[898,37117,16183],{},[902,37119,25785],{"encoding":904},[38,37121,5935],{}," než korunu — čím vyšší ",[883,37124,37126],{"className":37125},[886],[888,37127,37128],{"xmlns":890},[892,37129,37130,37138],{},[895,37131,37132,37134,37136],{},[898,37133,1741],{},[898,37135,1747],{},[898,37137,3455],{},[902,37139,29915],{"encoding":904},", tím silnější multiplikační efekt.",[724,37142,37143,37146,37147,37173,37174,37177,37178,1771,37199,37224,37225,2155],{},[38,37144,37145],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,37148,37150],{"className":37149},[886],[888,37151,37152],{"xmlns":890},[892,37153,37154,37170],{},[895,37155,37156],{},[3194,37157,37158],{"scriptlevel":2784,"displaystyle":1715},[2358,37159,37160,37162],{},[2505,37161,2507],{},[895,37163,37164,37166,37168],{},[2505,37165,2507],{},[1708,37167,2726],{},[898,37169,207],{},[902,37171,37172],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,37175,37176],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,37179,37181],{"className":37180},[886],[888,37182,37183],{"xmlns":890},[892,37184,37185,37197],{},[895,37186,37187,37189,37191,37193,37195],{},[898,37188,3455],{},[2247,37190,24176],{},[898,37192,24070],{},[2247,37194,24176],{},[898,37196,23999],{},[902,37198,30090],{"encoding":904},[883,37200,37202],{"className":37201},[886],[888,37203,37204],{"xmlns":890},[892,37205,37206,37222],{},[895,37207,37208,37210,37212,37214,37216,37218,37220],{},[898,37209,3455],{},[2247,37211,24176],{},[898,37213,24070],{},[2247,37215,24176],{},[898,37217,23999],{},[2247,37219,24176],{},[898,37221,24206],{},[902,37223,24209],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,37226,37228],{"className":37227,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,37230,37232],{"id":37231},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,37234,24050,37235,1343,37252,1771,37273,24055,37298,1695,37301,37322,37323,1729,37326,37339,37340,3136,37369,37386,37387,37390,37391,37393,37394,37415],{},[883,37236,37238],{"className":37237},[886],[888,37239,37240],{"xmlns":890},[892,37241,37242,37250],{},[895,37243,37244,37246,37248],{},[898,37245,3455],{},[2247,37247,24176],{},[898,37249,24070],{},[902,37251,24181],{"encoding":904},[883,37253,37255],{"className":37254},[886],[888,37256,37257],{"xmlns":890},[892,37258,37259,37271],{},[895,37260,37261,37263,37265,37267,37269],{},[898,37262,3455],{},[2247,37264,24176],{},[898,37266,24070],{},[2247,37268,24176],{},[898,37270,23999],{},[902,37272,30090],{"encoding":904},[883,37274,37276],{"className":37275},[886],[888,37277,37278],{"xmlns":890},[892,37279,37280,37296],{},[895,37281,37282,37284,37286,37288,37290,37292,37294],{},[898,37283,3455],{},[2247,37285,24176],{},[898,37287,24070],{},[2247,37289,24176],{},[898,37291,23999],{},[2247,37293,24176],{},[898,37295,24206],{},[902,37297,24209],{"encoding":904},[38,37299,37300],{},"investice konstantní",[883,37302,37304],{"className":37303},[886],[888,37305,37306],{"xmlns":890},[892,37307,37308,37320],{},[895,37309,37310,37312,37314],{},[898,37311,24070],{},[1708,37313,1710],{},[1753,37315,37316,37318],{},[898,37317,24070],{},[1708,37319,2417],{},[902,37321,24081],{"encoding":904},"). Reálnější je předpoklad, že ",[38,37324,37325],{},"investice závisejí na úrokové míře",[883,37327,37329],{"className":37328},[886],[888,37330,37331],{"xmlns":890},[892,37332,37333,37337],{},[895,37334,37335],{},[898,37336,5498],{},[902,37338,5498],{"encoding":904}," — klesající funkce ",[883,37341,37343],{"className":37342},[886],[888,37344,37345],{"xmlns":890},[892,37346,37347,37367],{},[895,37348,37349,37351,37353,37355,37357,37359,37361,37363,37365],{},[898,37350,24070],{},[1708,37352,1716],{"stretchy":1715},[898,37354,5498],{},[1708,37356,1721],{"stretchy":1715},[1708,37358,1710],{},[898,37360,14142],{},[898,37362,5498],{},[1708,37364,2019],{},[898,37366,2364],{},[902,37368,27633],{"encoding":904},[883,37370,37372],{"className":37371},[886],[888,37373,37374],{"xmlns":890},[892,37375,37376,37384],{},[895,37377,37378,37380,37382],{},[898,37379,14142],{},[1708,37381,2932],{},[2505,37383,2784],{},[902,37385,24401],{"encoding":904},". Přidáním ",[38,37388,37389],{},"trhu peněz"," k trhu zboží vzniká model ",[38,37392,23899],{}," se dvěma neznámými ",[883,37395,37397],{"className":37396},[886],[888,37398,37399],{"xmlns":890},[892,37400,37401,37413],{},[895,37402,37403,37405,37407,37409,37411],{},[1708,37404,1716],{"stretchy":1715},[898,37406,21035],{},[1708,37408,1883],{"separator":1882},[898,37410,5498],{},[1708,37412,1721],{"stretchy":1715},[902,37414,30020],{"encoding":904}," a dvěma rovnicemi:",[120,37417,37418,37468],{},[123,37419,37420,1695,37422,37424,37425,37446,37447,2155],{},[38,37421,27721],{},[614,37423,23941],{},") — klesající přímka v rovině ",[883,37426,37428],{"className":37427},[886],[888,37429,37430],{"xmlns":890},[892,37431,37432,37444],{},[895,37433,37434,37436,37438,37440,37442],{},[1708,37435,1716],{"stretchy":1715},[898,37437,5498],{},[1708,37439,1883],{"separator":1882},[898,37441,21035],{},[1708,37443,1721],{"stretchy":1715},[902,37445,24822],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,37448,37450],{"className":37449},[886],[888,37451,37452],{"xmlns":890},[892,37453,37454,37466],{},[895,37455,37456,37458,37460,37462,37464],{},[898,37457,21035],{},[1708,37459,1710],{},[898,37461,3455],{},[1708,37463,2019],{},[898,37465,24070],{},[902,37467,26625],{"encoding":904},[123,37469,37470,1695,37472,37474,37475,2980,37500,37546],{},[38,37471,27920],{},[614,37473,23948],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,37476,37478],{"className":37477},[886],[888,37479,37480],{"xmlns":890},[892,37481,37482,37498],{},[895,37483,37484,37490,37492],{},[1753,37485,37486,37488],{},[898,37487,1741],{},[898,37489,16117],{},[1708,37491,1710],{},[1753,37493,37494,37496],{},[898,37495,1741],{},[1708,37497,2417],{},[902,37499,25363],{"encoding":904},[883,37501,37503],{"className":37502},[886],[888,37504,37505],{"xmlns":890},[892,37506,37507,37543],{},[895,37508,37509,37515,37517,37523,37525,37527,37533,37535,37537],{},[1753,37510,37511,37513],{},[898,37512,1741],{},[898,37514,16117],{},[1708,37516,1710],{},[1743,37518,37519,37521],{},[898,37520,25121],{},[2505,37522,2507],{},[898,37524,21035],{},[1708,37526,2019],{},[1743,37528,37529,37531],{},[898,37530,25121],{},[2505,37532,3132],{},[898,37534,5498],{},[1708,37536,2019],{},[1743,37538,37539,37541],{},[898,37540,25121],{},[2505,37542,3121],{},[902,37544,37545],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,37548,37549,1729,37552,37585,37586,37588,37589,37591],{},[38,37550,37551],{},"Simultánní rovnovážný bod",[883,37553,37555],{"className":37554},[886],[888,37556,37557],{"xmlns":890},[892,37558,37559,37583],{},[895,37560,37561,37563,37565,37567,37573,37575,37581],{},[898,37562,16183],{},[1708,37564,1710],{},[1708,37566,1716],{"stretchy":1715},[1753,37568,37569,37571],{},[898,37570,5498],{},[898,37572,16183],{},[1708,37574,1883],{"separator":1882},[1753,37576,37577,37579],{},[898,37578,21035],{},[898,37580,16183],{},[1708,37582,1721],{"stretchy":1715},[902,37584,28012],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,37587,23986],{}," (posun IS) a ",[38,37590,24017],{}," (posun LM).",[724,37593,37594],{},[38,37595,37596,37597,1343,37619,1343,37641,1343,37663,37685,37686,2155],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,37598,37600],{"className":37599},[886],[888,37601,37602],{"xmlns":890},[892,37603,37604,37616],{},[895,37605,37606,37612,37614],{},[1753,37607,37608,37610],{},[898,37609,21035],{},[898,37611,16183],{},[1708,37613,1710],{},[2505,37615,26995],{},[902,37617,37618],{"encoding":904},"Y^E = 5000",[883,37620,37622],{"className":37621},[886],[888,37623,37624],{"xmlns":890},[892,37625,37626,37638],{},[895,37627,37628,37634,37636],{},[1753,37629,37630,37632],{},[898,37631,5498],{},[898,37633,16183],{},[1708,37635,1710],{},[2505,37637,3993],{},[902,37639,37640],{"encoding":904},"r^E = 5",[883,37642,37644],{"className":37643},[886],[888,37645,37646],{"xmlns":890},[892,37647,37648,37660],{},[895,37649,37650,37656,37658],{},[1753,37651,37652,37654],{},[898,37653,3455],{},[898,37655,16183],{},[1708,37657,1710],{},[2505,37659,27032],{},[902,37661,37662],{"encoding":904},"C^E = 4100",[883,37664,37666],{"className":37665},[886],[888,37667,37668],{"xmlns":890},[892,37669,37670,37682],{},[895,37671,37672,37678,37680],{},[1753,37673,37674,37676],{},[898,37675,24070],{},[898,37677,16183],{},[1708,37679,1710],{},[2505,37681,11732],{},[902,37683,37684],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,37687,945],{"className":37688,"dataFsResolvedFilePath":943,"href":944},[210],[115,37690,37692],{"id":37691},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,37694,37695,37759,37870,38013,38254,38322],{},[123,37696,37697,37700,37701,37723,37724,37758],{},[38,37698,37699],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,37702,37704],{"className":37703},[886],[888,37705,37706],{"xmlns":890},[892,37707,37708,37720],{},[895,37709,37710,37712,37714,37716,37718],{},[898,37711,23999],{},[898,37713,30164],{},[898,37715,1747],{},[1708,37717,2638],{},[898,37719,21035],{},[902,37721,37722],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,37725,37727],{"className":37726},[886],[888,37728,37729],{"xmlns":890},[892,37730,37731,37755],{},[895,37732,37733,37735,37737,37739,37741,37743,37745,37747,37749,37751,37753],{},[898,37734,23999],{},[898,37736,30164],{},[898,37738,1747],{},[1708,37740,1710],{},[898,37742,3455],{},[1708,37744,2019],{},[898,37746,24070],{},[1708,37748,2019],{},[898,37750,23999],{},[1708,37752,2019],{},[898,37754,24206],{},[902,37756,37757],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,37760,37761,37763,37764,37785,37786,1343,37809,37840,37841,37854,37855,2155],{},[38,37762,30398],{}," splňují ",[883,37765,37767],{"className":37766},[886],[888,37768,37769],{"xmlns":890},[892,37770,37771,37783],{},[895,37772,37773,37775,37777,37779,37781],{},[898,37774,21035],{},[1708,37776,1710],{},[898,37778,3455],{},[1708,37780,2019],{},[898,37782,1981],{},[902,37784,24579],{"encoding":904}," (7.2); lineární model ",[883,37787,37789],{"className":37788},[886],[888,37790,37791],{"xmlns":890},[892,37792,37793,37807],{},[895,37794,37795,37797,37799,37801,37803,37805],{},[898,37796,3455],{},[1708,37798,1710],{},[898,37800,207],{},[898,37802,21035],{},[1708,37804,2019],{},[898,37806,1923],{},[902,37808,30786],{"encoding":904},[883,37810,37812],{"className":37811},[886],[888,37813,37814],{"xmlns":890},[892,37815,37816,37838],{},[895,37817,37818,37820,37822,37824,37826,37828,37830,37832,37834,37836],{},[898,37819,1981],{},[1708,37821,1710],{},[1708,37823,1716],{"stretchy":1715},[2505,37825,2507],{},[1708,37827,2726],{},[898,37829,207],{},[1708,37831,1721],{"stretchy":1715},[898,37833,21035],{},[1708,37835,2726],{},[898,37837,1923],{},[902,37839,31035],{"encoding":904}," s autonomní spotřebou ",[883,37842,37844],{"className":37843},[886],[888,37845,37846],{"xmlns":890},[892,37847,37848,37852],{},[895,37849,37850],{},[898,37851,1923],{},[902,37853,1923],{"encoding":904}," a autonomními úsporami ",[883,37856,37858],{"className":37857},[886],[888,37859,37860],{"xmlns":890},[892,37861,37862,37868],{},[895,37863,37864,37866],{},[1708,37865,2726],{},[898,37867,1923],{},[902,37869,31114],{"encoding":904},[123,37871,37872,1729,37875,1343,37905,37935,37936,37966,37967,1343,37988,2155],{},[38,37873,37874],{},"Mezní sklony",[883,37876,37878],{"className":37877},[886],[888,37879,37880],{"xmlns":890},[892,37881,37882,37902],{},[895,37883,37884,37886,37888,37890,37892,37894,37896,37898,37900],{},[898,37885,1741],{},[898,37887,1747],{},[898,37889,3455],{},[1708,37891,1710],{},[898,37893,2364],{"mathvariant":1759},[898,37895,3455],{},[898,37897,1799],{"mathvariant":1759},[898,37899,2364],{"mathvariant":1759},[898,37901,21035],{},[902,37903,37904],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,37906,37908],{"className":37907},[886],[888,37909,37910],{"xmlns":890},[892,37911,37912,37932],{},[895,37913,37914,37916,37918,37920,37922,37924,37926,37928,37930],{},[898,37915,1741],{},[898,37917,1747],{},[898,37919,1981],{},[1708,37921,1710],{},[898,37923,2364],{"mathvariant":1759},[898,37925,1981],{},[898,37927,1799],{"mathvariant":1759},[898,37929,2364],{"mathvariant":1759},[898,37931,21035],{},[902,37933,37934],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,37937,37939],{"className":37938},[886],[888,37940,37941],{"xmlns":890},[892,37942,37943,37963],{},[895,37944,37945,37947,37949,37951,37953,37955,37957,37959,37961],{},[898,37946,1741],{},[898,37948,1747],{},[898,37950,3455],{},[1708,37952,2019],{},[898,37954,1741],{},[898,37956,1747],{},[898,37958,1981],{},[1708,37960,1710],{},[2505,37962,2507],{},[902,37964,37965],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,37968,37970],{"className":37969},[886],[888,37971,37972],{"xmlns":890},[892,37973,37974,37986],{},[895,37975,37976,37978,37980,37982,37984],{},[898,37977,1741],{},[898,37979,1747],{},[898,37981,3455],{},[1708,37983,1710],{},[898,37985,207],{},[902,37987,31753],{"encoding":904},[883,37989,37991],{"className":37990},[886],[888,37992,37993],{"xmlns":890},[892,37994,37995,38011],{},[895,37996,37997,37999,38001,38003,38005,38007,38009],{},[898,37998,1741],{},[898,38000,1747],{},[898,38002,1981],{},[1708,38004,1710],{},[2505,38006,2507],{},[1708,38008,2726],{},[898,38010,207],{},[902,38012,31779],{"encoding":904},[123,38014,38015,38018,38019],{},[38,38016,38017],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,38020,38021,38108,38177],{},[123,38022,38023,7468,38040,38061,38062,1883],{},[883,38024,38026],{"className":38025},[886],[888,38027,38028],{"xmlns":890},[892,38029,38030,38038],{},[895,38031,38032,38034,38036],{},[898,38033,3455],{},[2247,38035,24176],{},[898,38037,24070],{},[902,38039,24181],{"encoding":904},[883,38041,38043],{"className":38042},[886],[888,38044,38045],{"xmlns":890},[892,38046,38047,38059],{},[895,38048,38049,38051,38053,38055,38057],{},[898,38050,21035],{},[1708,38052,1710],{},[898,38054,3455],{},[1708,38056,2019],{},[898,38058,24070],{},[902,38060,26625],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,38063,38065],{"className":38064},[886],[888,38066,38067],{"xmlns":890},[892,38068,38069,38105],{},[895,38070,38071,38077,38079,38081,38083,38085,38091,38093,38095,38097,38099,38101,38103],{},[1753,38072,38073,38075],{},[898,38074,21035],{},[898,38076,16183],{},[1708,38078,1710],{},[1708,38080,1716],{"stretchy":1715},[898,38082,1923],{},[1708,38084,2019],{},[1753,38086,38087,38089],{},[898,38088,24070],{},[1708,38090,2417],{},[1708,38092,1721],{"stretchy":1715},[898,38094,1799],{"mathvariant":1759},[1708,38096,1716],{"stretchy":1715},[2505,38098,2507],{},[1708,38100,2726],{},[898,38102,207],{},[1708,38104,1721],{"stretchy":1715},[902,38106,38107],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,38109,38110,38131,38132,38151,38152,1883],{},[883,38111,38113],{"className":38112},[886],[888,38114,38115],{"xmlns":890},[892,38116,38117,38129],{},[895,38118,38119,38121,38123,38125,38127],{},[898,38120,3455],{},[2247,38122,24176],{},[898,38124,24070],{},[2247,38126,24176],{},[898,38128,23999],{},[902,38130,30090],{"encoding":904},": přidává vládu, zdanění ",[883,38133,38135],{"className":38134},[886],[888,38136,38137],{"xmlns":890},[892,38138,38139,38149],{},[895,38140,38141,38143,38145,38147],{},[898,38142,1978],{},[1708,38144,1716],{"stretchy":1715},[898,38146,21035],{},[1708,38148,1721],{"stretchy":1715},[902,38150,34077],{"encoding":904}," a disponibilní důchod ",[883,38153,38155],{"className":38154},[886],[888,38156,38157],{"xmlns":890},[892,38158,38159,38175],{},[895,38160,38161,38167,38169,38171,38173],{},[1743,38162,38163,38165],{},[898,38164,21035],{},[898,38166,16117],{},[1708,38168,1710],{},[898,38170,21035],{},[1708,38172,2726],{},[898,38174,1978],{},[902,38176,33576],{"encoding":904},[123,38178,38179,38204,38205,2980,38226,2155],{},[883,38180,38182],{"className":38181},[886],[888,38183,38184],{"xmlns":890},[892,38185,38186,38202],{},[895,38187,38188,38190,38192,38194,38196,38198,38200],{},[898,38189,3455],{},[2247,38191,24176],{},[898,38193,24070],{},[2247,38195,24176],{},[898,38197,23999],{},[2247,38199,24176],{},[898,38201,24206],{},[902,38203,24209],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,38206,38208],{"className":38207},[886],[888,38209,38210],{"xmlns":890},[892,38211,38212,38224],{},[895,38213,38214,38216,38218,38220,38222],{},[898,38215,24206],{},[1708,38217,1710],{},[898,38219,35110],{},[1708,38221,2726],{},[898,38223,1741],{},[902,38225,35117],{"encoding":904},[883,38227,38229],{"className":38228},[886],[888,38230,38231],{"xmlns":890},[892,38232,38233,38251],{},[895,38234,38235,38237,38239,38241,38243,38249],{},[898,38236,1741],{},[1708,38238,1710],{},[898,38240,1741],{},[1708,38242,1716],{"stretchy":1715},[1743,38244,38245,38247],{},[898,38246,21035],{},[898,38248,16117],{},[1708,38250,1721],{"stretchy":1715},[902,38252,38253],{"encoding":904},"M = M(Y_D)",[123,38255,38256,38259,38260,1729,38263,38321],{},[38,38257,38258],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,38261,38262],{},"multiplikátor investic",[883,38264,38266],{"className":38265},[886],[888,38267,38268],{"xmlns":890},[892,38269,38270,38318],{},[895,38271,38272,38274,38280,38282,38284,38290,38292,38294,38296,38298,38300,38302,38304,38306,38308,38310,38312,38314,38316],{},[898,38273,7252],{"mathvariant":1759},[1753,38275,38276,38278],{},[898,38277,21035],{},[898,38279,16183],{},[898,38281,1799],{"mathvariant":1759},[898,38283,7252],{"mathvariant":1759},[1753,38285,38286,38288],{},[898,38287,24070],{},[1708,38289,2417],{},[1708,38291,1710],{},[2505,38293,2507],{},[898,38295,1799],{"mathvariant":1759},[1708,38297,1716],{"stretchy":1715},[2505,38299,2507],{},[1708,38301,2726],{},[898,38303,207],{},[1708,38305,1721],{"stretchy":1715},[1708,38307,1710],{},[2505,38309,2507],{},[898,38311,1799],{"mathvariant":1759},[898,38313,1741],{},[898,38315,1747],{},[898,38317,1981],{},[902,38319,38320],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,38323,38324,38326,38327,38342,38343,13826,38360,38375,38376,38401,38402,2155],{},[38,38325,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,38328,38330],{"className":38329},[886],[888,38331,38332],{"xmlns":890},[892,38333,38334,38340],{},[895,38335,38336,38338],{},[898,38337,24070],{},[898,38339,1981],{},[902,38341,23938],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,38344,38346],{"className":38345},[886],[888,38347,38348],{"xmlns":890},[892,38349,38350,38358],{},[895,38351,38352,38354,38356],{},[898,38353,24070],{},[1708,38355,1710],{},[898,38357,1981],{},[902,38359,24597],{"encoding":904},[883,38361,38363],{"className":38362},[886],[888,38364,38365],{"xmlns":890},[892,38366,38367,38373],{},[895,38368,38369,38371],{},[898,38370,1658],{},[898,38372,1741],{},[902,38374,23945],{"encoding":904}," rovnováhu trhu peněz (",[883,38377,38379],{"className":38378},[886],[888,38380,38381],{"xmlns":890},[892,38382,38383,38399],{},[895,38384,38385,38391,38393],{},[1753,38386,38387,38389],{},[898,38388,1741],{},[898,38390,16117],{},[1708,38392,1710],{},[1753,38394,38395,38397],{},[898,38396,1741],{},[1708,38398,2417],{},[902,38400,25363],{"encoding":904},"); průsečík dává ",[883,38403,38405],{"className":38404},[886],[888,38406,38407],{"xmlns":890},[892,38408,38409,38429],{},[895,38410,38411,38413,38419,38421,38427],{},[1708,38412,1716],{"stretchy":1715},[1753,38414,38415,38417],{},[898,38416,21035],{},[898,38418,16183],{},[1708,38420,1883],{"separator":1882},[1753,38422,38423,38425],{},[898,38424,5498],{},[898,38426,16183],{},[1708,38428,1721],{"stretchy":1715},[902,38430,23982],{"encoding":904},[115,38432,12596],{"id":12595},[120,38434,38435,38473,38513,38603,38685,38739,38795,38854,38889,38894,38966,39041,39127,39189,39257,39315,39368,39407],{},[123,38436,38437,12636,38440,37758],{},[38,38438,38439],{},"Hrubý národní produkt (GNP)",[883,38441,38443],{"className":38442},[886],[888,38444,38445],{"xmlns":890},[892,38446,38447,38471],{},[895,38448,38449,38451,38453,38455,38457,38459,38461,38463,38465,38467,38469],{},[898,38450,23999],{},[898,38452,30164],{},[898,38454,1747],{},[1708,38456,1710],{},[898,38458,3455],{},[1708,38460,2019],{},[898,38462,24070],{},[1708,38464,2019],{},[898,38466,23999],{},[1708,38468,2019],{},[898,38470,24206],{},[902,38472,37757],{"encoding":904},[123,38474,38475,38491,38492,2155],{},[38,38476,38477,38478],{},"Národní důchod ",[883,38479,38481],{"className":38480},[886],[888,38482,38483],{"xmlns":890},[892,38484,38485,38489],{},[895,38486,38487],{},[898,38488,21035],{},[902,38490,21035],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,38493,38495],{"className":38494},[886],[888,38496,38497],{"xmlns":890},[892,38498,38499,38511],{},[895,38500,38501,38503,38505,38507,38509],{},[898,38502,23999],{},[898,38504,30164],{},[898,38506,1747],{},[1708,38508,2638],{},[898,38510,21035],{},[902,38512,37722],{"encoding":904},[123,38514,38515,38541,38542,1343,38565,1343,38586,2155],{},[38,38516,38517,38518],{},"Funkce spotřeby ",[883,38519,38521],{"className":38520},[886],[888,38522,38523],{"xmlns":890},[892,38524,38525,38539],{},[895,38526,38527,38529,38531,38533,38535,38537],{},[898,38528,3455],{},[1708,38530,1710],{},[898,38532,3455],{},[1708,38534,1716],{"stretchy":1715},[898,38536,21035],{},[1708,38538,1721],{"stretchy":1715},[902,38540,32602],{"encoding":904}," — lineární model ",[883,38543,38545],{"className":38544},[886],[888,38546,38547],{"xmlns":890},[892,38548,38549,38563],{},[895,38550,38551,38553,38555,38557,38559,38561],{},[898,38552,3455],{},[1708,38554,1710],{},[898,38556,207],{},[898,38558,21035],{},[1708,38560,2019],{},[898,38562,1923],{},[902,38564,30786],{"encoding":904},[883,38566,38568],{"className":38567},[886],[888,38569,38570],{"xmlns":890},[892,38571,38572,38584],{},[895,38573,38574,38576,38578,38580,38582],{},[2505,38575,2784],{},[1708,38577,2932],{},[898,38579,207],{},[1708,38581,2932],{},[2505,38583,2507],{},[902,38585,7040],{"encoding":904},[883,38587,38589],{"className":38588},[886],[888,38590,38591],{"xmlns":890},[892,38592,38593,38601],{},[895,38594,38595,38597,38599],{},[898,38596,1923],{},[1708,38598,2854],{},[2505,38600,2784],{},[902,38602,3172],{"encoding":904},[123,38604,38605,12636,38632,38653,38654,2155],{},[38,38606,38607,38608],{},"Funkce úspor ",[883,38609,38611],{"className":38610},[886],[888,38612,38613],{"xmlns":890},[892,38614,38615,38629],{},[895,38616,38617,38619,38621,38623,38625,38627],{},[898,38618,1981],{},[1708,38620,1710],{},[898,38622,1981],{},[1708,38624,1716],{"stretchy":1715},[898,38626,21035],{},[1708,38628,1721],{"stretchy":1715},[902,38630,38631],{"encoding":904},"S = S(Y)",[883,38633,38635],{"className":38634},[886],[888,38636,38637],{"xmlns":890},[892,38638,38639,38651],{},[895,38640,38641,38643,38645,38647,38649],{},[898,38642,21035],{},[1708,38644,1710],{},[898,38646,3455],{},[1708,38648,2019],{},[898,38650,1981],{},[902,38652,24579],{"encoding":904},"; lineární ",[883,38655,38657],{"className":38656},[886],[888,38658,38659],{"xmlns":890},[892,38660,38661,38683],{},[895,38662,38663,38665,38667,38669,38671,38673,38675,38677,38679,38681],{},[898,38664,1981],{},[1708,38666,1710],{},[1708,38668,1716],{"stretchy":1715},[2505,38670,2507],{},[1708,38672,2726],{},[898,38674,207],{},[1708,38676,1721],{"stretchy":1715},[898,38678,21035],{},[1708,38680,2726],{},[898,38682,1923],{},[902,38684,31035],{"encoding":904},[123,38686,38687,12636,38690,1343,38713,2155],{},[38,38688,38689],{},"Autonomní spotřeba\u002Fúspory",[883,38691,38693],{"className":38692},[886],[888,38694,38695],{"xmlns":890},[892,38696,38697,38711],{},[895,38698,38699,38701,38703,38705,38707,38709],{},[898,38700,3455],{},[1708,38702,1716],{"stretchy":1715},[2505,38704,2784],{},[1708,38706,1721],{"stretchy":1715},[1708,38708,1710],{},[898,38710,1923],{},[902,38712,31425],{"encoding":904},[883,38714,38716],{"className":38715},[886],[888,38717,38718],{"xmlns":890},[892,38719,38720,38736],{},[895,38721,38722,38724,38726,38728,38730,38732,38734],{},[898,38723,1981],{},[1708,38725,1716],{"stretchy":1715},[2505,38727,2784],{},[1708,38729,1721],{"stretchy":1715},[1708,38731,1710],{},[1708,38733,2726],{},[898,38735,1923],{},[902,38737,38738],{"encoding":904},"S(0) = -b",[123,38740,38741,38773,38774,2511],{},[38,38742,38743,38744],{},"Mezní sklon ke spotřebě ",[883,38745,38747],{"className":38746},[886],[888,38748,38749],{"xmlns":890},[892,38750,38751,38771],{},[895,38752,38753,38755,38757,38759,38761,38763,38765,38767,38769],{},[898,38754,1741],{},[898,38756,1747],{},[898,38758,3455],{},[1708,38760,1710],{},[898,38762,2364],{"mathvariant":1759},[898,38764,3455],{},[898,38766,1799],{"mathvariant":1759},[898,38768,2364],{"mathvariant":1759},[898,38770,21035],{},[902,38772,37904],{"encoding":904}," (v lineárním modelu ",[883,38775,38777],{"className":38776},[886],[888,38778,38779],{"xmlns":890},[892,38780,38781,38793],{},[895,38782,38783,38785,38787,38789,38791],{},[898,38784,1741],{},[898,38786,1747],{},[898,38788,3455],{},[1708,38790,1710],{},[898,38792,207],{},[902,38794,31753],{"encoding":904},[123,38796,38797,38773,38829,2511],{},[38,38798,38799,38800],{},"Mezní sklon k úsporám ",[883,38801,38803],{"className":38802},[886],[888,38804,38805],{"xmlns":890},[892,38806,38807,38827],{},[895,38808,38809,38811,38813,38815,38817,38819,38821,38823,38825],{},[898,38810,1741],{},[898,38812,1747],{},[898,38814,1981],{},[1708,38816,1710],{},[898,38818,2364],{"mathvariant":1759},[898,38820,1981],{},[898,38822,1799],{"mathvariant":1759},[898,38824,2364],{"mathvariant":1759},[898,38826,21035],{},[902,38828,37934],{"encoding":904},[883,38830,38832],{"className":38831},[886],[888,38833,38834],{"xmlns":890},[892,38835,38836,38852],{},[895,38837,38838,38840,38842,38844,38846,38848,38850],{},[898,38839,1741],{},[898,38841,1747],{},[898,38843,1981],{},[1708,38845,1710],{},[2505,38847,2507],{},[1708,38849,2726],{},[898,38851,207],{},[902,38853,31779],{"encoding":904},[123,38855,38856,1729,38859,38888],{},[38,38857,38858],{},"Vztah",[883,38860,38862],{"className":38861},[886],[888,38863,38864],{"xmlns":890},[892,38865,38866,38886],{},[895,38867,38868,38870,38872,38874,38876,38878,38880,38882,38884],{},[898,38869,1741],{},[898,38871,1747],{},[898,38873,3455],{},[1708,38875,2019],{},[898,38877,1741],{},[898,38879,1747],{},[898,38881,1981],{},[1708,38883,1710],{},[2505,38885,2507],{},[902,38887,37965],{"encoding":904}," (7.5).",[123,38890,38891,38893],{},[38,38892,32445],{}," — rovnováha agregátní poptávky a nabídky.",[123,38895,38896,38899,38900,9137,38921,2155],{},[38,38897,38898],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,38901,38903],{"className":38902},[886],[888,38904,38905],{"xmlns":890},[892,38906,38907,38919],{},[895,38908,38909,38911,38913,38915,38917],{},[898,38910,21035],{},[1708,38912,1710],{},[898,38914,3455],{},[1708,38916,2019],{},[898,38918,24070],{},[902,38920,26625],{"encoding":904},[883,38922,38924],{"className":38923},[886],[888,38925,38926],{"xmlns":890},[892,38927,38928,38964],{},[895,38929,38930,38936,38938,38940,38942,38944,38950,38952,38954,38956,38958,38960,38962],{},[1753,38931,38932,38934],{},[898,38933,21035],{},[898,38935,16183],{},[1708,38937,1710],{},[1708,38939,1716],{"stretchy":1715},[898,38941,1923],{},[1708,38943,2019],{},[1753,38945,38946,38948],{},[898,38947,24070],{},[1708,38949,2417],{},[1708,38951,1721],{"stretchy":1715},[898,38953,1799],{"mathvariant":1759},[1708,38955,1716],{"stretchy":1715},[2505,38957,2507],{},[1708,38959,2726],{},[898,38961,207],{},[1708,38963,1721],{"stretchy":1715},[902,38965,38107],{"encoding":904},[123,38967,38968,38971,38972,1343,38991,9137,39016,2155],{},[38,38969,38970],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,38973,38975],{"className":38974},[886],[888,38976,38977],{"xmlns":890},[892,38978,38979,38989],{},[895,38980,38981,38983,38985,38987],{},[898,38982,1978],{},[1708,38984,1716],{"stretchy":1715},[898,38986,21035],{},[1708,38988,1721],{"stretchy":1715},[902,38990,34077],{"encoding":904},[883,38992,38994],{"className":38993},[886],[888,38995,38996],{"xmlns":890},[892,38997,38998,39014],{},[895,38999,39000,39006,39008,39010,39012],{},[1743,39001,39002,39004],{},[898,39003,21035],{},[898,39005,16117],{},[1708,39007,1710],{},[898,39009,21035],{},[1708,39011,2726],{},[898,39013,1978],{},[902,39015,33576],{"encoding":904},[883,39017,39019],{"className":39018},[886],[888,39020,39021],{"xmlns":890},[892,39022,39023,39039],{},[895,39024,39025,39027,39029,39031,39033,39035,39037],{},[898,39026,21035],{},[1708,39028,1710],{},[898,39030,3455],{},[1708,39032,2019],{},[898,39034,24070],{},[1708,39036,2019],{},[898,39038,23999],{},[902,39040,33547],{"encoding":904},[123,39042,39043,39046,39047,39068,39069,9137,39093,2155],{},[38,39044,39045],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,39048,39050],{"className":39049},[886],[888,39051,39052],{"xmlns":890},[892,39053,39054,39066],{},[895,39055,39056,39058,39060,39062,39064],{},[898,39057,24206],{},[1708,39059,1710],{},[898,39061,35110],{},[1708,39063,2726],{},[898,39065,1741],{},[902,39067,35117],{"encoding":904},", importem ",[883,39070,39072],{"className":39071},[886],[888,39073,39074],{"xmlns":890},[892,39075,39076,39090],{},[895,39077,39078,39080,39082,39088],{},[898,39079,1741],{},[1708,39081,1716],{"stretchy":1715},[1743,39083,39084,39086],{},[898,39085,21035],{},[898,39087,16117],{},[1708,39089,1721],{"stretchy":1715},[902,39091,39092],{"encoding":904},"M(Y_D)",[883,39094,39096],{"className":39095},[886],[888,39097,39098],{"xmlns":890},[892,39099,39100,39124],{},[895,39101,39102,39104,39106,39108,39110,39112,39114,39116,39118,39120,39122],{},[898,39103,21035],{},[1708,39105,1710],{},[898,39107,3455],{},[1708,39109,2019],{},[898,39111,24070],{},[1708,39113,2019],{},[898,39115,23999],{},[1708,39117,2019],{},[898,39119,35110],{},[1708,39121,2726],{},[898,39123,1741],{},[902,39125,39126],{"encoding":904},"Y = C + I + G + B - M",[123,39128,39129,12636,39132,38321],{},[38,39130,39131],{},"Multiplikátor investic",[883,39133,39135],{"className":39134},[886],[888,39136,39137],{"xmlns":890},[892,39138,39139,39187],{},[895,39140,39141,39143,39149,39151,39153,39159,39161,39163,39165,39167,39169,39171,39173,39175,39177,39179,39181,39183,39185],{},[898,39142,7252],{"mathvariant":1759},[1753,39144,39145,39147],{},[898,39146,21035],{},[898,39148,16183],{},[898,39150,1799],{"mathvariant":1759},[898,39152,7252],{"mathvariant":1759},[1753,39154,39155,39157],{},[898,39156,24070],{},[1708,39158,2417],{},[1708,39160,1710],{},[2505,39162,2507],{},[898,39164,1799],{"mathvariant":1759},[1708,39166,1716],{"stretchy":1715},[2505,39168,2507],{},[1708,39170,2726],{},[898,39172,207],{},[1708,39174,1721],{"stretchy":1715},[1708,39176,1710],{},[2505,39178,2507],{},[898,39180,1799],{"mathvariant":1759},[898,39182,1741],{},[898,39184,1747],{},[898,39186,1981],{},[902,39188,38320],{"encoding":904},[123,39190,39191,12636,39222,1343,39239,39256],{},[38,39192,27603,39193],{},[883,39194,39196],{"className":39195},[886],[888,39197,39198],{"xmlns":890},[892,39199,39200,39220],{},[895,39201,39202,39204,39206,39208,39210,39212,39214,39216,39218],{},[898,39203,24070],{},[1708,39205,1716],{"stretchy":1715},[898,39207,5498],{},[1708,39209,1721],{"stretchy":1715},[1708,39211,1710],{},[898,39213,14142],{},[898,39215,5498],{},[1708,39217,2019],{},[898,39219,2364],{},[902,39221,27633],{"encoding":904},[883,39223,39225],{"className":39224},[886],[888,39226,39227],{"xmlns":890},[892,39228,39229,39237],{},[895,39230,39231,39233,39235],{},[898,39232,14142],{},[1708,39234,2932],{},[2505,39236,2784],{},[902,39238,24401],{"encoding":904},[883,39240,39242],{"className":39241},[886],[888,39243,39244],{"xmlns":890},[892,39245,39246,39254],{},[895,39247,39248,39250,39252],{},[898,39249,2364],{},[1708,39251,2854],{},[2505,39253,2784],{},[902,39255,24380],{"encoding":904},"; klesající.",[123,39258,39259,39261,39262,39264,39265,39314],{},[38,39260,27721],{}," — rovnováha na trhu zboží (",[614,39263,23941],{},"); ",[883,39266,39268],{"className":39267},[886],[888,39269,39270],{"xmlns":890},[892,39271,39272,39312],{},[895,39273,39274,39276,39278,39290,39292,39294],{},[898,39275,21035],{},[1708,39277,1710],{},[2358,39279,39280,39282],{},[898,39281,14142],{},[895,39283,39284,39286,39288],{},[2505,39285,2507],{},[1708,39287,2726],{},[898,39289,207],{},[898,39291,5498],{},[1708,39293,2019],{},[2358,39295,39296,39304],{},[895,39297,39298,39300,39302],{},[898,39299,1923],{},[1708,39301,2019],{},[898,39303,2364],{},[895,39305,39306,39308,39310],{},[2505,39307,2507],{},[1708,39309,2726],{},[898,39311,207],{},[902,39313,27774],{"encoding":904}," (7.14); klesající.",[123,39316,39317,39319,39320,39264,39322,39367],{},[38,39318,27920],{}," — rovnováha na trhu peněz (",[614,39321,23948],{},[883,39323,39325],{"className":39324},[886],[888,39326,39327],{"xmlns":890},[892,39328,39329,39365],{},[895,39330,39331,39337,39339,39345,39347,39349,39355,39357,39359],{},[1753,39332,39333,39335],{},[898,39334,1741],{},[1708,39336,2417],{},[1708,39338,1710],{},[1743,39340,39341,39343],{},[898,39342,25121],{},[2505,39344,2507],{},[898,39346,21035],{},[1708,39348,2019],{},[1743,39350,39351,39353],{},[898,39352,25121],{},[2505,39354,3132],{},[898,39356,5498],{},[1708,39358,2019],{},[1743,39360,39361,39363],{},[898,39362,25121],{},[2505,39364,3121],{},[902,39366,27968],{"encoding":904}," (7.15); rostoucí.",[123,39369,39370,12636,39373,2155],{},[38,39371,39372],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,39374,39376],{"className":39375},[886],[888,39377,39378],{"xmlns":890},[892,39379,39380,39404],{},[895,39381,39382,39388,39390,39396,39398],{},[1753,39383,39384,39386],{},[898,39385,1741],{},[898,39387,16117],{},[1708,39389,1710],{},[1743,39391,39392,39394],{},[898,39393,1658],{},[2505,39395,2507],{},[1708,39397,2019],{},[1743,39399,39400,39402],{},[898,39401,1658],{},[2505,39403,3132],{},[902,39405,39406],{"encoding":904},"M^D = L_1 + L_2",[123,39408,39409,27978,39411,25862,39424,1771,39439,39454,39455,2155],{},[38,39410,945],{},[883,39412,39414],{"className":39413},[886],[888,39415,39416],{"xmlns":890},[892,39417,39418,39422],{},[895,39419,39420],{},[898,39421,16183],{},[902,39423,16183],{"encoding":904},[883,39425,39427],{"className":39426},[886],[888,39428,39429],{"xmlns":890},[892,39430,39431,39437],{},[895,39432,39433,39435],{},[898,39434,24070],{},[898,39436,1981],{},[902,39438,23938],{"encoding":904},[883,39440,39442],{"className":39441},[886],[888,39443,39444],{"xmlns":890},[892,39445,39446,39452],{},[895,39447,39448,39450],{},[898,39449,1658],{},[898,39451,1741],{},[902,39453,23945],{"encoding":904}," určuje ",[883,39456,39458],{"className":39457},[886],[888,39459,39460],{"xmlns":890},[892,39461,39462,39482],{},[895,39463,39464,39466,39472,39474,39480],{},[1708,39465,1716],{"stretchy":1715},[1753,39467,39468,39470],{},[898,39469,21035],{},[898,39471,16183],{},[1708,39473,1883],{"separator":1882},[1753,39475,39476,39478],{},[898,39477,5498],{},[898,39479,16183],{},[1708,39481,1721],{"stretchy":1715},[902,39483,23982],{"encoding":904},[115,39485,13763],{"id":13762},[120,39487,39488,39495,39502],{},[123,39489,39490,1729,39492],{},[38,39491,13888],{},[207,39493,13894],{"className":39494,"dataFsResolvedFilePath":13892,"href":13893},[210],[123,39496,39497,1729,39499],{},[38,39498,13880],{},[207,39500,28089],{"className":39501,"dataFsResolvedFilePath":868,"href":869},[210],[123,39503,39504,39506],{},[38,39505,28104],{},[120,39507,39508,39514,39520,39526],{},[123,39509,39510,39513],{},[207,39511,28145],{"className":39512,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,39515,39516,39519],{},[207,39517,28112],{"className":39518,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,39521,39522,39525],{},[207,39523,14913],{"className":39524,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,39527,39528,39531,39532,1343,39549,39566],{},[207,39529,1145],{"className":39530,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,39533,39535],{"className":39534},[886],[888,39536,39537],{"xmlns":890},[892,39538,39539,39547],{},[895,39540,39541,39543,39545],{},[898,39542,1741],{},[898,39544,1747],{},[898,39546,3455],{},[902,39548,29915],{"encoding":904},[883,39550,39552],{"className":39551},[886],[888,39553,39554],{"xmlns":890},[892,39555,39556,39564],{},[895,39557,39558,39560,39562],{},[898,39559,1741],{},[898,39561,1747],{},[898,39563,1981],{},[902,39565,31523],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":39568},[39569,39570,39571,39572,39577,39580,39581,39588,39593,39598,39601,39602,39603,39604],{"id":23893,"depth":642,"text":23894},{"id":30024,"depth":642,"text":30025},{"id":30144,"depth":642,"text":30145},{"id":30397,"depth":642,"text":30398,"children":39573},[39574,39575,39576],{"id":30401,"depth":649,"text":30402},{"id":30612,"depth":649,"text":30613},{"id":31117,"depth":649,"text":31118},{"id":31435,"depth":642,"text":31436,"children":39578},[39579],{"id":31950,"depth":649,"text":31951},{"id":32444,"depth":642,"text":32445},{"id":32471,"depth":642,"text":32472,"children":39582},[39583,39584,39585,39587],{"id":32482,"depth":649,"text":32483},{"id":32552,"depth":649,"text":32553},{"id":32733,"depth":649,"text":39586},"Výpočet YEY^E",{"id":32876,"depth":649,"text":32877},{"id":33254,"depth":642,"text":33255,"children":39589},[39590,39591,39592],{"id":33258,"depth":649,"text":32483},{"id":33706,"depth":649,"text":32553},{"id":34362,"depth":649,"text":34363},{"id":35148,"depth":642,"text":35149,"children":39594},[39595,39596,39597],{"id":35152,"depth":649,"text":32483},{"id":35297,"depth":649,"text":32553},{"id":35567,"depth":649,"text":35568},{"id":36486,"depth":642,"text":36487,"children":39599},[39600],{"id":36682,"depth":649,"text":36683},{"id":37231,"depth":642,"text":37232},{"id":37691,"depth":642,"text":37692},{"id":12595,"depth":642,"text":12596},{"id":13762,"depth":642,"text":13763},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,28098,1143,39611,39612,39613,28145,29754],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":39616,"title":39617,"body":39618,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":48590,"navigation":664,"path":48591,"seo":48592,"sources":48593,"stem":48594,"tags":48595,"type":13951,"updated":677,"__hash__":48600},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":39619,"toc":48559},[39620,39623,39625,39854,39858,39911,39978,40090,40249,40253,40369,40373,40376,40498,40501,40694,40718,40786,40950,40968,41034,41412,41416,41423,41667,41723,41727,41791,41909,42040,42072,42192,42274,42277,42399,42591,42812,42816,42856,42961,43018,43118,43295,43425,43478,43481,43568,43572,43748,43752,43755,43840,43843,43900,44005,44009,44130,44133,44316,44319,44427,44636,44956,45004,45077,45151,45153,45377,45612,45880,45884,45887,45992,46049,46083,46130,46163,46247,46249,46481,46614,46691,46812,46967,46971,47112,47119,47343,47354,47358,47362,47467,47609,47719,47818,47822,47981,48090,48092,48485,48487],[12,39621,39617],{"id":39622},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,39624,23894],{"id":23893},[724,39626,39627,39629,39630,39664,39665,39668,39669,39700,39701,39747,39748,39751,39752,39794,39795,39813,39814,39818,39819,39849,39850,39853],{},[38,39628,913],{}," řeší, jaký svazek zboží ",[883,39631,39633],{"className":39632},[886],[888,39634,39635],{"xmlns":890},[892,39636,39637,39661],{},[895,39638,39639,39641,39649,39651,39659],{},[1708,39640,6940],{"stretchy":1715},[4754,39642,39643,39645,39647],{},[898,39644,1688],{},[2505,39646,2507],{},[1708,39648,2417],{},[1708,39650,1883],{"separator":1882},[4754,39652,39653,39655,39657],{},[898,39654,1688],{},[2505,39656,3132],{},[1708,39658,2417],{},[1708,39660,6981],{"stretchy":1715},[902,39662,39663],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,39666,39667],{},"primární úloha"," — maximalizace užitečnosti ",[883,39670,39672],{"className":39671},[886],[888,39673,39674],{"xmlns":890},[892,39675,39676,39698],{},[895,39677,39678,39680,39682,39688,39690,39696],{},[898,39679,900],{},[1708,39681,1716],{"stretchy":1715},[1743,39683,39684,39686],{},[898,39685,1688],{},[2505,39687,2507],{},[1708,39689,1883],{"separator":1882},[1743,39691,39692,39694],{},[898,39693,1688],{},[2505,39695,3132],{},[1708,39697,1721],{"stretchy":1715},[902,39699,28216],{"encoding":904}," při rozpočtovém omezení ",[883,39702,39704],{"className":39703},[886],[888,39705,39706],{"xmlns":890},[892,39707,39708,39744],{},[895,39709,39710,39716,39718,39724,39730,39732,39738],{},[1753,39711,39712,39714],{},[898,39713,21035],{},[1708,39715,2417],{},[1708,39717,1710],{},[1743,39719,39720,39722],{},[898,39721,1747],{},[2505,39723,2507],{},[1743,39725,39726,39728],{},[898,39727,1688],{},[2505,39729,2507],{},[1708,39731,2019],{},[1743,39733,39734,39736],{},[898,39735,1747],{},[2505,39737,3132],{},[1743,39739,39740,39742],{},[898,39741,1688],{},[2505,39743,3132],{},[902,39745,39746],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,39749,39750],{},"duální úloha"," — minimalizace výdajů ",[883,39753,39755],{"className":39754},[886],[888,39756,39757],{"xmlns":890},[892,39758,39759,39791],{},[895,39760,39761,39763,39765,39771,39777,39779,39785],{},[898,39762,16183],{},[1708,39764,1710],{},[1743,39766,39767,39769],{},[898,39768,1747],{},[2505,39770,2507],{},[1743,39772,39773,39775],{},[898,39774,1688],{},[2505,39776,2507],{},[1708,39778,2019],{},[1743,39780,39781,39783],{},[898,39782,1747],{},[2505,39784,3132],{},[1743,39786,39787,39789],{},[898,39788,1688],{},[2505,39790,3132],{},[902,39792,39793],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,39796,39798],{"className":39797},[886],[888,39799,39800],{"xmlns":890},[892,39801,39802,39810],{},[895,39803,39804],{},[1753,39805,39806,39808],{},[898,39807,900],{},[1708,39809,2417],{},[902,39811,39812],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,39815,39817],{"className":39816,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,39820,39822],{"className":39821},[886],[888,39823,39824],{"xmlns":890},[892,39825,39826,39846],{},[895,39827,39828,39830,39832,39838,39840],{},[2247,39829,13825],{},[1708,39831,1710],{},[1743,39833,39834,39836],{},[898,39835,1747],{},[2505,39837,2507],{},[898,39839,1799],{"mathvariant":1759},[1743,39841,39842,39844],{},[898,39843,1747],{},[2505,39845,3132],{},[902,39847,39848],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,39851,39852],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,39855,39857],{"id":39856},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,39859,39860,39861,39879,39880,39910],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,39862,39864],{"className":39863},[886],[888,39865,39866],{"xmlns":890},[892,39867,39868,39876],{},[895,39869,39870],{},[1753,39871,39872,39874],{},[898,39873,21035],{},[1708,39875,2417],{},[902,39877,39878],{"encoding":904},"Y^*"," a ceny ",[883,39881,39883],{"className":39882},[886],[888,39884,39885],{"xmlns":890},[892,39886,39887,39907],{},[895,39888,39889,39897,39899],{},[4754,39890,39891,39893,39895],{},[898,39892,1747],{},[2505,39894,2507],{},[1708,39896,2417],{},[1708,39898,1883],{"separator":1882},[4754,39900,39901,39903,39905],{},[898,39902,1747],{},[2505,39904,3132],{},[1708,39906,2417],{},[902,39908,39909],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,39912,39914],{"className":39913},[886],[888,39915,39916],{"xmlns":890,"display":2210},[892,39917,39918,39975],{},[2214,39919,39920],{"width":2216},[2218,39921,39922,39924,39968,39970],{},[2221,39923],{"width":2223},[2221,39925,39926],{},[895,39927,39928,39934,39936,39944,39950,39952,39960,39966],{},[1753,39929,39930,39932],{},[898,39931,21035],{},[1708,39933,2417],{},[1708,39935,1710],{},[4754,39937,39938,39940,39942],{},[898,39939,1747],{},[2505,39941,2507],{},[1708,39943,2417],{},[1743,39945,39946,39948],{},[898,39947,1688],{},[2505,39949,2507],{},[1708,39951,2019],{},[4754,39953,39954,39956,39958],{},[898,39955,1747],{},[2505,39957,3132],{},[1708,39959,2417],{},[1743,39961,39962,39964],{},[898,39963,1688],{},[2505,39965,3132],{},[1708,39967,1883],{"separator":1882},[2221,39969],{"width":2223},[2221,39971,39972],{},[2247,39973,39974],{},"(6.12)",[902,39976,39977],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,39979,39980,39981,39984,39985,1771,40021,40057,40058,40071,40072,40086,40087,2155],{},"geometricky ",[38,39982,39983],{},"rozpočtová přímka (budget line)"," procházející body ",[883,39986,39988],{"className":39987},[886],[888,39989,39990],{"xmlns":890},[892,39991,39992,40018],{},[895,39993,39994,39996,40002,40004,40012,40014,40016],{},[1708,39995,6940],{"stretchy":1715},[1753,39997,39998,40000],{},[898,39999,21035],{},[1708,40001,2417],{},[898,40003,1799],{"mathvariant":1759},[4754,40005,40006,40008,40010],{},[898,40007,1747],{},[2505,40009,2507],{},[1708,40011,2417],{},[1708,40013,1883],{"separator":1882},[2505,40015,2784],{},[1708,40017,6981],{"stretchy":1715},[902,40019,40020],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,40022,40024],{"className":40023},[886],[888,40025,40026],{"xmlns":890},[892,40027,40028,40054],{},[895,40029,40030,40032,40034,40036,40042,40044,40052],{},[1708,40031,6940],{"stretchy":1715},[2505,40033,2784],{},[1708,40035,1883],{"separator":1882},[1753,40037,40038,40040],{},[898,40039,21035],{},[1708,40041,2417],{},[898,40043,1799],{"mathvariant":1759},[4754,40045,40046,40048,40050],{},[898,40047,1747],{},[2505,40049,3132],{},[1708,40051,2417],{},[1708,40053,6981],{"stretchy":1715},[902,40055,40056],{"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 ",[883,40059,40061],{"className":40060},[886],[888,40062,40063],{"xmlns":890},[892,40064,40065,40069],{},[895,40066,40067],{},[898,40068,900],{},[902,40070,900],{"encoding":904},", indiferenční křivky a ",[883,40073,40075],{"className":40074},[886],[888,40076,40077],{"xmlns":890},[892,40078,40079,40083],{},[895,40080,40081],{},[2247,40082,13825],{},[902,40084,40085],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,40088,880],{"className":40089,"dataFsResolvedFilePath":878,"href":879},[210],[1636,40091,40092],{},[724,40093,40094,40096,40097,40100,40101,40114,40115,40117,40118,40131,40132,1729,40135,40175,40176,40193,40194,40211,40212,40229,40230,40248],{},[883,40095,6130],{}," Pozor — dvě úlohy, totéž řešení\n",[38,40098,40099],{},"Primární úloha"," (max ",[883,40102,40104],{"className":40103},[886],[888,40105,40106],{"xmlns":890},[892,40107,40108,40112],{},[895,40109,40110],{},[898,40111,900],{},[902,40113,900],{"encoding":904}," při pevném rozpočtu) a ",[38,40116,39750],{}," (min ",[883,40119,40121],{"className":40120},[886],[888,40122,40123],{"xmlns":890},[892,40124,40125,40129],{},[895,40126,40127],{},[898,40128,16183],{},[902,40130,16183],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,40133,40134],{},"tentýž bod",[883,40136,40138],{"className":40137},[886],[888,40139,40140],{"xmlns":890},[892,40141,40142,40172],{},[895,40143,40144,40150,40152,40160,40162,40170],{},[1753,40145,40146,40148],{},[898,40147,1688],{},[1708,40149,2417],{},[1708,40151,6940],{"stretchy":1715},[4754,40153,40154,40156,40158],{},[898,40155,1688],{},[2505,40157,2507],{},[1708,40159,2417],{},[1708,40161,1883],{"separator":1882},[4754,40163,40164,40166,40168],{},[898,40165,1688],{},[2505,40167,3132],{},[1708,40169,2417],{},[1708,40171,6981],{"stretchy":1715},[902,40173,40174],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,40177,40179],{"className":40178},[886],[888,40180,40181],{"xmlns":890},[892,40182,40183,40191],{},[895,40184,40185],{},[1753,40186,40187,40189],{},[898,40188,21035],{},[1708,40190,2417],{},[902,40192,39878],{"encoding":904}," a hledáme maximální ",[883,40195,40197],{"className":40196},[886],[888,40198,40199],{"xmlns":890},[892,40200,40201,40209],{},[895,40202,40203],{},[1753,40204,40205,40207],{},[898,40206,900],{},[1708,40208,2417],{},[902,40210,39812],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,40213,40215],{"className":40214},[886],[888,40216,40217],{"xmlns":890},[892,40218,40219,40227],{},[895,40220,40221],{},[1753,40222,40223,40225],{},[898,40224,900],{},[1708,40226,2417],{},[902,40228,39812],{"encoding":904}," a hledáme minimální ",[883,40231,40233],{"className":40232},[886],[888,40234,40235],{"xmlns":890},[892,40236,40237,40245],{},[895,40238,40239],{},[1753,40240,40241,40243],{},[898,40242,16183],{},[1708,40244,2417],{},[902,40246,40247],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,40250,40252],{"id":40251},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,40254,40255,40256,40287,40288,40364,40365,2155],{},"Úlohou je najít maximum ",[883,40257,40259],{"className":40258},[886],[888,40260,40261],{"xmlns":890},[892,40262,40263,40285],{},[895,40264,40265,40267,40269,40275,40277,40283],{},[898,40266,900],{},[1708,40268,1716],{"stretchy":1715},[1743,40270,40271,40273],{},[898,40272,1688],{},[2505,40274,2507],{},[1708,40276,1883],{"separator":1882},[1743,40278,40279,40281],{},[898,40280,1688],{},[2505,40282,3132],{},[1708,40284,1721],{"stretchy":1715},[902,40286,28216],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,40289,40291],{"className":40290},[886],[888,40292,40293],{"xmlns":890},[892,40294,40295,40361],{},[895,40296,40297,40299,40301,40307,40309,40315,40317,40319,40325,40327,40335,40341,40343,40351,40357,40359],{},[898,40298,22927],{},[1708,40300,1716],{"stretchy":1715},[1743,40302,40303,40305],{},[898,40304,1688],{},[2505,40306,2507],{},[1708,40308,1883],{"separator":1882},[1743,40310,40311,40313],{},[898,40312,1688],{},[2505,40314,3132],{},[1708,40316,1721],{"stretchy":1715},[1708,40318,1710],{},[1753,40320,40321,40323],{},[898,40322,21035],{},[1708,40324,2417],{},[1708,40326,2726],{},[4754,40328,40329,40331,40333],{},[898,40330,1747],{},[2505,40332,2507],{},[1708,40334,2417],{},[1743,40336,40337,40339],{},[898,40338,1688],{},[2505,40340,2507],{},[1708,40342,2726],{},[4754,40344,40345,40347,40349],{},[898,40346,1747],{},[2505,40348,3132],{},[1708,40350,2417],{},[1743,40352,40353,40355],{},[898,40354,1688],{},[2505,40356,3132],{},[1708,40358,1710],{},[2505,40360,2784],{},[902,40362,40363],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,40366,40368],{"className":40367,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,40370,40372],{"id":40371},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,40374,40375],{},"Sestavíme",[883,40377,40379],{"className":40378},[886],[888,40380,40381],{"xmlns":890,"display":2210},[892,40382,40383,40495],{},[2214,40384,40385],{"width":2216},[2218,40386,40387,40389,40488,40490],{},[2221,40388],{"width":2223},[2221,40390,40391],{},[895,40392,40393,40396,40398,40404,40406,40412,40414,40416,40418,40420,40422,40424,40430,40432,40438,40440,40442,40444,40446,40452,40454,40462,40468,40470,40478,40484,40486],{},[898,40394,1658],{"mathvariant":40395},"script",[1708,40397,1716],{"stretchy":1715},[1743,40399,40400,40402],{},[898,40401,1688],{},[2505,40403,2507],{},[1708,40405,1883],{"separator":1882},[1743,40407,40408,40410],{},[898,40409,1688],{},[2505,40411,3132],{},[1708,40413,1883],{"separator":1882},[898,40415,28315],{},[1708,40417,1721],{"stretchy":1715},[1708,40419,1710],{},[898,40421,900],{},[1708,40423,1716],{"stretchy":1715},[1743,40425,40426,40428],{},[898,40427,1688],{},[2505,40429,2507],{},[1708,40431,1883],{"separator":1882},[1743,40433,40434,40436],{},[898,40435,1688],{},[2505,40437,3132],{},[1708,40439,1721],{"stretchy":1715},[1708,40441,2019],{},[898,40443,28315],{},[1708,40445,1716],{"stretchy":1715},[1753,40447,40448,40450],{},[898,40449,21035],{},[1708,40451,2417],{},[1708,40453,2726],{},[4754,40455,40456,40458,40460],{},[898,40457,1747],{},[2505,40459,2507],{},[1708,40461,2417],{},[1743,40463,40464,40466],{},[898,40465,1688],{},[2505,40467,2507],{},[1708,40469,2726],{},[4754,40471,40472,40474,40476],{},[898,40473,1747],{},[2505,40475,3132],{},[1708,40477,2417],{},[1743,40479,40480,40482],{},[898,40481,1688],{},[2505,40483,3132],{},[1708,40485,1721],{"stretchy":1715},[898,40487,2155],{"mathvariant":1759},[2221,40489],{"width":2223},[2221,40491,40492],{},[2247,40493,40494],{},"(6.13)",[902,40496,40497],{"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}",[724,40499,40500],{},"Soustava prvního řádu:",[883,40502,40504],{"className":40503},[886],[888,40505,40506],{"xmlns":890,"display":2210},[892,40507,40508,40691],{},[2214,40509,40510],{"width":2216},[2218,40511,40512,40514,40684,40686],{},[2221,40513],{"width":2223},[2221,40515,40516],{},[2214,40517,40518,40568,40618],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,40519,40520,40532],{},[2221,40521,40522],{},[3194,40523,40524],{"scriptlevel":2784,"displaystyle":1882},[4754,40525,40526,40528,40530],{},[898,40527,1658],{"mathvariant":40395},[2505,40529,2507],{},[1708,40531,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,40533,40534],{},[3194,40535,40536],{"scriptlevel":2784,"displaystyle":1882},[895,40537,40538,40540,40542,40550,40552,40554,40562,40564,40566],{},[895,40539],{},[1708,40541,1710],{},[4754,40543,40544,40546,40548],{},[898,40545,900],{},[2505,40547,2507],{},[1708,40549,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,40551,2726],{},[898,40553,28315],{},[4754,40555,40556,40558,40560],{},[898,40557,1747],{},[2505,40559,2507],{},[1708,40561,2417],{},[1708,40563,1710],{},[2505,40565,2784],{},[1708,40567,1883],{"separator":1882},[2218,40569,40570,40582],{},[2221,40571,40572],{},[3194,40573,40574],{"scriptlevel":2784,"displaystyle":1882},[4754,40575,40576,40578,40580],{},[898,40577,1658],{"mathvariant":40395},[2505,40579,3132],{},[1708,40581,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,40583,40584],{},[3194,40585,40586],{"scriptlevel":2784,"displaystyle":1882},[895,40587,40588,40590,40592,40600,40602,40604,40612,40614,40616],{},[895,40589],{},[1708,40591,1710],{},[4754,40593,40594,40596,40598],{},[898,40595,900],{},[2505,40597,3132],{},[1708,40599,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,40601,2726],{},[898,40603,28315],{},[4754,40605,40606,40608,40610],{},[898,40607,1747],{},[2505,40609,3132],{},[1708,40611,2417],{},[1708,40613,1710],{},[2505,40615,2784],{},[1708,40617,1883],{"separator":1882},[2218,40619,40620,40632],{},[2221,40621,40622],{},[3194,40623,40624],{"scriptlevel":2784,"displaystyle":1882},[4754,40625,40626,40628,40630],{},[898,40627,1658],{"mathvariant":40395},[898,40629,28315],{},[1708,40631,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,40633,40634],{},[3194,40635,40636],{"scriptlevel":2784,"displaystyle":1882},[895,40637,40638,40640,40642,40648,40650,40658,40664,40666,40674,40680,40682],{},[895,40639],{},[1708,40641,1710],{},[1753,40643,40644,40646],{},[898,40645,21035],{},[1708,40647,2417],{},[1708,40649,2726],{},[4754,40651,40652,40654,40656],{},[898,40653,1747],{},[2505,40655,2507],{},[1708,40657,2417],{},[1743,40659,40660,40662],{},[898,40661,1688],{},[2505,40663,2507],{},[1708,40665,2726],{},[4754,40667,40668,40670,40672],{},[898,40669,1747],{},[2505,40671,3132],{},[1708,40673,2417],{},[1743,40675,40676,40678],{},[898,40677,1688],{},[2505,40679,3132],{},[1708,40681,1710],{},[2505,40683,24346],{},[2221,40685],{"width":2223},[2221,40687,40688],{},[2247,40689,40690],{},"(6.14)",[902,40692,40693],{"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}",[724,40695,40696,40697,40700,40701,40714,40715,2788],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,40698,40699],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,40702,40704],{"className":40703},[886],[888,40705,40706],{"xmlns":890},[892,40707,40708,40712],{},[895,40709,40710],{},[898,40711,28315],{},[902,40713,28368],{"encoding":904}," dostáváme ",[38,40716,40717],{},"podmínku optimality",[883,40719,40721],{"className":40720},[886],[888,40722,40723],{"xmlns":890,"display":2210},[892,40724,40725,40783],{},[895,40726,40727],{},[24717,40728,40729],{"notation":24719},[3194,40730,40731],{"scriptlevel":2784,"displaystyle":1715},[3194,40732,40733],{"scriptlevel":2784,"displaystyle":1715},[3194,40734,40735],{"scriptlevel":2784,"displaystyle":1882},[895,40736,40737,40739,40741,40743,40761,40763,40781],{},[2247,40738,4779],{},[2247,40740,13825],{},[1708,40742,1710],{},[2358,40744,40745,40753],{},[4754,40746,40747,40749,40751],{},[898,40748,900],{},[2505,40750,2507],{},[1708,40752,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,40754,40755,40757,40759],{},[898,40756,900],{},[2505,40758,3132],{},[1708,40760,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,40762,1710],{},[2358,40764,40765,40773],{},[4754,40766,40767,40769,40771],{},[898,40768,1747],{},[2505,40770,2507],{},[1708,40772,2417],{},[4754,40774,40775,40777,40779],{},[898,40776,1747],{},[2505,40778,3132],{},[1708,40780,2417],{},[2247,40782,4779],{},[902,40784,40785],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1636,40787,40788],{},[724,40789,40790,40792,40793,40827,40828,40831,40832,40850,40851,40869,40870,40900,40901,40918,40919,40949],{},[883,40791,2518],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,40794,40796],{"className":40795},[886],[888,40797,40798],{"xmlns":890},[892,40799,40800,40824],{},[895,40801,40802,40804,40806,40814,40816],{},[2247,40803,13825],{},[1708,40805,1710],{},[4754,40807,40808,40810,40812],{},[898,40809,1747],{},[2505,40811,2507],{},[1708,40813,2417],{},[898,40815,1799],{"mathvariant":1759},[4754,40817,40818,40820,40822],{},[898,40819,1747],{},[2505,40821,3132],{},[1708,40823,2417],{},[902,40825,40826],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,40829,40830],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,40833,40835],{"className":40834},[886],[888,40836,40837],{"xmlns":890},[892,40838,40839,40847],{},[895,40840,40841],{},[1743,40842,40843,40845],{},[898,40844,1688],{},[2505,40846,2507],{},[902,40848,40849],{"encoding":904},"Q_1"," za ",[883,40852,40854],{"className":40853},[886],[888,40855,40856],{"xmlns":890},[892,40857,40858,40866],{},[895,40859,40860],{},[1743,40861,40862,40864],{},[898,40863,1688],{},[2505,40865,3132],{},[902,40867,40868],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,40871,40873],{"className":40872},[886],[888,40874,40875],{"xmlns":890},[892,40876,40877,40897],{},[895,40878,40879,40881,40883,40889,40891],{},[2247,40880,13825],{},[1708,40882,2854],{},[1743,40884,40885,40887],{},[898,40886,1747],{},[2505,40888,2507],{},[898,40890,1799],{"mathvariant":1759},[1743,40892,40893,40895],{},[898,40894,1747],{},[2505,40896,3132],{},[902,40898,40899],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,40902,40904],{"className":40903},[886],[888,40905,40906],{"xmlns":890},[892,40907,40908,40916],{},[895,40909,40910],{},[1743,40911,40912,40914],{},[898,40913,1688],{},[2505,40915,2507],{},[902,40917,40849],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,40920,40922],{"className":40921},[886],[888,40923,40924],{"xmlns":890},[892,40925,40926,40946],{},[895,40927,40928,40930,40932,40938,40940],{},[2247,40929,13825],{},[1708,40931,2932],{},[1743,40933,40934,40936],{},[898,40935,1747],{},[2505,40937,2507],{},[898,40939,1799],{"mathvariant":1759},[1743,40941,40942,40944],{},[898,40943,1747],{},[2505,40945,3132],{},[902,40947,40948],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,40951,40953,40954,40967],{"id":40952},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,40955,40957],{"className":40956},[886],[888,40958,40959],{"xmlns":890},[892,40960,40961,40965],{},[895,40962,40963],{},[898,40964,28315],{},[902,40966,28368],{"encoding":904}," — mezní užitečnost důchodu",[724,40969,40970,40971,40989,40990,40993,40994,41011,41012,41029,41030,41033],{},"Lagrangeův multiplikátor ",[883,40972,40974],{"className":40973},[886],[888,40975,40976],{"xmlns":890},[892,40977,40978,40986],{},[895,40979,40980],{},[1753,40981,40982,40984],{},[898,40983,28315],{},[1708,40985,2417],{},[902,40987,40988],{"encoding":904},"\\lambda^*"," představuje ",[38,40991,40992],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,40995,40997],{"className":40996},[886],[888,40998,40999],{"xmlns":890},[892,41000,41001,41009],{},[895,41002,41003],{},[1753,41004,41005,41007],{},[898,41006,900],{},[1708,41008,2417],{},[902,41010,39812],{"encoding":904}," při jednotkové změně důchodu ",[883,41013,41015],{"className":41014},[886],[888,41016,41017],{"xmlns":890},[892,41018,41019,41027],{},[895,41020,41021],{},[1753,41022,41023,41025],{},[898,41024,21035],{},[1708,41026,2417],{},[902,41028,39878],{"encoding":904},". Je to ",[38,41031,41032],{},"stínová cena"," rozpočtového omezení.",[1636,41035,41036,41041],{},[724,41037,41038,41040],{},[883,41039,3465],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,41042,41043,41103,41190,41226,41313],{},[123,41044,41045,41048,41049,2155],{},[38,41046,41047],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,41050,41052],{"className":41051},[886],[888,41053,41054],{"xmlns":890},[892,41055,41056,41100],{},[895,41057,41058,41064,41066,41074,41080,41082,41090,41096,41098],{},[1753,41059,41060,41062],{},[898,41061,21035],{},[1708,41063,2417],{},[1708,41065,2726],{},[4754,41067,41068,41070,41072],{},[898,41069,1747],{},[2505,41071,2507],{},[1708,41073,2417],{},[1743,41075,41076,41078],{},[898,41077,1688],{},[2505,41079,2507],{},[1708,41081,2726],{},[4754,41083,41084,41086,41088],{},[898,41085,1747],{},[2505,41087,3132],{},[1708,41089,2417],{},[1743,41091,41092,41094],{},[898,41093,1688],{},[2505,41095,3132],{},[1708,41097,1710],{},[2505,41099,2784],{},[902,41101,41102],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,41104,41105,1729,41108,2155],{},[38,41106,41107],{},"Sestav Lagrangeovu funkci",[883,41109,41111],{"className":41110},[886],[888,41112,41113],{"xmlns":890},[892,41114,41115,41187],{},[895,41116,41117,41119,41121,41123,41125,41131,41133,41139,41141,41143,41145,41147,41153,41155,41163,41169,41171,41179,41185],{},[898,41118,1658],{"mathvariant":40395},[1708,41120,1710],{},[898,41122,900],{},[1708,41124,1716],{"stretchy":1715},[1743,41126,41127,41129],{},[898,41128,1688],{},[2505,41130,2507],{},[1708,41132,1883],{"separator":1882},[1743,41134,41135,41137],{},[898,41136,1688],{},[2505,41138,3132],{},[1708,41140,1721],{"stretchy":1715},[1708,41142,2019],{},[898,41144,28315],{},[1708,41146,1716],{"stretchy":1715},[1753,41148,41149,41151],{},[898,41150,21035],{},[1708,41152,2417],{},[1708,41154,2726],{},[4754,41156,41157,41159,41161],{},[898,41158,1747],{},[2505,41160,2507],{},[1708,41162,2417],{},[1743,41164,41165,41167],{},[898,41166,1688],{},[2505,41168,2507],{},[1708,41170,2726],{},[4754,41172,41173,41175,41177],{},[898,41174,1747],{},[2505,41176,3132],{},[1708,41178,2417],{},[1743,41180,41181,41183],{},[898,41182,1688],{},[2505,41184,3132],{},[1708,41186,1721],{"stretchy":1715},[902,41188,41189],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,41191,41192,22357,41195,41225],{},[38,41193,41194],{},"Spočítej parciální derivace",[883,41196,41198],{"className":41197},[886],[888,41199,41200],{"xmlns":890},[892,41201,41202,41222],{},[895,41203,41204,41210,41212,41218,41220],{},[1743,41205,41206,41208],{},[898,41207,1688],{},[2505,41209,2507],{},[1708,41211,1883],{"separator":1882},[1743,41213,41214,41216],{},[898,41215,1688],{},[2505,41217,3132],{},[1708,41219,1883],{"separator":1882},[898,41221,28315],{},[902,41223,41224],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,41227,41228,41244,41245,41278,41279,1771,41296,2155],{},[38,41229,41230,41231],{},"Vyluč ",[883,41232,41234],{"className":41233},[886],[888,41235,41236],{"xmlns":890},[892,41237,41238,41242],{},[895,41239,41240],{},[898,41241,28315],{},[902,41243,28368],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,41246,41248],{"className":41247},[886],[888,41249,41250],{"xmlns":890},[892,41251,41252,41276],{},[895,41253,41254,41256,41258,41266,41268],{},[2247,41255,13825],{},[1708,41257,1710],{},[4754,41259,41260,41262,41264],{},[898,41261,1747],{},[2505,41263,2507],{},[1708,41265,2417],{},[898,41267,1799],{"mathvariant":1759},[4754,41269,41270,41272,41274],{},[898,41271,1747],{},[2505,41273,3132],{},[1708,41275,2417],{},[902,41277,40826],{"encoding":904},", která dá vztah mezi ",[883,41280,41282],{"className":41281},[886],[888,41283,41284],{"xmlns":890},[892,41285,41286,41294],{},[895,41287,41288],{},[1743,41289,41290,41292],{},[898,41291,1688],{},[2505,41293,2507],{},[902,41295,40849],{"encoding":904},[883,41297,41299],{"className":41298},[886],[888,41300,41301],{"xmlns":890},[892,41302,41303,41311],{},[895,41304,41305],{},[1743,41306,41307,41309],{},[898,41308,1688],{},[2505,41310,3132],{},[902,41312,40868],{"encoding":904},[123,41314,41315,41318,41319,41349,41350,41367,41368,2155],{},[38,41316,41317],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,41320,41322],{"className":41321},[886],[888,41323,41324],{"xmlns":890},[892,41325,41326,41346],{},[895,41327,41328,41336,41338],{},[4754,41329,41330,41332,41334],{},[898,41331,1688],{},[2505,41333,2507],{},[1708,41335,2417],{},[1708,41337,1883],{"separator":1882},[4754,41339,41340,41342,41344],{},[898,41341,1688],{},[2505,41343,3132],{},[1708,41345,2417],{},[902,41347,41348],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,41351,41353],{"className":41352},[886],[888,41354,41355],{"xmlns":890},[892,41356,41357,41365],{},[895,41358,41359],{},[1753,41360,41361,41363],{},[898,41362,28315],{},[1708,41364,2417],{},[902,41366,40988],{"encoding":904}," a maximální užitečnost ",[883,41369,41371],{"className":41370},[886],[888,41372,41373],{"xmlns":890},[892,41374,41375,41409],{},[895,41376,41377,41383,41385,41387,41389,41397,41399,41407],{},[1753,41378,41379,41381],{},[898,41380,900],{},[1708,41382,2417],{},[1708,41384,1710],{},[898,41386,900],{},[1708,41388,1716],{"stretchy":1715},[4754,41390,41391,41393,41395],{},[898,41392,1688],{},[2505,41394,2507],{},[1708,41396,2417],{},[1708,41398,1883],{"separator":1882},[4754,41400,41401,41403,41405],{},[898,41402,1688],{},[2505,41404,3132],{},[1708,41406,2417],{},[1708,41408,1721],{"stretchy":1715},[902,41410,41411],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,41413,41415],{"id":41414},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,41417,41418],{},[3372,41419],{"alt":41420,"className":41421,"src":41422},"imek-uzitecnost-optimum",[210,3376],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,41424,41425],{},[614,41426,41427,41428,41477,41478,1771,41506,41534,41535,41569,41570,41609,41610,41628,41629,41647,41648,41666],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,41429,41431],{"className":41430},[886],[888,41432,41433],{"xmlns":890},[892,41434,41435,41475],{},[895,41436,41437,41443,41445,41453,41459,41461,41469],{},[1753,41438,41439,41441],{},[898,41440,21035],{},[1708,41442,2417],{},[1708,41444,1710],{},[4754,41446,41447,41449,41451],{},[898,41448,1747],{},[2505,41450,2507],{},[1708,41452,2417],{},[1743,41454,41455,41457],{},[898,41456,1688],{},[2505,41458,2507],{},[1708,41460,2019],{},[4754,41462,41463,41465,41467],{},[898,41464,1747],{},[2505,41466,3132],{},[1708,41468,2417],{},[1743,41470,41471,41473],{},[898,41472,1688],{},[2505,41474,3132],{},[902,41476,29170],{"encoding":904}," protíná osy v ",[883,41479,41481],{"className":41480},[886],[888,41482,41483],{"xmlns":890},[892,41484,41485,41503],{},[895,41486,41487,41493,41495],{},[1753,41488,41489,41491],{},[898,41490,21035],{},[1708,41492,2417],{},[898,41494,1799],{"mathvariant":1759},[4754,41496,41497,41499,41501],{},[898,41498,1747],{},[2505,41500,2507],{},[1708,41502,2417],{},[902,41504,41505],{"encoding":904},"Y^*\u002FP_1^*",[883,41507,41509],{"className":41508},[886],[888,41510,41511],{"xmlns":890},[892,41512,41513,41531],{},[895,41514,41515,41521,41523],{},[1753,41516,41517,41519],{},[898,41518,21035],{},[1708,41520,2417],{},[898,41522,1799],{"mathvariant":1759},[4754,41524,41525,41527,41529],{},[898,41526,1747],{},[2505,41528,3132],{},[1708,41530,2417],{},[902,41532,41533],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,41536,41538],{"className":41537},[886],[888,41539,41540],{"xmlns":890},[892,41541,41542,41566],{},[895,41543,41544,41550,41552,41558,41560],{},[1743,41545,41546,41548],{},[898,41547,14142],{},[2505,41549,2507],{},[1708,41551,2932],{},[1753,41553,41554,41556],{},[898,41555,14142],{},[1708,41557,2417],{},[1708,41559,2932],{},[1743,41561,41562,41564],{},[898,41563,14142],{},[2505,41565,3132],{},[902,41567,41568],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,41571,41573],{"className":41572},[886],[888,41574,41575],{"xmlns":890},[892,41576,41577,41607],{},[895,41578,41579,41585,41587,41595,41597,41605],{},[1753,41580,41581,41583],{},[898,41582,1688],{},[1708,41584,2417],{},[1708,41586,6940],{"stretchy":1715},[4754,41588,41589,41591,41593],{},[898,41590,1688],{},[2505,41592,2507],{},[1708,41594,2417],{},[1708,41596,1883],{"separator":1882},[4754,41598,41599,41601,41603],{},[898,41600,1688],{},[2505,41602,3132],{},[1708,41604,2417],{},[1708,41606,6981],{"stretchy":1715},[902,41608,40174],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,41611,41613],{"className":41612},[886],[888,41614,41615],{"xmlns":890},[892,41616,41617,41625],{},[895,41618,41619],{},[1753,41620,41621,41623],{},[898,41622,14142],{},[1708,41624,2417],{},[902,41626,41627],{"encoding":904},"c^*",". Křivka ",[883,41630,41632],{"className":41631},[886],[888,41633,41634],{"xmlns":890},[892,41635,41636,41644],{},[895,41637,41638],{},[1743,41639,41640,41642],{},[898,41641,14142],{},[2505,41643,2507],{},[902,41645,41646],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,41649,41651],{"className":41650},[886],[888,41652,41653],{"xmlns":890},[892,41654,41655,41663],{},[895,41656,41657],{},[1743,41658,41659,41661],{},[898,41660,14142],{},[2505,41662,3132],{},[902,41664,41665],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,41668,41669,41670,41673,41674,41692,41693,41722],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,41671,41672],{},"dotýkají",", tj. mají v bodě ",[883,41675,41677],{"className":41676},[886],[888,41678,41679],{"xmlns":890},[892,41680,41681,41689],{},[895,41682,41683],{},[1753,41684,41685,41687],{},[898,41686,1688],{},[1708,41688,2417],{},[902,41690,41691],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,41694,41696],{"className":41695},[886],[888,41697,41698],{"xmlns":890},[892,41699,41700,41720],{},[895,41701,41702,41704,41706,41712,41714],{},[2247,41703,13825],{},[1708,41705,1710],{},[1743,41707,41708,41710],{},[898,41709,1747],{},[2505,41711,2507],{},[898,41713,1799],{"mathvariant":1759},[1743,41715,41716,41718],{},[898,41717,1747],{},[2505,41719,3132],{},[902,41721,39848],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,41724,41726],{"id":41725},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,41728,3818,41729,7911],{},[883,41730,41732],{"className":41731},[886],[888,41733,41734],{"xmlns":890},[892,41735,41736,41788],{},[895,41737,41738,41740,41742,41748,41750,41756,41758,41760,41774],{},[898,41739,900],{},[1708,41741,1716],{"stretchy":1715},[1743,41743,41744,41746],{},[898,41745,1688],{},[2505,41747,2507],{},[1708,41749,1883],{"separator":1882},[1743,41751,41752,41754],{},[898,41753,1688],{},[2505,41755,3132],{},[1708,41757,1721],{"stretchy":1715},[1708,41759,1710],{},[4754,41761,41762,41764,41766],{},[898,41763,1688],{},[2505,41765,2507],{},[895,41767,41768,41770,41772],{},[2505,41769,2507],{},[898,41771,1799],{"mathvariant":1759},[2505,41773,3132],{},[4754,41775,41776,41778,41780],{},[898,41777,1688],{},[2505,41779,3132],{},[895,41781,41782,41784,41786],{},[2505,41783,2507],{},[898,41785,1799],{"mathvariant":1759},[2505,41787,3132],{},[902,41789,41790],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,41792,41793],{},[883,41794,41796],{"className":41795},[886],[888,41797,41798],{"xmlns":890},[892,41799,41800,41906],{},[895,41801,41802,41804,41806,41888,41890,41904],{},[2247,41803,13825],{},[1708,41805,1710],{},[2358,41807,41808,41848],{},[895,41809,41810,41818,41834],{},[3194,41811,41812],{"scriptlevel":2784,"displaystyle":1715},[2358,41813,41814,41816],{},[2505,41815,2507],{},[2505,41817,3132],{},[4754,41819,41820,41822,41824],{},[898,41821,1688],{},[2505,41823,2507],{},[895,41825,41826,41828,41830,41832],{},[1708,41827,2726],{},[2505,41829,2507],{},[898,41831,1799],{"mathvariant":1759},[2505,41833,3132],{},[4754,41835,41836,41838,41840],{},[898,41837,1688],{},[2505,41839,3132],{},[895,41841,41842,41844,41846],{},[2505,41843,2507],{},[898,41845,1799],{"mathvariant":1759},[2505,41847,3132],{},[895,41849,41850,41858,41872],{},[3194,41851,41852],{"scriptlevel":2784,"displaystyle":1715},[2358,41853,41854,41856],{},[2505,41855,2507],{},[2505,41857,3132],{},[4754,41859,41860,41862,41864],{},[898,41861,1688],{},[2505,41863,2507],{},[895,41865,41866,41868,41870],{},[2505,41867,2507],{},[898,41869,1799],{"mathvariant":1759},[2505,41871,3132],{},[4754,41873,41874,41876,41878],{},[898,41875,1688],{},[2505,41877,3132],{},[895,41879,41880,41882,41884,41886],{},[1708,41881,2726],{},[2505,41883,2507],{},[898,41885,1799],{"mathvariant":1759},[2505,41887,3132],{},[1708,41889,1710],{},[2358,41891,41892,41898],{},[1743,41893,41894,41896],{},[898,41895,1688],{},[2505,41897,3132],{},[1743,41899,41900,41902],{},[898,41901,1688],{},[2505,41903,2507],{},[898,41905,2155],{"mathvariant":1759},[902,41907,41908],{"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}.",[724,41910,41911,41912,2941,41956,41958,41959,41979,41980,42010,42011,2155],{},"Tedy ",[883,41913,41915],{"className":41914},[886],[888,41916,41917],{"xmlns":890},[892,41918,41919,41953],{},[895,41920,41921,41923,41925,41927,41929,41931,41933,41935,41943,41945],{},[2247,41922,13825],{},[1708,41924,1716],{"stretchy":1715},[2505,41926,11064],{},[1708,41928,1883],{"separator":1882},[2505,41930,11040],{},[1708,41932,1721],{"stretchy":1715},[1708,41934,1710],{},[3194,41936,41937],{"scriptlevel":2784,"displaystyle":1715},[2358,41938,41939,41941],{},[2505,41940,11040],{},[2505,41942,11064],{},[1708,41944,1710],{},[3194,41946,41947],{"scriptlevel":2784,"displaystyle":1715},[2358,41948,41949,41951],{},[2505,41950,3993],{},[2505,41952,3121],{},[902,41954,41955],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,41957,8418],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,41960,41962],{"className":41961},[886],[888,41963,41964],{"xmlns":890},[892,41965,41966,41976],{},[895,41967,41968],{},[3194,41969,41970],{"scriptlevel":2784,"displaystyle":1715},[2358,41971,41972,41974],{},[2505,41973,3993],{},[2505,41975,3121],{},[902,41977,41978],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,41981,41983],{"className":41982},[886],[888,41984,41985],{"xmlns":890},[892,41986,41987,42007],{},[895,41988,41989,41991,41993,41999,42001],{},[2247,41990,13825],{},[1708,41992,1710],{},[1743,41994,41995,41997],{},[898,41996,1688],{},[2505,41998,3132],{},[898,42000,1799],{"mathvariant":1759},[1743,42002,42003,42005],{},[898,42004,1688],{},[2505,42006,2507],{},[902,42008,42009],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,42012,42014],{"className":42013},[886],[888,42015,42016],{"xmlns":890},[892,42017,42018,42038],{},[895,42019,42020,42022,42024,42030,42032],{},[2247,42021,13825],{},[1708,42023,1710],{},[1743,42025,42026,42028],{},[898,42027,1747],{},[2505,42029,2507],{},[898,42031,1799],{"mathvariant":1759},[1743,42033,42034,42036],{},[898,42035,1747],{},[2505,42037,3132],{},[902,42039,39848],{"encoding":904},[115,42041,42043,42044],{"id":42042},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,42045,42047],{"className":42046},[886],[888,42048,42049],{"xmlns":890},[892,42050,42051,42069],{},[895,42052,42053,42055,42057,42063],{},[898,42054,900],{},[1708,42056,1710],{},[1743,42058,42059,42061],{},[898,42060,1688],{},[2505,42062,2507],{},[1743,42064,42065,42067],{},[898,42066,1688],{},[2505,42068,3132],{},[902,42070,42071],{"encoding":904},"U = Q_1 Q_2",[724,42073,42074,42075,1343,42121,1343,42145,1343,42169,42191],{},"Je dána ",[883,42076,42078],{"className":42077},[886],[888,42079,42080],{"xmlns":890},[892,42081,42082,42118],{},[895,42083,42084,42086,42088,42094,42096,42102,42104,42106,42112],{},[898,42085,900],{},[1708,42087,1716],{"stretchy":1715},[1743,42089,42090,42092],{},[898,42091,1688],{},[2505,42093,2507],{},[1708,42095,1883],{"separator":1882},[1743,42097,42098,42100],{},[898,42099,1688],{},[2505,42101,3132],{},[1708,42103,1721],{"stretchy":1715},[1708,42105,1710],{},[1743,42107,42108,42110],{},[898,42109,1688],{},[2505,42111,2507],{},[1743,42113,42114,42116],{},[898,42115,1688],{},[2505,42117,3132],{},[902,42119,42120],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,42122,42124],{"className":42123},[886],[888,42125,42126],{"xmlns":890},[892,42127,42128,42142],{},[895,42129,42130,42138,42140],{},[4754,42131,42132,42134,42136],{},[898,42133,1747],{},[2505,42135,2507],{},[1708,42137,2417],{},[1708,42139,1710],{},[2505,42141,3132],{},[902,42143,42144],{"encoding":904},"P_1^* = 2",[883,42146,42148],{"className":42147},[886],[888,42149,42150],{"xmlns":890},[892,42151,42152,42166],{},[895,42153,42154,42162,42164],{},[4754,42155,42156,42158,42160],{},[898,42157,1747],{},[2505,42159,3132],{},[1708,42161,2417],{},[1708,42163,1710],{},[2505,42165,3993],{},[902,42167,42168],{"encoding":904},"P_2^* = 5",[883,42170,42172],{"className":42171},[886],[888,42173,42174],{"xmlns":890},[892,42175,42176,42188],{},[895,42177,42178,42184,42186],{},[1753,42179,42180,42182],{},[898,42181,21035],{},[1708,42183,2417],{},[1708,42185,1710],{},[2505,42187,9238],{},[902,42189,42190],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,42193,42195],{"className":42194},[886],[888,42196,42197],{"xmlns":890,"display":2210},[892,42198,42199,42271],{},[895,42200,42201,42203,42205,42211,42213,42219,42221,42223,42225,42227,42233,42239,42241,42243,42245,42247,42249,42251,42257,42259,42261,42267,42269],{},[898,42202,1658],{"mathvariant":40395},[1708,42204,1716],{"stretchy":1715},[1743,42206,42207,42209],{},[898,42208,1688],{},[2505,42210,2507],{},[1708,42212,1883],{"separator":1882},[1743,42214,42215,42217],{},[898,42216,1688],{},[2505,42218,3132],{},[1708,42220,1883],{"separator":1882},[898,42222,28315],{},[1708,42224,1721],{"stretchy":1715},[1708,42226,1710],{},[1743,42228,42229,42231],{},[898,42230,1688],{},[2505,42232,2507],{},[1743,42234,42235,42237],{},[898,42236,1688],{},[2505,42238,3132],{},[1708,42240,2019],{},[898,42242,28315],{},[1708,42244,1716],{"stretchy":1715},[2505,42246,9238],{},[1708,42248,2726],{},[2505,42250,3132],{},[1743,42252,42253,42255],{},[898,42254,1688],{},[2505,42256,2507],{},[1708,42258,2726],{},[2505,42260,3993],{},[1743,42262,42263,42265],{},[898,42264,1688],{},[2505,42266,3132],{},[1708,42268,1721],{"stretchy":1715},[898,42270,2155],{"mathvariant":1759},[902,42272,42273],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,42275,42276],{},"Soustava:",[883,42278,42280],{"className":42279},[886],[888,42281,42282],{"xmlns":890,"display":2210},[892,42283,42284,42396],{},[2214,42285,42286,42320,42354],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,42287,42288,42306],{},[2221,42289,42290],{},[3194,42291,42292],{"scriptlevel":2784,"displaystyle":1882},[895,42293,42294,42300,42302,42304],{},[1743,42295,42296,42298],{},[898,42297,1688],{},[2505,42299,3132],{},[1708,42301,2726],{},[2505,42303,3132],{},[898,42305,28315],{},[2221,42307,42308],{},[3194,42309,42310],{"scriptlevel":2784,"displaystyle":1882},[895,42311,42312,42314,42316,42318],{},[895,42313],{},[1708,42315,1710],{},[2505,42317,2784],{},[1708,42319,1883],{"separator":1882},[2218,42321,42322,42340],{},[2221,42323,42324],{},[3194,42325,42326],{"scriptlevel":2784,"displaystyle":1882},[895,42327,42328,42334,42336,42338],{},[1743,42329,42330,42332],{},[898,42331,1688],{},[2505,42333,2507],{},[1708,42335,2726],{},[2505,42337,3993],{},[898,42339,28315],{},[2221,42341,42342],{},[3194,42343,42344],{"scriptlevel":2784,"displaystyle":1882},[895,42345,42346,42348,42350,42352],{},[895,42347],{},[1708,42349,1710],{},[2505,42351,2784],{},[1708,42353,1883],{"separator":1882},[2218,42355,42356,42384],{},[2221,42357,42358],{},[3194,42359,42360],{"scriptlevel":2784,"displaystyle":1882},[895,42361,42362,42364,42366,42368,42374,42376,42378],{},[2505,42363,9238],{},[1708,42365,2726],{},[2505,42367,3132],{},[1743,42369,42370,42372],{},[898,42371,1688],{},[2505,42373,2507],{},[1708,42375,2726],{},[2505,42377,3993],{},[1743,42379,42380,42382],{},[898,42381,1688],{},[2505,42383,3132],{},[2221,42385,42386],{},[3194,42387,42388],{"scriptlevel":2784,"displaystyle":1882},[895,42389,42390,42392,42394],{},[895,42391],{},[1708,42393,1710],{},[2505,42395,24346],{},[902,42397,42398],{"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}",[724,42400,42401,42402,1343,42426,42450,42451,17508,42491,42509,42510,42560,42561,2155],{},"Z prvních dvou rovnic ",[883,42403,42405],{"className":42404},[886],[888,42406,42407],{"xmlns":890},[892,42408,42409,42423],{},[895,42410,42411,42417,42419,42421],{},[1743,42412,42413,42415],{},[898,42414,1688],{},[2505,42416,3132],{},[1708,42418,1710],{},[2505,42420,3132],{},[898,42422,28315],{},[902,42424,42425],{"encoding":904},"Q_2 = 2\\lambda",[883,42427,42429],{"className":42428},[886],[888,42430,42431],{"xmlns":890},[892,42432,42433,42447],{},[895,42434,42435,42441,42443,42445],{},[1743,42436,42437,42439],{},[898,42438,1688],{},[2505,42440,2507],{},[1708,42442,1710],{},[2505,42444,3993],{},[898,42446,28315],{},[902,42448,42449],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,42452,42454],{"className":42453},[886],[888,42455,42456],{"xmlns":890},[892,42457,42458,42488],{},[895,42459,42460,42462,42464,42466,42468,42470,42472,42474,42476,42478,42480,42482,42484,42486],{},[2505,42461,9238],{},[1708,42463,1710],{},[2505,42465,3132],{},[1708,42467,3703],{},[2505,42469,3993],{},[898,42471,28315],{},[1708,42473,2019],{},[2505,42475,3993],{},[1708,42477,3703],{},[2505,42479,3132],{},[898,42481,28315],{},[1708,42483,1710],{},[2505,42485,4018],{},[898,42487,28315],{},[902,42489,42490],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,42492,42494],{"className":42493},[886],[888,42495,42496],{"xmlns":890},[892,42497,42498,42506],{},[895,42499,42500,42502,42504],{},[898,42501,28315],{},[1708,42503,1710],{},[2505,42505,3993],{},[902,42507,42508],{"encoding":904},"\\lambda = 5",". Odtud ",[38,42511,42512,1343,42536],{},[883,42513,42515],{"className":42514},[886],[888,42516,42517],{"xmlns":890},[892,42518,42519,42533],{},[895,42520,42521,42529,42531],{},[4754,42522,42523,42525,42527],{},[898,42524,1688],{},[2505,42526,2507],{},[1708,42528,2417],{},[1708,42530,1710],{},[2505,42532,4028],{},[902,42534,42535],{"encoding":904},"Q_1^* = 25",[883,42537,42539],{"className":42538},[886],[888,42540,42541],{"xmlns":890},[892,42542,42543,42557],{},[895,42544,42545,42553,42555],{},[4754,42546,42547,42549,42551],{},[898,42548,1688],{},[2505,42550,3132],{},[1708,42552,2417],{},[1708,42554,1710],{},[2505,42556,4003],{},[902,42558,42559],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,42562,42564],{"className":42563},[886],[888,42565,42566],{"xmlns":890},[892,42567,42568,42588],{},[895,42569,42570,42576,42578,42580,42582,42584,42586],{},[1753,42571,42572,42574],{},[898,42573,900],{},[1708,42575,2417],{},[1708,42577,1710],{},[2505,42579,4028],{},[1708,42581,3703],{},[2505,42583,4003],{},[1708,42585,1710],{},[2505,42587,11594],{},[902,42589,42590],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,42592,42593],{},[614,42594,42595,42596,39984,42634,1771,42658,42682,42683,42713,42714,42738,42739,42761,42762,2155],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,42597,42599],{"className":42598},[886],[888,42600,42601],{"xmlns":890},[892,42602,42603,42631],{},[895,42604,42605,42607,42609,42611,42617,42619,42621,42627,42629],{},[2505,42606,9238],{},[1708,42608,2726],{},[2505,42610,3132],{},[1743,42612,42613,42615],{},[898,42614,1688],{},[2505,42616,2507],{},[1708,42618,2726],{},[2505,42620,3993],{},[1743,42622,42623,42625],{},[898,42624,1688],{},[2505,42626,3132],{},[1708,42628,1710],{},[2505,42630,2784],{},[902,42632,42633],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,42635,42637],{"className":42636},[886],[888,42638,42639],{"xmlns":890},[892,42640,42641,42655],{},[895,42642,42643,42645,42647,42649,42651,42653],{},[898,42644,1786],{},[1708,42646,6940],{"stretchy":1715},[2505,42648,2784],{},[1708,42650,1883],{"separator":1882},[2505,42652,4018],{},[1708,42654,6981],{"stretchy":1715},[902,42656,42657],{"encoding":904},"A[0, 20]",[883,42659,42661],{"className":42660},[886],[888,42662,42663],{"xmlns":890},[892,42664,42665,42679],{},[895,42666,42667,42669,42671,42673,42675,42677],{},[898,42668,35110],{},[1708,42670,6940],{"stretchy":1715},[2505,42672,9704],{},[1708,42674,1883],{"separator":1882},[2505,42676,2784],{},[1708,42678,6981],{"stretchy":1715},[902,42680,42681],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,42684,42686],{"className":42685},[886],[888,42687,42688],{"xmlns":890},[892,42689,42690,42710],{},[895,42691,42692,42698,42700,42702,42704],{},[1743,42693,42694,42696],{},[898,42695,1688],{},[2505,42697,3132],{},[1708,42699,1710],{},[2505,42701,11594],{},[898,42703,1799],{"mathvariant":1759},[1743,42705,42706,42708],{},[898,42707,1688],{},[2505,42709,2507],{},[902,42711,42712],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,42715,42717],{"className":42716},[886],[888,42718,42719],{"xmlns":890},[892,42720,42721,42735],{},[895,42722,42723,42725,42727,42729,42731,42733],{},[898,42724,16183],{},[1708,42726,6940],{"stretchy":1715},[2505,42728,4028],{},[1708,42730,1883],{"separator":1882},[2505,42732,4003],{},[1708,42734,6981],{"stretchy":1715},[902,42736,42737],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,42740,42742],{"className":42741},[886],[888,42743,42744],{"xmlns":890},[892,42745,42746,42758],{},[895,42747,42748,42750],{},[1708,42749,2726],{},[3194,42751,42752],{"scriptlevel":2784,"displaystyle":1715},[2358,42753,42754,42756],{},[2505,42755,3132],{},[2505,42757,3993],{},[902,42759,42760],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,42763,42765],{"className":42764},[886],[888,42766,42767],{"xmlns":890},[892,42768,42769,42809],{},[895,42770,42771,42773,42775,42777,42779,42781,42783,42785,42787,42789,42797,42799,42801],{},[1708,42772,2726],{},[2247,42774,13825],{},[1708,42776,1716],{"stretchy":1715},[2505,42778,4028],{},[1708,42780,1883],{"separator":1882},[2505,42782,4003],{},[1708,42784,1721],{"stretchy":1715},[1708,42786,1710],{},[1708,42788,2726],{},[3194,42790,42791],{"scriptlevel":2784,"displaystyle":1715},[2358,42792,42793,42795],{},[2505,42794,4003],{},[2505,42796,4028],{},[1708,42798,1710],{},[1708,42800,2726],{},[3194,42802,42803],{"scriptlevel":2784,"displaystyle":1715},[2358,42804,42805,42807],{},[2505,42806,3132],{},[2505,42808,3993],{},[902,42810,42811],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,42813,42815],{"id":42814},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,42817,42818,42819,40850,42849,42852,42853,2788],{},"Považujeme-li v úloze ",[883,42820,42822],{"className":42821},[886],[888,42823,42824],{"xmlns":890},[892,42825,42826,42846],{},[895,42827,42828,42834,42836,42842,42844],{},[1743,42829,42830,42832],{},[898,42831,1747],{},[2505,42833,2507],{},[1708,42835,1883],{"separator":1882},[1743,42837,42838,42840],{},[898,42839,1747],{},[2505,42841,3132],{},[1708,42843,1883],{"separator":1882},[898,42845,21035],{},[902,42847,42848],{"encoding":904},"P_1, P_2, Y",[38,42850,42851],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,42854,42855],{},"Marshallovy poptávkové funkce",[883,42857,42859],{"className":42858},[886],[888,42860,42861],{"xmlns":890,"display":2210},[892,42862,42863,42958],{},[2214,42864,42865],{"width":2216},[2218,42866,42867,42869,42951,42953],{},[2221,42868],{"width":2223},[2221,42870,42871],{},[895,42872,42873,42879,42881,42887,42889,42895,42897,42903,42905,42907,42909,42911,42913,42919,42921,42927,42929,42935,42937,42943,42945,42947,42949],{},[1743,42874,42875,42877],{},[898,42876,1688],{},[2505,42878,2507],{},[1708,42880,1710],{},[1743,42882,42883,42885],{},[898,42884,16117],{},[2505,42886,2507],{},[1708,42888,1716],{"stretchy":1715},[1743,42890,42891,42893],{},[898,42892,1747],{},[2505,42894,2507],{},[1708,42896,1883],{"separator":1882},[1743,42898,42899,42901],{},[898,42900,1747],{},[2505,42902,3132],{},[1708,42904,1883],{"separator":1882},[898,42906,21035],{},[1708,42908,1721],{"stretchy":1715},[1708,42910,1883],{"separator":1882},[3213,42912],{"width":4750},[1743,42914,42915,42917],{},[898,42916,1688],{},[2505,42918,3132],{},[1708,42920,1710],{},[1743,42922,42923,42925],{},[898,42924,16117],{},[2505,42926,3132],{},[1708,42928,1716],{"stretchy":1715},[1743,42930,42931,42933],{},[898,42932,1747],{},[2505,42934,2507],{},[1708,42936,1883],{"separator":1882},[1743,42938,42939,42941],{},[898,42940,1747],{},[2505,42942,3132],{},[1708,42944,1883],{"separator":1882},[898,42946,21035],{},[1708,42948,1721],{"stretchy":1715},[1708,42950,1883],{"separator":1882},[2221,42952],{"width":2223},[2221,42954,42955],{},[2247,42956,42957],{},"(6.15)",[902,42959,42960],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,42962,42964],{"className":42963},[886],[888,42965,42966],{"xmlns":890,"display":2210},[892,42967,42968,43015],{},[2214,42969,42970],{"width":2216},[2218,42971,42972,42974,43008,43010],{},[2221,42973],{"width":2223},[2221,42975,42976],{},[895,42977,42978,42980,42982,42984,42986,42992,42994,43000,43002,43004,43006],{},[898,42979,28315],{},[1708,42981,1710],{},[898,42983,28315],{},[1708,42985,1716],{"stretchy":1715},[1743,42987,42988,42990],{},[898,42989,1747],{},[2505,42991,2507],{},[1708,42993,1883],{"separator":1882},[1743,42995,42996,42998],{},[898,42997,1747],{},[2505,42999,3132],{},[1708,43001,1883],{"separator":1882},[898,43003,21035],{},[1708,43005,1721],{"stretchy":1715},[898,43007,2155],{"mathvariant":1759},[2221,43009],{"width":2223},[2221,43011,43012],{},[2247,43013,43014],{},"(6.16)",[902,43016,43017],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,43019,43020,43050,43051,43117],{},[38,43021,43022,43023,2155],{},"Odvození pro ",[883,43024,43026],{"className":43025},[886],[888,43027,43028],{"xmlns":890},[892,43029,43030,43048],{},[895,43031,43032,43034,43036,43042],{},[898,43033,900],{},[1708,43035,1710],{},[1743,43037,43038,43040],{},[898,43039,1688],{},[2505,43041,2507],{},[1743,43043,43044,43046],{},[898,43045,1688],{},[2505,43047,3132],{},[902,43049,42071],{"encoding":904}," Lagrangeova funkce ",[883,43052,43054],{"className":43053},[886],[888,43055,43056],{"xmlns":890},[892,43057,43058,43114],{},[895,43059,43060,43062,43064,43070,43076,43078,43080,43082,43084,43086,43092,43098,43100,43106,43112],{},[898,43061,1658],{"mathvariant":40395},[1708,43063,1710],{},[1743,43065,43066,43068],{},[898,43067,1688],{},[2505,43069,2507],{},[1743,43071,43072,43074],{},[898,43073,1688],{},[2505,43075,3132],{},[1708,43077,2019],{},[898,43079,28315],{},[1708,43081,1716],{"stretchy":1715},[898,43083,21035],{},[1708,43085,2726],{},[1743,43087,43088,43090],{},[898,43089,1747],{},[2505,43091,2507],{},[1743,43093,43094,43096],{},[898,43095,1688],{},[2505,43097,2507],{},[1708,43099,2726],{},[1743,43101,43102,43104],{},[898,43103,1747],{},[2505,43105,3132],{},[1743,43107,43108,43110],{},[898,43109,1688],{},[2505,43111,3132],{},[1708,43113,1721],{"stretchy":1715},[902,43115,43116],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,43119,43121],{"className":43120},[886],[888,43122,43123],{"xmlns":890,"display":2210},[892,43124,43125,43292],{},[2214,43126,43127],{"width":2216},[2218,43128,43129,43131,43285,43287],{},[2221,43130],{"width":2223},[2221,43132,43133],{},[2214,43134,43135,43181,43227],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,43136,43137,43149],{},[2221,43138,43139],{},[3194,43140,43141],{"scriptlevel":2784,"displaystyle":1882},[4754,43142,43143,43145,43147],{},[898,43144,1658],{"mathvariant":40395},[2505,43146,2507],{},[1708,43148,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,43150,43151],{},[3194,43152,43153],{"scriptlevel":2784,"displaystyle":1882},[895,43154,43155,43157,43159,43165,43167,43169,43175,43177,43179],{},[895,43156],{},[1708,43158,1710],{},[1743,43160,43161,43163],{},[898,43162,1688],{},[2505,43164,3132],{},[1708,43166,2726],{},[898,43168,28315],{},[1743,43170,43171,43173],{},[898,43172,1747],{},[2505,43174,2507],{},[1708,43176,1710],{},[2505,43178,2784],{},[1708,43180,1883],{"separator":1882},[2218,43182,43183,43195],{},[2221,43184,43185],{},[3194,43186,43187],{"scriptlevel":2784,"displaystyle":1882},[4754,43188,43189,43191,43193],{},[898,43190,1658],{"mathvariant":40395},[2505,43192,3132],{},[1708,43194,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,43196,43197],{},[3194,43198,43199],{"scriptlevel":2784,"displaystyle":1882},[895,43200,43201,43203,43205,43211,43213,43215,43221,43223,43225],{},[895,43202],{},[1708,43204,1710],{},[1743,43206,43207,43209],{},[898,43208,1688],{},[2505,43210,2507],{},[1708,43212,2726],{},[898,43214,28315],{},[1743,43216,43217,43219],{},[898,43218,1747],{},[2505,43220,3132],{},[1708,43222,1710],{},[2505,43224,2784],{},[1708,43226,1883],{"separator":1882},[2218,43228,43229,43241],{},[2221,43230,43231],{},[3194,43232,43233],{"scriptlevel":2784,"displaystyle":1882},[4754,43234,43235,43237,43239],{},[898,43236,1658],{"mathvariant":40395},[898,43238,28315],{},[1708,43240,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,43242,43243],{},[3194,43244,43245],{"scriptlevel":2784,"displaystyle":1882},[895,43246,43247,43249,43251,43253,43255,43261,43267,43269,43275,43281,43283],{},[895,43248],{},[1708,43250,1710],{},[898,43252,21035],{},[1708,43254,2726],{},[1743,43256,43257,43259],{},[898,43258,1747],{},[2505,43260,2507],{},[1743,43262,43263,43265],{},[898,43264,1688],{},[2505,43266,2507],{},[1708,43268,2726],{},[1743,43270,43271,43273],{},[898,43272,1747],{},[2505,43274,3132],{},[1743,43276,43277,43279],{},[898,43278,1688],{},[2505,43280,3132],{},[1708,43282,1710],{},[2505,43284,24346],{},[2221,43286],{"width":2223},[2221,43288,43289],{},[2247,43290,43291],{},"(6.17)",[902,43293,43294],{"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}",[724,43296,43297,43298,43326,43327,43355,43356,43424],{},"Z prvních dvou: ",[883,43299,43301],{"className":43300},[886],[888,43302,43303],{"xmlns":890},[892,43304,43305,43323],{},[895,43306,43307,43313,43315,43321],{},[1743,43308,43309,43311],{},[898,43310,1688],{},[2505,43312,3132],{},[1708,43314,1710],{},[1743,43316,43317,43319],{},[898,43318,1747],{},[2505,43320,2507],{},[898,43322,28315],{},[902,43324,43325],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,43328,43330],{"className":43329},[886],[888,43331,43332],{"xmlns":890},[892,43333,43334,43352],{},[895,43335,43336,43342,43344,43350],{},[1743,43337,43338,43340],{},[898,43339,1688],{},[2505,43341,2507],{},[1708,43343,1710],{},[1743,43345,43346,43348],{},[898,43347,1747],{},[2505,43349,3132],{},[898,43351,28315],{},[902,43353,43354],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,43357,43359],{"className":43358},[886],[888,43360,43361],{"xmlns":890},[892,43362,43363,43421],{},[895,43364,43365,43367,43369,43375,43377,43383,43385,43387,43393,43395,43401,43403,43405,43407,43413,43419],{},[898,43366,21035],{},[1708,43368,1710],{},[1743,43370,43371,43373],{},[898,43372,1747],{},[2505,43374,2507],{},[1708,43376,3703],{},[1743,43378,43379,43381],{},[898,43380,1747],{},[2505,43382,3132],{},[898,43384,28315],{},[1708,43386,2019],{},[1743,43388,43389,43391],{},[898,43390,1747],{},[2505,43392,3132],{},[1708,43394,3703],{},[1743,43396,43397,43399],{},[898,43398,1747],{},[2505,43400,2507],{},[898,43402,28315],{},[1708,43404,1710],{},[2505,43406,3132],{},[1743,43408,43409,43411],{},[898,43410,1747],{},[2505,43412,2507],{},[1743,43414,43415,43417],{},[898,43416,1747],{},[2505,43418,3132],{},[898,43420,28315],{},[902,43422,43423],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,43426,43428],{"className":43427},[886],[888,43429,43430],{"xmlns":890,"display":2210},[892,43431,43432,43475],{},[2214,43433,43434],{"width":2216},[2218,43435,43436,43438,43468,43470],{},[2221,43437],{"width":2223},[2221,43439,43440],{},[895,43441,43442,43444,43446,43466],{},[898,43443,28315],{},[1708,43445,1710],{},[2358,43447,43448,43450],{},[898,43449,21035],{},[895,43451,43452,43454,43460],{},[2505,43453,3132],{},[1743,43455,43456,43458],{},[898,43457,1747],{},[2505,43459,2507],{},[1743,43461,43462,43464],{},[898,43463,1747],{},[2505,43465,3132],{},[898,43467,2155],{"mathvariant":1759},[2221,43469],{"width":2223},[2221,43471,43472],{},[2247,43473,43474],{},"(6.20)",[902,43476,43477],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,43479,43480],{},"Zpětně:",[883,43482,43484],{"className":43483},[886],[888,43485,43486],{"xmlns":890,"display":2210},[892,43487,43488,43565],{},[2214,43489,43490],{"width":2216},[2218,43491,43492,43494,43558,43560],{},[2221,43493],{"width":2223},[2221,43495,43496],{},[24717,43497,43498],{"notation":24719},[3194,43499,43500],{"scriptlevel":2784,"displaystyle":1715},[3194,43501,43502],{"scriptlevel":2784,"displaystyle":1715},[3194,43503,43504],{"scriptlevel":2784,"displaystyle":1882},[895,43505,43506,43508,43514,43516,43530,43532,43534,43540,43542,43556],{},[2247,43507,4779],{},[1743,43509,43510,43512],{},[898,43511,1688],{},[2505,43513,2507],{},[1708,43515,1710],{},[2358,43517,43518,43520],{},[898,43519,21035],{},[895,43521,43522,43524],{},[2505,43523,3132],{},[1743,43525,43526,43528],{},[898,43527,1747],{},[2505,43529,2507],{},[1708,43531,1883],{"separator":1882},[3213,43533],{"width":4750},[1743,43535,43536,43538],{},[898,43537,1688],{},[2505,43539,3132],{},[1708,43541,1710],{},[2358,43543,43544,43546],{},[898,43545,21035],{},[895,43547,43548,43550],{},[2505,43549,3132],{},[1743,43551,43552,43554],{},[898,43553,1747],{},[2505,43555,3132],{},[2247,43557,4779],{},[2221,43559],{"width":2223},[2221,43561,43562],{},[2247,43563,43564],{},"(6.21)",[902,43566,43567],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,43569,43571],{"id":43570},"engelova-funkce","Engelova funkce",[724,43573,3818,43574,43577,43578,43581,43582,31731,43599,1343,43629,43659,43660,43694,43695,1343,43721,43747],{},[38,43575,43576],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,43579,43580],{},"Engelovou funkcí",": pro ",[883,43583,43585],{"className":43584},[886],[888,43586,43587],{"xmlns":890},[892,43588,43589,43597],{},[895,43590,43591,43593,43595],{},[898,43592,21035],{},[1708,43594,1710],{},[2505,43596,9238],{},[902,43598,32181],{"encoding":904},[883,43600,43602],{"className":43601},[886],[888,43603,43604],{"xmlns":890},[892,43605,43606,43626],{},[895,43607,43608,43614,43616,43618,43620],{},[1743,43609,43610,43612],{},[898,43611,1688],{},[2505,43613,2507],{},[1708,43615,1710],{},[2505,43617,9704],{},[898,43619,1799],{"mathvariant":1759},[1743,43621,43622,43624],{},[898,43623,1747],{},[2505,43625,2507],{},[902,43627,43628],{"encoding":904},"Q_1 = 50\u002FP_1",[883,43630,43632],{"className":43631},[886],[888,43633,43634],{"xmlns":890},[892,43635,43636,43656],{},[895,43637,43638,43644,43646,43648,43650],{},[1743,43639,43640,43642],{},[898,43641,1688],{},[2505,43643,3132],{},[1708,43645,1710],{},[2505,43647,9704],{},[898,43649,1799],{"mathvariant":1759},[1743,43651,43652,43654],{},[898,43653,1747],{},[2505,43655,3132],{},[902,43657,43658],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,43661,43663],{"className":43662},[886],[888,43664,43665],{"xmlns":890},[892,43666,43667,43691],{},[895,43668,43669,43675,43677,43679,43681,43687,43689],{},[1743,43670,43671,43673],{},[898,43672,1747],{},[2505,43674,2507],{},[1708,43676,1710],{},[2505,43678,4003],{},[1708,43680,1883],{"separator":1882},[1743,43682,43683,43685],{},[898,43684,1747],{},[2505,43686,3132],{},[1708,43688,1710],{},[2505,43690,4018],{},[902,43692,43693],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,43696,43698],{"className":43697},[886],[888,43699,43700],{"xmlns":890},[892,43701,43702,43718],{},[895,43703,43704,43710,43712,43714,43716],{},[1743,43705,43706,43708],{},[898,43707,1688],{},[2505,43709,2507],{},[1708,43711,1710],{},[898,43713,21035],{},[898,43715,1799],{"mathvariant":1759},[2505,43717,4018],{},[902,43719,43720],{"encoding":904},"Q_1 = Y\u002F20",[883,43722,43724],{"className":43723},[886],[888,43725,43726],{"xmlns":890},[892,43727,43728,43744],{},[895,43729,43730,43736,43738,43740,43742],{},[1743,43731,43732,43734],{},[898,43733,1688],{},[2505,43735,3132],{},[1708,43737,1710],{},[898,43739,21035],{},[898,43741,1799],{"mathvariant":1759},[2505,43743,17132],{},[902,43745,43746],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,43749,43751],{"id":43750},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,43753,43754],{},"Výdaje spotřebitele jsou",[883,43756,43758],{"className":43757},[886],[888,43759,43760],{"xmlns":890,"display":2210},[892,43761,43762,43837],{},[2214,43763,43764],{"width":2216},[2218,43765,43766,43768,43830,43832],{},[2221,43767],{"width":2223},[2221,43769,43770],{},[895,43771,43772,43774,43776,43778,43780,43786,43788,43794,43796,43798,43806,43812,43814,43822,43828],{},[898,43773,16183],{},[1708,43775,1710],{},[898,43777,16183],{},[1708,43779,1716],{"stretchy":1715},[1743,43781,43782,43784],{},[898,43783,1688],{},[2505,43785,2507],{},[1708,43787,1883],{"separator":1882},[1743,43789,43790,43792],{},[898,43791,1688],{},[2505,43793,3132],{},[1708,43795,1721],{"stretchy":1715},[1708,43797,1710],{},[4754,43799,43800,43802,43804],{},[898,43801,1747],{},[2505,43803,2507],{},[1708,43805,2417],{},[1743,43807,43808,43810],{},[898,43809,1688],{},[2505,43811,2507],{},[1708,43813,2019],{},[4754,43815,43816,43818,43820],{},[898,43817,1747],{},[2505,43819,3132],{},[1708,43821,2417],{},[1743,43823,43824,43826],{},[898,43825,1688],{},[2505,43827,3132],{},[1708,43829,1883],{"separator":1882},[2221,43831],{"width":2223},[2221,43833,43834],{},[2247,43835,43836],{},"(6.22)",[902,43838,43839],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,43841,43842],{},"a je pevně zadána hladina užitečnosti",[883,43844,43846],{"className":43845},[886],[888,43847,43848],{"xmlns":890,"display":2210},[892,43849,43850,43897],{},[2214,43851,43852],{"width":2216},[2218,43853,43854,43856,43890,43892],{},[2221,43855],{"width":2223},[2221,43857,43858],{},[895,43859,43860,43866,43868,43870,43872,43878,43880,43886,43888],{},[1753,43861,43862,43864],{},[898,43863,900],{},[1708,43865,2417],{},[1708,43867,1710],{},[898,43869,900],{},[1708,43871,1716],{"stretchy":1715},[1743,43873,43874,43876],{},[898,43875,1688],{},[2505,43877,2507],{},[1708,43879,1883],{"separator":1882},[1743,43881,43882,43884],{},[898,43883,1688],{},[2505,43885,3132],{},[1708,43887,1721],{"stretchy":1715},[898,43889,2155],{"mathvariant":1759},[2221,43891],{"width":2223},[2221,43893,43894],{},[2247,43895,43896],{},"(6.23)",[902,43898,43899],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,43901,43902,43905,43906,43938,43939,2155],{},[38,43903,43904],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,43907,43909],{"className":43908},[886],[888,43910,43911],{"xmlns":890},[892,43912,43913,43935],{},[895,43914,43915,43917,43919,43925,43927,43933],{},[898,43916,16183],{},[1708,43918,1716],{"stretchy":1715},[1743,43920,43921,43923],{},[898,43922,1688],{},[2505,43924,2507],{},[1708,43926,1883],{"separator":1882},[1743,43928,43929,43931],{},[898,43930,1688],{},[2505,43932,3132],{},[1708,43934,1721],{"stretchy":1715},[902,43936,43937],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,43940,43942],{"className":43941},[886],[888,43943,43944],{"xmlns":890},[892,43945,43946,44002],{},[895,43947,43948,43950,43952,43958,43960,43966,43968,43970,43976,43978,43980,43982,43988,43990,43996,43998,44000],{},[898,43949,22927],{},[1708,43951,1716],{"stretchy":1715},[1743,43953,43954,43956],{},[898,43955,1688],{},[2505,43957,2507],{},[1708,43959,1883],{"separator":1882},[1743,43961,43962,43964],{},[898,43963,1688],{},[2505,43965,3132],{},[1708,43967,1721],{"stretchy":1715},[1708,43969,1710],{},[1753,43971,43972,43974],{},[898,43973,900],{},[1708,43975,2417],{},[1708,43977,2726],{},[898,43979,900],{},[1708,43981,1716],{"stretchy":1715},[1743,43983,43984,43986],{},[898,43985,1688],{},[2505,43987,2507],{},[1708,43989,1883],{"separator":1882},[1743,43991,43992,43994],{},[898,43993,1688],{},[2505,43995,3132],{},[1708,43997,1721],{"stretchy":1715},[1708,43999,1710],{},[2505,44001,2784],{},[902,44003,44004],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,44006,44008],{"id":44007},"lagrangeova-funkce","Lagrangeova funkce",[883,44010,44012],{"className":44011},[886],[888,44013,44014],{"xmlns":890,"display":2210},[892,44015,44016,44127],{},[2214,44017,44018],{"width":2216},[2218,44019,44020,44022,44120,44122],{},[2221,44021],{"width":2223},[2221,44023,44024],{},[895,44025,44026,44028,44030,44036,44038,44044,44046,44048,44050,44052,44060,44066,44068,44076,44082,44084,44086,44088,44094,44096,44098,44100,44106,44108,44114,44116,44118],{},[898,44027,1658],{"mathvariant":40395},[1708,44029,1716],{"stretchy":1715},[1743,44031,44032,44034],{},[898,44033,1688],{},[2505,44035,2507],{},[1708,44037,1883],{"separator":1882},[1743,44039,44040,44042],{},[898,44041,1688],{},[2505,44043,3132],{},[1708,44045,1883],{"separator":1882},[898,44047,28315],{},[1708,44049,1721],{"stretchy":1715},[1708,44051,1710],{},[4754,44053,44054,44056,44058],{},[898,44055,1747],{},[2505,44057,2507],{},[1708,44059,2417],{},[1743,44061,44062,44064],{},[898,44063,1688],{},[2505,44065,2507],{},[1708,44067,2019],{},[4754,44069,44070,44072,44074],{},[898,44071,1747],{},[2505,44073,3132],{},[1708,44075,2417],{},[1743,44077,44078,44080],{},[898,44079,1688],{},[2505,44081,3132],{},[1708,44083,2019],{},[898,44085,28315],{},[1708,44087,1716],{"stretchy":1715},[1753,44089,44090,44092],{},[898,44091,900],{},[1708,44093,2417],{},[1708,44095,2726],{},[898,44097,900],{},[1708,44099,1716],{"stretchy":1715},[1743,44101,44102,44104],{},[898,44103,1688],{},[2505,44105,2507],{},[1708,44107,1883],{"separator":1882},[1743,44109,44110,44112],{},[898,44111,1688],{},[2505,44113,3132],{},[1708,44115,1721],{"stretchy":1715},[1708,44117,1721],{"stretchy":1715},[898,44119,2155],{"mathvariant":1759},[2221,44121],{"width":2223},[2221,44123,44124],{},[2247,44125,44126],{},"(6.24)",[902,44128,44129],{"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}",[724,44131,44132],{},"Soustava podmínek prvního řádu:",[883,44134,44136],{"className":44135},[886],[888,44137,44138],{"xmlns":890,"display":2210},[892,44139,44140,44313],{},[2214,44141,44142],{"width":2216},[2218,44143,44144,44146,44306,44308],{},[2221,44145],{"width":2223},[2221,44147,44148],{},[2214,44149,44150,44200,44250],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,44151,44152,44164],{},[2221,44153,44154],{},[3194,44155,44156],{"scriptlevel":2784,"displaystyle":1882},[4754,44157,44158,44160,44162],{},[898,44159,1658],{"mathvariant":40395},[2505,44161,2507],{},[1708,44163,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,44165,44166],{},[3194,44167,44168],{"scriptlevel":2784,"displaystyle":1882},[895,44169,44170,44172,44174,44182,44184,44186,44194,44196,44198],{},[895,44171],{},[1708,44173,1710],{},[4754,44175,44176,44178,44180],{},[898,44177,1747],{},[2505,44179,2507],{},[1708,44181,2417],{},[1708,44183,2726],{},[898,44185,28315],{},[4754,44187,44188,44190,44192],{},[898,44189,900],{},[2505,44191,2507],{},[1708,44193,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,44195,1710],{},[2505,44197,2784],{},[1708,44199,1883],{"separator":1882},[2218,44201,44202,44214],{},[2221,44203,44204],{},[3194,44205,44206],{"scriptlevel":2784,"displaystyle":1882},[4754,44207,44208,44210,44212],{},[898,44209,1658],{"mathvariant":40395},[2505,44211,3132],{},[1708,44213,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,44215,44216],{},[3194,44217,44218],{"scriptlevel":2784,"displaystyle":1882},[895,44219,44220,44222,44224,44232,44234,44236,44244,44246,44248],{},[895,44221],{},[1708,44223,1710],{},[4754,44225,44226,44228,44230],{},[898,44227,1747],{},[2505,44229,3132],{},[1708,44231,2417],{},[1708,44233,2726],{},[898,44235,28315],{},[4754,44237,44238,44240,44242],{},[898,44239,900],{},[2505,44241,3132],{},[1708,44243,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,44245,1710],{},[2505,44247,2784],{},[1708,44249,1883],{"separator":1882},[2218,44251,44252,44264],{},[2221,44253,44254],{},[3194,44255,44256],{"scriptlevel":2784,"displaystyle":1882},[4754,44257,44258,44260,44262],{},[898,44259,1658],{"mathvariant":40395},[898,44261,28315],{},[1708,44263,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,44265,44266],{},[3194,44267,44268],{"scriptlevel":2784,"displaystyle":1882},[895,44269,44270,44272,44274,44280,44282,44284,44286,44292,44294,44300,44302,44304],{},[895,44271],{},[1708,44273,1710],{},[1753,44275,44276,44278],{},[898,44277,900],{},[1708,44279,2417],{},[1708,44281,2726],{},[898,44283,900],{},[1708,44285,1716],{"stretchy":1715},[1743,44287,44288,44290],{},[898,44289,1688],{},[2505,44291,2507],{},[1708,44293,1883],{"separator":1882},[1743,44295,44296,44298],{},[898,44297,1688],{},[2505,44299,3132],{},[1708,44301,1721],{"stretchy":1715},[1708,44303,1710],{},[2505,44305,24346],{},[2221,44307],{"width":2223},[2221,44309,44310],{},[2247,44311,44312],{},"(6.25)",[902,44314,44315],{"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}",[724,44317,44318],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,44320,44322],{"className":44321},[886],[888,44323,44324],{"xmlns":890,"display":2210},[892,44325,44326,44424],{},[2214,44327,44328],{"width":2216},[2218,44329,44330,44332,44417,44419],{},[2221,44331],{"width":2223},[2221,44333,44334],{},[895,44335,44336,44338,44340,44346,44348,44354,44356,44358,44360,44362,44364,44366,44415],{},[898,44337,16117],{},[1708,44339,1716],{"stretchy":1715},[1743,44341,44342,44344],{},[898,44343,1688],{},[2505,44345,2507],{},[1708,44347,1883],{"separator":1882},[1743,44349,44350,44352],{},[898,44351,1688],{},[2505,44353,3132],{},[1708,44355,1883],{"separator":1882},[898,44357,28315],{},[1708,44359,1721],{"stretchy":1715},[1708,44361,1710],{},[1708,44363,2726],{},[898,44365,28315],{},[895,44367,44368,44370,44382,44384,44397,44399,44401,44413],{},[1708,44369,1716],{"fence":1882},[4754,44371,44372,44374,44376],{},[898,44373,900],{},[2505,44375,14868],{},[895,44377,44378,44380],{},[1708,44379,1761],{"mathvariant":1759},[1708,44381,1761],{"mathvariant":1759},[1708,44383,2019],{},[4754,44385,44386,44388,44391],{},[898,44387,900],{},[2505,44389,44390],{},"22",[895,44392,44393,44395],{},[1708,44394,1761],{"mathvariant":1759},[1708,44396,1761],{"mathvariant":1759},[1708,44398,2019],{},[2505,44400,3132],{},[4754,44402,44403,44405,44407],{},[898,44404,900],{},[2505,44406,4090],{},[895,44408,44409,44411],{},[1708,44410,1761],{"mathvariant":1759},[1708,44412,1761],{"mathvariant":1759},[1708,44414,1721],{"fence":1882},[898,44416,2155],{"mathvariant":1759},[2221,44418],{"width":2223},[2221,44420,44421],{},[2247,44422,44423],{},"(6.26)",[902,44425,44426],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,44428,44429,44432,44433,44472,44473,44512,44513,44563,44564,44590,44591,44608,44609,44635],{},[38,44430,44431],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,44434,44436],{"className":44435},[886],[888,44437,44438],{"xmlns":890},[892,44439,44440,44470],{},[895,44441,44442,44448,44450,44458,44460,44468],{},[1753,44443,44444,44446],{},[898,44445,1688],{},[1708,44447,2417],{},[1708,44449,6940],{"stretchy":1715},[4754,44451,44452,44454,44456],{},[898,44453,1688],{},[2505,44455,2507],{},[1708,44457,2417],{},[1708,44459,1883],{"separator":1882},[4754,44461,44462,44464,44466],{},[898,44463,1688],{},[2505,44465,3132],{},[1708,44467,2417],{},[1708,44469,6981],{"stretchy":1715},[902,44471,40174],{"encoding":904}," dotyku křivky užitečnosti ",[883,44474,44476],{"className":44475},[886],[888,44477,44478],{"xmlns":890},[892,44479,44480,44510],{},[895,44481,44482,44488,44490,44492,44494,44500,44502,44508],{},[1753,44483,44484,44486],{},[898,44485,900],{},[1708,44487,2417],{},[1708,44489,1710],{},[898,44491,900],{},[1708,44493,1716],{"stretchy":1715},[1743,44495,44496,44498],{},[898,44497,1688],{},[2505,44499,2507],{},[1708,44501,1883],{"separator":1882},[1743,44503,44504,44506],{},[898,44505,1688],{},[2505,44507,3132],{},[1708,44509,1721],{"stretchy":1715},[902,44511,29536],{"encoding":904}," s přímkou výdajů ",[883,44514,44516],{"className":44515},[886],[888,44517,44518],{"xmlns":890},[892,44519,44520,44560],{},[895,44521,44522,44528,44530,44538,44544,44546,44554],{},[1753,44523,44524,44526],{},[898,44525,16183],{},[1708,44527,2417],{},[1708,44529,1710],{},[4754,44531,44532,44534,44536],{},[898,44533,1747],{},[2505,44535,2507],{},[1708,44537,2417],{},[1743,44539,44540,44542],{},[898,44541,1688],{},[2505,44543,2507],{},[1708,44545,2019],{},[4754,44547,44548,44550,44552],{},[898,44549,1747],{},[2505,44551,3132],{},[1708,44553,2417],{},[1743,44555,44556,44558],{},[898,44557,1688],{},[2505,44559,3132],{},[902,44561,44562],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,44565,44567],{"className":44566},[886],[888,44568,44569],{"xmlns":890},[892,44570,44571,44587],{},[895,44572,44573,44579,44581],{},[1743,44574,44575,44577],{},[898,44576,16183],{},[2505,44578,2784],{},[1708,44580,2932],{},[1753,44582,44583,44585],{},[898,44584,16183],{},[1708,44586,2417],{},[902,44588,44589],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,44592,44594],{"className":44593},[886],[888,44595,44596],{"xmlns":890},[892,44597,44598,44606],{},[895,44599,44600],{},[1753,44601,44602,44604],{},[898,44603,900],{},[1708,44605,2417],{},[902,44607,39812],{"encoding":904},", hladina ",[883,44610,44612],{"className":44611},[886],[888,44613,44614],{"xmlns":890},[892,44615,44616,44632],{},[895,44617,44618,44624,44626],{},[1743,44619,44620,44622],{},[898,44621,16183],{},[2505,44623,2507],{},[1708,44625,2854],{},[1753,44627,44628,44630],{},[898,44629,16183],{},[1708,44631,2417],{},[902,44633,44634],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1636,44637,44638,44643],{},[724,44639,44640,44642],{},[883,44641,3465],{}," Postup — duální úloha (minimalizace výdajů)",[152,44644,44645,44695,44781,44821,44896],{},[123,44646,44647,1729,44650,44694],{},[38,44648,44649],{},"Zapiš vazbu",[883,44651,44653],{"className":44652},[886],[888,44654,44655],{"xmlns":890},[892,44656,44657,44691],{},[895,44658,44659,44665,44667,44669,44671,44677,44679,44685,44687,44689],{},[1753,44660,44661,44663],{},[898,44662,900],{},[1708,44664,2417],{},[1708,44666,2726],{},[898,44668,900],{},[1708,44670,1716],{"stretchy":1715},[1743,44672,44673,44675],{},[898,44674,1688],{},[2505,44676,2507],{},[1708,44678,1883],{"separator":1882},[1743,44680,44681,44683],{},[898,44682,1688],{},[2505,44684,3132],{},[1708,44686,1721],{"stretchy":1715},[1708,44688,1710],{},[2505,44690,2784],{},[902,44692,44693],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,44696,44697,1729,44699,2155],{},[38,44698,41107],{},[883,44700,44702],{"className":44701},[886],[888,44703,44704],{"xmlns":890},[892,44705,44706,44778],{},[895,44707,44708,44710,44712,44720,44726,44728,44736,44742,44744,44746,44748,44754,44756,44758,44760,44766,44768,44774,44776],{},[898,44709,1658],{"mathvariant":40395},[1708,44711,1710],{},[4754,44713,44714,44716,44718],{},[898,44715,1747],{},[2505,44717,2507],{},[1708,44719,2417],{},[1743,44721,44722,44724],{},[898,44723,1688],{},[2505,44725,2507],{},[1708,44727,2019],{},[4754,44729,44730,44732,44734],{},[898,44731,1747],{},[2505,44733,3132],{},[1708,44735,2417],{},[1743,44737,44738,44740],{},[898,44739,1688],{},[2505,44741,3132],{},[1708,44743,2019],{},[898,44745,28315],{},[1708,44747,1716],{"stretchy":1715},[1753,44749,44750,44752],{},[898,44751,900],{},[1708,44753,2417],{},[1708,44755,2726],{},[898,44757,900],{},[1708,44759,1716],{"stretchy":1715},[1743,44761,44762,44764],{},[898,44763,1688],{},[2505,44765,2507],{},[1708,44767,1883],{"separator":1882},[1743,44769,44770,44772],{},[898,44771,1688],{},[2505,44773,3132],{},[1708,44775,1721],{"stretchy":1715},[1708,44777,1721],{"stretchy":1715},[902,44779,44780],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,44782,44783,44786,44787,44820],{},[38,44784,44785],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,44788,44790],{"className":44789},[886],[888,44791,44792],{"xmlns":890},[892,44793,44794,44818],{},[895,44795,44796,44798,44800,44808,44810],{},[2247,44797,13825],{},[1708,44799,1710],{},[4754,44801,44802,44804,44806],{},[898,44803,1747],{},[2505,44805,2507],{},[1708,44807,2417],{},[898,44809,1799],{"mathvariant":1759},[4754,44811,44812,44814,44816],{},[898,44813,1747],{},[2505,44815,3132],{},[1708,44817,2417],{},[902,44819,40826],{"encoding":904}," (stejná jako u maximalizace!).",[123,44822,44823,1729,44826,44866,44867,2155],{},[38,44824,44825],{},"Dosaď do vazby",[883,44827,44829],{"className":44828},[886],[888,44830,44831],{"xmlns":890},[892,44832,44833,44863],{},[895,44834,44835,44837,44839,44845,44847,44853,44855,44857],{},[898,44836,900],{},[1708,44838,1716],{"stretchy":1715},[1743,44840,44841,44843],{},[898,44842,1688],{},[2505,44844,2507],{},[1708,44846,1883],{"separator":1882},[1743,44848,44849,44851],{},[898,44850,1688],{},[2505,44852,3132],{},[1708,44854,1721],{"stretchy":1715},[1708,44856,1710],{},[1753,44858,44859,44861],{},[898,44860,900],{},[1708,44862,2417],{},[902,44864,44865],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,44868,44870],{"className":44869},[886],[888,44871,44872],{"xmlns":890},[892,44873,44874,44894],{},[895,44875,44876,44884,44886],{},[4754,44877,44878,44880,44882],{},[898,44879,1688],{},[2505,44881,2507],{},[1708,44883,2417],{},[1708,44885,1883],{"separator":1882},[4754,44887,44888,44890,44892],{},[898,44889,1688],{},[2505,44891,3132],{},[1708,44893,2417],{},[902,44895,41348],{"encoding":904},[123,44897,44898,1729,44901,44955],{},[38,44899,44900],{},"Vypočítej minimální výdaje",[883,44902,44904],{"className":44903},[886],[888,44905,44906],{"xmlns":890},[892,44907,44908,44952],{},[895,44909,44910,44916,44918,44926,44934,44936,44944],{},[1753,44911,44912,44914],{},[898,44913,16183],{},[1708,44915,2417],{},[1708,44917,1710],{},[4754,44919,44920,44922,44924],{},[898,44921,1747],{},[2505,44923,2507],{},[1708,44925,2417],{},[4754,44927,44928,44930,44932],{},[898,44929,1688],{},[2505,44931,2507],{},[1708,44933,2417],{},[1708,44935,2019],{},[4754,44937,44938,44940,44942],{},[898,44939,1747],{},[2505,44941,3132],{},[1708,44943,2417],{},[4754,44945,44946,44948,44950],{},[898,44947,1688],{},[2505,44949,3132],{},[1708,44951,2417],{},[902,44953,44954],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,44957,44959,44960],{"id":44958},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,44961,44963],{"className":44962},[886],[888,44964,44965],{"xmlns":890},[892,44966,44967,45001],{},[895,44968,44969,44971,44973,44987],{},[898,44970,900],{},[1708,44972,1710],{},[4754,44974,44975,44977,44979],{},[898,44976,1688],{},[2505,44978,2507],{},[895,44980,44981,44983,44985],{},[2505,44982,2507],{},[898,44984,1799],{"mathvariant":1759},[2505,44986,3132],{},[4754,44988,44989,44991,44993],{},[898,44990,1688],{},[2505,44992,3132],{},[895,44994,44995,44997,44999],{},[2505,44996,2507],{},[898,44998,1799],{"mathvariant":1759},[2505,45000,3132],{},[902,45002,45003],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,45005,45006,45007,1343,45029,1343,45053,42191],{},"Dáno ",[883,45008,45010],{"className":45009},[886],[888,45011,45012],{"xmlns":890},[892,45013,45014,45026],{},[895,45015,45016,45022,45024],{},[1753,45017,45018,45020],{},[898,45019,900],{},[1708,45021,2417],{},[1708,45023,1710],{},[2505,45025,3132],{},[902,45027,45028],{"encoding":904},"U^* = 2",[883,45030,45032],{"className":45031},[886],[888,45033,45034],{"xmlns":890},[892,45035,45036,45050],{},[895,45037,45038,45046,45048],{},[4754,45039,45040,45042,45044],{},[898,45041,1747],{},[2505,45043,2507],{},[1708,45045,2417],{},[1708,45047,1710],{},[2505,45049,11575],{},[902,45051,45052],{"encoding":904},"P_1^* = 0{,}25",[883,45054,45056],{"className":45055},[886],[888,45057,45058],{"xmlns":890},[892,45059,45060,45074],{},[895,45061,45062,45070,45072],{},[4754,45063,45064,45066,45068],{},[898,45065,1747],{},[2505,45067,3132],{},[1708,45069,2417],{},[1708,45071,1710],{},[2505,45073,2507],{},[902,45075,45076],{"encoding":904},"P_2^* = 1",[883,45078,45080],{"className":45079},[886],[888,45081,45082],{"xmlns":890,"display":2210},[892,45083,45084,45148],{},[895,45085,45086,45088,45090,45092,45098,45100,45106,45108,45110,45112,45114,45116,45130,45144,45146],{},[898,45087,1658],{"mathvariant":40395},[1708,45089,1710],{},[2505,45091,11575],{},[1743,45093,45094,45096],{},[898,45095,1688],{},[2505,45097,2507],{},[1708,45099,2019],{},[1743,45101,45102,45104],{},[898,45103,1688],{},[2505,45105,3132],{},[1708,45107,2019],{},[898,45109,28315],{},[1708,45111,1716],{"stretchy":1715},[2505,45113,3132],{},[1708,45115,2726],{},[4754,45117,45118,45120,45122],{},[898,45119,1688],{},[2505,45121,2507],{},[895,45123,45124,45126,45128],{},[2505,45125,2507],{},[898,45127,1799],{"mathvariant":1759},[2505,45129,3132],{},[4754,45131,45132,45134,45136],{},[898,45133,1688],{},[2505,45135,3132],{},[895,45137,45138,45140,45142],{},[2505,45139,2507],{},[898,45141,1799],{"mathvariant":1759},[2505,45143,3132],{},[1708,45145,1721],{"stretchy":1715},[898,45147,2155],{"mathvariant":1759},[902,45149,45150],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,45152,42276],{},[883,45154,45156],{"className":45155},[886],[888,45157,45158],{"xmlns":890,"display":2210},[892,45159,45160,45374],{},[2214,45161,45162,45238,45314],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,45163,45164,45176],{},[2221,45165,45166],{},[3194,45167,45168],{"scriptlevel":2784,"displaystyle":1882},[4754,45169,45170,45172,45174],{},[898,45171,1658],{"mathvariant":40395},[2505,45173,2507],{},[1708,45175,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,45177,45178],{},[3194,45179,45180],{"scriptlevel":2784,"displaystyle":1882},[895,45181,45182,45184,45186,45188,45190,45192,45194,45202,45218,45232,45234,45236],{},[895,45183],{},[1708,45185,1710],{},[2505,45187,11575],{},[1708,45189,2726],{},[898,45191,28315],{},[1708,45193,3703],{},[3194,45195,45196],{"scriptlevel":2784,"displaystyle":1715},[2358,45197,45198,45200],{},[2505,45199,2507],{},[2505,45201,3132],{},[4754,45203,45204,45206,45208],{},[898,45205,1688],{},[2505,45207,2507],{},[895,45209,45210,45212,45214,45216],{},[1708,45211,2726],{},[2505,45213,2507],{},[898,45215,1799],{"mathvariant":1759},[2505,45217,3132],{},[4754,45219,45220,45222,45224],{},[898,45221,1688],{},[2505,45223,3132],{},[895,45225,45226,45228,45230],{},[2505,45227,2507],{},[898,45229,1799],{"mathvariant":1759},[2505,45231,3132],{},[1708,45233,1710],{},[2505,45235,2784],{},[1708,45237,1883],{"separator":1882},[2218,45239,45240,45252],{},[2221,45241,45242],{},[3194,45243,45244],{"scriptlevel":2784,"displaystyle":1882},[4754,45245,45246,45248,45250],{},[898,45247,1658],{"mathvariant":40395},[2505,45249,3132],{},[1708,45251,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,45253,45254],{},[3194,45255,45256],{"scriptlevel":2784,"displaystyle":1882},[895,45257,45258,45260,45262,45264,45266,45268,45270,45278,45292,45308,45310,45312],{},[895,45259],{},[1708,45261,1710],{},[2505,45263,2507],{},[1708,45265,2726],{},[898,45267,28315],{},[1708,45269,3703],{},[3194,45271,45272],{"scriptlevel":2784,"displaystyle":1715},[2358,45273,45274,45276],{},[2505,45275,2507],{},[2505,45277,3132],{},[4754,45279,45280,45282,45284],{},[898,45281,1688],{},[2505,45283,2507],{},[895,45285,45286,45288,45290],{},[2505,45287,2507],{},[898,45289,1799],{"mathvariant":1759},[2505,45291,3132],{},[4754,45293,45294,45296,45298],{},[898,45295,1688],{},[2505,45297,3132],{},[895,45299,45300,45302,45304,45306],{},[1708,45301,2726],{},[2505,45303,2507],{},[898,45305,1799],{"mathvariant":1759},[2505,45307,3132],{},[1708,45309,1710],{},[2505,45311,2784],{},[1708,45313,1883],{"separator":1882},[2218,45315,45316,45328],{},[2221,45317,45318],{},[3194,45319,45320],{"scriptlevel":2784,"displaystyle":1882},[4754,45321,45322,45324,45326],{},[898,45323,1658],{"mathvariant":40395},[898,45325,28315],{},[1708,45327,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,45329,45330],{},[3194,45331,45332],{"scriptlevel":2784,"displaystyle":1882},[895,45333,45334,45336,45338,45340,45342,45356,45370,45372],{},[895,45335],{},[1708,45337,1710],{},[2505,45339,3132],{},[1708,45341,2726],{},[4754,45343,45344,45346,45348],{},[898,45345,1688],{},[2505,45347,2507],{},[895,45349,45350,45352,45354],{},[2505,45351,2507],{},[898,45353,1799],{"mathvariant":1759},[2505,45355,3132],{},[4754,45357,45358,45360,45362],{},[898,45359,1688],{},[2505,45361,3132],{},[895,45363,45364,45366,45368],{},[2505,45365,2507],{},[898,45367,1799],{"mathvariant":1759},[2505,45369,3132],{},[1708,45371,1710],{},[2505,45373,24346],{},[902,45375,45376],{"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}",[724,45378,45379,45380,5055,45410,45438,45439,17508,45501,1343,45551,45573,45574,2155],{},"Podílem prvních dvou rovnic: ",[883,45381,45383],{"className":45382},[886],[888,45384,45385],{"xmlns":890},[892,45386,45387,45407],{},[895,45388,45389,45391,45393,45399,45401],{},[2505,45390,11575],{},[1708,45392,1710],{},[1743,45394,45395,45397],{},[898,45396,1688],{},[2505,45398,3132],{},[898,45400,1799],{"mathvariant":1759},[1743,45402,45403,45405],{},[898,45404,1688],{},[2505,45406,2507],{},[902,45408,45409],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,45411,45413],{"className":45412},[886],[888,45414,45415],{"xmlns":890},[892,45416,45417,45435],{},[895,45418,45419,45425,45427,45429],{},[1743,45420,45421,45423],{},[898,45422,1688],{},[2505,45424,3132],{},[1708,45426,1710],{},[2505,45428,11575],{},[1743,45430,45431,45433],{},[898,45432,1688],{},[2505,45434,2507],{},[902,45436,45437],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,45440,45442],{"className":45441},[886],[888,45443,45444],{"xmlns":890},[892,45445,45446,45498],{},[895,45447,45448,45462,45464,45466,45472,45484,45486,45488,45494,45496],{},[4754,45449,45450,45452,45454],{},[898,45451,1688],{},[2505,45453,2507],{},[895,45455,45456,45458,45460],{},[2505,45457,2507],{},[898,45459,1799],{"mathvariant":1759},[2505,45461,3132],{},[1708,45463,1716],{"stretchy":1715},[2505,45465,11575],{},[1743,45467,45468,45470],{},[898,45469,1688],{},[2505,45471,2507],{},[1753,45473,45474,45476],{},[1708,45475,1721],{"stretchy":1715},[895,45477,45478,45480,45482],{},[2505,45479,2507],{},[898,45481,1799],{"mathvariant":1759},[2505,45483,3132],{},[1708,45485,1710],{},[2505,45487,6097],{},[1743,45489,45490,45492],{},[898,45491,1688],{},[2505,45493,2507],{},[1708,45495,1710],{},[2505,45497,3132],{},[902,45499,45500],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,45502,45503,1343,45527],{},[883,45504,45506],{"className":45505},[886],[888,45507,45508],{"xmlns":890},[892,45509,45510,45524],{},[895,45511,45512,45520,45522],{},[4754,45513,45514,45516,45518],{},[898,45515,1688],{},[2505,45517,2507],{},[1708,45519,2417],{},[1708,45521,1710],{},[2505,45523,5867],{},[902,45525,45526],{"encoding":904},"Q_1^* = 4",[883,45528,45530],{"className":45529},[886],[888,45531,45532],{"xmlns":890},[892,45533,45534,45548],{},[895,45535,45536,45544,45546],{},[4754,45537,45538,45540,45542],{},[898,45539,1688],{},[2505,45541,3132],{},[1708,45543,2417],{},[1708,45545,1710],{},[2505,45547,2507],{},[902,45549,45550],{"encoding":904},"Q_2^* = 1",[883,45552,45554],{"className":45553},[886],[888,45555,45556],{"xmlns":890},[892,45557,45558,45570],{},[895,45559,45560,45566,45568],{},[1753,45561,45562,45564],{},[898,45563,28315],{},[1708,45565,2417],{},[1708,45567,1710],{},[2505,45569,2507],{},[902,45571,45572],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,45575,45577],{"className":45576},[886],[888,45578,45579],{"xmlns":890},[892,45580,45581,45609],{},[895,45582,45583,45589,45591,45593,45595,45597,45599,45601,45603,45605,45607],{},[1753,45584,45585,45587],{},[898,45586,16183],{},[1708,45588,2417],{},[1708,45590,1710],{},[2505,45592,11575],{},[1708,45594,3703],{},[2505,45596,5867],{},[1708,45598,2019],{},[2505,45600,2507],{},[1708,45602,3703],{},[2505,45604,2507],{},[1708,45606,1710],{},[2505,45608,3132],{},[902,45610,45611],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,45613,45614,45617,45618,1343,45684,1343,45750,45816,45817,45854,45855,45877,45878,2155],{},[614,45615,45616],{},"Ověření postačující podmínky"," (6.26): ",[883,45619,45621],{"className":45620},[886],[888,45622,45623],{"xmlns":890},[892,45624,45625,45681],{},[895,45626,45627,45639,45641,45643,45651,45667],{},[4754,45628,45629,45631,45633],{},[898,45630,900],{},[2505,45632,14868],{},[895,45634,45635,45637],{},[1708,45636,1761],{"mathvariant":1759},[1708,45638,1761],{"mathvariant":1759},[1708,45640,1710],{},[1708,45642,2726],{},[3194,45644,45645],{"scriptlevel":2784,"displaystyle":1715},[2358,45646,45647,45649],{},[2505,45648,2507],{},[2505,45650,5867],{},[4754,45652,45653,45655,45657],{},[898,45654,1688],{},[2505,45656,2507],{},[895,45658,45659,45661,45663,45665],{},[1708,45660,2726],{},[2505,45662,3121],{},[898,45664,1799],{"mathvariant":1759},[2505,45666,3132],{},[4754,45668,45669,45671,45673],{},[898,45670,1688],{},[2505,45672,3132],{},[895,45674,45675,45677,45679],{},[2505,45676,2507],{},[898,45678,1799],{"mathvariant":1759},[2505,45680,3132],{},[902,45682,45683],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,45685,45687],{"className":45686},[886],[888,45688,45689],{"xmlns":890},[892,45690,45691,45747],{},[895,45692,45693,45705,45707,45709,45717,45731],{},[4754,45694,45695,45697,45699],{},[898,45696,900],{},[2505,45698,44390],{},[895,45700,45701,45703],{},[1708,45702,1761],{"mathvariant":1759},[1708,45704,1761],{"mathvariant":1759},[1708,45706,1710],{},[1708,45708,2726],{},[3194,45710,45711],{"scriptlevel":2784,"displaystyle":1715},[2358,45712,45713,45715],{},[2505,45714,2507],{},[2505,45716,5867],{},[4754,45718,45719,45721,45723],{},[898,45720,1688],{},[2505,45722,2507],{},[895,45724,45725,45727,45729],{},[2505,45726,2507],{},[898,45728,1799],{"mathvariant":1759},[2505,45730,3132],{},[4754,45732,45733,45735,45737],{},[898,45734,1688],{},[2505,45736,3132],{},[895,45738,45739,45741,45743,45745],{},[1708,45740,2726],{},[2505,45742,3121],{},[898,45744,1799],{"mathvariant":1759},[2505,45746,3132],{},[902,45748,45749],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,45751,45753],{"className":45752},[886],[888,45754,45755],{"xmlns":890},[892,45756,45757,45813],{},[895,45758,45759,45771,45773,45781,45797],{},[4754,45760,45761,45763,45765],{},[898,45762,900],{},[2505,45764,4090],{},[895,45766,45767,45769],{},[1708,45768,1761],{"mathvariant":1759},[1708,45770,1761],{"mathvariant":1759},[1708,45772,1710],{},[3194,45774,45775],{"scriptlevel":2784,"displaystyle":1715},[2358,45776,45777,45779],{},[2505,45778,2507],{},[2505,45780,5867],{},[4754,45782,45783,45785,45787],{},[898,45784,1688],{},[2505,45786,2507],{},[895,45788,45789,45791,45793,45795],{},[1708,45790,2726],{},[2505,45792,2507],{},[898,45794,1799],{"mathvariant":1759},[2505,45796,3132],{},[4754,45798,45799,45801,45803],{},[898,45800,1688],{},[2505,45802,3132],{},[895,45804,45805,45807,45809,45811],{},[1708,45806,2726],{},[2505,45808,2507],{},[898,45810,1799],{"mathvariant":1759},[2505,45812,3132],{},[902,45814,45815],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,45818,45820],{"className":45819},[886],[888,45821,45822],{"xmlns":890},[892,45823,45824,45851],{},[895,45825,45826,45828,45830,45832,45834,45836,45838,45840,45842,45844,45847,45849],{},[898,45827,16117],{},[1708,45829,1716],{"stretchy":1715},[2505,45831,5867],{},[1708,45833,1883],{"separator":1882},[2505,45835,2507],{},[1708,45837,1883],{"separator":1882},[2505,45839,2507],{},[1708,45841,1721],{"stretchy":1715},[1708,45843,1710],{},[2505,45845,45846],{},"0,28125",[1708,45848,2854],{},[2505,45850,2784],{},[902,45852,45853],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,45856,45858],{"className":45857},[886],[888,45859,45860],{"xmlns":890},[892,45861,45862,45874],{},[895,45863,45864,45866,45868,45870,45872],{},[1708,45865,6940],{"stretchy":1715},[2505,45867,5867],{},[1708,45869,1883],{"separator":1882},[2505,45871,2507],{},[1708,45873,6981],{"stretchy":1715},[902,45875,45876],{"encoding":904},"[4, 1]"," je vázané ",[38,45879,15724],{},[115,45881,45883],{"id":45882},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,45885,45886],{},"Obecně:",[883,45888,45890],{"className":45889},[886],[888,45891,45892],{"xmlns":890,"display":2210},[892,45893,45894,45989],{},[2214,45895,45896],{"width":2216},[2218,45897,45898,45900,45982,45984],{},[2221,45899],{"width":2223},[2221,45901,45902],{},[895,45903,45904,45910,45912,45918,45920,45926,45928,45934,45936,45938,45940,45942,45944,45950,45952,45958,45960,45966,45968,45974,45976,45978,45980],{},[1743,45905,45906,45908],{},[898,45907,1688],{},[2505,45909,2507],{},[1708,45911,1710],{},[1743,45913,45914,45916],{},[898,45915,16117],{},[2505,45917,2507],{},[1708,45919,1716],{"stretchy":1715},[1743,45921,45922,45924],{},[898,45923,1747],{},[2505,45925,2507],{},[1708,45927,1883],{"separator":1882},[1743,45929,45930,45932],{},[898,45931,1747],{},[2505,45933,3132],{},[1708,45935,1883],{"separator":1882},[898,45937,900],{},[1708,45939,1721],{"stretchy":1715},[1708,45941,1883],{"separator":1882},[3213,45943],{"width":4750},[1743,45945,45946,45948],{},[898,45947,1688],{},[2505,45949,3132],{},[1708,45951,1710],{},[1743,45953,45954,45956],{},[898,45955,16117],{},[2505,45957,3132],{},[1708,45959,1716],{"stretchy":1715},[1743,45961,45962,45964],{},[898,45963,1747],{},[2505,45965,2507],{},[1708,45967,1883],{"separator":1882},[1743,45969,45970,45972],{},[898,45971,1747],{},[2505,45973,3132],{},[1708,45975,1883],{"separator":1882},[898,45977,900],{},[1708,45979,1721],{"stretchy":1715},[1708,45981,1883],{"separator":1882},[2221,45983],{"width":2223},[2221,45985,45986],{},[2247,45987,45988],{},"(6.27)",[902,45990,45991],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,45993,45995],{"className":45994},[886],[888,45996,45997],{"xmlns":890,"display":2210},[892,45998,45999,46046],{},[2214,46000,46001],{"width":2216},[2218,46002,46003,46005,46039,46041],{},[2221,46004],{"width":2223},[2221,46006,46007],{},[895,46008,46009,46011,46013,46015,46017,46023,46025,46031,46033,46035,46037],{},[898,46010,28315],{},[1708,46012,1710],{},[898,46014,28315],{},[1708,46016,1716],{"stretchy":1715},[1743,46018,46019,46021],{},[898,46020,1747],{},[2505,46022,2507],{},[1708,46024,1883],{"separator":1882},[1743,46026,46027,46029],{},[898,46028,1747],{},[2505,46030,3132],{},[1708,46032,1883],{"separator":1882},[898,46034,900],{},[1708,46036,1721],{"stretchy":1715},[898,46038,2155],{"mathvariant":1759},[2221,46040],{"width":2223},[2221,46042,46043],{},[2247,46044,46045],{},"(6.28)",[902,46047,46048],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,46050,46051,46052,1729,46055,46068,46069,46082],{},"Hicksova poptávka závisí na ",[38,46053,46054],{},"hladině užitečnosti",[883,46056,46058],{"className":46057},[886],[888,46059,46060],{"xmlns":890},[892,46061,46062,46066],{},[895,46063,46064],{},[898,46065,900],{},[902,46067,900],{"encoding":904}," (nikoli na důchodu ",[883,46070,46072],{"className":46071},[886],[888,46073,46074],{"xmlns":890},[892,46075,46076,46080],{},[895,46077,46078],{},[898,46079,21035],{},[902,46081,21035],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,46084,46086,46087],{"id":46085},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,46088,46090],{"className":46089},[886],[888,46091,46092],{"xmlns":890},[892,46093,46094,46128],{},[895,46095,46096,46098,46100,46114],{},[898,46097,900],{},[1708,46099,1710],{},[4754,46101,46102,46104,46106],{},[898,46103,1688],{},[2505,46105,2507],{},[895,46107,46108,46110,46112],{},[2505,46109,2507],{},[898,46111,1799],{"mathvariant":1759},[2505,46113,3132],{},[4754,46115,46116,46118,46120],{},[898,46117,1688],{},[2505,46119,3132],{},[895,46121,46122,46124,46126],{},[2505,46123,2507],{},[898,46125,1799],{"mathvariant":1759},[2505,46127,3132],{},[902,46129,45003],{"encoding":904},[724,46131,46132,46162],{},[883,46133,46135],{"className":46134},[886],[888,46136,46137],{"xmlns":890},[892,46138,46139,46159],{},[895,46140,46141,46147,46149,46155,46157],{},[1743,46142,46143,46145],{},[898,46144,1747],{},[2505,46146,2507],{},[1708,46148,1883],{"separator":1882},[1743,46150,46151,46153],{},[898,46152,1747],{},[2505,46154,3132],{},[1708,46156,1883],{"separator":1882},[898,46158,900],{},[902,46160,46161],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,46164,46166],{"className":46165},[886],[888,46167,46168],{"xmlns":890,"display":2210},[892,46169,46170,46244],{},[895,46171,46172,46174,46176,46182,46188,46190,46196,46202,46204,46206,46208,46210,46212,46226,46240,46242],{},[898,46173,1658],{"mathvariant":40395},[1708,46175,1710],{},[1743,46177,46178,46180],{},[898,46179,1747],{},[2505,46181,2507],{},[1743,46183,46184,46186],{},[898,46185,1688],{},[2505,46187,2507],{},[1708,46189,2019],{},[1743,46191,46192,46194],{},[898,46193,1747],{},[2505,46195,3132],{},[1743,46197,46198,46200],{},[898,46199,1688],{},[2505,46201,3132],{},[1708,46203,2019],{},[898,46205,28315],{},[1708,46207,1716],{"stretchy":1715},[898,46209,900],{},[1708,46211,2726],{},[4754,46213,46214,46216,46218],{},[898,46215,1688],{},[2505,46217,2507],{},[895,46219,46220,46222,46224],{},[2505,46221,2507],{},[898,46223,1799],{"mathvariant":1759},[2505,46225,3132],{},[4754,46227,46228,46230,46232],{},[898,46229,1688],{},[2505,46231,3132],{},[895,46233,46234,46236,46238],{},[2505,46235,2507],{},[898,46237,1799],{"mathvariant":1759},[2505,46239,3132],{},[1708,46241,1721],{"stretchy":1715},[898,46243,2155],{"mathvariant":1759},[902,46245,46246],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,46248,42276],{},[883,46250,46252],{"className":46251},[886],[888,46253,46254],{"xmlns":890,"display":2210},[892,46255,46256,46478],{},[2214,46257,46258,46338,46418],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,46259,46260,46272],{},[2221,46261,46262],{},[3194,46263,46264],{"scriptlevel":2784,"displaystyle":1882},[4754,46265,46266,46268,46270],{},[898,46267,1658],{"mathvariant":40395},[2505,46269,2507],{},[1708,46271,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,46273,46274],{},[3194,46275,46276],{"scriptlevel":2784,"displaystyle":1882},[895,46277,46278,46280,46282,46288,46290,46292,46294,46302,46318,46332,46334,46336],{},[895,46279],{},[1708,46281,1710],{},[1743,46283,46284,46286],{},[898,46285,1747],{},[2505,46287,2507],{},[1708,46289,2726],{},[898,46291,28315],{},[1708,46293,3703],{},[3194,46295,46296],{"scriptlevel":2784,"displaystyle":1715},[2358,46297,46298,46300],{},[2505,46299,2507],{},[2505,46301,3132],{},[4754,46303,46304,46306,46308],{},[898,46305,1688],{},[2505,46307,2507],{},[895,46309,46310,46312,46314,46316],{},[1708,46311,2726],{},[2505,46313,2507],{},[898,46315,1799],{"mathvariant":1759},[2505,46317,3132],{},[4754,46319,46320,46322,46324],{},[898,46321,1688],{},[2505,46323,3132],{},[895,46325,46326,46328,46330],{},[2505,46327,2507],{},[898,46329,1799],{"mathvariant":1759},[2505,46331,3132],{},[1708,46333,1710],{},[2505,46335,2784],{},[1708,46337,1883],{"separator":1882},[2218,46339,46340,46352],{},[2221,46341,46342],{},[3194,46343,46344],{"scriptlevel":2784,"displaystyle":1882},[4754,46345,46346,46348,46350],{},[898,46347,1658],{"mathvariant":40395},[2505,46349,3132],{},[1708,46351,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,46353,46354],{},[3194,46355,46356],{"scriptlevel":2784,"displaystyle":1882},[895,46357,46358,46360,46362,46368,46370,46372,46374,46382,46396,46412,46414,46416],{},[895,46359],{},[1708,46361,1710],{},[1743,46363,46364,46366],{},[898,46365,1747],{},[2505,46367,3132],{},[1708,46369,2726],{},[898,46371,28315],{},[1708,46373,3703],{},[3194,46375,46376],{"scriptlevel":2784,"displaystyle":1715},[2358,46377,46378,46380],{},[2505,46379,2507],{},[2505,46381,3132],{},[4754,46383,46384,46386,46388],{},[898,46385,1688],{},[2505,46387,2507],{},[895,46389,46390,46392,46394],{},[2505,46391,2507],{},[898,46393,1799],{"mathvariant":1759},[2505,46395,3132],{},[4754,46397,46398,46400,46402],{},[898,46399,1688],{},[2505,46401,3132],{},[895,46403,46404,46406,46408,46410],{},[1708,46405,2726],{},[2505,46407,2507],{},[898,46409,1799],{"mathvariant":1759},[2505,46411,3132],{},[1708,46413,1710],{},[2505,46415,2784],{},[1708,46417,1883],{"separator":1882},[2218,46419,46420,46432],{},[2221,46421,46422],{},[3194,46423,46424],{"scriptlevel":2784,"displaystyle":1882},[4754,46425,46426,46428,46430],{},[898,46427,1658],{"mathvariant":40395},[898,46429,28315],{},[1708,46431,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2221,46433,46434],{},[3194,46435,46436],{"scriptlevel":2784,"displaystyle":1882},[895,46437,46438,46440,46442,46444,46446,46460,46474,46476],{},[895,46439],{},[1708,46441,1710],{},[898,46443,900],{},[1708,46445,2726],{},[4754,46447,46448,46450,46452],{},[898,46449,1688],{},[2505,46451,2507],{},[895,46453,46454,46456,46458],{},[2505,46455,2507],{},[898,46457,1799],{"mathvariant":1759},[2505,46459,3132],{},[4754,46461,46462,46464,46466],{},[898,46463,1688],{},[2505,46465,3132],{},[895,46467,46468,46470,46472],{},[2505,46469,2507],{},[898,46471,1799],{"mathvariant":1759},[2505,46473,3132],{},[1708,46475,1710],{},[2505,46477,24346],{},[902,46479,46480],{"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}",[724,46482,46483,46484,46554,46555,46613],{},"Podílem rovnic: ",[883,46485,46487],{"className":46486},[886],[888,46488,46489],{"xmlns":890},[892,46490,46491,46551],{},[895,46492,46493,46499,46501,46507,46509,46515,46517,46523,46525,46531,46537,46539,46545],{},[1743,46494,46495,46497],{},[898,46496,1747],{},[2505,46498,2507],{},[898,46500,1799],{"mathvariant":1759},[1743,46502,46503,46505],{},[898,46504,1747],{},[2505,46506,3132],{},[1708,46508,1710],{},[1743,46510,46511,46513],{},[898,46512,1688],{},[2505,46514,3132],{},[898,46516,1799],{"mathvariant":1759},[1743,46518,46519,46521],{},[898,46520,1688],{},[2505,46522,2507],{},[1708,46524,4782],{},[1743,46526,46527,46529],{},[898,46528,1747],{},[2505,46530,2507],{},[1743,46532,46533,46535],{},[898,46534,1688],{},[2505,46536,2507],{},[1708,46538,1710],{},[1743,46540,46541,46543],{},[898,46542,1747],{},[2505,46544,3132],{},[1743,46546,46547,46549],{},[898,46548,1688],{},[2505,46550,3132],{},[902,46552,46553],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,46556,46558],{"className":46557},[886],[888,46559,46560],{"xmlns":890},[892,46561,46562,46610],{},[895,46563,46564,46566,46568,46574,46580,46582,46588,46594,46596,46598,46604],{},[898,46565,16183],{},[1708,46567,1710],{},[1743,46569,46570,46572],{},[898,46571,1747],{},[2505,46573,2507],{},[1743,46575,46576,46578],{},[898,46577,1688],{},[2505,46579,2507],{},[1708,46581,2019],{},[1743,46583,46584,46586],{},[898,46585,1747],{},[2505,46587,3132],{},[1743,46589,46590,46592],{},[898,46591,1688],{},[2505,46593,3132],{},[1708,46595,1710],{},[2505,46597,3132],{},[1743,46599,46600,46602],{},[898,46601,1747],{},[2505,46603,2507],{},[1743,46605,46606,46608],{},[898,46607,1688],{},[2505,46609,2507],{},[902,46611,46612],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,46615,46617],{"className":46616},[886],[888,46618,46619],{"xmlns":890,"display":2210},[892,46620,46621,46688],{},[2214,46622,46623],{"width":2216},[2218,46624,46625,46627,46681,46683],{},[2221,46626],{"width":2223},[2221,46628,46629],{},[895,46630,46631,46637,46639,46653,46655,46657,46663,46665,46679],{},[1743,46632,46633,46635],{},[898,46634,1688],{},[2505,46636,2507],{},[1708,46638,1710],{},[2358,46640,46641,46643],{},[898,46642,16183],{},[895,46644,46645,46647],{},[2505,46646,3132],{},[1743,46648,46649,46651],{},[898,46650,1747],{},[2505,46652,2507],{},[1708,46654,1883],{"separator":1882},[3213,46656],{"width":4750},[1743,46658,46659,46661],{},[898,46660,1688],{},[2505,46662,3132],{},[1708,46664,1710],{},[2358,46666,46667,46669],{},[898,46668,16183],{},[895,46670,46671,46673],{},[2505,46672,3132],{},[1743,46674,46675,46677],{},[898,46676,1747],{},[2505,46678,3132],{},[898,46680,2155],{"mathvariant":1759},[2221,46682],{"width":2223},[2221,46684,46685],{},[2247,46686,46687],{},"(6.29)",[902,46689,46690],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,46692,46693,46694,5055,46776,4123],{},"Ze třetí rovnice ",[883,46695,46697],{"className":46696},[886],[888,46698,46699],{"xmlns":890},[892,46700,46701,46773],{},[895,46702,46703,46705,46707,46745,46747],{},[898,46704,900],{},[1708,46706,1710],{},[9351,46708,46709],{},[895,46710,46711,46727,46729],{},[3194,46712,46713],{"scriptlevel":2784,"displaystyle":1715},[2358,46714,46715,46717],{},[898,46716,16183],{},[895,46718,46719,46721],{},[2505,46720,3132],{},[1743,46722,46723,46725],{},[898,46724,1747],{},[2505,46726,2507],{},[1708,46728,3703],{},[3194,46730,46731],{"scriptlevel":2784,"displaystyle":1715},[2358,46732,46733,46735],{},[898,46734,16183],{},[895,46736,46737,46739],{},[2505,46738,3132],{},[1743,46740,46741,46743],{},[898,46742,1747],{},[2505,46744,3132],{},[1708,46746,1710],{},[3194,46748,46749],{"scriptlevel":2784,"displaystyle":1715},[2358,46750,46751,46753],{},[898,46752,16183],{},[895,46754,46755,46757],{},[2505,46756,3132],{},[9351,46758,46759],{},[895,46760,46761,46767],{},[1743,46762,46763,46765],{},[898,46764,1747],{},[2505,46766,2507],{},[1743,46768,46769,46771],{},[898,46770,1747],{},[2505,46772,3132],{},[902,46774,46775],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,46777,46779],{"className":46778},[886],[888,46780,46781],{"xmlns":890},[892,46782,46783,46809],{},[895,46784,46785,46787,46789,46791,46793],{},[898,46786,16183],{},[1708,46788,1710],{},[2505,46790,3132],{},[898,46792,900],{},[9351,46794,46795],{},[895,46796,46797,46803],{},[1743,46798,46799,46801],{},[898,46800,1747],{},[2505,46802,2507],{},[1743,46804,46805,46807],{},[898,46806,1747],{},[2505,46808,3132],{},[902,46810,46811],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",[883,46813,46815],{"className":46814},[886],[888,46816,46817],{"xmlns":890,"display":2210},[892,46818,46819,46964],{},[2214,46820,46821],{"width":2216},[2218,46822,46823,46825,46957,46959],{},[2221,46824],{"width":2223},[2221,46826,46827],{},[24717,46828,46829],{"notation":24719},[3194,46830,46831],{"scriptlevel":2784,"displaystyle":1715},[3194,46832,46833],{"scriptlevel":2784,"displaystyle":1715},[3194,46834,46835],{"scriptlevel":2784,"displaystyle":1882},[895,46836,46837,46839,46845,46847,46849,46865,46867,46873,46875,46881,46883,46889,46891,46893,46895,46897,46899,46905,46907,46909,46925,46927,46933,46935,46941,46943,46949,46951,46953,46955],{},[2247,46838,4779],{},[1743,46840,46841,46843],{},[898,46842,1688],{},[2505,46844,2507],{},[1708,46846,1710],{},[898,46848,900],{},[9351,46850,46851],{},[2358,46852,46853,46859],{},[1743,46854,46855,46857],{},[898,46856,1747],{},[2505,46858,3132],{},[1743,46860,46861,46863],{},[898,46862,1747],{},[2505,46864,2507],{},[1708,46866,1710],{},[1743,46868,46869,46871],{},[898,46870,16117],{},[2505,46872,2507],{},[1708,46874,1716],{"stretchy":1715},[1743,46876,46877,46879],{},[898,46878,1747],{},[2505,46880,2507],{},[1708,46882,1883],{"separator":1882},[1743,46884,46885,46887],{},[898,46886,1747],{},[2505,46888,3132],{},[1708,46890,1883],{"separator":1882},[898,46892,900],{},[1708,46894,1721],{"stretchy":1715},[1708,46896,1883],{"separator":1882},[3213,46898],{"width":4750},[1743,46900,46901,46903],{},[898,46902,1688],{},[2505,46904,3132],{},[1708,46906,1710],{},[898,46908,900],{},[9351,46910,46911],{},[2358,46912,46913,46919],{},[1743,46914,46915,46917],{},[898,46916,1747],{},[2505,46918,2507],{},[1743,46920,46921,46923],{},[898,46922,1747],{},[2505,46924,3132],{},[1708,46926,1710],{},[1743,46928,46929,46931],{},[898,46930,16117],{},[2505,46932,3132],{},[1708,46934,1716],{"stretchy":1715},[1743,46936,46937,46939],{},[898,46938,1747],{},[2505,46940,2507],{},[1708,46942,1883],{"separator":1882},[1743,46944,46945,46947],{},[898,46946,1747],{},[2505,46948,3132],{},[1708,46950,1883],{"separator":1882},[898,46952,900],{},[1708,46954,1721],{"stretchy":1715},[2247,46956,4779],{},[2221,46958],{"width":2223},[2221,46960,46961],{},[2247,46962,46963],{},"(6.30)",[902,46965,46966],{"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}",[115,46968,46970],{"id":46969},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,46972,46973,46974,46987,46988,47005,47006,47019,47020,47037,47038,47041,47042,47081,47082,47111],{},"Primární (max ",[883,46975,46977],{"className":46976},[886],[888,46978,46979],{"xmlns":890},[892,46980,46981,46985],{},[895,46982,46983],{},[898,46984,900],{},[902,46986,900],{"encoding":904}," při rozpočtu ",[883,46989,46991],{"className":46990},[886],[888,46992,46993],{"xmlns":890},[892,46994,46995,47003],{},[895,46996,46997],{},[1753,46998,46999,47001],{},[898,47000,21035],{},[1708,47002,2417],{},[902,47004,39878],{"encoding":904},") a duální (min ",[883,47007,47009],{"className":47008},[886],[888,47010,47011],{"xmlns":890},[892,47012,47013,47017],{},[895,47014,47015],{},[898,47016,16183],{},[902,47018,16183],{"encoding":904}," při užitečnosti ",[883,47021,47023],{"className":47022},[886],[888,47024,47025],{"xmlns":890},[892,47026,47027,47035],{},[895,47028,47029],{},[1753,47030,47031,47033],{},[898,47032,900],{},[1708,47034,2417],{},[902,47036,39812],{"encoding":904},") úloha jsou ",[38,47039,47040],{},"ekvivalentní",": mají tentýž bod optima ",[883,47043,47045],{"className":47044},[886],[888,47046,47047],{"xmlns":890},[892,47048,47049,47079],{},[895,47050,47051,47057,47059,47067,47069,47077],{},[1753,47052,47053,47055],{},[898,47054,1688],{},[1708,47056,2417],{},[1708,47058,6940],{"stretchy":1715},[4754,47060,47061,47063,47065],{},[898,47062,1688],{},[2505,47064,2507],{},[1708,47066,2417],{},[1708,47068,1883],{"separator":1882},[4754,47070,47071,47073,47075],{},[898,47072,1688],{},[2505,47074,3132],{},[1708,47076,2417],{},[1708,47078,6981],{"stretchy":1715},[902,47080,40174],{"encoding":904}," a v obou platí ",[883,47083,47085],{"className":47084},[886],[888,47086,47087],{"xmlns":890},[892,47088,47089,47109],{},[895,47090,47091,47093,47095,47101,47103],{},[2247,47092,13825],{},[1708,47094,1710],{},[1743,47096,47097,47099],{},[898,47098,1747],{},[2505,47100,2507],{},[898,47102,1799],{"mathvariant":1759},[1743,47104,47105,47107],{},[898,47106,1747],{},[2505,47108,3132],{},[902,47110,39848],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,47113,47114],{},[3372,47115],{"alt":47116,"className":47117,"src":47118},"imek-primarni-vs-dualni",[210,3376],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,47120,47121,47232],{},[123,47122,47123,47126,47127,47140,47141,47181,47182,2155],{},[38,47124,47125],{},"Primární"," (Marshall): zadáno ",[883,47128,47130],{"className":47129},[886],[888,47131,47132],{"xmlns":890},[892,47133,47134,47138],{},[895,47135,47136],{},[898,47137,21035],{},[902,47139,21035],{"encoding":904},", hledáme maximální ",[883,47142,47144],{"className":47143},[886],[888,47145,47146],{"xmlns":890},[892,47147,47148,47178],{},[895,47149,47150,47156,47158,47164,47166,47172,47174,47176],{},[1753,47151,47152,47154],{},[898,47153,900],{},[1708,47155,2417],{},[1708,47157,1716],{"stretchy":1715},[1743,47159,47160,47162],{},[898,47161,1747],{},[2505,47163,2507],{},[1708,47165,1883],{"separator":1882},[1743,47167,47168,47170],{},[898,47169,1747],{},[2505,47171,3132],{},[1708,47173,1883],{"separator":1882},[898,47175,21035],{},[1708,47177,1721],{"stretchy":1715},[902,47179,47180],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,47183,47185],{"className":47184},[886],[888,47186,47187],{"xmlns":890},[892,47188,47189,47229],{},[895,47190,47191,47197,47199,47207,47209,47215,47217,47223,47225,47227],{},[1743,47192,47193,47195],{},[898,47194,1688],{},[898,47196,29661],{},[1708,47198,1710],{},[4754,47200,47201,47203,47205],{},[898,47202,16117],{},[898,47204,29661],{},[898,47206,1741],{},[1708,47208,1716],{"stretchy":1715},[1743,47210,47211,47213],{},[898,47212,1747],{},[2505,47214,2507],{},[1708,47216,1883],{"separator":1882},[1743,47218,47219,47221],{},[898,47220,1747],{},[2505,47222,3132],{},[1708,47224,1883],{"separator":1882},[898,47226,21035],{},[1708,47228,1721],{"stretchy":1715},[902,47230,47231],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,47233,47234,47237,47238,47251,47252,47181,47292,2155],{},[38,47235,47236],{},"Duální"," (Hicks): zadáno ",[883,47239,47241],{"className":47240},[886],[888,47242,47243],{"xmlns":890},[892,47244,47245,47249],{},[895,47246,47247],{},[898,47248,900],{},[902,47250,900],{"encoding":904},", hledáme minimální ",[883,47253,47255],{"className":47254},[886],[888,47256,47257],{"xmlns":890},[892,47258,47259,47289],{},[895,47260,47261,47267,47269,47275,47277,47283,47285,47287],{},[1753,47262,47263,47265],{},[898,47264,16183],{},[1708,47266,2417],{},[1708,47268,1716],{"stretchy":1715},[1743,47270,47271,47273],{},[898,47272,1747],{},[2505,47274,2507],{},[1708,47276,1883],{"separator":1882},[1743,47278,47279,47281],{},[898,47280,1747],{},[2505,47282,3132],{},[1708,47284,1883],{"separator":1882},[898,47286,900],{},[1708,47288,1721],{"stretchy":1715},[902,47290,47291],{"encoding":904},"E^*(P_1, P_2, U)",[883,47293,47295],{"className":47294},[886],[888,47296,47297],{"xmlns":890},[892,47298,47299,47340],{},[895,47300,47301,47307,47309,47318,47320,47326,47328,47334,47336,47338],{},[1743,47302,47303,47305],{},[898,47304,1688],{},[898,47306,29661],{},[1708,47308,1710],{},[4754,47310,47311,47313,47315],{},[898,47312,16117],{},[898,47314,29661],{},[898,47316,47317],{},"H",[1708,47319,1716],{"stretchy":1715},[1743,47321,47322,47324],{},[898,47323,1747],{},[2505,47325,2507],{},[1708,47327,1883],{"separator":1882},[1743,47329,47330,47332],{},[898,47331,1747],{},[2505,47333,3132],{},[1708,47335,1883],{"separator":1882},[898,47337,900],{},[1708,47339,1721],{"stretchy":1715},[902,47341,47342],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,47344,47345,47346,47349,47350,47353],{},"Proč se studují obě? Marshallova poptávka je ",[38,47347,47348],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,47351,47352],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,47355,47357],{"id":47356},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,47359,47361],{"id":47360},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,47363,47364,47367,47368,47400,47401,47439,47440,47466],{},[38,47365,47366],{},"6.8"," Jsou dány užitečnost ",[883,47369,47371],{"className":47370},[886],[888,47372,47373],{"xmlns":890},[892,47374,47375,47397],{},[895,47376,47377,47379,47381,47389],{},[898,47378,900],{},[1708,47380,1710],{},[4754,47382,47383,47385,47387],{},[898,47384,1688],{},[2505,47386,2507],{},[2505,47388,6097],{},[4754,47390,47391,47393,47395],{},[898,47392,1688],{},[2505,47394,3132],{},[2505,47396,6097],{},[902,47398,47399],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,47402,47404],{"className":47403},[886],[888,47405,47406],{"xmlns":890},[892,47407,47408,47436],{},[895,47409,47410,47418,47420,47422,47424,47432,47434],{},[4754,47411,47412,47414,47416],{},[898,47413,1747],{},[2505,47415,2507],{},[1708,47417,2417],{},[1708,47419,1710],{},[2505,47421,5867],{},[1708,47423,1883],{"separator":1882},[4754,47425,47426,47428,47430],{},[898,47427,1747],{},[2505,47429,3132],{},[1708,47431,2417],{},[1708,47433,1710],{},[2505,47435,4003],{},[902,47437,47438],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,47441,47443],{"className":47442},[886],[888,47444,47445],{"xmlns":890},[892,47446,47447,47463],{},[895,47448,47449,47455,47457],{},[1743,47450,47451,47453],{},[898,47452,1688],{},[2505,47454,2507],{},[1708,47456,1883],{"separator":1882},[1743,47458,47459,47461],{},[898,47460,1688],{},[2505,47462,3132],{},[902,47464,47465],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,47468,47469,47472,47473,47515,47516,47547,47548,47570,47571,2155],{},[38,47470,47471],{},"6.9"," Jsou dány rozpočtové omezení ",[883,47474,47476],{"className":47475},[886],[888,47477,47478],{"xmlns":890},[892,47479,47480,47512],{},[895,47481,47482,47484,47486,47492,47498,47500,47506],{},[898,47483,21035],{},[1708,47485,1710],{},[1743,47487,47488,47490],{},[898,47489,1747],{},[2505,47491,2507],{},[1743,47493,47494,47496],{},[898,47495,1688],{},[2505,47497,2507],{},[1708,47499,2019],{},[1743,47501,47502,47504],{},[898,47503,1747],{},[2505,47505,3132],{},[1743,47507,47508,47510],{},[898,47509,1688],{},[2505,47511,3132],{},[902,47513,47514],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,47517,47519],{"className":47518},[886],[888,47520,47521],{"xmlns":890},[892,47522,47523,47545],{},[895,47524,47525,47527,47529,47537],{},[898,47526,900],{},[1708,47528,1710],{},[4754,47530,47531,47533,47535],{},[898,47532,1688],{},[2505,47534,2507],{},[2505,47536,6097],{},[4754,47538,47539,47541,47543],{},[898,47540,1688],{},[2505,47542,3132],{},[2505,47544,6097],{},[902,47546,47399],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,47549,47551],{"className":47550},[886],[888,47552,47553],{"xmlns":890},[892,47554,47555,47567],{},[895,47556,47557,47563,47565],{},[1753,47558,47559,47561],{},[898,47560,21035],{},[1708,47562,2417],{},[1708,47564,1710],{},[2505,47566,11040],{},[902,47568,47569],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,47572,47574],{"className":47573},[886],[888,47575,47576],{"xmlns":890},[892,47577,47578,47606],{},[895,47579,47580,47588,47590,47592,47594,47602,47604],{},[4754,47581,47582,47584,47586],{},[898,47583,1747],{},[2505,47585,2507],{},[1708,47587,2417],{},[1708,47589,1710],{},[2505,47591,3993],{},[1708,47593,1883],{"separator":1882},[4754,47595,47596,47598,47600],{},[898,47597,1747],{},[2505,47599,3132],{},[1708,47601,2417],{},[1708,47603,1710],{},[2505,47605,4003],{},[902,47607,47608],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,47610,47611,47614,47615,2980,47647,47677,47678,2155],{},[38,47612,47613],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,47616,47618],{"className":47617},[886],[888,47619,47620],{"xmlns":890},[892,47621,47622,47644],{},[895,47623,47624,47626,47628,47636],{},[898,47625,900],{},[1708,47627,1710],{},[4754,47629,47630,47632,47634],{},[898,47631,1688],{},[2505,47633,2507],{},[898,47635,207],{},[4754,47637,47638,47640,47642],{},[898,47639,1688],{},[2505,47641,3132],{},[898,47643,1923],{},[902,47645,47646],{"encoding":904},"U = Q_1^a Q_2^b",[883,47648,47650],{"className":47649},[886],[888,47651,47652],{"xmlns":890},[892,47653,47654,47674],{},[895,47655,47656,47658,47660,47662,47664,47666,47668,47670,47672],{},[898,47657,207],{},[1708,47659,1883],{"separator":1882},[898,47661,1923],{},[1708,47663,18420],{},[1708,47665,17245],{"stretchy":1715},[2505,47667,2784],{},[1708,47669,1883],{"separator":1882},[2505,47671,2507],{},[1708,47673,17262],{"stretchy":1715},[902,47675,47676],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,47679,47681],{"className":47680},[886],[888,47682,47683],{"xmlns":890},[892,47684,47685,47717],{},[895,47686,47687,47689,47691,47697,47703,47705,47711],{},[898,47688,21035],{},[1708,47690,1710],{},[1743,47692,47693,47695],{},[898,47694,1747],{},[2505,47696,2507],{},[1743,47698,47699,47701],{},[898,47700,1688],{},[2505,47702,2507],{},[1708,47704,2019],{},[1743,47706,47707,47709],{},[898,47708,1747],{},[2505,47710,3132],{},[1743,47712,47713,47715],{},[898,47714,1688],{},[2505,47716,3132],{},[902,47718,47514],{"encoding":904},[724,47720,47721,47724,47725,2980,47759,47677,47777,2155],{},[38,47722,47723],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,47726,47728],{"className":47727},[886],[888,47729,47730],{"xmlns":890},[892,47731,47732,47756],{},[895,47733,47734,47736,47738,47746,47748],{},[898,47735,900],{},[1708,47737,1710],{},[4754,47739,47740,47742,47744],{},[898,47741,1688],{},[2505,47743,2507],{},[898,47745,207],{},[1708,47747,2019],{},[4754,47749,47750,47752,47754],{},[898,47751,1688],{},[2505,47753,3132],{},[898,47755,207],{},[902,47757,47758],{"encoding":904},"U = Q_1^a + Q_2^a",[883,47760,47762],{"className":47761},[886],[888,47763,47764],{"xmlns":890},[892,47765,47766,47774],{},[895,47767,47768,47770,47772],{},[898,47769,207],{},[1708,47771,7060],{"mathvariant":1759},[2505,47773,2784],{},[902,47775,47776],{"encoding":904},"a \\neq 0",[883,47778,47780],{"className":47779},[886],[888,47781,47782],{"xmlns":890},[892,47783,47784,47816],{},[895,47785,47786,47788,47790,47796,47802,47804,47810],{},[898,47787,21035],{},[1708,47789,1710],{},[1743,47791,47792,47794],{},[898,47793,1747],{},[2505,47795,2507],{},[1743,47797,47798,47800],{},[898,47799,1688],{},[2505,47801,2507],{},[1708,47803,2019],{},[1743,47805,47806,47808],{},[898,47807,1747],{},[2505,47809,3132],{},[1743,47811,47812,47814],{},[898,47813,1688],{},[2505,47815,3132],{},[902,47817,47514],{"encoding":904},[198,47819,47821],{"id":47820},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,47823,47824,47367,47827,1343,47854,47876,47877,1343,47900,47924,47925,47950,47951,2155],{},[38,47825,47826],{},"6.12",[883,47828,47830],{"className":47829},[886],[888,47831,47832],{"xmlns":890},[892,47833,47834,47852],{},[895,47835,47836,47838,47840,47846],{},[898,47837,900],{},[1708,47839,1710],{},[1743,47841,47842,47844],{},[898,47843,1688],{},[2505,47845,2507],{},[1743,47847,47848,47850],{},[898,47849,1688],{},[2505,47851,3132],{},[902,47853,42071],{"encoding":904},[883,47855,47857],{"className":47856},[886],[888,47858,47859],{"xmlns":890},[892,47860,47861,47873],{},[895,47862,47863,47869,47871],{},[1753,47864,47865,47867],{},[898,47866,900],{},[1708,47868,2417],{},[1708,47870,1710],{},[2505,47872,4003],{},[902,47874,47875],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,47878,47880],{"className":47879},[886],[888,47881,47882],{"xmlns":890},[892,47883,47884,47898],{},[895,47885,47886,47894,47896],{},[4754,47887,47888,47890,47892],{},[898,47889,1747],{},[2505,47891,2507],{},[1708,47893,2417],{},[1708,47895,1710],{},[2505,47897,3132],{},[902,47899,42144],{"encoding":904},[883,47901,47903],{"className":47902},[886],[888,47904,47905],{"xmlns":890},[892,47906,47907,47921],{},[895,47908,47909,47917,47919],{},[4754,47910,47911,47913,47915],{},[898,47912,1747],{},[2505,47914,3132],{},[1708,47916,2417],{},[1708,47918,1710],{},[2505,47920,5867],{},[902,47922,47923],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,47926,47928],{"className":47927},[886],[888,47929,47930],{"xmlns":890},[892,47931,47932,47948],{},[895,47933,47934,47940,47942],{},[1743,47935,47936,47938],{},[898,47937,1688],{},[2505,47939,2507],{},[1708,47941,1883],{"separator":1882},[1743,47943,47944,47946],{},[898,47945,1688],{},[2505,47947,3132],{},[902,47949,47465],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,47952,47954],{"className":47953},[886],[888,47955,47956],{"xmlns":890},[892,47957,47958,47978],{},[895,47959,47960,47962,47964,47970,47972],{},[898,47961,900],{},[1708,47963,1710],{},[1743,47965,47966,47968],{},[898,47967,1688],{},[2505,47969,2507],{},[1708,47971,3703],{},[1743,47973,47974,47976],{},[898,47975,1688],{},[2505,47977,3132],{},[902,47979,47980],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,47982,47983,47986,47987,48028,48029,48051,48052,2155],{},[38,47984,47985],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,47988,47990],{"className":47989},[886],[888,47991,47992],{"xmlns":890},[892,47993,47994,48026],{},[895,47995,47996,47998,48000,48006,48012,48014,48020],{},[898,47997,16183],{},[1708,47999,1710],{},[1743,48001,48002,48004],{},[898,48003,1747],{},[2505,48005,2507],{},[1743,48007,48008,48010],{},[898,48009,1688],{},[2505,48011,2507],{},[1708,48013,2019],{},[1743,48015,48016,48018],{},[898,48017,1747],{},[2505,48019,3132],{},[1743,48021,48022,48024],{},[898,48023,1688],{},[2505,48025,3132],{},[902,48027,39793],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,48030,48032],{"className":48031},[886],[888,48033,48034],{"xmlns":890},[892,48035,48036,48048],{},[895,48037,48038,48044,48046],{},[1753,48039,48040,48042],{},[898,48041,900],{},[1708,48043,2417],{},[1708,48045,1710],{},[2505,48047,4028],{},[902,48049,48050],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,48053,48055],{"className":48054},[886],[888,48056,48057],{"xmlns":890},[892,48058,48059,48087],{},[895,48060,48061,48069,48071,48073,48075,48083,48085],{},[4754,48062,48063,48065,48067],{},[898,48064,1747],{},[2505,48066,2507],{},[1708,48068,2417],{},[1708,48070,1710],{},[2505,48072,4018],{},[1708,48074,1883],{"separator":1882},[4754,48076,48077,48079,48081],{},[898,48078,1747],{},[2505,48080,3132],{},[1708,48082,2417],{},[1708,48084,1710],{},[2505,48086,4853],{},[902,48088,48089],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,48091,12596],{"id":12595},[120,48093,48094,48151,48190,48210,48245,48299,48304,48310,48406,48451],{},[123,48095,48096,1729,48099,48148,48149,2155],{},[38,48097,48098],{},"Rozpočtové omezení (budget constraint)",[883,48100,48102],{"className":48101},[886],[888,48103,48104],{"xmlns":890},[892,48105,48106,48146],{},[895,48107,48108,48114,48116,48124,48130,48132,48140],{},[1753,48109,48110,48112],{},[898,48111,21035],{},[1708,48113,2417],{},[1708,48115,1710],{},[4754,48117,48118,48120,48122],{},[898,48119,1747],{},[2505,48121,2507],{},[1708,48123,2417],{},[1743,48125,48126,48128],{},[898,48127,1688],{},[2505,48129,2507],{},[1708,48131,2019],{},[4754,48133,48134,48136,48138],{},[898,48135,1747],{},[2505,48137,3132],{},[1708,48139,2417],{},[1743,48141,48142,48144],{},[898,48143,1688],{},[2505,48145,3132],{},[902,48147,29170],{"encoding":904}," — (6.12); ",[38,48150,39983],{},[123,48152,48153,48156,48157,2155],{},[38,48154,48155],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,48158,48160],{"className":48159},[886],[888,48161,48162],{"xmlns":890},[892,48163,48164,48188],{},[895,48165,48166,48168,48170,48178,48180],{},[2247,48167,13825],{},[1708,48169,1710],{},[4754,48171,48172,48174,48176],{},[898,48173,1747],{},[2505,48175,2507],{},[1708,48177,2417],{},[898,48179,1799],{"mathvariant":1759},[4754,48181,48182,48184,48186],{},[898,48183,1747],{},[2505,48185,3132],{},[1708,48187,2417],{},[902,48189,40826],{"encoding":904},[123,48191,48192,48207,48208,2155],{},[38,48193,40970,48194],{},[883,48195,48197],{"className":48196},[886],[888,48198,48199],{"xmlns":890},[892,48200,48201,48205],{},[895,48202,48203],{},[898,48204,28315],{},[902,48206,28368],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,48209,40992],{},[123,48211,48212,48215,48216,2155],{},[38,48213,48214],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,48217,48219],{"className":48218},[886],[888,48220,48221],{"xmlns":890},[892,48222,48223,48243],{},[895,48224,48225,48227,48229,48235,48237],{},[2247,48226,13825],{},[1708,48228,1710],{},[1743,48230,48231,48233],{},[898,48232,1747],{},[2505,48234,2507],{},[898,48236,1799],{"mathvariant":1759},[1743,48238,48239,48241],{},[898,48240,1747],{},[2505,48242,3132],{},[902,48244,39848],{"encoding":904},[123,48246,48247,12636,48250,48298],{},[38,48248,48249],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,48251,48253],{"className":48252},[886],[888,48254,48255],{"xmlns":890},[892,48256,48257,48295],{},[895,48258,48259,48265,48267,48273,48275,48281,48283,48289,48291,48293],{},[1743,48260,48261,48263],{},[898,48262,1688],{},[898,48264,29661],{},[1708,48266,1710],{},[1743,48268,48269,48271],{},[898,48270,16117],{},[898,48272,29661],{},[1708,48274,1716],{"stretchy":1715},[1743,48276,48277,48279],{},[898,48278,1747],{},[2505,48280,2507],{},[1708,48282,1883],{"separator":1882},[1743,48284,48285,48287],{},[898,48286,1747],{},[2505,48288,3132],{},[1708,48290,1883],{"separator":1882},[898,48292,21035],{},[1708,48294,1721],{"stretchy":1715},[902,48296,48297],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,48300,48301,48303],{},[38,48302,43571],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,48305,48306,48309],{},[38,48307,48308],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,48311,48312,12636,48314,48361,48362,48405],{},[38,48313,45883],{},[883,48315,48317],{"className":48316},[886],[888,48318,48319],{"xmlns":890},[892,48320,48321,48359],{},[895,48322,48323,48329,48331,48337,48339,48345,48347,48353,48355,48357],{},[1743,48324,48325,48327],{},[898,48326,1688],{},[898,48328,29661],{},[1708,48330,1710],{},[1743,48332,48333,48335],{},[898,48334,16117],{},[898,48336,29661],{},[1708,48338,1716],{"stretchy":1715},[1743,48340,48341,48343],{},[898,48342,1747],{},[2505,48344,2507],{},[1708,48346,1883],{"separator":1882},[1743,48348,48349,48351],{},[898,48350,1747],{},[2505,48352,3132],{},[1708,48354,1883],{"separator":1882},[898,48356,900],{},[1708,48358,1721],{"stretchy":1715},[902,48360,29694],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,48363,48365],{"className":48364},[886],[888,48366,48367],{"xmlns":890},[892,48368,48369,48403],{},[895,48370,48371,48373,48375,48389],{},[898,48372,900],{},[1708,48374,1710],{},[4754,48376,48377,48379,48381],{},[898,48378,1688],{},[2505,48380,2507],{},[895,48382,48383,48385,48387],{},[2505,48384,2507],{},[898,48386,1799],{"mathvariant":1759},[2505,48388,3132],{},[4754,48390,48391,48393,48395],{},[898,48392,1688],{},[2505,48394,3132],{},[895,48396,48397,48399,48401],{},[2505,48398,2507],{},[898,48400,1799],{"mathvariant":1759},[2505,48402,3132],{},[902,48404,45003],{"encoding":904},": (6.30).",[123,48407,48408,48450],{},[38,48409,48410,48411],{},"Bod dotyku ",[883,48412,48414],{"className":48413},[886],[888,48415,48416],{"xmlns":890},[892,48417,48418,48448],{},[895,48419,48420,48426,48428,48436,48438,48446],{},[1753,48421,48422,48424],{},[898,48423,1688],{},[1708,48425,2417],{},[1708,48427,6940],{"stretchy":1715},[4754,48429,48430,48432,48434],{},[898,48431,1688],{},[2505,48433,2507],{},[1708,48435,2417],{},[1708,48437,1883],{"separator":1882},[4754,48439,48440,48442,48444],{},[898,48441,1688],{},[2505,48443,3132],{},[1708,48445,2417],{},[1708,48447,6981],{"stretchy":1715},[902,48449,40174],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,48452,48453,48456,48457,48470,48471,48484],{},[38,48454,48455],{},"Dualita"," — ekvivalence max ",[883,48458,48460],{"className":48459},[886],[888,48461,48462],{"xmlns":890},[892,48463,48464,48468],{},[895,48465,48466],{},[898,48467,900],{},[902,48469,900],{"encoding":904}," a min ",[883,48472,48474],{"className":48473},[886],[888,48475,48476],{"xmlns":890},[892,48477,48478,48482],{},[895,48479,48480],{},[898,48481,16183],{},[902,48483,16183],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,48486,13763],{"id":13762},[120,48488,48489,48512,48528,48541,48552],{},[123,48490,48491,1729,48494,48497,48498,48511],{},[38,48492,48493],{},"Teorie před optimalizací:",[207,48495,880],{"className":48496,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,48499,48501],{"className":48500},[886],[888,48502,48503],{"xmlns":890},[892,48504,48505,48509],{},[895,48506,48507],{},[898,48508,900],{},[902,48510,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,48513,48514,1729,48517,48520,48521,48524,48525,2155],{},[38,48515,48516],{},"Matematický aparát:",[207,48518,793],{"className":48519,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,48522,784],{"className":48523,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,48526,2162],{"className":48527,"dataFsResolvedFilePath":764,"href":765},[210],[123,48529,48530,1729,48533,48536,48537,48540],{},[38,48531,48532],{},"Paralely:",[207,48534,22974],{"className":48535,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,48538,23828],{"className":48539,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,48542,48543,1729,48546,1343,48549],{},[38,48544,48545],{},"Přednášky:",[207,48547,1094],{"className":48548,"dataFsResolvedFilePath":838,"href":839},[210],[207,48550,1101],{"className":48551,"dataFsResolvedFilePath":868,"href":869},[210],[123,48553,48554,1729,48556],{},[38,48555,13888],{},[207,48557,13894],{"className":48558,"dataFsResolvedFilePath":13892,"href":13893},[210],{"title":641,"searchDepth":642,"depth":642,"links":48560},[48561,48562,48563,48568,48569,48570,48572,48575,48578,48580,48581,48583,48584,48588,48589],{"id":23893,"depth":642,"text":23894},{"id":39856,"depth":642,"text":39857},{"id":40251,"depth":642,"text":40252,"children":48564},[48565,48566],{"id":40371,"depth":649,"text":40372},{"id":40952,"depth":649,"text":48567},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":41414,"depth":642,"text":41415},{"id":41725,"depth":642,"text":41726},{"id":42042,"depth":642,"text":48571},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":42814,"depth":642,"text":42815,"children":48573},[48574],{"id":43570,"depth":649,"text":43571},{"id":43750,"depth":642,"text":43751,"children":48576},[48577],{"id":44007,"depth":649,"text":44008},{"id":44958,"depth":642,"text":48579},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":45882,"depth":642,"text":45883},{"id":46085,"depth":642,"text":48582},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":46969,"depth":642,"text":46970},{"id":47356,"depth":642,"text":47357,"children":48585},[48586,48587],{"id":47360,"depth":649,"text":47361},{"id":47820,"depth":649,"text":47821},{"id":12595,"depth":642,"text":12596},{"id":13762,"depth":642,"text":13763},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":39617,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,48596,1144,21676,48597,48598,48599],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":48602,"title":802,"body":48603,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":62636,"navigation":664,"path":62637,"seo":62638,"sources":62639,"stem":62640,"tags":62641,"type":13951,"updated":677,"__hash__":62647},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":48604,"toc":62592},[48605,48608,48634,48638,48645,48795,48807,48810,48812,48899,48903,48939,49012,49032,49157,49167,49180,49184,49189,49219,49281,49290,49294,49356,49363,49384,49501,49579,49583,49586,49645,49760,49765,49797,49859,49907,49962,49966,49987,50011,50059,50063,50075,50079,50188,50192,50208,50249,50260,50418,50428,50433,50437,50559,50569,50576,50580,50658,50669,50749,50755,50762,50901,50908,50911,50968,50972,51050,51096,51140,51146,51259,51263,51266,51461,51465,51702,51705,51859,52012,52014,52016,52096,52099,52204,52273,52282,52284,52287,52348,52357,52361,52394,52472,52511,52515,52564,52618,52622,52651,52680,52732,52739,52793,52871,52875,52918,52985,53029,53133,53152,53154,53158,53266,53270,53338,53387,53394,53479,53483,53555,53560,53608,53796,53800,53805,53981,53986,54045,54149,54153,54180,54184,54191,54355,54442,54447,54449,54452,54552,54702,54774,54848,54850,54854,54868,54872,55004,55059,55171,55248,55252,55309,55412,55470,55631,55635,55710,55782,55880,55938,56031,56084,56105,56159,56164,56242,56290,56377,56415,56503,56656,56692,56746,56749,56751,56753,56802,56809,56817,56904,56913,57000,57007,57009,57013,57238,57240,57244,57248,57316,57367,57570,57576,57587,57655,57661,58083,58087,58151,58175,58371,58377,58391,58459,58462,58502,58725,58793,59095,59504,59581,59747,59753,59756,59831,60284,60335,60741,60846,61509,61512,61589,61597,61671,61702,61704,61706,61750,61752,61754,61758,61988,61992,62083,62088,62182,62187,62360,62364,62482,62487,62536,62538,62540],[12,48606,802],{"id":48607},"poptávka-nabídka-a-tržní-rovnováha",[1636,48609,48610],{},[724,48611,48612,48614,48615,48618,48619,48622,48623,48626,48627,48629,48630,48633],{},[883,48613,2518],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,48616,48617],{},"poptávka",") a výrobce (",[38,48620,48621],{},"nabídka","), jejich interakci v ",[38,48624,48625],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,48628,29848],{},"). Uzavírá ji pojem ",[38,48631,48632],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,48635,48637],{"id":48636},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,48639,48640,48641,48644],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,48642,48643],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,48646,48647,48664,48705,48721],{},[123,48648,48649,48650,48663],{},"cena ",[883,48651,48653],{"className":48652},[886],[888,48654,48655],{"xmlns":890},[892,48656,48657,48661],{},[895,48658,48659],{},[898,48660,1747],{},[902,48662,1747],{"encoding":904}," zkoumaného zboží,",[123,48665,48666,48667,1883],{},"ceny alternativních zboží ",[883,48668,48670],{"className":48669},[886],[888,48671,48672],{"xmlns":890},[892,48673,48674,48702],{},[895,48675,48676,48682,48684,48690,48692,48694,48696],{},[1743,48677,48678,48680],{},[898,48679,1747],{},[2505,48681,2507],{},[1708,48683,1883],{"separator":1882},[1743,48685,48686,48688],{},[898,48687,1747],{},[2505,48689,3132],{},[1708,48691,1883],{"separator":1882},[1708,48693,21550],{},[1708,48695,1883],{"separator":1882},[1743,48697,48698,48700],{},[898,48699,1747],{},[898,48701,6676],{},[902,48703,48704],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,48706,48707,48708,1883],{},"důchod ",[883,48709,48711],{"className":48710},[886],[888,48712,48713],{"xmlns":890},[892,48714,48715,48719],{},[895,48716,48717],{},[898,48718,21035],{},[902,48720,21035],{"encoding":904},[123,48722,48723,48724,1661,48737,48750,48751,48764,48765,48779,48780,48794],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,48725,48727],{"className":48726},[886],[888,48728,48729],{"xmlns":890},[892,48730,48731,48735],{},[895,48732,48733],{},[898,48734,1658],{},[902,48736,1658],{"encoding":904},[883,48738,48740],{"className":48739},[886],[888,48741,48742],{"xmlns":890},[892,48743,48744,48748],{},[895,48745,48746],{},[898,48747,1673],{},[902,48749,1673],{"encoding":904},", půda ",[883,48752,48754],{"className":48753},[886],[888,48755,48756],{"xmlns":890},[892,48757,48758,48762],{},[895,48759,48760],{},[898,48761,16183],{},[902,48763,16183],{"encoding":904},"), technologie, počet výrobců ",[883,48766,48768],{"className":48767},[886],[888,48769,48770],{"xmlns":890},[892,48771,48772,48777],{},[895,48773,48774],{},[898,48775,48776],{},"O",[902,48778,48776],{"encoding":904},", počasí ",[883,48781,48783],{"className":48782},[886],[888,48784,48785],{"xmlns":890},[892,48786,48787,48792],{},[895,48788,48789],{},[898,48790,48791],{},"W",[902,48793,48791],{"encoding":904}," atd.",[724,48796,48797,48798,48800,48801,48803,48804,2155],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,48799,2758],{},"), hovoříme o ",[38,48802,1694],{},"; jinak jde o model ",[38,48805,48806],{},"vícefaktorový",[48808,48809],"hr",{},[115,48811,25046],{"id":48617},[1636,48813,48814],{},[724,48815,48816,48818,48819,48832,48833,48846,48847,48850,48851,48874,48875,2155],{},[883,48817,2518],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,48820,48822],{"className":48821},[886],[888,48823,48824],{"xmlns":890},[892,48825,48826,48830],{},[895,48827,48828],{},[898,48829,1688],{},[902,48831,1688],{"encoding":904}," na ceně ",[883,48834,48836],{"className":48835},[886],[888,48837,48838],{"xmlns":890},[892,48839,48840,48844],{},[895,48841,48842],{},[898,48843,1747],{},[902,48845,1747],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,48848,48849],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,48852,48854],{"className":48853},[886],[888,48855,48856],{"xmlns":890},[892,48857,48858,48872],{},[895,48859,48860,48862,48864,48866,48868,48870],{},[898,48861,1688],{},[1708,48863,1710],{},[898,48865,16117],{},[1708,48867,1716],{"stretchy":1715},[898,48869,1747],{},[1708,48871,1721],{"stretchy":1715},[902,48873,16126],{"encoding":904}," a jeho lineární verzí ",[883,48876,48878],{"className":48877},[886],[888,48879,48880],{"xmlns":890},[892,48881,48882,48896],{},[895,48883,48884,48886,48888,48890,48892,48894],{},[898,48885,1747],{},[1708,48887,1710],{},[898,48889,207],{},[898,48891,1688],{},[1708,48893,2019],{},[898,48895,1923],{},[902,48897,48898],{"encoding":904},"P = aQ + b",[198,48900,48902],{"id":48901},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,48904,48905,48906,48919,48920,48933,48934,1695,48936,2750],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,48907,48909],{"className":48908},[886],[888,48910,48911],{"xmlns":890},[892,48912,48913,48917],{},[895,48914,48915],{},[898,48916,1688],{},[902,48918,1688],{"encoding":904}," závisí na ceně ",[883,48921,48923],{"className":48922},[886],[888,48924,48925],{"xmlns":890},[892,48926,48927,48931],{},[895,48928,48929],{},[898,48930,1747],{},[902,48932,1747],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,48935,39852],{},[614,48937,48938],{},"demand function",[883,48940,48942],{"className":48941},[886],[888,48943,48944],{"xmlns":890,"display":2210},[892,48945,48946,49009],{},[2214,48947,48948],{"width":2216},[2218,48949,48950,48952,49002,49004],{},[2221,48951],{"width":2223},[2221,48953,48954],{},[895,48955,48956,48958,48960,48962,48964,48966,48968,48974,48976,48982,48984,48986,48988,48994,48996,48998,49000],{},[898,48957,1688],{},[1708,48959,1710],{},[898,48961,16117],{},[1708,48963,1716],{"stretchy":1715},[898,48965,1747],{},[1708,48967,1883],{"separator":1882},[1743,48969,48970,48972],{},[898,48971,1747],{},[2505,48973,2507],{},[1708,48975,1883],{"separator":1882},[1743,48977,48978,48980],{},[898,48979,1747],{},[2505,48981,3132],{},[1708,48983,1883],{"separator":1882},[1708,48985,21550],{},[1708,48987,1883],{"separator":1882},[1743,48989,48990,48992],{},[898,48991,1747],{},[898,48993,6676],{},[1708,48995,1883],{"separator":1882},[898,48997,21035],{},[1708,48999,1721],{"stretchy":1715},[898,49001,2155],{"mathvariant":1759},[2221,49003],{"width":2223},[2221,49005,49006],{},[2247,49007,49008],{},"(2.1)",[902,49010,49011],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,49013,49014,49015,49017,49018,49031],{},"Důležitou vlastností je ",[38,49016,6633],{},": změní-li se všechny nezávisle proměnné ",[883,49019,49021],{"className":49020},[886],[888,49022,49023],{"xmlns":890},[892,49024,49025,49029],{},[895,49026,49027],{},[898,49028,5498],{},[902,49030,5498],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,49033,49035],{"className":49034},[886],[888,49036,49037],{"xmlns":890,"display":2210},[892,49038,49039,49154],{},[2214,49040,49041],{"width":2216},[2218,49042,49043,49045,49147,49149],{},[2221,49044],{"width":2223},[2221,49046,49047],{},[895,49048,49049,49051,49053,49055,49057,49059,49061,49063,49065,49071,49073,49075,49081,49083,49085,49087,49089,49095,49097,49099,49101,49103,49105,49107,49109,49111,49113,49119,49121,49127,49129,49131,49133,49139,49141,49143,49145],{},[898,49050,1688],{},[1708,49052,1710],{},[898,49054,16117],{},[1708,49056,1716],{"stretchy":1715},[898,49058,5498],{},[898,49060,1747],{},[1708,49062,1883],{"separator":1882},[898,49064,5498],{},[1743,49066,49067,49069],{},[898,49068,1747],{},[2505,49070,2507],{},[1708,49072,1883],{"separator":1882},[898,49074,5498],{},[1743,49076,49077,49079],{},[898,49078,1747],{},[2505,49080,3132],{},[1708,49082,1883],{"separator":1882},[1708,49084,21550],{},[1708,49086,1883],{"separator":1882},[898,49088,5498],{},[1743,49090,49091,49093],{},[898,49092,1747],{},[898,49094,6676],{},[1708,49096,1883],{"separator":1882},[898,49098,5498],{},[898,49100,21035],{},[1708,49102,1721],{"stretchy":1715},[1708,49104,1710],{},[898,49106,16117],{},[1708,49108,1716],{"stretchy":1715},[898,49110,1747],{},[1708,49112,1883],{"separator":1882},[1743,49114,49115,49117],{},[898,49116,1747],{},[2505,49118,2507],{},[1708,49120,1883],{"separator":1882},[1743,49122,49123,49125],{},[898,49124,1747],{},[2505,49126,3132],{},[1708,49128,1883],{"separator":1882},[1708,49130,21550],{},[1708,49132,1883],{"separator":1882},[1743,49134,49135,49137],{},[898,49136,1747],{},[898,49138,6676],{},[1708,49140,1883],{"separator":1882},[898,49142,21035],{},[1708,49144,1721],{"stretchy":1715},[898,49146,2155],{"mathvariant":1759},[2221,49148],{"width":2223},[2221,49150,49151],{},[2247,49152,49153],{},"(2.2)",[902,49155,49156],{"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}",[1636,49158,49159],{},[724,49160,49161,49163,49164,2155],{},[883,49162,6130],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,49165,49166],{},"v jednofaktorových modelech neplatí",[724,49168,49169,49170,1343,49173,1771,49176,49179],{},"Rozlišuje se poptávka ",[38,49171,49172],{},"individuální",[38,49174,49175],{},"tržní",[38,49177,49178],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,49181,49183],{"id":49182},"jednofaktorové-modely","Jednofaktorové modely",[49185,49186,49188],"h4",{"id":49187},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,49190,49191,49192,49205,49206,2788],{},"Poptávané množství ",[883,49193,49195],{"className":49194},[886],[888,49196,49197],{"xmlns":890},[892,49198,49199,49203],{},[895,49200,49201],{},[898,49202,1688],{},[902,49204,1688],{"encoding":904}," závisí pouze na ceně ",[883,49207,49209],{"className":49208},[886],[888,49210,49211],{"xmlns":890},[892,49212,49213,49217],{},[895,49214,49215],{},[898,49216,1747],{},[902,49218,1747],{"encoding":904},[883,49220,49222],{"className":49221},[886],[888,49223,49224],{"xmlns":890,"display":2210},[892,49225,49226,49278],{},[2214,49227,49228],{"width":2216},[2218,49229,49230,49232,49271,49273],{},[2221,49231],{"width":2223},[2221,49233,49234],{},[895,49235,49236,49238,49240,49242,49244,49246,49248,49250,49252,49255,49257,49259,49261,49263,49265,49267,49269],{},[898,49237,1688],{},[1708,49239,1710],{},[898,49241,16117],{},[1708,49243,1716],{"stretchy":1715},[898,49245,1747],{},[1708,49247,1721],{"stretchy":1715},[1708,49249,1883],{"separator":1882},[3213,49251],{"width":3215},[2247,49253,49254],{},"resp.",[3213,49256],{"width":3215},[898,49258,1747],{},[1708,49260,1710],{},[898,49262,16117],{},[1708,49264,1716],{"stretchy":1715},[898,49266,1688],{},[1708,49268,1721],{"stretchy":1715},[898,49270,2155],{"mathvariant":1759},[2221,49272],{"width":2223},[2221,49274,49275],{},[2247,49276,49277],{},"(2.3)",[902,49279,49280],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,49282,49283,49284,1695,49287,2511],{},"Graf této funkce se nazývá ",[38,49285,49286],{},"křivka poptávky",[614,49288,49289],{},"demand curve",[49185,49291,49293],{"id":49292},"zákon-klesající-poptávky","Zákon klesající poptávky",[1636,49295,49296],{},[724,49297,49298],{},[38,49299,49300,49301,49314,49315,49328,49329,49314,49342,49355],{},"Roste-li cena ",[883,49302,49304],{"className":49303},[886],[888,49305,49306],{"xmlns":890},[892,49307,49308,49312],{},[895,49309,49310],{},[898,49311,1747],{},[902,49313,1747],{"encoding":904},", pak množství ",[883,49316,49318],{"className":49317},[886],[888,49319,49320],{"xmlns":890},[892,49321,49322,49326],{},[895,49323,49324],{},[898,49325,1688],{},[902,49327,1688],{"encoding":904}," klesá; klesá-li cena ",[883,49330,49332],{"className":49331},[886],[888,49333,49334],{"xmlns":890},[892,49335,49336,49340],{},[895,49337,49338],{},[898,49339,1747],{},[902,49341,1747],{"encoding":904},[883,49343,49345],{"className":49344},[886],[888,49346,49347],{"xmlns":890},[892,49348,49349,49353],{},[895,49350,49351],{},[898,49352,1688],{},[902,49354,1688],{"encoding":904}," roste.",[724,49357,49358,49359,49362],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,49360,49361],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1636,49364,49365,49370],{},[724,49366,49367,49369],{},[883,49368,2518],{}," Intuice — proč zákon platí",[120,49371,49372,49378],{},[123,49373,49374,49377],{},[38,49375,49376],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,49379,49380,49383],{},[38,49381,49382],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,49385,49386,49387,49400,49401,49414,49415,49441,49442,49468,49469,3033,49495,49498,49499,2155],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,49388,49390],{"className":49389},[886],[888,49391,49392],{"xmlns":890},[892,49393,49394,49398],{},[895,49395,49396],{},[898,49397,1747],{},[902,49399,1747],{"encoding":904}," se vynáší na svislou osu, množství ",[883,49402,49404],{"className":49403},[886],[888,49405,49406],{"xmlns":890},[892,49407,49408,49412],{},[895,49409,49410],{},[898,49411,1688],{},[902,49413,1688],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,49416,49418],{"className":49417},[886],[888,49419,49420],{"xmlns":890},[892,49421,49422,49438],{},[895,49423,49424,49426,49428,49430,49436],{},[1708,49425,6940],{"stretchy":1715},[2505,49427,2784],{},[1708,49429,1883],{"separator":1882},[1743,49431,49432,49434],{},[898,49433,1747],{},[2505,49435,2784],{},[1708,49437,6981],{"stretchy":1715},[902,49439,49440],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,49443,49445],{"className":49444},[886],[888,49446,49447],{"xmlns":890},[892,49448,49449,49465],{},[895,49450,49451,49453,49459,49461,49463],{},[1708,49452,6940],{"stretchy":1715},[1743,49454,49455,49457],{},[898,49456,1688],{},[2505,49458,2784],{},[1708,49460,1883],{"separator":1882},[2505,49462,2784],{},[1708,49464,6981],{"stretchy":1715},[902,49466,49467],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,49470,49472],{"className":49471},[886],[888,49473,49474],{"xmlns":890},[892,49475,49476,49492],{},[895,49477,49478,49480,49482,49484,49490],{},[1708,49479,1716],{"stretchy":1715},[2505,49481,2784],{},[1708,49483,1883],{"separator":1882},[1743,49485,49486,49488],{},[898,49487,1747],{},[2505,49489,2784],{},[1708,49491,1721],{"stretchy":1715},[902,49493,49494],{"encoding":904},"(0, P_0)",[38,49496,49497],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,49500,2863],{},[724,49502,49503],{},[614,49504,49505,49506,49528,49529,1771,49554,2155],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,49507,49509],{"className":49508},[886],[888,49510,49511],{"xmlns":890},[892,49512,49513,49525],{},[895,49514,49515,49517,49519,49521,49523],{},[1708,49516,1716],{"stretchy":1715},[898,49518,1688],{},[1708,49520,1883],{"separator":1882},[898,49522,1747],{},[1708,49524,1721],{"stretchy":1715},[902,49526,49527],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,49530,49532],{"className":49531},[886],[888,49533,49534],{"xmlns":890},[892,49535,49536,49552],{},[895,49537,49538,49540,49542,49544,49550],{},[1708,49539,6940],{"stretchy":1715},[2505,49541,2784],{},[1708,49543,1883],{"separator":1882},[1743,49545,49546,49548],{},[898,49547,1747],{},[2505,49549,2784],{},[1708,49551,6981],{"stretchy":1715},[902,49553,49440],{"encoding":904},[883,49555,49557],{"className":49556},[886],[888,49558,49559],{"xmlns":890},[892,49560,49561,49577],{},[895,49562,49563,49565,49571,49573,49575],{},[1708,49564,6940],{"stretchy":1715},[1743,49566,49567,49569],{},[898,49568,1688],{},[2505,49570,2784],{},[1708,49572,1883],{"separator":1882},[2505,49574,2784],{},[1708,49576,6981],{"stretchy":1715},[902,49578,49467],{"encoding":904},[49185,49580,49582],{"id":49581},"lineární-model-poptávky","Lineární model poptávky",[724,49584,49585],{},"Nejjednodušší závislostí je",[883,49587,49589],{"className":49588},[886],[888,49590,49591],{"xmlns":890,"display":2210},[892,49592,49593,49642],{},[2214,49594,49595],{"width":2216},[2218,49596,49597,49599,49635,49637],{},[2221,49598],{"width":2223},[2221,49600,49601],{},[895,49602,49603,49605,49607,49609,49611,49613,49615,49617,49619,49621,49623,49625,49627,49629,49631,49633],{},[898,49604,1747],{},[1708,49606,1710],{},[898,49608,207],{},[898,49610,1688],{},[1708,49612,2019],{},[898,49614,1923],{},[1708,49616,1883],{"separator":1882},[3213,49618],{"width":3215},[898,49620,207],{},[1708,49622,2932],{},[2505,49624,2784],{},[1708,49626,1883],{"separator":1882},[2247,49628,14279],{},[898,49630,1923],{},[1708,49632,2854],{},[2505,49634,24346],{},[2221,49636],{"width":2223},[2221,49638,49639],{},[2247,49640,49641],{},"(2.4)",[902,49643,49644],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,49646,49647,49648,2980,49684,1771,49708,19950,49734,49756,49757,2155],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,49649,49651],{"className":49650},[886],[888,49652,49653],{"xmlns":890},[892,49654,49655,49681],{},[895,49656,49657,49659,49661,49669,49671,49673],{},[898,49658,1688],{},[1708,49660,1710],{},[3194,49662,49663],{"scriptlevel":2784,"displaystyle":1715},[2358,49664,49665,49667],{},[2505,49666,2507],{},[898,49668,207],{},[898,49670,1747],{},[1708,49672,2726],{},[3194,49674,49675],{"scriptlevel":2784,"displaystyle":1715},[2358,49676,49677,49679],{},[898,49678,1923],{},[898,49680,207],{},[902,49682,49683],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,49685,49687],{"className":49686},[886],[888,49688,49689],{"xmlns":890},[892,49690,49691,49705],{},[895,49692,49693,49701,49703],{},[3194,49694,49695],{"scriptlevel":2784,"displaystyle":1715},[2358,49696,49697,49699],{},[2505,49698,2507],{},[898,49700,207],{},[1708,49702,2932],{},[2505,49704,2784],{},[902,49706,49707],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,49709,49711],{"className":49710},[886],[888,49712,49713],{"xmlns":890},[892,49714,49715,49731],{},[895,49716,49717,49719,49727,49729],{},[1708,49718,2726],{},[3194,49720,49721],{"scriptlevel":2784,"displaystyle":1715},[2358,49722,49723,49725],{},[898,49724,1923],{},[898,49726,207],{},[1708,49728,2854],{},[2505,49730,2784],{},[902,49732,49733],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,49735,49737],{"className":49736},[886],[888,49738,49739],{"xmlns":890},[892,49740,49741,49753],{},[895,49742,49743,49745,49747,49749,49751],{},[1708,49744,1716],{"stretchy":1715},[2505,49746,2784],{},[1708,49748,1883],{"separator":1882},[898,49750,1923],{},[1708,49752,1721],{"stretchy":1715},[902,49754,49755],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,49758,49759],{},"nedokonalé konkurenci",[49761,49762,49764],"h5",{"id":49763},"příklad-21","Příklad 2.1",[724,49766,49767,49770,49771,2155],{},[38,49768,49769],{},"Zadání:"," Lineární poptávka ",[883,49772,49774],{"className":49773},[886],[888,49775,49776],{"xmlns":890},[892,49777,49778,49794],{},[895,49779,49780,49782,49784,49786,49788,49790,49792],{},[898,49781,1747],{},[1708,49783,1710],{},[1708,49785,2726],{},[2505,49787,3132],{},[898,49789,1688],{},[1708,49791,2019],{},[2505,49793,4199],{},[902,49795,49796],{"encoding":904},"P = -2Q + 60",[724,49798,49799,49802,49803,49825,49826,2155],{},[38,49800,49801],{},"Řešení:"," Reálné cenové rozpětí je ",[883,49804,49806],{"className":49805},[886],[888,49807,49808],{"xmlns":890},[892,49809,49810,49822],{},[895,49811,49812,49814,49816,49818,49820],{},[1708,49813,1716],{"stretchy":1715},[2505,49815,2784],{},[1708,49817,1883],{"separator":1882},[2505,49819,4199],{},[1708,49821,1721],{"stretchy":1715},[902,49823,49824],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,49827,49829],{"className":49828},[886],[888,49830,49831],{"xmlns":890},[892,49832,49833,49856],{},[895,49834,49835,49837,49839,49841,49849,49851,49853],{},[898,49836,1688],{},[1708,49838,1710],{},[1708,49840,2726],{},[3194,49842,49843],{"scriptlevel":2784,"displaystyle":1715},[2358,49844,49845,49847],{},[2505,49846,2507],{},[2505,49848,3132],{},[898,49850,1747],{},[1708,49852,2019],{},[2505,49854,49855],{},"30",[902,49857,49858],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,49860,49861,49884],{},[19,49862,49863],{},[22,49864,49865,49880,49882],{},[25,49866,49867],{},[883,49868,49870],{"className":49869},[886],[888,49871,49872],{"xmlns":890},[892,49873,49874,49878],{},[895,49875,49876],{},[898,49877,1747],{},[902,49879,1747],{"encoding":904},[25,49881,17132],{},[25,49883,4018],{},[30,49885,49886],{},[22,49887,49888,49903,49905],{},[35,49889,49890],{},[883,49891,49893],{"className":49892},[886],[888,49894,49895],{"xmlns":890},[892,49896,49897,49901],{},[895,49898,49899],{},[898,49900,1688],{},[902,49902,1688],{"encoding":904},[35,49904,4003],{},[35,49906,4018],{},[724,49908,49909],{},[614,49910,49911,49912,1771,49934,2155],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,49913,49915],{"className":49914},[886],[888,49916,49917],{"xmlns":890},[892,49918,49919,49931],{},[895,49920,49921,49923,49925,49927,49929],{},[1708,49922,6940],{"stretchy":1715},[2505,49924,2784],{},[1708,49926,1883],{"separator":1882},[898,49928,1923],{},[1708,49930,6981],{"stretchy":1715},[902,49932,49933],{"encoding":904},"[0, b]",[883,49935,49937],{"className":49936},[886],[888,49938,49939],{"xmlns":890},[892,49940,49941,49959],{},[895,49942,49943,49945,49947,49949,49951,49953,49955,49957],{},[1708,49944,6940],{"stretchy":1715},[1708,49946,2726],{},[898,49948,1923],{},[898,49950,1799],{"mathvariant":1759},[898,49952,207],{},[1708,49954,1883],{"separator":1882},[2505,49956,2784],{},[1708,49958,6981],{"stretchy":1715},[902,49960,49961],{"encoding":904},"[-b\u002Fa, 0]",[49185,49963,49965],{"id":49964},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,49967,49968,49969,49986],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,49970,49972],{"className":49971},[886],[888,49973,49974],{"xmlns":890},[892,49975,49976,49984],{},[895,49977,49978],{},[1753,49979,49980,49982],{},[898,49981,1747],{},[1708,49983,2417],{},[902,49985,16331],{"encoding":904},", je funkce poptávky konstantní:",[883,49988,49990],{"className":49989},[886],[888,49991,49992],{"xmlns":890,"display":2210},[892,49993,49994,50008],{},[895,49995,49996,49998,50000,50006],{},[898,49997,1747],{},[1708,49999,1710],{},[1753,50001,50002,50004],{},[898,50003,1747],{},[1708,50005,2417],{},[898,50007,2155],{"mathvariant":1759},[902,50009,50010],{"encoding":904},"P = P^*.",[724,50012,50013],{},[614,50014,50015,50016,50037,50038,2155],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,50017,50019],{"className":50018},[886],[888,50020,50021],{"xmlns":890},[892,50022,50023,50035],{},[895,50024,50025,50027,50029,50031,50033],{},[1708,50026,1716],{"stretchy":1715},[898,50028,1688],{},[1708,50030,1883],{"separator":1882},[898,50032,1747],{},[1708,50034,1721],{"stretchy":1715},[902,50036,49527],{"encoding":904}," na úrovni ",[883,50039,50041],{"className":50040},[886],[888,50042,50043],{"xmlns":890},[892,50044,50045,50057],{},[895,50046,50047,50049,50051],{},[898,50048,1747],{},[1708,50050,1710],{},[1753,50052,50053,50055],{},[898,50054,1747],{},[1708,50056,2417],{},[902,50058,16285],{"encoding":904},[49185,50060,50062],{"id":50061},"giffenův-statek","Giffenův statek",[724,50064,50065,50066,50068,50069,50071,50072,2155],{},"Existují zboží, u nichž je křivka poptávky ",[38,50067,2082],{}," — tzv. ",[38,50070,50062],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,50073,50074],{},"podřadnému zboží",[49761,50076,50078],{"id":50077},"příklad-22","Příklad 2.2",[724,50080,50081,50084,50085,50103,50104,50126,50127,50145,50146,50164,50165,50187],{},[38,50082,50083],{},"Zadání a popis:"," Křivka ",[883,50086,50088],{"className":50087},[886],[888,50089,50090],{"xmlns":890},[892,50091,50092,50100],{},[895,50093,50094],{},[1743,50095,50096,50098],{},[898,50097,16117],{},[2505,50099,2507],{},[902,50101,50102],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,50105,50107],{"className":50106},[886],[888,50108,50109],{"xmlns":890},[892,50110,50111,50123],{},[895,50112,50113,50115,50117,50119,50121],{},[1708,50114,1716],{"stretchy":1715},[2505,50116,2784],{},[1708,50118,1883],{"separator":1882},[2505,50120,4853],{},[1708,50122,1721],{"stretchy":1715},[902,50124,50125],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,50128,50130],{"className":50129},[886],[888,50131,50132],{"xmlns":890},[892,50133,50134,50142],{},[895,50135,50136],{},[1743,50137,50138,50140],{},[898,50139,1688],{},[2505,50141,2784],{},[902,50143,50144],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,50147,50149],{"className":50148},[886],[888,50150,50151],{"xmlns":890},[892,50152,50153,50161],{},[895,50154,50155],{},[1743,50156,50157,50159],{},[898,50158,16117],{},[2505,50160,3132],{},[902,50162,50163],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,50166,50168],{"className":50167},[886],[888,50169,50170],{"xmlns":890},[892,50171,50172,50184],{},[895,50173,50174,50176,50178,50180,50182],{},[1708,50175,6940],{"stretchy":1715},[2505,50177,2784],{},[1708,50179,1883],{"separator":1882},[2505,50181,4023],{},[1708,50183,6981],{"stretchy":1715},[902,50185,50186],{"encoding":904},"[0, 21]"," centů.",[198,50189,50191],{"id":50190},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,50193,50194,50195,2788],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,50196,50198],{"className":50197},[886],[888,50199,50200],{"xmlns":890},[892,50201,50202,50206],{},[895,50203,50204],{},[898,50205,21035],{},[902,50207,21035],{"encoding":904},[883,50209,50211],{"className":50210},[886],[888,50212,50213],{"xmlns":890,"display":2210},[892,50214,50215,50246],{},[2214,50216,50217],{"width":2216},[2218,50218,50219,50221,50239,50241],{},[2221,50220],{"width":2223},[2221,50222,50223],{},[895,50224,50225,50227,50229,50231,50233,50235,50237],{},[898,50226,1688],{},[1708,50228,1710],{},[898,50230,16183],{},[1708,50232,1716],{"stretchy":1715},[898,50234,21035],{},[1708,50236,1721],{"stretchy":1715},[898,50238,2155],{"mathvariant":1759},[2221,50240],{"width":2223},[2221,50242,50243],{},[2247,50244,50245],{},"(2.5)",[902,50247,50248],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,50250,50251,50252,50255,50256,50259],{},"Funkce se nazývá ",[38,50253,50254],{},"Engelova",", její graf ",[38,50257,50258],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,50261,50262,50393],{},[123,50263,50264,12636,50267,50280,50281,50294,50295,50312,50313],{},[38,50265,50266],{},"Normální (superior) zboží",[883,50268,50270],{"className":50269},[886],[888,50271,50272],{"xmlns":890},[892,50273,50274,50278],{},[895,50275,50276],{},[898,50277,1688],{},[902,50279,1688],{"encoding":904}," roste s ",[883,50282,50284],{"className":50283},[886],[888,50285,50286],{"xmlns":890},[892,50287,50288,50292],{},[895,50289,50290],{},[898,50291,21035],{},[902,50293,21035],{"encoding":904},", nepřesáhne hodnotu ",[883,50296,50298],{"className":50297},[886],[888,50299,50300],{"xmlns":890},[892,50301,50302,50310],{},[895,50303,50304],{},[1743,50305,50306,50308],{},[898,50307,1688],{},[2505,50309,2784],{},[902,50311,50144],{"encoding":904},":\n",[120,50314,50315,50346],{},[123,50316,50317,50320,50321,50323,50324,2155],{},[38,50318,50319],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,50322,2940],{}," křivka, autonomní spotřeba ",[883,50325,50327],{"className":50326},[886],[888,50328,50329],{"xmlns":890},[892,50330,50331,50343],{},[895,50332,50333,50339,50341],{},[1743,50334,50335,50337],{},[898,50336,1688],{},[2505,50338,2507],{},[1708,50340,2854],{},[2505,50342,2784],{},[902,50344,50345],{"encoding":904},"Q_1 > 0",[123,50347,50348,50351,50352,50370,50371,50373,50374,1729,50391,2155],{},[38,50349,50350],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,50353,50355],{"className":50354},[886],[888,50356,50357],{"xmlns":890},[892,50358,50359,50367],{},[895,50360,50361],{},[1743,50362,50363,50365],{},[898,50364,21035],{},[2505,50366,2507],{},[902,50368,50369],{"encoding":904},"Y_1",", křivka je nejprve ",[38,50372,2863],{}," a od ",[883,50375,50377],{"className":50376},[886],[888,50378,50379],{"xmlns":890},[892,50380,50381,50389],{},[895,50382,50383],{},[1743,50384,50385,50387],{},[898,50386,21035],{},[2505,50388,2507],{},[902,50390,50369],{"encoding":904},[38,50392,2940],{},[123,50394,50395,50398,50399,50417],{},[38,50396,50397],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,50400,50402],{"className":50401},[886],[888,50403,50404],{"xmlns":890},[892,50405,50406,50414],{},[895,50407,50408],{},[1743,50409,50410,50412],{},[898,50411,21035],{},[2505,50413,2784],{},[902,50415,50416],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,50419,50420,50421,50424,50425,2511],{},"Mírou citlivosti je ",[614,50422,50423],{},"důchodová elasticita"," (viz ",[207,50426,15838],{"className":50427,"dataFsResolvedFilePath":848,"href":849},[210],[724,50429,50430],{},[614,50431,50432],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[49185,50434,50436],{"id":50435},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1636,50438,50439,50510,50553],{},[724,50440,50441,50443,50444,1729,50447,1729,50460,3136,50462,50475,50476,50479,50480,2155],{},[883,50442,6130],{}," Pozor — nezbytné ≠ podřadné\n",[38,50445,50446],{},"Nezbytné zboží:",[883,50448,50450],{"className":50449},[886],[888,50451,50452],{"xmlns":890},[892,50453,50454,50458],{},[895,50455,50456],{},[898,50457,1688],{},[902,50459,1688],{"encoding":904},[38,50461,19235],{},[883,50463,50465],{"className":50464},[886],[888,50466,50467],{"xmlns":890},[892,50468,50469,50473],{},[895,50470,50471],{},[898,50472,21035],{},[902,50474,21035],{"encoding":904},", ale ",[38,50477,50478],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,50481,50483],{"className":50482},[886],[888,50484,50485],{"xmlns":890},[892,50486,50487,50507],{},[895,50488,50489,50495,50497,50499,50501,50503,50505],{},[1743,50490,50491,50493],{},[898,50492,16183],{},[898,50494,21035],{},[1708,50496,18420],{},[1708,50498,1716],{"stretchy":1715},[2505,50500,2784],{},[1708,50502,1883],{"separator":1882},[2505,50504,2507],{},[1708,50506,1721],{"stretchy":1715},[902,50508,50509],{"encoding":904},"E_Y \\in (0, 1)",[724,50511,50512,1729,50515,1729,50528,50530,50531,2155],{},[38,50513,50514],{},"Podřadné zboží:",[883,50516,50518],{"className":50517},[886],[888,50519,50520],{"xmlns":890},[892,50521,50522,50526],{},[895,50523,50524],{},[898,50525,1688],{},[902,50527,1688],{"encoding":904},[38,50529,19255],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,50532,50534],{"className":50533},[886],[888,50535,50536],{"xmlns":890},[892,50537,50538,50550],{},[895,50539,50540,50546,50548],{},[1743,50541,50542,50544],{},[898,50543,16183],{},[898,50545,21035],{},[1708,50547,2932],{},[2505,50549,2784],{},[902,50551,50552],{"encoding":904},"E_Y \u003C 0",[724,50554,50555,50556,2155],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,50557,50558],{},"méně kusů, ne jen proporčně méně",[724,50560,50561,50564,50565,50568],{},[38,50562,50563],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,50566,50567],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,50570,50571],{},[3372,50572],{"alt":50573,"className":50574,"src":50575},"imek-engelovy-krivky-3typy",[210,3376],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[49761,50577,50579],{"id":50578},"české-příklady","České příklady",[16,50581,50582,50592],{},[19,50583,50584],{},[22,50585,50586,50589],{},[25,50587,50588],{},"Podřadné",[25,50590,50591],{},"Nahradí se za",[30,50593,50594,50602,50610,50618,50626,50634,50642,50650],{},[22,50595,50596,50599],{},[35,50597,50598],{},"Instantní polévky, ramen",[35,50600,50601],{},"Čerstvé jídlo, restaurace",[22,50603,50604,50607],{},[35,50605,50606],{},"MHD (autobus, tramvaj)",[35,50608,50609],{},"Vlastní auto, Uber, taxi",[22,50611,50612,50615],{},[35,50613,50614],{},"Mražené polotovary, pizza z mrazáku",[35,50616,50617],{},"Čerstvé suroviny, hotovky",[22,50619,50620,50623],{},[35,50621,50622],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,50624,50625],{},"Značkové produkty",[22,50627,50628,50631],{},[35,50629,50630],{},"Paštika Májka, obyčejný měkký salám",[35,50632,50633],{},"Kvalitní uzeniny, šunka od kosti",[22,50635,50636,50639],{},[35,50637,50638],{},"Second hand oblečení",[35,50640,50641],{},"Nové oblečení, značky",[22,50643,50644,50647],{},[35,50645,50646],{},"Krabicové víno, nejlevnější pivo",[35,50648,50649],{},"Lahvové víno, řemeslná piva",[22,50651,50652,50655],{},[35,50653,50654],{},"Ojetá auta nižších tříd",[35,50656,50657],{},"Nová auta, prémiové značky",[1636,50659,50660],{},[724,50661,50662,50664,50665,50668],{},[883,50663,3465],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,50666,50667],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,50670,50671,50674,50675,1695,50678,50700,50701,1695,50704,50725,50726,50744,50745,50748],{},[38,50672,50673],{},"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 ",[38,50676,50677],{},"luxus",[883,50679,50681],{"className":50680},[886],[888,50682,50683],{"xmlns":890},[892,50684,50685,50697],{},[895,50686,50687,50693,50695],{},[1743,50688,50689,50691],{},[898,50690,16183],{},[898,50692,21035],{},[1708,50694,2854],{},[2505,50696,2507],{},[902,50698,50699],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,50702,50703],{},"podřadné",[883,50705,50707],{"className":50706},[886],[888,50708,50709],{"xmlns":890},[892,50710,50711,50723],{},[895,50712,50713,50719,50721],{},[1743,50714,50715,50717],{},[898,50716,16183],{},[898,50718,21035],{},[1708,50720,2932],{},[2505,50722,2784],{},[902,50724,50552],{"encoding":904},"). Proto je ",[883,50727,50729],{"className":50728},[886],[888,50730,50731],{"xmlns":890},[892,50732,50733,50741],{},[895,50734,50735],{},[1743,50736,50737,50739],{},[898,50738,16183],{},[898,50740,21035],{},[902,50742,50743],{"encoding":904},"E_Y"," vždy ",[38,50746,50747],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,50750,50751,50752,50754],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,50753,50062],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,50756,50758,50759,1721],{"id":50757},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,50760,50761],{},"shift of demand",[724,50763,50764,50765,50783,50784,50801,50802,50815,50816,2486,50829,50851,50852,50869,50870,50896,50897,50900],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,50766,50768],{"className":50767},[886],[888,50769,50770],{"xmlns":890},[892,50771,50772,50780],{},[895,50773,50774],{},[1743,50775,50776,50778],{},[898,50777,1747],{},[2505,50779,2784],{},[902,50781,50782],{"encoding":904},"P_0"," odpovídá množství ",[883,50785,50787],{"className":50786},[886],[888,50788,50789],{"xmlns":890},[892,50790,50791,50799],{},[895,50792,50793],{},[1743,50794,50795,50797],{},[898,50796,1688],{},[2505,50798,2784],{},[902,50800,50144],{"encoding":904}," na křivce ",[883,50803,50805],{"className":50804},[886],[888,50806,50807],{"xmlns":890},[892,50808,50809,50813],{},[895,50810,50811],{},[898,50812,16117],{},[902,50814,16117],{"encoding":904},"; vzroste-li důchod z ",[883,50817,50819],{"className":50818},[886],[888,50820,50821],{"xmlns":890},[892,50822,50823,50827],{},[895,50824,50825],{},[898,50826,21035],{},[902,50828,21035],{"encoding":904},[883,50830,50832],{"className":50831},[886],[888,50833,50834],{"xmlns":890},[892,50835,50836,50848],{},[895,50837,50838,50844,50846],{},[1743,50839,50840,50842],{},[898,50841,21035],{},[2505,50843,2507],{},[1708,50845,2854],{},[898,50847,21035],{},[902,50849,50850],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,50853,50855],{"className":50854},[886],[888,50856,50857],{"xmlns":890},[892,50858,50859,50867],{},[895,50860,50861],{},[1743,50862,50863,50865],{},[898,50864,1747],{},[2505,50866,2784],{},[902,50868,50782],{"encoding":904}," odpovídá vyšší ",[883,50871,50873],{"className":50872},[886],[888,50874,50875],{"xmlns":890},[892,50876,50877,50893],{},[895,50878,50879,50885,50887],{},[1743,50880,50881,50883],{},[898,50882,1688],{},[2505,50884,2507],{},[1708,50886,2854],{},[1743,50888,50889,50891],{},[898,50890,1688],{},[2505,50892,2784],{},[902,50894,50895],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,50898,50899],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,50902,50903],{},[3372,50904],{"alt":50905,"className":50906,"src":50907},"imek-posun-vs-pohyb-po-krivce",[210,3376],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,50909,50910],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,50912,50913],{},[614,50914,50915,50916,25893,50946,50967],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,50917,50919],{"className":50918},[886],[888,50920,50921],{"xmlns":890},[892,50922,50923,50943],{},[895,50924,50925,50931,50933,50935,50937],{},[1743,50926,50927,50929],{},[898,50928,16117],{},[2505,50930,3132],{},[1708,50932,1883],{"separator":1882},[898,50934,16117],{},[1708,50936,1883],{"separator":1882},[1743,50938,50939,50941],{},[898,50940,16117],{},[2505,50942,2507],{},[902,50944,50945],{"encoding":904},"D_2, D, D_1",[883,50947,50949],{"className":50948},[886],[888,50950,50951],{"xmlns":890},[892,50952,50953,50965],{},[895,50954,50955,50957,50959,50961,50963],{},[1708,50956,1716],{"stretchy":1715},[898,50958,1688],{},[1708,50960,1883],{"separator":1882},[898,50962,1747],{},[1708,50964,1721],{"stretchy":1715},[902,50966,49527],{"encoding":904},", šipky naznačují posuny.",[49761,50969,50971],{"id":50970},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,50973,50974,50976,50977,51000,51001,51018,51019,51036,51037,2155],{},[38,50975,49769],{}," Poptávce ",[883,50978,50980],{"className":50979},[886],[888,50981,50982],{"xmlns":890},[892,50983,50984,50998],{},[895,50985,50986,50988,50990,50992,50994,50996],{},[898,50987,1747],{},[1708,50989,1710],{},[898,50991,16117],{},[1708,50993,1716],{"stretchy":1715},[898,50995,1688],{},[1708,50997,1721],{"stretchy":1715},[902,50999,16564],{"encoding":904}," odpovídá ceně ",[883,51002,51004],{"className":51003},[886],[888,51005,51006],{"xmlns":890},[892,51007,51008,51016],{},[895,51009,51010],{},[1743,51011,51012,51014],{},[898,51013,1747],{},[2505,51015,2784],{},[902,51017,50782],{"encoding":904}," množství ",[883,51020,51022],{"className":51021},[886],[888,51023,51024],{"xmlns":890},[892,51025,51026,51034],{},[895,51027,51028],{},[1743,51029,51030,51032],{},[898,51031,1688],{},[2505,51033,2784],{},[902,51035,50144],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,51038,51040],{"className":51039},[886],[888,51041,51042],{"xmlns":890},[892,51043,51044,51048],{},[895,51045,51046],{},[898,51047,1978],{},[902,51049,1978],{"encoding":904},[724,51051,51052,51054,51055,51072,51073,51095],{},[38,51053,49801],{}," Kupující nakupuje množství ",[883,51056,51058],{"className":51057},[886],[888,51059,51060],{"xmlns":890},[892,51061,51062,51070],{},[895,51063,51064],{},[1743,51065,51066,51068],{},[898,51067,1688],{},[2505,51069,2507],{},[902,51071,40849],{"encoding":904},", které odpovídá ceně ",[883,51074,51076],{"className":51075},[886],[888,51077,51078],{"xmlns":890},[892,51079,51080,51092],{},[895,51081,51082,51088,51090],{},[1743,51083,51084,51086],{},[898,51085,1747],{},[2505,51087,2784],{},[1708,51089,2019],{},[898,51091,1978],{},[902,51093,51094],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,51097,51099],{"className":51098},[886],[888,51100,51101],{"xmlns":890,"display":2210},[892,51102,51103,51137],{},[895,51104,51105,51107,51109,51115,51117,51119,51121,51123,51125,51127,51129,51131,51133,51135],{},[898,51106,1747],{},[1708,51108,1710],{},[1743,51110,51111,51113],{},[898,51112,16117],{},[2505,51114,2507],{},[1708,51116,1716],{"stretchy":1715},[898,51118,1688],{},[1708,51120,1721],{"stretchy":1715},[1708,51122,1710],{},[898,51124,16117],{},[1708,51126,1716],{"stretchy":1715},[898,51128,1688],{},[1708,51130,1721],{"stretchy":1715},[1708,51132,2726],{},[898,51134,1978],{},[1708,51136,1883],{"separator":1882},[902,51138,51139],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,51141,51142,51143,2155],{},"tj. dojde k ",[38,51144,51145],{},"posunu poptávky doleva",[724,51147,51148],{},[614,51149,51150,51151,51172,51173,1343,51190,1343,51203,51224,51225,1771,51242,2155],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,51152,51154],{"className":51153},[886],[888,51155,51156],{"xmlns":890},[892,51157,51158,51170],{},[895,51159,51160,51162,51164,51166,51168],{},[1708,51161,1716],{"stretchy":1715},[898,51163,1688],{},[1708,51165,1883],{"separator":1882},[898,51167,1747],{},[1708,51169,1721],{"stretchy":1715},[902,51171,49527],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,51174,51176],{"className":51175},[886],[888,51177,51178],{"xmlns":890},[892,51179,51180,51188],{},[895,51181,51182],{},[1743,51183,51184,51186],{},[898,51185,1747],{},[2505,51187,2784],{},[902,51189,50782],{"encoding":904},[883,51191,51193],{"className":51192},[886],[888,51194,51195],{"xmlns":890},[892,51196,51197,51201],{},[895,51198,51199],{},[898,51200,1978],{},[902,51202,1978],{"encoding":904},[883,51204,51206],{"className":51205},[886],[888,51207,51208],{"xmlns":890},[892,51209,51210,51222],{},[895,51211,51212,51218,51220],{},[1743,51213,51214,51216],{},[898,51215,1747],{},[2505,51217,2784],{},[1708,51219,2019],{},[898,51221,1978],{},[902,51223,51094],{"encoding":904},"; na vodorovné ",[883,51226,51228],{"className":51227},[886],[888,51229,51230],{"xmlns":890},[892,51231,51232,51240],{},[895,51233,51234],{},[1743,51235,51236,51238],{},[898,51237,1688],{},[2505,51239,2507],{},[902,51241,40849],{"encoding":904},[883,51243,51245],{"className":51244},[886],[888,51246,51247],{"xmlns":890},[892,51248,51249,51257],{},[895,51250,51251],{},[1743,51252,51253,51255],{},[898,51254,1688],{},[2505,51256,2784],{},[902,51258,50144],{"encoding":904},[198,51260,51262],{"id":51261},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,51264,51265],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,51267,51269],{"className":51268},[886],[888,51270,51271],{"xmlns":890,"display":2210},[892,51272,51273,51458],{},[2214,51274,51275],{"width":2216},[2218,51276,51277,51279,51451,51453],{},[2221,51278],{"width":2223},[2221,51280,51281],{},[2214,51282,51283,51367],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,51284,51285,51295],{},[2221,51286,51287],{},[3194,51288,51289],{"scriptlevel":2784,"displaystyle":1882},[1743,51290,51291,51293],{},[898,51292,1688],{},[2505,51294,2507],{},[2221,51296,51297],{},[3194,51298,51299],{"scriptlevel":2784,"displaystyle":1882},[895,51300,51301,51303,51305,51311,51313,51319,51321,51327,51329,51331,51337,51339,51345,51351,51353,51359,51365],{},[895,51302],{},[1708,51304,1710],{},[1743,51306,51307,51309],{},[898,51308,16117],{},[2505,51310,2507],{},[1708,51312,1716],{"stretchy":1715},[1743,51314,51315,51317],{},[898,51316,1747],{},[2505,51318,2507],{},[1708,51320,1883],{"separator":1882},[1743,51322,51323,51325],{},[898,51324,1747],{},[2505,51326,3132],{},[1708,51328,1721],{"stretchy":1715},[1708,51330,1710],{},[1743,51332,51333,51335],{},[898,51334,207],{},[2505,51336,2507],{},[1708,51338,2019],{},[1743,51340,51341,51343],{},[898,51342,1923],{},[2505,51344,2507],{},[1743,51346,51347,51349],{},[898,51348,1747],{},[2505,51350,2507],{},[1708,51352,2019],{},[1743,51354,51355,51357],{},[898,51356,14142],{},[2505,51358,2507],{},[1743,51360,51361,51363],{},[898,51362,1747],{},[2505,51364,3132],{},[1708,51366,1883],{"separator":1882},[2218,51368,51369,51379],{},[2221,51370,51371],{},[3194,51372,51373],{"scriptlevel":2784,"displaystyle":1882},[1743,51374,51375,51377],{},[898,51376,1688],{},[2505,51378,3132],{},[2221,51380,51381],{},[3194,51382,51383],{"scriptlevel":2784,"displaystyle":1882},[895,51384,51385,51387,51389,51395,51397,51403,51405,51411,51413,51415,51421,51423,51429,51435,51437,51443,51449],{},[895,51386],{},[1708,51388,1710],{},[1743,51390,51391,51393],{},[898,51392,16117],{},[2505,51394,3132],{},[1708,51396,1716],{"stretchy":1715},[1743,51398,51399,51401],{},[898,51400,1747],{},[2505,51402,2507],{},[1708,51404,1883],{"separator":1882},[1743,51406,51407,51409],{},[898,51408,1747],{},[2505,51410,3132],{},[1708,51412,1721],{"stretchy":1715},[1708,51414,1710],{},[1743,51416,51417,51419],{},[898,51418,207],{},[2505,51420,3132],{},[1708,51422,2019],{},[1743,51424,51425,51427],{},[898,51426,1923],{},[2505,51428,3132],{},[1743,51430,51431,51433],{},[898,51432,1747],{},[2505,51434,2507],{},[1708,51436,2019],{},[1743,51438,51439,51441],{},[898,51440,14142],{},[2505,51442,3132],{},[1743,51444,51445,51447],{},[898,51446,1747],{},[2505,51448,3132],{},[898,51450,2155],{"mathvariant":1759},[2221,51452],{"width":2223},[2221,51454,51455],{},[2247,51456,51457],{},"(2.6)",[902,51459,51460],{"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}",[49185,51462,51464],{"id":51463},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,51466,51467,51514,51561],{},[123,51468,51469,1343,51491,51513],{},[883,51470,51472],{"className":51471},[886],[888,51473,51474],{"xmlns":890},[892,51475,51476,51488],{},[895,51477,51478,51484,51486],{},[1743,51479,51480,51482],{},[898,51481,207],{},[2505,51483,2507],{},[1708,51485,2854],{},[2505,51487,2784],{},[902,51489,51490],{"encoding":904},"a_1 > 0",[883,51492,51494],{"className":51493},[886],[888,51495,51496],{"xmlns":890},[892,51497,51498,51510],{},[895,51499,51500,51506,51508],{},[1743,51501,51502,51504],{},[898,51503,207],{},[2505,51505,3132],{},[1708,51507,2854],{},[2505,51509,2784],{},[902,51511,51512],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,51515,51516,1343,51538,51560],{},[883,51517,51519],{"className":51518},[886],[888,51520,51521],{"xmlns":890},[892,51522,51523,51535],{},[895,51524,51525,51531,51533],{},[1743,51526,51527,51529],{},[898,51528,1923],{},[2505,51530,2507],{},[1708,51532,2932],{},[2505,51534,2784],{},[902,51536,51537],{"encoding":904},"b_1 \u003C 0",[883,51539,51541],{"className":51540},[886],[888,51542,51543],{"xmlns":890},[892,51544,51545,51557],{},[895,51546,51547,51553,51555],{},[1743,51548,51549,51551],{},[898,51550,14142],{},[2505,51552,3132],{},[1708,51554,2932],{},[2505,51556,2784],{},[902,51558,51559],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,51562,51563,51564,1343,51581,51599,51600],{},"zkřížené koeficienty ",[883,51565,51567],{"className":51566},[886],[888,51568,51569],{"xmlns":890},[892,51570,51571,51579],{},[895,51572,51573],{},[1743,51574,51575,51577],{},[898,51576,14142],{},[2505,51578,2507],{},[902,51580,41646],{"encoding":904},[883,51582,51584],{"className":51583},[886],[888,51585,51586],{"xmlns":890},[892,51587,51588,51596],{},[895,51589,51590],{},[1743,51591,51592,51594],{},[898,51593,1923],{},[2505,51595,3132],{},[902,51597,51598],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,51601,51602,51652],{},[123,51603,51604,51607,51608,1343,51630,1883],{},[38,51605,51606],{},"substituty"," (máslo vs. margarín): ",[883,51609,51611],{"className":51610},[886],[888,51612,51613],{"xmlns":890},[892,51614,51615,51627],{},[895,51616,51617,51623,51625],{},[1743,51618,51619,51621],{},[898,51620,14142],{},[2505,51622,2507],{},[1708,51624,2854],{},[2505,51626,2784],{},[902,51628,51629],{"encoding":904},"c_1 > 0",[883,51631,51633],{"className":51632},[886],[888,51634,51635],{"xmlns":890},[892,51636,51637,51649],{},[895,51638,51639,51645,51647],{},[1743,51640,51641,51643],{},[898,51642,1923],{},[2505,51644,3132],{},[1708,51646,2854],{},[2505,51648,2784],{},[902,51650,51651],{"encoding":904},"b_2 > 0",[123,51653,51654,51657,51658,1343,51680,2155],{},[38,51655,51656],{},"komplementy"," (auto vs. benzín): ",[883,51659,51661],{"className":51660},[886],[888,51662,51663],{"xmlns":890},[892,51664,51665,51677],{},[895,51666,51667,51673,51675],{},[1743,51668,51669,51671],{},[898,51670,14142],{},[2505,51672,2507],{},[1708,51674,2932],{},[2505,51676,2784],{},[902,51678,51679],{"encoding":904},"c_1 \u003C 0",[883,51681,51683],{"className":51682},[886],[888,51684,51685],{"xmlns":890},[892,51686,51687,51699],{},[895,51688,51689,51695,51697],{},[1743,51690,51691,51693],{},[898,51692,1923],{},[2505,51694,3132],{},[1708,51696,2932],{},[2505,51698,2784],{},[902,51700,51701],{"encoding":904},"b_2 \u003C 0",[724,51703,51704],{},"Schematicky:",[724,51706,51707,51710],{},[38,51708,51709],{},"Substituty",[883,51711,51713],{"className":51712},[886],[888,51714,51715],{"xmlns":890},[892,51716,51717,51856],{},[895,51718,51719,51725,51727,51742,51744,51764,51766,51786,51788,51790,51796,51798,51812,51814,51834,51836],{},[1743,51720,51721,51723],{},[898,51722,1688],{},[2505,51724,2507],{},[1708,51726,1710],{},[898,51728,51729],{},[51730,51731,51732,51740],"munder",{},[1708,51733,51734],{},[1743,51735,51736,51738],{},[898,51737,207],{},[2505,51739,2507],{},[1708,51741,2019],{"lspace":1760,"rspace":1760},[1708,51743,2019],{},[898,51745,51746],{},[51730,51747,51748,51762],{},[1708,51749,51750,51756],{},[1743,51751,51752,51754],{},[898,51753,1923],{},[2505,51755,2507],{},[1743,51757,51758,51760],{},[898,51759,1747],{},[2505,51761,2507],{},[1708,51763,2726],{"lspace":1760,"rspace":1760},[1708,51765,2019],{},[898,51767,51768],{},[51730,51769,51770,51784],{},[1708,51771,51772,51778],{},[1743,51773,51774,51776],{},[898,51775,14142],{},[2505,51777,2507],{},[1743,51779,51780,51782],{},[898,51781,1747],{},[2505,51783,3132],{},[1708,51785,2019],{"lspace":1760,"rspace":1760},[1708,51787,1883],{"separator":1882},[3213,51789],{"width":3215},[1743,51791,51792,51794],{},[898,51793,1688],{},[2505,51795,3132],{},[1708,51797,1710],{},[898,51799,51800],{},[51730,51801,51802,51810],{},[1708,51803,51804],{},[1743,51805,51806,51808],{},[898,51807,207],{},[2505,51809,3132],{},[1708,51811,2019],{"lspace":1760,"rspace":1760},[1708,51813,2019],{},[898,51815,51816],{},[51730,51817,51818,51832],{},[1708,51819,51820,51826],{},[1743,51821,51822,51824],{},[898,51823,1923],{},[2505,51825,3132],{},[1743,51827,51828,51830],{},[898,51829,1747],{},[2505,51831,2507],{},[1708,51833,2019],{"lspace":1760,"rspace":1760},[1708,51835,2019],{},[898,51837,51838],{},[51730,51839,51840,51854],{},[1708,51841,51842,51848],{},[1743,51843,51844,51846],{},[898,51845,14142],{},[2505,51847,3132],{},[1743,51849,51850,51852],{},[898,51851,1747],{},[2505,51853,3132],{},[1708,51855,2726],{"lspace":1760,"rspace":1760},[902,51857,51858],{"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}",[724,51860,51861,51864],{},[38,51862,51863],{},"Komplementy",[883,51865,51867],{"className":51866},[886],[888,51868,51869],{"xmlns":890},[892,51870,51871,52009],{},[895,51872,51873,51879,51881,51895,51897,51917,51919,51939,51941,51943,51949,51951,51965,51967,51987,51989],{},[1743,51874,51875,51877],{},[898,51876,1688],{},[2505,51878,2507],{},[1708,51880,1710],{},[898,51882,51883],{},[51730,51884,51885,51893],{},[1708,51886,51887],{},[1743,51888,51889,51891],{},[898,51890,207],{},[2505,51892,2507],{},[1708,51894,2019],{"lspace":1760,"rspace":1760},[1708,51896,2019],{},[898,51898,51899],{},[51730,51900,51901,51915],{},[1708,51902,51903,51909],{},[1743,51904,51905,51907],{},[898,51906,1923],{},[2505,51908,2507],{},[1743,51910,51911,51913],{},[898,51912,1747],{},[2505,51914,2507],{},[1708,51916,2726],{"lspace":1760,"rspace":1760},[1708,51918,2019],{},[898,51920,51921],{},[51730,51922,51923,51937],{},[1708,51924,51925,51931],{},[1743,51926,51927,51929],{},[898,51928,14142],{},[2505,51930,2507],{},[1743,51932,51933,51935],{},[898,51934,1747],{},[2505,51936,3132],{},[1708,51938,2726],{"lspace":1760,"rspace":1760},[1708,51940,1883],{"separator":1882},[3213,51942],{"width":3215},[1743,51944,51945,51947],{},[898,51946,1688],{},[2505,51948,3132],{},[1708,51950,1710],{},[898,51952,51953],{},[51730,51954,51955,51963],{},[1708,51956,51957],{},[1743,51958,51959,51961],{},[898,51960,207],{},[2505,51962,3132],{},[1708,51964,2019],{"lspace":1760,"rspace":1760},[1708,51966,2019],{},[898,51968,51969],{},[51730,51970,51971,51985],{},[1708,51972,51973,51979],{},[1743,51974,51975,51977],{},[898,51976,1923],{},[2505,51978,3132],{},[1743,51980,51981,51983],{},[898,51982,1747],{},[2505,51984,2507],{},[1708,51986,2726],{"lspace":1760,"rspace":1760},[1708,51988,2019],{},[898,51990,51991],{},[51730,51992,51993,52007],{},[1708,51994,51995,52001],{},[1743,51996,51997,51999],{},[898,51998,14142],{},[2505,52000,3132],{},[1743,52002,52003,52005],{},[898,52004,1747],{},[2505,52006,3132],{},[1708,52008,2726],{"lspace":1760,"rspace":1760},[902,52010,52011],{"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}",[48808,52013],{},[115,52015,25010],{"id":48621},[1636,52017,52018],{},[724,52019,52020,52022,52023,48832,52036,48846,52049,52052,52053,3136,52077,52095],{},[883,52021,2518],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,52024,52026],{"className":52025},[886],[888,52027,52028],{"xmlns":890},[892,52029,52030,52034],{},[895,52031,52032],{},[898,52033,1688],{},[902,52035,1688],{"encoding":904},[883,52037,52039],{"className":52038},[886],[888,52040,52041],{"xmlns":890},[892,52042,52043,52047],{},[895,52044,52045],{},[898,52046,1747],{},[902,52048,1747],{"encoding":904},[38,52050,52051],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,52054,52056],{"className":52055},[886],[888,52057,52058],{"xmlns":890},[892,52059,52060,52074],{},[895,52061,52062,52064,52066,52068,52070,52072],{},[898,52063,1747],{},[1708,52065,1710],{},[898,52067,14142],{},[898,52069,1688],{},[1708,52071,2019],{},[898,52073,2364],{},[902,52075,52076],{"encoding":904},"P = cQ + d",[883,52078,52080],{"className":52079},[886],[888,52081,52082],{"xmlns":890},[892,52083,52084,52092],{},[895,52085,52086,52088,52090],{},[898,52087,14142],{},[1708,52089,2854],{},[2505,52091,2784],{},[902,52093,52094],{"encoding":904},"c > 0"," je standardní aproximací.",[198,52097,48902],{"id":52098},"obecný-vícefaktorový-model-1",[724,52100,52101,1695,52104,52107,52108,52121,52122,1661,52135,48750,52148,52161,52162,52176,52177,48779,52190,52203],{},[38,52102,52103],{},"Nabízené množství",[614,52105,52106],{},"quantity supplied",") závisí na ceně ",[883,52109,52111],{"className":52110},[886],[888,52112,52113],{"xmlns":890},[892,52114,52115,52119],{},[895,52116,52117],{},[898,52118,1747],{},[902,52120,1747],{"encoding":904},", cenách výrobních faktorů (práce ",[883,52123,52125],{"className":52124},[886],[888,52126,52127],{"xmlns":890},[892,52128,52129,52133],{},[895,52130,52131],{},[898,52132,1658],{},[902,52134,1658],{"encoding":904},[883,52136,52138],{"className":52137},[886],[888,52139,52140],{"xmlns":890},[892,52141,52142,52146],{},[895,52143,52144],{},[898,52145,1673],{},[902,52147,1673],{"encoding":904},[883,52149,52151],{"className":52150},[886],[888,52152,52153],{"xmlns":890},[892,52154,52155,52159],{},[895,52156,52157],{},[898,52158,16183],{},[902,52160,16183],{"encoding":904},"), očekávání ",[883,52163,52165],{"className":52164},[886],[888,52166,52167],{"xmlns":890},[892,52168,52169,52174],{},[895,52170,52171],{},[898,52172,52173],{},"V",[902,52175,52173],{"encoding":904},", počtu výrobců ",[883,52178,52180],{"className":52179},[886],[888,52181,52182],{"xmlns":890},[892,52183,52184,52188],{},[895,52185,52186],{},[898,52187,48776],{},[902,52189,48776],{"encoding":904},[883,52191,52193],{"className":52192},[886],[888,52194,52195],{"xmlns":890},[892,52196,52197,52201],{},[895,52198,52199],{},[898,52200,48791],{},[902,52202,48791],{"encoding":904}," a dalších:",[883,52205,52207],{"className":52206},[886],[888,52208,52209],{"xmlns":890,"display":2210},[892,52210,52211,52270],{},[2214,52212,52213],{"width":2216},[2218,52214,52215,52217,52263,52265],{},[2221,52216],{"width":2223},[2221,52218,52219],{},[895,52220,52221,52223,52225,52227,52229,52231,52233,52235,52237,52239,52241,52243,52245,52247,52249,52251,52253,52255,52257,52259,52261],{},[898,52222,1688],{},[1708,52224,1710],{},[898,52226,1981],{},[1708,52228,1716],{"stretchy":1715},[898,52230,1747],{},[1708,52232,1883],{"separator":1882},[898,52234,1658],{},[1708,52236,1883],{"separator":1882},[898,52238,1673],{},[1708,52240,1883],{"separator":1882},[898,52242,16183],{},[1708,52244,1883],{"separator":1882},[898,52246,52173],{},[1708,52248,1883],{"separator":1882},[898,52250,48776],{},[1708,52252,1883],{"separator":1882},[898,52254,48791],{},[1708,52256,1883],{"separator":1882},[1708,52258,21550],{},[1708,52260,1721],{"stretchy":1715},[898,52262,2155],{"mathvariant":1759},[2221,52264],{"width":2223},[2221,52266,52267],{},[2247,52268,52269],{},"(2.7)",[902,52271,52272],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,52274,50251,52275,1695,52278,52281],{},[38,52276,52277],{},"funkce nabídky",[614,52279,52280],{},"supply function",") v širším slova smyslu.",[198,52283,10796],{"id":10795},[724,52285,52286],{},"V nejpřirozenějším jednofaktorovém modelu",[883,52288,52290],{"className":52289},[886],[888,52291,52292],{"xmlns":890,"display":2210},[892,52293,52294,52345],{},[2214,52295,52296],{"width":2216},[2218,52297,52298,52300,52338,52340],{},[2221,52299],{"width":2223},[2221,52301,52302],{},[895,52303,52304,52306,52308,52310,52312,52314,52316,52318,52320,52322,52324,52326,52328,52330,52332,52334,52336],{},[898,52305,1688],{},[1708,52307,1710],{},[898,52309,1981],{},[1708,52311,1716],{"stretchy":1715},[898,52313,1747],{},[1708,52315,1721],{"stretchy":1715},[1708,52317,1883],{"separator":1882},[3213,52319],{"width":3215},[2247,52321,49254],{},[3213,52323],{"width":3215},[898,52325,1747],{},[1708,52327,1710],{},[898,52329,1981],{},[1708,52331,1716],{"stretchy":1715},[898,52333,1688],{},[1708,52335,1721],{"stretchy":1715},[898,52337,2155],{"mathvariant":1759},[2221,52339],{"width":2223},[2221,52341,52342],{},[2247,52343,52344],{},"(2.8)",[902,52346,52347],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,52349,52350,52351,1695,52354,2511],{},"Graf je ",[38,52352,52353],{},"křivka nabídky",[614,52355,52356],{},"supply curve",[49185,52358,52360],{"id":52359},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1636,52362,52363],{},[724,52364,52365],{},[38,52366,49300,52367,52380,52381,49355],{},[883,52368,52370],{"className":52369},[886],[888,52371,52372],{"xmlns":890},[892,52373,52374,52378],{},[895,52375,52376],{},[898,52377,1747],{},[902,52379,1747],{"encoding":904},", pak nabízené množství ",[883,52382,52384],{"className":52383},[886],[888,52385,52386],{"xmlns":890},[892,52387,52388,52392],{},[895,52389,52390],{},[898,52391,1688],{},[902,52393,1688],{"encoding":904},[724,52395,52396,52397,52422,52423,52453,52454,52471],{},"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 ",[883,52398,52400],{"className":52399},[886],[888,52401,52402],{"xmlns":890},[892,52403,52404,52420],{},[895,52405,52406,52408,52410,52412,52418],{},[1708,52407,6940],{"stretchy":1715},[2505,52409,2784],{},[1708,52411,1883],{"separator":1882},[1743,52413,52414,52416],{},[898,52415,1747],{},[2505,52417,2784],{},[1708,52419,6981],{"stretchy":1715},[902,52421,49440],{"encoding":904}," na svislé ose (případně z ",[883,52424,52426],{"className":52425},[886],[888,52427,52428],{"xmlns":890},[892,52429,52430,52450],{},[895,52431,52432,52434,52440,52442,52448],{},[1708,52433,6940],{"stretchy":1715},[1743,52435,52436,52438],{},[898,52437,1688],{},[2505,52439,2507],{},[1708,52441,1883],{"separator":1882},[1743,52443,52444,52446],{},[898,52445,1747],{},[2505,52447,2507],{},[1708,52449,6981],{"stretchy":1715},[902,52451,52452],{"encoding":904},"[Q_1, P_1]","), kde ",[883,52455,52457],{"className":52456},[886],[888,52458,52459],{"xmlns":890},[892,52460,52461,52469],{},[895,52462,52463],{},[1743,52464,52465,52467],{},[898,52466,1747],{},[2505,52468,2784],{},[902,52470,50782],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,52473,52474],{},[614,52475,52476,52477,15667,52490,2155],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,52478,52480],{"className":52479},[886],[888,52481,52482],{"xmlns":890},[892,52483,52484,52488],{},[895,52485,52486],{},[898,52487,1981],{},[902,52489,1981],{"encoding":904},[883,52491,52493],{"className":52492},[886],[888,52494,52495],{"xmlns":890},[892,52496,52497,52509],{},[895,52498,52499,52501,52503,52505,52507],{},[1708,52500,1716],{"stretchy":1715},[898,52502,1688],{},[1708,52504,1883],{"separator":1882},[898,52506,1747],{},[1708,52508,1721],{"stretchy":1715},[902,52510,49527],{"encoding":904},[49185,52512,52514],{"id":52513},"lineární-model-nabídky","Lineární model nabídky",[883,52516,52518],{"className":52517},[886],[888,52519,52520],{"xmlns":890,"display":2210},[892,52521,52522,52561],{},[2214,52523,52524],{"width":2216},[2218,52525,52526,52528,52554,52556],{},[2221,52527],{"width":2223},[2221,52529,52530],{},[895,52531,52532,52534,52536,52538,52540,52542,52544,52546,52548,52550,52552],{},[898,52533,1747],{},[1708,52535,1710],{},[898,52537,14142],{},[898,52539,1688],{},[1708,52541,2019],{},[898,52543,2364],{},[1708,52545,1883],{"separator":1882},[3213,52547],{"width":3215},[898,52549,14142],{},[1708,52551,2854],{},[2505,52553,24346],{},[2221,52555],{"width":2223},[2221,52557,52558],{},[2247,52559,52560],{},"(2.9)",[902,52562,52563],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,52565,52566,52567,52603,52604,52617],{},"Alternativně ",[883,52568,52570],{"className":52569},[886],[888,52571,52572],{"xmlns":890},[892,52573,52574,52600],{},[895,52575,52576,52578,52580,52588,52590,52592],{},[898,52577,1688],{},[1708,52579,1710],{},[3194,52581,52582],{"scriptlevel":2784,"displaystyle":1715},[2358,52583,52584,52586],{},[2505,52585,2507],{},[898,52587,14142],{},[898,52589,1747],{},[1708,52591,2726],{},[3194,52593,52594],{"scriptlevel":2784,"displaystyle":1715},[2358,52595,52596,52598],{},[898,52597,2364],{},[898,52599,14142],{},[902,52601,52602],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,52605,52607],{"className":52606},[886],[888,52608,52609],{"xmlns":890},[892,52610,52611,52615],{},[895,52612,52613],{},[898,52614,1747],{},[902,52616,1747],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[49761,52619,52621],{"id":52620},"příklad-25","Příklad 2.5",[724,52623,52624,52626,52627,2155],{},[38,52625,49769],{}," Lineární nabídka ",[883,52628,52630],{"className":52629},[886],[888,52631,52632],{"xmlns":890},[892,52633,52634,52648],{},[895,52635,52636,52638,52640,52642,52644,52646],{},[898,52637,1747],{},[1708,52639,1710],{},[2505,52641,6097],{},[898,52643,1688],{},[1708,52645,2019],{},[2505,52647,4028],{},[902,52649,52650],{"encoding":904},"P = 0{,}5Q + 25",[724,52652,52653,52655,52656,2155],{},[38,52654,49801],{}," Alternativní tvar ",[883,52657,52659],{"className":52658},[886],[888,52660,52661],{"xmlns":890},[892,52662,52663,52677],{},[895,52664,52665,52667,52669,52671,52673,52675],{},[898,52666,1688],{},[1708,52668,1710],{},[2505,52670,3132],{},[898,52672,1747],{},[1708,52674,2726],{},[2505,52676,9704],{},[902,52678,52679],{"encoding":904},"Q = 2P - 50",[16,52681,52682,52707],{},[19,52683,52684],{},[22,52685,52686,52701,52703,52705],{},[25,52687,52688],{},[883,52689,52691],{"className":52690},[886],[888,52692,52693],{"xmlns":890},[892,52694,52695,52699],{},[895,52696,52697],{},[898,52698,1747],{},[902,52700,1747],{"encoding":904},[25,52702,49855],{},[25,52704,26919],{},[25,52706,17132],{},[30,52708,52709],{},[22,52710,52711,52726,52728,52730],{},[35,52712,52713],{},[883,52714,52716],{"className":52715},[886],[888,52717,52718],{"xmlns":890},[892,52719,52720,52724],{},[895,52721,52722],{},[898,52723,1688],{},[902,52725,1688],{"encoding":904},[35,52727,4003],{},[35,52729,4018],{},[35,52731,49855],{},[198,52733,52735,52736,1721],{"id":52734},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,52737,52738],{},"shift of supply",[724,52740,52741,52742,52745,52746,52763,52764,52789,52790,2155],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,52743,52744],{},"doprava",": při stejné ceně ",[883,52747,52749],{"className":52748},[886],[888,52750,52751],{"xmlns":890},[892,52752,52753,52761],{},[895,52754,52755],{},[1743,52756,52757,52759],{},[898,52758,1747],{},[2505,52760,2784],{},[902,52762,50782],{"encoding":904}," vyrobí výrobce větší ",[883,52765,52767],{"className":52766},[886],[888,52768,52769],{"xmlns":890},[892,52770,52771,52787],{},[895,52772,52773,52779,52781],{},[1743,52774,52775,52777],{},[898,52776,1688],{},[2505,52778,2507],{},[1708,52780,2854],{},[1743,52782,52783,52785],{},[898,52784,1688],{},[2505,52786,2784],{},[902,52788,50895],{"encoding":904},"); zdražení vstupů posune křivku ",[38,52791,52792],{},"doleva",[724,52794,52795],{},[614,52796,52797,52798,52811,52812,52830,52831,52849,52850,2155],{},"Obrázek 2.11: Původní ",[883,52799,52801],{"className":52800},[886],[888,52802,52803],{"xmlns":890},[892,52804,52805,52809],{},[895,52806,52807],{},[898,52808,1981],{},[902,52810,1981],{"encoding":904},", posunuté ",[883,52813,52815],{"className":52814},[886],[888,52816,52817],{"xmlns":890},[892,52818,52819,52827],{},[895,52820,52821],{},[1743,52822,52823,52825],{},[898,52824,1981],{},[2505,52826,2507],{},[902,52828,52829],{"encoding":904},"S_1"," (doprava) a ",[883,52832,52834],{"className":52833},[886],[888,52835,52836],{"xmlns":890},[892,52837,52838,52846],{},[895,52839,52840],{},[1743,52841,52842,52844],{},[898,52843,1981],{},[2505,52845,3132],{},[902,52847,52848],{"encoding":904},"S_2"," (doleva) v ",[883,52851,52853],{"className":52852},[886],[888,52854,52855],{"xmlns":890},[892,52856,52857,52869],{},[895,52858,52859,52861,52863,52865,52867],{},[1708,52860,1716],{"stretchy":1715},[898,52862,1688],{},[1708,52864,1883],{"separator":1882},[898,52866,1747],{},[1708,52868,1721],{"stretchy":1715},[902,52870,49527],{"encoding":904},[49761,52872,52874],{"id":52873},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,52876,52877,52879,52880,52904,52905,2155],{},[38,52878,49769],{}," Nabídka ",[883,52881,52883],{"className":52882},[886],[888,52884,52885],{"xmlns":890},[892,52886,52887,52901],{},[895,52888,52889,52891,52893,52895,52897,52899],{},[898,52890,1747],{},[1708,52892,1710],{},[898,52894,1981],{},[1708,52896,1716],{"stretchy":1715},[898,52898,1688],{},[1708,52900,1721],{"stretchy":1715},[902,52902,52903],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,52906,52908],{"className":52907},[886],[888,52909,52910],{"xmlns":890},[892,52911,52912,52916],{},[895,52913,52914],{},[898,52915,1978],{},[902,52917,1978],{"encoding":904},[724,52919,52920,52922,52923,52936,52937,52955,52956,52984],{},[38,52921,49801],{}," Spotřebitel zaplatí ",[883,52924,52926],{"className":52925},[886],[888,52927,52928],{"xmlns":890},[892,52929,52930,52934],{},[895,52931,52932],{},[898,52933,1747],{},[902,52935,1747],{"encoding":904},", výrobce obdrží ",[883,52938,52940],{"className":52939},[886],[888,52941,52942],{"xmlns":890},[892,52943,52944,52952],{},[895,52945,52946,52948,52950],{},[898,52947,1747],{},[1708,52949,2726],{},[898,52951,1978],{},[902,52953,52954],{"encoding":904},"P - T",". Z podmínky ",[883,52957,52959],{"className":52958},[886],[888,52960,52961],{"xmlns":890},[892,52962,52963,52981],{},[895,52964,52965,52967,52969,52971,52973,52975,52977,52979],{},[898,52966,1747],{},[1708,52968,2726],{},[898,52970,1978],{},[1708,52972,1710],{},[898,52974,1981],{},[1708,52976,1716],{"stretchy":1715},[898,52978,1688],{},[1708,52980,1721],{"stretchy":1715},[902,52982,52983],{"encoding":904},"P - T = S(Q)"," plyne",[883,52986,52988],{"className":52987},[886],[888,52989,52990],{"xmlns":890,"display":2210},[892,52991,52992,53026],{},[895,52993,52994,52996,52998,53004,53006,53008,53010,53012,53014,53016,53018,53020,53022,53024],{},[898,52995,1747],{},[1708,52997,1710],{},[1743,52999,53000,53002],{},[898,53001,1981],{},[2505,53003,2507],{},[1708,53005,1716],{"stretchy":1715},[898,53007,1688],{},[1708,53009,1721],{"stretchy":1715},[1708,53011,1710],{},[898,53013,1981],{},[1708,53015,1716],{"stretchy":1715},[898,53017,1688],{},[1708,53019,1721],{"stretchy":1715},[1708,53021,2019],{},[898,53023,1978],{},[898,53025,2155],{"mathvariant":1759},[902,53027,53028],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,53030,53031,53032,53045,53046,1729,53059,53062,53063,1771,53083,3033,53101,2155],{},"Křivka ",[883,53033,53035],{"className":53034},[886],[888,53036,53037],{"xmlns":890},[892,53038,53039,53043],{},[895,53040,53041],{},[898,53042,1981],{},[902,53044,1981],{"encoding":904}," se tedy posune o ",[883,53047,53049],{"className":53048},[886],[888,53050,53051],{"xmlns":890},[892,53052,53053,53057],{},[895,53054,53055],{},[898,53056,1978],{},[902,53058,1978],{"encoding":904},[38,53060,53061],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,53064,53066],{"className":53065},[886],[888,53067,53068],{"xmlns":890},[892,53069,53070,53080],{},[895,53071,53072,53074,53076,53078],{},[898,53073,1747],{},[1708,53075,1710],{},[2505,53077,3132],{},[898,53079,1688],{},[902,53081,53082],{"encoding":904},"P = 2Q",[883,53084,53086],{"className":53085},[886],[888,53087,53088],{"xmlns":890},[892,53089,53090,53098],{},[895,53091,53092,53094,53096],{},[898,53093,1978],{},[1708,53095,1710],{},[2505,53097,3947],{},[902,53099,53100],{"encoding":904},"T = 6",[883,53102,53104],{"className":53103},[886],[888,53105,53106],{"xmlns":890},[892,53107,53108,53130],{},[895,53109,53110,53116,53118,53120,53122,53124,53126,53128],{},[1743,53111,53112,53114],{},[898,53113,1981],{},[2505,53115,2507],{},[1708,53117,2788],{},[898,53119,1747],{},[1708,53121,1710],{},[2505,53123,3132],{},[898,53125,1688],{},[1708,53127,2019],{},[2505,53129,3947],{},[902,53131,53132],{"encoding":904},"S_1: P = 2Q + 6",[724,53134,53135],{},[614,53136,53137,53138,53151],{},"Obrázek 2.12: Posun nabídky o ",[883,53139,53141],{"className":53140},[886],[888,53142,53143],{"xmlns":890},[892,53144,53145,53149],{},[895,53146,53147],{},[898,53148,1978],{},[902,53150,1978],{"encoding":904}," svisle nahoru.",[48808,53153],{},[115,53155,53157],{"id":53156},"tržní-rovnováha","Tržní rovnováha",[1636,53159,53160],{},[724,53161,53162,53164,53165,1729,53168,53200,53201,1343,53224,53247,53248,53251,53252,53265],{},[883,53163,2518],{}," TL;DR\nV ",[38,53166,53167],{},"rovnovážném bodě",[883,53169,53171],{"className":53170},[886],[888,53172,53173],{"xmlns":890},[892,53174,53175,53197],{},[895,53176,53177,53179,53181,53187,53189,53195],{},[898,53178,16183],{},[1708,53180,6940],{"stretchy":1715},[1753,53182,53183,53185],{},[898,53184,1688],{},[898,53186,16183],{},[1708,53188,1883],{"separator":1882},[1753,53190,53191,53193],{},[898,53192,1747],{},[898,53194,16183],{},[1708,53196,6981],{"stretchy":1715},[902,53198,53199],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,53202,53204],{"className":53203},[886],[888,53205,53206],{"xmlns":890},[892,53207,53208,53222],{},[895,53209,53210,53212,53214,53216,53218,53220],{},[898,53211,1747],{},[1708,53213,1710],{},[898,53215,16117],{},[1708,53217,1716],{"stretchy":1715},[898,53219,1688],{},[1708,53221,1721],{"stretchy":1715},[902,53223,16564],{"encoding":904},[883,53225,53227],{"className":53226},[886],[888,53228,53229],{"xmlns":890},[892,53230,53231,53245],{},[895,53232,53233,53235,53237,53239,53241,53243],{},[898,53234,1747],{},[1708,53236,1710],{},[898,53238,1981],{},[1708,53240,1716],{"stretchy":1715},[898,53242,1688],{},[1708,53244,1721],{"stretchy":1715},[902,53246,52903],{"encoding":904},". Čtyři ",[38,53249,53250],{},"pravidla komparativní statiky"," popisují, jak se ",[883,53253,53255],{"className":53254},[886],[888,53256,53257],{"xmlns":890},[892,53258,53259,53263],{},[895,53260,53261],{},[898,53262,16183],{},[902,53264,16183],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,53267,53269],{"id":53268},"definice","Definice",[724,53271,53272,1695,53274,53277,53278,1729,53281,53299,53300,53331,53332,1695,53335,2511],{},[38,53273,53157],{},[614,53275,53276],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,53279,53280],{},"rovnovážné ceně",[883,53282,53284],{"className":53283},[886],[888,53285,53286],{"xmlns":890},[892,53287,53288,53296],{},[895,53289,53290],{},[1753,53291,53292,53294],{},[898,53293,1747],{},[898,53295,16183],{},[902,53297,53298],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,53301,53303],{"className":53302},[886],[888,53304,53305],{"xmlns":890},[892,53306,53307,53329],{},[895,53308,53309,53311,53313,53319,53321,53327],{},[898,53310,16183],{},[1708,53312,6940],{"stretchy":1715},[1753,53314,53315,53317],{},[898,53316,1688],{},[898,53318,16183],{},[1708,53320,1883],{"separator":1882},[1753,53322,53323,53325],{},[898,53324,1747],{},[898,53326,16183],{},[1708,53328,6981],{"stretchy":1715},[902,53330,53199],{"encoding":904}," se nazývá ",[38,53333,53334],{},"rovnovážný bod",[614,53336,53337],{},"equilibrium point",[724,53339,53340,53341,1343,53364,2155],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,53342,53344],{"className":53343},[886],[888,53345,53346],{"xmlns":890},[892,53347,53348,53362],{},[895,53349,53350,53352,53354,53356,53358,53360],{},[898,53351,1747],{},[1708,53353,1710],{},[898,53355,16117],{},[1708,53357,1716],{"stretchy":1715},[898,53359,1688],{},[1708,53361,1721],{"stretchy":1715},[902,53363,16564],{"encoding":904},[883,53365,53367],{"className":53366},[886],[888,53368,53369],{"xmlns":890},[892,53370,53371,53385],{},[895,53372,53373,53375,53377,53379,53381,53383],{},[898,53374,1747],{},[1708,53376,1710],{},[898,53378,1981],{},[1708,53380,1716],{"stretchy":1715},[898,53382,1688],{},[1708,53384,1721],{"stretchy":1715},[902,53386,52903],{"encoding":904},[724,53388,53389],{},[3372,53390],{"alt":53391,"className":53392,"src":53393},"imek-poptavka-nabidka-rovnovaha",[210,3376],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,53395,53396],{},[614,53397,53398,53399,53412,53413,25893,53426,53447,53448,2155],{},"Obrázek 2.13: Klesající ",[883,53400,53402],{"className":53401},[886],[888,53403,53404],{"xmlns":890},[892,53405,53406,53410],{},[895,53407,53408],{},[898,53409,16117],{},[902,53411,16117],{"encoding":904}," a rostoucí ",[883,53414,53416],{"className":53415},[886],[888,53417,53418],{"xmlns":890},[892,53419,53420,53424],{},[895,53421,53422],{},[898,53423,1981],{},[902,53425,1981],{"encoding":904},[883,53427,53429],{"className":53428},[886],[888,53430,53431],{"xmlns":890},[892,53432,53433,53445],{},[895,53434,53435,53437,53439,53441,53443],{},[1708,53436,1716],{"stretchy":1715},[898,53438,1688],{},[1708,53440,1883],{"separator":1882},[898,53442,1747],{},[1708,53444,1721],{"stretchy":1715},[902,53446,49527],{"encoding":904}," protínající se v ",[883,53449,53451],{"className":53450},[886],[888,53452,53453],{"xmlns":890},[892,53454,53455,53477],{},[895,53456,53457,53459,53461,53467,53469,53475],{},[898,53458,16183],{},[1708,53460,6940],{"stretchy":1715},[1753,53462,53463,53465],{},[898,53464,1688],{},[898,53466,16183],{},[1708,53468,1883],{"separator":1882},[1753,53470,53471,53473],{},[898,53472,1747],{},[898,53474,16183],{},[1708,53476,6981],{"stretchy":1715},[902,53478,53199],{"encoding":904},[198,53480,53482],{"id":53481},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,53484,53485,53487,53488,53522,53523,2155],{},[38,53486,49769],{}," Poptávka ",[883,53489,53491],{"className":53490},[886],[888,53492,53493],{"xmlns":890},[892,53494,53495,53519],{},[895,53496,53497,53499,53501,53503,53509,53511,53513,53515,53517],{},[898,53498,1747],{},[1708,53500,1710],{},[1708,53502,2726],{},[1753,53504,53505,53507],{},[898,53506,1688],{},[2505,53508,3132],{},[1708,53510,2726],{},[2505,53512,4003],{},[898,53514,1688],{},[1708,53516,2019],{},[2505,53518,9660],{},[902,53520,53521],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,53524,53526],{"className":53525},[886],[888,53527,53528],{"xmlns":890},[892,53529,53530,53552],{},[895,53531,53532,53534,53536,53542,53544,53546,53548,53550],{},[898,53533,1747],{},[1708,53535,1710],{},[1753,53537,53538,53540],{},[898,53539,1688],{},[2505,53541,3132],{},[1708,53543,2019],{},[2505,53545,4008],{},[898,53547,1688],{},[1708,53549,2019],{},[2505,53551,44390],{},[902,53553,53554],{"encoding":904},"P = Q^2 + 14Q + 22",[724,53556,53557,53559],{},[38,53558,49801],{}," Z rovnosti",[883,53561,53563],{"className":53562},[886],[888,53564,53565],{"xmlns":890,"display":2210},[892,53566,53567,53605],{},[895,53568,53569,53571,53577,53579,53581,53583,53585,53587,53589,53595,53597,53599,53601,53603],{},[1708,53570,2726],{},[1753,53572,53573,53575],{},[898,53574,1688],{},[2505,53576,3132],{},[1708,53578,2726],{},[2505,53580,4003],{},[898,53582,1688],{},[1708,53584,2019],{},[2505,53586,9660],{},[1708,53588,1710],{},[1753,53590,53591,53593],{},[898,53592,1688],{},[2505,53594,3132],{},[1708,53596,2019],{},[2505,53598,4008],{},[898,53600,1688],{},[1708,53602,2019],{},[2505,53604,44390],{},[902,53606,53607],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,53609,53610,53611,53646,53647,53680,53681,53698,53699,4972,53712,1343,53734,53771,53772,2155],{},"dostaneme ",[883,53612,53614],{"className":53613},[886],[888,53615,53616],{"xmlns":890},[892,53617,53618,53643],{},[895,53619,53620,53622,53628,53630,53633,53635,53637,53639,53641],{},[2505,53621,3132],{},[1753,53623,53624,53626],{},[898,53625,1688],{},[2505,53627,3132],{},[1708,53629,2019],{},[2505,53631,53632],{},"24",[898,53634,1688],{},[1708,53636,2726],{},[2505,53638,17536],{},[1708,53640,1710],{},[2505,53642,2784],{},[902,53644,53645],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,53648,53650],{"className":53649},[886],[888,53651,53652],{"xmlns":890},[892,53653,53654,53677],{},[895,53655,53656,53662,53664,53666,53668,53670,53673,53675],{},[1753,53657,53658,53660],{},[898,53659,1688],{},[2505,53661,3132],{},[1708,53663,2019],{},[2505,53665,4090],{},[898,53667,1688],{},[1708,53669,2726],{},[2505,53671,53672],{},"64",[1708,53674,1710],{},[2505,53676,2784],{},[902,53678,53679],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,53682,53684],{"className":53683},[886],[888,53685,53686],{"xmlns":890},[892,53687,53688,53695],{},[895,53689,53690,53692],{},[1708,53691,2726],{},[2505,53693,53694],{},"16",[902,53696,53697],{"encoding":904},"-16"," (nevyhovuje) a ",[883,53700,53702],{"className":53701},[886],[888,53703,53704],{"xmlns":890},[892,53705,53706,53710],{},[895,53707,53708],{},[2505,53709,5867],{},[902,53711,5867],{"encoding":904},[883,53713,53715],{"className":53714},[886],[888,53716,53717],{"xmlns":890},[892,53718,53719,53731],{},[895,53720,53721,53727,53729],{},[1753,53722,53723,53725],{},[898,53724,1688],{},[898,53726,16183],{},[1708,53728,1710],{},[2505,53730,5867],{},[902,53732,53733],{"encoding":904},"Q^E = 4",[883,53735,53737],{"className":53736},[886],[888,53738,53739],{"xmlns":890},[892,53740,53741,53768],{},[895,53742,53743,53749,53751,53753,53755,53757,53759,53761,53763,53765],{},[1753,53744,53745,53747],{},[898,53746,1747],{},[898,53748,16183],{},[1708,53750,1710],{},[1708,53752,2726],{},[2505,53754,53694],{},[1708,53756,2726],{},[2505,53758,17132],{},[1708,53760,2019],{},[2505,53762,9660],{},[1708,53764,1710],{},[2505,53766,53767],{},"94",[902,53769,53770],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,53773,53775],{"className":53774},[886],[888,53776,53777],{"xmlns":890},[892,53778,53779,53793],{},[895,53780,53781,53783,53785,53787,53789,53791],{},[898,53782,16183],{},[1708,53784,6940],{"stretchy":1715},[2505,53786,5867],{},[1708,53788,1883],{"separator":1882},[2505,53790,53767],{},[1708,53792,6981],{"stretchy":1715},[902,53794,53795],{"encoding":904},"E[4, 94]",[198,53797,53799],{"id":53798},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,53801,53802,53804],{},[38,53803,49769],{}," Poptávky a nabídky dvou zboží",[883,53806,53808],{"className":53807},[886],[888,53809,53810],{"xmlns":890,"display":2210},[892,53811,53812,53978],{},[2214,53813,53816,53904],{"rowspacing":32617,"columnalign":53814,"columnspacing":53815},"right left right left","0em 1em 0em",[2218,53817,53818,53828,53860,53870],{},[2221,53819,53820],{},[3194,53821,53822],{"scriptlevel":2784,"displaystyle":1882},[1743,53823,53824,53826],{},[898,53825,1688],{},[2505,53827,2507],{},[2221,53829,53830],{},[3194,53831,53832],{"scriptlevel":2784,"displaystyle":1882},[895,53833,53834,53836,53838,53840,53842,53844,53850,53852,53858],{},[895,53835],{},[1708,53837,1710],{},[2505,53839,17132],{},[1708,53841,2726],{},[2505,53843,3993],{},[1743,53845,53846,53848],{},[898,53847,1747],{},[2505,53849,2507],{},[1708,53851,2726],{},[1743,53853,53854,53856],{},[898,53855,1747],{},[2505,53857,3132],{},[1708,53859,1883],{"separator":1882},[2221,53861,53862],{},[3194,53863,53864],{"scriptlevel":2784,"displaystyle":1882},[1743,53865,53866,53868],{},[898,53867,1688],{},[2505,53869,3132],{},[2221,53871,53872],{},[3194,53873,53874],{"scriptlevel":2784,"displaystyle":1882},[895,53875,53876,53878,53880,53882,53884,53886,53892,53894,53896,53902],{},[895,53877],{},[1708,53879,1710],{},[2505,53881,9704],{},[1708,53883,2726],{},[2505,53885,3132],{},[1743,53887,53888,53890],{},[898,53889,1747],{},[2505,53891,2507],{},[1708,53893,2726],{},[2505,53895,5867],{},[1743,53897,53898,53900],{},[898,53899,1747],{},[2505,53901,3132],{},[1708,53903,1883],{"separator":1882},[2218,53905,53906,53916,53942,53952],{},[2221,53907,53908],{},[3194,53909,53910],{"scriptlevel":2784,"displaystyle":1882},[1743,53911,53912,53914],{},[898,53913,1688],{},[2505,53915,2507],{},[2221,53917,53918],{},[3194,53919,53920],{"scriptlevel":2784,"displaystyle":1882},[895,53921,53922,53924,53926,53928,53930,53932,53934,53940],{},[895,53923],{},[1708,53925,1710],{},[1708,53927,2726],{},[2505,53929,3121],{},[1708,53931,2019],{},[2505,53933,5867],{},[1743,53935,53936,53938],{},[898,53937,1747],{},[2505,53939,2507],{},[1708,53941,1883],{"separator":1882},[2221,53943,53944],{},[3194,53945,53946],{"scriptlevel":2784,"displaystyle":1882},[1743,53947,53948,53950],{},[898,53949,1688],{},[2505,53951,3132],{},[2221,53953,53954],{},[3194,53955,53956],{"scriptlevel":2784,"displaystyle":1882},[895,53957,53958,53960,53962,53964,53966,53968,53970,53976],{},[895,53959],{},[1708,53961,1710],{},[1708,53963,2726],{},[2505,53965,5967],{},[1708,53967,2019],{},[2505,53969,3121],{},[1743,53971,53972,53974],{},[898,53973,1747],{},[2505,53975,3132],{},[898,53977,2155],{"mathvariant":1759},[902,53979,53980],{"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}",[724,53982,53983,53985],{},[38,53984,49801],{}," Z rovností poptávek a nabídek dostaneme",[883,53987,53989],{"className":53988},[886],[888,53990,53991],{"xmlns":890,"display":2210},[892,53992,53993,54042],{},[895,53994,53995,53997,54003,54005,54011,54013,54015,54017,54019,54021,54027,54029,54031,54037,54039],{},[2505,53996,4635],{},[1743,53998,53999,54001],{},[898,54000,1747],{},[2505,54002,2507],{},[1708,54004,2019],{},[1743,54006,54007,54009],{},[898,54008,1747],{},[2505,54010,3132],{},[1708,54012,1710],{},[2505,54014,33062],{},[1708,54016,1883],{"separator":1882},[3213,54018],{"width":3215},[2505,54020,3132],{},[1743,54022,54023,54025],{},[898,54024,1747],{},[2505,54026,2507],{},[1708,54028,2019],{},[2505,54030,5967],{},[1743,54032,54033,54035],{},[898,54034,1747],{},[2505,54036,3132],{},[1708,54038,1710],{},[2505,54040,54041],{},"57.",[902,54043,54044],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,54046,54047,54048,1343,54072,54096,54097,1343,54121,54145,54146,54148],{},"Řešením je ",[883,54049,54051],{"className":54050},[886],[888,54052,54053],{"xmlns":890},[892,54054,54055,54069],{},[895,54056,54057,54065,54067],{},[4754,54058,54059,54061,54063],{},[898,54060,1747],{},[2505,54062,2507],{},[898,54064,16183],{},[1708,54066,1710],{},[2505,54068,5867],{},[902,54070,54071],{"encoding":904},"P_1^E = 4",[883,54073,54075],{"className":54074},[886],[888,54076,54077],{"xmlns":890},[892,54078,54079,54093],{},[895,54080,54081,54089,54091],{},[4754,54082,54083,54085,54087],{},[898,54084,1747],{},[2505,54086,3132],{},[898,54088,16183],{},[1708,54090,1710],{},[2505,54092,5967],{},[902,54094,54095],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,54098,54100],{"className":54099},[886],[888,54101,54102],{"xmlns":890},[892,54103,54104,54118],{},[895,54105,54106,54114,54116],{},[4754,54107,54108,54110,54112],{},[898,54109,1688],{},[2505,54111,2507],{},[898,54113,16183],{},[1708,54115,1710],{},[2505,54117,11015],{},[902,54119,54120],{"encoding":904},"Q_1^E = 13",[883,54122,54124],{"className":54123},[886],[888,54125,54126],{"xmlns":890},[892,54127,54128,54142],{},[895,54129,54130,54138,54140],{},[4754,54131,54132,54134,54136],{},[898,54133,1688],{},[2505,54135,3132],{},[898,54137,16183],{},[1708,54139,1710],{},[2505,54141,4008],{},[902,54143,54144],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,54147,51656],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,54150,54152],{"id":54151},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,54154,54155,54156,54173,54174,1695,54177,2511],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,54157,54159],{"className":54158},[886],[888,54160,54161],{"xmlns":890},[892,54162,54163,54171],{},[895,54164,54165],{},[1753,54166,54167,54169],{},[898,54168,1747],{},[898,54170,16183],{},[902,54172,53298],{"encoding":904},"; mechanismus popisuje ",[38,54175,54176],{},"teorém pavučiny",[614,54178,54179],{},"cobweb model",[198,54181,54183],{"id":54182},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,54185,54186],{},[3372,54187],{"alt":54188,"className":54189,"src":54190},"imek-komparativni-statika-4pripady",[210,3376],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1636,54192,54193,54234,54274,54314],{},[724,54194,54195,54198,54199,5283,54216,2155],{},[38,54196,54197],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,54200,54202],{"className":54201},[886],[888,54203,54204],{"xmlns":890},[892,54205,54206,54214],{},[895,54207,54208],{},[1753,54209,54210,54212],{},[898,54211,1747],{},[898,54213,16183],{},[902,54215,53298],{"encoding":904},[883,54217,54219],{"className":54218},[886],[888,54220,54221],{"xmlns":890},[892,54222,54223,54231],{},[895,54224,54225],{},[1753,54226,54227,54229],{},[898,54228,1688],{},[898,54230,16183],{},[902,54232,54233],{"encoding":904},"Q^E",[724,54235,54236,54239,54240,5283,54257,2155],{},[38,54237,54238],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,54241,54243],{"className":54242},[886],[888,54244,54245],{"xmlns":890},[892,54246,54247,54255],{},[895,54248,54249],{},[1753,54250,54251,54253],{},[898,54252,1747],{},[898,54254,16183],{},[902,54256,53298],{"encoding":904},[883,54258,54260],{"className":54259},[886],[888,54261,54262],{"xmlns":890},[892,54263,54264,54272],{},[895,54265,54266],{},[1753,54267,54268,54270],{},[898,54269,1688],{},[898,54271,16183],{},[902,54273,54233],{"encoding":904},[724,54275,54276,54279,54280,21260,54297,2155],{},[38,54277,54278],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,54281,54283],{"className":54282},[886],[888,54284,54285],{"xmlns":890},[892,54286,54287,54295],{},[895,54288,54289],{},[1753,54290,54291,54293],{},[898,54292,1747],{},[898,54294,16183],{},[902,54296,53298],{"encoding":904},[883,54298,54300],{"className":54299},[886],[888,54301,54302],{"xmlns":890},[892,54303,54304,54312],{},[895,54305,54306],{},[1753,54307,54308,54310],{},[898,54309,1688],{},[898,54311,16183],{},[902,54313,54233],{"encoding":904},[724,54315,54316,54319,54320,54337,54338,2155],{},[38,54317,54318],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,54321,54323],{"className":54322},[886],[888,54324,54325],{"xmlns":890},[892,54326,54327,54335],{},[895,54328,54329],{},[1753,54330,54331,54333],{},[898,54332,1747],{},[898,54334,16183],{},[902,54336,53298],{"encoding":904},", pokles ",[883,54339,54341],{"className":54340},[886],[888,54342,54343],{"xmlns":890},[892,54344,54345,54353],{},[895,54346,54347],{},[1753,54348,54349,54351],{},[898,54350,1688],{},[898,54352,16183],{},[902,54354,54233],{"encoding":904},[16,54356,54357,54402],{},[19,54358,54359],{},[22,54360,54361,54364,54383],{},[25,54362,54363],{},"Změna",[25,54365,54366],{},[883,54367,54369],{"className":54368},[886],[888,54370,54371],{"xmlns":890},[892,54372,54373,54381],{},[895,54374,54375],{},[1753,54376,54377,54379],{},[898,54378,1747],{},[898,54380,16183],{},[902,54382,53298],{"encoding":904},[25,54384,54385],{},[883,54386,54388],{"className":54387},[886],[888,54389,54390],{"xmlns":890},[892,54391,54392,54400],{},[895,54393,54394],{},[1753,54395,54396,54398],{},[898,54397,1688],{},[898,54399,16183],{},[902,54401,54233],{"encoding":904},[30,54403,54404,54414,54424,54433],{},[22,54405,54406,54409,54412],{},[35,54407,54408],{},"Růst poptávky",[35,54410,54411],{},"↑",[35,54413,54411],{},[22,54415,54416,54419,54422],{},[35,54417,54418],{},"Pokles poptávky",[35,54420,54421],{},"↓",[35,54423,54421],{},[22,54425,54426,54429,54431],{},[35,54427,54428],{},"Růst nabídky",[35,54430,54421],{},[35,54432,54411],{},[22,54434,54435,54438,54440],{},[35,54436,54437],{},"Pokles nabídky",[35,54439,54411],{},[35,54441,54421],{},[724,54443,54444],{},[614,54445,54446],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[48808,54448],{},[115,54450,811],{"id":54451},"zdanění-trhu",[1636,54453,54454,54543],{},[724,54455,54456,54458,54459,54472,54473,2941,54486,54489,54490,48618,54513,54538,54539,54542],{},[883,54457,2518],{}," TL;DR\nJednotková daň ",[883,54460,54462],{"className":54461},[886],[888,54463,54464],{"xmlns":890},[892,54465,54466,54470],{},[895,54467,54468],{},[898,54469,1978],{},[902,54471,1978],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,54474,54476],{"className":54475},[886],[888,54477,54478],{"xmlns":890},[892,54479,54480,54484],{},[895,54481,54482],{},[898,54483,1978],{},[902,54485,1978],{"encoding":904},[38,54487,54488],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,54491,54493],{"className":54492},[886],[888,54494,54495],{"xmlns":890},[892,54496,54497,54510],{},[895,54498,54499],{},[1743,54500,54501,54503],{},[898,54502,1978],{},[895,54504,54505,54508],{},[898,54506,54507],{},"s",[898,54509,724],{},[902,54511,54512],{"encoding":904},"T_{sp}",[883,54514,54516],{"className":54515},[886],[888,54517,54518],{"xmlns":890},[892,54519,54520,54535],{},[895,54521,54522],{},[1743,54523,54524,54526],{},[898,54525,1978],{},[895,54527,54528,54531,54533],{},[898,54529,54530],{},"v",[898,54532,14004],{},[898,54534,5498],{},[902,54536,54537],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,54540,54541],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,54544,54545],{},[614,54546,54547,54548,2155],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,54549,54551],{"className":54550,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,54553,54554,54555,54558,54559,54585,54586,54589,54590,54616,54617,54634,54635,54675,54676,1771,54689,2155],{},"Existují dvě formy zdanění — daň uložená ",[38,54556,54557],{},"výrobci"," (posun nabídky ",[883,54560,54562],{"className":54561},[886],[888,54563,54564],{"xmlns":890},[892,54565,54566,54582],{},[895,54567,54568,54574,54576,54578,54580],{},[1743,54569,54570,54572],{},[898,54571,1981],{},[2505,54573,2507],{},[1708,54575,1710],{},[898,54577,1981],{},[1708,54579,2019],{},[898,54581,1978],{},[902,54583,54584],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,54587,54588],{},"spotřebiteli"," (posun poptávky ",[883,54591,54593],{"className":54592},[886],[888,54594,54595],{"xmlns":890},[892,54596,54597,54613],{},[895,54598,54599,54605,54607,54609,54611],{},[1743,54600,54601,54603],{},[898,54602,16117],{},[2505,54604,3132],{},[1708,54606,1710],{},[898,54608,16117],{},[1708,54610,2726],{},[898,54612,1978],{},[902,54614,54615],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,54618,54620],{"className":54619},[886],[888,54621,54622],{"xmlns":890},[892,54623,54624,54632],{},[895,54625,54626],{},[1753,54627,54628,54630],{},[898,54629,1688],{},[898,54631,16183],{},[902,54633,54233],{"encoding":904}," klesá a vzniká rozklad daně ",[883,54636,54638],{"className":54637},[886],[888,54639,54640],{"xmlns":890},[892,54641,54642,54672],{},[895,54643,54644,54646,54648,54658,54660],{},[898,54645,1978],{},[1708,54647,1710],{},[1743,54649,54650,54652],{},[898,54651,1978],{},[895,54653,54654,54656],{},[898,54655,54507],{},[898,54657,724],{},[1708,54659,2019],{},[1743,54661,54662,54664],{},[898,54663,1978],{},[895,54665,54666,54668,54670],{},[898,54667,54530],{},[898,54669,14004],{},[898,54671,5498],{},[902,54673,54674],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,54677,54679],{"className":54678},[886],[888,54680,54681],{"xmlns":890},[892,54682,54683,54687],{},[895,54684,54685],{},[898,54686,16117],{},[902,54688,16117],{"encoding":904},[883,54690,54692],{"className":54691},[886],[888,54693,54694],{"xmlns":890},[892,54695,54696,54700],{},[895,54697,54698],{},[898,54699,1981],{},[902,54701,1981],{"encoding":904},[724,54703,54704,54705,54708,54709,1771,54739,54773],{},"Zásadním výsledkem kapitoly je ",[38,54706,54707],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,54710,54712],{"className":54711},[886],[888,54713,54714],{"xmlns":890},[892,54715,54716,54736],{},[895,54717,54718,54726,54728],{},[4754,54719,54720,54722,54724],{},[898,54721,1688],{},[2505,54723,2507],{},[898,54725,16183],{},[1708,54727,1710],{},[4754,54729,54730,54732,54734],{},[898,54731,1688],{},[2505,54733,3132],{},[898,54735,16183],{},[902,54737,54738],{"encoding":904},"Q_1^E = Q_2^E",[883,54740,54742],{"className":54741},[886],[888,54743,54744],{"xmlns":890},[892,54745,54746,54770],{},[895,54747,54748,54756,54758,54760,54762],{},[4754,54749,54750,54752,54754],{},[898,54751,1747],{},[2505,54753,2507],{},[898,54755,16183],{},[1708,54757,2726],{},[898,54759,1978],{},[1708,54761,1710],{},[4754,54763,54764,54766,54768],{},[898,54765,1747],{},[2505,54767,3132],{},[898,54769,16183],{},[902,54771,54772],{"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.",[724,54775,54776,54777,54780,54781,54807,54808,54836,54837,54840,54841,54844,54845,2155],{},"Podrobný výklad, Příklady ",[38,54778,54779],{},"2.9"," (daň výrobci, ",[883,54782,54784],{"className":54783},[886],[888,54785,54786],{"xmlns":890},[892,54787,54788,54804],{},[895,54789,54790,54800,54802],{},[1743,54791,54792,54794],{},[898,54793,1978],{},[895,54795,54796,54798],{},[898,54797,54507],{},[898,54799,724],{},[1708,54801,1710],{},[2505,54803,3132],{},[902,54805,54806],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,54809,54811],{"className":54810},[886],[888,54812,54813],{"xmlns":890},[892,54814,54815,54833],{},[895,54816,54817,54829,54831],{},[1743,54818,54819,54821],{},[898,54820,1978],{},[895,54822,54823,54825,54827],{},[898,54824,54530],{},[898,54826,14004],{},[898,54828,5498],{},[1708,54830,1710],{},[2505,54832,5867],{},[902,54834,54835],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,54838,54839],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,54842,54843],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,54846,54551],{"className":54847,"dataFsResolvedFilePath":809,"href":810},[210],[48808,54849],{},[115,54851,54853],{"id":54852},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1636,54855,54856],{},[724,54857,54858,54860,54861,54864,54865,54867],{},[883,54859,2518],{}," TL;DR\nMultiplikátory jsou ",[38,54862,54863],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,54866,2758],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,54869,54871],{"id":54870},"redukovaný-tvar","Redukovaný tvar",[724,54873,54874,54875,1695,54898,1343,54915,5149,54932,1695,54955,54972,54973,55003],{},"Pro lineární model ",[883,54876,54878],{"className":54877},[886],[888,54879,54880],{"xmlns":890},[892,54881,54882,54896],{},[895,54883,54884,54886,54888,54890,54892,54894],{},[898,54885,1747],{},[1708,54887,1710],{},[898,54889,207],{},[898,54891,1688],{},[1708,54893,2019],{},[898,54895,1923],{},[902,54897,48898],{"encoding":904},[883,54899,54901],{"className":54900},[886],[888,54902,54903],{"xmlns":890},[892,54904,54905,54913],{},[895,54906,54907,54909,54911],{},[898,54908,207],{},[1708,54910,2932],{},[2505,54912,2784],{},[902,54914,3154],{"encoding":904},[883,54916,54918],{"className":54917},[886],[888,54919,54920],{"xmlns":890},[892,54921,54922,54930],{},[895,54923,54924,54926,54928],{},[898,54925,1923],{},[1708,54927,2854],{},[2505,54929,2784],{},[902,54931,3172],{"encoding":904},[883,54933,54935],{"className":54934},[886],[888,54936,54937],{"xmlns":890},[892,54938,54939,54953],{},[895,54940,54941,54943,54945,54947,54949,54951],{},[898,54942,1747],{},[1708,54944,1710],{},[898,54946,14142],{},[898,54948,1688],{},[1708,54950,2019],{},[898,54952,2364],{},[902,54954,52076],{"encoding":904},[883,54956,54958],{"className":54957},[886],[888,54959,54960],{"xmlns":890},[892,54961,54962,54970],{},[895,54963,54964,54966,54968],{},[898,54965,14142],{},[1708,54967,2854],{},[2505,54969,2784],{},[902,54971,52094],{"encoding":904},") dává podmínka rovnováhy ",[883,54974,54976],{"className":54975},[886],[888,54977,54978],{"xmlns":890},[892,54979,54980,55000],{},[895,54981,54982,54984,54986,54988,54990,54992,54994,54996,54998],{},[898,54983,207],{},[898,54985,1688],{},[1708,54987,2019],{},[898,54989,1923],{},[1708,54991,1710],{},[898,54993,14142],{},[898,54995,1688],{},[1708,54997,2019],{},[898,54999,2364],{},[902,55001,55002],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,55005,55007],{"className":55006},[886],[888,55008,55009],{"xmlns":890,"display":2210},[892,55010,55011,55056],{},[2214,55012,55013],{"width":2216},[2218,55014,55015,55017,55049,55051],{},[2221,55016],{"width":2223},[2221,55018,55019],{},[895,55020,55021,55027,55029,55047],{},[1753,55022,55023,55025],{},[898,55024,1688],{},[898,55026,16183],{},[1708,55028,1710],{},[2358,55030,55031,55039],{},[895,55032,55033,55035,55037],{},[898,55034,1923],{},[1708,55036,2726],{},[898,55038,2364],{},[895,55040,55041,55043,55045],{},[898,55042,14142],{},[1708,55044,2726],{},[898,55046,207],{},[898,55048,2155],{"mathvariant":1759},[2221,55050],{"width":2223},[2221,55052,55053],{},[2247,55054,55055],{},"(2.10)",[902,55057,55058],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,55060,55061,55062,1695,55064,55067,55068,55085,55086,1729,55089,55115,55116,55129,55130,55148,55149,2511],{},"Vztah (2.10) je ",[38,55063,32813],{},[614,55065,55066],{},"reduced form",") pro ",[883,55069,55071],{"className":55070},[886],[888,55072,55073],{"xmlns":890},[892,55074,55075,55083],{},[895,55076,55077],{},[1753,55078,55079,55081],{},[898,55080,1688],{},[898,55082,16183],{},[902,55084,54233],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,55087,55088],{},"parametrů",[883,55090,55092],{"className":55091},[886],[888,55093,55094],{"xmlns":890},[892,55095,55096,55112],{},[895,55097,55098,55100,55102,55104,55106,55108,55110],{},[898,55099,207],{},[1708,55101,1883],{"separator":1882},[898,55103,1923],{},[1708,55105,1883],{"separator":1882},[898,55107,14142],{},[1708,55109,1883],{"separator":1882},[898,55111,2364],{},[902,55113,55114],{"encoding":904},"a, b, c, d",". Aby ",[883,55117,55119],{"className":55118},[886],[888,55120,55121],{"xmlns":890},[892,55122,55123,55127],{},[895,55124,55125],{},[898,55126,16183],{},[902,55128,16183],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,55131,55133],{"className":55132},[886],[888,55134,55135],{"xmlns":890},[892,55136,55137,55145],{},[895,55138,55139,55141,55143],{},[898,55140,1923],{},[1708,55142,2854],{},[898,55144,2364],{},[902,55146,55147],{"encoding":904},"b > d"," (neboť ",[883,55150,55152],{"className":55151},[886],[888,55153,55154],{"xmlns":890},[892,55155,55156,55168],{},[895,55157,55158,55160,55162,55164,55166],{},[898,55159,14142],{},[1708,55161,2726],{},[898,55163,207],{},[1708,55165,2854],{},[2505,55167,2784],{},[902,55169,55170],{"encoding":904},"c - a > 0",[724,55172,55173],{},[614,55174,55175,55176,55189,55190,55203,55204,13826,55217,53771,55234,55247],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,55177,55179],{"className":55178},[886],[888,55180,55181],{"xmlns":890},[892,55182,55183,55187],{},[895,55184,55185],{},[898,55186,1923],{},[902,55188,1923],{"encoding":904}," na ose ",[883,55191,55193],{"className":55192},[886],[888,55194,55195],{"xmlns":890},[892,55196,55197,55201],{},[895,55198,55199],{},[898,55200,1747],{},[902,55202,1747],{"encoding":904},") a nabídka (úsek ",[883,55205,55207],{"className":55206},[886],[888,55208,55209],{"xmlns":890},[892,55210,55211,55215],{},[895,55212,55213],{},[898,55214,2364],{},[902,55216,2364],{"encoding":904},[883,55218,55220],{"className":55219},[886],[888,55221,55222],{"xmlns":890},[892,55223,55224,55232],{},[895,55225,55226,55228,55230],{},[898,55227,1923],{},[1708,55229,2854],{},[898,55231,2364],{},[902,55233,55147],{"encoding":904},[883,55235,55237],{"className":55236},[886],[888,55238,55239],{"xmlns":890},[892,55240,55241,55245],{},[895,55242,55243],{},[898,55244,16183],{},[902,55246,16183],{"encoding":904}," v 1. kvadrantu.",[198,55249,55251],{"id":55250},"definice-multiplikátorů","Definice multiplikátorů",[724,55253,55254,55255,55280,55281,55294,55295,55308],{},"V komparativní statice jsou ",[883,55256,55258],{"className":55257},[886],[888,55259,55260],{"xmlns":890},[892,55261,55262,55278],{},[895,55263,55264,55266,55268,55270,55272,55274,55276],{},[898,55265,207],{},[1708,55267,1883],{"separator":1882},[898,55269,1923],{},[1708,55271,1883],{"separator":1882},[898,55273,14142],{},[1708,55275,1883],{"separator":1882},[898,55277,2364],{},[902,55279,55114],{"encoding":904}," exogenní proměnné a ",[883,55282,55284],{"className":55283},[886],[888,55285,55286],{"xmlns":890},[892,55287,55288,55292],{},[895,55289,55290],{},[898,55291,1688],{},[902,55293,1688],{"encoding":904}," endogenní. Přibližná změna ",[883,55296,55298],{"className":55297},[886],[888,55299,55300],{"xmlns":890},[892,55301,55302,55306],{},[895,55303,55304],{},[898,55305,1688],{},[902,55307,1688],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,55310,55312],{"className":55311},[886],[888,55313,55314],{"xmlns":890,"display":2210},[892,55315,55316,55409],{},[2214,55317,55318],{"width":2216},[2218,55319,55320,55322,55402,55404],{},[2221,55321],{"width":2223},[2221,55323,55324],{},[895,55325,55326,55328,55330,55332,55334,55336,55338,55346,55348,55350,55352,55354,55362,55364,55366,55368,55370,55378,55380,55382,55384,55386,55394,55396,55398,55400],{},[898,55327,2633],{"mathvariant":1759},[898,55329,1688],{},[1708,55331,2638],{},[898,55333,2364],{},[898,55335,1688],{},[1708,55337,1710],{},[4754,55339,55340,55342,55344],{},[898,55341,1688],{},[898,55343,207],{},[1708,55345,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,55347,2659],{},[898,55349,2364],{},[898,55351,207],{},[1708,55353,2019],{},[4754,55355,55356,55358,55360],{},[898,55357,1688],{},[898,55359,1923],{},[1708,55361,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,55363,2659],{},[898,55365,2364],{},[898,55367,1923],{},[1708,55369,2019],{},[4754,55371,55372,55374,55376],{},[898,55373,1688],{},[898,55375,14142],{},[1708,55377,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,55379,2659],{},[898,55381,2364],{},[898,55383,14142],{},[1708,55385,2019],{},[4754,55387,55388,55390,55392],{},[898,55389,1688],{},[898,55391,2364],{},[1708,55393,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,55395,2659],{},[898,55397,2364],{},[898,55399,2364],{},[898,55401,2155],{"mathvariant":1759},[2221,55403],{"width":2223},[2221,55405,55406],{},[2247,55407,55408],{},"(2.11)",[902,55410,55411],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,55413,55414,55415,6801,55465,1695,55467,2750],{},"Parciální derivace ",[883,55416,55418],{"className":55417},[886],[888,55419,55420],{"xmlns":890},[892,55421,55422,55462],{},[895,55423,55424,55432,55434,55442,55444,55452,55454],{},[4754,55425,55426,55428,55430],{},[898,55427,1688],{},[898,55429,207],{},[1708,55431,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55433,1883],{"separator":1882},[4754,55435,55436,55438,55440],{},[898,55437,1688],{},[898,55439,1923],{},[1708,55441,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55443,1883],{"separator":1882},[4754,55445,55446,55448,55450],{},[898,55447,1688],{},[898,55449,14142],{},[1708,55451,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55453,1883],{"separator":1882},[4754,55455,55456,55458,55460],{},[898,55457,1688],{},[898,55459,2364],{},[1708,55461,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,55463,55464],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d",[38,55466,29848],{},[614,55468,55469],{},"multipliers",[883,55471,55473],{"className":55472},[886],[888,55474,55475],{"xmlns":890,"display":2210},[892,55476,55477,55628],{},[2214,55478,55479],{"width":2216},[2218,55480,55481,55483,55621,55623],{},[2221,55482],{"width":2223},[2221,55484,55485],{},[895,55486,55487,55495,55497,55523,55525,55527,55535,55537,55549,55551,55553,55561,55563,55565,55591,55593,55595,55603,55605,55607,55619],{},[4754,55488,55489,55491,55493],{},[898,55490,1688],{},[898,55492,207],{},[1708,55494,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55496,1710],{},[2358,55498,55499,55507],{},[895,55500,55501,55503,55505],{},[898,55502,1923],{},[1708,55504,2726],{},[898,55506,2364],{},[895,55508,55509,55511,55513,55515,55517],{},[1708,55510,1716],{"stretchy":1715},[898,55512,14142],{},[1708,55514,2726],{},[898,55516,207],{},[1753,55518,55519,55521],{},[1708,55520,1721],{"stretchy":1715},[2505,55522,3132],{},[1708,55524,1883],{"separator":1882},[3213,55526],{"width":4750},[4754,55528,55529,55531,55533],{},[898,55530,1688],{},[898,55532,1923],{},[1708,55534,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55536,1710],{},[2358,55538,55539,55541],{},[2505,55540,2507],{},[895,55542,55543,55545,55547],{},[898,55544,14142],{},[1708,55546,2726],{},[898,55548,207],{},[1708,55550,1883],{"separator":1882},[3213,55552],{"width":4750},[4754,55554,55555,55557,55559],{},[898,55556,1688],{},[898,55558,14142],{},[1708,55560,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55562,1710],{},[1708,55564,2726],{},[2358,55566,55567,55575],{},[895,55568,55569,55571,55573],{},[898,55570,1923],{},[1708,55572,2726],{},[898,55574,2364],{},[895,55576,55577,55579,55581,55583,55585],{},[1708,55578,1716],{"stretchy":1715},[898,55580,14142],{},[1708,55582,2726],{},[898,55584,207],{},[1753,55586,55587,55589],{},[1708,55588,1721],{"stretchy":1715},[2505,55590,3132],{},[1708,55592,1883],{"separator":1882},[3213,55594],{"width":4750},[4754,55596,55597,55599,55601],{},[898,55598,1688],{},[898,55600,2364],{},[1708,55602,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55604,1710],{},[1708,55606,2726],{},[2358,55608,55609,55611],{},[2505,55610,2507],{},[895,55612,55613,55615,55617],{},[898,55614,14142],{},[1708,55616,2726],{},[898,55618,207],{},[898,55620,2155],{"mathvariant":1759},[2221,55622],{"width":2223},[2221,55624,55625],{},[2247,55626,55627],{},"(2.12)",[902,55629,55630],{"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}",[198,55632,55634],{"id":55633},"znaménka-a-interpretace","Znaménka a interpretace",[724,55636,55637,55638,1343,55655,1343,55672,1343,55689,55706,55707,2750],{},"Za podmínek ",[883,55639,55641],{"className":55640},[886],[888,55642,55643],{"xmlns":890},[892,55644,55645,55653],{},[895,55646,55647,55649,55651],{},[898,55648,207],{},[1708,55650,2932],{},[2505,55652,2784],{},[902,55654,3154],{"encoding":904},[883,55656,55658],{"className":55657},[886],[888,55659,55660],{"xmlns":890},[892,55661,55662,55670],{},[895,55663,55664,55666,55668],{},[898,55665,1923],{},[1708,55667,2854],{},[2505,55669,2784],{},[902,55671,3172],{"encoding":904},[883,55673,55675],{"className":55674},[886],[888,55676,55677],{"xmlns":890},[892,55678,55679,55687],{},[895,55680,55681,55683,55685],{},[898,55682,14142],{},[1708,55684,2854],{},[2505,55686,2784],{},[902,55688,52094],{"encoding":904},[883,55690,55692],{"className":55691},[886],[888,55693,55694],{"xmlns":890},[892,55695,55696,55704],{},[895,55697,55698,55700,55702],{},[898,55699,1923],{},[1708,55701,2854],{},[898,55703,2364],{},[902,55705,55147],{"encoding":904}," platí (znaménka se ",[38,55708,55709],{},"nemění",[883,55711,55713],{"className":55712},[886],[888,55714,55715],{"xmlns":890,"display":2210},[892,55716,55717,55779],{},[895,55718,55719,55727,55729,55731,55733,55735,55743,55745,55747,55749,55751,55759,55761,55763,55765,55767,55775,55777],{},[4754,55720,55721,55723,55725],{},[898,55722,1688],{},[898,55724,207],{},[1708,55726,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55728,2854],{},[2505,55730,2784],{},[1708,55732,1883],{"separator":1882},[3213,55734],{"width":3215},[4754,55736,55737,55739,55741],{},[898,55738,1688],{},[898,55740,1923],{},[1708,55742,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55744,2854],{},[2505,55746,2784],{},[1708,55748,1883],{"separator":1882},[3213,55750],{"width":3215},[4754,55752,55753,55755,55757],{},[898,55754,1688],{},[898,55756,14142],{},[1708,55758,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55760,2932],{},[2505,55762,2784],{},[1708,55764,1883],{"separator":1882},[3213,55766],{"width":3215},[4754,55768,55769,55771,55773],{},[898,55770,1688],{},[898,55772,2364],{},[1708,55774,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55776,2932],{},[2505,55778,24346],{},[902,55780,55781],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,55783,55784,55843],{},[123,55785,55786,1729,55789,55809,55810,55827,55828,1343,55841,2155],{},[38,55787,55788],{},"Kvantitativní smysl:",[883,55790,55792],{"className":55791},[886],[888,55793,55794],{"xmlns":890},[892,55795,55796,55806],{},[895,55797,55798],{},[4754,55799,55800,55802,55804],{},[898,55801,1688],{},[898,55803,14014],{},[1708,55805,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,55807,55808],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,55811,55813],{"className":55812},[886],[888,55814,55815],{"xmlns":890},[892,55816,55817,55825],{},[895,55818,55819],{},[1753,55820,55821,55823],{},[898,55822,1688],{},[898,55824,16183],{},[902,55826,54233],{"encoding":904}," při jednotkové změně parametru ",[883,55829,55831],{"className":55830},[886],[888,55832,55833],{"xmlns":890},[892,55834,55835,55839],{},[895,55836,55837],{},[898,55838,14014],{},[902,55840,14014],{"encoding":904},[614,55842,2758],{},[123,55844,55845,55848,55849,55866,55867,2155],{},[38,55846,55847],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,55850,55852],{"className":55851},[886],[888,55853,55854],{"xmlns":890},[892,55855,55856,55864],{},[895,55857,55858],{},[1753,55859,55860,55862],{},[898,55861,1688],{},[898,55863,16183],{},[902,55865,54233],{"encoding":904}," na růst ",[883,55868,55870],{"className":55869},[886],[888,55871,55872],{"xmlns":890},[892,55873,55874,55878],{},[895,55875,55876],{},[898,55877,14014],{},[902,55879,14014],{"encoding":904},[724,55881,55882,55883,55896,55897,55148,55914,2511],{},"Např. růst ",[883,55884,55886],{"className":55885},[886],[888,55887,55888],{"xmlns":890},[892,55889,55890,55894],{},[895,55891,55892],{},[898,55893,14142],{},[902,55895,14142],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,55898,55900],{"className":55899},[886],[888,55901,55902],{"xmlns":890},[892,55903,55904,55912],{},[895,55905,55906],{},[1753,55907,55908,55910],{},[898,55909,1688],{},[898,55911,16183],{},[902,55913,54233],{"encoding":904},[883,55915,55917],{"className":55916},[886],[888,55918,55919],{"xmlns":890},[892,55920,55921,55935],{},[895,55922,55923,55931,55933],{},[4754,55924,55925,55927,55929],{},[898,55926,1688],{},[898,55928,14142],{},[1708,55930,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,55932,2932],{},[2505,55934,2784],{},[902,55936,55937],{"encoding":904},"Q'_c \u003C 0",[724,55939,55940],{},[614,55941,55942,55943,55963,55964,9398,55988,56010,56011,2155],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,55944,55946],{"className":55945},[886],[888,55947,55948],{"xmlns":890},[892,55949,55950,55960],{},[895,55951,55952,55954,55956,55958],{},[898,55953,14142],{},[898,55955,1688],{},[1708,55957,2019],{},[898,55959,2364],{},[902,55961,55962],{"encoding":904},"cQ + d"," na strmější ",[883,55965,55967],{"className":55966},[886],[888,55968,55969],{"xmlns":890},[892,55970,55971,55985],{},[895,55972,55973,55979,55981,55983],{},[1743,55974,55975,55977],{},[898,55976,14142],{},[2505,55978,2507],{},[898,55980,1688],{},[1708,55982,2019],{},[898,55984,2364],{},[902,55986,55987],{"encoding":904},"c_1 Q + d",[883,55989,55991],{"className":55990},[886],[888,55992,55993],{"xmlns":890},[892,55994,55995,56007],{},[895,55996,55997,56003,56005],{},[1743,55998,55999,56001],{},[898,56000,14142],{},[2505,56002,2507],{},[1708,56004,2854],{},[898,56006,14142],{},[902,56008,56009],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,56012,56014],{"className":56013},[886],[888,56015,56016],{"xmlns":890},[892,56017,56018,56028],{},[895,56019,56020,56026],{},[1753,56021,56022,56024],{},[898,56023,1688],{},[898,56025,16183],{},[1708,56027,54421],{},[902,56029,56030],{"encoding":904},"Q^E \\downarrow",[724,56032,56033,56034,56066,56067,2155],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,56035,56037],{"className":56036},[886],[888,56038,56039],{"xmlns":890},[892,56040,56041,56063],{},[895,56042,56043,56045,56047,56049,56057,56059,56061],{},[898,56044,2633],{"mathvariant":1759},[898,56046,1688],{},[1708,56048,2638],{},[4754,56050,56051,56053,56055],{},[898,56052,1688],{},[898,56054,1923],{},[1708,56056,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,56058,2659],{},[898,56060,2364],{},[898,56062,1923],{},[902,56064,56065],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,56068,56070],{"className":56069},[886],[888,56071,56072],{"xmlns":890},[892,56073,56074,56082],{},[895,56075,56076],{},[1753,56077,56078,56080],{},[898,56079,1747],{},[898,56081,16183],{},[902,56083,53298],{"encoding":904},[198,56085,56087,56088],{"id":56086},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,56089,56091],{"className":56090},[886],[888,56092,56093],{"xmlns":890},[892,56094,56095,56103],{},[895,56096,56097],{},[1753,56098,56099,56101],{},[898,56100,1688],{},[898,56102,16183],{},[902,56104,54233],{"encoding":904},[724,56106,56107,53487,56109,53522,56135,2155],{},[38,56108,49769],{},[883,56110,56112],{"className":56111},[886],[888,56113,56114],{"xmlns":890},[892,56115,56116,56132],{},[895,56117,56118,56120,56122,56124,56126,56128,56130],{},[898,56119,1747],{},[1708,56121,1710],{},[1708,56123,2726],{},[2505,56125,3121],{},[898,56127,1688],{},[1708,56129,2019],{},[2505,56131,17132],{},[902,56133,56134],{"encoding":904},"P = -3Q + 40",[883,56136,56138],{"className":56137},[886],[888,56139,56140],{"xmlns":890},[892,56141,56142,56156],{},[895,56143,56144,56146,56148,56150,56152,56154],{},[898,56145,1747],{},[1708,56147,1710],{},[2505,56149,6097],{},[898,56151,1688],{},[1708,56153,2019],{},[2505,56155,4003],{},[902,56157,56158],{"encoding":904},"P = 0{,}5Q + 10",[724,56160,56161,56163],{},[38,56162,49801],{}," Rovnovážné množství",[883,56165,56167],{"className":56166},[886],[888,56168,56169],{"xmlns":890,"display":2210},[892,56170,56171,56239],{},[895,56172,56173,56179,56181,56199,56201,56225,56227,56234,56236],{},[1753,56174,56175,56177],{},[898,56176,1688],{},[898,56178,16183],{},[1708,56180,1710],{},[2358,56182,56183,56191],{},[895,56184,56185,56187,56189],{},[898,56186,1923],{},[1708,56188,2726],{},[898,56190,2364],{},[895,56192,56193,56195,56197],{},[898,56194,14142],{},[1708,56196,2726],{},[898,56198,207],{},[1708,56200,1710],{},[2358,56202,56203,56211],{},[895,56204,56205,56207,56209],{},[2505,56206,17132],{},[1708,56208,2726],{},[2505,56210,4003],{},[895,56212,56213,56215,56217,56219,56221,56223],{},[2505,56214,6097],{},[1708,56216,2726],{},[1708,56218,1716],{"stretchy":1715},[1708,56220,2726],{},[2505,56222,3121],{},[1708,56224,1721],{"stretchy":1715},[1708,56226,1710],{},[2358,56228,56229,56231],{},[2505,56230,49855],{},[2505,56232,56233],{},"3,5",[1708,56235,2638],{},[2505,56237,56238],{},"8,571.",[902,56240,56241],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,56243,56244,56289],{},[38,56245,56246,56247,14647,56260,2486,56274,56288],{},"(a) Změna ",[883,56248,56250],{"className":56249},[886],[888,56251,56252],{"xmlns":890},[892,56253,56254,56258],{},[895,56255,56256],{},[898,56257,14142],{},[902,56259,14142],{"encoding":904},[883,56261,56263],{"className":56262},[886],[888,56264,56265],{"xmlns":890},[892,56266,56267,56271],{},[895,56268,56269],{},[2505,56270,6097],{},[902,56272,56273],{"encoding":904},"0{,}5",[883,56275,56277],{"className":56276},[886],[888,56278,56279],{"xmlns":890},[892,56280,56281,56285],{},[895,56282,56283],{},[2505,56284,4097],{},[902,56286,56287],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,56291,56293],{"className":56292},[886],[888,56294,56295],{"xmlns":890,"display":2210},[892,56296,56297,56374],{},[895,56298,56299,56307,56309,56311,56313,56315,56317,56343,56345,56347,56349,56351,56353,56363,56365,56367,56369,56371],{},[4754,56300,56301,56303,56305],{},[898,56302,1688],{},[898,56304,14142],{},[1708,56306,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,56308,2659],{},[898,56310,2364],{},[898,56312,14142],{},[1708,56314,1710],{},[1708,56316,2726],{},[2358,56318,56319,56327],{},[895,56320,56321,56323,56325],{},[898,56322,1923],{},[1708,56324,2726],{},[898,56326,2364],{},[895,56328,56329,56331,56333,56335,56337],{},[1708,56330,1716],{"stretchy":1715},[898,56332,14142],{},[1708,56334,2726],{},[898,56336,207],{},[1753,56338,56339,56341],{},[1708,56340,1721],{"stretchy":1715},[2505,56342,3132],{},[2247,56344,2659],{},[898,56346,2364],{},[898,56348,14142],{},[1708,56350,1710],{},[1708,56352,2726],{},[2358,56354,56355,56357],{},[2505,56356,49855],{},[1753,56358,56359,56361],{},[2505,56360,56233],{},[2505,56362,3132],{},[1708,56364,3703],{},[2505,56366,10909],{},[1708,56368,2638],{},[1708,56370,2726],{},[2505,56372,56373],{},"0,245.",[902,56375,56376],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,56378,56379,56380,2155],{},"Nové rovnovážné množství ",[883,56381,56383],{"className":56382},[886],[888,56384,56385],{"xmlns":890},[892,56386,56387,56412],{},[895,56388,56389,56397,56399,56402,56404,56407,56409],{},[4754,56390,56391,56393,56395],{},[898,56392,1688],{},[2505,56394,2507],{},[898,56396,16183],{},[1708,56398,2638],{},[2505,56400,56401],{},"8,571",[1708,56403,2726],{},[2505,56405,56406],{},"0,245",[1708,56408,1710],{},[2505,56410,56411],{},"8,326",[902,56413,56414],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,56416,56417,56502],{},[38,56418,56419,56420,1343,56440,1343,56462,1343,56482,2155],{},"(b) Současné změny ",[883,56421,56423],{"className":56422},[886],[888,56424,56425],{"xmlns":890},[892,56426,56427,56437],{},[895,56428,56429,56431,56433,56435],{},[898,56430,2364],{},[898,56432,207],{},[1708,56434,1710],{},[2505,56436,6097],{},[902,56438,56439],{"encoding":904},"da = 0{,}5",[883,56441,56443],{"className":56442},[886],[888,56444,56445],{"xmlns":890},[892,56446,56447,56459],{},[895,56448,56449,56451,56453,56455,56457],{},[898,56450,2364],{},[898,56452,1923],{},[1708,56454,1710],{},[1708,56456,2726],{},[2505,56458,3993],{},[902,56460,56461],{"encoding":904},"db = -5",[883,56463,56465],{"className":56464},[886],[888,56466,56467],{"xmlns":890},[892,56468,56469,56479],{},[895,56470,56471,56473,56475,56477],{},[898,56472,2364],{},[898,56474,14142],{},[1708,56476,1710],{},[2505,56478,10909],{},[902,56480,56481],{"encoding":904},"dc = 0{,}1",[883,56483,56485],{"className":56484},[886],[888,56486,56487],{"xmlns":890},[892,56488,56489,56499],{},[895,56490,56491,56493,56495,56497],{},[898,56492,2364],{},[898,56494,2364],{},[1708,56496,1710],{},[2505,56498,2507],{},[902,56500,56501],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,56504,56506],{"className":56505},[886],[888,56507,56508],{"xmlns":890,"display":2210},[892,56509,56510,56653],{},[2214,56511,56512,56594,56630],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,56513,56514,56524],{},[2221,56515,56516],{},[3194,56517,56518],{"scriptlevel":2784,"displaystyle":1882},[895,56519,56520,56522],{},[898,56521,2633],{"mathvariant":1759},[898,56523,1688],{},[2221,56525,56526],{},[3194,56527,56528],{"scriptlevel":2784,"displaystyle":1882},[895,56529,56530,56532,56534,56544,56546,56548,56550,56556,56558,56560,56562,56564,56566,56568,56578,56580,56582,56584,56590,56592],{},[895,56531],{},[1708,56533,2638],{},[2358,56535,56536,56538],{},[2505,56537,49855],{},[1753,56539,56540,56542],{},[2505,56541,56233],{},[2505,56543,3132],{},[1708,56545,3703],{},[2505,56547,6097],{},[1708,56549,2019],{},[2358,56551,56552,56554],{},[2505,56553,2507],{},[2505,56555,56233],{},[1708,56557,3703],{},[1708,56559,1716],{"stretchy":1715},[1708,56561,2726],{},[2505,56563,3993],{},[1708,56565,1721],{"stretchy":1715},[1708,56567,2726],{},[2358,56569,56570,56572],{},[2505,56571,49855],{},[1753,56573,56574,56576],{},[2505,56575,56233],{},[2505,56577,3132],{},[1708,56579,3703],{},[2505,56581,10909],{},[1708,56583,2726],{},[2358,56585,56586,56588],{},[2505,56587,2507],{},[2505,56589,56233],{},[1708,56591,3703],{},[2505,56593,2507],{},[2218,56595,56596,56602],{},[2221,56597,56598],{},[3194,56599,56600],{"scriptlevel":2784,"displaystyle":1882},[895,56601],{},[2221,56603,56604],{},[3194,56605,56606],{"scriptlevel":2784,"displaystyle":1882},[895,56607,56608,56610,56612,56615,56617,56620,56622,56625,56627],{},[895,56609],{},[1708,56611,1710],{},[2505,56613,56614],{},"1,2245",[1708,56616,2726],{},[2505,56618,56619],{},"1,4286",[1708,56621,2726],{},[2505,56623,56624],{},"0,2449",[1708,56626,2726],{},[2505,56628,56629],{},"0,2857",[2218,56631,56632,56638],{},[2221,56633,56634],{},[3194,56635,56636],{"scriptlevel":2784,"displaystyle":1882},[895,56637],{},[2221,56639,56640],{},[3194,56641,56642],{"scriptlevel":2784,"displaystyle":1882},[895,56643,56644,56646,56648,56650],{},[895,56645],{},[1708,56647,2638],{},[1708,56649,2726],{},[2505,56651,56652],{},"0,735.",[902,56654,56655],{"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}",[724,56657,41911,56658,2155],{},[883,56659,56661],{"className":56660},[886],[888,56662,56663],{"xmlns":890},[892,56664,56665,56689],{},[895,56666,56667,56675,56677,56679,56681,56684,56686],{},[4754,56668,56669,56671,56673],{},[898,56670,1688],{},[2505,56672,2507],{},[898,56674,16183],{},[1708,56676,2638],{},[2505,56678,56401],{},[1708,56680,2726],{},[2505,56682,56683],{},"0,735",[1708,56685,1710],{},[2505,56687,56688],{},"7,836",[902,56690,56691],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1636,56693,56694],{},[724,56695,56696,56698,56699,56722,56723,56745],{},[883,56697,6130],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,56700,56702],{"className":56701},[886],[888,56703,56704],{"xmlns":890},[892,56705,56706,56719],{},[895,56707,56708,56710,56712,56714,56716],{},[898,56709,2633],{"mathvariant":1759},[898,56711,1688],{},[1708,56713,2638],{},[1708,56715,2726],{},[2505,56717,56718],{},"2,69",[902,56720,56721],{"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 ",[883,56724,56726],{"className":56725},[886],[888,56727,56728],{"xmlns":890},[892,56729,56730,56742],{},[895,56731,56732,56734,56736,56738,56740],{},[898,56733,2633],{"mathvariant":1759},[898,56735,1688],{},[1708,56737,2638],{},[1708,56739,2726],{},[2505,56741,56683],{},[902,56743,56744],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,56747,56748],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[48808,56750],{},[115,56752,820],{"id":23671},[1636,56754,56755],{},[724,56756,56757,1643,56759,1695,56762,5149,56778,1695,56781,56797,56798,2155],{},[883,56758,2518],{},[38,56760,56761],{},"Přebytek spotřebitele",[883,56763,56765],{"className":56764},[886],[888,56766,56767],{"xmlns":890},[892,56768,56769,56775],{},[895,56770,56771,56773],{},[898,56772,3455],{},[898,56774,1981],{},[902,56776,56777],{"encoding":904},"CS",[38,56779,56780],{},"přebytek výrobce",[883,56782,56784],{"className":56783},[886],[888,56785,56786],{"xmlns":890},[892,56787,56788,56794],{},[895,56789,56790,56792],{},[898,56791,1747],{},[898,56793,1981],{},[902,56795,56796],{"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 ",[207,56799,56801],{"className":56800,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,56803,56804],{},[3372,56805],{"alt":56806,"className":56807,"src":56808},"imek-prebytky-cs-ps",[210,3376],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,56810,56811,1695,56813,56816],{},[38,56812,56761],{},[614,56814,56815],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,56818,56820],{"className":56819},[886],[888,56821,56822],{"xmlns":890,"display":2210},[892,56823,56824,56901],{},[2214,56825,56826],{"width":2216},[2218,56827,56828,56830,56894,56896],{},[2221,56829],{"width":2223},[2221,56831,56832],{},[895,56833,56834,56836,56838,56840,56846,56848,56850,56862,56864,56866,56868,56870,56872,56874,56876,56878,56884,56886,56892],{},[898,56835,3455],{},[898,56837,1981],{},[1708,56839,1716],{"stretchy":1715},[1743,56841,56842,56844],{},[898,56843,1688],{},[2505,56845,2784],{},[1708,56847,1721],{"stretchy":1715},[1708,56849,1710],{},[4754,56851,56852,56854,56856],{},[1708,56853,23056],{},[2505,56855,2784],{},[1743,56857,56858,56860],{},[898,56859,1688],{},[2505,56861,2784],{},[898,56863,16117],{},[1708,56865,1716],{"stretchy":1715},[898,56867,1688],{},[1708,56869,1721],{"stretchy":1715},[2247,56871,2659],{},[898,56873,2364],{},[898,56875,1688],{},[1708,56877,2726],{},[1743,56879,56880,56882],{},[898,56881,1747],{},[2505,56883,2784],{},[2247,56885,2659],{},[1743,56887,56888,56890],{},[898,56889,1688],{},[2505,56891,2784],{},[898,56893,2155],{"mathvariant":1759},[2221,56895],{"width":2223},[2221,56897,56898],{},[2247,56899,56900],{},"(2.14)",[902,56902,56903],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,56905,56906,1695,56909,56912],{},[38,56907,56908],{},"Přebytek výrobce",[614,56910,56911],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,56914,56916],{"className":56915},[886],[888,56917,56918],{"xmlns":890,"display":2210},[892,56919,56920,56997],{},[2214,56921,56922],{"width":2216},[2218,56923,56924,56926,56990,56992],{},[2221,56925],{"width":2223},[2221,56927,56928],{},[895,56929,56930,56932,56934,56936,56942,56944,56946,56952,56954,56960,56962,56974,56976,56978,56980,56982,56984,56986,56988],{},[898,56931,1747],{},[898,56933,1981],{},[1708,56935,1716],{"stretchy":1715},[1743,56937,56938,56940],{},[898,56939,1688],{},[2505,56941,2784],{},[1708,56943,1721],{"stretchy":1715},[1708,56945,1710],{},[1743,56947,56948,56950],{},[898,56949,1747],{},[2505,56951,2784],{},[2247,56953,2659],{},[1743,56955,56956,56958],{},[898,56957,1688],{},[2505,56959,2784],{},[1708,56961,2726],{},[4754,56963,56964,56966,56968],{},[1708,56965,23056],{},[2505,56967,2784],{},[1743,56969,56970,56972],{},[898,56971,1688],{},[2505,56973,2784],{},[898,56975,1981],{},[1708,56977,1716],{"stretchy":1715},[898,56979,1688],{},[1708,56981,1721],{"stretchy":1715},[2247,56983,2659],{},[898,56985,2364],{},[898,56987,1688],{},[898,56989,2155],{"mathvariant":1759},[2221,56991],{"width":2223},[2221,56993,56994],{},[2247,56995,56996],{},"(2.15)",[902,56998,56999],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,57001,57002,57003,2155],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,57004,57006],{"className":57005,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[48808,57008],{},[115,57010,57012],{"id":57011},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,57014,57015,57046,57051,57057,57085,57091,57120,57126,57206,57232],{},[123,57016,57017,57019,57020,57045],{},[38,57018,49764],{}," — lineární poptávka ",[883,57021,57023],{"className":57022},[886],[888,57024,57025],{"xmlns":890},[892,57026,57027,57043],{},[895,57028,57029,57031,57033,57035,57037,57039,57041],{},[898,57030,1747],{},[1708,57032,1710],{},[1708,57034,2726],{},[2505,57036,3132],{},[898,57038,1688],{},[1708,57040,2019],{},[2505,57042,4199],{},[902,57044,49796],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,57047,57048,57050],{},[38,57049,50078],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,57052,57053,57056],{},[38,57054,57055],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,57058,57059,57061,57062,2155],{},[38,57060,52621],{}," — lineární nabídka ",[883,57063,57065],{"className":57064},[886],[888,57066,57067],{"xmlns":890},[892,57068,57069,57083],{},[895,57070,57071,57073,57075,57077,57079,57081],{},[898,57072,1747],{},[1708,57074,1710],{},[2505,57076,6097],{},[898,57078,1688],{},[1708,57080,2019],{},[2505,57082,4028],{},[902,57084,52650],{"encoding":904},[123,57086,57087,57090],{},[38,57088,57089],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,57092,57093,57096,57097,2155],{},[38,57094,57095],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,57098,57100],{"className":57099},[886],[888,57101,57102],{"xmlns":890},[892,57103,57104,57118],{},[895,57105,57106,57108,57110,57112,57114,57116],{},[898,57107,16183],{},[1708,57109,6940],{"stretchy":1715},[2505,57111,5867],{},[1708,57113,1883],{"separator":1882},[2505,57115,53767],{},[1708,57117,6981],{"stretchy":1715},[902,57119,53795],{"encoding":904},[123,57121,57122,57125],{},[38,57123,57124],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,57127,57128,57131,57132,57149,57150,1343,57175,57202,57203,14914],{},[38,57129,57130],{},"Příklad 2.9"," — daň ",[883,57133,57135],{"className":57134},[886],[888,57136,57137],{"xmlns":890},[892,57138,57139,57147],{},[895,57140,57141,57143,57145],{},[898,57142,1978],{},[1708,57144,1710],{},[2505,57146,3947],{},[902,57148,53100],{"encoding":904}," na výrobce; rozklad ",[883,57151,57153],{"className":57152},[886],[888,57154,57155],{"xmlns":890},[892,57156,57157,57173],{},[895,57158,57159,57169,57171],{},[1743,57160,57161,57163],{},[898,57162,1978],{},[895,57164,57165,57167],{},[898,57166,54507],{},[898,57168,724],{},[1708,57170,1710],{},[2505,57172,3132],{},[902,57174,54806],{"encoding":904},[883,57176,57178],{"className":57177},[886],[888,57179,57180],{"xmlns":890},[892,57181,57182,57200],{},[895,57183,57184,57196,57198],{},[1743,57185,57186,57188],{},[898,57187,1978],{},[895,57189,57190,57192,57194],{},[898,57191,54530],{},[898,57193,14004],{},[898,57195,5498],{},[1708,57197,1710],{},[2505,57199,5867],{},[902,57201,54835],{"encoding":904},". (Viz ",[207,57204,54551],{"className":57205,"dataFsResolvedFilePath":809,"href":810},[210],[123,57207,57208,57131,57211,57228,57229,14914],{},[38,57209,57210],{},"Příklad 2.10",[883,57212,57214],{"className":57213},[886],[888,57215,57216],{"xmlns":890},[892,57217,57218,57226],{},[895,57219,57220,57222,57224],{},[898,57221,1978],{},[1708,57223,1710],{},[2505,57225,3947],{},[902,57227,53100],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,57230,54551],{"className":57231,"dataFsResolvedFilePath":809,"href":810},[210],[123,57233,57234,57237],{},[38,57235,57236],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[48808,57239],{},[115,57241,57243],{"id":57242},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,57245,57247],{"id":57246},"základní-analýza-poptávky","Základní analýza poptávky",[724,57249,57250,57253,57254,57288,57289,57315],{},[38,57251,57252],{},"2.1"," Je dána poptávka ",[883,57255,57257],{"className":57256},[886],[888,57258,57259],{"xmlns":890},[892,57260,57261,57285],{},[895,57262,57263,57265,57267,57269,57271,57273,57275,57277,57279,57281,57283],{},[898,57264,1688],{},[1708,57266,1710],{},[898,57268,16117],{},[1708,57270,1716],{"stretchy":1715},[898,57272,1747],{},[1708,57274,1721],{"stretchy":1715},[1708,57276,1710],{},[2505,57278,4241],{},[1708,57280,2726],{},[2505,57282,3993],{},[898,57284,1747],{},[902,57286,57287],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,57290,57292],{"className":57291},[886],[888,57293,57294],{"xmlns":890},[892,57295,57296,57312],{},[895,57297,57298,57300,57302,57304,57306,57308,57310],{},[2505,57299,2784],{},[1708,57301,1883],{"separator":1882},[2505,57303,3993],{},[1708,57305,1883],{"separator":1882},[2505,57307,4003],{},[1708,57309,1883],{"separator":1882},[2505,57311,4853],{},[902,57313,57314],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,57317,57318,57321,57322,57340,57341,2750],{},[38,57319,57320],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,57323,57325],{"className":57324},[886],[888,57326,57327],{"xmlns":890},[892,57328,57329,57337],{},[895,57330,57331,57333,57335],{},[898,57332,1747],{},[1708,57334,1883],{"separator":1882},[898,57336,1688],{},[902,57338,57339],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,57342,57344],{"className":57343},[886],[888,57345,57346],{"xmlns":890},[892,57347,57348,57364],{},[895,57349,57350,57352,57354,57356,57358,57360,57362],{},[898,57351,207],{},[1708,57353,1883],{"separator":1882},[898,57355,1923],{},[1708,57357,1883],{"separator":1882},[898,57359,14142],{},[1708,57361,2854],{},[2505,57363,2784],{},[902,57365,57366],{"encoding":904},"a, b, c > 0",[120,57368,57369,57402,57433,57468,57499,57534],{},[123,57370,57371,57372],{},"(a) ",[883,57373,57375],{"className":57374},[886],[888,57376,57377],{"xmlns":890},[892,57378,57379,57399],{},[895,57380,57381,57383,57385],{},[898,57382,1688],{},[1708,57384,1710],{},[3194,57386,57387],{"scriptlevel":2784,"displaystyle":1882},[2358,57388,57389,57391],{},[898,57390,207],{},[895,57392,57393,57395,57397],{},[898,57394,1747],{},[1708,57396,2019],{},[898,57398,14142],{},[902,57400,57401],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,57403,57404,57405],{},"(b) ",[883,57406,57408],{"className":57407},[886],[888,57409,57410],{"xmlns":890},[892,57411,57412,57430],{},[895,57413,57414,57416,57418],{},[898,57415,1688],{},[1708,57417,1710],{},[9351,57419,57420],{},[895,57421,57422,57424,57426,57428],{},[898,57423,207],{},[1708,57425,2726],{},[898,57427,1923],{},[898,57429,1688],{},[902,57431,57432],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,57434,57435,57436],{},"(c) ",[883,57437,57439],{"className":57438},[886],[888,57440,57441],{"xmlns":890},[892,57442,57443,57465],{},[895,57444,57445,57447,57449],{},[898,57446,1688],{},[1708,57448,1710],{},[3194,57450,57451],{"scriptlevel":2784,"displaystyle":1882},[2358,57452,57453,57463],{},[895,57454,57455,57457,57459],{},[898,57456,207],{},[1708,57458,2726],{},[9351,57460,57461],{},[898,57462,1747],{},[898,57464,1923],{},[902,57466,57467],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,57469,57470,57471],{},"(d) ",[883,57472,57474],{"className":57473},[886],[888,57475,57476],{"xmlns":890},[892,57477,57478,57496],{},[895,57479,57480,57482,57484,57486,57488,57490],{},[898,57481,1747],{},[1708,57483,1710],{},[898,57485,207],{},[1708,57487,2726],{},[898,57489,1923],{},[1753,57491,57492,57494],{},[898,57493,1688],{},[2505,57495,3132],{},[902,57497,57498],{"encoding":904},"P = a - bQ^2",[123,57500,57501,57502],{},"(e) ",[883,57503,57505],{"className":57504},[886],[888,57506,57507],{"xmlns":890},[892,57508,57509,57531],{},[895,57510,57511,57513,57515,57517,57527,57529],{},[898,57512,1688],{},[1708,57514,1710],{},[898,57516,1923],{},[1753,57518,57519,57521],{},[898,57520,1747],{},[895,57522,57523,57525],{},[1708,57524,2726],{},[898,57526,207],{},[1708,57528,2019],{},[898,57530,14142],{},[902,57532,57533],{"encoding":904},"Q = bP^{-a} + c",[123,57535,57536,57537],{},"(f) ",[883,57538,57540],{"className":57539},[886],[888,57541,57542],{"xmlns":890},[892,57543,57544,57567],{},[895,57545,57546,57548,57550,57552,57554],{},[898,57547,1688],{},[1708,57549,1710],{},[898,57551,207],{},[1708,57553,3703],{},[1753,57555,57556,57559],{},[898,57557,57558],{},"e",[895,57560,57561,57563,57565],{},[1708,57562,2726],{},[898,57564,1923],{},[898,57566,1747],{},[902,57568,57569],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,57571,57572,57575],{},[38,57573,57574],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,57577,57578,57581,57584],{},[123,57579,57580],{},"(a) Cena substitutu.",[123,57582,57583],{},"(b) Cena komplementu.",[123,57585,57586],{},"(c) Výdaje na reklamu.",[724,57588,57589,57253,57591,57625,57626,57654],{},[38,57590,36494],{},[883,57592,57594],{"className":57593},[886],[888,57595,57596],{"xmlns":890},[892,57597,57598,57622],{},[895,57599,57600,57602,57604,57606,57608,57610,57612,57614,57616,57618,57620],{},[898,57601,1747],{},[1708,57603,1710],{},[898,57605,16117],{},[1708,57607,1716],{"stretchy":1715},[898,57609,1688],{},[1708,57611,1721],{"stretchy":1715},[1708,57613,1710],{},[2505,57615,4090],{},[1708,57617,2726],{},[2505,57619,3132],{},[898,57621,1688],{},[902,57623,57624],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,57627,57629],{"className":57628},[886],[888,57630,57631],{"xmlns":890},[892,57632,57633,57651],{},[895,57634,57635,57637,57639,57645,57647,57649],{},[898,57636,1747],{},[1708,57638,1710],{},[1753,57640,57641,57643],{},[898,57642,16117],{},[1708,57644,2417],{},[1708,57646,1716],{"stretchy":1715},[898,57648,1688],{},[1708,57650,1721],{"stretchy":1715},[902,57652,57653],{"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.",[724,57656,57657,57660],{},[38,57658,57659],{},"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:",[120,57662,57663,57747,57823,57909,57997],{},[123,57664,57371,57665,1343,57705,2155],{},[883,57666,57668],{"className":57667},[886],[888,57669,57670],{"xmlns":890},[892,57671,57672,57702],{},[895,57673,57674,57680,57682,57684,57686,57688,57694,57696],{},[1743,57675,57676,57678],{},[898,57677,35110],{},[2505,57679,2507],{},[1708,57681,1710],{},[2505,57683,4018],{},[1708,57685,2726],{},[2505,57687,5867],{},[1743,57689,57690,57692],{},[898,57691,1786],{},[2505,57693,2507],{},[1708,57695,2019],{},[1743,57697,57698,57700],{},[898,57699,1786],{},[2505,57701,3132],{},[902,57703,57704],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,57706,57708],{"className":57707},[886],[888,57709,57710],{"xmlns":890},[892,57711,57712,57744],{},[895,57713,57714,57720,57722,57724,57726,57728,57734,57736,57738],{},[1743,57715,57716,57718],{},[898,57717,35110],{},[2505,57719,3132],{},[1708,57721,1710],{},[2505,57723,4003],{},[1708,57725,2019],{},[2505,57727,3132],{},[1743,57729,57730,57732],{},[898,57731,1786],{},[2505,57733,2507],{},[1708,57735,2726],{},[2505,57737,5867],{},[1743,57739,57740,57742],{},[898,57741,1786],{},[2505,57743,3132],{},[902,57745,57746],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,57748,57404,57749,1343,57791,2155],{},[883,57750,57752],{"className":57751},[886],[888,57753,57754],{"xmlns":890},[892,57755,57756,57788],{},[895,57757,57758,57764,57766,57768,57770,57772,57778,57780,57782],{},[1743,57759,57760,57762],{},[898,57761,35110],{},[2505,57763,2507],{},[1708,57765,1710],{},[2505,57767,9704],{},[1708,57769,2726],{},[2505,57771,4003],{},[1743,57773,57774,57776],{},[898,57775,1786],{},[2505,57777,2507],{},[1708,57779,2726],{},[2505,57781,3947],{},[1743,57783,57784,57786],{},[898,57785,1786],{},[2505,57787,3132],{},[902,57789,57790],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,57792,57794],{"className":57793},[886],[888,57795,57796],{"xmlns":890},[892,57797,57798,57820],{},[895,57799,57800,57806,57808,57810,57812,57814],{},[1743,57801,57802,57804],{},[898,57803,35110],{},[2505,57805,3132],{},[1708,57807,1710],{},[2505,57809,4853],{},[1708,57811,2726],{},[2505,57813,4003],{},[1743,57815,57816,57818],{},[898,57817,1786],{},[2505,57819,3132],{},[902,57821,57822],{"encoding":904},"B_2 = 15 - 10A_2",[123,57824,57435,57825,1343,57867,2155],{},[883,57826,57828],{"className":57827},[886],[888,57829,57830],{"xmlns":890},[892,57831,57832,57864],{},[895,57833,57834,57840,57842,57844,57846,57848,57854,57856,57858],{},[1743,57835,57836,57838],{},[898,57837,35110],{},[2505,57839,2507],{},[1708,57841,1710],{},[2505,57843,49855],{},[1708,57845,2726],{},[2505,57847,3132],{},[1743,57849,57850,57852],{},[898,57851,1786],{},[2505,57853,2507],{},[1708,57855,2726],{},[2505,57857,5867],{},[1743,57859,57860,57862],{},[898,57861,1786],{},[2505,57863,3132],{},[902,57865,57866],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,57868,57870],{"className":57869},[886],[888,57871,57872],{"xmlns":890},[892,57873,57874,57906],{},[895,57875,57876,57882,57884,57886,57888,57890,57896,57898,57900],{},[1743,57877,57878,57880],{},[898,57879,35110],{},[2505,57881,3132],{},[1708,57883,1710],{},[2505,57885,4853],{},[1708,57887,2019],{},[2505,57889,3132],{},[1743,57891,57892,57894],{},[898,57893,1786],{},[2505,57895,2507],{},[1708,57897,2726],{},[2505,57899,3132],{},[1743,57901,57902,57904],{},[898,57903,1786],{},[2505,57905,3132],{},[902,57907,57908],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,57910,57470,57911,1343,57955,2155],{},[883,57912,57914],{"className":57913},[886],[888,57915,57916],{"xmlns":890},[892,57917,57918,57952],{},[895,57919,57920,57926,57928,57930,57932,57934,57936,57942,57944,57946],{},[1743,57921,57922,57924],{},[898,57923,35110],{},[2505,57925,2507],{},[1708,57927,1710],{},[1708,57929,2726],{},[2505,57931,4018],{},[1708,57933,2726],{},[2505,57935,3132],{},[1743,57937,57938,57940],{},[898,57939,1786],{},[2505,57941,2507],{},[1708,57943,2019],{},[2505,57945,3121],{},[1743,57947,57948,57950],{},[898,57949,1786],{},[2505,57951,3132],{},[902,57953,57954],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,57956,57958],{"className":57957},[886],[888,57959,57960],{"xmlns":890},[892,57961,57962,57994],{},[895,57963,57964,57970,57972,57974,57976,57978,57984,57986,57988],{},[1743,57965,57966,57968],{},[898,57967,35110],{},[2505,57969,3132],{},[1708,57971,1710],{},[2505,57973,4003],{},[1708,57975,2019],{},[2505,57977,3132],{},[1743,57979,57980,57982],{},[898,57981,1786],{},[2505,57983,2507],{},[1708,57985,2726],{},[2505,57987,3132],{},[1743,57989,57990,57992],{},[898,57991,1786],{},[2505,57993,3132],{},[902,57995,57996],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,57998,57501,57999,1343,58041,2155],{},[883,58000,58002],{"className":58001},[886],[888,58003,58004],{"xmlns":890},[892,58005,58006,58038],{},[895,58007,58008,58014,58016,58018,58020,58022,58028,58030,58032],{},[1743,58009,58010,58012],{},[898,58011,35110],{},[2505,58013,2507],{},[1708,58015,1710],{},[2505,58017,4018],{},[1708,58019,2019],{},[2505,58021,3132],{},[1743,58023,58024,58026],{},[898,58025,1786],{},[2505,58027,2507],{},[1708,58029,2019],{},[2505,58031,5867],{},[1743,58033,58034,58036],{},[898,58035,1786],{},[2505,58037,3132],{},[902,58039,58040],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,58042,58044],{"className":58043},[886],[888,58045,58046],{"xmlns":890},[892,58047,58048,58080],{},[895,58049,58050,58056,58058,58060,58062,58064,58070,58072,58074],{},[1743,58051,58052,58054],{},[898,58053,35110],{},[2505,58055,3132],{},[1708,58057,1710],{},[2505,58059,17132],{},[1708,58061,2726],{},[2505,58063,3121],{},[1743,58065,58066,58068],{},[898,58067,1786],{},[2505,58069,2507],{},[1708,58071,2019],{},[2505,58073,3993],{},[1743,58075,58076,58078],{},[898,58077,1786],{},[2505,58079,3132],{},[902,58081,58082],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,58084,58086],{"id":58085},"základní-analýza-nabídky","Základní analýza nabídky",[724,58088,58089,58092,58093,58127,58128,58150],{},[38,58090,58091],{},"2.6"," Je dána nabídka ",[883,58094,58096],{"className":58095},[886],[888,58097,58098],{"xmlns":890},[892,58099,58100,58124],{},[895,58101,58102,58104,58106,58108,58110,58112,58114,58116,58118,58120,58122],{},[898,58103,1747],{},[1708,58105,1710],{},[898,58107,1981],{},[1708,58109,1716],{"stretchy":1715},[898,58111,1688],{},[1708,58113,1721],{"stretchy":1715},[1708,58115,1710],{},[2505,58117,4018],{},[1708,58119,2019],{},[2505,58121,3958],{},[898,58123,1688],{},[902,58125,58126],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,58129,58131],{"className":58130},[886],[888,58132,58133],{"xmlns":890},[892,58134,58135,58147],{},[895,58136,58137,58139,58141,58143,58145],{},[2505,58138,4028],{},[1708,58140,1883],{"separator":1882},[2505,58142,49855],{},[1708,58144,1883],{"separator":1882},[2505,58146,26919],{},[902,58148,58149],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,58152,58153,58156,58157,58174],{},[38,58154,58155],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,58158,58160],{"className":58159},[886],[888,58161,58162],{"xmlns":890},[892,58163,58164,58172],{},[895,58165,58166,58168,58170],{},[898,58167,1747],{},[1708,58169,1883],{"separator":1882},[898,58171,1688],{},[902,58173,57339],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,58176,58177,58203,58231,58264,58298,58334],{},[123,58178,57371,58179],{},[883,58180,58182],{"className":58181},[886],[888,58183,58184],{"xmlns":890},[892,58185,58186,58200],{},[895,58187,58188,58190,58192,58194,58196,58198],{},[898,58189,1747],{},[1708,58191,1710],{},[2505,58193,49855],{},[1708,58195,2019],{},[2505,58197,3132],{},[898,58199,1688],{},[902,58201,58202],{"encoding":904},"P = 30 + 2Q",[123,58204,57404,58205],{},[883,58206,58208],{"className":58207},[886],[888,58209,58210],{"xmlns":890},[892,58211,58212,58228],{},[895,58213,58214,58216,58218,58220,58222,58224,58226],{},[898,58215,1688],{},[1708,58217,1710],{},[1708,58219,2726],{},[2505,58221,3121],{},[1708,58223,2019],{},[2505,58225,4090],{},[898,58227,1747],{},[902,58229,58230],{"encoding":904},"Q = -3 + 12P",[123,58232,57435,58233],{},[883,58234,58236],{"className":58235},[886],[888,58237,58238],{"xmlns":890},[892,58239,58240,58262],{},[895,58241,58242,58244,58246,58252,58254,58256,58258,58260],{},[898,58243,1747],{},[1708,58245,1710],{},[1753,58247,58248,58250],{},[898,58249,1688],{},[2505,58251,3132],{},[1708,58253,2019],{},[2505,58255,4008],{},[898,58257,1688],{},[1708,58259,2019],{},[2505,58261,44390],{},[902,58263,53554],{"encoding":904},[123,58265,57470,58266],{},[883,58267,58269],{"className":58268},[886],[888,58270,58271],{"xmlns":890},[892,58272,58273,58295],{},[895,58274,58275,58277,58279,58285,58287,58289,58291,58293],{},[898,58276,1747],{},[1708,58278,1710],{},[1753,58280,58281,58283],{},[898,58282,1688],{},[2505,58284,3132],{},[1708,58286,2019],{},[2505,58288,3132],{},[898,58290,1688],{},[1708,58292,2019],{},[2505,58294,4090],{},[902,58296,58297],{"encoding":904},"P = Q^2 + 2Q + 12",[123,58299,57501,58300],{},[883,58301,58303],{"className":58302},[886],[888,58304,58305],{"xmlns":890},[892,58306,58307,58331],{},[895,58308,58309,58311,58313,58315,58317,58319,58321,58323,58325],{},[898,58310,1688],{},[1708,58312,1710],{},[2505,58314,9660],{},[1708,58316,2019],{},[2505,58318,3993],{},[898,58320,1747],{},[1708,58322,2019],{},[2505,58324,10909],{},[1753,58326,58327,58329],{},[898,58328,1747],{},[2505,58330,3132],{},[902,58332,58333],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,58335,57536,58336],{},[883,58337,58339],{"className":58338},[886],[888,58340,58341],{"xmlns":890},[892,58342,58343,58368],{},[895,58344,58345,58347,58349,58351,58353,58355,58357,58359,58362],{},[898,58346,1688],{},[1708,58348,1710],{},[2505,58350,5967],{},[1708,58352,2019],{},[2505,58354,10909],{},[898,58356,1747],{},[1708,58358,2019],{},[2505,58360,58361],{},"0,004",[1753,58363,58364,58366],{},[898,58365,1747],{},[2505,58367,3132],{},[902,58369,58370],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,58372,58373,58376],{},[38,58374,58375],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,58378,58379,58382,58385,58388],{},[123,58380,58381],{},"(a) Sníží ceny surovin — vstupů.",[123,58383,58384],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,58386,58387],{},"(c) Zvýší ceny všech energií.",[123,58389,58390],{},"(d) Sníží daňové odvody státu.",[724,58392,58393,58092,58395,58429,58430,58458],{},[38,58394,54779],{},[883,58396,58398],{"className":58397},[886],[888,58399,58400],{"xmlns":890},[892,58401,58402,58426],{},[895,58403,58404,58406,58408,58410,58412,58414,58416,58418,58420,58422,58424],{},[898,58405,1747],{},[1708,58407,1710],{},[898,58409,1981],{},[1708,58411,1716],{"stretchy":1715},[898,58413,1688],{},[1708,58415,1721],{"stretchy":1715},[1708,58417,1710],{},[2505,58419,6097],{},[898,58421,1688],{},[1708,58423,2019],{},[2505,58425,4853],{},[902,58427,58428],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,58431,58433],{"className":58432},[886],[888,58434,58435],{"xmlns":890},[892,58436,58437,58455],{},[895,58438,58439,58441,58443,58449,58451,58453],{},[898,58440,1747],{},[1708,58442,1710],{},[1753,58444,58445,58447],{},[898,58446,1981],{},[1708,58448,2417],{},[1708,58450,1716],{"stretchy":1715},[898,58452,1688],{},[1708,58454,1721],{"stretchy":1715},[902,58456,58457],{"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.",[198,58460,53157],{"id":58461},"tržní-rovnováha-1",[724,58463,58464,58466,58467,58484,58485,2788],{},[38,58465,54839],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,58468,58470],{"className":58469},[886],[888,58471,58472],{"xmlns":890},[892,58473,58474,58482],{},[895,58475,58476],{},[1753,58477,58478,58480],{},[898,58479,1688],{},[898,58481,16183],{},[902,58483,54233],{"encoding":904}," a rovnovážnou cenu ",[883,58486,58488],{"className":58487},[886],[888,58489,58490],{"xmlns":890},[892,58491,58492,58500],{},[895,58493,58494],{},[1753,58495,58496,58498],{},[898,58497,1747],{},[898,58499,16183],{},[902,58501,53298],{"encoding":904},[120,58503,58504,58556,58607,58666],{},[123,58505,57371,58506,1343,58532,2155],{},[883,58507,58509],{"className":58508},[886],[888,58510,58511],{"xmlns":890},[892,58512,58513,58529],{},[895,58514,58515,58517,58519,58521,58523,58525,58527],{},[898,58516,1747],{},[1708,58518,1710],{},[1708,58520,2726],{},[2505,58522,3993],{},[898,58524,1688],{},[1708,58526,2019],{},[2505,58528,12513],{},[902,58530,58531],{"encoding":904},"P = -5Q + 80",[883,58533,58535],{"className":58534},[886],[888,58536,58537],{"xmlns":890},[892,58538,58539,58553],{},[895,58540,58541,58543,58545,58547,58549,58551],{},[898,58542,1747],{},[1708,58544,1710],{},[2505,58546,3132],{},[898,58548,1688],{},[1708,58550,2019],{},[2505,58552,4003],{},[902,58554,58555],{"encoding":904},"P = 2Q + 10",[123,58557,57404,58558,1343,58584,2155],{},[883,58559,58561],{"className":58560},[886],[888,58562,58563],{"xmlns":890},[892,58564,58565,58581],{},[895,58566,58567,58569,58571,58573,58575,58577,58579],{},[898,58568,1688],{},[1708,58570,1710],{},[1708,58572,2726],{},[2505,58574,6097],{},[898,58576,1747],{},[1708,58578,2019],{},[2505,58580,4028],{},[902,58582,58583],{"encoding":904},"Q = -0{,}5P + 25",[883,58585,58587],{"className":58586},[886],[888,58588,58589],{"xmlns":890},[892,58590,58591,58605],{},[895,58592,58593,58595,58597,58599,58601,58603],{},[898,58594,1688],{},[1708,58596,1710],{},[2505,58598,3132],{},[898,58600,1747],{},[1708,58602,2726],{},[2505,58604,9704],{},[902,58606,52679],{"encoding":904},[123,58608,57435,58609,1343,58635,2155],{},[883,58610,58612],{"className":58611},[886],[888,58613,58614],{"xmlns":890},[892,58615,58616,58632],{},[895,58617,58618,58620,58622,58624,58626,58628,58630],{},[898,58619,1747],{},[1708,58621,1710],{},[1708,58623,2726],{},[2505,58625,5867],{},[898,58627,1688],{},[1708,58629,2019],{},[2505,58631,15981],{},[902,58633,58634],{"encoding":904},"P = -4Q + 120",[883,58636,58638],{"className":58637},[886],[888,58639,58640],{"xmlns":890},[892,58641,58642,58663],{},[895,58643,58644,58646,58648,58656,58658,58660],{},[898,58645,1747],{},[1708,58647,1710],{},[3194,58649,58650],{"scriptlevel":2784,"displaystyle":1715},[2358,58651,58652,58654],{},[2505,58653,2507],{},[2505,58655,3121],{},[898,58657,1688],{},[1708,58659,2019],{},[2505,58661,58662],{},"29",[902,58664,58665],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,58667,57470,58668,1343,58697,2155],{},[883,58669,58671],{"className":58670},[886],[888,58672,58673],{"xmlns":890},[892,58674,58675,58694],{},[895,58676,58677,58679,58681,58683,58689,58691],{},[898,58678,1747],{},[1708,58680,1710],{},[1708,58682,2726],{},[1753,58684,58685,58687],{},[898,58686,1688],{},[2505,58688,3132],{},[1708,58690,2019],{},[2505,58692,58693],{},"52",[902,58695,58696],{"encoding":904},"P = -Q^2 + 52",[883,58698,58700],{"className":58699},[886],[888,58701,58702],{"xmlns":890},[892,58703,58704,58722],{},[895,58705,58706,58708,58710,58712,58718,58720],{},[898,58707,1747],{},[1708,58709,1710],{},[2505,58711,3132],{},[1753,58713,58714,58716],{},[898,58715,1688],{},[2505,58717,3132],{},[1708,58719,2019],{},[2505,58721,4003],{},[902,58723,58724],{"encoding":904},"P = 2Q^2 + 10",[724,58726,58727,58730,58731,58761,58762,58792],{},[38,58728,58729],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,58732,58734],{"className":58733},[886],[888,58735,58736],{"xmlns":890},[892,58737,58738,58758],{},[895,58739,58740,58748,58750],{},[4754,58741,58742,58744,58746],{},[898,58743,1688],{},[2505,58745,2507],{},[898,58747,16183],{},[1708,58749,1883],{"separator":1882},[4754,58751,58752,58754,58756],{},[898,58753,1688],{},[2505,58755,3132],{},[898,58757,16183],{},[902,58759,58760],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,58763,58765],{"className":58764},[886],[888,58766,58767],{"xmlns":890},[892,58768,58769,58789],{},[895,58770,58771,58779,58781],{},[4754,58772,58773,58775,58777],{},[898,58774,1747],{},[2505,58776,2507],{},[898,58778,16183],{},[1708,58780,1883],{"separator":1882},[4754,58782,58783,58785,58787],{},[898,58784,1747],{},[2505,58786,3132],{},[898,58788,16183],{},[902,58790,58791],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,58794,58795,58947],{},[123,58796,57371,58797,1343,58837,1343,58879,1343,58913,2155],{},[883,58798,58800],{"className":58799},[886],[888,58801,58802],{"xmlns":890},[892,58803,58804,58834],{},[895,58805,58806,58812,58814,58816,58818,58820,58826,58828],{},[1743,58807,58808,58810],{},[898,58809,1688],{},[2505,58811,2507],{},[1708,58813,1710],{},[2505,58815,4003],{},[1708,58817,2726],{},[2505,58819,3132],{},[1743,58821,58822,58824],{},[898,58823,1747],{},[2505,58825,2507],{},[1708,58827,2019],{},[1743,58829,58830,58832],{},[898,58831,1747],{},[2505,58833,3132],{},[902,58835,58836],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,58838,58840],{"className":58839},[886],[888,58841,58842],{"xmlns":890},[892,58843,58844,58876],{},[895,58845,58846,58852,58854,58856,58858,58860,58866,58868,58870],{},[1743,58847,58848,58850],{},[898,58849,1688],{},[2505,58851,3132],{},[1708,58853,1710],{},[2505,58855,3993],{},[1708,58857,2019],{},[2505,58859,3132],{},[1743,58861,58862,58864],{},[898,58863,1747],{},[2505,58865,2507],{},[1708,58867,2726],{},[2505,58869,3132],{},[1743,58871,58872,58874],{},[898,58873,1747],{},[2505,58875,3132],{},[902,58877,58878],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,58880,58882],{"className":58881},[886],[888,58883,58884],{"xmlns":890},[892,58885,58886,58910],{},[895,58887,58888,58894,58896,58898,58900,58902,58904],{},[1743,58889,58890,58892],{},[898,58891,1688],{},[2505,58893,2507],{},[1708,58895,1710],{},[1708,58897,2726],{},[2505,58899,3121],{},[1708,58901,2019],{},[2505,58903,3132],{},[1743,58905,58906,58908],{},[898,58907,1747],{},[2505,58909,2507],{},[902,58911,58912],{"encoding":904},"Q_1 = -3 + 2P_1",[883,58914,58916],{"className":58915},[886],[888,58917,58918],{"xmlns":890},[892,58919,58920,58944],{},[895,58921,58922,58928,58930,58932,58934,58936,58938],{},[1743,58923,58924,58926],{},[898,58925,1688],{},[2505,58927,3132],{},[1708,58929,1710],{},[1708,58931,2726],{},[2505,58933,3132],{},[1708,58935,2019],{},[2505,58937,3121],{},[1743,58939,58940,58942],{},[898,58941,1747],{},[2505,58943,3132],{},[902,58945,58946],{"encoding":904},"Q_2 = -2 + 3P_2",[123,58948,57404,58949,1343,58989,1343,59031,1343,59063,2155],{},[883,58950,58952],{"className":58951},[886],[888,58953,58954],{"xmlns":890},[892,58955,58956,58986],{},[895,58957,58958,58964,58966,58968,58970,58972,58978,58980],{},[1743,58959,58960,58962],{},[898,58961,1688],{},[2505,58963,2507],{},[1708,58965,1710],{},[2505,58967,9238],{},[1708,58969,2726],{},[2505,58971,3132],{},[1743,58973,58974,58976],{},[898,58975,1747],{},[2505,58977,2507],{},[1708,58979,2019],{},[1743,58981,58982,58984],{},[898,58983,1747],{},[2505,58985,3132],{},[902,58987,58988],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,58990,58992],{"className":58991},[886],[888,58993,58994],{"xmlns":890},[892,58995,58996,59028],{},[895,58997,58998,59004,59006,59008,59010,59012,59018,59020,59022],{},[1743,58999,59000,59002],{},[898,59001,1688],{},[2505,59003,3132],{},[1708,59005,1710],{},[2505,59007,3993],{},[1708,59009,2019],{},[2505,59011,3132],{},[1743,59013,59014,59016],{},[898,59015,1747],{},[2505,59017,2507],{},[1708,59019,2726],{},[2505,59021,3121],{},[1743,59023,59024,59026],{},[898,59025,1747],{},[2505,59027,3132],{},[902,59029,59030],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,59032,59034],{"className":59033},[886],[888,59035,59036],{"xmlns":890},[892,59037,59038,59060],{},[895,59039,59040,59046,59048,59050,59052,59054],{},[1743,59041,59042,59044],{},[898,59043,1688],{},[2505,59045,2507],{},[1708,59047,1710],{},[1708,59049,2726],{},[2505,59051,4003],{},[1708,59053,2019],{},[1743,59055,59056,59058],{},[898,59057,1747],{},[2505,59059,2507],{},[902,59061,59062],{"encoding":904},"Q_1 = -10 + P_1",[883,59064,59066],{"className":59065},[886],[888,59067,59068],{"xmlns":890},[892,59069,59070,59092],{},[895,59071,59072,59078,59080,59082,59084,59086],{},[1743,59073,59074,59076],{},[898,59075,1688],{},[2505,59077,3132],{},[1708,59079,1710],{},[2505,59081,3993],{},[1708,59083,2019],{},[2505,59085,3947],{},[1743,59087,59088,59090],{},[898,59089,1747],{},[2505,59091,3132],{},[902,59093,59094],{"encoding":904},"Q_2 = 5 + 6P_2",[724,59096,59097,59100,59101,1343,59149,1343,59195,59245,59246,1343,59278,1343,59312,2980,59346,1771,59364,59382,59383,59396,59397,59423,59424,58761,59464,2155],{},[38,59098,59099],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,59102,59104],{"className":59103},[886],[888,59105,59106],{"xmlns":890},[892,59107,59108,59146],{},[895,59109,59110,59116,59118,59120,59122,59128,59130,59132,59138,59140],{},[1743,59111,59112,59114],{},[898,59113,1688],{},[2505,59115,2507],{},[1708,59117,1710],{},[2505,59119,4853],{},[1708,59121,2726],{},[1743,59123,59124,59126],{},[898,59125,1747],{},[2505,59127,2507],{},[1708,59129,2019],{},[2505,59131,3132],{},[1743,59133,59134,59136],{},[898,59135,1747],{},[2505,59137,3132],{},[1708,59139,2019],{},[1743,59141,59142,59144],{},[898,59143,1747],{},[2505,59145,3121],{},[902,59147,59148],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,59150,59152],{"className":59151},[886],[888,59153,59154],{"xmlns":890},[892,59155,59156,59192],{},[895,59157,59158,59164,59166,59168,59170,59176,59178,59184,59186],{},[1743,59159,59160,59162],{},[898,59161,1688],{},[2505,59163,3132],{},[1708,59165,1710],{},[2505,59167,4635],{},[1708,59169,2019],{},[1743,59171,59172,59174],{},[898,59173,1747],{},[2505,59175,2507],{},[1708,59177,2726],{},[1743,59179,59180,59182],{},[898,59181,1747],{},[2505,59183,3132],{},[1708,59185,2726],{},[1743,59187,59188,59190],{},[898,59189,1747],{},[2505,59191,3121],{},[902,59193,59194],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,59196,59198],{"className":59197},[886],[888,59199,59200],{"xmlns":890},[892,59201,59202,59242],{},[895,59203,59204,59210,59212,59214,59216,59218,59224,59226,59232,59234,59236],{},[1743,59205,59206,59208],{},[898,59207,1688],{},[2505,59209,3121],{},[1708,59211,1710],{},[2505,59213,3998],{},[1708,59215,2019],{},[2505,59217,3132],{},[1743,59219,59220,59222],{},[898,59221,1747],{},[2505,59223,2507],{},[1708,59225,2726],{},[1743,59227,59228,59230],{},[898,59229,1747],{},[2505,59231,3132],{},[1708,59233,2726],{},[2505,59235,5867],{},[1743,59237,59238,59240],{},[898,59239,1747],{},[2505,59241,3121],{},[902,59243,59244],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,59247,59249],{"className":59248},[886],[888,59250,59251],{"xmlns":890},[892,59252,59253,59275],{},[895,59254,59255,59261,59263,59265,59267,59269],{},[1743,59256,59257,59259],{},[898,59258,1688],{},[2505,59260,2507],{},[1708,59262,1710],{},[1708,59264,2726],{},[2505,59266,5967],{},[1708,59268,2019],{},[1743,59270,59271,59273],{},[898,59272,1747],{},[2505,59274,2507],{},[902,59276,59277],{"encoding":904},"Q_1 = -7 + P_1",[883,59279,59281],{"className":59280},[886],[888,59282,59283],{"xmlns":890},[892,59284,59285,59309],{},[895,59286,59287,59293,59295,59297,59299,59301,59303],{},[1743,59288,59289,59291],{},[898,59290,1688],{},[2505,59292,3132],{},[1708,59294,1710],{},[1708,59296,2726],{},[2505,59298,5867],{},[1708,59300,2019],{},[2505,59302,5867],{},[1743,59304,59305,59307],{},[898,59306,1747],{},[2505,59308,3132],{},[902,59310,59311],{"encoding":904},"Q_2 = -4 + 4P_2",[883,59313,59315],{"className":59314},[886],[888,59316,59317],{"xmlns":890},[892,59318,59319,59343],{},[895,59320,59321,59327,59329,59331,59333,59335,59337],{},[1743,59322,59323,59325],{},[898,59324,1688],{},[2505,59326,3121],{},[1708,59328,1710],{},[1708,59330,2726],{},[2505,59332,3993],{},[1708,59334,2019],{},[2505,59336,3132],{},[1743,59338,59339,59341],{},[898,59340,1747],{},[2505,59342,3121],{},[902,59344,59345],{"encoding":904},"Q_3 = -5 + 2P_3",[883,59347,59349],{"className":59348},[886],[888,59350,59351],{"xmlns":890},[892,59352,59353,59361],{},[895,59354,59355],{},[1743,59356,59357,59359],{},[898,59358,1688],{},[898,59360,29661],{},[902,59362,59363],{"encoding":904},"Q_i",[883,59365,59367],{"className":59366},[886],[888,59368,59369],{"xmlns":890},[892,59370,59371,59379],{},[895,59372,59373],{},[1743,59374,59375,59377],{},[898,59376,1747],{},[898,59378,29661],{},[902,59380,59381],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,59384,59386],{"className":59385},[886],[888,59387,59388],{"xmlns":890},[892,59389,59390,59394],{},[895,59391,59392],{},[898,59393,29661],{},[902,59395,29661],{"encoding":904},"-tého zboží, ",[883,59398,59400],{"className":59399},[886],[888,59401,59402],{"xmlns":890},[892,59403,59404,59420],{},[895,59405,59406,59408,59410,59412,59414,59416,59418],{},[898,59407,29661],{},[1708,59409,1710],{},[2505,59411,2507],{},[1708,59413,1883],{"separator":1882},[2505,59415,3132],{},[1708,59417,1883],{"separator":1882},[2505,59419,3121],{},[902,59421,59422],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,59425,59427],{"className":59426},[886],[888,59428,59429],{"xmlns":890},[892,59430,59431,59461],{},[895,59432,59433,59441,59443,59451,59453],{},[4754,59434,59435,59437,59439],{},[898,59436,1688],{},[2505,59438,2507],{},[898,59440,16183],{},[1708,59442,1883],{"separator":1882},[4754,59444,59445,59447,59449],{},[898,59446,1688],{},[2505,59448,3132],{},[898,59450,16183],{},[1708,59452,1883],{"separator":1882},[4754,59454,59455,59457,59459],{},[898,59456,1688],{},[2505,59458,3121],{},[898,59460,16183],{},[902,59462,59463],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,59465,59467],{"className":59466},[886],[888,59468,59469],{"xmlns":890},[892,59470,59471,59501],{},[895,59472,59473,59481,59483,59491,59493],{},[4754,59474,59475,59477,59479],{},[898,59476,1747],{},[2505,59478,2507],{},[898,59480,16183],{},[1708,59482,1883],{"separator":1882},[4754,59484,59485,59487,59489],{},[898,59486,1747],{},[2505,59488,3132],{},[898,59490,16183],{},[1708,59492,1883],{"separator":1882},[4754,59494,59495,59497,59499],{},[898,59496,1747],{},[2505,59498,3121],{},[898,59500,16183],{},[902,59502,59503],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,59505,59506,59509,59510,59546,59547,2155],{},[38,59507,59508],{},"2.13"," Jsou dány poptávka ",[883,59511,59513],{"className":59512},[886],[888,59514,59515],{"xmlns":890},[892,59516,59517,59543],{},[895,59518,59519,59521,59523,59525,59527,59529,59531,59533,59535,59537,59539,59541],{},[898,59520,1747],{},[1708,59522,1710],{},[898,59524,16117],{},[1708,59526,1716],{"stretchy":1715},[898,59528,1688],{},[1708,59530,1721],{"stretchy":1715},[1708,59532,1710],{},[1708,59534,2726],{},[2505,59536,5867],{},[898,59538,1688],{},[1708,59540,2019],{},[2505,59542,12513],{},[902,59544,59545],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,59548,59550],{"className":59549},[886],[888,59551,59552],{"xmlns":890},[892,59553,59554,59578],{},[895,59555,59556,59558,59560,59562,59564,59566,59568,59570,59572,59574,59576],{},[898,59557,1747],{},[1708,59559,1710],{},[898,59561,1981],{},[1708,59563,1716],{"stretchy":1715},[898,59565,1688],{},[1708,59567,1721],{"stretchy":1715},[1708,59569,1710],{},[2505,59571,3121],{},[898,59573,1688],{},[1708,59575,2019],{},[2505,59577,4003],{},[902,59579,59580],{"encoding":904},"P = S(Q) = 3Q + 10",[120,59582,59583,59620,59684,59744],{},[123,59584,59585,59586,58484,59603,2155],{},"(a) Určete rovnovážné množství ",[883,59587,59589],{"className":59588},[886],[888,59590,59591],{"xmlns":890},[892,59592,59593,59601],{},[895,59594,59595],{},[1753,59596,59597,59599],{},[898,59598,1688],{},[898,59600,16183],{},[902,59602,54233],{"encoding":904},[883,59604,59606],{"className":59605},[886],[888,59607,59608],{"xmlns":890},[892,59609,59610,59618],{},[895,59611,59612],{},[1753,59613,59614,59616],{},[898,59615,1747],{},[898,59617,16183],{},[902,59619,53298],{"encoding":904},[123,59621,59622,59623,59641,59642,59662,59663,59683],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,59624,59626],{"className":59625},[886],[888,59627,59628],{"xmlns":890},[892,59629,59630,59638],{},[895,59631,59632,59634,59636],{},[898,59633,1978],{},[1708,59635,1710],{},[2505,59637,5967],{},[902,59639,59640],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,59643,59645],{"className":59644},[886],[888,59646,59647],{"xmlns":890},[892,59648,59649,59659],{},[895,59650,59651],{},[4754,59652,59653,59655,59657],{},[898,59654,1688],{},[2505,59656,2507],{},[898,59658,16183],{},[902,59660,59661],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,59664,59666],{"className":59665},[886],[888,59667,59668],{"xmlns":890},[892,59669,59670,59680],{},[895,59671,59672],{},[4754,59673,59674,59676,59678],{},[898,59675,1747],{},[2505,59677,2507],{},[898,59679,16183],{},[902,59681,59682],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,59685,59686,59687,59641,59704,59662,59724,59683],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,59688,59690],{"className":59689},[886],[888,59691,59692],{"xmlns":890},[892,59693,59694,59702],{},[895,59695,59696,59698,59700],{},[898,59697,1978],{},[1708,59699,1710],{},[2505,59701,5967],{},[902,59703,59640],{"encoding":904},[883,59705,59707],{"className":59706},[886],[888,59708,59709],{"xmlns":890},[892,59710,59711,59721],{},[895,59712,59713],{},[4754,59714,59715,59717,59719],{},[898,59716,1688],{},[2505,59718,3132],{},[898,59720,16183],{},[902,59722,59723],{"encoding":904},"Q_2^E",[883,59725,59727],{"className":59726},[886],[888,59728,59729],{"xmlns":890},[892,59730,59731,59741],{},[895,59732,59733],{},[4754,59734,59735,59737,59739],{},[898,59736,1747],{},[2505,59738,3132],{},[898,59740,16183],{},[902,59742,59743],{"encoding":904},"P_2^E",[123,59745,59746],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,59748,59749,59750,2155],{},"Viz též ",[207,59751,54551],{"className":59752,"dataFsResolvedFilePath":809,"href":810},[210],[198,59754,54853],{"id":59755},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,59757,59758,59509,59761,59546,59797,2155],{},[38,59759,59760],{},"2.14",[883,59762,59764],{"className":59763},[886],[888,59765,59766],{"xmlns":890},[892,59767,59768,59794],{},[895,59769,59770,59772,59774,59776,59778,59780,59782,59784,59786,59788,59790,59792],{},[898,59771,1747],{},[1708,59773,1710],{},[898,59775,207],{},[898,59777,1688],{},[1708,59779,2019],{},[898,59781,1923],{},[1708,59783,1710],{},[1708,59785,2726],{},[2505,59787,3132],{},[898,59789,1688],{},[1708,59791,2019],{},[2505,59793,9704],{},[902,59795,59796],{"encoding":904},"P = aQ + b = -2Q + 50",[883,59798,59800],{"className":59799},[886],[888,59801,59802],{"xmlns":890},[892,59803,59804,59828],{},[895,59805,59806,59808,59810,59812,59814,59816,59818,59820,59822,59824,59826],{},[898,59807,1747],{},[1708,59809,1710],{},[898,59811,14142],{},[898,59813,1688],{},[1708,59815,2019],{},[898,59817,2364],{},[1708,59819,1710],{},[2505,59821,4097],{},[898,59823,1688],{},[1708,59825,2019],{},[2505,59827,4018],{},[902,59829,59830],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,59832,59833,59869,59872,59958,60011,60091,60145],{},[123,59834,59585,59835,58484,59852,2155],{},[883,59836,59838],{"className":59837},[886],[888,59839,59840],{"xmlns":890},[892,59841,59842,59850],{},[895,59843,59844],{},[1753,59845,59846,59848],{},[898,59847,1688],{},[898,59849,16183],{},[902,59851,54233],{"encoding":904},[883,59853,59855],{"className":59854},[886],[888,59856,59857],{"xmlns":890},[892,59858,59859,59867],{},[895,59860,59861],{},[1753,59862,59863,59865],{},[898,59864,1747],{},[898,59866,16183],{},[902,59868,53298],{"encoding":904},[123,59870,59871],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,59873,59874,59875,59892,59893,14647,59906,2486,59922,59938,59939,2155],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,59876,59878],{"className":59877},[886],[888,59879,59880],{"xmlns":890},[892,59881,59882,59890],{},[895,59883,59884],{},[1753,59885,59886,59888],{},[898,59887,1688],{},[898,59889,16183],{},[902,59891,54233],{"encoding":904}," odpovídající změně ",[883,59894,59896],{"className":59895},[886],[888,59897,59898],{"xmlns":890},[892,59899,59900,59904],{},[895,59901,59902],{},[898,59903,207],{},[902,59905,207],{"encoding":904},[883,59907,59909],{"className":59908},[886],[888,59910,59911],{"xmlns":890},[892,59912,59913,59919],{},[895,59914,59915,59917],{},[1708,59916,2726],{},[2505,59918,3132],{},[902,59920,59921],{"encoding":904},"-2",[883,59923,59925],{"className":59924},[886],[888,59926,59927],{"xmlns":890},[892,59928,59929,59935],{},[895,59930,59931,59933],{},[1708,59932,2726],{},[2505,59934,3121],{},[902,59936,59937],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,59940,59942],{"className":59941},[886],[888,59943,59944],{"xmlns":890},[892,59945,59946,59956],{},[895,59947,59948],{},[4754,59949,59950,59952,59954],{},[898,59951,1688],{},[2505,59953,2507],{},[898,59955,16183],{},[902,59957,59661],{"encoding":904},[123,59959,59960,59961,59892,59978,59991,59992,2155],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,59962,59964],{"className":59963},[886],[888,59965,59966],{"xmlns":890},[892,59967,59968,59976],{},[895,59969,59970],{},[1753,59971,59972,59974],{},[898,59973,1688],{},[898,59975,16183],{},[902,59977,54233],{"encoding":904},[883,59979,59981],{"className":59980},[886],[888,59982,59983],{"xmlns":890},[892,59984,59985,59989],{},[895,59986,59987],{},[898,59988,1923],{},[902,59990,1923],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,59993,59995],{"className":59994},[886],[888,59996,59997],{"xmlns":890},[892,59998,59999,60009],{},[895,60000,60001],{},[4754,60002,60003,60005,60007],{},[898,60004,1688],{},[2505,60006,3132],{},[898,60008,16183],{},[902,60010,59723],{"encoding":904},[123,60012,60013,60014,59892,60031,14647,60044,2486,60057,59938,60071,2155],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,60015,60017],{"className":60016},[886],[888,60018,60019],{"xmlns":890},[892,60020,60021,60029],{},[895,60022,60023],{},[1753,60024,60025,60027],{},[898,60026,1688],{},[898,60028,16183],{},[902,60030,54233],{"encoding":904},[883,60032,60034],{"className":60033},[886],[888,60035,60036],{"xmlns":890},[892,60037,60038,60042],{},[895,60039,60040],{},[898,60041,14142],{},[902,60043,14142],{"encoding":904},[883,60045,60047],{"className":60046},[886],[888,60048,60049],{"xmlns":890},[892,60050,60051,60055],{},[895,60052,60053],{},[2505,60054,4097],{},[902,60056,56287],{"encoding":904},[883,60058,60060],{"className":60059},[886],[888,60061,60062],{"xmlns":890},[892,60063,60064,60068],{},[895,60065,60066],{},[2505,60067,6120],{},[902,60069,60070],{"encoding":904},"0{,}8",[883,60072,60074],{"className":60073},[886],[888,60075,60076],{"xmlns":890},[892,60077,60078,60088],{},[895,60079,60080],{},[4754,60081,60082,60084,60086],{},[898,60083,1688],{},[2505,60085,3121],{},[898,60087,16183],{},[902,60089,60090],{"encoding":904},"Q_3^E",[123,60092,60093,60094,59892,60111,60124,60125,2155],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,60095,60097],{"className":60096},[886],[888,60098,60099],{"xmlns":890},[892,60100,60101,60109],{},[895,60102,60103],{},[1753,60104,60105,60107],{},[898,60106,1688],{},[898,60108,16183],{},[902,60110,54233],{"encoding":904},[883,60112,60114],{"className":60113},[886],[888,60115,60116],{"xmlns":890},[892,60117,60118,60122],{},[895,60119,60120],{},[898,60121,2364],{},[902,60123,2364],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,60126,60128],{"className":60127},[886],[888,60129,60130],{"xmlns":890},[892,60131,60132,60142],{},[895,60133,60134],{},[4754,60135,60136,60138,60140],{},[898,60137,1688],{},[2505,60139,5867],{},[898,60141,16183],{},[902,60143,60144],{"encoding":904},"Q_4^E",[123,60146,60147,60148,60165,60166,60179,60180,33279,60193,1343,60208,33279,60221,1771,60235,33279,60248,60263,60264,2155],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,60149,60151],{"className":60150},[886],[888,60152,60153],{"xmlns":890},[892,60154,60155,60163],{},[895,60156,60157],{},[1753,60158,60159,60161],{},[898,60160,1688],{},[898,60162,16183],{},[902,60164,54233],{"encoding":904}," odpovídající změnám ",[883,60167,60169],{"className":60168},[886],[888,60170,60171],{"xmlns":890},[892,60172,60173,60177],{},[895,60174,60175],{},[898,60176,207],{},[902,60178,207],{"encoding":904}," o 1, ",[883,60181,60183],{"className":60182},[886],[888,60184,60185],{"xmlns":890},[892,60186,60187,60191],{},[895,60188,60189],{},[898,60190,1923],{},[902,60192,1923],{"encoding":904},[883,60194,60196],{"className":60195},[886],[888,60197,60198],{"xmlns":890},[892,60199,60200,60206],{},[895,60201,60202,60204],{},[1708,60203,2726],{},[2505,60205,4003],{},[902,60207,31319],{"encoding":904},[883,60209,60211],{"className":60210},[886],[888,60212,60213],{"xmlns":890},[892,60214,60215,60219],{},[895,60216,60217],{},[898,60218,14142],{},[902,60220,14142],{"encoding":904},[883,60222,60224],{"className":60223},[886],[888,60225,60226],{"xmlns":890},[892,60227,60228,60232],{},[895,60229,60230],{},[2505,60231,10909],{},[902,60233,60234],{"encoding":904},"0{,}1",[883,60236,60238],{"className":60237},[886],[888,60239,60240],{"xmlns":890},[892,60241,60242,60246],{},[895,60243,60244],{},[898,60245,2364],{},[902,60247,2364],{"encoding":904},[883,60249,60251],{"className":60250},[886],[888,60252,60253],{"xmlns":890},[892,60254,60255,60261],{},[895,60256,60257,60259],{},[1708,60258,2726],{},[2505,60260,4003],{},[902,60262,31319],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,60265,60267],{"className":60266},[886],[888,60268,60269],{"xmlns":890},[892,60270,60271,60281],{},[895,60272,60273],{},[4754,60274,60275,60277,60279],{},[898,60276,1688],{},[2505,60278,3993],{},[898,60280,16183],{},[902,60282,60283],{"encoding":904},"Q_5^E",[724,60285,60286,59509,60289,59546,60312,2155],{},[38,60287,60288],{},"2.15",[883,60290,60292],{"className":60291},[886],[888,60293,60294],{"xmlns":890},[892,60295,60296,60310],{},[895,60297,60298,60300,60302,60304,60306,60308],{},[898,60299,1747],{},[1708,60301,1710],{},[898,60303,207],{},[898,60305,1688],{},[1708,60307,2019],{},[898,60309,1923],{},[902,60311,48898],{"encoding":904},[883,60313,60315],{"className":60314},[886],[888,60316,60317],{"xmlns":890},[892,60318,60319,60333],{},[895,60320,60321,60323,60325,60327,60329,60331],{},[898,60322,1747],{},[1708,60324,1710],{},[898,60326,14142],{},[898,60328,1688],{},[1708,60330,2019],{},[898,60332,2364],{},[902,60334,52076],{"encoding":904},[120,60336,60337,60412,60429,60538,60591,60645],{},[123,60338,60339,60340,60353,60354,60379,60380,60411],{},"(a) Odvoďte redukovaný tvar pro ",[883,60341,60343],{"className":60342},[886],[888,60344,60345],{"xmlns":890},[892,60346,60347,60351],{},[895,60348,60349],{},[898,60350,1747],{},[902,60352,1747],{"encoding":904},". Stanovte podmínky pro ",[883,60355,60357],{"className":60356},[886],[888,60358,60359],{"xmlns":890},[892,60360,60361,60377],{},[895,60362,60363,60365,60367,60369,60371,60373,60375],{},[898,60364,207],{},[1708,60366,1883],{"separator":1882},[898,60368,1923],{},[1708,60370,1883],{"separator":1882},[898,60372,14142],{},[1708,60374,1883],{"separator":1882},[898,60376,2364],{},[902,60378,55114],{"encoding":904}," tak, aby rovnovážný bod ",[883,60381,60383],{"className":60382},[886],[888,60384,60385],{"xmlns":890},[892,60386,60387,60409],{},[895,60388,60389,60391,60393,60399,60401,60407],{},[898,60390,16183],{},[1708,60392,6940],{"stretchy":1715},[1753,60394,60395,60397],{},[898,60396,1688],{},[898,60398,16183],{},[1708,60400,1883],{"separator":1882},[1753,60402,60403,60405],{},[898,60404,1747],{},[898,60406,16183],{},[1708,60408,6981],{"stretchy":1715},[902,60410,53199],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,60413,60414,60415,60428],{},"(b) Vypočtěte multiplikátory pro ",[883,60416,60418],{"className":60417},[886],[888,60419,60420],{"xmlns":890},[892,60421,60422,60426],{},[895,60423,60424],{},[898,60425,1747],{},[902,60427,1747],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,60430,60431,60432,1343,60452,1343,60470,1343,60488,60506,60507,60524,60525,2155],{},"(c) Pro hodnoty parametrů ",[883,60433,60435],{"className":60434},[886],[888,60436,60437],{"xmlns":890},[892,60438,60439,60449],{},[895,60440,60441,60443,60445,60447],{},[898,60442,207],{},[1708,60444,1710],{},[1708,60446,2726],{},[2505,60448,3132],{},[902,60450,60451],{"encoding":904},"a = -2",[883,60453,60455],{"className":60454},[886],[888,60456,60457],{"xmlns":890},[892,60458,60459,60467],{},[895,60460,60461,60463,60465],{},[898,60462,1923],{},[1708,60464,1710],{},[2505,60466,17132],{},[902,60468,60469],{"encoding":904},"b = 40",[883,60471,60473],{"className":60472},[886],[888,60474,60475],{"xmlns":890},[892,60476,60477,60485],{},[895,60478,60479,60481,60483],{},[898,60480,14142],{},[1708,60482,1710],{},[2505,60484,6097],{},[902,60486,60487],{"encoding":904},"c = 0{,}5",[883,60489,60491],{"className":60490},[886],[888,60492,60493],{"xmlns":890},[892,60494,60495,60503],{},[895,60496,60497,60499,60501],{},[898,60498,2364],{},[1708,60500,1710],{},[2505,60502,4003],{},[902,60504,60505],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,60508,60510],{"className":60509},[886],[888,60511,60512],{"xmlns":890},[892,60513,60514,60522],{},[895,60515,60516],{},[1753,60517,60518,60520],{},[898,60519,1747],{},[898,60521,16183],{},[902,60523,53298],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,60526,60528],{"className":60527},[886],[888,60529,60530],{"xmlns":890},[892,60531,60532,60536],{},[895,60533,60534],{},[898,60535,1747],{},[902,60537,1747],{"encoding":904},[123,60539,60540,60541,59892,60558,60571,60572,2155],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,60542,60544],{"className":60543},[886],[888,60545,60546],{"xmlns":890},[892,60547,60548,60556],{},[895,60549,60550],{},[1753,60551,60552,60554],{},[898,60553,1747],{},[898,60555,16183],{},[902,60557,53298],{"encoding":904},[883,60559,60561],{"className":60560},[886],[888,60562,60563],{"xmlns":890},[892,60564,60565,60569],{},[895,60566,60567],{},[898,60568,207],{},[902,60570,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,60573,60575],{"className":60574},[886],[888,60576,60577],{"xmlns":890},[892,60578,60579,60589],{},[895,60580,60581],{},[4754,60582,60583,60585,60587],{},[898,60584,1747],{},[2505,60586,2507],{},[898,60588,16183],{},[902,60590,59682],{"encoding":904},[123,60592,60593,60594,60611,60612,60625,60626,2155],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,60595,60597],{"className":60596},[886],[888,60598,60599],{"xmlns":890},[892,60600,60601,60609],{},[895,60602,60603],{},[1753,60604,60605,60607],{},[898,60606,1747],{},[898,60608,16183],{},[902,60610,53298],{"encoding":904}," odpovídající poklesu ",[883,60613,60615],{"className":60614},[886],[888,60616,60617],{"xmlns":890},[892,60618,60619,60623],{},[895,60620,60621],{},[898,60622,207],{},[902,60624,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,60627,60629],{"className":60628},[886],[888,60630,60631],{"xmlns":890},[892,60632,60633,60643],{},[895,60634,60635],{},[4754,60636,60637,60639,60641],{},[898,60638,1747],{},[2505,60640,3132],{},[898,60642,16183],{},[902,60644,59743],{"encoding":904},[123,60646,60647,60648,60165,60665,60678,60679,2486,60692,1771,60707,60720,60721,2155],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,60649,60651],{"className":60650},[886],[888,60652,60653],{"xmlns":890},[892,60654,60655,60663],{},[895,60656,60657],{},[1753,60658,60659,60661],{},[898,60660,1747],{},[898,60662,16183],{},[902,60664,53298],{"encoding":904},[883,60666,60668],{"className":60667},[886],[888,60669,60670],{"xmlns":890},[892,60671,60672,60676],{},[895,60673,60674],{},[898,60675,207],{},[902,60677,207],{"encoding":904}," na 35, ",[883,60680,60682],{"className":60681},[886],[888,60683,60684],{"xmlns":890},[892,60685,60686,60690],{},[895,60687,60688],{},[898,60689,14142],{},[902,60691,14142],{"encoding":904},[883,60693,60695],{"className":60694},[886],[888,60696,60697],{"xmlns":890},[892,60698,60699,60704],{},[895,60700,60701],{},[2505,60702,60703],{},"0,7",[902,60705,60706],{"encoding":904},"0{,}7",[883,60708,60710],{"className":60709},[886],[888,60711,60712],{"xmlns":890},[892,60713,60714,60718],{},[895,60715,60716],{},[898,60717,2364],{},[902,60719,2364],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,60722,60724],{"className":60723},[886],[888,60725,60726],{"xmlns":890},[892,60727,60728,60738],{},[895,60729,60730],{},[4754,60731,60732,60734,60736],{},[898,60733,1747],{},[2505,60735,3121],{},[898,60737,16183],{},[902,60739,60740],{"encoding":904},"P_3^E",[724,60742,60743,59509,60746,59546,60774,2980,60802,1771,60828,2155],{},[38,60744,60745],{},"2.16",[883,60747,60749],{"className":60748},[886],[888,60750,60751],{"xmlns":890},[892,60752,60753,60771],{},[895,60754,60755,60757,60759,60761,60763,60765],{},[898,60756,1747],{},[1708,60758,1710],{},[898,60760,207],{},[1708,60762,2019],{},[898,60764,1923],{},[1753,60766,60767,60769],{},[898,60768,1688],{},[2505,60770,3132],{},[902,60772,60773],{"encoding":904},"P = a + bQ^2",[883,60775,60777],{"className":60776},[886],[888,60778,60779],{"xmlns":890},[892,60780,60781,60799],{},[895,60782,60783,60785,60787,60789,60791,60793],{},[898,60784,1747],{},[1708,60786,1710],{},[898,60788,14142],{},[1708,60790,2019],{},[898,60792,2364],{},[1753,60794,60795,60797],{},[898,60796,1688],{},[2505,60798,3132],{},[902,60800,60801],{"encoding":904},"P = c + dQ^2",[883,60803,60805],{"className":60804},[886],[888,60806,60807],{"xmlns":890},[892,60808,60809,60825],{},[895,60810,60811,60813,60815,60817,60819,60821,60823],{},[898,60812,207],{},[1708,60814,1883],{"separator":1882},[898,60816,14142],{},[1708,60818,1883],{"separator":1882},[898,60820,2364],{},[1708,60822,2854],{},[2505,60824,2784],{},[902,60826,60827],{"encoding":904},"a, c, d > 0",[883,60829,60831],{"className":60830},[886],[888,60832,60833],{"xmlns":890},[892,60834,60835,60843],{},[895,60836,60837,60839,60841],{},[898,60838,1923],{},[1708,60840,2932],{},[2505,60842,2784],{},[902,60844,60845],{"encoding":904},"b \u003C 0",[120,60847,60848,60896,60912,61019,61071,61123,61232,61248,61347,61400],{},[123,60849,60339,60850,60863,60864,60895],{},[883,60851,60853],{"className":60852},[886],[888,60854,60855],{"xmlns":890},[892,60856,60857,60861],{},[895,60858,60859],{},[898,60860,1688],{},[902,60862,1688],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,60865,60867],{"className":60866},[886],[888,60868,60869],{"xmlns":890},[892,60870,60871,60893],{},[895,60872,60873,60875,60877,60883,60885,60891],{},[898,60874,16183],{},[1708,60876,6940],{"stretchy":1715},[1753,60878,60879,60881],{},[898,60880,1688],{},[898,60882,16183],{},[1708,60884,1883],{"separator":1882},[1753,60886,60887,60889],{},[898,60888,1747],{},[898,60890,16183],{},[1708,60892,6981],{"stretchy":1715},[902,60894,53199],{"encoding":904}," patřil do 1. kvadrantu.",[123,60897,60414,60898,60911],{},[883,60899,60901],{"className":60900},[886],[888,60902,60903],{"xmlns":890},[892,60904,60905,60909],{},[895,60906,60907],{},[898,60908,1688],{},[902,60910,1688],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,60913,60431,60914,1343,60932,1343,60952,1343,60970,60988,60989,60524,61006,2155],{},[883,60915,60917],{"className":60916},[886],[888,60918,60919],{"xmlns":890},[892,60920,60921,60929],{},[895,60922,60923,60925,60927],{},[898,60924,207],{},[1708,60926,1710],{},[2505,60928,9238],{},[902,60930,60931],{"encoding":904},"a = 100",[883,60933,60935],{"className":60934},[886],[888,60936,60937],{"xmlns":890},[892,60938,60939,60949],{},[895,60940,60941,60943,60945,60947],{},[898,60942,1923],{},[1708,60944,1710],{},[1708,60946,2726],{},[2505,60948,2507],{},[902,60950,60951],{"encoding":904},"b = -1",[883,60953,60955],{"className":60954},[886],[888,60956,60957],{"xmlns":890},[892,60958,60959,60967],{},[895,60960,60961,60963,60965],{},[898,60962,14142],{},[1708,60964,1710],{},[2505,60966,4018],{},[902,60968,60969],{"encoding":904},"c = 20",[883,60971,60973],{"className":60972},[886],[888,60974,60975],{"xmlns":890},[892,60976,60977,60985],{},[895,60978,60979,60981,60983],{},[898,60980,2364],{},[1708,60982,1710],{},[2505,60984,2507],{},[902,60986,60987],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,60990,60992],{"className":60991},[886],[888,60993,60994],{"xmlns":890},[892,60995,60996,61004],{},[895,60997,60998],{},[1753,60999,61000,61002],{},[898,61001,1688],{},[898,61003,16183],{},[902,61005,54233],{"encoding":904},[883,61007,61009],{"className":61008},[886],[888,61010,61011],{"xmlns":890},[892,61012,61013,61017],{},[895,61014,61015],{},[898,61016,1688],{},[902,61018,1688],{"encoding":904},[123,61020,59960,61021,59892,61038,61051,61052,2155],{},[883,61022,61024],{"className":61023},[886],[888,61025,61026],{"xmlns":890},[892,61027,61028,61036],{},[895,61029,61030],{},[1753,61031,61032,61034],{},[898,61033,1688],{},[898,61035,16183],{},[902,61037,54233],{"encoding":904},[883,61039,61041],{"className":61040},[886],[888,61042,61043],{"xmlns":890},[892,61044,61045,61049],{},[895,61046,61047],{},[898,61048,207],{},[902,61050,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,61053,61055],{"className":61054},[886],[888,61056,61057],{"xmlns":890},[892,61058,61059,61069],{},[895,61060,61061],{},[4754,61062,61063,61065,61067],{},[898,61064,1688],{},[2505,61066,2507],{},[898,61068,16183],{},[902,61070,59661],{"encoding":904},[123,61072,60013,61073,59892,61090,61103,61104,2155],{},[883,61074,61076],{"className":61075},[886],[888,61077,61078],{"xmlns":890},[892,61079,61080,61088],{},[895,61081,61082],{},[1753,61083,61084,61086],{},[898,61085,1688],{},[898,61087,16183],{},[902,61089,54233],{"encoding":904},[883,61091,61093],{"className":61092},[886],[888,61094,61095],{"xmlns":890},[892,61096,61097,61101],{},[895,61098,61099],{},[898,61100,14142],{},[902,61102,14142],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,61105,61107],{"className":61106},[886],[888,61108,61109],{"xmlns":890},[892,61110,61111,61121],{},[895,61112,61113],{},[4754,61114,61115,61117,61119],{},[898,61116,1688],{},[2505,61118,3132],{},[898,61120,16183],{},[902,61122,59723],{"encoding":904},[123,61124,60093,61125,60165,61142,61155,61156,2486,61169,61184,61185,61198,61199,61212,61213,2155],{},[883,61126,61128],{"className":61127},[886],[888,61129,61130],{"xmlns":890},[892,61131,61132,61140],{},[895,61133,61134],{},[1753,61135,61136,61138],{},[898,61137,1688],{},[898,61139,16183],{},[902,61141,54233],{"encoding":904},[883,61143,61145],{"className":61144},[886],[888,61146,61147],{"xmlns":890},[892,61148,61149,61153],{},[895,61150,61151],{},[898,61152,207],{},[902,61154,207],{"encoding":904}," na 110, poklesu ",[883,61157,61159],{"className":61158},[886],[888,61160,61161],{"xmlns":890},[892,61162,61163,61167],{},[895,61164,61165],{},[898,61166,1923],{},[902,61168,1923],{"encoding":904},[883,61170,61172],{"className":61171},[886],[888,61173,61174],{"xmlns":890},[892,61175,61176,61182],{},[895,61177,61178,61180],{},[1708,61179,2726],{},[2505,61181,3132],{},[902,61183,59921],{"encoding":904},", růstu ",[883,61186,61188],{"className":61187},[886],[888,61189,61190],{"xmlns":890},[892,61191,61192,61196],{},[895,61193,61194],{},[898,61195,14142],{},[902,61197,14142],{"encoding":904}," na 25 a růstu ",[883,61200,61202],{"className":61201},[886],[888,61203,61204],{"xmlns":890},[892,61205,61206,61210],{},[895,61207,61208],{},[898,61209,2364],{},[902,61211,2364],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,61214,61216],{"className":61215},[886],[888,61217,61218],{"xmlns":890},[892,61219,61220,61230],{},[895,61221,61222],{},[4754,61223,61224,61226,61228],{},[898,61225,1688],{},[2505,61227,3121],{},[898,61229,16183],{},[902,61231,60090],{"encoding":904},[123,61233,61234,61235,60911],{},"(i) Vypočtěte multiplikátory pro ",[883,61236,61238],{"className":61237},[886],[888,61239,61240],{"xmlns":890},[892,61241,61242,61246],{},[895,61243,61244],{},[898,61245,1747],{},[902,61247,1747],{"encoding":904},[123,61249,61250,61251,60524,61268,61281,61282,59892,61299,2486,61312,61327,61328,2155],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,61252,61254],{"className":61253},[886],[888,61255,61256],{"xmlns":890},[892,61257,61258,61266],{},[895,61259,61260],{},[1753,61261,61262,61264],{},[898,61263,1747],{},[898,61265,16183],{},[902,61267,53298],{"encoding":904},[883,61269,61271],{"className":61270},[886],[888,61272,61273],{"xmlns":890},[892,61274,61275,61279],{},[895,61276,61277],{},[898,61278,1747],{},[902,61280,1747],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,61283,61285],{"className":61284},[886],[888,61286,61287],{"xmlns":890},[892,61288,61289,61297],{},[895,61290,61291],{},[1753,61292,61293,61295],{},[898,61294,1747],{},[898,61296,16183],{},[902,61298,53298],{"encoding":904},[883,61300,61302],{"className":61301},[886],[888,61303,61304],{"xmlns":890},[892,61305,61306,61310],{},[895,61307,61308],{},[898,61309,207],{},[902,61311,207],{"encoding":904},[883,61313,61315],{"className":61314},[886],[888,61316,61317],{"xmlns":890},[892,61318,61319,61325],{},[895,61320,61321,61323],{},[1708,61322,2726],{},[2505,61324,3121],{},[902,61326,59937],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,61329,61331],{"className":61330},[886],[888,61332,61333],{"xmlns":890},[892,61334,61335,61345],{},[895,61336,61337],{},[4754,61338,61339,61341,61343],{},[898,61340,1747],{},[2505,61342,2507],{},[898,61344,16183],{},[902,61346,59682],{"encoding":904},[123,61348,61349,61350,59892,61367,61380,61381,2155],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,61351,61353],{"className":61352},[886],[888,61354,61355],{"xmlns":890},[892,61356,61357,61365],{},[895,61358,61359],{},[1753,61360,61361,61363],{},[898,61362,1747],{},[898,61364,16183],{},[902,61366,53298],{"encoding":904},[883,61368,61370],{"className":61369},[886],[888,61371,61372],{"xmlns":890},[892,61373,61374,61378],{},[895,61375,61376],{},[898,61377,207],{},[902,61379,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,61382,61384],{"className":61383},[886],[888,61385,61386],{"xmlns":890},[892,61387,61388,61398],{},[895,61389,61390],{},[4754,61391,61392,61394,61396],{},[898,61393,1747],{},[2505,61395,3132],{},[898,61397,16183],{},[902,61399,59743],{"encoding":904},[123,61401,61402,61403,60611,61420,61433,61434,2486,61447,61184,61462,61475,61476,61489,61490,2155],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,61404,61406],{"className":61405},[886],[888,61407,61408],{"xmlns":890},[892,61409,61410,61418],{},[895,61411,61412],{},[1753,61413,61414,61416],{},[898,61415,1747],{},[898,61417,16183],{},[902,61419,53298],{"encoding":904},[883,61421,61423],{"className":61422},[886],[888,61424,61425],{"xmlns":890},[892,61426,61427,61431],{},[895,61428,61429],{},[898,61430,207],{},[902,61432,207],{"encoding":904}," na 90, poklesu ",[883,61435,61437],{"className":61436},[886],[888,61438,61439],{"xmlns":890},[892,61440,61441,61445],{},[895,61442,61443],{},[898,61444,1923],{},[902,61446,1923],{"encoding":904},[883,61448,61450],{"className":61449},[886],[888,61451,61452],{"xmlns":890},[892,61453,61454,61460],{},[895,61455,61456,61458],{},[1708,61457,2726],{},[2505,61459,3121],{},[902,61461,59937],{"encoding":904},[883,61463,61465],{"className":61464},[886],[888,61466,61467],{"xmlns":890},[892,61468,61469,61473],{},[895,61470,61471],{},[898,61472,14142],{},[902,61474,14142],{"encoding":904}," na 30 a růstu ",[883,61477,61479],{"className":61478},[886],[888,61480,61481],{"xmlns":890},[892,61482,61483,61487],{},[895,61484,61485],{},[898,61486,2364],{},[902,61488,2364],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,61491,61493],{"className":61492},[886],[888,61494,61495],{"xmlns":890},[892,61496,61497,61507],{},[895,61498,61499],{},[4754,61500,61501,61503,61505],{},[898,61502,1747],{},[2505,61504,3121],{},[898,61506,16183],{},[902,61508,60740],{"encoding":904},[198,61510,820],{"id":61511},"přebytek-spotřebitele-a-výrobce-1",[724,61513,61514,59509,61517,59546,61553,2155],{},[38,61515,61516],{},"2.17",[883,61518,61520],{"className":61519},[886],[888,61521,61522],{"xmlns":890},[892,61523,61524,61550],{},[895,61525,61526,61528,61530,61532,61534,61536,61538,61540,61542,61544],{},[898,61527,1747],{},[1708,61529,1710],{},[898,61531,16117],{},[1708,61533,1716],{"stretchy":1715},[898,61535,1688],{},[1708,61537,1721],{"stretchy":1715},[1708,61539,1710],{},[2505,61541,26919],{},[1708,61543,2726],{},[1753,61545,61546,61548],{},[898,61547,1688],{},[2505,61549,3132],{},[902,61551,61552],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,61554,61556],{"className":61555},[886],[888,61557,61558],{"xmlns":890},[892,61559,61560,61586],{},[895,61561,61562,61564,61566,61568,61570,61572,61574,61576,61578,61580],{},[898,61563,1747],{},[1708,61565,1710],{},[898,61567,1981],{},[1708,61569,1716],{"stretchy":1715},[898,61571,1688],{},[1708,61573,1721],{"stretchy":1715},[1708,61575,1710],{},[2505,61577,3121],{},[1708,61579,2019],{},[1753,61581,61582,61584],{},[898,61583,1688],{},[2505,61585,3132],{},[902,61587,61588],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,61590,61591,61594],{},[123,61592,61593],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,61595,61596],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,61598,61599,59509,61602,59546,61636,2155],{},[38,61600,61601],{},"2.18",[883,61603,61605],{"className":61604},[886],[888,61606,61607],{"xmlns":890},[892,61608,61609,61633],{},[895,61610,61611,61613,61615,61617,61619,61621,61623,61625,61627,61629,61631],{},[898,61612,1747],{},[1708,61614,1710],{},[898,61616,16117],{},[1708,61618,1716],{"stretchy":1715},[898,61620,1688],{},[1708,61622,1721],{"stretchy":1715},[1708,61624,1710],{},[2505,61626,4013],{},[1708,61628,2726],{},[2505,61630,3132],{},[898,61632,1688],{},[902,61634,61635],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,61637,61639],{"className":61638},[886],[888,61640,61641],{"xmlns":890},[892,61642,61643,61669],{},[895,61644,61645,61647,61649,61651,61653,61655,61657,61659,61661,61663],{},[898,61646,1747],{},[1708,61648,1710],{},[898,61650,1981],{},[1708,61652,1716],{"stretchy":1715},[898,61654,1688],{},[1708,61656,1721],{"stretchy":1715},[1708,61658,1710],{},[2505,61660,3121],{},[1708,61662,2019],{},[1753,61664,61665,61667],{},[898,61666,1688],{},[2505,61668,3132],{},[902,61670,61588],{"encoding":904},[120,61672,61673,61693,61696,61699],{},[123,61674,61675,61676,2155],{},"(a) Vypočtěte rovnovážné množství ",[883,61677,61679],{"className":61678},[886],[888,61680,61681],{"xmlns":890},[892,61682,61683,61691],{},[895,61684,61685],{},[1753,61686,61687,61689],{},[898,61688,1688],{},[898,61690,16183],{},[902,61692,54233],{"encoding":904},[123,61694,61695],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,61697,61698],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,61700,61701],{},"(c) Graficky interpretujte.",[48808,61703],{},[115,61705,10753],{"id":10752},[152,61707,61708,61711,61714,61717,61720,61723,61726,61729,61732,61735,61738,61741,61744,61747],{},[123,61709,61710],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,61712,61713],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,61715,61716],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,61718,61719],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,61721,61722],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,61724,61725],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,61727,61728],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,61730,61731],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,61733,61734],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,61736,61737],{},"K čemu slouží multiplikátory?",[123,61739,61740],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,61742,61743],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,61745,61746],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,61748,61749],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[48808,61751],{},[115,61753,12596],{"id":12595},[724,61755,61756],{},[38,61757,25046],{},[120,61759,61760,61795,61800,61830,61835,61898,61924,61929,61959,61968,61975,61981],{},[123,61761,61762,1695,61765,13826,61768,1729,61770,1343,61793],{},[38,61763,61764],{},"Poptávané množství",[614,61766,61767],{},"quantity demanded",[38,61769,39852],{},[883,61771,61773],{"className":61772},[886],[888,61774,61775],{"xmlns":890},[892,61776,61777,61791],{},[895,61778,61779,61781,61783,61785,61787,61789],{},[898,61780,1688],{},[1708,61782,1710],{},[898,61784,16117],{},[1708,61786,1716],{"stretchy":1715},[898,61788,1747],{},[1708,61790,1721],{"stretchy":1715},[902,61792,16126],{"encoding":904},[38,61794,49286],{},[123,61796,61797,61799],{},[38,61798,49293],{}," — substituční + důchodový efekt",[123,61801,61802,1729,61805],{},[38,61803,61804],{},"Reálné cenové rozpětí",[883,61806,61808],{"className":61807},[886],[888,61809,61810],{"xmlns":890},[892,61811,61812,61828],{},[895,61813,61814,61816,61818,61820,61826],{},[1708,61815,1716],{"stretchy":1715},[2505,61817,2784],{},[1708,61819,1883],{"separator":1882},[1743,61821,61822,61824],{},[898,61823,1747],{},[2505,61825,2784],{},[1708,61827,1721],{"stretchy":1715},[902,61829,49494],{"encoding":904},[123,61831,61832,22983],{},[38,61833,61834],{},"Homogenita poptávky",[123,61836,61837,1729,61840,1343,61863,1343,61880,61897],{},[38,61838,61839],{},"Lineární poptávka",[883,61841,61843],{"className":61842},[886],[888,61844,61845],{"xmlns":890},[892,61846,61847,61861],{},[895,61848,61849,61851,61853,61855,61857,61859],{},[898,61850,1747],{},[1708,61852,1710],{},[898,61854,207],{},[898,61856,1688],{},[1708,61858,2019],{},[898,61860,1923],{},[902,61862,48898],{"encoding":904},[883,61864,61866],{"className":61865},[886],[888,61867,61868],{"xmlns":890},[892,61869,61870,61878],{},[895,61871,61872,61874,61876],{},[898,61873,207],{},[1708,61875,2932],{},[2505,61877,2784],{},[902,61879,3154],{"encoding":904},[883,61881,61883],{"className":61882},[886],[888,61884,61885],{"xmlns":890},[892,61886,61887,61895],{},[895,61888,61889,61891,61893],{},[898,61890,1923],{},[1708,61892,2854],{},[2505,61894,2784],{},[902,61896,3172],{"encoding":904}," — nedokonalá konkurence",[123,61899,61900,12636,61903],{},[38,61901,61902],{},"Dokonalá konkurence",[883,61904,61906],{"className":61905},[886],[888,61907,61908],{"xmlns":890},[892,61909,61910,61922],{},[895,61911,61912,61914,61916],{},[898,61913,1747],{},[1708,61915,1710],{},[1753,61917,61918,61920],{},[898,61919,1747],{},[1708,61921,2417],{},[902,61923,16285],{"encoding":904},[123,61925,61926,61928],{},[38,61927,50062],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,61930,61931,1729,61933,1343,61957],{},[38,61932,43571],{},[883,61934,61936],{"className":61935},[886],[888,61937,61938],{"xmlns":890},[892,61939,61940,61954],{},[895,61941,61942,61944,61946,61948,61950,61952],{},[898,61943,1688],{},[1708,61945,1710],{},[898,61947,16183],{},[1708,61949,1716],{"stretchy":1715},[898,61951,21035],{},[1708,61953,1721],{"stretchy":1715},[902,61955,61956],{"encoding":904},"Q = E(Y)",[38,61958,50258],{},[123,61960,61961,61964,61965,61967],{},[38,61962,61963],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,61966,50703],{}," zboží",[123,61969,61970,1771,61972,61974],{},[38,61971,51709],{},[38,61973,51656],{}," — znaménka zkřížených koeficientů",[123,61976,61977,61980],{},[38,61978,61979],{},"Dvoukomoditní trh"," (2.6)",[123,61982,61983,1695,61986,1721],{},[38,61984,61985],{},"Posun poptávky",[614,61987,50761],{},[724,61989,61990],{},[38,61991,25010],{},[120,61993,61994,62027,62031,62076],{},[123,61995,61996,1695,61998,13826,62000,1729,62002,1343,62025],{},[38,61997,52103],{},[614,61999,52106],{},[38,62001,52277],{},[883,62003,62005],{"className":62004},[886],[888,62006,62007],{"xmlns":890},[892,62008,62009,62023],{},[895,62010,62011,62013,62015,62017,62019,62021],{},[898,62012,1688],{},[1708,62014,1710],{},[898,62016,1981],{},[1708,62018,1716],{"stretchy":1715},[898,62020,1747],{},[1708,62022,1721],{"stretchy":1715},[902,62024,20591],{"encoding":904},[38,62026,52353],{},[123,62028,62029],{},[38,62030,52360],{},[123,62032,62033,1729,62036,1343,62059],{},[38,62034,62035],{},"Lineární nabídka",[883,62037,62039],{"className":62038},[886],[888,62040,62041],{"xmlns":890},[892,62042,62043,62057],{},[895,62044,62045,62047,62049,62051,62053,62055],{},[898,62046,1747],{},[1708,62048,1710],{},[898,62050,14142],{},[898,62052,1688],{},[1708,62054,2019],{},[898,62056,2364],{},[902,62058,52076],{"encoding":904},[883,62060,62062],{"className":62061},[886],[888,62063,62064],{"xmlns":890},[892,62065,62066,62074],{},[895,62067,62068,62070,62072],{},[898,62069,14142],{},[1708,62071,2854],{},[2505,62073,2784],{},[902,62075,52094],{"encoding":904},[123,62077,62078,1695,62081,1721],{},[38,62079,62080],{},"Posun nabídky",[614,62082,52738],{},[724,62084,62085],{},[38,62086,62087],{},"Rovnováha a komparativní statika",[120,62089,62090,62169,62175],{},[123,62091,62092,1695,62094,13826,62096,1729,62099,1343,62116,1729,62119,1343,62136,1729,62138],{},[38,62093,53157],{},[614,62095,53276],{},[38,62097,62098],{},"rovnovážná cena",[883,62100,62102],{"className":62101},[886],[888,62103,62104],{"xmlns":890},[892,62105,62106,62114],{},[895,62107,62108],{},[1753,62109,62110,62112],{},[898,62111,1747],{},[898,62113,16183],{},[902,62115,53298],{"encoding":904},[38,62117,62118],{},"rovnovážné množství",[883,62120,62122],{"className":62121},[886],[888,62123,62124],{"xmlns":890},[892,62125,62126,62134],{},[895,62127,62128],{},[1753,62129,62130,62132],{},[898,62131,1688],{},[898,62133,16183],{},[902,62135,54233],{"encoding":904},[38,62137,53334],{},[883,62139,62141],{"className":62140},[886],[888,62142,62143],{"xmlns":890},[892,62144,62145,62167],{},[895,62146,62147,62149,62151,62157,62159,62165],{},[898,62148,16183],{},[1708,62150,6940],{"stretchy":1715},[1753,62152,62153,62155],{},[898,62154,1688],{},[898,62156,16183],{},[1708,62158,1883],{"separator":1882},[1753,62160,62161,62163],{},[898,62162,1747],{},[898,62164,16183],{},[1708,62166,6981],{"stretchy":1715},[902,62168,53199],{"encoding":904},[123,62170,62171,62174],{},[38,62172,62173],{},"Pravidla 1–4"," komparativní statiky",[123,62176,62177,1695,62180,1721],{},[38,62178,62179],{},"Teorém pavučiny",[614,62181,54179],{},[724,62183,62184],{},[38,62185,62186],{},"Zdanění",[120,62188,62189,62245,62293],{},[123,62190,62191,62193,62194,62219,62220,1721],{},[38,62192,62186],{}," — daň výrobci (",[883,62195,62197],{"className":62196},[886],[888,62198,62199],{"xmlns":890},[892,62200,62201,62217],{},[895,62202,62203,62209,62211,62213,62215],{},[1743,62204,62205,62207],{},[898,62206,1981],{},[2505,62208,2507],{},[1708,62210,1710],{},[898,62212,1981],{},[1708,62214,2019],{},[898,62216,1978],{},[902,62218,54584],{"encoding":904},") vs. daň spotřebiteli (",[883,62221,62223],{"className":62222},[886],[888,62224,62225],{"xmlns":890},[892,62226,62227,62243],{},[895,62228,62229,62235,62237,62239,62241],{},[1743,62230,62231,62233],{},[898,62232,16117],{},[2505,62234,3132],{},[1708,62236,1710],{},[898,62238,16117],{},[1708,62240,2726],{},[898,62242,1978],{},[902,62244,54615],{"encoding":904},[123,62246,62247,1729,62249,1343,62270],{},[38,62248,54488],{},[883,62250,62252],{"className":62251},[886],[888,62253,62254],{"xmlns":890},[892,62255,62256,62268],{},[895,62257,62258],{},[1743,62259,62260,62262],{},[898,62261,1978],{},[895,62263,62264,62266],{},[898,62265,54507],{},[898,62267,724],{},[902,62269,54512],{"encoding":904},[883,62271,62273],{"className":62272},[886],[888,62274,62275],{"xmlns":890},[892,62276,62277,62291],{},[895,62278,62279],{},[1743,62280,62281,62283],{},[898,62282,1978],{},[895,62284,62285,62287,62289],{},[898,62286,54530],{},[898,62288,14004],{},[898,62290,5498],{},[902,62292,54537],{"encoding":904},[123,62294,62295,1729,62298,1343,62327],{},[38,62296,62297],{},"Ekvivalence zdanění",[883,62299,62301],{"className":62300},[886],[888,62302,62303],{"xmlns":890},[892,62304,62305,62325],{},[895,62306,62307,62315,62317],{},[4754,62308,62309,62311,62313],{},[898,62310,1688],{},[2505,62312,2507],{},[898,62314,16183],{},[1708,62316,1710],{},[4754,62318,62319,62321,62323],{},[898,62320,1688],{},[2505,62322,3132],{},[898,62324,16183],{},[902,62326,54738],{"encoding":904},[883,62328,62330],{"className":62329},[886],[888,62331,62332],{"xmlns":890},[892,62333,62334,62358],{},[895,62335,62336,62344,62346,62348,62350],{},[4754,62337,62338,62340,62342],{},[898,62339,1747],{},[2505,62341,2507],{},[898,62343,16183],{},[1708,62345,2726],{},[898,62347,1978],{},[1708,62349,1710],{},[4754,62351,62352,62354,62356],{},[898,62353,1747],{},[2505,62355,3132],{},[898,62357,16183],{},[902,62359,54772],{"encoding":904},[724,62361,62362],{},[38,62363,38258],{},[120,62365,62366,62412,62443,62448,62454,62461],{},[123,62367,62368,1729,62370],{},[38,62369,54871],{},[883,62371,62373],{"className":62372},[886],[888,62374,62375],{"xmlns":890},[892,62376,62377,62409],{},[895,62378,62379,62385,62387,62389,62391,62393,62395,62397,62399,62401,62403,62405,62407],{},[1753,62380,62381,62383],{},[898,62382,1688],{},[898,62384,16183],{},[1708,62386,1710],{},[1708,62388,1716],{"stretchy":1715},[898,62390,1923],{},[1708,62392,2726],{},[898,62394,2364],{},[1708,62396,1721],{"stretchy":1715},[898,62398,1799],{"mathvariant":1759},[1708,62400,1716],{"stretchy":1715},[898,62402,14142],{},[1708,62404,2726],{},[898,62406,207],{},[1708,62408,1721],{"stretchy":1715},[902,62410,62411],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,62413,62414,1729,62417,62442],{},[38,62415,62416],{},"Parametry",[883,62418,62420],{"className":62419},[886],[888,62421,62422],{"xmlns":890},[892,62423,62424,62440],{},[895,62425,62426,62428,62430,62432,62434,62436,62438],{},[898,62427,207],{},[1708,62429,1883],{"separator":1882},[898,62431,1923],{},[1708,62433,1883],{"separator":1882},[898,62435,14142],{},[1708,62437,1883],{"separator":1882},[898,62439,2364],{},[902,62441,55114],{"encoding":904}," — exogenní proměnné",[123,62444,62445],{},[38,62446,62447],{},"Endogenní \u002F exogenní proměnná",[123,62449,62450,62453],{},[38,62451,62452],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,62455,62456,1343,62459],{},[38,62457,62458],{},"Komparativní statika",[38,62460,2758],{},[123,62462,62463,1729,62465,62481],{},[38,62464,14918],{},[883,62466,62468],{"className":62467},[886],[888,62469,62470],{"xmlns":890},[892,62471,62472,62478],{},[895,62473,62474,62476],{},[898,62475,2364],{},[898,62477,1688],{},[902,62479,62480],{"encoding":904},"dQ"," (2.11)",[724,62483,62484],{},[38,62485,62486],{},"Přebytky a ostatní",[120,62488,62489,62527],{},[123,62490,62491,1729,62493,62508,62509,1729,62511,62526],{},[38,62492,56761],{},[883,62494,62496],{"className":62495},[886],[888,62497,62498],{"xmlns":890},[892,62499,62500,62506],{},[895,62501,62502,62504],{},[898,62503,3455],{},[898,62505,1981],{},[902,62507,56777],{"encoding":904}," (2.14), ",[38,62510,56780],{},[883,62512,62514],{"className":62513},[886],[888,62515,62516],{"xmlns":890},[892,62517,62518,62524],{},[895,62519,62520,62522],{},[898,62521,1747],{},[898,62523,1981],{},[902,62525,56796],{"encoding":904}," (2.15)",[123,62528,62529,1343,62532,62535],{},[38,62530,62531],{},"Homo economicus",[38,62533,62534],{},"Marshallova formulace"," (1890)",[48808,62537],{},[115,62539,13763],{"id":13762},[120,62541,62542,62576,62585],{},[123,62543,62544,1729,62546,62549,62550,1343,62553,62556,62557,62560,62561,62564,62565,62568,62569,62572,62573],{},[38,62545,13770],{},[207,62547,811],{"className":62548,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,62551,820],{"className":62552,"dataFsResolvedFilePath":818,"href":819},[210],[207,62554,2162],{"className":62555,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,62558,775],{"className":62559,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,62562,784],{"className":62563,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,62566,793],{"className":62567,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,62570,13875],{"className":62571,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,62574,13830],{"className":62575,"dataFsResolvedFilePath":827,"href":828},[210],[123,62577,62578,1729,62581],{},[38,62579,62580],{},"Shrnutí přednášek:",[207,62582,62584],{"className":62583,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,62586,62587,1729,62589],{},[38,62588,13888],{},[207,62590,13894],{"className":62591,"dataFsResolvedFilePath":13892,"href":13893},[210],{"title":641,"searchDepth":642,"depth":642,"links":62593},[62594,62595,62603,62609,62616,62617,62624,62625,62626,62633,62634,62635],{"id":48636,"depth":642,"text":48637},{"id":48617,"depth":642,"text":25046,"children":62596},[62597,62598,62599,62600,62602],{"id":48901,"depth":649,"text":48902},{"id":49182,"depth":649,"text":49183},{"id":50190,"depth":649,"text":50191},{"id":50757,"depth":649,"text":62601},"Posun poptávky (shift of demand)",{"id":51261,"depth":649,"text":51262},{"id":48621,"depth":642,"text":25010,"children":62604},[62605,62606,62607],{"id":52098,"depth":649,"text":48902},{"id":10795,"depth":649,"text":10796},{"id":52734,"depth":649,"text":62608},"Posun nabídky (shift of supply)",{"id":53156,"depth":642,"text":53157,"children":62610},[62611,62612,62613,62614,62615],{"id":53268,"depth":649,"text":53269},{"id":53481,"depth":649,"text":53482},{"id":53798,"depth":649,"text":53799},{"id":54151,"depth":649,"text":54152},{"id":54182,"depth":649,"text":54183},{"id":54451,"depth":642,"text":811},{"id":54852,"depth":642,"text":54853,"children":62618},[62619,62620,62621,62622],{"id":54870,"depth":649,"text":54871},{"id":55250,"depth":649,"text":55251},{"id":55633,"depth":649,"text":55634},{"id":56086,"depth":649,"text":62623},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":23671,"depth":642,"text":820},{"id":57011,"depth":642,"text":57012},{"id":57242,"depth":642,"text":57243,"children":62627},[62628,62629,62630,62631,62632],{"id":57246,"depth":649,"text":57247},{"id":58085,"depth":649,"text":58086},{"id":58461,"depth":649,"text":53157},{"id":59755,"depth":649,"text":54853},{"id":61511,"depth":649,"text":820},{"id":10752,"depth":642,"text":10753},{"id":12595,"depth":642,"text":12596},{"id":13762,"depth":642,"text":13763},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,62642,62643,62644,29754,62645,62646],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":62649,"title":820,"body":62650,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":66926,"navigation":664,"path":66927,"seo":66928,"sources":66929,"stem":66930,"tags":66931,"type":13951,"updated":677,"__hash__":66936},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":62651,"toc":66904},[62652,62654,62722,62772,62774,62777,63035,63109,63114,63116,63135,63139,63215,63300,63302,63616,63709,63711,63730,63734,63808,63893,63896,64072,64077,64079,64498,64500,64504,64508,64744,64788,64888,64954,64957,64990,65166,65228,65358,65436,65547,65581,65779,65798,65817,65882,65886,65889,65934,65937,66055,66101,66103,66107,66455,66457,66459,66737,66739,66743,66778,66785,66858,66860,66862],[12,62653,820],{"id":23671},[1636,62655,62656],{},[724,62657,62658,1643,62660,1695,62662,62677,62678,1695,62680,62695,62696,62718,62719,2155],{},[883,62659,1642],{},[38,62661,56761],{},[883,62663,62665],{"className":62664},[886],[888,62666,62667],{"xmlns":890},[892,62668,62669,62675],{},[895,62670,62671,62673],{},[898,62672,3455],{},[898,62674,1981],{},[902,62676,56777],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,62679,56908],{},[883,62681,62683],{"className":62682},[886],[888,62684,62685],{"xmlns":890},[892,62686,62687,62693],{},[895,62688,62689,62691],{},[898,62690,1747],{},[898,62692,1981],{},[902,62694,56796],{"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 ",[883,62697,62699],{"className":62698},[886],[888,62700,62701],{"xmlns":890},[892,62702,62703,62715],{},[895,62704,62705,62707,62709,62711,62713],{},[898,62706,3455],{},[898,62708,1981],{},[1708,62710,2019],{},[898,62712,1747],{},[898,62714,1981],{},[902,62716,62717],{"encoding":904},"CS + PS"," měří ",[38,62720,62721],{},"celkový blahobyt trhu",[724,62723,62724,1695,62726,1343,62728,5149,62743,1695,62745,1343,62747,62762,62763,62767,62768,2155],{},[38,62725,56761],{},[614,62727,56815],{},[883,62729,62731],{"className":62730},[886],[888,62732,62733],{"xmlns":890},[892,62734,62735,62741],{},[895,62736,62737,62739],{},[898,62738,3455],{},[898,62740,1981],{},[902,62742,56777],{"encoding":904},[38,62744,56780],{},[614,62746,56911],{},[883,62748,62750],{"className":62749},[886],[888,62751,62752],{"xmlns":890},[892,62753,62754,62760],{},[895,62755,62756,62758],{},[898,62757,1747],{},[898,62759,1981],{},[902,62761,56796],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,62764,62766],{"className":62765,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,62769,62771],{"className":62770,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[48808,62773],{},[115,62775,1241],{"id":62776},"úvod",[724,62778,62779,62780,62803,62804,62827,62828,62845,62846,15851,62878,62910,62911,62937,62938,62941,62942,62945,62946,25893,62980,2980,63001,2155],{},"Je dána funkce poptávky ",[883,62781,62783],{"className":62782},[886],[888,62784,62785],{"xmlns":890},[892,62786,62787,62801],{},[895,62788,62789,62791,62793,62795,62797,62799],{},[898,62790,1747],{},[1708,62792,1710],{},[898,62794,16117],{},[1708,62796,1716],{"stretchy":1715},[898,62798,1688],{},[1708,62800,1721],{"stretchy":1715},[902,62802,16564],{"encoding":904},", resp. funkce nabídky ",[883,62805,62807],{"className":62806},[886],[888,62808,62809],{"xmlns":890},[892,62810,62811,62825],{},[895,62812,62813,62815,62817,62819,62821,62823],{},[898,62814,1747],{},[1708,62816,1710],{},[898,62818,1981],{},[1708,62820,1716],{"stretchy":1715},[898,62822,1688],{},[1708,62824,1721],{"stretchy":1715},[902,62826,52903],{"encoding":904},". Pro pevně zadané množství ",[883,62829,62831],{"className":62830},[886],[888,62832,62833],{"xmlns":890},[892,62834,62835,62843],{},[895,62836,62837],{},[1743,62838,62839,62841],{},[898,62840,1688],{},[2505,62842,2784],{},[902,62844,50144],{"encoding":904}," je odpovídající cena ",[883,62847,62849],{"className":62848},[886],[888,62850,62851],{"xmlns":890},[892,62852,62853,62875],{},[895,62854,62855,62861,62863,62865,62867,62873],{},[1743,62856,62857,62859],{},[898,62858,1747],{},[2505,62860,2784],{},[1708,62862,1710],{},[898,62864,16117],{},[1708,62866,1716],{"stretchy":1715},[1743,62868,62869,62871],{},[898,62870,1688],{},[2505,62872,2784],{},[1708,62874,1721],{"stretchy":1715},[902,62876,62877],{"encoding":904},"P_0 = D(Q_0)",[883,62879,62881],{"className":62880},[886],[888,62882,62883],{"xmlns":890},[892,62884,62885,62907],{},[895,62886,62887,62893,62895,62897,62899,62905],{},[1743,62888,62889,62891],{},[898,62890,1747],{},[2505,62892,2784],{},[1708,62894,1710],{},[898,62896,1981],{},[1708,62898,1716],{"stretchy":1715},[1743,62900,62901,62903],{},[898,62902,1688],{},[2505,62904,2784],{},[1708,62906,1721],{"stretchy":1715},[902,62908,62909],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,62912,62914],{"className":62913},[886],[888,62915,62916],{"xmlns":890},[892,62917,62918,62934],{},[895,62919,62920,62926,62928],{},[1743,62921,62922,62924],{},[898,62923,1747],{},[2505,62925,2784],{},[2247,62927,2659],{},[1743,62929,62930,62932],{},[898,62931,1688],{},[2505,62933,2784],{},[902,62935,62936],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,62939,62940],{},"výdaje spotřebitele",", nebo ",[38,62943,62944],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,62947,62949],{"className":62948},[886],[888,62950,62951],{"xmlns":890},[892,62952,62953,62977],{},[895,62954,62955,62957,62959,62965,62967,62969,62971],{},[2505,62956,2784],{},[2247,62958,2659],{},[1743,62960,62961,62963],{},[898,62962,1688],{},[2505,62964,2784],{},[2247,62966,2659],{},[898,62968,1786],{},[2247,62970,2659],{},[1743,62972,62973,62975],{},[898,62974,1747],{},[2505,62976,2784],{},[902,62978,62979],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,62981,62983],{"className":62982},[886],[888,62984,62985],{"xmlns":890},[892,62986,62987,62999],{},[895,62988,62989,62991,62993,62995,62997],{},[1708,62990,1716],{"stretchy":1715},[898,62992,1688],{},[1708,62994,1883],{"separator":1882},[898,62996,1747],{},[1708,62998,1721],{"stretchy":1715},[902,63000,49527],{"encoding":904},[883,63002,63004],{"className":63003},[886],[888,63005,63006],{"xmlns":890},[892,63007,63008,63032],{},[895,63009,63010,63012,63014,63016,63022,63024,63030],{},[898,63011,1786],{},[1708,63013,1710],{},[1708,63015,6940],{"stretchy":1715},[1743,63017,63018,63020],{},[898,63019,1688],{},[2505,63021,2784],{},[1708,63023,1883],{"separator":1882},[1743,63025,63026,63028],{},[898,63027,1747],{},[2505,63029,2784],{},[1708,63031,6981],{"stretchy":1715},[902,63033,63034],{"encoding":904},"A = [Q_0, P_0]",[1636,63036,63037,63041,63098],{},[724,63038,63039,7444],{},[883,63040,2518],{},[120,63042,63043,63070],{},[123,63044,63045,63046,63049,63050,5936,63052,63069],{},"Za jednotky zboží nakoupené ",[38,63047,63048],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,63051,5935],{},[883,63053,63055],{"className":63054},[886],[888,63056,63057],{"xmlns":890},[892,63058,63059,63067],{},[895,63060,63061],{},[1743,63062,63063,63065],{},[898,63064,1747],{},[2505,63066,2784],{},[902,63068,50782],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,63071,63072,63073,63075,63076,63079,63080,63097],{},"Za jednotky zboží prodané ",[38,63074,63048],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,63077,63078],{},"nižší"," cenu než ",[883,63081,63083],{"className":63082},[886],[888,63084,63085],{"xmlns":890},[892,63086,63087,63095],{},[895,63088,63089],{},[1743,63090,63091,63093],{},[898,63092,1747],{},[2505,63094,2784],{},[902,63096,50782],{"encoding":904}," — rozdíl je jeho přebytek.",[724,63099,63100,63101,63104,63105,63108],{},"Přebytek je tedy rozdíl mezi ",[614,63102,63103],{},"ochotou"," (platit \u002F prodávat) a ",[614,63106,63107],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,63110,63111],{},[3372,63112],{"alt":56806,"className":63113,"src":56808},[210,3376],[48808,63115],{},[115,63117,63119,63120,1721],{"id":63118},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,63121,63123],{"className":63122},[886],[888,63124,63125],{"xmlns":890},[892,63126,63127,63133],{},[895,63128,63129,63131],{},[898,63130,3455],{},[898,63132,1981],{},[902,63134,56777],{"encoding":904},[198,63136,63138],{"id":63137},"definice-vzorec-214","Definice (vzorec 2.14)",[724,63140,63141,63142,63165,63166,63183,63184,2788],{},"Pro poptávku ",[883,63143,63145],{"className":63144},[886],[888,63146,63147],{"xmlns":890},[892,63148,63149,63163],{},[895,63150,63151,63153,63155,63157,63159,63161],{},[898,63152,1747],{},[1708,63154,1710],{},[898,63156,16117],{},[1708,63158,1716],{"stretchy":1715},[898,63160,1688],{},[1708,63162,1721],{"stretchy":1715},[902,63164,16564],{"encoding":904}," a pevně zadané ",[883,63167,63169],{"className":63168},[886],[888,63170,63171],{"xmlns":890},[892,63172,63173,63181],{},[895,63174,63175],{},[1743,63176,63177,63179],{},[898,63178,1688],{},[2505,63180,2784],{},[902,63182,50144],{"encoding":904}," s cenou ",[883,63185,63187],{"className":63186},[886],[888,63188,63189],{"xmlns":890},[892,63190,63191,63213],{},[895,63192,63193,63199,63201,63203,63205,63211],{},[1743,63194,63195,63197],{},[898,63196,1747],{},[2505,63198,2784],{},[1708,63200,1710],{},[898,63202,16117],{},[1708,63204,1716],{"stretchy":1715},[1743,63206,63207,63209],{},[898,63208,1688],{},[2505,63210,2784],{},[1708,63212,1721],{"stretchy":1715},[902,63214,62877],{"encoding":904},[883,63216,63218],{"className":63217},[886],[888,63219,63220],{"xmlns":890,"display":2210},[892,63221,63222,63298],{},[2214,63223,63224],{"width":2216},[2218,63225,63226,63228,63292,63294],{},[2221,63227],{"width":2223},[2221,63229,63230],{},[895,63231,63232,63234,63236,63238,63244,63246,63248,63260,63262,63264,63266,63268,63270,63272,63274,63276,63282,63284,63290],{},[898,63233,3455],{},[898,63235,1981],{},[1708,63237,1716],{"stretchy":1715},[1743,63239,63240,63242],{},[898,63241,1688],{},[2505,63243,2784],{},[1708,63245,1721],{"stretchy":1715},[1708,63247,1710],{},[4754,63249,63250,63252,63254],{},[1708,63251,23056],{},[2505,63253,2784],{},[1743,63255,63256,63258],{},[898,63257,1688],{},[2505,63259,2784],{},[898,63261,16117],{},[1708,63263,1716],{"stretchy":1715},[898,63265,1688],{},[1708,63267,1721],{"stretchy":1715},[2247,63269,2659],{},[898,63271,2364],{},[898,63273,1688],{},[1708,63275,2726],{},[1743,63277,63278,63280],{},[898,63279,1747],{},[2505,63281,2784],{},[2247,63283,2659],{},[1743,63285,63286,63288],{},[898,63287,1688],{},[2505,63289,2784],{},[898,63291,2155],{"mathvariant":1759},[2221,63293],{"width":2223},[2221,63295,63296],{},[2247,63297,56900],{},[902,63299,56903],{"encoding":904},[198,63301,14425],{"id":14424},[120,63303,63304,63396,63458],{},[123,63305,63306,63346,63347,63373,63374,63377,63378,63395],{},[883,63307,63309],{"className":63308},[886],[888,63310,63311],{"xmlns":890},[892,63312,63313,63343],{},[895,63314,63315],{},[3194,63316,63317,63329,63331,63333,63335,63337,63339,63341],{"scriptlevel":2784,"displaystyle":1882},[4754,63318,63319,63321,63323],{},[1708,63320,23056],{},[2505,63322,2784],{},[1743,63324,63325,63327],{},[898,63326,1688],{},[2505,63328,2784],{},[898,63330,16117],{},[1708,63332,1716],{"stretchy":1715},[898,63334,1688],{},[1708,63336,1721],{"stretchy":1715},[2247,63338,2659],{},[898,63340,2364],{},[898,63342,1688],{},[902,63344,63345],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,63348,63350],{"className":63349},[886],[888,63351,63352],{"xmlns":890},[892,63353,63354,63370],{},[895,63355,63356,63358,63360,63362,63368],{},[1708,63357,6940],{"stretchy":1715},[2505,63359,2784],{},[1708,63361,1883],{"separator":1882},[1743,63363,63364,63366],{},[898,63365,1688],{},[2505,63367,2784],{},[1708,63369,6981],{"stretchy":1715},[902,63371,63372],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,63375,63376],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,63379,63381],{"className":63380},[886],[888,63382,63383],{"xmlns":890},[892,63384,63385,63393],{},[895,63386,63387],{},[1743,63388,63389,63391],{},[898,63390,1688],{},[2505,63392,2784],{},[902,63394,50144],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,63397,63398,63424,63425,2511],{},[883,63399,63401],{"className":63400},[886],[888,63402,63403],{"xmlns":890},[892,63404,63405,63421],{},[895,63406,63407,63413,63415],{},[1743,63408,63409,63411],{},[898,63410,1747],{},[2505,63412,2784],{},[2247,63414,2659],{},[1743,63416,63417,63419],{},[898,63418,1688],{},[2505,63420,2784],{},[902,63422,63423],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,63426,63428],{"className":63427},[886],[888,63429,63430],{"xmlns":890},[892,63431,63432,63456],{},[895,63433,63434,63436,63438,63444,63446,63448,63450],{},[2505,63435,2784],{},[2247,63437,2659],{},[1743,63439,63440,63442],{},[898,63441,1688],{},[2505,63443,2784],{},[2247,63445,2659],{},[898,63447,1786],{},[2247,63449,2659],{},[1743,63451,63452,63454],{},[898,63453,1747],{},[2505,63455,2784],{},[902,63457,62979],{"encoding":904},[123,63459,63460,63475,63476,63498,63499,63524,63525,2980,63551,1771,63583,2155],{},[883,63461,63463],{"className":63462},[886],[888,63464,63465],{"xmlns":890},[892,63466,63467,63473],{},[895,63468,63469,63471],{},[898,63470,3455],{},[898,63472,1981],{},[902,63474,56777],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,63477,63479],{"className":63478},[886],[888,63480,63481],{"xmlns":890},[892,63482,63483,63495],{},[895,63484,63485,63487,63489],{},[898,63486,1747],{},[1708,63488,1710],{},[1743,63490,63491,63493],{},[898,63492,1747],{},[2505,63494,2784],{},[902,63496,63497],{"encoding":904},"P = P_0"," v pásu ",[883,63500,63502],{"className":63501},[886],[888,63503,63504],{"xmlns":890},[892,63505,63506,63522],{},[895,63507,63508,63510,63512,63514,63520],{},[1708,63509,6940],{"stretchy":1715},[2505,63511,2784],{},[1708,63513,1883],{"separator":1882},[1743,63515,63516,63518],{},[898,63517,1688],{},[2505,63519,2784],{},[1708,63521,6981],{"stretchy":1715},[902,63523,63372],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,63526,63528],{"className":63527},[886],[888,63529,63530],{"xmlns":890},[892,63531,63532,63548],{},[895,63533,63534,63540,63542,63544,63546],{},[1743,63535,63536,63538],{},[898,63537,1747],{},[2505,63539,2784],{},[2247,63541,2659],{},[898,63543,35110],{},[2247,63545,2659],{},[898,63547,1786],{},[902,63549,63550],{"encoding":904},"P_0\\,B\\,A",[883,63552,63554],{"className":63553},[886],[888,63555,63556],{"xmlns":890},[892,63557,63558,63580],{},[895,63559,63560,63562,63564,63566,63568,63570,63572,63574,63576,63578],{},[898,63561,35110],{},[1708,63563,1710],{},[1708,63565,6940],{"stretchy":1715},[2505,63567,2784],{},[1708,63569,1883],{"separator":1882},[898,63571,16117],{},[1708,63573,1716],{"stretchy":1715},[2505,63575,2784],{},[1708,63577,1721],{"stretchy":1715},[1708,63579,6981],{"stretchy":1715},[902,63581,63582],{"encoding":904},"B = [0, D(0)]",[883,63584,63586],{"className":63585},[886],[888,63587,63588],{"xmlns":890},[892,63589,63590,63614],{},[895,63591,63592,63594,63596,63598,63604,63606,63612],{},[898,63593,1786],{},[1708,63595,1710],{},[1708,63597,6940],{"stretchy":1715},[1743,63599,63600,63602],{},[898,63601,1688],{},[2505,63603,2784],{},[1708,63605,1883],{"separator":1882},[1743,63607,63608,63610],{},[898,63609,1747],{},[2505,63611,2784],{},[1708,63613,6981],{"stretchy":1715},[902,63615,63034],{"encoding":904},[724,63617,63618],{},[614,63619,63620,63621,63634,63635,63668,63669,40989,63694,2155],{},"Obrázek 2.24: Křivka poptávky ",[883,63622,63624],{"className":63623},[886],[888,63625,63626],{"xmlns":890},[892,63627,63628,63632],{},[895,63629,63630],{},[898,63631,16117],{},[902,63633,16117],{"encoding":904},", bod ",[883,63636,63638],{"className":63637},[886],[888,63639,63640],{"xmlns":890},[892,63641,63642,63666],{},[895,63643,63644,63646,63648,63650,63656,63658,63664],{},[898,63645,1786],{},[1708,63647,1710],{},[1708,63649,6940],{"stretchy":1715},[1743,63651,63652,63654],{},[898,63653,1688],{},[2505,63655,2784],{},[1708,63657,1883],{"separator":1882},[1743,63659,63660,63662],{},[898,63661,1747],{},[2505,63663,2784],{},[1708,63665,6981],{"stretchy":1715},[902,63667,63034],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,63670,63672],{"className":63671},[886],[888,63673,63674],{"xmlns":890},[892,63675,63676,63692],{},[895,63677,63678,63684,63686,63688,63690],{},[1743,63679,63680,63682],{},[898,63681,1747],{},[2505,63683,2784],{},[2247,63685,2659],{},[898,63687,35110],{},[2247,63689,2659],{},[898,63691,1786],{},[902,63693,63550],{"encoding":904},[883,63695,63697],{"className":63696},[886],[888,63698,63699],{"xmlns":890},[892,63700,63701,63707],{},[895,63702,63703,63705],{},[898,63704,3455],{},[898,63706,1981],{},[902,63708,56777],{"encoding":904},[48808,63710],{},[115,63712,63714,63715,1721],{"id":63713},"přebytek-výrobce-psps","Přebytek výrobce (",[883,63716,63718],{"className":63717},[886],[888,63719,63720],{"xmlns":890},[892,63721,63722,63728],{},[895,63723,63724,63726],{},[898,63725,1747],{},[898,63727,1981],{},[902,63729,56796],{"encoding":904},[198,63731,63733],{"id":63732},"definice-vzorec-215","Definice (vzorec 2.15)",[724,63735,63736,63737,63165,63760,63183,63777,2788],{},"Analogicky — pro nabídku ",[883,63738,63740],{"className":63739},[886],[888,63741,63742],{"xmlns":890},[892,63743,63744,63758],{},[895,63745,63746,63748,63750,63752,63754,63756],{},[898,63747,1747],{},[1708,63749,1710],{},[898,63751,1981],{},[1708,63753,1716],{"stretchy":1715},[898,63755,1688],{},[1708,63757,1721],{"stretchy":1715},[902,63759,52903],{"encoding":904},[883,63761,63763],{"className":63762},[886],[888,63764,63765],{"xmlns":890},[892,63766,63767,63775],{},[895,63768,63769],{},[1743,63770,63771,63773],{},[898,63772,1688],{},[2505,63774,2784],{},[902,63776,50144],{"encoding":904},[883,63778,63780],{"className":63779},[886],[888,63781,63782],{"xmlns":890},[892,63783,63784,63806],{},[895,63785,63786,63792,63794,63796,63798,63804],{},[1743,63787,63788,63790],{},[898,63789,1747],{},[2505,63791,2784],{},[1708,63793,1710],{},[898,63795,1981],{},[1708,63797,1716],{"stretchy":1715},[1743,63799,63800,63802],{},[898,63801,1688],{},[2505,63803,2784],{},[1708,63805,1721],{"stretchy":1715},[902,63807,62909],{"encoding":904},[883,63809,63811],{"className":63810},[886],[888,63812,63813],{"xmlns":890,"display":2210},[892,63814,63815,63891],{},[2214,63816,63817],{"width":2216},[2218,63818,63819,63821,63885,63887],{},[2221,63820],{"width":2223},[2221,63822,63823],{},[895,63824,63825,63827,63829,63831,63837,63839,63841,63847,63849,63855,63857,63869,63871,63873,63875,63877,63879,63881,63883],{},[898,63826,1747],{},[898,63828,1981],{},[1708,63830,1716],{"stretchy":1715},[1743,63832,63833,63835],{},[898,63834,1688],{},[2505,63836,2784],{},[1708,63838,1721],{"stretchy":1715},[1708,63840,1710],{},[1743,63842,63843,63845],{},[898,63844,1747],{},[2505,63846,2784],{},[2247,63848,2659],{},[1743,63850,63851,63853],{},[898,63852,1688],{},[2505,63854,2784],{},[1708,63856,2726],{},[4754,63858,63859,63861,63863],{},[1708,63860,23056],{},[2505,63862,2784],{},[1743,63864,63865,63867],{},[898,63866,1688],{},[2505,63868,2784],{},[898,63870,1981],{},[1708,63872,1716],{"stretchy":1715},[898,63874,1688],{},[1708,63876,1721],{"stretchy":1715},[2247,63878,2659],{},[898,63880,2364],{},[898,63882,1688],{},[898,63884,2155],{"mathvariant":1759},[2221,63886],{"width":2223},[2221,63888,63889],{},[2247,63890,56996],{},[902,63892,56999],{"encoding":904},[198,63894,14425],{"id":63895},"geometrická-interpretace-1",[120,63897,63898,63946,64007],{},[123,63899,63900,12636,63925,63928,63929,2155],{},[883,63901,63903],{"className":63902},[886],[888,63904,63905],{"xmlns":890},[892,63906,63907,63923],{},[895,63908,63909,63915,63917],{},[1743,63910,63911,63913],{},[898,63912,1747],{},[2505,63914,2784],{},[2247,63916,2659],{},[1743,63918,63919,63921],{},[898,63920,1688],{},[2505,63922,2784],{},[902,63924,63423],{"encoding":904},[38,63926,63927],{},"tržba"," výrobce za prodané množství ",[883,63930,63932],{"className":63931},[886],[888,63933,63934],{"xmlns":890},[892,63935,63936,63944],{},[895,63937,63938],{},[1743,63939,63940,63942],{},[898,63941,1688],{},[2505,63943,2784],{},[902,63945,50144],{"encoding":904},[123,63947,63948,63988,63989,64006],{},[883,63949,63951],{"className":63950},[886],[888,63952,63953],{"xmlns":890},[892,63954,63955,63985],{},[895,63956,63957],{},[3194,63958,63959,63971,63973,63975,63977,63979,63981,63983],{"scriptlevel":2784,"displaystyle":1882},[4754,63960,63961,63963,63965],{},[1708,63962,23056],{},[2505,63964,2784],{},[1743,63966,63967,63969],{},[898,63968,1688],{},[2505,63970,2784],{},[898,63972,1981],{},[1708,63974,1716],{"stretchy":1715},[898,63976,1688],{},[1708,63978,1721],{"stretchy":1715},[2247,63980,2659],{},[898,63982,2364],{},[898,63984,1688],{},[902,63986,63987],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,63990,63992],{"className":63991},[886],[888,63993,63994],{"xmlns":890},[892,63995,63996,64004],{},[895,63997,63998],{},[1743,63999,64000,64002],{},[898,64001,1688],{},[2505,64003,2784],{},[902,64005,50144],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,64008,64009,64024,64025,64046,64047,2155],{},[883,64010,64012],{"className":64011},[886],[888,64013,64014],{"xmlns":890},[892,64015,64016,64022],{},[895,64017,64018,64020],{},[898,64019,1747],{},[898,64021,1981],{},[902,64023,56796],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,64026,64028],{"className":64027},[886],[888,64029,64030],{"xmlns":890},[892,64031,64032,64044],{},[895,64033,64034,64036,64038],{},[898,64035,1747],{},[1708,64037,1710],{},[1743,64039,64040,64042],{},[898,64041,1747],{},[2505,64043,2784],{},[902,64045,63497],{"encoding":904}," a křivkou nabídky v pásu ",[883,64048,64050],{"className":64049},[886],[888,64051,64052],{"xmlns":890},[892,64053,64054,64070],{},[895,64055,64056,64058,64060,64062,64068],{},[1708,64057,6940],{"stretchy":1715},[2505,64059,2784],{},[1708,64061,1883],{"separator":1882},[1743,64063,64064,64066],{},[898,64065,1688],{},[2505,64067,2784],{},[1708,64069,6981],{"stretchy":1715},[902,64071,63372],{"encoding":904},[724,64073,64074],{},[614,64075,64076],{},"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.",[48808,64078],{},[1636,64080,64081,64086],{},[724,64082,64083,64085],{},[883,64084,3465],{}," Postup výpočtu CS a PS",[152,64087,64088,64219,64329,64358,64491],{},[123,64089,64090,64091,64108,64109,64140,64141,64172,64173,2155],{},"Zjisti (nebo si zvol) množství ",[883,64092,64094],{"className":64093},[886],[888,64095,64096],{"xmlns":890},[892,64097,64098,64106],{},[895,64099,64100],{},[1743,64101,64102,64104],{},[898,64103,1688],{},[2505,64105,2784],{},[902,64107,50144],{"encoding":904}," a odpovídající cenu ",[883,64110,64112],{"className":64111},[886],[888,64113,64114],{"xmlns":890},[892,64115,64116,64138],{},[895,64117,64118,64124,64126,64128,64130,64136],{},[1743,64119,64120,64122],{},[898,64121,1747],{},[2505,64123,2784],{},[1708,64125,1710],{},[898,64127,16117],{},[1708,64129,1716],{"stretchy":1715},[1743,64131,64132,64134],{},[898,64133,1688],{},[2505,64135,2784],{},[1708,64137,1721],{"stretchy":1715},[902,64139,62877],{"encoding":904}," resp. ",[883,64142,64144],{"className":64143},[886],[888,64145,64146],{"xmlns":890},[892,64147,64148,64170],{},[895,64149,64150,64156,64158,64160,64162,64168],{},[1743,64151,64152,64154],{},[898,64153,1747],{},[2505,64155,2784],{},[1708,64157,1710],{},[898,64159,1981],{},[1708,64161,1716],{"stretchy":1715},[1743,64163,64164,64166],{},[898,64165,1688],{},[2505,64167,2784],{},[1708,64169,1721],{"stretchy":1715},[902,64171,62909],{"encoding":904},". V rovnováze platí ",[883,64174,64176],{"className":64175},[886],[888,64177,64178],{"xmlns":890},[892,64179,64180,64216],{},[895,64181,64182,64184,64186,64192,64194,64196,64198,64200,64206,64208,64210],{},[898,64183,16117],{},[1708,64185,1716],{"stretchy":1715},[1753,64187,64188,64190],{},[898,64189,1688],{},[898,64191,16183],{},[1708,64193,1721],{"stretchy":1715},[1708,64195,1710],{},[898,64197,1981],{},[1708,64199,1716],{"stretchy":1715},[1753,64201,64202,64204],{},[898,64203,1688],{},[898,64205,16183],{},[1708,64207,1721],{"stretchy":1715},[1708,64209,1710],{},[1753,64211,64212,64214],{},[898,64213,1747],{},[898,64215,16183],{},[902,64217,64218],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,64220,64221,64222,31989,64260,64275,64276,31989,64314,2511],{},"Spočti určitý integrál ",[883,64223,64225],{"className":64224},[886],[888,64226,64227],{"xmlns":890},[892,64228,64229,64257],{},[895,64230,64231,64243,64245,64247,64249,64251,64253,64255],{},[4754,64232,64233,64235,64237],{},[1708,64234,23056],{},[2505,64236,2784],{},[1743,64238,64239,64241],{},[898,64240,1688],{},[2505,64242,2784],{},[898,64244,16117],{},[1708,64246,1716],{"stretchy":1715},[898,64248,1688],{},[1708,64250,1721],{"stretchy":1715},[2247,64252,2659],{},[898,64254,2364],{},[898,64256,1688],{},[902,64258,64259],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,64261,64263],{"className":64262},[886],[888,64264,64265],{"xmlns":890},[892,64266,64267,64273],{},[895,64268,64269,64271],{},[898,64270,3455],{},[898,64272,1981],{},[902,64274,56777],{"encoding":904},") nebo ",[883,64277,64279],{"className":64278},[886],[888,64280,64281],{"xmlns":890},[892,64282,64283,64311],{},[895,64284,64285,64297,64299,64301,64303,64305,64307,64309],{},[4754,64286,64287,64289,64291],{},[1708,64288,23056],{},[2505,64290,2784],{},[1743,64292,64293,64295],{},[898,64294,1688],{},[2505,64296,2784],{},[898,64298,1981],{},[1708,64300,1716],{"stretchy":1715},[898,64302,1688],{},[1708,64304,1721],{"stretchy":1715},[2247,64306,2659],{},[898,64308,2364],{},[898,64310,1688],{},[902,64312,64313],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,64315,64317],{"className":64316},[886],[888,64318,64319],{"xmlns":890},[892,64320,64321,64327],{},[895,64322,64323,64325],{},[898,64324,1747],{},[898,64326,1981],{},[902,64328,56796],{"encoding":904},[123,64330,64331,64332,2155],{},"Sestav obdélník ",[883,64333,64335],{"className":64334},[886],[888,64336,64337],{"xmlns":890},[892,64338,64339,64355],{},[895,64340,64341,64347,64349],{},[1743,64342,64343,64345],{},[898,64344,1747],{},[2505,64346,2784],{},[1708,64348,3703],{},[1743,64350,64351,64353],{},[898,64352,1688],{},[2505,64354,2784],{},[902,64356,64357],{"encoding":904},"P_0 \\cdot Q_0",[123,64359,64360,64361],{},"Dosaď:\n",[120,64362,64363,64427],{},[123,64364,64365,64423,64424,64426],{},[883,64366,64368],{"className":64367},[886],[888,64369,64370],{"xmlns":890},[892,64371,64372,64420],{},[895,64373,64374,64376,64378,64380,64392,64394,64396,64398,64400,64402,64404,64406,64408,64414],{},[898,64375,3455],{},[898,64377,1981],{},[1708,64379,1710],{},[4754,64381,64382,64384,64386],{},[1708,64383,23056],{},[2505,64385,2784],{},[1743,64387,64388,64390],{},[898,64389,1688],{},[2505,64391,2784],{},[898,64393,16117],{},[1708,64395,1716],{"stretchy":1715},[898,64397,1688],{},[1708,64399,1721],{"stretchy":1715},[2247,64401,2659],{},[898,64403,2364],{},[898,64405,1688],{},[1708,64407,2726],{},[1743,64409,64410,64412],{},[898,64411,1747],{},[2505,64413,2784],{},[1743,64415,64416,64418],{},[898,64417,1688],{},[2505,64419,2784],{},[902,64421,64422],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,64425,9054],{}," obdélník)",[123,64428,64429,64487,64488,64490],{},[883,64430,64432],{"className":64431},[886],[888,64433,64434],{"xmlns":890},[892,64435,64436,64484],{},[895,64437,64438,64440,64442,64444,64450,64456,64458,64470,64472,64474,64476,64478,64480,64482],{},[898,64439,1747],{},[898,64441,1981],{},[1708,64443,1710],{},[1743,64445,64446,64448],{},[898,64447,1747],{},[2505,64449,2784],{},[1743,64451,64452,64454],{},[898,64453,1688],{},[2505,64455,2784],{},[1708,64457,2726],{},[4754,64459,64460,64462,64464],{},[1708,64461,23056],{},[2505,64463,2784],{},[1743,64465,64466,64468],{},[898,64467,1688],{},[2505,64469,2784],{},[898,64471,1981],{},[1708,64473,1716],{"stretchy":1715},[898,64475,1688],{},[1708,64477,1721],{"stretchy":1715},[2247,64479,2659],{},[898,64481,2364],{},[898,64483,1688],{},[902,64485,64486],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,64489,9054],{}," integrál)",[123,64492,64493,64494,64497],{},"Kontrola znaménka: obě hodnoty musí být ",[38,64495,64496],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[48808,64499],{},[115,64501,64503],{"id":64502},"příklady","Příklady",[198,64505,64507],{"id":64506},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1636,64509,64510],{},[724,64511,64512,64515,64516,59546,64539,64562,64563,1343,64583,1343,64600,1343,64617,64634,64635,64711,64712,64729,64730,64743],{},[883,64513,64514],{},"!example"," Zadání\nJsou dány poptávka ",[883,64517,64519],{"className":64518},[886],[888,64520,64521],{"xmlns":890},[892,64522,64523,64537],{},[895,64524,64525,64527,64529,64531,64533,64535],{},[898,64526,1747],{},[1708,64528,1710],{},[898,64530,207],{},[898,64532,1688],{},[1708,64534,2019],{},[898,64536,1923],{},[902,64538,48898],{"encoding":904},[883,64540,64542],{"className":64541},[886],[888,64543,64544],{"xmlns":890},[892,64545,64546,64560],{},[895,64547,64548,64550,64552,64554,64556,64558],{},[898,64549,1747],{},[1708,64551,1710],{},[898,64553,14142],{},[898,64555,1688],{},[1708,64557,2019],{},[898,64559,2364],{},[902,64561,52076],{"encoding":904}," s hodnotami ",[883,64564,64566],{"className":64565},[886],[888,64567,64568],{"xmlns":890},[892,64569,64570,64580],{},[895,64571,64572,64574,64576,64578],{},[898,64573,207],{},[1708,64575,1710],{},[1708,64577,2726],{},[2505,64579,3121],{},[902,64581,64582],{"encoding":904},"a = -3",[883,64584,64586],{"className":64585},[886],[888,64587,64588],{"xmlns":890},[892,64589,64590,64598],{},[895,64591,64592,64594,64596],{},[898,64593,1923],{},[1708,64595,1710],{},[2505,64597,17132],{},[902,64599,60469],{"encoding":904},[883,64601,64603],{"className":64602},[886],[888,64604,64605],{"xmlns":890},[892,64606,64607,64615],{},[895,64608,64609,64611,64613],{},[898,64610,14142],{},[1708,64612,1710],{},[2505,64614,6097],{},[902,64616,60487],{"encoding":904},[883,64618,64620],{"className":64619},[886],[888,64621,64622],{"xmlns":890},[892,64623,64624,64632],{},[895,64625,64626,64628,64630],{},[898,64627,2364],{},[1708,64629,1710],{},[2505,64631,4003],{},[902,64633,60505],{"encoding":904},".\nRovnovážné množství:\n",[883,64636,64638],{"className":64637},[886],[888,64639,64640],{"xmlns":890},[892,64641,64642,64708],{},[895,64643,64644,64650,64652,64670,64672,64696,64698,64704,64706],{},[1753,64645,64646,64648],{},[898,64647,1688],{},[898,64649,16183],{},[1708,64651,1710],{},[2358,64653,64654,64662],{},[895,64655,64656,64658,64660],{},[898,64657,1923],{},[1708,64659,2726],{},[898,64661,2364],{},[895,64663,64664,64666,64668],{},[898,64665,14142],{},[1708,64667,2726],{},[898,64669,207],{},[1708,64671,1710],{},[2358,64673,64674,64682],{},[895,64675,64676,64678,64680],{},[2505,64677,17132],{},[1708,64679,2726],{},[2505,64681,4003],{},[895,64683,64684,64686,64688,64690,64692,64694],{},[2505,64685,6097],{},[1708,64687,2726],{},[1708,64689,1716],{"stretchy":1715},[1708,64691,2726],{},[2505,64693,3121],{},[1708,64695,1721],{"stretchy":1715},[1708,64697,1710],{},[2358,64699,64700,64702],{},[2505,64701,49855],{},[2505,64703,56233],{},[1708,64705,17816],{},[2505,64707,56238],{},[902,64709,64710],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,64713,64715],{"className":64714},[886],[888,64716,64717],{"xmlns":890},[892,64718,64719,64727],{},[895,64720,64721],{},[1753,64722,64723,64725],{},[898,64724,1688],{},[898,64726,16183],{},[902,64728,54233],{"encoding":904}," (a) při změně samotného parametru ",[883,64731,64733],{"className":64732},[886],[888,64734,64735],{"xmlns":890},[892,64736,64737,64741],{},[895,64738,64739],{},[898,64740,14142],{},[902,64742,14142],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,64745,64746],{},[38,64747,64748,64749,14647,64762,2486,64775,21200],{},"Řešení (a) — změna ",[883,64750,64752],{"className":64751},[886],[888,64753,64754],{"xmlns":890},[892,64755,64756,64760],{},[895,64757,64758],{},[898,64759,14142],{},[902,64761,14142],{"encoding":904},[883,64763,64765],{"className":64764},[886],[888,64766,64767],{"xmlns":890},[892,64768,64769,64773],{},[895,64770,64771],{},[2505,64772,6097],{},[902,64774,56273],{"encoding":904},[883,64776,64778],{"className":64777},[886],[888,64779,64780],{"xmlns":890},[892,64781,64782,64786],{},[895,64783,64784],{},[2505,64785,4097],{},[902,64787,56287],{"encoding":904},[724,64789,64790,64791,64855,64856,2788],{},"Pomocí vzorce (2.13) pro ",[883,64792,64794],{"className":64793},[886],[888,64795,64796],{"xmlns":890},[892,64797,64798,64852],{},[895,64799,64800,64820,64822,64824],{},[3194,64801,64802],{"scriptlevel":2784,"displaystyle":1882},[2358,64803,64804,64814],{},[895,64805,64806,64808],{},[898,64807,7252],{"mathvariant":1759},[1753,64809,64810,64812],{},[898,64811,1688],{},[898,64813,16183],{},[895,64815,64816,64818],{},[898,64817,7252],{"mathvariant":1759},[898,64819,14142],{},[1708,64821,1710],{},[1708,64823,2726],{},[3194,64825,64826],{"scriptlevel":2784,"displaystyle":1882},[2358,64827,64828,64836],{},[895,64829,64830,64832,64834],{},[898,64831,1923],{},[1708,64833,2726],{},[898,64835,2364],{},[895,64837,64838,64840,64842,64844,64846],{},[1708,64839,1716],{"stretchy":1715},[898,64841,14142],{},[1708,64843,2726],{},[898,64845,207],{},[1753,64847,64848,64850],{},[1708,64849,1721],{"stretchy":1715},[2505,64851,3132],{},[902,64853,64854],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,64857,64859],{"className":64858},[886],[888,64860,64861],{"xmlns":890},[892,64862,64863,64885],{},[895,64864,64865,64867],{},[1708,64866,2726],{},[3194,64868,64869],{"scriptlevel":2784,"displaystyle":1882},[2358,64870,64871,64877],{},[1753,64872,64873,64875],{},[898,64874,1688],{},[898,64876,16183],{},[895,64878,64879,64881,64883],{},[898,64880,14142],{},[1708,64882,2726],{},[898,64884,207],{},[902,64886,64887],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,64889,64891],{"className":64890},[886],[888,64892,64893],{"xmlns":890,"display":2210},[892,64894,64895,64951],{},[895,64896,64897,64899,64905,64907,64909,64925,64927,64929,64931,64933,64935,64941,64943,64945,64947,64949],{},[898,64898,2364],{},[1753,64900,64901,64903],{},[898,64902,1688],{},[898,64904,16183],{},[1708,64906,1710],{},[1708,64908,2726],{},[2358,64910,64911,64917],{},[1753,64912,64913,64915],{},[898,64914,1688],{},[898,64916,16183],{},[895,64918,64919,64921,64923],{},[898,64920,14142],{},[1708,64922,2726],{},[898,64924,207],{},[2247,64926,2659],{},[898,64928,2364],{},[898,64930,14142],{},[1708,64932,1710],{},[1708,64934,2726],{},[2358,64936,64937,64939],{},[2505,64938,56401],{},[2505,64940,56233],{},[1708,64942,3703],{},[2505,64944,10909],{},[1708,64946,17816],{},[1708,64948,2726],{},[2505,64950,56373],{},[902,64952,64953],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,64955,64956],{},"Nové rovnovážné množství:",[883,64958,64960],{"className":64959},[886],[888,64961,64962],{"xmlns":890,"display":2210},[892,64963,64964,64987],{},[895,64965,64966,64974,64976,64978,64980,64982,64984],{},[4754,64967,64968,64970,64972],{},[898,64969,1688],{},[2505,64971,2507],{},[898,64973,16183],{},[1708,64975,2638],{},[2505,64977,56401],{},[1708,64979,2726],{},[2505,64981,56406],{},[1708,64983,1710],{},[2505,64985,64986],{},"8,326.",[902,64988,64989],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,64991,64992,1729,64995,1343,65022,1343,65044,1343,65066,17508,65088,1343,65107,1343,65128,1343,65147,2155],{},[38,64993,64994],{},"Řešení (b) — současná změna všech parametrů:",[883,64996,64998],{"className":64997},[886],[888,64999,65000],{"xmlns":890},[892,65001,65002,65019],{},[895,65003,65004,65006,65008,65010,65012,65014,65016],{},[898,65005,207],{},[1708,65007,2788],{},[1708,65009,2726],{},[2505,65011,3121],{},[1708,65013,9392],{},[1708,65015,2726],{},[2505,65017,65018],{},"2,5",[902,65020,65021],{"encoding":904},"a: -3 \\to -2{,}5",[883,65023,65025],{"className":65024},[886],[888,65026,65027],{"xmlns":890},[892,65028,65029,65041],{},[895,65030,65031,65033,65035,65037,65039],{},[898,65032,1923],{},[1708,65034,2788],{},[2505,65036,17132],{},[1708,65038,9392],{},[2505,65040,26919],{},[902,65042,65043],{"encoding":904},"b: 40 \\to 35",[883,65045,65047],{"className":65046},[886],[888,65048,65049],{"xmlns":890},[892,65050,65051,65063],{},[895,65052,65053,65055,65057,65059,65061],{},[898,65054,14142],{},[1708,65056,2788],{},[2505,65058,6097],{},[1708,65060,9392],{},[2505,65062,4097],{},[902,65064,65065],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,65067,65069],{"className":65068},[886],[888,65070,65071],{"xmlns":890},[892,65072,65073,65085],{},[895,65074,65075,65077,65079,65081,65083],{},[898,65076,2364],{},[1708,65078,2788],{},[2505,65080,4003],{},[1708,65082,9392],{},[2505,65084,14868],{},[902,65086,65087],{"encoding":904},"d: 10 \\to 11",[883,65089,65091],{"className":65090},[886],[888,65092,65093],{"xmlns":890},[892,65094,65095,65105],{},[895,65096,65097,65099,65101,65103],{},[898,65098,2364],{},[898,65100,207],{},[1708,65102,1710],{},[2505,65104,6097],{},[902,65106,56439],{"encoding":904},[883,65108,65110],{"className":65109},[886],[888,65111,65112],{"xmlns":890},[892,65113,65114,65126],{},[895,65115,65116,65118,65120,65122,65124],{},[898,65117,2364],{},[898,65119,1923],{},[1708,65121,1710],{},[1708,65123,2726],{},[2505,65125,3993],{},[902,65127,56461],{"encoding":904},[883,65129,65131],{"className":65130},[886],[888,65132,65133],{"xmlns":890},[892,65134,65135,65145],{},[895,65136,65137,65139,65141,65143],{},[898,65138,2364],{},[898,65140,14142],{},[1708,65142,1710],{},[2505,65144,10909],{},[902,65146,56481],{"encoding":904},[883,65148,65150],{"className":65149},[886],[888,65151,65152],{"xmlns":890},[892,65153,65154,65164],{},[895,65155,65156,65158,65160,65162],{},[898,65157,2364],{},[898,65159,2364],{},[1708,65161,1710],{},[2505,65163,2507],{},[902,65165,56501],{"encoding":904},[724,65167,65168,65169,65227],{},"Totální diferenciál ",[883,65170,65172],{"className":65171},[886],[888,65173,65174],{"xmlns":890},[892,65175,65176,65224],{},[895,65177,65178,65184,65186,65188,65190,65192,65194,65196,65198,65200,65202,65204],{},[1753,65179,65180,65182],{},[898,65181,1688],{},[898,65183,16183],{},[1708,65185,1716],{"stretchy":1715},[898,65187,207],{},[1708,65189,1883],{"separator":1882},[898,65191,1923],{},[1708,65193,1883],{"separator":1882},[898,65195,14142],{},[1708,65197,1883],{"separator":1882},[898,65199,2364],{},[1708,65201,1721],{"stretchy":1715},[1708,65203,1710],{},[3194,65205,65206],{"scriptlevel":2784,"displaystyle":1882},[2358,65207,65208,65216],{},[895,65209,65210,65212,65214],{},[898,65211,1923],{},[1708,65213,2726],{},[898,65215,2364],{},[895,65217,65218,65220,65222],{},[898,65219,14142],{},[1708,65221,2726],{},[898,65223,207],{},[902,65225,65226],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,65229,65231],{"className":65230},[886],[888,65232,65233],{"xmlns":890,"display":2210},[892,65234,65235,65355],{},[895,65236,65237,65239,65245,65247,65273,65275,65277,65279,65281,65293,65295,65297,65299,65301,65327,65329,65331,65333,65335,65347,65349,65351,65353],{},[898,65238,2364],{},[1753,65240,65241,65243],{},[898,65242,1688],{},[898,65244,16183],{},[1708,65246,1710],{},[2358,65248,65249,65257],{},[895,65250,65251,65253,65255],{},[898,65252,1923],{},[1708,65254,2726],{},[898,65256,2364],{},[895,65258,65259,65261,65263,65265,65267],{},[1708,65260,1716],{"stretchy":1715},[898,65262,14142],{},[1708,65264,2726],{},[898,65266,207],{},[1753,65268,65269,65271],{},[1708,65270,1721],{"stretchy":1715},[2505,65272,3132],{},[2247,65274,2659],{},[898,65276,2364],{},[898,65278,207],{},[1708,65280,2019],{},[2358,65282,65283,65285],{},[2505,65284,2507],{},[895,65286,65287,65289,65291],{},[898,65288,14142],{},[1708,65290,2726],{},[898,65292,207],{},[2247,65294,2659],{},[898,65296,2364],{},[898,65298,1923],{},[1708,65300,2726],{},[2358,65302,65303,65311],{},[895,65304,65305,65307,65309],{},[898,65306,1923],{},[1708,65308,2726],{},[898,65310,2364],{},[895,65312,65313,65315,65317,65319,65321],{},[1708,65314,1716],{"stretchy":1715},[898,65316,14142],{},[1708,65318,2726],{},[898,65320,207],{},[1753,65322,65323,65325],{},[1708,65324,1721],{"stretchy":1715},[2505,65326,3132],{},[2247,65328,2659],{},[898,65330,2364],{},[898,65332,14142],{},[1708,65334,2726],{},[2358,65336,65337,65339],{},[2505,65338,2507],{},[895,65340,65341,65343,65345],{},[898,65342,14142],{},[1708,65344,2726],{},[898,65346,207],{},[2247,65348,2659],{},[898,65350,2364],{},[898,65352,2364],{},[898,65354,2155],{"mathvariant":1759},[902,65356,65357],{"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.",[724,65359,65360,65361,1343,65383,1343,65414,2750],{},"Dosazením číselných hodnot (",[883,65362,65364],{"className":65363},[886],[888,65365,65366],{"xmlns":890},[892,65367,65368,65380],{},[895,65369,65370,65372,65374,65376,65378],{},[898,65371,14142],{},[1708,65373,2726],{},[898,65375,207],{},[1708,65377,1710],{},[2505,65379,56233],{},[902,65381,65382],{"encoding":904},"c - a = 3{,}5",[883,65384,65386],{"className":65385},[886],[888,65387,65388],{"xmlns":890},[892,65389,65390,65411],{},[895,65391,65392,65394,65396,65398,65400,65406,65408],{},[1708,65393,1716],{"stretchy":1715},[898,65395,14142],{},[1708,65397,2726],{},[898,65399,207],{},[1753,65401,65402,65404],{},[1708,65403,1721],{"stretchy":1715},[2505,65405,3132],{},[1708,65407,1710],{},[2505,65409,65410],{},"12,25",[902,65412,65413],{"encoding":904},"(c-a)^2 = 12{,}25",[883,65415,65417],{"className":65416},[886],[888,65418,65419],{"xmlns":890},[892,65420,65421,65433],{},[895,65422,65423,65425,65427,65429,65431],{},[898,65424,1923],{},[1708,65426,2726],{},[898,65428,2364],{},[1708,65430,1710],{},[2505,65432,49855],{},[902,65434,65435],{"encoding":904},"b - d = 30",[883,65437,65439],{"className":65438},[886],[888,65440,65441],{"xmlns":890,"display":2210},[892,65442,65443,65544],{},[895,65444,65445,65447,65453,65455,65463,65465,65467,65469,65471,65479,65481,65483,65485,65487,65489,65497,65499,65501,65503,65505,65513,65515,65517,65519,65521,65524,65526,65529,65531,65533,65535,65538,65540,65542],{},[898,65446,2364],{},[1753,65448,65449,65451],{},[898,65450,1688],{},[898,65452,16183],{},[1708,65454,2638],{},[3194,65456,65457],{"scriptlevel":2784,"displaystyle":1715},[2358,65458,65459,65461],{},[2505,65460,49855],{},[2505,65462,65410],{},[1708,65464,1716],{"stretchy":1715},[2505,65466,6097],{},[1708,65468,1721],{"stretchy":1715},[1708,65470,2019],{},[3194,65472,65473],{"scriptlevel":2784,"displaystyle":1715},[2358,65474,65475,65477],{},[2505,65476,2507],{},[2505,65478,56233],{},[1708,65480,1716],{"stretchy":1715},[1708,65482,2726],{},[2505,65484,3993],{},[1708,65486,1721],{"stretchy":1715},[1708,65488,2726],{},[3194,65490,65491],{"scriptlevel":2784,"displaystyle":1715},[2358,65492,65493,65495],{},[2505,65494,49855],{},[2505,65496,65410],{},[1708,65498,1716],{"stretchy":1715},[2505,65500,10909],{},[1708,65502,1721],{"stretchy":1715},[1708,65504,2726],{},[3194,65506,65507],{"scriptlevel":2784,"displaystyle":1715},[2358,65508,65509,65511],{},[2505,65510,2507],{},[2505,65512,56233],{},[1708,65514,1716],{"stretchy":1715},[2505,65516,2507],{},[1708,65518,1721],{"stretchy":1715},[1708,65520,17816],{},[2505,65522,65523],{},"1,224",[1708,65525,2726],{},[2505,65527,65528],{},"1,429",[1708,65530,2726],{},[2505,65532,56406],{},[1708,65534,2726],{},[2505,65536,65537],{},"0,286",[1708,65539,17816],{},[1708,65541,2726],{},[2505,65543,56652],{},[902,65545,65546],{"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.",[724,65548,41911,65549,2155],{},[883,65550,65552],{"className":65551},[886],[888,65553,65554],{"xmlns":890},[892,65555,65556,65578],{},[895,65557,65558,65566,65568,65570,65572,65574,65576],{},[4754,65559,65560,65562,65564],{},[898,65561,1688],{},[2505,65563,2507],{},[898,65565,16183],{},[1708,65567,2638],{},[2505,65569,56401],{},[1708,65571,2726],{},[2505,65573,56683],{},[1708,65575,17816],{},[2505,65577,56688],{},[902,65579,65580],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1636,65582,65583],{},[724,65584,65585,65587,65588,65609,65610,65636,65637,65640,65641,65737,65738,65761,65762,65778],{},[883,65586,6130],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,65589,65591],{"className":65590},[886],[888,65592,65593],{"xmlns":890},[892,65594,65595,65607],{},[895,65596,65597,65599,65601,65603,65605],{},[898,65598,2633],{"mathvariant":1759},[898,65600,1688],{},[1708,65602,2638],{},[1708,65604,2726],{},[2505,65606,56718],{},[902,65608,56721],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,65611,65613],{"className":65612},[886],[888,65614,65615],{"xmlns":890},[892,65616,65617,65633],{},[895,65618,65619,65621,65627,65629,65631],{},[898,65620,2364],{},[1753,65622,65623,65625],{},[898,65624,1688],{},[898,65626,16183],{},[1708,65628,17816],{},[1708,65630,2726],{},[2505,65632,56683],{},[902,65634,65635],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,65638,65639],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,65642,65644],{"className":65643},[886],[888,65645,65646],{"xmlns":890},[892,65647,65648,65734],{},[895,65649,65650,65658,65660,65694,65696,65720,65722,65729,65731],{},[4754,65651,65652,65654,65656],{},[898,65653,1688],{},[2505,65655,2507],{},[898,65657,16183],{},[1708,65659,1710],{},[2358,65661,65662,65678],{},[895,65663,65664,65670,65672],{},[1753,65665,65666,65668],{},[898,65667,1923],{},[1708,65669,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,65671,2726],{},[1753,65673,65674,65676],{},[898,65675,2364],{},[1708,65677,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[895,65679,65680,65686,65688],{},[1753,65681,65682,65684],{},[898,65683,14142],{},[1708,65685,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,65687,2726],{},[1753,65689,65690,65692],{},[898,65691,207],{},[1708,65693,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,65695,1710],{},[2358,65697,65698,65706],{},[895,65699,65700,65702,65704],{},[2505,65701,26919],{},[1708,65703,2726],{},[2505,65705,14868],{},[895,65707,65708,65710,65712,65714,65716,65718],{},[2505,65709,4097],{},[1708,65711,2726],{},[1708,65713,1716],{"stretchy":1715},[1708,65715,2726],{},[2505,65717,65018],{},[1708,65719,1721],{"stretchy":1715},[1708,65721,1710],{},[2358,65723,65724,65726],{},[2505,65725,53632],{},[2505,65727,65728],{},"3,1",[1708,65730,17816],{},[2505,65732,65733],{},"7,742",[902,65735,65736],{"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 ",[883,65739,65741],{"className":65740},[886],[888,65742,65743],{"xmlns":890},[892,65744,65745,65758],{},[895,65746,65747,65749,65751,65753,65755],{},[898,65748,2633],{"mathvariant":1759},[898,65750,1688],{},[1708,65752,17816],{},[1708,65754,2726],{},[2505,65756,65757],{},"0,829",[902,65759,65760],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,65763,65765],{"className":65764},[886],[888,65766,65767],{"xmlns":890},[892,65768,65769,65775],{},[895,65770,65771,65773],{},[1708,65772,2726],{},[2505,65774,56718],{},[902,65776,65777],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,65780,65781],{},[614,65782,65783,65784,65797],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,65785,65787],{"className":65786},[886],[888,65788,65789],{"xmlns":890},[892,65790,65791,65795],{},[895,65792,65793],{},[898,65794,1688],{},[902,65796,1688],{"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.",[198,65799,65801,65802],{"id":65800},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,65803,65805],{"className":65804},[886],[888,65806,65807],{"xmlns":890},[892,65808,65809,65815],{},[895,65810,65811,65813],{},[898,65812,1747],{},[898,65814,1981],{},[902,65816,56796],{"encoding":904},[1636,65818,65819],{},[724,65820,65821,65823,65824,65858,65859,65881],{},[883,65822,64514],{}," Zadání\nPro nabídku ",[883,65825,65827],{"className":65826},[886],[888,65828,65829],{"xmlns":890},[892,65830,65831,65855],{},[895,65832,65833,65835,65837,65839,65841,65843,65845,65847,65849,65851,65853],{},[898,65834,1747],{},[1708,65836,1710],{},[898,65838,1981],{},[1708,65840,1716],{"stretchy":1715},[898,65842,1688],{},[1708,65844,1721],{"stretchy":1715},[1708,65846,1710],{},[2505,65848,4003],{},[1708,65850,2019],{},[2505,65852,3132],{},[898,65854,1688],{},[902,65856,65857],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,65860,65862],{"className":65861},[886],[888,65863,65864],{"xmlns":890},[892,65865,65866,65878],{},[895,65867,65868,65874,65876],{},[1743,65869,65870,65872],{},[898,65871,1688],{},[2505,65873,2784],{},[1708,65875,1710],{},[2505,65877,4003],{},[902,65879,65880],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,65883,65884],{},[38,65885,34628],{},[724,65887,65888],{},"Odpovídající cena:",[883,65890,65892],{"className":65891},[886],[888,65893,65894],{"xmlns":890,"display":2210},[892,65895,65896,65931],{},[895,65897,65898,65904,65906,65908,65910,65912,65914,65916,65918,65920,65922,65924,65926,65928],{},[1743,65899,65900,65902],{},[898,65901,1747],{},[2505,65903,2784],{},[1708,65905,1710],{},[898,65907,1981],{},[1708,65909,1716],{"stretchy":1715},[2505,65911,4003],{},[1708,65913,1721],{"stretchy":1715},[1708,65915,1710],{},[2505,65917,4003],{},[1708,65919,2019],{},[2505,65921,3132],{},[1708,65923,3703],{},[2505,65925,4003],{},[1708,65927,1710],{},[2505,65929,65930],{},"30.",[902,65932,65933],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,65935,65936],{},"Dle vzorce (2.15):",[883,65938,65940],{"className":65939},[886],[888,65941,65942],{"xmlns":890,"display":2210},[892,65943,65944,66052],{},[895,65945,65946,65948,65950,65952,65954,65956,65958,65964,65970,65972,65980,65982,65984,65986,65988,65990,65992,65994,65996,65998,66000,66002,66004,66006,66008,66011,66013,66015,66017,66023,66031,66033,66035,66037,66039,66041,66043,66045,66047,66049],{},[898,65947,1747],{},[898,65949,1981],{},[1708,65951,1716],{"stretchy":1715},[2505,65953,4003],{},[1708,65955,1721],{"stretchy":1715},[1708,65957,1710],{},[1743,65959,65960,65962],{},[898,65961,1747],{},[2505,65963,2784],{},[1743,65965,65966,65968],{},[898,65967,1688],{},[2505,65969,2784],{},[1708,65971,2726],{},[4754,65973,65974,65976,65978],{},[1708,65975,23056],{},[2505,65977,2784],{},[2505,65979,4003],{},[1708,65981,1716],{"stretchy":1715},[2505,65983,4003],{},[1708,65985,2019],{},[2505,65987,3132],{},[898,65989,1688],{},[1708,65991,1721],{"stretchy":1715},[2247,65993,2659],{},[898,65995,2364],{},[898,65997,1688],{},[1708,65999,1710],{},[2505,66001,4003],{},[1708,66003,3703],{},[2505,66005,49855],{},[1708,66007,2726],{},[1708,66009,6940],{"fence":1715,"stretchy":1882,"minsize":66010,"maxsize":66010},"1.8em",[2505,66012,4003],{},[898,66014,1688],{},[1708,66016,2019],{},[1753,66018,66019,66021],{},[898,66020,1688],{},[2505,66022,3132],{},[4754,66024,66025,66027,66029],{},[1708,66026,6981],{"fence":1715,"stretchy":1882,"minsize":66010,"maxsize":66010},[2505,66028,2784],{},[2505,66030,4003],{},[1708,66032,1710],{},[2505,66034,11064],{},[1708,66036,2726],{},[1708,66038,1716],{"stretchy":1715},[2505,66040,9238],{},[1708,66042,2019],{},[2505,66044,9238],{},[1708,66046,1721],{"stretchy":1715},[1708,66048,1710],{},[2505,66050,66051],{},"100.",[902,66053,66054],{"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.",[724,66056,66057,66058,66079,66080,66100],{},"Přebytek výrobce při množství ",[883,66059,66061],{"className":66060},[886],[888,66062,66063],{"xmlns":890},[892,66064,66065,66077],{},[895,66066,66067,66073,66075],{},[1743,66068,66069,66071],{},[898,66070,1688],{},[2505,66072,2784],{},[1708,66074,1710],{},[2505,66076,4003],{},[902,66078,65880],{"encoding":904}," je tedy ",[883,66081,66083],{"className":66082},[886],[888,66084,66085],{"xmlns":890},[892,66086,66087,66097],{},[895,66088,66089,66091,66093,66095],{},[898,66090,1747],{},[898,66092,1981],{},[1708,66094,1710],{},[2505,66096,9238],{},[902,66098,66099],{"encoding":904},"PS = 100"," (peněžních jednotek).",[48808,66102],{},[115,66104,66106],{"id":66105},"cheat-sheet","Cheat sheet",[16,66108,66109,66122],{},[19,66110,66111],{},[22,66112,66113,66116,66119],{},[25,66114,66115],{},"Veličina",[25,66117,66118],{},"Vzorec",[25,66120,66121],{},"Geometrie",[30,66123,66124,66242,66356,66424],{},[22,66125,66126,66154,66210],{},[35,66127,66128],{},[883,66129,66131],{"className":66130},[886],[888,66132,66133],{"xmlns":890},[892,66134,66135,66151],{},[895,66136,66137,66139,66141,66143,66149],{},[898,66138,3455],{},[898,66140,1981],{},[1708,66142,1716],{"stretchy":1715},[1743,66144,66145,66147],{},[898,66146,1688],{},[2505,66148,2784],{},[1708,66150,1721],{"stretchy":1715},[902,66152,66153],{"encoding":904},"CS(Q_0)",[35,66155,66156],{},[883,66157,66159],{"className":66158},[886],[888,66160,66161],{"xmlns":890},[892,66162,66163,66207],{},[895,66164,66165],{},[3194,66166,66167,66179,66181,66183,66185,66187,66189,66191,66193,66195,66201],{"scriptlevel":2784,"displaystyle":1882},[4754,66168,66169,66171,66173],{},[1708,66170,23056],{},[2505,66172,2784],{},[1743,66174,66175,66177],{},[898,66176,1688],{},[2505,66178,2784],{},[898,66180,16117],{},[1708,66182,1716],{"stretchy":1715},[898,66184,1688],{},[1708,66186,1721],{"stretchy":1715},[2247,66188,2659],{},[898,66190,2364],{},[898,66192,1688],{},[1708,66194,2726],{},[1743,66196,66197,66199],{},[898,66198,1747],{},[2505,66200,2784],{},[1743,66202,66203,66205],{},[898,66204,1688],{},[2505,66206,2784],{},[902,66208,66209],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,66211,66212,66213,66216,66217,66220,66221],{},"plocha ",[38,66214,66215],{},"pod"," křivkou poptávky, ",[38,66218,66219],{},"nad"," čárou ",[883,66222,66224],{"className":66223},[886],[888,66225,66226],{"xmlns":890},[892,66227,66228,66240],{},[895,66229,66230,66232,66234],{},[898,66231,1747],{},[1708,66233,1710],{},[1743,66235,66236,66238],{},[898,66237,1747],{},[2505,66239,2784],{},[902,66241,63497],{"encoding":904},[22,66243,66244,66272,66328],{},[35,66245,66246],{},[883,66247,66249],{"className":66248},[886],[888,66250,66251],{"xmlns":890},[892,66252,66253,66269],{},[895,66254,66255,66257,66259,66261,66267],{},[898,66256,1747],{},[898,66258,1981],{},[1708,66260,1716],{"stretchy":1715},[1743,66262,66263,66265],{},[898,66264,1688],{},[2505,66266,2784],{},[1708,66268,1721],{"stretchy":1715},[902,66270,66271],{"encoding":904},"PS(Q_0)",[35,66273,66274],{},[883,66275,66277],{"className":66276},[886],[888,66278,66279],{"xmlns":890},[892,66280,66281,66325],{},[895,66282,66283],{},[3194,66284,66285,66291,66297,66299,66311,66313,66315,66317,66319,66321,66323],{"scriptlevel":2784,"displaystyle":1882},[1743,66286,66287,66289],{},[898,66288,1747],{},[2505,66290,2784],{},[1743,66292,66293,66295],{},[898,66294,1688],{},[2505,66296,2784],{},[1708,66298,2726],{},[4754,66300,66301,66303,66305],{},[1708,66302,23056],{},[2505,66304,2784],{},[1743,66306,66307,66309],{},[898,66308,1688],{},[2505,66310,2784],{},[898,66312,1981],{},[1708,66314,1716],{"stretchy":1715},[898,66316,1688],{},[1708,66318,1721],{"stretchy":1715},[2247,66320,2659],{},[898,66322,2364],{},[898,66324,1688],{},[902,66326,66327],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,66329,66212,66330,66332,66333,66220,66335],{},[38,66331,66219],{}," křivkou nabídky, ",[38,66334,66215],{},[883,66336,66338],{"className":66337},[886],[888,66339,66340],{"xmlns":890},[892,66341,66342,66354],{},[895,66343,66344,66346,66348],{},[898,66345,1747],{},[1708,66347,1710],{},[1743,66349,66350,66352],{},[898,66351,1747],{},[2505,66353,2784],{},[902,66355,63497],{"encoding":904},[22,66357,66358,66361,66388],{},[35,66359,66360],{},"Výdaje \u002F tržby",[35,66362,66363],{},[883,66364,66366],{"className":66365},[886],[888,66367,66368],{"xmlns":890},[892,66369,66370,66386],{},[895,66371,66372,66378,66380],{},[1743,66373,66374,66376],{},[898,66375,1747],{},[2505,66377,2784],{},[1708,66379,3703],{},[1743,66381,66382,66384],{},[898,66383,1688],{},[2505,66385,2784],{},[902,66387,64357],{"encoding":904},[35,66389,66390,66391],{},"obdélník ",[883,66392,66394],{"className":66393},[886],[888,66395,66396],{"xmlns":890},[892,66397,66398,66422],{},[895,66399,66400,66402,66404,66410,66412,66414,66416],{},[2505,66401,2784],{},[2247,66403,2659],{},[1743,66405,66406,66408],{},[898,66407,1688],{},[2505,66409,2784],{},[2247,66411,2659],{},[898,66413,1786],{},[2247,66415,2659],{},[1743,66417,66418,66420],{},[898,66419,1747],{},[2505,66421,2784],{},[902,66423,62979],{"encoding":904},[22,66425,66426,66429,66452],{},[35,66427,66428],{},"Celkový přebytek",[35,66430,66431],{},[883,66432,66434],{"className":66433},[886],[888,66435,66436],{"xmlns":890},[892,66437,66438,66450],{},[895,66439,66440,66442,66444,66446,66448],{},[898,66441,3455],{},[898,66443,1981],{},[1708,66445,2019],{},[898,66447,1747],{},[898,66449,1981],{},[902,66451,62717],{"encoding":904},[35,66453,66454],{},"součet obou ploch v rovnováze",[48808,66456],{},[115,66458,12596],{"id":12595},[120,66460,66461,66483,66505,66549,66593,66656,66684],{},[123,66462,66463,1695,66465,1343,66480,66482],{},[38,66464,56761],{},[883,66466,66468],{"className":66467},[886],[888,66469,66470],{"xmlns":890},[892,66471,66472,66478],{},[895,66473,66474,66476],{},[898,66475,3455],{},[898,66477,1981],{},[902,66479,56777],{"encoding":904},[614,66481,56815],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,66484,66485,1695,66487,1343,66502,66504],{},[38,66486,56908],{},[883,66488,66490],{"className":66489},[886],[888,66491,66492],{"xmlns":890},[892,66493,66494,66500],{},[895,66495,66496,66498],{},[898,66497,1747],{},[898,66499,1981],{},[902,66501,56796],{"encoding":904},[614,66503,56911],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,66506,66507,12636,66510,2155],{},[38,66508,66509],{},"Ochota platit",[883,66511,66513],{"className":66512},[886],[888,66514,66515],{"xmlns":890},[892,66516,66517,66547],{},[895,66518,66519],{},[3194,66520,66521,66533,66535,66537,66539,66541,66543,66545],{"scriptlevel":2784,"displaystyle":1882},[4754,66522,66523,66525,66527],{},[1708,66524,23056],{},[2505,66526,2784],{},[1743,66528,66529,66531],{},[898,66530,1688],{},[2505,66532,2784],{},[898,66534,16117],{},[1708,66536,1716],{"stretchy":1715},[898,66538,1688],{},[1708,66540,1721],{"stretchy":1715},[2247,66542,2659],{},[898,66544,2364],{},[898,66546,1688],{},[902,66548,63345],{"encoding":904},[123,66550,66551,12636,66554,2155],{},[38,66552,66553],{},"Minimální cena výrobce",[883,66555,66557],{"className":66556},[886],[888,66558,66559],{"xmlns":890},[892,66560,66561,66591],{},[895,66562,66563],{},[3194,66564,66565,66577,66579,66581,66583,66585,66587,66589],{"scriptlevel":2784,"displaystyle":1882},[4754,66566,66567,66569,66571],{},[1708,66568,23056],{},[2505,66570,2784],{},[1743,66572,66573,66575],{},[898,66574,1688],{},[2505,66576,2784],{},[898,66578,1981],{},[1708,66580,1716],{"stretchy":1715},[898,66582,1688],{},[1708,66584,1721],{"stretchy":1715},[2247,66586,2659],{},[898,66588,2364],{},[898,66590,1688],{},[902,66592,63987],{"encoding":904},[123,66594,66595,12636,66598,64487,66623,2511],{},[38,66596,66597],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,66599,66601],{"className":66600},[886],[888,66602,66603],{"xmlns":890},[892,66604,66605,66621],{},[895,66606,66607,66613,66615],{},[1743,66608,66609,66611],{},[898,66610,1747],{},[2505,66612,2784],{},[2247,66614,2659],{},[1743,66616,66617,66619],{},[898,66618,1688],{},[2505,66620,2784],{},[902,66622,63423],{"encoding":904},[883,66624,66626],{"className":66625},[886],[888,66627,66628],{"xmlns":890},[892,66629,66630,66654],{},[895,66631,66632,66634,66636,66642,66644,66646,66648],{},[2505,66633,2784],{},[2247,66635,2659],{},[1743,66637,66638,66640],{},[898,66639,1688],{},[2505,66641,2784],{},[2247,66643,2659],{},[898,66645,1786],{},[2247,66647,2659],{},[1743,66649,66650,66652],{},[898,66651,1747],{},[2505,66653,2784],{},[902,66655,62979],{"encoding":904},[123,66657,66658,66661,66662,66683],{},[38,66659,66660],{},"Celkový přebytek trhu"," — součet ",[883,66663,66665],{"className":66664},[886],[888,66666,66667],{"xmlns":890},[892,66668,66669,66681],{},[895,66670,66671,66673,66675,66677,66679],{},[898,66672,3455],{},[898,66674,1981],{},[1708,66676,2019],{},[898,66678,1747],{},[898,66680,1981],{},[902,66682,62717],{"encoding":904}," v rovnovážném bodě.",[123,66685,66686,66688,66689,1343,66702,66715,66716,2155],{},[38,66687,14425],{}," — plochy ohraničené křivkami ",[883,66690,66692],{"className":66691},[886],[888,66693,66694],{"xmlns":890},[892,66695,66696,66700],{},[895,66697,66698],{},[898,66699,16117],{},[902,66701,16117],{"encoding":904},[883,66703,66705],{"className":66704},[886],[888,66706,66707],{"xmlns":890},[892,66708,66709,66713],{},[895,66710,66711],{},[898,66712,1981],{},[902,66714,1981],{"encoding":904}," a přímkou ",[883,66717,66719],{"className":66718},[886],[888,66720,66721],{"xmlns":890},[892,66722,66723,66735],{},[895,66724,66725,66727,66729],{},[898,66726,1747],{},[1708,66728,1710],{},[1743,66730,66731,66733],{},[898,66732,1747],{},[2505,66734,2784],{},[902,66736,63497],{"encoding":904},[48808,66738],{},[115,66740,66742],{"id":66741},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,66744,66745,66746,66759,66760,66777],{},"Uvalení jednotkové daně ",[883,66747,66749],{"className":66748},[886],[888,66750,66751],{"xmlns":890},[892,66752,66753,66757],{},[895,66754,66755],{},[898,66756,1978],{},[902,66758,1978],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,66761,66763],{"className":66762},[886],[888,66764,66765],{"xmlns":890},[892,66766,66767,66775],{},[895,66768,66769],{},[1753,66770,66771,66773],{},[898,66772,1688],{},[898,66774,16183],{},[902,66776,54233],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,66779,66780],{},[3372,66781],{"alt":66782,"className":66783,"src":66784},"imek-prebytky-s-dani-deadweight",[210,3376],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,66786,66787,66788,66803,66804,66819,66820,64487,66823,66847,66848,1695,66851,66854,66855,2155],{},"Přebytek spotřebitele ",[883,66789,66791],{"className":66790},[886],[888,66792,66793],{"xmlns":890},[892,66794,66795,66801],{},[895,66796,66797,66799],{},[898,66798,3455],{},[898,66800,1981],{},[902,66802,56777],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,66805,66807],{"className":66806},[886],[888,66808,66809],{"xmlns":890},[892,66810,66811,66817],{},[895,66812,66813,66815],{},[898,66814,1747],{},[898,66816,1981],{},[902,66818,56796],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,66821,66822],{},"daňový příjem",[883,66824,66826],{"className":66825},[886],[888,66827,66828],{"xmlns":890},[892,66829,66830,66844],{},[895,66831,66832,66834,66836],{},[898,66833,1978],{},[1708,66835,3703],{},[4754,66837,66838,66840,66842],{},[898,66839,1688],{},[2505,66841,2507],{},[898,66843,16183],{},[902,66845,66846],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,66849,66850],{},"mrtvá ztráta",[614,66852,66853],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,66856,811],{"className":66857,"dataFsResolvedFilePath":809,"href":810},[210],[48808,66859],{},[115,66861,13763],{"id":13762},[120,66863,66864,66871,66883,66890,66897],{},[123,66865,66866,1729,66868],{},[38,66867,28094],{},[207,66869,802],{"className":66870,"dataFsResolvedFilePath":800,"href":801},[210],[123,66872,66873,1729,66875,66878,66879,66882],{},[38,66874,48516],{},[207,66876,775],{"className":66877,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,66880,2162],{"className":66881,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,66884,66885,1729,66887],{},[38,66886,28104],{},[207,66888,13830],{"className":66889,"dataFsResolvedFilePath":827,"href":828},[210],[123,66891,66892,1729,66894],{},[38,66893,62580],{},[207,66895,62584],{"className":66896,"dataFsResolvedFilePath":745,"href":746},[210],[123,66898,66899,1729,66901],{},[38,66900,13888],{},[207,66902,13894],{"className":66903,"dataFsResolvedFilePath":13892,"href":13893},[210],{"title":641,"searchDepth":642,"depth":642,"links":66905},[66906,66907,66912,66917,66922,66923,66924,66925],{"id":62776,"depth":642,"text":1241},{"id":63118,"depth":642,"text":66908,"children":66909},"Přebytek spotřebitele (CSCS)",[66910,66911],{"id":63137,"depth":649,"text":63138},{"id":14424,"depth":649,"text":14425},{"id":63713,"depth":642,"text":66913,"children":66914},"Přebytek výrobce (PSPS)",[66915,66916],{"id":63732,"depth":649,"text":63733},{"id":63895,"depth":649,"text":14425},{"id":64502,"depth":642,"text":64503,"children":66918},[66919,66920],{"id":64506,"depth":649,"text":64507},{"id":65800,"depth":649,"text":66921},"Příklad 2.13 — numerický výpočet PSPS",{"id":66105,"depth":642,"text":66106},{"id":12595,"depth":642,"text":12596},{"id":66741,"depth":642,"text":66742},{"id":13762,"depth":642,"text":13763},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,62646,66932,66933,23876,28112,66934,66935],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":66938,"title":66939,"body":66940,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":86254,"navigation":664,"path":86255,"seo":86256,"sources":86257,"stem":86258,"tags":86259,"type":13951,"updated":677,"__hash__":86265},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":66941,"toc":86218},[66942,66945,67131,67133,67224,67229,67554,67558,67565,67569,67614,67681,67712,67762,67797,67801,67860,67865,67931,68048,68150,68154,68177,68255,68298,68302,68331,68398,68404,68518,68522,68602,68639,68691,68889,68953,69040,69044,69047,69126,69129,69247,69266,69331,69335,69426,69494,69535,69588,69656,69693,69697,69755,69785,69996,70068,70120,70286,70379,70414,70418,70422,70459,70524,70579,70583,70606,70695,70799,70868,70872,70969,71082,71138,71192,71250,71311,71314,71350,71415,71445,71674,71732,71766,71770,71797,71876,71990,72011,72090,72092,72200,72204,72342,72664,72668,72671,72675,72724,72728,72982,73134,73141,73214,73398,73403,73746,73750,73773,73775,73796,73855,73865,73914,74056,74130,74225,74340,74438,74556,74560,74629,74634,74746,74891,74942,75054,75096,75100,75120,75181,75208,75270,75274,75296,75365,75645,75652,75682,75689,75882,75886,75964,75969,76045,76048,76136,76212,76278,76327,76429,76502,76623,76974,77087,77189,77193,77196,77203,77206,77242,77301,77310,77458,77681,77685,77748,77927,78019,78074,78078,78134,78204,78256,78277,78358,78361,78435,78479,78483,78524,78567,78593,78597,78668,78764,78826,78878,78981,79059,79082,79111,79115,79281,79398,79470,79785,79945,79949,80000,80061,80095,80125,80225,80267,80436,80441,80537,80575,80579,80698,80999,81001,81036,81040,81044,81171,81303,81624,81812,81890,81894,82199,82312,82458,82643,82749,82980,83095,83177,83296,83394,83435,83439,83494,83638,83792,83952,84044,84238,84550,84681,84810,84814,84886,84928,84979,84981,86176,86178],[12,66943,66939],{"id":66944},"příjem-náklady-zisk-a-nabídka-firmy",[1636,66946,66947],{},[724,66948,66949,1643,66951,1729,66954,66969,66970,1729,66973,66988,66989,1729,66992,67020,67021,67043,67044,67068,67069,67091,67092,67095,67096,67112,67113,2155],{},[883,66950,1642],{},[38,66952,66953],{},"Příjem",[883,66955,66957],{"className":66956},[886],[888,66958,66959],{"xmlns":890},[892,66960,66961,66967],{},[895,66962,66963,66965],{},[898,66964,1978],{},[898,66966,1975],{},[902,66968,16029],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,66971,66972],{},"náklady",[883,66974,66976],{"className":66975},[886],[888,66977,66978],{"xmlns":890},[892,66979,66980,66986],{},[895,66981,66982,66984],{},[898,66983,1978],{},[898,66985,3455],{},[902,66987,15197],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,66990,66991],{},"zisk",[883,66993,66995],{"className":66994},[886],[888,66996,66997],{"xmlns":890},[892,66998,66999,67017],{},[895,67000,67001,67003,67005,67007,67009,67011,67013,67015],{},[898,67002,1747],{},[898,67004,1975],{},[1708,67006,1710],{},[898,67008,1978],{},[898,67010,1975],{},[1708,67012,2726],{},[898,67014,1978],{},[898,67016,3455],{},[902,67018,67019],{"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: ",[883,67022,67024],{"className":67023},[886],[888,67025,67026],{"xmlns":890},[892,67027,67028,67040],{},[895,67029,67030,67032,67034,67036,67038],{},[898,67031,1786],{},[898,67033,3455],{},[1708,67035,1710],{},[898,67037,1741],{},[898,67039,3455],{},[902,67041,67042],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,67045,67047],{"className":67046},[886],[888,67048,67049],{"xmlns":890},[892,67050,67051,67065],{},[895,67052,67053,67055,67057,67059,67061,67063],{},[898,67054,1786],{},[898,67056,52173],{},[898,67058,3455],{},[1708,67060,1710],{},[898,67062,1741],{},[898,67064,3455],{},[902,67066,67067],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,67070,67072],{"className":67071},[886],[888,67073,67074],{"xmlns":890},[892,67075,67076,67088],{},[895,67077,67078,67080,67082,67084,67086],{},[898,67079,1741],{},[898,67081,1975],{},[1708,67083,1710],{},[898,67085,1741],{},[898,67087,3455],{},[902,67089,67090],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,67093,67094],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,67097,67099],{"className":67098},[886],[888,67100,67101],{"xmlns":890},[892,67102,67103,67109],{},[895,67104,67105,67107],{},[898,67106,1741],{},[898,67108,3455],{},[902,67110,67111],{"encoding":904},"MC"," nad bodem minima ",[883,67114,67116],{"className":67115},[886],[888,67117,67118],{"xmlns":890},[892,67119,67120,67128],{},[895,67121,67122,67124,67126],{},[898,67123,1786],{},[898,67125,52173],{},[898,67127,3455],{},[902,67129,67130],{"encoding":904},"AVC",[115,67132,1241],{"id":62776},[724,67134,67135,67136,67139,67140,67142,67143,1343,67146,1343,67149,67151,67152,67155,67156,67159,67160,67163,67164,14647,67179,1348,67194,14647,67209,2511],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,67137,67138],{},"příjmem"," (revenue) a ",[38,67141,66972],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,67144,67145],{},"zisku",[38,67147,67148],{},"bodů zvratu",[38,67150,13981],{}," a konstrukcí ",[38,67153,67154],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,67157,1145],{"className":67158,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,67161,23017],{"className":67162,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,67165,67167],{"className":67166},[886],[888,67168,67169],{"xmlns":890},[892,67170,67171,67177],{},[895,67172,67173,67175],{},[898,67174,1978],{},[898,67176,1975],{},[902,67178,16029],{"encoding":904},[883,67180,67182],{"className":67181},[886],[888,67183,67184],{"xmlns":890},[892,67185,67186,67192],{},[895,67187,67188,67190],{},[898,67189,1741],{},[898,67191,1975],{},[902,67193,18548],{"encoding":904},[883,67195,67197],{"className":67196},[886],[888,67198,67199],{"xmlns":890},[892,67200,67201,67207],{},[895,67202,67203,67205],{},[898,67204,1978],{},[898,67206,3455],{},[902,67208,15197],{"encoding":904},[883,67210,67212],{"className":67211},[886],[888,67213,67214],{"xmlns":890},[892,67215,67216,67222],{},[895,67217,67218,67220],{},[898,67219,1741],{},[898,67221,3455],{},[902,67223,67111],{"encoding":904},[724,67225,67226],{},[38,67227,67228],{},"Cílové znalosti:",[120,67230,67231,67394,67397,67400,67493,67540,67547],{},[123,67232,67233,67234,1343,67249,1343,67265,1771,67280,1343,67295,1343,67311,1343,67329,1343,67347,1343,67364,1343,67379,8197],{},"odvodit a interpretovat funkce ",[883,67235,67237],{"className":67236},[886],[888,67238,67239],{"xmlns":890},[892,67240,67241,67247],{},[895,67242,67243,67245],{},[898,67244,1978],{},[898,67246,1975],{},[902,67248,16029],{"encoding":904},[883,67250,67252],{"className":67251},[886],[888,67253,67254],{"xmlns":890},[892,67255,67256,67262],{},[895,67257,67258,67260],{},[898,67259,1786],{},[898,67261,1975],{},[902,67263,67264],{"encoding":904},"AR",[883,67266,67268],{"className":67267},[886],[888,67269,67270],{"xmlns":890},[892,67271,67272,67278],{},[895,67273,67274,67276],{},[898,67275,1741],{},[898,67277,1975],{},[902,67279,18548],{"encoding":904},[883,67281,67283],{"className":67282},[886],[888,67284,67285],{"xmlns":890},[892,67286,67287,67293],{},[895,67288,67289,67291],{},[898,67290,1978],{},[898,67292,3455],{},[902,67294,15197],{"encoding":904},[883,67296,67298],{"className":67297},[886],[888,67299,67300],{"xmlns":890},[892,67301,67302,67308],{},[895,67303,67304,67306],{},[898,67305,22325],{},[898,67307,3455],{},[902,67309,67310],{"encoding":904},"FC",[883,67312,67314],{"className":67313},[886],[888,67315,67316],{"xmlns":890},[892,67317,67318,67326],{},[895,67319,67320,67322,67324],{},[898,67321,1978],{},[898,67323,52173],{},[898,67325,3455],{},[902,67327,67328],{"encoding":904},"TVC",[883,67330,67332],{"className":67331},[886],[888,67333,67334],{"xmlns":890},[892,67335,67336,67344],{},[895,67337,67338,67340,67342],{},[898,67339,1786],{},[898,67341,22325],{},[898,67343,3455],{},[902,67345,67346],{"encoding":904},"AFC",[883,67348,67350],{"className":67349},[886],[888,67351,67352],{"xmlns":890},[892,67353,67354,67362],{},[895,67355,67356,67358,67360],{},[898,67357,1786],{},[898,67359,52173],{},[898,67361,3455],{},[902,67363,67130],{"encoding":904},[883,67365,67367],{"className":67366},[886],[888,67368,67369],{"xmlns":890},[892,67370,67371,67377],{},[895,67372,67373,67375],{},[898,67374,1786],{},[898,67376,3455],{},[902,67378,3458],{"encoding":904},[883,67380,67382],{"className":67381},[886],[888,67383,67384],{"xmlns":890},[892,67385,67386,67392],{},[895,67387,67388,67390],{},[898,67389,1741],{},[898,67391,3455],{},[902,67393,67111],{"encoding":904},[123,67395,67396],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,67398,67399],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,67401,67402,67403,67406,67407,53646,67449,8197],{},"osvojit si ",[38,67404,67405],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,67408,67410],{"className":67409},[886],[888,67411,67412],{"xmlns":890},[892,67413,67414,67446],{},[895,67415,67416,67418,67420,67422,67428,67430,67432,67434,67436,67438,67444],{},[898,67417,1786],{},[898,67419,3455],{},[1708,67421,1716],{"stretchy":1715},[1743,67423,67424,67426],{},[898,67425,1688],{},[2505,67427,2784],{},[1708,67429,1721],{"stretchy":1715},[1708,67431,1710],{},[898,67433,1741],{},[898,67435,3455],{},[1708,67437,1716],{"stretchy":1715},[1743,67439,67440,67442],{},[898,67441,1688],{},[2505,67443,2784],{},[1708,67445,1721],{"stretchy":1715},[902,67447,67448],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,67450,67452],{"className":67451},[886],[888,67453,67454],{"xmlns":890},[892,67455,67456,67490],{},[895,67457,67458,67460,67462,67464,67466,67472,67474,67476,67478,67480,67482,67488],{},[898,67459,1786],{},[898,67461,52173],{},[898,67463,3455],{},[1708,67465,1716],{"stretchy":1715},[1743,67467,67468,67470],{},[898,67469,1688],{},[2505,67471,2784],{},[1708,67473,1721],{"stretchy":1715},[1708,67475,1710],{},[898,67477,1741],{},[898,67479,3455],{},[1708,67481,1716],{"stretchy":1715},[1743,67483,67484,67486],{},[898,67485,1688],{},[2505,67487,2784],{},[1708,67489,1721],{"stretchy":1715},[902,67491,67492],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,67494,67402,67495,67406,67498,8197],{},[38,67496,67497],{},"princip maximalizace zisku",[883,67499,67501],{"className":67500},[886],[888,67502,67503],{"xmlns":890},[892,67504,67505,67537],{},[895,67506,67507,67509,67511,67513,67519,67521,67523,67525,67527,67529,67535],{},[898,67508,1741],{},[898,67510,1975],{},[1708,67512,1716],{"stretchy":1715},[1743,67514,67515,67517],{},[898,67516,1688],{},[2505,67518,2784],{},[1708,67520,1721],{"stretchy":1715},[1708,67522,1710],{},[898,67524,1741],{},[898,67526,3455],{},[1708,67528,1716],{"stretchy":1715},[1743,67530,67531,67533],{},[898,67532,1688],{},[2505,67534,2784],{},[1708,67536,1721],{"stretchy":1715},[902,67538,67539],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,67541,67542,67543,67546],{},"stanovit ",[38,67544,67545],{},"body zvratu"," a interval zisku;",[123,67548,67549,67550,67553],{},"zkonstruovat ",[38,67551,67552],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,67555,67557],{"id":67556},"příjem-firmy","Příjem firmy",[724,67559,67560],{},[3372,67561],{"alt":67562,"className":67563,"src":67564},"imek-ar-mr-dvojnasobny-sklon",[210,3376],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,67566,67568],{"id":67567},"celkový-příjem","Celkový příjem",[724,67570,67571,67572,1695,67587,67590,67591,7911],{},"Celkový příjem ",[883,67573,67575],{"className":67574},[886],[888,67576,67577],{"xmlns":890},[892,67578,67579,67585],{},[895,67580,67581,67583],{},[898,67582,1978],{},[898,67584,1975],{},[902,67586,16029],{"encoding":904},[38,67588,67589],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,67592,67594],{"className":67593},[886],[888,67595,67596],{"xmlns":890},[892,67597,67598,67612],{},[895,67599,67600,67602,67604,67606,67608,67610],{},[898,67601,1747],{},[1708,67603,1710],{},[898,67605,16117],{},[1708,67607,1716],{"stretchy":1715},[898,67609,1688],{},[1708,67611,1721],{"stretchy":1715},[902,67613,16564],{"encoding":904},[883,67615,67617],{"className":67616},[886],[888,67618,67619],{"xmlns":890,"display":2210},[892,67620,67621,67678],{},[2214,67622,67623],{"width":2216},[2218,67624,67625,67627,67671,67673],{},[2221,67626],{"width":2223},[2221,67628,67629],{},[895,67630,67631,67633,67635,67637,67639,67641,67643,67645,67647,67649,67651,67653,67655,67657,67659,67661,67663,67665,67667,67669],{},[898,67632,1978],{},[898,67634,1975],{},[1708,67636,1710],{},[898,67638,1978],{},[898,67640,1975],{},[1708,67642,1716],{"stretchy":1715},[898,67644,1688],{},[1708,67646,1721],{"stretchy":1715},[1708,67648,1710],{},[898,67650,1747],{},[1708,67652,3703],{},[898,67654,1688],{},[1708,67656,1710],{},[898,67658,16117],{},[1708,67660,1716],{"stretchy":1715},[898,67662,1688],{},[1708,67664,1721],{"stretchy":1715},[1708,67666,3703],{},[898,67668,1688],{},[898,67670,2155],{"mathvariant":1759},[2221,67672],{"width":2223},[2221,67674,67675],{},[2247,67676,67677],{},"(3.1)",[902,67679,67680],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,67682,67683,67684,67687,67688,67711],{},"Graf funkce se nazývá ",[38,67685,67686],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,67689,67691],{"className":67690},[886],[888,67692,67693],{"xmlns":890},[892,67694,67695,67709],{},[895,67696,67697,67699,67701,67703,67705,67707],{},[898,67698,1747],{},[1708,67700,1710],{},[898,67702,207],{},[898,67704,1688],{},[1708,67706,2019],{},[898,67708,1923],{},[902,67710,48898],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,67713,67715],{"className":67714},[886],[888,67716,67717],{"xmlns":890,"display":2210},[892,67718,67719,67759],{},[895,67720,67721,67723,67725,67727,67729,67731,67733,67735,67737,67739,67741,67743,67745,67751,67753,67755,67757],{},[898,67722,1978],{},[898,67724,1975],{},[1708,67726,1710],{},[898,67728,1688],{},[1708,67730,1716],{"stretchy":1715},[898,67732,207],{},[898,67734,1688],{},[1708,67736,2019],{},[898,67738,1923],{},[1708,67740,1721],{"stretchy":1715},[1708,67742,1710],{},[898,67744,207],{},[1753,67746,67747,67749],{},[898,67748,1688],{},[2505,67750,3132],{},[1708,67752,2019],{},[898,67754,1923],{},[898,67756,1688],{},[1708,67758,1883],{"separator":1882},[902,67760,67761],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,67763,67764,67765,67778,67779,67796],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,67766,67768],{"className":67767},[886],[888,67769,67770],{"xmlns":890},[892,67771,67772,67776],{},[895,67773,67774],{},[898,67775,900],{},[902,67777,900],{"encoding":904}," (jelikož ",[883,67780,67782],{"className":67781},[886],[888,67783,67784],{"xmlns":890},[892,67785,67786,67794],{},[895,67787,67788,67790,67792],{},[898,67789,207],{},[1708,67791,2932],{},[2505,67793,2784],{},[902,67795,3154],{"encoding":904},") procházející počátkem.",[49185,67798,67800],{"id":67799},"příklad-31","Příklad 3.1",[724,67802,67803,67806,67807,67843,67844,67859],{},[38,67804,67805],{},"Zadání."," Pro poptávku ",[883,67808,67810],{"className":67809},[886],[888,67811,67812],{"xmlns":890},[892,67813,67814,67840],{},[895,67815,67816,67818,67820,67822,67824,67826,67828,67830,67832,67834,67836,67838],{},[898,67817,1747],{},[1708,67819,1710],{},[898,67821,16117],{},[1708,67823,1716],{"stretchy":1715},[898,67825,1688],{},[1708,67827,1721],{"stretchy":1715},[1708,67829,1710],{},[1708,67831,2726],{},[2505,67833,3132],{},[898,67835,1688],{},[1708,67837,2019],{},[2505,67839,9238],{},[902,67841,67842],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,67845,67847],{"className":67846},[886],[888,67848,67849],{"xmlns":890},[892,67850,67851,67857],{},[895,67852,67853,67855],{},[898,67854,1978],{},[898,67856,1975],{},[902,67858,16029],{"encoding":904}," a charakterizujte jeho křivku.",[724,67861,67862,67864],{},[38,67863,34628],{}," Celkový příjem je",[883,67866,67868],{"className":67867},[886],[888,67869,67870],{"xmlns":890,"display":2210},[892,67871,67872,67928],{},[895,67873,67874,67876,67878,67880,67882,67884,67886,67888,67890,67892,67894,67896,67898,67900,67902,67904,67906,67908,67910,67912,67914,67920,67922,67924,67926],{},[898,67875,1978],{},[898,67877,1975],{},[1708,67879,1710],{},[898,67881,1978],{},[898,67883,1975],{},[1708,67885,1716],{"stretchy":1715},[898,67887,1688],{},[1708,67889,1721],{"stretchy":1715},[1708,67891,1710],{},[898,67893,1688],{},[1708,67895,1716],{"stretchy":1715},[1708,67897,2726],{},[2505,67899,3132],{},[898,67901,1688],{},[1708,67903,2019],{},[2505,67905,9238],{},[1708,67907,1721],{"stretchy":1715},[1708,67909,1710],{},[1708,67911,2726],{},[2505,67913,3132],{},[1753,67915,67916,67918],{},[898,67917,1688],{},[2505,67919,3132],{},[1708,67921,2019],{},[2505,67923,9238],{},[898,67925,1688],{},[898,67927,2155],{"mathvariant":1759},[902,67929,67930],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,67932,67933,67934,1771,67956,67978,67979,67997,67998,2155],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,67935,67937],{"className":67936},[886],[888,67938,67939],{"xmlns":890},[892,67940,67941,67953],{},[895,67942,67943,67949,67951],{},[1743,67944,67945,67947],{},[898,67946,1688],{},[2505,67948,2507],{},[1708,67950,1710],{},[2505,67952,2784],{},[902,67954,67955],{"encoding":904},"Q_1 = 0",[883,67957,67959],{"className":67958},[886],[888,67960,67961],{"xmlns":890},[892,67962,67963,67975],{},[895,67964,67965,67971,67973],{},[1743,67966,67967,67969],{},[898,67968,1688],{},[2505,67970,3132],{},[1708,67972,1710],{},[2505,67974,9704],{},[902,67976,67977],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,67980,67982],{"className":67981},[886],[888,67983,67984],{"xmlns":890},[892,67985,67986,67994],{},[895,67987,67988,67990,67992],{},[898,67989,1688],{},[1708,67991,1710],{},[2505,67993,4028],{},[902,67995,67996],{"encoding":904},"Q = 25"," ve výši ",[883,67999,68001],{"className":68000},[886],[888,68002,68003],{"xmlns":890},[892,68004,68005,68045],{},[895,68006,68007,68009,68018,68020,68022,68024,68026,68029,68031,68033,68035,68037,68039,68041,68043],{},[898,68008,1978],{},[1743,68010,68011,68013,68016],{},[898,68012,1975],{},[898,68014,68015],{},"max",[1708,68017,7149],{},[1708,68019,1710],{},[1708,68021,2726],{},[2505,68023,3132],{},[1708,68025,3703],{},[2505,68027,68028],{},"625",[1708,68030,2019],{},[2505,68032,9238],{},[1708,68034,3703],{},[2505,68036,4028],{},[1708,68038,1710],{},[2505,68040,2507],{},[2247,68042,2659],{},[2505,68044,11594],{},[902,68046,68047],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,68049,68050],{},[614,68051,68052,68053,68087,68088,1771,68101,68114,68115,3405,68133,2155],{},"Obrázek 3.1: Parabola ",[883,68054,68056],{"className":68055},[886],[888,68057,68058],{"xmlns":890},[892,68059,68060,68084],{},[895,68061,68062,68064,68066,68068,68070,68072,68078,68080,68082],{},[898,68063,1978],{},[898,68065,1975],{},[1708,68067,1710],{},[1708,68069,2726],{},[2505,68071,3132],{},[1753,68073,68074,68076],{},[898,68075,1688],{},[2505,68077,3132],{},[1708,68079,2019],{},[2505,68081,9238],{},[898,68083,1688],{},[902,68085,68086],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,68089,68091],{"className":68090},[886],[888,68092,68093],{"xmlns":890},[892,68094,68095,68099],{},[895,68096,68097],{},[2505,68098,2784],{},[902,68100,2784],{"encoding":904},[883,68102,68104],{"className":68103},[886],[888,68105,68106],{"xmlns":890},[892,68107,68108,68112],{},[895,68109,68110],{},[2505,68111,9704],{},[902,68113,9704],{"encoding":904}," a maximem ",[883,68116,68118],{"className":68117},[886],[888,68119,68120],{"xmlns":890},[892,68121,68122,68130],{},[895,68123,68124,68126,68128],{},[2505,68125,2507],{},[2247,68127,2659],{},[2505,68129,11594],{},[902,68131,68132],{"encoding":904},"1\\,250",[883,68134,68136],{"className":68135},[886],[888,68137,68138],{"xmlns":890},[892,68139,68140,68148],{},[895,68141,68142,68144,68146],{},[898,68143,1688],{},[1708,68145,1710],{},[2505,68147,4028],{},[902,68149,67996],{"encoding":904},[198,68151,68153],{"id":68152},"průměrný-příjem","Průměrný příjem",[724,68155,68156,1729,68158,1695,68173,68176],{},[38,68157,68153],{},[883,68159,68161],{"className":68160},[886],[888,68162,68163],{"xmlns":890},[892,68164,68165,68171],{},[895,68166,68167,68169],{},[898,68168,1786],{},[898,68170,1975],{},[902,68172,67264],{"encoding":904},[38,68174,68175],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,68178,68180],{"className":68179},[886],[888,68181,68182],{"xmlns":890,"display":2210},[892,68183,68184,68252],{},[895,68185,68186,68188,68190,68192,68194,68196,68198,68200,68202,68204,68220,68222,68240,68242,68244,68246,68248,68250],{},[898,68187,1786],{},[898,68189,1975],{},[1708,68191,1710],{},[898,68193,1786],{},[898,68195,1975],{},[1708,68197,1716],{"stretchy":1715},[898,68199,1688],{},[1708,68201,1721],{"stretchy":1715},[1708,68203,1710],{},[2358,68205,68206,68218],{},[895,68207,68208,68210,68212,68214,68216],{},[898,68209,1978],{},[898,68211,1975],{},[1708,68213,1716],{"stretchy":1715},[898,68215,1688],{},[1708,68217,1721],{"stretchy":1715},[898,68219,1688],{},[1708,68221,1710],{},[2358,68223,68224,68238],{},[895,68225,68226,68228,68230,68232,68234,68236],{},[898,68227,1688],{},[2247,68229,2659],{},[898,68231,16117],{},[1708,68233,1716],{"stretchy":1715},[898,68235,1688],{},[1708,68237,1721],{"stretchy":1715},[898,68239,1688],{},[1708,68241,1710],{},[898,68243,16117],{},[1708,68245,1716],{"stretchy":1715},[898,68247,1688],{},[1708,68249,1721],{"stretchy":1715},[898,68251,2155],{"mathvariant":1759},[902,68253,68254],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1636,68256,68257],{},[724,68258,68259,68262,68263,1343,68266,2155],{},[883,68260,68261],{},"!note"," Klíčové pozorování\n",[38,68264,68265],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,68267,68269],{"className":68268},[886],[888,68270,68271],{"xmlns":890},[892,68272,68273,68295],{},[895,68274,68275,68277,68279,68281,68283,68285,68287,68289,68291,68293],{},[898,68276,1786],{},[898,68278,1975],{},[1708,68280,1716],{"stretchy":1715},[898,68282,1688],{},[1708,68284,1721],{"stretchy":1715},[1708,68286,1710],{},[898,68288,16117],{},[1708,68290,1716],{"stretchy":1715},[898,68292,1688],{},[1708,68294,1721],{"stretchy":1715},[902,68296,68297],{"encoding":904},"AR(Q) = D(Q)",[198,68299,68301],{"id":68300},"mezní-příjem","Mezní příjem",[724,68303,68304,68305,1729,68308,1695,68323,68326,68327,68330],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,68306,68307],{},"mezní příjem",[883,68309,68311],{"className":68310},[886],[888,68312,68313],{"xmlns":890},[892,68314,68315,68321],{},[895,68316,68317,68319],{},[898,68318,1741],{},[898,68320,1975],{},[902,68322,18548],{"encoding":904},[38,68324,68325],{},"marginal revenue","), definovaný jako ",[207,68328,1145],{"className":68329,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,68332,68334],{"className":68333},[886],[888,68335,68336],{"xmlns":890,"display":2210},[892,68337,68338,68395],{},[2214,68339,68340],{"width":2216},[2218,68341,68342,68344,68388,68390],{},[2221,68343],{"width":2223},[2221,68345,68346],{},[895,68347,68348,68350,68352,68354,68370,68372,68374,68380,68382,68384,68386],{},[898,68349,1741],{},[898,68351,1975],{},[1708,68353,1710],{},[2358,68355,68356,68364],{},[895,68357,68358,68360,68362],{},[898,68359,2364],{"mathvariant":1759},[898,68361,1978],{},[898,68363,1975],{},[895,68365,68366,68368],{},[898,68367,2364],{"mathvariant":1759},[898,68369,1688],{},[1708,68371,1710],{},[898,68373,1978],{},[1753,68375,68376,68378],{},[898,68377,1975],{},[1708,68379,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,68381,1716],{"stretchy":1715},[898,68383,1688],{},[1708,68385,1721],{"stretchy":1715},[898,68387,2155],{"mathvariant":1759},[2221,68389],{"width":2223},[2221,68391,68392],{},[2247,68393,68394],{},"(3.2)",[902,68396,68397],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,68399,68400,68401,68403],{},"Mezní příjem udává ",[38,68402,14573],{}," celkového příjmu vzhledem k množství.",[1636,68405,68406],{},[724,68407,68408,68410,68411,68437,68438,68455,68456,2155],{},[883,68409,2518],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,68412,68414],{"className":68413},[886],[888,68415,68416],{"xmlns":890},[892,68417,68418,68434],{},[895,68419,68420,68422,68424,68426,68432],{},[898,68421,1741],{},[898,68423,1975],{},[1708,68425,1716],{"stretchy":1715},[1753,68427,68428,68430],{},[898,68429,1688],{},[1708,68431,2417],{},[1708,68433,1721],{"stretchy":1715},[902,68435,68436],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,68439,68441],{"className":68440},[886],[888,68442,68443],{"xmlns":890},[892,68444,68445,68453],{},[895,68446,68447],{},[1753,68448,68449,68451],{},[898,68450,1688],{},[1708,68452,2417],{},[902,68454,41691],{"encoding":904},". Jinak řečeno: ",[883,68457,68459],{"className":68458},[886],[888,68460,68461],{"xmlns":890},[892,68462,68463,68515],{},[895,68464,68465,68467,68469,68471,68477,68479,68481,68483,68485,68487,68493,68495,68497,68499,68501,68503,68505,68507,68513],{},[898,68466,1741],{},[898,68468,1975],{},[1708,68470,1716],{"stretchy":1715},[1753,68472,68473,68475],{},[898,68474,1688],{},[1708,68476,2417],{},[1708,68478,1721],{"stretchy":1715},[1708,68480,2638],{},[898,68482,1978],{},[898,68484,1975],{},[1708,68486,1716],{"stretchy":1715},[1753,68488,68489,68491],{},[898,68490,1688],{},[1708,68492,2417],{},[1708,68494,2019],{},[2505,68496,2507],{},[1708,68498,1721],{"stretchy":1715},[1708,68500,2726],{},[898,68502,1978],{},[898,68504,1975],{},[1708,68506,1716],{"stretchy":1715},[1753,68508,68509,68511],{},[898,68510,1688],{},[1708,68512,2417],{},[1708,68514,1721],{"stretchy":1715},[902,68516,68517],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[49185,68519,68521],{"id":68520},"příklad-32","Příklad 3.2",[724,68523,68524,67806,68526,67843,68560,68575,68576,2155],{},[38,68525,67805],{},[883,68527,68529],{"className":68528},[886],[888,68530,68531],{"xmlns":890},[892,68532,68533,68557],{},[895,68534,68535,68537,68539,68541,68543,68545,68547,68549,68551,68553,68555],{},[898,68536,1747],{},[1708,68538,1710],{},[898,68540,16117],{},[1708,68542,1716],{"stretchy":1715},[898,68544,1688],{},[1708,68546,1721],{"stretchy":1715},[1708,68548,1710],{},[2505,68550,9238],{},[1708,68552,2726],{},[2505,68554,3132],{},[898,68556,1688],{},[902,68558,68559],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,68561,68563],{"className":68562},[886],[888,68564,68565],{"xmlns":890},[892,68566,68567,68573],{},[895,68568,68569,68571],{},[898,68570,1741],{},[898,68572,1975],{},[902,68574,18548],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,68577,68579],{"className":68578},[886],[888,68580,68581],{"xmlns":890},[892,68582,68583,68599],{},[895,68584,68585,68587,68589,68591,68593,68595,68597],{},[898,68586,1688],{},[1708,68588,1710],{},[2505,68590,4853],{},[1708,68592,1883],{"separator":1882},[2505,68594,53694],{},[1708,68596,1883],{"separator":1882},[2505,68598,4018],{},[902,68600,68601],{"encoding":904},"Q = 15, 16, 20",[724,68603,68604,1729,68606,68638],{},[38,68605,34628],{},[883,68607,68609],{"className":68608},[886],[888,68610,68611],{"xmlns":890},[892,68612,68613,68635],{},[895,68614,68615,68617,68619,68621,68623,68625,68627,68629],{},[898,68616,1978],{},[898,68618,1975],{},[1708,68620,1710],{},[2505,68622,9238],{},[898,68624,1688],{},[1708,68626,2726],{},[2505,68628,3132],{},[1753,68630,68631,68633],{},[898,68632,1688],{},[2505,68634,3132],{},[902,68636,68637],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,68640,68642],{"className":68641},[886],[888,68643,68644],{"xmlns":890,"display":2210},[892,68645,68646,68688],{},[895,68647,68648,68650,68652,68654,68656,68658,68660,68662,68664,68670,68676,68678,68680,68682,68684,68686],{},[898,68649,1741],{},[898,68651,1975],{},[1708,68653,1710],{},[1708,68655,1716],{"stretchy":1715},[2505,68657,9238],{},[898,68659,1688],{},[1708,68661,2726],{},[2505,68663,3132],{},[1753,68665,68666,68668],{},[898,68667,1688],{},[2505,68669,3132],{},[1753,68671,68672,68674],{},[1708,68673,1721],{"stretchy":1715},[1708,68675,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,68677,1710],{},[2505,68679,9238],{},[1708,68681,2726],{},[2505,68683,5867],{},[898,68685,1688],{},[898,68687,2155],{"mathvariant":1759},[902,68689,68690],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,68692,3818,68693,3033,68711,68737,68738,8214,68751,68766,68767,68780,68781,33279,68794,8214,68807,68822,68823,68836,68837,68868,68869,68888],{},[883,68694,68696],{"className":68695},[886],[888,68697,68698],{"xmlns":890},[892,68699,68700,68708],{},[895,68701,68702,68704,68706],{},[898,68703,1688],{},[1708,68705,1710],{},[2505,68707,4853],{},[902,68709,68710],{"encoding":904},"Q = 15",[883,68712,68714],{"className":68713},[886],[888,68715,68716],{"xmlns":890},[892,68717,68718,68734],{},[895,68719,68720,68722,68724,68726,68728,68730,68732],{},[898,68721,1741],{},[898,68723,1975],{},[1708,68725,1716],{"stretchy":1715},[2505,68727,4853],{},[1708,68729,1721],{"stretchy":1715},[1708,68731,1710],{},[2505,68733,17132],{},[902,68735,68736],{"encoding":904},"MR(15) = 40",": při množství ",[883,68739,68741],{"className":68740},[886],[888,68742,68743],{"xmlns":890},[892,68744,68745,68749],{},[895,68746,68747],{},[2505,68748,4853],{},[902,68750,4853],{"encoding":904},[883,68752,68754],{"className":68753},[886],[888,68755,68756],{"xmlns":890},[892,68757,68758,68764],{},[895,68759,68760,68762],{},[898,68761,1978],{},[898,68763,1975],{},[902,68765,16029],{"encoding":904}," mění asi ",[883,68768,68770],{"className":68769},[886],[888,68771,68772],{"xmlns":890},[892,68773,68774,68778],{},[895,68775,68776],{},[2505,68777,17132],{},[902,68779,17132],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,68782,68784],{"className":68783},[886],[888,68785,68786],{"xmlns":890},[892,68787,68788,68792],{},[895,68789,68790],{},[898,68791,1688],{},[902,68793,1688],{"encoding":904},[883,68795,68797],{"className":68796},[886],[888,68798,68799],{"xmlns":890},[892,68800,68801,68805],{},[895,68802,68803],{},[2505,68804,2507],{},[902,68806,2507],{"encoding":904},[883,68808,68810],{"className":68809},[886],[888,68811,68812],{"xmlns":890},[892,68813,68814,68820],{},[895,68815,68816,68818],{},[898,68817,1978],{},[898,68819,1975],{},[902,68821,16029],{"encoding":904}," zvýší přibližně o ",[883,68824,68826],{"className":68825},[886],[888,68827,68828],{"xmlns":890},[892,68829,68830,68834],{},[895,68831,68832],{},[2505,68833,17132],{},[902,68835,17132],{"encoding":904},", tj. ze skutečné hodnoty ",[883,68838,68840],{"className":68839},[886],[888,68841,68842],{"xmlns":890},[892,68843,68844,68865],{},[895,68845,68846,68848,68850,68852,68854,68856,68858,68860,68862],{},[898,68847,1978],{},[898,68849,1975],{},[1708,68851,1716],{"stretchy":1715},[2505,68853,4853],{},[1708,68855,1721],{"stretchy":1715},[1708,68857,1710],{},[2505,68859,2507],{},[2247,68861,2659],{},[2505,68863,68864],{},"050",[902,68866,68867],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,68870,68872],{"className":68871},[886],[888,68873,68874],{"xmlns":890},[892,68875,68876,68885],{},[895,68877,68878,68880,68882],{},[2505,68879,2507],{},[2247,68881,2659],{},[2505,68883,68884],{},"090",[902,68886,68887],{"encoding":904},"1\\,090",". Skutečná změna je",[883,68890,68892],{"className":68891},[886],[888,68893,68894],{"xmlns":890,"display":2210},[892,68895,68896,68950],{},[895,68897,68898,68900,68902,68904,68906,68908,68910,68912,68914,68916,68918,68920,68922,68924,68926,68928,68930,68932,68934,68937,68939,68941,68943,68945,68947],{},[898,68899,2633],{"mathvariant":1759},[898,68901,1978],{},[898,68903,1975],{},[1708,68905,1710],{},[898,68907,1978],{},[898,68909,1975],{},[1708,68911,1716],{"stretchy":1715},[2505,68913,53694],{},[1708,68915,1721],{"stretchy":1715},[1708,68917,2726],{},[898,68919,1978],{},[898,68921,1975],{},[1708,68923,1716],{"stretchy":1715},[2505,68925,4853],{},[1708,68927,1721],{"stretchy":1715},[1708,68929,1710],{},[2505,68931,2507],{},[2247,68933,2659],{},[2505,68935,68936],{},"088",[1708,68938,2726],{},[2505,68940,2507],{},[2247,68942,2659],{},[2505,68944,68864],{},[1708,68946,1710],{},[2505,68948,68949],{},"38.",[902,68951,68952],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,68954,68955,68956,1343,68982,2941,69008,69023,69024,69039],{},"Podobně ",[883,68957,68959],{"className":68958},[886],[888,68960,68961],{"xmlns":890},[892,68962,68963,68979],{},[895,68964,68965,68967,68969,68971,68973,68975,68977],{},[898,68966,1741],{},[898,68968,1975],{},[1708,68970,1716],{"stretchy":1715},[2505,68972,53694],{},[1708,68974,1721],{"stretchy":1715},[1708,68976,1710],{},[2505,68978,4547],{},[902,68980,68981],{"encoding":904},"MR(16) = 36",[883,68983,68985],{"className":68984},[886],[888,68986,68987],{"xmlns":890},[892,68988,68989,69005],{},[895,68990,68991,68993,68995,68997,68999,69001,69003],{},[898,68992,1741],{},[898,68994,1975],{},[1708,68996,1716],{"stretchy":1715},[2505,68998,4018],{},[1708,69000,1721],{"stretchy":1715},[1708,69002,1710],{},[2505,69004,4018],{},[902,69006,69007],{"encoding":904},"MR(20) = 20",[883,69009,69011],{"className":69010},[886],[888,69012,69013],{"xmlns":890},[892,69014,69015,69021],{},[895,69016,69017,69019],{},[898,69018,1741],{},[898,69020,1975],{},[902,69022,18548],{"encoding":904}," je klesající funkce — rychlost změny ",[883,69025,69027],{"className":69026},[886],[888,69028,69029],{"xmlns":890},[892,69030,69031,69037],{},[895,69032,69033,69035],{},[898,69034,1978],{},[898,69036,1975],{},[902,69038,16029],{"encoding":904}," s růstem množství klesá.",[198,69041,69043],{"id":69042},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,69045,69046],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,69048,69050],{"className":69049},[886],[888,69051,69052],{"xmlns":890,"display":2210},[892,69053,69054,69123],{},[2214,69055,69056],{"width":2216},[2218,69057,69058,69060,69116,69118],{},[2221,69059],{"width":2223},[2221,69061,69062],{},[895,69063,69064,69066,69068,69070,69072,69074,69076,69078,69080,69082,69084,69086,69088,69090,69096,69098,69100,69102,69104,69106,69108,69110,69112,69114],{},[898,69065,2633],{"mathvariant":1759},[898,69067,1978],{},[898,69069,1975],{},[2247,69071,4779],{},[1708,69073,2638],{},[2247,69075,4779],{},[898,69077,2364],{"mathvariant":1759},[898,69079,1978],{},[898,69081,1975],{},[1708,69083,1710],{},[1708,69085,1716],{"stretchy":1715},[898,69087,1978],{},[898,69089,1975],{},[1753,69091,69092,69094],{},[1708,69093,1721],{"stretchy":1715},[1708,69095,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,69097,2659],{},[898,69099,2364],{"mathvariant":1759},[898,69101,1688],{},[1708,69103,1710],{},[898,69105,1741],{},[898,69107,1975],{},[2247,69109,2659],{},[898,69111,2364],{"mathvariant":1759},[898,69113,1688],{},[1708,69115,1883],{"separator":1882},[2221,69117],{"width":2223},[2221,69119,69120],{},[2247,69121,69122],{},"(3.3)",[902,69124,69125],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,69127,69128],{},"schematicky:",[883,69130,69132],{"className":69131},[886],[888,69133,69134],{"xmlns":890,"display":2210},[892,69135,69136,69244],{},[895,69137,69138,69176,69178,69180,69182,69211,69214,69242],{},[895,69139,69140,69143,69149,69152,69158,69161,69167,69173],{},[2247,69141,69142],{},"zm",[20297,69144,69145,69147],{"accent":1882},[2247,69146,57558],{},[1708,69148,36910],{},[2247,69150,69151],{},"na celkov",[20297,69153,69154,69156],{"accent":1882},[2247,69155,57558],{},[1708,69157,36829],{},[2247,69159,69160],{},"ho p",[20297,69162,69163,69165],{"accent":1882},[2247,69164,5498],{},[1708,69166,36910],{},[20297,69168,69169,69171],{"accent":1882},[2247,69170,36898],{},[1708,69172,36829],{},[2247,69174,69175],{},"jmu",[2247,69177,4779],{},[1708,69179,2638],{},[2247,69181,4779],{},[895,69183,69184,69187,69193,69196,69202,69208],{},[2247,69185,69186],{},"mezn",[20297,69188,69189,69191],{"accent":1882},[2247,69190,36898],{},[1708,69192,36829],{},[2247,69194,69195],{}," p",[20297,69197,69198,69200],{"accent":1882},[2247,69199,5498],{},[1708,69201,36910],{},[20297,69203,69204,69206],{"accent":1882},[2247,69205,36898],{},[1708,69207,36829],{},[2247,69209,69210],{},"jem",[1708,69212,69213],{},"×",[895,69215,69216,69218,69224,69227,69233,69236],{},[2247,69217,69142],{},[20297,69219,69220,69222],{"accent":1882},[2247,69221,57558],{},[1708,69223,36910],{},[2247,69225,69226],{},"na mno",[20297,69228,69229,69231],{"accent":1882},[2247,69230,21498],{},[1708,69232,36910],{},[2247,69234,69235],{},"stv",[20297,69237,69238,69240],{"accent":1882},[2247,69239,36898],{},[1708,69241,36829],{},[898,69243,2155],{"mathvariant":1759},[902,69245,69246],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,69248,69249,69250,69265],{},"Pro porovnání skutečná změna ",[883,69251,69253],{"className":69252},[886],[888,69254,69255],{"xmlns":890},[892,69256,69257,69263],{},[895,69258,69259,69261],{},[898,69260,1978],{},[898,69262,1975],{},[902,69264,16029],{"encoding":904}," je",[883,69267,69269],{"className":69268},[886],[888,69270,69271],{"xmlns":890,"display":2210},[892,69272,69273,69328],{},[2214,69274,69275],{"width":2216},[2218,69276,69277,69279,69321,69323],{},[2221,69278],{"width":2223},[2221,69280,69281],{},[895,69282,69283,69285,69287,69289,69291,69293,69295,69297,69299,69301,69303,69305,69307,69309,69311,69313,69315,69317,69319],{},[898,69284,2633],{"mathvariant":1759},[898,69286,1978],{},[898,69288,1975],{},[1708,69290,1710],{},[898,69292,1978],{},[898,69294,1975],{},[1708,69296,1716],{"stretchy":1715},[898,69298,1688],{},[1708,69300,2019],{},[898,69302,2364],{"mathvariant":1759},[898,69304,1688],{},[1708,69306,1721],{"stretchy":1715},[1708,69308,2726],{},[898,69310,1978],{},[898,69312,1975],{},[1708,69314,1716],{"stretchy":1715},[898,69316,1688],{},[1708,69318,1721],{"stretchy":1715},[898,69320,2155],{"mathvariant":1759},[2221,69322],{"width":2223},[2221,69324,69325],{},[2247,69326,69327],{},"(3.4)",[902,69329,69330],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[49185,69332,69334],{"id":69333},"příklad-33","Příklad 3.3",[724,69336,69337,3973,69339,69369,69370,14633,69385,14647,69398,2486,69411,69425],{},[38,69338,67805],{},[883,69340,69342],{"className":69341},[886],[888,69343,69344],{"xmlns":890},[892,69345,69346,69366],{},[895,69347,69348,69350,69352,69354,69356,69358,69360],{},[898,69349,1978],{},[898,69351,1975],{},[1708,69353,1710],{},[2505,69355,9238],{},[898,69357,1688],{},[1708,69359,2726],{},[1753,69361,69362,69364],{},[898,69363,1688],{},[2505,69365,3132],{},[902,69367,69368],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,69371,69373],{"className":69372},[886],[888,69374,69375],{"xmlns":890},[892,69376,69377,69383],{},[895,69378,69379,69381],{},[898,69380,1978],{},[898,69382,1975],{},[902,69384,16029],{"encoding":904},[883,69386,69388],{"className":69387},[886],[888,69389,69390],{"xmlns":890},[892,69391,69392,69396],{},[895,69393,69394],{},[898,69395,1688],{},[902,69397,1688],{"encoding":904},[883,69399,69401],{"className":69400},[886],[888,69402,69403],{"xmlns":890},[892,69404,69405,69409],{},[895,69406,69407],{},[2505,69408,4199],{},[902,69410,4199],{"encoding":904},[883,69412,69414],{"className":69413},[886],[888,69415,69416],{"xmlns":890},[892,69417,69418,69423],{},[895,69419,69420],{},[2505,69421,69422],{},"63",[902,69424,69422],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,69427,69428,1729,69430,69455,69456,1343,69474,2788],{},[38,69429,34628],{},[883,69431,69433],{"className":69432},[886],[888,69434,69435],{"xmlns":890},[892,69436,69437,69453],{},[895,69438,69439,69441,69443,69445,69447,69449,69451],{},[898,69440,1741],{},[898,69442,1975],{},[1708,69444,1710],{},[2505,69446,9238],{},[1708,69448,2726],{},[2505,69450,3132],{},[898,69452,1688],{},[902,69454,23323],{"encoding":904},", tedy při ",[883,69457,69459],{"className":69458},[886],[888,69460,69461],{"xmlns":890},[892,69462,69463,69471],{},[895,69464,69465,69467,69469],{},[898,69466,1688],{},[1708,69468,1710],{},[2505,69470,4199],{},[902,69472,69473],{"encoding":904},"Q = 60",[883,69475,69477],{"className":69476},[886],[888,69478,69479],{"xmlns":890},[892,69480,69481,69491],{},[895,69482,69483,69485,69487,69489],{},[898,69484,2364],{"mathvariant":1759},[898,69486,1688],{},[1708,69488,1710],{},[2505,69490,3121],{},[902,69492,69493],{"encoding":904},"\\mathrm{d}Q = 3",[883,69495,69497],{"className":69496},[886],[888,69498,69499],{"xmlns":890,"display":2210},[892,69500,69501,69532],{},[895,69502,69503,69505,69507,69509,69511,69513,69515,69517,69519,69521,69523,69525,69527,69529],{},[898,69504,2364],{"mathvariant":1759},[898,69506,1978],{},[898,69508,1975],{},[1708,69510,1710],{},[1708,69512,1716],{"stretchy":1715},[2505,69514,9238],{},[1708,69516,2726],{},[2505,69518,15981],{},[1708,69520,1721],{"stretchy":1715},[1708,69522,3703],{},[2505,69524,3121],{},[1708,69526,1710],{},[1708,69528,2726],{},[2505,69530,69531],{},"60.",[902,69533,69534],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,69536,69537,69538,4598,69568,69587],{},"Celkový příjem klesne z ",[883,69539,69541],{"className":69540},[886],[888,69542,69543],{"xmlns":890},[892,69544,69545,69565],{},[895,69546,69547,69549,69551,69553,69555,69557,69559,69561,69563],{},[898,69548,1978],{},[898,69550,1975],{},[1708,69552,1716],{"stretchy":1715},[2505,69554,4199],{},[1708,69556,1721],{"stretchy":1715},[1708,69558,1710],{},[2505,69560,3132],{},[2247,69562,2659],{},[2505,69564,11498],{},[902,69566,69567],{"encoding":904},"TR(60) = 2\\,400",[883,69569,69571],{"className":69570},[886],[888,69572,69573],{"xmlns":890},[892,69574,69575,69584],{},[895,69576,69577,69579,69581],{},[2505,69578,3132],{},[2247,69580,2659],{},[2505,69582,69583],{},"340",[902,69585,69586],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,69589,69591],{"className":69590},[886],[888,69592,69593],{"xmlns":890,"display":2210},[892,69594,69595,69653],{},[895,69596,69597,69599,69601,69603,69605,69607,69609,69611,69613,69615,69617,69619,69621,69623,69625,69627,69629,69631,69633,69636,69638,69640,69642,69644,69646,69648,69651],{},[898,69598,2633],{"mathvariant":1759},[898,69600,1978],{},[898,69602,1975],{},[1708,69604,1710],{},[898,69606,1978],{},[898,69608,1975],{},[1708,69610,1716],{"stretchy":1715},[2505,69612,69422],{},[1708,69614,1721],{"stretchy":1715},[1708,69616,2726],{},[898,69618,1978],{},[898,69620,1975],{},[1708,69622,1716],{"stretchy":1715},[2505,69624,4199],{},[1708,69626,1721],{"stretchy":1715},[1708,69628,1710],{},[2505,69630,3132],{},[2247,69632,2659],{},[2505,69634,69635],{},"331",[1708,69637,2726],{},[2505,69639,3132],{},[2247,69641,2659],{},[2505,69643,11498],{},[1708,69645,1710],{},[1708,69647,2726],{},[2505,69649,69650],{},"69",[1708,69652,1883],{"separator":1882},[902,69654,69655],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,69657,69658,69659,69674,69675,2155],{},"tj. ",[883,69660,69662],{"className":69661},[886],[888,69663,69664],{"xmlns":890},[892,69665,69666,69672],{},[895,69667,69668,69670],{},[898,69669,1978],{},[898,69671,1975],{},[902,69673,16029],{"encoding":904}," klesne na ",[883,69676,69678],{"className":69677},[886],[888,69679,69680],{"xmlns":890},[892,69681,69682,69690],{},[895,69683,69684,69686,69688],{},[2505,69685,3132],{},[2247,69687,2659],{},[2505,69689,69635],{},[902,69691,69692],{"encoding":904},"2\\,331",[198,69694,69696],{"id":69695},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,69698,69699,69700,1826,69723,43424],{},"Obecně pro lineární poptávku ",[883,69701,69703],{"className":69702},[886],[888,69704,69705],{"xmlns":890},[892,69706,69707,69721],{},[895,69708,69709,69711,69713,69715,69717,69719],{},[898,69710,1747],{},[1708,69712,1710],{},[898,69714,207],{},[898,69716,1688],{},[1708,69718,2019],{},[898,69720,1923],{},[902,69722,48898],{"encoding":904},[883,69724,69726],{"className":69725},[886],[888,69727,69728],{"xmlns":890},[892,69729,69730,69752],{},[895,69731,69732,69734,69736,69738,69740,69746,69748,69750],{},[898,69733,1978],{},[898,69735,1975],{},[1708,69737,1710],{},[898,69739,207],{},[1753,69741,69742,69744],{},[898,69743,1688],{},[2505,69745,3132],{},[1708,69747,2019],{},[898,69749,1923],{},[898,69751,1688],{},[902,69753,69754],{"encoding":904},"TR = aQ^2 + bQ",[883,69756,69758],{"className":69757},[886],[888,69759,69760],{"xmlns":890,"display":2210},[892,69761,69762,69782],{},[895,69763,69764,69766,69768,69770,69772,69774,69776,69778,69780],{},[898,69765,1741],{},[898,69767,1975],{},[1708,69769,1710],{},[2505,69771,3132],{},[898,69773,207],{},[898,69775,1688],{},[1708,69777,2019],{},[898,69779,1923],{},[898,69781,2155],{"mathvariant":1759},[902,69783,69784],{"encoding":904},"MR = 2aQ + b.",[724,69786,69787,69788,69803,69804,69819,69820,69833,69834,1695,69837,69853,69854,69867,69868,69883,69884,69899,69900,69915,69916,3405,69929,69959,69960,69979,69980,69995],{},"Křivky ",[883,69789,69791],{"className":69790},[886],[888,69792,69793],{"xmlns":890},[892,69794,69795,69801],{},[895,69796,69797,69799],{},[898,69798,1741],{},[898,69800,1975],{},[902,69802,18548],{"encoding":904}," a poptávky (resp. ",[883,69805,69807],{"className":69806},[886],[888,69808,69809],{"xmlns":890},[892,69810,69811,69817],{},[895,69812,69813,69815],{},[898,69814,1786],{},[898,69816,1975],{},[902,69818,67264],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,69821,69823],{"className":69822},[886],[888,69824,69825],{"xmlns":890},[892,69826,69827,69831],{},[895,69828,69829],{},[898,69830,1923],{},[902,69832,1923],{"encoding":904},", přičemž ",[38,69835,69836],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,69838,69840],{"className":69839},[886],[888,69841,69842],{"xmlns":890},[892,69843,69844,69850],{},[895,69845,69846,69848],{},[2505,69847,3132],{},[898,69849,207],{},[902,69851,69852],{"encoding":904},"2a"," vs. ",[883,69855,69857],{"className":69856},[886],[888,69858,69859],{"xmlns":890},[892,69860,69861,69865],{},[895,69862,69863],{},[898,69864,207],{},[902,69866,207],{"encoding":904},", obrázek 3.2). ",[883,69869,69871],{"className":69870},[886],[888,69872,69873],{"xmlns":890},[892,69874,69875,69881],{},[895,69876,69877,69879],{},[898,69878,1741],{},[898,69880,1975],{},[902,69882,18548],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,69885,69887],{"className":69886},[886],[888,69888,69889],{"xmlns":890},[892,69890,69891,69897],{},[895,69892,69893,69895],{},[898,69894,1978],{},[898,69896,1975],{},[902,69898,16029],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,69901,69903],{"className":69902},[886],[888,69904,69905],{"xmlns":890},[892,69906,69907,69913],{},[895,69908,69909,69911],{},[898,69910,1741],{},[898,69912,1975],{},[902,69914,18548],{"encoding":904}," osu ",[883,69917,69919],{"className":69918},[886],[888,69920,69921],{"xmlns":890},[892,69922,69923,69927],{},[895,69924,69925],{},[898,69926,1688],{},[902,69928,1688],{"encoding":904},[883,69930,69932],{"className":69931},[886],[888,69933,69934],{"xmlns":890},[892,69935,69936,69956],{},[895,69937,69938,69940,69942,69944],{},[898,69939,1688],{},[1708,69941,1710],{},[1708,69943,2726],{},[3194,69945,69946],{"scriptlevel":2784,"displaystyle":1715},[2358,69947,69948,69950],{},[898,69949,1923],{},[895,69951,69952,69954],{},[2505,69953,3132],{},[898,69955,207],{},[902,69957,69958],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,69961,69963],{"className":69962},[886],[888,69964,69965],{"xmlns":890},[892,69966,69967,69977],{},[895,69968,69969,69971,69973,69975],{},[898,69970,1741],{},[898,69972,1975],{},[1708,69974,1710],{},[2505,69976,2784],{},[902,69978,18997],{"encoding":904},", a dále ",[883,69981,69983],{"className":69982},[886],[888,69984,69985],{"xmlns":890},[892,69986,69987,69993],{},[895,69988,69989,69991],{},[898,69990,1978],{},[898,69992,1975],{},[902,69994,16029],{"encoding":904}," klesá.",[724,69997,69998,69999,70005,70006,70038,70039,70067],{},"V případě ",[38,70000,70001],{},[207,70002,70004],{"className":70003,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,70007,70009],{"className":70008},[886],[888,70010,70011],{"xmlns":890},[892,70012,70013,70035],{},[895,70014,70015,70017,70019,70021,70023,70025,70027,70029],{},[898,70016,1747],{},[1708,70018,1710],{},[898,70020,16117],{},[1708,70022,1716],{"stretchy":1715},[898,70024,1688],{},[1708,70026,1721],{"stretchy":1715},[1708,70028,1710],{},[1753,70030,70031,70033],{},[898,70032,1747],{},[1708,70034,2417],{},[902,70036,70037],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,70040,70042],{"className":70041},[886],[888,70043,70044],{"xmlns":890},[892,70045,70046,70064],{},[895,70047,70048,70050,70052,70054,70056,70058],{},[898,70049,1978],{},[898,70051,1975],{},[1708,70053,1710],{},[898,70055,1688],{},[1708,70057,3703],{},[1753,70059,70060,70062],{},[898,70061,1747],{},[1708,70063,2417],{},[902,70065,70066],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,70069,70071],{"className":70070},[886],[888,70072,70073],{"xmlns":890,"display":2210},[892,70074,70075,70117],{},[895,70076,70077,70079,70081,70083,70085,70087,70089,70095,70097,70099,70113,70115],{},[898,70078,1741],{},[898,70080,1975],{},[1708,70082,1710],{},[898,70084,1786],{},[898,70086,1975],{},[1708,70088,1710],{},[1753,70090,70091,70093],{},[898,70092,1747],{},[1708,70094,2417],{},[3213,70096],{"width":4750},[1708,70098,1716],{"stretchy":1715},[895,70100,70101,70104,70110],{},[2247,70102,70103],{},"obr",[20297,70105,70106,70108],{"accent":1882},[2247,70107,207],{},[1708,70109,36829],{},[2247,70111,70112],{},"zek 3.4",[1708,70114,1721],{"stretchy":1715},[898,70116,2155],{"mathvariant":1759},[902,70118,70119],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,70121,70122],{},[614,70123,70124,70125,1771,70151,70179,70180,70193,70194,70209,70210,15667,70223,1343,70249,15667,70264,2155],{},"Obrázek 3.2: Přímky ",[883,70126,70128],{"className":70127},[886],[888,70129,70130],{"xmlns":890},[892,70131,70132,70148],{},[895,70133,70134,70136,70138,70140,70142,70144,70146],{},[898,70135,1786],{},[898,70137,1975],{},[1708,70139,1710],{},[898,70141,207],{},[898,70143,1688],{},[1708,70145,2019],{},[898,70147,1923],{},[902,70149,70150],{"encoding":904},"AR = aQ + b",[883,70152,70154],{"className":70153},[886],[888,70155,70156],{"xmlns":890},[892,70157,70158,70176],{},[895,70159,70160,70162,70164,70166,70168,70170,70172,70174],{},[898,70161,1741],{},[898,70163,1975],{},[1708,70165,1710],{},[2505,70167,3132],{},[898,70169,207],{},[898,70171,1688],{},[1708,70173,2019],{},[898,70175,1923],{},[902,70177,70178],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,70181,70183],{"className":70182},[886],[888,70184,70185],{"xmlns":890},[892,70186,70187,70191],{},[895,70188,70189],{},[898,70190,1923],{},[902,70192,1923],{"encoding":904}," se svislou osou, ",[883,70195,70197],{"className":70196},[886],[888,70198,70199],{"xmlns":890},[892,70200,70201,70207],{},[895,70202,70203,70205],{},[898,70204,1741],{},[898,70206,1975],{},[902,70208,18548],{"encoding":904}," protíná osu ",[883,70211,70213],{"className":70212},[886],[888,70214,70215],{"xmlns":890},[892,70216,70217,70221],{},[895,70218,70219],{},[898,70220,1688],{},[902,70222,1688],{"encoding":904},[883,70224,70226],{"className":70225},[886],[888,70227,70228],{"xmlns":890},[892,70229,70230,70246],{},[895,70231,70232,70234],{},[1708,70233,2726],{},[3194,70235,70236],{"scriptlevel":2784,"displaystyle":1715},[2358,70237,70238,70240],{},[898,70239,1923],{},[895,70241,70242,70244],{},[2505,70243,3132],{},[898,70245,207],{},[902,70247,70248],{"encoding":904},"-\\tfrac{b}{2a}",[883,70250,70252],{"className":70251},[886],[888,70253,70254],{"xmlns":890},[892,70255,70256,70262],{},[895,70257,70258,70260],{},[898,70259,1786],{},[898,70261,1975],{},[902,70263,67264],{"encoding":904},[883,70265,70267],{"className":70266},[886],[888,70268,70269],{"xmlns":890},[892,70270,70271,70283],{},[895,70272,70273,70275],{},[1708,70274,2726],{},[3194,70276,70277],{"scriptlevel":2784,"displaystyle":1715},[2358,70278,70279,70281],{},[898,70280,1923],{},[898,70282,207],{},[902,70284,70285],{"encoding":904},"-\\tfrac{b}{a}",[724,70287,70288],{},[614,70289,70290,70291,70322,70323,70352,70353,2155],{},"Obrázek 3.3: Parabola ",[883,70292,70294],{"className":70293},[886],[888,70295,70296],{"xmlns":890},[892,70297,70298,70320],{},[895,70299,70300,70302,70304,70306,70308,70314,70316,70318],{},[898,70301,1978],{},[898,70303,1975],{},[1708,70305,1710],{},[898,70307,207],{},[1753,70309,70310,70312],{},[898,70311,1688],{},[2505,70313,3132],{},[1708,70315,2019],{},[898,70317,1923],{},[898,70319,1688],{},[902,70321,69754],{"encoding":904}," s maximem v ",[883,70324,70326],{"className":70325},[886],[888,70327,70328],{"xmlns":890},[892,70329,70330,70350],{},[895,70331,70332,70334,70336,70338],{},[898,70333,1688],{},[1708,70335,1710],{},[1708,70337,2726],{},[3194,70339,70340],{"scriptlevel":2784,"displaystyle":1715},[2358,70341,70342,70344],{},[898,70343,1923],{},[895,70345,70346,70348],{},[2505,70347,3132],{},[898,70349,207],{},[902,70351,69958],{"encoding":904}," a nulou v ",[883,70354,70356],{"className":70355},[886],[888,70357,70358],{"xmlns":890},[892,70359,70360,70376],{},[895,70361,70362,70364,70366,70368],{},[898,70363,1688],{},[1708,70365,1710],{},[1708,70367,2726],{},[3194,70369,70370],{"scriptlevel":2784,"displaystyle":1715},[2358,70371,70372,70374],{},[898,70373,1923],{},[898,70375,207],{},[902,70377,70378],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,70380,70381],{},[614,70382,70383,70384,2155],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,70385,70387],{"className":70386},[886],[888,70388,70389],{"xmlns":890},[892,70390,70391,70411],{},[895,70392,70393,70395,70397,70399,70401,70403,70405],{},[898,70394,1786],{},[898,70396,1975],{},[1708,70398,1710],{},[898,70400,1741],{},[898,70402,1975],{},[1708,70404,1710],{},[1753,70406,70407,70409],{},[898,70408,1747],{},[1708,70410,2417],{},[902,70412,70413],{"encoding":904},"AR = MR = P^*",[115,70415,70417],{"id":70416},"náklady-firmy","Náklady firmy",[198,70419,70421],{"id":70420},"celkové-náklady","Celkové náklady",[724,70423,70424,1729,70426,1695,70441,70444,70445,70458],{},[38,70425,70421],{},[883,70427,70429],{"className":70428},[886],[888,70430,70431],{"xmlns":890},[892,70432,70433,70439],{},[895,70434,70435,70437],{},[898,70436,1978],{},[898,70438,3455],{},[902,70440,15197],{"encoding":904},[38,70442,70443],{},"total cost",") jsou veškeré náklady na realizaci ",[883,70446,70448],{"className":70447},[886],[888,70449,70450],{"xmlns":890},[892,70451,70452,70456],{},[895,70453,70454],{},[898,70455,1688],{},[902,70457,1688],{"encoding":904}," jednotek produkce:",[883,70460,70462],{"className":70461},[886],[888,70463,70464],{"xmlns":890,"display":2210},[892,70465,70466,70521],{},[2214,70467,70468],{"width":2216},[2218,70469,70470,70472,70514,70516],{},[2221,70471],{"width":2223},[2221,70473,70474],{},[895,70475,70476,70478,70480,70482,70484,70486,70488,70490,70492,70494,70496,70498,70500,70502,70504,70506,70508,70510,70512],{},[898,70477,1978],{},[898,70479,3455],{},[1708,70481,1710],{},[898,70483,1978],{},[898,70485,3455],{},[1708,70487,1716],{"stretchy":1715},[898,70489,1688],{},[1708,70491,1721],{"stretchy":1715},[1708,70493,1710],{},[898,70495,22325],{},[898,70497,3455],{},[1708,70499,2019],{},[898,70501,1978],{},[898,70503,52173],{},[898,70505,3455],{},[1708,70507,1716],{"stretchy":1715},[898,70509,1688],{},[1708,70511,1721],{"stretchy":1715},[1708,70513,1883],{"separator":1882},[2221,70515],{"width":2223},[2221,70517,70518],{},[2247,70519,70520],{},"(3.5)",[902,70522,70523],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,70525,5411,70526,70541,70542,1695,70545,5149,70548,70541,70572,1695,70575,70578],{},[883,70527,70529],{"className":70528},[886],[888,70530,70531],{"xmlns":890},[892,70532,70533,70539],{},[895,70534,70535,70537],{},[898,70536,22325],{},[898,70538,3455],{},[902,70540,67310],{"encoding":904}," jsou ",[38,70543,70544],{},"fixní náklady",[38,70546,70547],{},"fixed cost",[883,70549,70551],{"className":70550},[886],[888,70552,70553],{"xmlns":890},[892,70554,70555,70569],{},[895,70556,70557,70559,70561,70563,70565,70567],{},[898,70558,1978],{},[898,70560,52173],{},[898,70562,3455],{},[1708,70564,1716],{"stretchy":1715},[898,70566,1688],{},[1708,70568,1721],{"stretchy":1715},[902,70570,70571],{"encoding":904},"TVC(Q)",[38,70573,70574],{},"celkové variabilní náklady",[38,70576,70577],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,70580,70582],{"id":70581},"průměrné-náklady","Průměrné náklady",[724,70584,70585,1729,70587,1695,70602,70605],{},[38,70586,70582],{},[883,70588,70590],{"className":70589},[886],[888,70591,70592],{"xmlns":890},[892,70593,70594,70600],{},[895,70595,70596,70598],{},[898,70597,1786],{},[898,70599,3455],{},[902,70601,3458],{"encoding":904},[38,70603,70604],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,70607,70609],{"className":70608},[886],[888,70610,70611],{"xmlns":890,"display":2210},[892,70612,70613,70692],{},[2214,70614,70615],{"width":2216},[2218,70616,70617,70619,70685,70687],{},[2221,70618],{"width":2223},[2221,70620,70621],{},[895,70622,70623,70625,70627,70629,70631,70633,70635,70637,70639,70641,70651,70653,70663,70665,70683],{},[898,70624,1786],{},[898,70626,3455],{},[1708,70628,1710],{},[898,70630,1786],{},[898,70632,3455],{},[1708,70634,1716],{"stretchy":1715},[898,70636,1688],{},[1708,70638,1721],{"stretchy":1715},[1708,70640,1710],{},[2358,70642,70643,70649],{},[895,70644,70645,70647],{},[898,70646,1978],{},[898,70648,3455],{},[898,70650,1688],{},[1708,70652,1710],{},[2358,70654,70655,70661],{},[895,70656,70657,70659],{},[898,70658,22325],{},[898,70660,3455],{},[898,70662,1688],{},[1708,70664,2019],{},[2358,70666,70667,70681],{},[895,70668,70669,70671,70673,70675,70677,70679],{},[898,70670,1978],{},[898,70672,52173],{},[898,70674,3455],{},[1708,70676,1716],{"stretchy":1715},[898,70678,1688],{},[1708,70680,1721],{"stretchy":1715},[898,70682,1688],{},[1708,70684,1883],{"separator":1882},[2221,70686],{"width":2223},[2221,70688,70689],{},[2247,70690,70691],{},"(3.6)",[902,70693,70694],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,70696,5411,70697,70541,70721,1729,70724,1695,70741,5149,70744,70541,70776,1729,70779,1695,70796,2750],{},[883,70698,70700],{"className":70699},[886],[888,70701,70702],{"xmlns":890},[892,70703,70704,70718],{},[895,70705,70706],{},[3194,70707,70708],{"scriptlevel":2784,"displaystyle":1715},[2358,70709,70710,70716],{},[895,70711,70712,70714],{},[898,70713,22325],{},[898,70715,3455],{},[898,70717,1688],{},[902,70719,70720],{"encoding":904},"\\tfrac{FC}{Q}",[38,70722,70723],{},"průměrné fixní náklady",[883,70725,70727],{"className":70726},[886],[888,70728,70729],{"xmlns":890},[892,70730,70731,70739],{},[895,70732,70733,70735,70737],{},[898,70734,1786],{},[898,70736,22325],{},[898,70738,3455],{},[902,70740,67346],{"encoding":904},[38,70742,70743],{},"average fixed cost",[883,70745,70747],{"className":70746},[886],[888,70748,70749],{"xmlns":890},[892,70750,70751,70773],{},[895,70752,70753],{},[3194,70754,70755],{"scriptlevel":2784,"displaystyle":1715},[2358,70756,70757,70771],{},[895,70758,70759,70761,70763,70765,70767,70769],{},[898,70760,1978],{},[898,70762,52173],{},[898,70764,3455],{},[1708,70766,1716],{"stretchy":1715},[898,70768,1688],{},[1708,70770,1721],{"stretchy":1715},[898,70772,1688],{},[902,70774,70775],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,70777,70778],{},"průměrné variabilní náklady",[883,70780,70782],{"className":70781},[886],[888,70783,70784],{"xmlns":890},[892,70785,70786,70794],{},[895,70787,70788,70790,70792],{},[898,70789,1786],{},[898,70791,52173],{},[898,70793,3455],{},[902,70795,67130],{"encoding":904},[38,70797,70798],{},"average variable cost",[883,70800,70802],{"className":70801},[886],[888,70803,70804],{"xmlns":890,"display":2210},[892,70805,70806,70865],{},[2214,70807,70808],{"width":2216},[2218,70809,70810,70812,70858,70860],{},[2221,70811],{"width":2223},[2221,70813,70814],{},[895,70815,70816,70818,70820,70822,70824,70826,70828,70830,70832,70834,70836,70838,70856],{},[898,70817,1786],{},[898,70819,52173],{},[898,70821,3455],{},[1708,70823,1710],{},[898,70825,1786],{},[898,70827,52173],{},[898,70829,3455],{},[1708,70831,1716],{"stretchy":1715},[898,70833,1688],{},[1708,70835,1721],{"stretchy":1715},[1708,70837,1710],{},[2358,70839,70840,70854],{},[895,70841,70842,70844,70846,70848,70850,70852],{},[898,70843,1978],{},[898,70845,52173],{},[898,70847,3455],{},[1708,70849,1716],{"stretchy":1715},[898,70851,1688],{},[1708,70853,1721],{"stretchy":1715},[898,70855,1688],{},[898,70857,2155],{"mathvariant":1759},[2221,70859],{"width":2223},[2221,70861,70862],{},[2247,70863,70864],{},"(3.7)",[902,70866,70867],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[49185,70869,70871],{"id":70870},"příklad-34","Příklad 3.4",[724,70873,70874,3973,70876,1771,70901,67843,70925,1771,70940,70955,70956,2155],{},[38,70875,67805],{},[883,70877,70879],{"className":70878},[886],[888,70880,70881],{"xmlns":890},[892,70882,70883,70898],{},[895,70884,70885,70887,70889,70891,70893,70895],{},[898,70886,22325],{},[898,70888,3455],{},[1708,70890,1710],{},[2505,70892,2507],{},[2247,70894,2659],{},[2505,70896,70897],{},"000",[902,70899,70900],{"encoding":904},"FC = 1\\,000",[883,70902,70904],{"className":70903},[886],[888,70905,70906],{"xmlns":890},[892,70907,70908,70922],{},[895,70909,70910,70912,70914,70916,70918,70920],{},[898,70911,1978],{},[898,70913,52173],{},[898,70915,3455],{},[1708,70917,1710],{},[2505,70919,5867],{},[898,70921,1688],{},[902,70923,70924],{"encoding":904},"TVC = 4Q",[883,70926,70928],{"className":70927},[886],[888,70929,70930],{"xmlns":890},[892,70931,70932,70938],{},[895,70933,70934,70936],{},[898,70935,1978],{},[898,70937,3455],{},[902,70939,15197],{"encoding":904},[883,70941,70943],{"className":70942},[886],[888,70944,70945],{"xmlns":890},[892,70946,70947,70953],{},[895,70948,70949,70951],{},[898,70950,1786],{},[898,70952,3455],{},[902,70954,3458],{"encoding":904}," a jejich chování s rostoucím ",[883,70957,70959],{"className":70958},[886],[888,70960,70961],{"xmlns":890},[892,70962,70963,70967],{},[895,70964,70965],{},[898,70966,1688],{},[902,70968,1688],{"encoding":904},[724,70970,70971,1729,70973,1771,71003,71039,71040,8214,71053,71068,71069,2788],{},[38,70972,34628],{},[883,70974,70976],{"className":70975},[886],[888,70977,70978],{"xmlns":890},[892,70979,70980,71000],{},[895,70981,70982,70984,70986,70988,70990,70992,70994,70996,70998],{},[898,70983,1978],{},[898,70985,3455],{},[1708,70987,1710],{},[2505,70989,2507],{},[2247,70991,2659],{},[2505,70993,70897],{},[1708,70995,2019],{},[2505,70997,5867],{},[898,70999,1688],{},[902,71001,71002],{"encoding":904},"TC = 1\\,000 + 4Q",[883,71004,71006],{"className":71005},[886],[888,71007,71008],{"xmlns":890},[892,71009,71010,71036],{},[895,71011,71012,71014,71016,71018,71032,71034],{},[898,71013,1786],{},[898,71015,3455],{},[1708,71017,1710],{},[3194,71019,71020],{"scriptlevel":2784,"displaystyle":1715},[2358,71021,71022,71030],{},[895,71023,71024,71026,71028],{},[2505,71025,2507],{},[2247,71027,2659],{},[2505,71029,70897],{},[898,71031,1688],{},[1708,71033,2019],{},[2505,71035,5867],{},[902,71037,71038],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,71041,71043],{"className":71042},[886],[888,71044,71045],{"xmlns":890},[892,71046,71047,71051],{},[895,71048,71049],{},[898,71050,1688],{},[902,71052,1688],{"encoding":904},[883,71054,71056],{"className":71055},[886],[888,71057,71058],{"xmlns":890},[892,71059,71060,71066],{},[895,71061,71062,71064],{},[898,71063,1786],{},[898,71065,3455],{},[902,71067,3458],{"encoding":904}," blíží ",[883,71070,71072],{"className":71071},[886],[888,71073,71074],{"xmlns":890},[892,71075,71076,71080],{},[895,71077,71078],{},[2505,71079,5867],{},[902,71081,5867],{"encoding":904},[883,71083,71085],{"className":71084},[886],[888,71086,71087],{"xmlns":890,"display":2210},[892,71088,71089,71135],{},[895,71090,71091,71108,71130,71132],{},[51730,71092,71093,71100],{},[895,71094,71095,71098],{},[898,71096,71097],{},"lim",[1708,71099,7149],{},[895,71101,71102,71104,71106],{},[898,71103,1688],{},[1708,71105,9392],{},[898,71107,18212],{"mathvariant":1759},[895,71109,71110,71112,71124,71126,71128],{},[1708,71111,1716],{"fence":1882},[2358,71113,71114,71122],{},[895,71115,71116,71118,71120],{},[2505,71117,2507],{},[2247,71119,2659],{},[2505,71121,70897],{},[898,71123,1688],{},[1708,71125,2019],{},[2505,71127,5867],{},[1708,71129,1721],{"fence":1882},[1708,71131,1710],{},[2505,71133,71134],{},"4.",[902,71136,71137],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,71139,71140,71178,71179,2155],{},[883,71141,71143],{"className":71142},[886],[888,71144,71145],{"xmlns":890},[892,71146,71147,71175],{},[895,71148,71149,71151,71153,71155,71157,71171,71173],{},[898,71150,1786],{},[898,71152,22325],{},[898,71154,3455],{},[1708,71156,1710],{},[3194,71158,71159],{"scriptlevel":2784,"displaystyle":1715},[2358,71160,71161,71169],{},[895,71162,71163,71165,71167],{},[2505,71164,2507],{},[2247,71166,2659],{},[2505,71168,70897],{},[898,71170,1688],{},[1708,71172,9392],{},[2505,71174,2784],{},[902,71176,71177],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,71180,71182],{"className":71181},[886],[888,71183,71184],{"xmlns":890},[892,71185,71186,71190],{},[895,71187,71188],{},[898,71189,1688],{},[902,71191,1688],{"encoding":904},[724,71193,71194],{},[614,71195,71196,71197,71226,71227,2155],{},"Obrázek 3.5: Přímka ",[883,71198,71200],{"className":71199},[886],[888,71201,71202],{"xmlns":890},[892,71203,71204,71224],{},[895,71205,71206,71208,71210,71212,71214,71216,71218,71220,71222],{},[898,71207,1978],{},[898,71209,3455],{},[1708,71211,1710],{},[2505,71213,2507],{},[2247,71215,2659],{},[2505,71217,70897],{},[1708,71219,2019],{},[2505,71221,5867],{},[898,71223,1688],{},[902,71225,71002],{"encoding":904}," protínající svislou osu ve výši ",[883,71228,71230],{"className":71229},[886],[888,71231,71232],{"xmlns":890},[892,71233,71234,71248],{},[895,71235,71236,71238,71240,71242,71244,71246],{},[898,71237,22325],{},[898,71239,3455],{},[1708,71241,1710],{},[2505,71243,2507],{},[2247,71245,2659],{},[2505,71247,70897],{},[902,71249,70900],{"encoding":904},[724,71251,71252],{},[614,71253,71254,71255,71290,71291,2155],{},"Obrázek 3.6: Hyperbola ",[883,71256,71258],{"className":71257},[886],[888,71259,71260],{"xmlns":890},[892,71261,71262,71288],{},[895,71263,71264,71266,71268,71270,71284,71286],{},[898,71265,1786],{},[898,71267,3455],{},[1708,71269,1710],{},[3194,71271,71272],{"scriptlevel":2784,"displaystyle":1715},[2358,71273,71274,71282],{},[895,71275,71276,71278,71280],{},[2505,71277,2507],{},[2247,71279,2659],{},[2505,71281,70897],{},[898,71283,1688],{},[1708,71285,2019],{},[2505,71287,5867],{},[902,71289,71038],{"encoding":904}," s vodorovnou asymptotou ",[883,71292,71294],{"className":71293},[886],[888,71295,71296],{"xmlns":890},[892,71297,71298,71308],{},[895,71299,71300,71302,71304,71306],{},[898,71301,1786],{},[898,71303,3455],{},[1708,71305,1710],{},[2505,71307,5867],{},[902,71309,71310],{"encoding":904},"AC = 4",[724,71312,71313],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,71315,71317],{"className":71316},[886],[888,71318,71319],{"xmlns":890,"display":2210},[892,71320,71321,71347],{},[895,71322,71323,71325,71327,71329,71331,71333,71335,71337,71339,71341,71343,71345],{},[898,71324,1978],{},[898,71326,52173],{},[898,71328,3455],{},[1708,71330,1710],{},[898,71332,1688],{},[1708,71334,3703],{},[898,71336,52173],{},[898,71338,3455],{},[1708,71340,1716],{"stretchy":1715},[898,71342,1688],{},[1708,71344,1721],{"stretchy":1715},[1708,71346,1883],{"separator":1882},[902,71348,71349],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,71351,5411,71352,70541,71380,71383,71384,71414],{},[883,71353,71355],{"className":71354},[886],[888,71356,71357],{"xmlns":890},[892,71358,71359,71377],{},[895,71360,71361,71363,71365,71367,71369,71371,71373,71375],{},[898,71362,52173],{},[898,71364,3455],{},[1708,71366,1710],{},[898,71368,52173],{},[898,71370,3455],{},[1708,71372,1716],{"stretchy":1715},[898,71374,1688],{},[1708,71376,1721],{"stretchy":1715},[902,71378,71379],{"encoding":904},"VC = VC(Q)",[38,71381,71382],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,71385,71387],{"className":71386},[886],[888,71388,71389],{"xmlns":890},[892,71390,71391,71411],{},[895,71392,71393,71395,71397,71399,71401,71403,71405,71407,71409],{},[898,71394,1978],{},[898,71396,52173],{},[898,71398,3455],{},[1708,71400,1716],{"stretchy":1715},[898,71402,1688],{},[1708,71404,1721],{"stretchy":1715},[1708,71406,1710],{},[898,71408,207],{},[898,71410,1688],{},[902,71412,71413],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,71416,71418],{"className":71417},[886],[888,71419,71420],{"xmlns":890,"display":2210},[892,71421,71422,71442],{},[895,71423,71424,71426,71428,71430,71432,71434,71436,71438,71440],{},[898,71425,1978],{},[898,71427,3455],{},[1708,71429,1710],{},[898,71431,22325],{},[898,71433,3455],{},[1708,71435,2019],{},[898,71437,207],{},[898,71439,1688],{},[898,71441,2155],{"mathvariant":1759},[902,71443,71444],{"encoding":904},"TC = FC + aQ.",[724,71446,71447,71448,71463,71464,71479,71480,71503,71504,71538,71539,71290,71552,71565,71566,1771,71614,71658,71659,2155],{},"Křivkou ",[883,71449,71451],{"className":71450},[886],[888,71452,71453],{"xmlns":890},[892,71454,71455,71461],{},[895,71456,71457,71459],{},[898,71458,1978],{},[898,71460,3455],{},[902,71462,15197],{"encoding":904}," je přímka se svislým průsečíkem ",[883,71465,71467],{"className":71466},[886],[888,71468,71469],{"xmlns":890},[892,71470,71471,71477],{},[895,71472,71473,71475],{},[898,71474,22325],{},[898,71476,3455],{},[902,71478,67310],{"encoding":904}," a sklonem ",[883,71481,71483],{"className":71482},[886],[888,71484,71485],{"xmlns":890},[892,71486,71487,71500],{},[895,71488,71489,71492,71494,71496,71498],{},[898,71490,71491],{},"tan",[1708,71493,7149],{},[898,71495,30728],{},[1708,71497,1710],{},[898,71499,207],{},[902,71501,71502],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,71505,71507],{"className":71506},[886],[888,71508,71509],{"xmlns":890},[892,71510,71511,71535],{},[895,71512,71513,71515,71517,71519,71531,71533],{},[898,71514,1786],{},[898,71516,3455],{},[1708,71518,1710],{},[3194,71520,71521],{"scriptlevel":2784,"displaystyle":1715},[2358,71522,71523,71529],{},[895,71524,71525,71527],{},[898,71526,22325],{},[898,71528,3455],{},[898,71530,1688],{},[1708,71532,2019],{},[898,71534,207],{},[902,71536,71537],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,71540,71542],{"className":71541},[886],[888,71543,71544],{"xmlns":890},[892,71545,71546,71550],{},[895,71547,71548],{},[898,71549,1658],{},[902,71551,1658],{"encoding":904},[883,71553,71555],{"className":71554},[886],[888,71556,71557],{"xmlns":890},[892,71558,71559,71563],{},[895,71560,71561],{},[898,71562,207],{},[902,71564,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,71567,71569],{"className":71568},[886],[888,71570,71571],{"xmlns":890},[892,71572,71573,71611],{},[895,71574,71575,71595,71607,71609],{},[1743,71576,71577,71583],{},[895,71578,71579,71581],{},[898,71580,71097],{},[1708,71582,7149],{},[895,71584,71585,71587,71589],{},[898,71586,1688],{},[1708,71588,9392],{},[1753,71590,71591,71593],{},[2505,71592,2784],{},[1708,71594,2019],{},[3194,71596,71597],{"scriptlevel":2784,"displaystyle":1715},[2358,71598,71599,71605],{},[895,71600,71601,71603],{},[898,71602,22325],{},[898,71604,3455],{},[898,71606,1688],{},[1708,71608,1710],{},[898,71610,18212],{"mathvariant":1759},[902,71612,71613],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,71615,71617],{"className":71616},[886],[888,71618,71619],{"xmlns":890},[892,71620,71621,71655],{},[895,71622,71623,71639,71651,71653],{},[1743,71624,71625,71631],{},[895,71626,71627,71629],{},[898,71628,71097],{},[1708,71630,7149],{},[895,71632,71633,71635,71637],{},[898,71634,1688],{},[1708,71636,9392],{},[898,71638,18212],{"mathvariant":1759},[3194,71640,71641],{"scriptlevel":2784,"displaystyle":1715},[2358,71642,71643,71649],{},[895,71644,71645,71647],{},[898,71646,22325],{},[898,71648,3455],{},[898,71650,1688],{},[1708,71652,1710],{},[2505,71654,2784],{},[902,71656,71657],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,71660,71662],{"className":71661},[886],[888,71663,71664],{"xmlns":890},[892,71665,71666,71672],{},[895,71667,71668,71670],{},[898,71669,1786],{},[898,71671,3455],{},[902,71673,3458],{"encoding":904},[724,71675,71676],{},[614,71677,71678,71679,71694,71695,71710,71711,2155],{},"Obrázek 3.7: Přímka ",[883,71680,71682],{"className":71681},[886],[888,71683,71684],{"xmlns":890},[892,71685,71686,71692],{},[895,71687,71688,71690],{},[898,71689,1978],{},[898,71691,3455],{},[902,71693,15197],{"encoding":904}," s osovým průsečíkem ve výši ",[883,71696,71698],{"className":71697},[886],[888,71699,71700],{"xmlns":890},[892,71701,71702,71708],{},[895,71703,71704,71706],{},[898,71705,22325],{},[898,71707,3455],{},[902,71709,67310],{"encoding":904}," a se sklonem ",[883,71712,71714],{"className":71713},[886],[888,71715,71716],{"xmlns":890},[892,71717,71718,71730],{},[895,71719,71720,71722,71724,71726,71728],{},[898,71721,71491],{},[1708,71723,7149],{},[898,71725,30728],{},[1708,71727,1710],{},[898,71729,207],{},[902,71731,71502],{"encoding":904},[724,71733,71734],{},[614,71735,71736,71737,71752,71753,2155],{},"Obrázek 3.8: Klesající hyperbola ",[883,71738,71740],{"className":71739},[886],[888,71741,71742],{"xmlns":890},[892,71743,71744,71750],{},[895,71745,71746,71748],{},[898,71747,1786],{},[898,71749,3455],{},[902,71751,3458],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,71754,71756],{"className":71755},[886],[888,71757,71758],{"xmlns":890},[892,71759,71760,71764],{},[895,71761,71762],{},[898,71763,207],{},[902,71765,207],{"encoding":904},[198,71767,71769],{"id":71768},"mezní-náklady","Mezní náklady",[724,71771,71772,1729,71774,1695,71789,71792,71793,71796],{},[38,71773,71769],{},[883,71775,71777],{"className":71776},[886],[888,71778,71779],{"xmlns":890},[892,71780,71781,71787],{},[895,71782,71783,71785],{},[898,71784,1741],{},[898,71786,3455],{},[902,71788,67111],{"encoding":904},[38,71790,71791],{},"marginal cost",") jsou ",[207,71794,1145],{"className":71795,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,71798,71800],{"className":71799},[886],[888,71801,71802],{"xmlns":890,"display":2210},[892,71803,71804,71873],{},[2214,71805,71806],{"width":2216},[2218,71807,71808,71810,71866,71868],{},[2221,71809],{"width":2223},[2221,71811,71812],{},[895,71813,71814,71816,71818,71820,71822,71824,71826,71828,71830,71832,71848,71850,71852,71858,71860,71862,71864],{},[898,71815,1741],{},[898,71817,3455],{},[1708,71819,1710],{},[898,71821,1741],{},[898,71823,3455],{},[1708,71825,1716],{"stretchy":1715},[898,71827,1688],{},[1708,71829,1721],{"stretchy":1715},[1708,71831,1710],{},[2358,71833,71834,71842],{},[895,71835,71836,71838,71840],{},[898,71837,2364],{"mathvariant":1759},[898,71839,1978],{},[898,71841,3455],{},[895,71843,71844,71846],{},[898,71845,2364],{"mathvariant":1759},[898,71847,1688],{},[1708,71849,1710],{},[898,71851,1978],{},[1753,71853,71854,71856],{},[898,71855,3455],{},[1708,71857,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,71859,1716],{"stretchy":1715},[898,71861,1688],{},[1708,71863,1721],{"stretchy":1715},[898,71865,2155],{"mathvariant":1759},[2221,71867],{"width":2223},[2221,71869,71870],{},[2247,71871,71872],{},"(3.8)",[902,71874,71875],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1636,71877,71878],{},[724,71879,71880,71882,71883,71909,71910,71927,71928,2155],{},[883,71881,2518],{}," Intuice — „kolik stojí další kus\"\n",[883,71884,71886],{"className":71885},[886],[888,71887,71888],{"xmlns":890},[892,71889,71890,71906],{},[895,71891,71892,71894,71896,71898,71904],{},[898,71893,1741],{},[898,71895,3455],{},[1708,71897,1716],{"stretchy":1715},[1753,71899,71900,71902],{},[898,71901,1688],{},[1708,71903,2417],{},[1708,71905,1721],{"stretchy":1715},[902,71907,71908],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,71911,71913],{"className":71912},[886],[888,71914,71915],{"xmlns":890},[892,71916,71917,71925],{},[895,71918,71919],{},[1753,71920,71921,71923],{},[898,71922,1688],{},[1708,71924,2417],{},[902,71926,41691],{"encoding":904},". Formálně ",[883,71929,71931],{"className":71930},[886],[888,71932,71933],{"xmlns":890},[892,71934,71935,71987],{},[895,71936,71937,71939,71941,71943,71949,71951,71953,71955,71957,71959,71965,71967,71969,71971,71973,71975,71977,71979,71985],{},[898,71938,1741],{},[898,71940,3455],{},[1708,71942,1716],{"stretchy":1715},[1753,71944,71945,71947],{},[898,71946,1688],{},[1708,71948,2417],{},[1708,71950,1721],{"stretchy":1715},[1708,71952,2638],{},[898,71954,1978],{},[898,71956,3455],{},[1708,71958,1716],{"stretchy":1715},[1753,71960,71961,71963],{},[898,71962,1688],{},[1708,71964,2417],{},[1708,71966,2019],{},[2505,71968,2507],{},[1708,71970,1721],{"stretchy":1715},[1708,71972,2726],{},[898,71974,1978],{},[898,71976,3455],{},[1708,71978,1716],{"stretchy":1715},[1753,71980,71981,71983],{},[898,71982,1688],{},[1708,71984,2417],{},[1708,71986,1721],{"stretchy":1715},[902,71988,71989],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,71991,71992,71993,2788],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,71994,71996],{"className":71995},[886],[888,71997,71998],{"xmlns":890},[892,71999,72000,72008],{},[895,72001,72002,72004,72006],{},[898,72003,2633],{"mathvariant":1759},[898,72005,1978],{},[898,72007,3455],{},[902,72009,72010],{"encoding":904},"\\Delta TC",[883,72012,72014],{"className":72013},[886],[888,72015,72016],{"xmlns":890,"display":2210},[892,72017,72018,72087],{},[2214,72019,72020],{"width":2216},[2218,72021,72022,72024,72080,72082],{},[2221,72023],{"width":2223},[2221,72025,72026],{},[895,72027,72028,72030,72032,72034,72036,72038,72040,72042,72044,72046,72048,72050,72052,72054,72060,72062,72064,72066,72068,72070,72072,72074,72076,72078],{},[898,72029,2633],{"mathvariant":1759},[898,72031,1978],{},[898,72033,3455],{},[2247,72035,4779],{},[1708,72037,2638],{},[2247,72039,4779],{},[898,72041,2364],{"mathvariant":1759},[898,72043,1978],{},[898,72045,3455],{},[1708,72047,1710],{},[1708,72049,1716],{"stretchy":1715},[898,72051,1978],{},[898,72053,3455],{},[1753,72055,72056,72058],{},[1708,72057,1721],{"stretchy":1715},[1708,72059,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[2247,72061,2659],{},[898,72063,2364],{"mathvariant":1759},[898,72065,1688],{},[1708,72067,1710],{},[898,72069,1741],{},[898,72071,3455],{},[2247,72073,2659],{},[898,72075,2364],{"mathvariant":1759},[898,72077,1688],{},[1708,72079,1883],{"separator":1882},[2221,72081],{"width":2223},[2221,72083,72084],{},[2247,72085,72086],{},"(3.9)",[902,72088,72089],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,72091,69128],{},[883,72093,72095],{"className":72094},[886],[888,72096,72097],{"xmlns":890,"display":2210},[892,72098,72099,72197],{},[895,72100,72101,72139,72141,72143,72145,72167,72169,72195],{},[895,72102,72103,72105,72111,72113,72119,72122,72128,72131],{},[2247,72104,69142],{},[20297,72106,72107,72109],{"accent":1882},[2247,72108,57558],{},[1708,72110,36910],{},[2247,72112,69151],{},[20297,72114,72115,72117],{"accent":1882},[2247,72116,14004],{},[1708,72118,36829],{},[2247,72120,72121],{},"ch n",[20297,72123,72124,72126],{"accent":1882},[2247,72125,207],{},[1708,72127,36829],{},[2247,72129,72130],{},"klad",[20297,72132,72133,72136],{"accent":1882},[2247,72134,72135],{},"u",[1708,72137,72138],{},"˚",[2247,72140,4779],{},[1708,72142,2638],{},[2247,72144,4779],{},[895,72146,72147,72149,72155,72158,72164],{},[2247,72148,69186],{},[20297,72150,72151,72153],{"accent":1882},[2247,72152,36898],{},[1708,72154,36829],{},[2247,72156,72157],{}," n",[20297,72159,72160,72162],{"accent":1882},[2247,72161,207],{},[1708,72163,36829],{},[2247,72165,72166],{},"klady",[1708,72168,69213],{},[895,72170,72171,72173,72179,72181,72187,72189],{},[2247,72172,69142],{},[20297,72174,72175,72177],{"accent":1882},[2247,72176,57558],{},[1708,72178,36910],{},[2247,72180,69226],{},[20297,72182,72183,72185],{"accent":1882},[2247,72184,21498],{},[1708,72186,36910],{},[2247,72188,69235],{},[20297,72190,72191,72193],{"accent":1882},[2247,72192,36898],{},[1708,72194,36829],{},[898,72196,2155],{"mathvariant":1759},[902,72198,72199],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[49185,72201,72203],{"id":72202},"příklad-35","Příklad 3.5",[724,72205,72206,3973,72208,67843,72244,72259,72260,72275,72276,14647,72289,2486,72302,72315,72316,2486,72329,2155],{},[38,72207,67805],{},[883,72209,72211],{"className":72210},[886],[888,72212,72213],{"xmlns":890},[892,72214,72215,72241],{},[895,72216,72217,72219,72221,72223,72225,72227,72229,72231,72233,72235],{},[898,72218,1978],{},[898,72220,3455],{},[1708,72222,1710],{},[2505,72224,20288],{},[1708,72226,2019],{},[2505,72228,3947],{},[898,72230,1688],{},[1708,72232,2019],{},[2505,72234,3132],{},[1753,72236,72237,72239],{},[898,72238,1688],{},[2505,72240,3132],{},[902,72242,72243],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,72245,72247],{"className":72246},[886],[888,72248,72249],{"xmlns":890},[892,72250,72251,72257],{},[895,72252,72253,72255],{},[898,72254,1741],{},[898,72256,3455],{},[902,72258,67111],{"encoding":904}," a odhadněte změny ",[883,72261,72263],{"className":72262},[886],[888,72264,72265],{"xmlns":890},[892,72266,72267,72273],{},[895,72268,72269,72271],{},[898,72270,1978],{},[898,72272,3455],{},[902,72274,15197],{"encoding":904}," při změnách ",[883,72277,72279],{"className":72278},[886],[888,72280,72281],{"xmlns":890},[892,72282,72283,72287],{},[895,72284,72285],{},[898,72286,1688],{},[902,72288,1688],{"encoding":904},[883,72290,72292],{"className":72291},[886],[888,72293,72294],{"xmlns":890},[892,72295,72296,72300],{},[895,72297,72298],{},[2505,72299,4853],{},[902,72301,4853],{"encoding":904},[883,72303,72305],{"className":72304},[886],[888,72306,72307],{"xmlns":890},[892,72308,72309,72313],{},[895,72310,72311],{},[2505,72312,53694],{},[902,72314,53694],{"encoding":904}," a z ",[883,72317,72319],{"className":72318},[886],[888,72320,72321],{"xmlns":890},[892,72322,72323,72327],{},[895,72324,72325],{},[2505,72326,4853],{},[902,72328,4853],{"encoding":904},[883,72330,72332],{"className":72331},[886],[888,72333,72334],{"xmlns":890},[892,72335,72336,72340],{},[895,72337,72338],{},[2505,72339,4090],{},[902,72341,4090],{"encoding":904},[724,72343,72344,1729,72346,2941,72372,1343,72399,72426,72427,72442,72443,72458,72459,72486,72487,72507,72508,32393,72529,72585,72586,14647,72599,2486,72612,3033,72625,2155],{},[38,72345,34628],{},[883,72347,72349],{"className":72348},[886],[888,72350,72351],{"xmlns":890},[892,72352,72353,72369],{},[895,72354,72355,72357,72359,72361,72363,72365,72367],{},[898,72356,1741],{},[898,72358,3455],{},[1708,72360,1710],{},[2505,72362,3947],{},[1708,72364,2019],{},[2505,72366,5867],{},[898,72368,1688],{},[902,72370,72371],{"encoding":904},"MC = 6 + 4Q",[883,72373,72375],{"className":72374},[886],[888,72376,72377],{"xmlns":890},[892,72378,72379,72396],{},[895,72380,72381,72383,72385,72387,72389,72391,72393],{},[898,72382,1741],{},[898,72384,3455],{},[1708,72386,1716],{"stretchy":1715},[2505,72388,4853],{},[1708,72390,1721],{"stretchy":1715},[1708,72392,1710],{},[2505,72394,72395],{},"66",[902,72397,72398],{"encoding":904},"MC(15) = 66",[883,72400,72402],{"className":72401},[886],[888,72403,72404],{"xmlns":890},[892,72405,72406,72423],{},[895,72407,72408,72410,72412,72414,72416,72418,72420],{},[898,72409,1741],{},[898,72411,3455],{},[1708,72413,1716],{"stretchy":1715},[2505,72415,4018],{},[1708,72417,1721],{"stretchy":1715},[1708,72419,1710],{},[2505,72421,72422],{},"86",[902,72424,72425],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,72428,72430],{"className":72429},[886],[888,72431,72432],{"xmlns":890},[892,72433,72434,72440],{},[895,72435,72436,72438],{},[898,72437,1978],{},[898,72439,3455],{},[902,72441,15197],{"encoding":904}," zvyšuje (",[883,72444,72446],{"className":72445},[886],[888,72447,72448],{"xmlns":890},[892,72449,72450,72456],{},[895,72451,72452,72454],{},[898,72453,1741],{},[898,72455,3455],{},[902,72457,67111],{"encoding":904}," je rostoucí). Z ",[883,72460,72462],{"className":72461},[886],[888,72463,72464],{"xmlns":890},[892,72465,72466,72483],{},[895,72467,72468,72470,72472,72474,72476,72478,72480],{},[898,72469,1978],{},[898,72471,3455],{},[1708,72473,1716],{"stretchy":1715},[2505,72475,4853],{},[1708,72477,1721],{"stretchy":1715},[1708,72479,1710],{},[2505,72481,72482],{},"740",[902,72484,72485],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,72488,72490],{"className":72489},[886],[888,72491,72492],{"xmlns":890},[892,72493,72494,72504],{},[895,72495,72496,72498,72500,72502],{},[898,72497,2364],{"mathvariant":1759},[898,72499,1688],{},[1708,72501,1710],{},[2505,72503,2507],{},[902,72505,72506],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,72509,72511],{"className":72510},[886],[888,72512,72513],{"xmlns":890},[892,72514,72515,72526],{},[895,72516,72517,72519,72521,72523],{},[898,72518,1978],{},[898,72520,3455],{},[1708,72522,2638],{},[2505,72524,72525],{},"806",[902,72527,72528],{"encoding":904},"TC \\approx 806",[883,72530,72532],{"className":72531},[886],[888,72533,72534],{"xmlns":890},[892,72535,72536,72582],{},[895,72537,72538,72540,72542,72544,72546,72548,72550,72552,72554,72556,72558,72560,72562,72564,72566,72568,72570,72573,72575,72577,72579],{},[898,72539,2633],{"mathvariant":1759},[898,72541,1978],{},[898,72543,3455],{},[1708,72545,1710],{},[898,72547,1978],{},[898,72549,3455],{},[1708,72551,1716],{"stretchy":1715},[2505,72553,53694],{},[1708,72555,1721],{"stretchy":1715},[1708,72557,2726],{},[898,72559,1978],{},[898,72561,3455],{},[1708,72563,1716],{"stretchy":1715},[2505,72565,4853],{},[1708,72567,1721],{"stretchy":1715},[1708,72569,1710],{},[2505,72571,72572],{},"808",[1708,72574,2726],{},[2505,72576,72482],{},[1708,72578,1710],{},[2505,72580,72581],{},"68",[902,72583,72584],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,72587,72589],{"className":72588},[886],[888,72590,72591],{"xmlns":890},[892,72592,72593,72597],{},[895,72594,72595],{},[898,72596,1688],{},[902,72598,1688],{"encoding":904},[883,72600,72602],{"className":72601},[886],[888,72603,72604],{"xmlns":890},[892,72605,72606,72610],{},[895,72607,72608],{},[2505,72609,4853],{},[902,72611,4853],{"encoding":904},[883,72613,72615],{"className":72614},[886],[888,72616,72617],{"xmlns":890},[892,72618,72619,72623],{},[895,72620,72621],{},[2505,72622,4090],{},[902,72624,4090],{"encoding":904},[883,72626,72628],{"className":72627},[886],[888,72629,72630],{"xmlns":890},[892,72631,72632,72661],{},[895,72633,72634,72636,72638,72640,72642,72644,72646,72648,72650,72652,72654,72656,72658],{},[898,72635,2633],{"mathvariant":1759},[898,72637,1978],{},[898,72639,3455],{},[1708,72641,2638],{},[2505,72643,72395],{},[1708,72645,3703],{},[1708,72647,1716],{"stretchy":1715},[1708,72649,2726],{},[2505,72651,3121],{},[1708,72653,1721],{"stretchy":1715},[1708,72655,1710],{},[1708,72657,2726],{},[2505,72659,72660],{},"198",[902,72662,72663],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,72665,72667],{"id":72666},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,72669,72670],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[49185,72672,72674],{"id":72673},"příklad-36","Příklad 3.6",[724,72676,72677,3973,72679,72723],{},[38,72678,67805],{},[883,72680,72682],{"className":72681},[886],[888,72683,72684],{"xmlns":890},[892,72685,72686,72720],{},[895,72687,72688,72690,72692,72694,72696,72698,72700,72702,72704,72706,72712,72714],{},[898,72689,1978],{},[898,72691,3455],{},[1708,72693,1710],{},[2505,72695,9238],{},[1708,72697,2019],{},[2505,72699,4028],{},[898,72701,1688],{},[1708,72703,2726],{},[2505,72705,3993],{},[1753,72707,72708,72710],{},[898,72709,1688],{},[2505,72711,3132],{},[1708,72713,2019],{},[1753,72715,72716,72718],{},[898,72717,1688],{},[2505,72719,3121],{},[902,72721,72722],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,72725,72726],{},[38,72727,34628],{},[883,72729,72731],{"className":72730},[886],[888,72732,72733],{"xmlns":890,"display":2210},[892,72734,72735,72979],{},[2214,72736,72737,72763,72811,72845,72887,72937],{"rowspacing":32617,"columnalign":32618,"columnspacing":1760},[2218,72738,72739,72749],{},[2221,72740,72741],{},[3194,72742,72743],{"scriptlevel":2784,"displaystyle":1882},[895,72744,72745,72747],{},[898,72746,22325],{},[898,72748,3455],{},[2221,72750,72751],{},[3194,72752,72753],{"scriptlevel":2784,"displaystyle":1882},[895,72754,72755,72757,72759,72761],{},[895,72756],{},[1708,72758,1710],{},[2505,72760,9238],{},[1708,72762,1883],{"separator":1882},[2218,72764,72765,72777],{},[2221,72766,72767],{},[3194,72768,72769],{"scriptlevel":2784,"displaystyle":1882},[895,72770,72771,72773,72775],{},[898,72772,1978],{},[898,72774,52173],{},[898,72776,3455],{},[2221,72778,72779],{},[3194,72780,72781],{"scriptlevel":2784,"displaystyle":1882},[895,72782,72783,72785,72787,72789,72791,72793,72795,72801,72803,72809],{},[895,72784],{},[1708,72786,1710],{},[2505,72788,4028],{},[898,72790,1688],{},[1708,72792,2726],{},[2505,72794,3993],{},[1753,72796,72797,72799],{},[898,72798,1688],{},[2505,72800,3132],{},[1708,72802,2019],{},[1753,72804,72805,72807],{},[898,72806,1688],{},[2505,72808,3121],{},[1708,72810,1883],{"separator":1882},[2218,72812,72813,72825],{},[2221,72814,72815],{},[3194,72816,72817],{"scriptlevel":2784,"displaystyle":1882},[895,72818,72819,72821,72823],{},[898,72820,1786],{},[898,72822,22325],{},[898,72824,3455],{},[2221,72826,72827],{},[3194,72828,72829],{"scriptlevel":2784,"displaystyle":1882},[895,72830,72831,72833,72835,72843],{},[895,72832],{},[1708,72834,1710],{},[3194,72836,72837],{"scriptlevel":2784,"displaystyle":1715},[2358,72838,72839,72841],{},[2505,72840,9238],{},[898,72842,1688],{},[1708,72844,1883],{"separator":1882},[2218,72846,72847,72859],{},[2221,72848,72849],{},[3194,72850,72851],{"scriptlevel":2784,"displaystyle":1882},[895,72852,72853,72855,72857],{},[898,72854,1786],{},[898,72856,52173],{},[898,72858,3455],{},[2221,72860,72861],{},[3194,72862,72863],{"scriptlevel":2784,"displaystyle":1882},[895,72864,72865,72867,72869,72871,72873,72875,72877,72879,72885],{},[895,72866],{},[1708,72868,1710],{},[2505,72870,4028],{},[1708,72872,2726],{},[2505,72874,3993],{},[898,72876,1688],{},[1708,72878,2019],{},[1753,72880,72881,72883],{},[898,72882,1688],{},[2505,72884,3132],{},[1708,72886,1883],{"separator":1882},[2218,72888,72889,72899],{},[2221,72890,72891],{},[3194,72892,72893],{"scriptlevel":2784,"displaystyle":1882},[895,72894,72895,72897],{},[898,72896,1786],{},[898,72898,3455],{},[2221,72900,72901],{},[3194,72902,72903],{"scriptlevel":2784,"displaystyle":1882},[895,72904,72905,72907,72909,72917,72919,72921,72923,72925,72927,72929,72935],{},[895,72906],{},[1708,72908,1710],{},[3194,72910,72911],{"scriptlevel":2784,"displaystyle":1715},[2358,72912,72913,72915],{},[2505,72914,9238],{},[898,72916,1688],{},[1708,72918,2019],{},[2505,72920,4028],{},[1708,72922,2726],{},[2505,72924,3993],{},[898,72926,1688],{},[1708,72928,2019],{},[1753,72930,72931,72933],{},[898,72932,1688],{},[2505,72934,3132],{},[1708,72936,1883],{"separator":1882},[2218,72938,72939,72949],{},[2221,72940,72941],{},[3194,72942,72943],{"scriptlevel":2784,"displaystyle":1882},[895,72944,72945,72947],{},[898,72946,1741],{},[898,72948,3455],{},[2221,72950,72951],{},[3194,72952,72953],{"scriptlevel":2784,"displaystyle":1882},[895,72954,72955,72957,72959,72961,72963,72965,72967,72969,72971,72977],{},[895,72956],{},[1708,72958,1710],{},[2505,72960,4028],{},[1708,72962,2726],{},[2505,72964,4003],{},[898,72966,1688],{},[1708,72968,2019],{},[2505,72970,3121],{},[1753,72972,72973,72975],{},[898,72974,1688],{},[2505,72976,3132],{},[898,72978,2155],{"mathvariant":1759},[902,72980,72981],{"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}",[724,72983,72984,72985,9137,73000,9137,73015,73030,73031,73046,73047,1343,73065,73046,73082,1343,73100,73046,73115,73133],{},"Význačné body ",[883,72986,72988],{"className":72987},[886],[888,72989,72990],{"xmlns":890},[892,72991,72992,72997],{},[895,72993,72994],{},[2505,72995,72996],{},"1,67",[902,72998,72999],{"encoding":904},"1{,}67",[883,73001,73003],{"className":73002},[886],[888,73004,73005],{"xmlns":890},[892,73006,73007,73012],{},[895,73008,73009],{},[2505,73010,73011],{},"2,50",[902,73013,73014],{"encoding":904},"2{,}50",[883,73016,73018],{"className":73017},[886],[888,73019,73020],{"xmlns":890},[892,73021,73022,73027],{},[895,73023,73024],{},[2505,73025,73026],{},"4,73",[902,73028,73029],{"encoding":904},"4{,}73"," odpovídají: ",[883,73032,73034],{"className":73033},[886],[888,73035,73036],{"xmlns":890},[892,73037,73038,73044],{},[895,73039,73040,73042],{},[898,73041,1741],{},[898,73043,3455],{},[902,73045,67111],{"encoding":904}," minimum v ",[883,73048,73050],{"className":73049},[886],[888,73051,73052],{"xmlns":890},[892,73053,73054,73062],{},[895,73055,73056,73058,73060],{},[898,73057,1688],{},[1708,73059,17816],{},[2505,73061,72996],{},[902,73063,73064],{"encoding":904},"Q \\doteq 1{,}67",[883,73066,73068],{"className":73067},[886],[888,73069,73070],{"xmlns":890},[892,73071,73072,73080],{},[895,73073,73074,73076,73078],{},[898,73075,1786],{},[898,73077,52173],{},[898,73079,3455],{},[902,73081,67130],{"encoding":904},[883,73083,73085],{"className":73084},[886],[888,73086,73087],{"xmlns":890},[892,73088,73089,73097],{},[895,73090,73091,73093,73095],{},[898,73092,1688],{},[1708,73094,1710],{},[2505,73096,73011],{},[902,73098,73099],{"encoding":904},"Q = 2{,}50",[883,73101,73103],{"className":73102},[886],[888,73104,73105],{"xmlns":890},[892,73106,73107,73113],{},[895,73108,73109,73111],{},[898,73110,1786],{},[898,73112,3455],{},[902,73114,3458],{"encoding":904},[883,73116,73118],{"className":73117},[886],[888,73119,73120],{"xmlns":890},[892,73121,73122,73130],{},[895,73123,73124,73126,73128],{},[898,73125,1688],{},[1708,73127,17816],{},[2505,73129,73026],{},[902,73131,73132],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,73135,73136],{},[3372,73137],{"alt":73138,"className":73139,"src":73140},"imek-ac-avc-mc",[210,3376],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,73142,73143],{},[614,73144,73145,73146,1771,73161,73178,73179,9137,73198,73213],{},"Obrázek 3.9: Kubické křivky ",[883,73147,73149],{"className":73148},[886],[888,73150,73151],{"xmlns":890},[892,73152,73153,73159],{},[895,73154,73155,73157],{},[898,73156,1978],{},[898,73158,3455],{},[902,73160,15197],{"encoding":904},[883,73162,73164],{"className":73163},[886],[888,73165,73166],{"xmlns":890},[892,73167,73168,73176],{},[895,73169,73170,73172,73174],{},[898,73171,1978],{},[898,73173,52173],{},[898,73175,3455],{},[902,73177,67328],{"encoding":904}," rostoucí od bodu ",[883,73180,73182],{"className":73181},[886],[888,73183,73184],{"xmlns":890},[892,73185,73186,73196],{},[895,73187,73188,73190,73192,73194],{},[898,73189,22325],{},[898,73191,3455],{},[1708,73193,1710],{},[2505,73195,9238],{},[902,73197,23520],{"encoding":904},[883,73199,73201],{"className":73200},[886],[888,73202,73203],{"xmlns":890},[892,73204,73205,73211],{},[895,73206,73207,73209],{},[898,73208,22325],{},[898,73210,3455],{},[902,73212,67310],{"encoding":904}," je vodorovná přímka.",[724,73215,73216],{},[614,73217,73218,73219,1343,73234,1343,73251,41048,73266,73279,73280,2941,73297,73312,73313,5283,73330,73345,73346,7468,73359,1343,73372,1343,73385,2155],{},"Obrázek 3.10: Křivky ",[883,73220,73222],{"className":73221},[886],[888,73223,73224],{"xmlns":890},[892,73225,73226,73232],{},[895,73227,73228,73230],{},[898,73229,1786],{},[898,73231,3455],{},[902,73233,3458],{"encoding":904},[883,73235,73237],{"className":73236},[886],[888,73238,73239],{"xmlns":890},[892,73240,73241,73249],{},[895,73242,73243,73245,73247],{},[898,73244,1786],{},[898,73246,52173],{},[898,73248,3455],{},[902,73250,67130],{"encoding":904},[883,73252,73254],{"className":73253},[886],[888,73255,73256],{"xmlns":890},[892,73257,73258,73264],{},[895,73259,73260,73262],{},[898,73261,1741],{},[898,73263,3455],{},[902,73265,67111],{"encoding":904},[883,73267,73269],{"className":73268},[886],[888,73270,73271],{"xmlns":890},[892,73272,73273,73277],{},[895,73274,73275],{},[898,73276,900],{},[902,73278,900],{"encoding":904}," a klesající hyperbola ",[883,73281,73283],{"className":73282},[886],[888,73284,73285],{"xmlns":890},[892,73286,73287,73295],{},[895,73288,73289,73291,73293],{},[898,73290,1786],{},[898,73292,22325],{},[898,73294,3455],{},[902,73296,67346],{"encoding":904},[883,73298,73300],{"className":73299},[886],[888,73301,73302],{"xmlns":890},[892,73303,73304,73310],{},[895,73305,73306,73308],{},[898,73307,1741],{},[898,73309,3455],{},[902,73311,67111],{"encoding":904}," protíná ",[883,73314,73316],{"className":73315},[886],[888,73317,73318],{"xmlns":890},[892,73319,73320,73328],{},[895,73321,73322,73324,73326],{},[898,73323,1786],{},[898,73325,52173],{},[898,73327,3455],{},[902,73329,67130],{"encoding":904},[883,73331,73333],{"className":73332},[886],[888,73334,73335],{"xmlns":890},[892,73336,73337,73343],{},[895,73338,73339,73341],{},[898,73340,1786],{},[898,73342,3455],{},[902,73344,3458],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,73347,73349],{"className":73348},[886],[888,73350,73351],{"xmlns":890},[892,73352,73353,73357],{},[895,73354,73355],{},[898,73356,1688],{},[902,73358,1688],{"encoding":904},[883,73360,73362],{"className":73361},[886],[888,73363,73364],{"xmlns":890},[892,73365,73366,73370],{},[895,73367,73368],{},[2505,73369,72996],{},[902,73371,72999],{"encoding":904},[883,73373,73375],{"className":73374},[886],[888,73376,73377],{"xmlns":890},[892,73378,73379,73383],{},[895,73380,73381],{},[2505,73382,73011],{},[902,73384,73014],{"encoding":904},[883,73386,73388],{"className":73387},[886],[888,73389,73390],{"xmlns":890},[892,73391,73392,73396],{},[895,73393,73394],{},[2505,73395,73026],{},[902,73397,73029],{"encoding":904},[724,73399,73400],{},[38,73401,73402],{},"Standardní vlastnosti:",[120,73404,73405,73440,73504,73572,73622,73642],{},[123,73406,73407,1771,73422,73439],{},[883,73408,73410],{"className":73409},[886],[888,73411,73412],{"xmlns":890},[892,73413,73414,73420],{},[895,73415,73416,73418],{},[898,73417,1978],{},[898,73419,3455],{},[902,73421,15197],{"encoding":904},[883,73423,73425],{"className":73424},[886],[888,73426,73427],{"xmlns":890},[892,73428,73429,73437],{},[895,73430,73431,73433,73435],{},[898,73432,1978],{},[898,73434,52173],{},[898,73436,3455],{},[902,73438,67328],{"encoding":904}," jsou kubické funkce;",[123,73441,73442,1343,73457,1343,73474,73489,73490,73503],{},[883,73443,73445],{"className":73444},[886],[888,73446,73447],{"xmlns":890},[892,73448,73449,73455],{},[895,73450,73451,73453],{},[898,73452,1786],{},[898,73454,3455],{},[902,73456,3458],{"encoding":904},[883,73458,73460],{"className":73459},[886],[888,73461,73462],{"xmlns":890},[892,73463,73464,73472],{},[895,73465,73466,73468,73470],{},[898,73467,1786],{},[898,73469,52173],{},[898,73471,3455],{},[902,73473,67130],{"encoding":904},[883,73475,73477],{"className":73476},[886],[888,73478,73479],{"xmlns":890},[892,73480,73481,73487],{},[895,73482,73483,73485],{},[898,73484,1741],{},[898,73486,3455],{},[902,73488,67111],{"encoding":904}," jsou křivky tvaru ",[883,73491,73493],{"className":73492},[886],[888,73494,73495],{"xmlns":890},[892,73496,73497,73501],{},[895,73498,73499],{},[898,73500,900],{},[902,73502,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,73505,73506,73521,73522,1343,73539,73556,73557,8197],{},[883,73507,73509],{"className":73508},[886],[888,73510,73511],{"xmlns":890},[892,73512,73513,73519],{},[895,73514,73515,73517],{},[898,73516,1741],{},[898,73518,3455],{},[902,73520,67111],{"encoding":904}," nabývá minima před ",[883,73523,73525],{"className":73524},[886],[888,73526,73527],{"xmlns":890},[892,73528,73529,73537],{},[895,73530,73531,73533,73535],{},[898,73532,1786],{},[898,73534,52173],{},[898,73536,3455],{},[902,73538,67130],{"encoding":904},[883,73540,73542],{"className":73541},[886],[888,73543,73544],{"xmlns":890},[892,73545,73546,73554],{},[895,73547,73548,73550,73552],{},[898,73549,1786],{},[898,73551,52173],{},[898,73553,3455],{},[902,73555,67130],{"encoding":904}," před ",[883,73558,73560],{"className":73559},[886],[888,73561,73562],{"xmlns":890},[892,73563,73564,73570],{},[895,73565,73566,73568],{},[898,73567,1786],{},[898,73569,3455],{},[902,73571,3458],{"encoding":904},[123,73573,73574,73312,73589,1771,73604,73621],{},[883,73575,73577],{"className":73576},[886],[888,73578,73579],{"xmlns":890},[892,73580,73581,73587],{},[895,73582,73583,73585],{},[898,73584,1741],{},[898,73586,3455],{},[902,73588,67111],{"encoding":904},[883,73590,73592],{"className":73591},[886],[888,73593,73594],{"xmlns":890},[892,73595,73596,73602],{},[895,73597,73598,73600],{},[898,73599,1786],{},[898,73601,3455],{},[902,73603,3458],{"encoding":904},[883,73605,73607],{"className":73606},[886],[888,73608,73609],{"xmlns":890},[892,73610,73611,73619],{},[895,73612,73613,73615,73617],{},[898,73614,1786],{},[898,73616,52173],{},[898,73618,3455],{},[902,73620,67130],{"encoding":904}," zdola právě v jejich minimech;",[123,73623,73624,73641],{},[883,73625,73627],{"className":73626},[886],[888,73628,73629],{"xmlns":890},[892,73630,73631,73639],{},[895,73632,73633,73635,73637],{},[898,73634,1786],{},[898,73636,22325],{},[898,73638,3455],{},[902,73640,67346],{"encoding":904}," je hyperbola, stále klesající;",[123,73643,73644,73676,73677,1771,73692,73709,73710,73723,73724,2511],{},[883,73645,73647],{"className":73646},[886],[888,73648,73649],{"xmlns":890},[892,73650,73651,73673],{},[895,73652,73653,73655,73657,73659,73661,73663,73665,73667,73669,73671],{},[898,73654,1786],{},[898,73656,3455],{},[1708,73658,1710],{},[898,73660,1786],{},[898,73662,22325],{},[898,73664,3455],{},[1708,73666,2019],{},[898,73668,1786],{},[898,73670,52173],{},[898,73672,3455],{},[902,73674,73675],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,73678,73680],{"className":73679},[886],[888,73681,73682],{"xmlns":890},[892,73683,73684,73690],{},[895,73685,73686,73688],{},[898,73687,1786],{},[898,73689,3455],{},[902,73691,3458],{"encoding":904},[883,73693,73695],{"className":73694},[886],[888,73696,73697],{"xmlns":890},[892,73698,73699,73707],{},[895,73700,73701,73703,73705],{},[898,73702,1786],{},[898,73704,52173],{},[898,73706,3455],{},[902,73708,67130],{"encoding":904}," klesá s rostoucím ",[883,73711,73713],{"className":73712},[886],[888,73714,73715],{"xmlns":890},[892,73716,73717,73721],{},[895,73718,73719],{},[898,73720,1688],{},[902,73722,1688],{"encoding":904}," (protože ",[883,73725,73727],{"className":73726},[886],[888,73728,73729],{"xmlns":890},[892,73730,73731,73743],{},[895,73732,73733,73735,73737,73739,73741],{},[898,73734,1786],{},[898,73736,22325],{},[898,73738,3455],{},[1708,73740,9392],{},[2505,73742,2784],{},[902,73744,73745],{"encoding":904},"AFC \\to 0",[115,73747,73749],{"id":73748},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,73751,73752,73753,73756,73757,73772],{},"Častou optimalizační úlohou je ",[38,73754,73755],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,73758,73760],{"className":73759},[886],[888,73761,73762],{"xmlns":890},[892,73763,73764,73770],{},[895,73765,73766,73768],{},[898,73767,1786],{},[898,73769,3455],{},[902,73771,3458],{"encoding":904}," minimální.",[198,73774,28284],{"id":28283},[724,73776,73777,73778,73795],{},"Mají-li průměrné náklady minimum v bodě ",[883,73779,73781],{"className":73780},[886],[888,73782,73783],{"xmlns":890},[892,73784,73785,73793],{},[895,73786,73787],{},[1743,73788,73789,73791],{},[898,73790,1688],{},[2505,73792,2784],{},[902,73794,50144],{"encoding":904},", pak platí",[883,73797,73799],{"className":73798},[886],[888,73800,73801],{"xmlns":890,"display":2210},[892,73802,73803,73852],{},[2214,73804,73805],{"width":2216},[2218,73806,73807,73809,73845,73847],{},[2221,73808],{"width":2223},[2221,73810,73811],{},[895,73812,73813,73815,73817,73819,73825,73827,73829,73831,73833,73835,73841,73843],{},[898,73814,1786],{},[898,73816,3455],{},[1708,73818,1716],{"stretchy":1715},[1743,73820,73821,73823],{},[898,73822,1688],{},[2505,73824,2784],{},[1708,73826,1721],{"stretchy":1715},[1708,73828,1710],{},[898,73830,1741],{},[898,73832,3455],{},[1708,73834,1716],{"stretchy":1715},[1743,73836,73837,73839],{},[898,73838,1688],{},[2505,73840,2784],{},[1708,73842,1721],{"stretchy":1715},[898,73844,2155],{"mathvariant":1759},[2221,73846],{"width":2223},[2221,73848,73849],{},[2247,73850,73851],{},"(3.10)",[902,73853,73854],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1636,73856,73857],{},[724,73858,73859,73861,73862],{},[883,73860,68261],{}," Princip\n",[38,73863,73864],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,73866,73867,73870,73871,73913],{},[38,73868,73869],{},"Odvození."," Z ",[883,73872,73874],{"className":73873},[886],[888,73875,73876],{"xmlns":890},[892,73877,73878,73910],{},[895,73879,73880,73882,73884,73886,73888,73890,73892],{},[898,73881,1786],{},[898,73883,3455],{},[1708,73885,1716],{"stretchy":1715},[898,73887,1688],{},[1708,73889,1721],{"stretchy":1715},[1708,73891,1710],{},[3194,73893,73894],{"scriptlevel":2784,"displaystyle":1715},[2358,73895,73896,73908],{},[895,73897,73898,73900,73902,73904,73906],{},[898,73899,1978],{},[898,73901,3455],{},[1708,73903,1716],{"stretchy":1715},[898,73905,1688],{},[1708,73907,1721],{"stretchy":1715},[898,73909,1688],{},[902,73911,73912],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,73915,73917],{"className":73916},[886],[888,73918,73919],{"xmlns":890,"display":2210},[892,73920,73921,74053],{},[895,73922,73923,73925,73931,73933,73935,73937,73939,73979,73981,74021,74023,74051],{},[898,73924,1786],{},[1753,73926,73927,73929],{},[898,73928,3455],{},[1708,73930,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,73932,1716],{"stretchy":1715},[898,73934,1688],{},[1708,73936,1721],{"stretchy":1715},[1708,73938,1710],{},[2358,73940,73941,73973],{},[895,73942,73943,73945,73951,73953,73955,73957,73959,73961,73963,73965,73967,73969,73971],{},[898,73944,1978],{},[1753,73946,73947,73949],{},[898,73948,3455],{},[1708,73950,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,73952,1716],{"stretchy":1715},[898,73954,1688],{},[1708,73956,1721],{"stretchy":1715},[1708,73958,3703],{},[898,73960,1688],{},[1708,73962,2726],{},[898,73964,1978],{},[898,73966,3455],{},[1708,73968,1716],{"stretchy":1715},[898,73970,1688],{},[1708,73972,1721],{"stretchy":1715},[1753,73974,73975,73977],{},[898,73976,1688],{},[2505,73978,3132],{},[1708,73980,1710],{},[2358,73982,73983,74015],{},[895,73984,73985,73987,73989,73991,73993,73995,73997,73999,74001,74003,74005,74007,74009,74011,74013],{},[898,73986,1741],{},[898,73988,3455],{},[1708,73990,1716],{"stretchy":1715},[898,73992,1688],{},[1708,73994,1721],{"stretchy":1715},[1708,73996,3703],{},[898,73998,1688],{},[1708,74000,2726],{},[898,74002,1786],{},[898,74004,3455],{},[1708,74006,1716],{"stretchy":1715},[898,74008,1688],{},[1708,74010,1721],{"stretchy":1715},[1708,74012,3703],{},[898,74014,1688],{},[1753,74016,74017,74019],{},[898,74018,1688],{},[2505,74020,3132],{},[1708,74022,1710],{},[2358,74024,74025,74049],{},[895,74026,74027,74029,74031,74033,74035,74037,74039,74041,74043,74045,74047],{},[898,74028,1741],{},[898,74030,3455],{},[1708,74032,1716],{"stretchy":1715},[898,74034,1688],{},[1708,74036,1721],{"stretchy":1715},[1708,74038,2726],{},[898,74040,1786],{},[898,74042,3455],{},[1708,74044,1716],{"stretchy":1715},[898,74046,1688],{},[1708,74048,1721],{"stretchy":1715},[898,74050,1688],{},[898,74052,2155],{"mathvariant":1759},[902,74054,74055],{"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}.",[724,74057,74058,74059,3405,74074,3033,74096,68638],{},"Nutnou podmínkou minima ",[883,74060,74062],{"className":74061},[886],[888,74063,74064],{"xmlns":890},[892,74065,74066,74072],{},[895,74067,74068,74070],{},[898,74069,1786],{},[898,74071,3455],{},[902,74073,3458],{"encoding":904},[883,74075,74077],{"className":74076},[886],[888,74078,74079],{"xmlns":890},[892,74080,74081,74093],{},[895,74082,74083,74089,74091],{},[1743,74084,74085,74087],{},[898,74086,1688],{},[2505,74088,2784],{},[1708,74090,2854],{},[2505,74092,2784],{},[902,74094,74095],{"encoding":904},"Q_0 > 0",[883,74097,74099],{"className":74098},[886],[888,74100,74101],{"xmlns":890},[892,74102,74103,74127],{},[895,74104,74105,74107,74113,74115,74121,74123,74125],{},[898,74106,1786],{},[1753,74108,74109,74111],{},[898,74110,3455],{},[1708,74112,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,74114,1716],{"stretchy":1715},[1743,74116,74117,74119],{},[898,74118,1688],{},[2505,74120,2784],{},[1708,74122,1721],{"stretchy":1715},[1708,74124,1710],{},[2505,74126,2784],{},[902,74128,74129],{"encoding":904},"AC'(Q_0) = 0",[883,74131,74133],{"className":74132},[886],[888,74134,74135],{"xmlns":890,"display":2210},[892,74136,74137,74222],{},[895,74138,74139,74179,74181,74183,74185,74188,74190,74192,74194,74196,74202,74204,74206,74208,74210,74212,74218,74220],{},[2358,74140,74141,74173],{},[895,74142,74143,74145,74147,74149,74155,74157,74159,74161,74163,74165,74171],{},[898,74144,1741],{},[898,74146,3455],{},[1708,74148,1716],{"stretchy":1715},[1743,74150,74151,74153],{},[898,74152,1688],{},[2505,74154,2784],{},[1708,74156,1721],{"stretchy":1715},[1708,74158,2726],{},[898,74160,1786],{},[898,74162,3455],{},[1708,74164,1716],{"stretchy":1715},[1743,74166,74167,74169],{},[898,74168,1688],{},[2505,74170,2784],{},[1708,74172,1721],{"stretchy":1715},[1743,74174,74175,74177],{},[898,74176,1688],{},[2505,74178,2784],{},[1708,74180,1710],{},[2505,74182,2784],{},[3213,74184],{"width":4750},[1708,74186,74187],{},"⟺",[3213,74189],{"width":4750},[898,74191,1741],{},[898,74193,3455],{},[1708,74195,1716],{"stretchy":1715},[1743,74197,74198,74200],{},[898,74199,1688],{},[2505,74201,2784],{},[1708,74203,1721],{"stretchy":1715},[1708,74205,1710],{},[898,74207,1786],{},[898,74209,3455],{},[1708,74211,1716],{"stretchy":1715},[1743,74213,74214,74216],{},[898,74215,1688],{},[2505,74217,2784],{},[1708,74219,1721],{"stretchy":1715},[898,74221,2155],{"mathvariant":1759},[902,74223,74224],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,74226,74227,1729,74230,73312,74245,74260,74261,74276,74277,3033,74294,74316,74317,74339],{},[38,74228,74229],{},"Geometrická interpretace.",[883,74231,74233],{"className":74232},[886],[888,74234,74235],{"xmlns":890},[892,74236,74237,74243],{},[895,74238,74239,74241],{},[898,74240,1741],{},[898,74242,3455],{},[902,74244,67111],{"encoding":904},[883,74246,74248],{"className":74247},[886],[888,74249,74250],{"xmlns":890},[892,74251,74252,74258],{},[895,74253,74254,74256],{},[898,74255,1786],{},[898,74257,3455],{},[902,74259,3458],{"encoding":904}," právě v bodě minima ",[883,74262,74264],{"className":74263},[886],[888,74265,74266],{"xmlns":890},[892,74267,74268,74274],{},[895,74269,74270,74272],{},[898,74271,1786],{},[898,74273,3455],{},[902,74275,3458],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,74278,74280],{"className":74279},[886],[888,74281,74282],{"xmlns":890},[892,74283,74284,74292],{},[895,74285,74286],{},[1743,74287,74288,74290],{},[898,74289,1688],{},[2505,74291,2784],{},[902,74293,50144],{"encoding":904},[883,74295,74297],{"className":74296},[886],[888,74298,74299],{"xmlns":890},[892,74300,74301,74313],{},[895,74302,74303,74305,74307,74309,74311],{},[898,74304,1741],{},[898,74306,3455],{},[1708,74308,2932],{},[898,74310,1786],{},[898,74312,3455],{},[902,74314,74315],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,74318,74320],{"className":74319},[886],[888,74321,74322],{"xmlns":890},[892,74323,74324,74336],{},[895,74325,74326,74328,74330,74332,74334],{},[898,74327,1741],{},[898,74329,3455],{},[1708,74331,2854],{},[898,74333,1786],{},[898,74335,3455],{},[902,74337,74338],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,74341,74342,74343,74385,74386,74403,74404,2155],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,74344,74346],{"className":74345},[886],[888,74347,74348],{"xmlns":890},[892,74349,74350,74382],{},[895,74351,74352,74354,74356,74358,74364,74366,74368,74370,74372,74374,74380],{},[898,74353,1786],{},[898,74355,3455],{},[1708,74357,1716],{"stretchy":1715},[1743,74359,74360,74362],{},[898,74361,1688],{},[2505,74363,2784],{},[1708,74365,1721],{"stretchy":1715},[1708,74367,1710],{},[898,74369,1741],{},[898,74371,3455],{},[1708,74373,1716],{"stretchy":1715},[1743,74375,74376,74378],{},[898,74377,1688],{},[2505,74379,2784],{},[1708,74381,1721],{"stretchy":1715},[902,74383,74384],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,74387,74389],{"className":74388},[886],[888,74390,74391],{"xmlns":890},[892,74392,74393,74401],{},[895,74394,74395],{},[1743,74396,74397,74399],{},[898,74398,1688],{},[2505,74400,2784],{},[902,74402,50144],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,74405,74407],{"className":74406},[886],[888,74408,74409],{"xmlns":890},[892,74410,74411,74435],{},[895,74412,74413,74415,74417,74419,74421,74423,74425,74427,74429,74431,74433],{},[898,74414,1786],{},[898,74416,3455],{},[1708,74418,1716],{"stretchy":1715},[898,74420,1688],{},[1708,74422,1721],{"stretchy":1715},[1708,74424,1710],{},[898,74426,1741],{},[898,74428,3455],{},[1708,74430,1716],{"stretchy":1715},[898,74432,1688],{},[1708,74434,1721],{"stretchy":1715},[902,74436,74437],{"encoding":904},"AC(Q) = MC(Q)",[1636,74439,74440],{},[724,74441,74442,74444,74445,1826,74463,74484,74485,1826,74488,74509,74510,74525,74526,69853,74541,2511],{},[883,74443,6130],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,74446,74447,74448],{},"minimum ",[883,74449,74451],{"className":74450},[886],[888,74452,74453],{"xmlns":890},[892,74454,74455,74461],{},[895,74456,74457,74459],{},[898,74458,1786],{},[898,74460,3455],{},[902,74462,3458],{"encoding":904},[883,74464,74466],{"className":74465},[886],[888,74467,74468],{"xmlns":890},[892,74469,74470,74482],{},[895,74471,74472,74474,74476,74478,74480],{},[898,74473,1786],{},[898,74475,3455],{},[1708,74477,1710],{},[898,74479,1741],{},[898,74481,3455],{},[902,74483,67042],{"encoding":904},", pro ",[38,74486,74487],{},"maximum zisku",[883,74489,74491],{"className":74490},[886],[888,74492,74493],{"xmlns":890},[892,74494,74495,74507],{},[895,74496,74497,74499,74501,74503,74505],{},[898,74498,1741],{},[898,74500,1975],{},[1708,74502,1710],{},[898,74504,1741],{},[898,74506,3455],{},[902,74508,67090],{"encoding":904},". Obě podmínky využívají ",[883,74511,74513],{"className":74512},[886],[888,74514,74515],{"xmlns":890},[892,74516,74517,74523],{},[895,74518,74519,74521],{},[898,74520,1741],{},[898,74522,3455],{},[902,74524,67111],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,74527,74529],{"className":74528},[886],[888,74530,74531],{"xmlns":890},[892,74532,74533,74539],{},[895,74534,74535,74537],{},[898,74536,1786],{},[898,74538,3455],{},[902,74540,3458],{"encoding":904},[883,74542,74544],{"className":74543},[886],[888,74545,74546],{"xmlns":890},[892,74547,74548,74554],{},[895,74549,74550,74552],{},[898,74551,1741],{},[898,74553,1975],{},[902,74555,18548],{"encoding":904},[49185,74557,74559],{"id":74558},"příklad-37","Příklad 3.7",[724,74561,74562,3973,74564,74598,74599,74612,74613,74628],{},[38,74563,67805],{},[883,74565,74567],{"className":74566},[886],[888,74568,74569],{"xmlns":890},[892,74570,74571,74595],{},[895,74572,74573,74575,74577,74579,74585,74587,74589,74591,74593],{},[898,74574,1978],{},[898,74576,3455],{},[1708,74578,1710],{},[1753,74580,74581,74583],{},[898,74582,1688],{},[2505,74584,3132],{},[1708,74586,2019],{},[2505,74588,3121],{},[898,74590,1688],{},[1708,74592,2019],{},[2505,74594,4547],{},[902,74596,74597],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,74600,74602],{"className":74601},[886],[888,74603,74604],{"xmlns":890},[892,74605,74606,74610],{},[895,74607,74608],{},[898,74609,1688],{},[902,74611,1688],{"encoding":904}," minimalizující ",[883,74614,74616],{"className":74615},[886],[888,74617,74618],{"xmlns":890},[892,74619,74620,74626],{},[895,74621,74622,74624],{},[898,74623,1786],{},[898,74625,3455],{},[902,74627,3458],{"encoding":904}," a ověřte princip (3.10).",[724,74630,74631,74633],{},[38,74632,34628],{}," Přímý výpočet:",[883,74635,74637],{"className":74636},[886],[888,74638,74639],{"xmlns":890,"display":2210},[892,74640,74641,74743],{},[895,74642,74643,74645,74647,74649,74671,74673,74675,74677,74679,74681,74687,74689,74691,74693,74695,74697,74703,74705,74707,74709,74719,74721,74741],{},[898,74644,1786],{},[898,74646,3455],{},[1708,74648,1710],{},[2358,74650,74651,74669],{},[895,74652,74653,74659,74661,74663,74665,74667],{},[1753,74654,74655,74657],{},[898,74656,1688],{},[2505,74658,3132],{},[1708,74660,2019],{},[2505,74662,3121],{},[898,74664,1688],{},[1708,74666,2019],{},[2505,74668,4547],{},[898,74670,1688],{},[1708,74672,1710],{},[898,74674,1688],{},[1708,74676,2019],{},[2505,74678,3121],{},[1708,74680,2019],{},[2358,74682,74683,74685],{},[2505,74684,4547],{},[898,74686,1688],{},[1708,74688,1883],{"separator":1882},[3213,74690],{"width":3215},[1708,74692,1716],{"stretchy":1715},[898,74694,1786],{},[898,74696,3455],{},[1753,74698,74699,74701],{},[1708,74700,1721],{"stretchy":1715},[1708,74702,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,74704,1710],{},[2505,74706,2507],{},[1708,74708,2726],{},[2358,74710,74711,74713],{},[2505,74712,4547],{},[1753,74714,74715,74717],{},[898,74716,1688],{},[2505,74718,3132],{},[1708,74720,1710],{},[2358,74722,74723,74735],{},[895,74724,74725,74731,74733],{},[1753,74726,74727,74729],{},[898,74728,1688],{},[2505,74730,3132],{},[1708,74732,2726],{},[2505,74734,4547],{},[1753,74736,74737,74739],{},[898,74738,1688],{},[2505,74740,3132],{},[898,74742,2155],{"mathvariant":1759},[902,74744,74745],{"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}.",[724,74747,74748,74788,74789,74813,74814,74864,74865,2155],{},[883,74749,74751],{"className":74750},[886],[888,74752,74753],{"xmlns":890},[892,74754,74755,74785],{},[895,74756,74757,74759,74761,74763,74769,74771,74773,74775,74781,74783],{},[1708,74758,1716],{"stretchy":1715},[898,74760,1786],{},[898,74762,3455],{},[1753,74764,74765,74767],{},[1708,74766,1721],{"stretchy":1715},[1708,74768,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,74770,1710],{},[2505,74772,2784],{},[1708,74774,4782],{},[1743,74776,74777,74779],{},[898,74778,1688],{},[2505,74780,2507],{},[1708,74782,1710],{},[2505,74784,3947],{},[902,74786,74787],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,74790,74792],{"className":74791},[886],[888,74793,74794],{"xmlns":890},[892,74795,74796,74810],{},[895,74797,74798,74804,74806,74808],{},[1743,74799,74800,74802],{},[898,74801,1688],{},[2505,74803,3132],{},[1708,74805,1710],{},[1708,74807,2726],{},[2505,74809,3947],{},[902,74811,74812],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,74815,74817],{"className":74816},[886],[888,74818,74819],{"xmlns":890},[892,74820,74821,74861],{},[895,74822,74823,74825,74827,74829,74839,74841,74843,74845,74847,74855,74857,74859],{},[1708,74824,1716],{"stretchy":1715},[898,74826,1786],{},[898,74828,3455],{},[1753,74830,74831,74833],{},[1708,74832,1721],{"stretchy":1715},[895,74834,74835,74837],{},[1708,74836,1761],{"mathvariant":1759},[1708,74838,1761],{"mathvariant":1759},[1708,74840,1716],{"stretchy":1715},[2505,74842,3947],{},[1708,74844,1721],{"stretchy":1715},[1708,74846,1710],{},[3194,74848,74849],{"scriptlevel":2784,"displaystyle":1715},[2358,74850,74851,74853],{},[2505,74852,2507],{},[2505,74854,3121],{},[1708,74856,2854],{},[2505,74858,2784],{},[1708,74860,4782],{},[902,74862,74863],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,74866,74868],{"className":74867},[886],[888,74869,74870],{"xmlns":890},[892,74871,74872,74888],{},[895,74873,74874,74876,74878,74880,74882,74884,74886],{},[898,74875,1786],{},[898,74877,3455],{},[1708,74879,1716],{"stretchy":1715},[2505,74881,3947],{},[1708,74883,1721],{"stretchy":1715},[1708,74885,1710],{},[2505,74887,4853],{},[902,74889,74890],{"encoding":904},"AC(6) = 15",[724,74892,74893,74894,74920,74921,2788],{},"Pomocí principu: ",[883,74895,74897],{"className":74896},[886],[888,74898,74899],{"xmlns":890},[892,74900,74901,74917],{},[895,74902,74903,74905,74907,74909,74911,74913,74915],{},[898,74904,1741],{},[898,74906,3455],{},[1708,74908,1710],{},[2505,74910,3132],{},[898,74912,1688],{},[1708,74914,2019],{},[2505,74916,3121],{},[902,74918,74919],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,74922,74924],{"className":74923},[886],[888,74925,74926],{"xmlns":890},[892,74927,74928,74940],{},[895,74929,74930,74932,74934,74936,74938],{},[898,74931,1786],{},[898,74933,3455],{},[1708,74935,1710],{},[898,74937,1741],{},[898,74939,3455],{},[902,74941,67042],{"encoding":904},[883,74943,74945],{"className":74944},[886],[888,74946,74947],{"xmlns":890,"display":2210},[892,74948,74949,75051],{},[895,74950,74951,74973,74975,74977,74979,74981,74983,74985,74987,74989,74995,74997,74999,75001,75003,75005,75007,75009,75015,75017,75019,75021,75023,75025,75027,75033,75035,75037,75039,75041,75043,75045,75047,75049],{},[2358,74952,74953,74971],{},[895,74954,74955,74961,74963,74965,74967,74969],{},[1753,74956,74957,74959],{},[898,74958,1688],{},[2505,74960,3132],{},[1708,74962,2019],{},[2505,74964,3121],{},[898,74966,1688],{},[1708,74968,2019],{},[2505,74970,4547],{},[898,74972,1688],{},[1708,74974,1710],{},[2505,74976,3132],{},[898,74978,1688],{},[1708,74980,2019],{},[2505,74982,3121],{},[2247,74984,4779],{},[1708,74986,4782],{},[2247,74988,4779],{},[1753,74990,74991,74993],{},[898,74992,1688],{},[2505,74994,3132],{},[1708,74996,2019],{},[2505,74998,3121],{},[898,75000,1688],{},[1708,75002,2019],{},[2505,75004,4547],{},[1708,75006,1710],{},[2505,75008,3132],{},[1753,75010,75011,75013],{},[898,75012,1688],{},[2505,75014,3132],{},[1708,75016,2019],{},[2505,75018,3121],{},[898,75020,1688],{},[2247,75022,4779],{},[1708,75024,4782],{},[2247,75026,4779],{},[1753,75028,75029,75031],{},[898,75030,1688],{},[2505,75032,3132],{},[1708,75034,1710],{},[2505,75036,4547],{},[2247,75038,4779],{},[1708,75040,4782],{},[2247,75042,4779],{},[898,75044,1688],{},[1708,75046,1710],{},[2505,75048,3947],{},[1708,75050,1883],{"separator":1882},[902,75052,75053],{"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,",[724,75055,75056,75057,75095],{},"a ",[883,75058,75060],{"className":75059},[886],[888,75061,75062],{"xmlns":890},[892,75063,75064,75092],{},[895,75065,75066,75068,75070,75072,75074,75076,75078,75080,75082,75084,75086,75088,75090],{},[898,75067,1786],{},[898,75069,3455],{},[1708,75071,1716],{"stretchy":1715},[2505,75073,3947],{},[1708,75075,1721],{"stretchy":1715},[1708,75077,1710],{},[898,75079,1741],{},[898,75081,3455],{},[1708,75083,1716],{"stretchy":1715},[2505,75085,3947],{},[1708,75087,1721],{"stretchy":1715},[1708,75089,1710],{},[2505,75091,4853],{},[902,75093,75094],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,75097,75099],{"id":75098},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,75101,75102,75103,2788],{},"Analogicky pro ",[883,75104,75106],{"className":75105},[886],[888,75107,75108],{"xmlns":890},[892,75109,75110,75118],{},[895,75111,75112,75114,75116],{},[898,75113,1786],{},[898,75115,52173],{},[898,75117,3455],{},[902,75119,67130],{"encoding":904},[883,75121,75123],{"className":75122},[886],[888,75124,75125],{"xmlns":890,"display":2210},[892,75126,75127,75178],{},[2214,75128,75129],{"width":2216},[2218,75130,75131,75133,75171,75173],{},[2221,75132],{"width":2223},[2221,75134,75135],{},[895,75136,75137,75139,75141,75143,75145,75151,75153,75155,75157,75159,75161,75167,75169],{},[898,75138,1786],{},[898,75140,52173],{},[898,75142,3455],{},[1708,75144,1716],{"stretchy":1715},[1743,75146,75147,75149],{},[898,75148,1688],{},[2505,75150,2784],{},[1708,75152,1721],{"stretchy":1715},[1708,75154,1710],{},[898,75156,1741],{},[898,75158,3455],{},[1708,75160,1716],{"stretchy":1715},[1743,75162,75163,75165],{},[898,75164,1688],{},[2505,75166,2784],{},[1708,75168,1721],{"stretchy":1715},[898,75170,2155],{"mathvariant":1759},[2221,75172],{"width":2223},[2221,75174,75175],{},[2247,75176,75177],{},"(3.11)",[902,75179,75180],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1636,75182,75183],{},[724,75184,75185,73861,75187],{},[883,75186,68261],{},[38,75188,75189,75190,75207],{},"V bodě minima průměrných variabilních nákladů se ",[883,75191,75193],{"className":75192},[886],[888,75194,75195],{"xmlns":890},[892,75196,75197,75205],{},[895,75198,75199,75201,75203],{},[898,75200,1786],{},[898,75202,52173],{},[898,75204,3455],{},[902,75206,67130],{"encoding":904}," rovnají mezním nákladům.",[724,75209,75210,75211,75233,75234,2155],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,75212,75214],{"className":75213},[886],[888,75215,75216],{"xmlns":890},[892,75217,75218,75230],{},[895,75219,75220,75226,75228],{},[1743,75221,75222,75224],{},[898,75223,1688],{},[2505,75225,2784],{},[1708,75227,1710],{},[2505,75229,65018],{},[902,75231,75232],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,75235,75237],{"className":75236},[886],[888,75238,75239],{"xmlns":890},[892,75240,75241,75267],{},[895,75242,75243,75245,75247,75249,75251,75253,75255,75257,75259,75261,75263,75265],{},[898,75244,1786],{},[898,75246,52173],{},[898,75248,3455],{},[1708,75250,1716],{"stretchy":1715},[898,75252,1688],{},[1708,75254,1721],{"stretchy":1715},[1708,75256,1710],{},[898,75258,1741],{},[898,75260,3455],{},[1708,75262,1716],{"stretchy":1715},[898,75264,1688],{},[1708,75266,1721],{"stretchy":1715},[902,75268,75269],{"encoding":904},"AVC(Q) = MC(Q)",[115,75271,75273],{"id":75272},"zisk-a-body-zvratu","Zisk a body zvratu",[724,75275,75276,1729,75279,75295],{},[38,75277,75278],{},"Zisk",[883,75280,75282],{"className":75281},[886],[888,75283,75284],{"xmlns":890},[892,75285,75286,75292],{},[895,75287,75288,75290],{},[898,75289,1747],{},[898,75291,1975],{},[902,75293,75294],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,75297,75299],{"className":75298},[886],[888,75300,75301],{"xmlns":890,"display":2210},[892,75302,75303,75362],{},[2214,75304,75305],{"width":2216},[2218,75306,75307,75309,75355,75357],{},[2221,75308],{"width":2223},[2221,75310,75311],{},[895,75312,75313,75315,75317,75319,75321,75323,75325,75327,75329,75331,75333,75335,75337,75339,75341,75343,75345,75347,75349,75351,75353],{},[898,75314,1747],{},[898,75316,1975],{},[1708,75318,1710],{},[898,75320,1747],{},[898,75322,1975],{},[1708,75324,1716],{"stretchy":1715},[898,75326,1688],{},[1708,75328,1721],{"stretchy":1715},[1708,75330,1710],{},[898,75332,1978],{},[898,75334,1975],{},[1708,75336,1716],{"stretchy":1715},[898,75338,1688],{},[1708,75340,1721],{"stretchy":1715},[1708,75342,2726],{},[898,75344,1978],{},[898,75346,3455],{},[1708,75348,1716],{"stretchy":1715},[898,75350,1688],{},[1708,75352,1721],{"stretchy":1715},[898,75354,2155],{"mathvariant":1759},[2221,75356],{"width":2223},[2221,75358,75359],{},[2247,75360,75361],{},"(3.12)",[902,75363,75364],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,75366,75367,75368,1771,75383,6801,75398,75400,75401,75404,75405,75421,75422,75437,75438,75453,75454,1343,75467,75480,75481,1343,75499,75517,75518,1695,75521,75524,75525,1348,75547,3033,75569,75591,75592,3033,75622,75644],{},"Body rovnosti ",[883,75369,75371],{"className":75370},[886],[888,75372,75373],{"xmlns":890},[892,75374,75375,75381],{},[895,75376,75377,75379],{},[898,75378,1978],{},[898,75380,1975],{},[902,75382,16029],{"encoding":904},[883,75384,75386],{"className":75385},[886],[888,75387,75388],{"xmlns":890},[892,75389,75390,75396],{},[895,75391,75392,75394],{},[898,75393,1978],{},[898,75395,3455],{},[902,75397,15197],{"encoding":904},[38,75399,67545],{}," (též vyrovnání, ",[614,75402,75403],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,75406,75408],{"className":75407},[886],[888,75409,75410],{"xmlns":890},[892,75411,75412,75418],{},[895,75413,75414,75416],{},[898,75415,52173],{},[898,75417,3455],{},[902,75419,75420],{"encoding":904},"VC",") je ",[883,75423,75425],{"className":75424},[886],[888,75426,75427],{"xmlns":890},[892,75428,75429,75435],{},[895,75430,75431,75433],{},[898,75432,1978],{},[898,75434,1975],{},[902,75436,16029],{"encoding":904}," kvadratická a ",[883,75439,75441],{"className":75440},[886],[888,75442,75443],{"xmlns":890},[892,75444,75445,75451],{},[895,75446,75447,75449],{},[898,75448,1978],{},[898,75450,3455],{},[902,75452,15197],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,75455,75457],{"className":75456},[886],[888,75458,75459],{"xmlns":890},[892,75460,75461,75465],{},[895,75462,75463],{},[898,75464,1786],{},[902,75466,1786],{"encoding":904},[883,75468,75470],{"className":75469},[886],[888,75471,75472],{"xmlns":890},[892,75473,75474,75478],{},[895,75475,75476],{},[898,75477,35110],{},[902,75479,35110],{"encoding":904}," odpovídajících množstvím ",[883,75482,75484],{"className":75483},[886],[888,75485,75486],{"xmlns":890},[892,75487,75488,75496],{},[895,75489,75490],{},[1743,75491,75492,75494],{},[898,75493,1688],{},[898,75495,1786],{},[902,75497,75498],{"encoding":904},"Q_A",[883,75500,75502],{"className":75501},[886],[888,75503,75504],{"xmlns":890},[892,75505,75506,75514],{},[895,75507,75508],{},[1743,75509,75510,75512],{},[898,75511,1688],{},[898,75513,35110],{},[902,75515,75516],{"encoding":904},"Q_B"," — firma je na ",[38,75519,75520],{},"prahu rentability",[614,75522,75523],{},"break even","). Pro ",[883,75526,75528],{"className":75527},[886],[888,75529,75530],{"xmlns":890},[892,75531,75532,75544],{},[895,75533,75534,75536,75538],{},[898,75535,1688],{},[1708,75537,2932],{},[1743,75539,75540,75542],{},[898,75541,1688],{},[898,75543,1786],{},[902,75545,75546],{"encoding":904},"Q \u003C Q_A",[883,75548,75550],{"className":75549},[886],[888,75551,75552],{"xmlns":890},[892,75553,75554,75566],{},[895,75555,75556,75558,75560],{},[898,75557,1688],{},[1708,75559,2854],{},[1743,75561,75562,75564],{},[898,75563,1688],{},[898,75565,35110],{},[902,75567,75568],{"encoding":904},"Q > Q_B",[883,75570,75572],{"className":75571},[886],[888,75573,75574],{"xmlns":890},[892,75575,75576,75588],{},[895,75577,75578,75580,75582,75584,75586],{},[898,75579,1978],{},[898,75581,3455],{},[1708,75583,2854],{},[898,75585,1978],{},[898,75587,1975],{},[902,75589,75590],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,75593,75595],{"className":75594},[886],[888,75596,75597],{"xmlns":890},[892,75598,75599,75619],{},[895,75600,75601,75607,75609,75611,75613],{},[1743,75602,75603,75605],{},[898,75604,1688],{},[898,75606,1786],{},[1708,75608,2932],{},[898,75610,1688],{},[1708,75612,2932],{},[1743,75614,75615,75617],{},[898,75616,1688],{},[898,75618,35110],{},[902,75620,75621],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,75623,75625],{"className":75624},[886],[888,75626,75627],{"xmlns":890},[892,75628,75629,75641],{},[895,75630,75631,75633,75635,75637,75639],{},[898,75632,1978],{},[898,75634,1975],{},[1708,75636,2854],{},[898,75638,1978],{},[898,75640,3455],{},[902,75642,75643],{"encoding":904},"TR > TC"," (zisk).",[1636,75646,75647],{},[724,75648,75649,75651],{},[883,75650,2518],{}," 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.",[724,75653,75654,75655,75681],{},"Body zvratu jsou řešení rovnice ",[883,75656,75658],{"className":75657},[886],[888,75659,75660],{"xmlns":890},[892,75661,75662,75678],{},[895,75663,75664,75666,75668,75670,75672,75674,75676],{},[898,75665,1747],{},[898,75667,1975],{},[1708,75669,1716],{"stretchy":1715},[898,75671,1688],{},[1708,75673,1721],{"stretchy":1715},[1708,75675,1710],{},[2505,75677,2784],{},[902,75679,75680],{"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.",[724,75683,75684],{},[3372,75685],{"alt":75686,"className":75687,"src":75688},"imek-tr-tc-body-zvratu",[210,3376],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,75690,75691],{},[614,75692,75693,75694,75709,75710,75725,75726,1771,75739,55189,75752,75765,75766,1771,75783,75800,75801,75821,75822,1771,75837,10064,75852,75881],{},"Obrázek 3.11: Body zvratu — křivky ",[883,75695,75697],{"className":75696},[886],[888,75698,75699],{"xmlns":890},[892,75700,75701,75707],{},[895,75702,75703,75705],{},[898,75704,1978],{},[898,75706,1975],{},[902,75708,16029],{"encoding":904}," (obrácená parabola) a ",[883,75711,75713],{"className":75712},[886],[888,75714,75715],{"xmlns":890},[892,75716,75717,75723],{},[895,75718,75719,75721],{},[898,75720,1978],{},[898,75722,3455],{},[902,75724,15197],{"encoding":904}," (přímka) se protínají v bodech ",[883,75727,75729],{"className":75728},[886],[888,75730,75731],{"xmlns":890},[892,75732,75733,75737],{},[895,75734,75735],{},[898,75736,1786],{},[902,75738,1786],{"encoding":904},[883,75740,75742],{"className":75741},[886],[888,75743,75744],{"xmlns":890},[892,75745,75746,75750],{},[895,75747,75748],{},[898,75749,35110],{},[902,75751,35110],{"encoding":904},[883,75753,75755],{"className":75754},[886],[888,75756,75757],{"xmlns":890},[892,75758,75759,75763],{},[895,75760,75761],{},[898,75762,1688],{},[902,75764,1688],{"encoding":904}," v hodnotách ",[883,75767,75769],{"className":75768},[886],[888,75770,75771],{"xmlns":890},[892,75772,75773,75781],{},[895,75774,75775],{},[1743,75776,75777,75779],{},[898,75778,1688],{},[898,75780,1786],{},[902,75782,75498],{"encoding":904},[883,75784,75786],{"className":75785},[886],[888,75787,75788],{"xmlns":890},[892,75789,75790,75798],{},[895,75791,75792],{},[1743,75793,75794,75796],{},[898,75795,1688],{},[898,75797,35110],{},[902,75799,75516],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,75802,75804],{"className":75803},[886],[888,75805,75806],{"xmlns":890},[892,75807,75808,75818],{},[895,75809,75810],{},[1743,75811,75812,75814,75816],{},[898,75813,1688],{},[898,75815,68015],{},[1708,75817,7149],{},[902,75819,75820],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,75823,75825],{"className":75824},[886],[888,75826,75827],{"xmlns":890},[892,75828,75829,75835],{},[895,75830,75831,75833],{},[898,75832,1978],{},[898,75834,1975],{},[902,75836,16029],{"encoding":904},[883,75838,75840],{"className":75839},[886],[888,75841,75842],{"xmlns":890},[892,75843,75844,75850],{},[895,75845,75846,75848],{},[898,75847,1978],{},[898,75849,3455],{},[902,75851,15197],{"encoding":904},[883,75853,75855],{"className":75854},[886],[888,75856,75857],{"xmlns":890},[892,75858,75859,75879],{},[895,75860,75861,75867,75869,75871,75873],{},[1743,75862,75863,75865],{},[898,75864,1688],{},[898,75866,1786],{},[1708,75868,2932],{},[898,75870,1688],{},[1708,75872,2932],{},[1743,75874,75875,75877],{},[898,75876,1688],{},[898,75878,35110],{},[902,75880,75621],{"encoding":904}," vyznačuje zisk.",[49185,75883,75885],{"id":75884},"příklad-38","Příklad 3.8",[724,75887,75888,75890,75891,1343,75911,1343,75937,75963],{},[38,75889,67805],{}," Dáno ",[883,75892,75894],{"className":75893},[886],[888,75895,75896],{"xmlns":890},[892,75897,75898,75908],{},[895,75899,75900,75902,75904,75906],{},[898,75901,22325],{},[898,75903,3455],{},[1708,75905,1710],{},[2505,75907,5867],{},[902,75909,75910],{"encoding":904},"FC = 4",[883,75912,75914],{"className":75913},[886],[888,75915,75916],{"xmlns":890},[892,75917,75918,75934],{},[895,75919,75920,75922,75924,75926,75928],{},[898,75921,1978],{},[898,75923,52173],{},[898,75925,3455],{},[1708,75927,1710],{},[1753,75929,75930,75932],{},[898,75931,1688],{},[2505,75933,3132],{},[902,75935,75936],{"encoding":904},"TVC = Q^2",[883,75938,75940],{"className":75939},[886],[888,75941,75942],{"xmlns":890},[892,75943,75944,75960],{},[895,75945,75946,75948,75950,75952,75954,75956,75958],{},[898,75947,1747],{},[1708,75949,1710],{},[1708,75951,2726],{},[2505,75953,3132],{},[898,75955,1688],{},[1708,75957,2019],{},[2505,75959,4635],{},[902,75961,75962],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,75965,75966,75968],{},[38,75967,34628],{}," Celkové náklady a příjem:",[883,75970,75972],{"className":75971},[886],[888,75973,75974],{"xmlns":890,"display":2210},[892,75975,75976,76042],{},[895,75977,75978,75980,75982,75984,75986,75988,75994,75996,75998,76000,76002,76004,76006,76008,76010,76012,76014,76016,76018,76020,76022,76024,76026,76028,76034,76036,76038,76040],{},[898,75979,1978],{},[898,75981,3455],{},[1708,75983,1710],{},[2505,75985,5867],{},[1708,75987,2019],{},[1753,75989,75990,75992],{},[898,75991,1688],{},[2505,75993,3132],{},[1708,75995,1883],{"separator":1882},[3213,75997],{"width":3215},[898,75999,1978],{},[898,76001,1975],{},[1708,76003,1710],{},[898,76005,1688],{},[1708,76007,3703],{},[1708,76009,1716],{"stretchy":1715},[1708,76011,2726],{},[2505,76013,3132],{},[898,76015,1688],{},[1708,76017,2019],{},[2505,76019,4635],{},[1708,76021,1721],{"stretchy":1715},[1708,76023,1710],{},[1708,76025,2726],{},[2505,76027,3132],{},[1753,76029,76030,76032],{},[898,76031,1688],{},[2505,76033,3132],{},[1708,76035,2019],{},[2505,76037,4635],{},[898,76039,1688],{},[898,76041,2155],{"mathvariant":1759},[902,76043,76044],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,76046,76047],{},"Zisk dle (3.12):",[883,76049,76051],{"className":76050},[886],[888,76052,76053],{"xmlns":890,"display":2210},[892,76054,76055,76133],{},[895,76056,76057,76059,76061,76063,76065,76067,76069,76071,76073,76075,76077,76079,76081,76087,76089,76091,76093,76095,76097,76099,76101,76103,76109,76111,76113,76115,76117,76123,76125,76127,76129,76131],{},[898,76058,1747],{},[898,76060,1975],{},[1708,76062,1710],{},[898,76064,1978],{},[898,76066,1975],{},[1708,76068,2726],{},[898,76070,1978],{},[898,76072,3455],{},[1708,76074,1710],{},[1708,76076,1716],{"stretchy":1715},[1708,76078,2726],{},[2505,76080,3132],{},[1753,76082,76083,76085],{},[898,76084,1688],{},[2505,76086,3132],{},[1708,76088,2019],{},[2505,76090,4635],{},[898,76092,1688],{},[1708,76094,1721],{"stretchy":1715},[1708,76096,2726],{},[1708,76098,1716],{"stretchy":1715},[2505,76100,5867],{},[1708,76102,2019],{},[1753,76104,76105,76107],{},[898,76106,1688],{},[2505,76108,3132],{},[1708,76110,1721],{"stretchy":1715},[1708,76112,1710],{},[1708,76114,2726],{},[2505,76116,3121],{},[1753,76118,76119,76121],{},[898,76120,1688],{},[2505,76122,3132],{},[1708,76124,2019],{},[2505,76126,4635],{},[898,76128,1688],{},[1708,76130,2726],{},[2505,76132,71134],{},[902,76134,76135],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,76137,76138,76141,76142,5055,76178,2788],{},[38,76139,76140],{},"Body zvratu"," jsou kořeny rovnice ",[883,76143,76145],{"className":76144},[886],[888,76146,76147],{"xmlns":890},[892,76148,76149,76175],{},[895,76150,76151,76153,76155,76161,76163,76165,76167,76169,76171,76173],{},[1708,76152,2726],{},[2505,76154,3121],{},[1753,76156,76157,76159],{},[898,76158,1688],{},[2505,76160,3132],{},[1708,76162,2019],{},[2505,76164,4635],{},[898,76166,1688],{},[1708,76168,2726],{},[2505,76170,5867],{},[1708,76172,1710],{},[2505,76174,2784],{},[902,76176,76177],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,76179,76181],{"className":76180},[886],[888,76182,76183],{"xmlns":890},[892,76184,76185,76209],{},[895,76186,76187,76189,76195,76197,76199,76201,76203,76205,76207],{},[2505,76188,3121],{},[1753,76190,76191,76193],{},[898,76192,1688],{},[2505,76194,3132],{},[1708,76196,2726],{},[2505,76198,4635],{},[898,76200,1688],{},[1708,76202,2019],{},[2505,76204,5867],{},[1708,76206,1710],{},[2505,76208,2784],{},[902,76210,76211],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,76213,76215],{"className":76214},[886],[888,76216,76217],{"xmlns":890,"display":2210},[892,76218,76219,76275],{},[895,76220,76221,76233,76235,76257,76259,76273],{},[1743,76222,76223,76225],{},[898,76224,1688],{},[895,76226,76227,76229,76231],{},[2505,76228,2507],{},[1708,76230,1883],{"separator":1882},[2505,76232,3132],{},[1708,76234,1710],{},[2358,76236,76237,76255],{},[895,76238,76239,76241,76244],{},[2505,76240,4635],{},[1708,76242,76243],{},"±",[9351,76245,76246],{},[895,76247,76248,76250,76252],{},[2505,76249,12358],{},[1708,76251,2726],{},[2505,76253,76254],{},"48",[2505,76256,3947],{},[1708,76258,1710],{},[2358,76260,76261,76271],{},[895,76262,76263,76265,76267],{},[2505,76264,4635],{},[1708,76266,76243],{},[9351,76268,76269],{},[2505,76270,20859],{},[2505,76272,3947],{},[1708,76274,1883],{"separator":1882},[902,76276,76277],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,76279,76280,76281,1771,76304,2155],{},"numericky ",[883,76282,76284],{"className":76283},[886],[888,76285,76286],{"xmlns":890},[892,76287,76288,76301],{},[895,76289,76290,76296,76298],{},[1743,76291,76292,76294],{},[898,76293,1688],{},[2505,76295,2507],{},[1708,76297,17816],{},[2505,76299,76300],{},"0,543",[902,76302,76303],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,76305,76307],{"className":76306},[886],[888,76308,76309],{"xmlns":890},[892,76310,76311,76324],{},[895,76312,76313,76319,76321],{},[1743,76314,76315,76317],{},[898,76316,1688],{},[2505,76318,3132],{},[1708,76320,17816],{},[2505,76322,76323],{},"2,457",[902,76325,76326],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,76328,76329,1729,76332,19465,76376,5055,76410,76428],{},[38,76330,76331],{},"Maximum zisku.",[883,76333,76335],{"className":76334},[886],[888,76336,76337],{"xmlns":890},[892,76338,76339,76373],{},[895,76340,76341,76343,76349,76351,76353,76355,76357,76359,76361,76363,76365,76367,76369,76371],{},[898,76342,1747],{},[1753,76344,76345,76347],{},[898,76346,1975],{},[1708,76348,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,76350,1710],{},[1708,76352,2726],{},[2505,76354,3947],{},[898,76356,1688],{},[1708,76358,2019],{},[2505,76360,4635],{},[1708,76362,1710],{},[2505,76364,2784],{},[1708,76366,4782],{},[898,76368,1688],{},[1708,76370,1710],{},[2505,76372,12222],{},[902,76374,76375],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,76377,76379],{"className":76378},[886],[888,76380,76381],{"xmlns":890},[892,76382,76383,76407],{},[895,76384,76385,76387,76397,76399,76401,76403,76405],{},[898,76386,1747],{},[1753,76388,76389,76391],{},[898,76390,1975],{},[895,76392,76393,76395],{},[1708,76394,1761],{"mathvariant":1759},[1708,76396,1761],{"mathvariant":1759},[1708,76398,1710],{},[1708,76400,2726],{},[2505,76402,3947],{},[1708,76404,2932],{},[2505,76406,2784],{},[902,76408,76409],{"encoding":904},"PR'' = -6 \u003C 0",[883,76411,76413],{"className":76412},[886],[888,76414,76415],{"xmlns":890},[892,76416,76417,76425],{},[895,76418,76419,76421,76423],{},[898,76420,1688],{},[1708,76422,1710],{},[2505,76424,12222],{},[902,76426,76427],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,76430,76432],{"className":76431},[886],[888,76433,76434],{"xmlns":890,"display":2210},[892,76435,76436,76499],{},[895,76437,76438,76440,76442,76444,76446,76448,76450,76452,76454,76456,76458,76460,76466,76468,76470,76472,76474,76476,76478,76480,76482,76485,76487,76490,76492,76494,76496],{},[898,76439,1747],{},[898,76441,1975],{},[1708,76443,1716],{"stretchy":1715},[2505,76445,12222],{},[1708,76447,1721],{"stretchy":1715},[1708,76449,1710],{},[1708,76451,2726],{},[2505,76453,3121],{},[1708,76455,3703],{},[1708,76457,1716],{"stretchy":1715},[2505,76459,12222],{},[1753,76461,76462,76464],{},[1708,76463,1721],{"stretchy":1715},[2505,76465,3132],{},[1708,76467,2019],{},[2505,76469,4635],{},[1708,76471,3703],{},[2505,76473,12222],{},[1708,76475,2726],{},[2505,76477,5867],{},[1708,76479,1710],{},[1708,76481,2726],{},[2505,76483,76484],{},"6,75",[1708,76486,2019],{},[2505,76488,76489],{},"13,5",[1708,76491,2726],{},[2505,76493,5867],{},[1708,76495,1710],{},[2505,76497,76498],{},"2,75.",[902,76500,76501],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,76503,76504,76505,1343,76550,76603,76604,76622],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,76506,76508],{"className":76507},[886],[888,76509,76510],{"xmlns":890},[892,76511,76512,76547],{},[895,76513,76514,76516,76522,76524,76526,76528,76530,76532,76534,76536,76538,76540,76542,76544],{},[898,76515,1978],{},[1753,76517,76518,76520],{},[898,76519,1975],{},[1708,76521,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,76523,1710],{},[1708,76525,2726],{},[2505,76527,5867],{},[898,76529,1688],{},[1708,76531,2019],{},[2505,76533,4635],{},[1708,76535,1710],{},[2505,76537,2784],{},[1708,76539,4782],{},[898,76541,1688],{},[1708,76543,1710],{},[2505,76545,76546],{},"2,25",[902,76548,76549],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,76551,76553],{"className":76552},[886],[888,76554,76555],{"xmlns":890},[892,76556,76557,76600],{},[895,76558,76559,76561,76569,76571,76573,76575,76577,76579,76581,76587,76589,76591,76593,76595,76597],{},[898,76560,1978],{},[1743,76562,76563,76565,76567],{},[898,76564,1975],{},[898,76566,68015],{},[1708,76568,7149],{},[1708,76570,1710],{},[1708,76572,2726],{},[2505,76574,3132],{},[1708,76576,3703],{},[1708,76578,1716],{"stretchy":1715},[2505,76580,76546],{},[1753,76582,76583,76585],{},[1708,76584,1721],{"stretchy":1715},[2505,76586,3132],{},[1708,76588,2019],{},[2505,76590,4635],{},[1708,76592,3703],{},[2505,76594,76546],{},[1708,76596,1710],{},[2505,76598,76599],{},"10,125",[902,76601,76602],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,76605,76607],{"className":76606},[886],[888,76608,76609],{"xmlns":890},[892,76610,76611,76619],{},[895,76612,76613,76615,76617],{},[898,76614,1688],{},[1708,76616,1710],{},[2505,76618,76546],{},[902,76620,76621],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1636,76624,76625],{},[724,76626,76627,76629,76630,1343,76652,76674,76675,1343,76692,76713,76714,76746,76747,76785,76786,14647,76804,76821,76822,1771,76850,76884,76885,19598,76923,1771,76947,2155],{},[883,76628,6130],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,76631,76633],{"className":76632},[886],[888,76634,76635],{"xmlns":890},[892,76636,76637,76649],{},[895,76638,76639,76645,76647],{},[1743,76640,76641,76643],{},[898,76642,1688],{},[2505,76644,2507],{},[1708,76646,1710],{},[2505,76648,6097],{},[902,76650,76651],{"encoding":904},"Q_1 = 0{,}5",[883,76653,76655],{"className":76654},[886],[888,76656,76657],{"xmlns":890},[892,76658,76659,76671],{},[895,76660,76661,76667,76669],{},[1743,76662,76663,76665],{},[898,76664,1688],{},[2505,76666,3132],{},[1708,76668,1710],{},[2505,76670,5867],{},[902,76672,76673],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,76676,76678],{"className":76677},[886],[888,76679,76680],{"xmlns":890},[892,76681,76682,76690],{},[895,76683,76684,76686,76688],{},[898,76685,1688],{},[1708,76687,1710],{},[2505,76689,76546],{},[902,76691,76621],{"encoding":904},[883,76693,76695],{"className":76694},[886],[888,76696,76697],{"xmlns":890},[892,76698,76699,76710],{},[895,76700,76701,76703,76705,76707],{},[898,76702,1747],{},[898,76704,1975],{},[1708,76706,1710],{},[2505,76708,76709],{},"6,125",[902,76711,76712],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,76715,76717],{"className":76716},[886],[888,76718,76719],{"xmlns":890},[892,76720,76721,76743],{},[895,76722,76723,76725,76731,76733,76735,76737,76739,76741],{},[898,76724,1747],{},[1753,76726,76727,76729],{},[898,76728,1975],{},[1708,76730,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,76732,1710],{},[1708,76734,2726],{},[2505,76736,5867],{},[898,76738,1688],{},[1708,76740,2019],{},[2505,76742,4635],{},[902,76744,76745],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,76748,76750],{"className":76749},[886],[888,76751,76752],{"xmlns":890},[892,76753,76754,76782],{},[895,76755,76756,76758,76760,76762,76764,76766,76772,76774,76776,76778,76780],{},[898,76757,1747],{},[898,76759,1975],{},[1708,76761,1710],{},[1708,76763,2726],{},[2505,76765,3132],{},[1753,76767,76768,76770],{},[898,76769,1688],{},[2505,76771,3132],{},[1708,76773,2019],{},[2505,76775,4635],{},[898,76777,1688],{},[1708,76779,2726],{},[2505,76781,5867],{},[902,76783,76784],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,76787,76789],{"className":76788},[886],[888,76790,76791],{"xmlns":890},[892,76792,76793,76801],{},[895,76794,76795],{},[1753,76796,76797,76799],{},[898,76798,1688],{},[2505,76800,3132],{},[902,76802,76803],{"encoding":904},"Q^2",[883,76805,76807],{"className":76806},[886],[888,76808,76809],{"xmlns":890},[892,76810,76811,76819],{},[895,76812,76813,76815,76817],{},[898,76814,1978],{},[898,76816,52173],{},[898,76818,3455],{},[902,76820,67328],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,76823,76825],{"className":76824},[886],[888,76826,76827],{"xmlns":890},[892,76828,76829,76847],{},[895,76830,76831,76833,76835,76837,76839,76841],{},[898,76832,1978],{},[898,76834,3455],{},[1708,76836,1710],{},[2505,76838,5867],{},[1708,76840,2019],{},[1753,76842,76843,76845],{},[898,76844,1688],{},[2505,76846,3132],{},[902,76848,76849],{"encoding":904},"TC = 4 + Q^2",[883,76851,76853],{"className":76852},[886],[888,76854,76855],{"xmlns":890},[892,76856,76857,76881],{},[895,76858,76859,76861,76863,76865,76867,76869,76875,76877,76879],{},[898,76860,1978],{},[898,76862,1975],{},[1708,76864,1710],{},[1708,76866,2726],{},[2505,76868,3132],{},[1753,76870,76871,76873],{},[898,76872,1688],{},[2505,76874,3132],{},[1708,76876,2019],{},[2505,76878,4635],{},[898,76880,1688],{},[902,76882,76883],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,76886,76888],{"className":76887},[886],[888,76889,76890],{"xmlns":890},[892,76891,76892,76920],{},[895,76893,76894,76896,76898,76900,76902,76904,76910,76912,76914,76916,76918],{},[898,76895,1747],{},[898,76897,1975],{},[1708,76899,1710],{},[1708,76901,2726],{},[2505,76903,3121],{},[1753,76905,76906,76908],{},[898,76907,1688],{},[2505,76909,3132],{},[1708,76911,2019],{},[2505,76913,4635],{},[898,76915,1688],{},[1708,76917,2726],{},[2505,76919,5867],{},[902,76921,76922],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,76924,76926],{"className":76925},[886],[888,76927,76928],{"xmlns":890},[892,76929,76930,76944],{},[895,76931,76932,76940,76942],{},[1743,76933,76934,76936,76938],{},[898,76935,1688],{},[898,76937,68015],{},[1708,76939,7149],{},[1708,76941,1710],{},[2505,76943,12222],{},[902,76945,76946],{"encoding":904},"Q_{\\max} = 1{,}5",[883,76948,76950],{"className":76949},[886],[888,76951,76952],{"xmlns":890},[892,76953,76954,76971],{},[895,76955,76956,76958,76966,76968],{},[898,76957,1747],{},[1743,76959,76960,76962,76964],{},[898,76961,1975],{},[898,76963,68015],{},[1708,76965,7149],{},[1708,76967,1710],{},[2505,76969,76970],{},"2,75",[902,76972,76973],{"encoding":904},"PR_{\\max} = 2{,}75",[724,76975,76976],{},[614,76977,76978,76979,77006,77007,77040,77041,1343,77064,2155],{},"Obrázek 3.12: Graf ",[883,76980,76982],{"className":76981},[886],[888,76983,76984],{"xmlns":890},[892,76985,76986,77004],{},[895,76987,76988,76990,76992,76994,76996,76998],{},[898,76989,1978],{},[898,76991,3455],{},[1708,76993,1710],{},[2505,76995,5867],{},[1708,76997,2019],{},[1753,76999,77000,77002],{},[898,77001,1688],{},[2505,77003,3132],{},[902,77005,76849],{"encoding":904}," (parabola) a ",[883,77008,77010],{"className":77009},[886],[888,77011,77012],{"xmlns":890},[892,77013,77014,77038],{},[895,77015,77016,77018,77020,77022,77024,77026,77032,77034,77036],{},[898,77017,1978],{},[898,77019,1975],{},[1708,77021,1710],{},[1708,77023,2726],{},[2505,77025,3132],{},[1753,77027,77028,77030],{},[898,77029,1688],{},[2505,77031,3132],{},[1708,77033,2019],{},[2505,77035,4635],{},[898,77037,1688],{},[902,77039,76883],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,77042,77044],{"className":77043},[886],[888,77045,77046],{"xmlns":890},[892,77047,77048,77061],{},[895,77049,77050,77056,77058],{},[1743,77051,77052,77054],{},[898,77053,1688],{},[2505,77055,2507],{},[1708,77057,17816],{},[2505,77059,77060],{},"0,54",[902,77062,77063],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,77065,77067],{"className":77066},[886],[888,77068,77069],{"xmlns":890},[892,77070,77071,77084],{},[895,77072,77073,77079,77081],{},[1743,77074,77075,77077],{},[898,77076,1688],{},[2505,77078,3132],{},[1708,77080,17816],{},[2505,77082,77083],{},"2,46",[902,77085,77086],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,77088,77089],{},[614,77090,77091,77092,70322,77129,77146,77147,1343,77168,2155],{},"Obrázek 3.13: Graf zisku ",[883,77093,77095],{"className":77094},[886],[888,77096,77097],{"xmlns":890},[892,77098,77099,77127],{},[895,77100,77101,77103,77105,77107,77109,77111,77117,77119,77121,77123,77125],{},[898,77102,1747],{},[898,77104,1975],{},[1708,77106,1710],{},[1708,77108,2726],{},[2505,77110,3121],{},[1753,77112,77113,77115],{},[898,77114,1688],{},[2505,77116,3132],{},[1708,77118,2019],{},[2505,77120,4635],{},[898,77122,1688],{},[1708,77124,2726],{},[2505,77126,5867],{},[902,77128,76922],{"encoding":904},[883,77130,77132],{"className":77131},[886],[888,77133,77134],{"xmlns":890},[892,77135,77136,77144],{},[895,77137,77138,77140,77142],{},[898,77139,1688],{},[1708,77141,1710],{},[2505,77143,12222],{},[902,77145,76427],{"encoding":904}," a nulami ",[883,77148,77150],{"className":77149},[886],[888,77151,77152],{"xmlns":890},[892,77153,77154,77166],{},[895,77155,77156,77162,77164],{},[1743,77157,77158,77160],{},[898,77159,1688],{},[2505,77161,2507],{},[1708,77163,17816],{},[2505,77165,77060],{},[902,77167,77063],{"encoding":904},[883,77169,77171],{"className":77170},[886],[888,77172,77173],{"xmlns":890},[892,77174,77175,77187],{},[895,77176,77177,77183,77185],{},[1743,77178,77179,77181],{},[898,77180,1688],{},[2505,77182,3132],{},[1708,77184,17816],{},[2505,77186,77083],{},[902,77188,77086],{"encoding":904},[115,77190,77192],{"id":77191},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,77194,77195],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,77197,77198],{},[3372,77199],{"alt":77200,"className":77201,"src":77202},"imek-max-zisku-dva-pohledy",[210,3376],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,77204,28284],{"id":77205},"princip-1",[724,77207,77208,77209,3405,77224,77241],{},"Má-li zisk ",[883,77210,77212],{"className":77211},[886],[888,77213,77214],{"xmlns":890},[892,77215,77216,77222],{},[895,77217,77218,77220],{},[898,77219,1747],{},[898,77221,1975],{},[902,77223,75294],{"encoding":904},[883,77225,77227],{"className":77226},[886],[888,77228,77229],{"xmlns":890},[892,77230,77231,77239],{},[895,77232,77233],{},[1743,77234,77235,77237],{},[898,77236,1688],{},[2505,77238,2784],{},[902,77240,50144],{"encoding":904}," maximum, pak platí",[883,77243,77245],{"className":77244},[886],[888,77246,77247],{"xmlns":890,"display":2210},[892,77248,77249,77298],{},[2214,77250,77251],{"width":2216},[2218,77252,77253,77255,77291,77293],{},[2221,77254],{"width":2223},[2221,77256,77257],{},[895,77258,77259,77261,77263,77265,77271,77273,77275,77277,77279,77281,77287,77289],{},[898,77260,1741],{},[898,77262,1975],{},[1708,77264,1716],{"stretchy":1715},[1743,77266,77267,77269],{},[898,77268,1688],{},[2505,77270,2784],{},[1708,77272,1721],{"stretchy":1715},[1708,77274,1710],{},[898,77276,1741],{},[898,77278,3455],{},[1708,77280,1716],{"stretchy":1715},[1743,77282,77283,77285],{},[898,77284,1688],{},[2505,77286,2784],{},[1708,77288,1721],{"stretchy":1715},[898,77290,2155],{"mathvariant":1759},[2221,77292],{"width":2223},[2221,77294,77295],{},[2247,77296,77297],{},"(3.13)",[902,77299,77300],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1636,77302,77303],{},[724,77304,77305,73861,77307],{},[883,77306,68261],{},[38,77308,77309],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,77311,77312,77314,77315,3033,77342,5055,77416,2155],{},[38,77313,3614],{}," (úloha 3.21): nutnou podmínkou maxima ",[883,77316,77318],{"className":77317},[886],[888,77319,77320],{"xmlns":890},[892,77321,77322,77340],{},[895,77323,77324,77326,77328,77330,77332,77334,77336,77338],{},[898,77325,1747],{},[898,77327,1975],{},[1708,77329,1710],{},[898,77331,1978],{},[898,77333,1975],{},[1708,77335,2726],{},[898,77337,1978],{},[898,77339,3455],{},[902,77341,67019],{"encoding":904},[883,77343,77345],{"className":77344},[886],[888,77346,77347],{"xmlns":890},[892,77348,77349,77413],{},[895,77350,77351,77353,77359,77361,77367,77369,77371,77373,77379,77381,77387,77389,77391,77393,77399,77401,77407,77409,77411],{},[898,77352,1747],{},[1753,77354,77355,77357],{},[898,77356,1975],{},[1708,77358,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,77360,1716],{"stretchy":1715},[1743,77362,77363,77365],{},[898,77364,1688],{},[2505,77366,2784],{},[1708,77368,1721],{"stretchy":1715},[1708,77370,1710],{},[898,77372,1978],{},[1753,77374,77375,77377],{},[898,77376,1975],{},[1708,77378,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,77380,1716],{"stretchy":1715},[1743,77382,77383,77385],{},[898,77384,1688],{},[2505,77386,2784],{},[1708,77388,1721],{"stretchy":1715},[1708,77390,2726],{},[898,77392,1978],{},[1753,77394,77395,77397],{},[898,77396,3455],{},[1708,77398,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,77400,1716],{"stretchy":1715},[1743,77402,77403,77405],{},[898,77404,1688],{},[2505,77406,2784],{},[1708,77408,1721],{"stretchy":1715},[1708,77410,1710],{},[2505,77412,2784],{},[902,77414,77415],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,77417,77419],{"className":77418},[886],[888,77420,77421],{"xmlns":890},[892,77422,77423,77455],{},[895,77424,77425,77427,77429,77431,77437,77439,77441,77443,77445,77447,77453],{},[898,77426,1741],{},[898,77428,1975],{},[1708,77430,1716],{"stretchy":1715},[1743,77432,77433,77435],{},[898,77434,1688],{},[2505,77436,2784],{},[1708,77438,1721],{"stretchy":1715},[1708,77440,1710],{},[898,77442,1741],{},[898,77444,3455],{},[1708,77446,1716],{"stretchy":1715},[1743,77448,77449,77451],{},[898,77450,1688],{},[2505,77452,2784],{},[1708,77454,1721],{"stretchy":1715},[902,77456,77457],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1636,77459,77460,77465],{},[724,77461,77462,77464],{},[883,77463,3465],{}," Postup — jak najít maximum zisku",[152,77466,77467,77531,77586,77623,77651],{},[123,77468,77469,77470,1771,77485,77500,77501,2511],{},"Sestavte ",[883,77471,77473],{"className":77472},[886],[888,77474,77475],{"xmlns":890},[892,77476,77477,77483],{},[895,77478,77479,77481],{},[898,77480,1978],{},[898,77482,1975],{},[902,77484,16029],{"encoding":904},[883,77486,77488],{"className":77487},[886],[888,77489,77490],{"xmlns":890},[892,77491,77492,77498],{},[895,77493,77494,77496],{},[898,77495,1978],{},[898,77497,3455],{},[902,77499,15197],{"encoding":904}," ze zadání (typicky ",[883,77502,77504],{"className":77503},[886],[888,77505,77506],{"xmlns":890},[892,77507,77508,77528],{},[895,77509,77510,77512,77514,77516,77518,77520,77522,77524,77526],{},[898,77511,1978],{},[898,77513,1975],{},[1708,77515,1710],{},[898,77517,1747],{},[1708,77519,1716],{"stretchy":1715},[898,77521,1688],{},[1708,77523,1721],{"stretchy":1715},[1708,77525,3703],{},[898,77527,1688],{},[902,77529,77530],{"encoding":904},"TR = P(Q) \\cdot Q",[123,77532,77533,77534,1771,77560,2155],{},"Vypočtěte ",[883,77535,77537],{"className":77536},[886],[888,77538,77539],{"xmlns":890},[892,77540,77541,77557],{},[895,77542,77543,77545,77547,77549,77551],{},[898,77544,1741],{},[898,77546,1975],{},[1708,77548,1710],{},[898,77550,1978],{},[1753,77552,77553,77555],{},[898,77554,1975],{},[1708,77556,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,77558,77559],{"encoding":904},"MR = TR'",[883,77561,77563],{"className":77562},[886],[888,77564,77565],{"xmlns":890},[892,77566,77567,77583],{},[895,77568,77569,77571,77573,77575,77577],{},[898,77570,1741],{},[898,77572,3455],{},[1708,77574,1710],{},[898,77576,1978],{},[1753,77578,77579,77581],{},[898,77580,3455],{},[1708,77582,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,77584,77585],{"encoding":904},"MC = TC'",[123,77587,77588,77589,2155],{},"Řešte rovnici ",[883,77590,77592],{"className":77591},[886],[888,77593,77594],{"xmlns":890},[892,77595,77596,77620],{},[895,77597,77598,77600,77602,77604,77606,77608,77610,77612,77614,77616,77618],{},[898,77599,1741],{},[898,77601,1975],{},[1708,77603,1716],{"stretchy":1715},[898,77605,1688],{},[1708,77607,1721],{"stretchy":1715},[1708,77609,1710],{},[898,77611,1741],{},[898,77613,3455],{},[1708,77615,1716],{"stretchy":1715},[898,77617,1688],{},[1708,77619,1721],{"stretchy":1715},[902,77621,77622],{"encoding":904},"MR(Q) = MC(Q)",[123,77624,77625,77626,77650],{},"Ověřte druhou derivaci ",[883,77627,77629],{"className":77628},[886],[888,77630,77631],{"xmlns":890},[892,77632,77633,77647],{},[895,77634,77635,77637],{},[898,77636,1747],{},[1753,77638,77639,77641],{},[898,77640,1975],{},[895,77642,77643,77645],{},[1708,77644,1761],{"mathvariant":1759},[1708,77646,1761],{"mathvariant":1759},[902,77648,77649],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,77652,8940,77653,77680],{},[883,77654,77656],{"className":77655},[886],[888,77657,77658],{"xmlns":890},[892,77659,77660,77678],{},[895,77661,77662,77664,77666,77668,77670,77672,77674,77676],{},[898,77663,1747],{},[898,77665,1975],{},[1708,77667,1710],{},[898,77669,1978],{},[898,77671,1975],{},[1708,77673,2726],{},[898,77675,1978],{},[898,77677,3455],{},[902,77679,67019],{"encoding":904}," pro hodnotu maxima.",[49185,77682,77684],{"id":77683},"příklad-39","Příklad 3.9",[724,77686,77687,67806,77689,1771,77711,77747],{},[38,77688,67805],{},[883,77690,77692],{"className":77691},[886],[888,77693,77694],{"xmlns":890},[892,77695,77696,77708],{},[895,77697,77698,77700,77702,77704,77706],{},[898,77699,1747],{},[1708,77701,1710],{},[2505,77703,49855],{},[1708,77705,2726],{},[898,77707,1688],{},[902,77709,77710],{"encoding":904},"P = 30 - Q",[883,77712,77714],{"className":77713},[886],[888,77715,77716],{"xmlns":890},[892,77717,77718,77744],{},[895,77719,77720,77722,77724,77726,77728,77734,77736,77738,77740,77742],{},[898,77721,1978],{},[898,77723,3455],{},[1708,77725,1710],{},[2505,77727,6097],{},[1753,77729,77730,77732],{},[898,77731,1688],{},[2505,77733,3132],{},[1708,77735,2019],{},[2505,77737,3947],{},[898,77739,1688],{},[1708,77741,2019],{},[2505,77743,5967],{},[902,77745,77746],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,77749,77750,1729,77752,1343,77782,77820,77821,9137,77865,77899,77900,2155],{},[38,77751,34628],{},[883,77753,77755],{"className":77754},[886],[888,77756,77757],{"xmlns":890},[892,77758,77759,77779],{},[895,77760,77761,77763,77765,77767,77769,77771,77773],{},[898,77762,1978],{},[898,77764,1975],{},[1708,77766,1710],{},[2505,77768,49855],{},[898,77770,1688],{},[1708,77772,2726],{},[1753,77774,77775,77777],{},[898,77776,1688],{},[2505,77778,3132],{},[902,77780,77781],{"encoding":904},"TR = 30Q - Q^2",[883,77783,77785],{"className":77784},[886],[888,77786,77787],{"xmlns":890},[892,77788,77789,77817],{},[895,77790,77791,77793,77795,77797,77799,77801,77807,77809,77811,77813,77815],{},[898,77792,1747],{},[898,77794,1975],{},[1708,77796,1710],{},[1708,77798,2726],{},[2505,77800,12222],{},[1753,77802,77803,77805],{},[898,77804,1688],{},[2505,77806,3132],{},[1708,77808,2019],{},[2505,77810,53632],{},[898,77812,1688],{},[1708,77814,2726],{},[2505,77816,5967],{},[902,77818,77819],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,77822,77824],{"className":77823},[886],[888,77825,77826],{"xmlns":890},[892,77827,77828,77862],{},[895,77829,77830,77832,77838,77840,77842,77844,77846,77848,77850,77852,77854,77856,77858,77860],{},[898,77831,1747],{},[1753,77833,77834,77836],{},[898,77835,1975],{},[1708,77837,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,77839,1710],{},[1708,77841,2726],{},[2505,77843,3121],{},[898,77845,1688],{},[1708,77847,2019],{},[2505,77849,53632],{},[1708,77851,1710],{},[2505,77853,2784],{},[1708,77855,4782],{},[898,77857,1688],{},[1708,77859,1710],{},[2505,77861,3998],{},[902,77863,77864],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,77866,77868],{"className":77867},[886],[888,77869,77870],{"xmlns":890},[892,77871,77872,77896],{},[895,77873,77874,77876,77886,77888,77890,77892,77894],{},[898,77875,1747],{},[1753,77877,77878,77880],{},[898,77879,1975],{},[895,77881,77882,77884],{},[1708,77883,1761],{"mathvariant":1759},[1708,77885,1761],{"mathvariant":1759},[1708,77887,1710],{},[1708,77889,2726],{},[2505,77891,3121],{},[1708,77893,2932],{},[2505,77895,2784],{},[902,77897,77898],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,77901,77903],{"className":77902},[886],[888,77904,77905],{"xmlns":890},[892,77906,77907,77924],{},[895,77908,77909,77911,77913,77915,77917,77919,77921],{},[898,77910,1747],{},[898,77912,1975],{},[1708,77914,1716],{"stretchy":1715},[2505,77916,3998],{},[1708,77918,1721],{"stretchy":1715},[1708,77920,1710],{},[2505,77922,77923],{},"89",[902,77925,77926],{"encoding":904},"PR(8) = 89",[724,77928,77929,77930,1343,77956,9137,77980,78018],{},"Ověření principu: ",[883,77931,77933],{"className":77932},[886],[888,77934,77935],{"xmlns":890},[892,77936,77937,77953],{},[895,77938,77939,77941,77943,77945,77947,77949,77951],{},[898,77940,1741],{},[898,77942,1975],{},[1708,77944,1710],{},[2505,77946,49855],{},[1708,77948,2726],{},[2505,77950,3132],{},[898,77952,1688],{},[902,77954,77955],{"encoding":904},"MR = 30 - 2Q",[883,77957,77959],{"className":77958},[886],[888,77960,77961],{"xmlns":890},[892,77962,77963,77977],{},[895,77964,77965,77967,77969,77971,77973,77975],{},[898,77966,1741],{},[898,77968,3455],{},[1708,77970,1710],{},[898,77972,1688],{},[1708,77974,2019],{},[2505,77976,3947],{},[902,77978,77979],{"encoding":904},"MC = Q + 6",[883,77981,77983],{"className":77982},[886],[888,77984,77985],{"xmlns":890},[892,77986,77987,78015],{},[895,77988,77989,77991,77993,77995,77997,77999,78001,78003,78005,78007,78009,78011,78013],{},[898,77990,1741],{},[898,77992,1975],{},[1708,77994,1716],{"stretchy":1715},[2505,77996,3998],{},[1708,77998,1721],{"stretchy":1715},[1708,78000,1710],{},[2505,78002,4008],{},[1708,78004,1710],{},[898,78006,1741],{},[898,78008,3455],{},[1708,78010,1716],{"stretchy":1715},[2505,78012,3998],{},[1708,78014,1721],{"stretchy":1715},[902,78016,78017],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,78020,78021,78022,78055,78056,78073],{},"V řadě případů — má-li rovnice ",[883,78023,78025],{"className":78024},[886],[888,78026,78027],{"xmlns":890},[892,78028,78029,78053],{},[895,78030,78031,78033,78035,78037,78039,78041,78043,78045,78047,78049,78051],{},[898,78032,1741],{},[898,78034,1975],{},[1708,78036,1716],{"stretchy":1715},[898,78038,1688],{},[1708,78040,1721],{"stretchy":1715},[1708,78042,1710],{},[898,78044,1741],{},[898,78046,3455],{},[1708,78048,1716],{"stretchy":1715},[898,78050,1688],{},[1708,78052,1721],{"stretchy":1715},[902,78054,77622],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,78057,78059],{"className":78058},[886],[888,78060,78061],{"xmlns":890},[892,78062,78063,78071],{},[895,78064,78065],{},[1743,78066,78067,78069],{},[898,78068,1688],{},[2505,78070,2784],{},[902,78072,50144],{"encoding":904}," — není třeba provádět test druhé derivace.",[49185,78075,78077],{"id":78076},"příklad-310","Příklad 3.10",[724,78079,78080,78082,78083,78087,78088,78101,78102,78133],{},[38,78081,67805],{}," Firma vyrábí minipočítače v ",[207,78084,78086],{"className":78085,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,78089,78091],{"className":78090},[886],[888,78092,78093],{"xmlns":890},[892,78094,78095,78099],{},[895,78096,78097],{},[2505,78098,11732],{},[902,78100,11732],{"encoding":904}," EUR\u002Fks. ",[883,78103,78105],{"className":78104},[886],[888,78106,78107],{"xmlns":890},[892,78108,78109,78130],{},[895,78110,78111,78113,78115,78117,78119,78121,78124],{},[898,78112,1978],{},[898,78114,3455],{},[1708,78116,1710],{},[2505,78118,9704],{},[1708,78120,2019],{},[2505,78122,78123],{},"28",[1753,78125,78126,78128],{},[898,78127,1688],{},[2505,78129,3132],{},[902,78131,78132],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,78135,78136,1729,78138,1343,78160,1343,78180,78203],{},[38,78137,34628],{},[883,78139,78141],{"className":78140},[886],[888,78142,78143],{"xmlns":890},[892,78144,78145,78157],{},[895,78146,78147,78149,78151,78153,78155],{},[898,78148,1978],{},[898,78150,1975],{},[1708,78152,1710],{},[2505,78154,11732],{},[898,78156,1688],{},[902,78158,78159],{"encoding":904},"TR = 900Q",[883,78161,78163],{"className":78162},[886],[888,78164,78165],{"xmlns":890},[892,78166,78167,78177],{},[895,78168,78169,78171,78173,78175],{},[898,78170,1741],{},[898,78172,1975],{},[1708,78174,1710],{},[2505,78176,11732],{},[902,78178,78179],{"encoding":904},"MR = 900",[883,78181,78183],{"className":78182},[886],[888,78184,78185],{"xmlns":890},[892,78186,78187,78200],{},[895,78188,78189,78191,78193,78195,78198],{},[898,78190,1741],{},[898,78192,3455],{},[1708,78194,1710],{},[2505,78196,78197],{},"56",[898,78199,1688],{},[902,78201,78202],{"encoding":904},"MC = 56Q",". Z principu:",[883,78205,78207],{"className":78206},[886],[888,78208,78209],{"xmlns":890,"display":2210},[892,78210,78211,78253],{},[895,78212,78213,78215,78217,78219,78221,78223,78225,78227,78229,78231,78239,78241,78244,78246,78248,78250],{},[2505,78214,11732],{},[1708,78216,1710],{},[2505,78218,78197],{},[898,78220,1688],{},[2247,78222,4779],{},[1708,78224,4782],{},[2247,78226,4779],{},[898,78228,1688],{},[1708,78230,1710],{},[3194,78232,78233],{"scriptlevel":2784,"displaystyle":1715},[2358,78234,78235,78237],{},[2505,78236,11732],{},[2505,78238,78197],{},[1708,78240,17816],{},[2505,78242,78243],{},"16,07",[2247,78245,4779],{},[1708,78247,2638],{},[2247,78249,4779],{},[2505,78251,78252],{},"16.",[902,78254,78255],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,78257,78258,78259,2788],{},"Zisk při ",[883,78260,78262],{"className":78261},[886],[888,78263,78264],{"xmlns":890},[892,78265,78266,78274],{},[895,78267,78268,78270,78272],{},[898,78269,1688],{},[1708,78271,1710],{},[2505,78273,53694],{},[902,78275,78276],{"encoding":904},"Q = 16",[883,78278,78280],{"className":78279},[886],[888,78281,78282],{"xmlns":890,"display":2210},[892,78283,78284,78355],{},[895,78285,78286,78288,78290,78292,78294,78296,78298,78300,78302,78304,78306,78308,78310,78312,78314,78316,78322,78324,78326,78328,78330,78332,78334,78336,78338,78341,78343,78345,78347,78350,78353],{},[898,78287,1747],{},[898,78289,1975],{},[1708,78291,1716],{"stretchy":1715},[2505,78293,53694],{},[1708,78295,1721],{"stretchy":1715},[1708,78297,1710],{},[2505,78299,11732],{},[1708,78301,3703],{},[2505,78303,53694],{},[1708,78305,2726],{},[1708,78307,1716],{"stretchy":1715},[2505,78309,9704],{},[1708,78311,2019],{},[2505,78313,78123],{},[1708,78315,3703],{},[1753,78317,78318,78320],{},[2505,78319,53694],{},[2505,78321,3132],{},[1708,78323,1721],{"stretchy":1715},[1708,78325,1710],{},[2505,78327,4008],{},[2247,78329,2659],{},[2505,78331,11498],{},[1708,78333,2726],{},[2505,78335,5967],{},[2247,78337,2659],{},[2505,78339,78340],{},"218",[1708,78342,1710],{},[2505,78344,5967],{},[2247,78346,2659],{},[2505,78348,78349],{},"182",[2247,78351,78352],{}," EUR",[898,78354,2155],{"mathvariant":1759},[902,78356,78357],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,78359,78360],{},"Pro srovnání při původních 30 ks:",[883,78362,78364],{"className":78363},[886],[888,78365,78366],{"xmlns":890,"display":2210},[892,78367,78368,78432],{},[895,78369,78370,78372,78374,78376,78378,78380,78382,78384,78386,78388,78390,78392,78394,78396,78398,78400,78402,78404,78406,78408,78410,78412,78414,78416,78418,78420,78422,78424,78426,78428,78430],{},[898,78371,1747],{},[898,78373,1975],{},[1708,78375,1716],{"stretchy":1715},[2505,78377,49855],{},[1708,78379,1721],{"stretchy":1715},[1708,78381,1710],{},[2505,78383,11732],{},[1708,78385,3703],{},[2505,78387,49855],{},[1708,78389,2726],{},[1708,78391,1716],{"stretchy":1715},[2505,78393,9704],{},[1708,78395,2019],{},[2505,78397,78123],{},[1708,78399,3703],{},[2505,78401,11732],{},[1708,78403,1721],{"stretchy":1715},[1708,78405,1710],{},[2505,78407,12110],{},[2247,78409,2659],{},[2505,78411,70897],{},[1708,78413,2726],{},[2505,78415,4028],{},[2247,78417,2659],{},[2505,78419,11594],{},[1708,78421,1710],{},[2505,78423,2507],{},[2247,78425,2659],{},[2505,78427,35599],{},[2247,78429,78352],{},[898,78431,2155],{"mathvariant":1759},[902,78433,78434],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,78436,78437,78440,78441,78459,78460,78478],{},[38,78438,78439],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,78442,78444],{"className":78443},[886],[888,78445,78446],{"xmlns":890},[892,78447,78448,78456],{},[895,78449,78450,78452,78454],{},[2505,78451,5967],{},[2247,78453,2659],{},[2505,78455,78349],{},[902,78457,78458],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,78461,78463],{"className":78462},[886],[888,78464,78465],{"xmlns":890},[892,78466,78467,78475],{},[895,78468,78469,78471,78473],{},[2505,78470,2507],{},[2247,78472,2659],{},[2505,78474,35599],{},[902,78476,78477],{"encoding":904},"1\\,750"," EUR.",[198,78480,78482],{"id":78481},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,78484,78485,78486,74385,78499,78523],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,78487,78489],{"className":78488},[886],[888,78490,78491],{"xmlns":890},[892,78492,78493,78497],{},[895,78494,78495],{},[898,78496,1747],{},[902,78498,1747],{"encoding":904},[883,78500,78502],{"className":78501},[886],[888,78503,78504],{"xmlns":890},[892,78505,78506,78520],{},[895,78507,78508,78510,78512,78514,78516,78518],{},[898,78509,1978],{},[898,78511,1975],{},[1708,78513,1710],{},[898,78515,1747],{},[1708,78517,3703],{},[898,78519,1688],{},[902,78521,78522],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,78525,78527],{"className":78526},[886],[888,78528,78529],{"xmlns":890,"display":2210},[892,78530,78531,78564],{},[2214,78532,78533],{"width":2216},[2218,78534,78535,78537,78557,78559],{},[2221,78536],{"width":2223},[2221,78538,78539],{},[895,78540,78541,78543,78545,78547,78549,78551,78553,78555],{},[898,78542,1747],{},[1708,78544,1710],{},[898,78546,1741],{},[898,78548,3455],{},[1708,78550,1716],{"stretchy":1715},[898,78552,1688],{},[1708,78554,1721],{"stretchy":1715},[898,78556,2155],{"mathvariant":1759},[2221,78558],{"width":2223},[2221,78560,78561],{},[2247,78562,78563],{},"(3.14)",[902,78565,78566],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,78568,78569,78570,2155],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,78571,78573],{"className":78572},[886],[888,78574,78575],{"xmlns":890},[892,78576,78577,78591],{},[895,78578,78579,78581],{},[898,78580,1747],{},[1753,78582,78583,78585],{},[898,78584,1975],{},[895,78586,78587,78589],{},[1708,78588,1761],{"mathvariant":1759},[1708,78590,1761],{"mathvariant":1759},[902,78592,77649],{"encoding":904},[49185,78594,78596],{"id":78595},"příklad-311","Příklad 3.11",[724,78598,78599,3973,78601,78648,78649,78667],{},[38,78600,67805],{},[883,78602,78604],{"className":78603},[886],[888,78605,78606],{"xmlns":890},[892,78607,78608,78645],{},[895,78609,78610,78612,78614,78616,78619,78625,78627,78629,78635,78637,78639,78641,78643],{},[898,78611,1978],{},[898,78613,3455],{},[1708,78615,1710],{},[2505,78617,78618],{},"0,04",[1753,78620,78621,78623],{},[898,78622,1688],{},[2505,78624,3121],{},[1708,78626,2726],{},[2505,78628,34403],{},[1753,78630,78631,78633],{},[898,78632,1688],{},[2505,78634,3132],{},[1708,78636,2019],{},[2505,78638,4003],{},[898,78640,1688],{},[1708,78642,2019],{},[2505,78644,3993],{},[902,78646,78647],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,78650,78652],{"className":78651},[886],[888,78653,78654],{"xmlns":890},[892,78655,78656,78664],{},[895,78657,78658,78660,78662],{},[898,78659,1747],{},[1708,78661,1710],{},[2505,78663,5867],{},[902,78665,78666],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,78669,78670,78672,78673,5055,78715,78749,78750,2788],{},[38,78671,34628],{}," Z (3.14): ",[883,78674,78676],{"className":78675},[886],[888,78677,78678],{"xmlns":890},[892,78679,78680,78712],{},[895,78681,78682,78684,78686,78688,78691,78697,78699,78702,78704,78706,78708,78710],{},[898,78683,1741],{},[898,78685,3455],{},[1708,78687,1710],{},[2505,78689,78690],{},"0,12",[1753,78692,78693,78695],{},[898,78694,1688],{},[2505,78696,3132],{},[1708,78698,2726],{},[2505,78700,78701],{},"1,8",[898,78703,1688],{},[1708,78705,2019],{},[2505,78707,4003],{},[1708,78709,1710],{},[2505,78711,5867],{},[902,78713,78714],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,78716,78718],{"className":78717},[886],[888,78719,78720],{"xmlns":890},[892,78721,78722,78746],{},[895,78723,78724,78726,78732,78734,78736,78738,78740,78742,78744],{},[2505,78725,78690],{},[1753,78727,78728,78730],{},[898,78729,1688],{},[2505,78731,3132],{},[1708,78733,2726],{},[2505,78735,78701],{},[898,78737,1688],{},[1708,78739,2019],{},[2505,78741,3947],{},[1708,78743,1710],{},[2505,78745,2784],{},[902,78747,78748],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,78751,78753],{"className":78752},[886],[888,78754,78755],{"xmlns":890},[892,78756,78757,78761],{},[895,78758,78759],{},[2505,78760,78690],{},[902,78762,78763],{"encoding":904},"0{,}12",[883,78765,78767],{"className":78766},[886],[888,78768,78769],{"xmlns":890,"display":2210},[892,78770,78771,78823],{},[895,78772,78773,78779,78781,78783,78785,78787,78789,78791,78793,78795,78797,78799,78805,78807,78809,78811,78813,78819,78821],{},[1753,78774,78775,78777],{},[898,78776,1688],{},[2505,78778,3132],{},[1708,78780,2726],{},[2505,78782,4853],{},[898,78784,1688],{},[1708,78786,2019],{},[2505,78788,9704],{},[1708,78790,1710],{},[2505,78792,2784],{},[2247,78794,4779],{},[1708,78796,4782],{},[2247,78798,4779],{},[1743,78800,78801,78803],{},[898,78802,1688],{},[2505,78804,2507],{},[1708,78806,1710],{},[2505,78808,3993],{},[1708,78810,1883],{"separator":1882},[2247,78812,4779],{},[1743,78814,78815,78817],{},[898,78816,1688],{},[2505,78818,3132],{},[1708,78820,1710],{},[2505,78822,31192],{},[902,78824,78825],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,78827,78828,78829,2788],{},"Dále ",[883,78830,78832],{"className":78831},[886],[888,78833,78834],{"xmlns":890},[892,78835,78836,78875],{},[895,78837,78838,78840,78850,78852,78854,78856,78862,78864,78866,78869,78871,78873],{},[898,78839,1747],{},[1753,78841,78842,78844],{},[898,78843,1975],{},[895,78845,78846,78848],{},[1708,78847,1761],{"mathvariant":1759},[1708,78849,1761],{"mathvariant":1759},[1708,78851,1710],{},[1708,78853,2726],{},[898,78855,1741],{},[1753,78857,78858,78860],{},[898,78859,3455],{},[1708,78861,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,78863,1710],{},[1708,78865,2726],{},[2505,78867,78868],{},"0,24",[898,78870,1688],{},[1708,78872,2019],{},[2505,78874,78701],{},[902,78876,78877],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,78879,78880,78930],{},[123,78881,78882,78926,78927,78929],{},[883,78883,78885],{"className":78884},[886],[888,78886,78887],{"xmlns":890},[892,78888,78889,78923],{},[895,78890,78891,78893,78903,78905,78907,78909,78911,78913,78915,78917,78919,78921],{},[898,78892,1747],{},[1753,78894,78895,78897],{},[898,78896,1975],{},[895,78898,78899,78901],{},[1708,78900,1761],{"mathvariant":1759},[1708,78902,1761],{"mathvariant":1759},[1708,78904,1716],{"stretchy":1715},[2505,78906,3993],{},[1708,78908,1721],{"stretchy":1715},[1708,78910,1710],{},[2505,78912,4097],{},[1708,78914,2854],{},[2505,78916,2784],{},[2247,78918,4779],{},[1708,78920,4782],{},[2247,78922,4779],{},[902,78924,78925],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,78928,15724],{}," zisku (minimalizace ztráty);",[123,78931,78932,78926,78978,78980],{},[883,78933,78935],{"className":78934},[886],[888,78936,78937],{"xmlns":890},[892,78938,78939,78975],{},[895,78940,78941,78943,78953,78955,78957,78959,78961,78963,78965,78967,78969,78971,78973],{},[898,78942,1747],{},[1753,78944,78945,78947],{},[898,78946,1975],{},[895,78948,78949,78951],{},[1708,78950,1761],{"mathvariant":1759},[1708,78952,1761],{"mathvariant":1759},[1708,78954,1716],{"stretchy":1715},[2505,78956,4003],{},[1708,78958,1721],{"stretchy":1715},[1708,78960,1710],{},[1708,78962,2726],{},[2505,78964,4097],{},[1708,78966,2932],{},[2505,78968,2784],{},[2247,78970,4779],{},[1708,78972,4782],{},[2247,78974,4779],{},[902,78976,78977],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,78979,15666],{}," zisku, avšak",[883,78982,78984],{"className":78983},[886],[888,78985,78986],{"xmlns":890,"display":2210},[892,78987,78988,79056],{},[895,78989,78990,78992,78994,78996,78998,79000,79002,79004,79006,79008,79010,79012,79014,79016,79018,79020,79022,79024,79026,79028,79030,79032,79034,79036,79038,79040,79042,79044,79046,79048,79050,79052,79054],{},[898,78991,1747],{},[898,78993,1975],{},[1708,78995,1716],{"stretchy":1715},[2505,78997,4003],{},[1708,78999,1721],{"stretchy":1715},[1708,79001,1710],{},[2505,79003,5867],{},[1708,79005,3703],{},[2505,79007,4003],{},[1708,79009,2726],{},[1708,79011,1716],{"stretchy":1715},[2505,79013,78618],{},[1708,79015,3703],{},[2505,79017,2507],{},[2247,79019,2659],{},[2505,79021,70897],{},[1708,79023,2726],{},[2505,79025,34403],{},[1708,79027,3703],{},[2505,79029,9238],{},[1708,79031,2019],{},[2505,79033,9238],{},[1708,79035,2019],{},[2505,79037,3993],{},[1708,79039,1721],{"stretchy":1715},[1708,79041,1710],{},[2505,79043,17132],{},[1708,79045,2726],{},[2505,79047,33039],{},[1708,79049,1710],{},[1708,79051,2726],{},[2505,79053,4853],{},[1708,79055,1883],{"separator":1882},[902,79057,79058],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,79060,79061,79062,2155],{},"tj. ztráta větší než ",[883,79063,79065],{"className":79064},[886],[888,79066,79067],{"xmlns":890},[892,79068,79069,79079],{},[895,79070,79071,79073,79075,79077],{},[898,79072,22325],{},[898,79074,3455],{},[1708,79076,1710],{},[2505,79078,3993],{},[902,79080,79081],{"encoding":904},"FC = 5",[724,79083,79084,79087,79088,79091,79092,2155],{},[38,79085,79086],{},"Závěr:"," firma by měla ",[38,79089,79090],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,79093,79095],{"className":79094},[886],[888,79096,79097],{"xmlns":890},[892,79098,79099,79109],{},[895,79100,79101,79103,79105,79107],{},[898,79102,22325],{},[898,79104,3455],{},[1708,79106,1710],{},[2505,79108,3993],{},[902,79110,79081],{"encoding":904},[115,79112,79114],{"id":79113},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,79116,79117,79118,79120,79121,79136,79137,79150,79151,79177,79178,79191,79192,79209,79210,3405,79227,79230,79231,79251,79252,79267,79268,2788],{},"Důležitým završením analýzy je konstrukce ",[38,79119,67094],{},". S nabízeným množstvím rostou mezní náklady ",[883,79122,79124],{"className":79123},[886],[888,79125,79126],{"xmlns":890},[892,79127,79128,79134],{},[895,79129,79130,79132],{},[898,79131,1741],{},[898,79133,3455],{},[902,79135,67111],{"encoding":904}," a tyto určují cenu ",[883,79138,79140],{"className":79139},[886],[888,79141,79142],{"xmlns":890},[892,79143,79144,79148],{},[895,79145,79146],{},[898,79147,1747],{},[902,79149,1747],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,79152,79154],{"className":79153},[886],[888,79155,79156],{"xmlns":890},[892,79157,79158,79174],{},[895,79159,79160,79162,79164,79166,79168,79170,79172],{},[898,79161,1747],{},[1708,79163,1710],{},[898,79165,1741],{},[898,79167,3455],{},[1708,79169,1716],{"stretchy":1715},[898,79171,1688],{},[1708,79173,1721],{"stretchy":1715},[902,79175,79176],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,79179,79181],{"className":79180},[886],[888,79182,79183],{"xmlns":890},[892,79184,79185,79189],{},[895,79186,79187],{},[898,79188,1747],{},[902,79190,1747],{"encoding":904}," však nemůže být nižší než ",[883,79193,79195],{"className":79194},[886],[888,79196,79197],{"xmlns":890},[892,79198,79199,79207],{},[895,79200,79201],{},[1753,79202,79203,79205],{},[898,79204,1747],{},[1708,79206,2417],{},[902,79208,16331],{"encoding":904}," odpovídající množství ",[883,79211,79213],{"className":79212},[886],[888,79214,79215],{"xmlns":890},[892,79216,79217,79225],{},[895,79218,79219],{},[1753,79220,79221,79223],{},[898,79222,1688],{},[1708,79224,2417],{},[902,79226,41691],{"encoding":904},[38,79228,79229],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,79232,79234],{"className":79233},[886],[888,79235,79236],{"xmlns":890},[892,79237,79238,79248],{},[895,79239,79240,79242],{},[2505,79241,2784],{},[1753,79243,79244,79246],{},[898,79245,1688],{},[1708,79247,2417],{},[902,79249,79250],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,79253,79255],{"className":79254},[886],[888,79256,79257],{"xmlns":890},[892,79258,79259,79265],{},[895,79260,79261,79263],{},[898,79262,1741],{},[898,79264,3455],{},[902,79266,67111],{"encoding":904}," nad bodem ",[883,79269,79271],{"className":79270},[886],[888,79272,79273],{"xmlns":890},[892,79274,79275,79279],{},[895,79276,79277],{},[898,79278,1786],{},[902,79280,1786],{"encoding":904},[883,79282,79284],{"className":79283},[886],[888,79285,79286],{"xmlns":890,"display":2210},[892,79287,79288,79395],{},[2214,79289,79290],{"width":2216},[2218,79291,79292,79294,79388,79390],{},[2221,79293],{"width":2223},[2221,79295,79296],{},[895,79297,79298,79300,79302,79304,79306,79308,79310,79312],{},[898,79299,1747],{},[1708,79301,1710],{},[898,79303,1981],{},[1708,79305,1716],{"stretchy":1715},[898,79307,1688],{},[1708,79309,1721],{"stretchy":1715},[1708,79311,1710],{},[895,79313,79314,79317],{},[1708,79315,79316],{"fence":1882},"{",[2214,79318,79321,79360],{"rowspacing":79319,"columnalign":79320,"columnspacing":4750},"0.36em","left left",[2218,79322,79323,79339],{},[2221,79324,79325],{},[3194,79326,79327],{"scriptlevel":2784,"displaystyle":1715},[895,79328,79329,79331,79333,79335,79337],{},[898,79330,1741],{},[898,79332,3455],{},[1708,79334,1716],{"stretchy":1715},[898,79336,1688],{},[1708,79338,1721],{"stretchy":1715},[2221,79340,79341],{},[3194,79342,79343],{"scriptlevel":2784,"displaystyle":1715},[895,79344,79345,79348,79350,79352,79358],{},[2247,79346,79347],{},"pro ",[898,79349,1688],{},[1708,79351,6762],{},[1753,79353,79354,79356],{},[898,79355,1688],{},[1708,79357,2417],{},[1708,79359,1883],{"separator":1882},[2218,79361,79362,79368],{},[2221,79363,79364],{},[3194,79365,79366],{"scriptlevel":2784,"displaystyle":1715},[2505,79367,2784],{},[2221,79369,79370],{},[3194,79371,79372],{"scriptlevel":2784,"displaystyle":1715},[895,79373,79374,79376,79378,79380,79386],{},[2247,79375,79347],{},[898,79377,1688],{},[1708,79379,2932],{},[1753,79381,79382,79384],{},[898,79383,1688],{},[1708,79385,2417],{},[1708,79387,1883],{"separator":1882},[2221,79389],{"width":2223},[2221,79391,79392],{},[2247,79393,79394],{},"(3.15)",[902,79396,79397],{"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}",[724,79399,5411,79400,79417,79418,79435,79436,53331,79466,79469],{},[883,79401,79403],{"className":79402},[886],[888,79404,79405],{"xmlns":890},[892,79406,79407,79415],{},[895,79408,79409],{},[1753,79410,79411,79413],{},[898,79412,1688],{},[1708,79414,2417],{},[902,79416,41691],{"encoding":904}," je bod minima ",[883,79419,79421],{"className":79420},[886],[888,79422,79423],{"xmlns":890},[892,79424,79425,79433],{},[895,79426,79427,79429,79431],{},[898,79428,1786],{},[898,79430,52173],{},[898,79432,3455],{},[902,79434,67130],{"encoding":904},". Bod ",[883,79437,79439],{"className":79438},[886],[888,79440,79441],{"xmlns":890},[892,79442,79443,79463],{},[895,79444,79445,79447,79453,79455,79461],{},[1708,79446,1716],{"stretchy":1715},[1753,79448,79449,79451],{},[898,79450,1688],{},[1708,79452,2417],{},[1708,79454,1883],{"separator":1882},[1753,79456,79457,79459],{},[898,79458,1747],{},[1708,79460,2417],{},[1708,79462,1721],{"stretchy":1715},[902,79464,79465],{"encoding":904},"(Q^*, P^*)",[38,79467,79468],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1636,79471,79472,79477],{},[724,79473,79474,79476],{},[883,79475,3465],{}," Postup — jak odvodit nabídku firmy",[152,79478,79479,79528,79623,79678,79749],{},[123,79480,79481,79482,1771,79504,2155],{},"Ze zadaných nákladů určete ",[883,79483,79485],{"className":79484},[886],[888,79486,79487],{"xmlns":890},[892,79488,79489,79501],{},[895,79490,79491,79493,79495,79497,79499],{},[898,79492,1741],{},[898,79494,3455],{},[1708,79496,1716],{"stretchy":1715},[898,79498,1688],{},[1708,79500,1721],{"stretchy":1715},[902,79502,79503],{"encoding":904},"MC(Q)",[883,79505,79507],{"className":79506},[886],[888,79508,79509],{"xmlns":890},[892,79510,79511,79525],{},[895,79512,79513,79515,79517,79519,79521,79523],{},[898,79514,1786],{},[898,79516,52173],{},[898,79518,3455],{},[1708,79520,1716],{"stretchy":1715},[898,79522,1688],{},[1708,79524,1721],{"stretchy":1715},[902,79526,79527],{"encoding":904},"AVC(Q)",[123,79529,79530,79531,79548,79549,79566,79567,79599,79600,2511],{},"Najděte ",[883,79532,79534],{"className":79533},[886],[888,79535,79536],{"xmlns":890},[892,79537,79538,79546],{},[895,79539,79540],{},[1753,79541,79542,79544],{},[898,79543,1688],{},[1708,79545,2417],{},[902,79547,41691],{"encoding":904}," jako bod minima ",[883,79550,79552],{"className":79551},[886],[888,79553,79554],{"xmlns":890},[892,79555,79556,79564],{},[895,79557,79558,79560,79562],{},[898,79559,1786],{},[898,79561,52173],{},[898,79563,3455],{},[902,79565,67130],{"encoding":904}," (řešením ",[883,79568,79570],{"className":79569},[886],[888,79571,79572],{"xmlns":890},[892,79573,79574,79596],{},[895,79575,79576,79578,79580,79586,79588,79590,79592,79594],{},[898,79577,1786],{},[898,79579,52173],{},[1753,79581,79582,79584],{},[898,79583,3455],{},[1708,79585,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,79587,1716],{"stretchy":1715},[898,79589,1688],{},[1708,79591,1721],{"stretchy":1715},[1708,79593,1710],{},[2505,79595,2784],{},[902,79597,79598],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,79601,79603],{"className":79602},[886],[888,79604,79605],{"xmlns":890},[892,79606,79607,79621],{},[895,79608,79609,79611,79613,79615,79617,79619],{},[898,79610,1786],{},[898,79612,52173],{},[898,79614,3455],{},[1708,79616,1710],{},[898,79618,1741],{},[898,79620,3455],{},[902,79622,67067],{"encoding":904},[123,79624,77533,79625,79677],{},[883,79626,79628],{"className":79627},[886],[888,79629,79630],{"xmlns":890},[892,79631,79632,79674],{},[895,79633,79634,79640,79642,79644,79646,79648,79654,79656,79658,79660,79662,79664,79666,79672],{},[1753,79635,79636,79638],{},[898,79637,1747],{},[1708,79639,2417],{},[1708,79641,1710],{},[898,79643,1741],{},[898,79645,3455],{},[1708,79647,1716],{"stretchy":1715},[1753,79649,79650,79652],{},[898,79651,1688],{},[1708,79653,2417],{},[1708,79655,1721],{"stretchy":1715},[1708,79657,1710],{},[898,79659,1786],{},[898,79661,52173],{},[898,79663,3455],{},[1708,79665,1716],{"stretchy":1715},[1753,79667,79668,79670],{},[898,79669,1688],{},[1708,79671,2417],{},[1708,79673,1721],{"stretchy":1715},[902,79675,79676],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,79679,79680,79681,10064,79713,79735,79736,2155],{},"Zapište nabídku: ",[883,79682,79684],{"className":79683},[886],[888,79685,79686],{"xmlns":890},[892,79687,79688,79710],{},[895,79689,79690,79692,79694,79696,79698,79700,79702,79704,79706,79708],{},[898,79691,1981],{},[1708,79693,1716],{"stretchy":1715},[898,79695,1688],{},[1708,79697,1721],{"stretchy":1715},[1708,79699,1710],{},[898,79701,1741],{},[898,79703,3455],{},[1708,79705,1716],{"stretchy":1715},[898,79707,1688],{},[1708,79709,1721],{"stretchy":1715},[902,79711,79712],{"encoding":904},"S(Q) = MC(Q)",[883,79714,79716],{"className":79715},[886],[888,79717,79718],{"xmlns":890},[892,79719,79720,79732],{},[895,79721,79722,79724,79726],{},[898,79723,1688],{},[1708,79725,6762],{},[1753,79727,79728,79730],{},[898,79729,1688],{},[1708,79731,2417],{},[902,79733,79734],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,79737,79739],{"className":79738},[886],[888,79740,79741],{"xmlns":890},[892,79742,79743,79747],{},[895,79744,79745],{},[2505,79746,2784],{},[902,79748,2784],{"encoding":904},[123,79750,79751,79752,79784],{},"V případě potřeby vyjádřete inverzi ",[883,79753,79755],{"className":79754},[886],[888,79756,79757],{"xmlns":890},[892,79758,79759,79781],{},[895,79760,79761,79763,79765,79775,79777,79779],{},[898,79762,1688],{},[1708,79764,1710],{},[1753,79766,79767,79769],{},[898,79768,1981],{},[895,79770,79771,79773],{},[1708,79772,2726],{},[2505,79774,2507],{},[1708,79776,1716],{"stretchy":1715},[898,79778,1747],{},[1708,79780,1721],{"stretchy":1715},[902,79782,79783],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,79786,79787],{},[614,79788,79789,79790,1343,79805,1771,79822,41048,79837,79850,79851,79876,79877,79890,79891,79908,79909,79926,79927,79944],{},"Obrázek 3.14: Křivky ",[883,79791,79793],{"className":79792},[886],[888,79794,79795],{"xmlns":890},[892,79796,79797,79803],{},[895,79798,79799,79801],{},[898,79800,1786],{},[898,79802,3455],{},[902,79804,3458],{"encoding":904},[883,79806,79808],{"className":79807},[886],[888,79809,79810],{"xmlns":890},[892,79811,79812,79820],{},[895,79813,79814,79816,79818],{},[898,79815,1786],{},[898,79817,52173],{},[898,79819,3455],{},[902,79821,67130],{"encoding":904},[883,79823,79825],{"className":79824},[886],[888,79826,79827],{"xmlns":890},[892,79828,79829,79835],{},[895,79830,79831,79833],{},[898,79832,1741],{},[898,79834,3455],{},[902,79836,67111],{"encoding":904},[883,79838,79840],{"className":79839},[886],[888,79841,79842],{"xmlns":890},[892,79843,79844,79848],{},[895,79845,79846],{},[898,79847,900],{},[902,79849,900],{"encoding":904},"; křivka nabídky ",[883,79852,79854],{"className":79853},[886],[888,79855,79856],{"xmlns":890},[892,79857,79858,79874],{},[895,79859,79860,79862,79864,79866,79868,79870,79872],{},[898,79861,1747],{},[1708,79863,1710],{},[898,79865,1741],{},[898,79867,3455],{},[1708,79869,1716],{"stretchy":1715},[898,79871,1688],{},[1708,79873,1721],{"stretchy":1715},[902,79875,79176],{"encoding":904}," začíná v bodě ",[883,79878,79880],{"className":79879},[886],[888,79881,79882],{"xmlns":890},[892,79883,79884,79888],{},[895,79885,79886],{},[898,79887,1786],{},[902,79889,1786],{"encoding":904}," odpovídajícím minimu ",[883,79892,79894],{"className":79893},[886],[888,79895,79896],{"xmlns":890},[892,79897,79898,79906],{},[895,79899,79900,79902,79904],{},[898,79901,1786],{},[898,79903,52173],{},[898,79905,3455],{},[902,79907,67130],{"encoding":904}," při ceně ",[883,79910,79912],{"className":79911},[886],[888,79913,79914],{"xmlns":890},[892,79915,79916,79924],{},[895,79917,79918],{},[1753,79919,79920,79922],{},[898,79921,1747],{},[1708,79923,2417],{},[902,79925,16331],{"encoding":904}," (minimální cena nabídky); pod ",[883,79928,79930],{"className":79929},[886],[888,79931,79932],{"xmlns":890},[892,79933,79934,79942],{},[895,79935,79936],{},[1753,79937,79938,79940],{},[898,79939,1688],{},[1708,79941,2417],{},[902,79943,41691],{"encoding":904}," je nabídka nulová.",[49185,79946,79948],{"id":79947},"příklad-312","Příklad 3.12",[724,79950,79951,3973,79953,79999],{},[38,79952,67805],{},[883,79954,79956],{"className":79955},[886],[888,79957,79958],{"xmlns":890},[892,79959,79960,79996],{},[895,79961,79962,79964,79966,79968,79970,79976,79978,79980,79986,79988,79990,79992,79994],{},[898,79963,1978],{},[898,79965,3455],{},[1708,79967,1710],{},[2505,79969,10909],{},[1753,79971,79972,79974],{},[898,79973,1688],{},[2505,79975,3121],{},[1708,79977,2726],{},[2505,79979,3132],{},[1753,79981,79982,79984],{},[898,79983,1688],{},[2505,79985,3132],{},[1708,79987,2019],{},[2505,79989,4853],{},[898,79991,1688],{},[1708,79993,2019],{},[2505,79995,4003],{},[902,79997,79998],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,80001,80002,1729,80004,80040,80041,2788],{},[38,80003,34628],{},[883,80005,80007],{"className":80006},[886],[888,80008,80009],{"xmlns":890},[892,80010,80011,80037],{},[895,80012,80013,80015,80017,80019,80021,80027,80029,80031,80033,80035],{},[898,80014,1741],{},[898,80016,3455],{},[1708,80018,1710],{},[2505,80020,6090],{},[1753,80022,80023,80025],{},[898,80024,1688],{},[2505,80026,3132],{},[1708,80028,2726],{},[2505,80030,5867],{},[898,80032,1688],{},[1708,80034,2019],{},[2505,80036,4853],{},[902,80038,80039],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,80042,80044],{"className":80043},[886],[888,80045,80046],{"xmlns":890},[892,80047,80048,80058],{},[895,80049,80050,80052,80054,80056],{},[898,80051,1747],{},[1708,80053,1710],{},[898,80055,1741],{},[898,80057,3455],{},[902,80059,80060],{"encoding":904},"P = MC",[883,80062,80064],{"className":80063},[886],[888,80065,80066],{"xmlns":890,"display":2210},[892,80067,80068,80092],{},[895,80069,80070,80072,80074,80076,80082,80084,80086,80088,80090],{},[898,80071,1747],{},[1708,80073,1710],{},[2505,80075,6090],{},[1753,80077,80078,80080],{},[898,80079,1688],{},[2505,80081,3132],{},[1708,80083,2726],{},[2505,80085,5867],{},[898,80087,1688],{},[1708,80089,2019],{},[2505,80091,4795],{},[902,80093,80094],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,80096,80097,80098,17303,80111,80124],{},"Vyjádření ",[883,80099,80101],{"className":80100},[886],[888,80102,80103],{"xmlns":890},[892,80104,80105,80109],{},[895,80106,80107],{},[898,80108,1688],{},[902,80110,1688],{"encoding":904},[883,80112,80114],{"className":80113},[886],[888,80115,80116],{"xmlns":890},[892,80117,80118,80122],{},[895,80119,80120],{},[898,80121,1747],{},[902,80123,1747],{"encoding":904}," doplněním na čtverec:",[883,80126,80128],{"className":80127},[886],[888,80129,80130],{"xmlns":890,"display":2210},[892,80131,80132,80222],{},[895,80133,80134,80136,80138,80140,80178,80180,80182,80204,80206,80220],{},[898,80135,1747],{},[1708,80137,1710],{},[2505,80139,6090],{},[895,80141,80142,80144,80166,80168,80176],{},[1708,80143,1716],{"fence":1882},[1753,80145,80146,80164],{},[895,80147,80148,80150,80152,80154,80162],{},[1708,80149,1716],{"fence":1882},[898,80151,1688],{},[1708,80153,2726],{},[3194,80155,80156],{"scriptlevel":2784,"displaystyle":1715},[2358,80157,80158,80160],{},[2505,80159,4018],{},[2505,80161,3121],{},[1708,80163,1721],{"fence":1882},[2505,80165,3132],{},[1708,80167,2019],{},[3194,80169,80170],{"scriptlevel":2784,"displaystyle":1715},[2358,80171,80172,80174],{},[2505,80173,9704],{},[2505,80175,4635],{},[1708,80177,1721],{"fence":1882},[1708,80179,1883],{"separator":1882},[3213,80181],{"width":3215},[1753,80183,80184,80202],{},[895,80185,80186,80188,80190,80192,80200],{},[1708,80187,1716],{"fence":1882},[898,80189,1688],{},[1708,80191,2726],{},[3194,80193,80194],{"scriptlevel":2784,"displaystyle":1715},[2358,80195,80196,80198],{},[2505,80197,4018],{},[2505,80199,3121],{},[1708,80201,1721],{"fence":1882},[2505,80203,3132],{},[1708,80205,1710],{},[2358,80207,80208,80218],{},[895,80209,80210,80212,80214,80216],{},[2505,80211,49855],{},[898,80213,1747],{},[1708,80215,2726],{},[2505,80217,9704],{},[2505,80219,4635],{},[1708,80221,1883],{"separator":1882},[902,80223,80224],{"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},",[883,80226,80228],{"className":80227},[886],[888,80229,80230],{"xmlns":890,"display":2210},[892,80231,80232,80264],{},[895,80233,80234,80236,80238,80244,80246,80262],{},[898,80235,1688],{},[1708,80237,1710],{},[2358,80239,80240,80242],{},[2505,80241,4018],{},[2505,80243,3121],{},[1708,80245,2019],{},[2358,80247,80248,80260],{},[9351,80249,80250],{},[895,80251,80252,80254,80256,80258],{},[2505,80253,49855],{},[898,80255,1747],{},[1708,80257,2726],{},[2505,80259,9704],{},[2505,80261,3121],{},[898,80263,2155],{"mathvariant":1759},[902,80265,80266],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,80268,78828,80269,1343,80307,1343,80355,80389,80390,2155],{},[883,80270,80272],{"className":80271},[886],[888,80273,80274],{"xmlns":890},[892,80275,80276,80304],{},[895,80277,80278,80280,80282,80284,80286,80288,80294,80296,80298,80300,80302],{},[898,80279,1786],{},[898,80281,52173],{},[898,80283,3455],{},[1708,80285,1710],{},[2505,80287,10909],{},[1753,80289,80290,80292],{},[898,80291,1688],{},[2505,80293,3132],{},[1708,80295,2726],{},[2505,80297,3132],{},[898,80299,1688],{},[1708,80301,2019],{},[2505,80303,4853],{},[902,80305,80306],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,80308,80310],{"className":80309},[886],[888,80311,80312],{"xmlns":890},[892,80313,80314,80352],{},[895,80315,80316,80318,80320,80326,80328,80330,80332,80334,80336,80338,80340,80342,80348,80350],{},[898,80317,1786],{},[898,80319,52173],{},[1753,80321,80322,80324],{},[898,80323,3455],{},[1708,80325,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,80327,1710],{},[2505,80329,3958],{},[898,80331,1688],{},[1708,80333,2726],{},[2505,80335,3132],{},[1708,80337,1710],{},[2505,80339,2784],{},[1708,80341,4782],{},[1753,80343,80344,80346],{},[898,80345,1688],{},[1708,80347,2417],{},[1708,80349,1710],{},[2505,80351,4003],{},[902,80353,80354],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,80356,80358],{"className":80357},[886],[888,80359,80360],{"xmlns":890},[892,80361,80362,80386],{},[895,80363,80364,80366,80368,80378,80380,80382,80384],{},[898,80365,1786],{},[898,80367,52173],{},[1753,80369,80370,80372],{},[898,80371,3455],{},[895,80373,80374,80376],{},[1708,80375,1761],{"mathvariant":1759},[1708,80377,1761],{"mathvariant":1759},[1708,80379,1710],{},[2505,80381,3958],{},[1708,80383,2854],{},[2505,80385,2784],{},[902,80387,80388],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,80391,80393],{"className":80392},[886],[888,80394,80395],{"xmlns":890},[892,80396,80397,80433],{},[895,80398,80399,80405,80407,80409,80411,80413,80415,80417,80419,80421,80423,80425,80427,80429,80431],{},[1753,80400,80401,80403],{},[898,80402,1747],{},[1708,80404,2417],{},[1708,80406,1710],{},[898,80408,1741],{},[898,80410,3455],{},[1708,80412,1716],{"stretchy":1715},[2505,80414,4003],{},[1708,80416,1721],{"stretchy":1715},[1708,80418,1710],{},[2505,80420,49855],{},[1708,80422,2726],{},[2505,80424,17132],{},[1708,80426,2019],{},[2505,80428,4853],{},[1708,80430,1710],{},[2505,80432,3993],{},[902,80434,80435],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,80437,80438],{},[38,80439,80440],{},"Závěr.",[883,80442,80444],{"className":80443},[886],[888,80445,80446],{"xmlns":890,"display":2210},[892,80447,80448,80534],{},[895,80449,80450,80452,80454,80456,80458,80460,80462,80464],{},[898,80451,1747],{},[1708,80453,1710],{},[898,80455,1981],{},[1708,80457,1716],{"stretchy":1715},[898,80459,1688],{},[1708,80461,1721],{"stretchy":1715},[1708,80463,1710],{},[895,80465,80466,80468],{},[1708,80467,79316],{"fence":1882},[2214,80469,80470,80512],{"rowspacing":79319,"columnalign":79320,"columnspacing":4750},[2218,80471,80472,80496],{},[2221,80473,80474],{},[3194,80475,80476],{"scriptlevel":2784,"displaystyle":1715},[895,80477,80478,80480,80486,80488,80490,80492,80494],{},[2505,80479,6090],{},[1753,80481,80482,80484],{},[898,80483,1688],{},[2505,80485,3132],{},[1708,80487,2726],{},[2505,80489,5867],{},[898,80491,1688],{},[1708,80493,2019],{},[2505,80495,4853],{},[2221,80497,80498],{},[3194,80499,80500],{"scriptlevel":2784,"displaystyle":1715},[895,80501,80502,80504,80506,80508,80510],{},[2247,80503,79347],{},[898,80505,1688],{},[1708,80507,6762],{},[2505,80509,4003],{},[1708,80511,1883],{"separator":1882},[2218,80513,80514,80520],{},[2221,80515,80516],{},[3194,80517,80518],{"scriptlevel":2784,"displaystyle":1715},[2505,80519,2784],{},[2221,80521,80522],{},[3194,80523,80524],{"scriptlevel":2784,"displaystyle":1715},[895,80525,80526,80528,80530,80532],{},[2247,80527,79347],{},[898,80529,1688],{},[1708,80531,2932],{},[2505,80533,31192],{},[902,80535,80536],{"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}",[724,80538,80539],{},[614,80540,80541,80542,80557,80558,2155],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,80543,80545],{"className":80544},[886],[888,80546,80547],{"xmlns":890},[892,80548,80549,80555],{},[895,80550,80551,80553],{},[898,80552,1741],{},[898,80554,3455],{},[902,80556,67111],{"encoding":904}," ležící nad minimem ",[883,80559,80561],{"className":80560},[886],[888,80562,80563],{"xmlns":890},[892,80564,80565,80573],{},[895,80566,80567,80569,80571],{},[898,80568,1786],{},[898,80570,52173],{},[898,80572,3455],{},[902,80574,67130],{"encoding":904},[115,80576,80578],{"id":80577},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,80580,80581,80582,80586,80587,80602,80603,80623,80624,1771,80627,80630,80631,80633,80634,2421,80656,80658,80659,1771,80661,70541,80664,1729,80667,53646,80682,80697],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,80583,80585],{"className":80584,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,80588,80590],{"className":80589},[886],[888,80591,80592],{"xmlns":890},[892,80593,80594,80600],{},[895,80595,80596,80598],{},[898,80597,1978],{},[898,80599,1975],{},[902,80601,16029],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,80604,80606],{"className":80605},[886],[888,80607,80608],{"xmlns":890},[892,80609,80610,80620],{},[895,80611,80612,80614,80616,80618],{},[898,80613,1978],{},[898,80615,1975],{},[898,80617,1799],{"mathvariant":1759},[898,80619,1688],{},[902,80621,80622],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,80625,80626],{},"fixních",[38,80628,80629],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,80632,76140],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,80635,80637],{"className":80636},[886],[888,80638,80639],{"xmlns":890},[892,80640,80641,80653],{},[895,80642,80643,80645,80647,80649,80651],{},[898,80644,1978],{},[898,80646,1975],{},[1708,80648,2726],{},[898,80650,1978],{},[898,80652,3455],{},[902,80654,80655],{"encoding":904},"TR - TC",[38,80657,66991],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,80660,68301],{},[38,80662,80663],{},"mezní náklady",[207,80665,1145],{"className":80666,"dataFsResolvedFilePath":764,"href":765},[210],[883,80668,80670],{"className":80669},[886],[888,80671,80672],{"xmlns":890},[892,80673,80674,80680],{},[895,80675,80676,80678],{},[898,80677,1978],{},[898,80679,1975],{},[902,80681,16029],{"encoding":904},[883,80683,80685],{"className":80684},[886],[888,80686,80687],{"xmlns":890},[892,80688,80689,80695],{},[895,80690,80691,80693],{},[898,80692,1978],{},[898,80694,3455],{},[902,80696,15197],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,80699,80700,80762,80828,80890],{},[123,80701,80702,80705,80706,1826,80721,2155],{},[38,80703,80704],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,80707,80709],{"className":80708},[886],[888,80710,80711],{"xmlns":890},[892,80712,80713,80719],{},[895,80714,80715,80717],{},[898,80716,1786],{},[898,80718,3455],{},[902,80720,3458],{"encoding":904},[883,80722,80724],{"className":80723},[886],[888,80725,80726],{"xmlns":890},[892,80727,80728,80760],{},[895,80729,80730,80732,80734,80736,80742,80744,80746,80748,80750,80752,80758],{},[898,80731,1786],{},[898,80733,3455],{},[1708,80735,1716],{"stretchy":1715},[1743,80737,80738,80740],{},[898,80739,1688],{},[2505,80741,2784],{},[1708,80743,1721],{"stretchy":1715},[1708,80745,1710],{},[898,80747,1741],{},[898,80749,3455],{},[1708,80751,1716],{"stretchy":1715},[1743,80753,80754,80756],{},[898,80755,1688],{},[2505,80757,2784],{},[1708,80759,1721],{"stretchy":1715},[902,80761,74384],{"encoding":904},[123,80763,80764,80705,80767,1826,80784,2155],{},[38,80765,80766],{},"Princip minimalizace průměrných variabilních nákladů:",[883,80768,80770],{"className":80769},[886],[888,80771,80772],{"xmlns":890},[892,80773,80774,80782],{},[895,80775,80776,80778,80780],{},[898,80777,1786],{},[898,80779,52173],{},[898,80781,3455],{},[902,80783,67130],{"encoding":904},[883,80785,80787],{"className":80786},[886],[888,80788,80789],{"xmlns":890},[892,80790,80791,80825],{},[895,80792,80793,80795,80797,80799,80801,80807,80809,80811,80813,80815,80817,80823],{},[898,80794,1786],{},[898,80796,52173],{},[898,80798,3455],{},[1708,80800,1716],{"stretchy":1715},[1743,80802,80803,80805],{},[898,80804,1688],{},[2505,80806,2784],{},[1708,80808,1721],{"stretchy":1715},[1708,80810,1710],{},[898,80812,1741],{},[898,80814,3455],{},[1708,80816,1716],{"stretchy":1715},[1743,80818,80819,80821],{},[898,80820,1688],{},[2505,80822,2784],{},[1708,80824,1721],{"stretchy":1715},[902,80826,80827],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,80829,80830,80833,80834,1826,80849,2155],{},[38,80831,80832],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,80835,80837],{"className":80836},[886],[888,80838,80839],{"xmlns":890},[892,80840,80841,80847],{},[895,80842,80843,80845],{},[898,80844,1747],{},[898,80846,1975],{},[902,80848,75294],{"encoding":904},[883,80850,80852],{"className":80851},[886],[888,80853,80854],{"xmlns":890},[892,80855,80856,80888],{},[895,80857,80858,80860,80862,80864,80870,80872,80874,80876,80878,80880,80886],{},[898,80859,1741],{},[898,80861,1975],{},[1708,80863,1716],{"stretchy":1715},[1743,80865,80866,80868],{},[898,80867,1688],{},[2505,80869,2784],{},[1708,80871,1721],{"stretchy":1715},[1708,80873,1710],{},[898,80875,1741],{},[898,80877,3455],{},[1708,80879,1716],{"stretchy":1715},[1743,80881,80882,80884],{},[898,80883,1688],{},[2505,80885,2784],{},[1708,80887,1721],{"stretchy":1715},[902,80889,77457],{"encoding":904},[123,80891,80892,1729,80895,10064,80931,79735,80952,2980,80965,79417,80982,2155],{},[38,80893,80894],{},"Funkce nabídky firmy:",[883,80896,80898],{"className":80897},[886],[888,80899,80900],{"xmlns":890},[892,80901,80902,80928],{},[895,80903,80904,80906,80908,80910,80912,80914,80916,80918,80920,80922,80924,80926],{},[898,80905,1747],{},[1708,80907,1710],{},[898,80909,1981],{},[1708,80911,1716],{"stretchy":1715},[898,80913,1688],{},[1708,80915,1721],{"stretchy":1715},[1708,80917,1710],{},[898,80919,1741],{},[898,80921,3455],{},[1708,80923,1716],{"stretchy":1715},[898,80925,1688],{},[1708,80927,1721],{"stretchy":1715},[902,80929,80930],{"encoding":904},"P = S(Q) = MC(Q)",[883,80932,80934],{"className":80933},[886],[888,80935,80936],{"xmlns":890},[892,80937,80938,80950],{},[895,80939,80940,80942,80944],{},[898,80941,1688],{},[1708,80943,6762],{},[1753,80945,80946,80948],{},[898,80947,1688],{},[1708,80949,2417],{},[902,80951,79734],{"encoding":904},[883,80953,80955],{"className":80954},[886],[888,80956,80957],{"xmlns":890},[892,80958,80959,80963],{},[895,80960,80961],{},[2505,80962,2784],{},[902,80964,2784],{"encoding":904},[883,80966,80968],{"className":80967},[886],[888,80969,80970],{"xmlns":890},[892,80971,80972,80980],{},[895,80973,80974],{},[1753,80975,80976,80978],{},[898,80977,1688],{},[1708,80979,2417],{},[902,80981,41691],{"encoding":904},[883,80983,80985],{"className":80984},[886],[888,80986,80987],{"xmlns":890},[892,80988,80989,80997],{},[895,80990,80991,80993,80995],{},[898,80992,1786],{},[898,80994,52173],{},[898,80996,3455],{},[902,80998,67130],{"encoding":904},[115,81000,10753],{"id":10752},[152,81002,81003,81006,81009,81012,81015,81018,81021,81024,81027,81030,81033],{},[123,81004,81005],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,81007,81008],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,81010,81011],{},"Jak se vypočte mezní příjem a co udává?",[123,81013,81014],{},"Z jakých složek se skládají celkové náklady?",[123,81016,81017],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,81019,81020],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,81022,81023],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,81025,81026],{},"Jak se vypočte zisk?",[123,81028,81029],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,81031,81032],{},"Co jsou body zvratu? Jak se najdou?",[123,81034,81035],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,81037,81039],{"id":81038},"úlohy-31328","Úlohy 3.1–3.28",[198,81041,81043],{"id":81042},"příjem-3135","Příjem (3.1–3.5)",[724,81045,81046,57253,81049,81077,81078,81093,81094,81109,81110,12381,81125,1343,81140,1343,81155,81170],{},[38,81047,81048],{},"3.1",[883,81050,81052],{"className":81051},[886],[888,81053,81054],{"xmlns":890},[892,81055,81056,81074],{},[895,81057,81058,81060,81062,81064,81066,81068,81070,81072],{},[898,81059,1747],{},[1708,81061,1710],{},[898,81063,16117],{},[1708,81065,1716],{"stretchy":1715},[898,81067,1688],{},[1708,81069,1721],{"stretchy":1715},[1708,81071,1710],{},[2505,81073,9238],{},[902,81075,81076],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,81079,81081],{"className":81080},[886],[888,81082,81083],{"xmlns":890},[892,81084,81085,81091],{},[895,81086,81087,81089],{},[898,81088,1978],{},[898,81090,1975],{},[902,81092,16029],{"encoding":904},", průměrný příjem ",[883,81095,81097],{"className":81096},[886],[888,81098,81099],{"xmlns":890},[892,81100,81101,81107],{},[895,81102,81103,81105],{},[898,81104,1786],{},[898,81106,1975],{},[902,81108,67264],{"encoding":904}," a mezní příjem ",[883,81111,81113],{"className":81112},[886],[888,81114,81115],{"xmlns":890},[892,81116,81117,81123],{},[895,81118,81119,81121],{},[898,81120,1741],{},[898,81122,1975],{},[902,81124,18548],{"encoding":904},[883,81126,81128],{"className":81127},[886],[888,81129,81130],{"xmlns":890},[892,81131,81132,81138],{},[895,81133,81134,81136],{},[898,81135,1978],{},[898,81137,1975],{},[902,81139,16029],{"encoding":904},[883,81141,81143],{"className":81142},[886],[888,81144,81145],{"xmlns":890},[892,81146,81147,81153],{},[895,81148,81149,81151],{},[898,81150,1786],{},[898,81152,1975],{},[902,81154,67264],{"encoding":904},[883,81156,81158],{"className":81157},[886],[888,81159,81160],{"xmlns":890},[892,81161,81162,81168],{},[895,81163,81164,81166],{},[898,81165,1741],{},[898,81167,1975],{},[902,81169,18548],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,81172,81173,57253,81176,81077,81212,81093,81227,81109,81242,12381,81257,1343,81272,1343,81287,81302],{},[38,81174,81175],{},"3.2",[883,81177,81179],{"className":81178},[886],[888,81180,81181],{"xmlns":890},[892,81182,81183,81209],{},[895,81184,81185,81187,81189,81191,81193,81195,81197,81199,81201,81203,81205,81207],{},[898,81186,1747],{},[1708,81188,1710],{},[898,81190,16117],{},[1708,81192,1716],{"stretchy":1715},[898,81194,1688],{},[1708,81196,1721],{"stretchy":1715},[1708,81198,1710],{},[1708,81200,2726],{},[2505,81202,6097],{},[898,81204,1688],{},[1708,81206,2019],{},[2505,81208,4018],{},[902,81210,81211],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,81213,81215],{"className":81214},[886],[888,81216,81217],{"xmlns":890},[892,81218,81219,81225],{},[895,81220,81221,81223],{},[898,81222,1978],{},[898,81224,1975],{},[902,81226,16029],{"encoding":904},[883,81228,81230],{"className":81229},[886],[888,81231,81232],{"xmlns":890},[892,81233,81234,81240],{},[895,81235,81236,81238],{},[898,81237,1786],{},[898,81239,1975],{},[902,81241,67264],{"encoding":904},[883,81243,81245],{"className":81244},[886],[888,81246,81247],{"xmlns":890},[892,81248,81249,81255],{},[895,81250,81251,81253],{},[898,81252,1741],{},[898,81254,1975],{},[902,81256,18548],{"encoding":904},[883,81258,81260],{"className":81259},[886],[888,81261,81262],{"xmlns":890},[892,81263,81264,81270],{},[895,81265,81266,81268],{},[898,81267,1978],{},[898,81269,1975],{},[902,81271,16029],{"encoding":904},[883,81273,81275],{"className":81274},[886],[888,81276,81277],{"xmlns":890},[892,81278,81279,81285],{},[895,81280,81281,81283],{},[898,81282,1786],{},[898,81284,1975],{},[902,81286,67264],{"encoding":904},[883,81288,81290],{"className":81289},[886],[888,81291,81292],{"xmlns":890},[892,81293,81294,81300],{},[895,81295,81296,81298],{},[898,81297,1741],{},[898,81299,1975],{},[902,81301,18548],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,81304,81305,57253,81308,81345,81346,81093,81361,81109,81376,11617,81391,10064,81406,81432,81433,81448,81449,1343,81464,10064,81479,81432,81504,81519,81520,81533,81534,81549,81550,81565,81566,1343,81579,1343,81594,1343,81609,2155],{},[38,81306,81307],{},"3.3",[883,81309,81311],{"className":81310},[886],[888,81312,81313],{"xmlns":890},[892,81314,81315,81342],{},[895,81316,81317,81319,81321,81323,81325,81327,81329,81331,81334,81336],{},[898,81318,1747],{},[1708,81320,1710],{},[898,81322,16117],{},[1708,81324,1716],{"stretchy":1715},[898,81326,1688],{},[1708,81328,1721],{"stretchy":1715},[1708,81330,1710],{},[2505,81332,81333],{},"1200",[1708,81335,2726],{},[1753,81337,81338,81340],{},[898,81339,1688],{},[2505,81341,3132],{},[902,81343,81344],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,81347,81349],{"className":81348},[886],[888,81350,81351],{"xmlns":890},[892,81352,81353,81359],{},[895,81354,81355,81357],{},[898,81356,1978],{},[898,81358,1975],{},[902,81360,16029],{"encoding":904},[883,81362,81364],{"className":81363},[886],[888,81365,81366],{"xmlns":890},[892,81367,81368,81374],{},[895,81369,81370,81372],{},[898,81371,1786],{},[898,81373,1975],{},[902,81375,67264],{"encoding":904},[883,81377,81379],{"className":81378},[886],[888,81380,81381],{"xmlns":890},[892,81382,81383,81389],{},[895,81384,81385,81387],{},[898,81386,1741],{},[898,81388,1975],{},[902,81390,18548],{"encoding":904},[883,81392,81394],{"className":81393},[886],[888,81395,81396],{"xmlns":890},[892,81397,81398,81404],{},[895,81399,81400,81402],{},[898,81401,1978],{},[898,81403,1975],{},[902,81405,16029],{"encoding":904},[883,81407,81409],{"className":81408},[886],[888,81410,81411],{"xmlns":890},[892,81412,81413,81429],{},[895,81414,81415,81417,81419,81421,81423,81425,81427],{},[898,81416,1688],{},[1708,81418,1710],{},[2505,81420,4003],{},[1708,81422,1883],{"separator":1882},[2505,81424,4018],{},[1708,81426,1883],{"separator":1882},[2505,81428,49855],{},[902,81430,81431],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,81434,81436],{"className":81435},[886],[888,81437,81438],{"xmlns":890},[892,81439,81440,81446],{},[895,81441,81442,81444],{},[898,81443,1978],{},[898,81445,1975],{},[902,81447,16029],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,81450,81452],{"className":81451},[886],[888,81453,81454],{"xmlns":890},[892,81455,81456,81462],{},[895,81457,81458,81460],{},[898,81459,1786],{},[898,81461,1975],{},[902,81463,67264],{"encoding":904},[883,81465,81467],{"className":81466},[886],[888,81468,81469],{"xmlns":890},[892,81470,81471,81477],{},[895,81472,81473,81475],{},[898,81474,1741],{},[898,81476,1975],{},[902,81478,18548],{"encoding":904},[883,81480,81482],{"className":81481},[886],[888,81483,81484],{"xmlns":890},[892,81485,81486,81502],{},[895,81487,81488,81490,81492,81494,81496,81498,81500],{},[898,81489,1688],{},[1708,81491,1710],{},[2505,81493,4003],{},[1708,81495,1883],{"separator":1882},[2505,81497,4018],{},[1708,81499,1883],{"separator":1882},[2505,81501,49855],{},[902,81503,81431],{"encoding":904},[883,81505,81507],{"className":81506},[886],[888,81508,81509],{"xmlns":890},[892,81510,81511,81517],{},[895,81512,81513,81515],{},[898,81514,1741],{},[898,81516,1975],{},[902,81518,18548],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,81521,81523],{"className":81522},[886],[888,81524,81525],{"xmlns":890},[892,81526,81527,81531],{},[895,81528,81529],{},[898,81530,1688],{},[902,81532,1688],{"encoding":904},", které maximalizuje ",[883,81535,81537],{"className":81536},[886],[888,81538,81539],{"xmlns":890},[892,81540,81541,81547],{},[895,81542,81543,81545],{},[898,81544,1978],{},[898,81546,1975],{},[902,81548,16029],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,81551,81553],{"className":81552},[886],[888,81554,81555],{"xmlns":890},[892,81556,81557,81563],{},[895,81558,81559,81561],{},[898,81560,1978],{},[898,81562,1975],{},[902,81564,16029],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,81567,81569],{"className":81568},[886],[888,81570,81571],{"xmlns":890},[892,81572,81573,81577],{},[895,81574,81575],{},[898,81576,16117],{},[902,81578,16117],{"encoding":904},[883,81580,81582],{"className":81581},[886],[888,81583,81584],{"xmlns":890},[892,81585,81586,81592],{},[895,81587,81588,81590],{},[898,81589,1978],{},[898,81591,1975],{},[902,81593,16029],{"encoding":904},[883,81595,81597],{"className":81596},[886],[888,81598,81599],{"xmlns":890},[892,81600,81601,81607],{},[895,81602,81603,81605],{},[898,81604,1786],{},[898,81606,1975],{},[902,81608,67264],{"encoding":904},[883,81610,81612],{"className":81611},[886],[888,81613,81614],{"xmlns":890},[892,81615,81616,81622],{},[895,81617,81618,81620],{},[898,81619,1741],{},[898,81621,1975],{},[902,81623,18548],{"encoding":904},[724,81625,81626,81629,81630,81660,81661,81676,81677,22048,81690,1343,81708,1343,81725,81743,81744,81766,81767,81782,81783,81796,81797,2155],{},[38,81627,81628],{},"3.4"," Je dán celkový příjem ",[883,81631,81633],{"className":81632},[886],[888,81634,81635],{"xmlns":890},[892,81636,81637,81657],{},[895,81638,81639,81641,81643,81645,81647,81649,81651],{},[898,81640,1978],{},[898,81642,1975],{},[1708,81644,1710],{},[2505,81646,81333],{},[898,81648,1688],{},[1708,81650,2726],{},[1753,81652,81653,81655],{},[898,81654,1688],{},[2505,81656,3121],{},[902,81658,81659],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,81662,81664],{"className":81663},[886],[888,81665,81666],{"xmlns":890},[892,81667,81668,81674],{},[895,81669,81670,81672],{},[898,81671,1978],{},[898,81673,1975],{},[902,81675,16029],{"encoding":904}," vzhledem ke ",[883,81678,81680],{"className":81679},[886],[888,81681,81682],{"xmlns":890},[892,81683,81684,81688],{},[895,81685,81686],{},[898,81687,1688],{},[902,81689,1688],{"encoding":904},[883,81691,81693],{"className":81692},[886],[888,81694,81695],{"xmlns":890},[892,81696,81697,81705],{},[895,81698,81699,81701,81703],{},[898,81700,1688],{},[1708,81702,1710],{},[2505,81704,3993],{},[902,81706,81707],{"encoding":904},"Q = 5",[883,81709,81711],{"className":81710},[886],[888,81712,81713],{"xmlns":890},[892,81714,81715,81723],{},[895,81716,81717,81719,81721],{},[898,81718,1688],{},[1708,81720,1710],{},[2505,81722,3998],{},[902,81724,17507],{"encoding":904},[883,81726,81728],{"className":81727},[886],[888,81729,81730],{"xmlns":890},[892,81731,81732,81740],{},[895,81733,81734,81736,81738],{},[898,81735,1688],{},[1708,81737,1710],{},[2505,81739,4090],{},[902,81741,81742],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,81745,81747],{"className":81746},[886],[888,81748,81749],{"xmlns":890},[892,81750,81751,81763],{},[895,81752,81753,81755,81757,81759,81761],{},[898,81754,1741],{},[898,81756,1975],{},[1708,81758,1716],{"stretchy":1715},[2505,81760,4003],{},[1708,81762,1721],{"stretchy":1715},[902,81764,81765],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,81768,81770],{"className":81769},[886],[888,81771,81772],{"xmlns":890},[892,81773,81774,81780],{},[895,81775,81776,81778],{},[898,81777,1978],{},[898,81779,1975],{},[902,81781,16029],{"encoding":904},", jestliže se ",[883,81784,81786],{"className":81785},[886],[888,81787,81788],{"xmlns":890},[892,81789,81790,81794],{},[895,81791,81792],{},[898,81793,1688],{},[902,81795,1688],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,81798,81800],{"className":81799},[886],[888,81801,81802],{"xmlns":890},[892,81803,81804,81810],{},[895,81805,81806,81808],{},[898,81807,1978],{},[898,81809,1975],{},[902,81811,16029],{"encoding":904},[724,81813,81814,81817,81818,81844,81845,81860,81861,81782,81876,81889],{},[38,81815,81816],{},"3.5"," Je dán mezní příjem ",[883,81819,81821],{"className":81820},[886],[888,81822,81823],{"xmlns":890},[892,81824,81825,81841],{},[895,81826,81827,81829,81831,81833,81835,81837,81839],{},[898,81828,1741],{},[898,81830,1975],{},[1708,81832,1710],{},[1708,81834,2726],{},[898,81836,1688],{},[1708,81838,2019],{},[2505,81840,4018],{},[902,81842,81843],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,81846,81848],{"className":81847},[886],[888,81849,81850],{"xmlns":890},[892,81851,81852,81858],{},[895,81853,81854,81856],{},[898,81855,1978],{},[898,81857,1975],{},[902,81859,16029],{"encoding":904},". (b) Vypočtěte změnu ",[883,81862,81864],{"className":81863},[886],[888,81865,81866],{"xmlns":890},[892,81867,81868,81874],{},[895,81869,81870,81872],{},[898,81871,1978],{},[898,81873,1975],{},[902,81875,16029],{"encoding":904},[883,81877,81879],{"className":81878},[886],[888,81880,81881],{"xmlns":890},[892,81882,81883,81887],{},[895,81884,81885],{},[898,81886,1688],{},[902,81888,1688],{"encoding":904}," změní z 8 na 12.",[198,81891,81893],{"id":81892},"náklady-36316","Náklady (3.6–3.16)",[724,81895,81896,81899,81900,81940,81941,81956,81957,81974,81975,81992,81993,82008,82009,82024,82025,11617,82040,1343,82055,1343,82072,1343,82089,1343,82104,1343,82119,10064,82134,82152,82153,1343,82168,1343,82183,82198],{},[38,81897,81898],{},"3.6"," Jsou dány celkové náklady ",[883,81901,81903],{"className":81902},[886],[888,81904,81905],{"xmlns":890},[892,81906,81907,81937],{},[895,81908,81909,81911,81913,81915,81917,81919,81921,81923,81925],{},[898,81910,1978],{},[898,81912,3455],{},[1708,81914,1710],{},[2505,81916,9238],{},[1708,81918,2019],{},[2505,81920,3132],{},[898,81922,1688],{},[1708,81924,2019],{},[3194,81926,81927],{"scriptlevel":2784,"displaystyle":1715},[2358,81928,81929,81935],{},[1753,81930,81931,81933],{},[898,81932,1688],{},[2505,81934,3132],{},[2505,81936,4003],{},[902,81938,81939],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,81942,81944],{"className":81943},[886],[888,81945,81946],{"xmlns":890},[892,81947,81948,81954],{},[895,81949,81950,81952],{},[898,81951,22325],{},[898,81953,3455],{},[902,81955,67310],{"encoding":904},", celkové variabilní náklady ",[883,81958,81960],{"className":81959},[886],[888,81961,81962],{"xmlns":890},[892,81963,81964,81972],{},[895,81965,81966,81968,81970],{},[898,81967,1978],{},[898,81969,52173],{},[898,81971,3455],{},[902,81973,67328],{"encoding":904},", průměrné variabilní náklady ",[883,81976,81978],{"className":81977},[886],[888,81979,81980],{"xmlns":890},[892,81981,81982,81990],{},[895,81983,81984,81986,81988],{},[898,81985,1786],{},[898,81987,52173],{},[898,81989,3455],{},[902,81991,67130],{"encoding":904},", variabilní náklady na jednotku ",[883,81994,81996],{"className":81995},[886],[888,81997,81998],{"xmlns":890},[892,81999,82000,82006],{},[895,82001,82002,82004],{},[898,82003,52173],{},[898,82005,3455],{},[902,82007,75420],{"encoding":904},", průměrné náklady ",[883,82010,82012],{"className":82011},[886],[888,82013,82014],{"xmlns":890},[892,82015,82016,82022],{},[895,82017,82018,82020],{},[898,82019,1786],{},[898,82021,3455],{},[902,82023,3458],{"encoding":904}," a mezní náklady ",[883,82026,82028],{"className":82027},[886],[888,82029,82030],{"xmlns":890},[892,82031,82032,82038],{},[895,82033,82034,82036],{},[898,82035,1741],{},[898,82037,3455],{},[902,82039,67111],{"encoding":904},[883,82041,82043],{"className":82042},[886],[888,82044,82045],{"xmlns":890},[892,82046,82047,82053],{},[895,82048,82049,82051],{},[898,82050,1978],{},[898,82052,3455],{},[902,82054,15197],{"encoding":904},[883,82056,82058],{"className":82057},[886],[888,82059,82060],{"xmlns":890},[892,82061,82062,82070],{},[895,82063,82064,82066,82068],{},[898,82065,1978],{},[898,82067,52173],{},[898,82069,3455],{},[902,82071,67328],{"encoding":904},[883,82073,82075],{"className":82074},[886],[888,82076,82077],{"xmlns":890},[892,82078,82079,82087],{},[895,82080,82081,82083,82085],{},[898,82082,1786],{},[898,82084,52173],{},[898,82086,3455],{},[902,82088,67130],{"encoding":904},[883,82090,82092],{"className":82091},[886],[888,82093,82094],{"xmlns":890},[892,82095,82096,82102],{},[895,82097,82098,82100],{},[898,82099,52173],{},[898,82101,3455],{},[902,82103,75420],{"encoding":904},[883,82105,82107],{"className":82106},[886],[888,82108,82109],{"xmlns":890},[892,82110,82111,82117],{},[895,82112,82113,82115],{},[898,82114,1786],{},[898,82116,3455],{},[902,82118,3458],{"encoding":904},[883,82120,82122],{"className":82121},[886],[888,82123,82124],{"xmlns":890},[892,82125,82126,82132],{},[895,82127,82128,82130],{},[898,82129,1741],{},[898,82131,3455],{},[902,82133,67111],{"encoding":904},[883,82135,82137],{"className":82136},[886],[888,82138,82139],{"xmlns":890},[892,82140,82141,82149],{},[895,82142,82143,82145,82147],{},[898,82144,1688],{},[1708,82146,1710],{},[2505,82148,9704],{},[902,82150,82151],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,82154,82156],{"className":82155},[886],[888,82157,82158],{"xmlns":890},[892,82159,82160,82166],{},[895,82161,82162,82164],{},[898,82163,1978],{},[898,82165,3455],{},[902,82167,15197],{"encoding":904},[883,82169,82171],{"className":82170},[886],[888,82172,82173],{"xmlns":890},[892,82174,82175,82181],{},[895,82176,82177,82179],{},[898,82178,1786],{},[898,82180,3455],{},[902,82182,3458],{"encoding":904},[883,82184,82186],{"className":82185},[886],[888,82187,82188],{"xmlns":890},[892,82189,82190,82196],{},[895,82191,82192,82194],{},[898,82193,1741],{},[898,82195,3455],{},[902,82197,67111],{"encoding":904}," rostou, resp. klesají.",[724,82200,82201,82204,82205,82024,82235,82250,82251,82266,82267,1343,82282,1343,82297,2155],{},[38,82202,82203],{},"3.7"," Jsou dány průměrné náklady ",[883,82206,82208],{"className":82207},[886],[888,82209,82210],{"xmlns":890},[892,82211,82212,82232],{},[895,82213,82214,82216,82218,82220,82228,82230],{},[898,82215,1786],{},[898,82217,3455],{},[1708,82219,1710],{},[3194,82221,82222],{"scriptlevel":2784,"displaystyle":1715},[2358,82223,82224,82226],{},[2505,82225,9238],{},[898,82227,1688],{},[1708,82229,2019],{},[2505,82231,4018],{},[902,82233,82234],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,82236,82238],{"className":82237},[886],[888,82239,82240],{"xmlns":890},[892,82241,82242,82248],{},[895,82243,82244,82246],{},[898,82245,1741],{},[898,82247,3455],{},[902,82249,67111],{"encoding":904},". (a) Určete celkové náklady ",[883,82252,82254],{"className":82253},[886],[888,82255,82256],{"xmlns":890},[892,82257,82258,82264],{},[895,82259,82260,82262],{},[898,82261,1978],{},[898,82263,3455],{},[902,82265,15197],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,82268,82270],{"className":82269},[886],[888,82271,82272],{"xmlns":890},[892,82273,82274,82280],{},[895,82275,82276,82278],{},[898,82277,1786],{},[898,82279,3455],{},[902,82281,3458],{"encoding":904},[883,82283,82285],{"className":82284},[886],[888,82286,82287],{"xmlns":890},[892,82288,82289,82295],{},[895,82290,82291,82293],{},[898,82292,1978],{},[898,82294,3455],{},[902,82296,15197],{"encoding":904},[883,82298,82300],{"className":82299},[886],[888,82301,82302],{"xmlns":890},[892,82303,82304,82310],{},[895,82305,82306,82308],{},[898,82307,1741],{},[898,82309,3455],{},[902,82311,67111],{"encoding":904},[724,82313,82314,81899,82317,82361,82362,1343,82379,1343,82394,1343,82411,1343,82426,1343,82443,2155],{},[38,82315,82316],{},"3.8",[883,82318,82320],{"className":82319},[886],[888,82321,82322],{"xmlns":890},[892,82323,82324,82358],{},[895,82325,82326,82328,82330,82332,82334,82336,82338,82340,82342,82344,82350,82352],{},[898,82327,1978],{},[898,82329,3455],{},[1708,82331,1710],{},[2505,82333,12513],{},[1708,82335,2019],{},[2505,82337,49855],{},[898,82339,1688],{},[1708,82341,2726],{},[2505,82343,3947],{},[1753,82345,82346,82348],{},[898,82347,1688],{},[2505,82349,3132],{},[1708,82351,2019],{},[1753,82353,82354,82356],{},[898,82355,1688],{},[2505,82357,3121],{},[902,82359,82360],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,82363,82365],{"className":82364},[886],[888,82366,82367],{"xmlns":890},[892,82368,82369,82377],{},[895,82370,82371,82373,82375],{},[898,82372,1978],{},[898,82374,52173],{},[898,82376,3455],{},[902,82378,67328],{"encoding":904},[883,82380,82382],{"className":82381},[886],[888,82383,82384],{"xmlns":890},[892,82385,82386,82392],{},[895,82387,82388,82390],{},[898,82389,22325],{},[898,82391,3455],{},[902,82393,67310],{"encoding":904},[883,82395,82397],{"className":82396},[886],[888,82398,82399],{"xmlns":890},[892,82400,82401,82409],{},[895,82402,82403,82405,82407],{},[898,82404,1786],{},[898,82406,52173],{},[898,82408,3455],{},[902,82410,67130],{"encoding":904},[883,82412,82414],{"className":82413},[886],[888,82415,82416],{"xmlns":890},[892,82417,82418,82424],{},[895,82419,82420,82422],{},[898,82421,1786],{},[898,82423,3455],{},[902,82425,3458],{"encoding":904},[883,82427,82429],{"className":82428},[886],[888,82430,82431],{"xmlns":890},[892,82432,82433,82441],{},[895,82434,82435,82437,82439],{},[898,82436,1786],{},[898,82438,22325],{},[898,82440,3455],{},[902,82442,67346],{"encoding":904},[883,82444,82446],{"className":82445},[886],[888,82447,82448],{"xmlns":890},[892,82449,82450,82456],{},[895,82451,82452,82454],{},[898,82453,1741],{},[898,82455,3455],{},[902,82457,67111],{"encoding":904},[724,82459,82460,81899,82463,82493,82494,81676,82509,10064,82522,1343,82540,1343,82558,81743,82576,81766,82598,82613,82614,82627,82628,2155],{},[38,82461,82462],{},"3.9",[883,82464,82466],{"className":82465},[886],[888,82467,82468],{"xmlns":890},[892,82469,82470,82490],{},[895,82471,82472,82474,82476,82478,82480,82482,82484],{},[898,82473,1978],{},[898,82475,3455],{},[1708,82477,1710],{},[2505,82479,11040],{},[1708,82481,2019],{},[2505,82483,4097],{},[1753,82485,82486,82488],{},[898,82487,1688],{},[2505,82489,3132],{},[902,82491,82492],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,82495,82497],{"className":82496},[886],[888,82498,82499],{"xmlns":890},[892,82500,82501,82507],{},[895,82502,82503,82505],{},[898,82504,1978],{},[898,82506,3455],{},[902,82508,15197],{"encoding":904},[883,82510,82512],{"className":82511},[886],[888,82513,82514],{"xmlns":890},[892,82515,82516,82520],{},[895,82517,82518],{},[898,82519,1688],{},[902,82521,1688],{"encoding":904},[883,82523,82525],{"className":82524},[886],[888,82526,82527],{"xmlns":890},[892,82528,82529,82537],{},[895,82530,82531,82533,82535],{},[898,82532,1688],{},[1708,82534,1710],{},[2505,82536,4003],{},[902,82538,82539],{"encoding":904},"Q = 10",[883,82541,82543],{"className":82542},[886],[888,82544,82545],{"xmlns":890},[892,82546,82547,82555],{},[895,82548,82549,82551,82553],{},[898,82550,1688],{},[1708,82552,1710],{},[2505,82554,4018],{},[902,82556,82557],{"encoding":904},"Q = 20",[883,82559,82561],{"className":82560},[886],[888,82562,82563],{"xmlns":890},[892,82564,82565,82573],{},[895,82566,82567,82569,82571],{},[898,82568,1688],{},[1708,82570,1710],{},[2505,82572,49855],{},[902,82574,82575],{"encoding":904},"Q = 30",[883,82577,82579],{"className":82578},[886],[888,82580,82581],{"xmlns":890},[892,82582,82583,82595],{},[895,82584,82585,82587,82589,82591,82593],{},[898,82586,1741],{},[898,82588,3455],{},[1708,82590,1716],{"stretchy":1715},[2505,82592,4853],{},[1708,82594,1721],{"stretchy":1715},[902,82596,82597],{"encoding":904},"MC(15)",[883,82599,82601],{"className":82600},[886],[888,82602,82603],{"xmlns":890},[892,82604,82605,82611],{},[895,82606,82607,82609],{},[898,82608,1978],{},[898,82610,3455],{},[902,82612,15197],{"encoding":904}," v důsledku změny ",[883,82615,82617],{"className":82616},[886],[888,82618,82619],{"xmlns":890},[892,82620,82621,82625],{},[895,82622,82623],{},[898,82624,1688],{},[902,82626,1688],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,82629,82631],{"className":82630},[886],[888,82632,82633],{"xmlns":890},[892,82634,82635,82641],{},[895,82636,82637,82639],{},[898,82638,1978],{},[898,82640,3455],{},[902,82642,15197],{"encoding":904},[724,82644,82645,82648,82649,82250,82685,82700,82701,81860,82720,82613,82735,82748],{},[38,82646,82647],{},"3.10"," Jsou dány mezní náklady ",[883,82650,82652],{"className":82651},[886],[888,82653,82654],{"xmlns":890},[892,82655,82656,82682],{},[895,82657,82658,82660,82662,82664,82666,82668,82670,82672,82674,82676],{},[898,82659,1741],{},[898,82661,3455],{},[1708,82663,1710],{},[2505,82665,4199],{},[1708,82667,2726],{},[2505,82669,53694],{},[898,82671,1688],{},[1708,82673,2019],{},[2505,82675,12222],{},[1753,82677,82678,82680],{},[898,82679,1688],{},[2505,82681,3132],{},[902,82683,82684],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,82686,82688],{"className":82687},[886],[888,82689,82690],{"xmlns":890},[892,82691,82692,82698],{},[895,82693,82694,82696],{},[898,82695,1978],{},[898,82697,3455],{},[902,82699,15197],{"encoding":904},", jestliže fixní náklady ",[883,82702,82704],{"className":82703},[886],[888,82705,82706],{"xmlns":890},[892,82707,82708,82718],{},[895,82709,82710,82712,82714,82716],{},[898,82711,22325],{},[898,82713,3455],{},[1708,82715,1710],{},[2505,82717,9238],{},[902,82719,23520],{"encoding":904},[883,82721,82723],{"className":82722},[886],[888,82724,82725],{"xmlns":890},[892,82726,82727,82733],{},[895,82728,82729,82731],{},[898,82730,1978],{},[898,82732,3455],{},[902,82734,15197],{"encoding":904},[883,82736,82738],{"className":82737},[886],[888,82739,82740],{"xmlns":890},[892,82741,82742,82746],{},[895,82743,82744],{},[898,82745,1688],{},[902,82747,1688],{"encoding":904}," z 15 na 20.",[724,82750,82751,81899,82754,12453,82797,82810,82811,82826,82827,82842,82843,82810,82856,82826,82873,82890,82891,82810,82904,82826,82919,82934,82935,82955,82956,82979],{},[38,82752,82753],{},"3.11",[883,82755,82757],{"className":82756},[886],[888,82758,82759],{"xmlns":890},[892,82760,82761,82795],{},[895,82762,82763,82765,82767,82769,82771,82773,82775,82777,82779,82781,82787,82789],{},[898,82764,1978],{},[898,82766,3455],{},[1708,82768,1710],{},[2505,82770,9238],{},[1708,82772,2019],{},[2505,82774,4028],{},[898,82776,1688],{},[1708,82778,2726],{},[2505,82780,3993],{},[1753,82782,82783,82785],{},[898,82784,1688],{},[2505,82786,3132],{},[1708,82788,2019],{},[1753,82790,82791,82793],{},[898,82792,1688],{},[2505,82794,3121],{},[902,82796,72722],{"encoding":904},[883,82798,82800],{"className":82799},[886],[888,82801,82802],{"xmlns":890},[892,82803,82804,82808],{},[895,82805,82806],{},[898,82807,1688],{},[902,82809,1688],{"encoding":904},", které minimalizuje ",[883,82812,82814],{"className":82813},[886],[888,82815,82816],{"xmlns":890},[892,82817,82818,82824],{},[895,82819,82820,82822],{},[898,82821,1741],{},[898,82823,3455],{},[902,82825,67111],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,82828,82830],{"className":82829},[886],[888,82831,82832],{"xmlns":890},[892,82833,82834,82840],{},[895,82835,82836,82838],{},[898,82837,1741],{},[898,82839,3455],{},[902,82841,67111],{"encoding":904},". (b) Určete ",[883,82844,82846],{"className":82845},[886],[888,82847,82848],{"xmlns":890},[892,82849,82850,82854],{},[895,82851,82852],{},[898,82853,1688],{},[902,82855,1688],{"encoding":904},[883,82857,82859],{"className":82858},[886],[888,82860,82861],{"xmlns":890},[892,82862,82863,82871],{},[895,82864,82865,82867,82869],{},[898,82866,1786],{},[898,82868,52173],{},[898,82870,3455],{},[902,82872,67130],{"encoding":904},[883,82874,82876],{"className":82875},[886],[888,82877,82878],{"xmlns":890},[892,82879,82880,82888],{},[895,82881,82882,82884,82886],{},[898,82883,1786],{},[898,82885,52173],{},[898,82887,3455],{},[902,82889,67130],{"encoding":904},". (c) Určete ",[883,82892,82894],{"className":82893},[886],[888,82895,82896],{"xmlns":890},[892,82897,82898,82902],{},[895,82899,82900],{},[898,82901,1688],{},[902,82903,1688],{"encoding":904},[883,82905,82907],{"className":82906},[886],[888,82908,82909],{"xmlns":890},[892,82910,82911,82917],{},[895,82912,82913,82915],{},[898,82914,1786],{},[898,82916,3455],{},[902,82918,3458],{"encoding":904},[883,82920,82922],{"className":82921},[886],[888,82923,82924],{"xmlns":890},[892,82925,82926,82932],{},[895,82927,82928,82930],{},[898,82929,1786],{},[898,82931,3455],{},[902,82933,3458],{"encoding":904}," (rada: hledaný kořen ",[883,82936,82938],{"className":82937},[886],[888,82939,82940],{"xmlns":890},[892,82941,82942,82952],{},[895,82943,82944,82946],{},[898,82945,1786],{},[1753,82947,82948,82950],{},[898,82949,3455],{},[1708,82951,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,82953,82954],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,82957,82959],{"className":82958},[886],[888,82960,82961],{"xmlns":890},[892,82962,82963,82976],{},[895,82964,82965,82967,82970,82972,82974],{},[1708,82966,1716],{"stretchy":1715},[2505,82968,82969],{},"4,7",[1708,82971,8197],{"separator":1882},[2505,82973,17200],{},[1708,82975,1721],{"stretchy":1715},[902,82977,82978],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,82981,82982,82985,82986,3405,83014,83031,83032,2980,83073,83094],{},[38,82983,82984],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,82987,82989],{"className":82988},[886],[888,82990,82991],{"xmlns":890},[892,82992,82993,83011],{},[895,82994,82995,82997,82999,83001,83003,83005,83007,83009],{},[898,82996,1786],{},[898,82998,3455],{},[1708,83000,1710],{},[898,83002,1786],{},[898,83004,3455],{},[1708,83006,1716],{"stretchy":1715},[898,83008,1688],{},[1708,83010,1721],{"stretchy":1715},[902,83012,83013],{"encoding":904},"AC = AC(Q)",[883,83015,83017],{"className":83016},[886],[888,83018,83019],{"xmlns":890},[892,83020,83021,83029],{},[895,83022,83023],{},[1743,83024,83025,83027],{},[898,83026,1688],{},[2505,83028,2784],{},[902,83030,50144],{"encoding":904}," minimum, pak platí ",[883,83033,83035],{"className":83034},[886],[888,83036,83037],{"xmlns":890},[892,83038,83039,83071],{},[895,83040,83041,83043,83045,83047,83053,83055,83057,83059,83061,83063,83069],{},[898,83042,1786],{},[898,83044,3455],{},[1708,83046,1716],{"stretchy":1715},[1743,83048,83049,83051],{},[898,83050,1688],{},[2505,83052,2784],{},[1708,83054,1721],{"stretchy":1715},[1708,83056,1710],{},[898,83058,1741],{},[898,83060,3455],{},[1708,83062,1716],{"stretchy":1715},[1743,83064,83065,83067],{},[898,83066,1688],{},[2505,83068,2784],{},[1708,83070,1721],{"stretchy":1715},[902,83072,74384],{"encoding":904},[883,83074,83076],{"className":83075},[886],[888,83077,83078],{"xmlns":890},[892,83079,83080,83092],{},[895,83081,83082,83084,83086,83088,83090],{},[898,83083,1741],{},[898,83085,3455],{},[1708,83087,1716],{"stretchy":1715},[898,83089,1688],{},[1708,83091,1721],{"stretchy":1715},[902,83093,79503],{"encoding":904}," jsou mezní náklady.",[724,83096,83097,81899,83100,82361,83134,82810,83147,82826,83162,2155],{},[38,83098,83099],{},"3.13",[883,83101,83103],{"className":83102},[886],[888,83104,83105],{"xmlns":890},[892,83106,83107,83131],{},[895,83108,83109,83111,83113,83115,83121,83123,83125,83127,83129],{},[898,83110,1978],{},[898,83112,3455],{},[1708,83114,1710],{},[1753,83116,83117,83119],{},[898,83118,1688],{},[2505,83120,3132],{},[1708,83122,2019],{},[2505,83124,3132],{},[898,83126,1688],{},[1708,83128,2019],{},[2505,83130,4028],{},[902,83132,83133],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,83135,83137],{"className":83136},[886],[888,83138,83139],{"xmlns":890},[892,83140,83141,83145],{},[895,83142,83143],{},[898,83144,1688],{},[902,83146,1688],{"encoding":904},[883,83148,83150],{"className":83149},[886],[888,83151,83152],{"xmlns":890},[892,83153,83154,83160],{},[895,83155,83156,83158],{},[898,83157,1786],{},[898,83159,3455],{},[902,83161,3458],{"encoding":904},[883,83163,83165],{"className":83164},[886],[888,83166,83167],{"xmlns":890},[892,83168,83169,83175],{},[895,83170,83171,83173],{},[898,83172,1786],{},[898,83174,3455],{},[902,83176,3458],{"encoding":904},[724,83178,83179,83182,83183,3405,83215,83031,83232,2980,83275,83094],{},[38,83180,83181],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,83184,83186],{"className":83185},[886],[888,83187,83188],{"xmlns":890},[892,83189,83190,83212],{},[895,83191,83192,83194,83196,83198,83200,83202,83204,83206,83208,83210],{},[898,83193,1786],{},[898,83195,52173],{},[898,83197,3455],{},[1708,83199,1710],{},[898,83201,1786],{},[898,83203,52173],{},[898,83205,3455],{},[1708,83207,1716],{"stretchy":1715},[898,83209,1688],{},[1708,83211,1721],{"stretchy":1715},[902,83213,83214],{"encoding":904},"AVC = AVC(Q)",[883,83216,83218],{"className":83217},[886],[888,83219,83220],{"xmlns":890},[892,83221,83222,83230],{},[895,83223,83224],{},[1743,83225,83226,83228],{},[898,83227,1688],{},[2505,83229,2784],{},[902,83231,50144],{"encoding":904},[883,83233,83235],{"className":83234},[886],[888,83236,83237],{"xmlns":890},[892,83238,83239,83273],{},[895,83240,83241,83243,83245,83247,83249,83255,83257,83259,83261,83263,83265,83271],{},[898,83242,1786],{},[898,83244,52173],{},[898,83246,3455],{},[1708,83248,1716],{"stretchy":1715},[1743,83250,83251,83253],{},[898,83252,1688],{},[2505,83254,2784],{},[1708,83256,1721],{"stretchy":1715},[1708,83258,1710],{},[898,83260,1741],{},[898,83262,3455],{},[1708,83264,1716],{"stretchy":1715},[1743,83266,83267,83269],{},[898,83268,1688],{},[2505,83270,2784],{},[1708,83272,1721],{"stretchy":1715},[902,83274,80827],{"encoding":904},[883,83276,83278],{"className":83277},[886],[888,83279,83280],{"xmlns":890},[892,83281,83282,83294],{},[895,83283,83284,83286,83288,83290,83292],{},[898,83285,1741],{},[898,83287,3455],{},[1708,83289,1716],{"stretchy":1715},[898,83291,1688],{},[1708,83293,1721],{"stretchy":1715},[902,83295,79503],{"encoding":904},[724,83297,83298,81899,83301,82361,83347,82810,83360,82826,83377,2155],{},[38,83299,83300],{},"3.15",[883,83302,83304],{"className":83303},[886],[888,83305,83306],{"xmlns":890},[892,83307,83308,83344],{},[895,83309,83310,83312,83314,83316,83318,83320,83322,83324,83326,83328,83334,83336,83338],{},[898,83311,1978],{},[898,83313,3455],{},[1708,83315,1710],{},[2505,83317,9704],{},[1708,83319,2019],{},[2505,83321,4853],{},[898,83323,1688],{},[1708,83325,2726],{},[2505,83327,3132],{},[1753,83329,83330,83332],{},[898,83331,1688],{},[2505,83333,3132],{},[1708,83335,2019],{},[2505,83337,3958],{},[1753,83339,83340,83342],{},[898,83341,1688],{},[2505,83343,3121],{},[902,83345,83346],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,83348,83350],{"className":83349},[886],[888,83351,83352],{"xmlns":890},[892,83353,83354,83358],{},[895,83355,83356],{},[898,83357,1688],{},[902,83359,1688],{"encoding":904},[883,83361,83363],{"className":83362},[886],[888,83364,83365],{"xmlns":890},[892,83366,83367,83375],{},[895,83368,83369,83371,83373],{},[898,83370,1786],{},[898,83372,52173],{},[898,83374,3455],{},[902,83376,67130],{"encoding":904},[883,83378,83380],{"className":83379},[886],[888,83381,83382],{"xmlns":890},[892,83383,83384,83392],{},[895,83385,83386,83388,83390],{},[898,83387,1786],{},[898,83389,52173],{},[898,83391,3455],{},[902,83393,67130],{"encoding":904},[724,83395,83396,83399,83400,83413,83414,83434],{},[38,83397,83398],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,83401,83403],{"className":83402},[886],[888,83404,83405],{"xmlns":890},[892,83406,83407,83411],{},[895,83408,83409],{},[898,83410,14014],{},[902,83412,14014],{"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 ",[883,83415,83417],{"className":83416},[886],[888,83418,83419],{"xmlns":890},[892,83420,83421,83431],{},[895,83422,83423,83425,83427,83429],{},[2505,83424,4003],{},[2247,83426,2659],{},[2505,83428,70897],{},[898,83430,14014],{},[902,83432,83433],{"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.",[198,83436,83438],{"id":83437},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,83440,83441,83444,83445,1771,83467,83493],{},[38,83442,83443],{},"3.17"," Jsou dány ",[883,83446,83448],{"className":83447},[886],[888,83449,83450],{"xmlns":890},[892,83451,83452,83464],{},[895,83453,83454,83456,83458,83460,83462],{},[898,83455,1978],{},[898,83457,1975],{},[1708,83459,1710],{},[2505,83461,4003],{},[898,83463,1688],{},[902,83465,83466],{"encoding":904},"TR = 10Q",[883,83468,83470],{"className":83469},[886],[888,83471,83472],{"xmlns":890},[892,83473,83474,83490],{},[895,83475,83476,83478,83480,83482,83484,83486,83488],{},[898,83477,1978],{},[898,83479,3455],{},[1708,83481,1710],{},[2505,83483,9238],{},[1708,83485,2019],{},[2505,83487,3993],{},[898,83489,1688],{},[902,83491,83492],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,83495,83496,83499,83500,5283,83515,83530,83531,1343,83553,2980,83580,83602,83603,83637],{},[38,83497,83498],{},"3.18"," Odvoďte, že jestliže ",[883,83501,83503],{"className":83502},[886],[888,83504,83505],{"xmlns":890},[892,83506,83507,83513],{},[895,83508,83509,83511],{},[898,83510,1978],{},[898,83512,1975],{},[902,83514,16029],{"encoding":904},[883,83516,83518],{"className":83517},[886],[888,83519,83520],{"xmlns":890},[892,83521,83522,83528],{},[895,83523,83524,83526],{},[898,83525,1978],{},[898,83527,3455],{},[902,83529,15197],{"encoding":904}," jsou lineární tvaru ",[883,83532,83534],{"className":83533},[886],[888,83535,83536],{"xmlns":890},[892,83537,83538,83550],{},[895,83539,83540,83542,83544,83546,83548],{},[898,83541,1978],{},[898,83543,1975],{},[1708,83545,1710],{},[898,83547,724],{},[898,83549,1688],{},[902,83551,83552],{"encoding":904},"TR = pQ",[883,83554,83556],{"className":83555},[886],[888,83557,83558],{"xmlns":890},[892,83559,83560,83577],{},[895,83561,83562,83564,83566,83568,83571,83573,83575],{},[898,83563,1978],{},[898,83565,3455],{},[1708,83567,1710],{},[898,83569,83570],{},"m",[1708,83572,2019],{},[898,83574,6676],{},[898,83576,1688],{},[902,83578,83579],{"encoding":904},"TC = m + nQ",[883,83581,83583],{"className":83582},[886],[888,83584,83585],{"xmlns":890},[892,83586,83587,83599],{},[895,83588,83589,83591,83593,83595,83597],{},[898,83590,83570],{},[1708,83592,1883],{"separator":1882},[898,83594,6676],{},[1708,83596,1883],{"separator":1882},[898,83598,724],{},[902,83600,83601],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,83604,83606],{"className":83605},[886],[888,83607,83608],{"xmlns":890},[892,83609,83610,83634],{},[895,83611,83612,83618,83620],{},[1753,83613,83614,83616],{},[898,83615,1688],{},[1708,83617,2417],{},[1708,83619,1710],{},[3194,83621,83622],{"scriptlevel":2784,"displaystyle":1715},[2358,83623,83624,83626],{},[898,83625,83570],{},[895,83627,83628,83630,83632],{},[898,83629,724],{},[1708,83631,2726],{},[898,83633,6676],{},[902,83635,83636],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,83639,83640,83444,83643,1771,83677,12453,83703,83716,83717,81549,83732,83747,83748,81533,83761,81549,83776,83791],{},[38,83641,83642],{},"3.19",[883,83644,83646],{"className":83645},[886],[888,83647,83648],{"xmlns":890},[892,83649,83650,83674],{},[895,83651,83652,83654,83656,83658,83660,83662,83668,83670,83672],{},[898,83653,1978],{},[898,83655,1975],{},[1708,83657,1710],{},[1708,83659,2726],{},[2505,83661,3132],{},[1753,83663,83664,83666],{},[898,83665,1688],{},[2505,83667,3132],{},[1708,83669,2019],{},[2505,83671,4008],{},[898,83673,1688],{},[902,83675,83676],{"encoding":904},"TR = -2Q^2 + 14Q",[883,83678,83680],{"className":83679},[886],[888,83681,83682],{"xmlns":890},[892,83683,83684,83700],{},[895,83685,83686,83688,83690,83692,83694,83696,83698],{},[898,83687,1978],{},[898,83689,3455],{},[1708,83691,1710],{},[2505,83693,3132],{},[898,83695,1688],{},[1708,83697,2019],{},[2505,83699,4003],{},[902,83701,83702],{"encoding":904},"TC = 2Q + 10",[883,83704,83706],{"className":83705},[886],[888,83707,83708],{"xmlns":890},[892,83709,83710,83714],{},[895,83711,83712],{},[898,83713,1688],{},[902,83715,1688],{"encoding":904},", které maximalizuje zisk ",[883,83718,83720],{"className":83719},[886],[888,83721,83722],{"xmlns":890},[892,83723,83724,83730],{},[895,83725,83726,83728],{},[898,83727,1747],{},[898,83729,1975],{},[902,83731,75294],{"encoding":904},[883,83733,83735],{"className":83734},[886],[888,83736,83737],{"xmlns":890},[892,83738,83739,83745],{},[895,83740,83741,83743],{},[898,83742,1747],{},[898,83744,1975],{},[902,83746,75294],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,83749,83751],{"className":83750},[886],[888,83752,83753],{"xmlns":890},[892,83754,83755,83759],{},[895,83756,83757],{},[898,83758,1688],{},[902,83760,1688],{"encoding":904},[883,83762,83764],{"className":83763},[886],[888,83765,83766],{"xmlns":890},[892,83767,83768,83774],{},[895,83769,83770,83772],{},[898,83771,1978],{},[898,83773,1975],{},[902,83775,16029],{"encoding":904},[883,83777,83779],{"className":83778},[886],[888,83780,83781],{"xmlns":890},[892,83782,83783,83789],{},[895,83784,83785,83787],{},[898,83786,1978],{},[898,83788,1975],{},[902,83790,16029],{"encoding":904},". (d) Graficky interpretujte.",[724,83793,83794,59509,83797,1343,83823,1343,83842,12453,83862,83716,83875,81549,83890,83905,83906,83928,83929,82979],{},[38,83795,83796],{},"3.20",[883,83798,83800],{"className":83799},[886],[888,83801,83802],{"xmlns":890},[892,83803,83804,83820],{},[895,83805,83806,83808,83810,83812,83814],{},[898,83807,1747],{},[1708,83809,1710],{},[2505,83811,11498],{},[1708,83813,2726],{},[1753,83815,83816,83818],{},[898,83817,1688],{},[2505,83819,3132],{},[902,83821,83822],{"encoding":904},"P = 400 - Q^2",[883,83824,83826],{"className":83825},[886],[888,83827,83828],{"xmlns":890},[892,83829,83830,83840],{},[895,83831,83832,83834,83836,83838],{},[898,83833,22325],{},[898,83835,3455],{},[1708,83837,1710],{},[2505,83839,9238],{},[902,83841,23520],{"encoding":904},[883,83843,83845],{"className":83844},[886],[888,83846,83847],{"xmlns":890},[892,83848,83849,83859],{},[895,83850,83851,83853,83855,83857],{},[898,83852,1741],{},[898,83854,3455],{},[1708,83856,1710],{},[2505,83858,4018],{},[902,83860,83861],{"encoding":904},"MC = 20",[883,83863,83865],{"className":83864},[886],[888,83866,83867],{"xmlns":890},[892,83868,83869,83873],{},[895,83870,83871],{},[898,83872,1688],{},[902,83874,1688],{"encoding":904},[883,83876,83878],{"className":83877},[886],[888,83879,83880],{"xmlns":890},[892,83881,83882,83888],{},[895,83883,83884,83886],{},[898,83885,1747],{},[898,83887,1975],{},[902,83889,75294],{"encoding":904},[883,83891,83893],{"className":83892},[886],[888,83894,83895],{"xmlns":890},[892,83896,83897,83903],{},[895,83898,83899,83901],{},[898,83900,1747],{},[898,83902,1975],{},[902,83904,75294],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,83907,83909],{"className":83908},[886],[888,83910,83911],{"xmlns":890},[892,83912,83913,83925],{},[895,83914,83915,83917,83919,83921,83923],{},[1708,83916,1716],{"stretchy":1715},[2505,83918,2784],{},[1708,83920,1883],{"separator":1882},[2505,83922,2507],{},[1708,83924,1721],{"stretchy":1715},[902,83926,83927],{"encoding":904},"(0, 1)",", druhý do ",[883,83930,83932],{"className":83931},[886],[888,83933,83934],{"xmlns":890},[892,83935,83936,83949],{},[895,83937,83938,83940,83943,83945,83947],{},[1708,83939,1716],{"stretchy":1715},[2505,83941,83942],{},"19",[1708,83944,1883],{"separator":1882},[2505,83946,4018],{},[1708,83948,1721],{"stretchy":1715},[902,83950,83951],{"encoding":904},"(19, 20)",[724,83953,83954,83957,83958,3405,83986,11189,84003,2155],{},[38,83955,83956],{},"3.21"," Dokažte, že má-li zisk ",[883,83959,83961],{"className":83960},[886],[888,83962,83963],{"xmlns":890},[892,83964,83965,83983],{},[895,83966,83967,83969,83971,83973,83975,83977,83979,83981],{},[898,83968,1747],{},[898,83970,1975],{},[1708,83972,1710],{},[898,83974,1747],{},[898,83976,1975],{},[1708,83978,1716],{"stretchy":1715},[898,83980,1688],{},[1708,83982,1721],{"stretchy":1715},[902,83984,83985],{"encoding":904},"PR = PR(Q)",[883,83987,83989],{"className":83988},[886],[888,83990,83991],{"xmlns":890},[892,83992,83993,84001],{},[895,83994,83995],{},[1743,83996,83997,83999],{},[898,83998,1688],{},[2505,84000,2784],{},[902,84002,50144],{"encoding":904},[883,84004,84006],{"className":84005},[886],[888,84007,84008],{"xmlns":890},[892,84009,84010,84042],{},[895,84011,84012,84014,84016,84018,84024,84026,84028,84030,84032,84034,84040],{},[898,84013,1741],{},[898,84015,1975],{},[1708,84017,1716],{"stretchy":1715},[1743,84019,84020,84022],{},[898,84021,1688],{},[2505,84023,2784],{},[1708,84025,1721],{"stretchy":1715},[1708,84027,1710],{},[898,84029,1741],{},[898,84031,3455],{},[1708,84033,1716],{"stretchy":1715},[1743,84035,84036,84038],{},[898,84037,1688],{},[2505,84039,2784],{},[1708,84041,1721],{"stretchy":1715},[902,84043,77457],{"encoding":904},[724,84045,84046,84049,84050,1771,84065,67843,84080,83716,84093,84108,84109,1343,84136,84173,84174,1343,84201,2155],{},[38,84047,84048],{},"3.22"," Pro zadané ",[883,84051,84053],{"className":84052},[886],[888,84054,84055],{"xmlns":890},[892,84056,84057,84063],{},[895,84058,84059,84061],{},[898,84060,1741],{},[898,84062,1975],{},[902,84064,18548],{"encoding":904},[883,84066,84068],{"className":84067},[886],[888,84069,84070],{"xmlns":890},[892,84071,84072,84078],{},[895,84073,84074,84076],{},[898,84075,1741],{},[898,84077,3455],{},[902,84079,67111],{"encoding":904},[883,84081,84083],{"className":84082},[886],[888,84084,84085],{"xmlns":890},[892,84086,84087,84091],{},[895,84088,84089],{},[898,84090,1688],{},[902,84092,1688],{"encoding":904},[883,84094,84096],{"className":84095},[886],[888,84097,84098],{"xmlns":890},[892,84099,84100,84106],{},[895,84101,84102,84104],{},[898,84103,1747],{},[898,84105,1975],{},[902,84107,75294],{"encoding":904},". (a) ",[883,84110,84112],{"className":84111},[886],[888,84113,84114],{"xmlns":890},[892,84115,84116,84133],{},[895,84117,84118,84120,84122,84124,84127,84129,84131],{},[898,84119,1741],{},[898,84121,1975],{},[1708,84123,1710],{},[2505,84125,84126],{},"236",[1708,84128,2726],{},[2505,84130,53694],{},[898,84132,1688],{},[902,84134,84135],{"encoding":904},"MR = 236 - 16Q",[883,84137,84139],{"className":84138},[886],[888,84140,84141],{"xmlns":890},[892,84142,84143,84170],{},[895,84144,84145,84147,84149,84151,84153,84159,84161,84164,84166,84168],{},[898,84146,1741],{},[898,84148,3455],{},[1708,84150,1710],{},[2505,84152,3121],{},[1753,84154,84155,84157],{},[898,84156,1688],{},[2505,84158,3132],{},[1708,84160,2726],{},[2505,84162,84163],{},"32",[898,84165,1688],{},[1708,84167,2019],{},[2505,84169,17662],{},[902,84171,84172],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,84175,84177],{"className":84176},[886],[888,84178,84179],{"xmlns":890},[892,84180,84181,84198],{},[895,84182,84183,84185,84187,84189,84192,84194,84196],{},[898,84184,1741],{},[898,84186,1975],{},[1708,84188,1710],{},[2505,84190,84191],{},"280",[1708,84193,2726],{},[2505,84195,4018],{},[898,84197,1688],{},[902,84199,84200],{"encoding":904},"MR = 280 - 20Q",[883,84202,84204],{"className":84203},[886],[888,84205,84206],{"xmlns":890},[892,84207,84208,84235],{},[895,84209,84210,84212,84214,84216,84219,84225,84227,84229,84231,84233],{},[898,84211,1741],{},[898,84213,3455],{},[1708,84215,1710],{},[2505,84217,84218],{},"1,6",[1753,84220,84221,84223],{},[898,84222,1688],{},[2505,84224,3132],{},[1708,84226,2726],{},[2505,84228,4853],{},[898,84230,1688],{},[1708,84232,2019],{},[2505,84234,4199],{},[902,84236,84237],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,84239,84240,84049,84243,1771,84258,67843,84273,81533,84286,81549,84301,84108,84316,1343,84347,84173,84383,1343,84415,84459,84460,1343,84492,2155],{},[38,84241,84242],{},"3.23",[883,84244,84246],{"className":84245},[886],[888,84247,84248],{"xmlns":890},[892,84249,84250,84256],{},[895,84251,84252,84254],{},[898,84253,1978],{},[898,84255,1975],{},[902,84257,16029],{"encoding":904},[883,84259,84261],{"className":84260},[886],[888,84262,84263],{"xmlns":890},[892,84264,84265,84271],{},[895,84266,84267,84269],{},[898,84268,1978],{},[898,84270,3455],{},[902,84272,15197],{"encoding":904},[883,84274,84276],{"className":84275},[886],[888,84277,84278],{"xmlns":890},[892,84279,84280,84284],{},[895,84281,84282],{},[898,84283,1688],{},[902,84285,1688],{"encoding":904},[883,84287,84289],{"className":84288},[886],[888,84290,84291],{"xmlns":890},[892,84292,84293,84299],{},[895,84294,84295,84297],{},[898,84296,1747],{},[898,84298,1975],{},[902,84300,75294],{"encoding":904},[883,84302,84304],{"className":84303},[886],[888,84305,84306],{"xmlns":890},[892,84307,84308,84314],{},[895,84309,84310,84312],{},[898,84311,1747],{},[898,84313,1975],{},[902,84315,75294],{"encoding":904},[883,84317,84319],{"className":84318},[886],[888,84320,84321],{"xmlns":890},[892,84322,84323,84344],{},[895,84324,84325,84327,84329,84331,84334,84336,84338],{},[898,84326,1978],{},[898,84328,1975],{},[1708,84330,1710],{},[2505,84332,84333],{},"125",[898,84335,1688],{},[1708,84337,2726],{},[1753,84339,84340,84342],{},[898,84341,1688],{},[2505,84343,3132],{},[902,84345,84346],{"encoding":904},"TR = 125Q - Q^2",[883,84348,84350],{"className":84349},[886],[888,84351,84352],{"xmlns":890},[892,84353,84354,84380],{},[895,84355,84356,84358,84360,84362,84364,84366,84368,84370,84372,84374],{},[898,84357,1978],{},[898,84359,3455],{},[1708,84361,1710],{},[2505,84363,11040],{},[1708,84365,2019],{},[2505,84367,3993],{},[898,84369,1688],{},[1708,84371,2019],{},[2505,84373,6097],{},[1753,84375,84376,84378],{},[898,84377,1688],{},[2505,84379,3132],{},[902,84381,84382],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,84384,84386],{"className":84385},[886],[888,84387,84388],{"xmlns":890},[892,84389,84390,84412],{},[895,84391,84392,84394,84396,84398,84400,84402,84404,84406],{},[898,84393,1978],{},[898,84395,1975],{},[1708,84397,1710],{},[2505,84399,4018],{},[898,84401,1688],{},[1708,84403,2726],{},[2505,84405,3132],{},[1753,84407,84408,84410],{},[898,84409,1688],{},[2505,84411,3132],{},[902,84413,84414],{"encoding":904},"TR = 20Q - 2Q^2",[883,84416,84418],{"className":84417},[886],[888,84419,84420],{"xmlns":890},[892,84421,84422,84456],{},[895,84423,84424,84426,84428,84430,84432,84434,84436,84438,84440,84442,84448,84450],{},[898,84425,1978],{},[898,84427,3455],{},[1708,84429,1710],{},[2505,84431,3132],{},[1708,84433,2019],{},[2505,84435,4018],{},[898,84437,1688],{},[1708,84439,2726],{},[2505,84441,3998],{},[1753,84443,84444,84446],{},[898,84445,1688],{},[2505,84447,3132],{},[1708,84449,2019],{},[1753,84451,84452,84454],{},[898,84453,1688],{},[2505,84455,3121],{},[902,84457,84458],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,84461,84463],{"className":84462},[886],[888,84464,84465],{"xmlns":890},[892,84466,84467,84489],{},[895,84468,84469,84471,84473,84475,84477,84479,84481,84483],{},[898,84470,1978],{},[898,84472,1975],{},[1708,84474,1710],{},[2505,84476,5867],{},[898,84478,1688],{},[1708,84480,2726],{},[2505,84482,11575],{},[1753,84484,84485,84487],{},[898,84486,1688],{},[2505,84488,3132],{},[902,84490,84491],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,84493,84495],{"className":84494},[886],[888,84496,84497],{"xmlns":890},[892,84498,84499,84547],{},[895,84500,84501,84503,84505,84507,84509,84511,84513,84515,84517,84533,84535],{},[898,84502,1978],{},[898,84504,3455],{},[1708,84506,1710],{},[2505,84508,5867],{},[1708,84510,2019],{},[2505,84512,3132],{},[898,84514,1688],{},[1708,84516,2726],{},[3194,84518,84519],{"scriptlevel":2784,"displaystyle":1715},[2358,84520,84521,84531],{},[895,84522,84523,84525],{},[2505,84524,3121],{},[1753,84526,84527,84529],{},[898,84528,1688],{},[2505,84530,3132],{},[2505,84532,4003],{},[1708,84534,2019],{},[3194,84536,84537],{"scriptlevel":2784,"displaystyle":1715},[2358,84538,84539,84545],{},[1753,84540,84541,84543],{},[898,84542,1688],{},[2505,84544,3121],{},[2505,84546,4018],{},[902,84548,84549],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,84551,84552,84555,84556,84586,84587,84619,84620,2980,84650,84680],{},[38,84553,84554],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,84557,84559],{"className":84558},[886],[888,84560,84561],{"xmlns":890},[892,84562,84563,84583],{},[895,84564,84565,84571,84573,84575,84577],{},[1743,84566,84567,84569],{},[898,84568,1747],{},[2505,84570,2507],{},[1708,84572,1710],{},[2505,84574,11040],{},[1708,84576,2726],{},[1743,84578,84579,84581],{},[898,84580,1688],{},[2505,84582,2507],{},[902,84584,84585],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,84588,84590],{"className":84589},[886],[888,84591,84592],{"xmlns":890},[892,84593,84594,84616],{},[895,84595,84596,84602,84604,84606,84608,84610],{},[1743,84597,84598,84600],{},[898,84599,1747],{},[2505,84601,3132],{},[1708,84603,1710],{},[2505,84605,11064],{},[1708,84607,2726],{},[2505,84609,12222],{},[1743,84611,84612,84614],{},[898,84613,1688],{},[2505,84615,3132],{},[902,84617,84618],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,84621,84623],{"className":84622},[886],[888,84624,84625],{"xmlns":890},[892,84626,84627,84647],{},[895,84628,84629,84631,84633,84635,84637,84639,84641,84643,84645],{},[898,84630,1978],{},[898,84632,3455],{},[1708,84634,1710],{},[2505,84636,9704],{},[2247,84638,2659],{},[2505,84640,70897],{},[1708,84642,2019],{},[2505,84644,4018],{},[898,84646,1688],{},[902,84648,84649],{"encoding":904},"TC = 50\\,000 + 20Q",[883,84651,84653],{"className":84652},[886],[888,84654,84655],{"xmlns":890},[892,84656,84657,84677],{},[895,84658,84659,84661,84663,84669,84671],{},[898,84660,1688],{},[1708,84662,1710],{},[1743,84664,84665,84667],{},[898,84666,1688],{},[2505,84668,2507],{},[1708,84670,2019],{},[1743,84672,84673,84675],{},[898,84674,1688],{},[2505,84676,3132],{},[902,84678,84679],{"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.",[724,84682,84683,84686,84687,84717,84718,84619,84750,2980,84780,84809],{},[38,84684,84685],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,84688,84690],{"className":84689},[886],[888,84691,84692],{"xmlns":890},[892,84693,84694,84714],{},[895,84695,84696,84702,84704,84706,84708],{},[1743,84697,84698,84700],{},[898,84699,1747],{},[2505,84701,2507],{},[1708,84703,1710],{},[2505,84705,11064],{},[1708,84707,2726],{},[1743,84709,84710,84712],{},[898,84711,1688],{},[2505,84713,2507],{},[902,84715,84716],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,84719,84721],{"className":84720},[886],[888,84722,84723],{"xmlns":890},[892,84724,84725,84747],{},[895,84726,84727,84733,84735,84737,84739,84741],{},[1743,84728,84729,84731],{},[898,84730,1747],{},[2505,84732,3132],{},[1708,84734,1710],{},[2505,84736,20288],{},[1708,84738,2726],{},[2505,84740,6097],{},[1743,84742,84743,84745],{},[898,84744,1688],{},[2505,84746,3132],{},[902,84748,84749],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,84751,84753],{"className":84752},[886],[888,84754,84755],{"xmlns":890},[892,84756,84757,84777],{},[895,84758,84759,84761,84763,84765,84767,84769,84771,84773,84775],{},[898,84760,1978],{},[898,84762,3455],{},[1708,84764,1710],{},[2505,84766,3993],{},[2247,84768,2659],{},[2505,84770,70897],{},[1708,84772,2019],{},[2505,84774,9238],{},[898,84776,1688],{},[902,84778,84779],{"encoding":904},"TC = 5\\,000 + 100Q",[883,84781,84783],{"className":84782},[886],[888,84784,84785],{"xmlns":890},[892,84786,84787,84807],{},[895,84788,84789,84791,84793,84799,84801],{},[898,84790,1688],{},[1708,84792,1710],{},[1743,84794,84795,84797],{},[898,84796,1688],{},[2505,84798,2507],{},[1708,84800,2019],{},[1743,84802,84803,84805],{},[898,84804,1688],{},[2505,84806,3132],{},[902,84808,84679],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,84811,84813],{"id":84812},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,84815,84816,84819,84820,84867,84868,84885],{},[38,84817,84818],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,84821,84823],{"className":84822},[886],[888,84824,84825],{"xmlns":890},[892,84826,84827,84864],{},[895,84828,84829,84831,84833,84835,84837,84840,84846,84848,84851,84857,84859,84862],{},[898,84830,1978],{},[898,84832,52173],{},[898,84834,3455],{},[1708,84836,1710],{},[2505,84838,84839],{},"0,85",[1753,84841,84842,84844],{},[898,84843,1688],{},[2505,84845,3121],{},[1708,84847,2726],{},[2505,84849,84850],{},"11,9",[1753,84852,84853,84855],{},[898,84854,1688],{},[2505,84856,3132],{},[1708,84858,2019],{},[2505,84860,84861],{},"102",[898,84863,1688],{},[902,84865,84866],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,84869,84871],{"className":84870},[886],[888,84872,84873],{"xmlns":890},[892,84874,84875,84883],{},[895,84876,84877],{},[1753,84878,84879,84881],{},[898,84880,1747],{},[1708,84882,2417],{},[902,84884,16331],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,84887,84888,82648,84891,84927],{},[38,84889,84890],{},"3.27",[883,84892,84894],{"className":84893},[886],[888,84895,84896],{"xmlns":890},[892,84897,84898,84924],{},[895,84899,84900,84902,84904,84906,84908,84914,84916,84918,84920,84922],{},[898,84901,1741],{},[898,84903,3455],{},[1708,84905,1710],{},[2505,84907,14887],{},[1753,84909,84910,84912],{},[898,84911,1688],{},[2505,84913,3132],{},[1708,84915,2726],{},[2505,84917,76254],{},[898,84919,1688],{},[1708,84921,2019],{},[2505,84923,11594],{},[902,84925,84926],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,84929,84930,81899,84933,84927],{},[38,84931,84932],{},"3.28",[883,84934,84936],{"className":84935},[886],[888,84937,84938],{"xmlns":890},[892,84939,84940,84976],{},[895,84941,84942,84944,84946,84948,84950,84956,84958,84960,84966,84968,84970,84972,84974],{},[898,84943,1978],{},[898,84945,3455],{},[1708,84947,1710],{},[2505,84949,6097],{},[1753,84951,84952,84954],{},[898,84953,1688],{},[2505,84955,3121],{},[1708,84957,2726],{},[2505,84959,5967],{},[1753,84961,84962,84964],{},[898,84963,1688],{},[2505,84965,3132],{},[1708,84967,2019],{},[2505,84969,4199],{},[898,84971,1688],{},[1708,84973,2019],{},[2505,84975,11040],{},[902,84977,84978],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,84980,12596],{"id":12595},[120,84982,84983,85011,85056,85128,85193,85233,85325,85431,85471,85585,85678,85742,85774,85834,85840,85904,85953,86007,86115,86170],{},[123,84984,84985,1729,84987,85010],{},[38,84986,67568],{},[883,84988,84990],{"className":84989},[886],[888,84991,84992],{"xmlns":890},[892,84993,84994,85008],{},[895,84995,84996,84998,85000,85002,85004,85006],{},[898,84997,1978],{},[898,84999,1975],{},[1708,85001,1710],{},[898,85003,1747],{},[1708,85005,3703],{},[898,85007,1688],{},[902,85009,78522],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,85012,85013,1729,85015,85055],{},[38,85014,68153],{},[883,85016,85018],{"className":85017},[886],[888,85019,85020],{"xmlns":890},[892,85021,85022,85052],{},[895,85023,85024,85026,85028,85030,85042,85044,85046,85048,85050],{},[898,85025,1786],{},[898,85027,1975],{},[1708,85029,1710],{},[3194,85031,85032],{"scriptlevel":2784,"displaystyle":1715},[2358,85033,85034,85040],{},[895,85035,85036,85038],{},[898,85037,1978],{},[898,85039,1975],{},[898,85041,1688],{},[1708,85043,1710],{},[898,85045,16117],{},[1708,85047,1716],{"stretchy":1715},[898,85049,1688],{},[1708,85051,1721],{"stretchy":1715},[902,85053,85054],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,85057,85058,1729,85060,85096,85097,85112,85113,2155],{},[38,85059,68301],{},[883,85061,85063],{"className":85062},[886],[888,85064,85065],{"xmlns":890},[892,85066,85067,85093],{},[895,85068,85069,85071,85073,85075],{},[898,85070,1741],{},[898,85072,1975],{},[1708,85074,1710],{},[3194,85076,85077],{"scriptlevel":2784,"displaystyle":1715},[2358,85078,85079,85087],{},[895,85080,85081,85083,85085],{},[898,85082,2364],{"mathvariant":1759},[898,85084,1978],{},[898,85086,1975],{},[895,85088,85089,85091],{},[898,85090,2364],{"mathvariant":1759},[898,85092,1688],{},[902,85094,85095],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,85098,85100],{"className":85099},[886],[888,85101,85102],{"xmlns":890},[892,85103,85104,85110],{},[895,85105,85106,85108],{},[898,85107,1978],{},[898,85109,1975],{},[902,85111,16029],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,85114,85116],{"className":85115},[886],[888,85117,85118],{"xmlns":890},[892,85119,85120,85126],{},[895,85121,85122,85124],{},[898,85123,1786],{},[898,85125,1975],{},[902,85127,67264],{"encoding":904},[123,85129,85130,1729,85133,1343,85163,2155],{},[38,85131,85132],{},"Diferenciál příjmu\u002Fnákladů",[883,85134,85136],{"className":85135},[886],[888,85137,85138],{"xmlns":890},[892,85139,85140,85160],{},[895,85141,85142,85144,85146,85148,85150,85152,85154,85156,85158],{},[898,85143,2633],{"mathvariant":1759},[898,85145,1978],{},[898,85147,1975],{},[1708,85149,2638],{},[898,85151,1741],{},[898,85153,1975],{},[2247,85155,2659],{},[898,85157,2364],{"mathvariant":1759},[898,85159,1688],{},[902,85161,85162],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,85164,85166],{"className":85165},[886],[888,85167,85168],{"xmlns":890},[892,85169,85170,85190],{},[895,85171,85172,85174,85176,85178,85180,85182,85184,85186,85188],{},[898,85173,2633],{"mathvariant":1759},[898,85175,1978],{},[898,85177,3455],{},[1708,85179,2638],{},[898,85181,1741],{},[898,85183,3455],{},[2247,85185,2659],{},[898,85187,2364],{"mathvariant":1759},[898,85189,1688],{},[902,85191,85192],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,85194,85195,1729,85197,2155],{},[38,85196,70421],{},[883,85198,85200],{"className":85199},[886],[888,85201,85202],{"xmlns":890},[892,85203,85204,85230],{},[895,85205,85206,85208,85210,85212,85214,85216,85218,85220,85222,85224,85226,85228],{},[898,85207,1978],{},[898,85209,3455],{},[1708,85211,1710],{},[898,85213,22325],{},[898,85215,3455],{},[1708,85217,2019],{},[898,85219,1978],{},[898,85221,52173],{},[898,85223,3455],{},[1708,85225,1716],{"stretchy":1715},[898,85227,1688],{},[1708,85229,1721],{"stretchy":1715},[902,85231,85232],{"encoding":904},"TC = FC + TVC(Q)",[123,85234,85235,1729,85238,1343,85253,1729,85255,1343,85278,1729,85281,2155],{},[38,85236,85237],{},"Fixní náklady",[883,85239,85241],{"className":85240},[886],[888,85242,85243],{"xmlns":890},[892,85244,85245,85251],{},[895,85246,85247,85249],{},[898,85248,22325],{},[898,85250,3455],{},[902,85252,67310],{"encoding":904},[38,85254,70574],{},[883,85256,85258],{"className":85257},[886],[888,85259,85260],{"xmlns":890},[892,85261,85262,85276],{},[895,85263,85264,85266,85268,85270,85272,85274],{},[898,85265,1978],{},[898,85267,52173],{},[898,85269,3455],{},[1708,85271,1716],{"stretchy":1715},[898,85273,1688],{},[1708,85275,1721],{"stretchy":1715},[902,85277,70571],{"encoding":904},[38,85279,85280],{},"variabilní náklady na jednotku",[883,85282,85284],{"className":85283},[886],[888,85285,85286],{"xmlns":890},[892,85287,85288,85322],{},[895,85289,85290,85292,85294,85296,85298,85300,85302],{},[898,85291,52173],{},[898,85293,3455],{},[1708,85295,1716],{"stretchy":1715},[898,85297,1688],{},[1708,85299,1721],{"stretchy":1715},[1708,85301,1710],{},[3194,85303,85304],{"scriptlevel":2784,"displaystyle":1715},[2358,85305,85306,85320],{},[895,85307,85308,85310,85312,85314,85316,85318],{},[898,85309,1978],{},[898,85311,52173],{},[898,85313,3455],{},[1708,85315,1716],{"stretchy":1715},[898,85317,1688],{},[1708,85319,1721],{"stretchy":1715},[898,85321,1688],{},[902,85323,85324],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,85326,85327,1729,85329,1343,85359,1729,85362,1343,85394,1729,85397,2155],{},[38,85328,70582],{},[883,85330,85332],{"className":85331},[886],[888,85333,85334],{"xmlns":890},[892,85335,85336,85356],{},[895,85337,85338,85340,85342,85344],{},[898,85339,1786],{},[898,85341,3455],{},[1708,85343,1710],{},[3194,85345,85346],{"scriptlevel":2784,"displaystyle":1715},[2358,85347,85348,85354],{},[895,85349,85350,85352],{},[898,85351,1978],{},[898,85353,3455],{},[898,85355,1688],{},[902,85357,85358],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,85360,85361],{},"průměrné fixní",[883,85363,85365],{"className":85364},[886],[888,85366,85367],{"xmlns":890},[892,85368,85369,85391],{},[895,85370,85371,85373,85375,85377,85379],{},[898,85372,1786],{},[898,85374,22325],{},[898,85376,3455],{},[1708,85378,1710],{},[3194,85380,85381],{"scriptlevel":2784,"displaystyle":1715},[2358,85382,85383,85389],{},[895,85384,85385,85387],{},[898,85386,22325],{},[898,85388,3455],{},[898,85390,1688],{},[902,85392,85393],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,85395,85396],{},"průměrné variabilní",[883,85398,85400],{"className":85399},[886],[888,85401,85402],{"xmlns":890},[892,85403,85404,85428],{},[895,85405,85406,85408,85410,85412,85414],{},[898,85407,1786],{},[898,85409,52173],{},[898,85411,3455],{},[1708,85413,1710],{},[3194,85415,85416],{"scriptlevel":2784,"displaystyle":1715},[2358,85417,85418,85426],{},[895,85419,85420,85422,85424],{},[898,85421,1978],{},[898,85423,52173],{},[898,85425,3455],{},[898,85427,1688],{},[902,85429,85430],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,85432,85433,1729,85435,2155],{},[38,85434,71769],{},[883,85436,85438],{"className":85437},[886],[888,85439,85440],{"xmlns":890},[892,85441,85442,85468],{},[895,85443,85444,85446,85448,85450],{},[898,85445,1741],{},[898,85447,3455],{},[1708,85449,1710],{},[3194,85451,85452],{"scriptlevel":2784,"displaystyle":1715},[2358,85453,85454,85462],{},[895,85455,85456,85458,85460],{},[898,85457,2364],{"mathvariant":1759},[898,85459,1978],{},[898,85461,3455],{},[895,85463,85464,85466],{},[898,85465,2364],{"mathvariant":1759},[898,85467,1688],{},[902,85469,85470],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,85472,85473,1729,85475,85523,85524,85537,85538,1343,85553,1343,85570,2155],{},[38,85474,72667],{},[883,85476,85478],{"className":85477},[886],[888,85479,85480],{"xmlns":890},[892,85481,85482,85520],{},[895,85483,85484,85486,85488,85490,85492,85494,85496,85498,85500,85502,85504,85510,85512,85514],{},[898,85485,1978],{},[898,85487,3455],{},[1708,85489,1710],{},[898,85491,22325],{},[898,85493,3455],{},[1708,85495,2019],{},[898,85497,207],{},[898,85499,1688],{},[1708,85501,2019],{},[898,85503,1923],{},[1753,85505,85506,85508],{},[898,85507,1688],{},[2505,85509,3132],{},[1708,85511,2019],{},[898,85513,14142],{},[1753,85515,85516,85518],{},[898,85517,1688],{},[2505,85519,3121],{},[902,85521,85522],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,85525,85527],{"className":85526},[886],[888,85528,85529],{"xmlns":890},[892,85530,85531,85535],{},[895,85532,85533],{},[898,85534,900],{},[902,85536,900],{"encoding":904},"-průběhem ",[883,85539,85541],{"className":85540},[886],[888,85542,85543],{"xmlns":890},[892,85544,85545,85551],{},[895,85546,85547,85549],{},[898,85548,1786],{},[898,85550,3455],{},[902,85552,3458],{"encoding":904},[883,85554,85556],{"className":85555},[886],[888,85557,85558],{"xmlns":890},[892,85559,85560,85568],{},[895,85561,85562,85564,85566],{},[898,85563,1786],{},[898,85565,52173],{},[898,85567,3455],{},[902,85569,67130],{"encoding":904},[883,85571,85573],{"className":85572},[886],[888,85574,85575],{"xmlns":890},[892,85576,85577,85583],{},[895,85578,85579,85581],{},[898,85580,1741],{},[898,85582,3455],{},[902,85584,67111],{"encoding":904},[123,85586,85587,85589,85590,1826,85605,85646,85647,73312,85662,85677],{},[38,85588,73749],{},": v bodě minima ",[883,85591,85593],{"className":85592},[886],[888,85594,85595],{"xmlns":890},[892,85596,85597,85603],{},[895,85598,85599,85601],{},[898,85600,1786],{},[898,85602,3455],{},[902,85604,3458],{"encoding":904},[883,85606,85608],{"className":85607},[886],[888,85609,85610],{"xmlns":890},[892,85611,85612,85644],{},[895,85613,85614,85616,85618,85620,85626,85628,85630,85632,85634,85636,85642],{},[898,85615,1786],{},[898,85617,3455],{},[1708,85619,1716],{"stretchy":1715},[1743,85621,85622,85624],{},[898,85623,1688],{},[2505,85625,2784],{},[1708,85627,1721],{"stretchy":1715},[1708,85629,1710],{},[898,85631,1741],{},[898,85633,3455],{},[1708,85635,1716],{"stretchy":1715},[1743,85637,85638,85640],{},[898,85639,1688],{},[2505,85641,2784],{},[1708,85643,1721],{"stretchy":1715},[902,85645,74384],{"encoding":904},"; geometricky ",[883,85648,85650],{"className":85649},[886],[888,85651,85652],{"xmlns":890},[892,85653,85654,85660],{},[895,85655,85656,85658],{},[898,85657,1741],{},[898,85659,3455],{},[902,85661,67111],{"encoding":904},[883,85663,85665],{"className":85664},[886],[888,85666,85667],{"xmlns":890},[892,85668,85669,85675],{},[895,85670,85671,85673],{},[898,85672,1786],{},[898,85674,3455],{},[902,85676,3458],{"encoding":904}," v jejím minimu.",[123,85679,85680,85589,85682,1826,85699,2155],{},[38,85681,75099],{},[883,85683,85685],{"className":85684},[886],[888,85686,85687],{"xmlns":890},[892,85688,85689,85697],{},[895,85690,85691,85693,85695],{},[898,85692,1786],{},[898,85694,52173],{},[898,85696,3455],{},[902,85698,67130],{"encoding":904},[883,85700,85702],{"className":85701},[886],[888,85703,85704],{"xmlns":890},[892,85705,85706,85740],{},[895,85707,85708,85710,85712,85714,85716,85722,85724,85726,85728,85730,85732,85738],{},[898,85709,1786],{},[898,85711,52173],{},[898,85713,3455],{},[1708,85715,1716],{"stretchy":1715},[1743,85717,85718,85720],{},[898,85719,1688],{},[2505,85721,2784],{},[1708,85723,1721],{"stretchy":1715},[1708,85725,1710],{},[898,85727,1741],{},[898,85729,3455],{},[1708,85731,1716],{"stretchy":1715},[1743,85733,85734,85736],{},[898,85735,1688],{},[2505,85737,2784],{},[1708,85739,1721],{"stretchy":1715},[902,85741,80827],{"encoding":904},[123,85743,85744,1729,85746,85773],{},[38,85745,75278],{},[883,85747,85749],{"className":85748},[886],[888,85750,85751],{"xmlns":890},[892,85752,85753,85771],{},[895,85754,85755,85757,85759,85761,85763,85765,85767,85769],{},[898,85756,1747],{},[898,85758,1975],{},[1708,85760,1710],{},[898,85762,1978],{},[898,85764,1975],{},[1708,85766,2726],{},[898,85768,1978],{},[898,85770,3455],{},[902,85772,67019],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,85775,85776,1695,85778,85780,85781,85807,85808,85833],{},[38,85777,76140],{},[614,85779,75403],{},") — hodnoty ",[883,85782,85784],{"className":85783},[886],[888,85785,85786],{"xmlns":890},[892,85787,85788,85804],{},[895,85789,85790,85796,85798],{},[1743,85791,85792,85794],{},[898,85793,1688],{},[898,85795,1786],{},[1708,85797,1883],{"separator":1882},[1743,85799,85800,85802],{},[898,85801,1688],{},[898,85803,35110],{},[902,85805,85806],{"encoding":904},"Q_A, Q_B"," splňující ",[883,85809,85811],{"className":85810},[886],[888,85812,85813],{"xmlns":890},[892,85814,85815,85831],{},[895,85816,85817,85819,85821,85823,85825,85827,85829],{},[898,85818,1747],{},[898,85820,1975],{},[1708,85822,1716],{"stretchy":1715},[898,85824,1688],{},[1708,85826,1721],{"stretchy":1715},[1708,85828,1710],{},[2505,85830,2784],{},[902,85832,75680],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,85835,85836,85839],{},[38,85837,85838],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,85841,85842,85844,85845,1826,85862,85903],{},[38,85843,77192],{}," — v bodě maxima zisku ",[883,85846,85848],{"className":85847},[886],[888,85849,85850],{"xmlns":890},[892,85851,85852,85860],{},[895,85853,85854],{},[1743,85855,85856,85858],{},[898,85857,1688],{},[2505,85859,2784],{},[902,85861,50144],{"encoding":904},[883,85863,85865],{"className":85864},[886],[888,85866,85867],{"xmlns":890},[892,85868,85869,85901],{},[895,85870,85871,85873,85875,85877,85883,85885,85887,85889,85891,85893,85899],{},[898,85872,1741],{},[898,85874,1975],{},[1708,85876,1716],{"stretchy":1715},[1743,85878,85879,85881],{},[898,85880,1688],{},[2505,85882,2784],{},[1708,85884,1721],{"stretchy":1715},[1708,85886,1710],{},[898,85888,1741],{},[898,85890,3455],{},[1708,85892,1716],{"stretchy":1715},[1743,85894,85895,85897],{},[898,85896,1688],{},[2505,85898,2784],{},[1708,85900,1721],{"stretchy":1715},[902,85902,77457],{"encoding":904}," (3.13).",[123,85905,85906,32163,85908,1826,85927,85952],{},[38,85907,78482],{},[883,85909,85911],{"className":85910},[886],[888,85912,85913],{"xmlns":890},[892,85914,85915,85924],{},[895,85916,85917,85919,85921],{},[898,85918,1747],{},[1708,85920,1710],{},[2247,85922,85923],{},"konst",[902,85925,85926],{"encoding":904},"P = \\text{konst}",[883,85928,85930],{"className":85929},[886],[888,85931,85932],{"xmlns":890},[892,85933,85934,85950],{},[895,85935,85936,85938,85940,85942,85944,85946,85948],{},[898,85937,1747],{},[1708,85939,1710],{},[898,85941,1741],{},[898,85943,3455],{},[1708,85945,1716],{"stretchy":1715},[898,85947,1688],{},[1708,85949,1721],{"stretchy":1715},[902,85951,79176],{"encoding":904}," (3.14).",[123,85954,85955,85958,85959,85988,85989,86006],{},[38,85956,85957],{},"Shutdown point"," — bod ",[883,85960,85962],{"className":85961},[886],[888,85963,85964],{"xmlns":890},[892,85965,85966,85986],{},[895,85967,85968,85970,85976,85978,85984],{},[1708,85969,1716],{"stretchy":1715},[1753,85971,85972,85974],{},[898,85973,1688],{},[1708,85975,2417],{},[1708,85977,1883],{"separator":1882},[1753,85979,85980,85982],{},[898,85981,1747],{},[1708,85983,2417],{},[1708,85985,1721],{"stretchy":1715},[902,85987,79465],{"encoding":904}," v minimu ",[883,85990,85992],{"className":85991},[886],[888,85993,85994],{"xmlns":890},[892,85995,85996,86004],{},[895,85997,85998,86000,86002],{},[898,85999,1786],{},[898,86001,52173],{},[898,86003,3455],{},[902,86005,67130],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,86008,86009,1729,86012,10064,86047,79735,86068,86081,86082,86097,86098,2155],{},[38,86010,86011],{},"Funkce nabídky firmy",[883,86013,86015],{"className":86014},[886],[888,86016,86017],{"xmlns":890},[892,86018,86019,86045],{},[895,86020,86021,86023,86025,86027,86029,86031,86033,86035,86037,86039,86041,86043],{},[898,86022,1747],{},[1708,86024,1710],{},[898,86026,1981],{},[1708,86028,1716],{"stretchy":1715},[898,86030,1688],{},[1708,86032,1721],{"stretchy":1715},[1708,86034,1710],{},[898,86036,1741],{},[898,86038,3455],{},[1708,86040,1716],{"stretchy":1715},[898,86042,1688],{},[1708,86044,1721],{"stretchy":1715},[902,86046,80930],{"encoding":904},[883,86048,86050],{"className":86049},[886],[888,86051,86052],{"xmlns":890},[892,86053,86054,86066],{},[895,86055,86056,86058,86060],{},[898,86057,1688],{},[1708,86059,6762],{},[1753,86061,86062,86064],{},[898,86063,1688],{},[1708,86065,2417],{},[902,86067,79734],{"encoding":904},[883,86069,86071],{"className":86070},[886],[888,86072,86073],{"xmlns":890},[892,86074,86075,86079],{},[895,86076,86077],{},[2505,86078,2784],{},[902,86080,2784],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,86083,86085],{"className":86084},[886],[888,86086,86087],{"xmlns":890},[892,86088,86089,86095],{},[895,86090,86091,86093],{},[898,86092,1741],{},[898,86094,3455],{},[902,86096,67111],{"encoding":904}," nad minimem ",[883,86099,86101],{"className":86100},[886],[888,86102,86103],{"xmlns":890},[892,86104,86105,86113],{},[895,86106,86107,86109,86111],{},[898,86108,1786],{},[898,86110,52173],{},[898,86112,3455],{},[902,86114,67130],{"encoding":904},[123,86116,86117,12636,86119,86140,86141,2155],{},[38,86118,61902],{},[883,86120,86122],{"className":86121},[886],[888,86123,86124],{"xmlns":890},[892,86125,86126,86138],{},[895,86127,86128,86130,86132],{},[898,86129,1747],{},[1708,86131,1710],{},[1753,86133,86134,86136],{},[898,86135,1747],{},[1708,86137,2417],{},[902,86139,16285],{"encoding":904}," konstantní ⇒ ",[883,86142,86144],{"className":86143},[886],[888,86145,86146],{"xmlns":890},[892,86147,86148,86168],{},[895,86149,86150,86152,86154,86156,86158,86160,86162],{},[898,86151,1786],{},[898,86153,1975],{},[1708,86155,1710],{},[898,86157,1741],{},[898,86159,1975],{},[1708,86161,1710],{},[1753,86163,86164,86166],{},[898,86165,1747],{},[1708,86167,2417],{},[902,86169,70413],{"encoding":904},[123,86171,86172,86175],{},[38,86173,86174],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,86177,13763],{"id":13762},[120,86179,86180,86199,86211],{},[123,86181,86182,1729,86184,1343,86187,1343,86190,1343,86193,1343,86196],{},[38,86183,13770],{},[207,86185,23828],{"className":86186,"dataFsResolvedFilePath":800,"href":801},[210],[207,86188,13875],{"className":86189,"dataFsResolvedFilePath":848,"href":849},[210],[207,86191,2162],{"className":86192,"dataFsResolvedFilePath":764,"href":765},[210],[207,86194,775],{"className":86195,"dataFsResolvedFilePath":773,"href":774},[210],[207,86197,859],{"className":86198,"dataFsResolvedFilePath":857,"href":858},[210],[123,86200,86201,1729,86203,1343,86207],{},[38,86202,48545],{},[207,86204,86206],{"className":86205,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,86208,86210],{"className":86209,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — 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Cobb-Douglasova funkce užitečnosti a optimalizace 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je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,97651,97652],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,97655,97657],{"className":97656},[886],[888,97658,97659],{"xmlns":890},[892,97660,97661,97681],{},[895,97662,97663,97665,97671,97673],{},[898,97664,1741],{},[1743,97666,97667,97669],{},[898,97668,900],{},[898,97670,29661],{},[1708,97672,1710],{},[4754,97674,97675,97677,97679],{},[898,97676,900],{},[898,97678,29661],{},[1708,97680,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,97682,97683],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,97686,97688],{"className":97687},[886],[888,97689,97690],{"xmlns":890},[892,97691,97692,97700],{},[895,97693,97694,97696,97698],{},[898,97695,900],{},[1708,97697,1710],{},[898,97699,14142],{},[902,97701,97702],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,97705,97707],{"className":97706},[886],[888,97708,97709],{"xmlns":890},[892,97710,97711,97741],{},[895,97712,97713,97715,97717,97719,97721,97723,97725,97731,97733,97735],{},[898,97714,1741],{},[898,97716,1975],{},[898,97718,3455],{},[898,97720,1981],{},[1708,97722,1710],{},[898,97724,1741],{},[1743,97726,97727,97729],{},[898,97728,900],{},[2505,97730,2507],{},[898,97732,1799],{"mathvariant":1759},[898,97734,1741],{},[1743,97736,97737,97739],{},[898,97738,900],{},[2505,97740,3132],{},[902,97742,97743],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,97746,97747],{},"teorii užitečnosti"," — funkce ",[883,97750,97752],{"className":97751},[886],[888,97753,97754],{"xmlns":890},[892,97755,97756,97760],{},[895,97757,97758],{},[898,97759,900],{},[902,97761,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,97764,97765],{},"Optimalizaci spotřebitele",[883,97767,97769],{"className":97768},[886],[888,97770,97771],{"xmlns":890},[892,97772,97773,97777],{},[895,97774,97775],{},[898,97776,900],{},[902,97778,900],{"encoding":904}," při rozpočtu, min ",[883,97781,97783],{"className":97782},[886],[888,97784,97785],{"xmlns":890},[892,97786,97787,97791],{},[895,97788,97789],{},[898,97790,16183],{},[902,97792,16183],{"encoding":904}," při dané ",[883,97795,97797],{"className":97796},[886],[888,97798,97799],{"xmlns":890},[892,97800,97801,97805],{},[895,97802,97803],{},[898,97804,900],{},[902,97806,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,97809,913],{"className":97810,"dataFsResolvedFilePath":911,"href":912},[210],[724,97812,97813,97814,97816,97817,2155],{},"Kapitola 6 knihy ",[614,97815,13894],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,97818,48596],{"className":97819,"dataFsResolvedFilePath":911,"href":912},[210],[115,97821,97823],{"id":97822},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,97825,97826],{},"Po prostudování této kapitoly byste měli umět:",[120,97828,97829,97835,97844,97849,97852,97858,97864,97867,97873],{},[123,97830,97831,97832,1883],{},"vyložit, co se rozumí termínem ",[38,97833,97834],{},"užitečnost",[123,97836,97837,97838,1771,97841,1883],{},"definovat pojmy ",[38,97839,97840],{},"svazek zboží",[38,97842,97843],{},"funkce užitečnosti",[123,97845,2043,97846,2050],{},[38,97847,97848],{},"mezní užitečnosti",[123,97850,97851],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,97853,2070,97854,97857],{},[38,97855,97856],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,97859,2093,97860,97863],{},[38,97861,97862],{},"křivky užitečnosti"," (indiferenční křivky),",[123,97865,97866],{},"vyjmenovat jejich základní vlastnosti,",[123,97868,2043,97869,97872],{},[38,97870,97871],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,97874,97875,97876,97879],{},"řešit ",[38,97877,97878],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,97881,97883],{"id":97882},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,97885,97886,97887,97891,97892,97895],{},"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 ",[207,97888,97890],{"className":97889,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,97893,97894],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,97897,97899],{"id":97898},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,97901,97902],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,97904,97905,97911],{},[123,97906,97907,97910],{},[38,97908,97909],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,97912,97913,97916,97917,97919],{},[38,97914,97915],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,97918,97652],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1636,97921,97922],{},[724,97923,97924,97926,97927,97930,97931,1729,97944,97947,97948,1771,97961,97980,97981,1343,98007,98034,98035,98038,98039,98042],{},[883,97925,6130],{}," Pozor — ordinalisté užitečnost ",[38,97928,97929],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,97932,97934],{"className":97933},[886],[888,97935,97936],{"xmlns":890},[892,97937,97938,97942],{},[895,97939,97940],{},[898,97941,900],{},[902,97943,900],{"encoding":904},[38,97945,97946],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,97949,97951],{"className":97950},[886],[888,97952,97953],{"xmlns":890},[892,97954,97955,97959],{},[895,97956,97957],{},[898,97958,900],{},[902,97960,900],{"encoding":904},[883,97962,97964],{"className":97963},[886],[888,97965,97966],{"xmlns":890},[892,97967,97968,97977],{},[895,97969,97970],{},[20297,97971,97972,97974],{"accent":1882},[898,97973,900],{},[1708,97975,97976],{},"~",[902,97978,97979],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,97982,97984],{"className":97983},[886],[888,97985,97986],{"xmlns":890},[892,97987,97988,98004],{},[895,97989,97990,97996,97998],{},[20297,97991,97992,97994],{"accent":1882},[898,97993,900],{},[1708,97995,97976],{},[1708,97997,1710],{},[1753,97999,98000,98002],{},[898,98001,900],{},[2505,98003,3132],{},[902,98005,98006],{"encoding":904},"\\tilde U = U^2",[883,98008,98010],{"className":98009},[886],[888,98011,98012],{"xmlns":890},[892,98013,98014,98031],{},[895,98015,98016,98022,98024,98027,98029],{},[20297,98017,98018,98020],{"accent":1882},[898,98019,900],{},[1708,98021,97976],{},[1708,98023,1710],{},[898,98025,98026],{},"ln",[1708,98028,7149],{},[898,98030,900],{},[902,98032,98033],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,98036,98037],{},"porovnání"," mezi svazky a ",[38,98040,98041],{},"poměry"," mezních veličin.",[724,98044,98045,98046,2788],{},"Ordinalistický přístup vychází z ",[38,98047,98048],{},"pěti hlavních předpokladů",[152,98050,98051,98057,98063,98181,98187],{},[123,98052,98053,98056],{},[38,98054,98055],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,98058,98059,98062],{},[38,98060,98061],{},"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.",[123,98064,98065,98068,98069,73556,98082,98095,98096,73556,98109,2941,98122,98125,98126,1771,98145,74385,98163,2155],{},[38,98066,98067],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,98070,98072],{"className":98071},[886],[888,98073,98074],{"xmlns":890},[892,98075,98076,98080],{},[895,98077,98078],{},[898,98079,1786],{},[902,98081,1786],{"encoding":904},[883,98083,98085],{"className":98084},[886],[888,98086,98087],{"xmlns":890},[892,98088,98089,98093],{},[895,98090,98091],{},[898,98092,35110],{},[902,98094,35110],{"encoding":904},", nebude jindy preferovat ",[883,98097,98099],{"className":98098},[886],[888,98100,98101],{"xmlns":890},[892,98102,98103,98107],{},[895,98104,98105],{},[898,98106,35110],{},[902,98108,35110],{"encoding":904},[883,98110,98112],{"className":98111},[886],[888,98113,98114],{"xmlns":890},[892,98115,98116,98120],{},[895,98117,98118],{},[898,98119,1786],{},[902,98121,1786],{"encoding":904},[38,98123,98124],{},"Tranzitivita",": pokud ",[883,98127,98129],{"className":98128},[886],[888,98130,98131],{"xmlns":890},[892,98132,98133,98142],{},[895,98134,98135,98137,98140],{},[898,98136,1786],{},[1708,98138,98139],{},"≻",[898,98141,35110],{},[902,98143,98144],{"encoding":904},"A \\succ B",[883,98146,98148],{"className":98147},[886],[888,98149,98150],{"xmlns":890},[892,98151,98152,98160],{},[895,98153,98154,98156,98158],{},[898,98155,35110],{},[1708,98157,98139],{},[898,98159,3455],{},[902,98161,98162],{"encoding":904},"B \\succ C",[883,98164,98166],{"className":98165},[886],[888,98167,98168],{"xmlns":890},[892,98169,98170,98178],{},[895,98171,98172,98174,98176],{},[898,98173,1786],{},[1708,98175,98139],{},[898,98177,3455],{},[902,98179,98180],{"encoding":904},"A \\succ C",[123,98182,98183,98186],{},[38,98184,98185],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,98188,98189,98192],{},[38,98190,98191],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,98194,98195,98196,98199,98200,2155],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,98197,98198],{},"preference"," a na příbuzné ",[614,98201,98202],{},"funkci užitečnosti",[115,98204,98206],{"id":98205},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,98208,98209,98210,98223,98224,98227,98228,98241],{},"Uvažujme ",[883,98211,98213],{"className":98212},[886],[888,98214,98215],{"xmlns":890},[892,98216,98217,98221],{},[895,98218,98219],{},[898,98220,6676],{},[902,98222,6676],{"encoding":904}," různých zboží. ",[38,98225,98226],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,98229,98231],{"className":98230},[886],[888,98232,98233],{"xmlns":890},[892,98234,98235,98239],{},[895,98236,98237],{},[898,98238,6676],{},[902,98240,6676],{"encoding":904},"-tice",[724,98243,98244],{},[883,98245,98247],{"className":98246},[886],[888,98248,98249],{"xmlns":890},[892,98250,98251,98277],{},[895,98252,98253,98255,98261,98263,98265,98267,98273,98275],{},[1708,98254,1716],{"stretchy":1715},[1743,98256,98257,98259],{},[898,98258,1688],{},[2505,98260,2507],{},[1708,98262,1883],{"separator":1882},[1708,98264,21550],{},[1708,98266,1883],{"separator":1882},[1743,98268,98269,98271],{},[898,98270,1688],{},[898,98272,6676],{},[1708,98274,1721],{"stretchy":1715},[1708,98276,1883],{"separator":1882},[902,98278,98279],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,98281,5411,98282,98299,98300,98313,98314,98317,98318,98321,98322,98325,98326,2788],{},[883,98283,98285],{"className":98284},[886],[888,98286,98287],{"xmlns":890},[892,98288,98289,98297],{},[895,98290,98291],{},[1743,98292,98293,98295],{},[898,98294,1688],{},[898,98296,29661],{},[902,98298,59363],{"encoding":904}," značí množství ",[883,98301,98303],{"className":98302},[886],[888,98304,98305],{"xmlns":890},[892,98306,98307,98311],{},[895,98308,98309],{},[898,98310,29661],{},[902,98312,29661],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,98315,98316],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,98319,98320],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,98323,98324],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,98327,98202],{},[883,98329,98331],{"className":98330},[886],[888,98332,98333],{"xmlns":890,"display":2210},[892,98334,98335,98382],{},[2214,98336,98337],{"width":2216},[2218,98338,98339,98341,98375,98377],{},[2221,98340],{"width":2223},[2221,98342,98343],{},[895,98344,98345,98347,98349,98351,98353,98359,98361,98363,98365,98371,98373],{},[898,98346,900],{},[1708,98348,1710],{},[898,98350,900],{},[1708,98352,1716],{"stretchy":1715},[1743,98354,98355,98357],{},[898,98356,1688],{},[2505,98358,2507],{},[1708,98360,1883],{"separator":1882},[1708,98362,21550],{},[1708,98364,1883],{"separator":1882},[1743,98366,98367,98369],{},[898,98368,1688],{},[898,98370,6676],{},[1708,98372,1721],{"stretchy":1715},[1708,98374,1883],{"separator":1882},[2221,98376],{"width":2223},[2221,98378,98379],{},[2247,98380,98381],{},"(6.1)",[902,98383,98384],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,98386,5411,98387,98417,98418,98440,98441,98444],{},[883,98388,98390],{"className":98389},[886],[888,98391,98392],{"xmlns":890},[892,98393,98394,98414],{},[895,98395,98396,98402,98404,98406,98408],{},[1743,98397,98398,98400],{},[898,98399,1688],{},[2505,98401,2507],{},[1708,98403,1883],{"separator":1882},[1708,98405,21550],{},[1708,98407,1883],{"separator":1882},[1743,98409,98410,98412],{},[898,98411,1688],{},[898,98413,6676],{},[902,98415,98416],{"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 ",[883,98419,98421],{"className":98420},[886],[888,98422,98423],{"xmlns":890},[892,98424,98425,98437],{},[895,98426,98427,98429,98431],{},[898,98428,900],{},[1708,98430,1883],{"separator":1882},[20297,98432,98433,98435],{"accent":1882},[898,98434,900],{},[1708,98436,97976],{},[902,98438,98439],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,98442,98443],{},"monotónní transformace"," zachovávající pořadí.",[724,98446,98447,98448,12636,98451,2155],{},"Dále se omezíme na funkce pro ",[38,98449,98450],{},"dvě zboží",[883,98452,98454],{"className":98453},[886],[888,98455,98456],{"xmlns":890},[892,98457,98458,98484],{},[895,98459,98460,98462,98464,98466,98468,98474,98476,98482],{},[898,98461,900],{},[1708,98463,1710],{},[898,98465,900],{},[1708,98467,1716],{"stretchy":1715},[1743,98469,98470,98472],{},[898,98471,1688],{},[2505,98473,2507],{},[1708,98475,1883],{"separator":1882},[1743,98477,98478,98480],{},[898,98479,1688],{},[2505,98481,3132],{},[1708,98483,1721],{"stretchy":1715},[902,98485,98486],{"encoding":904},"U = U(Q_1, Q_2)",[1636,98488,98489,98564],{},[724,98490,98491,98493,98494,2788],{},[883,98492,64514],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,98495,98497],{"className":98496},[886],[888,98498,98499],{"xmlns":890},[892,98500,98501,98561],{},[895,98502,98503,98505,98507,98509,98511,98517,98519,98525,98527,98533,98535,98537,98539],{},[898,98504,900],{},[1708,98506,1710],{},[898,98508,900],{},[1708,98510,1716],{"stretchy":1715},[1743,98512,98513,98515],{},[898,98514,1688],{},[2505,98516,2507],{},[1708,98518,1883],{"separator":1882},[1743,98520,98521,98523],{},[898,98522,1688],{},[2505,98524,3132],{},[1708,98526,1883],{"separator":1882},[1743,98528,98529,98531],{},[898,98530,1688],{},[2505,98532,3121],{},[1708,98534,1721],{"stretchy":1715},[1708,98536,1710],{},[2505,98538,3132],{},[9351,98540,98541],{},[895,98542,98543,98549,98555],{},[1743,98544,98545,98547],{},[898,98546,1688],{},[2505,98548,2507],{},[1743,98550,98551,98553],{},[898,98552,1688],{},[2505,98554,3132],{},[1743,98556,98557,98559],{},[898,98558,1688],{},[2505,98560,3121],{},[902,98562,98563],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,98565,98566,98759],{},[123,98567,98568,98569,98595,98596,24823,98622,1771,98681,17508,98741,8197],{},"svazek ",[883,98570,98572],{"className":98571},[886],[888,98573,98574],{"xmlns":890},[892,98575,98576,98592],{},[895,98577,98578,98580,98582,98584,98586,98588,98590],{},[1708,98579,1716],{"stretchy":1715},[2505,98581,53694],{},[1708,98583,1883],{"separator":1882},[2505,98585,5867],{},[1708,98587,1883],{"separator":1882},[2505,98589,53672],{},[1708,98591,1721],{"stretchy":1715},[902,98593,98594],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,98597,98599],{"className":98598},[886],[888,98600,98601],{"xmlns":890},[892,98602,98603,98619],{},[895,98604,98605,98607,98609,98611,98613,98615,98617],{},[1708,98606,1716],{"stretchy":1715},[2505,98608,4635],{},[1708,98610,1883],{"separator":1882},[2505,98612,4635],{},[1708,98614,1883],{"separator":1882},[2505,98616,12110],{},[1708,98618,1721],{"stretchy":1715},[902,98620,98621],{"encoding":904},"(9, 9, 27)",[883,98623,98625],{"className":98624},[886],[888,98626,98627],{"xmlns":890},[892,98628,98629,98678],{},[895,98630,98631,98633,98635,98637,98639,98641,98643,98645,98647,98649,98651,98665,98667,98669,98674,98676],{},[898,98632,900],{},[1708,98634,1716],{"stretchy":1715},[2505,98636,53694],{},[1708,98638,1883],{"separator":1882},[2505,98640,5867],{},[1708,98642,1883],{"separator":1882},[2505,98644,53672],{},[1708,98646,1721],{"stretchy":1715},[1708,98648,1710],{},[2505,98650,3132],{},[9351,98652,98653],{},[895,98654,98655,98657,98659,98661,98663],{},[2505,98656,53694],{},[1708,98658,3703],{},[2505,98660,5867],{},[1708,98662,3703],{},[2505,98664,53672],{},[1708,98666,1710],{},[2505,98668,3132],{},[9351,98670,98671],{},[2505,98672,98673],{},"4096",[1708,98675,1710],{},[2505,98677,17536],{},[902,98679,98680],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,98682,98684],{"className":98683},[886],[888,98685,98686],{"xmlns":890},[892,98687,98688,98738],{},[895,98689,98690,98692,98694,98696,98698,98700,98702,98704,98706,98708,98710,98724,98726,98728,98733,98735],{},[898,98691,900],{},[1708,98693,1716],{"stretchy":1715},[2505,98695,4635],{},[1708,98697,1883],{"separator":1882},[2505,98699,4635],{},[1708,98701,1883],{"separator":1882},[2505,98703,12110],{},[1708,98705,1721],{"stretchy":1715},[1708,98707,1710],{},[2505,98709,3132],{},[9351,98711,98712],{},[895,98713,98714,98716,98718,98720,98722],{},[2505,98715,4635],{},[1708,98717,3703],{},[2505,98719,4635],{},[1708,98721,3703],{},[2505,98723,12110],{},[1708,98725,1710],{},[2505,98727,3132],{},[9351,98729,98730],{},[2505,98731,98732],{},"2187",[1708,98734,17816],{},[2505,98736,98737],{},"93,53",[902,98739,98740],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,98742,98744],{"className":98743},[886],[888,98745,98746],{"xmlns":890},[892,98747,98748,98756],{},[895,98749,98750,98752,98754],{},[2505,98751,17536],{},[1708,98753,2854],{},[2505,98755,98737],{},[902,98757,98758],{"encoding":904},"128 > 93{,}53",[123,98760,98761,98762,1771,98788,98814,98815,1771,98855,98896,98897,98943,98944,1771,98970,14811,98996,1771,99014,99032,99033,2155],{},"svazky ",[883,98763,98765],{"className":98764},[886],[888,98766,98767],{"xmlns":890},[892,98768,98769,98785],{},[895,98770,98771,98773,98775,98777,98779,98781,98783],{},[1708,98772,1716],{"stretchy":1715},[2505,98774,5867],{},[1708,98776,1883],{"separator":1882},[2505,98778,3998],{},[1708,98780,1883],{"separator":1882},[2505,98782,3132],{},[1708,98784,1721],{"stretchy":1715},[902,98786,98787],{"encoding":904},"(4, 8, 2)",[883,98789,98791],{"className":98790},[886],[888,98792,98793],{"xmlns":890},[892,98794,98795,98811],{},[895,98796,98797,98799,98801,98803,98805,98807,98809],{},[1708,98798,1716],{"stretchy":1715},[2505,98800,53672],{},[1708,98802,1883],{"separator":1882},[2505,98804,2507],{},[1708,98806,1883],{"separator":1882},[2505,98808,5867],{},[1708,98810,1721],{"stretchy":1715},[902,98812,98813],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,98816,98818],{"className":98817},[886],[888,98819,98820],{"xmlns":890},[892,98821,98822,98852],{},[895,98823,98824,98826,98828,98830,98832,98834,98836,98838,98840,98842,98844,98848,98850],{},[898,98825,900],{},[1708,98827,1716],{"stretchy":1715},[2505,98829,5867],{},[1708,98831,1883],{"separator":1882},[2505,98833,3998],{},[1708,98835,1883],{"separator":1882},[2505,98837,3132],{},[1708,98839,1721],{"stretchy":1715},[1708,98841,1710],{},[2505,98843,3132],{},[9351,98845,98846],{},[2505,98847,53672],{},[1708,98849,1710],{},[2505,98851,53694],{},[902,98853,98854],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,98856,98858],{"className":98857},[886],[888,98859,98860],{"xmlns":890},[892,98861,98862,98893],{},[895,98863,98864,98866,98868,98870,98872,98874,98876,98878,98880,98882,98884,98889,98891],{},[898,98865,900],{},[1708,98867,1716],{"stretchy":1715},[2505,98869,53672],{},[1708,98871,1883],{"separator":1882},[2505,98873,2507],{},[1708,98875,1883],{"separator":1882},[2505,98877,5867],{},[1708,98879,1721],{"stretchy":1715},[1708,98881,1710],{},[2505,98883,3132],{},[9351,98885,98886],{},[2505,98887,98888],{},"256",[1708,98890,1710],{},[2505,98892,84163],{},[902,98894,98895],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,98898,98900],{"className":98899},[886],[888,98901,98902],{"xmlns":890},[892,98903,98904,98940],{},[895,98905,98906,98908,98910,98912,98914,98916,98918,98920,98922,98924,98926,98928,98930,98932,98934,98936,98938],{},[898,98907,900],{},[1708,98909,1716],{"stretchy":1715},[2505,98911,5867],{},[1708,98913,1883],{"separator":1882},[2505,98915,3998],{},[1708,98917,1883],{"separator":1882},[2505,98919,3132],{},[1708,98921,1721],{"stretchy":1715},[1708,98923,1710],{},[898,98925,900],{},[1708,98927,1716],{"stretchy":1715},[2505,98929,53672],{},[1708,98931,1883],{"separator":1882},[2505,98933,2507],{},[1708,98935,1883],{"separator":1882},[2505,98937,5867],{},[1708,98939,1721],{"stretchy":1715},[902,98941,98942],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,98945,98947],{"className":98946},[886],[888,98948,98949],{"xmlns":890},[892,98950,98951,98967],{},[895,98952,98953,98955,98957,98959,98961,98963,98965],{},[2505,98954,5867],{},[1708,98956,3703],{},[2505,98958,3998],{},[1708,98960,3703],{},[2505,98962,3132],{},[1708,98964,1710],{},[2505,98966,53672],{},[902,98968,98969],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,98971,98973],{"className":98972},[886],[888,98974,98975],{"xmlns":890},[892,98976,98977,98993],{},[895,98978,98979,98981,98983,98985,98987,98989,98991],{},[2505,98980,53672],{},[1708,98982,3703],{},[2505,98984,2507],{},[1708,98986,3703],{},[2505,98988,5867],{},[1708,98990,1710],{},[2505,98992,98888],{},[902,98994,98995],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,98997,98999],{"className":98998},[886],[888,99000,99001],{"xmlns":890},[892,99002,99003,99011],{},[895,99004,99005,99007,99009],{},[898,99006,900],{},[1708,99008,1710],{},[2505,99010,53694],{},[902,99012,99013],{"encoding":904},"U = 16",[883,99015,99017],{"className":99016},[886],[888,99018,99019],{"xmlns":890},[892,99020,99021,99029],{},[895,99022,99023,99025,99027],{},[898,99024,900],{},[1708,99026,1710],{},[2505,99028,84163],{},[902,99030,99031],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,99034,99036],{"className":99035},[886],[888,99037,99038],{"xmlns":890},[892,99039,99040,99060],{},[895,99041,99042,99048,99054],{},[1743,99043,99044,99046],{},[898,99045,1688],{},[2505,99047,2507],{},[1743,99049,99050,99052],{},[898,99051,1688],{},[2505,99053,3132],{},[1743,99055,99056,99058],{},[898,99057,1688],{},[2505,99059,3121],{},[902,99061,99062],{"encoding":904},"Q_1 Q_2 Q_3",[115,99064,99066],{"id":99065},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,99068,99069,99070,3033,99105,1729,99108,53646,99125,1695,99142,99145,99146,99149],{},"Pro funkci užitečnosti ",[883,99071,99073],{"className":99072},[886],[888,99074,99075],{"xmlns":890},[892,99076,99077,99103],{},[895,99078,99079,99081,99083,99085,99087,99093,99095,99101],{},[898,99080,900],{},[1708,99082,1710],{},[898,99084,900],{},[1708,99086,1716],{"stretchy":1715},[1743,99088,99089,99091],{},[898,99090,1688],{},[2505,99092,2507],{},[1708,99094,1883],{"separator":1882},[1743,99096,99097,99099],{},[898,99098,1688],{},[2505,99100,3132],{},[1708,99102,1721],{"stretchy":1715},[902,99104,98486],{"encoding":904},[38,99106,99107],{},"mezní užitečnost",[883,99109,99111],{"className":99110},[886],[888,99112,99113],{"xmlns":890},[892,99114,99115,99123],{},[895,99116,99117],{},[1743,99118,99119,99121],{},[898,99120,1688],{},[2505,99122,2507],{},[902,99124,40849],{"encoding":904},[883,99126,99128],{"className":99127},[886],[888,99129,99130],{"xmlns":890},[892,99131,99132,99140],{},[895,99133,99134],{},[1743,99135,99136,99138],{},[898,99137,1688],{},[2505,99139,3132],{},[902,99141,40868],{"encoding":904},[38,99143,99144],{},"marginal utility",") parciální ",[207,99147,1145],{"className":99148,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,99151,99153],{"className":99152},[886],[888,99154,99155],{"xmlns":890,"display":2210},[892,99156,99157,99256],{},[2214,99158,99159],{"width":2216},[2218,99160,99161,99163,99249,99251],{},[2221,99162],{"width":2223},[2221,99164,99165],{},[895,99166,99167,99169,99175,99177,99185,99187,99205,99207,99209,99211,99217,99219,99227,99229,99247],{},[898,99168,1741],{},[1743,99170,99171,99173],{},[898,99172,900],{},[2505,99174,2507],{},[1708,99176,1710],{},[4754,99178,99179,99181,99183],{},[898,99180,900],{},[2505,99182,2507],{},[1708,99184,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,99186,1710],{},[2358,99188,99189,99195],{},[895,99190,99191,99193],{},[898,99192,7252],{"mathvariant":1759},[898,99194,900],{},[895,99196,99197,99199],{},[898,99198,7252],{"mathvariant":1759},[1743,99200,99201,99203],{},[898,99202,1688],{},[2505,99204,2507],{},[1708,99206,1883],{"separator":1882},[3213,99208],{"width":4750},[898,99210,1741],{},[1743,99212,99213,99215],{},[898,99214,900],{},[2505,99216,3132],{},[1708,99218,1710],{},[4754,99220,99221,99223,99225],{},[898,99222,900],{},[2505,99224,3132],{},[1708,99226,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,99228,1710],{},[2358,99230,99231,99237],{},[895,99232,99233,99235],{},[898,99234,7252],{"mathvariant":1759},[898,99236,900],{},[895,99238,99239,99241],{},[898,99240,7252],{"mathvariant":1759},[1743,99242,99243,99245],{},[898,99244,1688],{},[2505,99246,3132],{},[898,99248,2155],{"mathvariant":1759},[2221,99250],{"width":2223},[2221,99252,99253],{},[2247,99254,99255],{},"(6.2)",[902,99257,99258],{"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}",[724,99260,99261,99262,99296,99297,99327,99328,1729,99331,2155],{},"Pro pevné ",[883,99263,99265],{"className":99264},[886],[888,99266,99267],{"xmlns":890},[892,99268,99269,99293],{},[895,99270,99271,99277,99279,99281,99283,99289,99291],{},[1743,99272,99273,99275],{},[898,99274,1688],{},[2505,99276,2507],{},[1708,99278,1710],{},[898,99280,207],{},[1708,99282,1883],{"separator":1882},[1743,99284,99285,99287],{},[898,99286,1688],{},[2505,99288,3132],{},[1708,99290,1710],{},[898,99292,1923],{},[902,99294,99295],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,99298,99300],{"className":99299},[886],[888,99301,99302],{"xmlns":890},[892,99303,99304,99324],{},[895,99305,99306,99308,99314,99316,99318,99320,99322],{},[898,99307,1741],{},[1743,99309,99310,99312],{},[898,99311,900],{},[2505,99313,2507],{},[1708,99315,1716],{"stretchy":1715},[898,99317,207],{},[1708,99319,1883],{"separator":1882},[898,99321,1923],{},[1708,99323,1721],{"stretchy":1715},[902,99325,99326],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,99329,99330],{},"v bodě (na hladině)",[883,99332,99334],{"className":99333},[886],[888,99335,99336],{"xmlns":890},[892,99337,99338,99350],{},[895,99339,99340,99342,99344,99346,99348],{},[1708,99341,6940],{"stretchy":1715},[898,99343,207],{},[1708,99345,1883],{"separator":1882},[898,99347,1923],{},[1708,99349,6981],{"stretchy":1715},[902,99351,7373],{"encoding":904},[1636,99353,99354],{},[724,99355,99356,99358,99359,99389,99418,99419,14587,99432,3405,99449,99470,99471,14647,99488,2486,99501,99518,99519,99541,99542,99571,99572,10064,99592,99609],{},[883,99357,2518],{}," Intuice — co říká ",[883,99360,99362],{"className":99361},[886],[888,99363,99364],{"xmlns":890},[892,99365,99366,99386],{},[895,99367,99368,99370,99376,99378,99380,99382,99384],{},[898,99369,1741],{},[1743,99371,99372,99374],{},[898,99373,900],{},[2505,99375,2507],{},[1708,99377,1716],{"stretchy":1715},[898,99379,207],{},[1708,99381,1883],{"separator":1882},[898,99383,1923],{},[1708,99385,1721],{"stretchy":1715},[902,99387,99388],{"encoding":904},"MU_1(a,b)",[883,99390,99392],{"className":99391},[886],[888,99393,99394],{"xmlns":890},[892,99395,99396,99416],{},[895,99397,99398,99400,99406,99408,99410,99412,99414],{},[898,99399,1741],{},[1743,99401,99402,99404],{},[898,99403,900],{},[2505,99405,2507],{},[1708,99407,1716],{"stretchy":1715},[898,99409,207],{},[1708,99411,1883],{"separator":1882},[898,99413,1923],{},[1708,99415,1721],{"stretchy":1715},[902,99417,99326],{"encoding":904}," je rychlost změny ",[883,99420,99422],{"className":99421},[886],[888,99423,99424],{"xmlns":890},[892,99425,99426,99430],{},[895,99427,99428],{},[898,99429,900],{},[902,99431,900],{"encoding":904},[883,99433,99435],{"className":99434},[886],[888,99436,99437],{"xmlns":890},[892,99438,99439,99447],{},[895,99440,99441],{},[1743,99442,99443,99445],{},[898,99444,1688],{},[2505,99446,2507],{},[902,99448,40849],{"encoding":904},[883,99450,99452],{"className":99451},[886],[888,99453,99454],{"xmlns":890},[892,99455,99456,99468],{},[895,99457,99458,99460,99462,99464,99466],{},[1708,99459,6940],{"stretchy":1715},[898,99461,207],{},[1708,99463,1883],{"separator":1882},[898,99465,1923],{},[1708,99467,6981],{"stretchy":1715},[902,99469,7373],{"encoding":904},". Přibližně: změní-li se ",[883,99472,99474],{"className":99473},[886],[888,99475,99476],{"xmlns":890},[892,99477,99478,99486],{},[895,99479,99480],{},[1743,99481,99482,99484],{},[898,99483,1688],{},[2505,99485,2507],{},[902,99487,40849],{"encoding":904},[883,99489,99491],{"className":99490},[886],[888,99492,99493],{"xmlns":890},[892,99494,99495,99499],{},[895,99496,99497],{},[898,99498,207],{},[902,99500,207],{"encoding":904},[883,99502,99504],{"className":99503},[886],[888,99505,99506],{"xmlns":890},[892,99507,99508,99516],{},[895,99509,99510,99512,99514],{},[898,99511,207],{},[1708,99513,2019],{},[2505,99515,2507],{},[902,99517,14678],{"encoding":904}," při pevném ",[883,99520,99522],{"className":99521},[886],[888,99523,99524],{"xmlns":890},[892,99525,99526,99538],{},[895,99527,99528,99534,99536],{},[1743,99529,99530,99532],{},[898,99531,1688],{},[2505,99533,3132],{},[1708,99535,1710],{},[898,99537,1923],{},[902,99539,99540],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,99543,99545],{"className":99544},[886],[888,99546,99547],{"xmlns":890},[892,99548,99549,99569],{},[895,99550,99551,99553,99559,99561,99563,99565,99567],{},[898,99552,1741],{},[1743,99554,99555,99557],{},[898,99556,900],{},[2505,99558,2507],{},[1708,99560,1716],{"stretchy":1715},[898,99562,207],{},[1708,99564,1883],{"separator":1882},[898,99566,1923],{},[1708,99568,1721],{"stretchy":1715},[902,99570,99326],{"encoding":904},". Stejně tak ",[883,99573,99575],{"className":99574},[886],[888,99576,99577],{"xmlns":890},[892,99578,99579,99589],{},[895,99580,99581,99583],{},[898,99582,1741],{},[1743,99584,99585,99587],{},[898,99586,900],{},[2505,99588,3132],{},[902,99590,99591],{"encoding":904},"MU_2",[883,99593,99595],{"className":99594},[886],[888,99596,99597],{"xmlns":890},[892,99598,99599,99607],{},[895,99600,99601],{},[1743,99602,99603,99605],{},[898,99604,1688],{},[2505,99606,3132],{},[902,99608,40868],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,99611,7527],{"id":99612},"totální-diferenciál",[724,99614,99615,99616,60165,99632,99662,99663,2788],{},"Přibližnou změnu užitečnosti ",[883,99617,99619],{"className":99618},[886],[888,99620,99621],{"xmlns":890},[892,99622,99623,99629],{},[895,99624,99625,99627],{},[898,99626,2633],{"mathvariant":1759},[898,99628,900],{},[902,99630,99631],{"encoding":904},"\\Delta U",[883,99633,99635],{"className":99634},[886],[888,99636,99637],{"xmlns":890},[892,99638,99639,99659],{},[895,99640,99641,99643,99649,99651,99653],{},[898,99642,2364],{"mathvariant":1759},[1743,99644,99645,99647],{},[898,99646,1688],{},[2505,99648,2507],{},[1708,99650,1883],{"separator":1882},[898,99652,2364],{"mathvariant":1759},[1743,99654,99655,99657],{},[898,99656,1688],{},[2505,99658,3132],{},[902,99660,99661],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,99664,99665],{},"totálního diferenciálu",[883,99667,99669],{"className":99668},[886],[888,99670,99671],{"xmlns":890,"display":2210},[892,99672,99673,99774],{},[2214,99674,99675],{"width":2216},[2218,99676,99677,99679,99767,99769],{},[2221,99678],{"width":2223},[2221,99680,99681],{},[895,99682,99683,99685,99687,99689,99691,99693,99695,99703,99705,99711,99713,99721,99723,99729,99731,99733,99739,99741,99747,99749,99751,99757,99759,99765],{},[898,99684,2633],{"mathvariant":1759},[898,99686,900],{},[1708,99688,2638],{},[898,99690,2364],{"mathvariant":1759},[898,99692,900],{},[1708,99694,1710],{},[4754,99696,99697,99699,99701],{},[898,99698,900],{},[2505,99700,2507],{},[1708,99702,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[898,99704,2364],{"mathvariant":1759},[1743,99706,99707,99709],{},[898,99708,1688],{},[2505,99710,2507],{},[1708,99712,2019],{},[4754,99714,99715,99717,99719],{},[898,99716,900],{},[2505,99718,3132],{},[1708,99720,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[898,99722,2364],{"mathvariant":1759},[1743,99724,99725,99727],{},[898,99726,1688],{},[2505,99728,3132],{},[1708,99730,1710],{},[898,99732,1741],{},[1743,99734,99735,99737],{},[898,99736,900],{},[2505,99738,2507],{},[898,99740,2364],{"mathvariant":1759},[1743,99742,99743,99745],{},[898,99744,1688],{},[2505,99746,2507],{},[1708,99748,2019],{},[898,99750,1741],{},[1743,99752,99753,99755],{},[898,99754,900],{},[2505,99756,3132],{},[898,99758,2364],{"mathvariant":1759},[1743,99760,99761,99763],{},[898,99762,1688],{},[2505,99764,3132],{},[898,99766,2155],{"mathvariant":1759},[2221,99768],{"width":2223},[2221,99770,99771],{},[2247,99772,99773],{},"(6.3)",[902,99775,99776],{"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}",[724,99778,2694,99779,2155],{},[883,99780,99782],{"className":99781},[886],[888,99783,99784],{"xmlns":890},[892,99785,99786,99856],{},[895,99787,99788,99790,99792,99794,99796,99798,99804,99806,99808,99814,99816,99822,99824,99826,99832,99834,99836,99838,99840,99846,99848,99854],{},[898,99789,2633],{"mathvariant":1759},[898,99791,900],{},[1708,99793,1710],{},[898,99795,900],{},[1708,99797,1716],{"stretchy":1715},[1743,99799,99800,99802],{},[898,99801,1688],{},[2505,99803,2507],{},[1708,99805,2019],{},[898,99807,2364],{"mathvariant":1759},[1743,99809,99810,99812],{},[898,99811,1688],{},[2505,99813,2507],{},[1708,99815,1883],{"separator":1882},[1743,99817,99818,99820],{},[898,99819,1688],{},[2505,99821,3132],{},[1708,99823,2019],{},[898,99825,2364],{"mathvariant":1759},[1743,99827,99828,99830],{},[898,99829,1688],{},[2505,99831,3132],{},[1708,99833,1721],{"stretchy":1715},[1708,99835,2726],{},[898,99837,900],{},[1708,99839,1716],{"stretchy":1715},[1743,99841,99842,99844],{},[898,99843,1688],{},[2505,99845,2507],{},[1708,99847,1883],{"separator":1882},[1743,99849,99850,99852],{},[898,99851,1688],{},[2505,99853,3132],{},[1708,99855,1721],{"stretchy":1715},[902,99857,99858],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,99860,99862],{"id":99861},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,99864,99865,99866,99869,99870,99873],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,99867,99868],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,99871,99872],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,99875,99876,99879,99880,53646,99906,99932,99933,1343,99965,99997,99998,1771,100052,100106],{},[38,99877,99878],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,99881,99883],{"className":99882},[886],[888,99884,99885],{"xmlns":890},[892,99886,99887,99903],{},[895,99888,99889,99895,99897],{},[1743,99890,99891,99893],{},[898,99892,1688],{},[2505,99894,3132],{},[1708,99896,1710],{},[1743,99898,99899,99901],{},[898,99900,207],{},[2505,99902,2784],{},[902,99904,99905],{"encoding":904},"Q_2 = a_0",[883,99907,99909],{"className":99908},[886],[888,99910,99911],{"xmlns":890},[892,99912,99913,99929],{},[895,99914,99915,99921,99923],{},[1743,99916,99917,99919],{},[898,99918,1688],{},[2505,99920,2507],{},[1708,99922,1710],{},[1743,99924,99925,99927],{},[898,99926,1923],{},[2505,99928,2784],{},[902,99930,99931],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,99934,99936],{"className":99935},[886],[888,99937,99938],{"xmlns":890},[892,99939,99940,99962],{},[895,99941,99942,99944,99946,99952,99954,99960],{},[898,99943,900],{},[1708,99945,1716],{"stretchy":1715},[1743,99947,99948,99950],{},[898,99949,1688],{},[2505,99951,2507],{},[1708,99953,1883],{"separator":1882},[1743,99955,99956,99958],{},[898,99957,207],{},[2505,99959,2784],{},[1708,99961,1721],{"stretchy":1715},[902,99963,99964],{"encoding":904},"U(Q_1, a_0)",[883,99966,99968],{"className":99967},[886],[888,99969,99970],{"xmlns":890},[892,99971,99972,99994],{},[895,99973,99974,99976,99978,99984,99986,99992],{},[898,99975,900],{},[1708,99977,1716],{"stretchy":1715},[1743,99979,99980,99982],{},[898,99981,1923],{},[2505,99983,2784],{},[1708,99985,1883],{"separator":1882},[1743,99987,99988,99990],{},[898,99989,1688],{},[2505,99991,3132],{},[1708,99993,1721],{"stretchy":1715},[902,99995,99996],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,99999,100001],{"className":100000},[886],[888,100002,100003],{"xmlns":890},[892,100004,100005,100049],{},[895,100006,100007,100045,100047],{},[3194,100008,100009],{"scriptlevel":2784,"displaystyle":1882},[2358,100010,100011,100035],{},[895,100012,100013,100015,100017,100019,100025,100027,100033],{},[898,100014,2364],{"mathvariant":1759},[898,100016,900],{},[1708,100018,1716],{"stretchy":1715},[1743,100020,100021,100023],{},[898,100022,1688],{},[2505,100024,2507],{},[1708,100026,1883],{"separator":1882},[1743,100028,100029,100031],{},[898,100030,207],{},[2505,100032,2784],{},[1708,100034,1721],{"stretchy":1715},[895,100036,100037,100039],{},[898,100038,2364],{"mathvariant":1759},[1743,100040,100041,100043],{},[898,100042,1688],{},[2505,100044,2507],{},[1708,100046,2854],{},[2505,100048,2784],{},[902,100050,100051],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,100053,100055],{"className":100054},[886],[888,100056,100057],{"xmlns":890},[892,100058,100059,100103],{},[895,100060,100061,100099,100101],{},[3194,100062,100063],{"scriptlevel":2784,"displaystyle":1882},[2358,100064,100065,100089],{},[895,100066,100067,100069,100071,100073,100079,100081,100087],{},[898,100068,2364],{"mathvariant":1759},[898,100070,900],{},[1708,100072,1716],{"stretchy":1715},[1743,100074,100075,100077],{},[898,100076,1923],{},[2505,100078,2784],{},[1708,100080,1883],{"separator":1882},[1743,100082,100083,100085],{},[898,100084,1688],{},[2505,100086,3132],{},[1708,100088,1721],{"stretchy":1715},[895,100090,100091,100093],{},[898,100092,2364],{"mathvariant":1759},[1743,100094,100095,100097],{},[898,100096,1688],{},[2505,100098,3132],{},[1708,100100,2854],{},[2505,100102,2784],{},[902,100104,100105],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,100108,100110],{"className":100109},[886],[888,100111,100112],{"xmlns":890,"display":2210},[892,100113,100114,100159],{},[2214,100115,100116],{"width":2216},[2218,100117,100118,100120,100152,100154],{},[2221,100119],{"width":2223},[2221,100121,100122],{},[895,100123,100124,100132,100134,100136,100138,100140,100148,100150],{},[4754,100125,100126,100128,100130],{},[898,100127,900],{},[2505,100129,2507],{},[1708,100131,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,100133,2854],{},[2505,100135,2784],{},[1708,100137,1883],{"separator":1882},[3213,100139],{"width":4750},[4754,100141,100142,100144,100146],{},[898,100143,900],{},[2505,100145,3132],{},[1708,100147,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,100149,2854],{},[2505,100151,24346],{},[2221,100153],{"width":2223},[2221,100155,100156],{},[2247,100157,100158],{},"(6.4)",[902,100160,100161],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,100163,100164,100165,100167],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,100166,64496],{}," — užitečnost roste s množstvím každého zboží.",[724,100169,100170,100173,100174,100204,100205,2788],{},[38,100171,100172],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,100175,100177],{"className":100176},[886],[888,100178,100179],{"xmlns":890},[892,100180,100181,100201],{},[895,100182,100183,100191,100193],{},[4754,100184,100185,100187,100189],{},[898,100186,900],{},[2505,100188,2507],{},[1708,100190,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,100192,1883],{"separator":1882},[4754,100194,100195,100197,100199],{},[898,100196,900],{},[2505,100198,3132],{},[1708,100200,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,100202,100203],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,100206,100207],{},"záporné",[883,100209,100211],{"className":100210},[886],[888,100212,100213],{"xmlns":890,"display":2210},[892,100214,100215,100268],{},[2214,100216,100217],{"width":2216},[2218,100218,100219,100221,100261,100263],{},[2221,100220],{"width":2223},[2221,100222,100223],{},[895,100224,100225,100237,100239,100241,100243,100245,100257,100259],{},[4754,100226,100227,100229,100231],{},[898,100228,900],{},[2505,100230,14868],{},[895,100232,100233,100235],{},[1708,100234,1761],{"mathvariant":1759},[1708,100236,1761],{"mathvariant":1759},[1708,100238,2932],{},[2505,100240,2784],{},[1708,100242,1883],{"separator":1882},[3213,100244],{"width":4750},[4754,100246,100247,100249,100251],{},[898,100248,900],{},[2505,100250,44390],{},[895,100252,100253,100255],{},[1708,100254,1761],{"mathvariant":1759},[1708,100256,1761],{"mathvariant":1759},[1708,100258,2932],{},[2505,100260,24346],{},[2221,100262],{"width":2223},[2221,100264,100265],{},[2247,100266,100267],{},"(6.5)",[902,100269,100270],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,100272,100273,100274,100277,100278,2155],{},"Podmínka (6.5) je známa jako ",[38,100275,100276],{},"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 ",[207,100279,100281],{"className":100280,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,100283,100284,100285,1771,100317,100349,100350,1771,100376,100402,100403,100431,100432,1771,100434,100436,100437,100472],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,100286,100288],{"className":100287},[886],[888,100289,100290],{"xmlns":890},[892,100291,100292,100314],{},[895,100293,100294,100296,100298,100304,100306,100312],{},[898,100295,900],{},[1708,100297,1716],{"stretchy":1715},[1743,100299,100300,100302],{},[898,100301,1688],{},[2505,100303,2507],{},[1708,100305,1883],{"separator":1882},[1743,100307,100308,100310],{},[898,100309,1923],{},[2505,100311,2784],{},[1708,100313,1721],{"stretchy":1715},[902,100315,100316],{"encoding":904},"U(Q_1, b_0)",[883,100318,100320],{"className":100319},[886],[888,100321,100322],{"xmlns":890},[892,100323,100324,100346],{},[895,100325,100326,100328,100330,100336,100338,100344],{},[898,100327,900],{},[1708,100329,1716],{"stretchy":1715},[1743,100331,100332,100334],{},[898,100333,207],{},[2505,100335,2784],{},[1708,100337,1883],{"separator":1882},[1743,100339,100340,100342],{},[898,100341,1688],{},[2505,100343,3132],{},[1708,100345,1721],{"stretchy":1715},[902,100347,100348],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,100351,100353],{"className":100352},[886],[888,100354,100355],{"xmlns":890},[892,100356,100357,100373],{},[895,100358,100359,100361,100363,100365,100371],{},[1708,100360,1716],{"stretchy":1715},[898,100362,900],{},[1708,100364,1883],{"separator":1882},[1743,100366,100367,100369],{},[898,100368,1688],{},[2505,100370,2507],{},[1708,100372,1721],{"stretchy":1715},[902,100374,100375],{"encoding":904},"(U, Q_1)",[883,100377,100379],{"className":100378},[886],[888,100380,100381],{"xmlns":890},[892,100382,100383,100399],{},[895,100384,100385,100387,100389,100391,100397],{},[1708,100386,1716],{"stretchy":1715},[898,100388,900],{},[1708,100390,1883],{"separator":1882},[1743,100392,100393,100395],{},[898,100394,1688],{},[2505,100396,3132],{},[1708,100398,1721],{"stretchy":1715},[902,100400,100401],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,100404,100406],{"className":100405},[886],[888,100407,100408],{"xmlns":890},[892,100409,100410,100428],{},[895,100411,100412,100414,100416,100418,100420,100422,100424,100426],{},[898,100413,900],{},[1708,100415,1716],{"stretchy":1715},[2505,100417,2784],{},[1708,100419,1883],{"separator":1882},[2505,100421,2784],{},[1708,100423,1721],{"stretchy":1715},[1708,100425,1710],{},[2505,100427,2784],{},[902,100429,100430],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,100433,2082],{},[38,100435,2940],{},". Typický tvar grafu ",[883,100438,100440],{"className":100439},[886],[888,100441,100442],{"xmlns":890},[892,100443,100444,100470],{},[895,100445,100446,100448,100450,100452,100454,100460,100462,100468],{},[898,100447,900],{},[1708,100449,1710],{},[898,100451,900],{},[1708,100453,1716],{"stretchy":1715},[1743,100455,100456,100458],{},[898,100457,1688],{},[2505,100459,2507],{},[1708,100461,1883],{"separator":1882},[1743,100463,100464,100466],{},[898,100465,1688],{},[2505,100467,3132],{},[1708,100469,1721],{"stretchy":1715},[902,100471,98486],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,100474,100475],{},[614,100476,100477,100478,99518,100506,100527,100528,99518,100556,100578],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,100479,100481],{"className":100480},[886],[888,100482,100483],{"xmlns":890},[892,100484,100485,100503],{},[895,100486,100487,100489,100491,100497,100499,100501],{},[898,100488,900],{},[1708,100490,1716],{"stretchy":1715},[1743,100492,100493,100495],{},[898,100494,1688],{},[2505,100496,2507],{},[1708,100498,1883],{"separator":1882},[898,100500,1923],{},[1708,100502,1721],{"stretchy":1715},[902,100504,100505],{"encoding":904},"U(Q_1, b)",[883,100507,100509],{"className":100508},[886],[888,100510,100511],{"xmlns":890},[892,100512,100513,100525],{},[895,100514,100515,100521,100523],{},[1743,100516,100517,100519],{},[898,100518,1688],{},[2505,100520,3132],{},[1708,100522,1710],{},[898,100524,1923],{},[902,100526,99540],{"encoding":904}," (vlevo) a ",[883,100529,100531],{"className":100530},[886],[888,100532,100533],{"xmlns":890},[892,100534,100535,100553],{},[895,100536,100537,100539,100541,100543,100545,100551],{},[898,100538,900],{},[1708,100540,1716],{"stretchy":1715},[898,100542,207],{},[1708,100544,1883],{"separator":1882},[1743,100546,100547,100549],{},[898,100548,1688],{},[2505,100550,3132],{},[1708,100552,1721],{"stretchy":1715},[902,100554,100555],{"encoding":904},"U(a, Q_2)",[883,100557,100559],{"className":100558},[886],[888,100560,100561],{"xmlns":890},[892,100562,100563,100575],{},[895,100564,100565,100571,100573],{},[1743,100566,100567,100569],{},[898,100568,1688],{},[2505,100570,2507],{},[1708,100572,1710],{},[898,100574,207],{},[902,100576,100577],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,100580,100581],{},[614,100582,100583,100584,100619,100620,100650,100651,1771,100674,100696,100697,2155],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,100585,100587],{"className":100586},[886],[888,100588,100589],{"xmlns":890},[892,100590,100591,100617],{},[895,100592,100593,100595,100597,100599,100601,100607,100609,100615],{},[898,100594,900],{},[1708,100596,1710],{},[898,100598,900],{},[1708,100600,1716],{"stretchy":1715},[1743,100602,100603,100605],{},[898,100604,1688],{},[2505,100606,2507],{},[1708,100608,1883],{"separator":1882},[1743,100610,100611,100613],{},[898,100612,1688],{},[2505,100614,3132],{},[1708,100616,1721],{"stretchy":1715},[902,100618,98486],{"encoding":904}," nad rovinou ",[883,100621,100623],{"className":100622},[886],[888,100624,100625],{"xmlns":890},[892,100626,100627,100647],{},[895,100628,100629,100631,100637,100639,100645],{},[1708,100630,1716],{"stretchy":1715},[1743,100632,100633,100635],{},[898,100634,1688],{},[2505,100636,2507],{},[1708,100638,1883],{"separator":1882},[1743,100640,100641,100643],{},[898,100642,1688],{},[2505,100644,3132],{},[1708,100646,1721],{"stretchy":1715},[902,100648,100649],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,100652,100654],{"className":100653},[886],[888,100655,100656],{"xmlns":890},[892,100657,100658,100671],{},[895,100659,100660,100666,100668],{},[1743,100661,100662,100664],{},[898,100663,1688],{},[2505,100665,2507],{},[1708,100667,1710],{},[2247,100669,100670],{},"const",[902,100672,100673],{"encoding":904},"Q_1 = \\text{const}",[883,100675,100677],{"className":100676},[886],[888,100678,100679],{"xmlns":890},[892,100680,100681,100693],{},[895,100682,100683,100689,100691],{},[1743,100684,100685,100687],{},[898,100686,1688],{},[2505,100688,3132],{},[1708,100690,1710],{},[2247,100692,100670],{},[902,100694,100695],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,100698,100700],{"className":100699},[886],[888,100701,100702],{"xmlns":890},[892,100703,100704,100730],{},[895,100705,100706,100708,100710,100716,100718,100724,100726,100728],{},[898,100707,900],{},[1708,100709,1716],{"stretchy":1715},[1743,100711,100712,100714],{},[898,100713,1688],{},[2505,100715,2507],{},[1708,100717,1883],{"separator":1882},[1743,100719,100720,100722],{},[898,100721,1688],{},[2505,100723,3132],{},[1708,100725,1721],{"stretchy":1715},[1708,100727,1710],{},[898,100729,14142],{},[902,100731,21671],{"encoding":904},[198,100733,100735,100736],{"id":100734},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,100737,100739],{"className":100738},[886],[888,100740,100741],{"xmlns":890},[892,100742,100743,100777],{},[895,100744,100745,100747,100749,100763],{},[898,100746,900],{},[1708,100748,1710],{},[4754,100750,100751,100753,100755],{},[898,100752,1688],{},[2505,100754,2507],{},[895,100756,100757,100759,100761],{},[2505,100758,2507],{},[898,100760,1799],{"mathvariant":1759},[2505,100762,3132],{},[4754,100764,100765,100767,100769],{},[898,100766,1688],{},[2505,100768,3132],{},[895,100770,100771,100773,100775],{},[2505,100772,2507],{},[898,100774,1799],{"mathvariant":1759},[2505,100776,3121],{},[902,100778,100779],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,100781,100782],{},[38,100783,100784],{},"Ověření (6.4) a (6.5).",[883,100786,100788],{"className":100787},[886],[888,100789,100790],{"xmlns":890,"display":2210},[892,100791,100792,100896],{},[895,100793,100794,100802,100804,100812,100828,100842,100844,100846,100854,100856,100864,100878,100894],{},[4754,100795,100796,100798,100800],{},[898,100797,900],{},[2505,100799,2507],{},[1708,100801,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,100803,1710],{},[3194,100805,100806],{"scriptlevel":2784,"displaystyle":1715},[2358,100807,100808,100810],{},[2505,100809,2507],{},[2505,100811,3132],{},[4754,100813,100814,100816,100818],{},[898,100815,1688],{},[2505,100817,2507],{},[895,100819,100820,100822,100824,100826],{},[1708,100821,2726],{},[2505,100823,2507],{},[898,100825,1799],{"mathvariant":1759},[2505,100827,3132],{},[4754,100829,100830,100832,100834],{},[898,100831,1688],{},[2505,100833,3132],{},[895,100835,100836,100838,100840],{},[2505,100837,2507],{},[898,100839,1799],{"mathvariant":1759},[2505,100841,3121],{},[1708,100843,1883],{"separator":1882},[3213,100845],{"width":4750},[4754,100847,100848,100850,100852],{},[898,100849,900],{},[2505,100851,3132],{},[1708,100853,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,100855,1710],{},[3194,100857,100858],{"scriptlevel":2784,"displaystyle":1715},[2358,100859,100860,100862],{},[2505,100861,2507],{},[2505,100863,3121],{},[4754,100865,100866,100868,100870],{},[898,100867,1688],{},[2505,100869,2507],{},[895,100871,100872,100874,100876],{},[2505,100873,2507],{},[898,100875,1799],{"mathvariant":1759},[2505,100877,3132],{},[4754,100879,100880,100882,100884],{},[898,100881,1688],{},[2505,100883,3132],{},[895,100885,100886,100888,100890,100892],{},[1708,100887,2726],{},[2505,100889,3132],{},[898,100891,1799],{"mathvariant":1759},[2505,100893,3121],{},[1708,100895,1883],{"separator":1882},[902,100897,100898],{"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},",[724,100900,100901,100902,100936],{},"zřejmě ",[883,100903,100905],{"className":100904},[886],[888,100906,100907],{"xmlns":890},[892,100908,100909,100933],{},[895,100910,100911,100919,100921,100929,100931],{},[4754,100912,100913,100915,100917],{},[898,100914,900],{},[2505,100916,2507],{},[1708,100918,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,100920,1883],{"separator":1882},[4754,100922,100923,100925,100927],{},[898,100924,900],{},[2505,100926,3132],{},[1708,100928,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,100930,2854],{},[2505,100932,2784],{},[902,100934,100935],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,100938,100940],{"className":100939},[886],[888,100941,100942],{"xmlns":890,"display":2210},[892,100943,100944,101060],{},[895,100945,100946,100958,100960,100962,100970,100986,101000,101002,101004,101016,101018,101020,101028,101042,101058],{},[4754,100947,100948,100950,100952],{},[898,100949,900],{},[2505,100951,14868],{},[895,100953,100954,100956],{},[1708,100955,1761],{"mathvariant":1759},[1708,100957,1761],{"mathvariant":1759},[1708,100959,1710],{},[1708,100961,2726],{},[3194,100963,100964],{"scriptlevel":2784,"displaystyle":1715},[2358,100965,100966,100968],{},[2505,100967,2507],{},[2505,100969,5867],{},[4754,100971,100972,100974,100976],{},[898,100973,1688],{},[2505,100975,2507],{},[895,100977,100978,100980,100982,100984],{},[1708,100979,2726],{},[2505,100981,3121],{},[898,100983,1799],{"mathvariant":1759},[2505,100985,3132],{},[4754,100987,100988,100990,100992],{},[898,100989,1688],{},[2505,100991,3132],{},[895,100993,100994,100996,100998],{},[2505,100995,2507],{},[898,100997,1799],{"mathvariant":1759},[2505,100999,3121],{},[1708,101001,1883],{"separator":1882},[3213,101003],{"width":4750},[4754,101005,101006,101008,101010],{},[898,101007,900],{},[2505,101009,44390],{},[895,101011,101012,101014],{},[1708,101013,1761],{"mathvariant":1759},[1708,101015,1761],{"mathvariant":1759},[1708,101017,1710],{},[1708,101019,2726],{},[3194,101021,101022],{"scriptlevel":2784,"displaystyle":1715},[2358,101023,101024,101026],{},[2505,101025,3132],{},[2505,101027,4635],{},[4754,101029,101030,101032,101034],{},[898,101031,1688],{},[2505,101033,2507],{},[895,101035,101036,101038,101040],{},[2505,101037,2507],{},[898,101039,1799],{"mathvariant":1759},[2505,101041,3132],{},[4754,101043,101044,101046,101048],{},[898,101045,1688],{},[2505,101047,3132],{},[895,101049,101050,101052,101054,101056],{},[1708,101051,2726],{},[2505,101053,3993],{},[898,101055,1799],{"mathvariant":1759},[2505,101057,3121],{},[1708,101059,1883],{"separator":1882},[902,101061,101062],{"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},",[724,101064,101065,101066,101108],{},"opět ",[883,101067,101069],{"className":101068},[886],[888,101070,101071],{"xmlns":890},[892,101072,101073,101105],{},[895,101074,101075,101087,101089,101101,101103],{},[4754,101076,101077,101079,101081],{},[898,101078,900],{},[2505,101080,14868],{},[895,101082,101083,101085],{},[1708,101084,1761],{"mathvariant":1759},[1708,101086,1761],{"mathvariant":1759},[1708,101088,1883],{"separator":1882},[4754,101090,101091,101093,101095],{},[898,101092,900],{},[2505,101094,44390],{},[895,101096,101097,101099],{},[1708,101098,1761],{"mathvariant":1759},[1708,101100,1761],{"mathvariant":1759},[1708,101102,2932],{},[2505,101104,2784],{},[902,101106,101107],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,101110,101111],{},[38,101112,101113,101114,2155],{},"(a) Mezní užitečnosti v bodě ",[883,101115,101117],{"className":101116},[886],[888,101118,101119],{"xmlns":890},[892,101120,101121,101133],{},[895,101122,101123,101125,101127,101129,101131],{},[1708,101124,6940],{"stretchy":1715},[2505,101126,9238],{},[1708,101128,1883],{"separator":1882},[2505,101130,20288],{},[1708,101132,6981],{"stretchy":1715},[902,101134,101135],{"encoding":904},"[100, 200]",[883,101137,101139],{"className":101138},[886],[888,101140,101141],{"xmlns":890,"display":2210},[892,101142,101143,101210],{},[895,101144,101145,101147,101153,101155,101157,101159,101161,101163,101165,101173,101175,101189,101191,101203,101205,101208],{},[898,101146,1741],{},[1743,101148,101149,101151],{},[898,101150,900],{},[2505,101152,2507],{},[1708,101154,1716],{"stretchy":1715},[2505,101156,9238],{},[1708,101158,1883],{"separator":1882},[2505,101160,20288],{},[1708,101162,1721],{"stretchy":1715},[1708,101164,1710],{},[3194,101166,101167],{"scriptlevel":2784,"displaystyle":1715},[2358,101168,101169,101171],{},[2505,101170,2507],{},[2505,101172,3132],{},[1708,101174,3703],{},[1753,101176,101177,101179],{},[2505,101178,9238],{},[895,101180,101181,101183,101185,101187],{},[1708,101182,2726],{},[2505,101184,2507],{},[898,101186,1799],{"mathvariant":1759},[2505,101188,3132],{},[1708,101190,3703],{},[1753,101192,101193,101195],{},[2505,101194,20288],{},[895,101196,101197,101199,101201],{},[2505,101198,2507],{},[898,101200,1799],{"mathvariant":1759},[2505,101202,3121],{},[1708,101204,17816],{},[2505,101206,101207],{},"0,4204",[1708,101209,1883],{"separator":1882},[902,101211,101212],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,101214,101216],{"className":101215},[886],[888,101217,101218],{"xmlns":890,"display":2210},[892,101219,101220,101285],{},[895,101221,101222,101224,101230,101232,101234,101236,101238,101240,101242,101250,101252,101264,101266,101280,101282],{},[898,101223,1741],{},[1743,101225,101226,101228],{},[898,101227,900],{},[2505,101229,3132],{},[1708,101231,1716],{"stretchy":1715},[2505,101233,9238],{},[1708,101235,1883],{"separator":1882},[2505,101237,20288],{},[1708,101239,1721],{"stretchy":1715},[1708,101241,1710],{},[3194,101243,101244],{"scriptlevel":2784,"displaystyle":1715},[2358,101245,101246,101248],{},[2505,101247,2507],{},[2505,101249,3121],{},[1708,101251,3703],{},[1753,101253,101254,101256],{},[2505,101255,9238],{},[895,101257,101258,101260,101262],{},[2505,101259,2507],{},[898,101261,1799],{"mathvariant":1759},[2505,101263,3132],{},[1708,101265,3703],{},[1753,101267,101268,101270],{},[2505,101269,20288],{},[895,101271,101272,101274,101276,101278],{},[1708,101273,2726],{},[2505,101275,3132],{},[898,101277,1799],{"mathvariant":1759},[2505,101279,3121],{},[1708,101281,17816],{},[2505,101283,101284],{},"0,63067.",[902,101286,101287],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,101289,101290,1729,101292,101327,101328,101349,101350,101367],{},[614,101291,8418],{},[883,101293,101295],{"className":101294},[886],[888,101296,101297],{"xmlns":890},[892,101298,101299,101324],{},[895,101300,101301,101303,101309,101311,101313,101315,101317,101319,101321],{},[898,101302,1741],{},[1743,101304,101305,101307],{},[898,101306,900],{},[2505,101308,3132],{},[1708,101310,1716],{"stretchy":1715},[2505,101312,9238],{},[1708,101314,1883],{"separator":1882},[2505,101316,20288],{},[1708,101318,1721],{"stretchy":1715},[1708,101320,17816],{},[2505,101322,101323],{},"0,63067",[902,101325,101326],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,101329,101331],{"className":101330},[886],[888,101332,101333],{"xmlns":890},[892,101334,101335,101347],{},[895,101336,101337,101339,101341,101343,101345],{},[1708,101338,6940],{"stretchy":1715},[2505,101340,9238],{},[1708,101342,1883],{"separator":1882},[2505,101344,20288],{},[1708,101346,6981],{"stretchy":1715},[902,101348,101135],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,101351,101353],{"className":101352},[886],[888,101354,101355],{"xmlns":890},[892,101356,101357,101365],{},[895,101358,101359],{},[1743,101360,101361,101363],{},[898,101362,1688],{},[2505,101364,3132],{},[902,101366,40868],{"encoding":904}," přibližně o 0,63067.",[724,101369,101370,101389,101390,51018,101411,101428,101429,101455,101456,101473,101474,2750],{},[38,101371,101372,101373,101388],{},"(b) Odhad změny ",[883,101374,101376],{"className":101375},[886],[888,101377,101378],{"xmlns":890},[892,101379,101380,101386],{},[895,101381,101382,101384],{},[898,101383,2633],{"mathvariant":1759},[898,101385,900],{},[902,101387,99631],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,101391,101393],{"className":101392},[886],[888,101394,101395],{"xmlns":890},[892,101396,101397,101409],{},[895,101398,101399,101401,101403,101405,101407],{},[1708,101400,6940],{"stretchy":1715},[2505,101402,9238],{},[1708,101404,1883],{"separator":1882},[2505,101406,20288],{},[1708,101408,6981],{"stretchy":1715},[902,101410,101135],{"encoding":904},[883,101412,101414],{"className":101413},[886],[888,101415,101416],{"xmlns":890},[892,101417,101418,101426],{},[895,101419,101420],{},[1743,101421,101422,101424],{},[898,101423,1688],{},[2505,101425,2507],{},[902,101427,40849],{"encoding":904}," na 98 (tj. ",[883,101430,101432],{"className":101431},[886],[888,101433,101434],{"xmlns":890},[892,101435,101436,101452],{},[895,101437,101438,101440,101446,101448,101450],{},[898,101439,2364],{"mathvariant":1759},[1743,101441,101442,101444],{},[898,101443,1688],{},[2505,101445,2507],{},[1708,101447,1710],{},[1708,101449,2726],{},[2505,101451,3132],{},[902,101453,101454],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,101457,101459],{"className":101458},[886],[888,101460,101461],{"xmlns":890},[892,101462,101463,101471],{},[895,101464,101465],{},[1743,101466,101467,101469],{},[898,101468,1688],{},[2505,101470,3132],{},[902,101472,40868],{"encoding":904}," o 3 (tj. ",[883,101475,101477],{"className":101476},[886],[888,101478,101479],{"xmlns":890},[892,101480,101481,101495],{},[895,101482,101483,101485,101491,101493],{},[898,101484,2364],{"mathvariant":1759},[1743,101486,101487,101489],{},[898,101488,1688],{},[2505,101490,3132],{},[1708,101492,1710],{},[2505,101494,3121],{},[902,101496,101497],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,101499,101501],{"className":101500},[886],[888,101502,101503],{"xmlns":890,"display":2210},[892,101504,101505,101556],{},[895,101506,101507,101509,101511,101513,101515,101517,101519,101521,101523,101525,101527,101529,101531,101533,101535,101537,101539,101541,101543,101546,101548,101551,101553],{},[898,101508,2633],{"mathvariant":1759},[898,101510,900],{},[1708,101512,2638],{},[898,101514,2364],{"mathvariant":1759},[898,101516,900],{},[1708,101518,1710],{},[2505,101520,101207],{},[1708,101522,3703],{},[1708,101524,1716],{"stretchy":1715},[1708,101526,2726],{},[2505,101528,3132],{},[1708,101530,1721],{"stretchy":1715},[1708,101532,2019],{},[2505,101534,101323],{},[1708,101536,3703],{},[2505,101538,3121],{},[1708,101540,1710],{},[1708,101542,2726],{},[2505,101544,101545],{},"0,8408",[1708,101547,2019],{},[2505,101549,101550],{},"1,89201",[1708,101552,17816],{},[2505,101554,101555],{},"1,05.",[902,101557,101558],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,101560,101561,101562,101565,101566,101617,101618,2155],{},"Užitečnost se tedy zvýší přibližně o ",[38,101563,101564],{},"1,05",". Skutečná změna je ",[883,101567,101569],{"className":101568},[886],[888,101570,101571],{"xmlns":890},[892,101572,101573,101614],{},[895,101574,101575,101577,101579,101581,101583,101585,101588,101590,101593,101595,101597,101599,101601,101603,101605,101607,101609,101611],{},[898,101576,2633],{"mathvariant":1759},[898,101578,900],{},[1708,101580,1710],{},[898,101582,900],{},[1708,101584,1716],{"stretchy":1715},[2505,101586,101587],{},"98",[1708,101589,1883],{"separator":1882},[2505,101591,101592],{},"203",[1708,101594,1721],{"stretchy":1715},[1708,101596,2726],{},[898,101598,900],{},[1708,101600,1716],{"stretchy":1715},[2505,101602,9238],{},[1708,101604,1883],{"separator":1882},[2505,101606,20288],{},[1708,101608,1721],{"stretchy":1715},[1708,101610,17816],{},[2505,101612,101613],{},"1,031",[902,101615,101616],{"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 ",[883,101619,101621],{"className":101620},[886],[888,101622,101623],{"xmlns":890},[892,101624,101625,101645],{},[895,101626,101627,101629,101635,101637,101639],{},[898,101628,2364],{"mathvariant":1759},[1743,101630,101631,101633],{},[898,101632,1688],{},[2505,101634,2507],{},[1708,101636,1883],{"separator":1882},[898,101638,2364],{"mathvariant":1759},[1743,101640,101641,101643],{},[898,101642,1688],{},[2505,101644,3132],{},[902,101646,99661],{"encoding":904},[115,101648,101650],{"id":101649},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,101652,101653],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,101655,101657],{"className":101656},[886],[888,101658,101659],{"xmlns":890,"display":2210},[892,101660,101661,101720],{},[2214,101662,101663],{"width":2216},[2218,101664,101665,101667,101713,101715],{},[2221,101666],{"width":2223},[2221,101668,101669],{},[895,101670,101671,101673,101675,101681,101683,101689,101691,101693,101701,101703,101711],{},[898,101672,900],{},[1708,101674,1716],{"stretchy":1715},[1743,101676,101677,101679],{},[898,101678,1688],{},[2505,101680,2507],{},[1708,101682,1883],{"separator":1882},[1743,101684,101685,101687],{},[898,101686,1688],{},[2505,101688,3132],{},[1708,101690,1721],{"stretchy":1715},[1708,101692,1710],{},[4754,101694,101695,101697,101699],{},[898,101696,1688],{},[2505,101698,2507],{},[898,101700,207],{},[1708,101702,3703],{},[4754,101704,101705,101707,101709],{},[898,101706,1688],{},[2505,101708,3132],{},[898,101710,1923],{},[1708,101712,1883],{"separator":1882},[2221,101714],{"width":2223},[2221,101716,101717],{},[2247,101718,101719],{},"(6.6)",[902,101721,101722],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,101724,5411,101725,101743,101744,101746,101747,101751,101752,101782,101783,101805],{},[883,101726,101728],{"className":101727},[886],[888,101729,101730],{"xmlns":890},[892,101731,101732,101740],{},[895,101733,101734,101736,101738],{},[898,101735,207],{},[1708,101737,1883],{"separator":1882},[898,101739,1923],{},[902,101741,101742],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,101745,1894],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,101748,101750],{"className":101749,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,101753,101755],{"className":101754},[886],[888,101756,101757],{"xmlns":890},[892,101758,101759,101779],{},[895,101760,101761,101763,101765,101767,101769,101771,101773,101775,101777],{},[898,101762,207],{},[1708,101764,1883],{"separator":1882},[898,101766,1923],{},[1708,101768,18420],{},[1708,101770,1716],{"stretchy":1715},[2505,101772,2784],{},[1708,101774,1883],{"separator":1882},[2505,101776,2507],{},[1708,101778,1721],{"stretchy":1715},[902,101780,101781],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,101784,101786],{"className":101785},[886],[888,101787,101788],{"xmlns":890},[892,101789,101790,101802],{},[895,101791,101792,101794,101796,101798,101800],{},[898,101793,1923],{},[1708,101795,1710],{},[2505,101797,2507],{},[1708,101799,2726],{},[898,101801,207],{},[902,101803,101804],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,101807,101808],{},[3372,101809],{"alt":101810,"className":101811,"src":101812},"imek-cobb-douglas-3d-plus-ic",[210,3376],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,101814,101816],{"className":101815},[886],[888,101817,101818],{"xmlns":890,"display":2210},[892,101819,101820,101870],{},[895,101821,101822,101824,101826,101832,101834,101840,101842,101844,101852,101854,101868],{},[898,101823,900],{},[1708,101825,1716],{"stretchy":1715},[1743,101827,101828,101830],{},[898,101829,1688],{},[2505,101831,2507],{},[1708,101833,1883],{"separator":1882},[1743,101835,101836,101838],{},[898,101837,1688],{},[2505,101839,3132],{},[1708,101841,1721],{"stretchy":1715},[1708,101843,1710],{},[4754,101845,101846,101848,101850],{},[898,101847,1688],{},[2505,101849,2507],{},[898,101851,207],{},[1708,101853,3703],{},[4754,101855,101856,101858,101860],{},[898,101857,1688],{},[2505,101859,3132],{},[895,101861,101862,101864,101866],{},[2505,101863,2507],{},[1708,101865,2726],{},[898,101867,207],{},[898,101869,2155],{"mathvariant":1759},[902,101871,101872],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1636,101874,101875,101924,102046,102180],{},[724,101876,101877,101879,101880],{},[883,101878,64514],{}," Příklad 6.3 — ověření vlastností pro ",[883,101881,101883],{"className":101882},[886],[888,101884,101885],{"xmlns":890},[892,101886,101887,101921],{},[895,101888,101889,101891,101893,101907],{},[898,101890,900],{},[1708,101892,1710],{},[4754,101894,101895,101897,101899],{},[898,101896,1688],{},[2505,101898,2507],{},[895,101900,101901,101903,101905],{},[2505,101902,2507],{},[898,101904,1799],{"mathvariant":1759},[2505,101906,5867],{},[4754,101908,101909,101911,101913],{},[898,101910,1688],{},[2505,101912,3132],{},[895,101914,101915,101917,101919],{},[2505,101916,3121],{},[898,101918,1799],{"mathvariant":1759},[2505,101920,5867],{},[902,101922,101923],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,101925,101927],{"className":101926},[886],[888,101928,101929],{"xmlns":890,"display":2210},[892,101930,101931,102043],{},[895,101932,101933,101941,101943,101951,101967,101981,101983,101985,101987,101989,101997,101999,102007,102021,102037,102039,102041],{},[4754,101934,101935,101937,101939],{},[898,101936,900],{},[2505,101938,2507],{},[1708,101940,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,101942,1710],{},[3194,101944,101945],{"scriptlevel":2784,"displaystyle":1715},[2358,101946,101947,101949],{},[2505,101948,2507],{},[2505,101950,5867],{},[4754,101952,101953,101955,101957],{},[898,101954,1688],{},[2505,101956,2507],{},[895,101958,101959,101961,101963,101965],{},[1708,101960,2726],{},[2505,101962,3121],{},[898,101964,1799],{"mathvariant":1759},[2505,101966,5867],{},[4754,101968,101969,101971,101973],{},[898,101970,1688],{},[2505,101972,3132],{},[895,101974,101975,101977,101979],{},[2505,101976,3121],{},[898,101978,1799],{"mathvariant":1759},[2505,101980,5867],{},[1708,101982,2854],{},[2505,101984,2784],{},[1708,101986,1883],{"separator":1882},[3213,101988],{"width":4750},[4754,101990,101991,101993,101995],{},[898,101992,900],{},[2505,101994,3132],{},[1708,101996,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,101998,1710],{},[3194,102000,102001],{"scriptlevel":2784,"displaystyle":1715},[2358,102002,102003,102005],{},[2505,102004,3121],{},[2505,102006,5867],{},[4754,102008,102009,102011,102013],{},[898,102010,1688],{},[2505,102012,2507],{},[895,102014,102015,102017,102019],{},[2505,102016,2507],{},[898,102018,1799],{"mathvariant":1759},[2505,102020,5867],{},[4754,102022,102023,102025,102027],{},[898,102024,1688],{},[2505,102026,3132],{},[895,102028,102029,102031,102033,102035],{},[1708,102030,2726],{},[2505,102032,2507],{},[898,102034,1799],{"mathvariant":1759},[2505,102036,5867],{},[1708,102038,2854],{},[2505,102040,2784],{},[1708,102042,1883],{"separator":1882},[902,102044,102045],{"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,",[883,102047,102049],{"className":102048},[886],[888,102050,102051],{"xmlns":890,"display":2210},[892,102052,102053,102177],{},[895,102054,102055,102067,102069,102071,102079,102095,102109,102111,102113,102115,102117,102129,102131,102133,102141,102155,102171,102173,102175],{},[4754,102056,102057,102059,102061],{},[898,102058,900],{},[2505,102060,14868],{},[895,102062,102063,102065],{},[1708,102064,1761],{"mathvariant":1759},[1708,102066,1761],{"mathvariant":1759},[1708,102068,1710],{},[1708,102070,2726],{},[3194,102072,102073],{"scriptlevel":2784,"displaystyle":1715},[2358,102074,102075,102077],{},[2505,102076,3121],{},[2505,102078,53694],{},[4754,102080,102081,102083,102085],{},[898,102082,1688],{},[2505,102084,2507],{},[895,102086,102087,102089,102091,102093],{},[1708,102088,2726],{},[2505,102090,5967],{},[898,102092,1799],{"mathvariant":1759},[2505,102094,5867],{},[4754,102096,102097,102099,102101],{},[898,102098,1688],{},[2505,102100,3132],{},[895,102102,102103,102105,102107],{},[2505,102104,3121],{},[898,102106,1799],{"mathvariant":1759},[2505,102108,5867],{},[1708,102110,2932],{},[2505,102112,2784],{},[1708,102114,1883],{"separator":1882},[3213,102116],{"width":4750},[4754,102118,102119,102121,102123],{},[898,102120,900],{},[2505,102122,44390],{},[895,102124,102125,102127],{},[1708,102126,1761],{"mathvariant":1759},[1708,102128,1761],{"mathvariant":1759},[1708,102130,1710],{},[1708,102132,2726],{},[3194,102134,102135],{"scriptlevel":2784,"displaystyle":1715},[2358,102136,102137,102139],{},[2505,102138,3121],{},[2505,102140,53694],{},[4754,102142,102143,102145,102147],{},[898,102144,1688],{},[2505,102146,2507],{},[895,102148,102149,102151,102153],{},[2505,102150,2507],{},[898,102152,1799],{"mathvariant":1759},[2505,102154,5867],{},[4754,102156,102157,102159,102161],{},[898,102158,1688],{},[2505,102160,3132],{},[895,102162,102163,102165,102167,102169],{},[1708,102164,2726],{},[2505,102166,3993],{},[898,102168,1799],{"mathvariant":1759},[2505,102170,5867],{},[1708,102172,2932],{},[2505,102174,2784],{},[1708,102176,1883],{"separator":1882},[902,102178,102179],{"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,",[724,102181,102182],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,102184,102186],{"id":102185},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,102188,102189,102192],{},[38,102190,102191],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,102194,102196],{"className":102195},[886],[888,102197,102198],{"xmlns":890,"display":2210},[892,102199,102200,102243],{},[2214,102201,102202],{"width":2216},[2218,102203,102204,102206,102236,102238],{},[2221,102205],{"width":2223},[2221,102207,102208],{},[895,102209,102210,102212,102214,102220,102222,102228,102230,102232,102234],{},[898,102211,900],{},[1708,102213,1716],{"stretchy":1715},[1743,102215,102216,102218],{},[898,102217,1688],{},[2505,102219,2507],{},[1708,102221,1883],{"separator":1882},[1743,102223,102224,102226],{},[898,102225,1688],{},[2505,102227,3132],{},[1708,102229,1721],{"stretchy":1715},[1708,102231,1710],{},[898,102233,14142],{},[1708,102235,1883],{"separator":1882},[2221,102237],{"width":2223},[2221,102239,102240],{},[2247,102241,102242],{},"(6.7)",[902,102244,102245],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,102247,5411,102248,102261],{},[883,102249,102251],{"className":102250},[886],[888,102252,102253],{"xmlns":890},[892,102254,102255,102259],{},[895,102256,102257],{},[898,102258,14142],{},[902,102260,14142],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,102263,102265],{"className":102264},[886],[888,102266,102267],{"xmlns":890,"display":2210},[892,102268,102269,102310],{},[2214,102270,102271],{"width":2216},[2218,102272,102273,102275,102303,102305],{},[2221,102274],{"width":2223},[2221,102276,102277],{},[895,102278,102279,102287,102289,102297,102299,102301],{},[4754,102280,102281,102283,102285],{},[898,102282,1688],{},[2505,102284,2507],{},[898,102286,207],{},[1708,102288,3703],{},[4754,102290,102291,102293,102295],{},[898,102292,1688],{},[2505,102294,3132],{},[898,102296,1923],{},[1708,102298,1710],{},[898,102300,14142],{},[898,102302,2155],{"mathvariant":1759},[2221,102304],{"width":2223},[2221,102306,102307],{},[2247,102308,102309],{},"(6.8)",[902,102311,102312],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,102314,102315,102316,8214,102346,1729,102349,102362,102363,102398,102399,102416,102417,102446,102447,102450],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,102317,102319],{"className":102318},[886],[888,102320,102321],{"xmlns":890},[892,102322,102323,102343],{},[895,102324,102325,102327,102333,102335,102341],{},[1708,102326,6940],{"stretchy":1715},[1743,102328,102329,102331],{},[898,102330,1688],{},[2505,102332,2507],{},[1708,102334,1883],{"separator":1882},[1743,102336,102337,102339],{},[898,102338,1688],{},[2505,102340,3132],{},[1708,102342,6981],{"stretchy":1715},[902,102344,102345],{"encoding":904},"[Q_1, Q_2]",[38,102347,102348],{},"stejnou úrovní uspokojení",[883,102350,102352],{"className":102351},[886],[888,102353,102354],{"xmlns":890},[892,102355,102356,102360],{},[895,102357,102358],{},[898,102359,14142],{},[902,102361,14142],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,102364,102366],{"className":102365},[886],[888,102367,102368],{"xmlns":890},[892,102369,102370,102396],{},[895,102371,102372,102374,102376,102378,102380,102386,102388,102394],{},[898,102373,900],{},[1708,102375,1710],{},[898,102377,900],{},[1708,102379,1716],{"stretchy":1715},[1743,102381,102382,102384],{},[898,102383,1688],{},[2505,102385,2507],{},[1708,102387,1883],{"separator":1882},[1743,102389,102390,102392],{},[898,102391,1688],{},[2505,102393,3132],{},[1708,102395,1721],{"stretchy":1715},[902,102397,98486],{"encoding":904}," s rovinami ",[883,102400,102402],{"className":102401},[886],[888,102403,102404],{"xmlns":890},[892,102405,102406,102414],{},[895,102407,102408,102410,102412],{},[898,102409,900],{},[1708,102411,1710],{},[898,102413,14142],{},[902,102415,97702],{"encoding":904}," rovnoběžnými s rovinou ",[883,102418,102420],{"className":102419},[886],[888,102421,102422],{"xmlns":890},[892,102423,102424,102444],{},[895,102425,102426,102428,102434,102436,102442],{},[1708,102427,1716],{"stretchy":1715},[1743,102429,102430,102432],{},[898,102431,1688],{},[2505,102433,2507],{},[1708,102435,1883],{"separator":1882},[1743,102437,102438,102440],{},[898,102439,1688],{},[2505,102441,3132],{},[1708,102443,1721],{"stretchy":1715},[902,102445,100649],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,102448,102449],{},"izokvantami"," produkčních funkcí.",[724,102452,102453],{},[614,102454,102455,102456,100527,102474,102492,102493,2155],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,102457,102459],{"className":102458},[886],[888,102460,102461],{"xmlns":890},[892,102462,102463,102471],{},[895,102464,102465,102467,102469],{},[898,102466,207],{},[1708,102468,2932],{},[898,102470,1923],{},[902,102472,102473],{"encoding":904},"a \u003C b",[883,102475,102477],{"className":102476},[886],[888,102478,102479],{"xmlns":890},[892,102480,102481,102489],{},[895,102482,102483,102485,102487],{},[898,102484,207],{},[1708,102486,2854],{},[898,102488,1923],{},[902,102490,102491],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,102494,102496],{"className":102495},[886],[888,102497,102498],{"xmlns":890},[892,102499,102500,102524],{},[895,102501,102502,102508,102510,102516,102518],{},[1743,102503,102504,102506],{},[898,102505,14142],{},[2505,102507,2784],{},[1708,102509,2932],{},[1743,102511,102512,102514],{},[898,102513,14142],{},[2505,102515,2507],{},[1708,102517,2932],{},[1743,102519,102520,102522],{},[898,102521,14142],{},[2505,102523,3132],{},[902,102525,102526],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,102528,102529],{},[614,102530,102531,102532,102561,102562,102620,102621,102639],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,102533,102535],{"className":102534},[886],[888,102536,102537],{"xmlns":890},[892,102538,102539,102559],{},[895,102540,102541,102543,102549,102551,102557],{},[1708,102542,1716],{"stretchy":1715},[1743,102544,102545,102547],{},[898,102546,1688],{},[2505,102548,2507],{},[1708,102550,1883],{"separator":1882},[1743,102552,102553,102555],{},[898,102554,1688],{},[2505,102556,3132],{},[1708,102558,1721],{"stretchy":1715},[902,102560,100649],{"encoding":904},"; body ",[883,102563,102565],{"className":102564},[886],[888,102566,102567],{"xmlns":890},[892,102568,102569,102617],{},[895,102570,102571,102573,102575,102577,102583,102585,102591,102593,102595,102597,102599,102601,102607,102609,102615],{},[898,102572,1786],{},[1708,102574,1710],{},[1708,102576,6940],{"stretchy":1715},[1743,102578,102579,102581],{},[898,102580,207],{},[2505,102582,2507],{},[1708,102584,1883],{"separator":1882},[1743,102586,102587,102589],{},[898,102588,207],{},[2505,102590,3132],{},[1708,102592,6981],{"stretchy":1715},[1708,102594,1883],{"separator":1882},[898,102596,35110],{},[1708,102598,1710],{},[1708,102600,6940],{"stretchy":1715},[1743,102602,102603,102605],{},[898,102604,1923],{},[2505,102606,2507],{},[1708,102608,1883],{"separator":1882},[1743,102610,102611,102613],{},[898,102612,1923],{},[2505,102614,3132],{},[1708,102616,6981],{"stretchy":1715},[902,102618,102619],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,102622,102624],{"className":102623},[886],[888,102625,102626],{"xmlns":890},[892,102627,102628,102636],{},[895,102629,102630,102632,102634],{},[898,102631,3455],{},[1708,102633,1883],{"separator":1882},[898,102635,16117],{},[902,102637,102638],{"encoding":904},"C, D"," na vyšší hladině.",[1636,102641,102642],{},[724,102643,102644,102646,102647,102709,102710,102754,102755,102789,102790,7468,102808,102789,102862,7468,102880,102956],{},[883,102645,64514],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,102648,102650],{"className":102649},[886],[888,102651,102652],{"xmlns":890},[892,102653,102654,102706],{},[895,102655,102656,102658,102660,102666,102668,102674,102676,102678,102692],{},[898,102657,900],{},[1708,102659,1716],{"stretchy":1715},[1743,102661,102662,102664],{},[898,102663,1688],{},[2505,102665,2507],{},[1708,102667,1883],{"separator":1882},[1743,102669,102670,102672],{},[898,102671,1688],{},[2505,102673,3132],{},[1708,102675,1721],{"stretchy":1715},[1708,102677,1710],{},[4754,102679,102680,102682,102684],{},[898,102681,1688],{},[2505,102683,2507],{},[895,102685,102686,102688,102690],{},[2505,102687,2507],{},[898,102689,1799],{"mathvariant":1759},[2505,102691,5867],{},[4754,102693,102694,102696,102698],{},[898,102695,1688],{},[2505,102697,3132],{},[895,102699,102700,102702,102704],{},[2505,102701,3121],{},[898,102703,1799],{"mathvariant":1759},[2505,102705,5867],{},[902,102707,102708],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,102711,102713],{"className":102712},[886],[888,102714,102715],{"xmlns":890},[892,102716,102717,102751],{},[895,102718,102719,102733,102747,102749],{},[4754,102720,102721,102723,102725],{},[898,102722,1688],{},[2505,102724,2507],{},[895,102726,102727,102729,102731],{},[2505,102728,2507],{},[898,102730,1799],{"mathvariant":1759},[2505,102732,5867],{},[4754,102734,102735,102737,102739],{},[898,102736,1688],{},[2505,102738,3132],{},[895,102740,102741,102743,102745],{},[2505,102742,3121],{},[898,102744,1799],{"mathvariant":1759},[2505,102746,5867],{},[1708,102748,1710],{},[898,102750,14142],{},[902,102752,102753],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,102756,102758],{"className":102757},[886],[888,102759,102760],{"xmlns":890},[892,102761,102762,102786],{},[895,102763,102764,102770,102778,102780],{},[1743,102765,102766,102768],{},[898,102767,1688],{},[2505,102769,2507],{},[4754,102771,102772,102774,102776],{},[898,102773,1688],{},[2505,102775,3132],{},[2505,102777,3121],{},[1708,102779,1710],{},[1753,102781,102782,102784],{},[898,102783,14142],{},[2505,102785,5867],{},[902,102787,102788],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,102791,102793],{"className":102792},[886],[888,102794,102795],{"xmlns":890},[892,102796,102797,102805],{},[895,102798,102799,102801,102803],{},[898,102800,14142],{},[1708,102802,1710],{},[2505,102804,2507],{},[902,102806,102807],{"encoding":904},"c = 1",[883,102809,102811],{"className":102810},[886],[888,102812,102813],{"xmlns":890},[892,102814,102815,102859],{},[895,102816,102817,102823,102825,102841,102843],{},[1743,102818,102819,102821],{},[898,102820,1688],{},[2505,102822,3132],{},[1708,102824,1710],{},[4754,102826,102827,102829,102831],{},[898,102828,1688],{},[2505,102830,2507],{},[895,102832,102833,102835,102837,102839],{},[1708,102834,2726],{},[2505,102836,2507],{},[898,102838,1799],{"mathvariant":1759},[2505,102840,3121],{},[1708,102842,1710],{},[3194,102844,102845],{"scriptlevel":2784,"displaystyle":1882},[2358,102846,102847,102849],{},[2505,102848,2507],{},[9358,102850,102851,102857],{},[1743,102852,102853,102855],{},[898,102854,1688],{},[2505,102856,2507],{},[2505,102858,3121],{},[902,102860,102861],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,102863,102865],{"className":102864},[886],[888,102866,102867],{"xmlns":890},[892,102868,102869,102877],{},[895,102870,102871,102873,102875],{},[898,102872,14142],{},[1708,102874,1710],{},[2505,102876,3132],{},[902,102878,102879],{"encoding":904},"c = 2",[883,102881,102883],{"className":102882},[886],[888,102884,102885],{"xmlns":890},[892,102886,102887,102953],{},[895,102888,102889,102895,102897,102909,102911,102927,102929],{},[1743,102890,102891,102893],{},[898,102892,1688],{},[2505,102894,3132],{},[1708,102896,1710],{},[1753,102898,102899,102901],{},[2505,102900,3132],{},[895,102902,102903,102905,102907],{},[2505,102904,5867],{},[898,102906,1799],{"mathvariant":1759},[2505,102908,3121],{},[1708,102910,3703],{},[4754,102912,102913,102915,102917],{},[898,102914,1688],{},[2505,102916,2507],{},[895,102918,102919,102921,102923,102925],{},[1708,102920,2726],{},[2505,102922,2507],{},[898,102924,1799],{"mathvariant":1759},[2505,102926,3121],{},[1708,102928,1710],{},[3194,102930,102931],{"scriptlevel":2784,"displaystyle":1882},[2358,102932,102933,102943],{},[895,102934,102935,102937],{},[2505,102936,3132],{},[9358,102938,102939,102941],{},[2505,102940,3132],{},[2505,102942,3121],{},[9358,102944,102945,102951],{},[1743,102946,102947,102949],{},[898,102948,1688],{},[2505,102950,2507],{},[2505,102952,3121],{},[902,102954,102955],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,102958,102960],{"id":102959},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,102962,102963],{},[3372,102964],{"alt":102965,"className":102966,"src":102967},"imek-ic-4vlastnosti-anotovane",[210,3376],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1636,102969,102970,102979,103026,103070,103076,103082],{},[724,102971,102972,102974,102975,102978],{},[883,102973,6130],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,102976,102977],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,102980,102981],{},[883,102982,102984],{"className":102983},[886],[888,102985,102986],{"xmlns":890},[892,102987,102988,103023],{},[895,102989,102990,102993,102995,102997,102999,103001,103019,103021],{},[898,102991,102992],{"mathvariant":1759},"tg",[1708,102994,7149],{},[898,102996,30728],{},[1708,102998,1710],{},[1708,103000,2726],{},[2358,103002,103003,103011],{},[4754,103004,103005,103007,103009],{},[898,103006,900],{},[2505,103008,2507],{},[1708,103010,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,103012,103013,103015,103017],{},[898,103014,900],{},[2505,103016,3132],{},[1708,103018,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,103020,2932],{},[2505,103022,2784],{},[902,103024,103025],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,103027,103028,103029,103069],{},"(derivace implicitně zadané funkce ",[883,103030,103032],{"className":103031},[886],[888,103033,103034],{"xmlns":890},[892,103035,103036,103066],{},[895,103037,103038,103040,103042,103048,103050,103056,103058,103060,103062,103064],{},[898,103039,900],{},[1708,103041,1716],{"stretchy":1715},[1743,103043,103044,103046],{},[898,103045,1688],{},[2505,103047,2507],{},[1708,103049,1883],{"separator":1882},[1743,103051,103052,103054],{},[898,103053,1688],{},[2505,103055,3132],{},[1708,103057,1721],{"stretchy":1715},[1708,103059,2726],{},[898,103061,14142],{},[1708,103063,1710],{},[2505,103065,2784],{},[902,103067,103068],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,103071,103072,103075],{},[38,103073,103074],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,103077,103078,103081],{},[38,103079,103080],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,103083,103084,103087,103088,103106,103107,103123,103124,103127],{},[38,103085,103086],{},"4° Konvexní."," Pro každé dva body ",[883,103089,103091],{"className":103090},[886],[888,103092,103093],{"xmlns":890},[892,103094,103095,103103],{},[895,103096,103097,103099,103101],{},[898,103098,1786],{},[1708,103100,1883],{"separator":1882},[898,103102,35110],{},[902,103104,103105],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,103108,103110],{"className":103109},[886],[888,103111,103112],{"xmlns":890},[892,103113,103114,103120],{},[895,103115,103116,103118],{},[898,103117,1786],{},[898,103119,35110],{},[902,103121,103122],{"encoding":904},"AB"," ve ",[38,103125,103126],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,103129,103130],{},[614,103131,103132,103133,103168,103169,2155],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,103134,103136],{"className":103135},[886],[888,103137,103138],{"xmlns":890},[892,103139,103140,103166],{},[895,103141,103142,103144,103146,103152,103154,103160,103162,103164],{},[898,103143,900],{},[1708,103145,1716],{"stretchy":1715},[1743,103147,103148,103150],{},[898,103149,1688],{},[2505,103151,2507],{},[1708,103153,1883],{"separator":1882},[1743,103155,103156,103158],{},[898,103157,1688],{},[2505,103159,3132],{},[1708,103161,1721],{"stretchy":1715},[1708,103163,1710],{},[898,103165,14142],{},[902,103167,21671],{"encoding":904}," s tečnou se sklonem ",[883,103170,103172],{"className":103171},[886],[888,103173,103174],{"xmlns":890},[892,103175,103176,103184],{},[895,103177,103178,103180,103182],{},[898,103179,102992],{"mathvariant":1759},[1708,103181,7149],{},[898,103183,30728],{},[902,103185,103186],{"encoding":904},"\\operatorname{tg}\\alpha",[115,103188,103190],{"id":103189},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,103192,103193,1729,103196,1695,103209,103212],{},[38,103194,103195],{},"Mezní míra komoditní substituce",[883,103197,103199],{"className":103198},[886],[888,103200,103201],{"xmlns":890},[892,103202,103203,103207],{},[895,103204,103205],{},[2247,103206,13825],{},[902,103208,40085],{"encoding":904},[38,103210,103211],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,103214,103216],{"className":103215},[886],[888,103217,103218],{"xmlns":890,"display":2210},[892,103219,103220,103307],{},[2214,103221,103222],{"width":2216},[2218,103223,103224,103226,103300,103302],{},[2221,103225],{"width":2223},[2221,103227,103228],{},[895,103229,103230,103232,103234,103236,103238,103244,103246,103252,103254,103256,103278,103280,103298],{},[2247,103231,13825],{},[1708,103233,1710],{},[2247,103235,13825],{},[1708,103237,1716],{"stretchy":1715},[1743,103239,103240,103242],{},[898,103241,1688],{},[2505,103243,2507],{},[1708,103245,1883],{"separator":1882},[1743,103247,103248,103250],{},[898,103249,1688],{},[2505,103251,3132],{},[1708,103253,1721],{"stretchy":1715},[1708,103255,1710],{},[2358,103257,103258,103268],{},[895,103259,103260,103262],{},[898,103261,1741],{},[1743,103263,103264,103266],{},[898,103265,900],{},[2505,103267,2507],{},[895,103269,103270,103272],{},[898,103271,1741],{},[1743,103273,103274,103276],{},[898,103275,900],{},[2505,103277,3132],{},[1708,103279,1710],{},[2358,103281,103282,103290],{},[4754,103283,103284,103286,103288],{},[898,103285,900],{},[2505,103287,2507],{},[1708,103289,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,103291,103292,103294,103296],{},[898,103293,900],{},[2505,103295,3132],{},[1708,103297,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[898,103299,2155],{"mathvariant":1759},[2221,103301],{"width":2223},[2221,103303,103304],{},[2247,103305,103306],{},"(6.9)",[902,103308,103309],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,103311,103312,103313,103347,103348,103380,103381,103416,103417,103430],{},"Geometricky: ",[883,103314,103316],{"className":103315},[886],[888,103317,103318],{"xmlns":890},[892,103319,103320,103344],{},[895,103321,103322,103324],{},[1708,103323,2726],{},[3194,103325,103326],{"scriptlevel":2784,"displaystyle":1715},[2358,103327,103328,103336],{},[4754,103329,103330,103332,103334],{},[898,103331,900],{},[2505,103333,2507],{},[1708,103335,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,103337,103338,103340,103342],{},[898,103339,900],{},[2505,103341,3132],{},[1708,103343,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,103345,103346],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,103349,103351],{"className":103350},[886],[888,103352,103353],{"xmlns":890},[892,103354,103355,103377],{},[895,103356,103357,103363,103365,103367,103369,103375],{},[1743,103358,103359,103361],{},[898,103360,1688],{},[2505,103362,3132],{},[1708,103364,1710],{},[898,103366,14009],{},[1708,103368,1716],{"stretchy":1715},[1743,103370,103371,103373],{},[898,103372,1688],{},[2505,103374,2507],{},[1708,103376,1721],{"stretchy":1715},[902,103378,103379],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,103382,103384],{"className":103383},[886],[888,103385,103386],{"xmlns":890},[892,103387,103388,103414],{},[895,103389,103390,103392,103394,103400,103402,103408,103410,103412],{},[898,103391,900],{},[1708,103393,1716],{"stretchy":1715},[1743,103395,103396,103398],{},[898,103397,1688],{},[2505,103399,2507],{},[1708,103401,1883],{"separator":1882},[1743,103403,103404,103406],{},[898,103405,1688],{},[2505,103407,3132],{},[1708,103409,1721],{"stretchy":1715},[1708,103411,1710],{},[898,103413,14142],{},[902,103415,21671],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,103418,103420],{"className":103419},[886],[888,103421,103422],{"xmlns":890},[892,103423,103424,103428],{},[895,103425,103426],{},[2247,103427,13825],{},[902,103429,40085],{"encoding":904}," chápeme jako velikost kompenzace.",[1636,103432,103433],{},[724,103434,103435,103437,103438,3033,103470,103508,103509,103526,103527,103544],{},[883,103436,2518],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,103439,103441],{"className":103440},[886],[888,103442,103443],{"xmlns":890},[892,103444,103445,103467],{},[895,103446,103447,103449,103451,103457,103459,103465],{},[2247,103448,13825],{},[1708,103450,1716],{"stretchy":1715},[1743,103452,103453,103455],{},[898,103454,1688],{},[2505,103456,2507],{},[1708,103458,1883],{"separator":1882},[1743,103460,103461,103463],{},[898,103462,1688],{},[2505,103464,3132],{},[1708,103466,1721],{"stretchy":1715},[902,103468,103469],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,103471,103472,103473,40850,103490,103507],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,103474,103476],{"className":103475},[886],[888,103477,103478],{"xmlns":890},[892,103479,103480,103488],{},[895,103481,103482],{},[1743,103483,103484,103486],{},[898,103485,1688],{},[2505,103487,2507],{},[902,103489,40849],{"encoding":904},[883,103491,103493],{"className":103492},[886],[888,103494,103495],{"xmlns":890},[892,103496,103497,103505],{},[895,103498,103499],{},[1743,103500,103501,103503],{},[898,103502,1688],{},[2505,103504,3132],{},[902,103506,40868],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,103510,103512],{"className":103511},[886],[888,103513,103514],{"xmlns":890},[892,103515,103516,103524],{},[895,103517,103518],{},[1743,103519,103520,103522],{},[898,103521,1688],{},[2505,103523,3132],{},[902,103525,40868],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,103528,103530],{"className":103529},[886],[888,103531,103532],{"xmlns":890},[892,103533,103534,103542],{},[895,103535,103536],{},[1743,103537,103538,103540],{},[898,103539,1688],{},[2505,103541,2507],{},[902,103543,40849],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,103546,103547,103548,7911],{},"Pro obecnou změnu ",[883,103549,103551],{"className":103550},[886],[888,103552,103553],{"xmlns":890},[892,103554,103555,103565],{},[895,103556,103557,103559],{},[898,103558,2364],{"mathvariant":1759},[1743,103560,103561,103563],{},[898,103562,1688],{},[2505,103564,2507],{},[902,103566,103567],{"encoding":904},"\\mathrm{d} Q_1",[883,103569,103571],{"className":103570},[886],[888,103572,103573],{"xmlns":890,"display":2210},[892,103574,103575,103628],{},[2214,103576,103577],{"width":2216},[2218,103578,103579,103581,103621,103623],{},[2221,103580],{"width":2223},[2221,103582,103583],{},[895,103584,103585,103587,103593,103595,103597,103603,103605,103607,103609,103611,103613,103619],{},[898,103586,2633],{"mathvariant":1759},[1743,103588,103589,103591],{},[898,103590,1688],{},[2505,103592,3132],{},[1708,103594,2638],{},[898,103596,2364],{"mathvariant":1759},[1743,103598,103599,103601],{},[898,103600,1688],{},[2505,103602,3132],{},[1708,103604,1710],{},[1708,103606,2726],{},[2247,103608,13825],{},[1708,103610,3703],{},[898,103612,2364],{"mathvariant":1759},[1743,103614,103615,103617],{},[898,103616,1688],{},[2505,103618,2507],{},[1708,103620,1883],{"separator":1882},[2221,103622],{"width":2223},[2221,103624,103625],{},[2247,103626,103627],{},"(6.10)",[902,103629,103630],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,103632,103634],{"className":103633},[886],[888,103635,103636],{"xmlns":890,"display":2210},[892,103637,103638,103685],{},[2214,103639,103640],{"width":2216},[2218,103641,103642,103644,103678,103680],{},[2221,103643],{"width":2223},[2221,103645,103646],{},[895,103647,103648,103650,103656,103658,103660,103666,103668,103670,103676],{},[898,103649,2364],{"mathvariant":1759},[1743,103651,103652,103654],{},[898,103653,1688],{},[2505,103655,2507],{},[1708,103657,1710],{},[1708,103659,2726],{},[2358,103661,103662,103664],{},[2505,103663,2507],{},[2247,103665,13825],{},[2247,103667,2659],{},[898,103669,2364],{"mathvariant":1759},[1743,103671,103672,103674],{},[898,103673,1688],{},[2505,103675,3132],{},[898,103677,2155],{"mathvariant":1759},[2221,103679],{"width":2223},[2221,103681,103682],{},[2247,103683,103684],{},"(6.11)",[902,103686,103687],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1636,103689,103690,103756,103873],{},[724,103691,103692,103694,103695,7911],{},[883,103693,64514],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,103696,103698],{"className":103697},[886],[888,103699,103700],{"xmlns":890},[892,103701,103702,103754],{},[895,103703,103704,103706,103708,103714,103716,103722,103724,103726,103740],{},[898,103705,900],{},[1708,103707,1716],{"stretchy":1715},[1743,103709,103710,103712],{},[898,103711,1688],{},[2505,103713,2507],{},[1708,103715,1883],{"separator":1882},[1743,103717,103718,103720],{},[898,103719,1688],{},[2505,103721,3132],{},[1708,103723,1721],{"stretchy":1715},[1708,103725,1710],{},[4754,103727,103728,103730,103732],{},[898,103729,1688],{},[2505,103731,2507],{},[895,103733,103734,103736,103738],{},[2505,103735,2507],{},[898,103737,1799],{"mathvariant":1759},[2505,103739,3132],{},[4754,103741,103742,103744,103746],{},[898,103743,1688],{},[2505,103745,3132],{},[895,103747,103748,103750,103752],{},[2505,103749,2507],{},[898,103751,1799],{"mathvariant":1759},[2505,103753,3132],{},[902,103755,41790],{"encoding":904},[724,103757,103758],{},[883,103759,103761],{"className":103760},[886],[888,103762,103763],{"xmlns":890},[892,103764,103765,103871],{},[895,103766,103767,103769,103771,103853,103855,103869],{},[2247,103768,13825],{},[1708,103770,1710],{},[2358,103772,103773,103813],{},[895,103774,103775,103783,103799],{},[3194,103776,103777],{"scriptlevel":2784,"displaystyle":1715},[2358,103778,103779,103781],{},[2505,103780,2507],{},[2505,103782,3132],{},[4754,103784,103785,103787,103789],{},[898,103786,1688],{},[2505,103788,2507],{},[895,103790,103791,103793,103795,103797],{},[1708,103792,2726],{},[2505,103794,2507],{},[898,103796,1799],{"mathvariant":1759},[2505,103798,3132],{},[4754,103800,103801,103803,103805],{},[898,103802,1688],{},[2505,103804,3132],{},[895,103806,103807,103809,103811],{},[2505,103808,2507],{},[898,103810,1799],{"mathvariant":1759},[2505,103812,3132],{},[895,103814,103815,103823,103837],{},[3194,103816,103817],{"scriptlevel":2784,"displaystyle":1715},[2358,103818,103819,103821],{},[2505,103820,2507],{},[2505,103822,3132],{},[4754,103824,103825,103827,103829],{},[898,103826,1688],{},[2505,103828,2507],{},[895,103830,103831,103833,103835],{},[2505,103832,2507],{},[898,103834,1799],{"mathvariant":1759},[2505,103836,3132],{},[4754,103838,103839,103841,103843],{},[898,103840,1688],{},[2505,103842,3132],{},[895,103844,103845,103847,103849,103851],{},[1708,103846,2726],{},[2505,103848,2507],{},[898,103850,1799],{"mathvariant":1759},[2505,103852,3132],{},[1708,103854,1710],{},[2358,103856,103857,103863],{},[1743,103858,103859,103861],{},[898,103860,1688],{},[2505,103862,3132],{},[1743,103864,103865,103867],{},[898,103866,1688],{},[2505,103868,2507],{},[898,103870,2155],{"mathvariant":1759},[902,103872,41908],{"encoding":904},[724,103874,41911,103875,2941,103918,41958,103920,103939],{},[883,103876,103878],{"className":103877},[886],[888,103879,103880],{"xmlns":890},[892,103881,103882,103916],{},[895,103883,103884,103886,103888,103890,103892,103894,103896,103898,103906,103908],{},[2247,103885,13825],{},[1708,103887,1716],{"stretchy":1715},[2505,103889,11064],{},[1708,103891,1883],{"separator":1882},[2505,103893,11040],{},[1708,103895,1721],{"stretchy":1715},[1708,103897,1710],{},[3194,103899,103900],{"scriptlevel":2784,"displaystyle":1715},[2358,103901,103902,103904],{},[2505,103903,11040],{},[2505,103905,11064],{},[1708,103907,1710],{},[3194,103909,103910],{"scriptlevel":2784,"displaystyle":1715},[2358,103911,103912,103914],{},[2505,103913,3993],{},[2505,103915,3121],{},[902,103917,41955],{"encoding":904},[614,103919,8418],{},[883,103921,103923],{"className":103922},[886],[888,103924,103925],{"xmlns":890},[892,103926,103927,103937],{},[895,103928,103929],{},[3194,103930,103931],{"scriptlevel":2784,"displaystyle":1715},[2358,103932,103933,103935],{},[2505,103934,3993],{},[2505,103936,3121],{},[902,103938,41978],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,103941,103942,103943,103947],{},"(Paralelou je ",[207,103944,103946],{"className":103945,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,103949,103951],{"id":103950},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,103953,103954,103955,103958],{},"Rámcově se v kapitole 6 studují ",[38,103956,103957],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,103960,103961,104097],{},[123,103962,103963,103965,103966,22048,103997,1729,104000,104049,104050,2155],{},[38,103964,40099],{}," — maximalizace ",[883,103967,103969],{"className":103968},[886],[888,103970,103971],{"xmlns":890},[892,103972,103973,103995],{},[895,103974,103975,103977,103979,103985,103987,103993],{},[898,103976,900],{},[1708,103978,1716],{"stretchy":1715},[1743,103980,103981,103983],{},[898,103982,1688],{},[2505,103984,2507],{},[1708,103986,1883],{"separator":1882},[1743,103988,103989,103991],{},[898,103990,1688],{},[2505,103992,3132],{},[1708,103994,1721],{"stretchy":1715},[902,103996,28216],{"encoding":904},[38,103998,103999],{},"rozpočtovém omezení",[883,104001,104003],{"className":104002},[886],[888,104004,104005],{"xmlns":890},[892,104006,104007,104047],{},[895,104008,104009,104015,104017,104025,104031,104033,104041],{},[1753,104010,104011,104013],{},[898,104012,21035],{},[1708,104014,2417],{},[1708,104016,1710],{},[4754,104018,104019,104021,104023],{},[898,104020,1747],{},[2505,104022,2507],{},[1708,104024,2417],{},[1743,104026,104027,104029],{},[898,104028,1688],{},[2505,104030,2507],{},[1708,104032,2019],{},[4754,104034,104035,104037,104039],{},[898,104036,1747],{},[2505,104038,3132],{},[1708,104040,2417],{},[1743,104042,104043,104045],{},[898,104044,1688],{},[2505,104046,3132],{},[902,104048,29170],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,104051,104053],{"className":104052},[886],[888,104054,104055],{"xmlns":890},[892,104056,104057,104095],{},[895,104058,104059,104065,104067,104073,104075,104081,104083,104089,104091,104093],{},[1743,104060,104061,104063],{},[898,104062,1688],{},[898,104064,29661],{},[1708,104066,1710],{},[1743,104068,104069,104071],{},[898,104070,16117],{},[898,104072,29661],{},[1708,104074,1716],{"stretchy":1715},[1743,104076,104077,104079],{},[898,104078,1747],{},[2505,104080,2507],{},[1708,104082,1883],{"separator":1882},[1743,104084,104085,104087],{},[898,104086,1747],{},[2505,104088,3132],{},[1708,104090,1883],{"separator":1882},[898,104092,21035],{},[1708,104094,1721],{"stretchy":1715},[902,104096,48297],{"encoding":904},[123,104098,104099,39751,104102,39794,104148,104165,104166,2155],{},[38,104100,104101],{},"Duální úloha",[883,104103,104105],{"className":104104},[886],[888,104106,104107],{"xmlns":890},[892,104108,104109,104145],{},[895,104110,104111,104113,104115,104123,104129,104131,104139],{},[898,104112,16183],{},[1708,104114,1710],{},[4754,104116,104117,104119,104121],{},[898,104118,1747],{},[2505,104120,2507],{},[1708,104122,2417],{},[1743,104124,104125,104127],{},[898,104126,1688],{},[2505,104128,2507],{},[1708,104130,2019],{},[4754,104132,104133,104135,104137],{},[898,104134,1747],{},[2505,104136,3132],{},[1708,104138,2417],{},[1743,104140,104141,104143],{},[898,104142,1688],{},[2505,104144,3132],{},[902,104146,104147],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,104149,104151],{"className":104150},[886],[888,104152,104153],{"xmlns":890},[892,104154,104155,104163],{},[895,104156,104157],{},[1753,104158,104159,104161],{},[898,104160,900],{},[1708,104162,2417],{},[902,104164,39812],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,104167,104169],{"className":104168},[886],[888,104170,104171],{"xmlns":890},[892,104172,104173,104211],{},[895,104174,104175,104181,104183,104189,104191,104197,104199,104205,104207,104209],{},[1743,104176,104177,104179],{},[898,104178,1688],{},[898,104180,29661],{},[1708,104182,1710],{},[1743,104184,104185,104187],{},[898,104186,16117],{},[898,104188,29661],{},[1708,104190,1716],{"stretchy":1715},[1743,104192,104193,104195],{},[898,104194,1747],{},[2505,104196,2507],{},[1708,104198,1883],{"separator":1882},[1743,104200,104201,104203],{},[898,104202,1747],{},[2505,104204,3132],{},[1708,104206,1883],{"separator":1882},[898,104208,900],{},[1708,104210,1721],{"stretchy":1715},[902,104212,29694],{"encoding":904},[724,104214,104215,104216,104219,104220,1729,104223,104262],{},"Obě úlohy se řeší ",[207,104217,39817],{"className":104218,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,104221,104222],{},"tentýž bod dotyku",[883,104224,104226],{"className":104225},[886],[888,104227,104228],{"xmlns":890},[892,104229,104230,104260],{},[895,104231,104232,104238,104240,104248,104250,104258],{},[1753,104233,104234,104236],{},[898,104235,1688],{},[1708,104237,2417],{},[1708,104239,6940],{"stretchy":1715},[4754,104241,104242,104244,104246],{},[898,104243,1688],{},[2505,104245,2507],{},[1708,104247,2417],{},[1708,104249,1883],{"separator":1882},[4754,104251,104252,104254,104256],{},[898,104253,1688],{},[2505,104255,3132],{},[1708,104257,2417],{},[1708,104259,6981],{"stretchy":1715},[902,104261,40174],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,104264,104266],{"className":104265},[886],[888,104267,104268],{"xmlns":890,"display":2210},[892,104269,104270,104316],{},[895,104271,104272,104274,104276,104294,104296,104314],{},[2247,104273,13825],{},[1708,104275,1710],{},[2358,104277,104278,104286],{},[4754,104279,104280,104282,104284],{},[898,104281,900],{},[2505,104283,2507],{},[1708,104285,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[4754,104287,104288,104290,104292],{},[898,104289,900],{},[2505,104291,3132],{},[1708,104293,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,104295,1710],{},[2358,104297,104298,104306],{},[4754,104299,104300,104302,104304],{},[898,104301,1747],{},[2505,104303,2507],{},[1708,104305,2417],{},[4754,104307,104308,104310,104312],{},[898,104309,1747],{},[2505,104311,3132],{},[1708,104313,2417],{},[898,104315,2155],{"mathvariant":1759},[902,104317,104318],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,104320,104321],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1636,104323,104324],{},[724,104325,104326,104328,104329,104332,104333,104336,104337,104364,104365,104399,104400,104434,104435,104478,104479,104482,104483,2155],{},[883,104327,2518],{}," Pro detailní postup viz ",[207,104330,48596],{"className":104331,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,104334,104335],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,104338,104340],{"className":104339},[886],[888,104341,104342],{"xmlns":890},[892,104343,104344,104362],{},[895,104345,104346,104348,104350,104356],{},[898,104347,900],{},[1708,104349,1710],{},[1743,104351,104352,104354],{},[898,104353,1688],{},[2505,104355,2507],{},[1743,104357,104358,104360],{},[898,104359,1688],{},[2505,104361,3132],{},[902,104363,42071],{"encoding":904}," s výsledkem ",[883,104366,104368],{"className":104367},[886],[888,104369,104370],{"xmlns":890},[892,104371,104372,104396],{},[895,104373,104374,104380,104382,104384,104386,104392,104394],{},[1743,104375,104376,104378],{},[898,104377,1688],{},[2505,104379,2507],{},[1708,104381,1710],{},[2505,104383,4028],{},[1708,104385,1883],{"separator":1882},[1743,104387,104388,104390],{},[898,104389,1688],{},[2505,104391,3132],{},[1708,104393,1710],{},[2505,104395,4003],{},[902,104397,104398],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,104401,104403],{"className":104402},[886],[888,104404,104405],{"xmlns":890},[892,104406,104407,104431],{},[895,104408,104409,104415,104417,104419,104421,104427,104429],{},[1743,104410,104411,104413],{},[898,104412,1688],{},[2505,104414,2507],{},[1708,104416,1710],{},[2505,104418,5867],{},[1708,104420,1883],{"separator":1882},[1743,104422,104423,104425],{},[898,104424,1688],{},[2505,104426,3132],{},[1708,104428,1710],{},[2505,104430,2507],{},[902,104432,104433],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,104436,104438],{"className":104437},[886],[888,104439,104440],{"xmlns":890},[892,104441,104442,104476],{},[895,104443,104444,104446,104448,104462],{},[898,104445,900],{},[1708,104447,1710],{},[4754,104449,104450,104452,104454],{},[898,104451,1688],{},[2505,104453,2507],{},[895,104455,104456,104458,104460],{},[2505,104457,2507],{},[898,104459,1799],{"mathvariant":1759},[2505,104461,3132],{},[4754,104463,104464,104466,104468],{},[898,104465,1688],{},[2505,104467,3132],{},[895,104469,104470,104472,104474],{},[2505,104471,2507],{},[898,104473,1799],{"mathvariant":1759},[2505,104475,3132],{},[902,104477,45003],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,104480,104481],{},"6.8–6.13"," jsou na stránce ",[207,104484,39617],{"className":104485,"dataFsResolvedFilePath":911,"href":912},[210],[115,104487,104489],{"id":104488},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,104491,104492,104493,104506,104507,104509,104510,104512,104513,104515,104516,104518,104519,104521,104522,104524,104525,1729,104527,104562,104563,104576,104577,104580,104581,104584,104585,2155],{},"Každá ",[883,104494,104496],{"className":104495},[886],[888,104497,104498],{"xmlns":890},[892,104499,104500,104504],{},[895,104501,104502],{},[898,104503,6676],{},[902,104505,6676],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,104508,97840],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,104511,98324],{}," a současně ",[38,104514,97843],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,104517,97848],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,104520,64496],{}," (6.4) a druhé parciální derivace ",[38,104523,100207],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,104526,21634],{},[883,104528,104530],{"className":104529},[886],[888,104531,104532],{"xmlns":890},[892,104533,104534,104560],{},[895,104535,104536,104538,104540,104546,104548,104554,104556,104558],{},[898,104537,900],{},[1708,104539,1716],{"stretchy":1715},[1743,104541,104542,104544],{},[898,104543,1688],{},[2505,104545,2507],{},[1708,104547,1883],{"separator":1882},[1743,104549,104550,104552],{},[898,104551,1688],{},[2505,104553,3132],{},[1708,104555,1721],{"stretchy":1715},[1708,104557,1710],{},[898,104559,14142],{},[902,104561,21671],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,104564,104566],{"className":104565},[886],[888,104567,104568],{"xmlns":890},[892,104569,104570,104574],{},[895,104571,104572],{},[2247,104573,13825],{},[902,104575,40085],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,104578,104579],{},"maximalizace užitečnosti"," a duální ",[38,104582,104583],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,104586,48596],{"className":104587,"dataFsResolvedFilePath":911,"href":912},[210],[115,104589,10753],{"id":10752},[152,104591,104592,104595,104598,104601,104604,104607,104610,104613,104616,104619],{},[123,104593,104594],{},"Co se zahrnuje pod termín užitečnost?",[123,104596,104597],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,104599,104600],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,104602,104603],{},"Jak se vypočítá mezní užitečnost?",[123,104605,104606],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,104608,104609],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,104611,104612],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,104614,104615],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,104617,104618],{},"Proč mají křivky užitečnosti záporný sklon?",[123,104620,104621],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,104623,104625],{"id":104624},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,104627,104628,104631,104632,10825,104674,1343,104702,1343,104730,104758],{},[38,104629,104630],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,104633,104635],{"className":104634},[886],[888,104636,104637],{"xmlns":890},[892,104638,104639,104671],{},[895,104640,104641,104643,104645,104651,104653,104655,104661,104663,104665],{},[898,104642,900],{},[1708,104644,1710],{},[1743,104646,104647,104649],{},[898,104648,1688],{},[2505,104650,2507],{},[1708,104652,2019],{},[2505,104654,12222],{},[1743,104656,104657,104659],{},[898,104658,1688],{},[2505,104660,3132],{},[1708,104662,2019],{},[2505,104664,3132],{},[1743,104666,104667,104669],{},[898,104668,1688],{},[2505,104670,3121],{},[902,104672,104673],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,104675,104677],{"className":104676},[886],[888,104678,104679],{"xmlns":890},[892,104680,104681,104699],{},[895,104682,104683,104685,104687,104689,104691,104693,104695,104697],{},[898,104684,900],{},[1708,104686,1716],{"stretchy":1715},[2505,104688,5867],{},[1708,104690,1883],{"separator":1882},[2505,104692,3132],{},[1708,104694,1883],{"separator":1882},[2505,104696,3132],{},[1708,104698,1721],{"stretchy":1715},[902,104700,104701],{"encoding":904},"U(4, 2, 2)",[883,104703,104705],{"className":104704},[886],[888,104706,104707],{"xmlns":890},[892,104708,104709,104727],{},[895,104710,104711,104713,104715,104717,104719,104721,104723,104725],{},[898,104712,900],{},[1708,104714,1716],{"stretchy":1715},[2505,104716,2507],{},[1708,104718,1883],{"separator":1882},[2505,104720,5867],{},[1708,104722,1883],{"separator":1882},[2505,104724,3132],{},[1708,104726,1721],{"stretchy":1715},[902,104728,104729],{"encoding":904},"U(1, 4, 2)",[883,104731,104733],{"className":104732},[886],[888,104734,104735],{"xmlns":890},[892,104736,104737,104755],{},[895,104738,104739,104741,104743,104745,104747,104749,104751,104753],{},[898,104740,900],{},[1708,104742,1716],{"stretchy":1715},[2505,104744,3132],{},[1708,104746,1883],{"separator":1882},[2505,104748,3121],{},[1708,104750,1883],{"separator":1882},[2505,104752,2507],{},[1708,104754,1721],{"stretchy":1715},[902,104756,104757],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,104760,104761,104764,104765,104817,104818,1343,104844,1343,104870,1343,104896,1343,104922,1343,104948,1343,104974,105000],{},[38,104762,104763],{},"6.2"," Je dána užitečnost ",[883,104766,104768],{"className":104767},[886],[888,104769,104770],{"xmlns":890},[892,104771,104772,104814],{},[895,104773,104774,104776,104778,104780,104794,104808],{},[898,104775,900],{},[1708,104777,1710],{},[2505,104779,3132],{},[4754,104781,104782,104784,104786],{},[898,104783,1688],{},[2505,104785,2507],{},[895,104787,104788,104790,104792],{},[2505,104789,2507],{},[898,104791,1799],{"mathvariant":1759},[2505,104793,3121],{},[4754,104795,104796,104798,104800],{},[898,104797,1688],{},[2505,104799,3132],{},[895,104801,104802,104804,104806],{},[2505,104803,2507],{},[898,104805,1799],{"mathvariant":1759},[2505,104807,3132],{},[1743,104809,104810,104812],{},[898,104811,1688],{},[2505,104813,3121],{},[902,104815,104816],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,104819,104821],{"className":104820},[886],[888,104822,104823],{"xmlns":890},[892,104824,104825,104841],{},[895,104826,104827,104829,104831,104833,104835,104837,104839],{},[1708,104828,1716],{"stretchy":1715},[2505,104830,4547],{},[1708,104832,1883],{"separator":1882},[2505,104834,12110],{},[1708,104836,1883],{"separator":1882},[2505,104838,4003],{},[1708,104840,1721],{"stretchy":1715},[902,104842,104843],{"encoding":904},"(36, 27, 10)",[883,104845,104847],{"className":104846},[886],[888,104848,104849],{"xmlns":890},[892,104850,104851,104867],{},[895,104852,104853,104855,104857,104859,104861,104863,104865],{},[1708,104854,1716],{"stretchy":1715},[2505,104856,53672],{},[1708,104858,1883],{"separator":1882},[2505,104860,3998],{},[1708,104862,1883],{"separator":1882},[2505,104864,4018],{},[1708,104866,1721],{"stretchy":1715},[902,104868,104869],{"encoding":904},"(64, 8, 20)",[883,104871,104873],{"className":104872},[886],[888,104874,104875],{"xmlns":890},[892,104876,104877,104893],{},[895,104878,104879,104881,104883,104885,104887,104889,104891],{},[1708,104880,1716],{"stretchy":1715},[2505,104882,4028],{},[1708,104884,1883],{"separator":1882},[2505,104886,53672],{},[1708,104888,1883],{"separator":1882},[2505,104890,3998],{},[1708,104892,1721],{"stretchy":1715},[902,104894,104895],{"encoding":904},"(25, 64, 8)",[883,104897,104899],{"className":104898},[886],[888,104900,104901],{"xmlns":890},[892,104902,104903,104919],{},[895,104904,104905,104907,104909,104911,104913,104915,104917],{},[1708,104906,1716],{"stretchy":1715},[2505,104908,5867],{},[1708,104910,1883],{"separator":1882},[2505,104912,84333],{},[1708,104914,1883],{"separator":1882},[2505,104916,3947],{},[1708,104918,1721],{"stretchy":1715},[902,104920,104921],{"encoding":904},"(4, 125, 6)",[883,104923,104925],{"className":104924},[886],[888,104926,104927],{"xmlns":890},[892,104928,104929,104945],{},[895,104930,104931,104933,104935,104937,104939,104941,104943],{},[1708,104932,1716],{"stretchy":1715},[2505,104934,4635],{},[1708,104936,1883],{"separator":1882},[2505,104938,17132],{},[1708,104940,1883],{"separator":1882},[2505,104942,4090],{},[1708,104944,1721],{"stretchy":1715},[902,104946,104947],{"encoding":904},"(9, 40, 12)",[883,104949,104951],{"className":104950},[886],[888,104952,104953],{"xmlns":890},[892,104954,104955,104971],{},[895,104956,104957,104959,104961,104963,104965,104967,104969],{},[1708,104958,1716],{"stretchy":1715},[2505,104960,4635],{},[1708,104962,1883],{"separator":1882},[2505,104964,53672],{},[1708,104966,1883],{"separator":1882},[2505,104968,3993],{},[1708,104970,1721],{"stretchy":1715},[902,104972,104973],{"encoding":904},"(9, 64, 5)",[883,104975,104977],{"className":104976},[886],[888,104978,104979],{"xmlns":890},[892,104980,104981,104997],{},[895,104982,104983,104985,104987,104989,104991,104993,104995],{},[1708,104984,1716],{"stretchy":1715},[2505,104986,53672],{},[1708,104988,1883],{"separator":1882},[2505,104990,3998],{},[1708,104992,1883],{"separator":1882},[2505,104994,4003],{},[1708,104996,1721],{"stretchy":1715},[902,104998,104999],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,105002,105003,104764,105006,105049,105050,105084,105085,10064,105115,105148,105149,105166,105167,105184],{},[38,105004,105005],{},"6.3",[883,105007,105009],{"className":105008},[886],[888,105010,105011],{"xmlns":890},[892,105012,105013,105047],{},[895,105014,105015,105017,105019,105033],{},[898,105016,900],{},[1708,105018,1710],{},[4754,105020,105021,105023,105025],{},[898,105022,1688],{},[2505,105024,2507],{},[895,105026,105027,105029,105031],{},[2505,105028,2507],{},[898,105030,1799],{"mathvariant":1759},[2505,105032,3132],{},[4754,105034,105035,105037,105039],{},[898,105036,1688],{},[2505,105038,3132],{},[895,105040,105041,105043,105045],{},[2505,105042,2507],{},[898,105044,1799],{"mathvariant":1759},[2505,105046,3132],{},[902,105048,45003],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,105051,105053],{"className":105052},[886],[888,105054,105055],{"xmlns":890},[892,105056,105057,105081],{},[895,105058,105059,105065,105067,105069,105071,105077,105079],{},[1743,105060,105061,105063],{},[898,105062,1688],{},[2505,105064,2507],{},[1708,105066,1710],{},[2505,105068,9704],{},[1708,105070,1883],{"separator":1882},[1743,105072,105073,105075],{},[898,105074,1688],{},[2505,105076,3132],{},[1708,105078,1710],{},[2505,105080,12513],{},[902,105082,105083],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,105086,105088],{"className":105087},[886],[888,105089,105090],{"xmlns":890},[892,105091,105092,105112],{},[895,105093,105094,105096,105102,105104,105106],{},[898,105095,1741],{},[1743,105097,105098,105100],{},[898,105099,900],{},[2505,105101,2507],{},[1708,105103,1883],{"separator":1882},[898,105105,1741],{},[1743,105107,105108,105110],{},[898,105109,900],{},[2505,105111,3132],{},[902,105113,105114],{"encoding":904},"MU_1, MU_2",[883,105116,105118],{"className":105117},[886],[888,105119,105120],{"xmlns":890},[892,105121,105122,105146],{},[895,105123,105124,105130,105132,105134,105136,105142,105144],{},[1743,105125,105126,105128],{},[898,105127,1688],{},[2505,105129,2507],{},[1708,105131,1710],{},[2505,105133,9704],{},[1708,105135,1883],{"separator":1882},[1743,105137,105138,105140],{},[898,105139,1688],{},[2505,105141,3132],{},[1708,105143,1710],{},[2505,105145,12513],{},[902,105147,105083],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,105150,105152],{"className":105151},[886],[888,105153,105154],{"xmlns":890},[892,105155,105156,105164],{},[895,105157,105158],{},[1743,105159,105160,105162],{},[898,105161,1688],{},[2505,105163,2507],{},[902,105165,40849],{"encoding":904}," na 60 a poklesu ",[883,105168,105170],{"className":105169},[886],[888,105171,105172],{"xmlns":890},[892,105173,105174,105182],{},[895,105175,105176],{},[1743,105177,105178,105180],{},[898,105179,1688],{},[2505,105181,3132],{},[902,105183,40868],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,105186,105187,105190,105191,105252,105253,2155],{},[38,105188,105189],{},"6.4"," Je dána funkce ",[883,105192,105194],{"className":105193},[886],[888,105195,105196],{"xmlns":890},[892,105197,105198,105250],{},[895,105199,105200,105202,105204,105210,105212,105218,105220,105222,105236],{},[898,105201,900],{},[1708,105203,1716],{"stretchy":1715},[1743,105205,105206,105208],{},[898,105207,1688],{},[2505,105209,2507],{},[1708,105211,1883],{"separator":1882},[1743,105213,105214,105216],{},[898,105215,1688],{},[2505,105217,3132],{},[1708,105219,1721],{"stretchy":1715},[1708,105221,1710],{},[4754,105223,105224,105226,105228],{},[898,105225,1688],{},[2505,105227,2507],{},[895,105229,105230,105232,105234],{},[2505,105231,2507],{},[898,105233,1799],{"mathvariant":1759},[2505,105235,3132],{},[4754,105237,105238,105240,105242],{},[898,105239,1688],{},[2505,105241,3132],{},[895,105243,105244,105246,105248],{},[2505,105245,2507],{},[898,105247,1799],{"mathvariant":1759},[2505,105249,3132],{},[902,105251,41790],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,105254,105256],{"className":105255},[886],[888,105257,105258],{"xmlns":890},[892,105259,105260,105350],{},[895,105261,105262,105264,105266,105272,105274,105276,105278,105280,105282,105284,105290,105292,105294,105296,105298,105300,105302,105304,105306,105312,105314,105316,105318,105320,105322,105324,105330,105332,105334,105336,105338,105340,105342,105348],{},[898,105263,900],{},[1708,105265,1716],{"stretchy":1715},[1743,105267,105268,105270],{},[898,105269,1688],{},[2505,105271,2507],{},[1708,105273,1883],{"separator":1882},[2505,105275,2507],{},[1708,105277,1721],{"stretchy":1715},[1708,105279,1883],{"separator":1882},[898,105281,900],{},[1708,105283,1716],{"stretchy":1715},[1743,105285,105286,105288],{},[898,105287,1688],{},[2505,105289,2507],{},[1708,105291,1883],{"separator":1882},[2505,105293,3132],{},[1708,105295,1721],{"stretchy":1715},[1708,105297,1883],{"separator":1882},[898,105299,900],{},[1708,105301,1716],{"stretchy":1715},[2505,105303,2507],{},[1708,105305,1883],{"separator":1882},[1743,105307,105308,105310],{},[898,105309,1688],{},[2505,105311,3132],{},[1708,105313,1721],{"stretchy":1715},[1708,105315,1883],{"separator":1882},[898,105317,900],{},[1708,105319,1716],{"stretchy":1715},[2505,105321,3132],{},[1708,105323,1883],{"separator":1882},[1743,105325,105326,105328],{},[898,105327,1688],{},[2505,105329,3132],{},[1708,105331,1721],{"stretchy":1715},[1708,105333,1883],{"separator":1882},[898,105335,900],{},[1708,105337,1716],{"stretchy":1715},[2505,105339,3121],{},[1708,105341,1883],{"separator":1882},[1743,105343,105344,105346],{},[898,105345,1688],{},[2505,105347,3132],{},[1708,105349,1721],{"stretchy":1715},[902,105351,105352],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,105354,105355,104764,105358,105402,105403,105511,105512,1343,105537,1343,105562,105604,105605,1343,105634,105659],{},[38,105356,105357],{},"6.5",[883,105359,105361],{"className":105360},[886],[888,105362,105363],{"xmlns":890},[892,105364,105365,105399],{},[895,105366,105367,105369,105371,105385],{},[898,105368,900],{},[1708,105370,1710],{},[4754,105372,105373,105375,105377],{},[898,105374,1688],{},[2505,105376,2507],{},[895,105378,105379,105381,105383],{},[2505,105380,3132],{},[898,105382,1799],{"mathvariant":1759},[2505,105384,3121],{},[4754,105386,105387,105389,105391],{},[898,105388,1688],{},[2505,105390,3132],{},[895,105392,105393,105395,105397],{},[2505,105394,2507],{},[898,105396,1799],{"mathvariant":1759},[2505,105398,3121],{},[902,105400,105401],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,105404,105406],{"className":105405},[886],[888,105407,105408],{"xmlns":890},[892,105409,105410,105508],{},[895,105411,105412,105414,105416,105422,105424,105430,105432,105434,105436,105438,105440,105442,105448,105450,105452,105454,105456,105458,105460,105466,105468,105470,105472,105474,105476,105478,105480,105482,105488,105490,105492,105494,105496,105498,105500,105506],{},[898,105413,900],{},[1708,105415,1716],{"stretchy":1715},[1743,105417,105418,105420],{},[898,105419,1688],{},[2505,105421,2507],{},[1708,105423,1883],{"separator":1882},[1743,105425,105426,105428],{},[898,105427,1688],{},[2505,105429,3132],{},[1708,105431,1721],{"stretchy":1715},[1708,105433,1710],{},[2505,105435,3132],{},[1708,105437,1883],{"separator":1882},[898,105439,900],{},[1708,105441,1716],{"stretchy":1715},[1743,105443,105444,105446],{},[898,105445,1688],{},[2505,105447,2507],{},[1708,105449,1883],{"separator":1882},[2505,105451,3121],{},[1708,105453,1721],{"stretchy":1715},[1708,105455,1883],{"separator":1882},[898,105457,900],{},[1708,105459,1716],{"stretchy":1715},[1743,105461,105462,105464],{},[898,105463,1688],{},[2505,105465,2507],{},[1708,105467,1883],{"separator":1882},[2505,105469,3132],{},[1708,105471,1721],{"stretchy":1715},[1708,105473,1883],{"separator":1882},[898,105475,900],{},[1708,105477,1716],{"stretchy":1715},[2505,105479,3132],{},[1708,105481,1883],{"separator":1882},[1743,105483,105484,105486],{},[898,105485,1688],{},[2505,105487,3132],{},[1708,105489,1721],{"stretchy":1715},[1708,105491,1883],{"separator":1882},[898,105493,900],{},[1708,105495,1716],{"stretchy":1715},[2505,105497,3121],{},[1708,105499,1883],{"separator":1882},[1743,105501,105502,105504],{},[898,105503,1688],{},[2505,105505,3132],{},[1708,105507,1721],{"stretchy":1715},[902,105509,105510],{"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 ",[883,105513,105515],{"className":105514},[886],[888,105516,105517],{"xmlns":890},[892,105518,105519,105534],{},[895,105520,105521,105523,105525,105527,105529,105532],{},[898,105522,1786],{},[1708,105524,6940],{"stretchy":1715},[2505,105526,12222],{},[1708,105528,8197],{"separator":1882},[2505,105530,105531],{},"3,555",[1708,105533,6981],{"stretchy":1715},[902,105535,105536],{"encoding":904},"A[1{,}5; 3{,}555]",[883,105538,105540],{"className":105539},[886],[888,105541,105542],{"xmlns":890},[892,105543,105544,105559],{},[895,105545,105546,105548,105550,105552,105554,105557],{},[898,105547,35110],{},[1708,105549,6940],{"stretchy":1715},[2505,105551,65018],{},[1708,105553,8197],{"separator":1882},[2505,105555,105556],{},"1,28",[1708,105558,6981],{"stretchy":1715},[902,105560,105561],{"encoding":904},"B[2{,}5; 1{,}28]",[883,105563,105565],{"className":105564},[886],[888,105566,105567],{"xmlns":890},[892,105568,105569,105601],{},[895,105570,105571,105573,105575,105577,105579,105581,105583,105589,105591,105593,105595,105597,105599],{},[898,105572,3455],{},[1708,105574,6940],{"stretchy":1715},[2505,105576,3132],{},[1708,105578,8197],{"separator":1882},[898,105580,900],{},[1708,105582,1716],{"stretchy":1715},[1743,105584,105585,105587],{},[898,105586,1688],{},[2505,105588,2507],{},[1708,105590,1883],{"separator":1882},[2505,105592,3121],{},[1708,105594,1721],{"stretchy":1715},[1708,105596,1710],{},[2505,105598,3121],{},[1708,105600,6981],{"stretchy":1715},[902,105602,105603],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,105606,105608],{"className":105607},[886],[888,105609,105610],{"xmlns":890},[892,105611,105612,105631],{},[895,105613,105614,105616,105618,105620,105622,105624,105626,105629],{},[898,105615,16117],{},[1708,105617,6940],{"stretchy":1715},[2505,105619,3121],{},[1708,105621,8197],{"separator":1882},[2505,105623,2507],{},[1708,105625,8197],{"separator":1882},[2505,105627,105628],{},"0,832",[1708,105630,6981],{"stretchy":1715},[902,105632,105633],{"encoding":904},"D[3; 1; 0{,}832]",[883,105635,105637],{"className":105636},[886],[888,105638,105639],{"xmlns":890},[892,105640,105641,105656],{},[895,105642,105643,105645,105647,105649,105651,105654],{},[898,105644,16183],{},[1708,105646,6940],{"stretchy":1715},[2505,105648,65018],{},[1708,105650,8197],{"separator":1882},[2505,105652,105653],{},"4,32",[1708,105655,6981],{"stretchy":1715},[902,105657,105658],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,105661,105662,104764,105665,105708,105709,10064,105722,105756,105757,105774,105775,105792],{},[38,105663,105664],{},"6.6",[883,105666,105668],{"className":105667},[886],[888,105669,105670],{"xmlns":890},[892,105671,105672,105706],{},[895,105673,105674,105676,105678,105692],{},[898,105675,900],{},[1708,105677,1710],{},[4754,105679,105680,105682,105684],{},[898,105681,1688],{},[2505,105683,2507],{},[895,105685,105686,105688,105690],{},[2505,105687,3132],{},[898,105689,1799],{"mathvariant":1759},[2505,105691,3121],{},[4754,105693,105694,105696,105698],{},[898,105695,1688],{},[2505,105697,3132],{},[895,105699,105700,105702,105704],{},[2505,105701,2507],{},[898,105703,1799],{"mathvariant":1759},[2505,105705,3121],{},[902,105707,105401],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,105710,105712],{"className":105711},[886],[888,105713,105714],{"xmlns":890},[892,105715,105716,105720],{},[895,105717,105718],{},[2247,105719,13825],{},[902,105721,40085],{"encoding":904},[883,105723,105725],{"className":105724},[886],[888,105726,105727],{"xmlns":890},[892,105728,105729,105753],{},[895,105730,105731,105737,105739,105741,105743,105749,105751],{},[1743,105732,105733,105735],{},[898,105734,1688],{},[2505,105736,2507],{},[1708,105738,1710],{},[2505,105740,9238],{},[1708,105742,1883],{"separator":1882},[1743,105744,105745,105747],{},[898,105746,1688],{},[2505,105748,3132],{},[1708,105750,1710],{},[2505,105752,20288],{},[902,105754,105755],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,105758,105760],{"className":105759},[886],[888,105761,105762],{"xmlns":890},[892,105763,105764,105772],{},[895,105765,105766],{},[1743,105767,105768,105770],{},[898,105769,1688],{},[2505,105771,2507],{},[902,105773,40849],{"encoding":904},", poklesne-li ",[883,105776,105778],{"className":105777},[886],[888,105779,105780],{"xmlns":890},[892,105781,105782,105790],{},[895,105783,105784],{},[1743,105785,105786,105788],{},[898,105787,1688],{},[2505,105789,3132],{},[902,105791,40868],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,105794,105795,105798,105799,105816,105817,105834,105835,105867,105868,105893,105894,105907,105908,1343,105932,1343,105956,2155],{},[38,105796,105797],{},"6.7"," Míra uspokojení z nákupu množství ",[883,105800,105802],{"className":105801},[886],[888,105803,105804],{"xmlns":890},[892,105805,105806,105814],{},[895,105807,105808],{},[1743,105809,105810,105812],{},[898,105811,1688],{},[2505,105813,2507],{},[902,105815,40849],{"encoding":904}," nealko nápojů a množství ",[883,105818,105820],{"className":105819},[886],[888,105821,105822],{"xmlns":890},[892,105823,105824,105832],{},[895,105825,105826],{},[1743,105827,105828,105830],{},[898,105829,1688],{},[2505,105831,3132],{},[902,105833,40868],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,105836,105838],{"className":105837},[886],[888,105839,105840],{"xmlns":890},[892,105841,105842,105864],{},[895,105843,105844,105846,105848],{},[898,105845,900],{},[1708,105847,1710],{},[9351,105849,105850],{},[895,105851,105852,105858],{},[1743,105853,105854,105856],{},[898,105855,1688],{},[2505,105857,2507],{},[1743,105859,105860,105862],{},[898,105861,1688],{},[2505,105863,3132],{},[902,105865,105866],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,105869,105871],{"className":105870},[886],[888,105872,105873],{"xmlns":890},[892,105874,105875,105891],{},[895,105876,105877,105883,105885],{},[1743,105878,105879,105881],{},[898,105880,1688],{},[2505,105882,2507],{},[1708,105884,1883],{"separator":1882},[1743,105886,105887,105889],{},[898,105888,1688],{},[2505,105890,3132],{},[902,105892,47465],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,105895,105897],{"className":105896},[886],[888,105898,105899],{"xmlns":890},[892,105900,105901,105905],{},[895,105902,105903],{},[2247,105904,13825],{},[902,105906,40085],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,105909,105911],{"className":105910},[886],[888,105912,105913],{"xmlns":890},[892,105914,105915,105929],{},[895,105916,105917,105919,105921,105923,105925,105927],{},[2247,105918,13825],{},[1708,105920,1716],{"stretchy":1715},[2505,105922,3993],{},[1708,105924,1883],{"separator":1882},[2505,105926,4018],{},[1708,105928,1721],{"stretchy":1715},[902,105930,105931],{"encoding":904},"\\text{MRCS}(5, 20)",[883,105933,105935],{"className":105934},[886],[888,105936,105937],{"xmlns":890},[892,105938,105939,105953],{},[895,105940,105941,105943,105945,105947,105949,105951],{},[2247,105942,13825],{},[1708,105944,1716],{"stretchy":1715},[2505,105946,4018],{},[1708,105948,1883],{"separator":1882},[2505,105950,3993],{},[1708,105952,1721],{"stretchy":1715},[902,105954,105955],{"encoding":904},"\\text{MRCS}(20, 5)",[883,105957,105959],{"className":105958},[886],[888,105960,105961],{"xmlns":890},[892,105962,105963,105977],{},[895,105964,105965,105967,105969,105971,105973,105975],{},[2247,105966,13825],{},[1708,105968,1716],{"stretchy":1715},[2505,105970,3132],{},[1708,105972,1883],{"separator":1882},[2505,105974,9704],{},[1708,105976,1721],{"stretchy":1715},[902,105978,105979],{"encoding":904},"\\text{MRCS}(2, 50)",[1636,105981,105982],{},[724,105983,105984,105986,105987,2155],{},[883,105985,3465],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,105988,105991],{"className":105989,"dataFsResolvedFilePath":911,"href":105990},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,105993,12596],{"id":12595},[120,105995,105996,106002,106007,106013,106066,106076,106122,106177,106240,106297,106352,106391],{},[123,105997,105998,106001],{},[38,105999,106000],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,106003,106004,106006],{},[38,106005,97899],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,106008,106009,106012],{},[38,106010,106011],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,106014,106015,106017,106018,106031,106032,2155],{},[38,106016,98226],{}," — uspořádaná ",[883,106019,106021],{"className":106020},[886],[888,106022,106023],{"xmlns":890},[892,106024,106025,106029],{},[895,106026,106027],{},[898,106028,6676],{},[902,106030,6676],{"encoding":904},"-tice ",[883,106033,106035],{"className":106034},[886],[888,106036,106037],{"xmlns":890},[892,106038,106039,106063],{},[895,106040,106041,106043,106049,106051,106053,106055,106061],{},[1708,106042,1716],{"stretchy":1715},[1743,106044,106045,106047],{},[898,106046,1688],{},[2505,106048,2507],{},[1708,106050,1883],{"separator":1882},[1708,106052,21550],{},[1708,106054,1883],{"separator":1882},[1743,106056,106057,106059],{},[898,106058,1688],{},[898,106060,6676],{},[1708,106062,1721],{"stretchy":1715},[902,106064,106065],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,106067,106068,106071,106072,106075],{},[38,106069,106070],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,106073,106074],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,106077,106078,1729,106081,106121],{},[38,106079,106080],{},"Funkce užitečnosti",[883,106082,106084],{"className":106083},[886],[888,106085,106086],{"xmlns":890},[892,106087,106088,106118],{},[895,106089,106090,106092,106094,106096,106098,106104,106106,106108,106110,106116],{},[898,106091,900],{},[1708,106093,1710],{},[898,106095,900],{},[1708,106097,1716],{"stretchy":1715},[1743,106099,106100,106102],{},[898,106101,1688],{},[2505,106103,2507],{},[1708,106105,1883],{"separator":1882},[1708,106107,21550],{},[1708,106109,1883],{"separator":1882},[1743,106111,106112,106114],{},[898,106113,1688],{},[898,106115,6676],{},[1708,106117,1721],{"stretchy":1715},[902,106119,106120],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,106123,106124,1729,106127,106156,106157,1729,106160,106176],{},[38,106125,106126],{},"Mezní užitečnost",[883,106128,106130],{"className":106129},[886],[888,106131,106132],{"xmlns":890},[892,106133,106134,106154],{},[895,106135,106136,106138,106144,106146],{},[898,106137,1741],{},[1743,106139,106140,106142],{},[898,106141,900],{},[898,106143,29661],{},[1708,106145,1710],{},[4754,106147,106148,106150,106152],{},[898,106149,900],{},[898,106151,29661],{},[1708,106153,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[902,106155,97683],{"encoding":904}," — vzorec (6.2); ",[38,106158,106159],{},"totální diferenciál",[883,106161,106163],{"className":106162},[886],[888,106164,106165],{"xmlns":890},[892,106166,106167,106173],{},[895,106168,106169,106171],{},[898,106170,2364],{"mathvariant":1759},[898,106172,900],{},[902,106174,106175],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,106178,106179,106181,106182,106206,106207,106239],{},[38,106180,99862],{}," — (6.4) ",[883,106183,106185],{"className":106184},[886],[888,106186,106187],{"xmlns":890},[892,106188,106189,106203],{},[895,106190,106191,106199,106201],{},[4754,106192,106193,106195,106197],{},[898,106194,900],{},[898,106196,29661],{},[1708,106198,1761],{"mathvariant":1759,"lspace":1760,"rspace":1760},[1708,106200,2854],{},[2505,106202,2784],{},[902,106204,106205],{"encoding":904},"U'_i > 0",", (6.5) ",[883,106208,106210],{"className":106209},[886],[888,106211,106212],{"xmlns":890},[892,106213,106214,106236],{},[895,106215,106216,106232,106234],{},[4754,106217,106218,106220,106226],{},[898,106219,900],{},[895,106221,106222,106224],{},[898,106223,29661],{},[898,106225,29661],{},[895,106227,106228,106230],{},[1708,106229,1761],{"mathvariant":1759},[1708,106231,1761],{"mathvariant":1759},[1708,106233,2932],{},[2505,106235,2784],{},[902,106237,106238],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,106241,106242,1729,106244,106275,106276,2155],{},[38,106243,101650],{},[883,106245,106247],{"className":106246},[886],[888,106248,106249],{"xmlns":890},[892,106250,106251,106273],{},[895,106252,106253,106255,106257,106265],{},[898,106254,900],{},[1708,106256,1710],{},[4754,106258,106259,106261,106263],{},[898,106260,1688],{},[2505,106262,2507],{},[898,106264,207],{},[4754,106266,106267,106269,106271],{},[898,106268,1688],{},[2505,106270,3132],{},[898,106272,1923],{},[902,106274,47646],{"encoding":904}," — (6.6), speciálně ",[883,106277,106279],{"className":106278},[886],[888,106280,106281],{"xmlns":890},[892,106282,106283,106295],{},[895,106284,106285,106287,106289,106291,106293],{},[898,106286,1923],{},[1708,106288,1710],{},[2505,106290,2507],{},[1708,106292,2726],{},[898,106294,207],{},[902,106296,101804],{"encoding":904},[123,106298,106299,1729,106302,106337,106338,106351],{},[38,106300,106301],{},"Křivky užitečnosti (indiferenční)",[883,106303,106305],{"className":106304},[886],[888,106306,106307],{"xmlns":890},[892,106308,106309,106335],{},[895,106310,106311,106313,106315,106321,106323,106329,106331,106333],{},[898,106312,900],{},[1708,106314,1716],{"stretchy":1715},[1743,106316,106317,106319],{},[898,106318,1688],{},[2505,106320,2507],{},[1708,106322,1883],{"separator":1882},[1743,106324,106325,106327],{},[898,106326,1688],{},[2505,106328,3132],{},[1708,106330,1721],{"stretchy":1715},[1708,106332,1710],{},[898,106334,14142],{},[902,106336,21671],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,106339,106341],{"className":106340},[886],[888,106342,106343],{"xmlns":890},[892,106344,106345,106349],{},[895,106346,106347],{},[898,106348,900],{},[902,106350,900],{"encoding":904},", konvexní.",[123,106353,106354,1729,106356,106390],{},[38,106355,103195],{},[883,106357,106359],{"className":106358},[886],[888,106360,106361],{"xmlns":890},[892,106362,106363,106387],{},[895,106364,106365,106367,106369,106371,106377,106379,106381],{},[2247,106366,13825],{},[1708,106368,1710],{},[898,106370,1741],{},[1743,106372,106373,106375],{},[898,106374,900],{},[2505,106376,2507],{},[898,106378,1799],{"mathvariant":1759},[898,106380,1741],{},[1743,106382,106383,106385],{},[898,106384,900],{},[2505,106386,3132],{},[902,106388,106389],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,106392,106393,1729,106396,21672,106425,106428],{},[38,106394,106395],{},"Podmínka optimality",[883,106397,106399],{"className":106398},[886],[888,106400,106401],{"xmlns":890},[892,106402,106403,106423],{},[895,106404,106405,106407,106409,106415,106417],{},[2247,106406,13825],{},[1708,106408,1710],{},[1743,106410,106411,106413],{},[898,106412,1747],{},[2505,106414,2507],{},[898,106416,1799],{"mathvariant":1759},[1743,106418,106419,106421],{},[898,106420,1747],{},[2505,106422,3132],{},[902,106424,39848],{"encoding":904},[207,106426,48596],{"className":106427,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,106430,13763],{"id":13762},[120,106432,106433,106470,106511,106521],{},[123,106434,106435,1729,106438,106441,106442,106455,106456,106469],{},[38,106436,106437],{},"Navazující téma:",[207,106439,913],{"className":106440,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,106443,106445],{"className":106444},[886],[888,106446,106447],{"xmlns":890},[892,106448,106449,106453],{},[895,106450,106451],{},[898,106452,900],{},[902,106454,900],{"encoding":904},", min ",[883,106457,106459],{"className":106458},[886],[888,106460,106461],{"xmlns":890},[892,106462,106463,106467],{},[895,106464,106465],{},[898,106466,16183],{},[902,106468,16183],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,106471,106472,1729,106475,22979,106478,13774,106481,106484,106485,106488,106489,13826,106507,106510],{},[38,106473,106474],{},"Související pojmy:",[207,106476,784],{"className":106477,"dataFsResolvedFilePath":782,"href":783},[210],[207,106479,2162],{"className":106480,"dataFsResolvedFilePath":764,"href":765},[210],[207,106482,22974],{"className":106483,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,106486,23828],{"className":106487,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,106490,106492],{"className":106491},[886],[888,106493,106494],{"xmlns":890},[892,106495,106496,106504],{},[895,106497,106498],{},[1743,106499,106500,106502],{},[898,106501,16117],{},[898,106503,29661],{},[902,106505,106506],{"encoding":904},"D_i",[207,106508,793],{"className":106509,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,106512,106513,1729,106515,1343,106518],{},[38,106514,48545],{},[207,106516,1094],{"className":106517,"dataFsResolvedFilePath":838,"href":839},[210],[207,106519,1101],{"className":106520,"dataFsResolvedFilePath":868,"href":869},[210],[123,106522,106523,1729,106525],{},[38,106524,13888],{},[207,106526,13894],{"className":106527,"dataFsResolvedFilePath":13892,"href":13893},[210],{"title":641,"searchDepth":642,"depth":642,"links":106529},[106530,106531,106532,106535,106536,106539,106543,106544,106547,106548,106549,106550,106551,106552,106553],{"id":23893,"depth":642,"text":23894},{"id":97822,"depth":642,"text":97823},{"id":97882,"depth":642,"text":97883,"children":106533},[106534],{"id":97898,"depth":649,"text":97899},{"id":98205,"depth":642,"text":98206},{"id":99065,"depth":642,"text":99066,"children":106537},[106538],{"id":99612,"depth":649,"text":7527},{"id":99861,"depth":642,"text":99862,"children":106540},[106541],{"id":100734,"depth":649,"text":106542},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":101649,"depth":642,"text":101650},{"id":102185,"depth":642,"text":102186,"children":106545},[106546],{"id":102959,"depth":649,"text":102960},{"id":103189,"depth":642,"text":103190},{"id":103950,"depth":642,"text":103951},{"id":104488,"depth":642,"text":104489},{"id":10752,"depth":642,"text":10753},{"id":104624,"depth":642,"text":104625},{"id":12595,"depth":642,"text":12596},{"id":13762,"depth":642,"text":13763},{},"\u002Ftopics\u002Fuzitecnost",{"title":97606,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,21676,106560,13948,23009,106561],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":106564,"title":757,"body":106565,"course":1128,"courses":659,"created":1129,"description":106838,"extension":661,"meta":106839,"navigation":664,"path":106840,"seo":106841,"sources":106842,"stem":106843,"tags":106844,"type":13951,"updated":677,"__hash__":106850},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":106566,"toc":106830},[106567,106570,106577,106584,106588,106598,106600,106634,106638,106681,106684,106742,106746,106776,106780,106801,106803],[12,106568,757],{"id":106569},"základy-matematické-ekonomie",[724,106571,106572,106573,106576],{},"Úvodní pojmy a princip modelování v ",[207,106574,28252],{"className":106575,"dataFsResolvedFilePath":13892,"href":13893},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,106578,106579],{},[3372,106580],{"alt":106581,"className":106582,"src":106583},"imek-model-promenne",[210,3376],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,106585,106587],{"id":106586},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,106589,106590,106593,106594,106597],{},[38,106591,106592],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,106595,106596],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,106599,12596],{"id":12595},[120,106601,106602,106608,106614,106620,106629],{},[123,106603,106604,106607],{},[38,106605,106606],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,106609,106610,106613],{},[38,106611,106612],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,106615,106616,106619],{},[38,106617,106618],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,106621,106622,12636,106625,106628],{},[38,106623,106624],{},"Ceteris paribus",[614,106626,106627],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,106630,106631,106633],{},[38,106632,62458],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,106635,106637],{"id":106636},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,106639,106640,106680],{},[883,106641,106643],{"className":106642},[886],[888,106644,106645],{"xmlns":890},[892,106646,106647,106677],{},[895,106648,106649,106651,106653,106655,106657,106659,106661,106663,106665,106667,106669,106671,106673,106675],{},[898,106650,1688],{},[1708,106652,1710],{},[898,106654,16117],{},[1708,106656,1716],{"stretchy":1715},[898,106658,1747],{},[1708,106660,1883],{"separator":1882},[898,106662,21035],{},[1708,106664,1883],{"separator":1882},[898,106666,30164],{},[1708,106668,1883],{"separator":1882},[898,106670,900],{},[1708,106672,1883],{"separator":1882},[1708,106674,21550],{},[1708,106676,1721],{"stretchy":1715},[902,106678,106679],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,106682,106683],{},"Zjednodušení:",[120,106685,106686,106714],{},[123,106687,106688,1729,106691],{},[38,106689,106690],{},"Jednofaktorový model:",[883,106692,106694],{"className":106693},[886],[888,106695,106696],{"xmlns":890},[892,106697,106698,106712],{},[895,106699,106700,106702,106704,106706,106708,106710],{},[898,106701,1688],{},[1708,106703,1710],{},[898,106705,16117],{},[1708,106707,1716],{"stretchy":1715},[898,106709,1747],{},[1708,106711,1721],{"stretchy":1715},[902,106713,16126],{"encoding":904},[123,106715,106716,1729,106719],{},[38,106717,106718],{},"Inverzní zápis:",[883,106720,106722],{"className":106721},[886],[888,106723,106724],{"xmlns":890},[892,106725,106726,106740],{},[895,106727,106728,106730,106732,106734,106736,106738],{},[898,106729,1747],{},[1708,106731,1710],{},[898,106733,16117],{},[1708,106735,1716],{"stretchy":1715},[898,106737,1688],{},[1708,106739,1721],{"stretchy":1715},[902,106741,16564],{"encoding":904},[115,106743,106745],{"id":106744},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,106747,106748,106757],{},[123,106749,106750,106753,106754,2511],{},[38,106751,106752],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,106755,28112],{"className":106756,"dataFsResolvedFilePath":800,"href":801},[210],[123,106758,106759,106762,106763,106766,106767,106770,106771,106775],{},[38,106760,106761],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,106764,1145],{"className":106765,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,106768,28125],{"className":106769,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,106772,106774],{"className":106773,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,106777,106779],{"id":106778},"konvence-z-přednášek","Konvence z přednášek",[120,106781,106782,106789,106795],{},[123,106783,106784,106785,106788],{},"Symbol ",[106786,106787,2638],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,106790,106791,106792,2155],{},"Numerické výsledky ",[38,106793,106794],{},"na 3 desetinná místa",[123,106796,15835,106797,106800],{},[614,106798,106799],{},"jednotková změna"," má standardní význam (změna o 1).",[115,106802,13763],{"id":13762},[120,106804,106805,106810,106818],{},[123,106806,106807,106809],{},[38,106808,13871],{}," —",[123,106811,106812,1729,106814],{},[38,106813,15753],{},[207,106815,106817],{"className":106816,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,106819,106820,1729,106822,1343,106826],{},[38,106821,15761],{},[207,106823,106825],{"className":106824,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,106827,106829],{"className":106828,"dataFsResolvedFilePath":13892,"href":13893},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":106831},[106832,106833,106834,106835,106836,106837],{"id":106586,"depth":642,"text":106587},{"id":12595,"depth":642,"text":12596},{"id":106636,"depth":642,"text":106637},{"id":106744,"depth":642,"text":106745},{"id":106778,"depth":642,"text":106779},{"id":13762,"depth":642,"text":13763},"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":106838},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,106845,106846,106847,106848,106849],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":106852,"title":106853,"body":106854,"course":1128,"courses":659,"created":13938,"description":641,"extension":661,"meta":111126,"navigation":664,"path":111127,"seo":111128,"sources":111129,"stem":111130,"tags":111131,"type":13951,"updated":677,"__hash__":111135},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":106855,"toc":111109},[106856,106859,106953,106957,106979,106993,107045,107047,107051,107114,107157,107176,107339,107438,107441,107508,107512,107641,107680,107710,107822,107867,107933,107986,108062,108118,108120,108124,108188,108232,108252,108413,108416,108500,108597,108600,108666,108670,108719,108745,108850,108914,108919,109015,109062,109064,109067,109089,109131,109138,109171,109173,109244,109298,109407,109411,109500,109576,109840,109878,109880,109884,109887,109894,110205,110208,110266,110446,110475,110477,110481,110487,110625,110634,110636,110638,111063,111065,111067],[12,106857,106853],{"id":106858},"zdanění-trhu-dopady-daně-na-rovnováhu",[1636,106860,106861],{},[724,106862,106863,54458,106865,106878,106879,106882,106883,106885,106886,106889,106890,106911,106912,106935,106936,106939,106940,2155],{},[883,106864,2518],{},[883,106866,106868],{"className":106867},[886],[888,106869,106870],{"xmlns":890},[892,106871,106872,106876],{},[895,106873,106874],{},[898,106875,1978],{},[902,106877,1978],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,106880,106881],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,106884,97890],{}," (je-li uložena spotřebiteli). Výsledné ",[38,106887,106888],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,106891,106893],{"className":106892},[886],[888,106894,106895],{"xmlns":890},[892,106896,106897,106909],{},[895,106898,106899],{},[1743,106900,106901,106903],{},[898,106902,1978],{},[895,106904,106905,106907],{},[898,106906,54507],{},[898,106908,724],{},[902,106910,54512],{"encoding":904}," (spotřebitel) a ",[883,106913,106915],{"className":106914},[886],[888,106916,106917],{"xmlns":890},[892,106918,106919,106933],{},[895,106920,106921],{},[1743,106922,106923,106925],{},[898,106924,1978],{},[895,106926,106927,106929,106931],{},[898,106928,54530],{},[898,106930,14004],{},[898,106932,5498],{},[902,106934,54537],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,106937,106938],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,106941,106943],{"className":106942},[886],[888,106944,106945],{"xmlns":890},[892,106946,106947,106951],{},[895,106948,106949],{},[898,106950,1978],{},[902,106952,1978],{"encoding":904},[115,106954,106956],{"id":106955},"dvě-formy-zdanění","Dvě formy zdanění",[724,106958,106959,106960,106978],{},"Uvažujme jednotkovou daň ",[883,106961,106963],{"className":106962},[886],[888,106964,106965],{"xmlns":890},[892,106966,106967,106975],{},[895,106968,106969,106971,106973],{},[898,106970,1978],{},[1708,106972,2854],{},[2505,106974,2784],{},[902,106976,106977],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,106980,106981,106987],{},[123,106982,106983,106986],{},[38,106984,106985],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,106988,106989,106992],{},[38,106990,106991],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,106994,106995,106996,107009,107010,107013,107014,2155],{},"V obou případech dochází k posunu jedné z křivek o ",[883,106997,106999],{"className":106998},[886],[888,107000,107001],{"xmlns":890},[892,107002,107003,107007],{},[895,107004,107005],{},[898,107006,1978],{},[902,107008,1978],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,107011,107012],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,107015,107017],{"className":107016},[886],[888,107018,107019],{"xmlns":890},[892,107020,107021,107043],{},[895,107022,107023,107025,107027,107033,107035,107041],{},[898,107024,16183],{},[1708,107026,6940],{"stretchy":1715},[1753,107028,107029,107031],{},[898,107030,1688],{},[898,107032,16183],{},[1708,107034,1883],{"separator":1882},[1753,107036,107037,107039],{},[898,107038,1747],{},[898,107040,16183],{},[1708,107042,6981],{"stretchy":1715},[902,107044,53199],{"encoding":904},[48808,107046],{},[115,107048,107050],{"id":107049},"daň-uložená-výrobci","Daň uložená výrobci",[724,107052,107053,107054,107067,107068,107085,107086,107113],{},"Je-li daň ",[883,107055,107057],{"className":107056},[886],[888,107058,107059],{"xmlns":890},[892,107060,107061,107065],{},[895,107062,107063],{},[898,107064,1978],{},[902,107066,1978],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,107069,107071],{"className":107070},[886],[888,107072,107073],{"xmlns":890},[892,107074,107075,107083],{},[895,107076,107077,107079,107081],{},[898,107078,1747],{},[1708,107080,2726],{},[898,107082,1978],{},[902,107084,52954],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,107087,107089],{"className":107088},[886],[888,107090,107091],{"xmlns":890},[892,107092,107093,107111],{},[895,107094,107095,107097,107099,107101,107103,107105,107107,107109],{},[898,107096,1747],{},[1708,107098,2726],{},[898,107100,1978],{},[1708,107102,1710],{},[898,107104,1981],{},[1708,107106,1716],{"stretchy":1715},[898,107108,1688],{},[1708,107110,1721],{"stretchy":1715},[902,107112,52983],{"encoding":904}," nová funkce nabídky:",[883,107115,107117],{"className":107116},[886],[888,107118,107119],{"xmlns":890,"display":2210},[892,107120,107121,107155],{},[895,107122,107123,107125,107127,107133,107135,107137,107139,107141,107143,107145,107147,107149,107151,107153],{},[898,107124,1747],{},[1708,107126,1710],{},[1743,107128,107129,107131],{},[898,107130,1981],{},[2505,107132,2507],{},[1708,107134,1716],{"stretchy":1715},[898,107136,1688],{},[1708,107138,1721],{"stretchy":1715},[1708,107140,1710],{},[898,107142,1981],{},[1708,107144,1716],{"stretchy":1715},[898,107146,1688],{},[1708,107148,1721],{"stretchy":1715},[1708,107150,2019],{},[898,107152,1978],{},[898,107154,2155],{"mathvariant":1759},[902,107156,53028],{"encoding":904},[724,107158,107159,107160,1729,107173,107175],{},"Nabídka se tedy posouvá o ",[883,107161,107163],{"className":107162},[886],[888,107164,107165],{"xmlns":890},[892,107166,107167,107171],{},[895,107168,107169],{},[898,107170,1978],{},[902,107172,1978],{"encoding":904},[38,107174,53061],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,107177,107178,107179,107219,107220,1771,107248,107276,107277,107296,107297,107321,107322,2511],{},"Nový rovnovážný bod ",[883,107180,107182],{"className":107181},[886],[888,107183,107184],{"xmlns":890},[892,107185,107186,107216],{},[895,107187,107188,107194,107196,107204,107206,107214],{},[1743,107189,107190,107192],{},[898,107191,16183],{},[2505,107193,2507],{},[1708,107195,6940],{"stretchy":1715},[4754,107197,107198,107200,107202],{},[898,107199,1688],{},[2505,107201,2507],{},[898,107203,16183],{},[1708,107205,1883],{"separator":1882},[4754,107207,107208,107210,107212],{},[898,107209,1747],{},[2505,107211,2507],{},[898,107213,16183],{},[1708,107215,6981],{"stretchy":1715},[902,107217,107218],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,107221,107223],{"className":107222},[886],[888,107224,107225],{"xmlns":890},[892,107226,107227,107245],{},[895,107228,107229,107237,107239],{},[4754,107230,107231,107233,107235],{},[898,107232,1688],{},[2505,107234,2507],{},[898,107236,16183],{},[1708,107238,2932],{},[1753,107240,107241,107243],{},[898,107242,1688],{},[898,107244,16183],{},[902,107246,107247],{"encoding":904},"Q_1^E \u003C Q^E",[883,107249,107251],{"className":107250},[886],[888,107252,107253],{"xmlns":890},[892,107254,107255,107273],{},[895,107256,107257,107265,107267],{},[4754,107258,107259,107261,107263],{},[898,107260,1747],{},[2505,107262,2507],{},[898,107264,16183],{},[1708,107266,2854],{},[1753,107268,107269,107271],{},[898,107270,1747],{},[898,107272,16183],{},[902,107274,107275],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,107278,107280],{"className":107279},[886],[888,107281,107282],{"xmlns":890},[892,107283,107284,107294],{},[895,107285,107286],{},[4754,107287,107288,107290,107292],{},[898,107289,1747],{},[2505,107291,2507],{},[898,107293,16183],{},[902,107295,59682],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,107298,107300],{"className":107299},[886],[888,107301,107302],{"xmlns":890},[892,107303,107304,107318],{},[895,107305,107306,107314,107316],{},[4754,107307,107308,107310,107312],{},[898,107309,1747],{},[2505,107311,2507],{},[898,107313,16183],{},[1708,107315,2726],{},[898,107317,1978],{},[902,107319,107320],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,107323,107325],{"className":107324},[886],[888,107326,107327],{"xmlns":890},[892,107328,107329,107337],{},[895,107330,107331],{},[1753,107332,107333,107335],{},[898,107334,1747],{},[898,107336,16183],{},[902,107338,53298],{"encoding":904},[724,107340,107341],{},[614,107342,107343,107344,107374,107375,107388,107389,3136,107406,107419,107420,2155],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,107345,107347],{"className":107346},[886],[888,107348,107349],{"xmlns":890},[892,107350,107351,107371],{},[895,107352,107353,107355,107357,107363,107365,107367,107369],{},[898,107354,1981],{},[1708,107356,9392],{},[1743,107358,107359,107361],{},[898,107360,1981],{},[2505,107362,2507],{},[1708,107364,1710],{},[898,107366,1981],{},[1708,107368,2019],{},[898,107370,1978],{},[902,107372,107373],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,107376,107378],{"className":107377},[886],[888,107379,107380],{"xmlns":890},[892,107381,107382,107386],{},[895,107383,107384],{},[898,107385,1978],{},[902,107387,1978],{"encoding":904},". Průsečík ",[883,107390,107392],{"className":107391},[886],[888,107393,107394],{"xmlns":890},[892,107395,107396,107404],{},[895,107397,107398],{},[1743,107399,107400,107402],{},[898,107401,1981],{},[2505,107403,2507],{},[902,107405,52829],{"encoding":904},[883,107407,107409],{"className":107408},[886],[888,107410,107411],{"xmlns":890},[892,107412,107413,107417],{},[895,107414,107415],{},[898,107416,16117],{},[902,107418,16117],{"encoding":904}," je nový rovnovážný bod ",[883,107421,107423],{"className":107422},[886],[888,107424,107425],{"xmlns":890},[892,107426,107427,107435],{},[895,107428,107429],{},[1743,107430,107431,107433],{},[898,107432,16183],{},[2505,107434,2507],{},[902,107436,107437],{"encoding":904},"E_1",[198,107439,57130],{"id":107440},"příklad-29",[724,107442,107443,53487,107445,53522,107469,107489,107490,107507],{},[38,107444,49769],{},[883,107446,107448],{"className":107447},[886],[888,107449,107450],{"xmlns":890},[892,107451,107452,107466],{},[895,107453,107454,107456,107458,107460,107462,107464],{},[898,107455,1747],{},[1708,107457,1710],{},[2505,107459,4090],{},[1708,107461,2726],{},[2505,107463,3132],{},[898,107465,1688],{},[902,107467,107468],{"encoding":904},"P = 12 - 2Q",[883,107470,107472],{"className":107471},[886],[888,107473,107474],{"xmlns":890},[892,107475,107476,107486],{},[895,107477,107478,107480,107482,107484],{},[898,107479,1747],{},[1708,107481,1710],{},[2505,107483,5867],{},[898,107485,1688],{},[902,107487,107488],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,107491,107493],{"className":107492},[886],[888,107494,107495],{"xmlns":890},[892,107496,107497,107505],{},[895,107498,107499,107501,107503],{},[898,107500,1978],{},[1708,107502,1710],{},[2505,107504,3947],{},[902,107506,53100],{"encoding":904}," Kč.",[724,107509,107510],{},[38,107511,49801],{},[724,107513,107514,107517,107518,17489,107544,17508,107564,1343,107586,107616,107617,2155],{},[614,107515,107516],{},"Bez daně."," Z rovnosti ",[883,107519,107521],{"className":107520},[886],[888,107522,107523],{"xmlns":890},[892,107524,107525,107541],{},[895,107526,107527,107529,107531,107533,107535,107537,107539],{},[2505,107528,4090],{},[1708,107530,2726],{},[2505,107532,3132],{},[898,107534,1688],{},[1708,107536,1710],{},[2505,107538,5867],{},[898,107540,1688],{},[902,107542,107543],{"encoding":904},"12 - 2Q = 4Q",[883,107545,107547],{"className":107546},[886],[888,107548,107549],{"xmlns":890},[892,107550,107551,107561],{},[895,107552,107553,107555,107557,107559],{},[2505,107554,3947],{},[898,107556,1688],{},[1708,107558,1710],{},[2505,107560,4090],{},[902,107562,107563],{"encoding":904},"6Q = 12",[883,107565,107567],{"className":107566},[886],[888,107568,107569],{"xmlns":890},[892,107570,107571,107583],{},[895,107572,107573,107579,107581],{},[1753,107574,107575,107577],{},[898,107576,1688],{},[898,107578,16183],{},[1708,107580,1710],{},[2505,107582,3132],{},[902,107584,107585],{"encoding":904},"Q^E = 2",[883,107587,107589],{"className":107588},[886],[888,107590,107591],{"xmlns":890},[892,107592,107593,107613],{},[895,107594,107595,107601,107603,107605,107607,107609,107611],{},[1753,107596,107597,107599],{},[898,107598,1747],{},[898,107600,16183],{},[1708,107602,1710],{},[2505,107604,5867],{},[1708,107606,3703],{},[2505,107608,3132],{},[1708,107610,1710],{},[2505,107612,3998],{},[902,107614,107615],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,107618,107620],{"className":107619},[886],[888,107621,107622],{"xmlns":890},[892,107623,107624,107638],{},[895,107625,107626,107628,107630,107632,107634,107636],{},[898,107627,16183],{},[1708,107629,6940],{"stretchy":1715},[2505,107631,3132],{},[1708,107633,1883],{"separator":1882},[2505,107635,3998],{},[1708,107637,6981],{"stretchy":1715},[902,107639,107640],{"encoding":904},"E[2, 8]",[724,107642,107643,107646,107647,107679],{},[614,107644,107645],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,107648,107650],{"className":107649},[886],[888,107651,107652],{"xmlns":890},[892,107653,107654,107676],{},[895,107655,107656,107662,107664,107666,107668,107670,107672,107674],{},[1743,107657,107658,107660],{},[898,107659,1981],{},[2505,107661,2507],{},[1708,107663,2788],{},[898,107665,1747],{},[1708,107667,1710],{},[2505,107669,5867],{},[898,107671,1688],{},[1708,107673,2019],{},[2505,107675,3947],{},[902,107677,107678],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,107681,107683],{"className":107682},[886],[888,107684,107685],{"xmlns":890,"display":2210},[892,107686,107687,107707],{},[895,107688,107689,107691,107693,107695,107697,107699,107701,107703,107705],{},[2505,107690,4090],{},[1708,107692,2726],{},[2505,107694,3132],{},[898,107696,1688],{},[1708,107698,1710],{},[2505,107700,5867],{},[898,107702,1688],{},[1708,107704,2019],{},[2505,107706,3947],{},[902,107708,107709],{"encoding":904},"12 - 2Q = 4Q + 6",[724,107711,107712,107713,17508,107733,1343,107757,107793,107794,2155],{},"plyne ",[883,107714,107716],{"className":107715},[886],[888,107717,107718],{"xmlns":890},[892,107719,107720,107730],{},[895,107721,107722,107724,107726,107728],{},[2505,107723,3947],{},[898,107725,1688],{},[1708,107727,1710],{},[2505,107729,3947],{},[902,107731,107732],{"encoding":904},"6Q = 6",[883,107734,107736],{"className":107735},[886],[888,107737,107738],{"xmlns":890},[892,107739,107740,107754],{},[895,107741,107742,107750,107752],{},[4754,107743,107744,107746,107748],{},[898,107745,1688],{},[2505,107747,2507],{},[898,107749,16183],{},[1708,107751,1710],{},[2505,107753,2507],{},[902,107755,107756],{"encoding":904},"Q_1^E = 1",[883,107758,107760],{"className":107759},[886],[888,107761,107762],{"xmlns":890},[892,107763,107764,107790],{},[895,107765,107766,107774,107776,107778,107780,107782,107784,107786,107788],{},[4754,107767,107768,107770,107772],{},[898,107769,1747],{},[2505,107771,2507],{},[898,107773,16183],{},[1708,107775,1710],{},[2505,107777,5867],{},[1708,107779,3703],{},[2505,107781,2507],{},[1708,107783,2019],{},[2505,107785,3947],{},[1708,107787,1710],{},[2505,107789,4003],{},[902,107791,107792],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,107795,107797],{"className":107796},[886],[888,107798,107799],{"xmlns":890},[892,107800,107801,107819],{},[895,107802,107803,107809,107811,107813,107815,107817],{},[1743,107804,107805,107807],{},[898,107806,16183],{},[2505,107808,2507],{},[1708,107810,6940],{"stretchy":1715},[2505,107812,2507],{},[1708,107814,1883],{"separator":1882},[2505,107816,4003],{},[1708,107818,6981],{"stretchy":1715},[902,107820,107821],{"encoding":904},"E_1[1, 10]",[724,107823,107824,107827,107828,107852,107853,107866],{},[614,107825,107826],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,107829,107831],{"className":107830},[886],[888,107832,107833],{"xmlns":890},[892,107834,107835,107849],{},[895,107836,107837,107845,107847],{},[4754,107838,107839,107841,107843],{},[898,107840,1747],{},[2505,107842,2507],{},[898,107844,16183],{},[1708,107846,1710],{},[2505,107848,4003],{},[902,107850,107851],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,107854,107856],{"className":107855},[886],[888,107857,107858],{"xmlns":890},[892,107859,107860,107864],{},[895,107861,107862],{},[2505,107863,3998],{},[902,107865,3998],{"encoding":904},", navýšení je",[883,107868,107870],{"className":107869},[886],[888,107871,107872],{"xmlns":890,"display":2210},[892,107873,107874,107930],{},[895,107875,107876,107886,107888,107896,107898,107904,107906,107908,107910,107912,107914,107916,107918,107928],{},[1743,107877,107878,107880],{},[898,107879,1978],{},[895,107881,107882,107884],{},[898,107883,54507],{},[898,107885,724],{},[1708,107887,1710],{},[4754,107889,107890,107892,107894],{},[898,107891,1747],{},[2505,107893,2507],{},[898,107895,16183],{},[1708,107897,2726],{},[1753,107899,107900,107902],{},[898,107901,1747],{},[898,107903,16183],{},[1708,107905,1710],{},[2505,107907,4003],{},[1708,107909,2726],{},[2505,107911,3998],{},[1708,107913,1710],{},[2505,107915,3132],{},[2247,107917,14279],{},[895,107919,107920,107922],{},[2247,107921,1673],{},[20297,107923,107924,107926],{"accent":1882},[2247,107925,14142],{},[1708,107927,36910],{},[898,107929,2155],{"mathvariant":1759},[902,107931,107932],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,107934,107935,107936,107852,107972,107985],{},"Výrobci zůstává čistá cena ",[883,107937,107939],{"className":107938},[886],[888,107940,107941],{"xmlns":890},[892,107942,107943,107969],{},[895,107944,107945,107953,107955,107957,107959,107961,107963,107965,107967],{},[4754,107946,107947,107949,107951],{},[898,107948,1747],{},[2505,107950,2507],{},[898,107952,16183],{},[1708,107954,2726],{},[898,107956,1978],{},[1708,107958,1710],{},[2505,107960,4003],{},[1708,107962,2726],{},[2505,107964,3947],{},[1708,107966,1710],{},[2505,107968,5867],{},[902,107970,107971],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,107973,107975],{"className":107974},[886],[888,107976,107977],{"xmlns":890},[892,107978,107979,107983],{},[895,107980,107981],{},[2505,107982,3998],{},[902,107984,3998],{"encoding":904},", pokles je",[883,107987,107989],{"className":107988},[886],[888,107990,107991],{"xmlns":890,"display":2210},[892,107992,107993,108059],{},[895,107994,107995,108007,108009,108015,108017,108019,108027,108029,108031,108033,108035,108037,108039,108041,108043,108045,108047,108057],{},[1743,107996,107997,107999],{},[898,107998,1978],{},[895,108000,108001,108003,108005],{},[898,108002,54530],{},[898,108004,14004],{},[898,108006,5498],{},[1708,108008,1710],{},[1753,108010,108011,108013],{},[898,108012,1747],{},[898,108014,16183],{},[1708,108016,2726],{},[1708,108018,1716],{"stretchy":1715},[4754,108020,108021,108023,108025],{},[898,108022,1747],{},[2505,108024,2507],{},[898,108026,16183],{},[1708,108028,2726],{},[898,108030,1978],{},[1708,108032,1721],{"stretchy":1715},[1708,108034,1710],{},[2505,108036,3998],{},[1708,108038,2726],{},[2505,108040,5867],{},[1708,108042,1710],{},[2505,108044,5867],{},[2247,108046,14279],{},[895,108048,108049,108051],{},[2247,108050,1673],{},[20297,108052,108053,108055],{"accent":1882},[2247,108054,14142],{},[1708,108056,36910],{},[898,108058,2155],{"mathvariant":1759},[902,108060,108061],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,108063,108064,108065,108117],{},"Kontrola: ",[883,108066,108068],{"className":108067},[886],[888,108069,108070],{"xmlns":890},[892,108071,108072,108114],{},[895,108073,108074,108084,108086,108098,108100,108102,108104,108106,108108,108110,108112],{},[1743,108075,108076,108078],{},[898,108077,1978],{},[895,108079,108080,108082],{},[898,108081,54507],{},[898,108083,724],{},[1708,108085,2019],{},[1743,108087,108088,108090],{},[898,108089,1978],{},[895,108091,108092,108094,108096],{},[898,108093,54530],{},[898,108095,14004],{},[898,108097,5498],{},[1708,108099,1710],{},[2505,108101,3132],{},[1708,108103,2019],{},[2505,108105,5867],{},[1708,108107,1710],{},[2505,108109,3947],{},[1708,108111,1710],{},[898,108113,1978],{},[902,108115,108116],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[48808,108119],{},[115,108121,108123],{"id":108122},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,108125,107053,108126,108139,108140,108158,108159,108187],{},[883,108127,108129],{"className":108128},[886],[888,108130,108131],{"xmlns":890},[892,108132,108133,108137],{},[895,108134,108135],{},[898,108136,1978],{},[902,108138,1978],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,108141,108143],{"className":108142},[886],[888,108144,108145],{"xmlns":890},[892,108146,108147,108155],{},[895,108148,108149,108151,108153],{},[898,108150,1747],{},[1708,108152,2019],{},[898,108154,1978],{},[902,108156,108157],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,108160,108162],{"className":108161},[886],[888,108163,108164],{"xmlns":890},[892,108165,108166,108184],{},[895,108167,108168,108170,108172,108174,108176,108178,108180,108182],{},[898,108169,1747],{},[1708,108171,2019],{},[898,108173,1978],{},[1708,108175,1710],{},[898,108177,16117],{},[1708,108179,1716],{"stretchy":1715},[898,108181,1688],{},[1708,108183,1721],{"stretchy":1715},[902,108185,108186],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,108189,108191],{"className":108190},[886],[888,108192,108193],{"xmlns":890,"display":2210},[892,108194,108195,108229],{},[895,108196,108197,108199,108201,108207,108209,108211,108213,108215,108217,108219,108221,108223,108225,108227],{},[898,108198,1747],{},[1708,108200,1710],{},[1743,108202,108203,108205],{},[898,108204,16117],{},[2505,108206,3132],{},[1708,108208,1716],{"stretchy":1715},[898,108210,1688],{},[1708,108212,1721],{"stretchy":1715},[1708,108214,1710],{},[898,108216,16117],{},[1708,108218,1716],{"stretchy":1715},[898,108220,1688],{},[1708,108222,1721],{"stretchy":1715},[1708,108224,2726],{},[898,108226,1978],{},[898,108228,2155],{"mathvariant":1759},[902,108230,108231],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,108233,108234,108235,1729,108248,108251],{},"Poptávka se tedy posouvá o ",[883,108236,108238],{"className":108237},[886],[888,108239,108240],{"xmlns":890},[892,108241,108242,108246],{},[895,108243,108244],{},[898,108245,1978],{},[902,108247,1978],{"encoding":904},[38,108249,108250],{},"svisle dolů",". Nabídka se nemění.",[724,108253,107178,108254,107219,108294,1771,108322,108350,108351,108370,108371,108395,108396,2511],{},[883,108255,108257],{"className":108256},[886],[888,108258,108259],{"xmlns":890},[892,108260,108261,108291],{},[895,108262,108263,108269,108271,108279,108281,108289],{},[1743,108264,108265,108267],{},[898,108266,16183],{},[2505,108268,3132],{},[1708,108270,6940],{"stretchy":1715},[4754,108272,108273,108275,108277],{},[898,108274,1688],{},[2505,108276,3132],{},[898,108278,16183],{},[1708,108280,1883],{"separator":1882},[4754,108282,108283,108285,108287],{},[898,108284,1747],{},[2505,108286,3132],{},[898,108288,16183],{},[1708,108290,6981],{"stretchy":1715},[902,108292,108293],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,108295,108297],{"className":108296},[886],[888,108298,108299],{"xmlns":890},[892,108300,108301,108319],{},[895,108302,108303,108311,108313],{},[4754,108304,108305,108307,108309],{},[898,108306,1688],{},[2505,108308,3132],{},[898,108310,16183],{},[1708,108312,2932],{},[1753,108314,108315,108317],{},[898,108316,1688],{},[898,108318,16183],{},[902,108320,108321],{"encoding":904},"Q_2^E \u003C Q^E",[883,108323,108325],{"className":108324},[886],[888,108326,108327],{"xmlns":890},[892,108328,108329,108347],{},[895,108330,108331,108339,108341],{},[4754,108332,108333,108335,108337],{},[898,108334,1747],{},[2505,108336,3132],{},[898,108338,16183],{},[1708,108340,2932],{},[1753,108342,108343,108345],{},[898,108344,1747],{},[898,108346,16183],{},[902,108348,108349],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,108352,108354],{"className":108353},[886],[888,108355,108356],{"xmlns":890},[892,108357,108358,108368],{},[895,108359,108360],{},[4754,108361,108362,108364,108366],{},[898,108363,1747],{},[2505,108365,3132],{},[898,108367,16183],{},[902,108369,59743],{"encoding":904},", spotřebitel platí celkem ",[883,108372,108374],{"className":108373},[886],[888,108375,108376],{"xmlns":890},[892,108377,108378,108392],{},[895,108379,108380,108388,108390],{},[4754,108381,108382,108384,108386],{},[898,108383,1747],{},[2505,108385,3132],{},[898,108387,16183],{},[1708,108389,2019],{},[898,108391,1978],{},[902,108393,108394],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,108397,108399],{"className":108398},[886],[888,108400,108401],{"xmlns":890},[892,108402,108403,108411],{},[895,108404,108405],{},[1753,108406,108407,108409],{},[898,108408,1747],{},[898,108410,16183],{},[902,108412,53298],{"encoding":904},[724,108414,108415],{},"Daňové břemeno:",[883,108417,108419],{"className":108418},[886],[888,108420,108421],{"xmlns":890,"display":2210},[892,108422,108423,108497],{},[895,108424,108425,108435,108437,108439,108447,108449,108451,108453,108455,108461,108463,108465,108477,108479,108485,108487,108495],{},[1743,108426,108427,108429],{},[898,108428,1978],{},[895,108430,108431,108433],{},[898,108432,54507],{},[898,108434,724],{},[1708,108436,1710],{},[1708,108438,1716],{"stretchy":1715},[4754,108440,108441,108443,108445],{},[898,108442,1747],{},[2505,108444,3132],{},[898,108446,16183],{},[1708,108448,2019],{},[898,108450,1978],{},[1708,108452,1721],{"stretchy":1715},[1708,108454,2726],{},[1753,108456,108457,108459],{},[898,108458,1747],{},[898,108460,16183],{},[1708,108462,1883],{"separator":1882},[3213,108464],{"width":3215},[1743,108466,108467,108469],{},[898,108468,1978],{},[895,108470,108471,108473,108475],{},[898,108472,54530],{},[898,108474,14004],{},[898,108476,5498],{},[1708,108478,1710],{},[1753,108480,108481,108483],{},[898,108482,1747],{},[898,108484,16183],{},[1708,108486,2726],{},[4754,108488,108489,108491,108493],{},[898,108490,1747],{},[2505,108492,3132],{},[898,108494,16183],{},[898,108496,2155],{"mathvariant":1759},[902,108498,108499],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,108501,108502],{},[614,108503,108504,108505,108535,108536,107388,108549,3136,108566,107419,108579,2155],{},"Obrázek 2.19: Posun ",[883,108506,108508],{"className":108507},[886],[888,108509,108510],{"xmlns":890},[892,108511,108512,108532],{},[895,108513,108514,108516,108518,108524,108526,108528,108530],{},[898,108515,16117],{},[1708,108517,9392],{},[1743,108519,108520,108522],{},[898,108521,16117],{},[2505,108523,3132],{},[1708,108525,1710],{},[898,108527,16117],{},[1708,108529,2726],{},[898,108531,1978],{},[902,108533,108534],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,108537,108539],{"className":108538},[886],[888,108540,108541],{"xmlns":890},[892,108542,108543,108547],{},[895,108544,108545],{},[898,108546,1978],{},[902,108548,1978],{"encoding":904},[883,108550,108552],{"className":108551},[886],[888,108553,108554],{"xmlns":890},[892,108555,108556,108564],{},[895,108557,108558],{},[1743,108559,108560,108562],{},[898,108561,16117],{},[2505,108563,3132],{},[902,108565,50163],{"encoding":904},[883,108567,108569],{"className":108568},[886],[888,108570,108571],{"xmlns":890},[892,108572,108573,108577],{},[895,108574,108575],{},[898,108576,1981],{},[902,108578,1981],{"encoding":904},[883,108580,108582],{"className":108581},[886],[888,108583,108584],{"xmlns":890},[892,108585,108586,108594],{},[895,108587,108588],{},[1743,108589,108590,108592],{},[898,108591,16183],{},[2505,108593,3132],{},[902,108595,108596],{"encoding":904},"E_2",[198,108598,57210],{"id":108599},"příklad-210",[724,108601,108602,108604,108605,53522,108628,108647,108648,108665],{},[38,108603,49769],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,108606,108608],{"className":108607},[886],[888,108609,108610],{"xmlns":890},[892,108611,108612,108626],{},[895,108613,108614,108616,108618,108620,108622,108624],{},[898,108615,1747],{},[1708,108617,1710],{},[2505,108619,4090],{},[1708,108621,2726],{},[2505,108623,3132],{},[898,108625,1688],{},[902,108627,107468],{"encoding":904},[883,108629,108631],{"className":108630},[886],[888,108632,108633],{"xmlns":890},[892,108634,108635,108645],{},[895,108636,108637,108639,108641,108643],{},[898,108638,1747],{},[1708,108640,1710],{},[2505,108642,5867],{},[898,108644,1688],{},[902,108646,107488],{"encoding":904},". Daň ",[883,108649,108651],{"className":108650},[886],[888,108652,108653],{"xmlns":890},[892,108654,108655,108663],{},[895,108656,108657,108659,108661],{},[898,108658,1978],{},[1708,108660,1710],{},[2505,108662,3947],{},[902,108664,53100],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,108667,108668],{},[38,108669,49801],{},[724,108671,108672,108673,107679],{},"Nová poptávka je ",[883,108674,108676],{"className":108675},[886],[888,108677,108678],{"xmlns":890},[892,108679,108680,108716],{},[895,108681,108682,108688,108690,108692,108694,108696,108698,108700,108702,108704,108706,108708,108710,108712,108714],{},[1743,108683,108684,108686],{},[898,108685,16117],{},[2505,108687,3132],{},[1708,108689,2788],{},[898,108691,1747],{},[1708,108693,1710],{},[2505,108695,4090],{},[1708,108697,2726],{},[2505,108699,3132],{},[898,108701,1688],{},[1708,108703,2726],{},[2505,108705,3947],{},[1708,108707,1710],{},[2505,108709,3947],{},[1708,108711,2726],{},[2505,108713,3132],{},[898,108715,1688],{},[902,108717,108718],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,108720,108722],{"className":108721},[886],[888,108723,108724],{"xmlns":890,"display":2210},[892,108725,108726,108742],{},[895,108727,108728,108730,108732,108734,108736,108738,108740],{},[2505,108729,3947],{},[1708,108731,2726],{},[2505,108733,3132],{},[898,108735,1688],{},[1708,108737,1710],{},[2505,108739,5867],{},[898,108741,1688],{},[902,108743,108744],{"encoding":904},"6 - 2Q = 4Q",[724,108746,107712,108747,17508,108766,1343,108790,107793,108822,2155],{},[883,108748,108750],{"className":108749},[886],[888,108751,108752],{"xmlns":890},[892,108753,108754,108764],{},[895,108755,108756,108758,108760,108762],{},[2505,108757,3947],{},[898,108759,1688],{},[1708,108761,1710],{},[2505,108763,3947],{},[902,108765,107732],{"encoding":904},[883,108767,108769],{"className":108768},[886],[888,108770,108771],{"xmlns":890},[892,108772,108773,108787],{},[895,108774,108775,108783,108785],{},[4754,108776,108777,108779,108781],{},[898,108778,1688],{},[2505,108780,3132],{},[898,108782,16183],{},[1708,108784,1710],{},[2505,108786,2507],{},[902,108788,108789],{"encoding":904},"Q_2^E = 1",[883,108791,108793],{"className":108792},[886],[888,108794,108795],{"xmlns":890},[892,108796,108797,108819],{},[895,108798,108799,108807,108809,108811,108813,108815,108817],{},[4754,108800,108801,108803,108805],{},[898,108802,1747],{},[2505,108804,3132],{},[898,108806,16183],{},[1708,108808,1710],{},[2505,108810,5867],{},[1708,108812,3703],{},[2505,108814,2507],{},[1708,108816,1710],{},[2505,108818,5867],{},[902,108820,108821],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,108823,108825],{"className":108824},[886],[888,108826,108827],{"xmlns":890},[892,108828,108829,108847],{},[895,108830,108831,108837,108839,108841,108843,108845],{},[1743,108832,108833,108835],{},[898,108834,16183],{},[2505,108836,3132],{},[1708,108838,6940],{"stretchy":1715},[2505,108840,2507],{},[1708,108842,1883],{"separator":1882},[2505,108844,5867],{},[1708,108846,6981],{"stretchy":1715},[902,108848,108849],{"encoding":904},"E_2[1, 4]",[724,108851,108852,108853,108889,108890,107507],{},"Spotřebitel platí celkem ",[883,108854,108856],{"className":108855},[886],[888,108857,108858],{"xmlns":890},[892,108859,108860,108886],{},[895,108861,108862,108870,108872,108874,108876,108878,108880,108882,108884],{},[4754,108863,108864,108866,108868],{},[898,108865,1747],{},[2505,108867,3132],{},[898,108869,16183],{},[1708,108871,2019],{},[898,108873,1978],{},[1708,108875,1710],{},[2505,108877,5867],{},[1708,108879,2019],{},[2505,108881,3947],{},[1708,108883,1710],{},[2505,108885,4003],{},[902,108887,108888],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,108891,108893],{"className":108892},[886],[888,108894,108895],{"xmlns":890},[892,108896,108897,108911],{},[895,108898,108899,108907,108909],{},[4754,108900,108901,108903,108905],{},[898,108902,1747],{},[2505,108904,3132],{},[898,108906,16183],{},[1708,108908,1710],{},[2505,108910,5867],{},[902,108912,108913],{"encoding":904},"P_2^E = 4",[724,108915,108916],{},[614,108917,108918],{},"Rozklad daňového břemene:",[883,108920,108922],{"className":108921},[886],[888,108923,108924],{"xmlns":890,"display":2210},[892,108925,108926,109012],{},[895,108927,108928,108938,108940,108942,108944,108946,108948,108950,108952,108954,108956,108958,108960,108970,108972,108974,108986,108988,108990,108992,108994,108996,108998,109000,109010],{},[1743,108929,108930,108932],{},[898,108931,1978],{},[895,108933,108934,108936],{},[898,108935,54507],{},[898,108937,724],{},[1708,108939,1710],{},[1708,108941,1716],{"stretchy":1715},[2505,108943,5867],{},[1708,108945,2019],{},[2505,108947,3947],{},[1708,108949,1721],{"stretchy":1715},[1708,108951,2726],{},[2505,108953,3998],{},[1708,108955,1710],{},[2505,108957,3132],{},[2247,108959,14279],{},[895,108961,108962,108964],{},[2247,108963,1673],{},[20297,108965,108966,108968],{"accent":1882},[2247,108967,14142],{},[1708,108969,36910],{},[1708,108971,1883],{"separator":1882},[3213,108973],{"width":3215},[1743,108975,108976,108978],{},[898,108977,1978],{},[895,108979,108980,108982,108984],{},[898,108981,54530],{},[898,108983,14004],{},[898,108985,5498],{},[1708,108987,1710],{},[2505,108989,3998],{},[1708,108991,2726],{},[2505,108993,5867],{},[1708,108995,1710],{},[2505,108997,5867],{},[2247,108999,14279],{},[895,109001,109002,109004],{},[2247,109003,1673],{},[20297,109005,109006,109008],{"accent":1882},[2247,109007,14142],{},[1708,109009,36910],{},[898,109011,2155],{"mathvariant":1759},[902,109013,109014],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,109016,109017,109018,2155],{},"Opět ",[883,109019,109021],{"className":109020},[886],[888,109022,109023],{"xmlns":890},[892,109024,109025,109059],{},[895,109026,109027,109037,109039,109051,109053,109055,109057],{},[1743,109028,109029,109031],{},[898,109030,1978],{},[895,109032,109033,109035],{},[898,109034,54507],{},[898,109036,724],{},[1708,109038,2019],{},[1743,109040,109041,109043],{},[898,109042,1978],{},[895,109044,109045,109047,109049],{},[898,109046,54530],{},[898,109048,14004],{},[898,109050,5498],{},[1708,109052,1710],{},[2505,109054,3947],{},[1708,109056,1710],{},[898,109058,1978],{},[902,109060,109061],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[48808,109063],{},[115,109065,54488],{"id":109066},"daňové-břemeno",[724,109068,109069,1695,109071,109074,109075,109088],{},[38,109070,54488],{},[614,109072,109073],{},"tax burden",") je rozdělení zaplacené daně ",[883,109076,109078],{"className":109077},[886],[888,109079,109080],{"xmlns":890},[892,109081,109082,109086],{},[895,109083,109084],{},[898,109085,1978],{},[902,109087,1978],{"encoding":904}," mezi spotřebitele a výrobce:",[883,109090,109092],{"className":109091},[886],[888,109093,109094],{"xmlns":890,"display":2210},[892,109095,109096,109128],{},[895,109097,109098,109100,109102,109112,109114,109126],{},[898,109099,1978],{},[1708,109101,1710],{},[1743,109103,109104,109106],{},[898,109105,1978],{},[895,109107,109108,109110],{},[898,109109,54507],{},[898,109111,724],{},[1708,109113,2019],{},[1743,109115,109116,109118],{},[898,109117,1978],{},[895,109119,109120,109122,109124],{},[898,109121,54530],{},[898,109123,14004],{},[898,109125,5498],{},[898,109127,2155],{"mathvariant":1759},[902,109129,109130],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,109132,109133],{},[3372,109134],{"alt":109135,"className":109136,"src":109137},"imek-dan-rozklad-bremene-sklony",[210,3376],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1636,109139,109140],{},[724,109141,109142,109144,109145,1771,109158,2155],{},[883,109143,2518],{}," 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 ",[883,109146,109148],{"className":109147},[886],[888,109149,109150],{"xmlns":890},[892,109151,109152,109156],{},[895,109153,109154],{},[898,109155,16117],{},[902,109157,16117],{"encoding":904},[883,109159,109161],{"className":109160},[886],[888,109162,109163],{"xmlns":890},[892,109164,109165,109169],{},[895,109166,109167],{},[898,109168,1981],{},[902,109170,1981],{"encoding":904},[198,109172,14425],{"id":14424},[724,109174,109175,109176,109197,109198,109211,109212,109229,109230,109243],{},"V grafu ",[883,109177,109179],{"className":109178},[886],[888,109180,109181],{"xmlns":890},[892,109182,109183,109195],{},[895,109184,109185,109187,109189,109191,109193],{},[1708,109186,1716],{"stretchy":1715},[898,109188,1688],{},[1708,109190,1883],{"separator":1882},[898,109192,1747],{},[1708,109194,1721],{"stretchy":1715},[902,109196,49527],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,109199,109201],{"className":109200},[886],[888,109202,109203],{"xmlns":890},[892,109204,109205,109209],{},[895,109206,109207],{},[898,109208,1978],{},[902,109210,1978],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,109213,109215],{"className":109214},[886],[888,109216,109217],{"xmlns":890},[892,109218,109219,109227],{},[895,109220,109221],{},[1753,109222,109223,109225],{},[898,109224,1747],{},[898,109226,16183],{},[902,109228,53298],{"encoding":904},", rozdělí se úsečka ",[883,109231,109233],{"className":109232},[886],[888,109234,109235],{"xmlns":890},[892,109236,109237,109241],{},[895,109238,109239],{},[898,109240,1978],{},[902,109242,1978],{"encoding":904}," na dvě části:",[120,109245,109246,109271],{},[123,109247,109248,109249,109270],{},"horní část odpovídá ",[883,109250,109252],{"className":109251},[886],[888,109253,109254],{"xmlns":890},[892,109255,109256,109268],{},[895,109257,109258],{},[1743,109259,109260,109262],{},[898,109261,1978],{},[895,109263,109264,109266],{},[898,109265,54507],{},[898,109267,724],{},[902,109269,54512],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,109272,109273,109274,109297],{},"dolní část odpovídá ",[883,109275,109277],{"className":109276},[886],[888,109278,109279],{"xmlns":890},[892,109280,109281,109295],{},[895,109282,109283],{},[1743,109284,109285,109287],{},[898,109286,1978],{},[895,109288,109289,109291,109293],{},[898,109290,54530],{},[898,109292,14004],{},[898,109294,5498],{},[902,109296,54537],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,109299,109300],{},[614,109301,109302,109303,2486,109316,109337,109338,109361,109362,1771,109383,109406],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,109304,109306],{"className":109305},[886],[888,109307,109308],{"xmlns":890},[892,109309,109310,109314],{},[895,109311,109312],{},[898,109313,1978],{},[902,109315,1978],{"encoding":904},[883,109317,109319],{"className":109318},[886],[888,109320,109321],{"xmlns":890},[892,109322,109323,109335],{},[895,109324,109325],{},[1743,109326,109327,109329],{},[898,109328,1978],{},[895,109330,109331,109333],{},[898,109332,54507],{},[898,109334,724],{},[902,109336,54512],{"encoding":904}," (nahoře) a ",[883,109339,109341],{"className":109340},[886],[888,109342,109343],{"xmlns":890},[892,109344,109345,109359],{},[895,109346,109347],{},[1743,109348,109349,109351],{},[898,109350,1978],{},[895,109352,109353,109355,109357],{},[898,109354,54530],{},[898,109356,14004],{},[898,109358,5498],{},[902,109360,54537],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,109363,109365],{"className":109364},[886],[888,109366,109367],{"xmlns":890},[892,109368,109369,109381],{},[895,109370,109371],{},[1743,109372,109373,109375],{},[898,109374,1978],{},[895,109376,109377,109379],{},[898,109378,54507],{},[898,109380,724],{},[902,109382,54512],{"encoding":904},[883,109384,109386],{"className":109385},[886],[888,109387,109388],{"xmlns":890},[892,109389,109390,109404],{},[895,109391,109392],{},[1743,109393,109394,109396],{},[898,109395,1978],{},[895,109397,109398,109400,109402],{},[898,109399,54530],{},[898,109401,14004],{},[898,109403,5498],{},[902,109405,54537],{"encoding":904}," je v obou případech stejná.",[198,109408,109410],{"id":109409},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,109412,109413,109414,109417,109418,1695,109441,109458,109459,1695,109482,109499],{},"Platí obecně: ",[38,109415,109416],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,109419,109421],{"className":109420},[886],[888,109422,109423],{"xmlns":890},[892,109424,109425,109439],{},[895,109426,109427,109429,109431,109433,109435,109437],{},[898,109428,1747],{},[1708,109430,1710],{},[898,109432,207],{},[898,109434,1688],{},[1708,109436,2019],{},[898,109438,1923],{},[902,109440,48898],{"encoding":904},[883,109442,109444],{"className":109443},[886],[888,109445,109446],{"xmlns":890},[892,109447,109448,109456],{},[895,109449,109450,109452,109454],{},[898,109451,207],{},[1708,109453,2932],{},[2505,109455,2784],{},[902,109457,3154],{"encoding":904},") a lineární nabídku ",[883,109460,109462],{"className":109461},[886],[888,109463,109464],{"xmlns":890},[892,109465,109466,109480],{},[895,109467,109468,109470,109472,109474,109476,109478],{},[898,109469,1747],{},[1708,109471,1710],{},[898,109473,14142],{},[898,109475,1688],{},[1708,109477,2019],{},[898,109479,2364],{},[902,109481,52076],{"encoding":904},[883,109483,109485],{"className":109484},[886],[888,109486,109487],{"xmlns":890},[892,109488,109489,109497],{},[895,109490,109491,109493,109495],{},[898,109492,14142],{},[1708,109494,2854],{},[2505,109496,2784],{},[902,109498,52094],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,109501,109503],{"className":109502},[886],[888,109504,109505],{"xmlns":890,"display":2210},[892,109506,109507,109573],{},[895,109508,109509,109533,109535,109545,109547,109571],{},[2358,109510,109511,109521],{},[1743,109512,109513,109515],{},[898,109514,1978],{},[895,109516,109517,109519],{},[898,109518,54507],{},[898,109520,724],{},[1743,109522,109523,109525],{},[898,109524,1978],{},[895,109526,109527,109529,109531],{},[898,109528,54530],{},[898,109530,14004],{},[898,109532,5498],{},[1708,109534,1710],{},[2358,109536,109537,109539],{},[898,109538,14142],{},[895,109540,109541,109543],{},[1708,109542,2726],{},[898,109544,207],{},[1708,109546,1710],{},[2358,109548,109549,109561],{},[895,109550,109551,109554,109557,109559],{},[898,109552,109553],{"mathvariant":1759},"∣",[2247,109555,109556],{},"sklon ",[898,109558,1981],{},[898,109560,109553],{"mathvariant":1759},[895,109562,109563,109565,109567,109569],{},[898,109564,109553],{"mathvariant":1759},[2247,109566,109556],{},[898,109568,16117],{},[898,109570,109553],{"mathvariant":1759},[898,109572,2155],{"mathvariant":1759},[902,109574,109575],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1636,109577,109578,109583],{},[724,109579,109580,109582],{},[883,109581,3465],{}," Postup výpočtu rozkladu",[152,109584,109585,109620,109673,109752],{},[123,109586,109587,109588,109619],{},"Spočti rovnovážný bod ",[883,109589,109591],{"className":109590},[886],[888,109592,109593],{"xmlns":890},[892,109594,109595,109617],{},[895,109596,109597,109599,109601,109607,109609,109615],{},[898,109598,16183],{},[1708,109600,6940],{"stretchy":1715},[1753,109602,109603,109605],{},[898,109604,1688],{},[898,109606,16183],{},[1708,109608,1883],{"separator":1882},[1753,109610,109611,109613],{},[898,109612,1747],{},[898,109614,16183],{},[1708,109616,6981],{"stretchy":1715},[902,109618,53199],{"encoding":904}," bez daně.",[123,109621,109622,109623,1348,109648,2511],{},"Urči posunutou křivku (",[883,109624,109626],{"className":109625},[886],[888,109627,109628],{"xmlns":890},[892,109629,109630,109646],{},[895,109631,109632,109638,109640,109642,109644],{},[1743,109633,109634,109636],{},[898,109635,1981],{},[2505,109637,2507],{},[1708,109639,1710],{},[898,109641,1981],{},[1708,109643,2019],{},[898,109645,1978],{},[902,109647,54584],{"encoding":904},[883,109649,109651],{"className":109650},[886],[888,109652,109653],{"xmlns":890},[892,109654,109655,109671],{},[895,109656,109657,109663,109665,109667,109669],{},[1743,109658,109659,109661],{},[898,109660,16117],{},[2505,109662,3132],{},[1708,109664,1710],{},[898,109666,16117],{},[1708,109668,2726],{},[898,109670,1978],{},[902,109672,54615],{"encoding":904},[123,109674,109675,109676,15851,109695,5149,109714,15851,109733,2511],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,109677,109679],{"className":109678},[886],[888,109680,109681],{"xmlns":890},[892,109682,109683,109693],{},[895,109684,109685],{},[4754,109686,109687,109689,109691],{},[898,109688,1688],{},[2505,109690,2507],{},[898,109692,16183],{},[902,109694,59661],{"encoding":904},[883,109696,109698],{"className":109697},[886],[888,109699,109700],{"xmlns":890},[892,109701,109702,109712],{},[895,109703,109704],{},[4754,109705,109706,109708,109710],{},[898,109707,1688],{},[2505,109709,3132],{},[898,109711,16183],{},[902,109713,59723],{"encoding":904},[883,109715,109717],{"className":109716},[886],[888,109718,109719],{"xmlns":890},[892,109720,109721,109731],{},[895,109722,109723],{},[4754,109724,109725,109727,109729],{},[898,109726,1747],{},[2505,109728,2507],{},[898,109730,16183],{},[902,109732,59682],{"encoding":904},[883,109734,109736],{"className":109735},[886],[888,109737,109738],{"xmlns":890},[892,109739,109740,109750],{},[895,109741,109742],{},[4754,109743,109744,109746,109748],{},[898,109745,1747],{},[2505,109747,3132],{},[898,109749,16183],{},[902,109751,59743],{"encoding":904},[123,109753,109754,109755,1771,109776,109799,109800,2155],{},"Dopočítej ",[883,109756,109758],{"className":109757},[886],[888,109759,109760],{"xmlns":890},[892,109761,109762,109774],{},[895,109763,109764],{},[1743,109765,109766,109768],{},[898,109767,1978],{},[895,109769,109770,109772],{},[898,109771,54507],{},[898,109773,724],{},[902,109775,54512],{"encoding":904},[883,109777,109779],{"className":109778},[886],[888,109780,109781],{"xmlns":890},[892,109782,109783,109797],{},[895,109784,109785],{},[1743,109786,109787,109789],{},[898,109788,1978],{},[895,109790,109791,109793,109795],{},[898,109792,54530],{},[898,109794,14004],{},[898,109796,5498],{},[902,109798,54537],{"encoding":904}," z definice, vždy ověř ",[883,109801,109803],{"className":109802},[886],[888,109804,109805],{"xmlns":890},[892,109806,109807,109837],{},[895,109808,109809,109819,109821,109833,109835],{},[1743,109810,109811,109813],{},[898,109812,1978],{},[895,109814,109815,109817],{},[898,109816,54507],{},[898,109818,724],{},[1708,109820,2019],{},[1743,109822,109823,109825],{},[898,109824,1978],{},[895,109826,109827,109829,109831],{},[898,109828,54530],{},[898,109830,14004],{},[898,109832,5498],{},[1708,109834,1710],{},[898,109836,1978],{},[902,109838,109839],{"encoding":904},"T_{sp} + T_{vyr} = T",[1636,109841,109842],{},[724,109843,109844,109846,109847,109850,109851,1771,109864,109877],{},[883,109845,6130],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,109848,109849],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,109852,109854],{"className":109853},[886],[888,109855,109856],{"xmlns":890},[892,109857,109858,109862],{},[895,109859,109860],{},[898,109861,16117],{},[902,109863,16117],{"encoding":904},[883,109865,109867],{"className":109866},[886],[888,109868,109869],{"xmlns":890},[892,109870,109871,109875],{},[895,109872,109873],{},[898,109874,1981],{},[902,109876,1981],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[48808,109879],{},[115,109881,109883],{"id":109882},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,109885,109886],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,109888,109889],{},[3372,109890],{"alt":109891,"className":109892,"src":109893},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,3376],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,109895,109896,109908],{},[19,109897,109898],{},[22,109899,109900,109902,109905],{},[25,109901,66115],{},[25,109903,109904],{},"(a) daň výrobci",[25,109906,109907],{},"(b) daň spotřebiteli",[30,109909,109910,109965,110032,110092],{},[22,109911,109912,109915,109940],{},[35,109913,109914],{},"Rovnovážné množství",[35,109916,109917],{},[883,109918,109920],{"className":109919},[886],[888,109921,109922],{"xmlns":890},[892,109923,109924,109938],{},[895,109925,109926,109934,109936],{},[4754,109927,109928,109930,109932],{},[898,109929,1688],{},[2505,109931,2507],{},[898,109933,16183],{},[1708,109935,1710],{},[2505,109937,2507],{},[902,109939,107756],{"encoding":904},[35,109941,109942],{},[883,109943,109945],{"className":109944},[886],[888,109946,109947],{"xmlns":890},[892,109948,109949,109963],{},[895,109950,109951,109959,109961],{},[4754,109952,109953,109955,109957],{},[898,109954,1688],{},[2505,109956,3132],{},[898,109958,16183],{},[1708,109960,1710],{},[2505,109962,2507],{},[902,109964,108789],{"encoding":904},[22,109966,109967,109970,109995],{},[35,109968,109969],{},"Cena placená spotřebitelem",[35,109971,109972],{},[883,109973,109975],{"className":109974},[886],[888,109976,109977],{"xmlns":890},[892,109978,109979,109993],{},[895,109980,109981,109989,109991],{},[4754,109982,109983,109985,109987],{},[898,109984,1747],{},[2505,109986,2507],{},[898,109988,16183],{},[1708,109990,1710],{},[2505,109992,4003],{},[902,109994,107851],{"encoding":904},[35,109996,109997],{},[883,109998,110000],{"className":109999},[886],[888,110001,110002],{"xmlns":890},[892,110003,110004,110030],{},[895,110005,110006,110014,110016,110018,110020,110022,110024,110026,110028],{},[4754,110007,110008,110010,110012],{},[898,110009,1747],{},[2505,110011,3132],{},[898,110013,16183],{},[1708,110015,2019],{},[898,110017,1978],{},[1708,110019,1710],{},[2505,110021,5867],{},[1708,110023,2019],{},[2505,110025,3947],{},[1708,110027,1710],{},[2505,110029,4003],{},[902,110031,108888],{"encoding":904},[22,110033,110034,110037,110067],{},[35,110035,110036],{},"Cena přijímaná výrobcem",[35,110038,110039],{},[883,110040,110042],{"className":110041},[886],[888,110043,110044],{"xmlns":890},[892,110045,110046,110064],{},[895,110047,110048,110056,110058,110060,110062],{},[4754,110049,110050,110052,110054],{},[898,110051,1747],{},[2505,110053,2507],{},[898,110055,16183],{},[1708,110057,2726],{},[898,110059,1978],{},[1708,110061,1710],{},[2505,110063,5867],{},[902,110065,110066],{"encoding":904},"P_1^E - T = 4",[35,110068,110069],{},[883,110070,110072],{"className":110071},[886],[888,110073,110074],{"xmlns":890},[892,110075,110076,110090],{},[895,110077,110078,110086,110088],{},[4754,110079,110080,110082,110084],{},[898,110081,1747],{},[2505,110083,3132],{},[898,110085,16183],{},[1708,110087,1710],{},[2505,110089,5867],{},[902,110091,108913],{"encoding":904},[22,110093,110094,110097,110151],{},[35,110095,110096],{},"Rozklad břemene",[35,110098,110099,1343,110124],{},[883,110100,110102],{"className":110101},[886],[888,110103,110104],{"xmlns":890},[892,110105,110106,110122],{},[895,110107,110108,110118,110120],{},[1743,110109,110110,110112],{},[898,110111,1978],{},[895,110113,110114,110116],{},[898,110115,54507],{},[898,110117,724],{},[1708,110119,1710],{},[2505,110121,3132],{},[902,110123,54806],{"encoding":904},[883,110125,110127],{"className":110126},[886],[888,110128,110129],{"xmlns":890},[892,110130,110131,110149],{},[895,110132,110133,110145,110147],{},[1743,110134,110135,110137],{},[898,110136,1978],{},[895,110138,110139,110141,110143],{},[898,110140,54530],{},[898,110142,14004],{},[898,110144,5498],{},[1708,110146,1710],{},[2505,110148,5867],{},[902,110150,54835],{"encoding":904},[35,110152,110153,1343,110178],{},[883,110154,110156],{"className":110155},[886],[888,110157,110158],{"xmlns":890},[892,110159,110160,110176],{},[895,110161,110162,110172,110174],{},[1743,110163,110164,110166],{},[898,110165,1978],{},[895,110167,110168,110170],{},[898,110169,54507],{},[898,110171,724],{},[1708,110173,1710],{},[2505,110175,3132],{},[902,110177,54806],{"encoding":904},[883,110179,110181],{"className":110180},[886],[888,110182,110183],{"xmlns":890},[892,110184,110185,110203],{},[895,110186,110187,110199,110201],{},[1743,110188,110189,110191],{},[898,110190,1978],{},[895,110192,110193,110195,110197],{},[898,110194,54530],{},[898,110196,14004],{},[898,110198,5498],{},[1708,110200,1710],{},[2505,110202,5867],{},[902,110204,54835],{"encoding":904},[724,110206,110207],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,110209,110211],{"className":110210},[886],[888,110212,110213],{"xmlns":890,"display":2210},[892,110214,110215,110263],{},[895,110216,110217,110225,110227,110235,110237,110239,110247,110249,110251,110253,110261],{},[4754,110218,110219,110221,110223],{},[898,110220,1688],{},[2505,110222,2507],{},[898,110224,16183],{},[1708,110226,1710],{},[4754,110228,110229,110231,110233],{},[898,110230,1688],{},[2505,110232,3132],{},[898,110234,16183],{},[1708,110236,1883],{"separator":1882},[3213,110238],{"width":3215},[4754,110240,110241,110243,110245],{},[898,110242,1747],{},[2505,110244,2507],{},[898,110246,16183],{},[1708,110248,2726],{},[898,110250,1978],{},[1708,110252,1710],{},[4754,110254,110255,110257,110259],{},[898,110256,1747],{},[2505,110258,3132],{},[898,110260,16183],{},[898,110262,2155],{"mathvariant":1759},[902,110264,110265],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1636,110267,110268,110287,110441],{},[724,110269,110270,110272,110273,110286],{},[883,110271,3465],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,110274,110276],{"className":110275},[886],[888,110277,110278],{"xmlns":890},[892,110279,110280,110284],{},[895,110281,110282],{},[898,110283,1978],{},[902,110285,1978],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,110288,110289,110321,110357,110394],{},[123,110290,110291,110292,1883],{},"rovnovážná množství obou režimů, ",[883,110293,110295],{"className":110294},[886],[888,110296,110297],{"xmlns":890},[892,110298,110299,110319],{},[895,110300,110301,110309,110311],{},[4754,110302,110303,110305,110307],{},[898,110304,1688],{},[2505,110306,2507],{},[898,110308,16183],{},[1708,110310,1710],{},[4754,110312,110313,110315,110317],{},[898,110314,1688],{},[2505,110316,3132],{},[898,110318,16183],{},[902,110320,54738],{"encoding":904},[123,110322,110323,110324,1883],{},"čistá cena přijímaná výrobcem, ",[883,110325,110327],{"className":110326},[886],[888,110328,110329],{"xmlns":890},[892,110330,110331,110355],{},[895,110332,110333,110341,110343,110345,110347],{},[4754,110334,110335,110337,110339],{},[898,110336,1747],{},[2505,110338,2507],{},[898,110340,16183],{},[1708,110342,2726],{},[898,110344,1978],{},[1708,110346,1710],{},[4754,110348,110349,110351,110353],{},[898,110350,1747],{},[2505,110352,3132],{},[898,110354,16183],{},[902,110356,54772],{"encoding":904},[123,110358,110359,110360,1883],{},"celková cena placená spotřebitelem, ",[883,110361,110363],{"className":110362},[886],[888,110364,110365],{"xmlns":890},[892,110366,110367,110391],{},[895,110368,110369,110377,110379,110387,110389],{},[4754,110370,110371,110373,110375],{},[898,110372,1747],{},[2505,110374,2507],{},[898,110376,16183],{},[1708,110378,1710],{},[4754,110380,110381,110383,110385],{},[898,110382,1747],{},[2505,110384,3132],{},[898,110386,16183],{},[1708,110388,2019],{},[898,110390,1978],{},[902,110392,110393],{"encoding":904},"P_1^E = P_2^E + T",[123,110395,110396,110397,1771,110418,2155],{},"rozklad daňového břemene ",[883,110398,110400],{"className":110399},[886],[888,110401,110402],{"xmlns":890},[892,110403,110404,110416],{},[895,110405,110406],{},[1743,110407,110408,110410],{},[898,110409,1978],{},[895,110411,110412,110414],{},[898,110413,54507],{},[898,110415,724],{},[902,110417,54512],{"encoding":904},[883,110419,110421],{"className":110420},[886],[888,110422,110423],{"xmlns":890},[892,110424,110425,110439],{},[895,110426,110427],{},[1743,110428,110429,110431],{},[898,110430,1978],{},[895,110432,110433,110435,110437],{},[898,110434,54530],{},[898,110436,14004],{},[898,110438,5498],{},[902,110440,54537],{"encoding":904},[724,110442,110443,110444,2155],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,110445,47040],{},[724,110447,110448,110449,1771,110462,2511],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,110450,110452],{"className":110451},[886],[888,110453,110454],{"xmlns":890},[892,110455,110456,110460],{},[895,110457,110458],{},[898,110459,16117],{},[902,110461,16117],{"encoding":904},[883,110463,110465],{"className":110464},[886],[888,110466,110467],{"xmlns":890},[892,110468,110469,110473],{},[895,110470,110471],{},[898,110472,1981],{},[902,110474,1981],{"encoding":904},[48808,110476],{},[115,110478,110480],{"id":110479},"úlohy","Úlohy",[724,110482,110483,110484,2750],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,110485,28112],{"className":110486,"dataFsResolvedFilePath":800,"href":801},[210],[120,110488,110489,110519,110550],{},[123,110490,110491,110494,110495,110518],{},[38,110492,110493],{},"Úloha 2.4"," — Poptávka ",[883,110496,110498],{"className":110497},[886],[888,110499,110500],{"xmlns":890},[892,110501,110502,110516],{},[895,110503,110504,110506,110508,110510,110512,110514],{},[898,110505,1747],{},[1708,110507,1710],{},[2505,110509,4090],{},[1708,110511,2726],{},[2505,110513,3132],{},[898,110515,1688],{},[902,110517,107468],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,110520,110521,110524,110525,110549],{},[38,110522,110523],{},"Úloha 2.9"," — Nabídka ",[883,110526,110528],{"className":110527},[886],[888,110529,110530],{"xmlns":890},[892,110531,110532,110546],{},[895,110533,110534,110536,110538,110540,110542,110544],{},[898,110535,1747],{},[1708,110537,1710],{},[2505,110539,6097],{},[898,110541,1688],{},[1708,110543,2019],{},[2505,110545,4853],{},[902,110547,110548],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,110551,110552,110555,110556,1771,110582,110606,110607,110624],{},[38,110553,110554],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,110557,110559],{"className":110558},[886],[888,110560,110561],{"xmlns":890},[892,110562,110563,110579],{},[895,110564,110565,110567,110569,110571,110573,110575,110577],{},[898,110566,1747],{},[1708,110568,1710],{},[1708,110570,2726],{},[2505,110572,5867],{},[898,110574,1688],{},[1708,110576,2019],{},[2505,110578,12513],{},[902,110580,110581],{"encoding":904},"P = -4Q + 80",[883,110583,110585],{"className":110584},[886],[888,110586,110587],{"xmlns":890},[892,110588,110589,110603],{},[895,110590,110591,110593,110595,110597,110599,110601],{},[898,110592,1747],{},[1708,110594,1710],{},[2505,110596,3121],{},[898,110598,1688],{},[1708,110600,2019],{},[2505,110602,4003],{},[902,110604,110605],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,110608,110610],{"className":110609},[886],[888,110611,110612],{"xmlns":890},[892,110613,110614,110622],{},[895,110615,110616,110618,110620],{},[898,110617,1978],{},[1708,110619,1710],{},[2505,110621,5967],{},[902,110623,59640],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,110626,110627,110628,110630,110631,110633],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,110629,57055],{}," (posun poptávky při zdanění kupujícího) a ",[38,110632,57089],{}," (posun nabídky při zdanění výrobce).",[48808,110635],{},[115,110637,12596],{"id":12595},[120,110639,110640,110659,110717,110774,110857,110903,110946,110991,111057],{},[123,110641,110642,1729,110645,110658],{},[38,110643,110644],{},"Jednotková daň",[883,110646,110648],{"className":110647},[886],[888,110649,110650],{"xmlns":890},[892,110651,110652,110656],{},[895,110653,110654],{},[898,110655,1978],{},[902,110657,1978],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,110660,110661,110663,110664,110702,110703,110716],{},[38,110662,107050],{}," — posun nabídky ",[883,110665,110667],{"className":110666},[886],[888,110668,110669],{"xmlns":890},[892,110670,110671,110699],{},[895,110672,110673,110679,110681,110683,110685,110687,110689,110691,110693,110695,110697],{},[1743,110674,110675,110677],{},[898,110676,1981],{},[2505,110678,2507],{},[1708,110680,1716],{"stretchy":1715},[898,110682,1688],{},[1708,110684,1721],{"stretchy":1715},[1708,110686,1710],{},[898,110688,1981],{},[1708,110690,1716],{"stretchy":1715},[898,110692,1688],{},[1708,110694,1721],{"stretchy":1715},[1708,110696,2019],{},[898,110698,1978],{},[902,110700,110701],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,110704,110706],{"className":110705},[886],[888,110707,110708],{"xmlns":890},[892,110709,110710,110714],{},[895,110711,110712],{},[898,110713,1978],{},[902,110715,1978],{"encoding":904}," svisle nahoru)",[123,110718,110719,110721,110722,110702,110760,110773],{},[38,110720,108123],{}," — posun poptávky ",[883,110723,110725],{"className":110724},[886],[888,110726,110727],{"xmlns":890},[892,110728,110729,110757],{},[895,110730,110731,110737,110739,110741,110743,110745,110747,110749,110751,110753,110755],{},[1743,110732,110733,110735],{},[898,110734,16117],{},[2505,110736,3132],{},[1708,110738,1716],{"stretchy":1715},[898,110740,1688],{},[1708,110742,1721],{"stretchy":1715},[1708,110744,1710],{},[898,110746,16117],{},[1708,110748,1716],{"stretchy":1715},[898,110750,1688],{},[1708,110752,1721],{"stretchy":1715},[1708,110754,2726],{},[898,110756,1978],{},[902,110758,110759],{"encoding":904},"D_2(Q) = D(Q) - T",[883,110761,110763],{"className":110762},[886],[888,110764,110765],{"xmlns":890},[892,110766,110767,110771],{},[895,110768,110769],{},[898,110770,1978],{},[902,110772,1978],{"encoding":904}," svisle dolů)",[123,110775,110776,12636,110779,53646,110818],{},[38,110777,110778],{},"Rovnovážný bod s daní",[883,110780,110782],{"className":110781},[886],[888,110783,110784],{"xmlns":890},[892,110785,110786,110816],{},[895,110787,110788,110794,110796,110804,110806,110814],{},[1743,110789,110790,110792],{},[898,110791,16183],{},[2505,110793,2507],{},[1708,110795,6940],{"stretchy":1715},[4754,110797,110798,110800,110802],{},[898,110799,1688],{},[2505,110801,2507],{},[898,110803,16183],{},[1708,110805,1883],{"separator":1882},[4754,110807,110808,110810,110812],{},[898,110809,1747],{},[2505,110811,2507],{},[898,110813,16183],{},[1708,110815,6981],{"stretchy":1715},[902,110817,107218],{"encoding":904},[883,110819,110821],{"className":110820},[886],[888,110822,110823],{"xmlns":890},[892,110824,110825,110855],{},[895,110826,110827,110833,110835,110843,110845,110853],{},[1743,110828,110829,110831],{},[898,110830,16183],{},[2505,110832,3132],{},[1708,110834,6940],{"stretchy":1715},[4754,110836,110837,110839,110841],{},[898,110838,1688],{},[2505,110840,3132],{},[898,110842,16183],{},[1708,110844,1883],{"separator":1882},[4754,110846,110847,110849,110851],{},[898,110848,1747],{},[2505,110850,3132],{},[898,110852,16183],{},[1708,110854,6981],{"stretchy":1715},[902,110856,108293],{"encoding":904},[123,110858,110859,1695,110861,110863,110864],{},[38,110860,54488],{},[614,110862,109073],{},") — rozklad ",[883,110865,110867],{"className":110866},[886],[888,110868,110869],{"xmlns":890},[892,110870,110871,110901],{},[895,110872,110873,110875,110877,110887,110889],{},[898,110874,1978],{},[1708,110876,1710],{},[1743,110878,110879,110881],{},[898,110880,1978],{},[895,110882,110883,110885],{},[898,110884,54507],{},[898,110886,724],{},[1708,110888,2019],{},[1743,110890,110891,110893],{},[898,110892,1978],{},[895,110894,110895,110897,110899],{},[898,110896,54530],{},[898,110898,14004],{},[898,110900,5498],{},[902,110902,54674],{"encoding":904},[123,110904,110905,110928,110929,1721],{},[38,110906,110907],{},[883,110908,110910],{"className":110909},[886],[888,110911,110912],{"xmlns":890},[892,110913,110914,110926],{},[895,110915,110916],{},[1743,110917,110918,110920],{},[898,110919,1978],{},[895,110921,110922,110924],{},[898,110923,54507],{},[898,110925,724],{},[902,110927,54512],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,110930,110932],{"className":110931},[886],[888,110933,110934],{"xmlns":890},[892,110935,110936,110944],{},[895,110937,110938],{},[1753,110939,110940,110942],{},[898,110941,1747],{},[898,110943,16183],{},[902,110945,53298],{"encoding":904},[123,110947,110948,110973,110974,1721],{},[38,110949,110950],{},[883,110951,110953],{"className":110952},[886],[888,110954,110955],{"xmlns":890},[892,110956,110957,110971],{},[895,110958,110959],{},[1743,110960,110961,110963],{},[898,110962,1978],{},[895,110964,110965,110967,110969],{},[898,110966,54530],{},[898,110968,14004],{},[898,110970,5498],{},[902,110972,54537],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,110975,110977],{"className":110976},[886],[888,110978,110979],{"xmlns":890},[892,110980,110981,110989],{},[895,110982,110983],{},[1753,110984,110985,110987],{},[898,110986,1747],{},[898,110988,16183],{},[902,110990,53298],{"encoding":904},[123,110992,110993,12636,110995,1343,111024],{},[38,110994,62297],{},[883,110996,110998],{"className":110997},[886],[888,110999,111000],{"xmlns":890},[892,111001,111002,111022],{},[895,111003,111004,111012,111014],{},[4754,111005,111006,111008,111010],{},[898,111007,1688],{},[2505,111009,2507],{},[898,111011,16183],{},[1708,111013,1710],{},[4754,111015,111016,111018,111020],{},[898,111017,1688],{},[2505,111019,3132],{},[898,111021,16183],{},[902,111023,54738],{"encoding":904},[883,111025,111027],{"className":111026},[886],[888,111028,111029],{"xmlns":890},[892,111030,111031,111055],{},[895,111032,111033,111041,111043,111045,111047],{},[4754,111034,111035,111037,111039],{},[898,111036,1747],{},[2505,111038,2507],{},[898,111040,16183],{},[1708,111042,2726],{},[898,111044,1978],{},[1708,111046,1710],{},[4754,111048,111049,111051,111053],{},[898,111050,1747],{},[2505,111052,3132],{},[898,111054,16183],{},[902,111056,54772],{"encoding":904},[123,111058,111059,111062],{},[38,111060,111061],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[48808,111064],{},[115,111066,13763],{"id":13762},[120,111068,111069,111077,111095,111102],{},[123,111070,111071,1729,111074],{},[38,111072,111073],{},"Kontext (hub):",[207,111075,802],{"className":111076,"dataFsResolvedFilePath":800,"href":801},[210],[123,111078,111079,1729,111081,111084,111085,13826,111087,111090,111091,111094],{},[38,111080,13770],{},[207,111082,820],{"className":111083,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,111086,66853],{},[207,111088,2162],{"className":111089,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,111092,13875],{"className":111093,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,111096,111097,1729,111099],{},[38,111098,62580],{},[207,111100,62584],{"className":111101,"dataFsResolvedFilePath":745,"href":746},[210],[123,111103,111104,1729,111106],{},[38,111105,13888],{},[207,111107,13894],{"className":111108,"dataFsResolvedFilePath":13892,"href":13893},[210],{"title":641,"searchDepth":642,"depth":642,"links":111110},[111111,111112,111115,111118,111122,111123,111124,111125],{"id":106955,"depth":642,"text":106956},{"id":107049,"depth":642,"text":107050,"children":111113},[111114],{"id":107440,"depth":649,"text":57130},{"id":108122,"depth":642,"text":108123,"children":111116},[111117],{"id":108599,"depth":649,"text":57210},{"id":109066,"depth":642,"text":54488,"children":111119},[111120,111121],{"id":14424,"depth":649,"text":14425},{"id":109409,"depth":649,"text":109410},{"id":109882,"depth":642,"text":109883},{"id":110479,"depth":642,"text":110480},{"id":12595,"depth":642,"text":12596},{"id":13762,"depth":642,"text":13763},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":106853,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,62645,111132,111133,111134,28112],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[111137,111139,111141,111145,111149,111153,111157,111159],{"slug":28125,"path":783,"title":21474,"snippet":111138},"… osti $U(Q_1, Q_2) = c$ — viz uzitecnost. - **Izokvanty** produkce $Q(L, K) = c$ — viz \u003C\u003Cprodukce>>. ## Parciální derivace Pro $f(x, y)$ derivujeme jako kdyby druhá proměnná byla konstant …",{"slug":1128,"path":13893,"title":681,"snippet":111140},"… - Cenová, křížová a důchodová elasticita (jedno- i vícefaktorový model) - \u003C\u003Cprodukce>> — Cobb-Douglasova, CES, lineární, Leontiefova, izokvanty, MRTS, Eulerova věta ### Blok 3 …",{"slug":111142,"path":746,"title":111143,"snippet":111144},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… |Elasticita]] (Blok 2) — navazuje na příjem (vliv elasticity na TR) a využívá derivace. - \u003C\u003Cprodukce>> (Blok 2) — využívá parciální derivace. - [[uzitecnost|Užitečno …",{"slug":111146,"path":839,"title":111147,"snippet":111148},"imek-blok-02","KS 2. blok — Elasticita a produkce","… model, pravidla pro TR, klasifikace (elastická \u002F jednotkově elastická \u002F neelastická). 2. \u003C\u003Cprodukce>> — jednofaktorový a dvoufaktorový model $Q(L)$ resp. $Q(L, K)$, Cobb-Douglas, CES, lineárn …",{"slug":111150,"path":1109,"title":111151,"snippet":111152},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… echnické substituce $MRTS = MP_L\u002FMP_K$. **Příklady 5.1–5.6**, **Úlohy 5.1–5.17**. Topic: \u003C\u003Cprodukce>>. ### Kapitola 6 — Užitečnost *(str. 113–131)* Pojetí užitečnosti (kardinalistický vs. o …",{"slug":111154,"path":959,"title":111155,"snippet":111156},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… řadné zboží (s růstem důchodu přestáváš kupovat) --- ## 8. Produkce **Základní téma:** \u003C\u003Cprodukce>> ### Produkční funkce $$Q = Q(L, K)$$ **Původ:** axiomatický zápis — produkce závisí na …",{"slug":48596,"path":912,"title":39617,"snippet":111158},"… ych|Funkce více proměnných]] (parciální derivace), Derivace. - **Paralely:** \u003C\u003Cprodukce>> (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), [[poptavka-nabidka|Poptávka a nabídk …",{"slug":14913,"path":828,"title":66939,"snippet":111160},"… vka a nabídka]], Elasticita, Derivace, Integrál, \u003C\u003Cprodukce>> - **Přednášky:** KS 1. blok — souhrn, [[imek-blok-02|KS 2. blok — souhrn …",[111162,111163],{"slug":111146,"title":111147,"path":839,"sharedTags":13956},{"slug":21676,"title":97606,"path":879,"sharedTags":642},1777154971915]