[{"data":1,"prerenderedAt":106808},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-imek-vzorce-prehled":1626,"course-stats-imek":8880,"course-topics-imek":8884,"backlinks-imek-vzorce-prehled":106796,"related-imek-vzorce-prehled":106799},{"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":8879},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":8868,"description":641,"extension":661,"meta":8869,"navigation":664,"path":8870,"seo":8871,"sources":8872,"stem":8873,"tags":8874,"type":8877,"updated":677,"__hash__":8878},"outputs\u002Foutputs\u002Fimek-vzorce-prehled.md","ImeK — kompletní přehled vzorců se zdroji a intuicí",{"type":9,"value":1631,"toc":8781},[1632,1635,1667,1671,1851,1854,1858,1867,1871,1928,1937,1979,1983,2030,2057,2062,2066,2098,2103,2108,2112,2153,2158,2168,2170,2174,2183,2205,2313,2318,2341,2345,2434,2526,2574,2632,2634,2638,2646,2650,2678,2683,2702,2706,2748,2798,2822,2826,2863,2899,2939,2941,2945,2952,2956,2997,3002,3043,3047,3123,3128,3166,3170,3206,3240,3248,3250,3254,3262,3266,3311,3354,3359,3363,3409,3448,3457,3461,3505,3576,3581,3583,3587,3594,3702,3790,3812,3814,3818,3826,3830,3872,3926,3931,3981,4029,4034,4087,4091,4126,4144,4168,4172,4210,4266,4301,4442,4446,4505,4510,4515,4519,4646,4688,4692,4802,4804,4808,4816,4819,4851,4856,4861,4865,4931,4936,4966,4970,5000,5005,5063,5067,5103,5108,5135,5212,5252,5256,5302,5307,5317,5321,5380,5421,5512,5514,5518,5526,5530,5568,5573,5582,5586,5660,5665,5713,5717,5763,5768,5816,5818,5822,5830,5834,5878,5883,5919,5923,6023,6036,6060,6064,6147,6165,6173,6175,6179,6186,6190,6263,6268,6326,6330,6402,6407,6433,6437,6466,6471,6480,6482,6486,6494,6498,6569,6638,6700,6719,6723,6771,6776,6781,6785,6865,6870,6878,6882,6940,6945,6954,6956,6960,6967,6971,7011,7016,7021,7025,7049,7054,7059,7063,7113,7159,7195,7199,7261,7266,7357,7361,7393,7420,7425,7429,7458,7491,7533,7538,7543,7547,7575,7580,7636,7640,7684,7735,7773,7777,7841,7881,7988,7990,7994,8002,8006,8062,8067,8090,8094,8148,8217,8307,8311,8361,8462,8518,8522,8608,8610,8614,8648,8682,8686],[12,1633,1629],{"id":1634},"imek-kompletní-přehled-vzorců-se-zdroji-a-intuicí",[1636,1637,1638],"blockquote",{},[724,1639,1640,1643,1644,1647,1648,1654,1655,1658,1659,1662,1663,1666],{},[883,1641,1642],{},"!abstract"," TL;DR\nReferenční přehled ",[38,1645,1646],{},"všech klíčových vzorců"," kurzu ",[207,1649,1653],{"className":1650,"dataFsResolvedFilePath":1651,"href":1652},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie"," v ",[38,1656,1657],{},"základním (definičním) tvaru"," — od poptávky a nabídky přes optimalizaci firmy a spotřebitele až po IS-LM. Pro každý vzorec: ",[38,1660,1661],{},"kde se v materiálech bere"," (odkaz do příslušné topic stránky) a ",[38,1664,1665],{},"intuice"," (co vzorec znamená ekonomicky).",[115,1668,1670],{"id":1669},"jak-číst-tento-přehled","Jak číst tento přehled",[120,1672,1673,1790,1793,1844],{},[123,1674,1675,1676,1679,1680,1737,1738,1785,1786,1789],{},"Všechny vzorce jsou zapsané ",[38,1677,1678],{},"v definičním tvaru"," — tj. tak, jak vznikají z prvních principů, beze snahy o algebraická zjednodušení. Když v jiném textu narazíš na „hezčí\" tvar (např. ",[883,1681,1683],{"className":1682},[886],[888,1684,1685],{"xmlns":890},[892,1686,1687,1734],{},[895,1688,1689,1692,1696,1699,1702,1706,1710,1713,1716,1725,1727,1729,1732],{},[898,1690,1691],{},"E",[1693,1694,1695],"mo",{},"=",[1693,1697,1698],{},"−",[898,1700,1701],{},"P",[898,1703,1705],{"mathvariant":1704},"normal","\u002F",[1693,1707,1709],{"stretchy":1708},"false","(",[898,1711,1712],{},"Q",[1693,1714,1715],{},"⋅",[1717,1718,1719,1721],"msup",{},[898,1720,1701],{},[1693,1722,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},"0em","′",[1693,1726,1709],{"stretchy":1708},[898,1728,1712],{},[1693,1730,1731],{"stretchy":1708},")",[1693,1733,1731],{"stretchy":1708},[902,1735,1736],{"encoding":904},"E = -P\u002F(Q \\cdot P'(Q))"," místo ",[883,1739,1741],{"className":1740},[886],[888,1742,1743],{"xmlns":890},[892,1744,1745,1782],{},[895,1746,1747,1749,1751,1753,1755,1757,1759,1761,1765,1767,1769,1772,1774,1776,1778,1780],{},[898,1748,1691],{},[1693,1750,1695],{},[1693,1752,1698],{},[898,1754,1701],{},[898,1756,1705],{"mathvariant":1704},[898,1758,1712],{},[1693,1760,1715],{},[1762,1763,1764],"mn",{},"1",[898,1766,1705],{"mathvariant":1704},[1693,1768,1709],{"stretchy":1708},[898,1770,1771],{},"d",[898,1773,1701],{},[898,1775,1705],{"mathvariant":1704},[898,1777,1771],{},[898,1779,1712],{},[1693,1781,1731],{"stretchy":1708},[902,1783,1784],{"encoding":904},"E = -P\u002FQ \\cdot 1\u002F(dP\u002FdQ)","), je to zpravidla ",[38,1787,1788],{},"jen dosazení jednoho kousku do druhého",".",[123,1791,1792],{},"Každý vzorec má vlastní řádek (displayed math), ne inline, aby byl čitelný.",[123,1794,1795,1796,1818,1819,1843],{},"Notace ",[883,1797,1799],{"className":1798},[886],[888,1800,1801],{"xmlns":890},[892,1802,1803,1815],{},[895,1804,1805,1807,1809,1811,1813],{},[898,1806,1771],{},[898,1808,1701],{},[898,1810,1705],{"mathvariant":1704},[898,1812,1771],{},[898,1814,1712],{},[902,1816,1817],{"encoding":904},"dP\u002FdQ"," je totéž co ",[883,1820,1822],{"className":1821},[886],[888,1823,1824],{"xmlns":890},[892,1825,1826,1840],{},[895,1827,1828,1834,1836,1838],{},[1717,1829,1830,1832],{},[898,1831,1701],{},[1693,1833,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,1835,1709],{"stretchy":1708},[898,1837,1712],{},[1693,1839,1731],{"stretchy":1708},[902,1841,1842],{"encoding":904},"P'(Q)"," — používám první tvar, protože je explicitnější.",[123,1845,1846,1847,1850],{},"Prokliky vedou vždy na ",[38,1848,1849],{},"primární topic stránku",", kde najdeš úplné odvození, příklady a úlohy.",[1852,1853],"hr",{},[115,1855,1857],{"id":1856},"_1-poptávka-a-nabídka","1. Poptávka a nabídka",[724,1859,1860,1863,1864],{},[38,1861,1862],{},"Základní téma:"," ",[207,1865,802],{"className":1866,"dataFsResolvedFilePath":800,"href":801},[210],[198,1868,1870],{"id":1869},"lineární-poptávka","Lineární poptávka",[724,1872,1873],{},[883,1874,1876],{"className":1875},[886],[888,1877,1878],{"xmlns":890},[892,1879,1880,1925],{},[895,1881,1882,1884,1886,1888,1890,1893,1896,1900,1904,1906,1909,1912,1914,1918,1920,1923],{},[898,1883,1701],{},[1693,1885,1695],{},[898,1887,207],{},[898,1889,1712],{},[1693,1891,1892],{},"+",[898,1894,1895],{},"b",[1693,1897,1899],{"separator":1898},"true",",",[1901,1902],"mspace",{"width":1903},"2em",[898,1905,207],{},[1693,1907,1908],{},"\u003C",[1762,1910,1911],{},"0",[1693,1913,1899],{"separator":1898},[1915,1916,1917],"mtext",{},"  ",[898,1919,1895],{},[1693,1921,1922],{},">",[1762,1924,1911],{},[902,1926,1927],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0, \\; b > 0",[724,1929,1930,1933,1934,1789],{},[38,1931,1932],{},"Původ:"," axiom — lineární aproximace vztahu ceny a množství pro nedokonalou konkurenci (vzorec 2.4). Odpovídá ",[38,1935,1936],{},"zákonu klesající poptávky",[724,1938,1939,1942,1943,1956,1957,1789],{},[38,1940,1941],{},"Intuice:"," čím vyšší cena, tím méně lidé kupují. Sklon ",[883,1944,1946],{"className":1945},[886],[888,1947,1948],{"xmlns":890},[892,1949,1950,1954],{},[895,1951,1952],{},[898,1953,207],{},[902,1955,207],{"encoding":904}," je záporný — klesající přímka v rovině ",[883,1958,1960],{"className":1959},[886],[888,1961,1962],{"xmlns":890},[892,1963,1964,1976],{},[895,1965,1966,1968,1970,1972,1974],{},[1693,1967,1709],{"stretchy":1708},[898,1969,1712],{},[1693,1971,1899],{"separator":1898},[898,1973,1701],{},[1693,1975,1731],{"stretchy":1708},[902,1977,1978],{"encoding":904},"(Q, P)",[198,1980,1982],{"id":1981},"lineární-nabídka","Lineární nabídka",[724,1984,1985],{},[883,1986,1988],{"className":1987},[886],[888,1989,1990],{"xmlns":890},[892,1991,1992,2027],{},[895,1993,1994,1996,1998,2001,2003,2005,2007,2009,2011,2013,2015,2017,2019,2021,2023,2025],{},[898,1995,1701],{},[1693,1997,1695],{},[898,1999,2000],{},"c",[898,2002,1712],{},[1693,2004,1892],{},[898,2006,1771],{},[1693,2008,1899],{"separator":1898},[1901,2010],{"width":1903},[898,2012,2000],{},[1693,2014,1922],{},[1762,2016,1911],{},[1693,2018,1899],{"separator":1898},[1915,2020,1917],{},[898,2022,1895],{},[1693,2024,1922],{},[898,2026,1771],{},[902,2028,2029],{"encoding":904},"P = cQ + d, \\qquad c > 0, \\; b > d",[724,2031,2032,1863,2034,2037,2038,2056],{},[38,2033,1932],{},[38,2035,2036],{},"zákon rostoucí nabídky"," (vzorec 2.9). Podmínka ",[883,2039,2041],{"className":2040},[886],[888,2042,2043],{"xmlns":890},[892,2044,2045,2053],{},[895,2046,2047,2049,2051],{},[898,2048,1895],{},[1693,2050,1922],{},[898,2052,1771],{},[902,2054,2055],{"encoding":904},"b > d"," zajišťuje, že rovnovážný bod leží v 1. kvadrantu.",[724,2058,2059,2061],{},[38,2060,1941],{}," výrobce je ochoten vyrobit víc, jen když cena stoupne — rostou mu mezní náklady.",[198,2063,2065],{"id":2064},"rovnovážná-rovnice","Rovnovážná rovnice",[724,2067,2068],{},[883,2069,2071],{"className":2070},[886],[888,2072,2073],{"xmlns":890},[892,2074,2075,2095],{},[895,2076,2077,2079,2081,2083,2085,2087,2089,2091,2093],{},[898,2078,207],{},[898,2080,1712],{},[1693,2082,1892],{},[898,2084,1895],{},[1693,2086,1695],{},[898,2088,2000],{},[898,2090,1712],{},[1693,2092,1892],{},[898,2094,1771],{},[902,2096,2097],{"encoding":904},"aQ + b = cQ + d",[724,2099,2100,2102],{},[38,2101,1932],{}," v rovnováze je poptávané množství rovno nabízenému, takže obě rovnice platí současně.",[724,2104,2105,2107],{},[38,2106,1941],{}," cena, při které se střetne „chci koupit\" s „chci prodat\". Geometricky — průsečík obou křivek.",[198,2109,2111],{"id":2110},"redukovaný-tvar-rovnovážného-množství","Redukovaný tvar rovnovážného množství",[724,2113,2114],{},[883,2115,2117],{"className":2116},[886],[888,2118,2119],{"xmlns":890},[892,2120,2121,2150],{},[895,2122,2123,2129,2131],{},[1717,2124,2125,2127],{},[898,2126,1712],{},[898,2128,1691],{},[1693,2130,1695],{},[2132,2133,2134,2142],"mfrac",{},[895,2135,2136,2138,2140],{},[898,2137,1895],{},[1693,2139,1698],{},[898,2141,1771],{},[895,2143,2144,2146,2148],{},[898,2145,2000],{},[1693,2147,1698],{},[898,2149,207],{},[902,2151,2152],{"encoding":904},"Q^E = \\frac{b - d}{c - a}",[724,2154,2155,2157],{},[38,2156,1932],{}," algebraické řešení rovnováhy (vzorec 2.10).",[724,2159,2160,2162,2163,2167],{},[38,2161,1941],{}," rovnovážné množství jako explicitní funkce parametrů. Čím větší mezera ",[2164,2165,2166],"code",{},"b - d"," mezi „maximální cenou poptávky\" a „minimální cenou nabídky\", tím větší trh.",[1852,2169],{},[115,2171,2173],{"id":2172},"_2-multiplikátory-komparativní-statiky","2. Multiplikátory komparativní statiky",[724,2175,2176,1863,2178,2182],{},[38,2177,1862],{},[207,2179,2181],{"className":2180,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka"," (sekce „Multiplikátory pro mikroekonomické proměnné\")",[198,2184,2186,2187],{"id":2185},"totální-diferenciál-qeqe","Totální diferenciál ",[883,2188,2190],{"className":2189},[886],[888,2191,2192],{"xmlns":890},[892,2193,2194,2202],{},[895,2195,2196],{},[1717,2197,2198,2200],{},[898,2199,1712],{},[898,2201,1691],{},[902,2203,2204],{"encoding":904},"Q^E",[724,2206,2207],{},[883,2208,2210],{"className":2209},[886],[888,2211,2212],{"xmlns":890},[892,2213,2214,2310],{},[895,2215,2216,2218,2220,2222,2237,2240,2242,2244,2246,2260,2262,2264,2266,2268,2282,2284,2286,2288,2290,2304,2306,2308],{},[898,2217,1771],{},[898,2219,1712],{},[1693,2221,1695],{},[2132,2223,2224,2231],{},[895,2225,2226,2229],{},[898,2227,2228],{"mathvariant":1704},"∂",[898,2230,1712],{},[895,2232,2233,2235],{},[898,2234,2228],{"mathvariant":1704},[898,2236,207],{},[1915,2238,2239],{}," ",[898,2241,1771],{},[898,2243,207],{},[1693,2245,1892],{},[2132,2247,2248,2254],{},[895,2249,2250,2252],{},[898,2251,2228],{"mathvariant":1704},[898,2253,1712],{},[895,2255,2256,2258],{},[898,2257,2228],{"mathvariant":1704},[898,2259,1895],{},[1915,2261,2239],{},[898,2263,1771],{},[898,2265,1895],{},[1693,2267,1892],{},[2132,2269,2270,2276],{},[895,2271,2272,2274],{},[898,2273,2228],{"mathvariant":1704},[898,2275,1712],{},[895,2277,2278,2280],{},[898,2279,2228],{"mathvariant":1704},[898,2281,2000],{},[1915,2283,2239],{},[898,2285,1771],{},[898,2287,2000],{},[1693,2289,1892],{},[2132,2291,2292,2298],{},[895,2293,2294,2296],{},[898,2295,2228],{"mathvariant":1704},[898,2297,1712],{},[895,2299,2300,2302],{},[898,2301,2228],{"mathvariant":1704},[898,2303,1771],{},[1915,2305,2239],{},[898,2307,1771],{},[898,2309,1771],{},[902,2311,2312],{"encoding":904},"dQ = \\frac{\\partial Q}{\\partial a}\\,da + \\frac{\\partial Q}{\\partial b}\\,db + \\frac{\\partial Q}{\\partial c}\\,dc + \\frac{\\partial Q}{\\partial d}\\,dd",[724,2314,2315,2317],{},[38,2316,1932],{}," lineární aproximace změny funkce více proměnných (vzorec 2.11).",[724,2319,2320,2322,2323,2340],{},[38,2321,1941],{}," jak se změní ",[883,2324,2326],{"className":2325},[886],[888,2327,2328],{"xmlns":890},[892,2329,2330,2338],{},[895,2331,2332],{},[1717,2333,2334,2336],{},[898,2335,1712],{},[898,2337,1691],{},[902,2339,2204],{"encoding":904}," při současné změně všech parametrů. Každý parametr přispívá samostatně (ceteris paribus) a výsledky se sčítají.",[198,2342,2344],{"id":2343},"jednotlivé-multiplikátory","Jednotlivé multiplikátory",[724,2346,2347],{},[883,2348,2350],{"className":2349},[886],[888,2351,2352],{"xmlns":890},[892,2353,2354,2431],{},[895,2355,2356,2370,2372,2399,2401,2403,2417,2419],{},[2132,2357,2358,2364],{},[895,2359,2360,2362],{},[898,2361,2228],{"mathvariant":1704},[898,2363,1712],{},[895,2365,2366,2368],{},[898,2367,2228],{"mathvariant":1704},[898,2369,207],{},[1693,2371,1695],{},[2132,2373,2374,2382],{},[895,2375,2376,2378,2380],{},[898,2377,1895],{},[1693,2379,1698],{},[898,2381,1771],{},[895,2383,2384,2386,2388,2390,2392],{},[1693,2385,1709],{"stretchy":1708},[898,2387,2000],{},[1693,2389,1698],{},[898,2391,207],{},[1717,2393,2394,2396],{},[1693,2395,1731],{"stretchy":1708},[1762,2397,2398],{},"2",[1693,2400,1899],{"separator":1898},[1901,2402],{"width":1903},[2132,2404,2405,2411],{},[895,2406,2407,2409],{},[898,2408,2228],{"mathvariant":1704},[898,2410,1712],{},[895,2412,2413,2415],{},[898,2414,2228],{"mathvariant":1704},[898,2416,1895],{},[1693,2418,1695],{},[2132,2420,2421,2423],{},[1762,2422,1764],{},[895,2424,2425,2427,2429],{},[898,2426,2000],{},[1693,2428,1698],{},[898,2430,207],{},[902,2432,2433],{"encoding":904},"\\frac{\\partial Q}{\\partial a} = \\frac{b-d}{(c-a)^2}, \\qquad \\frac{\\partial Q}{\\partial b} = \\frac{1}{c-a}",[724,2435,2436],{},[883,2437,2439],{"className":2438},[886],[888,2440,2441],{"xmlns":890},[892,2442,2443,2523],{},[895,2444,2445,2459,2461,2463,2489,2491,2493,2507,2509,2511],{},[2132,2446,2447,2453],{},[895,2448,2449,2451],{},[898,2450,2228],{"mathvariant":1704},[898,2452,1712],{},[895,2454,2455,2457],{},[898,2456,2228],{"mathvariant":1704},[898,2458,2000],{},[1693,2460,1695],{},[1693,2462,1698],{},[2132,2464,2465,2473],{},[895,2466,2467,2469,2471],{},[898,2468,1895],{},[1693,2470,1698],{},[898,2472,1771],{},[895,2474,2475,2477,2479,2481,2483],{},[1693,2476,1709],{"stretchy":1708},[898,2478,2000],{},[1693,2480,1698],{},[898,2482,207],{},[1717,2484,2485,2487],{},[1693,2486,1731],{"stretchy":1708},[1762,2488,2398],{},[1693,2490,1899],{"separator":1898},[1901,2492],{"width":1903},[2132,2494,2495,2501],{},[895,2496,2497,2499],{},[898,2498,2228],{"mathvariant":1704},[898,2500,1712],{},[895,2502,2503,2505],{},[898,2504,2228],{"mathvariant":1704},[898,2506,1771],{},[1693,2508,1695],{},[1693,2510,1698],{},[2132,2512,2513,2515],{},[1762,2514,1764],{},[895,2516,2517,2519,2521],{},[898,2518,2000],{},[1693,2520,1698],{},[898,2522,207],{},[902,2524,2525],{"encoding":904},"\\frac{\\partial Q}{\\partial c} = -\\frac{b-d}{(c-a)^2}, \\qquad \\frac{\\partial Q}{\\partial d} = -\\frac{1}{c-a}",[724,2527,2528,2530,2531,2573],{},[38,2529,1932],{}," parciální derivace redukovaného tvaru ",[883,2532,2534],{"className":2533},[886],[888,2535,2536],{"xmlns":890},[892,2537,2538,2570],{},[895,2539,2540,2546,2548,2550,2552,2554,2556,2558,2560,2562,2564,2566,2568],{},[1717,2541,2542,2544],{},[898,2543,1712],{},[898,2545,1691],{},[1693,2547,1695],{},[1693,2549,1709],{"stretchy":1708},[898,2551,1895],{},[1693,2553,1698],{},[898,2555,1771],{},[1693,2557,1731],{"stretchy":1708},[898,2559,1705],{"mathvariant":1704},[1693,2561,1709],{"stretchy":1708},[898,2563,2000],{},[1693,2565,1698],{},[898,2567,207],{},[1693,2569,1731],{"stretchy":1708},[902,2571,2572],{"encoding":904},"Q^E = (b-d)\u002F(c-a)"," (vzorec 2.12).",[724,2575,2576,2578,2579,2593,2594,2612,2613,2631],{},[38,2577,1941],{}," „O kolik se posune rovnovážné množství, když zvednu parametr ",[883,2580,2582],{"className":2581},[886],[888,2583,2584],{"xmlns":890},[892,2585,2586,2591],{},[895,2587,2588],{},[898,2589,2590],{},"x",[902,2592,2590],{"encoding":904}," o jednotku?\" Znaménka zůstávají stálá: u ",[883,2595,2597],{"className":2596},[886],[888,2598,2599],{"xmlns":890},[892,2600,2601,2609],{},[895,2602,2603,2605,2607],{},[898,2604,207],{},[1693,2606,1899],{"separator":1898},[898,2608,1895],{},[902,2610,2611],{"encoding":904},"a, b"," kladná, u ",[883,2614,2616],{"className":2615},[886],[888,2617,2618],{"xmlns":890},[892,2619,2620,2628],{},[895,2621,2622,2624,2626],{},[898,2623,2000],{},[1693,2625,1899],{"separator":1898},[898,2627,1771],{},[902,2629,2630],{"encoding":904},"c, d"," záporná.",[1852,2633],{},[115,2635,2637],{"id":2636},"_3-příjem-firmy","3. Příjem firmy",[724,2639,2640,1863,2642],{},[38,2641,1862],{},[207,2643,2645],{"className":2644,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk a nabídka firmy",[198,2647,2649],{"id":2648},"celkový-příjem","Celkový příjem",[724,2651,2652],{},[883,2653,2655],{"className":2654},[886],[888,2656,2657],{"xmlns":890},[892,2658,2659,2675],{},[895,2660,2661,2664,2667,2669,2671,2673],{},[898,2662,2663],{},"T",[898,2665,2666],{},"R",[1693,2668,1695],{},[898,2670,1701],{},[1693,2672,1715],{},[898,2674,1712],{},[902,2676,2677],{"encoding":904},"TR = P \\cdot Q",[724,2679,2680,2682],{},[38,2681,1932],{}," definice (3.1) — tržba jako cena krát množství.",[724,2684,2685,2687,2688,2701],{},[38,2686,1941],{}," co firma inkasuje za prodej ",[883,2689,2691],{"className":2690},[886],[888,2692,2693],{"xmlns":890},[892,2694,2695,2699],{},[895,2696,2697],{},[898,2698,1712],{},[902,2700,1712],{"encoding":904}," kusů.",[198,2703,2705],{"id":2704},"průměrný-příjem","Průměrný příjem",[724,2707,2708],{},[883,2709,2711],{"className":2710},[886],[888,2712,2713],{"xmlns":890},[892,2714,2715,2745],{},[895,2716,2717,2720,2722,2724,2734,2736,2739,2741,2743],{},[898,2718,2719],{},"A",[898,2721,2666],{},[1693,2723,1695],{},[2132,2725,2726,2732],{},[895,2727,2728,2730],{},[898,2729,2663],{},[898,2731,2666],{},[898,2733,1712],{},[1693,2735,1695],{},[898,2737,2738],{},"D",[1693,2740,1709],{"stretchy":1708},[898,2742,1712],{},[1693,2744,1731],{"stretchy":1708},[902,2746,2747],{"encoding":904},"AR = \\frac{TR}{Q} = D(Q)",[724,2749,2750,2752,2753,2783,2784,2797],{},[38,2751,1932],{}," podíl; po dosazení ",[883,2754,2756],{"className":2755},[886],[888,2757,2758],{"xmlns":890},[892,2759,2760,2780],{},[895,2761,2762,2764,2766,2768,2770,2772,2774,2776,2778],{},[898,2763,2663],{},[898,2765,2666],{},[1693,2767,1695],{},[898,2769,2738],{},[1693,2771,1709],{"stretchy":1708},[898,2773,1712],{},[1693,2775,1731],{"stretchy":1708},[1693,2777,1715],{},[898,2779,1712],{},[902,2781,2782],{"encoding":904},"TR = D(Q) \\cdot Q"," se ",[883,2785,2787],{"className":2786},[886],[888,2788,2789],{"xmlns":890},[892,2790,2791,2795],{},[895,2792,2793],{},[898,2794,1712],{},[902,2796,1712],{"encoding":904}," vykrátí.",[724,2799,2800,2802,2803],{},[38,2801,1941],{}," průměrný příjem na kus = cena = křivka poptávky. ",[38,2804,2805,2821],{},[883,2806,2808],{"className":2807},[886],[888,2809,2810],{"xmlns":890},[892,2811,2812,2818],{},[895,2813,2814,2816],{},[898,2815,2719],{},[898,2817,2666],{},[902,2819,2820],{"encoding":904},"AR"," a poptávka jsou doslova tatáž křivka.",[198,2823,2825],{"id":2824},"mezní-příjem","Mezní příjem",[724,2827,2828],{},[883,2829,2831],{"className":2830},[886],[888,2832,2833],{"xmlns":890},[892,2834,2835,2860],{},[895,2836,2837,2840,2842,2844],{},[898,2838,2839],{},"M",[898,2841,2666],{},[1693,2843,1695],{},[2132,2845,2846,2854],{},[895,2847,2848,2850,2852],{},[898,2849,1771],{},[898,2851,2663],{},[898,2853,2666],{},[895,2855,2856,2858],{},[898,2857,1771],{},[898,2859,1712],{},[902,2861,2862],{"encoding":904},"MR = \\frac{dTR}{dQ}",[724,2864,2865,2867,2868,2884,2885,2898],{},[38,2866,1932],{}," derivace ",[883,2869,2871],{"className":2870},[886],[888,2872,2873],{"xmlns":890},[892,2874,2875,2881],{},[895,2876,2877,2879],{},[898,2878,2663],{},[898,2880,2666],{},[902,2882,2883],{"encoding":904},"TR"," podle ",[883,2886,2888],{"className":2887},[886],[888,2889,2890],{"xmlns":890},[892,2891,2892,2896],{},[895,2893,2894],{},[898,2895,1712],{},[902,2897,1712],{"encoding":904}," (vzorec 3.2).",[724,2900,2901,2903,2904,1863,2920,2923,2924,1789],{},[38,2902,1941],{}," „o kolik naroste tržba, když prodám o jeden kus víc\". Pro lineární poptávku má ",[883,2905,2907],{"className":2906},[886],[888,2908,2909],{"xmlns":890},[892,2910,2911,2917],{},[895,2912,2913,2915],{},[898,2914,2839],{},[898,2916,2666],{},[902,2918,2919],{"encoding":904},"MR",[38,2921,2922],{},"dvojnásobný sklon"," oproti ",[883,2925,2927],{"className":2926},[886],[888,2928,2929],{"xmlns":890},[892,2930,2931,2937],{},[895,2932,2933,2935],{},[898,2934,2719],{},[898,2936,2666],{},[902,2938,2820],{"encoding":904},[1852,2940],{},[115,2942,2944],{"id":2943},"_4-náklady-firmy","4. Náklady firmy",[724,2946,2947,1863,2949],{},[38,2948,1862],{},[207,2950,2645],{"className":2951,"dataFsResolvedFilePath":827,"href":828},[210],[198,2953,2955],{"id":2954},"celkové-náklady","Celkové náklady",[724,2957,2958],{},[883,2959,2961],{"className":2960},[886],[888,2962,2963],{"xmlns":890},[892,2964,2965,2994],{},[895,2966,2967,2969,2972,2974,2977,2979,2981,2983,2986,2988,2990,2992],{},[898,2968,2663],{},[898,2970,2971],{},"C",[1693,2973,1695],{},[898,2975,2976],{},"F",[898,2978,2971],{},[1693,2980,1892],{},[898,2982,2663],{},[898,2984,2985],{},"V",[898,2987,2971],{},[1693,2989,1709],{"stretchy":1708},[898,2991,1712],{},[1693,2993,1731],{"stretchy":1708},[902,2995,2996],{"encoding":904},"TC = FC + TVC(Q)",[724,2998,2999,3001],{},[38,3000,1932],{}," definice (3.5) — rozklad na fixní a variabilní část.",[724,3003,3004,3006,3007,3023,3024,3042],{},[38,3005,1941],{}," co zaplatíš, ať vyrobíš cokoli (",[883,3008,3010],{"className":3009},[886],[888,3011,3012],{"xmlns":890},[892,3013,3014,3020],{},[895,3015,3016,3018],{},[898,3017,2976],{},[898,3019,2971],{},[902,3021,3022],{"encoding":904},"FC",") + co zaplatíš za samotnou výrobu (",[883,3025,3027],{"className":3026},[886],[888,3028,3029],{"xmlns":890},[892,3030,3031,3039],{},[895,3032,3033,3035,3037],{},[898,3034,2663],{},[898,3036,2985],{},[898,3038,2971],{},[902,3040,3041],{"encoding":904},"TVC",").",[198,3044,3046],{"id":3045},"průměrné-náklady","Průměrné náklady",[724,3048,3049],{},[883,3050,3052],{"className":3051},[886],[888,3053,3054],{"xmlns":890},[892,3055,3056,3120],{},[895,3057,3058,3060,3062,3064,3074,3076,3078,3080,3082,3084,3086,3096,3098,3100,3102,3104,3106,3108],{},[898,3059,2719],{},[898,3061,2971],{},[1693,3063,1695],{},[2132,3065,3066,3072],{},[895,3067,3068,3070],{},[898,3069,2663],{},[898,3071,2971],{},[898,3073,1712],{},[1693,3075,1899],{"separator":1898},[1901,3077],{"width":1903},[898,3079,2719],{},[898,3081,2976],{},[898,3083,2971],{},[1693,3085,1695],{},[2132,3087,3088,3094],{},[895,3089,3090,3092],{},[898,3091,2976],{},[898,3093,2971],{},[898,3095,1712],{},[1693,3097,1899],{"separator":1898},[1901,3099],{"width":1903},[898,3101,2719],{},[898,3103,2985],{},[898,3105,2971],{},[1693,3107,1695],{},[2132,3109,3110,3118],{},[895,3111,3112,3114,3116],{},[898,3113,2663],{},[898,3115,2985],{},[898,3117,2971],{},[898,3119,1712],{},[902,3121,3122],{"encoding":904},"AC = \\frac{TC}{Q}, \\qquad AFC = \\frac{FC}{Q}, \\qquad AVC = \\frac{TVC}{Q}",[724,3124,3125,3127],{},[38,3126,1932],{}," definiční podíly (vzorce 3.6, 3.7).",[724,3129,3130,3132,3133,3151,3152,3165],{},[38,3131,1941],{}," průměrný náklad na kus. ",[883,3134,3136],{"className":3135},[886],[888,3137,3138],{"xmlns":890},[892,3139,3140,3148],{},[895,3141,3142,3144,3146],{},[898,3143,2719],{},[898,3145,2976],{},[898,3147,2971],{},[902,3149,3150],{"encoding":904},"AFC"," s rostoucím ",[883,3153,3155],{"className":3154},[886],[888,3156,3157],{"xmlns":890},[892,3158,3159,3163],{},[895,3160,3161],{},[898,3162,1712],{},[902,3164,1712],{"encoding":904}," jde k nule (fixní náklad se rozředí přes víc kusů).",[198,3167,3169],{"id":3168},"mezní-náklady","Mezní náklady",[724,3171,3172],{},[883,3173,3175],{"className":3174},[886],[888,3176,3177],{"xmlns":890},[892,3178,3179,3203],{},[895,3180,3181,3183,3185,3187],{},[898,3182,2839],{},[898,3184,2971],{},[1693,3186,1695],{},[2132,3188,3189,3197],{},[895,3190,3191,3193,3195],{},[898,3192,1771],{},[898,3194,2663],{},[898,3196,2971],{},[895,3198,3199,3201],{},[898,3200,1771],{},[898,3202,1712],{},[902,3204,3205],{"encoding":904},"MC = \\frac{dTC}{dQ}",[724,3207,3208,2867,3210,2884,3226,3239],{},[38,3209,1932],{},[883,3211,3213],{"className":3212},[886],[888,3214,3215],{"xmlns":890},[892,3216,3217,3223],{},[895,3218,3219,3221],{},[898,3220,2663],{},[898,3222,2971],{},[902,3224,3225],{"encoding":904},"TC",[883,3227,3229],{"className":3228},[886],[888,3230,3231],{"xmlns":890},[892,3232,3233,3237],{},[895,3234,3235],{},[898,3236,1712],{},[902,3238,1712],{"encoding":904}," (vzorec 3.8).",[724,3241,3242,3244,3245,1789],{},[38,3243,1941],{}," „kolik mě stojí vyrobit ještě jeden kus navíc\". Fixní náklady z derivace vypadnou → ",[38,3246,3247],{},"mezní rozhodování nezávisí na fixních nákladech",[1852,3249],{},[115,3251,3253],{"id":3252},"_5-optimalizační-principy-firmy","5. Optimalizační principy firmy",[724,3255,3256,1863,3258],{},[38,3257,1862],{},[207,3259,3261],{"className":3260,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk",[198,3263,3265],{"id":3264},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,3267,3268],{},[883,3269,3271],{"className":3270},[886],[888,3272,3273],{"xmlns":890},[892,3274,3275,3308],{},[895,3276,3277,3279,3281,3283,3290,3292,3294,3296,3298,3300,3306],{},[898,3278,2719],{},[898,3280,2971],{},[1693,3282,1709],{"stretchy":1708},[3284,3285,3286,3288],"msub",{},[898,3287,1712],{},[1762,3289,1911],{},[1693,3291,1731],{"stretchy":1708},[1693,3293,1695],{},[898,3295,2839],{},[898,3297,2971],{},[1693,3299,1709],{"stretchy":1708},[3284,3301,3302,3304],{},[898,3303,1712],{},[1762,3305,1911],{},[1693,3307,1731],{"stretchy":1708},[902,3309,3310],{"encoding":904},"AC(Q_0) = MC(Q_0)",[724,3312,3313,3315,3316,3332,3333,3353],{},[38,3314,1932],{}," nutná podmínka minima ",[883,3317,3319],{"className":3318},[886],[888,3320,3321],{"xmlns":890},[892,3322,3323,3329],{},[895,3324,3325,3327],{},[898,3326,2719],{},[898,3328,2971],{},[902,3330,3331],{"encoding":904},"AC",", odvozeno derivací podílu ",[883,3334,3336],{"className":3335},[886],[888,3337,3338],{"xmlns":890},[892,3339,3340,3350],{},[895,3341,3342,3344,3346,3348],{},[898,3343,2663],{},[898,3345,2971],{},[898,3347,1705],{"mathvariant":1704},[898,3349,1712],{},[902,3351,3352],{"encoding":904},"TC\u002FQ"," (vzorec 3.10).",[724,3355,3356,3358],{},[38,3357,1941],{}," analogie se známkovým průměrem — průměr klesá, když další známka (mezní) je pod průměrem; roste, když nad; je v extrému, když se rovnají.",[198,3360,3362],{"id":3361},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,3364,3365],{},[883,3366,3368],{"className":3367},[886],[888,3369,3370],{"xmlns":890},[892,3371,3372,3406],{},[895,3373,3374,3376,3378,3380,3382,3388,3390,3392,3394,3396,3398,3404],{},[898,3375,2719],{},[898,3377,2985],{},[898,3379,2971],{},[1693,3381,1709],{"stretchy":1708},[3284,3383,3384,3386],{},[898,3385,1712],{},[1762,3387,1911],{},[1693,3389,1731],{"stretchy":1708},[1693,3391,1695],{},[898,3393,2839],{},[898,3395,2971],{},[1693,3397,1709],{"stretchy":1708},[3284,3399,3400,3402],{},[898,3401,1712],{},[1762,3403,1911],{},[1693,3405,1731],{"stretchy":1708},[902,3407,3408],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[724,3410,3411,3413,3414,3429,3430,3447],{},[38,3412,1932],{}," stejné odvození jako u ",[883,3415,3417],{"className":3416},[886],[888,3418,3419],{"xmlns":890},[892,3420,3421,3427],{},[895,3422,3423,3425],{},[898,3424,2719],{},[898,3426,2971],{},[902,3428,3331],{"encoding":904},", ale s ",[883,3431,3433],{"className":3432},[886],[888,3434,3435],{"xmlns":890},[892,3436,3437,3445],{},[895,3438,3439,3441,3443],{},[898,3440,2663],{},[898,3442,2985],{},[898,3444,2971],{},[902,3446,3041],{"encoding":904}," (vzorec 3.11).",[724,3449,3450,3452,3453,3456],{},[38,3451,1941],{}," identifikuje ",[38,3454,3455],{},"shutdown point"," — kritický bod pro nabídku firmy. Pod ním se firmě nevyplatí produkovat.",[198,3458,3460],{"id":3459},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,3462,3463],{},[883,3464,3466],{"className":3465},[886],[888,3467,3468],{"xmlns":890},[892,3469,3470,3502],{},[895,3471,3472,3474,3476,3478,3484,3486,3488,3490,3492,3494,3500],{},[898,3473,2839],{},[898,3475,2666],{},[1693,3477,1709],{"stretchy":1708},[3284,3479,3480,3482],{},[898,3481,1712],{},[1762,3483,1911],{},[1693,3485,1731],{"stretchy":1708},[1693,3487,1695],{},[898,3489,2839],{},[898,3491,2971],{},[1693,3493,1709],{"stretchy":1708},[3284,3495,3496,3498],{},[898,3497,1712],{},[1762,3499,1911],{},[1693,3501,1731],{"stretchy":1708},[902,3503,3504],{"encoding":904},"MR(Q_0) = MC(Q_0)",[724,3506,3507,3509,3510,3538,3539,3575],{},[38,3508,1932],{}," nutná podmínka maxima zisku ",[883,3511,3513],{"className":3512},[886],[888,3514,3515],{"xmlns":890},[892,3516,3517,3535],{},[895,3518,3519,3521,3523,3525,3527,3529,3531,3533],{},[898,3520,1701],{},[898,3522,2666],{},[1693,3524,1695],{},[898,3526,2663],{},[898,3528,2666],{},[1693,3530,1698],{},[898,3532,2663],{},[898,3534,2971],{},[902,3536,3537],{"encoding":904},"PR = TR - TC",": derivace ",[883,3540,3542],{"className":3541},[886],[888,3543,3544],{"xmlns":890},[892,3545,3546,3572],{},[895,3547,3548,3550,3556,3558,3560,3562,3564,3566,3568,3570],{},[898,3549,1701],{},[1717,3551,3552,3554],{},[898,3553,2666],{},[1693,3555,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,3557,1695],{},[898,3559,2839],{},[898,3561,2666],{},[1693,3563,1698],{},[898,3565,2839],{},[898,3567,2971],{},[1693,3569,1695],{},[1762,3571,1911],{},[902,3573,3574],{"encoding":904},"PR' = MR - MC = 0"," (vzorec 3.13).",[724,3577,3578,3580],{},[38,3579,1941],{}," vyrábím dál, dokud další kus přináší víc peněz, než stojí. Zastavím se, když se vyrovnají.",[1852,3582],{},[115,3584,3586],{"id":3585},"_6-nabídka-firmy","6. Nabídka firmy",[724,3588,3589,1863,3591],{},[38,3590,1862],{},[207,3592,3261],{"className":3593,"dataFsResolvedFilePath":827,"href":828},[210],[724,3595,3596],{},[883,3597,3599],{"className":3598},[886],[888,3600,3601],{"xmlns":890},[892,3602,3603,3699],{},[895,3604,3605,3607,3609,3612,3614,3616,3618,3620],{},[898,3606,1701],{},[1693,3608,1695],{},[898,3610,3611],{},"S",[1693,3613,1709],{"stretchy":1708},[898,3615,1712],{},[1693,3617,1731],{"stretchy":1708},[1693,3619,1695],{},[895,3621,3622,3625],{},[1693,3623,3624],{"fence":1898},"{",[3626,3627,3631,3673],"mtable",{"rowspacing":3628,"columnalign":3629,"columnspacing":3630},"0.36em","left left","1em",[3632,3633,3634,3652],"mtr",{},[3635,3636,3637],"mtd",{},[3638,3639,3640],"mstyle",{"scriptlevel":1911,"displaystyle":1708},[895,3641,3642,3644,3646,3648,3650],{},[898,3643,2839],{},[898,3645,2971],{},[1693,3647,1709],{"stretchy":1708},[898,3649,1712],{},[1693,3651,1731],{"stretchy":1708},[3635,3653,3654],{},[3638,3655,3656],{"scriptlevel":1911,"displaystyle":1708},[895,3657,3658,3661,3663,3666],{},[1915,3659,3660],{},"pro ",[898,3662,1712],{},[1693,3664,3665],{},"≥",[1717,3667,3668,3670],{},[898,3669,1712],{},[1693,3671,3672],{},"∗",[3632,3674,3675,3681],{},[3635,3676,3677],{},[3638,3678,3679],{"scriptlevel":1911,"displaystyle":1708},[1762,3680,1911],{},[3635,3682,3683],{},[3638,3684,3685],{"scriptlevel":1911,"displaystyle":1708},[895,3686,3687,3689,3691,3693],{},[1915,3688,3660],{},[898,3690,1712],{},[1693,3692,1908],{},[1717,3694,3695,3697],{},[898,3696,1712],{},[1693,3698,3672],{},[902,3700,3701],{"encoding":904},"P = S(Q) = \\begin{cases} MC(Q) & \\text{pro } Q \\geq Q^* \\\\ 0 & \\text{pro } Q \u003C Q^* \\end{cases}",[724,3703,3704,3706,3707,3727,3728,3752,3753,3771,3772,1789],{},[38,3705,1932],{}," kombinace principu ",[883,3708,3710],{"className":3709},[886],[888,3711,3712],{"xmlns":890},[892,3713,3714,3724],{},[895,3715,3716,3718,3720,3722],{},[898,3717,1701],{},[1693,3719,1695],{},[898,3721,2839],{},[898,3723,2971],{},[902,3725,3726],{"encoding":904},"P = MC"," a podmínky, že cena musí pokrýt alespoň ",[883,3729,3731],{"className":3730},[886],[888,3732,3733],{"xmlns":890},[892,3734,3735,3749],{},[895,3736,3737,3740,3743,3745,3747],{},[898,3738,3739],{},"min",[1693,3741,3742],{},"⁡",[898,3744,2719],{},[898,3746,2985],{},[898,3748,2971],{},[902,3750,3751],{"encoding":904},"\\min AVC"," (vzorec 3.15). ",[883,3754,3756],{"className":3755},[886],[888,3757,3758],{"xmlns":890},[892,3759,3760,3768],{},[895,3761,3762],{},[1717,3763,3764,3766],{},[898,3765,1712],{},[1693,3767,3672],{},[902,3769,3770],{"encoding":904},"Q^*"," je bod minima ",[883,3773,3775],{"className":3774},[886],[888,3776,3777],{"xmlns":890},[892,3778,3779,3787],{},[895,3780,3781,3783,3785],{},[898,3782,2719],{},[898,3784,2985],{},[898,3786,2971],{},[902,3788,3789],{"encoding":904},"AVC",[724,3791,3792,3794,3795,3811],{},[38,3793,1941],{}," nabídková křivka je rostoucí část ",[883,3796,3798],{"className":3797},[886],[888,3799,3800],{"xmlns":890},[892,3801,3802,3808],{},[895,3803,3804,3806],{},[898,3805,2839],{},[898,3807,2971],{},[902,3809,3810],{"encoding":904},"MC"," nad shutdown bodem. Pod ním firma raději zavře — ztráta z fixních nákladů je menší než ztráta z pokračování výroby pod náklady.",[1852,3813],{},[115,3815,3817],{"id":3816},"_7-elasticita-poptávky","7. Elasticita poptávky",[724,3819,3820,1863,3822],{},[38,3821,1862],{},[207,3823,3825],{"className":3824,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita poptávky a nabídky",[198,3827,3829],{"id":3828},"cenová-elasticita-poptávky-definiční-tvar","Cenová elasticita poptávky (definiční tvar)",[724,3831,3832],{},[883,3833,3835],{"className":3834},[886],[888,3836,3837],{"xmlns":890},[892,3838,3839,3869],{},[895,3840,3841,3843,3845,3847,3853,3855],{},[898,3842,1691],{},[1693,3844,1695],{},[1693,3846,1698],{},[2132,3848,3849,3851],{},[898,3850,1701],{},[898,3852,1712],{},[1693,3854,1715],{},[2132,3856,3857,3863],{},[895,3858,3859,3861],{},[898,3860,1771],{},[898,3862,1712],{},[895,3864,3865,3867],{},[898,3866,1771],{},[898,3868,1701],{},[902,3870,3871],{"encoding":904},"E = -\\frac{P}{Q} \\cdot \\frac{dQ}{dP}",[724,3873,3874,3876,3877,3907,3908,1789],{},[38,3875,1932],{}," limitní přechod z průměrné (obloukové) elasticity ",[883,3878,3880],{"className":3879},[886],[888,3881,3882],{"xmlns":890},[892,3883,3884,3904],{},[895,3885,3886,3888,3891,3893,3896,3898,3900,3902],{},[1693,3887,1698],{},[898,3889,3890],{"mathvariant":1704},"Δ",[898,3892,1712],{},[898,3894,3895],{"mathvariant":1704},"%",[898,3897,1705],{"mathvariant":1704},[898,3899,3890],{"mathvariant":1704},[898,3901,1701],{},[898,3903,3895],{"mathvariant":1704},[902,3905,3906],{"encoding":904},"-\\Delta Q\\% \u002F \\Delta P\\%"," (vzorec 4.5). Znaménko minus překlápí záporný výsledek (poptávka klesá), aby ",[883,3909,3911],{"className":3910},[886],[888,3912,3913],{"xmlns":890},[892,3914,3915,3923],{},[895,3916,3917,3919,3921],{},[898,3918,1691],{},[1693,3920,3665],{},[1762,3922,1911],{},[902,3924,3925],{"encoding":904},"E \\geq 0",[724,3927,3928,3930],{},[38,3929,1941],{}," „o kolik % se změní množství, když cena vzroste o 1 %\". Bezrozměrná míra citlivosti.",[198,3932,3934,3935,3956,3957,1731],{"id":3933},"převod-na-dpdqdpdq-když-je-poptávka-zadaná-jako-pdqp-dq","Převod na ",[883,3936,3938],{"className":3937},[886],[888,3939,3940],{"xmlns":890},[892,3941,3942,3954],{},[895,3943,3944,3946,3948,3950,3952],{},[898,3945,1771],{},[898,3947,1701],{},[898,3949,1705],{"mathvariant":1704},[898,3951,1771],{},[898,3953,1712],{},[902,3955,1817],{"encoding":904}," (když je poptávka zadaná jako ",[883,3958,3960],{"className":3959},[886],[888,3961,3962],{"xmlns":890},[892,3963,3964,3978],{},[895,3965,3966,3968,3970,3972,3974,3976],{},[898,3967,1701],{},[1693,3969,1695],{},[898,3971,2738],{},[1693,3973,1709],{"stretchy":1708},[898,3975,1712],{},[1693,3977,1731],{"stretchy":1708},[902,3979,3980],{"encoding":904},"P = D(Q)",[724,3982,3983],{},[883,3984,3986],{"className":3985},[886],[888,3987,3988],{"xmlns":890},[892,3989,3990,4026],{},[895,3991,3992,4006,4008],{},[2132,3993,3994,4000],{},[895,3995,3996,3998],{},[898,3997,1771],{},[898,3999,1712],{},[895,4001,4002,4004],{},[898,4003,1771],{},[898,4005,1701],{},[1693,4007,1695],{},[2132,4009,4010,4012],{},[1762,4011,1764],{},[2132,4013,4014,4020],{},[895,4015,4016,4018],{},[898,4017,1771],{},[898,4019,1701],{},[895,4021,4022,4024],{},[898,4023,1771],{},[898,4025,1712],{},[902,4027,4028],{"encoding":904},"\\frac{dQ}{dP} = \\frac{1}{\\frac{dP}{dQ}}",[724,4030,4031,4033],{},[38,4032,1932],{}," pravidlo pro derivaci inverzní funkce (vzorec 4.9).",[724,4035,4036,4038,4039,4059,4060,2884,4073,4086],{},[38,4037,1941],{}," když znám ",[883,4040,4042],{"className":4041},[886],[888,4043,4044],{"xmlns":890},[892,4045,4046,4056],{},[895,4047,4048,4050,4052,4054],{},[898,4049,1701],{},[1693,4051,1709],{"stretchy":1708},[898,4053,1712],{},[1693,4055,1731],{"stretchy":1708},[902,4057,4058],{"encoding":904},"P(Q)"," a potřebuju derivaci ",[883,4061,4063],{"className":4062},[886],[888,4064,4065],{"xmlns":890},[892,4066,4067,4071],{},[895,4068,4069],{},[898,4070,1712],{},[902,4072,1712],{"encoding":904},[883,4074,4076],{"className":4075},[886],[888,4077,4078],{"xmlns":890},[892,4079,4080,4084],{},[895,4081,4082],{},[898,4083,1701],{},[902,4085,1701],{"encoding":904},", stačí ji převrátit.",[198,4088,4090],{"id":4089},"procentní-odhad-změny","Procentní odhad změny",[724,4092,4093],{},[883,4094,4096],{"className":4095},[886],[888,4097,4098],{"xmlns":890},[892,4099,4100,4123],{},[895,4101,4102,4104,4106,4108,4111,4113,4115,4117,4119,4121],{},[898,4103,3890],{"mathvariant":1704},[898,4105,1712],{},[898,4107,3895],{"mathvariant":1704},[1693,4109,4110],{},"≈",[1693,4112,1698],{},[898,4114,1691],{},[1693,4116,1715],{},[898,4118,3890],{"mathvariant":1704},[898,4120,1701],{},[898,4122,3895],{"mathvariant":1704},[902,4124,4125],{"encoding":904},"\\Delta Q\\% \\approx -E \\cdot \\Delta P\\%",[724,4127,4128,4130,4131,1789],{},[38,4129,1932],{}," vzorec (4.11) — plyne přímo z definice ",[883,4132,4134],{"className":4133},[886],[888,4135,4136],{"xmlns":890},[892,4137,4138,4142],{},[895,4139,4140],{},[898,4141,1691],{},[902,4143,1691],{"encoding":904},[724,4145,4146,4148,4149,4167],{},[38,4147,1941],{}," při ",[883,4150,4152],{"className":4151},[886],[888,4153,4154],{"xmlns":890},[892,4155,4156,4164],{},[895,4157,4158,4160,4162],{},[898,4159,1691],{},[1693,4161,1695],{},[1762,4163,2398],{},[902,4165,4166],{"encoding":904},"E = 2"," a zdražení o 3 % klesne množství přibližně o 6 %.",[198,4169,4171],{"id":4170},"vztah-mr-a-elasticity","Vztah MR a elasticity",[724,4173,4174],{},[883,4175,4177],{"className":4176},[886],[888,4178,4179],{"xmlns":890},[892,4180,4181,4207],{},[895,4182,4183,4185,4187,4189,4191],{},[898,4184,2839],{},[898,4186,2666],{},[1693,4188,1695],{},[898,4190,1701],{},[895,4192,4193,4195,4197,4199,4205],{},[1693,4194,1709],{"fence":1898},[1762,4196,1764],{},[1693,4198,1698],{},[2132,4200,4201,4203],{},[1762,4202,1764],{},[898,4204,1691],{},[1693,4206,1731],{"fence":1898},[902,4208,4209],{"encoding":904},"MR = P\\left(1 - \\frac{1}{E}\\right)",[724,4211,4212,4214,4215,2884,4238,4251,4252,4265],{},[38,4213,1932],{}," derivací ",[883,4216,4218],{"className":4217},[886],[888,4219,4220],{"xmlns":890},[892,4221,4222,4236],{},[895,4223,4224,4226,4228,4230,4232,4234],{},[898,4225,2663],{},[898,4227,2666],{},[1693,4229,1695],{},[898,4231,1701],{},[1693,4233,1715],{},[898,4235,1712],{},[902,4237,2677],{"encoding":904},[883,4239,4241],{"className":4240},[886],[888,4242,4243],{"xmlns":890},[892,4244,4245,4249],{},[895,4246,4247],{},[898,4248,1712],{},[902,4250,1712],{"encoding":904}," a dosazením ",[883,4253,4255],{"className":4254},[886],[888,4256,4257],{"xmlns":890},[892,4258,4259,4263],{},[895,4260,4261],{},[898,4262,1691],{},[902,4264,1691],{"encoding":904}," (vzorec 4.12).",[724,4267,4268,4270,4271,4286,4287,4300],{},[38,4269,1941],{}," most mezi ",[883,4272,4274],{"className":4273},[886],[888,4275,4276],{"xmlns":890},[892,4277,4278,4284],{},[895,4279,4280,4282],{},[898,4281,2839],{},[898,4283,2666],{},[902,4285,2919],{"encoding":904}," a ",[883,4288,4290],{"className":4289},[886],[888,4291,4292],{"xmlns":890},[892,4293,4294,4298],{},[895,4295,4296],{},[898,4297,1691],{},[902,4299,1691],{"encoding":904},":",[120,4302,4303,4345,4386],{},[123,4304,4305,4323,4324,4344],{},[883,4306,4308],{"className":4307},[886],[888,4309,4310],{"xmlns":890},[892,4311,4312,4320],{},[895,4313,4314,4316,4318],{},[898,4315,1691],{},[1693,4317,1922],{},[1762,4319,1764],{},[902,4321,4322],{"encoding":904},"E > 1"," → ",[883,4325,4327],{"className":4326},[886],[888,4328,4329],{"xmlns":890},[892,4330,4331,4341],{},[895,4332,4333,4335,4337,4339],{},[898,4334,2839],{},[898,4336,2666],{},[1693,4338,1922],{},[1762,4340,1911],{},[902,4342,4343],{"encoding":904},"MR > 0"," → vyplatí se snížit cenu",[123,4346,4347,4323,4365,4385],{},[883,4348,4350],{"className":4349},[886],[888,4351,4352],{"xmlns":890},[892,4353,4354,4362],{},[895,4355,4356,4358,4360],{},[898,4357,1691],{},[1693,4359,1908],{},[1762,4361,1764],{},[902,4363,4364],{"encoding":904},"E \u003C 1",[883,4366,4368],{"className":4367},[886],[888,4369,4370],{"xmlns":890},[892,4371,4372,4382],{},[895,4373,4374,4376,4378,4380],{},[898,4375,2839],{},[898,4377,2666],{},[1693,4379,1908],{},[1762,4381,1911],{},[902,4383,4384],{"encoding":904},"MR \u003C 0"," → vyplatí se zvýšit cenu",[123,4387,4388,4323,4406,4426,4427],{},[883,4389,4391],{"className":4390},[886],[888,4392,4393],{"xmlns":890},[892,4394,4395,4403],{},[895,4396,4397,4399,4401],{},[898,4398,1691],{},[1693,4400,1695],{},[1762,4402,1764],{},[902,4404,4405],{"encoding":904},"E = 1",[883,4407,4409],{"className":4408},[886],[888,4410,4411],{"xmlns":890},[892,4412,4413,4423],{},[895,4414,4415,4417,4419,4421],{},[898,4416,2839],{},[898,4418,2666],{},[1693,4420,1695],{},[1762,4422,1911],{},[902,4424,4425],{"encoding":904},"MR = 0"," → maximum ",[883,4428,4430],{"className":4429},[886],[888,4431,4432],{"xmlns":890},[892,4433,4434,4440],{},[895,4435,4436,4438],{},[898,4437,2663],{},[898,4439,2666],{},[902,4441,2883],{"encoding":904},[198,4443,4445],{"id":4444},"elasticita-nabídky","Elasticita nabídky",[724,4447,4448],{},[883,4449,4451],{"className":4450},[886],[888,4452,4453],{"xmlns":890},[892,4454,4455,4502],{},[895,4456,4457,4478,4480,4486,4488],{},[3284,4458,4459,4461],{},[898,4460,1691],{},[895,4462,4463,4466,4475],{},[1915,4464,4465],{},"nab",[4467,4468,4469,4472],"mover",{"accent":1898},[1915,4470,4471],{},"ı",[1693,4473,4474],{},"ˊ",[1915,4476,4477],{},"dky",[1693,4479,1695],{},[2132,4481,4482,4484],{},[898,4483,1701],{},[898,4485,1712],{},[1693,4487,1715],{},[2132,4489,4490,4496],{},[895,4491,4492,4494],{},[898,4493,1771],{},[898,4495,1712],{},[895,4497,4498,4500],{},[898,4499,1771],{},[898,4501,1701],{},[902,4503,4504],{"encoding":904},"E_{\\text{nabídky}} = \\frac{P}{Q} \\cdot \\frac{dQ}{dP}",[724,4506,4507,4509],{},[38,4508,1932],{}," analogie elasticity poptávky (vzorec 4.13). Bez minusu, protože nabídka roste s cenou.",[724,4511,4512,4514],{},[38,4513,1941],{}," „o kolik % vzroste nabídka, když cena o 1 %\".",[198,4516,4518],{"id":4517},"vícefaktorové-elasticity","Vícefaktorové elasticity",[724,4520,4521],{},[883,4522,4524],{"className":4523},[886],[888,4525,4526],{"xmlns":890},[892,4527,4528,4643],{},[895,4529,4530,4536,4538,4540,4546,4548,4562,4564,4566,4576,4578,4588,4590,4608,4610,4612,4619,4621,4627,4629],{},[3284,4531,4532,4534],{},[898,4533,1691],{},[898,4535,1701],{},[1693,4537,1695],{},[1693,4539,1698],{},[2132,4541,4542,4544],{},[898,4543,1701],{},[898,4545,1712],{},[1915,4547,2239],{},[2132,4549,4550,4556],{},[895,4551,4552,4554],{},[898,4553,2228],{"mathvariant":1704},[898,4555,1712],{},[895,4557,4558,4560],{},[898,4559,2228],{"mathvariant":1704},[898,4561,1701],{},[1693,4563,1899],{"separator":1898},[1901,4565],{"width":1903},[3284,4567,4568,4570],{},[898,4569,1691],{},[3284,4571,4572,4574],{},[898,4573,1701],{},[898,4575,2719],{},[1693,4577,1695],{},[2132,4579,4580,4586],{},[3284,4581,4582,4584],{},[898,4583,1701],{},[898,4585,2719],{},[898,4587,1712],{},[1915,4589,2239],{},[2132,4591,4592,4598],{},[895,4593,4594,4596],{},[898,4595,2228],{"mathvariant":1704},[898,4597,1712],{},[895,4599,4600,4602],{},[898,4601,2228],{"mathvariant":1704},[3284,4603,4604,4606],{},[898,4605,1701],{},[898,4607,2719],{},[1693,4609,1899],{"separator":1898},[1901,4611],{"width":1903},[3284,4613,4614,4616],{},[898,4615,1691],{},[898,4617,4618],{},"Y",[1693,4620,1695],{},[2132,4622,4623,4625],{},[898,4624,4618],{},[898,4626,1712],{},[1915,4628,2239],{},[2132,4630,4631,4637],{},[895,4632,4633,4635],{},[898,4634,2228],{"mathvariant":1704},[898,4636,1712],{},[895,4638,4639,4641],{},[898,4640,2228],{"mathvariant":1704},[898,4642,4618],{},[902,4644,4645],{"encoding":904},"E_P = -\\frac{P}{Q}\\,\\frac{\\partial Q}{\\partial P}, \\qquad E_{P_A} = \\frac{P_A}{Q}\\,\\frac{\\partial Q}{\\partial P_A}, \\qquad E_Y = \\frac{Y}{Q}\\,\\frac{\\partial Q}{\\partial Y}",[724,4647,4648,4650,4651,4687],{},[38,4649,1932],{}," vícefaktorový model ",[883,4652,4654],{"className":4653},[886],[888,4655,4656],{"xmlns":890},[892,4657,4658,4684],{},[895,4659,4660,4662,4664,4666,4668,4670,4672,4678,4680,4682],{},[898,4661,1712],{},[1693,4663,1695],{},[898,4665,2738],{},[1693,4667,1709],{"stretchy":1708},[898,4669,1701],{},[1693,4671,1899],{"separator":1898},[3284,4673,4674,4676],{},[898,4675,1701],{},[898,4677,2719],{},[1693,4679,1899],{"separator":1898},[898,4681,4618],{},[1693,4683,1731],{"stretchy":1708},[902,4685,4686],{"encoding":904},"Q = D(P, P_A, Y)"," (vzorce 4.18–4.20).",[724,4689,4690],{},[38,4691,1941],{},[120,4693,4694,4723,4752,4777],{},[123,4695,4696,4722],{},[883,4697,4699],{"className":4698},[886],[888,4700,4701],{"xmlns":890},[892,4702,4703,4719],{},[895,4704,4705,4715,4717],{},[3284,4706,4707,4709],{},[898,4708,1691],{},[3284,4710,4711,4713],{},[898,4712,1701],{},[898,4714,2719],{},[1693,4716,1922],{},[1762,4718,1911],{},[902,4720,4721],{"encoding":904},"E_{P_A} > 0"," → substitut (máslo vs. margarín)",[123,4724,4725,4751],{},[883,4726,4728],{"className":4727},[886],[888,4729,4730],{"xmlns":890},[892,4731,4732,4748],{},[895,4733,4734,4744,4746],{},[3284,4735,4736,4738],{},[898,4737,1691],{},[3284,4739,4740,4742],{},[898,4741,1701],{},[898,4743,2719],{},[1693,4745,1908],{},[1762,4747,1911],{},[902,4749,4750],{"encoding":904},"E_{P_A} \u003C 0"," → komplement (auto + benzín)",[123,4753,4754,4776],{},[883,4755,4757],{"className":4756},[886],[888,4758,4759],{"xmlns":890},[892,4760,4761,4773],{},[895,4762,4763,4769,4771],{},[3284,4764,4765,4767],{},[898,4766,1691],{},[898,4768,4618],{},[1693,4770,1922],{},[1762,4772,1911],{},[902,4774,4775],{"encoding":904},"E_Y > 0"," → normální zboží (luxus, standard)",[123,4778,4779,4801],{},[883,4780,4782],{"className":4781},[886],[888,4783,4784],{"xmlns":890},[892,4785,4786,4798],{},[895,4787,4788,4794,4796],{},[3284,4789,4790,4792],{},[898,4791,1691],{},[898,4793,4618],{},[1693,4795,1908],{},[1762,4797,1911],{},[902,4799,4800],{"encoding":904},"E_Y \u003C 0"," → podřadné zboží (s růstem důchodu přestáváš kupovat)",[1852,4803],{},[115,4805,4807],{"id":4806},"_8-produkce","8. Produkce",[724,4809,4810,1863,4812],{},[38,4811,1862],{},[207,4813,4815],{"className":4814,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce — produkční funkce, Cobb-Douglas, MRTS",[198,4817,859],{"id":4818},"produkční-funkce",[724,4820,4821],{},[883,4822,4824],{"className":4823},[886],[888,4825,4826],{"xmlns":890},[892,4827,4828,4848],{},[895,4829,4830,4832,4834,4836,4838,4841,4843,4846],{},[898,4831,1712],{},[1693,4833,1695],{},[898,4835,1712],{},[1693,4837,1709],{"stretchy":1708},[898,4839,4840],{},"L",[1693,4842,1899],{"separator":1898},[898,4844,4845],{},"K",[1693,4847,1731],{"stretchy":1708},[902,4849,4850],{"encoding":904},"Q = Q(L, K)",[724,4852,4853,4855],{},[38,4854,1932],{}," axiomatický zápis — produkce závisí na práci a kapitálu (vzorec 5.6).",[724,4857,4858,4860],{},[38,4859,1941],{}," kolik se vyrobí z daného množství práce a kapitálu.",[198,4862,4864],{"id":4863},"mezní-produkty","Mezní produkty",[724,4866,4867],{},[883,4868,4870],{"className":4869},[886],[888,4871,4872],{"xmlns":890},[892,4873,4874,4928],{},[895,4875,4876,4878,4884,4886,4900,4902,4904,4906,4912,4914],{},[898,4877,2839],{},[3284,4879,4880,4882],{},[898,4881,1701],{},[898,4883,4840],{},[1693,4885,1695],{},[2132,4887,4888,4894],{},[895,4889,4890,4892],{},[898,4891,2228],{"mathvariant":1704},[898,4893,1712],{},[895,4895,4896,4898],{},[898,4897,2228],{"mathvariant":1704},[898,4899,4840],{},[1693,4901,1899],{"separator":1898},[1901,4903],{"width":1903},[898,4905,2839],{},[3284,4907,4908,4910],{},[898,4909,1701],{},[898,4911,4845],{},[1693,4913,1695],{},[2132,4915,4916,4922],{},[895,4917,4918,4920],{},[898,4919,2228],{"mathvariant":1704},[898,4921,1712],{},[895,4923,4924,4926],{},[898,4925,2228],{"mathvariant":1704},[898,4927,4845],{},[902,4929,4930],{"encoding":904},"MP_L = \\frac{\\partial Q}{\\partial L}, \\qquad MP_K = \\frac{\\partial Q}{\\partial K}",[724,4932,4933,4935],{},[38,4934,1932],{}," parciální derivace produkční funkce (vzorec 5.2 a jeho 2F rozšíření).",[724,4937,4938,4940,4941,4944,4945,4965],{},[38,4939,1941],{}," „o kolik vzroste produkce, když přidám 1 pracovníka navíc (kapitál pevný)\". Podle ",[38,4942,4943],{},"zákona klesajících výnosů"," se od jistého bodu ",[883,4946,4948],{"className":4947},[886],[888,4949,4950],{"xmlns":890},[892,4951,4952,4962],{},[895,4953,4954,4956],{},[898,4955,2839],{},[3284,4957,4958,4960],{},[898,4959,1701],{},[898,4961,4840],{},[902,4963,4964],{"encoding":904},"MP_L"," začne snižovat.",[198,4967,4969],{"id":4968},"průměrný-produkt-práce","Průměrný produkt práce",[724,4971,4972],{},[883,4973,4975],{"className":4974},[886],[888,4976,4977],{"xmlns":890},[892,4978,4979,4997],{},[895,4980,4981,4983,4989,4991],{},[898,4982,2719],{},[3284,4984,4985,4987],{},[898,4986,1701],{},[898,4988,4840],{},[1693,4990,1695],{},[2132,4992,4993,4995],{},[898,4994,1712],{},[898,4996,4840],{},[902,4998,4999],{"encoding":904},"AP_L = \\frac{Q}{L}",[724,5001,5002,5004],{},[38,5003,1932],{}," definice (vzorec 5.4).",[724,5006,5007,5009,5010,5040,5041,3042],{},[38,5008,1941],{}," produktivita na pracovníka. V maximu platí ",[883,5011,5013],{"className":5012},[886],[888,5014,5015],{"xmlns":890},[892,5016,5017,5037],{},[895,5018,5019,5021,5027,5029,5031],{},[898,5020,2839],{},[3284,5022,5023,5025],{},[898,5024,1701],{},[898,5026,4840],{},[1693,5028,1695],{},[898,5030,2719],{},[3284,5032,5033,5035],{},[898,5034,1701],{},[898,5036,4840],{},[902,5038,5039],{"encoding":904},"MP_L = AP_L"," (stejná logika jako ",[883,5042,5044],{"className":5043},[886],[888,5045,5046],{"xmlns":890},[892,5047,5048,5060],{},[895,5049,5050,5052,5054,5056,5058],{},[898,5051,2719],{},[898,5053,2971],{},[1693,5055,1695],{},[898,5057,2839],{},[898,5059,2971],{},[902,5061,5062],{"encoding":904},"AC = MC",[198,5064,5066],{"id":5065},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,5068,5069],{},[883,5070,5072],{"className":5071},[886],[888,5073,5074],{"xmlns":890},[892,5075,5076,5100],{},[895,5077,5078,5080,5082,5084,5086,5092,5094],{},[898,5079,1712],{},[1693,5081,1695],{},[898,5083,2719],{},[1693,5085,1715],{},[1717,5087,5088,5090],{},[898,5089,4840],{},[898,5091,207],{},[1693,5093,1715],{},[1717,5095,5096,5098],{},[898,5097,4845],{},[898,5099,1895],{},[902,5101,5102],{"encoding":904},"Q = A \\cdot L^a \\cdot K^b",[724,5104,5105,5107],{},[38,5106,1932],{}," standardní funkční tvar v ekonomii (vzorec 5.7).",[724,5109,5110,5112,5113,5131,5132,4300],{},[38,5111,1941],{}," součet ",[883,5114,5116],{"className":5115},[886],[888,5117,5118],{"xmlns":890},[892,5119,5120,5128],{},[895,5121,5122,5124,5126],{},[898,5123,207],{},[1693,5125,1892],{},[898,5127,1895],{},[902,5129,5130],{"encoding":904},"a + b"," rozhoduje o ",[38,5133,5134],{},"výnosech z rozsahu",[120,5136,5137,5162,5187],{},[123,5138,5139,5161],{},[883,5140,5142],{"className":5141},[886],[888,5143,5144],{"xmlns":890},[892,5145,5146,5158],{},[895,5147,5148,5150,5152,5154,5156],{},[898,5149,207],{},[1693,5151,1892],{},[898,5153,1895],{},[1693,5155,1695],{},[1762,5157,1764],{},[902,5159,5160],{"encoding":904},"a + b = 1"," → konstantní",[123,5163,5164,5186],{},[883,5165,5167],{"className":5166},[886],[888,5168,5169],{"xmlns":890},[892,5170,5171,5183],{},[895,5172,5173,5175,5177,5179,5181],{},[898,5174,207],{},[1693,5176,1892],{},[898,5178,1895],{},[1693,5180,1922],{},[1762,5182,1764],{},[902,5184,5185],{"encoding":904},"a + b > 1"," → rostoucí",[123,5188,5189,5211],{},[883,5190,5192],{"className":5191},[886],[888,5193,5194],{"xmlns":890},[892,5195,5196,5208],{},[895,5197,5198,5200,5202,5204,5206],{},[898,5199,207],{},[1693,5201,1892],{},[898,5203,1895],{},[1693,5205,1908],{},[1762,5207,1764],{},[902,5209,5210],{"encoding":904},"a + b \u003C 1"," → klesající",[724,5213,5214,5215,5251],{},"Speciálně ",[883,5216,5218],{"className":5217},[886],[888,5219,5220],{"xmlns":890},[892,5221,5222,5248],{},[895,5223,5224,5226,5228,5230,5236],{},[898,5225,1712],{},[1693,5227,1695],{},[898,5229,2719],{},[1717,5231,5232,5234],{},[898,5233,4840],{},[898,5235,207],{},[1717,5237,5238,5240],{},[898,5239,4845],{},[895,5241,5242,5244,5246],{},[1762,5243,1764],{},[1693,5245,1698],{},[898,5247,207],{},[902,5249,5250],{"encoding":904},"Q = A L^a K^{1-a}"," (ryzí CD) má vždy konstantní výnosy.",[198,5253,5255],{"id":5254},"mezní-míra-technické-substituce","Mezní míra technické substituce",[724,5257,5258],{},[883,5259,5261],{"className":5260},[886],[888,5262,5263],{"xmlns":890},[892,5264,5265,5299],{},[895,5266,5267,5269,5271,5273,5275,5277],{},[898,5268,2839],{},[898,5270,2666],{},[898,5272,2663],{},[898,5274,3611],{},[1693,5276,1695],{},[2132,5278,5279,5289],{},[895,5280,5281,5283],{},[898,5282,2839],{},[3284,5284,5285,5287],{},[898,5286,1701],{},[898,5288,4840],{},[895,5290,5291,5293],{},[898,5292,2839],{},[3284,5294,5295,5297],{},[898,5296,1701],{},[898,5298,4845],{},[902,5300,5301],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K}",[724,5303,5304,5306],{},[38,5305,1932],{}," definice (vzorec 5.14).",[724,5308,5309,5311,5312,5316],{},[38,5310,1941],{}," „kolik jednotek kapitálu nahradí 1 jednotka práce, aby produkce zůstala stejná\". Je to sklon izokvanty. Přesná analogie ",[207,5313,5315],{"className":5314,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS"," z teorie užitečnosti.",[198,5318,5320],{"id":5319},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,5322,5323],{},[883,5324,5326],{"className":5325},[886],[888,5327,5328],{"xmlns":890},[892,5329,5330,5377],{},[895,5331,5332,5334,5336,5338,5344,5346,5348,5350,5352,5358,5360,5363,5365,5367,5369,5371,5373,5375],{},[898,5333,4840],{},[1693,5335,1715],{},[898,5337,2839],{},[3284,5339,5340,5342],{},[898,5341,1701],{},[898,5343,4840],{},[1693,5345,1892],{},[898,5347,4845],{},[1693,5349,1715],{},[898,5351,2839],{},[3284,5353,5354,5356],{},[898,5355,1701],{},[898,5357,4845],{},[1693,5359,1695],{},[898,5361,5362],{},"n",[1693,5364,1715],{},[898,5366,1712],{},[1693,5368,1709],{"stretchy":1708},[898,5370,4840],{},[1693,5372,1899],{"separator":1898},[898,5374,4845],{},[1693,5376,1731],{"stretchy":1708},[902,5378,5379],{"encoding":904},"L \\cdot MP_L + K \\cdot MP_K = n \\cdot Q(L, K)",[724,5381,5382,5384,5385,5398,5399,1789],{},[38,5383,1932],{}," matematická věta o homogenních funkcích stupně ",[883,5386,5388],{"className":5387},[886],[888,5389,5390],{"xmlns":890},[892,5391,5392,5396],{},[895,5393,5394],{},[898,5395,5362],{},[902,5397,5362],{"encoding":904}," (vzorec 5.12). Pro Cobb-Douglase je ",[883,5400,5402],{"className":5401},[886],[888,5403,5404],{"xmlns":890},[892,5405,5406,5418],{},[895,5407,5408,5410,5412,5414,5416],{},[898,5409,5362],{},[1693,5411,1695],{},[898,5413,207],{},[1693,5415,1892],{},[898,5417,1895],{},[902,5419,5420],{"encoding":904},"n = a + b",[724,5422,5423,5425,5426,5444,5445,5448,5449,5473,5474,5498,5499,1789],{},[38,5424,1941],{}," při konstantních výnosech (",[883,5427,5429],{"className":5428},[886],[888,5430,5431],{"xmlns":890},[892,5432,5433,5441],{},[895,5434,5435,5437,5439],{},[898,5436,5362],{},[1693,5438,1695],{},[1762,5440,1764],{},[902,5442,5443],{"encoding":904},"n = 1",") se celý produkt rozdělí mezi vstupy podle jejich mezních produktů — ",[38,5446,5447],{},"důchodové pravidlo",". Práce dostane ",[883,5450,5452],{"className":5451},[886],[888,5453,5454],{"xmlns":890},[892,5455,5456,5470],{},[895,5457,5458,5460,5462,5464],{},[898,5459,4840],{},[1693,5461,1715],{},[898,5463,2839],{},[3284,5465,5466,5468],{},[898,5467,1701],{},[898,5469,4840],{},[902,5471,5472],{"encoding":904},"L \\cdot MP_L",", kapitál ",[883,5475,5477],{"className":5476},[886],[888,5478,5479],{"xmlns":890},[892,5480,5481,5495],{},[895,5482,5483,5485,5487,5489],{},[898,5484,4845],{},[1693,5486,1715],{},[898,5488,2839],{},[3284,5490,5491,5493],{},[898,5492,1701],{},[898,5494,4845],{},[902,5496,5497],{"encoding":904},"K \\cdot MP_K",", a to přesně vyčerpá ",[883,5500,5502],{"className":5501},[886],[888,5503,5504],{"xmlns":890},[892,5505,5506,5510],{},[895,5507,5508],{},[898,5509,1712],{},[902,5511,1712],{"encoding":904},[1852,5513],{},[115,5515,5517],{"id":5516},"_9-užitečnost","9. Užitečnost",[724,5519,5520,1863,5522],{},[38,5521,1862],{},[207,5523,5525],{"className":5524,"dataFsResolvedFilePath":878,"href":879},[210],"Užitečnost, Cobb-Douglas a MRCS",[198,5527,5529],{"id":5528},"funkce-užitečnosti","Funkce užitečnosti",[724,5531,5532],{},[883,5533,5535],{"className":5534},[886],[888,5536,5537],{"xmlns":890},[892,5538,5539,5565],{},[895,5540,5541,5543,5545,5547,5549,5555,5557,5563],{},[898,5542,900],{},[1693,5544,1695],{},[898,5546,900],{},[1693,5548,1709],{"stretchy":1708},[3284,5550,5551,5553],{},[898,5552,1712],{},[1762,5554,1764],{},[1693,5556,1899],{"separator":1898},[3284,5558,5559,5561],{},[898,5560,1712],{},[1762,5562,2398],{},[1693,5564,1731],{"stretchy":1708},[902,5566,5567],{"encoding":904},"U = U(Q_1, Q_2)",[724,5569,5570,5572],{},[38,5571,1932],{}," axiom — užitečnost jako funkce svazku zboží (vzorec 6.1).",[724,5574,5575,5577,5578,5581],{},[38,5576,1941],{}," číselné „skóre\" uspokojení. V ordinalistickém pojetí jen k ",[38,5579,5580],{},"uspořádání"," svazků, ne k měření absolutních hodnot.",[198,5583,5585],{"id":5584},"mezní-užitek","Mezní užitek",[724,5587,5588],{},[883,5589,5591],{"className":5590},[886],[888,5592,5593],{"xmlns":890},[892,5594,5595,5657],{},[895,5596,5597,5599,5605,5607,5625,5627,5629,5631,5637,5639],{},[898,5598,2839],{},[3284,5600,5601,5603],{},[898,5602,900],{},[1762,5604,1764],{},[1693,5606,1695],{},[2132,5608,5609,5615],{},[895,5610,5611,5613],{},[898,5612,2228],{"mathvariant":1704},[898,5614,900],{},[895,5616,5617,5619],{},[898,5618,2228],{"mathvariant":1704},[3284,5620,5621,5623],{},[898,5622,1712],{},[1762,5624,1764],{},[1693,5626,1899],{"separator":1898},[1901,5628],{"width":1903},[898,5630,2839],{},[3284,5632,5633,5635],{},[898,5634,900],{},[1762,5636,2398],{},[1693,5638,1695],{},[2132,5640,5641,5647],{},[895,5642,5643,5645],{},[898,5644,2228],{"mathvariant":1704},[898,5646,900],{},[895,5648,5649,5651],{},[898,5650,2228],{"mathvariant":1704},[3284,5652,5653,5655],{},[898,5654,1712],{},[1762,5656,2398],{},[902,5658,5659],{"encoding":904},"MU_1 = \\frac{\\partial U}{\\partial Q_1}, \\qquad MU_2 = \\frac{\\partial U}{\\partial Q_2}",[724,5661,5662,5664],{},[38,5663,1932],{}," parciální derivace (vzorec 6.2).",[724,5666,5667,5669,5670,5673,5674,5677,5678,5712],{},[38,5668,1941],{}," „užitek z další jednotky zboží\". Musí být ",[38,5671,5672],{},"kladný"," (víc je lepší) a ",[38,5675,5676],{},"klesající"," (zákon klesající mezní užitečnosti — ",[883,5679,5681],{"className":5680},[886],[888,5682,5683],{"xmlns":890},[892,5684,5685,5709],{},[895,5686,5687,5705,5707],{},[5688,5689,5690,5692,5699],"msubsup",{},[898,5691,900],{},[895,5693,5694,5697],{},[898,5695,5696],{},"i",[898,5698,5696],{},[895,5700,5701,5703],{},[1693,5702,1724],{"mathvariant":1704},[1693,5704,1724],{"mathvariant":1704},[1693,5706,1908],{},[1762,5708,1911],{},[902,5710,5711],{"encoding":904},"U''_{ii} \u003C 0",", 1. sklenice vody = záchrana, 10. už skoro nic).",[198,5714,5716],{"id":5715},"mezní-míra-komoditní-substituce","Mezní míra komoditní substituce",[724,5718,5719],{},[883,5720,5722],{"className":5721},[886],[888,5723,5724],{"xmlns":890},[892,5725,5726,5760],{},[895,5727,5728,5730,5732,5734,5736,5738],{},[898,5729,2839],{},[898,5731,2666],{},[898,5733,2971],{},[898,5735,3611],{},[1693,5737,1695],{},[2132,5739,5740,5750],{},[895,5741,5742,5744],{},[898,5743,2839],{},[3284,5745,5746,5748],{},[898,5747,900],{},[1762,5749,1764],{},[895,5751,5752,5754],{},[898,5753,2839],{},[3284,5755,5756,5758],{},[898,5757,900],{},[1762,5759,2398],{},[902,5761,5762],{"encoding":904},"MRCS = \\frac{MU_1}{MU_2}",[724,5764,5765,5767],{},[38,5766,1932],{}," definice (vzorec 6.9).",[724,5769,5770,5772,5773,5791,5792,5810,5811,5815],{},[38,5771,1941],{}," „kolik ",[883,5774,5776],{"className":5775},[886],[888,5777,5778],{"xmlns":890},[892,5779,5780,5788],{},[895,5781,5782],{},[3284,5783,5784,5786],{},[898,5785,1712],{},[1762,5787,2398],{},[902,5789,5790],{"encoding":904},"Q_2"," obětuji za 1 jednotku ",[883,5793,5795],{"className":5794},[886],[888,5796,5797],{"xmlns":890},[892,5798,5799,5807],{},[895,5800,5801],{},[3284,5802,5803,5805],{},[898,5804,1712],{},[1762,5806,1764],{},[902,5808,5809],{"encoding":904},"Q_1"," navíc, aby zůstalo stejné uspokojení\". Absolutní hodnota sklonu indiferenční křivky. Analogie ",[207,5812,5814],{"className":5813,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS"," z teorie produkce.",[1852,5817],{},[115,5819,5821],{"id":5820},"_10-optimalizace-spotřebitele","10. Optimalizace spotřebitele",[724,5823,5824,1863,5826],{},[38,5825,1862],{},[207,5827,5829],{"className":5828,"dataFsResolvedFilePath":911,"href":912},[210],"Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",[198,5831,5833],{"id":5832},"rozpočtové-omezení","Rozpočtové omezení",[724,5835,5836],{},[883,5837,5839],{"className":5838},[886],[888,5840,5841],{"xmlns":890},[892,5842,5843,5875],{},[895,5844,5845,5847,5849,5855,5861,5863,5869],{},[898,5846,4618],{},[1693,5848,1695],{},[3284,5850,5851,5853],{},[898,5852,1701],{},[1762,5854,1764],{},[3284,5856,5857,5859],{},[898,5858,1712],{},[1762,5860,1764],{},[1693,5862,1892],{},[3284,5864,5865,5867],{},[898,5866,1701],{},[1762,5868,2398],{},[3284,5870,5871,5873],{},[898,5872,1712],{},[1762,5874,2398],{},[902,5876,5877],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2",[724,5879,5880,5882],{},[38,5881,1932],{}," identita (vzorec 6.12) — veškerý důchod rozdělen mezi dvě zboží.",[724,5884,5885,5887,5888,5918],{},[38,5886,1941],{}," geometricky přímka v rovině ",[883,5889,5891],{"className":5890},[886],[888,5892,5893],{"xmlns":890},[892,5894,5895,5915],{},[895,5896,5897,5899,5905,5907,5913],{},[1693,5898,1709],{"stretchy":1708},[3284,5900,5901,5903],{},[898,5902,1712],{},[1762,5904,1764],{},[1693,5906,1899],{"separator":1898},[3284,5908,5909,5911],{},[898,5910,1712],{},[1762,5912,2398],{},[1693,5914,1731],{"stretchy":1708},[902,5916,5917],{"encoding":904},"(Q_1, Q_2)",". Pod ní (a na ní) leží dostupné svazky.",[198,5920,5922],{"id":5921},"lagrangeova-funkce-maximalizace-užitečnosti","Lagrangeova funkce (maximalizace užitečnosti)",[724,5924,5925],{},[883,5926,5928],{"className":5927},[886],[888,5929,5930],{"xmlns":890},[892,5931,5932,6020],{},[895,5933,5934,5937,5939,5945,5947,5953,5955,5958,5960,5962,5964,5966,5972,5974,5980,5982,5984,5986,5988,5990,5992,5998,6004,6006,6012,6018],{},[898,5935,4840],{"mathvariant":5936},"script",[1693,5938,1709],{"stretchy":1708},[3284,5940,5941,5943],{},[898,5942,1712],{},[1762,5944,1764],{},[1693,5946,1899],{"separator":1898},[3284,5948,5949,5951],{},[898,5950,1712],{},[1762,5952,2398],{},[1693,5954,1899],{"separator":1898},[898,5956,5957],{},"λ",[1693,5959,1731],{"stretchy":1708},[1693,5961,1695],{},[898,5963,900],{},[1693,5965,1709],{"stretchy":1708},[3284,5967,5968,5970],{},[898,5969,1712],{},[1762,5971,1764],{},[1693,5973,1899],{"separator":1898},[3284,5975,5976,5978],{},[898,5977,1712],{},[1762,5979,2398],{},[1693,5981,1731],{"stretchy":1708},[1693,5983,1892],{},[898,5985,5957],{},[1693,5987,1709],{"stretchy":1708},[898,5989,4618],{},[1693,5991,1698],{},[3284,5993,5994,5996],{},[898,5995,1701],{},[1762,5997,1764],{},[3284,5999,6000,6002],{},[898,6001,1712],{},[1762,6003,1764],{},[1693,6005,1698],{},[3284,6007,6008,6010],{},[898,6009,1701],{},[1762,6011,2398],{},[3284,6013,6014,6016],{},[898,6015,1712],{},[1762,6017,2398],{},[1693,6019,1731],{"stretchy":1708},[902,6021,6022],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda(Y - P_1 Q_1 - P_2 Q_2)",[724,6024,6025,6027,6028,6032,6033],{},[38,6026,1932],{}," nástroj ",[207,6029,6031],{"className":6030,"dataFsResolvedFilePath":791,"href":792},[210],"Lagrangeovy metody"," pro vázanou optimalizaci (vzorec 6.13). ",[38,6034,6035],{},"Pozor: plus, ne mínus.",[724,6037,6038,6040,6041,6055,6056,6059],{},[38,6039,1941],{}," trik převádějící vázanou optimalizaci na volnou. ",[883,6042,6044],{"className":6043},[886],[888,6045,6046],{"xmlns":890},[892,6047,6048,6052],{},[895,6049,6050],{},[898,6051,5957],{},[902,6053,6054],{"encoding":904},"\\lambda"," je ",[38,6057,6058],{},"stínová cena"," rozpočtu — mezní užitek dalšího kusu důchodu.",[198,6061,6063],{"id":6062},"podmínka-optimality-gossenův-2-zákon","Podmínka optimality (Gossenův 2. zákon)",[724,6065,6066],{},[883,6067,6069],{"className":6068},[886],[888,6070,6071],{"xmlns":890},[892,6072,6073,6144],{},[895,6074,6075,6093,6095,6113,6115,6118,6120,6122,6124,6126,6128,6130],{},[2132,6076,6077,6087],{},[895,6078,6079,6081],{},[898,6080,2839],{},[3284,6082,6083,6085],{},[898,6084,900],{},[1762,6086,1764],{},[3284,6088,6089,6091],{},[898,6090,1701],{},[1762,6092,1764],{},[1693,6094,1695],{},[2132,6096,6097,6107],{},[895,6098,6099,6101],{},[898,6100,2839],{},[3284,6102,6103,6105],{},[898,6104,900],{},[1762,6106,2398],{},[3284,6108,6109,6111],{},[898,6110,1701],{},[1762,6112,2398],{},[1901,6114],{"width":1903},[1693,6116,6117],{},"⟺",[1901,6119],{"width":1903},[898,6121,2839],{},[898,6123,2666],{},[898,6125,2971],{},[898,6127,3611],{},[1693,6129,1695],{},[2132,6131,6132,6138],{},[3284,6133,6134,6136],{},[898,6135,1701],{},[1762,6137,1764],{},[3284,6139,6140,6142],{},[898,6141,1701],{},[1762,6143,2398],{},[902,6145,6146],{"encoding":904},"\\frac{MU_1}{P_1} = \\frac{MU_2}{P_2} \\qquad \\Longleftrightarrow \\qquad MRCS = \\frac{P_1}{P_2}",[724,6148,6149,6151,6152,1789],{},[38,6150,1932],{}," z Lagrangeových rovnic (6.14) vyloučením ",[883,6153,6155],{"className":6154},[886],[888,6156,6157],{"xmlns":890},[892,6158,6159,6163],{},[895,6160,6161],{},[898,6162,5957],{},[902,6164,6054],{"encoding":904},[724,6166,6167,1863,6169,6172],{},[38,6168,1941],{},[38,6170,6171],{},"za každou korunu utracenou za zboží 1 dostanu stejný mezní užitek jako za zboží 2",". Kdyby to neplatilo, vyplatila by se realokace. Ekvivalentně: sklon indiferenční křivky = sklon rozpočtové přímky (tečnost).",[1852,6174],{},[115,6176,6178],{"id":6177},"_11-přebytky-spotřebitele-a-výrobce","11. Přebytky spotřebitele a výrobce",[724,6180,6181,1863,6183],{},[38,6182,1862],{},[207,6184,820],{"className":6185,"dataFsResolvedFilePath":818,"href":819},[210],[198,6187,6189],{"id":6188},"přebytek-spotřebitele","Přebytek spotřebitele",[724,6191,6192],{},[883,6193,6195],{"className":6194},[886],[888,6196,6197],{"xmlns":890},[892,6198,6199,6260],{},[895,6200,6201,6203,6205,6207,6213,6215,6217,6230,6232,6234,6236,6238,6240,6242,6244,6246,6252,6254],{},[898,6202,2971],{},[898,6204,3611],{},[1693,6206,1709],{"stretchy":1708},[3284,6208,6209,6211],{},[898,6210,1712],{},[1762,6212,1911],{},[1693,6214,1731],{"stretchy":1708},[1693,6216,1695],{},[5688,6218,6219,6222,6224],{},[1693,6220,6221],{},"∫",[1762,6223,1911],{},[3284,6225,6226,6228],{},[898,6227,1712],{},[1762,6229,1911],{},[898,6231,2738],{},[1693,6233,1709],{"stretchy":1708},[898,6235,1712],{},[1693,6237,1731],{"stretchy":1708},[1915,6239,2239],{},[898,6241,1771],{},[898,6243,1712],{},[1693,6245,1698],{},[3284,6247,6248,6250],{},[898,6249,1701],{},[1762,6251,1911],{},[1693,6253,1715],{},[3284,6255,6256,6258],{},[898,6257,1712],{},[1762,6259,1911],{},[902,6261,6262],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0 \\cdot Q_0",[724,6264,6265,6267],{},[38,6266,1932],{}," definice (vzorec 2.14).",[724,6269,6270,1863,6272,6275,6276,6294,6295,6325],{},[38,6271,1941],{},[38,6273,6274],{},"integrál = celková ochota platit"," (součet mezních užitků za všechny jednotky od 0 do ",[883,6277,6279],{"className":6278},[886],[888,6280,6281],{"xmlns":890},[892,6282,6283,6291],{},[895,6284,6285],{},[3284,6286,6287,6289],{},[898,6288,1712],{},[1762,6290,1911],{},[902,6292,6293],{"encoding":904},"Q_0","); ",[38,6296,6297,6298,6324],{},"obdélník ",[883,6299,6301],{"className":6300},[886],[888,6302,6303],{"xmlns":890},[892,6304,6305,6321],{},[895,6306,6307,6313,6315],{},[3284,6308,6309,6311],{},[898,6310,1701],{},[1762,6312,1911],{},[1693,6314,1715],{},[3284,6316,6317,6319],{},[898,6318,1712],{},[1762,6320,1911],{},[902,6322,6323],{"encoding":904},"P_0 \\cdot Q_0"," = skutečně zaplaceno",". Rozdíl = „co jsem ušetřil, že mám trh a nemusím za každou jednotku platit svou maximální ochotu\".",[198,6327,6329],{"id":6328},"přebytek-výrobce","Přebytek výrobce",[724,6331,6332],{},[883,6333,6335],{"className":6334},[886],[888,6336,6337],{"xmlns":890},[892,6338,6339,6399],{},[895,6340,6341,6343,6345,6347,6353,6355,6357,6363,6365,6371,6373,6385,6387,6389,6391,6393,6395,6397],{},[898,6342,1701],{},[898,6344,3611],{},[1693,6346,1709],{"stretchy":1708},[3284,6348,6349,6351],{},[898,6350,1712],{},[1762,6352,1911],{},[1693,6354,1731],{"stretchy":1708},[1693,6356,1695],{},[3284,6358,6359,6361],{},[898,6360,1701],{},[1762,6362,1911],{},[1693,6364,1715],{},[3284,6366,6367,6369],{},[898,6368,1712],{},[1762,6370,1911],{},[1693,6372,1698],{},[5688,6374,6375,6377,6379],{},[1693,6376,6221],{},[1762,6378,1911],{},[3284,6380,6381,6383],{},[898,6382,1712],{},[1762,6384,1911],{},[898,6386,3611],{},[1693,6388,1709],{"stretchy":1708},[898,6390,1712],{},[1693,6392,1731],{"stretchy":1708},[1915,6394,2239],{},[898,6396,1771],{},[898,6398,1712],{},[902,6400,6401],{"encoding":904},"PS(Q_0) = P_0 \\cdot Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[724,6403,6404,6406],{},[38,6405,1932],{}," definice (vzorec 2.15).",[724,6408,6409,6411,6412,6432],{},[38,6410,1941],{}," zrcadlo — tržba mínus minimální cena, za kterou by výrobce jednotky dodal (integrál z ",[883,6413,6415],{"className":6414},[886],[888,6416,6417],{"xmlns":890},[892,6418,6419,6429],{},[895,6420,6421,6423,6425,6427],{},[898,6422,3611],{},[1693,6424,1709],{"stretchy":1708},[898,6426,1712],{},[1693,6428,1731],{"stretchy":1708},[902,6430,6431],{"encoding":904},"S(Q)"," odpovídá celkovým variabilním nákladům).",[198,6434,6436],{"id":6435},"celkový-blahobyt-trhu","Celkový blahobyt trhu",[724,6438,6439],{},[883,6440,6442],{"className":6441},[886],[888,6443,6444],{"xmlns":890},[892,6445,6446,6463],{},[895,6447,6448,6451,6453,6455,6457,6459,6461],{},[898,6449,6450],{},"W",[1693,6452,1695],{},[898,6454,2971],{},[898,6456,3611],{},[1693,6458,1892],{},[898,6460,1701],{},[898,6462,3611],{},[902,6464,6465],{"encoding":904},"W = CS + PS",[724,6467,6468,6470],{},[38,6469,1932],{}," součet obou přebytků.",[724,6472,6473,6475,6476,6479],{},[38,6474,1941],{}," čistý ekonomický přínos trhu pro obě strany dohromady. Maximalizuje se v rovnováze ",[38,6477,6478],{},"bez daně"," — jakýkoli zásah (daň, regulace) blahobyt snižuje (mrtvá ztráta).",[1852,6481],{},[115,6483,6485],{"id":6484},"_12-zdanění-trhu","12. Zdanění trhu",[724,6487,6488,1863,6490],{},[38,6489,1862],{},[207,6491,6493],{"className":6492,"dataFsResolvedFilePath":809,"href":810},[210],"Zdanění trhu — dopady daně na rovnováhu",[198,6495,6497],{"id":6496},"posun-křivek-při-zdanění","Posun křivek při zdanění",[724,6499,6500],{},[883,6501,6503],{"className":6502},[886],[888,6504,6505],{"xmlns":890},[892,6506,6507,6566],{},[895,6508,6509,6511,6513,6519,6521,6523,6525,6527,6529,6531,6533,6535,6537,6539,6541],{},[898,6510,1701],{},[1693,6512,1695],{},[3284,6514,6515,6517],{},[898,6516,3611],{},[1762,6518,1764],{},[1693,6520,1709],{"stretchy":1708},[898,6522,1712],{},[1693,6524,1731],{"stretchy":1708},[1693,6526,1695],{},[898,6528,3611],{},[1693,6530,1709],{"stretchy":1708},[898,6532,1712],{},[1693,6534,1731],{"stretchy":1708},[1693,6536,1892],{},[898,6538,2663],{},[1901,6540],{"width":3630},[895,6542,6543,6546,6553,6556,6563],{},[1915,6544,6545],{},"(da",[4467,6547,6548,6550],{"accent":1898},[1915,6549,5362],{},[1693,6551,6552],{},"ˇ",[1915,6554,6555],{}," v",[4467,6557,6558,6561],{"accent":1898},[1915,6559,6560],{},"y",[1693,6562,4474],{},[1915,6564,6565],{},"robci)",[902,6567,6568],{"encoding":904},"P = S_1(Q) = S(Q) + T \\quad \\text{(daň výrobci)}",[724,6570,6571],{},[883,6572,6574],{"className":6573},[886],[888,6575,6576],{"xmlns":890},[892,6577,6578,6635],{},[895,6579,6580,6582,6584,6590,6592,6594,6596,6598,6600,6602,6604,6606,6608,6610,6612],{},[898,6581,1701],{},[1693,6583,1695],{},[3284,6585,6586,6588],{},[898,6587,2738],{},[1762,6589,2398],{},[1693,6591,1709],{"stretchy":1708},[898,6593,1712],{},[1693,6595,1731],{"stretchy":1708},[1693,6597,1695],{},[898,6599,2738],{},[1693,6601,1709],{"stretchy":1708},[898,6603,1712],{},[1693,6605,1731],{"stretchy":1708},[1693,6607,1698],{},[898,6609,2663],{},[1901,6611],{"width":3630},[895,6613,6614,6616,6622,6625,6632],{},[1915,6615,6545],{},[4467,6617,6618,6620],{"accent":1898},[1915,6619,5362],{},[1693,6621,6552],{},[1915,6623,6624],{}," spot",[4467,6626,6627,6630],{"accent":1898},[1915,6628,6629],{},"r",[1693,6631,6552],{},[1915,6633,6634],{},"ebiteli)",[902,6636,6637],{"encoding":904},"P = D_2(Q) = D(Q) - T \\quad \\text{(daň spotřebiteli)}",[724,6639,6640,6642,6643,6671,6672,1789],{},[38,6641,1932],{}," odvození z rovnic ",[883,6644,6646],{"className":6645},[886],[888,6647,6648],{"xmlns":890},[892,6649,6650,6668],{},[895,6651,6652,6654,6656,6658,6660,6662,6664,6666],{},[898,6653,1701],{},[1693,6655,1698],{},[898,6657,2663],{},[1693,6659,1695],{},[898,6661,3611],{},[1693,6663,1709],{"stretchy":1708},[898,6665,1712],{},[1693,6667,1731],{"stretchy":1708},[902,6669,6670],{"encoding":904},"P - T = S(Q)"," resp. ",[883,6673,6675],{"className":6674},[886],[888,6676,6677],{"xmlns":890},[892,6678,6679,6697],{},[895,6680,6681,6683,6685,6687,6689,6691,6693,6695],{},[898,6682,1701],{},[1693,6684,1892],{},[898,6686,2663],{},[1693,6688,1695],{},[898,6690,2738],{},[1693,6692,1709],{"stretchy":1708},[898,6694,1712],{},[1693,6696,1731],{"stretchy":1708},[902,6698,6699],{"encoding":904},"P + T = D(Q)",[724,6701,6702,6704,6705,6718],{},[38,6703,1941],{}," daň uložená komukoli posune jednu z křivek o ",[883,6706,6708],{"className":6707},[886],[888,6709,6710],{"xmlns":890},[892,6711,6712,6716],{},[895,6713,6714],{},[898,6715,2663],{},[902,6717,2663],{"encoding":904}," svisle. Výsledek je ekonomicky tentýž (viz ekvivalence níže).",[198,6720,6722],{"id":6721},"rozklad-daňového-břemene","Rozklad daňového břemene",[724,6724,6725],{},[883,6726,6728],{"className":6727},[886],[888,6729,6730],{"xmlns":890},[892,6731,6732,6768],{},[895,6733,6734,6736,6738,6749,6751],{},[898,6735,2663],{},[1693,6737,1695],{},[3284,6739,6740,6742],{},[898,6741,2663],{},[895,6743,6744,6747],{},[898,6745,6746],{},"s",[898,6748,724],{},[1693,6750,1892],{},[3284,6752,6753,6755],{},[898,6754,2663],{},[895,6756,6757,6760,6766],{},[1915,6758,6759],{},"v",[4467,6761,6762,6764],{"accent":1898},[1915,6763,6560],{},[1693,6765,4474],{},[1915,6767,6629],{},[902,6769,6770],{"encoding":904},"T = T_{sp} + T_{\\text{výr}}",[724,6772,6773,6775],{},[38,6774,1932],{}," definice rozkladu.",[724,6777,6778,6780],{},[38,6779,1941],{}," daň nese vždy obě strany. Spotřebitel platí víc, výrobce dostane míň — součet = daň.",[198,6782,6784],{"id":6783},"poměr-daňového-břemene-lineární-model","Poměr daňového břemene (lineární model)",[724,6786,6787],{},[883,6788,6790],{"className":6789},[886],[888,6791,6792],{"xmlns":890},[892,6793,6794,6862],{},[895,6795,6796,6824,6826,6836,6838],{},[2132,6797,6798,6808],{},[3284,6799,6800,6802],{},[898,6801,2663],{},[895,6803,6804,6806],{},[898,6805,6746],{},[898,6807,724],{},[3284,6809,6810,6812],{},[898,6811,2663],{},[895,6813,6814,6816,6822],{},[1915,6815,6759],{},[4467,6817,6818,6820],{"accent":1898},[1915,6819,6560],{},[1693,6821,4474],{},[1915,6823,6629],{},[1693,6825,1695],{},[2132,6827,6828,6830],{},[898,6829,2000],{},[895,6831,6832,6834],{},[1693,6833,1698],{},[898,6835,207],{},[1693,6837,1695],{},[2132,6839,6840,6852],{},[895,6841,6842,6845,6848,6850],{},[898,6843,6844],{"mathvariant":1704},"∣",[1915,6846,6847],{},"sklon ",[898,6849,3611],{},[898,6851,6844],{"mathvariant":1704},[895,6853,6854,6856,6858,6860],{},[898,6855,6844],{"mathvariant":1704},[1915,6857,6847],{},[898,6859,2738],{},[898,6861,6844],{"mathvariant":1704},[902,6863,6864],{"encoding":904},"\\frac{T_{sp}}{T_{\\text{výr}}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}",[724,6866,6867,6869],{},[38,6868,1932],{}," odvozeno z rozkladu pro lineární model.",[724,6871,6872,1863,6874,6877],{},[38,6873,1941],{},[38,6875,6876],{},"čím strmější křivka (méně elastická strana), tím větší podíl daně",". Poptávka strmější → lidé stejně kupují → platí víc spotřebitel. Nabídka strmější → výrobci nemohou reagovat → platí víc výrobce.",[198,6879,6881],{"id":6880},"věta-o-ekvivalenci-zdanění","Věta o ekvivalenci zdanění",[724,6883,6884],{},[883,6885,6887],{"className":6886},[886],[888,6888,6889],{"xmlns":890},[892,6890,6891,6937],{},[895,6892,6893,6901,6903,6911,6913,6915,6923,6925,6927,6929],{},[5688,6894,6895,6897,6899],{},[898,6896,1712],{},[1762,6898,1764],{},[898,6900,1691],{},[1693,6902,1695],{},[5688,6904,6905,6907,6909],{},[898,6906,1712],{},[1762,6908,2398],{},[898,6910,1691],{},[1693,6912,1899],{"separator":1898},[1901,6914],{"width":1903},[5688,6916,6917,6919,6921],{},[898,6918,1701],{},[1762,6920,1764],{},[898,6922,1691],{},[1693,6924,1698],{},[898,6926,2663],{},[1693,6928,1695],{},[5688,6930,6931,6933,6935],{},[898,6932,1701],{},[1762,6934,2398],{},[898,6936,1691],{},[902,6938,6939],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E",[724,6941,6942,6944],{},[38,6943,1932],{}," porovnáním obou forem zdanění.",[724,6946,6947,6949,6950,6953],{},[38,6948,1941],{}," zákon může psát, kdo „platí\" daň — ekonomicky je to jedno. Rozdělení je určeno ",[38,6951,6952],{},"tvarem křivek",", ne paragrafem.",[1852,6955],{},[115,6957,6959],{"id":6958},"_13-makroekonomie-národní-důchod","13. Makroekonomie — národní důchod",[724,6961,6962,1863,6964],{},[38,6963,1862],{},[207,6965,936],{"className":6966,"dataFsResolvedFilePath":934,"href":935},[210],[198,6968,6970],{"id":6969},"hnp-výdajovou-metodou","HNP výdajovou metodou",[724,6972,6973],{},[883,6974,6976],{"className":6975},[886],[888,6977,6978],{"xmlns":890},[892,6979,6980,7008],{},[895,6981,6982,6985,6988,6990,6992,6994,6996,6999,7001,7003,7005],{},[898,6983,6984],{},"G",[898,6986,6987],{},"N",[898,6989,1701],{},[1693,6991,1695],{},[898,6993,2971],{},[1693,6995,1892],{},[898,6997,6998],{},"I",[1693,7000,1892],{},[898,7002,6984],{},[1693,7004,1892],{},[898,7006,7007],{},"X",[902,7009,7010],{"encoding":904},"GNP = C + I + G + X",[724,7012,7013,7015],{},[38,7014,1932],{}," definice (vzorec 7.1).",[724,7017,7018,7020],{},[38,7019,1941],{}," celková výroba = spotřeba domácností + investice firem + vládní výdaje + čistý export.",[198,7022,7024],{"id":7023},"rozklad-důchodu","Rozklad důchodu",[724,7026,7027],{},[883,7028,7030],{"className":7029},[886],[888,7031,7032],{"xmlns":890},[892,7033,7034,7046],{},[895,7035,7036,7038,7040,7042,7044],{},[898,7037,4618],{},[1693,7039,1695],{},[898,7041,2971],{},[1693,7043,1892],{},[898,7045,3611],{},[902,7047,7048],{"encoding":904},"Y = C + S",[724,7050,7051,7053],{},[38,7052,1932],{}," identita (vzorec 7.2) — každou korunu důchodu buď utratím, nebo uspořím.",[724,7055,7056,7058],{},[38,7057,1941],{}," důchod neumí „zmizet\" — buď spotřeba, nebo úspory.",[198,7060,7062],{"id":7061},"lineární-modely-spotřeby-a-úspor","Lineární modely spotřeby a úspor",[724,7064,7065],{},[883,7066,7068],{"className":7067},[886],[888,7069,7070],{"xmlns":890},[892,7071,7072,7110],{},[895,7073,7074,7076,7078,7080,7082,7084,7086,7088,7090,7092,7094,7096,7098,7100,7102,7104,7106,7108],{},[898,7075,2971],{},[1693,7077,1695],{},[898,7079,207],{},[898,7081,4618],{},[1693,7083,1892],{},[898,7085,1895],{},[1693,7087,1899],{"separator":1898},[1901,7089],{"width":1903},[898,7091,3611],{},[1693,7093,1695],{},[1693,7095,1709],{"stretchy":1708},[1762,7097,1764],{},[1693,7099,1698],{},[898,7101,207],{},[1693,7103,1731],{"stretchy":1708},[898,7105,4618],{},[1693,7107,1698],{},[898,7109,1895],{},[902,7111,7112],{"encoding":904},"C = aY + b, \\qquad S = (1-a)Y - b",[724,7114,7115,7117,7118,1343,7140,7158],{},[38,7116,1932],{}," lineární aproximace s předpokladem ",[883,7119,7121],{"className":7120},[886],[888,7122,7123],{"xmlns":890},[892,7124,7125,7137],{},[895,7126,7127,7129,7131,7133,7135],{},[1762,7128,1911],{},[1693,7130,1908],{},[898,7132,207],{},[1693,7134,1908],{},[1762,7136,1764],{},[902,7138,7139],{"encoding":904},"0 \u003C a \u003C 1",[883,7141,7143],{"className":7142},[886],[888,7144,7145],{"xmlns":890},[892,7146,7147,7155],{},[895,7148,7149,7151,7153],{},[898,7150,1895],{},[1693,7152,1922],{},[1762,7154,1911],{},[902,7156,7157],{"encoding":904},"b > 0"," (vzorce 7.3, 7.4).",[724,7160,7161,1863,7163,7176,7177,7180,7181,7194],{},[38,7162,1941],{},[883,7164,7166],{"className":7165},[886],[888,7167,7168],{"xmlns":890},[892,7169,7170,7174],{},[895,7171,7172],{},[898,7173,1895],{},[902,7175,1895],{"encoding":904}," = ",[38,7178,7179],{},"autonomní spotřeba"," (co utratím i s nulovým příjmem — ze starých úspor). ",[883,7182,7184],{"className":7183},[886],[888,7185,7186],{"xmlns":890},[892,7187,7188,7192],{},[895,7189,7190],{},[898,7191,207],{},[902,7193,207],{"encoding":904}," = sklon — kolik z každé nové koruny utratím.",[198,7196,7198],{"id":7197},"mezní-sklony","Mezní sklony",[724,7200,7201],{},[883,7202,7204],{"className":7203},[886],[888,7205,7206],{"xmlns":890},[892,7207,7208,7258],{},[895,7209,7210,7212,7214,7216,7218,7232,7234,7236,7238,7240,7242,7244],{},[898,7211,2839],{},[898,7213,1701],{},[898,7215,2971],{},[1693,7217,1695],{},[2132,7219,7220,7226],{},[895,7221,7222,7224],{},[898,7223,1771],{},[898,7225,2971],{},[895,7227,7228,7230],{},[898,7229,1771],{},[898,7231,4618],{},[1693,7233,1899],{"separator":1898},[1901,7235],{"width":1903},[898,7237,2839],{},[898,7239,1701],{},[898,7241,3611],{},[1693,7243,1695],{},[2132,7245,7246,7252],{},[895,7247,7248,7250],{},[898,7249,1771],{},[898,7251,3611],{},[895,7253,7254,7256],{},[898,7255,1771],{},[898,7257,4618],{},[902,7259,7260],{"encoding":904},"MPC = \\frac{dC}{dY}, \\qquad MPS = \\frac{dS}{dY}",[724,7262,7263,7265],{},[38,7264,1932],{}," definice derivací (článek 7.2).",[724,7267,7268,7270,7271,7289,7290,7308,7309,1343,7331,1789],{},[38,7269,1941],{}," z dodatečné koruny důchodu utratím ",[883,7272,7274],{"className":7273},[886],[888,7275,7276],{"xmlns":890},[892,7277,7278,7286],{},[895,7279,7280,7282,7284],{},[898,7281,2839],{},[898,7283,1701],{},[898,7285,2971],{},[902,7287,7288],{"encoding":904},"MPC"," Kč a ušetřím ",[883,7291,7293],{"className":7292},[886],[888,7294,7295],{"xmlns":890},[892,7296,7297,7305],{},[895,7298,7299,7301,7303],{},[898,7300,2839],{},[898,7302,1701],{},[898,7304,3611],{},[902,7306,7307],{"encoding":904},"MPS"," Kč. V lineárním modelu ",[883,7310,7312],{"className":7311},[886],[888,7313,7314],{"xmlns":890},[892,7315,7316,7328],{},[895,7317,7318,7320,7322,7324,7326],{},[898,7319,2839],{},[898,7321,1701],{},[898,7323,2971],{},[1693,7325,1695],{},[898,7327,207],{},[902,7329,7330],{"encoding":904},"MPC = a",[883,7332,7334],{"className":7333},[886],[888,7335,7336],{"xmlns":890},[892,7337,7338,7354],{},[895,7339,7340,7342,7344,7346,7348,7350,7352],{},[898,7341,2839],{},[898,7343,1701],{},[898,7345,3611],{},[1693,7347,1695],{},[1762,7349,1764],{},[1693,7351,1698],{},[898,7353,207],{},[902,7355,7356],{"encoding":904},"MPS = 1 - a",[198,7358,7360],{"id":7359},"identita-mpc-mps","Identita MPC + MPS",[724,7362,7363],{},[883,7364,7366],{"className":7365},[886],[888,7367,7368],{"xmlns":890},[892,7369,7370,7390],{},[895,7371,7372,7374,7376,7378,7380,7382,7384,7386,7388],{},[898,7373,2839],{},[898,7375,1701],{},[898,7377,2971],{},[1693,7379,1892],{},[898,7381,2839],{},[898,7383,1701],{},[898,7385,3611],{},[1693,7387,1695],{},[1762,7389,1764],{},[902,7391,7392],{"encoding":904},"MPC + MPS = 1",[724,7394,7395,7397,7398,7419],{},[38,7396,1932],{}," derivace identity ",[883,7399,7401],{"className":7400},[886],[888,7402,7403],{"xmlns":890},[892,7404,7405,7417],{},[895,7406,7407,7409,7411,7413,7415],{},[898,7408,4618],{},[1693,7410,1695],{},[898,7412,2971],{},[1693,7414,1892],{},[898,7416,3611],{},[902,7418,7048],{"encoding":904}," (vzorec 7.5).",[724,7421,7422,7424],{},[38,7423,1941],{}," koruna navíc buď jde na spotřebu, nebo na úspory — nic jiného se s ní stát nemůže.",[198,7426,7428],{"id":7427},"podmínky-rovnováhy-jednotlivých-modelů","Podmínky rovnováhy jednotlivých modelů",[724,7430,7431],{},[883,7432,7434],{"className":7433},[886],[888,7435,7436],{"xmlns":890},[892,7437,7438,7455],{},[895,7439,7440,7442,7444,7446,7448,7450,7452],{},[898,7441,4618],{},[1693,7443,1695],{},[898,7445,2971],{},[1693,7447,1892],{},[898,7449,6998],{},[1901,7451],{"width":1903},[1915,7453,7454],{},"(C-I)",[902,7456,7457],{"encoding":904},"Y = C + I \\qquad \\text{(C-I)}",[724,7459,7460],{},[883,7461,7463],{"className":7462},[886],[888,7464,7465],{"xmlns":890},[892,7466,7467,7488],{},[895,7468,7469,7471,7473,7475,7477,7479,7481,7483,7485],{},[898,7470,4618],{},[1693,7472,1695],{},[898,7474,2971],{},[1693,7476,1892],{},[898,7478,6998],{},[1693,7480,1892],{},[898,7482,6984],{},[1901,7484],{"width":1903},[1915,7486,7487],{},"(C-I-G)",[902,7489,7490],{"encoding":904},"Y = C + I + G \\qquad \\text{(C-I-G)}",[724,7492,7493],{},[883,7494,7496],{"className":7495},[886],[888,7497,7498],{"xmlns":890},[892,7499,7500,7530],{},[895,7501,7502,7504,7506,7508,7510,7512,7514,7516,7518,7521,7523,7525,7527],{},[898,7503,4618],{},[1693,7505,1695],{},[898,7507,2971],{},[1693,7509,1892],{},[898,7511,6998],{},[1693,7513,1892],{},[898,7515,6984],{},[1693,7517,1892],{},[898,7519,7520],{},"B",[1693,7522,1698],{},[898,7524,2839],{},[1901,7526],{"width":1903},[1915,7528,7529],{},"(C-I-G-X)",[902,7531,7532],{"encoding":904},"Y = C + I + G + B - M \\qquad \\text{(C-I-G-X)}",[724,7534,7535,7537],{},[38,7536,1932],{}," rozšiřující se modely (vzorce 7.6, 7.8, 7.10).",[724,7539,7540,7542],{},[38,7541,1941],{}," produkce = spotřeba všech sektorů. Postupné bohatnutí modelu — soukromí → + vláda → + zahraničí.",[198,7544,7546],{"id":7545},"disponibilní-důchod","Disponibilní důchod",[724,7548,7549],{},[883,7550,7552],{"className":7551},[886],[888,7553,7554],{"xmlns":890},[892,7555,7556,7572],{},[895,7557,7558,7564,7566,7568,7570],{},[3284,7559,7560,7562],{},[898,7561,4618],{},[898,7563,2738],{},[1693,7565,1695],{},[898,7567,4618],{},[1693,7569,1698],{},[898,7571,2663],{},[902,7573,7574],{"encoding":904},"Y_D = Y - T",[724,7576,7577,7579],{},[38,7578,1932],{}," definice (model C-I-G).",[724,7581,7582,7584,7585,7603,7604,7617,7618,7621,7622,7635],{},[38,7583,1941],{}," co domácnostem zbývá po zaplacení daní — spotřeba závisí na ",[883,7586,7588],{"className":7587},[886],[888,7589,7590],{"xmlns":890},[892,7591,7592,7600],{},[895,7593,7594],{},[3284,7595,7596,7598],{},[898,7597,4618],{},[898,7599,2738],{},[902,7601,7602],{"encoding":904},"Y_D",", ne na ",[883,7605,7607],{"className":7606},[886],[888,7608,7609],{"xmlns":890},[892,7610,7611,7615],{},[895,7612,7613],{},[898,7614,4618],{},[902,7616,4618],{"encoding":904},". ",[38,7619,7620],{},"Nejčastější zdroj chyb"," — nesmí se zaměňovat s ",[883,7623,7625],{"className":7624},[886],[888,7626,7627],{"xmlns":890},[892,7628,7629,7633],{},[895,7630,7631],{},[898,7632,4618],{},[902,7634,4618],{"encoding":904}," v podmínce rovnováhy.",[198,7637,7639],{"id":7638},"rovnovážný-důchod-redukovaný-tvar-c-i","Rovnovážný důchod (redukovaný tvar, C-I)",[724,7641,7642],{},[883,7643,7645],{"className":7644},[886],[888,7646,7647],{"xmlns":890},[892,7648,7649,7681],{},[895,7650,7651,7657,7659],{},[1717,7652,7653,7655],{},[898,7654,4618],{},[898,7656,1691],{},[1693,7658,1695],{},[2132,7660,7661,7673],{},[895,7662,7663,7665,7667],{},[898,7664,1895],{},[1693,7666,1892],{},[1717,7668,7669,7671],{},[898,7670,6998],{},[1693,7672,3672],{},[895,7674,7675,7677,7679],{},[1762,7676,1764],{},[1693,7678,1698],{},[898,7680,207],{},[902,7682,7683],{"encoding":904},"Y^E = \\frac{b + I^*}{1 - a}",[724,7685,7686,7688,7689,7721,7722,1789],{},[38,7687,1932],{}," řešení rovnice ",[883,7690,7692],{"className":7691},[886],[888,7693,7694],{"xmlns":890},[892,7695,7696,7718],{},[895,7697,7698,7700,7702,7704,7706,7708,7710,7712],{},[898,7699,4618],{},[1693,7701,1695],{},[898,7703,207],{},[898,7705,4618],{},[1693,7707,1892],{},[898,7709,1895],{},[1693,7711,1892],{},[1717,7713,7714,7716],{},[898,7715,6998],{},[1693,7717,3672],{},[902,7719,7720],{"encoding":904},"Y = aY + b + I^*"," pro ",[883,7723,7725],{"className":7724},[886],[888,7726,7727],{"xmlns":890},[892,7728,7729,7733],{},[895,7730,7731],{},[898,7732,4618],{},[902,7734,4618],{"encoding":904},[724,7736,7737,7739,7740,7758,7759,7772],{},[38,7738,1941],{}," rovnovážný důchod je násobkem autonomních výdajů. Jmenovatel ",[883,7741,7743],{"className":7742},[886],[888,7744,7745],{"xmlns":890},[892,7746,7747,7755],{},[895,7748,7749,7751,7753],{},[1762,7750,1764],{},[1693,7752,1698],{},[898,7754,207],{},[902,7756,7757],{"encoding":904},"1 - a"," je klíčový — vysoké ",[883,7760,7762],{"className":7761},[886],[888,7763,7764],{"xmlns":890},[892,7765,7766,7770],{},[895,7767,7768],{},[898,7769,207],{},[902,7771,207],{"encoding":904}," (ochota utrácet) → silná multiplikace.",[198,7774,7776],{"id":7775},"keynesův-multiplikátor-investic","Keynesův multiplikátor investic",[724,7778,7779],{},[883,7780,7782],{"className":7781},[886],[888,7783,7784],{"xmlns":890},[892,7785,7786,7838],{},[895,7787,7788,7810,7812,7824,7826],{},[2132,7789,7790,7800],{},[895,7791,7792,7794],{},[898,7793,2228],{"mathvariant":1704},[1717,7795,7796,7798],{},[898,7797,4618],{},[898,7799,1691],{},[895,7801,7802,7804],{},[898,7803,2228],{"mathvariant":1704},[1717,7805,7806,7808],{},[898,7807,6998],{},[1693,7809,3672],{},[1693,7811,1695],{},[2132,7813,7814,7816],{},[1762,7815,1764],{},[895,7817,7818,7820,7822],{},[1762,7819,1764],{},[1693,7821,1698],{},[898,7823,207],{},[1693,7825,1695],{},[2132,7827,7828,7830],{},[1762,7829,1764],{},[895,7831,7832,7834,7836],{},[898,7833,2839],{},[898,7835,1701],{},[898,7837,3611],{},[902,7839,7840],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1-a} = \\frac{1}{MPS}",[724,7842,7843,2530,7845,2884,7863,1789],{},[38,7844,1932],{},[883,7846,7848],{"className":7847},[886],[888,7849,7850],{"xmlns":890},[892,7851,7852,7860],{},[895,7853,7854],{},[1717,7855,7856,7858],{},[898,7857,4618],{},[898,7859,1691],{},[902,7861,7862],{"encoding":904},"Y^E",[883,7864,7866],{"className":7865},[886],[888,7867,7868],{"xmlns":890},[892,7869,7870,7878],{},[895,7871,7872],{},[1717,7873,7874,7876],{},[898,7875,6998],{},[1693,7877,3672],{},[902,7879,7880],{"encoding":904},"I^*",[724,7882,7883,1863,7885,7888,7889,7902,7903,7921,7922,7969,7970,7987],{},[38,7884,1941],{},[38,7886,7887],{},"1 Kč navíc v investicích zvýší důchod o víc než 1 Kč."," Jedna utracená koruna se stane něčím důchodem, z něj se utratí ",[883,7890,7892],{"className":7891},[886],[888,7893,7894],{"xmlns":890},[892,7895,7896,7900],{},[895,7897,7898],{},[898,7899,207],{},[902,7901,207],{"encoding":904}," Kč, z toho ",[883,7904,7906],{"className":7905},[886],[888,7907,7908],{"xmlns":890},[892,7909,7910,7918],{},[895,7911,7912],{},[1717,7913,7914,7916],{},[898,7915,207],{},[1762,7917,2398],{},[902,7919,7920],{"encoding":904},"a^2"," Kč… geometrická řada ",[883,7923,7925],{"className":7924},[886],[888,7926,7927],{"xmlns":890},[892,7928,7929,7966],{},[895,7930,7931,7933,7935,7937,7939,7945,7947,7950,7952,7954,7956,7958,7960,7962,7964],{},[1762,7932,1764],{},[1693,7934,1892],{},[898,7936,207],{},[1693,7938,1892],{},[1717,7940,7941,7943],{},[898,7942,207],{},[1762,7944,2398],{},[1693,7946,1892],{},[1693,7948,7949],{},"⋯",[1693,7951,1695],{},[1762,7953,1764],{},[898,7955,1705],{"mathvariant":1704},[1693,7957,1709],{"stretchy":1708},[1762,7959,1764],{},[1693,7961,1698],{},[898,7963,207],{},[1693,7965,1731],{"stretchy":1708},[902,7967,7968],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)",". Čím vyšší ",[883,7971,7973],{"className":7972},[886],[888,7974,7975],{"xmlns":890},[892,7976,7977,7985],{},[895,7978,7979,7981,7983],{},[898,7980,2839],{},[898,7982,1701],{},[898,7984,2971],{},[902,7986,7288],{"encoding":904},", tím silnější násobení.",[1852,7989],{},[115,7991,7993],{"id":7992},"_14-is-lm-analýza","14. IS-LM analýza",[724,7995,7996,1863,7998],{},[38,7997,1862],{},[207,7999,8001],{"className":8000,"dataFsResolvedFilePath":943,"href":944},[210],"IS-LM analýza — simultánní rovnováha",[198,8003,8005],{"id":8004},"funkce-investic","Funkce investic",[724,8007,8008],{},[883,8009,8011],{"className":8010},[886],[888,8012,8013],{"xmlns":890},[892,8014,8015,8059],{},[895,8016,8017,8019,8021,8023,8025,8027,8029,8031,8033,8035,8037,8039,8041,8043,8045,8047,8049,8051,8053,8055,8057],{},[898,8018,6998],{},[1693,8020,1695],{},[898,8022,6998],{},[1693,8024,1709],{"stretchy":1708},[898,8026,6629],{},[1693,8028,1731],{"stretchy":1708},[1693,8030,1695],{},[898,8032,2000],{},[898,8034,6629],{},[1693,8036,1892],{},[898,8038,1771],{},[1693,8040,1899],{"separator":1898},[1901,8042],{"width":1903},[898,8044,2000],{},[1693,8046,1908],{},[1762,8048,1911],{},[1693,8050,1899],{"separator":1898},[1915,8052,1917],{},[898,8054,1771],{},[1693,8056,1922],{},[1762,8058,1911],{},[902,8060,8061],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0, \\; d > 0",[724,8063,8064,8066],{},[38,8065,1932],{}," lineární model investic v závislosti na úrokové míře (vzorec 7.11).",[724,8068,8069,8071,8072,1789],{},[38,8070,1941],{}," vyšší úroková sazba → dražší úvěr → menší investice. Proto ",[883,8073,8075],{"className":8074},[886],[888,8076,8077],{"xmlns":890},[892,8078,8079,8087],{},[895,8080,8081,8083,8085],{},[898,8082,2000],{},[1693,8084,1908],{},[1762,8086,1911],{},[902,8088,8089],{"encoding":904},"c \u003C 0",[198,8091,8093],{"id":8092},"křivka-is-trh-zboží","Křivka IS (trh zboží)",[724,8095,8096],{},[883,8097,8099],{"className":8098},[886],[888,8100,8101],{"xmlns":890},[892,8102,8103,8145],{},[895,8104,8105,8107,8109,8121,8123,8125,8127],{},[898,8106,4618],{},[1693,8108,1695],{},[2132,8110,8111,8113],{},[898,8112,2000],{},[895,8114,8115,8117,8119],{},[1762,8116,1764],{},[1693,8118,1698],{},[898,8120,207],{},[1915,8122,2239],{},[898,8124,6629],{},[1693,8126,1892],{},[2132,8128,8129,8137],{},[895,8130,8131,8133,8135],{},[898,8132,1895],{},[1693,8134,1892],{},[898,8136,1771],{},[895,8138,8139,8141,8143],{},[1762,8140,1764],{},[1693,8142,1698],{},[898,8144,207],{},[902,8146,8147],{"encoding":904},"Y = \\frac{c}{1-a}\\,r + \\frac{b+d}{1-a}",[724,8149,8150,8152,8153,8175,8176,4286,8196,8216],{},[38,8151,1932],{}," z rovnováhy ",[883,8154,8156],{"className":8155},[886],[888,8157,8158],{"xmlns":890},[892,8159,8160,8172],{},[895,8161,8162,8164,8166,8168,8170],{},[898,8163,4618],{},[1693,8165,1695],{},[898,8167,2971],{},[1693,8169,1892],{},[898,8171,6998],{},[902,8173,8174],{"encoding":904},"Y = C + I"," dosazením lineárních funkcí ",[883,8177,8179],{"className":8178},[886],[888,8180,8181],{"xmlns":890},[892,8182,8183,8193],{},[895,8184,8185,8187,8189,8191],{},[898,8186,2971],{},[1693,8188,1709],{"stretchy":1708},[898,8190,4618],{},[1693,8192,1731],{"stretchy":1708},[902,8194,8195],{"encoding":904},"C(Y)",[883,8197,8199],{"className":8198},[886],[888,8200,8201],{"xmlns":890},[892,8202,8203,8213],{},[895,8204,8205,8207,8209,8211],{},[898,8206,6998],{},[1693,8208,1709],{"stretchy":1708},[898,8210,6629],{},[1693,8212,1731],{"stretchy":1708},[902,8214,8215],{"encoding":904},"I(r)"," (vzorec 7.14).",[724,8218,8219,8221,8222,8244,8245,8248,8249,8266,8267,8280,8281,8280,8294,1789],{},[38,8220,1941],{}," kombinace ",[883,8223,8225],{"className":8224},[886],[888,8226,8227],{"xmlns":890},[892,8228,8229,8241],{},[895,8230,8231,8233,8235,8237,8239],{},[1693,8232,1709],{"stretchy":1708},[898,8234,4618],{},[1693,8236,1899],{"separator":1898},[898,8238,6629],{},[1693,8240,1731],{"stretchy":1708},[902,8242,8243],{"encoding":904},"(Y, r)",", pro které ",[38,8246,8247],{},"Investice = Savings",". Klesající přímka (protože ",[883,8250,8252],{"className":8251},[886],[888,8253,8254],{"xmlns":890},[892,8255,8256,8264],{},[895,8257,8258,8260,8262],{},[898,8259,2000],{},[1693,8261,1908],{},[1762,8263,1911],{},[902,8265,8089],{"encoding":904},"): vyšší ",[883,8268,8270],{"className":8269},[886],[888,8271,8272],{"xmlns":890},[892,8273,8274,8278],{},[895,8275,8276],{},[898,8277,6629],{},[902,8279,6629],{"encoding":904}," → nižší ",[883,8282,8284],{"className":8283},[886],[888,8285,8286],{"xmlns":890},[892,8287,8288,8292],{},[895,8289,8290],{},[898,8291,6998],{},[902,8293,6998],{"encoding":904},[883,8295,8297],{"className":8296},[886],[888,8298,8299],{"xmlns":890},[892,8300,8301,8305],{},[895,8302,8303],{},[898,8304,4618],{},[902,8306,4618],{"encoding":904},[198,8308,8310],{"id":8309},"křivka-lm-trh-peněz","Křivka LM (trh peněz)",[724,8312,8313],{},[883,8314,8316],{"className":8315},[886],[888,8317,8318],{"xmlns":890},[892,8319,8320,8358],{},[895,8321,8322,8328,8330,8337,8339,8341,8347,8349,8351],{},[1717,8323,8324,8326],{},[898,8325,2839],{},[1693,8327,3672],{},[1693,8329,1695],{},[3284,8331,8332,8335],{},[898,8333,8334],{},"k",[1762,8336,1764],{},[898,8338,4618],{},[1693,8340,1892],{},[3284,8342,8343,8345],{},[898,8344,8334],{},[1762,8346,2398],{},[898,8348,6629],{},[1693,8350,1892],{},[3284,8352,8353,8355],{},[898,8354,8334],{},[1762,8356,8357],{},"3",[902,8359,8360],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3",[724,8362,8363,8365,8366,8392,8393,8413,8414,8442,8443,8461],{},[38,8364,1932],{}," rovnováha na trhu peněz ",[883,8367,8369],{"className":8368},[886],[888,8370,8371],{"xmlns":890},[892,8372,8373,8389],{},[895,8374,8375,8381,8383],{},[1717,8376,8377,8379],{},[898,8378,2839],{},[898,8380,2738],{},[1693,8382,1695],{},[1717,8384,8385,8387],{},[898,8386,2839],{},[898,8388,3611],{},[902,8390,8391],{"encoding":904},"M^D = M^S"," — poptávka (transakční ",[883,8394,8396],{"className":8395},[886],[888,8397,8398],{"xmlns":890},[892,8399,8400,8410],{},[895,8401,8402,8408],{},[3284,8403,8404,8406],{},[898,8405,8334],{},[1762,8407,1764],{},[898,8409,4618],{},[902,8411,8412],{"encoding":904},"k_1 Y"," + spekulační ",[883,8415,8417],{"className":8416},[886],[888,8418,8419],{"xmlns":890},[892,8420,8421,8439],{},[895,8422,8423,8429,8431,8433],{},[3284,8424,8425,8427],{},[898,8426,8334],{},[1762,8428,2398],{},[898,8430,6629],{},[1693,8432,1892],{},[3284,8434,8435,8437],{},[898,8436,8334],{},[1762,8438,8357],{},[902,8440,8441],{"encoding":904},"k_2 r + k_3",") = pevná nabídka ",[883,8444,8446],{"className":8445},[886],[888,8447,8448],{"xmlns":890},[892,8449,8450,8458],{},[895,8451,8452],{},[1717,8453,8454,8456],{},[898,8455,2839],{},[1693,8457,3672],{},[902,8459,8460],{"encoding":904},"M^*"," (vzorec 7.15).",[724,8463,8464,1863,8466,8468,8469,8471,8472,8485,8486,8503,8504,8517],{},[38,8465,1941],{},[38,8467,4840],{},"iquidity of ",[38,8470,2839],{},"oney. Rostoucí přímka: vyšší ",[883,8473,8475],{"className":8474},[886],[888,8476,8477],{"xmlns":890},[892,8478,8479,8483],{},[895,8480,8481],{},[898,8482,4618],{},[902,8484,4618],{"encoding":904}," → větší transakční poptávka po penězích → při pevné nabídce ",[883,8487,8489],{"className":8488},[886],[888,8490,8491],{"xmlns":890},[892,8492,8493,8501],{},[895,8494,8495],{},[1717,8496,8497,8499],{},[898,8498,2839],{},[1693,8500,3672],{},[902,8502,8460],{"encoding":904}," musí ",[883,8505,8507],{"className":8506},[886],[888,8508,8509],{"xmlns":890},[892,8510,8511,8515],{},[895,8512,8513],{},[898,8514,6629],{},[902,8516,6629],{"encoding":904}," vzrůst, aby se trh vyrovnal.",[198,8519,8521],{"id":8520},"simultánní-rovnováha","Simultánní rovnováha",[724,8523,8524,8525,8555,8556,8559,8560,1343,8573,8586,8587,8590,8591,3042],{},"Řešení soustavy (IS) a (LM) dá ",[883,8526,8528],{"className":8527},[886],[888,8529,8530],{"xmlns":890},[892,8531,8532,8552],{},[895,8533,8534,8536,8542,8544,8550],{},[1693,8535,1709],{"stretchy":1708},[1717,8537,8538,8540],{},[898,8539,4618],{},[898,8541,1691],{},[1693,8543,1899],{"separator":1898},[1717,8545,8546,8548],{},[898,8547,6629],{},[898,8549,1691],{},[1693,8551,1731],{"stretchy":1708},[902,8553,8554],{"encoding":904},"(Y^E, r^E)"," — průsečík obou křivek. Rámec pro analýzu ",[38,8557,8558],{},"fiskální politiky"," (posun IS změnou ",[883,8561,8563],{"className":8562},[886],[888,8564,8565],{"xmlns":890},[892,8566,8567,8571],{},[895,8568,8569],{},[898,8570,6984],{},[902,8572,6984],{"encoding":904},[883,8574,8576],{"className":8575},[886],[888,8577,8578],{"xmlns":890},[892,8579,8580,8584],{},[895,8581,8582],{},[898,8583,2663],{},[902,8585,2663],{"encoding":904},") a ",[38,8588,8589],{},"monetární politiky"," (posun LM změnou ",[883,8592,8594],{"className":8593},[886],[888,8595,8596],{"xmlns":890},[892,8597,8598,8606],{},[895,8599,8600],{},[1717,8601,8602,8604],{},[898,8603,2839],{},[1693,8605,3672],{},[902,8607,8460],{"encoding":904},[1852,8609],{},[115,8611,8613],{"id":8612},"jak-tenhle-přehled-efektivně-používat","Jak tenhle přehled efektivně používat",[1636,8615,8616,8622],{},[724,8617,8618,8621],{},[883,8619,8620],{},"!tip"," K čemu se hodí",[120,8623,8624,8630,8636,8642],{},[123,8625,8626,8629],{},[38,8627,8628],{},"Před zkouškou"," — rychlá revize všech klíčových vztahů bez nutnosti procházet jednotlivé topic stránky.",[123,8631,8632,8635],{},[38,8633,8634],{},"Při řešení úlohy"," — najdi vzorec, klikni na primární topic a najdeš plné odvození + řešené příklady.",[123,8637,8638,8641],{},[38,8639,8640],{},"Při nejistotě"," — zda jsi správně zapamatoval vzorec: porovnej s definičním tvarem zde.",[123,8643,8644,8647],{},[38,8645,8646],{},"Při nepochopení"," — přečti si „Intuice\" — často lepší než odvození.",[1636,8649,8650,8656],{},[724,8651,8652,8655],{},[883,8653,8654],{},"!warning"," Co tu není",[120,8657,8658,8664,8670,8676],{},[123,8659,8660,8663],{},[38,8661,8662],{},"Úlohy a jejich řešení"," — ty jsou na primárních topic stránkách.",[123,8665,8666,8669],{},[38,8667,8668],{},"Obrázky a geometrické interpretace"," — většina je na topic stránkách a v knize Mezník.",[123,8671,8672,8675],{},[38,8673,8674],{},"Otázky k sebehodnocení"," — viz konce jednotlivých topic stránek.",[123,8677,8678,8681],{},[38,8679,8680],{},"Podrobná odvození"," — vzorce jsou zde jen ve finálním tvaru; odvození viz příslušné kapitoly.",[115,8683,8685],{"id":8684},"navigace","Navigace",[120,8687,8688,8696,8710,8718,8736,8770],{},[123,8689,8690,1863,8693],{},[38,8691,8692],{},"Kurz:",[207,8694,681],{"className":8695,"dataFsResolvedFilePath":1651,"href":1652},[210],[123,8697,8698,1863,8701,1343,8704,1343,8707],{},[38,8699,8700],{},"Souhrny přednášek:",[207,8702,1087],{"className":8703,"dataFsResolvedFilePath":745,"href":746},[210],[207,8705,1094],{"className":8706,"dataFsResolvedFilePath":838,"href":839},[210],[207,8708,1101],{"className":8709,"dataFsResolvedFilePath":868,"href":869},[210],[123,8711,8712,1863,8715],{},[38,8713,8714],{},"Primární zdroj:",[207,8716,1110],{"className":8717,"dataFsResolvedFilePath":1108,"href":1109},[210],[123,8719,8720,1863,8723,1343,8727,1343,8730,1343,8733],{},[38,8721,8722],{},"Matematický aparát:",[207,8724,8726],{"className":8725,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace",[207,8728,775],{"className":8729,"dataFsResolvedFilePath":773,"href":774},[210],[207,8731,784],{"className":8732,"dataFsResolvedFilePath":782,"href":783},[210],[207,8734,793],{"className":8735,"dataFsResolvedFilePath":791,"href":792},[210],[123,8737,8738,1863,8741,1343,8744,1343,8748,1343,8752,1343,8756,1343,8760,1343,8764,1343,8767],{},[38,8739,8740],{},"Mikroekonomie:",[207,8742,2181],{"className":8743,"dataFsResolvedFilePath":800,"href":801},[210],[207,8745,8747],{"className":8746,"dataFsResolvedFilePath":809,"href":810},[210],"Zdanění",[207,8749,8751],{"className":8750,"dataFsResolvedFilePath":818,"href":819},[210],"Přebytky",[207,8753,8755],{"className":8754,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem\u002Fnáklady\u002Fzisk",[207,8757,8759],{"className":8758,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita",[207,8761,8763],{"className":8762,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce",[207,8765,880],{"className":8766,"dataFsResolvedFilePath":878,"href":879},[210],[207,8768,913],{"className":8769,"dataFsResolvedFilePath":911,"href":912},[210],[123,8771,8772,1863,8775,1343,8778],{},[38,8773,8774],{},"Makroekonomie:",[207,8776,936],{"className":8777,"dataFsResolvedFilePath":934,"href":935},[210],[207,8779,945],{"className":8780,"dataFsResolvedFilePath":943,"href":944},[210],{"title":641,"searchDepth":642,"depth":642,"links":8782},[8783,8784,8790,8795,8800,8805,8810,8811,8820,8828,8833,8838,8843,8849,8860,8866,8867],{"id":1669,"depth":642,"text":1670},{"id":1856,"depth":642,"text":1857,"children":8785},[8786,8787,8788,8789],{"id":1869,"depth":649,"text":1870},{"id":1981,"depth":649,"text":1982},{"id":2064,"depth":649,"text":2065},{"id":2110,"depth":649,"text":2111},{"id":2172,"depth":642,"text":2173,"children":8791},[8792,8794],{"id":2185,"depth":649,"text":8793},"Totální diferenciál QEQ^E",{"id":2343,"depth":649,"text":2344},{"id":2636,"depth":642,"text":2637,"children":8796},[8797,8798,8799],{"id":2648,"depth":649,"text":2649},{"id":2704,"depth":649,"text":2705},{"id":2824,"depth":649,"text":2825},{"id":2943,"depth":642,"text":2944,"children":8801},[8802,8803,8804],{"id":2954,"depth":649,"text":2955},{"id":3045,"depth":649,"text":3046},{"id":3168,"depth":649,"text":3169},{"id":3252,"depth":642,"text":3253,"children":8806},[8807,8808,8809],{"id":3264,"depth":649,"text":3265},{"id":3361,"depth":649,"text":3362},{"id":3459,"depth":649,"text":3460},{"id":3585,"depth":642,"text":3586},{"id":3816,"depth":642,"text":3817,"children":8812},[8813,8814,8816,8817,8818,8819],{"id":3828,"depth":649,"text":3829},{"id":3933,"depth":649,"text":8815},"Převod na dP\u002FdQdP\u002FdQ (když je poptávka zadaná jako P=D(Q)P = D(Q))",{"id":4089,"depth":649,"text":4090},{"id":4170,"depth":649,"text":4171},{"id":4444,"depth":649,"text":4445},{"id":4517,"depth":649,"text":4518},{"id":4806,"depth":642,"text":4807,"children":8821},[8822,8823,8824,8825,8826,8827],{"id":4818,"depth":649,"text":859},{"id":4863,"depth":649,"text":4864},{"id":4968,"depth":649,"text":4969},{"id":5065,"depth":649,"text":5066},{"id":5254,"depth":649,"text":5255},{"id":5319,"depth":649,"text":5320},{"id":5516,"depth":642,"text":5517,"children":8829},[8830,8831,8832],{"id":5528,"depth":649,"text":5529},{"id":5584,"depth":649,"text":5585},{"id":5715,"depth":649,"text":5716},{"id":5820,"depth":642,"text":5821,"children":8834},[8835,8836,8837],{"id":5832,"depth":649,"text":5833},{"id":5921,"depth":649,"text":5922},{"id":6062,"depth":649,"text":6063},{"id":6177,"depth":642,"text":6178,"children":8839},[8840,8841,8842],{"id":6188,"depth":649,"text":6189},{"id":6328,"depth":649,"text":6329},{"id":6435,"depth":649,"text":6436},{"id":6484,"depth":642,"text":6485,"children":8844},[8845,8846,8847,8848],{"id":6496,"depth":649,"text":6497},{"id":6721,"depth":649,"text":6722},{"id":6783,"depth":649,"text":6784},{"id":6880,"depth":649,"text":6881},{"id":6958,"depth":642,"text":6959,"children":8850},[8851,8852,8853,8854,8855,8856,8857,8858,8859],{"id":6969,"depth":649,"text":6970},{"id":7023,"depth":649,"text":7024},{"id":7061,"depth":649,"text":7062},{"id":7197,"depth":649,"text":7198},{"id":7359,"depth":649,"text":7360},{"id":7427,"depth":649,"text":7428},{"id":7545,"depth":649,"text":7546},{"id":7638,"depth":649,"text":7639},{"id":7775,"depth":649,"text":7776},{"id":7992,"depth":642,"text":7993,"children":8861},[8862,8863,8864,8865],{"id":8004,"depth":649,"text":8005},{"id":8092,"depth":649,"text":8093},{"id":8309,"depth":649,"text":8310},{"id":8520,"depth":649,"text":8521},{"id":8612,"depth":642,"text":8613},{"id":8684,"depth":642,"text":8685},"2026-04-24",{},"\u002Foutputs\u002Fimek-vzorce-prehled",{"title":1629,"description":641},[1138],"outputs\u002Fimek-vzorce-prehled",[1128,8875,8876,1142,1143],"vzorce","prehled","output","d4vLCigxcNxRA2f9zyt6i4Sve5b_RPzT7MmymVCWkEs","outputs",{"zapisku":1625,"topics":8881,"summaries":8882,"outputs":8883},15,5,1,[8885,10747,16423,17970,18840,23099,24703,34554,43540,57586,61874,81175,93276,102228,102515],{"id":8886,"title":8887,"body":8888,"course":1128,"courses":659,"created":1129,"description":10735,"extension":661,"meta":10736,"navigation":664,"path":10737,"seo":10738,"sources":10739,"stem":10740,"tags":10741,"type":10745,"updated":677,"__hash__":10746},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":8889,"toc":10718},[8890,8893,8912,8916,8993,8996,9119,9266,9268,9348,9352,9412,9462,9471,9475,9610,9660,9664,9705,9773,9842,9850,9854,9892,9964,9968,10049,10097,10140,10144,10148,10218,10222,10272,10349,10356,10359,10412,10681,10683],[12,8891,8887],{"id":8892},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,8894,8895,8896,8900,8901,8904,8905,8908,8909,1789],{},"Matematický aparát kurzu ",[207,8897,8899],{"className":8898,"dataFsResolvedFilePath":1651,"href":1652},[210],"ImeK",". Bez derivace se neobejdou ",[38,8902,8903],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,8906,8907],{},"maximalizace zisku"," ani ",[38,8910,8911],{},"minimalizace nákladů",[115,8913,8915],{"id":8914},"funkce-a-polynomy","Funkce a polynomy",[724,8917,8918,8919,8944,8945,8958,8959,8972,8973,1789],{},"Funkce jedné proměnné ",[883,8920,8922],{"className":8921},[886],[888,8923,8924],{"xmlns":890},[892,8925,8926,8941],{},[895,8927,8928,8930,8932,8935,8937,8939],{},[898,8929,6560],{},[1693,8931,1695],{},[898,8933,8934],{},"f",[1693,8936,1709],{"stretchy":1708},[898,8938,2590],{},[1693,8940,1731],{"stretchy":1708},[902,8942,8943],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,8946,8948],{"className":8947},[886],[888,8949,8950],{"xmlns":890},[892,8951,8952,8956],{},[895,8953,8954],{},[898,8955,2590],{},[902,8957,2590],{"encoding":904}," (nezávislá) → ",[883,8960,8962],{"className":8961},[886],[888,8963,8964],{"xmlns":890},[892,8965,8966,8970],{},[895,8967,8968],{},[898,8969,6560],{},[902,8971,6560],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,8974,8976],{"className":8975},[886],[888,8977,8978],{"xmlns":890},[892,8979,8980,8990],{},[895,8981,8982,8984,8986,8988],{},[898,8983,8934],{},[1693,8985,1709],{"stretchy":1708},[898,8987,207],{},[1693,8989,1731],{"stretchy":1708},[902,8991,8992],{"encoding":904},"f(a)",[724,8994,8995],{},"Polynomy:",[120,8997,8998,9029,9069],{},[123,8999,9000],{},[152,9001,9002],{},[123,9003,9004,9005],{},"stupně: ",[883,9006,9008],{"className":9007},[886],[888,9009,9010],{"xmlns":890},[892,9011,9012,9026],{},[895,9013,9014,9016,9018,9020,9022,9024],{},[898,9015,6560],{},[1693,9017,1695],{},[898,9019,207],{},[898,9021,2590],{},[1693,9023,1892],{},[898,9025,1895],{},[902,9027,9028],{"encoding":904},"y = ax + b",[123,9030,9031],{},[152,9032,9033],{"start":642},[123,9034,9004,9035],{},[883,9036,9038],{"className":9037},[886],[888,9039,9040],{"xmlns":890},[892,9041,9042,9066],{},[895,9043,9044,9046,9048,9050,9056,9058,9060,9062,9064],{},[898,9045,6560],{},[1693,9047,1695],{},[898,9049,207],{},[1717,9051,9052,9054],{},[898,9053,2590],{},[1762,9055,2398],{},[1693,9057,1892],{},[898,9059,1895],{},[898,9061,2590],{},[1693,9063,1892],{},[898,9065,2000],{},[902,9067,9068],{"encoding":904},"y = ax^2 + bx + c",[123,9070,9071],{},[152,9072,9073],{"start":649},[123,9074,9004,9075],{},[883,9076,9078],{"className":9077},[886],[888,9079,9080],{"xmlns":890},[892,9081,9082,9116],{},[895,9083,9084,9086,9088,9090,9096,9098,9100,9106,9108,9110,9112,9114],{},[898,9085,6560],{},[1693,9087,1695],{},[898,9089,207],{},[1717,9091,9092,9094],{},[898,9093,2590],{},[1762,9095,8357],{},[1693,9097,1892],{},[898,9099,1895],{},[1717,9101,9102,9104],{},[898,9103,2590],{},[1762,9105,2398],{},[1693,9107,1892],{},[898,9109,2000],{},[898,9111,2590],{},[1693,9113,1892],{},[898,9115,1771],{},[902,9117,9118],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,9120,9121,1863,9124,9180,9181,9218,9219,1789],{},[38,9122,9123],{},"Příklad rozkladu:",[883,9125,9127],{"className":9126},[886],[888,9128,9129],{"xmlns":890},[892,9130,9131,9177],{},[895,9132,9133,9135,9137,9143,9145,9148,9150,9152,9155,9157,9159,9161,9163,9165,9167,9169,9171,9173,9175],{},[898,9134,6560],{},[1693,9136,1695],{},[1717,9138,9139,9141],{},[898,9140,2590],{},[1762,9142,2398],{},[1693,9144,1698],{},[1762,9146,9147],{},"5",[898,9149,2590],{},[1693,9151,1892],{},[1762,9153,9154],{},"6",[1693,9156,1695],{},[1693,9158,1709],{"stretchy":1708},[898,9160,2590],{},[1693,9162,1698],{},[1762,9164,2398],{},[1693,9166,1731],{"stretchy":1708},[1693,9168,1709],{"stretchy":1708},[898,9170,2590],{},[1693,9172,1698],{},[1762,9174,8357],{},[1693,9176,1731],{"stretchy":1708},[902,9178,9179],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,9182,9184],{"className":9183},[886],[888,9185,9186],{"xmlns":890},[892,9187,9188,9215],{},[895,9189,9190,9196,9198,9200,9202,9205,9211,9213],{},[3284,9191,9192,9194],{},[898,9193,2590],{},[1762,9195,1764],{},[1693,9197,1695],{},[1762,9199,2398],{},[1693,9201,1899],{"separator":1898},[1915,9203,9204],{}," ",[3284,9206,9207,9209],{},[898,9208,2590],{},[1762,9210,2398],{},[1693,9212,1695],{},[1762,9214,8357],{},[902,9216,9217],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,9220,9222],{"className":9221},[886],[888,9223,9224],{"xmlns":890},[892,9225,9226,9263],{},[895,9227,9228,9230,9232,9234,9236,9238,9246,9252,9254],{},[898,9229,6560],{},[1693,9231,1695],{},[1693,9233,1709],{"stretchy":1708},[898,9235,2590],{},[1693,9237,1698],{},[3638,9239,9240],{"scriptlevel":1911,"displaystyle":1708},[2132,9241,9242,9244],{},[1762,9243,9147],{},[1762,9245,2398],{},[1717,9247,9248,9250],{},[1693,9249,1731],{"stretchy":1708},[1762,9251,2398],{},[1693,9253,1698],{},[3638,9255,9256],{"scriptlevel":1911,"displaystyle":1708},[2132,9257,9258,9260],{},[1762,9259,1764],{},[1762,9261,9262],{},"4",[902,9264,9265],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,9267,8726],{"id":1145},[724,9269,9270,9271,1348,9295,9323,9324,1789],{},"Označení ",[883,9272,9274],{"className":9273},[886],[888,9275,9276],{"xmlns":890},[892,9277,9278,9292],{},[895,9279,9280,9286,9288,9290],{},[1717,9281,9282,9284],{},[898,9283,8934],{},[1693,9285,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9287,1709],{"stretchy":1708},[898,9289,2590],{},[1693,9291,1731],{"stretchy":1708},[902,9293,9294],{"encoding":904},"f'(x)",[883,9296,9298],{"className":9297},[886],[888,9299,9300],{"xmlns":890},[892,9301,9302,9320],{},[895,9303,9304],{},[3638,9305,9306],{"scriptlevel":1911,"displaystyle":1898},[2132,9307,9308,9314],{},[895,9309,9310,9312],{},[898,9311,1771],{},[898,9313,6560],{},[895,9315,9316,9318],{},[898,9317,1771],{},[898,9319,2590],{},[902,9321,9322],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,9325,9327],{"className":9326},[886],[888,9328,9329],{"xmlns":890},[892,9330,9331,9345],{},[895,9332,9333,9339,9341,9343],{},[1717,9334,9335,9337],{},[898,9336,8934],{},[1693,9338,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9340,1709],{"stretchy":1708},[898,9342,207],{},[1693,9344,1731],{"stretchy":1708},[902,9346,9347],{"encoding":904},"f'(a)",[198,9349,9351],{"id":9350},"geometrická-interpretace","Geometrická interpretace",[724,9353,9354,7176,9377,9380,9381,9411],{},[883,9355,9357],{"className":9356},[886],[888,9358,9359],{"xmlns":890},[892,9360,9361,9375],{},[895,9362,9363,9369,9371,9373],{},[1717,9364,9365,9367],{},[898,9366,8934],{},[1693,9368,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9370,1709],{"stretchy":1708},[898,9372,207],{},[1693,9374,1731],{"stretchy":1708},[902,9376,9347],{"encoding":904},[38,9378,9379],{},"sklon tečny"," ke grafu funkce v bodě ",[883,9382,9384],{"className":9383},[886],[888,9385,9386],{"xmlns":890},[892,9387,9388,9408],{},[895,9389,9390,9393,9395,9397,9399,9401,9403,9405],{},[1693,9391,9392],{"stretchy":1708},"[",[898,9394,207],{},[1693,9396,1899],{"separator":1898},[898,9398,8934],{},[1693,9400,1709],{"stretchy":1708},[898,9402,207],{},[1693,9404,1731],{"stretchy":1708},[1693,9406,9407],{"stretchy":1708},"]",[902,9409,9410],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,9413,9414],{},[883,9415,9417],{"className":9416},[886],[888,9418,9419],{"xmlns":890},[892,9420,9421,9459],{},[895,9422,9423,9425,9427,9429,9431,9433,9435,9437,9443,9445,9447,9449,9451,9453,9455,9457],{},[898,9424,6560],{},[1693,9426,1698],{},[898,9428,8934],{},[1693,9430,1709],{"stretchy":1708},[898,9432,207],{},[1693,9434,1731],{"stretchy":1708},[1693,9436,1695],{},[1717,9438,9439,9441],{},[898,9440,8934],{},[1693,9442,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9444,1709],{"stretchy":1708},[898,9446,207],{},[1693,9448,1731],{"stretchy":1708},[1693,9450,1709],{"stretchy":1708},[898,9452,2590],{},[1693,9454,1698],{},[898,9456,207],{},[1693,9458,1731],{"stretchy":1708},[902,9460,9461],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,9463,9464],{},[9465,9466],"img",{"alt":9467,"className":9468,"src":9470},"imek-derivace-tecna",[210,9469],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,9472,9474],{"id":9473},"inženýrská-interpretace","Inženýrská interpretace",[724,9476,9477,7176,9500,1863,9503,9516,9517,9530,9531,9549,9550,9563,9564,9577,9578,9591,9592,4300],{},[883,9478,9480],{"className":9479},[886],[888,9481,9482],{"xmlns":890},[892,9483,9484,9498],{},[895,9485,9486,9492,9494,9496],{},[1717,9487,9488,9490],{},[898,9489,8934],{},[1693,9491,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9493,1709],{"stretchy":1708},[898,9495,207],{},[1693,9497,1731],{"stretchy":1708},[902,9499,9347],{"encoding":904},[38,9501,9502],{},"rychlost změny",[883,9504,9506],{"className":9505},[886],[888,9507,9508],{"xmlns":890},[892,9509,9510,9514],{},[895,9511,9512],{},[898,9513,6560],{},[902,9515,6560],{"encoding":904}," vzhledem k ",[883,9518,9520],{"className":9519},[886],[888,9521,9522],{"xmlns":890},[892,9523,9524,9528],{},[895,9525,9526],{},[898,9527,2590],{},[902,9529,2590],{"encoding":904}," v bodě ",[883,9532,9534],{"className":9533},[886],[888,9535,9536],{"xmlns":890},[892,9537,9538,9546],{},[895,9539,9540,9542,9544],{},[898,9541,2590],{},[1693,9543,1695],{},[898,9545,207],{},[902,9547,9548],{"encoding":904},"x = a","; přibližná změna ",[883,9551,9553],{"className":9552},[886],[888,9554,9555],{"xmlns":890},[892,9556,9557,9561],{},[895,9558,9559],{},[898,9560,6560],{},[902,9562,6560],{"encoding":904}," při změně ",[883,9565,9567],{"className":9566},[886],[888,9568,9569],{"xmlns":890},[892,9570,9571,9575],{},[895,9572,9573],{},[898,9574,2590],{},[902,9576,2590],{"encoding":904}," z ",[883,9579,9581],{"className":9580},[886],[888,9582,9583],{"xmlns":890},[892,9584,9585,9589],{},[895,9586,9587],{},[898,9588,207],{},[902,9590,207],{"encoding":904}," na ",[883,9593,9595],{"className":9594},[886],[888,9596,9597],{"xmlns":890},[892,9598,9599,9607],{},[895,9600,9601,9603,9605],{},[898,9602,207],{},[1693,9604,1892],{},[1762,9606,1764],{},[902,9608,9609],{"encoding":904},"a+1",[724,9611,9612],{},[883,9613,9615],{"className":9614},[886],[888,9616,9617],{"xmlns":890},[892,9618,9619,9657],{},[895,9620,9621,9623,9625,9627,9629,9631,9633,9635,9637,9639,9641,9643,9645,9651,9653,9655],{},[898,9622,8934],{},[1693,9624,1709],{"stretchy":1708},[898,9626,207],{},[1693,9628,1892],{},[1762,9630,1764],{},[1693,9632,1731],{"stretchy":1708},[1693,9634,4110],{},[898,9636,8934],{},[1693,9638,1709],{"stretchy":1708},[898,9640,207],{},[1693,9642,1731],{"stretchy":1708},[1693,9644,1892],{},[1717,9646,9647,9649],{},[898,9648,8934],{},[1693,9650,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9652,1709],{"stretchy":1708},[898,9654,207],{},[1693,9656,1731],{"stretchy":1708},[902,9658,9659],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,9661,9663],{"id":9662},"příklad-mezní-náklady","Příklad — mezní náklady",[724,9665,9666,9667,1789],{},"Celkové náklady ",[883,9668,9670],{"className":9669},[886],[888,9671,9672],{"xmlns":890},[892,9673,9674,9702],{},[895,9675,9676,9678,9680,9682,9685,9687,9689,9691,9693,9696],{},[898,9677,2663],{},[898,9679,2971],{},[1693,9681,1695],{},[1762,9683,9684],{},"1000",[1693,9686,1892],{},[1762,9688,2398],{},[898,9690,1712],{},[1693,9692,1892],{},[1762,9694,9695],{},"0,1",[1717,9697,9698,9700],{},[898,9699,1712],{},[1762,9701,2398],{},[902,9703,9704],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,9706,9707,9708,9745,9746,1789],{},"Mezní náklady: ",[883,9709,9711],{"className":9710},[886],[888,9712,9713],{"xmlns":890},[892,9714,9715,9742],{},[895,9716,9717,9719,9721,9723,9725,9731,9733,9735,9737,9740],{},[898,9718,2839],{},[898,9720,2971],{},[1693,9722,1695],{},[898,9724,2663],{},[1717,9726,9727,9729],{},[898,9728,2971],{},[1693,9730,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9732,1695],{},[1762,9734,2398],{},[1693,9736,1892],{},[1762,9738,9739],{},"0,2",[898,9741,1712],{},[902,9743,9744],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,9747,9749],{"className":9748},[886],[888,9750,9751],{"xmlns":890},[892,9752,9753,9770],{},[895,9754,9755,9757,9759,9761,9764,9766,9768],{},[898,9756,2839],{},[898,9758,2971],{},[1693,9760,1709],{"stretchy":1708},[1762,9762,9763],{},"10",[1693,9765,1731],{"stretchy":1708},[1693,9767,1695],{},[1762,9769,9262],{},[902,9771,9772],{"encoding":904},"MC(10) = 4",[724,9774,9775,1863,9778,7617,9826,1863,9829,1789],{},[38,9776,9777],{},"Skutečný přírůstek:",[883,9779,9781],{"className":9780},[886],[888,9782,9783],{"xmlns":890},[892,9784,9785,9823],{},[895,9786,9787,9789,9791,9793,9795,9797,9799,9801,9804,9806,9808,9810,9812,9814,9816,9818,9820],{},[898,9788,3890],{"mathvariant":1704},[898,9790,2663],{},[898,9792,2971],{},[1693,9794,1695],{},[898,9796,2663],{},[898,9798,2971],{},[1693,9800,1709],{"stretchy":1708},[1762,9802,9803],{},"11",[1693,9805,1731],{"stretchy":1708},[1693,9807,1698],{},[898,9809,2663],{},[898,9811,2971],{},[1693,9813,1709],{"stretchy":1708},[1762,9815,9763],{},[1693,9817,1731],{"stretchy":1708},[1693,9819,1695],{},[1762,9821,9822],{},"4,2",[902,9824,9825],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,9827,9828],{},"Přibližný (lineární):",[883,9830,9832],{"className":9831},[886],[888,9833,9834],{"xmlns":890},[892,9835,9836,9840],{},[895,9837,9838],{},[1762,9839,9262],{},[902,9841,9262],{"encoding":904},[724,9843,9844,9845,9849],{},"(Viz aplikace v ",[207,9846,9848],{"className":9847,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,9851,9853],{"id":9852},"diferenciál","Diferenciál",[724,9855,9856],{},[883,9857,9859],{"className":9858},[886],[888,9860,9861],{"xmlns":890},[892,9862,9863,9889],{},[895,9864,9865,9867,9869,9871,9877,9879,9881,9883,9885,9887],{},[898,9866,1771],{},[898,9868,8934],{},[1693,9870,1695],{},[1717,9872,9873,9875],{},[898,9874,8934],{},[1693,9876,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,9878,1709],{"stretchy":1708},[898,9880,2590],{},[1693,9882,1731],{"stretchy":1708},[1915,9884,2239],{},[898,9886,1771],{},[898,9888,2590],{},[902,9890,9891],{"encoding":904},"df = f'(x)\\, dx",[724,9893,9894,9895,9911,9912,9960,9961,1789],{},"Pro malá ",[883,9896,9898],{"className":9897},[886],[888,9899,9900],{"xmlns":890},[892,9901,9902,9908],{},[895,9903,9904,9906],{},[898,9905,1771],{},[898,9907,2590],{},[902,9909,9910],{"encoding":904},"dx"," platí: ",[883,9913,9915],{"className":9914},[886],[888,9916,9917],{"xmlns":890},[892,9918,9919,9957],{},[895,9920,9921,9923,9925,9927,9929,9931,9933,9935,9937,9939,9941,9943,9945,9947,9949,9951,9953,9955],{},[898,9922,3890],{"mathvariant":1704},[898,9924,8934],{},[1693,9926,1695],{},[898,9928,8934],{},[1693,9930,1709],{"stretchy":1708},[898,9932,2590],{},[1693,9934,1892],{},[898,9936,1771],{},[898,9938,2590],{},[1693,9940,1731],{"stretchy":1708},[1693,9942,1698],{},[898,9944,8934],{},[1693,9946,1709],{"stretchy":1708},[898,9948,2590],{},[1693,9950,1731],{"stretchy":1708},[1693,9952,4110],{},[898,9954,1771],{},[898,9956,8934],{},[902,9958,9959],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,9962,9963],{},"lineární odhad přírůstku",[198,9965,9967],{"id":9966},"příklad","Příklad",[724,9969,9970,10001,10002,10027,10028,10048],{},[883,9971,9973],{"className":9972},[886],[888,9974,9975],{"xmlns":890},[892,9976,9977,9998],{},[895,9978,9979,9981,9983,9985,9988,9990,9992],{},[898,9980,2663],{},[898,9982,2971],{},[1693,9984,1695],{},[1762,9986,9987],{},"100",[1693,9989,1892],{},[1762,9991,9695],{},[1717,9993,9994,9996],{},[898,9995,1712],{},[1762,9997,2398],{},[902,9999,10000],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,10003,10005],{"className":10004},[886],[888,10006,10007],{"xmlns":890},[892,10008,10009,10024],{},[895,10010,10011,10013,10015,10018,10021],{},[898,10012,1712],{},[1693,10014,4300],{},[1762,10016,10017],{},"50",[1693,10019,10020],{},"→",[1762,10022,10023],{},"60",[902,10025,10026],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,10029,10031],{"className":10030},[886],[888,10032,10033],{"xmlns":890},[892,10034,10035,10045],{},[895,10036,10037,10039,10041,10043],{},[898,10038,1771],{},[898,10040,1712],{},[1693,10042,1695],{},[1762,10044,9763],{},[902,10046,10047],{"encoding":904},"dQ = 10","):",[724,10050,10051],{},[883,10052,10054],{"className":10053},[886],[888,10055,10056],{"xmlns":890},[892,10057,10058,10094],{},[895,10059,10060,10062,10064,10066,10068,10070,10072,10074,10076,10078,10080,10082,10084,10086,10088,10090,10092],{},[898,10061,1771],{},[898,10063,2663],{},[898,10065,2971],{},[1693,10067,1695],{},[1762,10069,9739],{},[898,10071,1712],{},[1693,10073,1715],{},[898,10075,1771],{},[898,10077,1712],{},[1693,10079,1695],{},[1762,10081,9739],{},[1693,10083,1715],{},[1762,10085,10017],{},[1693,10087,1715],{},[1762,10089,9763],{},[1693,10091,1695],{},[1762,10093,9987],{},[902,10095,10096],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,10098,10099,10100,10123,10124,10139],{},"Přesná změna: ",[883,10101,10103],{"className":10102},[886],[888,10104,10105],{"xmlns":890},[892,10106,10107,10120],{},[895,10108,10109,10111,10113,10115,10117],{},[898,10110,3890],{"mathvariant":1704},[898,10112,2663],{},[898,10114,2971],{},[1693,10116,1695],{},[1762,10118,10119],{},"110",[902,10121,10122],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,10125,10127],{"className":10126},[886],[888,10128,10129],{"xmlns":890},[892,10130,10131,10137],{},[895,10132,10133,10135],{},[898,10134,2663],{},[898,10136,2971],{},[902,10138,3225],{"encoding":904}," je konvexní.",[115,10141,10143],{"id":10142},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,10145,10147],{"id":10146},"nutná-podmínka","Nutná podmínka",[724,10149,10150,10151,9530,10171,10184,10185,10213,10214,10217],{},"Má-li ",[883,10152,10154],{"className":10153},[886],[888,10155,10156],{"xmlns":890},[892,10157,10158,10168],{},[895,10159,10160,10162,10164,10166],{},[898,10161,8934],{},[1693,10163,1709],{"stretchy":1708},[898,10165,2590],{},[1693,10167,1731],{"stretchy":1708},[902,10169,10170],{"encoding":904},"f(x)",[883,10172,10174],{"className":10173},[886],[888,10175,10176],{"xmlns":890},[892,10177,10178,10182],{},[895,10179,10180],{},[898,10181,207],{},[902,10183,207],{"encoding":904}," extrém, pak ",[883,10186,10188],{"className":10187},[886],[888,10189,10190],{"xmlns":890},[892,10191,10192,10210],{},[895,10193,10194,10200,10202,10204,10206,10208],{},[1717,10195,10196,10198],{},[898,10197,8934],{},[1693,10199,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,10201,1709],{"stretchy":1708},[898,10203,207],{},[1693,10205,1731],{"stretchy":1708},[1693,10207,1695],{},[1762,10209,1911],{},[902,10211,10212],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,10215,10216],{},"stacionární"," (podezřelé) body.",[198,10219,10221],{"id":10220},"postačující-podmínka","Postačující podmínka",[724,10223,10224,10225,10238,10239,4300],{},"Pro stacionární bod ",[883,10226,10228],{"className":10227},[886],[888,10229,10230],{"xmlns":890},[892,10231,10232,10236],{},[895,10233,10234],{},[898,10235,207],{},[902,10237,207],{"encoding":904},", je-li ",[883,10240,10242],{"className":10241},[886],[888,10243,10244],{"xmlns":890},[892,10245,10246,10269],{},[895,10247,10248,10258,10260,10262,10264,10267],{},[1717,10249,10250,10252],{},[898,10251,8934],{},[895,10253,10254,10256],{},[1693,10255,1724],{"mathvariant":1704},[1693,10257,1724],{"mathvariant":1704},[1693,10259,1709],{"stretchy":1708},[898,10261,207],{},[1693,10263,1731],{"stretchy":1708},[1693,10265,10266],{"mathvariant":1704},"≠",[1762,10268,1911],{},[902,10270,10271],{"encoding":904},"f''(a) \\neq 0",[120,10273,10274,10312],{},[123,10275,10276,10308,10309],{},[883,10277,10279],{"className":10278},[886],[888,10280,10281],{"xmlns":890},[892,10282,10283,10305],{},[895,10284,10285,10295,10297,10299,10301,10303],{},[1717,10286,10287,10289],{},[898,10288,8934],{},[895,10290,10291,10293],{},[1693,10292,1724],{"mathvariant":1704},[1693,10294,1724],{"mathvariant":1704},[1693,10296,1709],{"stretchy":1708},[898,10298,207],{},[1693,10300,1731],{"stretchy":1708},[1693,10302,1922],{},[1762,10304,1911],{},[902,10306,10307],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,10310,10311],{},"lokální minimum",[123,10313,10314,10308,10346],{},[883,10315,10317],{"className":10316},[886],[888,10318,10319],{"xmlns":890},[892,10320,10321,10343],{},[895,10322,10323,10333,10335,10337,10339,10341],{},[1717,10324,10325,10327],{},[898,10326,8934],{},[895,10328,10329,10331],{},[1693,10330,1724],{"mathvariant":1704},[1693,10332,1724],{"mathvariant":1704},[1693,10334,1709],{"stretchy":1708},[898,10336,207],{},[1693,10338,1731],{"stretchy":1708},[1693,10340,1908],{},[1762,10342,1911],{},[902,10344,10345],{"encoding":904},"f''(a) \u003C 0",[38,10347,10348],{},"lokální maximum",[724,10350,10351],{},[9465,10352],{"alt":10353,"className":10354,"src":10355},"imek-extremy-1d",[210,9469],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,10357,9967],{"id":10358},"příklad-1",[724,10360,10361],{},[883,10362,10364],{"className":10363},[886],[888,10365,10366],{"xmlns":890},[892,10367,10368,10409],{},[895,10369,10370,10372,10374,10376,10378,10380,10382,10388,10390,10392,10398,10400,10403,10405,10407],{},[898,10371,8934],{},[1693,10373,1709],{"stretchy":1708},[898,10375,2590],{},[1693,10377,1731],{"stretchy":1708},[1693,10379,1695],{},[1762,10381,2398],{},[1717,10383,10384,10386],{},[898,10385,2590],{},[1762,10387,8357],{},[1693,10389,1698],{},[1762,10391,8357],{},[1717,10393,10394,10396],{},[898,10395,2590],{},[1762,10397,2398],{},[1693,10399,1698],{},[1762,10401,10402],{},"12",[898,10404,2590],{},[1693,10406,1892],{},[1762,10408,8357],{},[902,10410,10411],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,10413,10414,10525,10565,10627],{},[123,10415,10416,10488,10489],{},[883,10417,10419],{"className":10418},[886],[888,10420,10421],{"xmlns":890},[892,10422,10423,10485],{},[895,10424,10425,10431,10433,10435,10437,10439,10441,10447,10449,10451,10453,10455,10457,10459,10461,10463,10465,10467,10469,10471,10473,10475,10477,10479,10481,10483],{},[1717,10426,10427,10429],{},[898,10428,8934],{},[1693,10430,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,10432,1709],{"stretchy":1708},[898,10434,2590],{},[1693,10436,1731],{"stretchy":1708},[1693,10438,1695],{},[1762,10440,9154],{},[1717,10442,10443,10445],{},[898,10444,2590],{},[1762,10446,2398],{},[1693,10448,1698],{},[1762,10450,9154],{},[898,10452,2590],{},[1693,10454,1698],{},[1762,10456,10402],{},[1693,10458,1695],{},[1762,10460,9154],{},[1693,10462,1709],{"stretchy":1708},[898,10464,2590],{},[1693,10466,1892],{},[1762,10468,1764],{},[1693,10470,1731],{"stretchy":1708},[1693,10472,1709],{"stretchy":1708},[898,10474,2590],{},[1693,10476,1698],{},[1762,10478,2398],{},[1693,10480,1731],{"stretchy":1708},[1693,10482,1695],{},[1762,10484,1911],{},[902,10486,10487],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,10490,10492],{"className":10491},[886],[888,10493,10494],{"xmlns":890},[892,10495,10496,10522],{},[895,10497,10498,10504,10506,10508,10510,10512,10518,10520],{},[3284,10499,10500,10502],{},[898,10501,2590],{},[1762,10503,1764],{},[1693,10505,1695],{},[1693,10507,1698],{},[1762,10509,1764],{},[1693,10511,1899],{"separator":1898},[3284,10513,10514,10516],{},[898,10515,2590],{},[1762,10517,2398],{},[1693,10519,1695],{},[1762,10521,2398],{},[902,10523,10524],{"encoding":904},"x_1 = -1, x_2 = 2",[123,10526,10527],{},[883,10528,10530],{"className":10529},[886],[888,10531,10532],{"xmlns":890},[892,10533,10534,10562],{},[895,10535,10536,10546,10548,10550,10552,10554,10556,10558,10560],{},[1717,10537,10538,10540],{},[898,10539,8934],{},[895,10541,10542,10544],{},[1693,10543,1724],{"mathvariant":1704},[1693,10545,1724],{"mathvariant":1704},[1693,10547,1709],{"stretchy":1708},[898,10549,2590],{},[1693,10551,1731],{"stretchy":1708},[1693,10553,1695],{},[1762,10555,10402],{},[898,10557,2590],{},[1693,10559,1698],{},[1762,10561,9154],{},[902,10563,10564],{"encoding":904},"f''(x) = 12x - 6",[123,10566,10567,10308,10608,1654,10611],{},[883,10568,10570],{"className":10569},[886],[888,10571,10572],{"xmlns":890},[892,10573,10574,10605],{},[895,10575,10576,10586,10588,10590,10592,10594,10596,10598,10601,10603],{},[1717,10577,10578,10580],{},[898,10579,8934],{},[895,10581,10582,10584],{},[1693,10583,1724],{"mathvariant":1704},[1693,10585,1724],{"mathvariant":1704},[1693,10587,1709],{"stretchy":1708},[1693,10589,1698],{},[1762,10591,1764],{},[1693,10593,1731],{"stretchy":1708},[1693,10595,1695],{},[1693,10597,1698],{},[1762,10599,10600],{},"18",[1693,10602,1908],{},[1762,10604,1911],{},[902,10606,10607],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,10609,10610],{},"maximum",[883,10612,10614],{"className":10613},[886],[888,10615,10616],{"xmlns":890},[892,10617,10618,10624],{},[895,10619,10620,10622],{},[1693,10621,1698],{},[1762,10623,1764],{},[902,10625,10626],{"encoding":904},"-1",[123,10628,10629,10308,10665,1654,10668],{},[883,10630,10632],{"className":10631},[886],[888,10633,10634],{"xmlns":890},[892,10635,10636,10662],{},[895,10637,10638,10648,10650,10652,10654,10656,10658,10660],{},[1717,10639,10640,10642],{},[898,10641,8934],{},[895,10643,10644,10646],{},[1693,10645,1724],{"mathvariant":1704},[1693,10647,1724],{"mathvariant":1704},[1693,10649,1709],{"stretchy":1708},[1762,10651,2398],{},[1693,10653,1731],{"stretchy":1708},[1693,10655,1695],{},[1762,10657,10600],{},[1693,10659,1922],{},[1762,10661,1911],{},[902,10663,10664],{"encoding":904},"f''(2) = 18 > 0",[38,10666,10667],{},"minimum",[883,10669,10671],{"className":10670},[886],[888,10672,10673],{"xmlns":890},[892,10674,10675,10679],{},[895,10676,10677],{},[1762,10678,2398],{},[902,10680,2398],{"encoding":904},[115,10682,8685],{"id":8684},[120,10684,10685,10693,10701],{},[123,10686,10687,1863,10690],{},[38,10688,10689],{},"Předchozí:",[207,10691,757],{"className":10692,"dataFsResolvedFilePath":755,"href":756},[210],[123,10694,10695,1863,10698],{},[38,10696,10697],{},"Navazující:",[207,10699,775],{"className":10700,"dataFsResolvedFilePath":773,"href":774},[210],[123,10702,10703,1863,10706,10709,10710,10713,10714,10717],{},[38,10704,10705],{},"Souvislosti:",[207,10707,784],{"className":10708,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,10711,3261],{"className":10712,"dataFsResolvedFilePath":827,"href":828},[210]," (aplikace mezních veličin), ",[207,10715,8759],{"className":10716,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":10719},[10720,10721,10726,10729,10734],{"id":8914,"depth":642,"text":8915},{"id":1145,"depth":642,"text":8726,"children":10722},[10723,10724,10725],{"id":9350,"depth":649,"text":9351},{"id":9473,"depth":649,"text":9474},{"id":9662,"depth":649,"text":9663},{"id":9852,"depth":642,"text":9853,"children":10727},[10728],{"id":9966,"depth":649,"text":9967},{"id":10142,"depth":642,"text":10143,"children":10730},[10731,10732,10733],{"id":10146,"depth":649,"text":10147},{"id":10220,"depth":649,"text":10221},{"id":10358,"depth":649,"text":9967},{"id":8684,"depth":642,"text":8685},"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":8887,"description":10735},[1135],"topics\u002Fderivace",[1128,1145,10742,10743,10744],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":10748,"title":3825,"body":10749,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":16412,"navigation":664,"path":16413,"seo":16414,"sources":16415,"stem":16416,"tags":16417,"type":10745,"updated":677,"__hash__":16422},"topics\u002Ftopics\u002Felasticita.md",{"type":9,"value":10750,"toc":16384},[10751,10754,10774,10778,10804,10808,10849,10938,10981,10985,11009,11016,11020,11030,11042,11046,11074,11083,11138,11144,11147,11153,11180,11186,11282,11437,11725,11729,11809,11815,11819,11917,11983,12151,12155,12233,12264,12291,12297,12329,12407,12494,12498,12561,12567,12570,12576,12690,12773,12816,12820,12866,12873,13190,13195,13219,13248,13315,13411,13415,13422,13429,13499,13619,13703,13706,13712,14036,14040,14203,14211,14347,14355,14593,14601,14604,14609,14865,14869,15042,15176,15213,15256,15259,15389,15479,15497,15501,15508,15514,15574,15577,15601,15604,15610,15613,15619,15622,15626,15664,15722,15911,15915,15987,15993,16000,16004,16010,16151,16155,16161,16197,16202,16379],[12,10752,3825],{"id":10753},"elasticita-poptávky-a-nabídky",[1636,10755,10756],{},[724,10757,10758,10760,10761,10763,10764,10767,10768,4286,10771,1789],{},[883,10759,1642],{}," TL;DR\n",[38,10762,8759],{}," 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: ",[38,10765,10766],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,10769,10770],{},"křížově-cenovou elasticitu",[38,10772,10773],{},"důchodovou elasticitu",[115,10775,10777],{"id":10776},"úvod-motivace","Úvod — motivace",[724,10779,10780,10781,10784,10785,10788,10789,10792,10793,10796,10797,10800,10801,3042],{},"Termín ",[614,10782,10783],{},"elasticita"," (alternativně ",[614,10786,10787],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,10790,10791],{},"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 ",[614,10794,10795],{},"cenové elasticity poptávky"," (resp. ",[614,10798,10799],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,10802,8726],{"className":10803,"dataFsResolvedFilePath":764,"href":765},[210],[198,10805,10807],{"id":10806},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,10809,10810,10811,10829,10830,10848],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,10812,10814],{"className":10813},[886],[888,10815,10816],{"xmlns":890},[892,10817,10818,10826],{},[895,10819,10820,10822,10824],{},[898,10821,1701],{},[1693,10823,1695],{},[1762,10825,9763],{},[902,10827,10828],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,10831,10833],{"className":10832},[886],[888,10834,10835],{"xmlns":890},[892,10836,10837,10845],{},[895,10838,10839,10841,10843],{},[898,10840,1712],{},[1693,10842,1695],{},[1762,10844,9987],{},[902,10846,10847],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,10850,10851,10895],{},[123,10852,10853,10856,10857,10894],{},[38,10854,10855],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,10858,10860],{"className":10859},[886],[888,10861,10862],{"xmlns":890},[892,10863,10864,10891],{},[895,10865,10866,10868,10871,10873,10875,10877,10879,10882,10884,10886,10888],{},[1915,10867,1917],{},[1693,10869,10870],{},"⇒",[1915,10872,1917],{},[898,10874,2663],{},[898,10876,2666],{},[1693,10878,1695],{},[1762,10880,10881],{},"9",[1693,10883,1715],{},[1762,10885,10119],{},[1693,10887,1695],{},[1762,10889,10890],{},"990",[902,10892,10893],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,10896,10897,10900,10901,10937],{},[38,10898,10899],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,10902,10904],{"className":10903},[886],[888,10905,10906],{"xmlns":890},[892,10907,10908,10934],{},[895,10909,10910,10912,10914,10916,10918,10920,10922,10924,10926,10929,10931],{},[1915,10911,1917],{},[1693,10913,10870],{},[1915,10915,1917],{},[898,10917,2663],{},[898,10919,2666],{},[1693,10921,1695],{},[1762,10923,10881],{},[1693,10925,1715],{},[1762,10927,10928],{},"120",[1693,10930,1695],{},[1762,10932,10933],{},"1080",[902,10935,10936],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,10939,10940,10941,10944,10945,10948,10949,10952,10953,10956,10957,10960,10961,10976,10977,10980],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,10942,10943],{},"nerozumné",", na Trhu 2 ",[38,10946,10947],{},"rozumné",". Trh 2 je ",[38,10950,10951],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,10954,10955],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,10958,10959],{},"neelastická"," a vyššího ",[883,10962,10964],{"className":10963},[886],[888,10965,10966],{"xmlns":890},[892,10967,10968,10974],{},[895,10969,10970,10972],{},[898,10971,2663],{},[898,10973,2666],{},[902,10975,2883],{"encoding":904}," lze naopak dosáhnout ",[614,10978,10979],{},"zvýšením"," ceny.",[198,10982,10984],{"id":10983},"hypotéza-41","Hypotéza 4.1",[1636,10986,10987],{},[724,10988,10989,10990],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,10991,10993],{"className":10992},[886],[888,10994,10995],{"xmlns":890},[892,10996,10997,11006],{},[895,10998,10999,11001,11004],{},[1693,11000,1709],{"stretchy":1708},[1762,11002,11003],{},"4.1",[1693,11005,1731],{"stretchy":1708},[902,11007,11008],{"encoding":904},"(4.1)",[724,11010,11011,11012,11015],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,11013,11014],{},"procentní změny"," obou faktorů.",[115,11017,11019],{"id":11018},"pojem-elasticity","Pojem elasticity",[724,11021,11022,11023,11025,11026,11029],{},"Obecně ",[38,11024,10783],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,11027,11028],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1636,11031,11032],{},[724,11033,11034,11037,11038,11041],{},[883,11035,11036],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,11039,11040],{},"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.",[115,11043,11045],{"id":11044},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,11047,11048,11049,11073],{},"Nechť ",[883,11050,11052],{"className":11051},[886],[888,11053,11054],{"xmlns":890},[892,11055,11056,11070],{},[895,11057,11058,11060,11062,11064,11066,11068],{},[898,11059,1712],{},[1693,11061,1695],{},[898,11063,2738],{},[1693,11065,1709],{"stretchy":1708},[898,11067,1701],{},[1693,11069,1731],{"stretchy":1708},[902,11071,11072],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,11075,11076],{},[883,11077,11082],{"className":11078,"title":11080,"style":11081},[11079],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,11084,11085,11086,4286,11102,11118,11119,11137],{},"Znaménko minus je korekce: změny ",[883,11087,11089],{"className":11088},[886],[888,11090,11091],{"xmlns":890},[892,11092,11093,11099],{},[895,11094,11095,11097],{},[898,11096,3890],{"mathvariant":1704},[898,11098,1712],{},[902,11100,11101],{"encoding":904},"\\Delta Q",[883,11103,11105],{"className":11104},[886],[888,11106,11107],{"xmlns":890},[892,11108,11109,11115],{},[895,11110,11111,11113],{},[898,11112,3890],{"mathvariant":1704},[898,11114,1701],{},[902,11116,11117],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,11120,11122],{"className":11121},[886],[888,11123,11124],{"xmlns":890},[892,11125,11126,11134],{},[895,11127,11128],{},[1717,11129,11130,11132],{},[898,11131,1691],{},[898,11133,2719],{},[902,11135,11136],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,11139,11140],{},[883,11141,11143],{"className":11142,"title":11080,"style":11081},[11079],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,11145,11146],{},"Po dosazení:",[724,11148,11149],{},[883,11150,11152],{"className":11151,"title":11080,"style":11081},[11079],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,11154,11155,11156,11176,11177,11179],{},"Limitním přechodem ",[883,11157,11159],{"className":11158},[886],[888,11160,11161],{"xmlns":890},[892,11162,11163,11173],{},[895,11164,11165,11167,11169,11171],{},[898,11166,3890],{"mathvariant":1704},[898,11168,1701],{},[1693,11170,10020],{},[1762,11172,1911],{},[902,11174,11175],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,11178,10795],{}," (price elasticity of demand):",[724,11181,11182],{},[883,11183,11185],{"className":11184,"title":11080,"style":11081},[11079],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,11187,11188,11189,11212,11213,2783,11235,11259,11260,11281],{},"kde ",[883,11190,11192],{"className":11191},[886],[888,11193,11194],{"xmlns":890},[892,11195,11196,11210],{},[895,11197,11198,11200,11202,11204,11206,11208],{},[898,11199,1712],{},[1693,11201,1695],{},[898,11203,2738],{},[1693,11205,1709],{"stretchy":1708},[898,11207,1701],{},[1693,11209,1731],{"stretchy":1708},[902,11211,11072],{"encoding":904},". Pro pevnou cenu ",[883,11214,11216],{"className":11215},[886],[888,11217,11218],{"xmlns":890},[892,11219,11220,11232],{},[895,11221,11222,11224,11226],{},[898,11223,1701],{},[1693,11225,1695],{},[1717,11227,11228,11230],{},[898,11229,1701],{},[1693,11231,3672],{},[902,11233,11234],{"encoding":904},"P = P^*",[883,11236,11238],{"className":11237},[886],[888,11239,11240],{"xmlns":890},[892,11241,11242,11256],{},[895,11243,11244,11246,11248,11254],{},[898,11245,1691],{},[1693,11247,1709],{"stretchy":1708},[1717,11249,11250,11252],{},[898,11251,1701],{},[1693,11253,3672],{},[1693,11255,1731],{"stretchy":1708},[902,11257,11258],{"encoding":904},"E(P^*)"," nazývá ",[614,11261,11262,11263],{},"elasticita poptávky při ceně ",[883,11264,11266],{"className":11265},[886],[888,11267,11268],{"xmlns":890},[892,11269,11270,11278],{},[895,11271,11272],{},[1717,11273,11274,11276],{},[898,11275,1701],{},[1693,11277,3672],{},[902,11279,11280],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1636,11283,11284],{},[724,11285,11286,11288,11289,11307,11308,11336,11337,11365,11366,1343,11383,1343,11400,11417,11418,11433,11434,1789],{},[883,11287,8654],{}," Pozor na znaménko\nV (4.5) je ",[38,11290,11291,11292],{},"explicitní ",[883,11293,11295],{"className":11294},[886],[888,11296,11297],{"xmlns":890},[892,11298,11299,11305],{},[895,11300,11301,11303],{},[1693,11302,1698],{},[1762,11304,1764],{},[902,11306,10626],{"encoding":904}," právě proto, že ",[883,11309,11311],{"className":11310},[886],[888,11312,11313],{"xmlns":890},[892,11314,11315,11333],{},[895,11316,11317,11323,11325,11327,11329,11331],{},[1717,11318,11319,11321],{},[898,11320,1712],{},[1693,11322,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,11324,1709],{"stretchy":1708},[898,11326,1701],{},[1693,11328,1731],{"stretchy":1708},[1693,11330,1908],{},[1762,11332,1911],{},[902,11334,11335],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,11338,11340],{"className":11339},[886],[888,11341,11342],{"xmlns":890},[892,11343,11344,11362],{},[895,11345,11346,11348,11350,11356,11358,11360],{},[898,11347,1691],{},[1693,11349,1709],{"stretchy":1708},[1717,11351,11352,11354],{},[898,11353,1701],{},[1693,11355,3672],{},[1693,11357,1731],{"stretchy":1708},[1693,11359,3665],{},[1762,11361,1911],{},[902,11363,11364],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,11367,11369],{"className":11368},[886],[888,11370,11371],{"xmlns":890},[892,11372,11373,11381],{},[895,11374,11375,11377,11379],{},[898,11376,1691],{},[1693,11378,1922],{},[1762,11380,1764],{},[902,11382,4322],{"encoding":904},[883,11384,11386],{"className":11385},[886],[888,11387,11388],{"xmlns":890},[892,11389,11390,11398],{},[895,11391,11392,11394,11396],{},[898,11393,1691],{},[1693,11395,1908],{},[1762,11397,1764],{},[902,11399,4364],{"encoding":904},[883,11401,11403],{"className":11402},[886],[888,11404,11405],{"xmlns":890},[892,11406,11407,11415],{},[895,11408,11409,11411,11413],{},[898,11410,1691],{},[1693,11412,1695],{},[1762,11414,1764],{},[902,11416,4405],{"encoding":904},". V některých starších pramenech se ",[883,11419,11421],{"className":11420},[886],[888,11422,11423],{"xmlns":890},[892,11424,11425,11431],{},[895,11426,11427,11429],{},[1693,11428,1698],{},[1762,11430,1764],{},[902,11432,10626],{"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 ",[38,11435,11436],{},"absolutní hodnotou",[1636,11438,11439,11458],{},[724,11440,11441,11443,11444,11457],{},[883,11442,8620],{}," Postup: jak spočítat ",[883,11445,11447],{"className":11446},[886],[888,11448,11449],{"xmlns":890},[892,11450,11451,11455],{},[895,11452,11453],{},[898,11454,1691],{},[902,11456,1691],{"encoding":904}," v bodě",[152,11459,11460,11511,11550,11603,11668],{},[123,11461,11462,11463,11486,11487,11510],{},"Zapište ",[883,11464,11466],{"className":11465},[886],[888,11467,11468],{"xmlns":890},[892,11469,11470,11484],{},[895,11471,11472,11474,11476,11478,11480,11482],{},[898,11473,1712],{},[1693,11475,1695],{},[898,11477,2738],{},[1693,11479,1709],{"stretchy":1708},[898,11481,1701],{},[1693,11483,1731],{"stretchy":1708},[902,11485,11072],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,11488,11490],{"className":11489},[886],[888,11491,11492],{"xmlns":890},[892,11493,11494,11508],{},[895,11495,11496,11498,11500,11502,11504,11506],{},[898,11497,1701],{},[1693,11499,1695],{},[898,11501,2738],{},[1693,11503,1709],{"stretchy":1708},[898,11505,1712],{},[1693,11507,1731],{"stretchy":1708},[902,11509,3980],{"encoding":904},", použijte vztah (4.9).",[123,11512,11513,11514,1789],{},"Spočítejte derivaci ",[883,11515,11517],{"className":11516},[886],[888,11518,11519],{"xmlns":890},[892,11520,11521,11547],{},[895,11522,11523,11529,11531,11533,11535,11537,11539,11541,11543,11545],{},[1717,11524,11525,11527],{},[898,11526,1712],{},[1693,11528,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,11530,1709],{"stretchy":1708},[898,11532,1701],{},[1693,11534,1731],{"stretchy":1708},[1693,11536,1695],{},[898,11538,1771],{"mathvariant":1704},[898,11540,1712],{},[898,11542,1705],{"mathvariant":1704},[898,11544,1771],{"mathvariant":1704},[898,11546,1701],{},[902,11548,11549],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,11551,11552,11553,11570,11571,1789],{},"Dosaďte zadanou cenu ",[883,11554,11556],{"className":11555},[886],[888,11557,11558],{"xmlns":890},[892,11559,11560,11568],{},[895,11561,11562],{},[1717,11563,11564,11566],{},[898,11565,1701],{},[1693,11567,3672],{},[902,11569,11280],{"encoding":904}," a dopočítejte odpovídající ",[883,11572,11574],{"className":11573},[886],[888,11575,11576],{"xmlns":890},[892,11577,11578,11600],{},[895,11579,11580,11586,11588,11590,11592,11598],{},[1717,11581,11582,11584],{},[898,11583,1712],{},[1693,11585,3672],{},[1693,11587,1695],{},[898,11589,2738],{},[1693,11591,1709],{"stretchy":1708},[1717,11593,11594,11596],{},[898,11595,1701],{},[1693,11597,3672],{},[1693,11599,1731],{"stretchy":1708},[902,11601,11602],{"encoding":904},"Q^* = D(P^*)",[123,11604,11605,11606,1789],{},"Dosaďte do (4.5): ",[883,11607,11609],{"className":11608},[886],[888,11610,11611],{"xmlns":890},[892,11612,11613,11665],{},[895,11614,11615,11617,11619,11625,11627,11629,11631,11647,11649,11655,11657,11663],{},[898,11616,1691],{},[1693,11618,1709],{"stretchy":1708},[1717,11620,11621,11623],{},[898,11622,1701],{},[1693,11624,3672],{},[1693,11626,1731],{"stretchy":1708},[1693,11628,1695],{},[1693,11630,1698],{},[3638,11632,11633],{"scriptlevel":1911,"displaystyle":1898},[2132,11634,11635,11641],{},[1717,11636,11637,11639],{},[898,11638,1701],{},[1693,11640,3672],{},[1717,11642,11643,11645],{},[898,11644,1712],{},[1693,11646,3672],{},[1915,11648,2239],{},[1717,11650,11651,11653],{},[898,11652,1712],{},[1693,11654,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,11656,1709],{"stretchy":1708},[1717,11658,11659,11661],{},[898,11660,1701],{},[1693,11662,3672],{},[1693,11664,1731],{"stretchy":1708},[902,11666,11667],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,11669,11670,11671,11688,11689,11706,11707,11724],{},"Klasifikujte: ",[883,11672,11674],{"className":11673},[886],[888,11675,11676],{"xmlns":890},[892,11677,11678,11686],{},[895,11679,11680,11682,11684],{},[898,11681,1691],{},[1693,11683,1922],{},[1762,11685,1764],{},[902,11687,4322],{"encoding":904}," elastická, ",[883,11690,11692],{"className":11691},[886],[888,11693,11694],{"xmlns":890},[892,11695,11696,11704],{},[895,11697,11698,11700,11702],{},[898,11699,1691],{},[1693,11701,1695],{},[1762,11703,1764],{},[902,11705,4405],{"encoding":904}," jednotková, ",[883,11708,11710],{"className":11709},[886],[888,11711,11712],{"xmlns":890},[892,11713,11714,11722],{},[895,11715,11716,11718,11720],{},[898,11717,1691],{},[1693,11719,1908],{},[1762,11721,1764],{},[902,11723,4364],{"encoding":904}," neelastická.",[198,11726,11728],{"id":11727},"interpretace-46","Interpretace (4.6)",[1636,11730,11731],{},[724,11732,11733,11734,11757,11758,11771,11772,11789,11790],{},"Číslo ",[883,11735,11737],{"className":11736},[886],[888,11738,11739],{"xmlns":890},[892,11740,11741,11755],{},[895,11742,11743,11745,11747,11753],{},[898,11744,1691],{},[1693,11746,1709],{"stretchy":1708},[1717,11748,11749,11751],{},[898,11750,1701],{},[1693,11752,3672],{},[1693,11754,1731],{"stretchy":1708},[902,11756,11258],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,11759,11761],{"className":11760},[886],[888,11762,11763],{"xmlns":890},[892,11764,11765,11769],{},[895,11766,11767],{},[898,11768,1712],{},[902,11770,1712],{"encoding":904},", jestliže se cena ",[883,11773,11775],{"className":11774},[886],[888,11776,11777],{"xmlns":890},[892,11778,11779,11787],{},[895,11780,11781],{},[1717,11782,11783,11785],{},[898,11784,1701],{},[1693,11786,3672],{},[902,11788,11280],{"encoding":904}," změní o 1 %. ",[883,11791,11793],{"className":11792},[886],[888,11794,11795],{"xmlns":890},[892,11796,11797,11806],{},[895,11798,11799,11801,11804],{},[1693,11800,1709],{"stretchy":1708},[1762,11802,11803],{},"4.6",[1693,11805,1731],{"stretchy":1708},[902,11807,11808],{"encoding":904},"(4.6)",[724,11810,11811,11814],{},[38,11812,11813],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,11816,11818],{"id":11817},"příklad-41","Příklad 4.1",[724,11820,11821,11822,11856,11857,1343,11883,4300],{},"Poptávka ",[883,11823,11825],{"className":11824},[886],[888,11826,11827],{"xmlns":890},[892,11828,11829,11853],{},[895,11830,11831,11833,11835,11837,11839,11841,11843,11845,11847,11849,11851],{},[898,11832,1701],{},[1693,11834,1695],{},[898,11836,2738],{},[1693,11838,1709],{"stretchy":1708},[898,11840,1712],{},[1693,11842,1731],{"stretchy":1708},[1693,11844,1695],{},[1762,11846,10017],{},[1693,11848,1698],{},[1762,11850,2398],{},[898,11852,1712],{},[902,11854,11855],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,11858,11860],{"className":11859},[886],[888,11861,11862],{"xmlns":890},[892,11863,11864,11880],{},[895,11865,11866,11868,11870,11873,11875,11878],{},[898,11867,1712],{},[1693,11869,1695],{},[1762,11871,11872],{},"25",[1693,11874,1698],{},[1762,11876,11877],{},"0,5",[898,11879,1701],{},[902,11881,11882],{"encoding":904},"Q = 25 - 0{,}5P",[883,11884,11886],{"className":11885},[886],[888,11887,11888],{"xmlns":890},[892,11889,11890,11914],{},[895,11891,11892,11908,11910,11912],{},[3638,11893,11894],{"scriptlevel":1911,"displaystyle":1898},[2132,11895,11896,11902],{},[895,11897,11898,11900],{},[898,11899,1771],{"mathvariant":1704},[898,11901,1712],{},[895,11903,11904,11906],{},[898,11905,1771],{"mathvariant":1704},[898,11907,1701],{},[1693,11909,1695],{},[1693,11911,1698],{},[1762,11913,11877],{},[902,11915,11916],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,11918,11919],{},[883,11920,11922],{"className":11921},[886],[888,11923,11924],{"xmlns":890},[892,11925,11926,11980],{},[895,11927,11928,11930,11932,11934,11948,11950,11952,11954,11956,11958,11960,11978],{},[898,11929,1691],{},[1693,11931,1695],{},[1693,11933,1698],{},[2132,11935,11936,11938],{},[898,11937,1701],{},[895,11939,11940,11942,11944,11946],{},[1762,11941,11872],{},[1693,11943,1698],{},[1762,11945,11877],{},[898,11947,1701],{},[1693,11949,1715],{},[1693,11951,1709],{"stretchy":1708},[1693,11953,1698],{},[1762,11955,11877],{},[1693,11957,1731],{"stretchy":1708},[1693,11959,1695],{},[2132,11961,11962,11968],{},[895,11963,11964,11966],{},[1762,11965,11877],{},[898,11967,1701],{},[895,11969,11970,11972,11974,11976],{},[1762,11971,11872],{},[1693,11973,1698],{},[1762,11975,11877],{},[898,11977,1701],{},[898,11979,1789],{"mathvariant":1704},[902,11981,11982],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,11984,11985,11986,1343,12010,1343,12040,1343,12064,12089,12090,12113,12114,9591,12132,3042],{},"Potom ",[883,11987,11989],{"className":11988},[886],[888,11990,11991],{"xmlns":890},[892,11992,11993,12007],{},[895,11994,11995,11997,11999,12001,12003,12005],{},[898,11996,1691],{},[1693,11998,1709],{"stretchy":1708},[1762,12000,1911],{},[1693,12002,1731],{"stretchy":1708},[1693,12004,1695],{},[1762,12006,1911],{},[902,12008,12009],{"encoding":904},"E(0)=0",[883,12011,12013],{"className":12012},[886],[888,12014,12015],{"xmlns":890},[892,12016,12017,12037],{},[895,12018,12019,12021,12023,12025,12027,12029],{},[898,12020,1691],{},[1693,12022,1709],{"stretchy":1708},[1762,12024,9763],{},[1693,12026,1731],{"stretchy":1708},[1693,12028,1695],{},[3638,12030,12031],{"scriptlevel":1911,"displaystyle":1708},[2132,12032,12033,12035],{},[1762,12034,1764],{},[1762,12036,9262],{},[902,12038,12039],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,12041,12043],{"className":12042},[886],[888,12044,12045],{"xmlns":890},[892,12046,12047,12061],{},[895,12048,12049,12051,12053,12055,12057,12059],{},[898,12050,1691],{},[1693,12052,1709],{"stretchy":1708},[1762,12054,11872],{},[1693,12056,1731],{"stretchy":1708},[1693,12058,1695],{},[1762,12060,1764],{},[902,12062,12063],{"encoding":904},"E(25)=1",[883,12065,12067],{"className":12066},[886],[888,12068,12069],{"xmlns":890},[892,12070,12071,12086],{},[895,12072,12073,12075,12077,12080,12082,12084],{},[898,12074,1691],{},[1693,12076,1709],{"stretchy":1708},[1762,12078,12079],{},"40",[1693,12081,1731],{"stretchy":1708},[1693,12083,1695],{},[1762,12085,9262],{},[902,12087,12088],{"encoding":904},"E(40)=4",". Např. ",[883,12091,12093],{"className":12092},[886],[888,12094,12095],{"xmlns":890},[892,12096,12097,12111],{},[895,12098,12099,12101,12103,12105,12107,12109],{},[898,12100,1691],{},[1693,12102,1709],{"stretchy":1708},[1762,12104,12079],{},[1693,12106,1731],{"stretchy":1708},[1693,12108,1695],{},[1762,12110,9262],{},[902,12112,12088],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,12115,12117],{"className":12116},[886],[888,12118,12119],{"xmlns":890},[892,12120,12121,12129],{},[895,12122,12123,12125,12127],{},[898,12124,1712],{},[1693,12126,1695],{},[1762,12128,9147],{},[902,12130,12131],{"encoding":904},"Q=5",[883,12133,12135],{"className":12134},[886],[888,12136,12137],{"xmlns":890},[892,12138,12139,12148],{},[895,12140,12141,12143,12145],{},[898,12142,1712],{},[1693,12144,1695],{},[1762,12146,12147],{},"4,8",[902,12149,12150],{"encoding":904},"Q=4{,}8",[198,12152,12154],{"id":12153},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,12156,12157,12213],{},[123,12158,12159,12162,12163,12180,12181,1789],{},[38,12160,12161],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,12164,12166],{"className":12165},[886],[888,12167,12168],{"xmlns":890},[892,12169,12170,12178],{},[895,12171,12172],{},[1717,12173,12174,12176],{},[898,12175,1691],{},[898,12177,2719],{},[902,12179,11136],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,12182,12184],{"className":12183},[886],[888,12185,12186],{"xmlns":890},[892,12187,12188,12210],{},[895,12189,12190,12193,12195,12197,12199,12201,12203,12205,12207],{},[1693,12191,12192],{"stretchy":1708},"⟨",[898,12194,1701],{},[1693,12196,1899],{"separator":1898},[1915,12198,2239],{},[898,12200,1701],{},[1693,12202,1892],{},[898,12204,3890],{"mathvariant":1704},[898,12206,1701],{},[1693,12208,12209],{"stretchy":1708},"⟩",[902,12211,12212],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,12214,12215,12218,12219,12232],{},[38,12216,12217],{},"Bodová"," (okamžitá) elasticita: ",[883,12220,12222],{"className":12221},[886],[888,12223,12224],{"xmlns":890},[892,12225,12226,12230],{},[895,12227,12228],{},[898,12229,1691],{},[902,12231,1691],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,12234,12236,12237,12250,12251],{"id":12235},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,12238,12240],{"className":12239},[886],[888,12241,12242],{"xmlns":890},[892,12243,12244,12248],{},[895,12245,12246],{},[898,12247,1701],{},[902,12249,1701],{"encoding":904}," jako funkce ",[883,12252,12254],{"className":12253},[886],[888,12255,12256],{"xmlns":890},[892,12257,12258,12262],{},[895,12259,12260],{},[898,12261,1712],{},[902,12263,1712],{"encoding":904},[724,12265,12266,12267,12290],{},"Pokud je poptávka zadaná ve tvaru ",[883,12268,12270],{"className":12269},[886],[888,12271,12272],{"xmlns":890},[892,12273,12274,12288],{},[895,12275,12276,12278,12280,12282,12284,12286],{},[898,12277,1701],{},[1693,12279,1695],{},[898,12281,2738],{},[1693,12283,1709],{"stretchy":1708},[898,12285,1712],{},[1693,12287,1731],{"stretchy":1708},[902,12289,3980],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,12292,12293],{},[883,12294,12296],{"className":12295,"title":11080,"style":11081},[11079],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,12298,12299,1863,12302,12328],{},[38,12300,12301],{},"Příklad 4.3.",[883,12303,12305],{"className":12304},[886],[888,12306,12307],{"xmlns":890},[892,12308,12309,12325],{},[895,12310,12311,12313,12315,12317,12319],{},[898,12312,1701],{},[1693,12314,1695],{},[1762,12316,9987],{},[1693,12318,1698],{},[1717,12320,12321,12323],{},[898,12322,1712],{},[1762,12324,2398],{},[902,12326,12327],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,12330,12331],{},[883,12332,12334],{"className":12333},[886],[888,12335,12336],{"xmlns":890},[892,12337,12338,12404],{},[895,12339,12340,12342,12344,12346,12362,12364,12376,12378,12402],{},[898,12341,1691],{},[1693,12343,1695],{},[1693,12345,1698],{},[2132,12347,12348,12360],{},[895,12349,12350,12352,12354],{},[1762,12351,9987],{},[1693,12353,1698],{},[1717,12355,12356,12358],{},[898,12357,1712],{},[1762,12359,2398],{},[898,12361,1712],{},[1693,12363,1715],{},[2132,12365,12366,12368],{},[1762,12367,1764],{},[895,12369,12370,12372,12374],{},[1693,12371,1698],{},[1762,12373,2398],{},[898,12375,1712],{},[1693,12377,1695],{},[2132,12379,12380,12392],{},[895,12381,12382,12384,12386],{},[1762,12383,9987],{},[1693,12385,1698],{},[1717,12387,12388,12390],{},[898,12389,1712],{},[1762,12391,2398],{},[895,12393,12394,12396],{},[1762,12395,2398],{},[1717,12397,12398,12400],{},[898,12399,1712],{},[1762,12401,2398],{},[898,12403,1789],{"mathvariant":1704},[902,12405,12406],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,12408,12409,12410,12437,12438,12457,12458,1789],{},"Z rovnice ",[883,12411,12413],{"className":12412},[886],[888,12414,12415],{"xmlns":890},[892,12416,12417,12434],{},[895,12418,12419,12421,12423,12429,12431],{},[1762,12420,9987],{},[1693,12422,1698],{},[1717,12424,12425,12427],{},[898,12426,1712],{},[1762,12428,2398],{},[1693,12430,1695],{},[1762,12432,12433],{},"36",[902,12435,12436],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,12439,12441],{"className":12440},[886],[888,12442,12443],{"xmlns":890},[892,12444,12445,12454],{},[895,12446,12447,12449,12451],{},[898,12448,1712],{},[1693,12450,1695],{},[1762,12452,12453],{},"8",[902,12455,12456],{"encoding":904},"Q = 8",", tedy ",[883,12459,12461],{"className":12460},[886],[888,12462,12463],{"xmlns":890},[892,12464,12465,12491],{},[895,12466,12467,12469,12471,12473,12475,12477,12486,12488],{},[898,12468,1691],{},[1693,12470,1709],{"stretchy":1708},[1762,12472,12453],{},[1693,12474,1731],{"stretchy":1708},[1693,12476,1695],{},[3638,12478,12479],{"scriptlevel":1911,"displaystyle":1708},[2132,12480,12481,12483],{},[1762,12482,12433],{},[1762,12484,12485],{},"128",[1693,12487,1695],{},[1762,12489,12490],{},"0,281",[902,12492,12493],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,12495,12497],{"id":12496},"přibližné-změny","Přibližné změny",[724,12499,12500,12501,12537,12538,12560],{},"Diferenciál ",[883,12502,12504],{"className":12503},[886],[888,12505,12506],{"xmlns":890},[892,12507,12508,12534],{},[895,12509,12510,12512,12514,12516,12522,12524,12526,12528,12530,12532],{},[898,12511,1771],{"mathvariant":1704},[898,12513,1712],{},[1693,12515,1695],{},[1717,12517,12518,12520],{},[898,12519,1712],{},[1693,12521,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,12523,1709],{"stretchy":1708},[898,12525,1701],{},[1693,12527,1731],{"stretchy":1708},[1915,12529,2239],{},[898,12531,1771],{"mathvariant":1704},[898,12533,1701],{},[902,12535,12536],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,12539,12541],{"className":12540},[886],[888,12542,12543],{"xmlns":890},[892,12544,12545,12557],{},[895,12546,12547,12549,12551,12553,12555],{},[898,12548,1771],{"mathvariant":1704},[898,12550,1701],{},[1693,12552,1695],{},[898,12554,3890],{"mathvariant":1704},[898,12556,1701],{},[902,12558,12559],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,12562,12563],{},[883,12564,12566],{"className":12565,"title":11080,"style":11081},[11079],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,12568,12569],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,12571,12572],{},[883,12573,12575],{"className":12574,"title":11080,"style":11081},[11079],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,12577,12578,1863,12581,12616,12617,12636,12637,12671,12672,12689],{},[38,12579,12580],{},"Příklad 4.5.",[883,12582,12584],{"className":12583},[886],[888,12585,12586],{"xmlns":890},[892,12587,12588,12613],{},[895,12589,12590,12592,12594,12596,12602,12604,12606,12608,12610],{},[898,12591,1701],{},[1693,12593,1695],{},[1693,12595,1698],{},[1717,12597,12598,12600],{},[898,12599,1712],{},[1762,12601,2398],{},[1693,12603,1698],{},[1762,12605,9262],{},[898,12607,1712],{},[1693,12609,1892],{},[1762,12611,12612],{},"96",[902,12614,12615],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,12618,12620],{"className":12619},[886],[888,12621,12622],{"xmlns":890},[892,12623,12624,12633],{},[895,12625,12626,12628,12630],{},[898,12627,1701],{},[1693,12629,1695],{},[1762,12631,12632],{},"51",[902,12634,12635],{"encoding":904},"P=51",". Z rovnice ",[883,12638,12640],{"className":12639},[886],[888,12641,12642],{"xmlns":890},[892,12643,12644,12668],{},[895,12645,12646,12648,12650,12652,12658,12660,12662,12664,12666],{},[1762,12647,12632],{},[1693,12649,1695],{},[1693,12651,1698],{},[1717,12653,12654,12656],{},[898,12655,1712],{},[1762,12657,2398],{},[1693,12659,1698],{},[1762,12661,9262],{},[898,12663,1712],{},[1693,12665,1892],{},[1762,12667,12612],{},[902,12669,12670],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,12673,12675],{"className":12674},[886],[888,12676,12677],{"xmlns":890},[892,12678,12679,12687],{},[895,12680,12681,12683,12685],{},[898,12682,1712],{},[1693,12684,1695],{},[1762,12686,9147],{},[902,12688,12131],{"encoding":904},". Elasticita:",[724,12691,12692],{},[883,12693,12695],{"className":12694},[886],[888,12696,12697],{"xmlns":890},[892,12698,12699,12770],{},[895,12700,12701,12703,12705,12743,12745,12747,12749,12751,12753,12755,12757,12764,12767],{},[898,12702,1691],{},[1693,12704,1695],{},[2132,12706,12707,12727],{},[895,12708,12709,12711,12717,12719,12721,12723,12725],{},[1693,12710,1698],{},[1717,12712,12713,12715],{},[898,12714,1712],{},[1762,12716,2398],{},[1693,12718,1698],{},[1762,12720,9262],{},[898,12722,1712],{},[1693,12724,1892],{},[1762,12726,12612],{},[895,12728,12729,12731,12733,12735,12737,12739,12741],{},[898,12730,1712],{},[1693,12732,1709],{"stretchy":1708},[1762,12734,2398],{},[898,12736,1712],{},[1693,12738,1892],{},[1762,12740,9262],{},[1693,12742,1731],{"stretchy":1708},[1693,12744,1899],{"separator":1898},[1901,12746],{"width":1903},[898,12748,1691],{},[1693,12750,1709],{"stretchy":1708},[1762,12752,9147],{},[1693,12754,1731],{"stretchy":1708},[1693,12756,1695],{},[2132,12758,12759,12761],{},[1762,12760,12632],{},[1762,12762,12763],{},"70",[1693,12765,12766],{},"≐",[1762,12768,12769],{},"0,728.",[902,12771,12772],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,12774,12775,12776,1789],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,12777,12779],{"className":12778},[886],[888,12780,12781],{"xmlns":890},[892,12782,12783,12813],{},[895,12784,12785,12787,12789,12791,12793,12795,12798,12800,12802,12804,12806,12809,12811],{},[898,12786,3890],{"mathvariant":1704},[898,12788,1712],{},[898,12790,3895],{"mathvariant":1704},[1693,12792,4110],{},[1693,12794,1698],{},[1762,12796,12797],{},"0,728",[1693,12799,1715],{},[1762,12801,2398],{},[1693,12803,1695],{},[1693,12805,1698],{},[1762,12807,12808],{},"1,456",[1915,12810,2239],{},[898,12812,3895],{"mathvariant":1704},[902,12814,12815],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,12817,12819],{"id":12818},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,12821,12822,12823,12846,12847,4300],{},"V závislosti na hodnotě ",[883,12824,12826],{"className":12825},[886],[888,12827,12828],{"xmlns":890},[892,12829,12830,12844],{},[895,12831,12832,12834,12836,12842],{},[898,12833,1691],{},[1693,12835,1709],{"stretchy":1708},[1717,12837,12838,12840],{},[898,12839,1701],{},[1693,12841,3672],{},[1693,12843,1731],{"stretchy":1708},[902,12845,11258],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,12848,12850],{"className":12849},[886],[888,12851,12852],{"xmlns":890},[892,12853,12854,12863],{},[895,12855,12856,12858,12861],{},[1693,12857,1709],{"stretchy":1708},[1762,12859,12860],{},"4.7",[1693,12862,1731],{"stretchy":1708},[902,12864,12865],{"encoding":904},"(4.7)",[724,12867,12868],{},[9465,12869],{"alt":12870,"className":12871,"src":12872},"imek-typy-elasticity-5panelu",[210,9469],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,12874,12875,12914],{},[19,12876,12877],{},[22,12878,12879,12905,12908,12911],{},[25,12880,12881,12882],{},"Hodnota ",[883,12883,12885],{"className":12884},[886],[888,12886,12887],{"xmlns":890},[892,12888,12889,12903],{},[895,12890,12891,12893,12895,12901],{},[898,12892,1691],{},[1693,12894,1709],{"stretchy":1708},[1717,12896,12897,12899],{},[898,12898,1701],{},[1693,12900,3672],{},[1693,12902,1731],{"stretchy":1708},[902,12904,11258],{"encoding":904},[25,12906,12907],{},"Typ poptávky",[25,12909,12910],{},"Termín",[25,12912,12913],{},"Význam",[30,12915,12916,12949,13011,13086,13143],{},[22,12917,12918,12938,12943,12946],{},[35,12919,12920],{},[883,12921,12923],{"className":12922},[886],[888,12924,12925],{"xmlns":890},[892,12926,12927,12935],{},[895,12928,12929,12931,12933],{},[898,12930,1691],{},[1693,12932,1695],{},[1762,12934,1911],{},[902,12936,12937],{"encoding":904},"E = 0",[35,12939,12940],{},[38,12941,12942],{},"dokonale neelastická",[35,12944,12945],{},"perfectly inelastic",[35,12947,12948],{},"množství se nemění bez ohledu na cenu",[22,12950,12951,12975,12979,12982],{},[35,12952,12953],{},[883,12954,12956],{"className":12955},[886],[888,12957,12958],{"xmlns":890},[892,12959,12960,12972],{},[895,12961,12962,12964,12966,12968,12970],{},[1762,12963,1911],{},[1693,12965,1908],{},[898,12967,1691],{},[1693,12969,1908],{},[1762,12971,1764],{},[902,12973,12974],{"encoding":904},"0 \u003C E \u003C 1",[35,12976,12977],{},[38,12978,10959],{},[35,12980,12981],{},"inelastic",[35,12983,12984,12997,12998],{},[883,12985,12987],{"className":12986},[886],[888,12988,12989],{"xmlns":890},[892,12990,12991,12995],{},[895,12992,12993],{},[898,12994,1712],{},[902,12996,1712],{"encoding":904}," se mění pomaleji než ",[883,12999,13001],{"className":13000},[886],[888,13002,13003],{"xmlns":890},[892,13004,13005,13009],{},[895,13006,13007],{},[898,13008,1701],{},[902,13010,1701],{"encoding":904},[22,13012,13013,13032,13037,13040],{},[35,13014,13015],{},[883,13016,13018],{"className":13017},[886],[888,13019,13020],{"xmlns":890},[892,13021,13022,13030],{},[895,13023,13024,13026,13028],{},[898,13025,1691],{},[1693,13027,1695],{},[1762,13029,1764],{},[902,13031,4405],{"encoding":904},[35,13033,13034],{},[38,13035,13036],{},"jednotkově elastická",[35,13038,13039],{},"unit elastic",[35,13041,13042,13055,13056,13069,13070,13085],{},[883,13043,13045],{"className":13044},[886],[888,13046,13047],{"xmlns":890},[892,13048,13049,13053],{},[895,13050,13051],{},[898,13052,1712],{},[902,13054,1712],{"encoding":904}," i ",[883,13057,13059],{"className":13058},[886],[888,13060,13061],{"xmlns":890},[892,13062,13063,13067],{},[895,13064,13065],{},[898,13066,1701],{},[902,13068,1701],{"encoding":904}," se mění stejně rychle; ",[883,13071,13073],{"className":13072},[886],[888,13074,13075],{"xmlns":890},[892,13076,13077,13083],{},[895,13078,13079,13081],{},[898,13080,2663],{},[898,13082,2666],{},[902,13084,2883],{"encoding":904}," má maximum",[22,13087,13088,13107,13111,13114],{},[35,13089,13090],{},[883,13091,13093],{"className":13092},[886],[888,13094,13095],{"xmlns":890},[892,13096,13097,13105],{},[895,13098,13099,13101,13103],{},[898,13100,1691],{},[1693,13102,1922],{},[1762,13104,1764],{},[902,13106,4322],{"encoding":904},[35,13108,13109],{},[38,13110,10955],{},[35,13112,13113],{},"elastic",[35,13115,13116,13129,13130],{},[883,13117,13119],{"className":13118},[886],[888,13120,13121],{"xmlns":890},[892,13122,13123,13127],{},[895,13124,13125],{},[898,13126,1712],{},[902,13128,1712],{"encoding":904}," se mění rychleji než ",[883,13131,13133],{"className":13132},[886],[888,13134,13135],{"xmlns":890},[892,13136,13137,13141],{},[895,13138,13139],{},[898,13140,1701],{},[902,13142,1701],{"encoding":904},[22,13144,13145,13166,13171,13174],{},[35,13146,13147],{},[883,13148,13150],{"className":13149},[886],[888,13151,13152],{"xmlns":890},[892,13153,13154,13163],{},[895,13155,13156,13158,13160],{},[898,13157,1691],{},[1693,13159,10020],{},[898,13161,13162],{"mathvariant":1704},"∞",[902,13164,13165],{"encoding":904},"E \\to \\infty",[35,13167,13168],{},[38,13169,13170],{},"dokonale elastická",[35,13172,13173],{},"perfectly elastic",[35,13175,13176,13177],{},"sebemenší změna ceny úplně mění ",[883,13178,13180],{"className":13179},[886],[888,13181,13182],{"xmlns":890},[892,13183,13184,13188],{},[895,13185,13186],{},[898,13187,1712],{},[902,13189,1712],{"encoding":904},[724,13191,13192],{},[38,13193,13194],{},"Pravidlo růstu elasticity s cenou:",[1636,13196,13197],{},[724,13198,13199,13200],{},"S rostoucí cenou elasticita poptávky roste. ",[883,13201,13203],{"className":13202},[886],[888,13204,13205],{"xmlns":890},[892,13206,13207,13216],{},[895,13208,13209,13211,13214],{},[1693,13210,1709],{"stretchy":1708},[1762,13212,13213],{},"4.8",[1693,13215,1731],{"stretchy":1708},[902,13217,13218],{"encoding":904},"(4.8)",[724,13220,13221,13222,13225,13226,13229,13230,13247],{},"Z toho plyne, že při ",[614,13223,13224],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,13227,13228],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,13231,13233],{"className":13232},[886],[888,13234,13235],{"xmlns":890},[892,13236,13237,13245],{},[895,13238,13239],{},[1717,13240,13241,13243],{},[898,13242,1701],{},[1693,13244,3672],{},[902,13246,11280],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1636,13249,13250,13255],{},[724,13251,13252,13254],{},[883,13253,8620],{}," Postup: jak klasifikovat poptávku",[152,13256,13257,13284,13287],{},[123,13258,13259,13260,13283],{},"Spočítejte ",[883,13261,13263],{"className":13262},[886],[888,13264,13265],{"xmlns":890},[892,13266,13267,13281],{},[895,13268,13269,13271,13273,13279],{},[898,13270,1691],{},[1693,13272,1709],{"stretchy":1708},[1717,13274,13275,13277],{},[898,13276,1701],{},[1693,13278,3672],{},[1693,13280,1731],{"stretchy":1708},[902,13282,11258],{"encoding":904}," dle (4.5).",[123,13285,13286],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,13288,13289,13290,13314],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,13291,13293],{"className":13292},[886],[888,13294,13295],{"xmlns":890},[892,13296,13297,13311],{},[895,13298,13299,13301,13303,13305,13307,13309],{},[898,13300,1691],{},[1693,13302,1709],{"stretchy":1708},[898,13304,1701],{},[1693,13306,1731],{"stretchy":1708},[1693,13308,1695],{},[1762,13310,1764],{},[902,13312,13313],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,13316,13317,13320,13321,7721,13338,13356,13357,13384,13385,1789],{},[38,13318,13319],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,13322,13324],{"className":13323},[886],[888,13325,13326],{"xmlns":890},[892,13327,13328,13336],{},[895,13329,13330,13332,13334],{},[898,13331,1691],{},[1693,13333,1695],{},[1762,13335,1764],{},[902,13337,4405],{"encoding":904},[883,13339,13341],{"className":13340},[886],[888,13342,13343],{"xmlns":890},[892,13344,13345,13353],{},[895,13346,13347,13349,13351],{},[898,13348,1701],{},[1693,13350,1695],{},[1762,13352,11872],{},[902,13354,13355],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,13358,13360],{"className":13359},[886],[888,13361,13362],{"xmlns":890},[892,13363,13364,13381],{},[895,13365,13366,13368,13371,13373,13375,13377,13379],{},[898,13367,1701],{},[1693,13369,13370],{},"∈",[1693,13372,12192],{"stretchy":1708},[1762,13374,1911],{},[1693,13376,1899],{"separator":1898},[1762,13378,11872],{},[1693,13380,1731],{"stretchy":1708},[902,13382,13383],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,13386,13388],{"className":13387},[886],[888,13389,13390],{"xmlns":890},[892,13391,13392,13408],{},[895,13393,13394,13396,13398,13400,13402,13404,13406],{},[898,13395,1701],{},[1693,13397,13370],{},[1693,13399,1709],{"stretchy":1708},[1762,13401,11872],{},[1693,13403,1899],{"separator":1898},[1762,13405,10017],{},[1693,13407,12209],{"stretchy":1708},[902,13409,13410],{"encoding":904},"P \\in (25, 50\\rangle",[115,13412,13414],{"id":13413},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,13416,13417],{},[9465,13418],{"alt":13419,"className":13420,"src":13421},"imek-elasticita-tr",[210,9469],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,13423,13424],{},[9465,13425],{"alt":13426,"className":13427,"src":13428},"imek-elasticita-podel-linearni-poptavky",[210,9469],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,13430,13431,13432,13482,13483,13498],{},"Pro celkový příjem platí ",[883,13433,13435],{"className":13434},[886],[888,13436,13437],{"xmlns":890},[892,13438,13439,13479],{},[895,13440,13441,13443,13445,13447,13449,13451,13453,13455,13457,13459,13461,13463,13465,13467,13469,13471,13473,13475,13477],{},[898,13442,2663],{},[898,13444,2666],{},[1693,13446,1695],{},[898,13448,2663],{},[898,13450,2666],{},[1693,13452,1709],{"stretchy":1708},[898,13454,1712],{},[1693,13456,1731],{"stretchy":1708},[1693,13458,1695],{},[898,13460,1701],{},[1693,13462,1715],{},[898,13464,1712],{},[1693,13466,1695],{},[898,13468,1712],{},[1693,13470,1715],{},[898,13472,2738],{},[1693,13474,1709],{"stretchy":1708},[898,13476,1712],{},[1693,13478,1731],{"stretchy":1708},[902,13480,13481],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,13484,13486],{"className":13485},[886],[888,13487,13488],{"xmlns":890},[892,13489,13490,13496],{},[895,13491,13492,13494],{},[898,13493,2839],{},[898,13495,2666],{},[902,13497,2919],{"encoding":904}," odvodíme:",[724,13500,13501],{},[883,13502,13504],{"className":13503},[886],[888,13505,13506],{"xmlns":890},[892,13507,13508,13616],{},[895,13509,13510,13512,13514,13516,13518,13524,13526,13528,13530,13532,13534,13536,13538,13540,13542,13544,13546,13552,13554,13556,13558,13560,13562,13564,13566,13580,13582,13584],{},[898,13511,2839],{},[898,13513,2666],{},[1693,13515,1695],{},[898,13517,2663],{},[1717,13519,13520,13522],{},[898,13521,2666],{},[1693,13523,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,13525,1709],{"stretchy":1708},[898,13527,1712],{},[1693,13529,1731],{"stretchy":1708},[1693,13531,1695],{},[898,13533,2738],{},[1693,13535,1709],{"stretchy":1708},[898,13537,1712],{},[1693,13539,1731],{"stretchy":1708},[1693,13541,1892],{},[898,13543,1712],{},[1915,13545,2239],{},[1717,13547,13548,13550],{},[898,13549,2738],{},[1693,13551,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,13553,1709],{"stretchy":1708},[898,13555,1712],{},[1693,13557,1731],{"stretchy":1708},[1693,13559,1695],{},[898,13561,1701],{},[1693,13563,1892],{},[898,13565,1712],{},[2132,13567,13568,13574],{},[895,13569,13570,13572],{},[898,13571,1771],{"mathvariant":1704},[898,13573,1701],{},[895,13575,13576,13578],{},[898,13577,1771],{"mathvariant":1704},[898,13579,1712],{},[1693,13581,1695],{},[898,13583,1701],{},[895,13585,13586,13588,13590,13592,13598,13600,13614],{},[1693,13587,1709],{"fence":1898},[1762,13589,1764],{},[1693,13591,1892],{},[2132,13593,13594,13596],{},[898,13595,1712],{},[898,13597,1701],{},[1693,13599,1715],{},[2132,13601,13602,13608],{},[895,13603,13604,13606],{},[898,13605,1771],{"mathvariant":1704},[898,13607,1701],{},[895,13609,13610,13612],{},[898,13611,1771],{"mathvariant":1704},[898,13613,1712],{},[1693,13615,1731],{"fence":1898},[902,13617,13618],{"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)",[724,13620,13621],{},[883,13622,13624],{"className":13623},[886],[888,13625,13626],{"xmlns":890},[892,13627,13628,13700],{},[895,13629,13630,13632,13634,13676,13678,13680],{},[1693,13631,1695],{},[898,13633,1701],{},[895,13635,13636,13638,13640,13642,13674],{},[1693,13637,1709],{"fence":1898},[1762,13639,1764],{},[1693,13641,1892],{},[2132,13643,13644,13646],{},[1762,13645,1764],{},[895,13647,13648,13656,13658],{},[3638,13649,13650],{"scriptlevel":1911,"displaystyle":1708},[2132,13651,13652,13654],{},[898,13653,1701],{},[898,13655,1712],{},[1693,13657,1715],{},[3638,13659,13660],{"scriptlevel":1911,"displaystyle":1708},[2132,13661,13662,13668],{},[895,13663,13664,13666],{},[898,13665,1771],{"mathvariant":1704},[898,13667,1712],{},[895,13669,13670,13672],{},[898,13671,1771],{"mathvariant":1704},[898,13673,1701],{},[1693,13675,1731],{"fence":1898},[1693,13677,1695],{},[898,13679,1701],{},[895,13681,13682,13684,13686,13688,13698],{},[1693,13683,1709],{"fence":1898},[1762,13685,1764],{},[1693,13687,1892],{},[2132,13689,13690,13692],{},[1762,13691,1764],{},[895,13693,13694,13696],{},[1693,13695,1698],{},[898,13697,1691],{},[1693,13699,1731],{"fence":1898},[902,13701,13702],{"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)",[724,13704,13705],{},"a tedy",[724,13707,13708],{},[883,13709,13711],{"className":13710,"title":11080,"style":11081},[11079],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1636,13713,13714,13783,14030],{},[724,13715,13716,13718,13719,13753,13754,13769,13770,4300],{},[883,13717,11036],{}," Intuice: vztah ",[883,13720,13722],{"className":13721},[886],[888,13723,13724],{"xmlns":890},[892,13725,13726,13750],{},[895,13727,13728,13730,13732,13734,13736,13738,13740,13742,13744,13746,13748],{},[898,13729,2839],{},[898,13731,2666],{},[1693,13733,1695],{},[898,13735,1701],{},[1693,13737,1709],{"stretchy":1708},[1762,13739,1764],{},[1693,13741,1698],{},[1762,13743,1764],{},[898,13745,1705],{"mathvariant":1704},[898,13747,1691],{},[1693,13749,1731],{"stretchy":1708},[902,13751,13752],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,13755,13757],{"className":13756},[886],[888,13758,13759],{"xmlns":890},[892,13760,13761,13767],{},[895,13762,13763,13765],{},[898,13764,2839],{},[898,13766,2666],{},[902,13768,2919],{"encoding":904}," jednoznačně určuje hodnota ",[883,13771,13773],{"className":13772},[886],[888,13774,13775],{"xmlns":890},[892,13776,13777,13781],{},[895,13778,13779],{},[898,13780,1691],{},[902,13782,1691],{"encoding":904},[120,13784,13785,13894,13962],{},[123,13786,13787,13804,13805,1863,13819,1863,13845,1863,13858,13877,13878,13893],{},[883,13788,13790],{"className":13789},[886],[888,13791,13792],{"xmlns":890},[892,13793,13794,13802],{},[895,13795,13796,13798,13800],{},[898,13797,1691],{},[1693,13799,1922],{},[1762,13801,1764],{},[902,13803,4322],{"encoding":904}," (elastická) ",[883,13806,13808],{"className":13807},[886],[888,13809,13810],{"xmlns":890},[892,13811,13812,13816],{},[895,13813,13814],{},[1693,13815,10870],{},[902,13817,13818],{"encoding":904},"\\Rightarrow",[883,13820,13822],{"className":13821},[886],[888,13823,13824],{"xmlns":890},[892,13825,13826,13842],{},[895,13827,13828,13830,13832,13834,13836,13838,13840],{},[1762,13829,1764],{},[1693,13831,1698],{},[1762,13833,1764],{},[898,13835,1705],{"mathvariant":1704},[898,13837,1691],{},[1693,13839,1922],{},[1762,13841,1911],{},[902,13843,13844],{"encoding":904},"1 - 1\u002FE > 0",[883,13846,13848],{"className":13847},[886],[888,13849,13850],{"xmlns":890},[892,13851,13852,13856],{},[895,13853,13854],{},[1693,13855,10870],{},[902,13857,13818],{"encoding":904},[883,13859,13861],{"className":13860},[886],[888,13862,13863],{"xmlns":890},[892,13864,13865,13875],{},[895,13866,13867,13869,13871,13873],{},[898,13868,2839],{},[898,13870,2666],{},[1693,13872,1922],{},[1762,13874,1911],{},[902,13876,4343],{"encoding":904}," — ",[883,13879,13881],{"className":13880},[886],[888,13882,13883],{"xmlns":890},[892,13884,13885,13891],{},[895,13886,13887,13889],{},[898,13888,2663],{},[898,13890,2666],{},[902,13892,2883],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,13895,13896,13913,13914,1863,13927,13877,13946,13961],{},[883,13897,13899],{"className":13898},[886],[888,13900,13901],{"xmlns":890},[892,13902,13903,13911],{},[895,13904,13905,13907,13909],{},[898,13906,1691],{},[1693,13908,1695],{},[1762,13910,1764],{},[902,13912,4405],{"encoding":904}," (jednotková) ",[883,13915,13917],{"className":13916},[886],[888,13918,13919],{"xmlns":890},[892,13920,13921,13925],{},[895,13922,13923],{},[1693,13924,10870],{},[902,13926,13818],{"encoding":904},[883,13928,13930],{"className":13929},[886],[888,13931,13932],{"xmlns":890},[892,13933,13934,13944],{},[895,13935,13936,13938,13940,13942],{},[898,13937,2839],{},[898,13939,2666],{},[1693,13941,1695],{},[1762,13943,1911],{},[902,13945,4425],{"encoding":904},[883,13947,13949],{"className":13948},[886],[888,13950,13951],{"xmlns":890},[892,13952,13953,13959],{},[895,13954,13955,13957],{},[898,13956,2663],{},[898,13958,2666],{},[902,13960,2883],{"encoding":904}," je extrém (maximum).",[123,13963,13964,13981,13982,1863,13995,13877,14014,14029],{},[883,13965,13967],{"className":13966},[886],[888,13968,13969],{"xmlns":890},[892,13970,13971,13979],{},[895,13972,13973,13975,13977],{},[898,13974,1691],{},[1693,13976,1908],{},[1762,13978,1764],{},[902,13980,4364],{"encoding":904}," (neelastická) ",[883,13983,13985],{"className":13984},[886],[888,13986,13987],{"xmlns":890},[892,13988,13989,13993],{},[895,13990,13991],{},[1693,13992,10870],{},[902,13994,13818],{"encoding":904},[883,13996,13998],{"className":13997},[886],[888,13999,14000],{"xmlns":890},[892,14001,14002,14012],{},[895,14003,14004,14006,14008,14010],{},[898,14005,2839],{},[898,14007,2666],{},[1693,14009,1908],{},[1762,14011,1911],{},[902,14013,4384],{"encoding":904},[883,14015,14017],{"className":14016},[886],[888,14018,14019],{"xmlns":890},[892,14020,14021,14027],{},[895,14022,14023,14025],{},[898,14024,2663],{},[898,14026,2666],{},[902,14028,2883],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,14031,14032,14033,1789],{},"Viz také ",[207,14034,3261],{"className":14035,"dataFsResolvedFilePath":827,"href":828},[210],[198,14037,14039],{"id":14038},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,14041,14042,14062,14063,14089,14090,14105,14106,14119,14120,14133,14134,14147,14148,14164,14165,1863,14180,14183,14184,14164,14200,1789],{},[38,14043,14044,14045,3042],{},"(a) Poptávka elastická (",[883,14046,14048],{"className":14047},[886],[888,14049,14050],{"xmlns":890},[892,14051,14052,14060],{},[895,14053,14054,14056,14058],{},[898,14055,1691],{},[1693,14057,1922],{},[1762,14059,1764],{},[902,14061,4322],{"encoding":904}," Z (4.12) plyne ",[883,14064,14066],{"className":14065},[886],[888,14067,14068],{"xmlns":890},[892,14069,14070,14086],{},[895,14071,14072,14074,14076,14078,14080,14082,14084],{},[898,14073,2839],{},[898,14075,2666],{},[1693,14077,1709],{"stretchy":1708},[898,14079,1712],{},[1693,14081,1731],{"stretchy":1708},[1693,14083,1922],{},[1762,14085,1911],{},[902,14087,14088],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,14091,14093],{"className":14092},[886],[888,14094,14095],{"xmlns":890},[892,14096,14097,14103],{},[895,14098,14099,14101],{},[898,14100,2663],{},[898,14102,2666],{},[902,14104,2883],{"encoding":904}," je rostoucí funkcí ",[883,14107,14109],{"className":14108},[886],[888,14110,14111],{"xmlns":890},[892,14112,14113,14117],{},[895,14114,14115],{},[898,14116,1712],{},[902,14118,1712],{"encoding":904},". Avšak růst ",[883,14121,14123],{"className":14122},[886],[888,14124,14125],{"xmlns":890},[892,14126,14127,14131],{},[895,14128,14129],{},[898,14130,1712],{},[902,14132,1712],{"encoding":904}," je odezvou na pokles ceny ",[883,14135,14137],{"className":14136},[886],[888,14138,14139],{"xmlns":890},[892,14140,14141,14145],{},[895,14142,14143],{},[898,14144,1701],{},[902,14146,1701],{"encoding":904},". Tudíž s ",[614,14149,14150,14151],{},"poklesem ceny ",[883,14152,14154],{"className":14153},[886],[888,14155,14156],{"xmlns":890},[892,14157,14158,14162],{},[895,14159,14160],{},[898,14161,1701],{},[902,14163,1701],{"encoding":904}," celkový příjem ",[883,14166,14168],{"className":14167},[886],[888,14169,14170],{"xmlns":890},[892,14171,14172,14178],{},[895,14173,14174,14176],{},[898,14175,2663],{},[898,14177,2666],{},[902,14179,2883],{"encoding":904},[614,14181,14182],{},"roste"," a s ",[614,14185,14186,14187],{},"růstem ceny ",[883,14188,14190],{"className":14189},[886],[888,14191,14192],{"xmlns":890},[892,14193,14194,14198],{},[895,14195,14196],{},[898,14197,1701],{},[902,14199,1701],{"encoding":904},[614,14201,14202],{},"klesá",[1636,14204,14205],{},[724,14206,14207,14210],{},[38,14208,14209],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,14212,14213,14062,14233,1343,14259,14274,14275,14288,14289,14302,14303,14316,14317,14164,14330,1863,14345,1789],{},[38,14214,14215,14216,3042],{},"(b) Poptávka neelastická (",[883,14217,14219],{"className":14218},[886],[888,14220,14221],{"xmlns":890},[892,14222,14223,14231],{},[895,14224,14225,14227,14229],{},[898,14226,1691],{},[1693,14228,1908],{},[1762,14230,1764],{},[902,14232,4364],{"encoding":904},[883,14234,14236],{"className":14235},[886],[888,14237,14238],{"xmlns":890},[892,14239,14240,14256],{},[895,14241,14242,14244,14246,14248,14250,14252,14254],{},[898,14243,2839],{},[898,14245,2666],{},[1693,14247,1709],{"stretchy":1708},[898,14249,1712],{},[1693,14251,1731],{"stretchy":1708},[1693,14253,1908],{},[1762,14255,1911],{},[902,14257,14258],{"encoding":904},"MR(Q) \u003C 0",[883,14260,14262],{"className":14261},[886],[888,14263,14264],{"xmlns":890},[892,14265,14266,14272],{},[895,14267,14268,14270],{},[898,14269,2663],{},[898,14271,2666],{},[902,14273,2883],{"encoding":904}," je klesající funkce ",[883,14276,14278],{"className":14277},[886],[888,14279,14280],{"xmlns":890},[892,14281,14282,14286],{},[895,14283,14284],{},[898,14285,1712],{},[902,14287,1712],{"encoding":904},", tj. s růstem ",[883,14290,14292],{"className":14291},[886],[888,14293,14294],{"xmlns":890},[892,14295,14296,14300],{},[895,14297,14298],{},[898,14299,1712],{},[902,14301,1712],{"encoding":904}," (s poklesem ceny ",[883,14304,14306],{"className":14305},[886],[888,14307,14308],{"xmlns":890},[892,14309,14310,14314],{},[895,14311,14312],{},[898,14313,1701],{},[902,14315,1701],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,14318,14320],{"className":14319},[886],[888,14321,14322],{"xmlns":890},[892,14323,14324,14328],{},[895,14325,14326],{},[898,14327,1701],{},[902,14329,1701],{"encoding":904},[883,14331,14333],{"className":14332},[886],[888,14334,14335],{"xmlns":890},[892,14336,14337,14343],{},[895,14338,14339,14341],{},[898,14340,2663],{},[898,14342,2666],{},[902,14344,2883],{"encoding":904},[614,14346,14182],{},[1636,14348,14349],{},[724,14350,14351,14354],{},[38,14352,14353],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,14356,14357,14062,14377,14396,14397,14412,14413,14483,14484,4286,14512,14545,14546,12457,14574,14589,14590,1789],{},[38,14358,14359,14360,3042],{},"(c) Jednotková elasticita (",[883,14361,14363],{"className":14362},[886],[888,14364,14365],{"xmlns":890},[892,14366,14367,14375],{},[895,14368,14369,14371,14373],{},[898,14370,1691],{},[1693,14372,1695],{},[1762,14374,1764],{},[902,14376,4405],{"encoding":904},[883,14378,14380],{"className":14379},[886],[888,14381,14382],{"xmlns":890},[892,14383,14384,14394],{},[895,14385,14386,14388,14390,14392],{},[898,14387,2839],{},[898,14389,2666],{},[1693,14391,1695],{},[1762,14393,1911],{},[902,14395,4425],{"encoding":904}," — nutná podmínka extrému ",[883,14398,14400],{"className":14399},[886],[888,14401,14402],{"xmlns":890},[892,14403,14404,14410],{},[895,14405,14406,14408],{},[898,14407,2663],{},[898,14409,2666],{},[902,14411,2883],{"encoding":904},". Dále ",[883,14414,14416],{"className":14415},[886],[888,14417,14418],{"xmlns":890},[892,14419,14420,14480],{},[895,14421,14422,14424,14434,14436,14438,14444,14446,14452,14454,14456,14458,14460,14462,14464,14474,14476,14478],{},[898,14423,2663],{},[1717,14425,14426,14428],{},[898,14427,2666],{},[895,14429,14430,14432],{},[1693,14431,1724],{"mathvariant":1704},[1693,14433,1724],{"mathvariant":1704},[1693,14435,1695],{},[898,14437,2839],{},[1717,14439,14440,14442],{},[898,14441,2666],{},[1693,14443,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,14445,1695],{},[1717,14447,14448,14450],{},[898,14449,2738],{},[1693,14451,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,14453,1709],{"stretchy":1708},[898,14455,1712],{},[1693,14457,1731],{"stretchy":1708},[1693,14459,1892],{},[898,14461,1712],{},[1915,14463,2239],{},[1717,14465,14466,14468],{},[898,14467,2738],{},[895,14469,14470,14472],{},[1693,14471,1724],{"mathvariant":1704},[1693,14473,1724],{"mathvariant":1704},[1693,14475,1709],{"stretchy":1708},[898,14477,1712],{},[1693,14479,1731],{"stretchy":1708},[902,14481,14482],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,14485,14487],{"className":14486},[886],[888,14488,14489],{"xmlns":890},[892,14490,14491,14509],{},[895,14492,14493,14499,14501,14503,14505,14507],{},[1717,14494,14495,14497],{},[898,14496,2738],{},[1693,14498,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,14500,1709],{"stretchy":1708},[898,14502,1712],{},[1693,14504,1731],{"stretchy":1708},[1693,14506,1908],{},[1762,14508,1911],{},[902,14510,14511],{"encoding":904},"D'(Q) \u003C 0",[883,14513,14515],{"className":14514},[886],[888,14516,14517],{"xmlns":890},[892,14518,14519,14542],{},[895,14520,14521,14531,14533,14535,14537,14540],{},[1717,14522,14523,14525],{},[898,14524,2738],{},[895,14526,14527,14529],{},[1693,14528,1724],{"mathvariant":1704},[1693,14530,1724],{"mathvariant":1704},[1693,14532,1709],{"stretchy":1708},[898,14534,1712],{},[1693,14536,1731],{"stretchy":1708},[1693,14538,14539],{},"≤",[1762,14541,1911],{},[902,14543,14544],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,14547,14549],{"className":14548},[886],[888,14550,14551],{"xmlns":890},[892,14552,14553,14571],{},[895,14554,14555,14557,14567,14569],{},[898,14556,2663],{},[1717,14558,14559,14561],{},[898,14560,2666],{},[895,14562,14563,14565],{},[1693,14564,1724],{"mathvariant":1704},[1693,14566,1724],{"mathvariant":1704},[1693,14568,1908],{},[1762,14570,1911],{},[902,14572,14573],{"encoding":904},"TR'' \u003C 0",[883,14575,14577],{"className":14576},[886],[888,14578,14579],{"xmlns":890},[892,14580,14581,14587],{},[895,14582,14583,14585],{},[898,14584,2663],{},[898,14586,2666],{},[902,14588,2883],{"encoding":904}," nabývá ",[38,14591,14592],{},"maxima",[1636,14594,14595],{},[724,14596,14597,14600],{},[38,14598,14599],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,14602,14603],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,14605,14606],{},[38,14607,14608],{},"Souhrnná tabulka Pravidel 1–3:",[16,14610,14611,14715],{},[19,14612,14613],{},[22,14614,14615,14618,14633,14650,14681,14712],{},[25,14616,14617],{},"Charakter poptávky",[25,14619,14620],{},[883,14621,14623],{"className":14622},[886],[888,14624,14625],{"xmlns":890},[892,14626,14627,14631],{},[895,14628,14629],{},[898,14630,1691],{},[902,14632,1691],{"encoding":904},[25,14634,14635],{},[883,14636,14638],{"className":14637},[886],[888,14639,14640],{"xmlns":890},[892,14641,14642,14648],{},[895,14643,14644,14646],{},[898,14645,2839],{},[898,14647,2666],{},[902,14649,2919],{"encoding":904},[25,14651,14652,14653,1863,14666],{},"Pokles ceny ",[883,14654,14656],{"className":14655},[886],[888,14657,14658],{"xmlns":890},[892,14659,14660,14664],{},[895,14661,14662],{},[1693,14663,10870],{},[902,14665,13818],{"encoding":904},[883,14667,14669],{"className":14668},[886],[888,14670,14671],{"xmlns":890},[892,14672,14673,14679],{},[895,14674,14675,14677],{},[898,14676,2663],{},[898,14678,2666],{},[902,14680,2883],{"encoding":904},[25,14682,14683,14684,1863,14697],{},"Růst ceny ",[883,14685,14687],{"className":14686},[886],[888,14688,14689],{"xmlns":890},[892,14690,14691,14695],{},[895,14692,14693],{},[1693,14694,10870],{},[902,14696,13818],{"encoding":904},[883,14698,14700],{"className":14699},[886],[888,14701,14702],{"xmlns":890},[892,14703,14704,14710],{},[895,14705,14706,14708],{},[898,14707,2663],{},[898,14709,2666],{},[902,14711,2883],{"encoding":904},[25,14713,14714],{},"Doporučení",[30,14716,14717,14766,14816],{},[22,14718,14719,14721,14739,14757,14759,14761],{},[35,14720,10955],{},[35,14722,14723],{},[883,14724,14726],{"className":14725},[886],[888,14727,14728],{"xmlns":890},[892,14729,14730,14736],{},[895,14731,14732,14734],{},[1693,14733,1922],{},[1762,14735,1764],{},[902,14737,14738],{"encoding":904},"> 1",[35,14740,14741],{},[883,14742,14744],{"className":14743},[886],[888,14745,14746],{"xmlns":890},[892,14747,14748,14754],{},[895,14749,14750,14752],{},[1693,14751,1922],{},[1762,14753,1911],{},[902,14755,14756],{"encoding":904},"> 0",[35,14758,14182],{},[35,14760,14202],{},[35,14762,14763],{},[38,14764,14765],{},"snížit cenu",[22,14767,14768,14771,14789,14807,14809,14811],{},[35,14769,14770],{},"jednotková",[35,14772,14773],{},[883,14774,14776],{"className":14775},[886],[888,14777,14778],{"xmlns":890},[892,14779,14780,14786],{},[895,14781,14782,14784],{},[1693,14783,1695],{},[1762,14785,1764],{},[902,14787,14788],{"encoding":904},"= 1",[35,14790,14791],{},[883,14792,14794],{"className":14793},[886],[888,14795,14796],{"xmlns":890},[892,14797,14798,14804],{},[895,14799,14800,14802],{},[1693,14801,1695],{},[1762,14803,1911],{},[902,14805,14806],{"encoding":904},"= 0",[35,14808,10610],{},[35,14810,10610],{},[35,14812,14813],{},[38,14814,14815],{},"držet cenu",[22,14817,14818,14820,14838,14856,14858,14860],{},[35,14819,10959],{},[35,14821,14822],{},[883,14823,14825],{"className":14824},[886],[888,14826,14827],{"xmlns":890},[892,14828,14829,14835],{},[895,14830,14831,14833],{},[1693,14832,1908],{},[1762,14834,1764],{},[902,14836,14837],{"encoding":904},"\u003C 1",[35,14839,14840],{},[883,14841,14843],{"className":14842},[886],[888,14844,14845],{"xmlns":890},[892,14846,14847,14853],{},[895,14848,14849,14851],{},[1693,14850,1908],{},[1762,14852,1911],{},[902,14854,14855],{"encoding":904},"\u003C 0",[35,14857,14202],{},[35,14859,14182],{},[35,14861,14862],{},[38,14863,14864],{},"zvýšit cenu",[198,14866,14868],{"id":14867},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,14870,14871,14872,14897,14898,14920,14921,14934,14935,14948,14949,6055,14962,12457,14989,15041],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,14873,14875],{"className":14874},[886],[888,14876,14877],{"xmlns":890},[892,14878,14879,14895],{},[895,14880,14881,14883,14885,14887,14889],{},[898,14882,1701],{},[1693,14884,1695],{},[1762,14886,9987],{},[1693,14888,1698],{},[1717,14890,14891,14893],{},[898,14892,1712],{},[1762,14894,2398],{},[902,14896,12327],{"encoding":904},". Reálné cenové rozpětí je ",[883,14899,14901],{"className":14900},[886],[888,14902,14903],{"xmlns":890},[892,14904,14905,14917],{},[895,14906,14907,14909,14911,14913,14915],{},[1693,14908,12192],{"stretchy":1708},[1762,14910,1764],{},[1693,14912,1899],{"separator":1898},[1762,14914,9987],{},[1693,14916,12209],{"stretchy":1708},[902,14918,14919],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,14922,14924],{"className":14923},[886],[888,14925,14926],{"xmlns":890},[892,14927,14928,14932],{},[895,14929,14930],{},[898,14931,1712],{},[902,14933,1712],{"encoding":904}," jako funkci ",[883,14936,14938],{"className":14937},[886],[888,14939,14940],{"xmlns":890},[892,14941,14942,14946],{},[895,14943,14944],{},[898,14945,1701],{},[902,14947,1701],{"encoding":904},"; pro nezáporné ",[883,14950,14952],{"className":14951},[886],[888,14953,14954],{"xmlns":890},[892,14955,14956,14960],{},[895,14957,14958],{},[898,14959,1712],{},[902,14961,1712],{"encoding":904},[883,14963,14965],{"className":14964},[886],[888,14966,14967],{"xmlns":890},[892,14968,14969,14986],{},[895,14970,14971,14973,14975],{},[898,14972,1712],{},[1693,14974,1695],{},[14976,14977,14978],"msqrt",{},[895,14979,14980,14982,14984],{},[1762,14981,9987],{},[1693,14983,1698],{},[898,14985,1701],{},[902,14987,14988],{"encoding":904},"Q = \\sqrt{100 - P}",[883,14990,14992],{"className":14991},[886],[888,14993,14994],{"xmlns":890},[892,14995,14996,15038],{},[895,14997,14998,15014,15016,15018],{},[3638,14999,15000],{"scriptlevel":1911,"displaystyle":1898},[2132,15001,15002,15008],{},[895,15003,15004,15006],{},[898,15005,1771],{"mathvariant":1704},[898,15007,1712],{},[895,15009,15010,15012],{},[898,15011,1771],{"mathvariant":1704},[898,15013,1701],{},[1693,15015,1695],{},[1693,15017,1698],{},[3638,15019,15020],{"scriptlevel":1911,"displaystyle":1898},[2132,15021,15022,15024],{},[1762,15023,1764],{},[895,15025,15026,15028],{},[1762,15027,2398],{},[14976,15029,15030],{},[895,15031,15032,15034,15036],{},[1762,15033,9987],{},[1693,15035,1698],{},[898,15037,1701],{},[902,15039,15040],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,15043,15044],{},[883,15045,15047],{"className":15046},[886],[888,15048,15049],{"xmlns":890},[892,15050,15051,15173],{},[895,15052,15053,15055,15057,15059,15061,15063,15065,15071,15073,15087,15089,15091,15105,15107,15133,15135,15153,15155,15171],{},[898,15054,1691],{},[1693,15056,1709],{"stretchy":1708},[898,15058,1701],{},[1693,15060,1731],{"stretchy":1708},[1693,15062,1695],{},[1693,15064,1698],{},[2132,15066,15067,15069],{},[898,15068,1701],{},[898,15070,1712],{},[1693,15072,1715],{},[2132,15074,15075,15081],{},[895,15076,15077,15079],{},[898,15078,1771],{"mathvariant":1704},[898,15080,1712],{},[895,15082,15083,15085],{},[898,15084,1771],{"mathvariant":1704},[898,15086,1701],{},[1693,15088,1695],{},[1693,15090,1698],{},[2132,15092,15093,15095],{},[898,15094,1701],{},[14976,15096,15097],{},[895,15098,15099,15101,15103],{},[1762,15100,9987],{},[1693,15102,1698],{},[898,15104,1701],{},[1693,15106,1715],{},[895,15108,15109,15111,15113,15131],{},[1693,15110,1709],{"fence":1898},[1693,15112,1698],{},[2132,15114,15115,15117],{},[1762,15116,1764],{},[895,15118,15119,15121],{},[1762,15120,2398],{},[14976,15122,15123],{},[895,15124,15125,15127,15129],{},[1762,15126,9987],{},[1693,15128,1698],{},[898,15130,1701],{},[1693,15132,1731],{"fence":1898},[1693,15134,1695],{},[2132,15136,15137,15139],{},[898,15138,1701],{},[895,15140,15141,15143,15145,15147,15149,15151],{},[1762,15142,2398],{},[1693,15144,1709],{"stretchy":1708},[1762,15146,9987],{},[1693,15148,1698],{},[898,15150,1701],{},[1693,15152,1731],{"stretchy":1708},[1693,15154,1695],{},[2132,15156,15157,15163],{},[895,15158,15159,15161],{},[1762,15160,11877],{},[898,15162,1701],{},[895,15164,15165,15167,15169],{},[1762,15166,9987],{},[1693,15168,1698],{},[898,15170,1701],{},[898,15172,1789],{"mathvariant":1704},[902,15174,15175],{"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}.",[724,15177,15178,15179,4300],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,15180,15182],{"className":15181},[886],[888,15183,15184],{"xmlns":890},[892,15185,15186,15210],{},[895,15187,15188,15206,15208],{},[3638,15189,15190],{"scriptlevel":1911,"displaystyle":1898},[2132,15191,15192,15198],{},[895,15193,15194,15196],{},[1762,15195,11877],{},[898,15197,1701],{},[895,15199,15200,15202,15204],{},[1762,15201,9987],{},[1693,15203,1698],{},[898,15205,1701],{},[1693,15207,1695],{},[1762,15209,1764],{},[902,15211,15212],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,15214,15215],{},[883,15216,15218],{"className":15217},[886],[888,15219,15220],{"xmlns":890},[892,15221,15222,15253],{},[895,15223,15224,15230,15232,15239,15241,15244,15251],{},[1717,15225,15226,15228],{},[898,15227,1701],{},[1693,15229,3672],{},[1693,15231,1695],{},[2132,15233,15234,15237],{},[1762,15235,15236],{},"200",[1762,15238,8357],{},[1693,15240,12766],{},[1762,15242,15243],{},"66,",[4467,15245,15246,15248],{"accent":1898},[1762,15247,9154],{},[1693,15249,15250],{"stretchy":1898},"‾",[898,15252,1789],{"mathvariant":1704},[902,15254,15255],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,15257,15258],{},"S využitím vlastnosti (4.8):",[120,15260,15261,15307,15349],{},[123,15262,15263,15264,15299,15300,15302,15303,15306],{},"Při cenách ",[883,15265,15267],{"className":15266},[886],[888,15268,15269],{"xmlns":890},[892,15270,15271,15296],{},[895,15272,15273,15275,15277,15279,15281,15284,15286,15288,15294],{},[898,15274,1701],{},[1693,15276,13370],{},[1693,15278,12192],{"stretchy":1708},[1762,15280,1764],{},[1693,15282,15283],{"separator":1898},";",[1915,15285,2239],{},[1762,15287,15243],{},[4467,15289,15290,15292],{"accent":1898},[1762,15291,9154],{},[1693,15293,15250],{"stretchy":1898},[1693,15295,1731],{"stretchy":1708},[902,15297,15298],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,15301,10959],{}," — dle ",[614,15304,15305],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,15308,15263,15309,15299,15343,15302,15345,15348],{},[883,15310,15312],{"className":15311},[886],[888,15313,15314],{"xmlns":890},[892,15315,15316,15340],{},[895,15317,15318,15320,15322,15324,15326,15332,15334,15336,15338],{},[898,15319,1701],{},[1693,15321,13370],{},[1693,15323,1709],{"stretchy":1708},[1762,15325,15243],{},[4467,15327,15328,15330],{"accent":1898},[1762,15329,9154],{},[1693,15331,15250],{"stretchy":1898},[1693,15333,15283],{"separator":1898},[1915,15335,2239],{},[1762,15337,9987],{},[1693,15339,12209],{"stretchy":1708},[902,15341,15342],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,15344,10955],{},[614,15346,15347],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,15350,15351,15352,15355,15356,15384,15385,15388],{},"Dle ",[614,15353,15354],{},"Pravidla 3"," je při ceně ",[883,15357,15359],{"className":15358},[886],[888,15360,15361],{"xmlns":890},[892,15362,15363,15381],{},[895,15364,15365,15371,15373,15375],{},[1717,15366,15367,15369],{},[898,15368,1701],{},[1693,15370,3672],{},[1693,15372,1695],{},[1762,15374,15243],{},[4467,15376,15377,15379],{"accent":1898},[1762,15378,9154],{},[1693,15380,15250],{"stretchy":1898},[902,15382,15383],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,15386,15387],{},"maxima celkového příjmu"," ve výši",[724,15390,15391],{},[883,15392,15394],{"className":15393},[886],[888,15395,15396],{"xmlns":890},[892,15397,15398,15476],{},[895,15399,15400,15402,15404,15406,15412,15414,15416,15422,15424,15438,15440,15446,15448,15456,15458,15471,15473],{},[898,15401,2663],{},[898,15403,2666],{},[1693,15405,1709],{"stretchy":1708},[1717,15407,15408,15410],{},[898,15409,1701],{},[1693,15411,3672],{},[1693,15413,1731],{"stretchy":1708},[1693,15415,1695],{},[1717,15417,15418,15420],{},[898,15419,1701],{},[1693,15421,3672],{},[1693,15423,1715],{},[14976,15425,15426],{},[895,15427,15428,15430,15432],{},[1762,15429,9987],{},[1693,15431,1698],{},[1717,15433,15434,15436],{},[898,15435,1701],{},[1693,15437,3672],{},[1693,15439,1695],{},[2132,15441,15442,15444],{},[1762,15443,15236],{},[1762,15445,8357],{},[1693,15447,1715],{},[14976,15449,15450],{},[2132,15451,15452,15454],{},[1762,15453,9987],{},[1762,15455,8357],{},[1693,15457,1695],{},[2132,15459,15460,15463],{},[1762,15461,15462],{},"2000",[895,15464,15465,15467],{},[1762,15466,8357],{},[14976,15468,15469],{},[1762,15470,8357],{},[1693,15472,12766],{},[1762,15474,15475],{},"384,9.",[902,15477,15478],{"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.",[724,15480,15481,15482,1789],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,15483,15485],{"className":15484},[886],[888,15486,15487],{"xmlns":890},[892,15488,15489,15495],{},[895,15490,15491,15493],{},[898,15492,2663],{},[898,15494,2666],{},[902,15496,2883],{"encoding":904},[115,15498,15500],{"id":15499},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,15502,15503,15504,15507],{},"Analogicky se definuje ",[38,15505,15506],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,15509,15510],{},[883,15511,15513],{"className":15512,"title":11080,"style":11081},[11079],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,15515,11188,15516,15540,15541,15573],{},[883,15517,15519],{"className":15518},[886],[888,15520,15521],{"xmlns":890},[892,15522,15523,15537],{},[895,15524,15525,15527,15529,15531,15533,15535],{},[898,15526,1712],{},[1693,15528,1695],{},[898,15530,3611],{},[1693,15532,1709],{"stretchy":1708},[898,15534,1701],{},[1693,15536,1731],{"stretchy":1708},[902,15538,15539],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,15542,15544],{"className":15543},[886],[888,15545,15546],{"xmlns":890},[892,15547,15548,15570],{},[895,15549,15550,15566,15568],{},[3638,15551,15552],{"scriptlevel":1911,"displaystyle":1898},[2132,15553,15554,15560],{},[895,15555,15556,15558],{},[898,15557,1771],{"mathvariant":1704},[898,15559,1712],{},[895,15561,15562,15564],{},[898,15563,1771],{"mathvariant":1704},[898,15565,1701],{},[1693,15567,1922],{},[1762,15569,1911],{},[902,15571,15572],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,15575,15576],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1636,15578,15579],{},[724,15580,15581,15582],{},"S rostoucí cenou elasticita nabídky roste. ",[883,15583,15585],{"className":15584},[886],[888,15586,15587],{"xmlns":890},[892,15588,15589,15598],{},[895,15590,15591,15593,15596],{},[1693,15592,1709],{"stretchy":1708},[1762,15594,15595],{},"4.14",[1693,15597,1731],{"stretchy":1708},[902,15599,15600],{"encoding":904},"(4.14)",[724,15602,15603],{},"Pro nominální změny platí",[724,15605,15606],{},[883,15607,15609],{"className":15608,"title":11080,"style":11081},[11079],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,15611,15612],{},"a pro procentní změny",[724,15614,15615],{},[883,15616,15618],{"className":15617,"title":11080,"style":11081},[11079],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,15620,15621],{},"(bez znaménka minus).",[198,15623,15625],{"id":15624},"příklad-47","Příklad 4.7",[724,15627,15628,15629,4300],{},"Nabídka ",[883,15630,15632],{"className":15631},[886],[888,15633,15634],{"xmlns":890},[892,15635,15636,15661],{},[895,15637,15638,15640,15642,15644,15650,15652,15654,15656,15658],{},[898,15639,1712],{},[1693,15641,1695],{},[1762,15643,9695],{},[1717,15645,15646,15648],{},[898,15647,1701],{},[1762,15649,2398],{},[1693,15651,1892],{},[1762,15653,9147],{},[898,15655,1701],{},[1693,15657,1892],{},[1762,15659,15660],{},"150",[902,15662,15663],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,15665,15666],{},[883,15667,15669],{"className":15668},[886],[888,15670,15671],{"xmlns":890},[892,15672,15673,15719],{},[895,15674,15675,15677,15679,15703,15705,15707,15709,15711,15713,15715,15717],{},[898,15676,1691],{},[1693,15678,1695],{},[2132,15680,15681,15683],{},[898,15682,1701],{},[895,15684,15685,15687,15693,15695,15697,15699,15701],{},[1762,15686,9695],{},[1717,15688,15689,15691],{},[898,15690,1701],{},[1762,15692,2398],{},[1693,15694,1892],{},[1762,15696,9147],{},[898,15698,1701],{},[1693,15700,1892],{},[1762,15702,15660],{},[1915,15704,2239],{},[1693,15706,1709],{"stretchy":1708},[1762,15708,9739],{},[898,15710,1701],{},[1693,15712,1892],{},[1762,15714,9147],{},[1693,15716,1731],{"stretchy":1708},[898,15718,1789],{"mathvariant":1704},[902,15720,15721],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,15723,11985,15724,1343,15754,1343,15781,15817,15818,15843,15844,15862,15863,1789],{},[883,15725,15727],{"className":15726},[886],[888,15728,15729],{"xmlns":890},[892,15730,15731,15751],{},[895,15732,15733,15735,15737,15739,15741,15743],{},[898,15734,1691],{},[1693,15736,1709],{"stretchy":1708},[1762,15738,9763],{},[1693,15740,1731],{"stretchy":1708},[1693,15742,1695],{},[3638,15744,15745],{"scriptlevel":1911,"displaystyle":1708},[2132,15746,15747,15749],{},[1762,15748,1764],{},[1762,15750,8357],{},[902,15752,15753],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,15755,15757],{"className":15756},[886],[888,15758,15759],{"xmlns":890},[892,15760,15761,15778],{},[895,15762,15763,15765,15767,15772,15774,15776],{},[898,15764,1691],{},[1693,15766,1709],{"stretchy":1708},[14976,15768,15769],{},[1762,15770,15771],{},"1500",[1693,15773,1731],{"stretchy":1708},[1693,15775,1695],{},[1762,15777,1764],{},[902,15779,15780],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,15782,15784],{"className":15783},[886],[888,15785,15786],{"xmlns":890},[892,15787,15788,15814],{},[895,15789,15790,15792,15794,15796,15798,15800,15809,15811],{},[898,15791,1691],{},[1693,15793,1709],{"stretchy":1708},[1762,15795,9987],{},[1693,15797,1731],{"stretchy":1708},[1693,15799,1695],{},[3638,15801,15802],{"scriptlevel":1911,"displaystyle":1708},[2132,15803,15804,15806],{},[1762,15805,10017],{},[1762,15807,15808],{},"33",[1693,15810,12766],{},[1762,15812,15813],{},"1,515",[902,15815,15816],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,15819,15821],{"className":15820},[886],[888,15822,15823],{"xmlns":890},[892,15824,15825,15840],{},[895,15826,15827,15829,15831,15835,15837],{},[898,15828,1701],{},[1693,15830,1922],{},[14976,15832,15833],{},[1762,15834,15771],{},[1693,15836,4110],{},[1762,15838,15839],{},"38,7",[902,15841,15842],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,15845,15847],{"className":15846},[886],[888,15848,15849],{"xmlns":890},[892,15850,15851,15859],{},[895,15852,15853,15855,15857],{},[898,15854,1701],{},[1693,15856,1908],{},[1762,15858,15839],{},[902,15860,15861],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,15864,15866],{"className":15865},[886],[888,15867,15868],{"xmlns":890},[892,15869,15870,15908],{},[895,15871,15872,15874,15876,15878,15880,15888,15890,15893,15895,15898,15904,15906],{},[898,15873,3890],{"mathvariant":1704},[898,15875,1712],{},[898,15877,3895],{"mathvariant":1704},[1693,15879,4110],{},[3638,15881,15882],{"scriptlevel":1911,"displaystyle":1708},[2132,15883,15884,15886],{},[1762,15885,1764],{},[1762,15887,8357],{},[1693,15889,1715],{},[1762,15891,15892],{},"20",[1693,15894,1695],{},[1762,15896,15897],{},"6,",[4467,15899,15900,15902],{"accent":1898},[1762,15901,9154],{},[1693,15903,15250],{"stretchy":1898},[1915,15905,2239],{},[898,15907,3895],{"mathvariant":1704},[902,15909,15910],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,15912,15914],{"id":15913},"vícefaktorový-model","Vícefaktorový model",[724,15916,15917,15918,15931,15932,1863,15935,15948,15949,1863,15952,15970,15971,1863,15974,4300],{},"Předpokládejme, že poptávané množství ",[883,15919,15921],{"className":15920},[886],[888,15922,15923],{"xmlns":890},[892,15924,15925,15929],{},[895,15926,15927],{},[898,15928,1712],{},[902,15930,1712],{"encoding":904}," závisí na ",[38,15933,15934],{},"ceně základního zboží",[883,15936,15938],{"className":15937},[886],[888,15939,15940],{"xmlns":890},[892,15941,15942,15946],{},[895,15943,15944],{},[898,15945,1701],{},[902,15947,1701],{"encoding":904},", na ",[38,15950,15951],{},"ceně alternativního zboží",[883,15953,15955],{"className":15954},[886],[888,15956,15957],{"xmlns":890},[892,15958,15959,15967],{},[895,15960,15961],{},[3284,15962,15963,15965],{},[898,15964,1701],{},[898,15966,2719],{},[902,15968,15969],{"encoding":904},"P_A"," a na ",[38,15972,15973],{},"důchodu",[883,15975,15977],{"className":15976},[886],[888,15978,15979],{"xmlns":890},[892,15980,15981,15985],{},[895,15982,15983],{},[898,15984,4618],{},[902,15986,4618],{"encoding":904},[724,15988,15989],{},[883,15990,15992],{"className":15991,"title":11080,"style":11081},[11079],"Q = D(P, P_A, Y). \\tag{4.17}",[724,15994,15995,15996,15999],{},"V analogii jednofaktorového modelu pracujeme s ",[38,15997,15998],{},"parciálními derivacemi"," funkce poptávky.",[198,16001,16003],{"id":16002},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,16005,16006],{},[883,16007,16009],{"className":16008,"title":11080,"style":11081},[11079],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,16011,11188,16012,16032,16033,16046,16047,7617,16069,1863,16072,16118,16119,16132,16133,16150],{},[883,16013,16015],{"className":16014},[886],[888,16016,16017],{"xmlns":890},[892,16018,16019,16029],{},[895,16020,16021],{},[5688,16022,16023,16025,16027],{},[898,16024,1712],{},[898,16026,1701],{},[1693,16028,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,16030,16031],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,16034,16036],{"className":16035},[886],[888,16037,16038],{"xmlns":890},[892,16039,16040,16044],{},[895,16041,16042],{},[898,16043,1701],{},[902,16045,1701],{"encoding":904},". Vždy ",[883,16048,16050],{"className":16049},[886],[888,16051,16052],{"xmlns":890},[892,16053,16054,16066],{},[895,16055,16056,16062,16064],{},[3284,16057,16058,16060],{},[898,16059,1691],{},[898,16061,1701],{},[1693,16063,3665],{},[1762,16065,1911],{},[902,16067,16068],{"encoding":904},"E_P \\ge 0",[614,16070,16071],{},"Interpretace:",[883,16073,16075],{"className":16074},[886],[888,16076,16077],{"xmlns":890},[892,16078,16079,16115],{},[895,16080,16081,16087,16089,16095,16097,16105,16107,16113],{},[3284,16082,16083,16085],{},[898,16084,1691],{},[898,16086,1701],{},[1693,16088,1709],{"stretchy":1708},[1717,16090,16091,16093],{},[898,16092,1701],{},[1693,16094,3672],{},[1693,16096,1899],{"separator":1898},[5688,16098,16099,16101,16103],{},[898,16100,1701],{},[898,16102,2719],{},[1693,16104,3672],{},[1693,16106,1899],{"separator":1898},[1717,16108,16109,16111],{},[898,16110,4618],{},[1693,16112,3672],{},[1693,16114,1731],{"stretchy":1708},[902,16116,16117],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,16120,16122],{"className":16121},[886],[888,16123,16124],{"xmlns":890},[892,16125,16126,16130],{},[895,16127,16128],{},[898,16129,1712],{},[902,16131,1712],{"encoding":904}," při 1% změně ",[883,16134,16136],{"className":16135},[886],[888,16137,16138],{"xmlns":890},[892,16139,16140,16148],{},[895,16141,16142],{},[1717,16143,16144,16146],{},[898,16145,1701],{},[1693,16147,3672],{},[902,16149,11280],{"encoding":904},", ceteris paribus.",[198,16152,16154],{"id":16153},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,16156,16157],{},[883,16158,16160],{"className":16159,"title":11080,"style":11081},[11079],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,16162,16163,16118,16165,16178,16179,16196],{},[614,16164,16071],{},[883,16166,16168],{"className":16167},[886],[888,16169,16170],{"xmlns":890},[892,16171,16172,16176],{},[895,16173,16174],{},[898,16175,1712],{},[902,16177,1712],{"encoding":904}," základního zboží při 1% změně ceny ",[883,16180,16182],{"className":16181},[886],[888,16183,16184],{"xmlns":890},[892,16185,16186,16194],{},[895,16187,16188],{},[3284,16189,16190,16192],{},[898,16191,1701],{},[898,16193,2719],{},[902,16195,15969],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,16198,16199],{},[38,16200,16201],{},"Znaménko závisí na povaze alternativního zboží:",[120,16203,16204,16292],{},[123,16205,16206,16207,16210,16211,16228,16229,1863,16242,1789],{},"Je-li alternativní zboží ",[38,16208,16209],{},"komplement",", růst ",[883,16212,16214],{"className":16213},[886],[888,16215,16216],{"xmlns":890},[892,16217,16218,16226],{},[895,16219,16220],{},[3284,16221,16222,16224],{},[898,16223,1701],{},[898,16225,2719],{},[902,16227,15969],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,16230,16232],{"className":16231},[886],[888,16233,16234],{"xmlns":890},[892,16235,16236,16240],{},[895,16237,16238],{},[898,16239,1712],{},[902,16241,1712],{"encoding":904},[883,16243,16245],{"className":16244},[886],[888,16246,16247],{"xmlns":890},[892,16248,16249,16289],{},[895,16250,16251,16253,16255,16267,16269,16271,16273,16275,16285,16287],{},[1693,16252,10870],{},[1915,16254,1917],{},[5688,16256,16257,16259,16265],{},[898,16258,1712],{},[3284,16260,16261,16263],{},[898,16262,1701],{},[898,16264,2719],{},[1693,16266,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,16268,1908],{},[1762,16270,1911],{},[1693,16272,1899],{"separator":1898},[1915,16274,1917],{},[3284,16276,16277,16279],{},[898,16278,1691],{},[3284,16280,16281,16283],{},[898,16282,1701],{},[898,16284,2719],{},[1693,16286,1908],{},[1762,16288,1911],{},[902,16290,16291],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,16293,16206,16294,16210,16297,16314,16315,16328,16329,1789],{},[38,16295,16296],{},"substitut",[883,16298,16300],{"className":16299},[886],[888,16301,16302],{"xmlns":890},[892,16303,16304,16312],{},[895,16305,16306],{},[3284,16307,16308,16310],{},[898,16309,1701],{},[898,16311,2719],{},[902,16313,15969],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,16316,16318],{"className":16317},[886],[888,16319,16320],{"xmlns":890},[892,16321,16322,16326],{},[895,16323,16324],{},[898,16325,1712],{},[902,16327,1712],{"encoding":904}," roste ",[883,16330,16332],{"className":16331},[886],[888,16333,16334],{"xmlns":890},[892,16335,16336,16376],{},[895,16337,16338,16340,16342,16354,16356,16358,16360,16362,16372,16374],{},[1693,16339,10870],{},[1915,16341,1917],{},[5688,16343,16344,16346,16352],{},[898,16345,1712],{},[3284,16347,16348,16350],{},[898,16349,1701],{},[898,16351,2719],{},[1693,16353,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,16355,1922],{},[1762,16357,1911],{},[1693,16359,1899],{"separator":1898},[1915,16361,1917],{},[3284,16363,16364,16366],{},[898,16365,1691],{},[3284,16367,16368,16370],{},[898,16369,1701],{},[898,16371,2719],{},[1693,16373,1922],{},[1762,16375,1911],{},[902,16377,16378],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,16380,16383],{"className":16381,"title":16382,"style":11081},[11079],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":16385},[16386,16390,16391,16399,16400,16404,16407],{"id":10776,"depth":642,"text":10777,"children":16387},[16388,16389],{"id":10806,"depth":649,"text":10807},{"id":10983,"depth":649,"text":10984},{"id":11018,"depth":642,"text":11019},{"id":11044,"depth":642,"text":11045,"children":16392},[16393,16394,16395,16396,16398],{"id":11727,"depth":649,"text":11728},{"id":11817,"depth":649,"text":11818},{"id":12153,"depth":649,"text":12154},{"id":12235,"depth":649,"text":16397},"Výpočet, je-li dáno PP jako funkce QQ",{"id":12496,"depth":649,"text":12497},{"id":12818,"depth":642,"text":12819},{"id":13413,"depth":642,"text":13414,"children":16401},[16402,16403],{"id":14038,"depth":649,"text":14039},{"id":14867,"depth":649,"text":14868},{"id":15499,"depth":642,"text":15500,"children":16405},[16406],{"id":15624,"depth":649,"text":15625},{"id":15913,"depth":642,"text":15914,"children":16408},[16409,16410],{"id":16002,"depth":649,"text":16003},{"id":16153,"depth":649,"text":16154},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":3825,"description":641},[1138,1136],"topics\u002Felasticita",[1128,10783,16418,16419,16420,16421],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":16424,"title":16425,"body":16426,"course":1128,"courses":659,"created":1129,"description":17958,"extension":661,"meta":17959,"navigation":664,"path":17960,"seo":17961,"sources":17962,"stem":17963,"tags":17964,"type":10745,"updated":677,"__hash__":17969},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":16427,"toc":17943},[16428,16431,16505,16512,16516,16580,16667,16671,16698,16764,16819,16823,16850,16942,16944,16976,17146,17150,17220,17268,17272,17331,17437,17450,17454,17456,17484,17549,17551,17558,17646,17671,17869,17873,17909,17911],[12,16429,16425],{"id":16430},"kalkul-funkcí-více-proměnných",[724,16432,16433,16434,16437,16438,1343,16467,1789],{},"Většina ekonomických veličin závisí na ",[38,16435,16436],{},"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 ",[883,16439,16441],{"className":16440},[886],[888,16442,16443],{"xmlns":890},[892,16444,16445,16464],{},[895,16446,16447,16450,16452,16454,16456,16458,16460,16462],{},[898,16448,16449],{},"z",[1693,16451,1695],{},[898,16453,8934],{},[1693,16455,1709],{"stretchy":1708},[898,16457,2590],{},[1693,16459,1899],{"separator":1898},[898,16461,6560],{},[1693,16463,1731],{"stretchy":1708},[902,16465,16466],{"encoding":904},"z = f(x, y)",[883,16468,16470],{"className":16469},[886],[888,16471,16472],{"xmlns":890},[892,16473,16474,16502],{},[895,16475,16476,16479,16481,16483,16485,16487,16489,16491,16493,16495,16497,16499],{},[898,16477,16478],{},"w",[1693,16480,1695],{},[898,16482,8934],{},[1693,16484,1709],{"stretchy":1708},[898,16486,2590],{},[1693,16488,1899],{"separator":1898},[898,16490,6560],{},[1693,16492,1899],{"separator":1898},[898,16494,16449],{},[1693,16496,1731],{"stretchy":1708},[1693,16498,1899],{"separator":1898},[1693,16500,16501],{},"…",[902,16503,16504],{"encoding":904},"w = f(x, y, z), \\ldots",[724,16506,16507],{},[9465,16508],{"alt":16509,"className":16510,"src":16511},"imek-funkce-2d-vrstevnice",[210,9469],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,16513,16515],{"id":16514},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,16517,16518,16519,16546,16547,16575,16576,16579],{},"Pro ",[883,16520,16522],{"className":16521},[886],[888,16523,16524],{"xmlns":890},[892,16525,16526,16544],{},[895,16527,16528,16530,16532,16534,16536,16538,16540,16542],{},[898,16529,16449],{},[1693,16531,1695],{},[898,16533,8934],{},[1693,16535,1709],{"stretchy":1708},[898,16537,2590],{},[1693,16539,1899],{"separator":1898},[898,16541,6560],{},[1693,16543,1731],{"stretchy":1708},[902,16545,16466],{"encoding":904}," se křivkou s předpisem ",[883,16548,16550],{"className":16549},[886],[888,16551,16552],{"xmlns":890},[892,16553,16554,16572],{},[895,16555,16556,16558,16560,16562,16564,16566,16568,16570],{},[898,16557,8934],{},[1693,16559,1709],{"stretchy":1708},[898,16561,2590],{},[1693,16563,1899],{"separator":1898},[898,16565,6560],{},[1693,16567,1731],{"stretchy":1708},[1693,16569,1695],{},[898,16571,2000],{},[902,16573,16574],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,16577,16578],{},"vrstevnice"," funkce. V ekonomii:",[120,16581,16582,16629],{},[123,16583,16584,16587,16588,16624,16625,1789],{},[38,16585,16586],{},"Indiferenční křivky"," užitečnosti ",[883,16589,16591],{"className":16590},[886],[888,16592,16593],{"xmlns":890},[892,16594,16595,16621],{},[895,16596,16597,16599,16601,16607,16609,16615,16617,16619],{},[898,16598,900],{},[1693,16600,1709],{"stretchy":1708},[3284,16602,16603,16605],{},[898,16604,1712],{},[1762,16606,1764],{},[1693,16608,1899],{"separator":1898},[3284,16610,16611,16613],{},[898,16612,1712],{},[1762,16614,2398],{},[1693,16616,1731],{"stretchy":1708},[1693,16618,1695],{},[898,16620,2000],{},[902,16622,16623],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,16626,16628],{"className":16627,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,16630,16631,16634,16635,16624,16663,1789],{},[38,16632,16633],{},"Izokvanty"," produkce ",[883,16636,16638],{"className":16637},[886],[888,16639,16640],{"xmlns":890},[892,16641,16642,16660],{},[895,16643,16644,16646,16648,16650,16652,16654,16656,16658],{},[898,16645,1712],{},[1693,16647,1709],{"stretchy":1708},[898,16649,4840],{},[1693,16651,1899],{"separator":1898},[898,16653,4845],{},[1693,16655,1731],{"stretchy":1708},[1693,16657,1695],{},[898,16659,2000],{},[902,16661,16662],{"encoding":904},"Q(L, K) = c",[207,16664,16666],{"className":16665,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,16668,16670],{"id":16669},"parciální-derivace","Parciální derivace",[724,16672,16518,16673,16697],{},[883,16674,16676],{"className":16675},[886],[888,16677,16678],{"xmlns":890},[892,16679,16680,16694],{},[895,16681,16682,16684,16686,16688,16690,16692],{},[898,16683,8934],{},[1693,16685,1709],{"stretchy":1708},[898,16687,2590],{},[1693,16689,1899],{"separator":1898},[898,16691,6560],{},[1693,16693,1731],{"stretchy":1708},[902,16695,16696],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,16699,16700],{},[883,16701,16703],{"className":16702},[886],[888,16704,16705],{"xmlns":890},[892,16706,16707,16761],{},[895,16708,16709,16717,16719,16733,16735,16737,16745,16747],{},[5688,16710,16711,16713,16715],{},[898,16712,8934],{},[898,16714,2590],{},[1693,16716,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,16718,1695],{},[2132,16720,16721,16727],{},[895,16722,16723,16725],{},[898,16724,2228],{"mathvariant":1704},[898,16726,8934],{},[895,16728,16729,16731],{},[898,16730,2228],{"mathvariant":1704},[898,16732,2590],{},[1693,16734,1899],{"separator":1898},[1901,16736],{"width":1903},[5688,16738,16739,16741,16743],{},[898,16740,8934],{},[898,16742,6560],{},[1693,16744,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,16746,1695],{},[2132,16748,16749,16755],{},[895,16750,16751,16753],{},[898,16752,2228],{"mathvariant":1704},[898,16754,8934],{},[895,16756,16757,16759],{},[898,16758,2228],{"mathvariant":1704},[898,16760,6560],{},[902,16762,16763],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,16765,16766,16767,1789],{},"Hodnoty v bodě: ",[883,16768,16770],{"className":16769},[886],[888,16771,16772],{"xmlns":890},[892,16773,16774,16816],{},[895,16775,16776,16784,16786,16788,16790,16792,16794,16796,16798,16806,16808,16810,16812,16814],{},[5688,16777,16778,16780,16782],{},[898,16779,8934],{},[898,16781,2590],{},[1693,16783,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,16785,1709],{"stretchy":1708},[898,16787,207],{},[1693,16789,1899],{"separator":1898},[898,16791,1895],{},[1693,16793,1731],{"stretchy":1708},[1693,16795,1899],{"separator":1898},[1915,16797,9204],{},[5688,16799,16800,16802,16804],{},[898,16801,8934],{},[898,16803,6560],{},[1693,16805,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,16807,1709],{"stretchy":1708},[898,16809,207],{},[1693,16811,1899],{"separator":1898},[898,16813,1895],{},[1693,16815,1731],{"stretchy":1708},[902,16817,16818],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,16820,16822],{"id":16821},"ekonomické-značení","Ekonomické značení",[724,16824,16825,16826,4300],{},"Pro produkční funkci ",[883,16827,16829],{"className":16828},[886],[888,16830,16831],{"xmlns":890},[892,16832,16833,16847],{},[895,16834,16835,16837,16839,16841,16843,16845],{},[898,16836,1712],{},[1693,16838,1709],{"stretchy":1708},[898,16840,4840],{},[1693,16842,1899],{"separator":1898},[898,16844,4845],{},[1693,16846,1731],{"stretchy":1708},[902,16848,16849],{"encoding":904},"Q(L, K)",[120,16851,16852,16897],{},[123,16853,16854,7176,16874,16877,16878,1731],{},[883,16855,16857],{"className":16856},[886],[888,16858,16859],{"xmlns":890},[892,16860,16861,16871],{},[895,16862,16863],{},[5688,16864,16865,16867,16869],{},[898,16866,1712],{},[898,16868,4840],{},[1693,16870,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,16872,16873],{"encoding":904},"Q'_L",[38,16875,16876],{},"mezní produkt práce"," (",[883,16879,16881],{"className":16880},[886],[888,16882,16883],{"xmlns":890},[892,16884,16885,16895],{},[895,16886,16887,16889],{},[898,16888,2839],{},[3284,16890,16891,16893],{},[898,16892,1701],{},[898,16894,4840],{},[902,16896,4964],{"encoding":904},[123,16898,16899,7176,16919,16877,16922,1731],{},[883,16900,16902],{"className":16901},[886],[888,16903,16904],{"xmlns":890},[892,16905,16906,16916],{},[895,16907,16908],{},[5688,16909,16910,16912,16914],{},[898,16911,1712],{},[898,16913,4845],{},[1693,16915,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,16917,16918],{"encoding":904},"Q'_K",[38,16920,16921],{},"mezní produkt kapitálu",[883,16923,16925],{"className":16924},[886],[888,16926,16927],{"xmlns":890},[892,16928,16929,16939],{},[895,16930,16931,16933],{},[898,16932,2839],{},[3284,16934,16935,16937],{},[898,16936,1701],{},[898,16938,4845],{},[902,16940,16941],{"encoding":904},"MP_K",[198,16943,9474],{"id":9473},[724,16945,16946,4300],{},[883,16947,16949],{"className":16948},[886],[888,16950,16951],{"xmlns":890},[892,16952,16953,16973],{},[895,16954,16955,16963,16965,16967,16969,16971],{},[5688,16956,16957,16959,16961],{},[898,16958,8934],{},[898,16960,2590],{},[1693,16962,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,16964,1709],{"stretchy":1708},[898,16966,207],{},[1693,16968,1899],{"separator":1898},[898,16970,1895],{},[1693,16972,1731],{"stretchy":1708},[902,16974,16975],{"encoding":904},"f'_x(a, b)",[120,16977,16978,17035],{},[123,16979,16980,16981,16994,16995,4148,17008,17034],{},"rychlost změny ",[883,16982,16984],{"className":16983},[886],[888,16985,16986],{"xmlns":890},[892,16987,16988,16992],{},[895,16989,16990],{},[898,16991,8934],{},[902,16993,8934],{"encoding":904}," vůči ",[883,16996,16998],{"className":16997},[886],[888,16999,17000],{"xmlns":890},[892,17001,17002,17006],{},[895,17003,17004],{},[898,17005,2590],{},[902,17007,2590],{"encoding":904},[883,17009,17011],{"className":17010},[886],[888,17012,17013],{"xmlns":890},[892,17014,17015,17031],{},[895,17016,17017,17019,17021,17023,17025,17027,17029],{},[898,17018,2590],{},[1693,17020,1695],{},[898,17022,207],{},[1693,17024,1899],{"separator":1898},[898,17026,6560],{},[1693,17028,1695],{},[898,17030,1895],{},[902,17032,17033],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,17036,17037,17038,9563,17051,17064,17065,17083,17084,1789],{},"přibližná změna ",[883,17039,17041],{"className":17040},[886],[888,17042,17043],{"xmlns":890},[892,17044,17045,17049],{},[895,17046,17047],{},[898,17048,8934],{},[902,17050,8934],{"encoding":904},[883,17052,17054],{"className":17053},[886],[888,17055,17056],{"xmlns":890},[892,17057,17058,17062],{},[895,17059,17060],{},[898,17061,2590],{},[902,17063,2590],{"encoding":904}," o 1 (a pevném ",[883,17066,17068],{"className":17067},[886],[888,17069,17070],{"xmlns":890},[892,17071,17072,17080],{},[895,17073,17074,17076,17078],{},[898,17075,6560],{},[1693,17077,1695],{},[898,17079,1895],{},[902,17081,17082],{"encoding":904},"y = b","): ",[883,17085,17087],{"className":17086},[886],[888,17088,17089],{"xmlns":890},[892,17090,17091,17143],{},[895,17092,17093,17095,17097,17099,17101,17103,17105,17107,17109,17111,17113,17115,17117,17119,17121,17123,17125,17133,17135,17137,17139,17141],{},[898,17094,8934],{},[1693,17096,1709],{"stretchy":1708},[898,17098,207],{},[1693,17100,1892],{},[1762,17102,1764],{},[1693,17104,1899],{"separator":1898},[898,17106,1895],{},[1693,17108,1731],{"stretchy":1708},[1693,17110,4110],{},[898,17112,8934],{},[1693,17114,1709],{"stretchy":1708},[898,17116,207],{},[1693,17118,1899],{"separator":1898},[898,17120,1895],{},[1693,17122,1731],{"stretchy":1708},[1693,17124,1892],{},[5688,17126,17127,17129,17131],{},[898,17128,8934],{},[898,17130,2590],{},[1693,17132,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17134,1709],{"stretchy":1708},[898,17136,207],{},[1693,17138,1899],{"separator":1898},[898,17140,1895],{},[1693,17142,1731],{"stretchy":1708},[902,17144,17145],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,17147,17149],{"id":17148},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,17151,17152],{},[883,17153,17155],{"className":17154},[886],[888,17156,17157],{"xmlns":890},[892,17158,17159,17217],{},[895,17160,17161,17163,17165,17167,17175,17177,17179,17181,17183,17185,17187,17189,17191,17193,17201,17203,17205,17207,17209,17211,17213,17215],{},[898,17162,1771],{},[898,17164,8934],{},[1693,17166,1695],{},[5688,17168,17169,17171,17173],{},[898,17170,8934],{},[898,17172,2590],{},[1693,17174,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17176,1709],{"stretchy":1708},[898,17178,2590],{},[1693,17180,1899],{"separator":1898},[898,17182,6560],{},[1693,17184,1731],{"stretchy":1708},[1915,17186,2239],{},[898,17188,1771],{},[898,17190,2590],{},[1693,17192,1892],{},[5688,17194,17195,17197,17199],{},[898,17196,8934],{},[898,17198,6560],{},[1693,17200,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17202,1709],{"stretchy":1708},[898,17204,2590],{},[1693,17206,1899],{"separator":1898},[898,17208,6560],{},[1693,17210,1731],{"stretchy":1708},[1915,17212,2239],{},[898,17214,1771],{},[898,17216,6560],{},[902,17218,17219],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,17221,9894,17222,17244,17245,17267],{},[883,17223,17225],{"className":17224},[886],[888,17226,17227],{"xmlns":890},[892,17228,17229,17241],{},[895,17230,17231,17233,17235,17237,17239],{},[898,17232,1771],{},[898,17234,2590],{},[1693,17236,1899],{"separator":1898},[898,17238,1771],{},[898,17240,6560],{},[902,17242,17243],{"encoding":904},"dx, dy"," platí ",[883,17246,17248],{"className":17247},[886],[888,17249,17250],{"xmlns":890},[892,17251,17252,17264],{},[895,17253,17254,17256,17258,17260,17262],{},[898,17255,3890],{"mathvariant":1704},[898,17257,8934],{},[1693,17259,4110],{},[898,17261,1771],{},[898,17263,8934],{},[902,17265,17266],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,17269,17271],{"id":17270},"implicitní-funkce","Implicitní funkce",[724,17273,17274,17275,17303,17304,2884,17317,17330],{},"Je-li vztah dán rovnicí ",[883,17276,17278],{"className":17277},[886],[888,17279,17280],{"xmlns":890},[892,17281,17282,17300],{},[895,17283,17284,17286,17288,17290,17292,17294,17296,17298],{},[898,17285,2976],{},[1693,17287,1709],{"stretchy":1708},[898,17289,2590],{},[1693,17291,1899],{"separator":1898},[898,17293,6560],{},[1693,17295,1731],{"stretchy":1708},[1693,17297,1695],{},[1762,17299,1911],{},[902,17301,17302],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,17305,17307],{"className":17306},[886],[888,17308,17309],{"xmlns":890},[892,17310,17311,17315],{},[895,17312,17313],{},[898,17314,6560],{},[902,17316,6560],{"encoding":904},[883,17318,17320],{"className":17319},[886],[888,17321,17322],{"xmlns":890},[892,17323,17324,17328],{},[895,17325,17326],{},[898,17327,2590],{},[902,17329,2590],{"encoding":904}," (nebo naopak):",[724,17332,17333],{},[883,17334,17336],{"className":17335},[886],[888,17337,17338],{"xmlns":890},[892,17339,17340,17434],{},[895,17341,17342,17348,17350,17364,17366,17368,17386,17388,17390,17396,17398,17412,17414,17416],{},[1717,17343,17344,17346],{},[898,17345,6560],{},[1693,17347,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17349,1695],{},[2132,17351,17352,17358],{},[895,17353,17354,17356],{},[898,17355,1771],{},[898,17357,6560],{},[895,17359,17360,17362],{},[898,17361,1771],{},[898,17363,2590],{},[1693,17365,1695],{},[1693,17367,1698],{},[2132,17369,17370,17378],{},[5688,17371,17372,17374,17376],{},[898,17373,2976],{},[898,17375,2590],{},[1693,17377,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,17379,17380,17382,17384],{},[898,17381,2976],{},[898,17383,6560],{},[1693,17385,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17387,1899],{"separator":1898},[1901,17389],{"width":1903},[1717,17391,17392,17394],{},[898,17393,2590],{},[1693,17395,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17397,1695],{},[2132,17399,17400,17406],{},[895,17401,17402,17404],{},[898,17403,1771],{},[898,17405,2590],{},[895,17407,17408,17410],{},[898,17409,1771],{},[898,17411,6560],{},[1693,17413,1695],{},[1693,17415,1698],{},[2132,17417,17418,17426],{},[5688,17419,17420,17422,17424],{},[898,17421,2976],{},[898,17423,6560],{},[1693,17425,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,17427,17428,17430,17432],{},[898,17429,2976],{},[898,17431,2590],{},[1693,17433,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,17435,17436],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,17438,17439,17440,17443,17444,4286,17447,1789],{},"Tato vzorec dává ",[38,17441,17442],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,17445,5814],{"className":17446,"dataFsResolvedFilePath":857,"href":858},[210],[207,17448,5315],{"className":17449,"dataFsResolvedFilePath":878,"href":879},[210],[115,17451,17453],{"id":17452},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,17455,10147],{"id":10146},[724,17457,17458,17459,17483],{},"V bodě extrému ",[883,17460,17462],{"className":17461},[886],[888,17463,17464],{"xmlns":890},[892,17465,17466,17480],{},[895,17467,17468,17470,17472,17474,17476,17478],{},[898,17469,2719],{},[1693,17471,9392],{"stretchy":1708},[898,17473,207],{},[1693,17475,1899],{"separator":1898},[898,17477,1895],{},[1693,17479,9407],{"stretchy":1708},[902,17481,17482],{"encoding":904},"A[a, b]"," musí platit současně:",[724,17485,17486],{},[883,17487,17489],{"className":17488},[886],[888,17490,17491],{"xmlns":890},[892,17492,17493,17546],{},[895,17494,17495,17503,17505,17507,17509,17511,17513,17515,17517,17519,17522,17524,17532,17534,17536,17538,17540,17542,17544],{},[5688,17496,17497,17499,17501],{},[898,17498,8934],{},[898,17500,2590],{},[1693,17502,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17504,1709],{"stretchy":1708},[898,17506,207],{},[1693,17508,1899],{"separator":1898},[898,17510,1895],{},[1693,17512,1731],{"stretchy":1708},[1693,17514,1695],{},[1762,17516,1911],{},[1915,17518,1917],{},[1693,17520,17521],{},"∧",[1915,17523,1917],{},[5688,17525,17526,17528,17530],{},[898,17527,8934],{},[898,17529,6560],{},[1693,17531,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,17533,1709],{"stretchy":1708},[898,17535,207],{},[1693,17537,1899],{"separator":1898},[898,17539,1895],{},[1693,17541,1731],{"stretchy":1708},[1693,17543,1695],{},[1762,17545,1911],{},[902,17547,17548],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,17550,10221],{"id":10220},[724,17552,17553,17554,17557],{},"Definujeme ",[38,17555,17556],{},"diskriminant"," (Hessián zjednodušeně):",[724,17559,17560],{},[883,17561,17563],{"className":17562},[886],[888,17564,17565],{"xmlns":890},[892,17566,17567,17643],{},[895,17568,17569,17571,17573,17575,17577,17579,17581,17583,17599,17601,17617,17619,17621,17637],{},[898,17570,2738],{},[1693,17572,1709],{"stretchy":1708},[898,17574,2590],{},[1693,17576,1899],{"separator":1898},[898,17578,6560],{},[1693,17580,1731],{"stretchy":1708},[1693,17582,1695],{},[5688,17584,17585,17587,17593],{},[898,17586,8934],{},[895,17588,17589,17591],{},[898,17590,2590],{},[898,17592,2590],{},[895,17594,17595,17597],{},[1693,17596,1724],{"mathvariant":1704},[1693,17598,1724],{"mathvariant":1704},[1693,17600,1715],{},[5688,17602,17603,17605,17611],{},[898,17604,8934],{},[895,17606,17607,17609],{},[898,17608,6560],{},[898,17610,6560],{},[895,17612,17613,17615],{},[1693,17614,1724],{"mathvariant":1704},[1693,17616,1724],{"mathvariant":1704},[1693,17618,1698],{},[1693,17620,1709],{"stretchy":1708},[5688,17622,17623,17625,17631],{},[898,17624,8934],{},[895,17626,17627,17629],{},[898,17628,2590],{},[898,17630,6560],{},[895,17632,17633,17635],{},[1693,17634,1724],{"mathvariant":1704},[1693,17636,1724],{"mathvariant":1704},[1717,17638,17639,17641],{},[1693,17640,1731],{"stretchy":1708},[1762,17642,2398],{},[902,17644,17645],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,17647,17648,17649,4300],{},"V podezřelém bodě ",[883,17650,17652],{"className":17651},[886],[888,17653,17654],{"xmlns":890},[892,17655,17656,17668],{},[895,17657,17658,17660,17662,17664,17666],{},[1693,17659,9392],{"stretchy":1708},[898,17661,207],{},[1693,17663,1899],{"separator":1898},[898,17665,1895],{},[1693,17667,9407],{"stretchy":1708},[902,17669,17670],{"encoding":904},"[a, b]",[152,17672,17673,17800,17836],{},[123,17674,17675,17705,17706],{},[38,17676,17677,4300],{},[883,17678,17680],{"className":17679},[886],[888,17681,17682],{"xmlns":890},[892,17683,17684,17702],{},[895,17685,17686,17688,17690,17692,17694,17696,17698,17700],{},[898,17687,2738],{},[1693,17689,1709],{"stretchy":1708},[898,17691,207],{},[1693,17693,1899],{"separator":1898},[898,17695,1895],{},[1693,17697,1731],{"stretchy":1708},[1693,17699,1922],{},[1762,17701,1911],{},[902,17703,17704],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,17707,17708,17754],{},[123,17709,17710,10308,17752],{},[883,17711,17713],{"className":17712},[886],[888,17714,17715],{"xmlns":890},[892,17716,17717,17749],{},[895,17718,17719,17735,17737,17739,17741,17743,17745,17747],{},[5688,17720,17721,17723,17729],{},[898,17722,8934],{},[895,17724,17725,17727],{},[898,17726,2590],{},[898,17728,2590],{},[895,17730,17731,17733],{},[1693,17732,1724],{"mathvariant":1704},[1693,17734,1724],{"mathvariant":1704},[1693,17736,1709],{"stretchy":1708},[898,17738,207],{},[1693,17740,1899],{"separator":1898},[898,17742,1895],{},[1693,17744,1731],{"stretchy":1708},[1693,17746,1922],{},[1762,17748,1911],{},[902,17750,17751],{"encoding":904},"f''_{xx}(a, b) > 0",[38,17753,10667],{},[123,17755,17756,10308,17798],{},[883,17757,17759],{"className":17758},[886],[888,17760,17761],{"xmlns":890},[892,17762,17763,17795],{},[895,17764,17765,17781,17783,17785,17787,17789,17791,17793],{},[5688,17766,17767,17769,17775],{},[898,17768,8934],{},[895,17770,17771,17773],{},[898,17772,2590],{},[898,17774,2590],{},[895,17776,17777,17779],{},[1693,17778,1724],{"mathvariant":1704},[1693,17780,1724],{"mathvariant":1704},[1693,17782,1709],{"stretchy":1708},[898,17784,207],{},[1693,17786,1899],{"separator":1898},[898,17788,1895],{},[1693,17790,1731],{"stretchy":1708},[1693,17792,1908],{},[1762,17794,1911],{},[902,17796,17797],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,17799,10610],{},[123,17801,17802,1863,17832,17835],{},[38,17803,17804,4300],{},[883,17805,17807],{"className":17806},[886],[888,17808,17809],{"xmlns":890},[892,17810,17811,17829],{},[895,17812,17813,17815,17817,17819,17821,17823,17825,17827],{},[898,17814,2738],{},[1693,17816,1709],{"stretchy":1708},[898,17818,207],{},[1693,17820,1899],{"separator":1898},[898,17822,1895],{},[1693,17824,1731],{"stretchy":1708},[1693,17826,1908],{},[1762,17828,1911],{},[902,17830,17831],{"encoding":904},"D(a, b) \u003C 0",[38,17833,17834],{},"sedlo"," (v daném bodě extrém není).",[123,17837,17838,17868],{},[38,17839,17840,4300],{},[883,17841,17843],{"className":17842},[886],[888,17844,17845],{"xmlns":890},[892,17846,17847,17865],{},[895,17848,17849,17851,17853,17855,17857,17859,17861,17863],{},[898,17850,2738],{},[1693,17852,1709],{"stretchy":1708},[898,17854,207],{},[1693,17856,1899],{"separator":1898},[898,17858,1895],{},[1693,17860,1731],{"stretchy":1708},[1693,17862,1695],{},[1762,17864,1911],{},[902,17866,17867],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,17870,17872],{"id":17871},"vázané-extrémy","Vázané extrémy",[724,17874,17875,17876,17905,17906,1789],{},"Pro extrémy s omezující podmínkou ",[883,17877,17879],{"className":17878},[886],[888,17880,17881],{"xmlns":890},[892,17882,17883,17902],{},[895,17884,17885,17888,17890,17892,17894,17896,17898,17900],{},[898,17886,17887],{},"g",[1693,17889,1709],{"stretchy":1708},[898,17891,2590],{},[1693,17893,1899],{"separator":1898},[898,17895,6560],{},[1693,17897,1731],{"stretchy":1708},[1693,17899,1695],{},[1762,17901,1911],{},[902,17903,17904],{"encoding":904},"g(x, y) = 0"," se používá ",[207,17907,793],{"className":17908,"dataFsResolvedFilePath":791,"href":792},[210],[115,17910,8685],{"id":8684},[120,17912,17913,17920,17927],{},[123,17914,17915,1863,17917],{},[38,17916,10689],{},[207,17918,775],{"className":17919,"dataFsResolvedFilePath":773,"href":774},[210],[123,17921,17922,1863,17924],{},[38,17923,10697],{},[207,17925,793],{"className":17926,"dataFsResolvedFilePath":791,"href":792},[210],[123,17928,17929,1863,17931,17934,17935,17938,17939,17942],{},[38,17930,10705],{},[207,17932,8763],{"className":17933,"dataFsResolvedFilePath":857,"href":858},[210]," (parciální derivace = mezní produkty), ",[207,17936,880],{"className":17937,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,17940,8759],{"className":17941,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":17944},[17945,17946,17950,17951,17952,17956,17957],{"id":16514,"depth":642,"text":16515},{"id":16669,"depth":642,"text":16670,"children":17947},[17948,17949],{"id":16821,"depth":649,"text":16822},{"id":9473,"depth":649,"text":9474},{"id":17148,"depth":642,"text":17149},{"id":17270,"depth":642,"text":17271},{"id":17452,"depth":642,"text":17453,"children":17953},[17954,17955],{"id":10146,"depth":649,"text":10147},{"id":10220,"depth":649,"text":10221},{"id":17871,"depth":642,"text":17872},{"id":8684,"depth":642,"text":8685},"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":16425,"description":17958},[1135],"topics\u002Ffunkce-vice-promennych",[1128,17965,10742,17966,17967,17968],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":17971,"title":775,"body":17972,"course":1128,"courses":659,"created":1129,"description":18826,"extension":661,"meta":18827,"navigation":664,"path":18828,"seo":18829,"sources":18830,"stem":18831,"tags":18832,"type":10745,"updated":677,"__hash__":18839},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":17973,"toc":18816},[17974,17977,17988,17992,18036,18116,18120,18196,18238,18245,18249,18253,18282,18340,18387,18425,18429,18479,18531,18583,18627,18630,18633,18705,18708,18780,18786,18788],[12,17975,775],{"id":17976},"integrál",[724,17978,17979,17980,17983,17984,17987],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,17981,17982],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,17985,17986],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,17989,17991],{"id":17990},"neurčitý-integrál","Neurčitý integrál",[724,17993,17994],{},[883,17995,17997],{"className":17996},[886],[888,17998,17999],{"xmlns":890},[892,18000,18001,18033],{},[895,18002,18003,18005,18007,18009,18011,18013,18015,18017,18019,18021,18023,18025,18027,18029,18031],{},[898,18004,2976],{},[1693,18006,1709],{"stretchy":1708},[898,18008,2590],{},[1693,18010,1731],{"stretchy":1708},[1693,18012,1695],{},[1693,18014,6221],{},[898,18016,8934],{},[1693,18018,1709],{"stretchy":1708},[898,18020,2590],{},[1693,18022,1731],{"stretchy":1708},[1915,18024,2239],{},[898,18026,1771],{},[898,18028,2590],{},[1693,18030,1892],{},[898,18032,2971],{},[902,18034,18035],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,18037,11188,18038,7617,18072,6055,18085,18088,18089,1343,18102,18115],{},[883,18039,18041],{"className":18040},[886],[888,18042,18043],{"xmlns":890},[892,18044,18045,18069],{},[895,18046,18047,18053,18055,18057,18059,18061,18063,18065,18067],{},[1717,18048,18049,18051],{},[898,18050,2976],{},[1693,18052,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,18054,1709],{"stretchy":1708},[898,18056,2590],{},[1693,18058,1731],{"stretchy":1708},[1693,18060,1695],{},[898,18062,8934],{},[1693,18064,1709],{"stretchy":1708},[898,18066,2590],{},[1693,18068,1731],{"stretchy":1708},[902,18070,18071],{"encoding":904},"F'(x) = f(x)",[883,18073,18075],{"className":18074},[886],[888,18076,18077],{"xmlns":890},[892,18078,18079,18083],{},[895,18080,18081],{},[898,18082,2976],{},[902,18084,2976],{"encoding":904},[38,18086,18087],{},"primitivní funkce"," k ",[883,18090,18092],{"className":18091},[886],[888,18093,18094],{"xmlns":890},[892,18095,18096,18100],{},[895,18097,18098],{},[898,18099,8934],{},[902,18101,8934],{"encoding":904},[883,18103,18105],{"className":18104},[886],[888,18106,18107],{"xmlns":890},[892,18108,18109,18113],{},[895,18110,18111],{},[898,18112,2971],{},[902,18114,2971],{"encoding":904}," konstanta.",[115,18117,18119],{"id":18118},"určitý-integrál","Určitý integrál",[724,18121,18122],{},[883,18123,18125],{"className":18124},[886],[888,18126,18127],{"xmlns":890},[892,18128,18129,18193],{},[895,18130,18131,18139,18141,18143,18145,18147,18149,18151,18153,18155,18157,18159,18161,18163,18165,18173,18175,18177,18179,18181,18183,18185,18187,18189,18191],{},[5688,18132,18133,18135,18137],{},[1693,18134,6221],{},[898,18136,207],{},[898,18138,1895],{},[898,18140,8934],{},[1693,18142,1709],{"stretchy":1708},[898,18144,2590],{},[1693,18146,1731],{"stretchy":1708},[1915,18148,2239],{},[898,18150,1771],{},[898,18152,2590],{},[1693,18154,1695],{},[1693,18156,9392],{"stretchy":1708},[898,18158,2976],{},[1693,18160,1709],{"stretchy":1708},[898,18162,2590],{},[1693,18164,1731],{"stretchy":1708},[5688,18166,18167,18169,18171],{},[1693,18168,9407],{"stretchy":1708},[898,18170,207],{},[898,18172,1895],{},[1693,18174,1695],{},[898,18176,2976],{},[1693,18178,1709],{"stretchy":1708},[898,18180,1895],{},[1693,18182,1731],{"stretchy":1708},[1693,18184,1698],{},[898,18186,2976],{},[1693,18188,1709],{"stretchy":1708},[898,18190,207],{},[1693,18192,1731],{"stretchy":1708},[902,18194,18195],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,18197,18198,18199,1863,18202,18215,18216,18237],{},"Geometricky ",[38,18200,18201],{},"plocha pod grafem",[883,18203,18205],{"className":18204},[886],[888,18206,18207],{"xmlns":890},[892,18208,18209,18213],{},[895,18210,18211],{},[898,18212,8934],{},[902,18214,8934],{"encoding":904}," na intervalu ",[883,18217,18219],{"className":18218},[886],[888,18220,18221],{"xmlns":890},[892,18222,18223,18235],{},[895,18224,18225,18227,18229,18231,18233],{},[1693,18226,9392],{"stretchy":1708},[898,18228,207],{},[1693,18230,1899],{"separator":1898},[898,18232,1895],{},[1693,18234,9407],{"stretchy":1708},[902,18236,17670],{"encoding":904}," (orientovaná).",[724,18239,18240],{},[9465,18241],{"alt":18242,"className":18243,"src":18244},"imek-integral-plocha",[210,9469],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,18246,18248],{"id":18247},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,18250,18252],{"id":18251},"příklad-tr-z-mr","Příklad — TR z MR",[724,18254,18255,18256,1789],{},"Mezní příjem ",[883,18257,18259],{"className":18258},[886],[888,18260,18261],{"xmlns":890},[892,18262,18263,18279],{},[895,18264,18265,18267,18269,18271,18273,18275,18277],{},[898,18266,2839],{},[898,18268,2666],{},[1693,18270,1695],{},[1762,18272,9987],{},[1693,18274,1698],{},[1762,18276,2398],{},[898,18278,1712],{},[902,18280,18281],{"encoding":904},"MR = 100 - 2Q",[724,18283,18284],{},[883,18285,18287],{"className":18286},[886],[888,18288,18289],{"xmlns":890},[892,18290,18291,18337],{},[895,18292,18293,18295,18297,18299,18301,18303,18305,18307,18309,18311,18313,18315,18317,18319,18321,18323,18325,18327,18333,18335],{},[898,18294,2663],{},[898,18296,2666],{},[1693,18298,1695],{},[1693,18300,6221],{},[1693,18302,1709],{"stretchy":1708},[1762,18304,9987],{},[1693,18306,1698],{},[1762,18308,2398],{},[898,18310,1712],{},[1693,18312,1731],{"stretchy":1708},[1915,18314,2239],{},[898,18316,1771],{},[898,18318,1712],{},[1693,18320,1695],{},[1762,18322,9987],{},[898,18324,1712],{},[1693,18326,1698],{},[1717,18328,18329,18331],{},[898,18330,1712],{},[1762,18332,2398],{},[1693,18334,1892],{},[898,18336,2000],{},[902,18338,18339],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,18341,18342,18343,10308,18369,4300],{},"Okrajová podmínka ",[883,18344,18346],{"className":18345},[886],[888,18347,18348],{"xmlns":890},[892,18349,18350,18366],{},[895,18351,18352,18354,18356,18358,18360,18362,18364],{},[898,18353,2663],{},[898,18355,2666],{},[1693,18357,1709],{"stretchy":1708},[1762,18359,1911],{},[1693,18361,1731],{"stretchy":1708},[1693,18363,1695],{},[1762,18365,1911],{},[902,18367,18368],{"encoding":904},"TR(0) = 0",[883,18370,18372],{"className":18371},[886],[888,18373,18374],{"xmlns":890},[892,18375,18376,18384],{},[895,18377,18378,18380,18382],{},[898,18379,2000],{},[1693,18381,1695],{},[1762,18383,1911],{},[902,18385,18386],{"encoding":904},"c = 0",[724,18388,18389],{},[883,18390,18392],{"className":18391},[886],[888,18393,18394],{"xmlns":890},[892,18395,18396,18422],{},[895,18397,18398,18400,18402,18404,18406,18408,18410,18412,18414,18416],{},[898,18399,2663],{},[898,18401,2666],{},[1693,18403,1709],{"stretchy":1708},[898,18405,1712],{},[1693,18407,1731],{"stretchy":1708},[1693,18409,1695],{},[1762,18411,9987],{},[898,18413,1712],{},[1693,18415,1698],{},[1717,18417,18418,18420],{},[898,18419,1712],{},[1762,18421,2398],{},[902,18423,18424],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,18426,18428],{"id":18427},"příklad-tc-z-mc","Příklad — TC z MC",[724,18430,18431,18432,18458,18459,1789],{},"Mezní náklady ",[883,18433,18435],{"className":18434},[886],[888,18436,18437],{"xmlns":890},[892,18438,18439,18455],{},[895,18440,18441,18443,18445,18447,18449,18451,18453],{},[898,18442,2839],{},[898,18444,2971],{},[1693,18446,1695],{},[1762,18448,2398],{},[1693,18450,1892],{},[1762,18452,9739],{},[898,18454,1712],{},[902,18456,18457],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,18460,18462],{"className":18461},[886],[888,18463,18464],{"xmlns":890},[892,18465,18466,18476],{},[895,18467,18468,18470,18472,18474],{},[898,18469,2976],{},[898,18471,2971],{},[1693,18473,1695],{},[1762,18475,9987],{},[902,18477,18478],{"encoding":904},"FC = 100",[724,18480,18481],{},[883,18482,18484],{"className":18483},[886],[888,18485,18486],{"xmlns":890},[892,18487,18488,18528],{},[895,18489,18490,18492,18494,18496,18498,18500,18502,18504,18506,18508,18510,18512,18514,18516,18518,18524,18526],{},[898,18491,2663],{},[898,18493,2971],{},[1693,18495,1695],{},[1693,18497,6221],{},[898,18499,2839],{},[898,18501,2971],{},[1915,18503,2239],{},[898,18505,1771],{},[898,18507,1712],{},[1693,18509,1695],{},[1762,18511,2398],{},[898,18513,1712],{},[1693,18515,1892],{},[1762,18517,9695],{},[1717,18519,18520,18522],{},[898,18521,1712],{},[1762,18523,2398],{},[1693,18525,1892],{},[898,18527,2000],{},[902,18529,18530],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,18532,18342,18533,10308,18565,4300],{},[883,18534,18536],{"className":18535},[886],[888,18537,18538],{"xmlns":890},[892,18539,18540,18562],{},[895,18541,18542,18544,18546,18548,18550,18552,18554,18556,18558,18560],{},[898,18543,2663],{},[898,18545,2971],{},[1693,18547,1709],{"stretchy":1708},[1762,18549,1911],{},[1693,18551,1731],{"stretchy":1708},[1693,18553,1695],{},[898,18555,2976],{},[898,18557,2971],{},[1693,18559,1695],{},[1762,18561,9987],{},[902,18563,18564],{"encoding":904},"TC(0) = FC = 100",[883,18566,18568],{"className":18567},[886],[888,18569,18570],{"xmlns":890},[892,18571,18572,18580],{},[895,18573,18574,18576,18578],{},[898,18575,2000],{},[1693,18577,1695],{},[1762,18579,9987],{},[902,18581,18582],{"encoding":904},"c = 100",[724,18584,18585],{},[883,18586,18588],{"className":18587},[886],[888,18589,18590],{"xmlns":890},[892,18591,18592,18624],{},[895,18593,18594,18596,18598,18600,18602,18604,18606,18608,18610,18612,18614,18616,18618],{},[898,18595,2663],{},[898,18597,2971],{},[1693,18599,1709],{"stretchy":1708},[898,18601,1712],{},[1693,18603,1731],{"stretchy":1708},[1693,18605,1695],{},[1762,18607,9987],{},[1693,18609,1892],{},[1762,18611,2398],{},[898,18613,1712],{},[1693,18615,1892],{},[1762,18617,9695],{},[1717,18619,18620,18622],{},[898,18621,1712],{},[1762,18623,2398],{},[902,18625,18626],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,18628,820],{"id":18629},"přebytek-spotřebitele-a-výrobce",[724,18631,18632],{},"Přebytek spotřebitele:",[724,18634,18635],{},[883,18636,18638],{"className":18637},[886],[888,18639,18640],{"xmlns":890},[892,18641,18642,18702],{},[895,18643,18644,18646,18648,18650,18656,18658,18660,18672,18674,18676,18678,18680,18682,18684,18686,18688,18694,18696],{},[898,18645,2971],{},[898,18647,3611],{},[1693,18649,1709],{"stretchy":1708},[3284,18651,18652,18654],{},[898,18653,1712],{},[1762,18655,1911],{},[1693,18657,1731],{"stretchy":1708},[1693,18659,1695],{},[5688,18661,18662,18664,18666],{},[1693,18663,6221],{},[1762,18665,1911],{},[3284,18667,18668,18670],{},[898,18669,1712],{},[1762,18671,1911],{},[898,18673,2738],{},[1693,18675,1709],{"stretchy":1708},[898,18677,1712],{},[1693,18679,1731],{"stretchy":1708},[1915,18681,2239],{},[898,18683,1771],{},[898,18685,1712],{},[1693,18687,1698],{},[3284,18689,18690,18692],{},[898,18691,1701],{},[1762,18693,1911],{},[1915,18695,2239],{},[3284,18697,18698,18700],{},[898,18699,1712],{},[1762,18701,1911],{},[902,18703,18704],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,18706,18707],{},"Přebytek výrobce:",[724,18709,18710],{},[883,18711,18713],{"className":18712},[886],[888,18714,18715],{"xmlns":890},[892,18716,18717,18777],{},[895,18718,18719,18721,18723,18725,18731,18733,18735,18741,18743,18749,18751,18763,18765,18767,18769,18771,18773,18775],{},[898,18720,1701],{},[898,18722,3611],{},[1693,18724,1709],{"stretchy":1708},[3284,18726,18727,18729],{},[898,18728,1712],{},[1762,18730,1911],{},[1693,18732,1731],{"stretchy":1708},[1693,18734,1695],{},[3284,18736,18737,18739],{},[898,18738,1701],{},[1762,18740,1911],{},[1915,18742,2239],{},[3284,18744,18745,18747],{},[898,18746,1712],{},[1762,18748,1911],{},[1693,18750,1698],{},[5688,18752,18753,18755,18757],{},[1693,18754,6221],{},[1762,18756,1911],{},[3284,18758,18759,18761],{},[898,18760,1712],{},[1762,18762,1911],{},[898,18764,3611],{},[1693,18766,1709],{"stretchy":1708},[898,18768,1712],{},[1693,18770,1731],{"stretchy":1708},[1915,18772,2239],{},[898,18774,1771],{},[898,18776,1712],{},[902,18778,18779],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,18781,18782,18783,1789],{},"Detailně viz ",[207,18784,2181],{"className":18785,"dataFsResolvedFilePath":800,"href":801},[210],[115,18787,8685],{"id":8684},[120,18789,18790,18797,18804],{},[123,18791,18792,1863,18794],{},[38,18793,10689],{},[207,18795,766],{"className":18796,"dataFsResolvedFilePath":764,"href":765},[210],[123,18798,18799,1863,18801],{},[38,18800,10697],{},[207,18802,784],{"className":18803,"dataFsResolvedFilePath":782,"href":783},[210],[123,18805,18806,1863,18808,18811,18812,18815],{},[38,18807,10705],{},[207,18809,3261],{"className":18810,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,18813,2181],{"className":18814,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":18817},[18818,18819,18820,18825],{"id":17990,"depth":642,"text":17991},{"id":18118,"depth":642,"text":18119},{"id":18247,"depth":642,"text":18248,"children":18821},[18822,18823,18824],{"id":18251,"depth":649,"text":18252},{"id":18427,"depth":649,"text":18428},{"id":18629,"depth":649,"text":820},{"id":8684,"depth":642,"text":8685},"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":18826},[1135],"topics\u002Fintegral",[1128,18833,18834,18835,18836,18837,18838],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":18841,"title":18842,"body":18843,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":23087,"navigation":664,"path":23088,"seo":23089,"sources":23090,"stem":23091,"tags":23092,"type":10745,"updated":677,"__hash__":23098},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":18844,"toc":23075},[18845,18848,18852,18988,18995,18999,19068,19106,19208,19212,19242,19308,19353,19356,19425,19428,19463,19499,19503,19550,19557,19603,19649,19652,19731,19828,19911,19915,19959,19989,19995,20024,20046,20095,20148,20214,20217,20283,20312,20371,20387,20474,20571,20702,20706,20862,21011,21389,21393,21396,21455,21458,21544,21571,21609,21612,21649,21689,21723,21725,21762,21794,21892,21897,22021,22073,22154,22293,22297,22417,22424,22535,22542,22546,23018,23020],[12,18846,18842],{"id":18847},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,18849,18851],{"id":18850},"tldr","TL;DR",[724,18853,18854,18857,18858,16877,18861,18874,18875,18888,18889,18892,18893,1343,18896,18899,18900,1343,18903,18906,18907,1863,18910,18939,18940,8559,18942,1343,18955,8586,18968,18970,18971,3042],{},[38,18855,18856],{},"IS-LM"," je makroekonomický model se ",[38,18859,18860],{},"dvěma neznámými",[883,18862,18864],{"className":18863},[886],[888,18865,18866],{"xmlns":890},[892,18867,18868,18872],{},[895,18869,18870],{},[898,18871,4618],{},[902,18873,4618],{"encoding":904}," — národní důchod a ",[883,18876,18878],{"className":18877},[886],[888,18879,18880],{"xmlns":890},[892,18881,18882,18886],{},[895,18883,18884],{},[898,18885,6629],{},[902,18887,6629],{"encoding":904}," — úroková míra) a ",[38,18890,18891],{},"dvěma trhy",": trhem zboží (křivka ",[38,18894,18895],{},"IS",[614,18897,18898],{},"Investment = Savings",") a trhem peněz (křivka ",[38,18901,18902],{},"LM",[614,18904,18905],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,18908,18909],{},"simultánní rovnováhu",[883,18911,18913],{"className":18912},[886],[888,18914,18915],{"xmlns":890},[892,18916,18917,18937],{},[895,18918,18919,18921,18927,18929,18935],{},[1693,18920,1709],{"stretchy":1708},[1717,18922,18923,18925],{},[898,18924,4618],{},[898,18926,1691],{},[1693,18928,1899],{"separator":1898},[1717,18930,18931,18933],{},[898,18932,6629],{},[898,18934,1691],{},[1693,18936,1731],{"stretchy":1708},[902,18938,8554],{"encoding":904},", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,18941,8558],{},[883,18943,18945],{"className":18944},[886],[888,18946,18947],{"xmlns":890},[892,18948,18949,18953],{},[895,18950,18951],{},[898,18952,6984],{},[902,18954,6984],{"encoding":904},[883,18956,18958],{"className":18957},[886],[888,18959,18960],{"xmlns":890},[892,18961,18962,18966],{},[895,18963,18964],{},[898,18965,2663],{},[902,18967,2663],{"encoding":904},[38,18969,8589],{}," (posun LM změnou nabídky peněz ",[883,18972,18974],{"className":18973},[886],[888,18975,18976],{"xmlns":890},[892,18977,18978,18986],{},[895,18979,18980],{},[1717,18981,18982,18984],{},[898,18983,2839],{},[1693,18985,3672],{},[902,18987,8460],{"encoding":904},[724,18989,18990],{},[9465,18991],{"alt":18992,"className":18993,"src":18994},"imek-is-lm-model",[210,9469],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,18996,18998],{"id":18997},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,19000,19001,19002,19006,19007,16877,19010,19032,19033,19036,19037,19053,19054,19067],{},"V modelech ",[207,19003,19005],{"className":19004,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,19008,19009],{},"investice pokládány za konstantní",[883,19011,19013],{"className":19012},[886],[888,19014,19015],{"xmlns":890},[892,19016,19017,19029],{},[895,19018,19019,19021,19023],{},[898,19020,6998],{},[1693,19022,1695],{},[1717,19024,19025,19027],{},[898,19026,6998],{},[1693,19028,3672],{},[902,19030,19031],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,19034,19035],{},"ceně peněz",", tedy na ",[38,19038,19039,19040],{},"úrokové míře ",[883,19041,19043],{"className":19042},[886],[888,19044,19045],{"xmlns":890},[892,19046,19047,19051],{},[895,19048,19049],{},[898,19050,6629],{},[902,19052,6629],{"encoding":904},": čím vyšší ",[883,19055,19057],{"className":19056},[886],[888,19058,19059],{"xmlns":890},[892,19060,19061,19065],{},[895,19062,19063],{},[898,19064,6629],{},[902,19066,6629],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,19069,19070,19100],{},[123,19071,19072,1863,19075,19099],{},[38,19073,19074],{},"funkci investic",[883,19076,19078],{"className":19077},[886],[888,19079,19080],{"xmlns":890},[892,19081,19082,19096],{},[895,19083,19084,19086,19088,19090,19092,19094],{},[898,19085,6998],{},[1693,19087,1695],{},[898,19089,6998],{},[1693,19091,1709],{"stretchy":1708},[898,19093,6629],{},[1693,19095,1731],{"stretchy":1708},[902,19097,19098],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,19101,19102,19105],{},[38,19103,19104],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1636,19107,19108],{},[724,19109,19110,19112,19113,19132,19133,19159,19160,19173,19174,19203,19204,19207],{},[883,19111,8654],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,19114,19116],{"className":19115},[886],[888,19117,19118],{"xmlns":890},[892,19119,19120,19129],{},[895,19121,19122,19124,19127],{},[898,19123,2971],{},[1915,19125,19126],{},"-",[898,19128,6998],{},[902,19130,19131],{"encoding":904},"C\\text{-}I"," až ",[883,19134,19136],{"className":19135},[886],[888,19137,19138],{"xmlns":890},[892,19139,19140,19156],{},[895,19141,19142,19144,19146,19148,19150,19152,19154],{},[898,19143,2971],{},[1915,19145,19126],{},[898,19147,6998],{},[1915,19149,19126],{},[898,19151,6984],{},[1915,19153,19126],{},[898,19155,7007],{},[902,19157,19158],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,19161,19163],{"className":19162},[886],[888,19164,19165],{"xmlns":890},[892,19166,19167,19171],{},[895,19168,19169],{},[898,19170,4618],{},[902,19172,4618],{"encoding":904},". V IS-LM jsou ",[38,19175,19176,19177,4286,19190],{},"dvě neznámé ",[883,19178,19180],{"className":19179},[886],[888,19181,19182],{"xmlns":890},[892,19183,19184,19188],{},[895,19185,19186],{},[898,19187,4618],{},[902,19189,4618],{"encoding":904},[883,19191,19193],{"className":19192},[886],[888,19194,19195],{"xmlns":890},[892,19196,19197,19201],{},[895,19198,19199],{},[898,19200,6629],{},[902,19202,6629],{"encoding":904},", a proto potřebujeme ",[38,19205,19206],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,19209,19211],{"id":19210},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,19213,19214,19215,19228,19229,4300],{},"Lineární závislost investic ",[883,19216,19218],{"className":19217},[886],[888,19219,19220],{"xmlns":890},[892,19221,19222,19226],{},[895,19223,19224],{},[898,19225,6998],{},[902,19227,6998],{"encoding":904}," na úrokové míře ",[883,19230,19232],{"className":19231},[886],[888,19233,19234],{"xmlns":890},[892,19235,19236,19240],{},[895,19237,19238],{},[898,19239,6629],{},[902,19241,6629],{"encoding":904},[724,19243,19244],{},[883,19245,19247],{"className":19246},[886],[888,19248,19249],{"xmlns":890},[892,19250,19251,19305],{},[895,19252,19253,19255,19257,19259,19261,19263,19265,19267,19269,19271,19273,19275,19277,19279,19281,19283,19285,19287,19289,19291,19293,19296,19298,19300,19303],{},[898,19254,6998],{},[1693,19256,1695],{},[898,19258,6998],{},[1693,19260,1709],{"stretchy":1708},[898,19262,6629],{},[1693,19264,1731],{"stretchy":1708},[1693,19266,1695],{},[898,19268,2000],{},[898,19270,6629],{},[1693,19272,1892],{},[898,19274,1771],{},[1693,19276,1899],{"separator":1898},[1901,19278],{"width":1903},[898,19280,2000],{},[1693,19282,1908],{},[1762,19284,1911],{},[1693,19286,1899],{"separator":1898},[1915,19288,9204],{},[898,19290,1771],{},[1693,19292,1922],{},[1762,19294,19295],{},"0.",[1901,19297],{"width":1903},[1693,19299,1709],{"stretchy":1708},[1762,19301,19302],{},"7.11",[1693,19304,1731],{"stretchy":1708},[902,19306,19307],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,19309,19310,19331],{},[123,19311,19312,19330],{},[883,19313,19315],{"className":19314},[886],[888,19316,19317],{"xmlns":890},[892,19318,19319,19327],{},[895,19320,19321,19323,19325],{},[898,19322,1771],{},[1693,19324,1922],{},[1762,19326,1911],{},[902,19328,19329],{"encoding":904},"d > 0"," zřejmé,",[123,19332,19333,19350,19351,1789],{},[883,19334,19336],{"className":19335},[886],[888,19337,19338],{"xmlns":890},[892,19339,19340,19348],{},[895,19341,19342,19344,19346],{},[898,19343,2000],{},[1693,19345,1908],{},[1762,19347,1911],{},[902,19349,8089],{"encoding":904},", protože růst úrokové míry tlumí investice — funkce investic je ",[38,19352,5676],{},[724,19354,19355],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,19357,19358],{},[883,19359,19361],{"className":19360},[886],[888,19362,19363],{"xmlns":890},[892,19364,19365,19422],{},[895,19366,19367,19369,19371,19373,19375,19377,19379,19381,19383,19385,19387,19389,19391,19393,19395,19397,19399,19401,19403,19405,19407,19409,19411,19413,19415,19417,19420],{},[898,19368,2971],{},[1693,19370,1695],{},[898,19372,2971],{},[1693,19374,1709],{"stretchy":1708},[898,19376,4618],{},[1693,19378,1731],{"stretchy":1708},[1693,19380,1695],{},[898,19382,207],{},[898,19384,4618],{},[1693,19386,1892],{},[898,19388,1895],{},[1693,19390,1899],{"separator":1898},[1901,19392],{"width":1903},[1762,19394,1911],{},[1693,19396,1908],{},[898,19398,207],{},[1693,19400,1908],{},[1762,19402,1764],{},[1693,19404,1899],{"separator":1898},[1915,19406,9204],{},[898,19408,1895],{},[1693,19410,1922],{},[1762,19412,19295],{},[1901,19414],{"width":1903},[1693,19416,1709],{"stretchy":1708},[1762,19418,19419],{},"7.12",[1693,19421,1731],{"stretchy":1708},[902,19423,19424],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,19426,19427],{},"Podmínka rovnováhy na trhu zboží:",[724,19429,19430],{},[883,19431,19433],{"className":19432},[886],[888,19434,19435],{"xmlns":890},[892,19436,19437,19460],{},[895,19438,19439,19441,19443,19445,19447,19449,19451,19453,19455,19458],{},[898,19440,4618],{},[1693,19442,1695],{},[898,19444,2971],{},[1693,19446,1892],{},[898,19448,6998],{},[898,19450,1789],{"mathvariant":1704},[1901,19452],{"width":1903},[1693,19454,1709],{"stretchy":1708},[1762,19456,19457],{},"7.13",[1693,19459,1731],{"stretchy":1708},[902,19461,19462],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,19464,19465,19466,1863,19469,19495,19496,1789],{},"To dává ",[38,19467,19468],{},"tři rovnice o čtyřech neznámých",[883,19470,19472],{"className":19471},[886],[888,19473,19474],{"xmlns":890},[892,19475,19476,19492],{},[895,19477,19478,19480,19482,19484,19486,19488,19490],{},[898,19479,4618],{},[1693,19481,1899],{"separator":1898},[898,19483,2971],{},[1693,19485,1899],{"separator":1898},[898,19487,6998],{},[1693,19489,1899],{"separator":1898},[898,19491,6629],{},[902,19493,19494],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,19497,19498],{},"rovnováhy na trhu peněz",[115,19500,19502],{"id":19501},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,19504,19505,19506,12437,19527,19545,19546,19549],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,19507,19509],{"className":19508},[886],[888,19510,19511],{"xmlns":890},[892,19512,19513,19525],{},[895,19514,19515,19517,19519,19521,19523],{},[898,19516,4618],{},[1693,19518,1695],{},[898,19520,2971],{},[1693,19522,1892],{},[898,19524,3611],{},[902,19526,7048],{"encoding":904},[883,19528,19530],{"className":19529},[886],[888,19531,19532],{"xmlns":890},[892,19533,19534,19542],{},[895,19535,19536,19538,19540],{},[898,19537,6998],{},[1693,19539,1695],{},[898,19541,3611],{},[902,19543,19544],{"encoding":904},"I = S"," (plánované ",[38,19547,19548],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,19551,19552],{},[9465,19553],{"alt":19554,"className":19555,"src":19556},"imek-odvozeni-is-4panelu",[210,9469],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,19558,19559],{},[883,19560,19562],{"className":19561},[886],[888,19563,19564],{"xmlns":890},[892,19565,19566,19600],{},[895,19567,19568,19570,19572,19574,19576,19578,19580,19582,19584,19586,19588,19590,19592,19594,19596,19598],{},[898,19569,4618],{},[1693,19571,1695],{},[1693,19573,1709],{"stretchy":1708},[898,19575,207],{},[898,19577,4618],{},[1693,19579,1892],{},[898,19581,1895],{},[1693,19583,1731],{"stretchy":1708},[1693,19585,1892],{},[1693,19587,1709],{"stretchy":1708},[898,19589,2000],{},[898,19591,6629],{},[1693,19593,1892],{},[898,19595,1771],{},[1693,19597,1731],{"stretchy":1708},[1693,19599,1899],{"separator":1898},[902,19601,19602],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,19604,19605],{},[883,19606,19608],{"className":19607},[886],[888,19609,19610],{"xmlns":890},[892,19611,19612,19646],{},[895,19613,19614,19616,19618,19620,19622,19624,19626,19628,19630,19632,19634,19636,19638,19640,19642,19644],{},[1693,19615,1709],{"stretchy":1708},[1762,19617,1764],{},[1693,19619,1698],{},[898,19621,207],{},[1693,19623,1731],{"stretchy":1708},[898,19625,4618],{},[1693,19627,1698],{},[898,19629,2000],{},[898,19631,6629],{},[1693,19633,1698],{},[898,19635,1895],{},[1693,19637,1698],{},[898,19639,1771],{},[1693,19641,1695],{},[1762,19643,1911],{},[1693,19645,1899],{"separator":1898},[902,19647,19648],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,19650,19651],{},"odkud",[724,19653,19654],{},[883,19655,19657],{"className":19656},[886],[888,19658,19659],{"xmlns":890},[892,19660,19661,19728],{},[895,19662,19663,19719,19721,19723,19726],{},[19664,19665,19667],"menclose",{"notation":19666},"box",[3638,19668,19669],{"scriptlevel":1911,"displaystyle":1708},[3638,19670,19671],{"scriptlevel":1911,"displaystyle":1708},[3638,19672,19673],{"scriptlevel":1911,"displaystyle":1898},[895,19674,19675,19677,19679,19681,19693,19695,19697,19699,19717],{},[1915,19676,2239],{},[898,19678,4618],{},[1693,19680,1695],{},[2132,19682,19683,19685],{},[898,19684,2000],{},[895,19686,19687,19689,19691],{},[1762,19688,1764],{},[1693,19690,1698],{},[898,19692,207],{},[1915,19694,2239],{},[898,19696,6629],{},[1693,19698,1892],{},[2132,19700,19701,19709],{},[895,19702,19703,19705,19707],{},[898,19704,1895],{},[1693,19706,1892],{},[898,19708,1771],{},[895,19710,19711,19713,19715],{},[1762,19712,1764],{},[1693,19714,1698],{},[898,19716,207],{},[1915,19718,2239],{},[1901,19720],{"width":1903},[1693,19722,1709],{"stretchy":1708},[1762,19724,19725],{},"7.14",[1693,19727,1731],{"stretchy":1708},[902,19729,19730],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,19732,19733,19734,16877,19737,19740,19741,19744,19745,19747,19748,19770,19771,19799,19800,19821,19822,19824,19825,19827],{},"Tento vztah se nazývá ",[38,19735,19736],{},"funkce IS",[614,19738,19739],{},"IS schedule",") a její graf ",[38,19742,19743],{},"křivka IS",". Křivka je ",[38,19746,5676],{}," přímka v rovině ",[883,19749,19751],{"className":19750},[886],[888,19752,19753],{"xmlns":890},[892,19754,19755,19767],{},[895,19756,19757,19759,19761,19763,19765],{},[1693,19758,1709],{"stretchy":1708},[898,19760,6629],{},[1693,19762,1899],{"separator":1898},[898,19764,4618],{},[1693,19766,1731],{"stretchy":1708},[902,19768,19769],{"encoding":904},"(r, Y)",", neboť ",[883,19772,19774],{"className":19773},[886],[888,19775,19776],{"xmlns":890},[892,19777,19778,19796],{},[895,19779,19780,19792,19794],{},[2132,19781,19782,19784],{},[898,19783,2000],{},[895,19785,19786,19788,19790],{},[1762,19787,1764],{},[1693,19789,1698],{},[898,19791,207],{},[1693,19793,1908],{},[1762,19795,1911],{},[902,19797,19798],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,19801,19803],{"className":19802},[886],[888,19804,19805],{"xmlns":890},[892,19806,19807,19819],{},[895,19808,19809,19811,19813,19815,19817],{},[1693,19810,1709],{"stretchy":1708},[898,19812,6629],{},[1693,19814,1899],{"separator":1898},[898,19816,4618],{},[1693,19818,1731],{"stretchy":1708},[902,19820,19769],{"encoding":904},", pro které plánované ",[38,19823,6998],{},"nvestment = ",[38,19826,3611],{},"avings.",[1636,19829,19830],{},[724,19831,19832,19834,19835,19848,19849,1863,19852,19865,19866,19879,19880,4286,19893,19906,19907,19910],{},[883,19833,11036],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,19836,19838],{"className":19837},[886],[888,19839,19840],{"xmlns":890},[892,19841,19842,19846],{},[895,19843,19844],{},[898,19845,6629],{},[902,19847,6629],{"encoding":904}," → levnější úvěr → ",[38,19850,19851],{},"více investic",[883,19853,19855],{"className":19854},[886],[888,19856,19857],{"xmlns":890},[892,19858,19859,19863],{},[895,19860,19861],{},[898,19862,6998],{},[902,19864,6998],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,19867,19869],{"className":19868},[886],[888,19870,19871],{"xmlns":890},[892,19872,19873,19877],{},[895,19874,19875],{},[898,19876,4618],{},[902,19878,4618],{"encoding":904},". Vztah mezi ",[883,19881,19883],{"className":19882},[886],[888,19884,19885],{"xmlns":890},[892,19886,19887,19891],{},[895,19888,19889],{},[898,19890,6629],{},[902,19892,6629],{"encoding":904},[883,19894,19896],{"className":19895},[886],[888,19897,19898],{"xmlns":890},[892,19899,19900,19904],{},[895,19901,19902],{},[898,19903,4618],{},[902,19905,4618],{"encoding":904}," na trhu zboží je proto ",[38,19908,19909],{},"nepřímý"," (klesající křivka).",[115,19912,19914],{"id":19913},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,19916,19917,19918,19936,19937,7617,19955,19958],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,19919,19921],{"className":19920},[886],[888,19922,19923],{"xmlns":890},[892,19924,19925,19933],{},[895,19926,19927],{},[1717,19928,19929,19931],{},[898,19930,2839],{},[898,19932,2738],{},[902,19934,19935],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,19938,19940],{"className":19939},[886],[888,19941,19942],{"xmlns":890},[892,19943,19944,19952],{},[895,19945,19946],{},[1717,19947,19948,19950],{},[898,19949,2839],{},[898,19951,3611],{},[902,19953,19954],{"encoding":904},"M^S",[38,19956,19957],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,19960,19961],{},[883,19962,19964],{"className":19963},[886],[888,19965,19966],{"xmlns":890},[892,19967,19968,19986],{},[895,19969,19970,19976,19978,19984],{},[1717,19971,19972,19974],{},[898,19973,2839],{},[898,19975,3611],{},[1693,19977,1695],{},[1717,19979,19980,19982],{},[898,19981,2839],{},[1693,19983,3672],{},[898,19985,1789],{"mathvariant":1704},[902,19987,19988],{"encoding":904},"M^S = M^*.",[724,19990,19991,19994],{},[38,19992,19993],{},"Poptávka"," po penězích má tři zdroje:",[120,19996,19997,20006,20015],{},[123,19998,19999,16877,20002,20005],{},[38,20000,20001],{},"transakční poptávka",[614,20003,20004],{},"transactions demand",") — peníze pro nákup zboží,",[123,20007,20008,16877,20011,20014],{},[38,20009,20010],{},"opatrnostní poptávka",[614,20012,20013],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,20016,20017,16877,20020,20023],{},[38,20018,20019],{},"spekulační poptávka",[614,20021,20022],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,20025,20026,20027,20045],{},"Součet transakční a opatrnostní poptávky ",[883,20028,20030],{"className":20029},[886],[888,20031,20032],{"xmlns":890},[892,20033,20034,20042],{},[895,20035,20036],{},[3284,20037,20038,20040],{},[898,20039,4840],{},[1762,20041,1764],{},[902,20043,20044],{"encoding":904},"L_1"," je úměrný důchodu:",[724,20047,20048],{},[883,20049,20051],{"className":20050},[886],[888,20052,20053],{"xmlns":890},[892,20054,20055,20092],{},[895,20056,20057,20063,20065,20071,20073,20075,20077,20079,20081,20087,20089],{},[3284,20058,20059,20061],{},[898,20060,4840],{},[1762,20062,1764],{},[1693,20064,1695],{},[3284,20066,20067,20069],{},[898,20068,8334],{},[1762,20070,1764],{},[898,20072,4618],{},[1693,20074,1899],{"separator":1898},[1901,20076],{"width":1903},[1762,20078,1911],{},[1693,20080,1908],{},[3284,20082,20083,20085],{},[898,20084,8334],{},[1762,20086,1764],{},[1693,20088,1908],{},[1762,20090,20091],{},"1.",[902,20093,20094],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,20096,20097,20098,20116,20117,1343,20130,20147],{},"Spekulační poptávka ",[883,20099,20101],{"className":20100},[886],[888,20102,20103],{"xmlns":890},[892,20104,20105,20113],{},[895,20106,20107],{},[3284,20108,20109,20111],{},[898,20110,4840],{},[1762,20112,2398],{},[902,20114,20115],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,20118,20120],{"className":20119},[886],[888,20121,20122],{"xmlns":890},[892,20123,20124,20128],{},[895,20125,20126],{},[898,20127,6629],{},[902,20129,6629],{"encoding":904},[883,20131,20133],{"className":20132},[886],[888,20134,20135],{"xmlns":890},[892,20136,20137,20145],{},[895,20138,20139],{},[3284,20140,20141,20143],{},[898,20142,4840],{},[1762,20144,2398],{},[902,20146,20115],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,20149,20150],{},[883,20151,20153],{"className":20152},[886],[888,20154,20155],{"xmlns":890},[892,20156,20157,20211],{},[895,20158,20159,20165,20167,20173,20175,20177,20183,20185,20187,20193,20195,20197,20199,20201,20207,20209],{},[3284,20160,20161,20163],{},[898,20162,4840],{},[1762,20164,2398],{},[1693,20166,1695],{},[3284,20168,20169,20171],{},[898,20170,8334],{},[1762,20172,2398],{},[898,20174,6629],{},[1693,20176,1892],{},[3284,20178,20179,20181],{},[898,20180,8334],{},[1762,20182,8357],{},[1693,20184,1899],{"separator":1898},[1901,20186],{"width":1903},[3284,20188,20189,20191],{},[898,20190,8334],{},[1762,20192,2398],{},[1693,20194,1908],{},[1762,20196,1911],{},[1693,20198,1899],{"separator":1898},[1915,20200,9204],{},[3284,20202,20203,20205],{},[898,20204,8334],{},[1762,20206,8357],{},[1693,20208,1922],{},[1762,20210,19295],{},[902,20212,20213],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,20215,20216],{},"Celková poptávka po penězích:",[724,20218,20219],{},[883,20220,20222],{"className":20221},[886],[888,20223,20224],{"xmlns":890},[892,20225,20226,20280],{},[895,20227,20228,20234,20236,20242,20244,20250,20252,20258,20260,20262,20268,20270,20272,20278],{},[1717,20229,20230,20232],{},[898,20231,2839],{},[898,20233,2738],{},[1693,20235,1695],{},[3284,20237,20238,20240],{},[898,20239,4840],{},[1762,20241,1764],{},[1693,20243,1892],{},[3284,20245,20246,20248],{},[898,20247,4840],{},[1762,20249,2398],{},[1693,20251,1695],{},[3284,20253,20254,20256],{},[898,20255,8334],{},[1762,20257,1764],{},[898,20259,4618],{},[1693,20261,1892],{},[3284,20263,20264,20266],{},[898,20265,8334],{},[1762,20267,2398],{},[898,20269,6629],{},[1693,20271,1892],{},[3284,20273,20274,20276],{},[898,20275,8334],{},[1762,20277,8357],{},[898,20279,1789],{"mathvariant":1704},[902,20281,20282],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,20284,20285,20286,4300],{},"Podmínka rovnováhy na trhu peněz ",[883,20287,20289],{"className":20288},[886],[888,20290,20291],{"xmlns":890},[892,20292,20293,20309],{},[895,20294,20295,20301,20303],{},[1717,20296,20297,20299],{},[898,20298,2839],{},[898,20300,2738],{},[1693,20302,1695],{},[1717,20304,20305,20307],{},[898,20306,2839],{},[1693,20308,3672],{},[902,20310,20311],{"encoding":904},"M^D = M^*",[724,20313,20314],{},[883,20315,20317],{"className":20316},[886],[888,20318,20319],{"xmlns":890},[892,20320,20321,20368],{},[895,20322,20323,20329,20331,20337,20339,20341,20347,20349,20351,20357,20359,20361,20363,20366],{},[1717,20324,20325,20327],{},[898,20326,2839],{},[1693,20328,3672],{},[1693,20330,1695],{},[3284,20332,20333,20335],{},[898,20334,8334],{},[1762,20336,1764],{},[898,20338,4618],{},[1693,20340,1892],{},[3284,20342,20343,20345],{},[898,20344,8334],{},[1762,20346,2398],{},[898,20348,6629],{},[1693,20350,1892],{},[3284,20352,20353,20355],{},[898,20354,8334],{},[1762,20356,8357],{},[1693,20358,1899],{"separator":1898},[1901,20360],{"width":1903},[1693,20362,1709],{"stretchy":1708},[1762,20364,20365],{},"7.15",[1693,20367,1731],{"stretchy":1708},[902,20369,20370],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,20372,20373,20374,10048],{},"po úpravě (vyjádření ",[883,20375,20377],{"className":20376},[886],[888,20378,20379],{"xmlns":890},[892,20380,20381,20385],{},[895,20382,20383],{},[898,20384,4618],{},[902,20386,4618],{"encoding":904},[724,20388,20389],{},[883,20390,20392],{"className":20391},[886],[888,20393,20394],{"xmlns":890},[892,20395,20396,20471],{},[895,20397,20398,20462,20464,20466,20469],{},[19664,20399,20400],{"notation":19666},[3638,20401,20402],{"scriptlevel":1911,"displaystyle":1708},[3638,20403,20404],{"scriptlevel":1911,"displaystyle":1708},[3638,20405,20406],{"scriptlevel":1911,"displaystyle":1898},[895,20407,20408,20410,20412,20414,20416,20430,20432,20434,20436,20460],{},[1915,20409,2239],{},[898,20411,4618],{},[1693,20413,1695],{},[1693,20415,1698],{},[2132,20417,20418,20424],{},[3284,20419,20420,20422],{},[898,20421,8334],{},[1762,20423,2398],{},[3284,20425,20426,20428],{},[898,20427,8334],{},[1762,20429,1764],{},[1915,20431,2239],{},[898,20433,6629],{},[1693,20435,1892],{},[2132,20437,20438,20454],{},[895,20439,20440,20446,20448],{},[1717,20441,20442,20444],{},[898,20443,2839],{},[1693,20445,3672],{},[1693,20447,1698],{},[3284,20449,20450,20452],{},[898,20451,8334],{},[1762,20453,8357],{},[3284,20455,20456,20458],{},[898,20457,8334],{},[1762,20459,1764],{},[1915,20461,2239],{},[1901,20463],{"width":1903},[1693,20465,1709],{"stretchy":1708},[1762,20467,20468],{},"7.16",[1693,20470,1731],{"stretchy":1708},[902,20472,20473],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,20475,19733,20476,16877,20479,20482,20483,19744,20486,19747,20489,19770,20510,20542,20543,20565,20566,8468,20568,20570],{},[38,20477,20478],{},"funkce LM",[614,20480,20481],{},"LM schedule","), její graf ",[38,20484,20485],{},"křivka LM",[38,20487,20488],{},"rostoucí",[883,20490,20492],{"className":20491},[886],[888,20493,20494],{"xmlns":890},[892,20495,20496,20508],{},[895,20497,20498,20500,20502,20504,20506],{},[1693,20499,1709],{"stretchy":1708},[898,20501,6629],{},[1693,20503,1899],{"separator":1898},[898,20505,4618],{},[1693,20507,1731],{"stretchy":1708},[902,20509,19769],{"encoding":904},[883,20511,20513],{"className":20512},[886],[888,20514,20515],{"xmlns":890},[892,20516,20517,20539],{},[895,20518,20519,20521,20535,20537],{},[1693,20520,1698],{},[2132,20522,20523,20529],{},[3284,20524,20525,20527],{},[898,20526,8334],{},[1762,20528,2398],{},[3284,20530,20531,20533],{},[898,20532,8334],{},[1762,20534,1764],{},[1693,20536,1922],{},[1762,20538,1911],{},[902,20540,20541],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,20544,20546],{"className":20545},[886],[888,20547,20548],{"xmlns":890},[892,20549,20550,20562],{},[895,20551,20552,20558,20560],{},[3284,20553,20554,20556],{},[898,20555,8334],{},[1762,20557,2398],{},[1693,20559,1908],{},[1762,20561,1911],{},[902,20563,20564],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,20567,4840],{},[38,20569,2839],{},"oney.",[1636,20572,20573],{},[724,20574,20575,20577,20578,20591,20592,20620,20621,20638,20639,20652,20653,20670,20671,4286,20684,20697,20698,20701],{},[883,20576,11036],{}," Intuice — proč LM roste\nVyšší důchod ",[883,20579,20581],{"className":20580},[886],[888,20582,20583],{"xmlns":890},[892,20584,20585,20589],{},[895,20586,20587],{},[898,20588,4618],{},[902,20590,4618],{"encoding":904}," → větší transakční poptávka po penězích ",[883,20593,20595],{"className":20594},[886],[888,20596,20597],{"xmlns":890},[892,20598,20599,20617],{},[895,20600,20601,20607,20609,20615],{},[3284,20602,20603,20605],{},[898,20604,4840],{},[1762,20606,1764],{},[1693,20608,1695],{},[3284,20610,20611,20613],{},[898,20612,8334],{},[1762,20614,1764],{},[898,20616,4618],{},[902,20618,20619],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,20622,20624],{"className":20623},[886],[888,20625,20626],{"xmlns":890},[892,20627,20628,20636],{},[895,20629,20630],{},[1717,20631,20632,20634],{},[898,20633,2839],{},[1693,20635,3672],{},[902,20637,8460],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,20640,20642],{"className":20641},[886],[888,20643,20644],{"xmlns":890},[892,20645,20646,20650],{},[895,20647,20648],{},[898,20649,6629],{},[902,20651,6629],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,20654,20656],{"className":20655},[886],[888,20657,20658],{"xmlns":890},[892,20659,20660,20668],{},[895,20661,20662],{},[3284,20663,20664,20666],{},[898,20665,4840],{},[1762,20667,2398],{},[902,20669,20115],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,20672,20674],{"className":20673},[886],[888,20675,20676],{"xmlns":890},[892,20677,20678,20682],{},[895,20679,20680],{},[898,20681,4618],{},[902,20683,4618],{"encoding":904},[883,20685,20687],{"className":20686},[886],[888,20688,20689],{"xmlns":890},[892,20690,20691,20695],{},[895,20692,20693],{},[898,20694,6629],{},[902,20696,6629],{"encoding":904}," na trhu peněz je proto ",[38,20699,20700],{},"přímý"," (rostoucí křivka).",[115,20703,20705],{"id":20704},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,20707,20708,20709,20712,20713,1863,20716,4286,20733,1863,20736,20754,20755,20773,20774,20792,20793,20809,20810,4286,20825,20840,20841,1789],{},"Řešením ",[38,20710,20711],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,20714,20715],{},"rovnovážný důchod",[883,20717,20719],{"className":20718},[886],[888,20720,20721],{"xmlns":890},[892,20722,20723,20731],{},[895,20724,20725],{},[1717,20726,20727,20729],{},[898,20728,4618],{},[898,20730,1691],{},[902,20732,7862],{"encoding":904},[38,20734,20735],{},"rovnovážnou úrokovou míru",[883,20737,20739],{"className":20738},[886],[888,20740,20741],{"xmlns":890},[892,20742,20743,20751],{},[895,20744,20745],{},[1717,20746,20747,20749],{},[898,20748,6629],{},[898,20750,1691],{},[902,20752,20753],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,20756,20758],{"className":20757},[886],[888,20759,20760],{"xmlns":890},[892,20761,20762,20770],{},[895,20763,20764],{},[1717,20765,20766,20768],{},[898,20767,6998],{},[898,20769,1691],{},[902,20771,20772],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,20775,20777],{"className":20776},[886],[888,20778,20779],{"xmlns":890},[892,20780,20781,20789],{},[895,20782,20783],{},[1717,20784,20785,20787],{},[898,20786,2971],{},[898,20788,1691],{},[902,20790,20791],{"encoding":904},"C^E",". Graficky jde o ",[38,20794,20795,20796],{},"průsečík ",[883,20797,20799],{"className":20798},[886],[888,20800,20801],{"xmlns":890},[892,20802,20803,20807],{},[895,20804,20805],{},[898,20806,1691],{},[902,20808,1691],{"encoding":904}," křivek ",[883,20811,20813],{"className":20812},[886],[888,20814,20815],{"xmlns":890},[892,20816,20817,20823],{},[895,20818,20819,20821],{},[898,20820,6998],{},[898,20822,3611],{},[902,20824,18895],{"encoding":904},[883,20826,20828],{"className":20827},[886],[888,20829,20830],{"xmlns":890},[892,20831,20832,20838],{},[895,20833,20834,20836],{},[898,20835,4840],{},[898,20837,2839],{},[902,20839,18902],{"encoding":904}," v rovině ",[883,20842,20844],{"className":20843},[886],[888,20845,20846],{"xmlns":890},[892,20847,20848,20860],{},[895,20849,20850,20852,20854,20856,20858],{},[1693,20851,1709],{"stretchy":1708},[898,20853,6629],{},[1693,20855,1899],{"separator":1898},[898,20857,4618],{},[1693,20859,1731],{"stretchy":1708},[902,20861,19769],{"encoding":904},[724,20863,20864],{},[614,20865,20866,20867,20888,20889,20904,20905,20920,20921,20934,20935,20952,20953,8586,20966,20952,20983,20996,20997,21010],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,20868,20870],{"className":20869},[886],[888,20871,20872],{"xmlns":890},[892,20873,20874,20886],{},[895,20875,20876,20878,20880,20882,20884],{},[1693,20877,1709],{"stretchy":1708},[898,20879,6629],{},[1693,20881,1899],{"separator":1898},[898,20883,4618],{},[1693,20885,1731],{"stretchy":1708},[902,20887,19769],{"encoding":904},". Rostoucí přímka ",[883,20890,20892],{"className":20891},[886],[888,20893,20894],{"xmlns":890},[892,20895,20896,20902],{},[895,20897,20898,20900],{},[898,20899,4840],{},[898,20901,2839],{},[902,20903,18902],{"encoding":904}," a klesající přímka ",[883,20906,20908],{"className":20907},[886],[888,20909,20910],{"xmlns":890},[892,20911,20912,20918],{},[895,20913,20914,20916],{},[898,20915,6998],{},[898,20917,3611],{},[902,20919,18895],{"encoding":904}," se protínají v bodě ",[883,20922,20924],{"className":20923},[886],[888,20925,20926],{"xmlns":890},[892,20927,20928,20932],{},[895,20929,20930],{},[898,20931,1691],{},[902,20933,1691],{"encoding":904}," se souřadnicemi ",[883,20936,20938],{"className":20937},[886],[888,20939,20940],{"xmlns":890},[892,20941,20942,20950],{},[895,20943,20944],{},[1717,20945,20946,20948],{},[898,20947,6629],{},[898,20949,1691],{},[902,20951,20753],{"encoding":904}," (na ose ",[883,20954,20956],{"className":20955},[886],[888,20957,20958],{"xmlns":890},[892,20959,20960,20964],{},[895,20961,20962],{},[898,20963,6629],{},[902,20965,6629],{"encoding":904},[883,20967,20969],{"className":20968},[886],[888,20970,20971],{"xmlns":890},[892,20972,20973,20981],{},[895,20974,20975],{},[1717,20976,20977,20979],{},[898,20978,4618],{},[898,20980,1691],{},[902,20982,7862],{"encoding":904},[883,20984,20986],{"className":20985},[886],[888,20987,20988],{"xmlns":890},[892,20989,20990,20994],{},[895,20991,20992],{},[898,20993,4618],{},[902,20995,4618],{"encoding":904},"); tečkované čáry z ",[883,20998,21000],{"className":20999},[886],[888,21001,21002],{"xmlns":890},[892,21003,21004,21008],{},[895,21005,21006],{},[898,21007,1691],{},[902,21009,1691],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1636,21012,21013,21018],{},[724,21014,21015,21017],{},[883,21016,8620],{}," Postup — jak najít IS-LM rovnováhu",[152,21019,21020,21094,21162,21220,21293],{},[123,21021,21022,21025,21026,4286,21045,21064,21065,4286,21078,21091,21092,1789],{},[38,21023,21024],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,21027,21029],{"className":21028},[886],[888,21030,21031],{"xmlns":890},[892,21032,21033,21043],{},[895,21034,21035,21037,21039,21041],{},[898,21036,2971],{},[1693,21038,1709],{"stretchy":1708},[898,21040,4618],{},[1693,21042,1731],{"stretchy":1708},[902,21044,8195],{"encoding":904},[883,21046,21048],{"className":21047},[886],[888,21049,21050],{"xmlns":890},[892,21051,21052,21062],{},[895,21053,21054,21056,21058,21060],{},[898,21055,6998],{},[1693,21057,1709],{"stretchy":1708},[898,21059,6629],{},[1693,21061,1731],{"stretchy":1708},[902,21063,8215],{"encoding":904}," a vyjádři vztah mezi ",[883,21066,21068],{"className":21067},[886],[888,21069,21070],{"xmlns":890},[892,21071,21072,21076],{},[895,21073,21074],{},[898,21075,4618],{},[902,21077,4618],{"encoding":904},[883,21079,21081],{"className":21080},[886],[888,21082,21083],{"xmlns":890},[892,21084,21085,21089],{},[895,21086,21087],{},[898,21088,6629],{},[902,21090,6629],{"encoding":904}," — dostaneš rovnici ",[38,21093,18895],{},[123,21095,21096,21099,21100,4286,21117,21134,21135,21091,21160,1789],{},[38,21097,21098],{},"Z trhu peněz (7.15)"," dosaď ",[883,21101,21103],{"className":21102},[886],[888,21104,21105],{"xmlns":890},[892,21106,21107,21115],{},[895,21108,21109],{},[3284,21110,21111,21113],{},[898,21112,4840],{},[1762,21114,1764],{},[902,21116,20044],{"encoding":904},[883,21118,21120],{"className":21119},[886],[888,21121,21122],{"xmlns":890},[892,21123,21124,21132],{},[895,21125,21126],{},[3284,21127,21128,21130],{},[898,21129,4840],{},[1762,21131,2398],{},[902,21133,20115],{"encoding":904}," a vztah ",[883,21136,21138],{"className":21137},[886],[888,21139,21140],{"xmlns":890},[892,21141,21142,21158],{},[895,21143,21144,21150,21152],{},[1717,21145,21146,21148],{},[898,21147,2839],{},[898,21149,2738],{},[1693,21151,1695],{},[1717,21153,21154,21156],{},[898,21155,2839],{},[1693,21157,3672],{},[902,21159,20311],{"encoding":904},[38,21161,18902],{},[123,21163,21164,21167,21168,4286,21181,21194,21195,21219],{},[38,21165,21166],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,21169,21171],{"className":21170},[886],[888,21172,21173],{"xmlns":890},[892,21174,21175,21179],{},[895,21176,21177],{},[898,21178,4618],{},[902,21180,4618],{"encoding":904},[883,21182,21184],{"className":21183},[886],[888,21185,21186],{"xmlns":890},[892,21187,21188,21192],{},[895,21189,21190],{},[898,21191,6629],{},[902,21193,6629],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,21196,21198],{"className":21197},[886],[888,21199,21200],{"xmlns":890},[892,21201,21202,21216],{},[895,21203,21204,21206,21208,21210,21212,21214],{},[898,21205,4618],{},[1693,21207,1695],{},[898,21209,8934],{},[1693,21211,1709],{"stretchy":1708},[898,21213,6629],{},[1693,21215,1731],{"stretchy":1708},[902,21217,21218],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,21221,21222,1863,21225,4286,21259,1789],{},[38,21223,21224],{},"Zpětně dopočítej",[883,21226,21228],{"className":21227},[886],[888,21229,21230],{"xmlns":890},[892,21231,21232,21256],{},[895,21233,21234,21240,21242,21244,21246,21252,21254],{},[1717,21235,21236,21238],{},[898,21237,2971],{},[898,21239,1691],{},[1693,21241,1695],{},[898,21243,207],{},[1915,21245,2239],{},[1717,21247,21248,21250],{},[898,21249,4618],{},[898,21251,1691],{},[1693,21253,1892],{},[898,21255,1895],{},[902,21257,21258],{"encoding":904},"C^E = a\\,Y^E + b",[883,21260,21262],{"className":21261},[886],[888,21263,21264],{"xmlns":890},[892,21265,21266,21290],{},[895,21267,21268,21274,21276,21278,21280,21286,21288],{},[1717,21269,21270,21272],{},[898,21271,6998],{},[898,21273,1691],{},[1693,21275,1695],{},[898,21277,2000],{},[1915,21279,2239],{},[1717,21281,21282,21284],{},[898,21283,6629],{},[898,21285,1691],{},[1693,21287,1892],{},[898,21289,1771],{},[902,21291,21292],{"encoding":904},"I^E = c\\,r^E + d",[123,21294,21295,21298,21299,21333,21334,21388],{},[38,21296,21297],{},"Ověř:"," musí platit ",[883,21300,21302],{"className":21301},[886],[888,21303,21304],{"xmlns":890},[892,21305,21306,21330],{},[895,21307,21308,21314,21316,21322,21324],{},[1717,21309,21310,21312],{},[898,21311,4618],{},[898,21313,1691],{},[1693,21315,1695],{},[1717,21317,21318,21320],{},[898,21319,2971],{},[898,21321,1691],{},[1693,21323,1892],{},[1717,21325,21326,21328],{},[898,21327,6998],{},[898,21329,1691],{},[902,21331,21332],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,21335,21337],{"className":21336},[886],[888,21338,21339],{"xmlns":890},[892,21340,21341,21385],{},[895,21342,21343,21349,21351,21357,21363,21365,21371,21377,21379],{},[1717,21344,21345,21347],{},[898,21346,2839],{},[1693,21348,3672],{},[1693,21350,1695],{},[3284,21352,21353,21355],{},[898,21354,8334],{},[1762,21356,1764],{},[1717,21358,21359,21361],{},[898,21360,4618],{},[898,21362,1691],{},[1693,21364,1892],{},[3284,21366,21367,21369],{},[898,21368,8334],{},[1762,21370,2398],{},[1717,21372,21373,21375],{},[898,21374,6629],{},[898,21376,1691],{},[1693,21378,1892],{},[3284,21380,21381,21383],{},[898,21382,8334],{},[1762,21384,8357],{},[902,21386,21387],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,21390,21392],{"id":21391},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,21394,21395],{},"Pro trh zboží jsou dány:",[120,21397,21398,21426],{},[123,21399,21400,21401,1899],{},"spotřeba ",[883,21402,21404],{"className":21403},[886],[888,21405,21406],{"xmlns":890},[892,21407,21408,21423],{},[895,21409,21410,21412,21414,21417,21419,21421],{},[898,21411,2971],{},[1693,21413,1695],{},[1762,21415,21416],{},"0,8",[898,21418,4618],{},[1693,21420,1892],{},[1762,21422,9987],{},[902,21424,21425],{"encoding":904},"C = 0{,}8Y + 100",[123,21427,21428,21429,1789],{},"investice ",[883,21430,21432],{"className":21431},[886],[888,21433,21434],{"xmlns":890},[892,21435,21436,21452],{},[895,21437,21438,21440,21442,21444,21446,21448,21450],{},[898,21439,6998],{},[1693,21441,1695],{},[1693,21443,1698],{},[1762,21445,15892],{},[898,21447,6629],{},[1693,21449,1892],{},[1762,21451,9684],{},[902,21453,21454],{"encoding":904},"I = -20r + 1000",[724,21456,21457],{},"Pro trh peněz:",[120,21459,21460,21486,21518],{},[123,21461,21462,1899],{},[883,21463,21465],{"className":21464},[886],[888,21466,21467],{"xmlns":890},[892,21468,21469,21483],{},[895,21470,21471,21477,21479,21481],{},[3284,21472,21473,21475],{},[898,21474,4840],{},[1762,21476,1764],{},[1693,21478,1695],{},[1762,21480,9695],{},[898,21482,4618],{},[902,21484,21485],{"encoding":904},"L_1 = 0{,}1Y",[123,21487,21488,1899],{},[883,21489,21491],{"className":21490},[886],[888,21492,21493],{"xmlns":890},[892,21494,21495,21515],{},[895,21496,21497,21503,21505,21507,21509,21511,21513],{},[3284,21498,21499,21501],{},[898,21500,4840],{},[1762,21502,2398],{},[1693,21504,1695],{},[1693,21506,1698],{},[1762,21508,11872],{},[898,21510,6629],{},[1693,21512,1892],{},[1762,21514,15462],{},[902,21516,21517],{"encoding":904},"L_2 = -25r + 2000",[123,21519,21520,21521,1789],{},"nabídka peněz ",[883,21522,21524],{"className":21523},[886],[888,21525,21526],{"xmlns":890},[892,21527,21528,21541],{},[895,21529,21530,21536,21538],{},[1717,21531,21532,21534],{},[898,21533,2839],{},[1693,21535,3672],{},[1693,21537,1695],{},[1762,21539,21540],{},"2375",[902,21542,21543],{"encoding":904},"M^* = 2375",[724,21545,21546,21549,21550,4300],{},[38,21547,21548],{},"Funkce IS"," — dosazením do (7.13) ",[883,21551,21553],{"className":21552},[886],[888,21554,21555],{"xmlns":890},[892,21556,21557,21569],{},[895,21558,21559,21561,21563,21565,21567],{},[898,21560,4618],{},[1693,21562,1695],{},[898,21564,2971],{},[1693,21566,1892],{},[898,21568,6998],{},[902,21570,8174],{"encoding":904},[724,21572,21573],{},[883,21574,21576],{"className":21575},[886],[888,21577,21578],{"xmlns":890},[892,21579,21580,21606],{},[895,21581,21582,21584,21586,21588,21590,21592,21594,21596,21598,21600,21602,21604],{},[898,21583,4618],{},[1693,21585,1695],{},[1762,21587,21416],{},[898,21589,4618],{},[1693,21591,1892],{},[1762,21593,9987],{},[1693,21595,1698],{},[1762,21597,15892],{},[898,21599,6629],{},[1693,21601,1892],{},[1762,21603,9684],{},[1693,21605,1899],{"separator":1898},[902,21607,21608],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,21610,21611],{},"tj.",[724,21613,21614],{},[883,21615,21617],{"className":21616},[886],[888,21618,21619],{"xmlns":890},[892,21620,21621,21646],{},[895,21622,21623,21625,21627,21629,21631,21633,21635,21638,21640,21642,21644],{},[1762,21624,9739],{},[898,21626,4618],{},[1693,21628,1892],{},[1762,21630,15892],{},[898,21632,6629],{},[1693,21634,1695],{},[1762,21636,21637],{},"1100.",[1901,21639],{"width":1903},[1693,21641,1709],{"stretchy":1708},[1915,21643,18895],{},[1693,21645,1731],{"stretchy":1708},[902,21647,21648],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,21650,21651,21654,21655,4300],{},[38,21652,21653],{},"Funkce LM"," — dosazením do (7.15) ",[883,21656,21658],{"className":21657},[886],[888,21659,21660],{"xmlns":890},[892,21661,21662,21686],{},[895,21663,21664,21670,21672,21678,21680],{},[1717,21665,21666,21668],{},[898,21667,2839],{},[1693,21669,3672],{},[1693,21671,1695],{},[3284,21673,21674,21676],{},[898,21675,4840],{},[1762,21677,1764],{},[1693,21679,1892],{},[3284,21681,21682,21684],{},[898,21683,4840],{},[1762,21685,2398],{},[902,21687,21688],{"encoding":904},"M^* = L_1 + L_2",[724,21690,21691],{},[883,21692,21694],{"className":21693},[886],[888,21695,21696],{"xmlns":890},[892,21697,21698,21720],{},[895,21699,21700,21702,21704,21706,21708,21710,21712,21714,21716,21718],{},[1762,21701,21540],{},[1693,21703,1695],{},[1762,21705,9695],{},[898,21707,4618],{},[1693,21709,1698],{},[1762,21711,11872],{},[898,21713,6629],{},[1693,21715,1892],{},[1762,21717,15462],{},[1693,21719,1899],{"separator":1898},[902,21721,21722],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,21724,21611],{},[724,21726,21727],{},[883,21728,21730],{"className":21729},[886],[888,21731,21732],{"xmlns":890},[892,21733,21734,21759],{},[895,21735,21736,21738,21740,21742,21744,21746,21748,21751,21753,21755,21757],{},[1762,21737,9695],{},[898,21739,4618],{},[1693,21741,1698],{},[1762,21743,11872],{},[898,21745,6629],{},[1693,21747,1695],{},[1762,21749,21750],{},"375.",[1901,21752],{"width":1903},[1693,21754,1709],{"stretchy":1708},[1915,21756,18902],{},[1693,21758,1731],{"stretchy":1708},[902,21760,21761],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,21763,21764,21767,21768,21793],{},[38,21765,21766],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,21769,21771],{"className":21770},[886],[888,21772,21773],{"xmlns":890},[892,21774,21775,21790],{},[895,21776,21777,21779,21781,21784,21786,21788],{},[898,21778,4618],{},[1693,21780,1695],{},[1762,21782,21783],{},"5500",[1693,21785,1698],{},[1762,21787,9987],{},[898,21789,6629],{},[902,21791,21792],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,21795,21796],{},[883,21797,21799],{"className":21798},[886],[888,21800,21801],{"xmlns":890},[892,21802,21803,21889],{},[895,21804,21805,21807,21809,21811,21813,21815,21817,21819,21821,21823,21825,21827,21830,21832,21835,21837,21840,21842,21844,21846,21848,21850,21852,21854,21856,21858,21860,21862,21865,21867,21869,21872,21874,21876,21878,21884,21886],{},[1762,21806,9695],{},[1693,21808,1709],{"stretchy":1708},[1762,21810,21783],{},[1693,21812,1698],{},[1762,21814,9987],{},[898,21816,6629],{},[1693,21818,1731],{"stretchy":1708},[1693,21820,1698],{},[1762,21822,11872],{},[898,21824,6629],{},[1693,21826,1695],{},[1762,21828,21829],{},"375",[1915,21831,1917],{},[1693,21833,21834],{},"⟹",[1915,21836,1917],{},[1762,21838,21839],{},"550",[1693,21841,1698],{},[1762,21843,9763],{},[898,21845,6629],{},[1693,21847,1698],{},[1762,21849,11872],{},[898,21851,6629],{},[1693,21853,1695],{},[1762,21855,21829],{},[1915,21857,1917],{},[1693,21859,21834],{},[1915,21861,1917],{},[1762,21863,21864],{},"35",[898,21866,6629],{},[1693,21868,1695],{},[1762,21870,21871],{},"175",[1915,21873,1917],{},[1693,21875,21834],{},[1915,21877,1917],{},[1717,21879,21880,21882],{},[898,21881,6629],{},[898,21883,1691],{},[1693,21885,1695],{},[1762,21887,21888],{},"5.",[902,21890,21891],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,21893,21894],{},[38,21895,21896],{},"Zpětné dosazení:",[120,21898,21899,21945,21982],{},[123,21900,21901,1899],{},[883,21902,21904],{"className":21903},[886],[888,21905,21906],{"xmlns":890},[892,21907,21908,21942],{},[895,21909,21910,21916,21918,21920,21922,21924,21926,21928,21930,21932,21934,21937,21939],{},[1717,21911,21912,21914],{},[898,21913,4618],{},[898,21915,1691],{},[1693,21917,1695],{},[1762,21919,21783],{},[1693,21921,1698],{},[1762,21923,9987],{},[1693,21925,1715],{},[1762,21927,9147],{},[1693,21929,1695],{},[1762,21931,21783],{},[1693,21933,1698],{},[1762,21935,21936],{},"500",[1693,21938,1695],{},[1762,21940,21941],{},"5000",[902,21943,21944],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,21946,21947,1899],{},[883,21948,21950],{"className":21949},[886],[888,21951,21952],{"xmlns":890},[892,21953,21954,21979],{},[895,21955,21956,21962,21964,21966,21968,21970,21972,21974,21976],{},[1717,21957,21958,21960],{},[898,21959,2971],{},[898,21961,1691],{},[1693,21963,1695],{},[1762,21965,21416],{},[1693,21967,1715],{},[1762,21969,21941],{},[1693,21971,1892],{},[1762,21973,9987],{},[1693,21975,1695],{},[1762,21977,21978],{},"4100",[902,21980,21981],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,21983,21984,1789],{},[883,21985,21987],{"className":21986},[886],[888,21988,21989],{"xmlns":890},[892,21990,21991,22018],{},[895,21992,21993,21999,22001,22003,22005,22007,22009,22011,22013,22015],{},[1717,21994,21995,21997],{},[898,21996,6998],{},[898,21998,1691],{},[1693,22000,1695],{},[1693,22002,1698],{},[1762,22004,15892],{},[1693,22006,1715],{},[1762,22008,9147],{},[1693,22010,1892],{},[1762,22012,9684],{},[1693,22014,1695],{},[1762,22016,22017],{},"900",[902,22019,22020],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,22022,22023,1863,22026,22072],{},[38,22024,22025],{},"Ověření:",[883,22027,22029],{"className":22028},[886],[888,22030,22031],{"xmlns":890},[892,22032,22033,22069],{},[895,22034,22035,22041,22043,22049,22051,22053,22055,22057,22059,22061,22063],{},[1717,22036,22037,22039],{},[898,22038,2971],{},[898,22040,1691],{},[1693,22042,1892],{},[1717,22044,22045,22047],{},[898,22046,6998],{},[898,22048,1691],{},[1693,22050,1695],{},[1762,22052,21978],{},[1693,22054,1892],{},[1762,22056,22017],{},[1693,22058,1695],{},[1762,22060,21941],{},[1693,22062,1695],{},[1717,22064,22065,22067],{},[898,22066,4618],{},[898,22068,1691],{},[902,22070,22071],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,22074,22075],{},[883,22076,22078],{"className":22077},[886],[888,22079,22080],{"xmlns":890},[892,22081,22082,22151],{},[895,22083,22084],{},[19664,22085,22086],{"notation":19666},[3638,22087,22088],{"scriptlevel":1911,"displaystyle":1708},[3638,22089,22090],{"scriptlevel":1911,"displaystyle":1708},[3638,22091,22092],{"scriptlevel":1911,"displaystyle":1898},[895,22093,22094,22096,22102,22104,22106,22108,22110,22116,22118,22120,22122,22124,22130,22132,22134,22136,22138,22144,22146,22149],{},[1915,22095,2239],{},[1717,22097,22098,22100],{},[898,22099,4618],{},[898,22101,1691],{},[1693,22103,1695],{},[1762,22105,21941],{},[1693,22107,1899],{"separator":1898},[1901,22109],{"width":3630},[1717,22111,22112,22114],{},[898,22113,6629],{},[898,22115,1691],{},[1693,22117,1695],{},[1762,22119,9147],{},[1693,22121,1899],{"separator":1898},[1901,22123],{"width":3630},[1717,22125,22126,22128],{},[898,22127,2971],{},[898,22129,1691],{},[1693,22131,1695],{},[1762,22133,21978],{},[1693,22135,1899],{"separator":1898},[1901,22137],{"width":3630},[1717,22139,22140,22142],{},[898,22141,6998],{},[898,22143,1691],{},[1693,22145,1695],{},[1762,22147,22148],{},"900.",[1915,22150,2239],{},[902,22152,22153],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,22155,22156],{},[614,22157,22158,22159,22172,22173,22186,22187,22202,22203,22216,22217,22232,22233,22246,22247,22260,22261,1789],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,22160,22162],{"className":22161},[886],[888,22163,22164],{"xmlns":890},[892,22165,22166,22170],{},[895,22167,22168],{},[898,22169,4618],{},[902,22171,4618],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,22174,22176],{"className":22175},[886],[888,22177,22178],{"xmlns":890},[892,22179,22180,22184],{},[895,22181,22182],{},[898,22183,6629],{},[902,22185,6629],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,22188,22190],{"className":22189},[886],[888,22191,22192],{"xmlns":890},[892,22193,22194,22200],{},[895,22195,22196,22198],{},[898,22197,4840],{},[898,22199,2839],{},[902,22201,18902],{"encoding":904}," stoupá z oblasti nízkých ",[883,22204,22206],{"className":22205},[886],[888,22207,22208],{"xmlns":890},[892,22209,22210,22214],{},[895,22211,22212],{},[898,22213,6629],{},[902,22215,6629],{"encoding":904},", přímka ",[883,22218,22220],{"className":22219},[886],[888,22221,22222],{"xmlns":890},[892,22223,22224,22230],{},[895,22225,22226,22228],{},[898,22227,6998],{},[898,22229,3611],{},[902,22231,18895],{"encoding":904}," klesá a protíná osu ",[883,22234,22236],{"className":22235},[886],[888,22237,22238],{"xmlns":890},[892,22239,22240,22244],{},[895,22241,22242],{},[898,22243,6629],{},[902,22245,6629],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,22248,22250],{"className":22249},[886],[888,22251,22252],{"xmlns":890},[892,22253,22254,22258],{},[895,22255,22256],{},[898,22257,1691],{},[902,22259,1691],{"encoding":904}," leží v bodě ",[883,22262,22264],{"className":22263},[886],[888,22265,22266],{"xmlns":890},[892,22267,22268,22290],{},[895,22269,22270,22272,22274,22276,22278,22280,22282,22284,22286,22288],{},[1693,22271,9392],{"stretchy":1708},[898,22273,6629],{},[1693,22275,1695],{},[1762,22277,9147],{},[1693,22279,1899],{"separator":1898},[1915,22281,9204],{},[898,22283,4618],{},[1693,22285,1695],{},[1762,22287,21941],{},[1693,22289,9407],{"stretchy":1708},[902,22291,22292],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,22294,22296],{"id":22295},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,22298,22299,22302,22303,22316,22317,13877,22330,22333,22334,22352,22353,22370,22371,22388,22389,22402,22403,22416],{},[38,22300,22301],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,22304,22306],{"className":22305},[886],[888,22307,22308],{"xmlns":890},[892,22309,22310,22314],{},[895,22311,22312],{},[898,22313,6984],{},[902,22315,6984],{"encoding":904}," nebo snížení daní ",[883,22318,22320],{"className":22319},[886],[888,22321,22322],{"xmlns":890},[892,22323,22324,22328],{},[895,22325,22326],{},[898,22327,2663],{},[902,22329,2663],{"encoding":904},[38,22331,22332],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,22335,22337],{"className":22336},[886],[888,22338,22339],{"xmlns":890},[892,22340,22341,22349],{},[895,22342,22343],{},[1717,22344,22345,22347],{},[898,22346,1691],{},[1693,22348,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,22350,22351],{"encoding":904},"E'"," má vyšší ",[883,22354,22356],{"className":22355},[886],[888,22357,22358],{"xmlns":890},[892,22359,22360,22368],{},[895,22361,22362],{},[1717,22363,22364,22366],{},[898,22365,4618],{},[898,22367,1691],{},[902,22369,7862],{"encoding":904}," i vyšší ",[883,22372,22374],{"className":22373},[886],[888,22375,22376],{"xmlns":890},[892,22377,22378,22386],{},[895,22379,22380],{},[1717,22381,22382,22384],{},[898,22383,6629],{},[898,22385,1691],{},[902,22387,20753],{"encoding":904}," (vyšší ",[883,22390,22392],{"className":22391},[886],[888,22393,22394],{"xmlns":890},[892,22395,22396,22400],{},[895,22397,22398],{},[898,22399,4618],{},[902,22401,4618],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,22404,22406],{"className":22405},[886],[888,22407,22408],{"xmlns":890},[892,22409,22410,22414],{},[895,22411,22412],{},[898,22413,6629],{},[902,22415,6629],{"encoding":904}," nahoru).",[724,22418,22419],{},[9465,22420],{"alt":22421,"className":22422,"src":22423},"imek-posun-is-lm-politiky",[210,9469],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,22425,22426,22429,22430,22447,22448,22451,22452,22469,22470,22487,22488,22501,22502,22521,22522,3042],{},[38,22427,22428],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,22431,22433],{"className":22432},[886],[888,22434,22435],{"xmlns":890},[892,22436,22437,22445],{},[895,22438,22439],{},[1717,22440,22441,22443],{},[898,22442,2839],{},[1693,22444,3672],{},[902,22446,8460],{"encoding":904}," národní bankou — ",[38,22449,22450],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,22453,22455],{"className":22454},[886],[888,22456,22457],{"xmlns":890},[892,22458,22459,22467],{},[895,22460,22461],{},[1717,22462,22463,22465],{},[898,22464,6629],{},[898,22466,1691],{},[902,22468,20753],{"encoding":904}," a vyšší ",[883,22471,22473],{"className":22472},[886],[888,22474,22475],{"xmlns":890},[892,22476,22477,22485],{},[895,22478,22479],{},[1717,22480,22481,22483],{},[898,22482,4618],{},[898,22484,1691],{},[902,22486,7862],{"encoding":904}," (nižší ",[883,22489,22491],{"className":22490},[886],[888,22492,22493],{"xmlns":890},[892,22494,22495,22499],{},[895,22496,22497],{},[898,22498,6629],{},[902,22500,6629],{"encoding":904}," povzbuzuje investice ",[883,22503,22505],{"className":22504},[886],[888,22506,22507],{"xmlns":890},[892,22508,22509,22519],{},[895,22510,22511,22513,22515,22517],{},[898,22512,6998],{},[1693,22514,1709],{"stretchy":1708},[898,22516,6629],{},[1693,22518,1731],{"stretchy":1708},[902,22520,8215],{"encoding":904},", ty zvedají ",[883,22523,22525],{"className":22524},[886],[888,22526,22527],{"xmlns":890},[892,22528,22529,22533],{},[895,22530,22531],{},[898,22532,4618],{},[902,22534,4618],{"encoding":904},[724,22536,22537,22538,22541],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,22539,22540],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,22543,22545],{"id":22544},"klíčové-pojmy","Klíčové pojmy",[120,22547,22548,22621,22667,22749,22798,22865,22921,22961,22994],{},[123,22549,22550,13877,22583,1343,22600,22617,22618,22620],{},[38,22551,22552,22553],{},"Funkce investic ",[883,22554,22556],{"className":22555},[886],[888,22557,22558],{"xmlns":890},[892,22559,22560,22580],{},[895,22561,22562,22564,22566,22568,22570,22572,22574,22576,22578],{},[898,22563,6998],{},[1693,22565,1709],{"stretchy":1708},[898,22567,6629],{},[1693,22569,1731],{"stretchy":1708},[1693,22571,1695],{},[898,22573,2000],{},[898,22575,6629],{},[1693,22577,1892],{},[898,22579,1771],{},[902,22581,22582],{"encoding":904},"I(r) = cr + d",[883,22584,22586],{"className":22585},[886],[888,22587,22588],{"xmlns":890},[892,22589,22590,22598],{},[895,22591,22592,22594,22596],{},[898,22593,2000],{},[1693,22595,1908],{},[1762,22597,1911],{},[902,22599,8089],{"encoding":904},[883,22601,22603],{"className":22602},[886],[888,22604,22605],{"xmlns":890},[892,22606,22607,22615],{},[895,22608,22609,22611,22613],{},[898,22610,1771],{},[1693,22612,1922],{},[1762,22614,1911],{},[902,22616,19329],{"encoding":904},"; ",[38,22619,5676],{}," funkce úrokové míry.",[123,22622,22623,22626,22627,22648,22649,22666],{},[38,22624,22625],{},"Trh zboží"," — rovnováha ",[883,22628,22630],{"className":22629},[886],[888,22631,22632],{"xmlns":890},[892,22633,22634,22646],{},[895,22635,22636,22638,22640,22642,22644],{},[898,22637,4618],{},[1693,22639,1695],{},[898,22641,2971],{},[1693,22643,1892],{},[898,22645,6998],{},[902,22647,8174],{"encoding":904},", ekvivalentně ",[883,22650,22652],{"className":22651},[886],[888,22653,22654],{"xmlns":890},[892,22655,22656,22664],{},[895,22657,22658,22660,22662],{},[898,22659,6998],{},[1693,22661,1695],{},[898,22663,3611],{},[902,22665,19544],{"encoding":904}," (investice = úspory).",[123,22668,22669,16877,22672,22674,22675,22725,22726,19747,22728,1789],{},[38,22670,22671],{},"Křivka IS",[614,22673,18898],{},") — ",[883,22676,22678],{"className":22677},[886],[888,22679,22680],{"xmlns":890},[892,22681,22682,22722],{},[895,22683,22684,22686,22688,22700,22702,22704],{},[898,22685,4618],{},[1693,22687,1695],{},[2132,22689,22690,22692],{},[898,22691,2000],{},[895,22693,22694,22696,22698],{},[1762,22695,1764],{},[1693,22697,1698],{},[898,22699,207],{},[898,22701,6629],{},[1693,22703,1892],{},[2132,22705,22706,22714],{},[895,22707,22708,22710,22712],{},[898,22709,1895],{},[1693,22711,1892],{},[898,22713,1771],{},[895,22715,22716,22718,22720],{},[1762,22717,1764],{},[1693,22719,1698],{},[898,22721,207],{},[902,22723,22724],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,22727,5676],{},[883,22729,22731],{"className":22730},[886],[888,22732,22733],{"xmlns":890},[892,22734,22735,22747],{},[895,22736,22737,22739,22741,22743,22745],{},[1693,22738,1709],{"stretchy":1708},[898,22740,6629],{},[1693,22742,1899],{"separator":1898},[898,22744,4618],{},[1693,22746,1731],{"stretchy":1708},[902,22748,19769],{"encoding":904},[123,22750,22751,22626,22754,22779,22780,1789],{},[38,22752,22753],{},"Trh peněz",[883,22755,22757],{"className":22756},[886],[888,22758,22759],{"xmlns":890},[892,22760,22761,22777],{},[895,22762,22763,22769,22771],{},[1717,22764,22765,22767],{},[898,22766,2839],{},[898,22768,2738],{},[1693,22770,1695],{},[1717,22772,22773,22775],{},[898,22774,2839],{},[898,22776,3611],{},[902,22778,8391],{"encoding":904}," při pevné nabídce ",[883,22781,22783],{"className":22782},[886],[888,22784,22785],{"xmlns":890},[892,22786,22787,22795],{},[895,22788,22789],{},[1717,22790,22791,22793],{},[898,22792,2839],{},[1693,22794,3672],{},[902,22796,22797],{"encoding":904},"M^* ",[123,22799,22800,13877,22803,1789],{},[38,22801,22802],{},"Transakční, opatrnostní, spekulační poptávka",[883,22804,22806],{"className":22805},[886],[888,22807,22808],{"xmlns":890},[892,22809,22810,22862],{},[895,22811,22812,22818,22820,22826,22828,22834,22836,22842,22844,22846,22852,22854,22856],{},[1717,22813,22814,22816],{},[898,22815,2839],{},[898,22817,2738],{},[1693,22819,1695],{},[3284,22821,22822,22824],{},[898,22823,4840],{},[1762,22825,1764],{},[1693,22827,1892],{},[3284,22829,22830,22832],{},[898,22831,4840],{},[1762,22833,2398],{},[1693,22835,1695],{},[3284,22837,22838,22840],{},[898,22839,8334],{},[1762,22841,1764],{},[898,22843,4618],{},[1693,22845,1892],{},[3284,22847,22848,22850],{},[898,22849,8334],{},[1762,22851,2398],{},[898,22853,6629],{},[1693,22855,1892],{},[3284,22857,22858,22860],{},[898,22859,8334],{},[1762,22861,8357],{},[902,22863,22864],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,22866,22867,16877,22870,22674,22872,22917,22918,22920],{},[38,22868,22869],{},"Křivka LM",[614,22871,18905],{},[883,22873,22875],{"className":22874},[886],[888,22876,22877],{"xmlns":890},[892,22878,22879,22915],{},[895,22880,22881,22887,22889,22895,22897,22899,22905,22907,22909],{},[1717,22882,22883,22885],{},[898,22884,2839],{},[1693,22886,3672],{},[1693,22888,1695],{},[3284,22890,22891,22893],{},[898,22892,8334],{},[1762,22894,1764],{},[898,22896,4618],{},[1693,22898,1892],{},[3284,22900,22901,22903],{},[898,22902,8334],{},[1762,22904,2398],{},[898,22906,6629],{},[1693,22908,1892],{},[3284,22910,22911,22913],{},[898,22912,8334],{},[1762,22914,8357],{},[902,22916,8360],{"encoding":904}," (7.15); ",[38,22919,20488],{}," přímka.",[123,22922,22923,22925,22926,22960],{},[38,22924,8521],{}," — průsečík ",[883,22927,22929],{"className":22928},[886],[888,22930,22931],{"xmlns":890},[892,22932,22933,22957],{},[895,22934,22935,22937,22939,22941,22947,22949,22955],{},[898,22936,1691],{},[1693,22938,1695],{},[1693,22940,1709],{"stretchy":1708},[1717,22942,22943,22945],{},[898,22944,6629],{},[898,22946,1691],{},[1693,22948,1899],{"separator":1898},[1717,22950,22951,22953],{},[898,22952,4618],{},[898,22954,1691],{},[1693,22956,1731],{"stretchy":1708},[902,22958,22959],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,22962,22963,22966,22967,1343,22980,22993],{},[38,22964,22965],{},"Fiskální politika"," — nástroje ",[883,22968,22970],{"className":22969},[886],[888,22971,22972],{"xmlns":890},[892,22973,22974,22978],{},[895,22975,22976],{},[898,22977,6984],{},[902,22979,6984],{"encoding":904},[883,22981,22983],{"className":22982},[886],[888,22984,22985],{"xmlns":890},[892,22986,22987,22991],{},[895,22988,22989],{},[898,22990,2663],{},[902,22992,2663],{"encoding":904}," posouvající křivku IS.",[123,22995,22996,22999,23000,23017],{},[38,22997,22998],{},"Monetární politika"," — nástroj ",[883,23001,23003],{"className":23002},[886],[888,23004,23005],{"xmlns":890},[892,23006,23007,23015],{},[895,23008,23009],{},[1717,23010,23011,23013],{},[898,23012,2839],{},[1693,23014,3672],{},[902,23016,8460],{"encoding":904}," posouvající křivku LM.",[115,23019,8685],{"id":8684},[120,23021,23022,23029,23038,23048],{},[123,23023,23024,1863,23026],{},[38,23025,8692],{},[207,23027,1653],{"className":23028,"dataFsResolvedFilePath":1651,"href":1652},[210],[123,23030,23031,1863,23034],{},[38,23032,23033],{},"Přednáška:",[207,23035,23037],{"className":23036,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,23039,23040,1863,23043,23047],{},[38,23041,23042],{},"Nadřazené téma:",[207,23044,23046],{"className":23045,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,23049,23050,23053],{},[38,23051,23052],{},"Související:",[120,23054,23055,23062,23068],{},[123,23056,23057,23061],{},[207,23058,23060],{"className":23059,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,23063,23064,23067],{},[207,23065,1145],{"className":23066,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,23069,23070,23074],{},[207,23071,23073],{"className":23072,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":23076},[23077,23078,23079,23080,23081,23082,23083,23084,23085,23086],{"id":18850,"depth":642,"text":18851},{"id":18997,"depth":642,"text":18998},{"id":19210,"depth":642,"text":19211},{"id":19501,"depth":642,"text":19502},{"id":19913,"depth":642,"text":19914},{"id":20704,"depth":642,"text":20705},{"id":21391,"depth":642,"text":21392},{"id":22295,"depth":642,"text":22296},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fis-lm",{"title":18842,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,23093,1143,23094,23095,23096,23097,23046],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":23100,"title":23101,"body":23102,"course":659,"courses":24692,"created":1129,"description":24693,"extension":661,"meta":24694,"navigation":664,"path":24695,"seo":24696,"sources":24697,"stem":24698,"tags":24699,"type":10745,"updated":677,"__hash__":24702},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":23103,"toc":24680},[23104,23107,23203,23210,23230,23234,23239,23301,23319,23321,23324,23460,23462,23672,23706,23843,23847,23911,23927,23955,23959,24057,24061,24065,24118,24224,24438,24442,24485,24591,24642,24644],[12,23105,23101],{"id":23106},"lagrangeova-metoda-vázané-extrémy",[724,23108,23109,23110,10796,23133,23165,23166,23169,23170,23197,23198,23202],{},"Hledáme extrém funkce ",[883,23111,23113],{"className":23112},[886],[888,23114,23115],{"xmlns":890},[892,23116,23117,23131],{},[895,23118,23119,23121,23123,23125,23127,23129],{},[898,23120,8934],{},[1693,23122,1709],{"stretchy":1708},[898,23124,2590],{},[1693,23126,1899],{"separator":1898},[898,23128,6560],{},[1693,23130,1731],{"stretchy":1708},[902,23132,16696],{"encoding":904},[883,23134,23136],{"className":23135},[886],[888,23137,23138],{"xmlns":890},[892,23139,23140,23162],{},[895,23141,23142,23144,23146,23152,23154,23160],{},[898,23143,900],{},[1693,23145,1709],{"stretchy":1708},[3284,23147,23148,23150],{},[898,23149,1712],{},[1762,23151,1764],{},[1693,23153,1899],{"separator":1898},[3284,23155,23156,23158],{},[898,23157,1712],{},[1762,23159,2398],{},[1693,23161,1731],{"stretchy":1708},[902,23163,23164],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,23167,23168],{},"podmíněný"," rovnicí ",[883,23171,23173],{"className":23172},[886],[888,23174,23175],{"xmlns":890},[892,23176,23177,23195],{},[895,23178,23179,23181,23183,23185,23187,23189,23191,23193],{},[898,23180,17887],{},[1693,23182,1709],{"stretchy":1708},[898,23184,2590],{},[1693,23186,1899],{"separator":1898},[898,23188,6560],{},[1693,23190,1731],{"stretchy":1708},[1693,23192,1695],{},[1762,23194,1911],{},[902,23196,17904],{"encoding":904},". V ",[207,23199,23201],{"className":23200,"dataFsResolvedFilePath":1651,"href":1652},[210],"matematické ekonomii"," se používá pro:",[724,23204,23205],{},[9465,23206],{"alt":23207,"className":23208,"src":23209},"imek-lagrange-tecnost",[210,9469],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,23211,23212,23221,23227],{},[123,23213,23214,23217,23218,1731],{},[38,23215,23216],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,23219,16628],{"className":23220,"dataFsResolvedFilePath":878,"href":879},[210],[123,23222,23223,23226],{},[38,23224,23225],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,23228,23229],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,23231,23233],{"id":23232},"princip","Princip",[724,23235,17553,23236,4300],{},[38,23237,23238],{},"Lagrangeovu funkci",[724,23240,23241],{},[883,23242,23244],{"className":23243},[886],[888,23245,23246],{"xmlns":890},[892,23247,23248,23298],{},[895,23249,23250,23252,23254,23256,23258,23260,23262,23264,23266,23268,23270,23272,23274,23276,23278,23280,23282,23284,23286,23288,23290,23292,23294,23296],{},[898,23251,4840],{},[1693,23253,1709],{"stretchy":1708},[898,23255,2590],{},[1693,23257,1899],{"separator":1898},[898,23259,6560],{},[1693,23261,1899],{"separator":1898},[898,23263,5957],{},[1693,23265,1731],{"stretchy":1708},[1693,23267,1695],{},[898,23269,8934],{},[1693,23271,1709],{"stretchy":1708},[898,23273,2590],{},[1693,23275,1899],{"separator":1898},[898,23277,6560],{},[1693,23279,1731],{"stretchy":1708},[1693,23281,1892],{},[898,23283,5957],{},[1915,23285,2239],{},[898,23287,17887],{},[1693,23289,1709],{"stretchy":1708},[898,23291,2590],{},[1693,23293,1899],{"separator":1898},[898,23295,6560],{},[1693,23297,1731],{"stretchy":1708},[902,23299,23300],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,23302,11188,23303,6055,23316,1789],{},[883,23304,23306],{"className":23305},[886],[888,23307,23308],{"xmlns":890},[892,23309,23310,23314],{},[895,23311,23312],{},[898,23313,5957],{},[902,23315,6054],{"encoding":904},[38,23317,23318],{},"Lagrangeův multiplikátor",[115,23320,10147],{"id":10146},[724,23322,23323],{},"Řešíme soustavu:",[724,23325,23326,23374,23422],{},[883,23327,23329],{"className":23328},[886],[888,23330,23331],{"xmlns":890},[892,23332,23333,23371],{},[895,23334,23335,23343,23345,23353,23355,23357,23359,23367,23369],{},[5688,23336,23337,23339,23341],{},[898,23338,4840],{},[898,23340,2590],{},[1693,23342,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23344,1695],{},[5688,23346,23347,23349,23351],{},[898,23348,8934],{},[898,23350,2590],{},[1693,23352,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23354,1892],{},[898,23356,5957],{},[1915,23358,2239],{},[5688,23360,23361,23363,23365],{},[898,23362,17887],{},[898,23364,2590],{},[1693,23366,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23368,1695],{},[1762,23370,1911],{},[902,23372,23373],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,23375,23377],{"className":23376},[886],[888,23378,23379],{"xmlns":890},[892,23380,23381,23419],{},[895,23382,23383,23391,23393,23401,23403,23405,23407,23415,23417],{},[5688,23384,23385,23387,23389],{},[898,23386,4840],{},[898,23388,6560],{},[1693,23390,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23392,1695],{},[5688,23394,23395,23397,23399],{},[898,23396,8934],{},[898,23398,6560],{},[1693,23400,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23402,1892],{},[898,23404,5957],{},[1915,23406,2239],{},[5688,23408,23409,23411,23413],{},[898,23410,17887],{},[898,23412,6560],{},[1693,23414,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23416,1695],{},[1762,23418,1911],{},[902,23420,23421],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,23423,23425],{"className":23424},[886],[888,23426,23427],{"xmlns":890},[892,23428,23429,23457],{},[895,23430,23431,23439,23441,23443,23445,23447,23449,23451,23453,23455],{},[5688,23432,23433,23435,23437],{},[898,23434,4840],{},[898,23436,5957],{},[1693,23438,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23440,1695],{},[898,23442,17887],{},[1693,23444,1709],{"stretchy":1708},[898,23446,2590],{},[1693,23448,1899],{"separator":1898},[898,23450,6560],{},[1693,23452,1731],{"stretchy":1708},[1693,23454,1695],{},[1762,23456,1911],{},[902,23458,23459],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,23461,10221],{"id":10220},[724,23463,23464],{},[883,23465,23467],{"className":23466},[886],[888,23468,23469],{"xmlns":890},[892,23470,23471,23669],{},[895,23472,23473,23475,23477,23479,23481,23483,23485,23487,23489,23491,23493,23509,23511,23513,23529,23531,23533,23541,23547,23549,23551,23567,23569,23571,23587,23589,23591,23599,23605,23607,23609,23611,23627,23629,23631,23647,23649,23651,23659,23661],{},[898,23474,2738],{},[1693,23476,1709],{"stretchy":1708},[898,23478,2590],{},[1693,23480,1899],{"separator":1898},[898,23482,6560],{},[1693,23484,1899],{"separator":1898},[898,23486,5957],{},[1693,23488,1731],{"stretchy":1708},[1693,23490,1695],{},[1693,23492,1709],{"stretchy":1708},[5688,23494,23495,23497,23503],{},[898,23496,8934],{},[895,23498,23499,23501],{},[898,23500,2590],{},[898,23502,2590],{},[895,23504,23505,23507],{},[1693,23506,1724],{"mathvariant":1704},[1693,23508,1724],{"mathvariant":1704},[1693,23510,1892],{},[898,23512,5957],{},[5688,23514,23515,23517,23523],{},[898,23516,17887],{},[895,23518,23519,23521],{},[898,23520,2590],{},[898,23522,2590],{},[895,23524,23525,23527],{},[1693,23526,1724],{"mathvariant":1704},[1693,23528,1724],{"mathvariant":1704},[1693,23530,1731],{"stretchy":1708},[1693,23532,1709],{"stretchy":1708},[5688,23534,23535,23537,23539],{},[898,23536,17887],{},[898,23538,6560],{},[1693,23540,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1717,23542,23543,23545],{},[1693,23544,1731],{"stretchy":1708},[1762,23546,2398],{},[1693,23548,1892],{},[1693,23550,1709],{"stretchy":1708},[5688,23552,23553,23555,23561],{},[898,23554,8934],{},[895,23556,23557,23559],{},[898,23558,6560],{},[898,23560,6560],{},[895,23562,23563,23565],{},[1693,23564,1724],{"mathvariant":1704},[1693,23566,1724],{"mathvariant":1704},[1693,23568,1892],{},[898,23570,5957],{},[5688,23572,23573,23575,23581],{},[898,23574,17887],{},[895,23576,23577,23579],{},[898,23578,6560],{},[898,23580,6560],{},[895,23582,23583,23585],{},[1693,23584,1724],{"mathvariant":1704},[1693,23586,1724],{"mathvariant":1704},[1693,23588,1731],{"stretchy":1708},[1693,23590,1709],{"stretchy":1708},[5688,23592,23593,23595,23597],{},[898,23594,17887],{},[898,23596,2590],{},[1693,23598,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1717,23600,23601,23603],{},[1693,23602,1731],{"stretchy":1708},[1762,23604,2398],{},[1693,23606,1698],{},[1762,23608,2398],{},[1693,23610,1709],{"stretchy":1708},[5688,23612,23613,23615,23621],{},[898,23614,8934],{},[895,23616,23617,23619],{},[898,23618,2590],{},[898,23620,6560],{},[895,23622,23623,23625],{},[1693,23624,1724],{"mathvariant":1704},[1693,23626,1724],{"mathvariant":1704},[1693,23628,1892],{},[898,23630,5957],{},[5688,23632,23633,23635,23641],{},[898,23634,17887],{},[895,23636,23637,23639],{},[898,23638,2590],{},[898,23640,6560],{},[895,23642,23643,23645],{},[1693,23644,1724],{"mathvariant":1704},[1693,23646,1724],{"mathvariant":1704},[1693,23648,1731],{"stretchy":1708},[1915,23650,2239],{},[5688,23652,23653,23655,23657],{},[898,23654,17887],{},[898,23656,2590],{},[1693,23658,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,23660,2239],{},[5688,23662,23663,23665,23667],{},[898,23664,17887],{},[898,23666,6560],{},[1693,23668,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,23670,23671],{"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",[724,23673,23674,23675,23705],{},"Je-li ",[883,23676,23678],{"className":23677},[886],[888,23679,23680],{"xmlns":890},[892,23681,23682,23702],{},[895,23683,23684,23686,23688,23690,23692,23694,23700],{},[1693,23685,9392],{"stretchy":1708},[898,23687,207],{},[1693,23689,1899],{"separator":1898},[898,23691,1895],{},[1693,23693,1899],{"separator":1898},[3284,23695,23696,23698],{},[898,23697,5957],{},[1762,23699,1911],{},[1693,23701,9407],{"stretchy":1708},[902,23703,23704],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,23707,23708,23776],{},[123,23709,23710,10308,23746,23748,23749],{},[883,23711,23713],{"className":23712},[886],[888,23714,23715],{"xmlns":890},[892,23716,23717,23743],{},[895,23718,23719,23721,23723,23725,23727,23729,23731,23737,23739,23741],{},[898,23720,2738],{},[1693,23722,1709],{"stretchy":1708},[898,23724,207],{},[1693,23726,1899],{"separator":1898},[898,23728,1895],{},[1693,23730,1899],{"separator":1898},[3284,23732,23733,23735],{},[898,23734,5957],{},[1762,23736,1911],{},[1693,23738,1731],{"stretchy":1708},[1693,23740,1908],{},[1762,23742,1911],{},[902,23744,23745],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,23747,10610],{}," vázané podmínkou ",[883,23750,23752],{"className":23751},[886],[888,23753,23754],{"xmlns":890},[892,23755,23756,23774],{},[895,23757,23758,23760,23762,23764,23766,23768,23770,23772],{},[898,23759,17887],{},[1693,23761,1709],{"stretchy":1708},[898,23763,2590],{},[1693,23765,1899],{"separator":1898},[898,23767,6560],{},[1693,23769,1731],{"stretchy":1708},[1693,23771,1695],{},[1762,23773,1911],{},[902,23775,17904],{"encoding":904},[123,23777,23778,10308,23814,23748,23816],{},[883,23779,23781],{"className":23780},[886],[888,23782,23783],{"xmlns":890},[892,23784,23785,23811],{},[895,23786,23787,23789,23791,23793,23795,23797,23799,23805,23807,23809],{},[898,23788,2738],{},[1693,23790,1709],{"stretchy":1708},[898,23792,207],{},[1693,23794,1899],{"separator":1898},[898,23796,1895],{},[1693,23798,1899],{"separator":1898},[3284,23800,23801,23803],{},[898,23802,5957],{},[1762,23804,1911],{},[1693,23806,1731],{"stretchy":1708},[1693,23808,1922],{},[1762,23810,1911],{},[902,23812,23813],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,23815,10667],{},[883,23817,23819],{"className":23818},[886],[888,23820,23821],{"xmlns":890},[892,23822,23823,23841],{},[895,23824,23825,23827,23829,23831,23833,23835,23837,23839],{},[898,23826,17887],{},[1693,23828,1709],{"stretchy":1708},[898,23830,2590],{},[1693,23832,1899],{"separator":1898},[898,23834,6560],{},[1693,23836,1731],{"stretchy":1708},[1693,23838,1695],{},[1762,23840,1911],{},[902,23842,17904],{"encoding":904},[115,23844,23846],{"id":23845},"význam-multiplikátoru","Význam multiplikátoru",[724,23848,23849],{},[883,23850,23852],{"className":23851},[886],[888,23853,23854],{"xmlns":890},[892,23855,23856,23908],{},[895,23857,23858,23860,23862,23884,23886],{},[898,23859,5957],{},[1693,23861,1695],{},[2132,23863,23864,23872],{},[5688,23865,23866,23868,23870],{},[898,23867,8934],{},[898,23869,2590],{},[1693,23871,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[895,23873,23874,23876],{},[1693,23875,1698],{},[5688,23877,23878,23880,23882],{},[898,23879,17887],{},[898,23881,2590],{},[1693,23883,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,23885,1695],{},[2132,23887,23888,23896],{},[5688,23889,23890,23892,23894],{},[898,23891,8934],{},[898,23893,6560],{},[1693,23895,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[895,23897,23898,23900],{},[1693,23899,1698],{},[5688,23901,23902,23904,23906],{},[898,23903,17887],{},[898,23905,6560],{},[1693,23907,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,23909,23910],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,23912,23913,23926],{},[883,23914,23916],{"className":23915},[886],[888,23917,23918],{"xmlns":890},[892,23919,23920,23924],{},[895,23921,23922],{},[898,23923,5957],{},[902,23925,6054],{"encoding":904}," udává:",[120,23928,23929,23935],{},[123,23930,23931,23932],{},"konstantní ",[38,23933,23934],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,23936,23937,23940,23941,23954],{},[38,23938,23939],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,23942,23944],{"className":23943},[886],[888,23945,23946],{"xmlns":890},[892,23947,23948,23952],{},[895,23949,23950],{},[898,23951,8934],{},[902,23953,8934],{"encoding":904},", uvolní-li se omezení o jednotku",[115,23956,23958],{"id":23957},"alternativní-postup","Alternativní postup",[724,23960,23961,23962,23989,23990,24014,24015,24039,24040,24053,24054,1789],{},"Lze-li z ",[883,23963,23965],{"className":23964},[886],[888,23966,23967],{"xmlns":890},[892,23968,23969,23987],{},[895,23970,23971,23973,23975,23977,23979,23981,23983,23985],{},[898,23972,17887],{},[1693,23974,1709],{"stretchy":1708},[898,23976,2590],{},[1693,23978,1899],{"separator":1898},[898,23980,6560],{},[1693,23982,1731],{"stretchy":1708},[1693,23984,1695],{},[1762,23986,1911],{},[902,23988,17904],{"encoding":904}," vyjádřit ",[883,23991,23993],{"className":23992},[886],[888,23994,23995],{"xmlns":890},[892,23996,23997,24011],{},[895,23998,23999,24001,24003,24005,24007,24009],{},[898,24000,6560],{},[1693,24002,1695],{},[898,24004,6560],{},[1693,24006,1709],{"stretchy":1708},[898,24008,2590],{},[1693,24010,1731],{"stretchy":1708},[902,24012,24013],{"encoding":904},"y = y(x)"," (nebo ",[883,24016,24018],{"className":24017},[886],[888,24019,24020],{"xmlns":890},[892,24021,24022,24036],{},[895,24023,24024,24026,24028,24030,24032,24034],{},[898,24025,2590],{},[1693,24027,1695],{},[898,24029,2590],{},[1693,24031,1709],{"stretchy":1708},[898,24033,6560],{},[1693,24035,1731],{"stretchy":1708},[902,24037,24038],{"encoding":904},"x = x(y)","), dosadíme do ",[883,24041,24043],{"className":24042},[886],[888,24044,24045],{"xmlns":890},[892,24046,24047,24051],{},[895,24048,24049],{},[898,24050,8934],{},[902,24052,8934],{"encoding":904}," a převedeme na ",[38,24055,24056],{},"extrém funkce jedné proměnné",[115,24058,24060],{"id":24059},"použití-v-imek","Použití v ImeK",[198,24062,24064],{"id":24063},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,24066,24067,24068,1789],{},"Rozpočtové omezení: ",[883,24069,24071],{"className":24070},[886],[888,24072,24073],{"xmlns":890},[892,24074,24075,24115],{},[895,24076,24077,24083,24085,24093,24099,24101,24109],{},[1717,24078,24079,24081],{},[898,24080,4618],{},[1693,24082,3672],{},[1693,24084,1695],{},[5688,24086,24087,24089,24091],{},[898,24088,1701],{},[1762,24090,1764],{},[1693,24092,3672],{},[3284,24094,24095,24097],{},[898,24096,1712],{},[1762,24098,1764],{},[1693,24100,1892],{},[5688,24102,24103,24105,24107],{},[898,24104,1701],{},[1762,24106,2398],{},[1693,24108,3672],{},[3284,24110,24111,24113],{},[898,24112,1712],{},[1762,24114,2398],{},[902,24116,24117],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,24119,24120],{},[883,24121,24123],{"className":24122},[886],[888,24124,24125],{"xmlns":890},[892,24126,24127,24221],{},[895,24128,24129,24131,24133,24139,24141,24147,24149,24151,24153,24155,24157,24159,24165,24167,24173,24175,24177,24179,24181,24187,24189,24197,24203,24205,24213,24219],{},[898,24130,4840],{},[1693,24132,1709],{"stretchy":1708},[3284,24134,24135,24137],{},[898,24136,1712],{},[1762,24138,1764],{},[1693,24140,1899],{"separator":1898},[3284,24142,24143,24145],{},[898,24144,1712],{},[1762,24146,2398],{},[1693,24148,1899],{"separator":1898},[898,24150,5957],{},[1693,24152,1731],{"stretchy":1708},[1693,24154,1695],{},[898,24156,900],{},[1693,24158,1709],{"stretchy":1708},[3284,24160,24161,24163],{},[898,24162,1712],{},[1762,24164,1764],{},[1693,24166,1899],{"separator":1898},[3284,24168,24169,24171],{},[898,24170,1712],{},[1762,24172,2398],{},[1693,24174,1731],{"stretchy":1708},[1693,24176,1892],{},[898,24178,5957],{},[1693,24180,1709],{"stretchy":1708},[1717,24182,24183,24185],{},[898,24184,4618],{},[1693,24186,3672],{},[1693,24188,1698],{},[5688,24190,24191,24193,24195],{},[898,24192,1701],{},[1762,24194,1764],{},[1693,24196,3672],{},[3284,24198,24199,24201],{},[898,24200,1712],{},[1762,24202,1764],{},[1693,24204,1698],{},[5688,24206,24207,24209,24211],{},[898,24208,1701],{},[1762,24210,2398],{},[1693,24212,3672],{},[3284,24214,24215,24217],{},[898,24216,1712],{},[1762,24218,2398],{},[1693,24220,1731],{"stretchy":1708},[902,24222,24223],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,24225,24226,24227,1343,24259,1343,24291,24340,24341,24395,24396,1789],{},"Soustava: ",[883,24228,24230],{"className":24229},[886],[888,24231,24232],{"xmlns":890},[892,24233,24234,24256],{},[895,24235,24236,24244,24246,24248],{},[5688,24237,24238,24240,24242],{},[898,24239,900],{},[1762,24241,1764],{},[1693,24243,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,24245,1695],{},[898,24247,5957],{},[5688,24249,24250,24252,24254],{},[898,24251,1701],{},[1762,24253,1764],{},[1693,24255,3672],{},[902,24257,24258],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,24260,24262],{"className":24261},[886],[888,24263,24264],{"xmlns":890},[892,24265,24266,24288],{},[895,24267,24268,24276,24278,24280],{},[5688,24269,24270,24272,24274],{},[898,24271,900],{},[1762,24273,2398],{},[1693,24275,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,24277,1695],{},[898,24279,5957],{},[5688,24281,24282,24284,24286],{},[898,24283,1701],{},[1762,24285,2398],{},[1693,24287,3672],{},[902,24289,24290],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,24292,24294],{"className":24293},[886],[888,24295,24296],{"xmlns":890},[892,24297,24298,24338],{},[895,24299,24300,24306,24308,24316,24322,24324,24332],{},[1717,24301,24302,24304],{},[898,24303,4618],{},[1693,24305,3672],{},[1693,24307,1695],{},[5688,24309,24310,24312,24314],{},[898,24311,1701],{},[1762,24313,1764],{},[1693,24315,3672],{},[3284,24317,24318,24320],{},[898,24319,1712],{},[1762,24321,1764],{},[1693,24323,1892],{},[5688,24325,24326,24328,24330],{},[898,24327,1701],{},[1762,24329,2398],{},[1693,24331,3672],{},[3284,24333,24334,24336],{},[898,24335,1712],{},[1762,24337,2398],{},[902,24339,24117],{"encoding":904},". Z prvních dvou: ",[883,24342,24344],{"className":24343},[886],[888,24345,24346],{"xmlns":890},[892,24347,24348,24392],{},[895,24349,24350,24370,24372],{},[3638,24351,24352],{"scriptlevel":1911,"displaystyle":1708},[2132,24353,24354,24362],{},[5688,24355,24356,24358,24360],{},[898,24357,900],{},[1762,24359,1764],{},[1693,24361,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,24363,24364,24366,24368],{},[898,24365,900],{},[1762,24367,2398],{},[1693,24369,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,24371,1695],{},[3638,24373,24374],{"scriptlevel":1911,"displaystyle":1708},[2132,24375,24376,24384],{},[5688,24377,24378,24380,24382],{},[898,24379,1701],{},[1762,24381,1764],{},[1693,24383,3672],{},[5688,24385,24386,24388,24390],{},[898,24387,1701],{},[1762,24389,2398],{},[1693,24391,3672],{},[902,24393,24394],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,24397,24399],{"className":24398},[886],[888,24400,24401],{"xmlns":890},[892,24402,24403,24435],{},[895,24404,24405,24407,24409,24411,24413,24415],{},[898,24406,2839],{},[898,24408,2666],{},[898,24410,2971],{},[898,24412,3611],{},[1693,24414,1695],{},[3638,24416,24417],{"scriptlevel":1911,"displaystyle":1708},[2132,24418,24419,24427],{},[5688,24420,24421,24423,24425],{},[898,24422,1701],{},[1762,24424,1764],{},[1693,24426,3672],{},[5688,24428,24429,24431,24433],{},[898,24430,1701],{},[1762,24432,2398],{},[1693,24434,3672],{},[902,24436,24437],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,24439,24441],{"id":24440},"minimalizace-výdajů","Minimalizace výdajů",[724,24443,24444,24445,1789],{},"Podmínka dané užitečnosti ",[883,24446,24448],{"className":24447},[886],[888,24449,24450],{"xmlns":890},[892,24451,24452,24482],{},[895,24453,24454,24460,24462,24464,24466,24472,24474,24480],{},[1717,24455,24456,24458],{},[898,24457,900],{},[1693,24459,3672],{},[1693,24461,1695],{},[898,24463,900],{},[1693,24465,1709],{"stretchy":1708},[3284,24467,24468,24470],{},[898,24469,1712],{},[1762,24471,1764],{},[1693,24473,1899],{"separator":1898},[3284,24475,24476,24478],{},[898,24477,1712],{},[1762,24479,2398],{},[1693,24481,1731],{"stretchy":1708},[902,24483,24484],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,24486,24487],{},[883,24488,24490],{"className":24489},[886],[888,24491,24492],{"xmlns":890},[892,24493,24494,24588],{},[895,24495,24496,24498,24500,24506,24508,24514,24516,24518,24520,24522,24530,24536,24538,24546,24552,24554,24556,24558,24564,24566,24568,24570,24576,24578,24584,24586],{},[898,24497,4840],{},[1693,24499,1709],{"stretchy":1708},[3284,24501,24502,24504],{},[898,24503,1712],{},[1762,24505,1764],{},[1693,24507,1899],{"separator":1898},[3284,24509,24510,24512],{},[898,24511,1712],{},[1762,24513,2398],{},[1693,24515,1899],{"separator":1898},[898,24517,5957],{},[1693,24519,1731],{"stretchy":1708},[1693,24521,1695],{},[5688,24523,24524,24526,24528],{},[898,24525,1701],{},[1762,24527,1764],{},[1693,24529,3672],{},[3284,24531,24532,24534],{},[898,24533,1712],{},[1762,24535,1764],{},[1693,24537,1892],{},[5688,24539,24540,24542,24544],{},[898,24541,1701],{},[1762,24543,2398],{},[1693,24545,3672],{},[3284,24547,24548,24550],{},[898,24549,1712],{},[1762,24551,2398],{},[1693,24553,1892],{},[898,24555,5957],{},[1693,24557,1709],{"stretchy":1708},[1717,24559,24560,24562],{},[898,24561,900],{},[1693,24563,3672],{},[1693,24565,1698],{},[898,24567,900],{},[1693,24569,1709],{"stretchy":1708},[3284,24571,24572,24574],{},[898,24573,1712],{},[1762,24575,1764],{},[1693,24577,1899],{"separator":1898},[3284,24579,24580,24582],{},[898,24581,1712],{},[1762,24583,2398],{},[1693,24585,1731],{"stretchy":1708},[1693,24587,1731],{"stretchy":1708},[902,24589,24590],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,24592,24593,24594,1789],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,24595,24597],{"className":24596},[886],[888,24598,24599],{"xmlns":890},[892,24600,24601,24639],{},[895,24602,24603,24609,24611,24617,24619,24625,24627,24633,24635,24637],{},[3284,24604,24605,24607],{},[898,24606,1712],{},[898,24608,5696],{},[1693,24610,1695],{},[3284,24612,24613,24615],{},[898,24614,2738],{},[898,24616,5696],{},[1693,24618,1709],{"stretchy":1708},[3284,24620,24621,24623],{},[898,24622,1701],{},[1762,24624,1764],{},[1693,24626,1899],{"separator":1898},[3284,24628,24629,24631],{},[898,24630,1701],{},[1762,24632,2398],{},[1693,24634,1899],{"separator":1898},[898,24636,900],{},[1693,24638,1731],{"stretchy":1708},[902,24640,24641],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,24643,8685],{"id":8684},[120,24645,24646,24653,24660,24669],{},[123,24647,24648,1863,24650],{},[38,24649,10689],{},[207,24651,784],{"className":24652,"dataFsResolvedFilePath":782,"href":783},[210],[123,24654,24655,1863,24657],{},[38,24656,10697],{},[207,24658,2181],{"className":24659,"dataFsResolvedFilePath":800,"href":801},[210],[123,24661,24662,1863,24665,24668],{},[38,24663,24664],{},"Aplikace v kurzu:",[207,24666,880],{"className":24667,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,24670,24671,1863,24673,1343,24676,24679],{},[38,24672,10705],{},[207,24674,936],{"className":24675,"dataFsResolvedFilePath":934,"href":935},[210],[207,24677,1400],{"className":24678,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":24681},[24682,24683,24684,24685,24686,24687,24691],{"id":23232,"depth":642,"text":23233},{"id":10146,"depth":642,"text":10147},{"id":10220,"depth":642,"text":10221},{"id":23845,"depth":642,"text":23846},{"id":23957,"depth":642,"text":23958},{"id":24059,"depth":642,"text":24060,"children":24688},[24689,24690],{"id":24063,"depth":649,"text":24064},{"id":24440,"depth":649,"text":24441},{"id":8684,"depth":642,"text":8685},[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":23101,"description":24693},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,24700,24701],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":24704,"title":936,"body":24705,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":34544,"navigation":664,"path":34545,"seo":34546,"sources":34547,"stem":34548,"tags":34549,"type":10745,"updated":677,"__hash__":34553},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":24706,"toc":34506},[24707,24710,24712,24835,24966,24970,24973,25086,25090,25117,25164,25167,25233,25278,25281,25307,25338,25342,25346,25390,25434,25496,25551,25554,25558,25561,25608,25703,25809,25815,25892,25921,26060,26064,26093,26143,26290,26379,26383,26409,26447,26473,26511,26573,26648,26724,26782,26848,26892,26896,26954,27003,27048,27261,27381,27387,27391,27414,27418,27425,27429,27460,27495,27499,27549,27634,27676,27697,27758,27818,27822,27893,27961,28033,28148,28196,28200,28203,28244,28283,28306,28420,28582,28589,28616,28646,28649,28726,28879,28963,29302,29306,29430,29566,29702,29755,29758,30008,30088,30092,30095,30153,30185,30188,30237,30240,30311,30507,30511,30662,30892,30930,30983,31029,31032,31088,31137,31341,31431,31435,31451,31458,31626,31630,31701,31781,31859,31938,32083,32171,32175,32358,32489,32534,32631,32635,33371,33373,34423,34425],[12,24708,936],{"id":24709},"národní-důchod",[115,24711,18851],{"id":18850},[724,24713,24714,24715,1863,24719,24722,24723,1863,24726,24739,24740,24743,24744,24747,24748,24751,24752,24754,24755,1863,24757,24774,24775,24792,24793,24796,24797,3042],{},"Kapitola 7 ",[207,24716,24718],{"className":24717,"dataFsResolvedFilePath":1651,"href":1652},[210],"Matematické ekonomie",[38,24720,24721],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,24724,24725],{},"národním důchodem",[883,24727,24729],{"className":24728},[886],[888,24730,24731],{"xmlns":890},[892,24732,24733,24737],{},[895,24734,24735],{},[898,24736,4618],{},[902,24738,4618],{"encoding":904},". Budují se postupně bohatší modely — ",[38,24741,24742],{},"C-I"," (jen spotřeba a investice) → ",[38,24745,24746],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,24749,24750],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,24753,18856],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,24756,20715],{},[883,24758,24760],{"className":24759},[886],[888,24761,24762],{"xmlns":890},[892,24763,24764,24772],{},[895,24765,24766],{},[1717,24767,24768,24770],{},[898,24769,4618],{},[898,24771,1691],{},[902,24773,7862],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,24776,24778],{"className":24777},[886],[888,24779,24780],{"xmlns":890},[892,24781,24782,24790],{},[895,24783,24784],{},[1717,24785,24786,24788],{},[898,24787,4618],{},[898,24789,1691],{},[902,24791,7862],{"encoding":904}," na exogenní veličiny popisují ",[38,24794,24795],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,24798,24800],{"className":24799},[886],[888,24801,24802],{"xmlns":890},[892,24803,24804,24832],{},[895,24805,24806,24808,24810,24812,24814,24816,24818,24820,24822,24824,24826,24828,24830],{},[1762,24807,1764],{},[898,24809,1705],{"mathvariant":1704},[1693,24811,1709],{"stretchy":1708},[1762,24813,1764],{},[1693,24815,1698],{},[898,24817,207],{},[1693,24819,1731],{"stretchy":1708},[1693,24821,1695],{},[1762,24823,1764],{},[898,24825,1705],{"mathvariant":1704},[898,24827,2839],{},[898,24829,1701],{},[898,24831,3611],{},[902,24833,24834],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1636,24836,24837],{},[724,24838,24839,24841,24842,24845,24846,24863,24864,24894,24895,24940,24941,24943,24944,24965],{},[883,24840,11036],{}," Intuice\n",[38,24843,24844],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,24847,24849],{"className":24848},[886],[888,24850,24851],{"xmlns":890},[892,24852,24853,24861],{},[895,24854,24855,24857,24859],{},[898,24856,2839],{},[898,24858,1701],{},[898,24860,2971],{},[902,24862,7288],{"encoding":904}," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,24865,24867],{"className":24866},[886],[888,24868,24869],{"xmlns":890},[892,24870,24871,24891],{},[895,24872,24873,24875,24877,24879,24881,24883,24885,24887,24889],{},[898,24874,2839],{},[898,24876,1701],{},[898,24878,3611],{},[1693,24880,1695],{},[1762,24882,1764],{},[1693,24884,1698],{},[898,24886,2839],{},[898,24888,1701],{},[898,24890,2971],{},[902,24892,24893],{"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 ",[883,24896,24898],{"className":24897},[886],[888,24899,24900],{"xmlns":890},[892,24901,24902,24938],{},[895,24903,24904,24906,24908,24910,24912,24918,24920,24922,24924,24926,24928,24930,24932,24934,24936],{},[1762,24905,1764],{},[1693,24907,1892],{},[898,24909,207],{},[1693,24911,1892],{},[1717,24913,24914,24916],{},[898,24915,207],{},[1762,24917,2398],{},[1693,24919,1892],{},[1693,24921,7949],{},[1693,24923,1695],{},[1762,24925,1764],{},[898,24927,1705],{"mathvariant":1704},[1693,24929,1709],{"stretchy":1708},[1762,24931,1764],{},[1693,24933,1698],{},[898,24935,207],{},[1693,24937,1731],{"stretchy":1708},[902,24939,7968],{"encoding":904},"). ",[38,24942,18856],{}," 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 ",[883,24945,24947],{"className":24946},[886],[888,24948,24949],{"xmlns":890},[892,24950,24951,24963],{},[895,24952,24953,24955,24957,24959,24961],{},[1693,24954,1709],{"stretchy":1708},[898,24956,4618],{},[1693,24958,1899],{"separator":1898},[898,24960,6629],{},[1693,24962,1731],{"stretchy":1708},[902,24964,8243],{"encoding":904}," jsou oba trhy v rovnováze současně.",[115,24967,24969],{"id":24968},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,24971,24972],{},"Po prostudování kapitoly by čtenář měl umět:",[120,24974,24975,24978,24981,24984,24987,24990,24993,25083],{},[123,24976,24977],{},"popsat zjednodušený model národní ekonomiky,",[123,24979,24980],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,24982,24983],{},"popsat lineární model spotřeby a úspor,",[123,24985,24986],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,24988,24989],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,24991,24992],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,24994,24995,24996,1343,25013,1343,25035,4286,25060,25082],{},"popsat modely ",[883,24997,24999],{"className":24998},[886],[888,25000,25001],{"xmlns":890},[892,25002,25003,25011],{},[895,25004,25005,25007,25009],{},[898,25006,2971],{},[1915,25008,19126],{},[898,25010,6998],{},[902,25012,19131],{"encoding":904},[883,25014,25016],{"className":25015},[886],[888,25017,25018],{"xmlns":890},[892,25019,25020,25032],{},[895,25021,25022,25024,25026,25028,25030],{},[898,25023,2971],{},[1915,25025,19126],{},[898,25027,6998],{},[1915,25029,19126],{},[898,25031,6984],{},[902,25033,25034],{"encoding":904},"C\\text{-}I\\text{-}G",[883,25036,25038],{"className":25037},[886],[888,25039,25040],{"xmlns":890},[892,25041,25042,25058],{},[895,25043,25044,25046,25048,25050,25052,25054,25056],{},[898,25045,2971],{},[1915,25047,19126],{},[898,25049,6998],{},[1915,25051,19126],{},[898,25053,6984],{},[1915,25055,19126],{},[898,25057,7007],{},[902,25059,19158],{"encoding":904},[883,25061,25063],{"className":25062},[886],[888,25064,25065],{"xmlns":890},[892,25066,25067,25079],{},[895,25068,25069,25071,25073,25075,25077],{},[898,25070,6998],{},[898,25072,3611],{},[1915,25074,19126],{},[898,25076,4840],{},[898,25078,2839],{},[902,25080,25081],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,25084,25085],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,25087,25089],{"id":25088},"gnp-a-národní-důchod","GNP a národní důchod",[724,25091,25092,1863,25095,16877,25113,25116],{},[38,25093,25094],{},"Hrubý národní produkt",[883,25096,25098],{"className":25097},[886],[888,25099,25100],{"xmlns":890},[892,25101,25102,25110],{},[895,25103,25104,25106,25108],{},[898,25105,6984],{},[898,25107,6987],{},[898,25109,1701],{},[902,25111,25112],{"encoding":904},"GNP",[614,25114,25115],{},"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:",[724,25118,25119],{},[883,25120,25122],{"className":25121},[886],[888,25123,25124],{"xmlns":890},[892,25125,25126,25161],{},[895,25127,25128,25130,25132,25134,25136,25138,25140,25142,25144,25146,25148,25150,25152,25154,25156,25159],{},[898,25129,6984],{},[898,25131,6987],{},[898,25133,1701],{},[1693,25135,1695],{},[898,25137,2971],{},[1693,25139,1892],{},[898,25141,6998],{},[1693,25143,1892],{},[898,25145,6984],{},[1693,25147,1892],{},[898,25149,7007],{},[1693,25151,1899],{"separator":1898},[1901,25153],{"width":1903},[1693,25155,1709],{"stretchy":1708},[1762,25157,25158],{},"7.1",[1693,25160,1731],{"stretchy":1708},[902,25162,25163],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,25165,25166],{},"kde",[120,25168,25169,25185,25201,25217],{},[123,25170,25171,25184],{},[883,25172,25174],{"className":25173},[886],[888,25175,25176],{"xmlns":890},[892,25177,25178,25182],{},[895,25179,25180],{},[898,25181,2971],{},[902,25183,2971],{"encoding":904}," — výdaje domácností na spotřebu,",[123,25186,25187,25200],{},[883,25188,25190],{"className":25189},[886],[888,25191,25192],{"xmlns":890},[892,25193,25194,25198],{},[895,25195,25196],{},[898,25197,6998],{},[902,25199,6998],{"encoding":904}," — hrubé domácí investice,",[123,25202,25203,25216],{},[883,25204,25206],{"className":25205},[886],[888,25207,25208],{"xmlns":890},[892,25209,25210,25214],{},[895,25211,25212],{},[898,25213,6984],{},[902,25215,6984],{"encoding":904}," — vládní výdaje,",[123,25218,25219,25232],{},[883,25220,25222],{"className":25221},[886],[888,25223,25224],{"xmlns":890},[892,25225,25226,25230],{},[895,25227,25228],{},[898,25229,7007],{},[902,25231,7007],{"encoding":904}," — čistý export.",[724,25234,25235,25236,25253,25254,25257,25258,1863,25261,16877,25274,25277],{},"K měření ",[883,25237,25239],{"className":25238},[886],[888,25240,25241],{"xmlns":890},[892,25242,25243,25251],{},[895,25244,25245,25247,25249],{},[898,25246,6984],{},[898,25248,6987],{},[898,25250,1701],{},[902,25252,25112],{"encoding":904}," se užívá ",[38,25255,25256],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,25259,25260],{},"národní důchod",[883,25262,25264],{"className":25263},[886],[888,25265,25266],{"xmlns":890},[892,25267,25268,25272],{},[895,25269,25270],{},[898,25271,4618],{},[902,25273,4618],{"encoding":904},[614,25275,25276],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,25279,25280],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,25282,25283],{},[883,25284,25286],{"className":25285},[886],[888,25287,25288],{"xmlns":890},[892,25289,25290,25304],{},[895,25291,25292,25294,25296,25298,25300,25302],{},[898,25293,6984],{},[898,25295,6987],{},[898,25297,1701],{},[1693,25299,4110],{},[898,25301,4618],{},[1693,25303,1899],{"separator":1898},[902,25305,25306],{"encoding":904},"GNP \\approx Y,",[724,25308,25309,25310,16877,25313,25316,25317,25330,25331,25334,25335,1789],{},"a užívá se společného názvu ",[38,25311,25312],{},"důchod",[614,25314,25315],{},"income",") s označením ",[883,25318,25320],{"className":25319},[886],[888,25321,25322],{"xmlns":890},[892,25323,25324,25328],{},[895,25325,25326],{},[898,25327,4618],{},[902,25329,4618],{"encoding":904},". Domácnosti důchod použijí ke ",[38,25332,25333],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,25336,25337],{},"úspor",[115,25339,25341],{"id":25340},"spotřeba-a-úspory","Spotřeba a úspory",[198,25343,25345],{"id":25344},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,25347,25348,25349,25362,25363,25376,25377,4300],{},"Jak spotřeba ",[883,25350,25352],{"className":25351},[886],[888,25353,25354],{"xmlns":890},[892,25355,25356,25360],{},[895,25357,25358],{},[898,25359,2971],{},[902,25361,2971],{"encoding":904},", tak úspory ",[883,25364,25366],{"className":25365},[886],[888,25367,25368],{"xmlns":890},[892,25369,25370,25374],{},[895,25371,25372],{},[898,25373,3611],{},[902,25375,3611],{"encoding":904}," závisejí na důchodu ",[883,25378,25380],{"className":25379},[886],[888,25381,25382],{"xmlns":890},[892,25383,25384,25388],{},[895,25385,25386],{},[898,25387,4618],{},[902,25389,4618],{"encoding":904},[724,25391,25392],{},[883,25393,25395],{"className":25394},[886],[888,25396,25397],{"xmlns":890},[892,25398,25399,25431],{},[895,25400,25401,25403,25405,25407,25409,25411,25413,25415,25417,25419,25421,25423,25425,25427,25429],{},[898,25402,2971],{},[1693,25404,1695],{},[898,25406,2971],{},[1693,25408,1709],{"stretchy":1708},[898,25410,4618],{},[1693,25412,1731],{"stretchy":1708},[1693,25414,1899],{"separator":1898},[1901,25416],{"width":1903},[898,25418,3611],{},[1693,25420,1695],{},[898,25422,3611],{},[1693,25424,1709],{"stretchy":1708},[898,25426,4618],{},[1693,25428,1731],{"stretchy":1708},[898,25430,1789],{"mathvariant":1704},[902,25432,25433],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,25435,25436,6055,25455,16877,25458,25461,25462,6055,25482,16877,25485,25488,25489,4286,25492,25495],{},[883,25437,25439],{"className":25438},[886],[888,25440,25441],{"xmlns":890},[892,25442,25443,25453],{},[895,25444,25445,25447,25449,25451],{},[898,25446,2971],{},[1693,25448,1709],{"stretchy":1708},[898,25450,4618],{},[1693,25452,1731],{"stretchy":1708},[902,25454,8195],{"encoding":904},[38,25456,25457],{},"funkce spotřeby",[614,25459,25460],{},"consumption function","), ",[883,25463,25465],{"className":25464},[886],[888,25466,25467],{"xmlns":890},[892,25468,25469,25479],{},[895,25470,25471,25473,25475,25477],{},[898,25472,3611],{},[1693,25474,1709],{"stretchy":1708},[898,25476,4618],{},[1693,25478,1731],{"stretchy":1708},[902,25480,25481],{"encoding":904},"S(Y)",[38,25483,25484],{},"funkce úspor",[614,25486,25487],{},"savings function","); jejich grafy se nazývají ",[38,25490,25491],{},"křivka spotřeby",[38,25493,25494],{},"křivka úspor",". Platí základní identita",[724,25497,25498],{},[883,25499,25501],{"className":25500},[886],[888,25502,25503],{"xmlns":890},[892,25504,25505,25548],{},[895,25506,25507,25509,25511,25513,25515,25517,25519,25521,25523,25525,25527,25529,25531,25533,25535,25537,25539,25541,25543,25546],{},[898,25508,4618],{},[1693,25510,1695],{},[898,25512,2971],{},[1693,25514,1892],{},[898,25516,3611],{},[1693,25518,1695],{},[898,25520,2971],{},[1693,25522,1709],{"stretchy":1708},[898,25524,4618],{},[1693,25526,1731],{"stretchy":1708},[1693,25528,1892],{},[898,25530,3611],{},[1693,25532,1709],{"stretchy":1708},[898,25534,4618],{},[1693,25536,1731],{"stretchy":1708},[898,25538,1789],{"mathvariant":1704},[1901,25540],{"width":1903},[1693,25542,1709],{"stretchy":1708},[1762,25544,25545],{},"7.2",[1693,25547,1731],{"stretchy":1708},[902,25549,25550],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,25552,25553],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,25555,25557],{"id":25556},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,25559,25560],{},"Nejjednodušší model předpokládá lineární tvar",[724,25562,25563],{},[883,25564,25566],{"className":25565},[886],[888,25567,25568],{"xmlns":890},[892,25569,25570,25605],{},[895,25571,25572,25574,25576,25578,25580,25582,25584,25586,25588,25590,25592,25594,25596,25598,25600,25603],{},[898,25573,2971],{},[1693,25575,1695],{},[898,25577,2971],{},[1693,25579,1709],{"stretchy":1708},[898,25581,4618],{},[1693,25583,1731],{"stretchy":1708},[1693,25585,1695],{},[898,25587,207],{},[898,25589,4618],{},[1693,25591,1892],{},[898,25593,1895],{},[1693,25595,1899],{"separator":1898},[1901,25597],{"width":1903},[1693,25599,1709],{"stretchy":1708},[1762,25601,25602],{},"7.3",[1693,25604,1731],{"stretchy":1708},[902,25606,25607],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,25609,11188,25610,4286,25627,25648,25649,25689,25690,1789],{},[883,25611,25613],{"className":25612},[886],[888,25614,25615],{"xmlns":890},[892,25616,25617,25625],{},[895,25618,25619,25621,25623],{},[898,25620,1895],{},[1693,25622,1922],{},[1762,25624,1911],{},[902,25626,7157],{"encoding":904},[883,25628,25630],{"className":25629},[886],[888,25631,25632],{"xmlns":890},[892,25633,25634,25646],{},[895,25635,25636,25638,25640,25642,25644],{},[1762,25637,1911],{},[1693,25639,1908],{},[898,25641,207],{},[1693,25643,1908],{},[1762,25645,1764],{},[902,25647,7139],{"encoding":904},". Směrnice ",[883,25650,25652],{"className":25651},[886],[888,25653,25654],{"xmlns":890},[892,25655,25656,25686],{},[895,25657,25658,25660,25662,25669,25671,25674,25676,25678,25680,25682,25684],{},[898,25659,207],{},[1693,25661,1695],{},[895,25663,25664,25667],{},[898,25665,25666],{"mathvariant":1704},"t",[898,25668,17887],{"mathvariant":1704},[1915,25670,2239],{},[898,25672,25673],{},"α",[1693,25675,1695],{},[898,25677,3890],{"mathvariant":1704},[898,25679,2971],{},[898,25681,1705],{"mathvariant":1704},[898,25683,3890],{"mathvariant":1704},[898,25685,4618],{},[902,25687,25688],{"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 ",[883,25691,25693],{"className":25692},[886],[888,25694,25695],{"xmlns":890},[892,25696,25697,25701],{},[895,25698,25699],{},[898,25700,4618],{},[902,25702,4618],{"encoding":904},[724,25704,25705],{},[614,25706,25707,25708,25732,25733,25771,25772,25788,25789,1789],{},"Obrázek 7.1 — Přímka spotřeby ",[883,25709,25711],{"className":25710},[886],[888,25712,25713],{"xmlns":890},[892,25714,25715,25729],{},[895,25716,25717,25719,25721,25723,25725,25727],{},[898,25718,2971],{},[1693,25720,1695],{},[898,25722,207],{},[898,25724,4618],{},[1693,25726,1892],{},[898,25728,1895],{},[902,25730,25731],{"encoding":904},"C = aY + b"," se směrnicí ",[883,25734,25736],{"className":25735},[886],[888,25737,25738],{"xmlns":890},[892,25739,25740,25768],{},[895,25741,25742,25744,25746,25752,25754,25756,25758,25760,25762,25764,25766],{},[898,25743,207],{},[1693,25745,1695],{},[895,25747,25748,25750],{},[898,25749,25666],{"mathvariant":1704},[898,25751,17887],{"mathvariant":1704},[1915,25753,2239],{},[898,25755,25673],{},[1693,25757,1695],{},[898,25759,3890],{"mathvariant":1704},[898,25761,2971],{},[898,25763,1705],{"mathvariant":1704},[898,25765,3890],{"mathvariant":1704},[898,25767,4618],{},[902,25769,25770],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,25773,25775],{"className":25774},[886],[888,25776,25777],{"xmlns":890},[892,25778,25779,25785],{},[895,25780,25781,25783],{},[898,25782,3890],{"mathvariant":1704},[898,25784,2971],{},[902,25786,25787],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,25790,25792],{"className":25791},[886],[888,25793,25794],{"xmlns":890},[892,25795,25796,25806],{},[895,25797,25798,25800,25802,25804],{},[898,25799,3890],{"mathvariant":1704},[898,25801,4618],{},[1693,25803,1695],{},[1762,25805,1764],{},[902,25807,25808],{"encoding":904},"\\Delta Y = 1",[724,25810,25811,25812,4300],{},"Dosazením do (7.2) plyne ",[38,25813,25814],{},"lineární model úspor",[724,25816,25817],{},[883,25818,25820],{"className":25819},[886],[888,25821,25822],{"xmlns":890},[892,25823,25824,25889],{},[895,25825,25826,25828,25830,25832,25834,25836,25838,25840,25842,25844,25846,25848,25850,25852,25854,25856,25858,25860,25862,25864,25866,25868,25870,25872,25874,25876,25878,25880,25882,25884,25887],{},[898,25827,3611],{},[1693,25829,1695],{},[898,25831,4618],{},[1693,25833,1698],{},[898,25835,2971],{},[1693,25837,1709],{"stretchy":1708},[898,25839,4618],{},[1693,25841,1731],{"stretchy":1708},[1693,25843,1695],{},[898,25845,4618],{},[1693,25847,1698],{},[1693,25849,1709],{"stretchy":1708},[898,25851,207],{},[898,25853,4618],{},[1693,25855,1892],{},[898,25857,1895],{},[1693,25859,1731],{"stretchy":1708},[1693,25861,1695],{},[1693,25863,1709],{"stretchy":1708},[1762,25865,1764],{},[1693,25867,1698],{},[898,25869,207],{},[1693,25871,1731],{"stretchy":1708},[898,25873,4618],{},[1693,25875,1698],{},[898,25877,1895],{},[898,25879,1789],{"mathvariant":1704},[1901,25881],{"width":1903},[1693,25883,1709],{"stretchy":1708},[1762,25885,25886],{},"7.4",[1693,25888,1731],{"stretchy":1708},[902,25890,25891],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,25893,25894,25895,3042],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,25896,25898],{"className":25897},[886],[888,25899,25900],{"xmlns":890},[892,25901,25902,25918],{},[895,25903,25904,25906,25908,25910,25912,25914,25916],{},[1762,25905,1911],{},[1693,25907,1908],{},[1762,25909,1764],{},[1693,25911,1698],{},[898,25913,207],{},[1693,25915,1908],{},[1762,25917,1764],{},[902,25919,25920],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,25922,25923],{},[614,25924,25925,25926,4286,25949,25981,25982,9530,25995,26025,26026,9530,26044,1789],{},"Obrázek 7.2 — Přímky ",[883,25927,25929],{"className":25928},[886],[888,25930,25931],{"xmlns":890},[892,25932,25933,25947],{},[895,25934,25935,25937,25939,25941,25943,25945],{},[898,25936,2971],{},[1693,25938,1695],{},[898,25940,207],{},[898,25942,4618],{},[1693,25944,1892],{},[898,25946,1895],{},[902,25948,25731],{"encoding":904},[883,25950,25952],{"className":25951},[886],[888,25953,25954],{"xmlns":890},[892,25955,25956,25978],{},[895,25957,25958,25960,25962,25964,25966,25968,25970,25972,25974,25976],{},[898,25959,3611],{},[1693,25961,1695],{},[1693,25963,1709],{"stretchy":1708},[1762,25965,1764],{},[1693,25967,1698],{},[898,25969,207],{},[1693,25971,1731],{"stretchy":1708},[898,25973,4618],{},[1693,25975,1698],{},[898,25977,1895],{},[902,25979,25980],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,25983,25985],{"className":25984},[886],[888,25986,25987],{"xmlns":890},[892,25988,25989,25993],{},[895,25990,25991],{},[898,25992,4618],{},[902,25994,4618],{"encoding":904},[883,25996,25998],{"className":25997},[886],[888,25999,26000],{"xmlns":890},[892,26001,26002,26022],{},[895,26003,26004,26006,26008,26010,26012,26014,26016,26018,26020],{},[898,26005,4618],{},[1693,26007,1695],{},[898,26009,1895],{},[898,26011,1705],{"mathvariant":1704},[1693,26013,1709],{"stretchy":1708},[1762,26015,1764],{},[1693,26017,1698],{},[898,26019,207],{},[1693,26021,1731],{"stretchy":1708},[902,26023,26024],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,26027,26029],{"className":26028},[886],[888,26030,26031],{"xmlns":890},[892,26032,26033,26041],{},[895,26034,26035,26037,26039],{},[898,26036,2971],{},[1693,26038,1899],{"separator":1898},[898,26040,3611],{},[902,26042,26043],{"encoding":904},"C, S",[883,26045,26047],{"className":26046},[886],[888,26048,26049],{"xmlns":890},[892,26050,26051,26057],{},[895,26052,26053,26055],{},[1693,26054,1698],{},[898,26056,1895],{},[902,26058,26059],{"encoding":904},"-b",[198,26061,26063],{"id":26062},"příklad-71","Příklad 7.1",[724,26065,26066,26067,26092],{},"Pro spotřebu ",[883,26068,26070],{"className":26069},[886],[888,26071,26072],{"xmlns":890},[892,26073,26074,26089],{},[895,26075,26076,26078,26080,26083,26085,26087],{},[898,26077,2971],{},[1693,26079,1695],{},[1762,26081,26082],{},"0,4",[898,26084,4618],{},[1693,26086,1892],{},[1762,26088,9763],{},[902,26090,26091],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,26094,26095],{},[883,26096,26098],{"className":26097},[886],[888,26099,26100],{"xmlns":890},[892,26101,26102,26140],{},[895,26103,26104,26106,26108,26110,26112,26114,26116,26118,26120,26122,26124,26126,26128,26130,26133,26135,26137],{},[898,26105,3611],{},[1693,26107,1695],{},[898,26109,4618],{},[1693,26111,1698],{},[898,26113,2971],{},[1693,26115,1695],{},[898,26117,4618],{},[1693,26119,1698],{},[1762,26121,26082],{},[898,26123,4618],{},[1693,26125,1698],{},[1762,26127,9763],{},[1693,26129,1695],{},[1762,26131,26132],{},"0,6",[898,26134,4618],{},[1693,26136,1698],{},[1762,26138,26139],{},"10.",[902,26141,26142],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,26144,26145],{},[614,26146,26147,26148,4286,26171,26195,26196,6055,26209,26233,26234,6055,26251,26267,26268,1789],{},"Obrázek 7.3 — Přímky ",[883,26149,26151],{"className":26150},[886],[888,26152,26153],{"xmlns":890},[892,26154,26155,26169],{},[895,26156,26157,26159,26161,26163,26165,26167],{},[898,26158,2971],{},[1693,26160,1695],{},[1762,26162,26082],{},[898,26164,4618],{},[1693,26166,1892],{},[1762,26168,9763],{},[902,26170,26091],{"encoding":904},[883,26172,26174],{"className":26173},[886],[888,26175,26176],{"xmlns":890},[892,26177,26178,26192],{},[895,26179,26180,26182,26184,26186,26188,26190],{},[898,26181,3611],{},[1693,26183,1695],{},[1762,26185,26132],{},[898,26187,4618],{},[1693,26189,1698],{},[1762,26191,9763],{},[902,26193,26194],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,26197,26199],{"className":26198},[886],[888,26200,26201],{"xmlns":890},[892,26202,26203,26207],{},[895,26204,26205],{},[898,26206,4618],{},[902,26208,4618],{"encoding":904},[883,26210,26212],{"className":26211},[886],[888,26213,26214],{"xmlns":890},[892,26215,26216,26230],{},[895,26217,26218,26220,26223],{},[1693,26219,4110],{},[1762,26221,26222],{},"16,",[4467,26224,26225,26227],{"accent":1898},[1762,26226,9154],{},[1693,26228,26229],{},"ˉ",[902,26231,26232],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,26235,26237],{"className":26236},[886],[888,26238,26239],{"xmlns":890},[892,26240,26241,26249],{},[895,26242,26243,26245,26247],{},[898,26244,2971],{},[1693,26246,1899],{"separator":1898},[898,26248,3611],{},[902,26250,26043],{"encoding":904},[883,26252,26254],{"className":26253},[886],[888,26255,26256],{"xmlns":890},[892,26257,26258,26264],{},[895,26259,26260,26262],{},[1693,26261,1698],{},[1762,26263,9763],{},[902,26265,26266],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,26269,26271],{"className":26270},[886],[888,26272,26273],{"xmlns":890},[892,26274,26275,26287],{},[895,26276,26277,26279,26281,26283,26285],{},[1693,26278,1709],{"stretchy":1708},[1762,26280,1911],{},[1693,26282,1899],{"separator":1898},[1762,26284,9763],{},[1693,26286,1731],{"stretchy":1708},[902,26288,26289],{"encoding":904},"(0, 10)",[724,26291,26292,26293,6055,26311,26341,26342,16877,26345,26348,26349,6055,26373,16877,26375,26378],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,26294,26296],{"className":26295},[886],[888,26297,26298],{"xmlns":890},[892,26299,26300,26308],{},[895,26301,26302,26304,26306],{},[898,26303,4618],{},[1693,26305,1695],{},[1762,26307,1911],{},[902,26309,26310],{"encoding":904},"Y = 0",[883,26312,26314],{"className":26313},[886],[888,26315,26316],{"xmlns":890},[892,26317,26318,26338],{},[895,26319,26320,26322,26324,26326,26328,26330,26332,26334,26336],{},[898,26321,3611],{},[1693,26323,1709],{"stretchy":1708},[1762,26325,1911],{},[1693,26327,1731],{"stretchy":1708},[1693,26329,1695],{},[1693,26331,1698],{},[898,26333,1895],{},[1693,26335,1908],{},[1762,26337,1911],{},[902,26339,26340],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,26343,26344],{},"autonomních úsporách",[614,26346,26347],{},"autonomous savings","). Analogicky ",[883,26350,26352],{"className":26351},[886],[888,26353,26354],{"xmlns":890},[892,26355,26356,26370],{},[895,26357,26358,26360,26362,26364,26366,26368],{},[898,26359,2971],{},[1693,26361,1709],{"stretchy":1708},[1762,26363,1911],{},[1693,26365,1731],{"stretchy":1708},[1693,26367,1695],{},[898,26369,1895],{},[902,26371,26372],{"encoding":904},"C(0) = b",[38,26374,7179],{},[614,26376,26377],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,26380,26382],{"id":26381},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,26384,26385,1863,26388,16877,26405,26408],{},[38,26386,26387],{},"Mezní sklon ke spotřebě",[883,26389,26391],{"className":26390},[886],[888,26392,26393],{"xmlns":890},[892,26394,26395,26403],{},[895,26396,26397,26399,26401],{},[898,26398,2839],{},[898,26400,1701],{},[898,26402,2971],{},[902,26404,7288],{"encoding":904},[614,26406,26407],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,26410,26411],{},[883,26412,26414],{"className":26413},[886],[888,26415,26416],{"xmlns":890},[892,26417,26418,26444],{},[895,26419,26420,26422,26424,26426,26428,26442],{},[898,26421,2839],{},[898,26423,1701],{},[898,26425,2971],{},[1693,26427,1695],{},[2132,26429,26430,26436],{},[895,26431,26432,26434],{},[898,26433,1771],{"mathvariant":1704},[898,26435,2971],{},[895,26437,26438,26440],{},[898,26439,1771],{"mathvariant":1704},[898,26441,4618],{},[898,26443,1789],{"mathvariant":1704},[902,26445,26446],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,26448,26449,1863,26452,16877,26469,26472],{},[38,26450,26451],{},"Mezní sklon k úsporám",[883,26453,26455],{"className":26454},[886],[888,26456,26457],{"xmlns":890},[892,26458,26459,26467],{},[895,26460,26461,26463,26465],{},[898,26462,2839],{},[898,26464,1701],{},[898,26466,3611],{},[902,26468,7307],{"encoding":904},[614,26470,26471],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,26474,26475],{},[883,26476,26478],{"className":26477},[886],[888,26479,26480],{"xmlns":890},[892,26481,26482,26508],{},[895,26483,26484,26486,26488,26490,26492,26506],{},[898,26485,2839],{},[898,26487,1701],{},[898,26489,3611],{},[1693,26491,1695],{},[2132,26493,26494,26500],{},[895,26495,26496,26498],{},[898,26497,1771],{"mathvariant":1704},[898,26499,3611],{},[895,26501,26502,26504],{},[898,26503,1771],{"mathvariant":1704},[898,26505,4618],{},[898,26507,1789],{"mathvariant":1704},[902,26509,26510],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,26512,26513,26514,26572],{},"Z (7.2) plyne ",[883,26515,26517],{"className":26516},[886],[888,26518,26519],{"xmlns":890},[892,26520,26521,26569],{},[895,26522,26523,26537,26539,26553,26555],{},[2132,26524,26525,26531],{},[895,26526,26527,26529],{},[898,26528,1771],{"mathvariant":1704},[898,26530,4618],{},[895,26532,26533,26535],{},[898,26534,1771],{"mathvariant":1704},[898,26536,4618],{},[1693,26538,1695],{},[2132,26540,26541,26547],{},[895,26542,26543,26545],{},[898,26544,1771],{"mathvariant":1704},[898,26546,2971],{},[895,26548,26549,26551],{},[898,26550,1771],{"mathvariant":1704},[898,26552,4618],{},[1693,26554,1892],{},[2132,26556,26557,26563],{},[895,26558,26559,26561],{},[898,26560,1771],{"mathvariant":1704},[898,26562,3611],{},[895,26564,26565,26567],{},[898,26566,1771],{"mathvariant":1704},[898,26568,4618],{},[902,26570,26571],{"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",[724,26574,26575],{},[883,26576,26578],{"className":26577},[886],[888,26579,26580],{"xmlns":890},[892,26581,26582,26645],{},[895,26583,26584,26636,26638,26640,26643],{},[19664,26585,26586],{"notation":19666},[3638,26587,26588],{"scriptlevel":1911,"displaystyle":1708},[3638,26589,26590],{"scriptlevel":1911,"displaystyle":1708},[3638,26591,26592],{"scriptlevel":1911,"displaystyle":1898},[895,26593,26594,26596,26598,26600,26602,26604,26606,26608,26610,26612,26614,26616,26618,26620,26622,26624,26626,26628,26630,26632,26634],{},[898,26595,2839],{},[898,26597,1701],{},[898,26599,2971],{},[1693,26601,1892],{},[898,26603,2839],{},[898,26605,1701],{},[898,26607,3611],{},[1693,26609,1695],{},[1762,26611,1764],{},[1693,26613,1899],{"separator":1898},[1901,26615],{"width":1903},[898,26617,2839],{},[898,26619,1701],{},[898,26621,3611],{},[1693,26623,1695],{},[1762,26625,1764],{},[1693,26627,1698],{},[898,26629,2839],{},[898,26631,1701],{},[898,26633,2971],{},[898,26635,1789],{"mathvariant":1704},[1901,26637],{"width":1903},[1693,26639,1709],{"stretchy":1708},[1762,26641,26642],{},"7.5",[1693,26644,1731],{"stretchy":1708},[902,26646,26647],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,26649,26650,1863,26653,26676,26677,4286,26698,26723],{},[38,26651,26652],{},"Pro lineární model",[883,26654,26656],{"className":26655},[886],[888,26657,26658],{"xmlns":890},[892,26659,26660,26674],{},[895,26661,26662,26664,26666,26668,26670,26672],{},[898,26663,2971],{},[1693,26665,1695],{},[898,26667,207],{},[898,26669,4618],{},[1693,26671,1892],{},[898,26673,1895],{},[902,26675,25731],{"encoding":904}," vychází ",[883,26678,26680],{"className":26679},[886],[888,26681,26682],{"xmlns":890},[892,26683,26684,26696],{},[895,26685,26686,26688,26690,26692,26694],{},[898,26687,2839],{},[898,26689,1701],{},[898,26691,2971],{},[1693,26693,1695],{},[898,26695,207],{},[902,26697,7330],{"encoding":904},[883,26699,26701],{"className":26700},[886],[888,26702,26703],{"xmlns":890},[892,26704,26705,26721],{},[895,26706,26707,26709,26711,26713,26715,26717,26719],{},[898,26708,2839],{},[898,26710,1701],{},[898,26712,3611],{},[1693,26714,1695],{},[1762,26716,1764],{},[1693,26718,1698],{},[898,26720,207],{},[902,26722,7356],{"encoding":904}," — tedy směrnice přímek spotřeby a úspor.",[724,26725,26726,26729,26730,26752,26753,26781],{},[38,26727,26728],{},"Interpretace diferenciálem."," Pro pevné ",[883,26731,26733],{"className":26732},[886],[888,26734,26735],{"xmlns":890},[892,26736,26737,26749],{},[895,26738,26739,26741,26743],{},[898,26740,4618],{},[1693,26742,1695],{},[1717,26744,26745,26747],{},[898,26746,4618],{},[1693,26748,3672],{},[902,26750,26751],{"encoding":904},"Y = Y^*"," udává ",[883,26754,26756],{"className":26755},[886],[888,26757,26758],{"xmlns":890},[892,26759,26760,26778],{},[895,26761,26762,26764,26766,26768,26770,26776],{},[898,26763,2839],{},[898,26765,1701],{},[898,26767,2971],{},[1693,26769,1709],{"stretchy":1708},[1717,26771,26772,26774],{},[898,26773,4618],{},[1693,26775,3672],{},[1693,26777,1731],{"stretchy":1708},[902,26779,26780],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,26783,26784],{},[883,26785,26787],{"className":26786},[886],[888,26788,26789],{"xmlns":890},[892,26790,26791,26845],{},[895,26792,26793,26795,26797,26799,26801,26803,26805,26811,26813,26815,26817,26819,26821,26823,26825,26827,26829,26831,26833,26835,26837,26839,26841,26843],{},[898,26794,3890],{"mathvariant":1704},[898,26796,2971],{},[1693,26798,4110],{},[898,26800,1771],{"mathvariant":1704},[898,26802,2971],{},[1693,26804,1695],{},[1717,26806,26807,26809],{},[898,26808,2971],{},[1693,26810,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,26812,1709],{"stretchy":1708},[898,26814,4618],{},[1693,26816,1731],{"stretchy":1708},[1915,26818,2239],{},[898,26820,1771],{"mathvariant":1704},[898,26822,4618],{},[1693,26824,1695],{},[898,26826,2839],{},[898,26828,1701],{},[898,26830,2971],{},[1693,26832,1709],{"stretchy":1708},[898,26834,4618],{},[1693,26836,1731],{"stretchy":1708},[1915,26838,2239],{},[898,26840,1771],{"mathvariant":1704},[898,26842,4618],{},[898,26844,1789],{"mathvariant":1704},[902,26846,26847],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,26849,26850,26851,26887,26888,26891],{},"Analogicky ",[883,26852,26854],{"className":26853},[886],[888,26855,26856],{"xmlns":890},[892,26857,26858,26884],{},[895,26859,26860,26862,26864,26866,26868,26870,26872,26874,26876,26878,26880,26882],{},[898,26861,3890],{"mathvariant":1704},[898,26863,3611],{},[1693,26865,4110],{},[898,26867,2839],{},[898,26869,1701],{},[898,26871,3611],{},[1693,26873,1709],{"stretchy":1708},[898,26875,4618],{},[1693,26877,1731],{"stretchy":1708},[1915,26879,2239],{},[898,26881,1771],{"mathvariant":1704},[898,26883,4618],{},[902,26885,26886],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,26889,1145],{"className":26890,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,26893,26895],{"id":26894},"příklad-72","Příklad 7.2",[724,26897,26066,26898,26933,26934,26953],{},[883,26899,26901],{"className":26900},[886],[888,26902,26903],{"xmlns":890},[892,26904,26905,26930],{},[895,26906,26907,26909,26911,26914,26920,26922,26924,26926,26928],{},[898,26908,2971],{},[1693,26910,1695],{},[1762,26912,26913],{},"0,001",[1717,26915,26916,26918],{},[898,26917,4618],{},[1762,26919,2398],{},[1693,26921,1892],{},[1762,26923,9739],{},[898,26925,4618],{},[1693,26927,1892],{},[1762,26929,10017],{},[902,26931,26932],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,26935,26937],{"className":26936},[886],[888,26938,26939],{"xmlns":890},[892,26940,26941,26950],{},[895,26942,26943,26945,26947],{},[898,26944,4618],{},[1693,26946,1908],{},[1762,26948,26949],{},"400",[902,26951,26952],{"encoding":904},"Y \u003C 400",") platí",[724,26955,26956],{},[883,26957,26959],{"className":26958},[886],[888,26960,26961],{"xmlns":890},[892,26962,26963,27000],{},[895,26964,26965,26967,26969,26971,26973,26987,26989,26992,26994,26996,26998],{},[898,26966,2839],{},[898,26968,1701],{},[898,26970,2971],{},[1693,26972,1695],{},[2132,26974,26975,26981],{},[895,26976,26977,26979],{},[898,26978,1771],{"mathvariant":1704},[898,26980,2971],{},[895,26982,26983,26985],{},[898,26984,1771],{"mathvariant":1704},[898,26986,4618],{},[1693,26988,1695],{},[1762,26990,26991],{},"0,002",[898,26993,4618],{},[1693,26995,1892],{},[1762,26997,9739],{},[1693,26999,1899],{"separator":1898},[902,27001,27002],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,27004,27005],{},[883,27006,27008],{"className":27007},[886],[888,27009,27010],{"xmlns":890},[892,27011,27012,27045],{},[895,27013,27014,27016,27018,27020,27022,27024,27026,27028,27030,27032,27034,27036,27038,27040,27042],{},[898,27015,2839],{},[898,27017,1701],{},[898,27019,3611],{},[1693,27021,1695],{},[1762,27023,1764],{},[1693,27025,1698],{},[898,27027,2839],{},[898,27029,1701],{},[898,27031,2971],{},[1693,27033,1695],{},[1693,27035,1698],{},[1762,27037,26991],{},[898,27039,4618],{},[1693,27041,1892],{},[1762,27043,27044],{},"0,8.",[902,27046,27047],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,27049,27050,27130,27209],{},[123,27051,27052,1343,27080,27108,27109,6055,27127,1789],{},[883,27053,27055],{"className":27054},[886],[888,27056,27057],{"xmlns":890},[892,27058,27059,27077],{},[895,27060,27061,27063,27065,27067,27069,27071,27073,27075],{},[898,27062,2839],{},[898,27064,1701],{},[898,27066,2971],{},[1693,27068,1709],{"stretchy":1708},[1762,27070,9987],{},[1693,27072,1731],{"stretchy":1708},[1693,27074,1695],{},[1762,27076,26082],{},[902,27078,27079],{"encoding":904},"MPC(100) = 0{,}4",[883,27081,27083],{"className":27082},[886],[888,27084,27085],{"xmlns":890},[892,27086,27087,27105],{},[895,27088,27089,27091,27093,27095,27097,27099,27101,27103],{},[898,27090,2839],{},[898,27092,1701],{},[898,27094,3611],{},[1693,27096,1709],{"stretchy":1708},[1762,27098,9987],{},[1693,27100,1731],{"stretchy":1708},[1693,27102,1695],{},[1762,27104,26132],{},[902,27106,27107],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,27110,27112],{"className":27111},[886],[888,27113,27114],{"xmlns":890},[892,27115,27116,27124],{},[895,27117,27118,27120,27122],{},[898,27119,4618],{},[1693,27121,1695],{},[1762,27123,9987],{},[902,27125,27126],{"encoding":904},"Y = 100",[38,27128,27129],{},"větší sklon k úsporám",[123,27131,27132,1343,27160,27108,27188,6055,27206,1789],{},[883,27133,27135],{"className":27134},[886],[888,27136,27137],{"xmlns":890},[892,27138,27139,27157],{},[895,27140,27141,27143,27145,27147,27149,27151,27153,27155],{},[898,27142,2839],{},[898,27144,1701],{},[898,27146,2971],{},[1693,27148,1709],{"stretchy":1708},[1762,27150,15236],{},[1693,27152,1731],{"stretchy":1708},[1693,27154,1695],{},[1762,27156,26132],{},[902,27158,27159],{"encoding":904},"MPC(200) = 0{,}6",[883,27161,27163],{"className":27162},[886],[888,27164,27165],{"xmlns":890},[892,27166,27167,27185],{},[895,27168,27169,27171,27173,27175,27177,27179,27181,27183],{},[898,27170,2839],{},[898,27172,1701],{},[898,27174,3611],{},[1693,27176,1709],{"stretchy":1708},[1762,27178,15236],{},[1693,27180,1731],{"stretchy":1708},[1693,27182,1695],{},[1762,27184,26082],{},[902,27186,27187],{"encoding":904},"MPS(200) = 0{,}4",[883,27189,27191],{"className":27190},[886],[888,27192,27193],{"xmlns":890},[892,27194,27195,27203],{},[895,27196,27197,27199,27201],{},[898,27198,4618],{},[1693,27200,1695],{},[1762,27202,15236],{},[902,27204,27205],{"encoding":904},"Y = 200",[38,27207,27208],{},"větší sklon ke spotřebě",[123,27210,27211,27212,27230,27231,3042],{},"Přesně při ",[883,27213,27215],{"className":27214},[886],[888,27216,27217],{"xmlns":890},[892,27218,27219,27227],{},[895,27220,27221,27223,27225],{},[898,27222,4618],{},[1693,27224,1695],{},[1762,27226,15660],{},[902,27228,27229],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,27232,27234],{"className":27233},[886],[888,27235,27236],{"xmlns":890},[892,27237,27238,27258],{},[895,27239,27240,27242,27244,27246,27248,27250,27252,27254,27256],{},[898,27241,2839],{},[898,27243,1701],{},[898,27245,2971],{},[1693,27247,1695],{},[898,27249,2839],{},[898,27251,1701],{},[898,27253,3611],{},[1693,27255,1695],{},[1762,27257,11877],{},[902,27259,27260],{"encoding":904},"MPC = MPS = 0{,}5",[724,27262,27263,27264,27281,27282,27296,27297,9591,27310,27324,27325,27338,27339,27380],{},"Interpretace: při ",[883,27265,27267],{"className":27266},[886],[888,27268,27269],{"xmlns":890},[892,27270,27271,27279],{},[895,27272,27273,27275,27277],{},[898,27274,4618],{},[1693,27276,1695],{},[1762,27278,9987],{},[902,27280,27126],{"encoding":904}," se spotřeba mění ",[883,27283,27285],{"className":27284},[886],[888,27286,27287],{"xmlns":890},[892,27288,27289,27293],{},[895,27290,27291],{},[1762,27292,26082],{},[902,27294,27295],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,27298,27300],{"className":27299},[886],[888,27301,27302],{"xmlns":890},[892,27303,27304,27308],{},[895,27305,27306],{},[1762,27307,9987],{},[902,27309,9987],{"encoding":904},[883,27311,27313],{"className":27312},[886],[888,27314,27315],{"xmlns":890},[892,27316,27317,27322],{},[895,27318,27319],{},[1762,27320,27321],{},"101",[902,27323,27321],{"encoding":904},", změní se spotřeba přibližně o ",[883,27326,27328],{"className":27327},[886],[888,27329,27330],{"xmlns":890},[892,27331,27332,27336],{},[895,27333,27334],{},[1762,27335,26082],{},[902,27337,27295],{"encoding":904},". Skutečná změna ",[883,27340,27342],{"className":27341},[886],[888,27343,27344],{"xmlns":890},[892,27345,27346,27377],{},[895,27347,27348,27350,27352,27354,27356,27358,27360,27362,27364,27366,27368,27370,27372,27374],{},[898,27349,3890],{"mathvariant":1704},[898,27351,2971],{},[1693,27353,1695],{},[898,27355,2971],{},[1693,27357,1709],{"stretchy":1708},[1762,27359,27321],{},[1693,27361,1731],{"stretchy":1708},[1693,27363,1698],{},[898,27365,2971],{},[1693,27367,1709],{"stretchy":1708},[1762,27369,9987],{},[1693,27371,1731],{"stretchy":1708},[1693,27373,1695],{},[1762,27375,27376],{},"0,401",[902,27378,27379],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,27382,27383,27384],{},"Obecný trend: ",[38,27385,27386],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,27388,27390],{"id":27389},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,27392,27393,27394,16877,27397,27400,27401,16877,27404,8586,27407,16877,27410,27413],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,27395,27396],{},"makroekonomická rovnováha",[614,27398,27399],{},"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 ",[38,27402,27403],{},"agregátní poptávky",[614,27405,27406],{},"aggregate demand",[38,27408,27409],{},"agregátní nabídky",[614,27411,27412],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,27415,27417],{"id":27416},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,27419,27420],{},[9465,27421],{"alt":27422,"className":27423,"src":27424},"imek-keynesian-kriz",[210,9469],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,27426,27428],{"id":27427},"zadání-modelu","Zadání modelu",[724,27430,27431,27432,27445,27446,27459],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,27433,27435],{"className":27434},[886],[888,27436,27437],{"xmlns":890},[892,27438,27439,27443],{},[895,27440,27441],{},[898,27442,2971],{},[902,27444,2971],{"encoding":904}," a investice ",[883,27447,27449],{"className":27448},[886],[888,27450,27451],{"xmlns":890},[892,27452,27453,27457],{},[895,27454,27455],{},[898,27456,6998],{},[902,27458,6998],{"encoding":904},". Podmínka rovnováhy:",[724,27461,27462],{},[883,27463,27465],{"className":27464},[886],[888,27466,27467],{"xmlns":890},[892,27468,27469,27492],{},[895,27470,27471,27473,27475,27477,27479,27481,27483,27485,27487,27490],{},[898,27472,4618],{},[1693,27474,1695],{},[898,27476,2971],{},[1693,27478,1892],{},[898,27480,6998],{},[898,27482,1789],{"mathvariant":1704},[1901,27484],{"width":1903},[1693,27486,1709],{"stretchy":1708},[1762,27488,27489],{},"7.6",[1693,27491,1731],{"stretchy":1708},[902,27493,27494],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,27496,27498],{"id":27497},"soustava-rovnic","Soustava rovnic",[724,27500,27501,27502,27523,27524,27548],{},"Pro pevně zadané (plánované) investice ",[883,27503,27505],{"className":27504},[886],[888,27506,27507],{"xmlns":890},[892,27508,27509,27521],{},[895,27510,27511,27513,27515],{},[898,27512,6998],{},[1693,27514,1695],{},[1717,27516,27517,27519],{},[898,27518,6998],{},[1693,27520,3672],{},[902,27522,19031],{"encoding":904}," a funkci spotřeby ",[883,27525,27527],{"className":27526},[886],[888,27528,27529],{"xmlns":890},[892,27530,27531,27545],{},[895,27532,27533,27535,27537,27539,27541,27543],{},[898,27534,2971],{},[1693,27536,1695],{},[898,27538,2971],{},[1693,27540,1709],{"stretchy":1708},[898,27542,4618],{},[1693,27544,1731],{"stretchy":1708},[902,27546,27547],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,27550,27551],{},[883,27552,27554],{"className":27553},[886],[888,27555,27556],{"xmlns":890},[892,27557,27558,27631],{},[895,27559,27560,27622,27624,27626,27629],{},[3626,27561,27564,27594],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},"0.25em","right left",[3632,27565,27566,27572],{},[3635,27567,27568],{},[3638,27569,27570],{"scriptlevel":1911,"displaystyle":1898},[898,27571,4618],{},[3635,27573,27574],{},[3638,27575,27576],{"scriptlevel":1911,"displaystyle":1898},[895,27577,27578,27580,27582,27584,27586,27592],{},[895,27579],{},[1693,27581,1695],{},[898,27583,2971],{},[1693,27585,1892],{},[1717,27587,27588,27590],{},[898,27589,6998],{},[1693,27591,3672],{},[1693,27593,1899],{"separator":1898},[3632,27595,27596,27602],{},[3635,27597,27598],{},[3638,27599,27600],{"scriptlevel":1911,"displaystyle":1898},[898,27601,2971],{},[3635,27603,27604],{},[3638,27605,27606],{"scriptlevel":1911,"displaystyle":1898},[895,27607,27608,27610,27612,27614,27616,27618,27620],{},[895,27609],{},[1693,27611,1695],{},[898,27613,2971],{},[1693,27615,1709],{"stretchy":1708},[898,27617,4618],{},[1693,27619,1731],{"stretchy":1708},[1693,27621,1899],{"separator":1898},[1901,27623],{"width":1903},[1693,27625,1709],{"stretchy":1708},[1762,27627,27628],{},"7.7",[1693,27630,1731],{"stretchy":1708},[902,27632,27633],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,27635,27636,27637,1863,27639,4286,27656,1863,27659,1789],{},"jejímž řešením jsou ",[38,27638,20715],{},[883,27640,27642],{"className":27641},[886],[888,27643,27644],{"xmlns":890},[892,27645,27646,27654],{},[895,27647,27648],{},[1717,27649,27650,27652],{},[898,27651,4618],{},[898,27653,1691],{},[902,27655,7862],{"encoding":904},[38,27657,27658],{},"rovnovážná spotřeba",[883,27660,27662],{"className":27661},[886],[888,27663,27664],{"xmlns":890},[892,27665,27666,27674],{},[895,27667,27668],{},[1717,27669,27670,27672],{},[898,27671,2971],{},[898,27673,1691],{},[902,27675,20791],{"encoding":904},[198,27677,27679,27680],{"id":27678},"výpočet-yeye","Výpočet ",[883,27681,27683],{"className":27682},[886],[888,27684,27685],{"xmlns":890},[892,27686,27687,27695],{},[895,27688,27689],{},[1717,27690,27691,27693],{},[898,27692,4618],{},[898,27694,1691],{},[902,27696,7862],{"encoding":904},[724,27698,27699,27700,27723,27724,14545,27755],{},"Pro lineární spotřebu ",[883,27701,27703],{"className":27702},[886],[888,27704,27705],{"xmlns":890},[892,27706,27707,27721],{},[895,27708,27709,27711,27713,27715,27717,27719],{},[898,27710,2971],{},[1693,27712,1695],{},[898,27714,207],{},[898,27716,4618],{},[1693,27718,1892],{},[898,27720,1895],{},[902,27722,25731],{"encoding":904}," plyne z (7.7) rovnice ",[883,27725,27727],{"className":27726},[886],[888,27728,27729],{"xmlns":890},[892,27730,27731,27753],{},[895,27732,27733,27735,27737,27739,27741,27743,27745,27747],{},[898,27734,4618],{},[1693,27736,1695],{},[898,27738,207],{},[898,27740,4618],{},[1693,27742,1892],{},[898,27744,1895],{},[1693,27746,1892],{},[1717,27748,27749,27751],{},[898,27750,6998],{},[1693,27752,3672],{},[902,27754,7720],{"encoding":904},[38,27756,27757],{},"redukovaný tvar",[724,27759,27760],{},[883,27761,27763],{"className":27762},[886],[888,27764,27765],{"xmlns":890},[892,27766,27767,27815],{},[895,27768,27769],{},[19664,27770,27771],{"notation":19666},[3638,27772,27773],{"scriptlevel":1911,"displaystyle":1708},[3638,27774,27775],{"scriptlevel":1911,"displaystyle":1708},[3638,27776,27777],{"scriptlevel":1911,"displaystyle":1898},[895,27778,27779,27781,27787,27789,27811,27813],{},[1915,27780,2239],{},[1717,27782,27783,27785],{},[898,27784,4618],{},[898,27786,1691],{},[1693,27788,1695],{},[2132,27790,27791,27803],{},[895,27792,27793,27795,27797],{},[898,27794,1895],{},[1693,27796,1892],{},[1717,27798,27799,27801],{},[898,27800,6998],{},[1693,27802,3672],{},[895,27804,27805,27807,27809],{},[1762,27806,1764],{},[1693,27808,1698],{},[898,27810,207],{},[898,27812,1789],{"mathvariant":1704},[1915,27814,2239],{},[902,27816,27817],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,27819,27821],{"id":27820},"příklad-73","Příklad 7.3",[724,27823,27824,27825,6055,27842,4286,27866,27892],{},"V modelu ",[883,27826,27828],{"className":27827},[886],[888,27829,27830],{"xmlns":890},[892,27831,27832,27840],{},[895,27833,27834,27836,27838],{},[898,27835,2971],{},[1915,27837,19126],{},[898,27839,6998],{},[902,27841,19131],{"encoding":904},[883,27843,27845],{"className":27844},[886],[888,27846,27847],{"xmlns":890},[892,27848,27849,27863],{},[895,27850,27851,27853,27855,27857,27859,27861],{},[898,27852,2971],{},[1693,27854,1695],{},[1762,27856,26132],{},[898,27858,4618],{},[1693,27860,1892],{},[1762,27862,9763],{},[902,27864,27865],{"encoding":904},"C = 0{,}6Y + 10",[883,27867,27869],{"className":27868},[886],[888,27870,27871],{"xmlns":890},[892,27872,27873,27889],{},[895,27874,27875,27877,27879,27881,27883],{},[898,27876,6998],{},[1693,27878,1695],{},[1762,27880,10402],{},[1693,27882,1695],{},[1717,27884,27885,27887],{},[898,27886,6998],{},[1693,27888,3672],{},[902,27890,27891],{"encoding":904},"I = 12 = I^*",". Soustava",[724,27894,27895],{},[883,27896,27898],{"className":27897},[886],[888,27899,27900],{"xmlns":890},[892,27901,27902,27958],{},[3626,27903,27904,27930],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,27905,27906,27912],{},[3635,27907,27908],{},[3638,27909,27910],{"scriptlevel":1911,"displaystyle":1898},[898,27911,4618],{},[3635,27913,27914],{},[3638,27915,27916],{"scriptlevel":1911,"displaystyle":1898},[895,27917,27918,27920,27922,27924,27926,27928],{},[895,27919],{},[1693,27921,1695],{},[898,27923,2971],{},[1693,27925,1892],{},[1762,27927,10402],{},[1693,27929,1899],{"separator":1898},[3632,27931,27932,27938],{},[3635,27933,27934],{},[3638,27935,27936],{"scriptlevel":1911,"displaystyle":1898},[898,27937,2971],{},[3635,27939,27940],{},[3638,27941,27942],{"scriptlevel":1911,"displaystyle":1898},[895,27943,27944,27946,27948,27950,27952,27954,27956],{},[895,27945],{},[1693,27947,1695],{},[1762,27949,26132],{},[898,27951,4618],{},[1693,27953,1892],{},[1762,27955,9763],{},[1693,27957,1899],{"separator":1898},[902,27959,27960],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,27962,27963,27964,1343,27987,28010,28011,3042],{},"má řešení ",[883,27965,27967],{"className":27966},[886],[888,27968,27969],{"xmlns":890},[892,27970,27971,27984],{},[895,27972,27973,27979,27981],{},[1717,27974,27975,27977],{},[898,27976,4618],{},[898,27978,1691],{},[1693,27980,1695],{},[1762,27982,27983],{},"55",[902,27985,27986],{"encoding":904},"Y^E = 55",[883,27988,27990],{"className":27989},[886],[888,27991,27992],{"xmlns":890},[892,27993,27994,28007],{},[895,27995,27996,28002,28004],{},[1717,27997,27998,28000],{},[898,27999,2971],{},[898,28001,1691],{},[1693,28003,1695],{},[1762,28005,28006],{},"43",[902,28008,28009],{"encoding":904},"C^E = 43"," (a ",[883,28012,28014],{"className":28013},[886],[888,28015,28016],{"xmlns":890},[892,28017,28018,28030],{},[895,28019,28020,28026,28028],{},[1717,28021,28022,28024],{},[898,28023,3611],{},[898,28025,1691],{},[1693,28027,1695],{},[1762,28029,10402],{},[902,28031,28032],{"encoding":904},"S^E = 12",[724,28034,28035],{},[614,28036,28037,28038,28060,28061,8586,28082,28105,28106,1789],{},"Obrázek 7.5 — Přímky ",[883,28039,28041],{"className":28040},[886],[888,28042,28043],{"xmlns":890},[892,28044,28045,28057],{},[895,28046,28047,28049,28051,28053,28055],{},[898,28048,2971],{},[1693,28050,1695],{},[898,28052,4618],{},[1693,28054,1698],{},[1762,28056,10402],{},[902,28058,28059],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,28062,28064],{"className":28063},[886],[888,28065,28066],{"xmlns":890},[892,28067,28068,28080],{},[895,28069,28070,28072,28074,28076,28078],{},[898,28071,4618],{},[1693,28073,1695],{},[898,28075,2971],{},[1693,28077,1892],{},[898,28079,6998],{},[902,28081,8174],{"encoding":904},[883,28083,28085],{"className":28084},[886],[888,28086,28087],{"xmlns":890},[892,28088,28089,28103],{},[895,28090,28091,28093,28095,28097,28099,28101],{},[898,28092,2971],{},[1693,28094,1695],{},[1762,28096,26132],{},[898,28098,4618],{},[1693,28100,1892],{},[1762,28102,9763],{},[902,28104,27865],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,28107,28109],{"className":28108},[886],[888,28110,28111],{"xmlns":890},[892,28112,28113,28145],{},[895,28114,28115,28117,28123,28125,28131,28133,28135,28137,28139,28141,28143],{},[1693,28116,9392],{"stretchy":1708},[1717,28118,28119,28121],{},[898,28120,4618],{},[898,28122,1691],{},[1693,28124,1899],{"separator":1898},[1717,28126,28127,28129],{},[898,28128,2971],{},[898,28130,1691],{},[1693,28132,9407],{"stretchy":1708},[1693,28134,1695],{},[1693,28136,9392],{"stretchy":1708},[1762,28138,27983],{},[1693,28140,1899],{"separator":1898},[1762,28142,28006],{},[1693,28144,9407],{"stretchy":1708},[902,28146,28147],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,28149,28150,28153,28154,28171,28172,1789],{},[38,28151,28152],{},"Komentář k přechodu."," Model ",[883,28155,28157],{"className":28156},[886],[888,28158,28159],{"xmlns":890},[892,28160,28161,28169],{},[895,28162,28163,28165,28167],{},[898,28164,2971],{},[1915,28166,19126],{},[898,28168,6998],{},[902,28170,19131],{"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 ",[38,28173,28174,28175],{},"model ",[883,28176,28178],{"className":28177},[886],[888,28179,28180],{"xmlns":890},[892,28181,28182,28194],{},[895,28183,28184,28186,28188,28190,28192],{},[898,28185,2971],{},[1915,28187,19126],{},[898,28189,6998],{},[1915,28191,19126],{},[898,28193,6984],{},[902,28195,25034],{"encoding":904},[115,28197,28199],{"id":28198},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,28201,27428],{"id":28202},"zadání-modelu-1",[724,28204,28205,28206,28223,28224,1863,28227,16877,28240,28243],{},"Rozšíření modelu ",[883,28207,28209],{"className":28208},[886],[888,28210,28211],{"xmlns":890},[892,28212,28213,28221],{},[895,28214,28215,28217,28219],{},[898,28216,2971],{},[1915,28218,19126],{},[898,28220,6998],{},[902,28222,19131],{"encoding":904}," o ",[38,28225,28226],{},"vládní výdaje",[883,28228,28230],{"className":28229},[886],[888,28231,28232],{"xmlns":890},[892,28233,28234,28238],{},[895,28235,28236],{},[898,28237,6984],{},[902,28239,6984],{"encoding":904},[614,28241,28242],{},"government expenditure","). Podmínka rovnováhy:",[724,28245,28246],{},[883,28247,28249],{"className":28248},[886],[888,28250,28251],{"xmlns":890},[892,28252,28253,28280],{},[895,28254,28255,28257,28259,28261,28263,28265,28267,28269,28271,28273,28275,28278],{},[898,28256,4618],{},[1693,28258,1695],{},[898,28260,2971],{},[1693,28262,1892],{},[898,28264,6998],{},[1693,28266,1892],{},[898,28268,6984],{},[898,28270,1789],{"mathvariant":1704},[1901,28272],{"width":1903},[1693,28274,1709],{"stretchy":1708},[1762,28276,28277],{},"7.8",[1693,28279,1731],{"stretchy":1708},[902,28281,28282],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,28284,28285,28286,1863,28289,16877,28302,28305],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,28287,28288],{},"zdaněním domácností",[883,28290,28292],{"className":28291},[886],[888,28293,28294],{"xmlns":890},[892,28295,28296,28300],{},[895,28297,28298],{},[898,28299,2663],{},[902,28301,2663],{"encoding":904},[614,28303,28304],{},"taxation","). Zdanění bývá:",[120,28307,28308,28341,28366],{},[123,28309,28310,28311,1899],{},"úměrné důchodu: ",[883,28312,28314],{"className":28313},[886],[888,28315,28316],{"xmlns":890},[892,28317,28318,28338],{},[895,28319,28320,28322,28324,28326,28328,28330,28332,28334,28336],{},[898,28321,2663],{},[1693,28323,1695],{},[898,28325,2663],{},[1693,28327,1709],{"stretchy":1708},[898,28329,4618],{},[1693,28331,1731],{"stretchy":1708},[1693,28333,1695],{},[898,28335,25666],{},[898,28337,4618],{},[902,28339,28340],{"encoding":904},"T = T(Y) = tY",[123,28342,28343,28344,1899],{},"fixní: ",[883,28345,28347],{"className":28346},[886],[888,28348,28349],{"xmlns":890},[892,28350,28351,28363],{},[895,28352,28353,28355,28357],{},[898,28354,2663],{},[1693,28356,1695],{},[1717,28358,28359,28361],{},[898,28360,2663],{},[1693,28362,3672],{},[902,28364,28365],{"encoding":904},"T = T^*",[123,28367,28368,28369,28397,28398,1789],{},"kombinované: ",[883,28370,28372],{"className":28371},[886],[888,28373,28374],{"xmlns":890},[892,28375,28376,28394],{},[895,28377,28378,28380,28382,28388,28390,28392],{},[898,28379,2663],{},[1693,28381,1695],{},[1717,28383,28384,28386],{},[898,28385,2663],{},[1693,28387,3672],{},[1693,28389,1892],{},[898,28391,25666],{},[898,28393,4618],{},[902,28395,28396],{"encoding":904},"T = T^* + tY",", kde ",[883,28399,28401],{"className":28400},[886],[888,28402,28403],{"xmlns":890},[892,28404,28405,28417],{},[895,28406,28407,28409,28411,28413,28415],{},[1762,28408,1911],{},[1693,28410,14539],{},[898,28412,25666],{},[1693,28414,1908],{},[1762,28416,1764],{},[902,28418,28419],{"encoding":904},"0 \\le t \u003C 1",[1636,28421,28422],{},[724,28423,28424,28426,28427,28448,28449,28452,28453,28466,28467,8586,28493,1863,28496,28521,28522,28550,28551,4286,28564,28581],{},[883,28425,8654],{}," Pozor na disponibilní důchod\nV modelu ",[883,28428,28430],{"className":28429},[886],[888,28431,28432],{"xmlns":890},[892,28433,28434,28446],{},[895,28435,28436,28438,28440,28442,28444],{},[898,28437,2971],{},[1915,28439,19126],{},[898,28441,6998],{},[1915,28443,19126],{},[898,28445,6984],{},[902,28447,25034],{"encoding":904}," je nutné ",[38,28450,28451],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,28454,28456],{"className":28455},[886],[888,28457,28458],{"xmlns":890},[892,28459,28460,28464],{},[895,28461,28462],{},[898,28463,4618],{},[902,28465,4618],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,28468,28470],{"className":28469},[886],[888,28471,28472],{"xmlns":890},[892,28473,28474,28490],{},[895,28475,28476,28478,28480,28482,28484,28486,28488],{},[898,28477,4618],{},[1693,28479,1695],{},[898,28481,2971],{},[1693,28483,1892],{},[898,28485,6998],{},[1693,28487,1892],{},[898,28489,6984],{},[902,28491,28492],{"encoding":904},"Y = C + I + G",[38,28494,28495],{},"disponibilní důchod",[883,28497,28499],{"className":28498},[886],[888,28500,28501],{"xmlns":890},[892,28502,28503,28519],{},[895,28504,28505,28511,28513,28515,28517],{},[3284,28506,28507,28509],{},[898,28508,4618],{},[898,28510,2738],{},[1693,28512,1695],{},[898,28514,4618],{},[1693,28516,1698],{},[898,28518,2663],{},[902,28520,7574],{"encoding":904}," (na něm závisí spotřeba domácností, ",[883,28523,28525],{"className":28524},[886],[888,28526,28527],{"xmlns":890},[892,28528,28529,28547],{},[895,28530,28531,28533,28535,28537,28539,28545],{},[898,28532,2971],{},[1693,28534,1695],{},[898,28536,2971],{},[1693,28538,1709],{"stretchy":1708},[3284,28540,28541,28543],{},[898,28542,4618],{},[898,28544,2738],{},[1693,28546,1731],{"stretchy":1708},[902,28548,28549],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,28552,28554],{"className":28553},[886],[888,28555,28556],{"xmlns":890},[892,28557,28558,28562],{},[895,28559,28560],{},[898,28561,4618],{},[902,28563,4618],{"encoding":904},[883,28565,28567],{"className":28566},[886],[888,28568,28569],{"xmlns":890},[892,28570,28571,28579],{},[895,28572,28573],{},[3284,28574,28575,28577],{},[898,28576,4618],{},[898,28578,2738],{},[902,28580,7602],{"encoding":904}," ve funkci spotřeby je nejčastější zdroj chyb.",[724,28583,28584,16877,28586,1731],{},[38,28585,7546],{},[614,28587,28588],{},"disposable income",[724,28590,28591],{},[883,28592,28594],{"className":28593},[886],[888,28595,28596],{"xmlns":890},[892,28597,28598,28614],{},[895,28599,28600,28606,28608,28610,28612],{},[3284,28601,28602,28604],{},[898,28603,4618],{},[898,28605,2738],{},[1693,28607,1695],{},[898,28609,4618],{},[1693,28611,1698],{},[898,28613,2663],{},[902,28615,7574],{"encoding":904},[724,28617,28618,28619,1789],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,28620,28622],{"className":28621},[886],[888,28623,28624],{"xmlns":890},[892,28625,28626,28644],{},[895,28627,28628,28630,28632,28634,28636,28642],{},[898,28629,2971],{},[1693,28631,1695],{},[898,28633,2971],{},[1693,28635,1709],{"stretchy":1708},[3284,28637,28638,28640],{},[898,28639,4618],{},[898,28641,2738],{},[1693,28643,1731],{"stretchy":1708},[902,28645,28549],{"encoding":904},[198,28647,27498],{"id":28648},"soustava-rovnic-1",[724,28650,28651,28652,1343,28673,28695,28696,4300],{},"Pro pevně zadané ",[883,28653,28655],{"className":28654},[886],[888,28656,28657],{"xmlns":890},[892,28658,28659,28671],{},[895,28660,28661,28663,28665],{},[898,28662,6998],{},[1693,28664,1695],{},[1717,28666,28667,28669],{},[898,28668,6998],{},[1693,28670,3672],{},[902,28672,19031],{"encoding":904},[883,28674,28676],{"className":28675},[886],[888,28677,28678],{"xmlns":890},[892,28679,28680,28692],{},[895,28681,28682,28684,28686],{},[898,28683,6984],{},[1693,28685,1695],{},[1717,28687,28688,28690],{},[898,28689,6984],{},[1693,28691,3672],{},[902,28693,28694],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,28697,28699],{"className":28698},[886],[888,28700,28701],{"xmlns":890},[892,28702,28703,28723],{},[895,28704,28705,28707,28709,28711,28713,28719,28721],{},[898,28706,4618],{},[1693,28708,1899],{"separator":1898},[898,28710,2971],{},[1693,28712,1899],{"separator":1898},[3284,28714,28715,28717],{},[898,28716,4618],{},[898,28718,2738],{},[1693,28720,1899],{"separator":1898},[898,28722,2663],{},[902,28724,28725],{"encoding":904},"Y, C, Y_D, T",[724,28727,28728],{},[883,28729,28731],{"className":28730},[886],[888,28732,28733],{"xmlns":890},[892,28734,28735,28876],{},[895,28736,28737,28867,28869,28871,28874],{},[3626,28738,28739,28777,28805,28837],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,28740,28741,28747],{},[3635,28742,28743],{},[3638,28744,28745],{"scriptlevel":1911,"displaystyle":1898},[898,28746,4618],{},[3635,28748,28749],{},[3638,28750,28751],{"scriptlevel":1911,"displaystyle":1898},[895,28752,28753,28755,28757,28759,28761,28767,28769,28775],{},[895,28754],{},[1693,28756,1695],{},[898,28758,2971],{},[1693,28760,1892],{},[1717,28762,28763,28765],{},[898,28764,6998],{},[1693,28766,3672],{},[1693,28768,1892],{},[1717,28770,28771,28773],{},[898,28772,6984],{},[1693,28774,3672],{},[1693,28776,1899],{"separator":1898},[3632,28778,28779,28785],{},[3635,28780,28781],{},[3638,28782,28783],{"scriptlevel":1911,"displaystyle":1898},[898,28784,2663],{},[3635,28786,28787],{},[3638,28788,28789],{"scriptlevel":1911,"displaystyle":1898},[895,28790,28791,28793,28795,28797,28799,28801,28803],{},[895,28792],{},[1693,28794,1695],{},[898,28796,2663],{},[1693,28798,1709],{"stretchy":1708},[898,28800,4618],{},[1693,28802,1731],{"stretchy":1708},[1693,28804,1899],{"separator":1898},[3632,28806,28807,28813],{},[3635,28808,28809],{},[3638,28810,28811],{"scriptlevel":1911,"displaystyle":1898},[898,28812,2971],{},[3635,28814,28815],{},[3638,28816,28817],{"scriptlevel":1911,"displaystyle":1898},[895,28818,28819,28821,28823,28825,28827,28833,28835],{},[895,28820],{},[1693,28822,1695],{},[898,28824,2971],{},[1693,28826,1709],{"stretchy":1708},[3284,28828,28829,28831],{},[898,28830,4618],{},[898,28832,2738],{},[1693,28834,1731],{"stretchy":1708},[1693,28836,1899],{"separator":1898},[3632,28838,28839,28849],{},[3635,28840,28841],{},[3638,28842,28843],{"scriptlevel":1911,"displaystyle":1898},[3284,28844,28845,28847],{},[898,28846,4618],{},[898,28848,2738],{},[3635,28850,28851],{},[3638,28852,28853],{"scriptlevel":1911,"displaystyle":1898},[895,28854,28855,28857,28859,28861,28863,28865],{},[895,28856],{},[1693,28858,1695],{},[898,28860,4618],{},[1693,28862,1698],{},[898,28864,2663],{},[1693,28866,1899],{"separator":1898},[1901,28868],{"width":1903},[1693,28870,1709],{"stretchy":1708},[1762,28872,28873],{},"7.9",[1693,28875,1731],{"stretchy":1708},[902,28877,28878],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,28880,28881,28882,28926,28927,1789],{},"s řešeními ",[883,28883,28885],{"className":28884},[886],[888,28886,28887],{"xmlns":890},[892,28888,28889,28923],{},[895,28890,28891,28897,28899,28905,28907,28913,28915],{},[1717,28892,28893,28895],{},[898,28894,4618],{},[898,28896,1691],{},[1693,28898,1899],{"separator":1898},[1717,28900,28901,28903],{},[898,28902,2971],{},[898,28904,1691],{},[1693,28906,1899],{"separator":1898},[1717,28908,28909,28911],{},[898,28910,2663],{},[898,28912,1691],{},[1693,28914,1899],{"separator":1898},[5688,28916,28917,28919,28921],{},[898,28918,4618],{},[898,28920,2738],{},[898,28922,1691],{},[902,28924,28925],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,28928,28930],{"className":28929},[886],[888,28931,28932],{"xmlns":890},[892,28933,28934,28960],{},[895,28935,28936,28942,28944,28952,28954],{},[1717,28937,28938,28940],{},[898,28939,3611],{},[898,28941,1691],{},[1693,28943,1695],{},[5688,28945,28946,28948,28950],{},[898,28947,4618],{},[898,28949,2738],{},[898,28951,1691],{},[1693,28953,1698],{},[1717,28955,28956,28958],{},[898,28957,2971],{},[898,28959,1691],{},[902,28961,28962],{"encoding":904},"S^E = Y_D^E - C^E",[1636,28964,28965,28970],{},[724,28966,28967,28969],{},[883,28968,8620],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,28971,28972,28995,29078,29133,29223],{},[123,28973,28974,28977,28978,1789],{},[38,28975,28976],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,28979,28981],{"className":28980},[886],[888,28982,28983],{"xmlns":890},[892,28984,28985,28993],{},[895,28986,28987],{},[3284,28988,28989,28991],{},[898,28990,4618],{},[898,28992,2738],{},[902,28994,7602],{"encoding":904},[123,28996,28997,29046,29047,29064,29065,1789],{},[38,28998,28999,29000,29020,29021],{},"Dosaď ",[883,29001,29003],{"className":29002},[886],[888,29004,29005],{"xmlns":890},[892,29006,29007,29017],{},[895,29008,29009,29011,29013,29015],{},[898,29010,2663],{},[1693,29012,1709],{"stretchy":1708},[898,29014,4618],{},[1693,29016,1731],{"stretchy":1708},[902,29018,29019],{"encoding":904},"T(Y)"," do ",[883,29022,29024],{"className":29023},[886],[888,29025,29026],{"xmlns":890},[892,29027,29028,29044],{},[895,29029,29030,29036,29038,29040,29042],{},[3284,29031,29032,29034],{},[898,29033,4618],{},[898,29035,2738],{},[1693,29037,1695],{},[898,29039,4618],{},[1693,29041,1698],{},[898,29043,2663],{},[902,29045,7574],{"encoding":904}," — dostaneš ",[883,29048,29050],{"className":29049},[886],[888,29051,29052],{"xmlns":890},[892,29053,29054,29062],{},[895,29055,29056],{},[3284,29057,29058,29060],{},[898,29059,4618],{},[898,29061,2738],{},[902,29063,7602],{"encoding":904}," jako lineární funkci ",[883,29066,29068],{"className":29067},[886],[888,29069,29070],{"xmlns":890},[892,29071,29072,29076],{},[895,29073,29074],{},[898,29075,4618],{},[902,29077,4618],{"encoding":904},[123,29079,29080,29046,29107,29064,29120,1789],{},[38,29081,28999,29082,29106],{},[883,29083,29085],{"className":29084},[886],[888,29086,29087],{"xmlns":890},[892,29088,29089,29103],{},[895,29090,29091,29097,29099,29101],{},[3284,29092,29093,29095],{},[898,29094,4618],{},[898,29096,2738],{},[1693,29098,1709],{"stretchy":1708},[898,29100,4618],{},[1693,29102,1731],{"stretchy":1708},[902,29104,29105],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,29108,29110],{"className":29109},[886],[888,29111,29112],{"xmlns":890},[892,29113,29114,29118],{},[895,29115,29116],{},[898,29117,2971],{},[902,29119,2971],{"encoding":904},[883,29121,29123],{"className":29122},[886],[888,29124,29125],{"xmlns":890},[892,29126,29127,29131],{},[895,29128,29129],{},[898,29130,4618],{},[902,29132,4618],{"encoding":904},[123,29134,29135,1863,29157,29191,29192,29205,29206,1789],{},[38,29136,28999,29137,29156],{},[883,29138,29140],{"className":29139},[886],[888,29141,29142],{"xmlns":890},[892,29143,29144,29154],{},[895,29145,29146,29148,29150,29152],{},[898,29147,2971],{},[1693,29149,1709],{"stretchy":1708},[898,29151,4618],{},[1693,29153,1731],{"stretchy":1708},[902,29155,8195],{"encoding":904}," do podmínky rovnováhy",[883,29158,29160],{"className":29159},[886],[888,29161,29162],{"xmlns":890},[892,29163,29164,29188],{},[895,29165,29166,29168,29170,29172,29174,29180,29182],{},[898,29167,4618],{},[1693,29169,1695],{},[898,29171,2971],{},[1693,29173,1892],{},[1717,29175,29176,29178],{},[898,29177,6998],{},[1693,29179,3672],{},[1693,29181,1892],{},[1717,29183,29184,29186],{},[898,29185,6984],{},[1693,29187,3672],{},[902,29189,29190],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,29193,29195],{"className":29194},[886],[888,29196,29197],{"xmlns":890},[892,29198,29199,29203],{},[895,29200,29201],{},[898,29202,4618],{},[902,29204,4618],{"encoding":904},", odtud ",[883,29207,29209],{"className":29208},[886],[888,29210,29211],{"xmlns":890},[892,29212,29213,29221],{},[895,29214,29215],{},[1717,29216,29217,29219],{},[898,29218,4618],{},[898,29220,1691],{},[902,29222,7862],{"encoding":904},[123,29224,29225,29228,29229,1343,29247,1343,29267,1343,29284,1789],{},[38,29226,29227],{},"Zpětným dosazením"," dopočítej ",[883,29230,29232],{"className":29231},[886],[888,29233,29234],{"xmlns":890},[892,29235,29236,29244],{},[895,29237,29238],{},[1717,29239,29240,29242],{},[898,29241,2663],{},[898,29243,1691],{},[902,29245,29246],{"encoding":904},"T^E",[883,29248,29250],{"className":29249},[886],[888,29251,29252],{"xmlns":890},[892,29253,29254,29264],{},[895,29255,29256],{},[5688,29257,29258,29260,29262],{},[898,29259,4618],{},[898,29261,2738],{},[898,29263,1691],{},[902,29265,29266],{"encoding":904},"Y_D^E",[883,29268,29270],{"className":29269},[886],[888,29271,29272],{"xmlns":890},[892,29273,29274,29282],{},[895,29275,29276],{},[1717,29277,29278,29280],{},[898,29279,2971],{},[898,29281,1691],{},[902,29283,20791],{"encoding":904},[883,29285,29287],{"className":29286},[886],[888,29288,29289],{"xmlns":890},[892,29290,29291,29299],{},[895,29292,29293],{},[1717,29294,29295,29297],{},[898,29296,3611],{},[898,29298,1691],{},[902,29300,29301],{"encoding":904},"S^E",[198,29303,29305],{"id":29304},"příklad-74","Příklad 7.4",[724,29307,27824,29308,29329,29330,1343,29361,1343,29385,1343,29407,29429],{},[883,29309,29311],{"className":29310},[886],[888,29312,29313],{"xmlns":890},[892,29314,29315,29327],{},[895,29316,29317,29319,29321,29323,29325],{},[898,29318,2971],{},[1915,29320,19126],{},[898,29322,6998],{},[1915,29324,19126],{},[898,29326,6984],{},[902,29328,25034],{"encoding":904}," jsou dány ",[883,29331,29333],{"className":29332},[886],[888,29334,29335],{"xmlns":890},[892,29336,29337,29358],{},[895,29338,29339,29341,29343,29346,29348,29354,29356],{},[898,29340,2971],{},[1693,29342,1695],{},[1762,29344,29345],{},"0,9",[1915,29347,2239],{},[3284,29349,29350,29352],{},[898,29351,4618],{},[898,29353,2738],{},[1693,29355,1892],{},[1762,29357,12763],{},[902,29359,29360],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,29362,29364],{"className":29363},[886],[888,29365,29366],{"xmlns":890},[892,29367,29368,29382],{},[895,29369,29370,29372,29374,29376,29378,29380],{},[898,29371,2663],{},[1693,29373,1695],{},[1762,29375,9739],{},[898,29377,4618],{},[1693,29379,1892],{},[1762,29381,11872],{},[902,29383,29384],{"encoding":904},"T = 0{,}2Y + 25",[883,29386,29388],{"className":29387},[886],[888,29389,29390],{"xmlns":890},[892,29391,29392,29404],{},[895,29393,29394,29400,29402],{},[1717,29395,29396,29398],{},[898,29397,6998],{},[1693,29399,3672],{},[1693,29401,1695],{},[1762,29403,21864],{},[902,29405,29406],{"encoding":904},"I^* = 35",[883,29408,29410],{"className":29409},[886],[888,29411,29412],{"xmlns":890},[892,29413,29414,29426],{},[895,29415,29416,29422,29424],{},[1717,29417,29418,29420],{},[898,29419,6984],{},[1693,29421,3672],{},[1693,29423,1695],{},[1762,29425,15892],{},[902,29427,29428],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,29431,29432],{},[883,29433,29435],{"className":29434},[886],[888,29436,29437],{"xmlns":890},[892,29438,29439,29563],{},[3626,29440,29441,29471,29499,29533],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,29442,29443,29449],{},[3635,29444,29445],{},[3638,29446,29447],{"scriptlevel":1911,"displaystyle":1898},[898,29448,4618],{},[3635,29450,29451],{},[3638,29452,29453],{"scriptlevel":1911,"displaystyle":1898},[895,29454,29455,29457,29459,29461,29463,29465,29467,29469],{},[895,29456],{},[1693,29458,1695],{},[898,29460,2971],{},[1693,29462,1892],{},[1762,29464,21864],{},[1693,29466,1892],{},[1762,29468,15892],{},[1693,29470,1899],{"separator":1898},[3632,29472,29473,29479],{},[3635,29474,29475],{},[3638,29476,29477],{"scriptlevel":1911,"displaystyle":1898},[898,29478,2663],{},[3635,29480,29481],{},[3638,29482,29483],{"scriptlevel":1911,"displaystyle":1898},[895,29484,29485,29487,29489,29491,29493,29495,29497],{},[895,29486],{},[1693,29488,1695],{},[1762,29490,9739],{},[898,29492,4618],{},[1693,29494,1892],{},[1762,29496,11872],{},[1693,29498,1899],{"separator":1898},[3632,29500,29501,29507],{},[3635,29502,29503],{},[3638,29504,29505],{"scriptlevel":1911,"displaystyle":1898},[898,29506,2971],{},[3635,29508,29509],{},[3638,29510,29511],{"scriptlevel":1911,"displaystyle":1898},[895,29512,29513,29515,29517,29519,29521,29527,29529,29531],{},[895,29514],{},[1693,29516,1695],{},[1762,29518,29345],{},[1915,29520,2239],{},[3284,29522,29523,29525],{},[898,29524,4618],{},[898,29526,2738],{},[1693,29528,1892],{},[1762,29530,12763],{},[1693,29532,1899],{"separator":1898},[3632,29534,29535,29545],{},[3635,29536,29537],{},[3638,29538,29539],{"scriptlevel":1911,"displaystyle":1898},[3284,29540,29541,29543],{},[898,29542,4618],{},[898,29544,2738],{},[3635,29546,29547],{},[3638,29548,29549],{"scriptlevel":1911,"displaystyle":1898},[895,29550,29551,29553,29555,29557,29559,29561],{},[895,29552],{},[1693,29554,1695],{},[898,29556,4618],{},[1693,29558,1698],{},[898,29560,2663],{},[898,29562,1789],{"mathvariant":1704},[902,29564,29565],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,29567,29568,29571,29572,29626,29627,29673,29674,4300],{},[38,29569,29570],{},"Řešení."," Z definice ",[883,29573,29575],{"className":29574},[886],[888,29576,29577],{"xmlns":890},[892,29578,29579,29623],{},[895,29580,29581,29587,29589,29591,29593,29595,29597,29599,29601,29603,29605,29607,29609,29611,29613,29615,29617,29619,29621],{},[3284,29582,29583,29585],{},[898,29584,4618],{},[898,29586,2738],{},[1693,29588,1695],{},[898,29590,4618],{},[1693,29592,1698],{},[898,29594,2663],{},[1693,29596,1695],{},[898,29598,4618],{},[1693,29600,1698],{},[1693,29602,1709],{"stretchy":1708},[1762,29604,9739],{},[898,29606,4618],{},[1693,29608,1892],{},[1762,29610,11872],{},[1693,29612,1731],{"stretchy":1708},[1693,29614,1695],{},[1762,29616,21416],{},[898,29618,4618],{},[1693,29620,1698],{},[1762,29622,11872],{},[902,29624,29625],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,29628,29630],{"className":29629},[886],[888,29631,29632],{"xmlns":890},[892,29633,29634,29670],{},[895,29635,29636,29638,29640,29642,29644,29646,29648,29650,29652,29654,29656,29658,29660,29663,29665,29667],{},[898,29637,2971],{},[1693,29639,1695],{},[1762,29641,29345],{},[1693,29643,1709],{"stretchy":1708},[1762,29645,21416],{},[898,29647,4618],{},[1693,29649,1698],{},[1762,29651,11872],{},[1693,29653,1731],{"stretchy":1708},[1693,29655,1892],{},[1762,29657,12763],{},[1693,29659,1695],{},[1762,29661,29662],{},"0,72",[898,29664,4618],{},[1693,29666,1892],{},[1762,29668,29669],{},"47,5",[902,29671,29672],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,29675,29677],{"className":29676},[886],[888,29678,29679],{"xmlns":890},[892,29680,29681,29699],{},[895,29682,29683,29685,29687,29689,29691,29693,29695,29697],{},[898,29684,4618],{},[1693,29686,1695],{},[1762,29688,29662],{},[898,29690,4618],{},[1693,29692,1892],{},[1762,29694,29669],{},[1693,29696,1892],{},[1762,29698,27983],{},[902,29700,29701],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,29703,29704],{},[883,29705,29707],{"className":29706},[886],[888,29708,29709],{"xmlns":890},[892,29710,29711,29752],{},[895,29712,29713,29716,29718,29720,29723,29725,29727,29729,29735,29737,29747,29749],{},[1762,29714,29715],{},"0,28",[898,29717,4618],{},[1693,29719,1695],{},[1762,29721,29722],{},"102,5",[1915,29724,1917],{},[1693,29726,21834],{},[1915,29728,1917],{},[1717,29730,29731,29733],{},[898,29732,4618],{},[898,29734,1691],{},[1693,29736,1695],{},[3638,29738,29739],{"scriptlevel":1911,"displaystyle":1708},[2132,29740,29741,29744],{},[1762,29742,29743],{},"5125",[1762,29745,29746],{},"14",[1693,29748,12766],{},[1762,29750,29751],{},"366,071.",[902,29753,29754],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,29756,29757],{},"Rovnovážné veličiny:",[120,29759,29760,29795,29847,29901,29949],{},[123,29761,29762,1899],{},[883,29763,29765],{"className":29764},[886],[888,29766,29767],{"xmlns":890},[892,29768,29769,29792],{},[895,29770,29771,29777,29779,29787,29789],{},[1717,29772,29773,29775],{},[898,29774,4618],{},[898,29776,1691],{},[1693,29778,1695],{},[3638,29780,29781],{"scriptlevel":1911,"displaystyle":1708},[2132,29782,29783,29785],{},[1762,29784,29743],{},[1762,29786,29746],{},[1693,29788,12766],{},[1762,29790,29791],{},"366,071",[902,29793,29794],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,29796,29797,1899],{},[883,29798,29800],{"className":29799},[886],[888,29801,29802],{"xmlns":890},[892,29803,29804,29844],{},[895,29805,29806,29812,29814,29816,29818,29824,29826,29828,29830,29839,29841],{},[1717,29807,29808,29810],{},[898,29809,2663],{},[898,29811,1691],{},[1693,29813,1695],{},[1762,29815,9739],{},[1915,29817,2239],{},[1717,29819,29820,29822],{},[898,29821,4618],{},[898,29823,1691],{},[1693,29825,1892],{},[1762,29827,11872],{},[1693,29829,1695],{},[3638,29831,29832],{"scriptlevel":1911,"displaystyle":1708},[2132,29833,29834,29837],{},[1762,29835,29836],{},"1375",[1762,29838,29746],{},[1693,29840,12766],{},[1762,29842,29843],{},"98,214",[902,29845,29846],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,29848,29849,1899],{},[883,29850,29852],{"className":29851},[886],[888,29853,29854],{"xmlns":890},[892,29855,29856,29898],{},[895,29857,29858,29866,29868,29874,29876,29882,29884,29893,29895],{},[5688,29859,29860,29862,29864],{},[898,29861,4618],{},[898,29863,2738],{},[898,29865,1691],{},[1693,29867,1695],{},[1717,29869,29870,29872],{},[898,29871,4618],{},[898,29873,1691],{},[1693,29875,1698],{},[1717,29877,29878,29880],{},[898,29879,2663],{},[898,29881,1691],{},[1693,29883,1695],{},[3638,29885,29886],{"scriptlevel":1911,"displaystyle":1708},[2132,29887,29888,29891],{},[1762,29889,29890],{},"3750",[1762,29892,29746],{},[1693,29894,12766],{},[1762,29896,29897],{},"267,857",[902,29899,29900],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,29902,29903,1899],{},[883,29904,29906],{"className":29905},[886],[888,29907,29908],{"xmlns":890},[892,29909,29910,29946],{},[895,29911,29912,29918,29920,29926,29928,29930,29932,29941,29943],{},[1717,29913,29914,29916],{},[898,29915,2971],{},[898,29917,1691],{},[1693,29919,1695],{},[1717,29921,29922,29924],{},[898,29923,4618],{},[898,29925,1691],{},[1693,29927,1698],{},[1762,29929,27983],{},[1693,29931,1695],{},[3638,29933,29934],{"scriptlevel":1911,"displaystyle":1708},[2132,29935,29936,29939],{},[1762,29937,29938],{},"4355",[1762,29940,29746],{},[1693,29942,12766],{},[1762,29944,29945],{},"311,071",[902,29947,29948],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,29950,29951,30007],{},[883,29952,29954],{"className":29953},[886],[888,29955,29956],{"xmlns":890},[892,29957,29958,30004],{},[895,29959,29960,29966,29968,29976,29978,29984,29986,29988,29997,29999,30001],{},[1717,29961,29962,29964],{},[898,29963,3611],{},[898,29965,1691],{},[1693,29967,1695],{},[5688,29969,29970,29972,29974],{},[898,29971,4618],{},[898,29973,2738],{},[898,29975,1691],{},[1693,29977,1698],{},[1717,29979,29980,29982],{},[898,29981,2971],{},[898,29983,1691],{},[1693,29985,1695],{},[1693,29987,1698],{},[3638,29989,29990],{"scriptlevel":1911,"displaystyle":1708},[2132,29991,29992,29995],{},[1762,29993,29994],{},"605",[1762,29996,29746],{},[1693,29998,12766],{},[1693,30000,1698],{},[1762,30002,30003],{},"43,214",[902,30005,30006],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,30009,30010,28153,30012,30033,30034,30037,30038,30060,30061,1789],{},[38,30011,28152],{},[883,30013,30015],{"className":30014},[886],[888,30016,30017],{"xmlns":890},[892,30018,30019,30031],{},[895,30020,30021,30023,30025,30027,30029],{},[898,30022,2971],{},[1915,30024,19126],{},[898,30026,6998],{},[1915,30028,19126],{},[898,30030,6984],{},[902,30032,25034],{"encoding":904}," stále uvažuje ",[38,30035,30036],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,30039,30041],{"className":30040},[886],[888,30042,30043],{"xmlns":890},[892,30044,30045,30057],{},[895,30046,30047,30049,30051,30053,30055],{},[898,30048,7007],{},[1693,30050,1695],{},[898,30052,7520],{},[1693,30054,1698],{},[898,30056,2839],{},[902,30058,30059],{"encoding":904},"X = B - M"," dává ",[38,30062,28174,30063],{},[883,30064,30066],{"className":30065},[886],[888,30067,30068],{"xmlns":890},[892,30069,30070,30086],{},[895,30071,30072,30074,30076,30078,30080,30082,30084],{},[898,30073,2971],{},[1915,30075,19126],{},[898,30077,6998],{},[1915,30079,19126],{},[898,30081,6984],{},[1915,30083,19126],{},[898,30085,7007],{},[902,30087,19158],{"encoding":904},[115,30089,30091],{"id":30090},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,30093,27428],{"id":30094},"zadání-modelu-2",[724,30096,30097,30098,1863,30101,28397,30122,30135,30136,8586,30139,30152],{},"Rozšíření o ",[38,30099,30100],{},"čistý export",[883,30102,30104],{"className":30103},[886],[888,30105,30106],{"xmlns":890},[892,30107,30108,30120],{},[895,30109,30110,30112,30114,30116,30118],{},[898,30111,7007],{},[1693,30113,1695],{},[898,30115,7520],{},[1693,30117,1698],{},[898,30119,2839],{},[902,30121,30059],{"encoding":904},[883,30123,30125],{"className":30124},[886],[888,30126,30127],{"xmlns":890},[892,30128,30129,30133],{},[895,30130,30131],{},[898,30132,7520],{},[902,30134,7520],{"encoding":904}," je hrubý export (",[614,30137,30138],{},"brutto export",[883,30140,30142],{"className":30141},[886],[888,30143,30144],{"xmlns":890},[892,30145,30146,30150],{},[895,30147,30148],{},[898,30149,2839],{},[902,30151,2839],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,30154,30155],{},[883,30156,30158],{"className":30157},[886],[888,30159,30160],{"xmlns":890},[892,30161,30162,30182],{},[895,30163,30164,30166,30168,30170,30172,30178,30180],{},[898,30165,2839],{},[1693,30167,1695],{},[898,30169,2839],{},[1693,30171,1709],{"stretchy":1708},[3284,30173,30174,30176],{},[898,30175,4618],{},[898,30177,2738],{},[1693,30179,1731],{"stretchy":1708},[898,30181,1789],{"mathvariant":1704},[902,30183,30184],{"encoding":904},"M = M(Y_D).",[724,30186,30187],{},"Podmínka rovnováhy:",[724,30189,30190],{},[883,30191,30193],{"className":30192},[886],[888,30194,30195],{"xmlns":890},[892,30196,30197,30234],{},[895,30198,30199,30201,30203,30205,30207,30209,30211,30213,30215,30217,30219,30221,30223,30225,30227,30230,30232],{},[898,30200,4618],{},[1693,30202,1695],{},[898,30204,2971],{},[1693,30206,1892],{},[898,30208,6998],{},[1693,30210,1892],{},[898,30212,6984],{},[1693,30214,1892],{},[898,30216,7520],{},[1693,30218,1698],{},[898,30220,2839],{},[898,30222,1789],{"mathvariant":1704},[1901,30224],{"width":1903},[1693,30226,1709],{"stretchy":1708},[1762,30228,30229],{},"7.10",[1915,30231,207],{},[1693,30233,1731],{"stretchy":1708},[902,30235,30236],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,30238,27498],{"id":30239},"soustava-rovnic-2",[724,30241,28651,30242,30276,30277,4300],{},[883,30243,30245],{"className":30244},[886],[888,30246,30247],{"xmlns":890},[892,30248,30249,30273],{},[895,30250,30251,30257,30259,30265,30267],{},[1717,30252,30253,30255],{},[898,30254,6998],{},[1693,30256,3672],{},[1693,30258,1899],{"separator":1898},[1717,30260,30261,30263],{},[898,30262,6984],{},[1693,30264,3672],{},[1693,30266,1899],{"separator":1898},[1717,30268,30269,30271],{},[898,30270,7520],{},[1693,30272,3672],{},[902,30274,30275],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,30278,30280],{"className":30279},[886],[888,30281,30282],{"xmlns":890},[892,30283,30284,30308],{},[895,30285,30286,30288,30290,30292,30294,30296,30298,30304,30306],{},[898,30287,4618],{},[1693,30289,1899],{"separator":1898},[898,30291,2971],{},[1693,30293,1899],{"separator":1898},[898,30295,2663],{},[1693,30297,1899],{"separator":1898},[3284,30299,30300,30302],{},[898,30301,4618],{},[898,30303,2738],{},[1693,30305,1899],{"separator":1898},[898,30307,2839],{},[902,30309,30310],{"encoding":904},"Y, C, T, Y_D, M",[724,30312,30313],{},[883,30314,30316],{"className":30315},[886],[888,30317,30318],{"xmlns":890},[892,30319,30320,30504],{},[895,30321,30322,30496,30498,30500,30502],{},[3626,30323,30324,30356,30386,30414,30446],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,30325,30326,30332],{},[3635,30327,30328],{},[3638,30329,30330],{"scriptlevel":1911,"displaystyle":1898},[898,30331,2971],{},[3635,30333,30334],{},[3638,30335,30336],{"scriptlevel":1911,"displaystyle":1898},[895,30337,30338,30340,30342,30344,30346,30352,30354],{},[895,30339],{},[1693,30341,1695],{},[898,30343,2971],{},[1693,30345,1709],{"stretchy":1708},[3284,30347,30348,30350],{},[898,30349,4618],{},[898,30351,2738],{},[1693,30353,1731],{"stretchy":1708},[1693,30355,1899],{"separator":1898},[3632,30357,30358,30368],{},[3635,30359,30360],{},[3638,30361,30362],{"scriptlevel":1911,"displaystyle":1898},[3284,30363,30364,30366],{},[898,30365,4618],{},[898,30367,2738],{},[3635,30369,30370],{},[3638,30371,30372],{"scriptlevel":1911,"displaystyle":1898},[895,30373,30374,30376,30378,30380,30382,30384],{},[895,30375],{},[1693,30377,1695],{},[898,30379,4618],{},[1693,30381,1698],{},[898,30383,2663],{},[1693,30385,1899],{"separator":1898},[3632,30387,30388,30394],{},[3635,30389,30390],{},[3638,30391,30392],{"scriptlevel":1911,"displaystyle":1898},[898,30393,2663],{},[3635,30395,30396],{},[3638,30397,30398],{"scriptlevel":1911,"displaystyle":1898},[895,30399,30400,30402,30404,30406,30408,30410,30412],{},[895,30401],{},[1693,30403,1695],{},[898,30405,2663],{},[1693,30407,1709],{"stretchy":1708},[898,30409,4618],{},[1693,30411,1731],{"stretchy":1708},[1693,30413,1899],{"separator":1898},[3632,30415,30416,30422],{},[3635,30417,30418],{},[3638,30419,30420],{"scriptlevel":1911,"displaystyle":1898},[898,30421,2839],{},[3635,30423,30424],{},[3638,30425,30426],{"scriptlevel":1911,"displaystyle":1898},[895,30427,30428,30430,30432,30434,30436,30442,30444],{},[895,30429],{},[1693,30431,1695],{},[898,30433,2839],{},[1693,30435,1709],{"stretchy":1708},[3284,30437,30438,30440],{},[898,30439,4618],{},[898,30441,2738],{},[1693,30443,1731],{"stretchy":1708},[1693,30445,1899],{"separator":1898},[3632,30447,30448,30454],{},[3635,30449,30450],{},[3638,30451,30452],{"scriptlevel":1911,"displaystyle":1898},[898,30453,4618],{},[3635,30455,30456],{},[3638,30457,30458],{"scriptlevel":1911,"displaystyle":1898},[895,30459,30460,30462,30464,30466,30468,30474,30476,30482,30484,30490,30492,30494],{},[895,30461],{},[1693,30463,1695],{},[898,30465,2971],{},[1693,30467,1892],{},[1717,30469,30470,30472],{},[898,30471,6998],{},[1693,30473,3672],{},[1693,30475,1892],{},[1717,30477,30478,30480],{},[898,30479,6984],{},[1693,30481,3672],{},[1693,30483,1892],{},[1717,30485,30486,30488],{},[898,30487,7520],{},[1693,30489,3672],{},[1693,30491,1698],{},[898,30493,2839],{},[898,30495,1789],{"mathvariant":1704},[1901,30497],{"width":1903},[1693,30499,1709],{"stretchy":1708},[1762,30501,30229],{},[1693,30503,1731],{"stretchy":1708},[902,30505,30506],{"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)",[198,30508,30510],{"id":30509},"příklad-75","Příklad 7.5",[724,30512,30513,30514,1343,30546,1343,30573,1343,30594,1343,30616,1343,30638,30661],{},"Dáno: ",[883,30515,30517],{"className":30516},[886],[888,30518,30519],{"xmlns":890},[892,30520,30521,30543],{},[895,30522,30523,30525,30527,30530,30532,30538,30540],{},[898,30524,2971],{},[1693,30526,1695],{},[1762,30528,30529],{},"0,75",[1915,30531,2239],{},[3284,30533,30534,30536],{},[898,30535,4618],{},[898,30537,2738],{},[1693,30539,1892],{},[1762,30541,30542],{},"750",[902,30544,30545],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,30547,30549],{"className":30548},[886],[888,30550,30551],{"xmlns":890},[892,30552,30553,30570],{},[895,30554,30555,30557,30559,30562,30564],{},[898,30556,2839],{},[1693,30558,1695],{},[1762,30560,30561],{},"0,15",[1915,30563,2239],{},[3284,30565,30566,30568],{},[898,30567,4618],{},[898,30569,2738],{},[902,30571,30572],{"encoding":904},"M = 0{,}15\\,Y_D",[883,30574,30576],{"className":30575},[886],[888,30577,30578],{"xmlns":890},[892,30579,30580,30591],{},[895,30581,30582,30584,30586,30589],{},[898,30583,2663],{},[1693,30585,1695],{},[1762,30587,30588],{},"0,25",[898,30590,4618],{},[902,30592,30593],{"encoding":904},"T = 0{,}25Y",[883,30595,30597],{"className":30596},[886],[888,30598,30599],{"xmlns":890},[892,30600,30601,30613],{},[895,30602,30603,30609,30611],{},[1717,30604,30605,30607],{},[898,30606,6998],{},[1693,30608,3672],{},[1693,30610,1695],{},[1762,30612,21936],{},[902,30614,30615],{"encoding":904},"I^* = 500",[883,30617,30619],{"className":30618},[886],[888,30620,30621],{"xmlns":890},[892,30622,30623,30635],{},[895,30624,30625,30631,30633],{},[1717,30626,30627,30629],{},[898,30628,6984],{},[1693,30630,3672],{},[1693,30632,1695],{},[1762,30634,15660],{},[902,30636,30637],{"encoding":904},"G^* = 150",[883,30639,30641],{"className":30640},[886],[888,30642,30643],{"xmlns":890},[892,30644,30645,30658],{},[895,30646,30647,30653,30655],{},[1717,30648,30649,30651],{},[898,30650,7520],{},[1693,30652,3672],{},[1693,30654,1695],{},[1762,30656,30657],{},"800",[902,30659,30660],{"encoding":904},"B^* = 800",". Soustava:",[724,30663,30664],{},[883,30665,30667],{"className":30666},[886],[888,30668,30669],{"xmlns":890},[892,30670,30671,30889],{},[3626,30672,30673,30719,30761,30797,30839],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,30674,30675,30691],{},[3635,30676,30677],{},[3638,30678,30679],{"scriptlevel":1911,"displaystyle":1898},[895,30680,30681,30683,30685,30687,30689],{},[1693,30682,1709],{"stretchy":1708},[898,30684,6629],{},[1762,30686,1764],{},[1693,30688,1731],{"stretchy":1708},[1915,30690,9204],{},[3635,30692,30693],{},[3638,30694,30695],{"scriptlevel":1911,"displaystyle":1898},[895,30696,30697,30699,30701,30703,30705,30707,30713,30715,30717],{},[895,30698],{},[898,30700,2971],{},[1693,30702,1695],{},[1762,30704,30529],{},[1915,30706,2239],{},[3284,30708,30709,30711],{},[898,30710,4618],{},[898,30712,2738],{},[1693,30714,1892],{},[1762,30716,30542],{},[1693,30718,1899],{"separator":1898},[3632,30720,30721,30737],{},[3635,30722,30723],{},[3638,30724,30725],{"scriptlevel":1911,"displaystyle":1898},[895,30726,30727,30729,30731,30733,30735],{},[1693,30728,1709],{"stretchy":1708},[898,30730,6629],{},[1762,30732,2398],{},[1693,30734,1731],{"stretchy":1708},[1915,30736,9204],{},[3635,30738,30739],{},[3638,30740,30741],{"scriptlevel":1911,"displaystyle":1898},[895,30742,30743,30745,30751,30753,30755,30757,30759],{},[895,30744],{},[3284,30746,30747,30749],{},[898,30748,4618],{},[898,30750,2738],{},[1693,30752,1695],{},[898,30754,4618],{},[1693,30756,1698],{},[898,30758,2663],{},[1693,30760,1899],{"separator":1898},[3632,30762,30763,30779],{},[3635,30764,30765],{},[3638,30766,30767],{"scriptlevel":1911,"displaystyle":1898},[895,30768,30769,30771,30773,30775,30777],{},[1693,30770,1709],{"stretchy":1708},[898,30772,6629],{},[1762,30774,8357],{},[1693,30776,1731],{"stretchy":1708},[1915,30778,9204],{},[3635,30780,30781],{},[3638,30782,30783],{"scriptlevel":1911,"displaystyle":1898},[895,30784,30785,30787,30789,30791,30793,30795],{},[895,30786],{},[898,30788,2663],{},[1693,30790,1695],{},[1762,30792,30588],{},[898,30794,4618],{},[1693,30796,1899],{"separator":1898},[3632,30798,30799,30815],{},[3635,30800,30801],{},[3638,30802,30803],{"scriptlevel":1911,"displaystyle":1898},[895,30804,30805,30807,30809,30811,30813],{},[1693,30806,1709],{"stretchy":1708},[898,30808,6629],{},[1762,30810,9262],{},[1693,30812,1731],{"stretchy":1708},[1915,30814,9204],{},[3635,30816,30817],{},[3638,30818,30819],{"scriptlevel":1911,"displaystyle":1898},[895,30820,30821,30823,30825,30827,30829,30831,30837],{},[895,30822],{},[898,30824,2839],{},[1693,30826,1695],{},[1762,30828,30561],{},[1915,30830,2239],{},[3284,30832,30833,30835],{},[898,30834,4618],{},[898,30836,2738],{},[1693,30838,1899],{"separator":1898},[3632,30840,30841,30857],{},[3635,30842,30843],{},[3638,30844,30845],{"scriptlevel":1911,"displaystyle":1898},[895,30846,30847,30849,30851,30853,30855],{},[1693,30848,1709],{"stretchy":1708},[898,30850,6629],{},[1762,30852,9147],{},[1693,30854,1731],{"stretchy":1708},[1915,30856,9204],{},[3635,30858,30859],{},[3638,30860,30861],{"scriptlevel":1911,"displaystyle":1898},[895,30862,30863,30865,30867,30869,30871,30873,30875,30877,30879,30881,30883,30885,30887],{},[895,30864],{},[898,30866,4618],{},[1693,30868,1695],{},[898,30870,2971],{},[1693,30872,1892],{},[1762,30874,21936],{},[1693,30876,1892],{},[1762,30878,15660],{},[1693,30880,1892],{},[1762,30882,30657],{},[1693,30884,1698],{},[898,30886,2839],{},[898,30888,1789],{"mathvariant":1704},[902,30890,30891],{"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}",[724,30893,30894,30895,30929],{},"Postupná substituce — z (r3) do (r2): ",[883,30896,30898],{"className":30897},[886],[888,30899,30900],{"xmlns":890},[892,30901,30902,30926],{},[895,30903,30904,30910,30912,30914,30916,30918,30920,30922,30924],{},[3284,30905,30906,30908],{},[898,30907,4618],{},[898,30909,2738],{},[1693,30911,1695],{},[898,30913,4618],{},[1693,30915,1698],{},[1762,30917,30588],{},[898,30919,4618],{},[1693,30921,1695],{},[1762,30923,30529],{},[898,30925,4618],{},[902,30927,30928],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,30931,30932],{},[883,30933,30935],{"className":30934},[886],[888,30936,30937],{"xmlns":890},[892,30938,30939,30980],{},[895,30940,30941,30943,30945,30947,30949,30951,30953,30955,30957,30959,30961,30963,30965,30967,30969,30972,30974,30976,30978],{},[1693,30942,1709],{"stretchy":1708},[898,30944,6629],{},[1762,30946,9154],{},[1693,30948,1731],{"stretchy":1708},[1915,30950,9204],{},[898,30952,2971],{},[1693,30954,1695],{},[1762,30956,30529],{},[1693,30958,1715],{},[1762,30960,30529],{},[898,30962,4618],{},[1693,30964,1892],{},[1762,30966,30542],{},[1693,30968,1695],{},[1762,30970,30971],{},"0,5625",[898,30973,4618],{},[1693,30975,1892],{},[1762,30977,30542],{},[1693,30979,1899],{"separator":1898},[902,30981,30982],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,30984,30985],{},[883,30986,30988],{"className":30987},[886],[888,30989,30990],{"xmlns":890},[892,30991,30992,31026],{},[895,30993,30994,30996,30998,31001,31003,31005,31007,31009,31011,31013,31015,31017,31019,31022,31024],{},[1693,30995,1709],{"stretchy":1708},[898,30997,6629],{},[1762,30999,31000],{},"7",[1693,31002,1731],{"stretchy":1708},[1915,31004,9204],{},[898,31006,2839],{},[1693,31008,1695],{},[1762,31010,30561],{},[1693,31012,1715],{},[1762,31014,30529],{},[898,31016,4618],{},[1693,31018,1695],{},[1762,31020,31021],{},"0,1125",[898,31023,4618],{},[898,31025,1789],{"mathvariant":1704},[902,31027,31028],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,31030,31031],{},"Dosazením do (r5):",[724,31033,31034],{},[883,31035,31037],{"className":31036},[886],[888,31038,31039],{"xmlns":890},[892,31040,31041,31085],{},[895,31042,31043,31045,31047,31049,31051,31053,31055,31057,31059,31061,31063,31065,31067,31069,31071,31073,31075,31078,31080,31082],{},[898,31044,4618],{},[1693,31046,1695],{},[1762,31048,30971],{},[898,31050,4618],{},[1693,31052,1892],{},[1762,31054,30542],{},[1693,31056,1892],{},[1762,31058,21936],{},[1693,31060,1892],{},[1762,31062,15660],{},[1693,31064,1892],{},[1762,31066,30657],{},[1693,31068,1698],{},[1762,31070,31021],{},[898,31072,4618],{},[1693,31074,1695],{},[1762,31076,31077],{},"0,45",[898,31079,4618],{},[1693,31081,1892],{},[1762,31083,31084],{},"2200.",[902,31086,31087],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,31089,31090,31091,12457,31113,31136],{},"Odtud ",[883,31092,31094],{"className":31093},[886],[888,31095,31096],{"xmlns":890},[892,31097,31098,31110],{},[895,31099,31100,31103,31105,31107],{},[1762,31101,31102],{},"0,55",[898,31104,4618],{},[1693,31106,1695],{},[1762,31108,31109],{},"2200",[902,31111,31112],{"encoding":904},"0{,}55Y = 2200",[883,31114,31116],{"className":31115},[886],[888,31117,31118],{"xmlns":890},[892,31119,31120,31133],{},[895,31121,31122,31128,31130],{},[1717,31123,31124,31126],{},[898,31125,4618],{},[898,31127,1691],{},[1693,31129,1695],{},[1762,31131,31132],{},"4000",[902,31134,31135],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,31138,31139,31162,31194,31229,31262,31298],{},[123,31140,31141,1899],{},[883,31142,31144],{"className":31143},[886],[888,31145,31146],{"xmlns":890},[892,31147,31148,31160],{},[895,31149,31150,31156,31158],{},[1717,31151,31152,31154],{},[898,31153,4618],{},[898,31155,1691],{},[1693,31157,1695],{},[1762,31159,31132],{},[902,31161,31135],{"encoding":904},[123,31163,31164,1899],{},[883,31165,31167],{"className":31166},[886],[888,31168,31169],{"xmlns":890},[892,31170,31171,31191],{},[895,31172,31173,31179,31181,31183,31185,31187,31189],{},[1717,31174,31175,31177],{},[898,31176,2663],{},[898,31178,1691],{},[1693,31180,1695],{},[1762,31182,30588],{},[1693,31184,1715],{},[1762,31186,31132],{},[1693,31188,1695],{},[1762,31190,9684],{},[902,31192,31193],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,31195,31196,1899],{},[883,31197,31199],{"className":31198},[886],[888,31200,31201],{"xmlns":890},[892,31202,31203,31226],{},[895,31204,31205,31213,31215,31217,31219,31221,31223],{},[5688,31206,31207,31209,31211],{},[898,31208,4618],{},[898,31210,2738],{},[898,31212,1691],{},[1693,31214,1695],{},[1762,31216,30529],{},[1693,31218,1715],{},[1762,31220,31132],{},[1693,31222,1695],{},[1762,31224,31225],{},"3000",[902,31227,31228],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,31230,31231,1899],{},[883,31232,31234],{"className":31233},[886],[888,31235,31236],{"xmlns":890},[892,31237,31238,31259],{},[895,31239,31240,31246,31248,31250,31252,31254,31256],{},[1717,31241,31242,31244],{},[898,31243,2839],{},[898,31245,1691],{},[1693,31247,1695],{},[1762,31249,30561],{},[1693,31251,1715],{},[1762,31253,31225],{},[1693,31255,1695],{},[1762,31257,31258],{},"450",[902,31260,31261],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,31263,31264,1899],{},[883,31265,31267],{"className":31266},[886],[888,31268,31269],{"xmlns":890},[892,31270,31271,31295],{},[895,31272,31273,31279,31281,31283,31285,31287,31289,31291,31293],{},[1717,31274,31275,31277],{},[898,31276,2971],{},[898,31278,1691],{},[1693,31280,1695],{},[1762,31282,30529],{},[1693,31284,1715],{},[1762,31286,31225],{},[1693,31288,1892],{},[1762,31290,30542],{},[1693,31292,1695],{},[1762,31294,31225],{},[902,31296,31297],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,31299,31300,31340],{},[883,31301,31303],{"className":31302},[886],[888,31304,31305],{"xmlns":890},[892,31306,31307,31337],{},[895,31308,31309,31315,31317,31325,31327,31333,31335],{},[1717,31310,31311,31313],{},[898,31312,3611],{},[898,31314,1691],{},[1693,31316,1695],{},[5688,31318,31319,31321,31323],{},[898,31320,4618],{},[898,31322,2738],{},[898,31324,1691],{},[1693,31326,1698],{},[1717,31328,31329,31331],{},[898,31330,2971],{},[898,31332,1691],{},[1693,31334,1695],{},[1762,31336,1911],{},[902,31338,31339],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,31342,31343,31345,31346,1343,31363,4286,31384,31409,31410,31413,31414,31427,31428,1789],{},[38,31344,28152],{}," Modely ",[883,31347,31349],{"className":31348},[886],[888,31350,31351],{"xmlns":890},[892,31352,31353,31361],{},[895,31354,31355,31357,31359],{},[898,31356,2971],{},[1915,31358,19126],{},[898,31360,6998],{},[902,31362,19131],{"encoding":904},[883,31364,31366],{"className":31365},[886],[888,31367,31368],{"xmlns":890},[892,31369,31370,31382],{},[895,31371,31372,31374,31376,31378,31380],{},[898,31373,2971],{},[1915,31375,19126],{},[898,31377,6998],{},[1915,31379,19126],{},[898,31381,6984],{},[902,31383,25034],{"encoding":904},[883,31385,31387],{"className":31386},[886],[888,31388,31389],{"xmlns":890},[892,31390,31391,31407],{},[895,31392,31393,31395,31397,31399,31401,31403,31405],{},[898,31394,2971],{},[1915,31396,19126],{},[898,31398,6998],{},[1915,31400,19126],{},[898,31402,6984],{},[1915,31404,19126],{},[898,31406,7007],{},[902,31408,19158],{"encoding":904}," pokládají investice za ",[38,31411,31412],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,31415,31417],{"className":31416},[886],[888,31418,31419],{"xmlns":890},[892,31420,31421,31425],{},[895,31422,31423],{},[898,31424,6629],{},[902,31426,6629],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,31429,31430],{},"model IS-LM",[115,31432,31434],{"id":31433},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,31436,31437,31438,31442,31443,31446,31447,31450],{},"V článku ",[207,31439,31441],{"className":31440,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,31444,31445],{},"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 ",[38,31448,31449],{},"výraznější"," než v mikroekonomických modelech.",[724,31452,31453],{},[9465,31454],{"alt":31455,"className":31456,"src":31457},"imek-multiplikatorovy-efekt-chain",[210,9469],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,31459,19001,31460,1343,31477,1343,31498,31523,31524,31527,31528,31545,31546,31564,31565,31583,31584,31587,31588,1343,31605,31622,31623,31625],{},[883,31461,31463],{"className":31462},[886],[888,31464,31465],{"xmlns":890},[892,31466,31467,31475],{},[895,31468,31469,31471,31473],{},[898,31470,2971],{},[1915,31472,19126],{},[898,31474,6998],{},[902,31476,19131],{"encoding":904},[883,31478,31480],{"className":31479},[886],[888,31481,31482],{"xmlns":890},[892,31483,31484,31496],{},[895,31485,31486,31488,31490,31492,31494],{},[898,31487,2971],{},[1915,31489,19126],{},[898,31491,6998],{},[1915,31493,19126],{},[898,31495,6984],{},[902,31497,25034],{"encoding":904},[883,31499,31501],{"className":31500},[886],[888,31502,31503],{"xmlns":890},[892,31504,31505,31521],{},[895,31506,31507,31509,31511,31513,31515,31517,31519],{},[898,31508,2971],{},[1915,31510,19126],{},[898,31512,6998],{},[1915,31514,19126],{},[898,31516,6984],{},[1915,31518,19126],{},[898,31520,7007],{},[902,31522,19158],{"encoding":904}," se vyšetřuje vliv změn ",[38,31525,31526],{},"exogenních"," veličin (plánovaných investic ",[883,31529,31531],{"className":31530},[886],[888,31532,31533],{"xmlns":890},[892,31534,31535,31543],{},[895,31536,31537],{},[1717,31538,31539,31541],{},[898,31540,6998],{},[1693,31542,3672],{},[902,31544,7880],{"encoding":904},", vládních výdajů ",[883,31547,31549],{"className":31548},[886],[888,31550,31551],{"xmlns":890},[892,31552,31553,31561],{},[895,31554,31555],{},[1717,31556,31557,31559],{},[898,31558,6984],{},[1693,31560,3672],{},[902,31562,31563],{"encoding":904},"G^*",", exportu ",[883,31566,31568],{"className":31567},[886],[888,31569,31570],{"xmlns":890},[892,31571,31572,31580],{},[895,31573,31574],{},[1717,31575,31576,31578],{},[898,31577,7520],{},[1693,31579,3672],{},[902,31581,31582],{"encoding":904},"B^*",") na změny ",[38,31585,31586],{},"endogenních"," rovnovážných veličin (",[883,31589,31591],{"className":31590},[886],[888,31592,31593],{"xmlns":890},[892,31594,31595,31603],{},[895,31596,31597],{},[1717,31598,31599,31601],{},[898,31600,4618],{},[898,31602,1691],{},[902,31604,7862],{"encoding":904},[883,31606,31608],{"className":31607},[886],[888,31609,31610],{"xmlns":890},[892,31611,31612,31620],{},[895,31613,31614],{},[1717,31615,31616,31618],{},[898,31617,2971],{},[898,31619,1691],{},[902,31621,20791],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,31624,24795],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,31627,31629],{"id":31628},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,31631,27699,31632,31655,31656,31700],{},[883,31633,31635],{"className":31634},[886],[888,31636,31637],{"xmlns":890},[892,31638,31639,31653],{},[895,31640,31641,31643,31645,31647,31649,31651],{},[898,31642,2971],{},[1693,31644,1695],{},[898,31646,207],{},[898,31648,4618],{},[1693,31650,1892],{},[898,31652,1895],{},[902,31654,25731],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,31657,31659],{"className":31658},[886],[888,31660,31661],{"xmlns":890},[892,31662,31663,31697],{},[895,31664,31665,31671,31673],{},[1717,31666,31667,31669],{},[898,31668,4618],{},[898,31670,1691],{},[1693,31672,1695],{},[3638,31674,31675],{"scriptlevel":1911,"displaystyle":1898},[2132,31676,31677,31689],{},[895,31678,31679,31681,31683],{},[898,31680,1895],{},[1693,31682,1892],{},[1717,31684,31685,31687],{},[898,31686,6998],{},[1693,31688,3672],{},[895,31690,31691,31693,31695],{},[1762,31692,1764],{},[1693,31694,1698],{},[898,31696,207],{},[902,31698,31699],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,31702,31703],{},[883,31704,31706],{"className":31705},[886],[888,31707,31708],{"xmlns":890},[892,31709,31710,31778],{},[895,31711,31712,31730,31732,31762,31764],{},[2132,31713,31714,31724],{},[895,31715,31716,31718],{},[898,31717,2228],{"mathvariant":1704},[1717,31719,31720,31722],{},[898,31721,4618],{},[898,31723,1691],{},[895,31725,31726,31728],{},[898,31727,2228],{"mathvariant":1704},[898,31729,207],{},[1693,31731,1695],{},[2132,31733,31734,31746],{},[895,31735,31736,31738,31740],{},[898,31737,1895],{},[1693,31739,1892],{},[1717,31741,31742,31744],{},[898,31743,6998],{},[1693,31745,3672],{},[895,31747,31748,31750,31752,31754,31756],{},[1693,31749,1709],{"stretchy":1708},[1762,31751,1764],{},[1693,31753,1698],{},[898,31755,207],{},[1717,31757,31758,31760],{},[1693,31759,1731],{"stretchy":1708},[1762,31761,2398],{},[1901,31763],{"width":1903},[895,31765,31766,31769,31775],{},[1915,31767,31768],{},"(multiplik",[4467,31770,31771,31773],{"accent":1898},[1915,31772,207],{},[1693,31774,4474],{},[1915,31776,31777],{},"tor MPC)",[902,31779,31780],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,31782,31783],{},[883,31784,31786],{"className":31785},[886],[888,31787,31788],{"xmlns":890},[892,31789,31790,31856],{},[895,31791,31792,31810,31812,31824,31826],{},[2132,31793,31794,31804],{},[895,31795,31796,31798],{},[898,31797,2228],{"mathvariant":1704},[1717,31799,31800,31802],{},[898,31801,4618],{},[898,31803,1691],{},[895,31805,31806,31808],{},[898,31807,2228],{"mathvariant":1704},[898,31809,1895],{},[1693,31811,1695],{},[2132,31813,31814,31816],{},[1762,31815,1764],{},[895,31817,31818,31820,31822],{},[1762,31819,1764],{},[1693,31821,1698],{},[898,31823,207],{},[1901,31825],{"width":1903},[895,31827,31828,31830,31836,31839,31845,31847,31853],{},[1915,31829,31768],{},[4467,31831,31832,31834],{"accent":1898},[1915,31833,207],{},[1693,31835,4474],{},[1915,31837,31838],{},"tor autonomn",[4467,31840,31841,31843],{"accent":1898},[1915,31842,4471],{},[1693,31844,4474],{},[1915,31846,6624],{},[4467,31848,31849,31851],{"accent":1898},[1915,31850,6629],{},[1693,31852,6552],{},[1915,31854,31855],{},"eby)",[902,31857,31858],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,31860,31861],{},[883,31862,31864],{"className":31863},[886],[888,31865,31866],{"xmlns":890},[892,31867,31868,31935],{},[895,31869,31870,31892,31894,31906,31908,31920,31922],{},[2132,31871,31872,31882],{},[895,31873,31874,31876],{},[898,31875,2228],{"mathvariant":1704},[1717,31877,31878,31880],{},[898,31879,4618],{},[898,31881,1691],{},[895,31883,31884,31886],{},[898,31885,2228],{"mathvariant":1704},[1717,31887,31888,31890],{},[898,31889,6998],{},[1693,31891,3672],{},[1693,31893,1695],{},[2132,31895,31896,31898],{},[1762,31897,1764],{},[895,31899,31900,31902,31904],{},[1762,31901,1764],{},[1693,31903,1698],{},[898,31905,207],{},[1693,31907,1695],{},[2132,31909,31910,31912],{},[1762,31911,1764],{},[895,31913,31914,31916,31918],{},[898,31915,2839],{},[898,31917,1701],{},[898,31919,3611],{},[1901,31921],{"width":1903},[895,31923,31924,31926,31932],{},[1915,31925,31768],{},[4467,31927,31928,31930],{"accent":1898},[1915,31929,207],{},[1693,31931,4474],{},[1915,31933,31934],{},"tor investic)",[902,31936,31937],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1636,31939,31940],{},[724,31941,31942,31944,31945,31948,31949,31962,31963,31980,31981,31998,31999,32043,32044,28223,32061,32064,32065,32082],{},[883,31943,11036],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,31946,31947],{},"důchodem","; z něj se utratí ",[883,31950,31952],{"className":31951},[886],[888,31953,31954],{"xmlns":890},[892,31955,31956,31960],{},[895,31957,31958],{},[898,31959,207],{},[902,31961,207],{"encoding":904}," Kč (= ",[883,31964,31966],{"className":31965},[886],[888,31967,31968],{"xmlns":890},[892,31969,31970,31978],{},[895,31971,31972,31974,31976],{},[898,31973,2839],{},[898,31975,1701],{},[898,31977,2971],{},[902,31979,7288],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,31982,31984],{"className":31983},[886],[888,31985,31986],{"xmlns":890},[892,31987,31988,31996],{},[895,31989,31990],{},[1717,31991,31992,31994],{},[898,31993,207],{},[1762,31995,2398],{},[902,31997,7920],{"encoding":904}," Kč… Součet geometrické řady ",[883,32000,32002],{"className":32001},[886],[888,32003,32004],{"xmlns":890},[892,32005,32006,32040],{},[895,32007,32008,32010,32012,32014,32016,32022,32024,32026,32028],{},[1762,32009,1764],{},[1693,32011,1892],{},[898,32013,207],{},[1693,32015,1892],{},[1717,32017,32018,32020],{},[898,32019,207],{},[1762,32021,2398],{},[1693,32023,1892],{},[1693,32025,7949],{},[1693,32027,1695],{},[2132,32029,32030,32032],{},[1762,32031,1764],{},[895,32033,32034,32036,32038],{},[1762,32035,1764],{},[1693,32037,1698],{},[898,32039,207],{},[902,32041,32042],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,32045,32047],{"className":32046},[886],[888,32048,32049],{"xmlns":890},[892,32050,32051,32059],{},[895,32052,32053],{},[1717,32054,32055,32057],{},[898,32056,4618],{},[898,32058,1691],{},[902,32060,7862],{"encoding":904},[38,32062,32063],{},"více"," než korunu — čím vyšší ",[883,32066,32068],{"className":32067},[886],[888,32069,32070],{"xmlns":890},[892,32071,32072,32080],{},[895,32073,32074,32076,32078],{},[898,32075,2839],{},[898,32077,1701],{},[898,32079,2971],{},[902,32081,7288],{"encoding":904},", tím silnější multiplikační efekt.",[724,32084,32085,32088,32089,32115,32116,32119,32120,4286,32141,32166,32167,1789],{},[38,32086,32087],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,32090,32092],{"className":32091},[886],[888,32093,32094],{"xmlns":890},[892,32095,32096,32112],{},[895,32097,32098],{},[3638,32099,32100],{"scriptlevel":1911,"displaystyle":1708},[2132,32101,32102,32104],{},[1762,32103,1764],{},[895,32105,32106,32108,32110],{},[1762,32107,1764],{},[1693,32109,1698],{},[898,32111,207],{},[902,32113,32114],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,32117,32118],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,32121,32123],{"className":32122},[886],[888,32124,32125],{"xmlns":890},[892,32126,32127,32139],{},[895,32128,32129,32131,32133,32135,32137],{},[898,32130,2971],{},[1915,32132,19126],{},[898,32134,6998],{},[1915,32136,19126],{},[898,32138,6984],{},[902,32140,25034],{"encoding":904},[883,32142,32144],{"className":32143},[886],[888,32145,32146],{"xmlns":890},[892,32147,32148,32164],{},[895,32149,32150,32152,32154,32156,32158,32160,32162],{},[898,32151,2971],{},[1915,32153,19126],{},[898,32155,6998],{},[1915,32157,19126],{},[898,32159,6984],{},[1915,32161,19126],{},[898,32163,7007],{},[902,32165,19158],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,32168,32170],{"className":32169,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,32172,32174],{"id":32173},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,32176,19001,32177,1343,32194,4286,32215,19006,32240,16877,32243,32264,32265,1863,32268,32281,32282,12537,32311,32328,32329,32332,32333,32335,32336,32357],{},[883,32178,32180],{"className":32179},[886],[888,32181,32182],{"xmlns":890},[892,32183,32184,32192],{},[895,32185,32186,32188,32190],{},[898,32187,2971],{},[1915,32189,19126],{},[898,32191,6998],{},[902,32193,19131],{"encoding":904},[883,32195,32197],{"className":32196},[886],[888,32198,32199],{"xmlns":890},[892,32200,32201,32213],{},[895,32202,32203,32205,32207,32209,32211],{},[898,32204,2971],{},[1915,32206,19126],{},[898,32208,6998],{},[1915,32210,19126],{},[898,32212,6984],{},[902,32214,25034],{"encoding":904},[883,32216,32218],{"className":32217},[886],[888,32219,32220],{"xmlns":890},[892,32221,32222,32238],{},[895,32223,32224,32226,32228,32230,32232,32234,32236],{},[898,32225,2971],{},[1915,32227,19126],{},[898,32229,6998],{},[1915,32231,19126],{},[898,32233,6984],{},[1915,32235,19126],{},[898,32237,7007],{},[902,32239,19158],{"encoding":904},[38,32241,32242],{},"investice konstantní",[883,32244,32246],{"className":32245},[886],[888,32247,32248],{"xmlns":890},[892,32249,32250,32262],{},[895,32251,32252,32254,32256],{},[898,32253,6998],{},[1693,32255,1695],{},[1717,32257,32258,32260],{},[898,32259,6998],{},[1693,32261,3672],{},[902,32263,19031],{"encoding":904},"). Reálnější je předpoklad, že ",[38,32266,32267],{},"investice závisejí na úrokové míře",[883,32269,32271],{"className":32270},[886],[888,32272,32273],{"xmlns":890},[892,32274,32275,32279],{},[895,32276,32277],{},[898,32278,6629],{},[902,32280,6629],{"encoding":904}," — klesající funkce ",[883,32283,32285],{"className":32284},[886],[888,32286,32287],{"xmlns":890},[892,32288,32289,32309],{},[895,32290,32291,32293,32295,32297,32299,32301,32303,32305,32307],{},[898,32292,6998],{},[1693,32294,1709],{"stretchy":1708},[898,32296,6629],{},[1693,32298,1731],{"stretchy":1708},[1693,32300,1695],{},[898,32302,2000],{},[898,32304,6629],{},[1693,32306,1892],{},[898,32308,1771],{},[902,32310,22582],{"encoding":904},[883,32312,32314],{"className":32313},[886],[888,32315,32316],{"xmlns":890},[892,32317,32318,32326],{},[895,32319,32320,32322,32324],{},[898,32321,2000],{},[1693,32323,1908],{},[1762,32325,1911],{},[902,32327,8089],{"encoding":904},". Přidáním ",[38,32330,32331],{},"trhu peněz"," k trhu zboží vzniká model ",[38,32334,18856],{}," se dvěma neznámými ",[883,32337,32339],{"className":32338},[886],[888,32340,32341],{"xmlns":890},[892,32342,32343,32355],{},[895,32344,32345,32347,32349,32351,32353],{},[1693,32346,1709],{"stretchy":1708},[898,32348,4618],{},[1693,32350,1899],{"separator":1898},[898,32352,6629],{},[1693,32354,1731],{"stretchy":1708},[902,32356,8243],{"encoding":904}," a dvěma rovnicemi:",[120,32359,32360,32410],{},[123,32361,32362,16877,32364,32366,32367,32388,32389,1789],{},[38,32363,22671],{},[614,32365,18898],{},") — klesající přímka v rovině ",[883,32368,32370],{"className":32369},[886],[888,32371,32372],{"xmlns":890},[892,32373,32374,32386],{},[895,32375,32376,32378,32380,32382,32384],{},[1693,32377,1709],{"stretchy":1708},[898,32379,6629],{},[1693,32381,1899],{"separator":1898},[898,32383,4618],{},[1693,32385,1731],{"stretchy":1708},[902,32387,19769],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,32390,32392],{"className":32391},[886],[888,32393,32394],{"xmlns":890},[892,32395,32396,32408],{},[895,32397,32398,32400,32402,32404,32406],{},[898,32399,4618],{},[1693,32401,1695],{},[898,32403,2971],{},[1693,32405,1892],{},[898,32407,6998],{},[902,32409,8174],{"encoding":904},[123,32411,32412,16877,32414,32416,32417,28397,32442,32488],{},[38,32413,22869],{},[614,32415,18905],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,32418,32420],{"className":32419},[886],[888,32421,32422],{"xmlns":890},[892,32423,32424,32440],{},[895,32425,32426,32432,32434],{},[1717,32427,32428,32430],{},[898,32429,2839],{},[898,32431,2738],{},[1693,32433,1695],{},[1717,32435,32436,32438],{},[898,32437,2839],{},[1693,32439,3672],{},[902,32441,20311],{"encoding":904},[883,32443,32445],{"className":32444},[886],[888,32446,32447],{"xmlns":890},[892,32448,32449,32485],{},[895,32450,32451,32457,32459,32465,32467,32469,32475,32477,32479],{},[1717,32452,32453,32455],{},[898,32454,2839],{},[898,32456,2738],{},[1693,32458,1695],{},[3284,32460,32461,32463],{},[898,32462,8334],{},[1762,32464,1764],{},[898,32466,4618],{},[1693,32468,1892],{},[3284,32470,32471,32473],{},[898,32472,8334],{},[1762,32474,2398],{},[898,32476,6629],{},[1693,32478,1892],{},[3284,32480,32481,32483],{},[898,32482,8334],{},[1762,32484,8357],{},[902,32486,32487],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,32490,32491,1863,32494,32527,32528,32530,32531,32533],{},[38,32492,32493],{},"Simultánní rovnovážný bod",[883,32495,32497],{"className":32496},[886],[888,32498,32499],{"xmlns":890},[892,32500,32501,32525],{},[895,32502,32503,32505,32507,32509,32515,32517,32523],{},[898,32504,1691],{},[1693,32506,1695],{},[1693,32508,1709],{"stretchy":1708},[1717,32510,32511,32513],{},[898,32512,6629],{},[898,32514,1691],{},[1693,32516,1899],{"separator":1898},[1717,32518,32519,32521],{},[898,32520,4618],{},[898,32522,1691],{},[1693,32524,1731],{"stretchy":1708},[902,32526,22959],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,32529,8558],{}," (posun IS) a ",[38,32532,8589],{}," (posun LM).",[724,32535,32536],{},[38,32537,32538,32539,1343,32561,1343,32583,1343,32605,32627,32628,1789],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,32540,32542],{"className":32541},[886],[888,32543,32544],{"xmlns":890},[892,32545,32546,32558],{},[895,32547,32548,32554,32556],{},[1717,32549,32550,32552],{},[898,32551,4618],{},[898,32553,1691],{},[1693,32555,1695],{},[1762,32557,21941],{},[902,32559,32560],{"encoding":904},"Y^E = 5000",[883,32562,32564],{"className":32563},[886],[888,32565,32566],{"xmlns":890},[892,32567,32568,32580],{},[895,32569,32570,32576,32578],{},[1717,32571,32572,32574],{},[898,32573,6629],{},[898,32575,1691],{},[1693,32577,1695],{},[1762,32579,9147],{},[902,32581,32582],{"encoding":904},"r^E = 5",[883,32584,32586],{"className":32585},[886],[888,32587,32588],{"xmlns":890},[892,32589,32590,32602],{},[895,32591,32592,32598,32600],{},[1717,32593,32594,32596],{},[898,32595,2971],{},[898,32597,1691],{},[1693,32599,1695],{},[1762,32601,21978],{},[902,32603,32604],{"encoding":904},"C^E = 4100",[883,32606,32608],{"className":32607},[886],[888,32609,32610],{"xmlns":890},[892,32611,32612,32624],{},[895,32613,32614,32620,32622],{},[1717,32615,32616,32618],{},[898,32617,6998],{},[898,32619,1691],{},[1693,32621,1695],{},[1762,32623,22017],{},[902,32625,32626],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,32629,945],{"className":32630,"dataFsResolvedFilePath":943,"href":944},[210],[115,32632,32634],{"id":32633},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,32636,32637,32700,32811,32952,33194,33262],{},[123,32638,32639,32642,32643,32665,32666,32699],{},[38,32640,32641],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,32644,32646],{"className":32645},[886],[888,32647,32648],{"xmlns":890},[892,32649,32650,32662],{},[895,32651,32652,32654,32656,32658,32660],{},[898,32653,6984],{},[898,32655,6987],{},[898,32657,1701],{},[1693,32659,4110],{},[898,32661,4618],{},[902,32663,32664],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,32667,32669],{"className":32668},[886],[888,32670,32671],{"xmlns":890},[892,32672,32673,32697],{},[895,32674,32675,32677,32679,32681,32683,32685,32687,32689,32691,32693,32695],{},[898,32676,6984],{},[898,32678,6987],{},[898,32680,1701],{},[1693,32682,1695],{},[898,32684,2971],{},[1693,32686,1892],{},[898,32688,6998],{},[1693,32690,1892],{},[898,32692,6984],{},[1693,32694,1892],{},[898,32696,7007],{},[902,32698,7010],{"encoding":904}," (7.1).",[123,32701,32702,32704,32705,32726,32727,1343,32750,32781,32782,32795,32796,1789],{},[38,32703,25341],{}," splňují ",[883,32706,32708],{"className":32707},[886],[888,32709,32710],{"xmlns":890},[892,32711,32712,32724],{},[895,32713,32714,32716,32718,32720,32722],{},[898,32715,4618],{},[1693,32717,1695],{},[898,32719,2971],{},[1693,32721,1892],{},[898,32723,3611],{},[902,32725,7048],{"encoding":904}," (7.2); lineární model ",[883,32728,32730],{"className":32729},[886],[888,32731,32732],{"xmlns":890},[892,32733,32734,32748],{},[895,32735,32736,32738,32740,32742,32744,32746],{},[898,32737,2971],{},[1693,32739,1695],{},[898,32741,207],{},[898,32743,4618],{},[1693,32745,1892],{},[898,32747,1895],{},[902,32749,25731],{"encoding":904},[883,32751,32753],{"className":32752},[886],[888,32754,32755],{"xmlns":890},[892,32756,32757,32779],{},[895,32758,32759,32761,32763,32765,32767,32769,32771,32773,32775,32777],{},[898,32760,3611],{},[1693,32762,1695],{},[1693,32764,1709],{"stretchy":1708},[1762,32766,1764],{},[1693,32768,1698],{},[898,32770,207],{},[1693,32772,1731],{"stretchy":1708},[898,32774,4618],{},[1693,32776,1698],{},[898,32778,1895],{},[902,32780,25980],{"encoding":904}," s autonomní spotřebou ",[883,32783,32785],{"className":32784},[886],[888,32786,32787],{"xmlns":890},[892,32788,32789,32793],{},[895,32790,32791],{},[898,32792,1895],{},[902,32794,1895],{"encoding":904}," a autonomními úsporami ",[883,32797,32799],{"className":32798},[886],[888,32800,32801],{"xmlns":890},[892,32802,32803,32809],{},[895,32804,32805,32807],{},[1693,32806,1698],{},[898,32808,1895],{},[902,32810,26059],{"encoding":904},[123,32812,32813,1863,32815,1343,32845,32875,32876,32905,32906,1343,32927,1789],{},[38,32814,7198],{},[883,32816,32818],{"className":32817},[886],[888,32819,32820],{"xmlns":890},[892,32821,32822,32842],{},[895,32823,32824,32826,32828,32830,32832,32834,32836,32838,32840],{},[898,32825,2839],{},[898,32827,1701],{},[898,32829,2971],{},[1693,32831,1695],{},[898,32833,1771],{"mathvariant":1704},[898,32835,2971],{},[898,32837,1705],{"mathvariant":1704},[898,32839,1771],{"mathvariant":1704},[898,32841,4618],{},[902,32843,32844],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,32846,32848],{"className":32847},[886],[888,32849,32850],{"xmlns":890},[892,32851,32852,32872],{},[895,32853,32854,32856,32858,32860,32862,32864,32866,32868,32870],{},[898,32855,2839],{},[898,32857,1701],{},[898,32859,3611],{},[1693,32861,1695],{},[898,32863,1771],{"mathvariant":1704},[898,32865,3611],{},[898,32867,1705],{"mathvariant":1704},[898,32869,1771],{"mathvariant":1704},[898,32871,4618],{},[902,32873,32874],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,32877,32879],{"className":32878},[886],[888,32880,32881],{"xmlns":890},[892,32882,32883,32903],{},[895,32884,32885,32887,32889,32891,32893,32895,32897,32899,32901],{},[898,32886,2839],{},[898,32888,1701],{},[898,32890,2971],{},[1693,32892,1892],{},[898,32894,2839],{},[898,32896,1701],{},[898,32898,3611],{},[1693,32900,1695],{},[1762,32902,1764],{},[902,32904,7392],{"encoding":904}," (7.5). V lineárním modelu ",[883,32907,32909],{"className":32908},[886],[888,32910,32911],{"xmlns":890},[892,32912,32913,32925],{},[895,32914,32915,32917,32919,32921,32923],{},[898,32916,2839],{},[898,32918,1701],{},[898,32920,2971],{},[1693,32922,1695],{},[898,32924,207],{},[902,32926,7330],{"encoding":904},[883,32928,32930],{"className":32929},[886],[888,32931,32932],{"xmlns":890},[892,32933,32934,32950],{},[895,32935,32936,32938,32940,32942,32944,32946,32948],{},[898,32937,2839],{},[898,32939,1701],{},[898,32941,3611],{},[1693,32943,1695],{},[1762,32945,1764],{},[1693,32947,1698],{},[898,32949,207],{},[902,32951,7356],{"encoding":904},[123,32953,32954,32957,32958],{},[38,32955,32956],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,32959,32960,33048,33117],{},[123,32961,32962,32979,32980,33001,33002,1899],{},[883,32963,32965],{"className":32964},[886],[888,32966,32967],{"xmlns":890},[892,32968,32969,32977],{},[895,32970,32971,32973,32975],{},[898,32972,2971],{},[1915,32974,19126],{},[898,32976,6998],{},[902,32978,19131],{"encoding":904},": ",[883,32981,32983],{"className":32982},[886],[888,32984,32985],{"xmlns":890},[892,32986,32987,32999],{},[895,32988,32989,32991,32993,32995,32997],{},[898,32990,4618],{},[1693,32992,1695],{},[898,32994,2971],{},[1693,32996,1892],{},[898,32998,6998],{},[902,33000,8174],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,33003,33005],{"className":33004},[886],[888,33006,33007],{"xmlns":890},[892,33008,33009,33045],{},[895,33010,33011,33017,33019,33021,33023,33025,33031,33033,33035,33037,33039,33041,33043],{},[1717,33012,33013,33015],{},[898,33014,4618],{},[898,33016,1691],{},[1693,33018,1695],{},[1693,33020,1709],{"stretchy":1708},[898,33022,1895],{},[1693,33024,1892],{},[1717,33026,33027,33029],{},[898,33028,6998],{},[1693,33030,3672],{},[1693,33032,1731],{"stretchy":1708},[898,33034,1705],{"mathvariant":1704},[1693,33036,1709],{"stretchy":1708},[1762,33038,1764],{},[1693,33040,1698],{},[898,33042,207],{},[1693,33044,1731],{"stretchy":1708},[902,33046,33047],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,33049,33050,33071,33072,33091,33092,1899],{},[883,33051,33053],{"className":33052},[886],[888,33054,33055],{"xmlns":890},[892,33056,33057,33069],{},[895,33058,33059,33061,33063,33065,33067],{},[898,33060,2971],{},[1915,33062,19126],{},[898,33064,6998],{},[1915,33066,19126],{},[898,33068,6984],{},[902,33070,25034],{"encoding":904},": přidává vládu, zdanění ",[883,33073,33075],{"className":33074},[886],[888,33076,33077],{"xmlns":890},[892,33078,33079,33089],{},[895,33080,33081,33083,33085,33087],{},[898,33082,2663],{},[1693,33084,1709],{"stretchy":1708},[898,33086,4618],{},[1693,33088,1731],{"stretchy":1708},[902,33090,29019],{"encoding":904}," a disponibilní důchod ",[883,33093,33095],{"className":33094},[886],[888,33096,33097],{"xmlns":890},[892,33098,33099,33115],{},[895,33100,33101,33107,33109,33111,33113],{},[3284,33102,33103,33105],{},[898,33104,4618],{},[898,33106,2738],{},[1693,33108,1695],{},[898,33110,4618],{},[1693,33112,1698],{},[898,33114,2663],{},[902,33116,7574],{"encoding":904},[123,33118,33119,33144,33145,28397,33166,1789],{},[883,33120,33122],{"className":33121},[886],[888,33123,33124],{"xmlns":890},[892,33125,33126,33142],{},[895,33127,33128,33130,33132,33134,33136,33138,33140],{},[898,33129,2971],{},[1915,33131,19126],{},[898,33133,6998],{},[1915,33135,19126],{},[898,33137,6984],{},[1915,33139,19126],{},[898,33141,7007],{},[902,33143,19158],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,33146,33148],{"className":33147},[886],[888,33149,33150],{"xmlns":890},[892,33151,33152,33164],{},[895,33153,33154,33156,33158,33160,33162],{},[898,33155,7007],{},[1693,33157,1695],{},[898,33159,7520],{},[1693,33161,1698],{},[898,33163,2839],{},[902,33165,30059],{"encoding":904},[883,33167,33169],{"className":33168},[886],[888,33170,33171],{"xmlns":890},[892,33172,33173,33191],{},[895,33174,33175,33177,33179,33181,33183,33189],{},[898,33176,2839],{},[1693,33178,1695],{},[898,33180,2839],{},[1693,33182,1709],{"stretchy":1708},[3284,33184,33185,33187],{},[898,33186,4618],{},[898,33188,2738],{},[1693,33190,1731],{"stretchy":1708},[902,33192,33193],{"encoding":904},"M = M(Y_D)",[123,33195,33196,33199,33200,1863,33203,33261],{},[38,33197,33198],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,33201,33202],{},"multiplikátor investic",[883,33204,33206],{"className":33205},[886],[888,33207,33208],{"xmlns":890},[892,33209,33210,33258],{},[895,33211,33212,33214,33220,33222,33224,33230,33232,33234,33236,33238,33240,33242,33244,33246,33248,33250,33252,33254,33256],{},[898,33213,2228],{"mathvariant":1704},[1717,33215,33216,33218],{},[898,33217,4618],{},[898,33219,1691],{},[898,33221,1705],{"mathvariant":1704},[898,33223,2228],{"mathvariant":1704},[1717,33225,33226,33228],{},[898,33227,6998],{},[1693,33229,3672],{},[1693,33231,1695],{},[1762,33233,1764],{},[898,33235,1705],{"mathvariant":1704},[1693,33237,1709],{"stretchy":1708},[1762,33239,1764],{},[1693,33241,1698],{},[898,33243,207],{},[1693,33245,1731],{"stretchy":1708},[1693,33247,1695],{},[1762,33249,1764],{},[898,33251,1705],{"mathvariant":1704},[898,33253,2839],{},[898,33255,1701],{},[898,33257,3611],{},[902,33259,33260],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,33263,33264,33266,33267,33282,33283,25461,33300,33315,33316,33341,33342,1789],{},[38,33265,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,33268,33270],{"className":33269},[886],[888,33271,33272],{"xmlns":890},[892,33273,33274,33280],{},[895,33275,33276,33278],{},[898,33277,6998],{},[898,33279,3611],{},[902,33281,18895],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,33284,33286],{"className":33285},[886],[888,33287,33288],{"xmlns":890},[892,33289,33290,33298],{},[895,33291,33292,33294,33296],{},[898,33293,6998],{},[1693,33295,1695],{},[898,33297,3611],{},[902,33299,19544],{"encoding":904},[883,33301,33303],{"className":33302},[886],[888,33304,33305],{"xmlns":890},[892,33306,33307,33313],{},[895,33308,33309,33311],{},[898,33310,4840],{},[898,33312,2839],{},[902,33314,18902],{"encoding":904}," rovnováhu trhu peněz (",[883,33317,33319],{"className":33318},[886],[888,33320,33321],{"xmlns":890},[892,33322,33323,33339],{},[895,33324,33325,33331,33333],{},[1717,33326,33327,33329],{},[898,33328,2839],{},[898,33330,2738],{},[1693,33332,1695],{},[1717,33334,33335,33337],{},[898,33336,2839],{},[1693,33338,3672],{},[902,33340,20311],{"encoding":904},"); průsečík dává ",[883,33343,33345],{"className":33344},[886],[888,33346,33347],{"xmlns":890},[892,33348,33349,33369],{},[895,33350,33351,33353,33359,33361,33367],{},[1693,33352,1709],{"stretchy":1708},[1717,33354,33355,33357],{},[898,33356,4618],{},[898,33358,1691],{},[1693,33360,1899],{"separator":1898},[1717,33362,33363,33365],{},[898,33364,6629],{},[898,33366,1691],{},[1693,33368,1731],{"stretchy":1708},[902,33370,8554],{"encoding":904},[115,33372,22545],{"id":22544},[120,33374,33375,33413,33453,33543,33625,33679,33735,33794,33829,33834,33906,33981,34067,34129,34197,34254,34307,34346],{},[123,33376,33377,13877,33380,32699],{},[38,33378,33379],{},"Hrubý národní produkt (GNP)",[883,33381,33383],{"className":33382},[886],[888,33384,33385],{"xmlns":890},[892,33386,33387,33411],{},[895,33388,33389,33391,33393,33395,33397,33399,33401,33403,33405,33407,33409],{},[898,33390,6984],{},[898,33392,6987],{},[898,33394,1701],{},[1693,33396,1695],{},[898,33398,2971],{},[1693,33400,1892],{},[898,33402,6998],{},[1693,33404,1892],{},[898,33406,6984],{},[1693,33408,1892],{},[898,33410,7007],{},[902,33412,7010],{"encoding":904},[123,33414,33415,33431,33432,1789],{},[38,33416,33417,33418],{},"Národní důchod ",[883,33419,33421],{"className":33420},[886],[888,33422,33423],{"xmlns":890},[892,33424,33425,33429],{},[895,33426,33427],{},[898,33428,4618],{},[902,33430,4618],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,33433,33435],{"className":33434},[886],[888,33436,33437],{"xmlns":890},[892,33438,33439,33451],{},[895,33440,33441,33443,33445,33447,33449],{},[898,33442,6984],{},[898,33444,6987],{},[898,33446,1701],{},[1693,33448,4110],{},[898,33450,4618],{},[902,33452,32664],{"encoding":904},[123,33454,33455,33481,33482,1343,33505,1343,33526,1789],{},[38,33456,33457,33458],{},"Funkce spotřeby ",[883,33459,33461],{"className":33460},[886],[888,33462,33463],{"xmlns":890},[892,33464,33465,33479],{},[895,33466,33467,33469,33471,33473,33475,33477],{},[898,33468,2971],{},[1693,33470,1695],{},[898,33472,2971],{},[1693,33474,1709],{"stretchy":1708},[898,33476,4618],{},[1693,33478,1731],{"stretchy":1708},[902,33480,27547],{"encoding":904}," — lineární model ",[883,33483,33485],{"className":33484},[886],[888,33486,33487],{"xmlns":890},[892,33488,33489,33503],{},[895,33490,33491,33493,33495,33497,33499,33501],{},[898,33492,2971],{},[1693,33494,1695],{},[898,33496,207],{},[898,33498,4618],{},[1693,33500,1892],{},[898,33502,1895],{},[902,33504,25731],{"encoding":904},[883,33506,33508],{"className":33507},[886],[888,33509,33510],{"xmlns":890},[892,33511,33512,33524],{},[895,33513,33514,33516,33518,33520,33522],{},[1762,33515,1911],{},[1693,33517,1908],{},[898,33519,207],{},[1693,33521,1908],{},[1762,33523,1764],{},[902,33525,7139],{"encoding":904},[883,33527,33529],{"className":33528},[886],[888,33530,33531],{"xmlns":890},[892,33532,33533,33541],{},[895,33534,33535,33537,33539],{},[898,33536,1895],{},[1693,33538,1922],{},[1762,33540,1911],{},[902,33542,7157],{"encoding":904},[123,33544,33545,13877,33572,33593,33594,1789],{},[38,33546,33547,33548],{},"Funkce úspor ",[883,33549,33551],{"className":33550},[886],[888,33552,33553],{"xmlns":890},[892,33554,33555,33569],{},[895,33556,33557,33559,33561,33563,33565,33567],{},[898,33558,3611],{},[1693,33560,1695],{},[898,33562,3611],{},[1693,33564,1709],{"stretchy":1708},[898,33566,4618],{},[1693,33568,1731],{"stretchy":1708},[902,33570,33571],{"encoding":904},"S = S(Y)",[883,33573,33575],{"className":33574},[886],[888,33576,33577],{"xmlns":890},[892,33578,33579,33591],{},[895,33580,33581,33583,33585,33587,33589],{},[898,33582,4618],{},[1693,33584,1695],{},[898,33586,2971],{},[1693,33588,1892],{},[898,33590,3611],{},[902,33592,7048],{"encoding":904},"; lineární ",[883,33595,33597],{"className":33596},[886],[888,33598,33599],{"xmlns":890},[892,33600,33601,33623],{},[895,33602,33603,33605,33607,33609,33611,33613,33615,33617,33619,33621],{},[898,33604,3611],{},[1693,33606,1695],{},[1693,33608,1709],{"stretchy":1708},[1762,33610,1764],{},[1693,33612,1698],{},[898,33614,207],{},[1693,33616,1731],{"stretchy":1708},[898,33618,4618],{},[1693,33620,1698],{},[898,33622,1895],{},[902,33624,25980],{"encoding":904},[123,33626,33627,13877,33630,1343,33653,1789],{},[38,33628,33629],{},"Autonomní spotřeba\u002Fúspory",[883,33631,33633],{"className":33632},[886],[888,33634,33635],{"xmlns":890},[892,33636,33637,33651],{},[895,33638,33639,33641,33643,33645,33647,33649],{},[898,33640,2971],{},[1693,33642,1709],{"stretchy":1708},[1762,33644,1911],{},[1693,33646,1731],{"stretchy":1708},[1693,33648,1695],{},[898,33650,1895],{},[902,33652,26372],{"encoding":904},[883,33654,33656],{"className":33655},[886],[888,33657,33658],{"xmlns":890},[892,33659,33660,33676],{},[895,33661,33662,33664,33666,33668,33670,33672,33674],{},[898,33663,3611],{},[1693,33665,1709],{"stretchy":1708},[1762,33667,1911],{},[1693,33669,1731],{"stretchy":1708},[1693,33671,1695],{},[1693,33673,1698],{},[898,33675,1895],{},[902,33677,33678],{"encoding":904},"S(0) = -b",[123,33680,33681,33713,33714,3042],{},[38,33682,33683,33684],{},"Mezní sklon ke spotřebě ",[883,33685,33687],{"className":33686},[886],[888,33688,33689],{"xmlns":890},[892,33690,33691,33711],{},[895,33692,33693,33695,33697,33699,33701,33703,33705,33707,33709],{},[898,33694,2839],{},[898,33696,1701],{},[898,33698,2971],{},[1693,33700,1695],{},[898,33702,1771],{"mathvariant":1704},[898,33704,2971],{},[898,33706,1705],{"mathvariant":1704},[898,33708,1771],{"mathvariant":1704},[898,33710,4618],{},[902,33712,32844],{"encoding":904}," (v lineárním modelu ",[883,33715,33717],{"className":33716},[886],[888,33718,33719],{"xmlns":890},[892,33720,33721,33733],{},[895,33722,33723,33725,33727,33729,33731],{},[898,33724,2839],{},[898,33726,1701],{},[898,33728,2971],{},[1693,33730,1695],{},[898,33732,207],{},[902,33734,7330],{"encoding":904},[123,33736,33737,33713,33769,3042],{},[38,33738,33739,33740],{},"Mezní sklon k úsporám ",[883,33741,33743],{"className":33742},[886],[888,33744,33745],{"xmlns":890},[892,33746,33747,33767],{},[895,33748,33749,33751,33753,33755,33757,33759,33761,33763,33765],{},[898,33750,2839],{},[898,33752,1701],{},[898,33754,3611],{},[1693,33756,1695],{},[898,33758,1771],{"mathvariant":1704},[898,33760,3611],{},[898,33762,1705],{"mathvariant":1704},[898,33764,1771],{"mathvariant":1704},[898,33766,4618],{},[902,33768,32874],{"encoding":904},[883,33770,33772],{"className":33771},[886],[888,33773,33774],{"xmlns":890},[892,33775,33776,33792],{},[895,33777,33778,33780,33782,33784,33786,33788,33790],{},[898,33779,2839],{},[898,33781,1701],{},[898,33783,3611],{},[1693,33785,1695],{},[1762,33787,1764],{},[1693,33789,1698],{},[898,33791,207],{},[902,33793,7356],{"encoding":904},[123,33795,33796,1863,33799,33828],{},[38,33797,33798],{},"Vztah",[883,33800,33802],{"className":33801},[886],[888,33803,33804],{"xmlns":890},[892,33805,33806,33826],{},[895,33807,33808,33810,33812,33814,33816,33818,33820,33822,33824],{},[898,33809,2839],{},[898,33811,1701],{},[898,33813,2971],{},[1693,33815,1892],{},[898,33817,2839],{},[898,33819,1701],{},[898,33821,3611],{},[1693,33823,1695],{},[1762,33825,1764],{},[902,33827,7392],{"encoding":904}," (7.5).",[123,33830,33831,33833],{},[38,33832,27390],{}," — rovnováha agregátní poptávky a nabídky.",[123,33835,33836,33839,33840,22617,33861,1789],{},[38,33837,33838],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,33841,33843],{"className":33842},[886],[888,33844,33845],{"xmlns":890},[892,33846,33847,33859],{},[895,33848,33849,33851,33853,33855,33857],{},[898,33850,4618],{},[1693,33852,1695],{},[898,33854,2971],{},[1693,33856,1892],{},[898,33858,6998],{},[902,33860,8174],{"encoding":904},[883,33862,33864],{"className":33863},[886],[888,33865,33866],{"xmlns":890},[892,33867,33868,33904],{},[895,33869,33870,33876,33878,33880,33882,33884,33890,33892,33894,33896,33898,33900,33902],{},[1717,33871,33872,33874],{},[898,33873,4618],{},[898,33875,1691],{},[1693,33877,1695],{},[1693,33879,1709],{"stretchy":1708},[898,33881,1895],{},[1693,33883,1892],{},[1717,33885,33886,33888],{},[898,33887,6998],{},[1693,33889,3672],{},[1693,33891,1731],{"stretchy":1708},[898,33893,1705],{"mathvariant":1704},[1693,33895,1709],{"stretchy":1708},[1762,33897,1764],{},[1693,33899,1698],{},[898,33901,207],{},[1693,33903,1731],{"stretchy":1708},[902,33905,33047],{"encoding":904},[123,33907,33908,33911,33912,1343,33931,22617,33956,1789],{},[38,33909,33910],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,33913,33915],{"className":33914},[886],[888,33916,33917],{"xmlns":890},[892,33918,33919,33929],{},[895,33920,33921,33923,33925,33927],{},[898,33922,2663],{},[1693,33924,1709],{"stretchy":1708},[898,33926,4618],{},[1693,33928,1731],{"stretchy":1708},[902,33930,29019],{"encoding":904},[883,33932,33934],{"className":33933},[886],[888,33935,33936],{"xmlns":890},[892,33937,33938,33954],{},[895,33939,33940,33946,33948,33950,33952],{},[3284,33941,33942,33944],{},[898,33943,4618],{},[898,33945,2738],{},[1693,33947,1695],{},[898,33949,4618],{},[1693,33951,1698],{},[898,33953,2663],{},[902,33955,7574],{"encoding":904},[883,33957,33959],{"className":33958},[886],[888,33960,33961],{"xmlns":890},[892,33962,33963,33979],{},[895,33964,33965,33967,33969,33971,33973,33975,33977],{},[898,33966,4618],{},[1693,33968,1695],{},[898,33970,2971],{},[1693,33972,1892],{},[898,33974,6998],{},[1693,33976,1892],{},[898,33978,6984],{},[902,33980,28492],{"encoding":904},[123,33982,33983,33986,33987,34008,34009,22617,34033,1789],{},[38,33984,33985],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,33988,33990],{"className":33989},[886],[888,33991,33992],{"xmlns":890},[892,33993,33994,34006],{},[895,33995,33996,33998,34000,34002,34004],{},[898,33997,7007],{},[1693,33999,1695],{},[898,34001,7520],{},[1693,34003,1698],{},[898,34005,2839],{},[902,34007,30059],{"encoding":904},", importem ",[883,34010,34012],{"className":34011},[886],[888,34013,34014],{"xmlns":890},[892,34015,34016,34030],{},[895,34017,34018,34020,34022,34028],{},[898,34019,2839],{},[1693,34021,1709],{"stretchy":1708},[3284,34023,34024,34026],{},[898,34025,4618],{},[898,34027,2738],{},[1693,34029,1731],{"stretchy":1708},[902,34031,34032],{"encoding":904},"M(Y_D)",[883,34034,34036],{"className":34035},[886],[888,34037,34038],{"xmlns":890},[892,34039,34040,34064],{},[895,34041,34042,34044,34046,34048,34050,34052,34054,34056,34058,34060,34062],{},[898,34043,4618],{},[1693,34045,1695],{},[898,34047,2971],{},[1693,34049,1892],{},[898,34051,6998],{},[1693,34053,1892],{},[898,34055,6984],{},[1693,34057,1892],{},[898,34059,7520],{},[1693,34061,1698],{},[898,34063,2839],{},[902,34065,34066],{"encoding":904},"Y = C + I + G + B - M",[123,34068,34069,13877,34072,33261],{},[38,34070,34071],{},"Multiplikátor investic",[883,34073,34075],{"className":34074},[886],[888,34076,34077],{"xmlns":890},[892,34078,34079,34127],{},[895,34080,34081,34083,34089,34091,34093,34099,34101,34103,34105,34107,34109,34111,34113,34115,34117,34119,34121,34123,34125],{},[898,34082,2228],{"mathvariant":1704},[1717,34084,34085,34087],{},[898,34086,4618],{},[898,34088,1691],{},[898,34090,1705],{"mathvariant":1704},[898,34092,2228],{"mathvariant":1704},[1717,34094,34095,34097],{},[898,34096,6998],{},[1693,34098,3672],{},[1693,34100,1695],{},[1762,34102,1764],{},[898,34104,1705],{"mathvariant":1704},[1693,34106,1709],{"stretchy":1708},[1762,34108,1764],{},[1693,34110,1698],{},[898,34112,207],{},[1693,34114,1731],{"stretchy":1708},[1693,34116,1695],{},[1762,34118,1764],{},[898,34120,1705],{"mathvariant":1704},[898,34122,2839],{},[898,34124,1701],{},[898,34126,3611],{},[902,34128,33260],{"encoding":904},[123,34130,34131,13877,34162,1343,34179,34196],{},[38,34132,22552,34133],{},[883,34134,34136],{"className":34135},[886],[888,34137,34138],{"xmlns":890},[892,34139,34140,34160],{},[895,34141,34142,34144,34146,34148,34150,34152,34154,34156,34158],{},[898,34143,6998],{},[1693,34145,1709],{"stretchy":1708},[898,34147,6629],{},[1693,34149,1731],{"stretchy":1708},[1693,34151,1695],{},[898,34153,2000],{},[898,34155,6629],{},[1693,34157,1892],{},[898,34159,1771],{},[902,34161,22582],{"encoding":904},[883,34163,34165],{"className":34164},[886],[888,34166,34167],{"xmlns":890},[892,34168,34169,34177],{},[895,34170,34171,34173,34175],{},[898,34172,2000],{},[1693,34174,1908],{},[1762,34176,1911],{},[902,34178,8089],{"encoding":904},[883,34180,34182],{"className":34181},[886],[888,34183,34184],{"xmlns":890},[892,34185,34186,34194],{},[895,34187,34188,34190,34192],{},[898,34189,1771],{},[1693,34191,1922],{},[1762,34193,1911],{},[902,34195,19329],{"encoding":904},"; klesající.",[123,34198,34199,34201,34202,6294,34204,34253],{},[38,34200,22671],{}," — rovnováha na trhu zboží (",[614,34203,18898],{},[883,34205,34207],{"className":34206},[886],[888,34208,34209],{"xmlns":890},[892,34210,34211,34251],{},[895,34212,34213,34215,34217,34229,34231,34233],{},[898,34214,4618],{},[1693,34216,1695],{},[2132,34218,34219,34221],{},[898,34220,2000],{},[895,34222,34223,34225,34227],{},[1762,34224,1764],{},[1693,34226,1698],{},[898,34228,207],{},[898,34230,6629],{},[1693,34232,1892],{},[2132,34234,34235,34243],{},[895,34236,34237,34239,34241],{},[898,34238,1895],{},[1693,34240,1892],{},[898,34242,1771],{},[895,34244,34245,34247,34249],{},[1762,34246,1764],{},[1693,34248,1698],{},[898,34250,207],{},[902,34252,22724],{"encoding":904}," (7.14); klesající.",[123,34255,34256,34258,34259,6294,34261,34306],{},[38,34257,22869],{}," — rovnováha na trhu peněz (",[614,34260,18905],{},[883,34262,34264],{"className":34263},[886],[888,34265,34266],{"xmlns":890},[892,34267,34268,34304],{},[895,34269,34270,34276,34278,34284,34286,34288,34294,34296,34298],{},[1717,34271,34272,34274],{},[898,34273,2839],{},[1693,34275,3672],{},[1693,34277,1695],{},[3284,34279,34280,34282],{},[898,34281,8334],{},[1762,34283,1764],{},[898,34285,4618],{},[1693,34287,1892],{},[3284,34289,34290,34292],{},[898,34291,8334],{},[1762,34293,2398],{},[898,34295,6629],{},[1693,34297,1892],{},[3284,34299,34300,34302],{},[898,34301,8334],{},[1762,34303,8357],{},[902,34305,8360],{"encoding":904}," (7.15); rostoucí.",[123,34308,34309,13877,34312,1789],{},[38,34310,34311],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,34313,34315],{"className":34314},[886],[888,34316,34317],{"xmlns":890},[892,34318,34319,34343],{},[895,34320,34321,34327,34329,34335,34337],{},[1717,34322,34323,34325],{},[898,34324,2839],{},[898,34326,2738],{},[1693,34328,1695],{},[3284,34330,34331,34333],{},[898,34332,4840],{},[1762,34334,1764],{},[1693,34336,1892],{},[3284,34338,34339,34341],{},[898,34340,4840],{},[1762,34342,2398],{},[902,34344,34345],{"encoding":904},"M^D = L_1 + L_2",[123,34347,34348,22925,34350,20809,34363,4286,34378,34393,34394,1789],{},[38,34349,945],{},[883,34351,34353],{"className":34352},[886],[888,34354,34355],{"xmlns":890},[892,34356,34357,34361],{},[895,34358,34359],{},[898,34360,1691],{},[902,34362,1691],{"encoding":904},[883,34364,34366],{"className":34365},[886],[888,34367,34368],{"xmlns":890},[892,34369,34370,34376],{},[895,34371,34372,34374],{},[898,34373,6998],{},[898,34375,3611],{},[902,34377,18895],{"encoding":904},[883,34379,34381],{"className":34380},[886],[888,34382,34383],{"xmlns":890},[892,34384,34385,34391],{},[895,34386,34387,34389],{},[898,34388,4840],{},[898,34390,2839],{},[902,34392,18902],{"encoding":904}," určuje ",[883,34395,34397],{"className":34396},[886],[888,34398,34399],{"xmlns":890},[892,34400,34401,34421],{},[895,34402,34403,34405,34411,34413,34419],{},[1693,34404,1709],{"stretchy":1708},[1717,34406,34407,34409],{},[898,34408,4618],{},[898,34410,1691],{},[1693,34412,1899],{"separator":1898},[1717,34414,34415,34417],{},[898,34416,6629],{},[898,34418,1691],{},[1693,34420,1731],{"stretchy":1708},[902,34422,8554],{"encoding":904},[115,34424,8685],{"id":8684},[120,34426,34427,34434,34441],{},[123,34428,34429,1863,34431],{},[38,34430,8692],{},[207,34432,1653],{"className":34433,"dataFsResolvedFilePath":1651,"href":1652},[210],[123,34435,34436,1863,34438],{},[38,34437,23033],{},[207,34439,23037],{"className":34440,"dataFsResolvedFilePath":868,"href":869},[210],[123,34442,34443,34445],{},[38,34444,23052],{},[120,34446,34447,34453,34459,34465],{},[123,34448,34449,34452],{},[207,34450,23093],{"className":34451,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,34454,34455,34458],{},[207,34456,23060],{"className":34457,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,34460,34461,34464],{},[207,34462,9848],{"className":34463,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,34466,34467,34470,34471,1343,34488,34505],{},[207,34468,1145],{"className":34469,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,34472,34474],{"className":34473},[886],[888,34475,34476],{"xmlns":890},[892,34477,34478,34486],{},[895,34479,34480,34482,34484],{},[898,34481,2839],{},[898,34483,1701],{},[898,34485,2971],{},[902,34487,7288],{"encoding":904},[883,34489,34491],{"className":34490},[886],[888,34492,34493],{"xmlns":890},[892,34494,34495,34503],{},[895,34496,34497,34499,34501],{},[898,34498,2839],{},[898,34500,1701],{},[898,34502,3611],{},[902,34504,7307],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":34507},[34508,34509,34510,34511,34516,34519,34520,34527,34532,34537,34540,34541,34542,34543],{"id":18850,"depth":642,"text":18851},{"id":24968,"depth":642,"text":24969},{"id":25088,"depth":642,"text":25089},{"id":25340,"depth":642,"text":25341,"children":34512},[34513,34514,34515],{"id":25344,"depth":649,"text":25345},{"id":25556,"depth":649,"text":25557},{"id":26062,"depth":649,"text":26063},{"id":26381,"depth":642,"text":26382,"children":34517},[34518],{"id":26894,"depth":649,"text":26895},{"id":27389,"depth":642,"text":27390},{"id":27416,"depth":642,"text":27417,"children":34521},[34522,34523,34524,34526],{"id":27427,"depth":649,"text":27428},{"id":27497,"depth":649,"text":27498},{"id":27678,"depth":649,"text":34525},"Výpočet YEY^E",{"id":27820,"depth":649,"text":27821},{"id":28198,"depth":642,"text":28199,"children":34528},[34529,34530,34531],{"id":28202,"depth":649,"text":27428},{"id":28648,"depth":649,"text":27498},{"id":29304,"depth":649,"text":29305},{"id":30090,"depth":642,"text":30091,"children":34533},[34534,34535,34536],{"id":30094,"depth":649,"text":27428},{"id":30239,"depth":649,"text":27498},{"id":30509,"depth":649,"text":30510},{"id":31433,"depth":642,"text":31434,"children":34538},[34539],{"id":31628,"depth":649,"text":31629},{"id":32173,"depth":642,"text":32174},{"id":32633,"depth":642,"text":32634},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,23046,1143,34550,34551,34552,23093,24701],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":34555,"title":5829,"body":34556,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":43529,"navigation":664,"path":43530,"seo":43531,"sources":43532,"stem":43533,"tags":43534,"type":10745,"updated":677,"__hash__":43539},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md",{"type":9,"value":34557,"toc":43498},[34558,34561,34563,34792,34796,34849,34919,35031,35190,35194,35310,35314,35317,35438,35441,35634,35658,35726,35888,35906,35971,36349,36353,36360,36604,36659,36663,36728,36846,36978,37010,37130,37212,37215,37337,37530,37751,37755,37795,37900,37957,38057,38234,38364,38417,38420,38507,38511,38687,38691,38694,38779,38782,38839,38944,38948,39069,39072,39255,39258,39366,39575,39895,39943,40016,40090,40092,40316,40551,40819,40823,40826,40931,40988,41022,41069,41102,41186,41188,41420,41553,41630,41752,41907,41911,42052,42059,42283,42294,42298,42302,42407,42548,42658,42757,42761,42920,43030,43032,43425,43427],[12,34559,5829],{"id":34560},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,34562,18851],{"id":18850},[724,34564,34565,34567,34568,34602,34603,34606,34607,34638,34639,34685,34686,34689,34690,34732,34733,34751,34752,34756,34757,34787,34788,34791],{},[38,34566,913],{}," řeší, jaký svazek zboží ",[883,34569,34571],{"className":34570},[886],[888,34572,34573],{"xmlns":890},[892,34574,34575,34599],{},[895,34576,34577,34579,34587,34589,34597],{},[1693,34578,9392],{"stretchy":1708},[5688,34580,34581,34583,34585],{},[898,34582,1712],{},[1762,34584,1764],{},[1693,34586,3672],{},[1693,34588,1899],{"separator":1898},[5688,34590,34591,34593,34595],{},[898,34592,1712],{},[1762,34594,2398],{},[1693,34596,3672],{},[1693,34598,9407],{"stretchy":1708},[902,34600,34601],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,34604,34605],{},"primární úloha"," — maximalizace užitečnosti ",[883,34608,34610],{"className":34609},[886],[888,34611,34612],{"xmlns":890},[892,34613,34614,34636],{},[895,34615,34616,34618,34620,34626,34628,34634],{},[898,34617,900],{},[1693,34619,1709],{"stretchy":1708},[3284,34621,34622,34624],{},[898,34623,1712],{},[1762,34625,1764],{},[1693,34627,1899],{"separator":1898},[3284,34629,34630,34632],{},[898,34631,1712],{},[1762,34633,2398],{},[1693,34635,1731],{"stretchy":1708},[902,34637,23164],{"encoding":904}," při rozpočtovém omezení ",[883,34640,34642],{"className":34641},[886],[888,34643,34644],{"xmlns":890},[892,34645,34646,34682],{},[895,34647,34648,34654,34656,34662,34668,34670,34676],{},[1717,34649,34650,34652],{},[898,34651,4618],{},[1693,34653,3672],{},[1693,34655,1695],{},[3284,34657,34658,34660],{},[898,34659,1701],{},[1762,34661,1764],{},[3284,34663,34664,34666],{},[898,34665,1712],{},[1762,34667,1764],{},[1693,34669,1892],{},[3284,34671,34672,34674],{},[898,34673,1701],{},[1762,34675,2398],{},[3284,34677,34678,34680],{},[898,34679,1712],{},[1762,34681,2398],{},[902,34683,34684],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,34687,34688],{},"duální úloha"," — minimalizace výdajů ",[883,34691,34693],{"className":34692},[886],[888,34694,34695],{"xmlns":890},[892,34696,34697,34729],{},[895,34698,34699,34701,34703,34709,34715,34717,34723],{},[898,34700,1691],{},[1693,34702,1695],{},[3284,34704,34705,34707],{},[898,34706,1701],{},[1762,34708,1764],{},[3284,34710,34711,34713],{},[898,34712,1712],{},[1762,34714,1764],{},[1693,34716,1892],{},[3284,34718,34719,34721],{},[898,34720,1701],{},[1762,34722,2398],{},[3284,34724,34725,34727],{},[898,34726,1712],{},[1762,34728,2398],{},[902,34730,34731],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,34734,34736],{"className":34735},[886],[888,34737,34738],{"xmlns":890},[892,34739,34740,34748],{},[895,34741,34742],{},[1717,34743,34744,34746],{},[898,34745,900],{},[1693,34747,3672],{},[902,34749,34750],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,34753,34755],{"className":34754,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,34758,34760],{"className":34759},[886],[888,34761,34762],{"xmlns":890},[892,34763,34764,34784],{},[895,34765,34766,34768,34770,34776,34778],{},[1915,34767,5315],{},[1693,34769,1695],{},[3284,34771,34772,34774],{},[898,34773,1701],{},[1762,34775,1764],{},[898,34777,1705],{"mathvariant":1704},[3284,34779,34780,34782],{},[898,34781,1701],{},[1762,34783,2398],{},[902,34785,34786],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,34789,34790],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,34793,34795],{"id":34794},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,34797,34798,34799,34817,34818,34848],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,34800,34802],{"className":34801},[886],[888,34803,34804],{"xmlns":890},[892,34805,34806,34814],{},[895,34807,34808],{},[1717,34809,34810,34812],{},[898,34811,4618],{},[1693,34813,3672],{},[902,34815,34816],{"encoding":904},"Y^*"," a ceny ",[883,34819,34821],{"className":34820},[886],[888,34822,34823],{"xmlns":890},[892,34824,34825,34845],{},[895,34826,34827,34835,34837],{},[5688,34828,34829,34831,34833],{},[898,34830,1701],{},[1762,34832,1764],{},[1693,34834,3672],{},[1693,34836,1899],{"separator":1898},[5688,34838,34839,34841,34843],{},[898,34840,1701],{},[1762,34842,2398],{},[1693,34844,3672],{},[902,34846,34847],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,34850,34852],{"className":34851},[886],[888,34853,34855],{"xmlns":890,"display":34854},"block",[892,34856,34857,34916],{},[3626,34858,34860],{"width":34859},"100%",[3632,34861,34862,34865,34909,34911],{},[3635,34863],{"width":34864},"50%",[3635,34866,34867],{},[895,34868,34869,34875,34877,34885,34891,34893,34901,34907],{},[1717,34870,34871,34873],{},[898,34872,4618],{},[1693,34874,3672],{},[1693,34876,1695],{},[5688,34878,34879,34881,34883],{},[898,34880,1701],{},[1762,34882,1764],{},[1693,34884,3672],{},[3284,34886,34887,34889],{},[898,34888,1712],{},[1762,34890,1764],{},[1693,34892,1892],{},[5688,34894,34895,34897,34899],{},[898,34896,1701],{},[1762,34898,2398],{},[1693,34900,3672],{},[3284,34902,34903,34905],{},[898,34904,1712],{},[1762,34906,2398],{},[1693,34908,1899],{"separator":1898},[3635,34910],{"width":34864},[3635,34912,34913],{},[1915,34914,34915],{},"(6.12)",[902,34917,34918],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,34920,34921,34922,34925,34926,4286,34962,34998,34999,35012,35013,35027,35028,1789],{},"geometricky ",[38,34923,34924],{},"rozpočtová přímka (budget line)"," procházející body ",[883,34927,34929],{"className":34928},[886],[888,34930,34931],{"xmlns":890},[892,34932,34933,34959],{},[895,34934,34935,34937,34943,34945,34953,34955,34957],{},[1693,34936,9392],{"stretchy":1708},[1717,34938,34939,34941],{},[898,34940,4618],{},[1693,34942,3672],{},[898,34944,1705],{"mathvariant":1704},[5688,34946,34947,34949,34951],{},[898,34948,1701],{},[1762,34950,1764],{},[1693,34952,3672],{},[1693,34954,1899],{"separator":1898},[1762,34956,1911],{},[1693,34958,9407],{"stretchy":1708},[902,34960,34961],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,34963,34965],{"className":34964},[886],[888,34966,34967],{"xmlns":890},[892,34968,34969,34995],{},[895,34970,34971,34973,34975,34977,34983,34985,34993],{},[1693,34972,9392],{"stretchy":1708},[1762,34974,1911],{},[1693,34976,1899],{"separator":1898},[1717,34978,34979,34981],{},[898,34980,4618],{},[1693,34982,3672],{},[898,34984,1705],{"mathvariant":1704},[5688,34986,34987,34989,34991],{},[898,34988,1701],{},[1762,34990,2398],{},[1693,34992,3672],{},[1693,34994,9407],{"stretchy":1708},[902,34996,34997],{"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 ",[883,35000,35002],{"className":35001},[886],[888,35003,35004],{"xmlns":890},[892,35005,35006,35010],{},[895,35007,35008],{},[898,35009,900],{},[902,35011,900],{"encoding":904},", indiferenční křivky a ",[883,35014,35016],{"className":35015},[886],[888,35017,35018],{"xmlns":890},[892,35019,35020,35024],{},[895,35021,35022],{},[1915,35023,5315],{},[902,35025,35026],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,35029,880],{"className":35030,"dataFsResolvedFilePath":878,"href":879},[210],[1636,35032,35033],{},[724,35034,35035,35037,35038,35041,35042,35055,35056,35058,35059,35072,35073,1863,35076,35116,35117,35134,35135,35152,35153,35170,35171,35189],{},[883,35036,8654],{}," Pozor — dvě úlohy, totéž řešení\n",[38,35039,35040],{},"Primární úloha"," (max ",[883,35043,35045],{"className":35044},[886],[888,35046,35047],{"xmlns":890},[892,35048,35049,35053],{},[895,35050,35051],{},[898,35052,900],{},[902,35054,900],{"encoding":904}," při pevném rozpočtu) a ",[38,35057,34688],{}," (min ",[883,35060,35062],{"className":35061},[886],[888,35063,35064],{"xmlns":890},[892,35065,35066,35070],{},[895,35067,35068],{},[898,35069,1691],{},[902,35071,1691],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,35074,35075],{},"tentýž bod",[883,35077,35079],{"className":35078},[886],[888,35080,35081],{"xmlns":890},[892,35082,35083,35113],{},[895,35084,35085,35091,35093,35101,35103,35111],{},[1717,35086,35087,35089],{},[898,35088,1712],{},[1693,35090,3672],{},[1693,35092,9392],{"stretchy":1708},[5688,35094,35095,35097,35099],{},[898,35096,1712],{},[1762,35098,1764],{},[1693,35100,3672],{},[1693,35102,1899],{"separator":1898},[5688,35104,35105,35107,35109],{},[898,35106,1712],{},[1762,35108,2398],{},[1693,35110,3672],{},[1693,35112,9407],{"stretchy":1708},[902,35114,35115],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,35118,35120],{"className":35119},[886],[888,35121,35122],{"xmlns":890},[892,35123,35124,35132],{},[895,35125,35126],{},[1717,35127,35128,35130],{},[898,35129,4618],{},[1693,35131,3672],{},[902,35133,34816],{"encoding":904}," a hledáme maximální ",[883,35136,35138],{"className":35137},[886],[888,35139,35140],{"xmlns":890},[892,35141,35142,35150],{},[895,35143,35144],{},[1717,35145,35146,35148],{},[898,35147,900],{},[1693,35149,3672],{},[902,35151,34750],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,35154,35156],{"className":35155},[886],[888,35157,35158],{"xmlns":890},[892,35159,35160,35168],{},[895,35161,35162],{},[1717,35163,35164,35166],{},[898,35165,900],{},[1693,35167,3672],{},[902,35169,34750],{"encoding":904}," a hledáme minimální ",[883,35172,35174],{"className":35173},[886],[888,35175,35176],{"xmlns":890},[892,35177,35178,35186],{},[895,35179,35180],{},[1717,35181,35182,35184],{},[898,35183,1691],{},[1693,35185,3672],{},[902,35187,35188],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,35191,35193],{"id":35192},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,35195,35196,35197,35228,35229,35305,35306,1789],{},"Úlohou je najít maximum ",[883,35198,35200],{"className":35199},[886],[888,35201,35202],{"xmlns":890},[892,35203,35204,35226],{},[895,35205,35206,35208,35210,35216,35218,35224],{},[898,35207,900],{},[1693,35209,1709],{"stretchy":1708},[3284,35211,35212,35214],{},[898,35213,1712],{},[1762,35215,1764],{},[1693,35217,1899],{"separator":1898},[3284,35219,35220,35222],{},[898,35221,1712],{},[1762,35223,2398],{},[1693,35225,1731],{"stretchy":1708},[902,35227,23164],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,35230,35232],{"className":35231},[886],[888,35233,35234],{"xmlns":890},[892,35235,35236,35302],{},[895,35237,35238,35240,35242,35248,35250,35256,35258,35260,35266,35268,35276,35282,35284,35292,35298,35300],{},[898,35239,17887],{},[1693,35241,1709],{"stretchy":1708},[3284,35243,35244,35246],{},[898,35245,1712],{},[1762,35247,1764],{},[1693,35249,1899],{"separator":1898},[3284,35251,35252,35254],{},[898,35253,1712],{},[1762,35255,2398],{},[1693,35257,1731],{"stretchy":1708},[1693,35259,1695],{},[1717,35261,35262,35264],{},[898,35263,4618],{},[1693,35265,3672],{},[1693,35267,1698],{},[5688,35269,35270,35272,35274],{},[898,35271,1701],{},[1762,35273,1764],{},[1693,35275,3672],{},[3284,35277,35278,35280],{},[898,35279,1712],{},[1762,35281,1764],{},[1693,35283,1698],{},[5688,35285,35286,35288,35290],{},[898,35287,1701],{},[1762,35289,2398],{},[1693,35291,3672],{},[3284,35293,35294,35296],{},[898,35295,1712],{},[1762,35297,2398],{},[1693,35299,1695],{},[1762,35301,1911],{},[902,35303,35304],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,35307,35309],{"className":35308,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,35311,35313],{"id":35312},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,35315,35316],{},"Sestavíme",[883,35318,35320],{"className":35319},[886],[888,35321,35322],{"xmlns":890,"display":34854},[892,35323,35324,35435],{},[3626,35325,35326],{"width":34859},[3632,35327,35328,35330,35428,35430],{},[3635,35329],{"width":34864},[3635,35331,35332],{},[895,35333,35334,35336,35338,35344,35346,35352,35354,35356,35358,35360,35362,35364,35370,35372,35378,35380,35382,35384,35386,35392,35394,35402,35408,35410,35418,35424,35426],{},[898,35335,4840],{"mathvariant":5936},[1693,35337,1709],{"stretchy":1708},[3284,35339,35340,35342],{},[898,35341,1712],{},[1762,35343,1764],{},[1693,35345,1899],{"separator":1898},[3284,35347,35348,35350],{},[898,35349,1712],{},[1762,35351,2398],{},[1693,35353,1899],{"separator":1898},[898,35355,5957],{},[1693,35357,1731],{"stretchy":1708},[1693,35359,1695],{},[898,35361,900],{},[1693,35363,1709],{"stretchy":1708},[3284,35365,35366,35368],{},[898,35367,1712],{},[1762,35369,1764],{},[1693,35371,1899],{"separator":1898},[3284,35373,35374,35376],{},[898,35375,1712],{},[1762,35377,2398],{},[1693,35379,1731],{"stretchy":1708},[1693,35381,1892],{},[898,35383,5957],{},[1693,35385,1709],{"stretchy":1708},[1717,35387,35388,35390],{},[898,35389,4618],{},[1693,35391,3672],{},[1693,35393,1698],{},[5688,35395,35396,35398,35400],{},[898,35397,1701],{},[1762,35399,1764],{},[1693,35401,3672],{},[3284,35403,35404,35406],{},[898,35405,1712],{},[1762,35407,1764],{},[1693,35409,1698],{},[5688,35411,35412,35414,35416],{},[898,35413,1701],{},[1762,35415,2398],{},[1693,35417,3672],{},[3284,35419,35420,35422],{},[898,35421,1712],{},[1762,35423,2398],{},[1693,35425,1731],{"stretchy":1708},[898,35427,1789],{"mathvariant":1704},[3635,35429],{"width":34864},[3635,35431,35432],{},[1915,35433,35434],{},"(6.13)",[902,35436,35437],{"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}",[724,35439,35440],{},"Soustava prvního řádu:",[883,35442,35444],{"className":35443},[886],[888,35445,35446],{"xmlns":890,"display":34854},[892,35447,35448,35631],{},[3626,35449,35450],{"width":34859},[3632,35451,35452,35454,35624,35626],{},[3635,35453],{"width":34864},[3635,35455,35456],{},[3626,35457,35458,35508,35558],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,35459,35460,35472],{},[3635,35461,35462],{},[3638,35463,35464],{"scriptlevel":1911,"displaystyle":1898},[5688,35465,35466,35468,35470],{},[898,35467,4840],{"mathvariant":5936},[1762,35469,1764],{},[1693,35471,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,35473,35474],{},[3638,35475,35476],{"scriptlevel":1911,"displaystyle":1898},[895,35477,35478,35480,35482,35490,35492,35494,35502,35504,35506],{},[895,35479],{},[1693,35481,1695],{},[5688,35483,35484,35486,35488],{},[898,35485,900],{},[1762,35487,1764],{},[1693,35489,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,35491,1698],{},[898,35493,5957],{},[5688,35495,35496,35498,35500],{},[898,35497,1701],{},[1762,35499,1764],{},[1693,35501,3672],{},[1693,35503,1695],{},[1762,35505,1911],{},[1693,35507,1899],{"separator":1898},[3632,35509,35510,35522],{},[3635,35511,35512],{},[3638,35513,35514],{"scriptlevel":1911,"displaystyle":1898},[5688,35515,35516,35518,35520],{},[898,35517,4840],{"mathvariant":5936},[1762,35519,2398],{},[1693,35521,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,35523,35524],{},[3638,35525,35526],{"scriptlevel":1911,"displaystyle":1898},[895,35527,35528,35530,35532,35540,35542,35544,35552,35554,35556],{},[895,35529],{},[1693,35531,1695],{},[5688,35533,35534,35536,35538],{},[898,35535,900],{},[1762,35537,2398],{},[1693,35539,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,35541,1698],{},[898,35543,5957],{},[5688,35545,35546,35548,35550],{},[898,35547,1701],{},[1762,35549,2398],{},[1693,35551,3672],{},[1693,35553,1695],{},[1762,35555,1911],{},[1693,35557,1899],{"separator":1898},[3632,35559,35560,35572],{},[3635,35561,35562],{},[3638,35563,35564],{"scriptlevel":1911,"displaystyle":1898},[5688,35565,35566,35568,35570],{},[898,35567,4840],{"mathvariant":5936},[898,35569,5957],{},[1693,35571,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,35573,35574],{},[3638,35575,35576],{"scriptlevel":1911,"displaystyle":1898},[895,35577,35578,35580,35582,35588,35590,35598,35604,35606,35614,35620,35622],{},[895,35579],{},[1693,35581,1695],{},[1717,35583,35584,35586],{},[898,35585,4618],{},[1693,35587,3672],{},[1693,35589,1698],{},[5688,35591,35592,35594,35596],{},[898,35593,1701],{},[1762,35595,1764],{},[1693,35597,3672],{},[3284,35599,35600,35602],{},[898,35601,1712],{},[1762,35603,1764],{},[1693,35605,1698],{},[5688,35607,35608,35610,35612],{},[898,35609,1701],{},[1762,35611,2398],{},[1693,35613,3672],{},[3284,35615,35616,35618],{},[898,35617,1712],{},[1762,35619,2398],{},[1693,35621,1695],{},[1762,35623,19295],{},[3635,35625],{"width":34864},[3635,35627,35628],{},[1915,35629,35630],{},"(6.14)",[902,35632,35633],{"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}",[724,35635,35636,35637,35640,35641,35654,35655,4300],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,35638,35639],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,35642,35644],{"className":35643},[886],[888,35645,35646],{"xmlns":890},[892,35647,35648,35652],{},[895,35649,35650],{},[898,35651,5957],{},[902,35653,6054],{"encoding":904}," dostáváme ",[38,35656,35657],{},"podmínku optimality",[883,35659,35661],{"className":35660},[886],[888,35662,35663],{"xmlns":890,"display":34854},[892,35664,35665,35723],{},[895,35666,35667],{},[19664,35668,35669],{"notation":19666},[3638,35670,35671],{"scriptlevel":1911,"displaystyle":1708},[3638,35672,35673],{"scriptlevel":1911,"displaystyle":1708},[3638,35674,35675],{"scriptlevel":1911,"displaystyle":1898},[895,35676,35677,35679,35681,35683,35701,35703,35721],{},[1915,35678,1917],{},[1915,35680,5315],{},[1693,35682,1695],{},[2132,35684,35685,35693],{},[5688,35686,35687,35689,35691],{},[898,35688,900],{},[1762,35690,1764],{},[1693,35692,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,35694,35695,35697,35699],{},[898,35696,900],{},[1762,35698,2398],{},[1693,35700,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,35702,1695],{},[2132,35704,35705,35713],{},[5688,35706,35707,35709,35711],{},[898,35708,1701],{},[1762,35710,1764],{},[1693,35712,3672],{},[5688,35714,35715,35717,35719],{},[898,35716,1701],{},[1762,35718,2398],{},[1693,35720,3672],{},[1915,35722,1917],{},[902,35724,35725],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1636,35727,35728],{},[724,35729,35730,35732,35733,35767,35768,35771,35772,35789,35790,35807,35808,35838,35839,35856,35857,35887],{},[883,35731,11036],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,35734,35736],{"className":35735},[886],[888,35737,35738],{"xmlns":890},[892,35739,35740,35764],{},[895,35741,35742,35744,35746,35754,35756],{},[1915,35743,5315],{},[1693,35745,1695],{},[5688,35747,35748,35750,35752],{},[898,35749,1701],{},[1762,35751,1764],{},[1693,35753,3672],{},[898,35755,1705],{"mathvariant":1704},[5688,35757,35758,35760,35762],{},[898,35759,1701],{},[1762,35761,2398],{},[1693,35763,3672],{},[902,35765,35766],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,35769,35770],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,35773,35775],{"className":35774},[886],[888,35776,35777],{"xmlns":890},[892,35778,35779,35787],{},[895,35780,35781],{},[3284,35782,35783,35785],{},[898,35784,1712],{},[1762,35786,1764],{},[902,35788,5809],{"encoding":904}," za ",[883,35791,35793],{"className":35792},[886],[888,35794,35795],{"xmlns":890},[892,35796,35797,35805],{},[895,35798,35799],{},[3284,35800,35801,35803],{},[898,35802,1712],{},[1762,35804,2398],{},[902,35806,5790],{"encoding":904}," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,35809,35811],{"className":35810},[886],[888,35812,35813],{"xmlns":890},[892,35814,35815,35835],{},[895,35816,35817,35819,35821,35827,35829],{},[1915,35818,5315],{},[1693,35820,1922],{},[3284,35822,35823,35825],{},[898,35824,1701],{},[1762,35826,1764],{},[898,35828,1705],{"mathvariant":1704},[3284,35830,35831,35833],{},[898,35832,1701],{},[1762,35834,2398],{},[902,35836,35837],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,35840,35842],{"className":35841},[886],[888,35843,35844],{"xmlns":890},[892,35845,35846,35854],{},[895,35847,35848],{},[3284,35849,35850,35852],{},[898,35851,1712],{},[1762,35853,1764],{},[902,35855,5809],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,35858,35860],{"className":35859},[886],[888,35861,35862],{"xmlns":890},[892,35863,35864,35884],{},[895,35865,35866,35868,35870,35876,35878],{},[1915,35867,5315],{},[1693,35869,1908],{},[3284,35871,35872,35874],{},[898,35873,1701],{},[1762,35875,1764],{},[898,35877,1705],{"mathvariant":1704},[3284,35879,35880,35882],{},[898,35881,1701],{},[1762,35883,2398],{},[902,35885,35886],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,35889,35891,35892,35905],{"id":35890},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,35893,35895],{"className":35894},[886],[888,35896,35897],{"xmlns":890},[892,35898,35899,35903],{},[895,35900,35901],{},[898,35902,5957],{},[902,35904,6054],{"encoding":904}," — mezní užitečnost důchodu",[724,35907,35908,35909,35927,35928,35931,35932,35949,35950,35967,35968,35970],{},"Lagrangeův multiplikátor ",[883,35910,35912],{"className":35911},[886],[888,35913,35914],{"xmlns":890},[892,35915,35916,35924],{},[895,35917,35918],{},[1717,35919,35920,35922],{},[898,35921,5957],{},[1693,35923,3672],{},[902,35925,35926],{"encoding":904},"\\lambda^*"," představuje ",[38,35929,35930],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,35933,35935],{"className":35934},[886],[888,35936,35937],{"xmlns":890},[892,35938,35939,35947],{},[895,35940,35941],{},[1717,35942,35943,35945],{},[898,35944,900],{},[1693,35946,3672],{},[902,35948,34750],{"encoding":904}," při jednotkové změně důchodu ",[883,35951,35953],{"className":35952},[886],[888,35954,35955],{"xmlns":890},[892,35956,35957,35965],{},[895,35958,35959],{},[1717,35960,35961,35963],{},[898,35962,4618],{},[1693,35964,3672],{},[902,35966,34816],{"encoding":904},". Je to ",[38,35969,6058],{}," rozpočtového omezení.",[1636,35972,35973,35978],{},[724,35974,35975,35977],{},[883,35976,8620],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,35979,35980,36040,36127,36163,36250],{},[123,35981,35982,35985,35986,1789],{},[38,35983,35984],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,35987,35989],{"className":35988},[886],[888,35990,35991],{"xmlns":890},[892,35992,35993,36037],{},[895,35994,35995,36001,36003,36011,36017,36019,36027,36033,36035],{},[1717,35996,35997,35999],{},[898,35998,4618],{},[1693,36000,3672],{},[1693,36002,1698],{},[5688,36004,36005,36007,36009],{},[898,36006,1701],{},[1762,36008,1764],{},[1693,36010,3672],{},[3284,36012,36013,36015],{},[898,36014,1712],{},[1762,36016,1764],{},[1693,36018,1698],{},[5688,36020,36021,36023,36025],{},[898,36022,1701],{},[1762,36024,2398],{},[1693,36026,3672],{},[3284,36028,36029,36031],{},[898,36030,1712],{},[1762,36032,2398],{},[1693,36034,1695],{},[1762,36036,1911],{},[902,36038,36039],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,36041,36042,1863,36045,1789],{},[38,36043,36044],{},"Sestav Lagrangeovu funkci",[883,36046,36048],{"className":36047},[886],[888,36049,36050],{"xmlns":890},[892,36051,36052,36124],{},[895,36053,36054,36056,36058,36060,36062,36068,36070,36076,36078,36080,36082,36084,36090,36092,36100,36106,36108,36116,36122],{},[898,36055,4840],{"mathvariant":5936},[1693,36057,1695],{},[898,36059,900],{},[1693,36061,1709],{"stretchy":1708},[3284,36063,36064,36066],{},[898,36065,1712],{},[1762,36067,1764],{},[1693,36069,1899],{"separator":1898},[3284,36071,36072,36074],{},[898,36073,1712],{},[1762,36075,2398],{},[1693,36077,1731],{"stretchy":1708},[1693,36079,1892],{},[898,36081,5957],{},[1693,36083,1709],{"stretchy":1708},[1717,36085,36086,36088],{},[898,36087,4618],{},[1693,36089,3672],{},[1693,36091,1698],{},[5688,36093,36094,36096,36098],{},[898,36095,1701],{},[1762,36097,1764],{},[1693,36099,3672],{},[3284,36101,36102,36104],{},[898,36103,1712],{},[1762,36105,1764],{},[1693,36107,1698],{},[5688,36109,36110,36112,36114],{},[898,36111,1701],{},[1762,36113,2398],{},[1693,36115,3672],{},[3284,36117,36118,36120],{},[898,36119,1712],{},[1762,36121,2398],{},[1693,36123,1731],{"stretchy":1708},[902,36125,36126],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,36128,36129,2884,36132,36162],{},[38,36130,36131],{},"Spočítej parciální derivace",[883,36133,36135],{"className":36134},[886],[888,36136,36137],{"xmlns":890},[892,36138,36139,36159],{},[895,36140,36141,36147,36149,36155,36157],{},[3284,36142,36143,36145],{},[898,36144,1712],{},[1762,36146,1764],{},[1693,36148,1899],{"separator":1898},[3284,36150,36151,36153],{},[898,36152,1712],{},[1762,36154,2398],{},[1693,36156,1899],{"separator":1898},[898,36158,5957],{},[902,36160,36161],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,36164,36165,36181,36182,36215,36216,4286,36233,1789],{},[38,36166,36167,36168],{},"Vyluč ",[883,36169,36171],{"className":36170},[886],[888,36172,36173],{"xmlns":890},[892,36174,36175,36179],{},[895,36176,36177],{},[898,36178,5957],{},[902,36180,6054],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,36183,36185],{"className":36184},[886],[888,36186,36187],{"xmlns":890},[892,36188,36189,36213],{},[895,36190,36191,36193,36195,36203,36205],{},[1915,36192,5315],{},[1693,36194,1695],{},[5688,36196,36197,36199,36201],{},[898,36198,1701],{},[1762,36200,1764],{},[1693,36202,3672],{},[898,36204,1705],{"mathvariant":1704},[5688,36206,36207,36209,36211],{},[898,36208,1701],{},[1762,36210,2398],{},[1693,36212,3672],{},[902,36214,35766],{"encoding":904},", která dá vztah mezi ",[883,36217,36219],{"className":36218},[886],[888,36220,36221],{"xmlns":890},[892,36222,36223,36231],{},[895,36224,36225],{},[3284,36226,36227,36229],{},[898,36228,1712],{},[1762,36230,1764],{},[902,36232,5809],{"encoding":904},[883,36234,36236],{"className":36235},[886],[888,36237,36238],{"xmlns":890},[892,36239,36240,36248],{},[895,36241,36242],{},[3284,36243,36244,36246],{},[898,36245,1712],{},[1762,36247,2398],{},[902,36249,5790],{"encoding":904},[123,36251,36252,36255,36256,36286,36287,36304,36305,1789],{},[38,36253,36254],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,36257,36259],{"className":36258},[886],[888,36260,36261],{"xmlns":890},[892,36262,36263,36283],{},[895,36264,36265,36273,36275],{},[5688,36266,36267,36269,36271],{},[898,36268,1712],{},[1762,36270,1764],{},[1693,36272,3672],{},[1693,36274,1899],{"separator":1898},[5688,36276,36277,36279,36281],{},[898,36278,1712],{},[1762,36280,2398],{},[1693,36282,3672],{},[902,36284,36285],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,36288,36290],{"className":36289},[886],[888,36291,36292],{"xmlns":890},[892,36293,36294,36302],{},[895,36295,36296],{},[1717,36297,36298,36300],{},[898,36299,5957],{},[1693,36301,3672],{},[902,36303,35926],{"encoding":904}," a maximální užitečnost ",[883,36306,36308],{"className":36307},[886],[888,36309,36310],{"xmlns":890},[892,36311,36312,36346],{},[895,36313,36314,36320,36322,36324,36326,36334,36336,36344],{},[1717,36315,36316,36318],{},[898,36317,900],{},[1693,36319,3672],{},[1693,36321,1695],{},[898,36323,900],{},[1693,36325,1709],{"stretchy":1708},[5688,36327,36328,36330,36332],{},[898,36329,1712],{},[1762,36331,1764],{},[1693,36333,3672],{},[1693,36335,1899],{"separator":1898},[5688,36337,36338,36340,36342],{},[898,36339,1712],{},[1762,36341,2398],{},[1693,36343,3672],{},[1693,36345,1731],{"stretchy":1708},[902,36347,36348],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,36350,36352],{"id":36351},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,36354,36355],{},[9465,36356],{"alt":36357,"className":36358,"src":36359},"imek-uzitecnost-optimum",[210,9469],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,36361,36362],{},[614,36363,36364,36365,36414,36415,4286,36443,36471,36472,36506,36507,36546,36547,36565,36566,36584,36585,36603],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,36366,36368],{"className":36367},[886],[888,36369,36370],{"xmlns":890},[892,36371,36372,36412],{},[895,36373,36374,36380,36382,36390,36396,36398,36406],{},[1717,36375,36376,36378],{},[898,36377,4618],{},[1693,36379,3672],{},[1693,36381,1695],{},[5688,36383,36384,36386,36388],{},[898,36385,1701],{},[1762,36387,1764],{},[1693,36389,3672],{},[3284,36391,36392,36394],{},[898,36393,1712],{},[1762,36395,1764],{},[1693,36397,1892],{},[5688,36399,36400,36402,36404],{},[898,36401,1701],{},[1762,36403,2398],{},[1693,36405,3672],{},[3284,36407,36408,36410],{},[898,36409,1712],{},[1762,36411,2398],{},[902,36413,24117],{"encoding":904}," protíná osy v ",[883,36416,36418],{"className":36417},[886],[888,36419,36420],{"xmlns":890},[892,36421,36422,36440],{},[895,36423,36424,36430,36432],{},[1717,36425,36426,36428],{},[898,36427,4618],{},[1693,36429,3672],{},[898,36431,1705],{"mathvariant":1704},[5688,36433,36434,36436,36438],{},[898,36435,1701],{},[1762,36437,1764],{},[1693,36439,3672],{},[902,36441,36442],{"encoding":904},"Y^*\u002FP_1^*",[883,36444,36446],{"className":36445},[886],[888,36447,36448],{"xmlns":890},[892,36449,36450,36468],{},[895,36451,36452,36458,36460],{},[1717,36453,36454,36456],{},[898,36455,4618],{},[1693,36457,3672],{},[898,36459,1705],{"mathvariant":1704},[5688,36461,36462,36464,36466],{},[898,36463,1701],{},[1762,36465,2398],{},[1693,36467,3672],{},[902,36469,36470],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,36473,36475],{"className":36474},[886],[888,36476,36477],{"xmlns":890},[892,36478,36479,36503],{},[895,36480,36481,36487,36489,36495,36497],{},[3284,36482,36483,36485],{},[898,36484,2000],{},[1762,36486,1764],{},[1693,36488,1908],{},[1717,36490,36491,36493],{},[898,36492,2000],{},[1693,36494,3672],{},[1693,36496,1908],{},[3284,36498,36499,36501],{},[898,36500,2000],{},[1762,36502,2398],{},[902,36504,36505],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,36508,36510],{"className":36509},[886],[888,36511,36512],{"xmlns":890},[892,36513,36514,36544],{},[895,36515,36516,36522,36524,36532,36534,36542],{},[1717,36517,36518,36520],{},[898,36519,1712],{},[1693,36521,3672],{},[1693,36523,9392],{"stretchy":1708},[5688,36525,36526,36528,36530],{},[898,36527,1712],{},[1762,36529,1764],{},[1693,36531,3672],{},[1693,36533,1899],{"separator":1898},[5688,36535,36536,36538,36540],{},[898,36537,1712],{},[1762,36539,2398],{},[1693,36541,3672],{},[1693,36543,9407],{"stretchy":1708},[902,36545,35115],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,36548,36550],{"className":36549},[886],[888,36551,36552],{"xmlns":890},[892,36553,36554,36562],{},[895,36555,36556],{},[1717,36557,36558,36560],{},[898,36559,2000],{},[1693,36561,3672],{},[902,36563,36564],{"encoding":904},"c^*",". Křivka ",[883,36567,36569],{"className":36568},[886],[888,36570,36571],{"xmlns":890},[892,36572,36573,36581],{},[895,36574,36575],{},[3284,36576,36577,36579],{},[898,36578,2000],{},[1762,36580,1764],{},[902,36582,36583],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,36586,36588],{"className":36587},[886],[888,36589,36590],{"xmlns":890},[892,36591,36592,36600],{},[895,36593,36594],{},[3284,36595,36596,36598],{},[898,36597,2000],{},[1762,36599,2398],{},[902,36601,36602],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,36605,36606,36607,36610,36611,36628,36629,36658],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,36608,36609],{},"dotýkají",", tj. mají v bodě ",[883,36612,36614],{"className":36613},[886],[888,36615,36616],{"xmlns":890},[892,36617,36618,36626],{},[895,36619,36620],{},[1717,36621,36622,36624],{},[898,36623,1712],{},[1693,36625,3672],{},[902,36627,3770],{"encoding":904}," společnou tečnu. To přímo převádí podmínku ",[883,36630,36632],{"className":36631},[886],[888,36633,36634],{"xmlns":890},[892,36635,36636,36656],{},[895,36637,36638,36640,36642,36648,36650],{},[1915,36639,5315],{},[1693,36641,1695],{},[3284,36643,36644,36646],{},[898,36645,1701],{},[1762,36647,1764],{},[898,36649,1705],{"mathvariant":1704},[3284,36651,36652,36654],{},[898,36653,1701],{},[1762,36655,2398],{},[902,36657,34786],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,36660,36662],{"id":36661},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,36664,16518,36665,36727],{},[883,36666,36668],{"className":36667},[886],[888,36669,36670],{"xmlns":890},[892,36671,36672,36724],{},[895,36673,36674,36676,36678,36684,36686,36692,36694,36696,36710],{},[898,36675,900],{},[1693,36677,1709],{"stretchy":1708},[3284,36679,36680,36682],{},[898,36681,1712],{},[1762,36683,1764],{},[1693,36685,1899],{"separator":1898},[3284,36687,36688,36690],{},[898,36689,1712],{},[1762,36691,2398],{},[1693,36693,1731],{"stretchy":1708},[1693,36695,1695],{},[5688,36697,36698,36700,36702],{},[898,36699,1712],{},[1762,36701,1764],{},[895,36703,36704,36706,36708],{},[1762,36705,1764],{},[898,36707,1705],{"mathvariant":1704},[1762,36709,2398],{},[5688,36711,36712,36714,36716],{},[898,36713,1712],{},[1762,36715,2398],{},[895,36717,36718,36720,36722],{},[1762,36719,1764],{},[898,36721,1705],{"mathvariant":1704},[1762,36723,2398],{},[902,36725,36726],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,36729,36730],{},[883,36731,36733],{"className":36732},[886],[888,36734,36735],{"xmlns":890},[892,36736,36737,36843],{},[895,36738,36739,36741,36743,36825,36827,36841],{},[1915,36740,5315],{},[1693,36742,1695],{},[2132,36744,36745,36785],{},[895,36746,36747,36755,36771],{},[3638,36748,36749],{"scriptlevel":1911,"displaystyle":1708},[2132,36750,36751,36753],{},[1762,36752,1764],{},[1762,36754,2398],{},[5688,36756,36757,36759,36761],{},[898,36758,1712],{},[1762,36760,1764],{},[895,36762,36763,36765,36767,36769],{},[1693,36764,1698],{},[1762,36766,1764],{},[898,36768,1705],{"mathvariant":1704},[1762,36770,2398],{},[5688,36772,36773,36775,36777],{},[898,36774,1712],{},[1762,36776,2398],{},[895,36778,36779,36781,36783],{},[1762,36780,1764],{},[898,36782,1705],{"mathvariant":1704},[1762,36784,2398],{},[895,36786,36787,36795,36809],{},[3638,36788,36789],{"scriptlevel":1911,"displaystyle":1708},[2132,36790,36791,36793],{},[1762,36792,1764],{},[1762,36794,2398],{},[5688,36796,36797,36799,36801],{},[898,36798,1712],{},[1762,36800,1764],{},[895,36802,36803,36805,36807],{},[1762,36804,1764],{},[898,36806,1705],{"mathvariant":1704},[1762,36808,2398],{},[5688,36810,36811,36813,36815],{},[898,36812,1712],{},[1762,36814,2398],{},[895,36816,36817,36819,36821,36823],{},[1693,36818,1698],{},[1762,36820,1764],{},[898,36822,1705],{"mathvariant":1704},[1762,36824,2398],{},[1693,36826,1695],{},[2132,36828,36829,36835],{},[3284,36830,36831,36833],{},[898,36832,1712],{},[1762,36834,2398],{},[3284,36836,36837,36839],{},[898,36838,1712],{},[1762,36840,1764],{},[898,36842,1789],{"mathvariant":1704},[902,36844,36845],{"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}.",[724,36847,36848,36849,7617,36894,36896,36897,36917,36918,36948,36949,1789],{},"Tedy ",[883,36850,36852],{"className":36851},[886],[888,36853,36854],{"xmlns":890},[892,36855,36856,36891],{},[895,36857,36858,36860,36862,36865,36867,36869,36871,36873,36881,36883],{},[1915,36859,5315],{},[1693,36861,1709],{"stretchy":1708},[1762,36863,36864],{},"300",[1693,36866,1899],{"separator":1898},[1762,36868,21936],{},[1693,36870,1731],{"stretchy":1708},[1693,36872,1695],{},[3638,36874,36875],{"scriptlevel":1911,"displaystyle":1708},[2132,36876,36877,36879],{},[1762,36878,21936],{},[1762,36880,36864],{},[1693,36882,1695],{},[3638,36884,36885],{"scriptlevel":1911,"displaystyle":1708},[2132,36886,36887,36889],{},[1762,36888,9147],{},[1762,36890,8357],{},[902,36892,36893],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,36895,16071],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,36898,36900],{"className":36899},[886],[888,36901,36902],{"xmlns":890},[892,36903,36904,36914],{},[895,36905,36906],{},[3638,36907,36908],{"scriptlevel":1911,"displaystyle":1708},[2132,36909,36910,36912],{},[1762,36911,9147],{},[1762,36913,8357],{},[902,36915,36916],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,36919,36921],{"className":36920},[886],[888,36922,36923],{"xmlns":890},[892,36924,36925,36945],{},[895,36926,36927,36929,36931,36937,36939],{},[1915,36928,5315],{},[1693,36930,1695],{},[3284,36932,36933,36935],{},[898,36934,1712],{},[1762,36936,2398],{},[898,36938,1705],{"mathvariant":1704},[3284,36940,36941,36943],{},[898,36942,1712],{},[1762,36944,1764],{},[902,36946,36947],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,36950,36952],{"className":36951},[886],[888,36953,36954],{"xmlns":890},[892,36955,36956,36976],{},[895,36957,36958,36960,36962,36968,36970],{},[1915,36959,5315],{},[1693,36961,1695],{},[3284,36963,36964,36966],{},[898,36965,1701],{},[1762,36967,1764],{},[898,36969,1705],{"mathvariant":1704},[3284,36971,36972,36974],{},[898,36973,1701],{},[1762,36975,2398],{},[902,36977,34786],{"encoding":904},[115,36979,36981,36982],{"id":36980},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,36983,36985],{"className":36984},[886],[888,36986,36987],{"xmlns":890},[892,36988,36989,37007],{},[895,36990,36991,36993,36995,37001],{},[898,36992,900],{},[1693,36994,1695],{},[3284,36996,36997,36999],{},[898,36998,1712],{},[1762,37000,1764],{},[3284,37002,37003,37005],{},[898,37004,1712],{},[1762,37006,2398],{},[902,37008,37009],{"encoding":904},"U = Q_1 Q_2",[724,37011,37012,37013,1343,37059,1343,37083,1343,37107,37129],{},"Je dána ",[883,37014,37016],{"className":37015},[886],[888,37017,37018],{"xmlns":890},[892,37019,37020,37056],{},[895,37021,37022,37024,37026,37032,37034,37040,37042,37044,37050],{},[898,37023,900],{},[1693,37025,1709],{"stretchy":1708},[3284,37027,37028,37030],{},[898,37029,1712],{},[1762,37031,1764],{},[1693,37033,1899],{"separator":1898},[3284,37035,37036,37038],{},[898,37037,1712],{},[1762,37039,2398],{},[1693,37041,1731],{"stretchy":1708},[1693,37043,1695],{},[3284,37045,37046,37048],{},[898,37047,1712],{},[1762,37049,1764],{},[3284,37051,37052,37054],{},[898,37053,1712],{},[1762,37055,2398],{},[902,37057,37058],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,37060,37062],{"className":37061},[886],[888,37063,37064],{"xmlns":890},[892,37065,37066,37080],{},[895,37067,37068,37076,37078],{},[5688,37069,37070,37072,37074],{},[898,37071,1701],{},[1762,37073,1764],{},[1693,37075,3672],{},[1693,37077,1695],{},[1762,37079,2398],{},[902,37081,37082],{"encoding":904},"P_1^* = 2",[883,37084,37086],{"className":37085},[886],[888,37087,37088],{"xmlns":890},[892,37089,37090,37104],{},[895,37091,37092,37100,37102],{},[5688,37093,37094,37096,37098],{},[898,37095,1701],{},[1762,37097,2398],{},[1693,37099,3672],{},[1693,37101,1695],{},[1762,37103,9147],{},[902,37105,37106],{"encoding":904},"P_2^* = 5",[883,37108,37110],{"className":37109},[886],[888,37111,37112],{"xmlns":890},[892,37113,37114,37126],{},[895,37115,37116,37122,37124],{},[1717,37117,37118,37120],{},[898,37119,4618],{},[1693,37121,3672],{},[1693,37123,1695],{},[1762,37125,9987],{},[902,37127,37128],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,37131,37133],{"className":37132},[886],[888,37134,37135],{"xmlns":890,"display":34854},[892,37136,37137,37209],{},[895,37138,37139,37141,37143,37149,37151,37157,37159,37161,37163,37165,37171,37177,37179,37181,37183,37185,37187,37189,37195,37197,37199,37205,37207],{},[898,37140,4840],{"mathvariant":5936},[1693,37142,1709],{"stretchy":1708},[3284,37144,37145,37147],{},[898,37146,1712],{},[1762,37148,1764],{},[1693,37150,1899],{"separator":1898},[3284,37152,37153,37155],{},[898,37154,1712],{},[1762,37156,2398],{},[1693,37158,1899],{"separator":1898},[898,37160,5957],{},[1693,37162,1731],{"stretchy":1708},[1693,37164,1695],{},[3284,37166,37167,37169],{},[898,37168,1712],{},[1762,37170,1764],{},[3284,37172,37173,37175],{},[898,37174,1712],{},[1762,37176,2398],{},[1693,37178,1892],{},[898,37180,5957],{},[1693,37182,1709],{"stretchy":1708},[1762,37184,9987],{},[1693,37186,1698],{},[1762,37188,2398],{},[3284,37190,37191,37193],{},[898,37192,1712],{},[1762,37194,1764],{},[1693,37196,1698],{},[1762,37198,9147],{},[3284,37200,37201,37203],{},[898,37202,1712],{},[1762,37204,2398],{},[1693,37206,1731],{"stretchy":1708},[898,37208,1789],{"mathvariant":1704},[902,37210,37211],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,37213,37214],{},"Soustava:",[883,37216,37218],{"className":37217},[886],[888,37219,37220],{"xmlns":890,"display":34854},[892,37221,37222,37334],{},[3626,37223,37224,37258,37292],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,37225,37226,37244],{},[3635,37227,37228],{},[3638,37229,37230],{"scriptlevel":1911,"displaystyle":1898},[895,37231,37232,37238,37240,37242],{},[3284,37233,37234,37236],{},[898,37235,1712],{},[1762,37237,2398],{},[1693,37239,1698],{},[1762,37241,2398],{},[898,37243,5957],{},[3635,37245,37246],{},[3638,37247,37248],{"scriptlevel":1911,"displaystyle":1898},[895,37249,37250,37252,37254,37256],{},[895,37251],{},[1693,37253,1695],{},[1762,37255,1911],{},[1693,37257,1899],{"separator":1898},[3632,37259,37260,37278],{},[3635,37261,37262],{},[3638,37263,37264],{"scriptlevel":1911,"displaystyle":1898},[895,37265,37266,37272,37274,37276],{},[3284,37267,37268,37270],{},[898,37269,1712],{},[1762,37271,1764],{},[1693,37273,1698],{},[1762,37275,9147],{},[898,37277,5957],{},[3635,37279,37280],{},[3638,37281,37282],{"scriptlevel":1911,"displaystyle":1898},[895,37283,37284,37286,37288,37290],{},[895,37285],{},[1693,37287,1695],{},[1762,37289,1911],{},[1693,37291,1899],{"separator":1898},[3632,37293,37294,37322],{},[3635,37295,37296],{},[3638,37297,37298],{"scriptlevel":1911,"displaystyle":1898},[895,37299,37300,37302,37304,37306,37312,37314,37316],{},[1762,37301,9987],{},[1693,37303,1698],{},[1762,37305,2398],{},[3284,37307,37308,37310],{},[898,37309,1712],{},[1762,37311,1764],{},[1693,37313,1698],{},[1762,37315,9147],{},[3284,37317,37318,37320],{},[898,37319,1712],{},[1762,37321,2398],{},[3635,37323,37324],{},[3638,37325,37326],{"scriptlevel":1911,"displaystyle":1898},[895,37327,37328,37330,37332],{},[895,37329],{},[1693,37331,1695],{},[1762,37333,19295],{},[902,37335,37336],{"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}",[724,37338,37339,37340,1343,37364,37388,37389,12457,37429,37447,37448,37498,37499,1789],{},"Z prvních dvou rovnic ",[883,37341,37343],{"className":37342},[886],[888,37344,37345],{"xmlns":890},[892,37346,37347,37361],{},[895,37348,37349,37355,37357,37359],{},[3284,37350,37351,37353],{},[898,37352,1712],{},[1762,37354,2398],{},[1693,37356,1695],{},[1762,37358,2398],{},[898,37360,5957],{},[902,37362,37363],{"encoding":904},"Q_2 = 2\\lambda",[883,37365,37367],{"className":37366},[886],[888,37368,37369],{"xmlns":890},[892,37370,37371,37385],{},[895,37372,37373,37379,37381,37383],{},[3284,37374,37375,37377],{},[898,37376,1712],{},[1762,37378,1764],{},[1693,37380,1695],{},[1762,37382,9147],{},[898,37384,5957],{},[902,37386,37387],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,37390,37392],{"className":37391},[886],[888,37393,37394],{"xmlns":890},[892,37395,37396,37426],{},[895,37397,37398,37400,37402,37404,37406,37408,37410,37412,37414,37416,37418,37420,37422,37424],{},[1762,37399,9987],{},[1693,37401,1695],{},[1762,37403,2398],{},[1693,37405,1715],{},[1762,37407,9147],{},[898,37409,5957],{},[1693,37411,1892],{},[1762,37413,9147],{},[1693,37415,1715],{},[1762,37417,2398],{},[898,37419,5957],{},[1693,37421,1695],{},[1762,37423,15892],{},[898,37425,5957],{},[902,37427,37428],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,37430,37432],{"className":37431},[886],[888,37433,37434],{"xmlns":890},[892,37435,37436,37444],{},[895,37437,37438,37440,37442],{},[898,37439,5957],{},[1693,37441,1695],{},[1762,37443,9147],{},[902,37445,37446],{"encoding":904},"\\lambda = 5",". Odtud ",[38,37449,37450,1343,37474],{},[883,37451,37453],{"className":37452},[886],[888,37454,37455],{"xmlns":890},[892,37456,37457,37471],{},[895,37458,37459,37467,37469],{},[5688,37460,37461,37463,37465],{},[898,37462,1712],{},[1762,37464,1764],{},[1693,37466,3672],{},[1693,37468,1695],{},[1762,37470,11872],{},[902,37472,37473],{"encoding":904},"Q_1^* = 25",[883,37475,37477],{"className":37476},[886],[888,37478,37479],{"xmlns":890},[892,37480,37481,37495],{},[895,37482,37483,37491,37493],{},[5688,37484,37485,37487,37489],{},[898,37486,1712],{},[1762,37488,2398],{},[1693,37490,3672],{},[1693,37492,1695],{},[1762,37494,9763],{},[902,37496,37497],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,37500,37502],{"className":37501},[886],[888,37503,37504],{"xmlns":890},[892,37505,37506,37527],{},[895,37507,37508,37514,37516,37518,37520,37522,37524],{},[1717,37509,37510,37512],{},[898,37511,900],{},[1693,37513,3672],{},[1693,37515,1695],{},[1762,37517,11872],{},[1693,37519,1715],{},[1762,37521,9763],{},[1693,37523,1695],{},[1762,37525,37526],{},"250",[902,37528,37529],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,37531,37532],{},[614,37533,37534,37535,34925,37573,4286,37597,37621,37622,37652,37653,37677,37678,37700,37701,1789],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,37536,37538],{"className":37537},[886],[888,37539,37540],{"xmlns":890},[892,37541,37542,37570],{},[895,37543,37544,37546,37548,37550,37556,37558,37560,37566,37568],{},[1762,37545,9987],{},[1693,37547,1698],{},[1762,37549,2398],{},[3284,37551,37552,37554],{},[898,37553,1712],{},[1762,37555,1764],{},[1693,37557,1698],{},[1762,37559,9147],{},[3284,37561,37562,37564],{},[898,37563,1712],{},[1762,37565,2398],{},[1693,37567,1695],{},[1762,37569,1911],{},[902,37571,37572],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,37574,37576],{"className":37575},[886],[888,37577,37578],{"xmlns":890},[892,37579,37580,37594],{},[895,37581,37582,37584,37586,37588,37590,37592],{},[898,37583,2719],{},[1693,37585,9392],{"stretchy":1708},[1762,37587,1911],{},[1693,37589,1899],{"separator":1898},[1762,37591,15892],{},[1693,37593,9407],{"stretchy":1708},[902,37595,37596],{"encoding":904},"A[0, 20]",[883,37598,37600],{"className":37599},[886],[888,37601,37602],{"xmlns":890},[892,37603,37604,37618],{},[895,37605,37606,37608,37610,37612,37614,37616],{},[898,37607,7520],{},[1693,37609,9392],{"stretchy":1708},[1762,37611,10017],{},[1693,37613,1899],{"separator":1898},[1762,37615,1911],{},[1693,37617,9407],{"stretchy":1708},[902,37619,37620],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,37623,37625],{"className":37624},[886],[888,37626,37627],{"xmlns":890},[892,37628,37629,37649],{},[895,37630,37631,37637,37639,37641,37643],{},[3284,37632,37633,37635],{},[898,37634,1712],{},[1762,37636,2398],{},[1693,37638,1695],{},[1762,37640,37526],{},[898,37642,1705],{"mathvariant":1704},[3284,37644,37645,37647],{},[898,37646,1712],{},[1762,37648,1764],{},[902,37650,37651],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,37654,37656],{"className":37655},[886],[888,37657,37658],{"xmlns":890},[892,37659,37660,37674],{},[895,37661,37662,37664,37666,37668,37670,37672],{},[898,37663,1691],{},[1693,37665,9392],{"stretchy":1708},[1762,37667,11872],{},[1693,37669,1899],{"separator":1898},[1762,37671,9763],{},[1693,37673,9407],{"stretchy":1708},[902,37675,37676],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,37679,37681],{"className":37680},[886],[888,37682,37683],{"xmlns":890},[892,37684,37685,37697],{},[895,37686,37687,37689],{},[1693,37688,1698],{},[3638,37690,37691],{"scriptlevel":1911,"displaystyle":1708},[2132,37692,37693,37695],{},[1762,37694,2398],{},[1762,37696,9147],{},[902,37698,37699],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,37702,37704],{"className":37703},[886],[888,37705,37706],{"xmlns":890},[892,37707,37708,37748],{},[895,37709,37710,37712,37714,37716,37718,37720,37722,37724,37726,37728,37736,37738,37740],{},[1693,37711,1698],{},[1915,37713,5315],{},[1693,37715,1709],{"stretchy":1708},[1762,37717,11872],{},[1693,37719,1899],{"separator":1898},[1762,37721,9763],{},[1693,37723,1731],{"stretchy":1708},[1693,37725,1695],{},[1693,37727,1698],{},[3638,37729,37730],{"scriptlevel":1911,"displaystyle":1708},[2132,37731,37732,37734],{},[1762,37733,9763],{},[1762,37735,11872],{},[1693,37737,1695],{},[1693,37739,1698],{},[3638,37741,37742],{"scriptlevel":1911,"displaystyle":1708},[2132,37743,37744,37746],{},[1762,37745,2398],{},[1762,37747,9147],{},[902,37749,37750],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,37752,37754],{"id":37753},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,37756,37757,37758,35789,37788,37791,37792,4300],{},"Považujeme-li v úloze ",[883,37759,37761],{"className":37760},[886],[888,37762,37763],{"xmlns":890},[892,37764,37765,37785],{},[895,37766,37767,37773,37775,37781,37783],{},[3284,37768,37769,37771],{},[898,37770,1701],{},[1762,37772,1764],{},[1693,37774,1899],{"separator":1898},[3284,37776,37777,37779],{},[898,37778,1701],{},[1762,37780,2398],{},[1693,37782,1899],{"separator":1898},[898,37784,4618],{},[902,37786,37787],{"encoding":904},"P_1, P_2, Y",[38,37789,37790],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,37793,37794],{},"Marshallovy poptávkové funkce",[883,37796,37798],{"className":37797},[886],[888,37799,37800],{"xmlns":890,"display":34854},[892,37801,37802,37897],{},[3626,37803,37804],{"width":34859},[3632,37805,37806,37808,37890,37892],{},[3635,37807],{"width":34864},[3635,37809,37810],{},[895,37811,37812,37818,37820,37826,37828,37834,37836,37842,37844,37846,37848,37850,37852,37858,37860,37866,37868,37874,37876,37882,37884,37886,37888],{},[3284,37813,37814,37816],{},[898,37815,1712],{},[1762,37817,1764],{},[1693,37819,1695],{},[3284,37821,37822,37824],{},[898,37823,2738],{},[1762,37825,1764],{},[1693,37827,1709],{"stretchy":1708},[3284,37829,37830,37832],{},[898,37831,1701],{},[1762,37833,1764],{},[1693,37835,1899],{"separator":1898},[3284,37837,37838,37840],{},[898,37839,1701],{},[1762,37841,2398],{},[1693,37843,1899],{"separator":1898},[898,37845,4618],{},[1693,37847,1731],{"stretchy":1708},[1693,37849,1899],{"separator":1898},[1901,37851],{"width":3630},[3284,37853,37854,37856],{},[898,37855,1712],{},[1762,37857,2398],{},[1693,37859,1695],{},[3284,37861,37862,37864],{},[898,37863,2738],{},[1762,37865,2398],{},[1693,37867,1709],{"stretchy":1708},[3284,37869,37870,37872],{},[898,37871,1701],{},[1762,37873,1764],{},[1693,37875,1899],{"separator":1898},[3284,37877,37878,37880],{},[898,37879,1701],{},[1762,37881,2398],{},[1693,37883,1899],{"separator":1898},[898,37885,4618],{},[1693,37887,1731],{"stretchy":1708},[1693,37889,1899],{"separator":1898},[3635,37891],{"width":34864},[3635,37893,37894],{},[1915,37895,37896],{},"(6.15)",[902,37898,37899],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,37901,37903],{"className":37902},[886],[888,37904,37905],{"xmlns":890,"display":34854},[892,37906,37907,37954],{},[3626,37908,37909],{"width":34859},[3632,37910,37911,37913,37947,37949],{},[3635,37912],{"width":34864},[3635,37914,37915],{},[895,37916,37917,37919,37921,37923,37925,37931,37933,37939,37941,37943,37945],{},[898,37918,5957],{},[1693,37920,1695],{},[898,37922,5957],{},[1693,37924,1709],{"stretchy":1708},[3284,37926,37927,37929],{},[898,37928,1701],{},[1762,37930,1764],{},[1693,37932,1899],{"separator":1898},[3284,37934,37935,37937],{},[898,37936,1701],{},[1762,37938,2398],{},[1693,37940,1899],{"separator":1898},[898,37942,4618],{},[1693,37944,1731],{"stretchy":1708},[898,37946,1789],{"mathvariant":1704},[3635,37948],{"width":34864},[3635,37950,37951],{},[1915,37952,37953],{},"(6.16)",[902,37955,37956],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,37958,37959,37989,37990,38056],{},[38,37960,37961,37962,1789],{},"Odvození pro ",[883,37963,37965],{"className":37964},[886],[888,37966,37967],{"xmlns":890},[892,37968,37969,37987],{},[895,37970,37971,37973,37975,37981],{},[898,37972,900],{},[1693,37974,1695],{},[3284,37976,37977,37979],{},[898,37978,1712],{},[1762,37980,1764],{},[3284,37982,37983,37985],{},[898,37984,1712],{},[1762,37986,2398],{},[902,37988,37009],{"encoding":904}," Lagrangeova funkce ",[883,37991,37993],{"className":37992},[886],[888,37994,37995],{"xmlns":890},[892,37996,37997,38053],{},[895,37998,37999,38001,38003,38009,38015,38017,38019,38021,38023,38025,38031,38037,38039,38045,38051],{},[898,38000,4840],{"mathvariant":5936},[1693,38002,1695],{},[3284,38004,38005,38007],{},[898,38006,1712],{},[1762,38008,1764],{},[3284,38010,38011,38013],{},[898,38012,1712],{},[1762,38014,2398],{},[1693,38016,1892],{},[898,38018,5957],{},[1693,38020,1709],{"stretchy":1708},[898,38022,4618],{},[1693,38024,1698],{},[3284,38026,38027,38029],{},[898,38028,1701],{},[1762,38030,1764],{},[3284,38032,38033,38035],{},[898,38034,1712],{},[1762,38036,1764],{},[1693,38038,1698],{},[3284,38040,38041,38043],{},[898,38042,1701],{},[1762,38044,2398],{},[3284,38046,38047,38049],{},[898,38048,1712],{},[1762,38050,2398],{},[1693,38052,1731],{"stretchy":1708},[902,38054,38055],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,38058,38060],{"className":38059},[886],[888,38061,38062],{"xmlns":890,"display":34854},[892,38063,38064,38231],{},[3626,38065,38066],{"width":34859},[3632,38067,38068,38070,38224,38226],{},[3635,38069],{"width":34864},[3635,38071,38072],{},[3626,38073,38074,38120,38166],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,38075,38076,38088],{},[3635,38077,38078],{},[3638,38079,38080],{"scriptlevel":1911,"displaystyle":1898},[5688,38081,38082,38084,38086],{},[898,38083,4840],{"mathvariant":5936},[1762,38085,1764],{},[1693,38087,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,38089,38090],{},[3638,38091,38092],{"scriptlevel":1911,"displaystyle":1898},[895,38093,38094,38096,38098,38104,38106,38108,38114,38116,38118],{},[895,38095],{},[1693,38097,1695],{},[3284,38099,38100,38102],{},[898,38101,1712],{},[1762,38103,2398],{},[1693,38105,1698],{},[898,38107,5957],{},[3284,38109,38110,38112],{},[898,38111,1701],{},[1762,38113,1764],{},[1693,38115,1695],{},[1762,38117,1911],{},[1693,38119,1899],{"separator":1898},[3632,38121,38122,38134],{},[3635,38123,38124],{},[3638,38125,38126],{"scriptlevel":1911,"displaystyle":1898},[5688,38127,38128,38130,38132],{},[898,38129,4840],{"mathvariant":5936},[1762,38131,2398],{},[1693,38133,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,38135,38136],{},[3638,38137,38138],{"scriptlevel":1911,"displaystyle":1898},[895,38139,38140,38142,38144,38150,38152,38154,38160,38162,38164],{},[895,38141],{},[1693,38143,1695],{},[3284,38145,38146,38148],{},[898,38147,1712],{},[1762,38149,1764],{},[1693,38151,1698],{},[898,38153,5957],{},[3284,38155,38156,38158],{},[898,38157,1701],{},[1762,38159,2398],{},[1693,38161,1695],{},[1762,38163,1911],{},[1693,38165,1899],{"separator":1898},[3632,38167,38168,38180],{},[3635,38169,38170],{},[3638,38171,38172],{"scriptlevel":1911,"displaystyle":1898},[5688,38173,38174,38176,38178],{},[898,38175,4840],{"mathvariant":5936},[898,38177,5957],{},[1693,38179,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,38181,38182],{},[3638,38183,38184],{"scriptlevel":1911,"displaystyle":1898},[895,38185,38186,38188,38190,38192,38194,38200,38206,38208,38214,38220,38222],{},[895,38187],{},[1693,38189,1695],{},[898,38191,4618],{},[1693,38193,1698],{},[3284,38195,38196,38198],{},[898,38197,1701],{},[1762,38199,1764],{},[3284,38201,38202,38204],{},[898,38203,1712],{},[1762,38205,1764],{},[1693,38207,1698],{},[3284,38209,38210,38212],{},[898,38211,1701],{},[1762,38213,2398],{},[3284,38215,38216,38218],{},[898,38217,1712],{},[1762,38219,2398],{},[1693,38221,1695],{},[1762,38223,19295],{},[3635,38225],{"width":34864},[3635,38227,38228],{},[1915,38229,38230],{},"(6.17)",[902,38232,38233],{"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}",[724,38235,38236,38237,38265,38266,38294,38295,38363],{},"Z prvních dvou: ",[883,38238,38240],{"className":38239},[886],[888,38241,38242],{"xmlns":890},[892,38243,38244,38262],{},[895,38245,38246,38252,38254,38260],{},[3284,38247,38248,38250],{},[898,38249,1712],{},[1762,38251,2398],{},[1693,38253,1695],{},[3284,38255,38256,38258],{},[898,38257,1701],{},[1762,38259,1764],{},[898,38261,5957],{},[902,38263,38264],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,38267,38269],{"className":38268},[886],[888,38270,38271],{"xmlns":890},[892,38272,38273,38291],{},[895,38274,38275,38281,38283,38289],{},[3284,38276,38277,38279],{},[898,38278,1712],{},[1762,38280,1764],{},[1693,38282,1695],{},[3284,38284,38285,38287],{},[898,38286,1701],{},[1762,38288,2398],{},[898,38290,5957],{},[902,38292,38293],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,38296,38298],{"className":38297},[886],[888,38299,38300],{"xmlns":890},[892,38301,38302,38360],{},[895,38303,38304,38306,38308,38314,38316,38322,38324,38326,38332,38334,38340,38342,38344,38346,38352,38358],{},[898,38305,4618],{},[1693,38307,1695],{},[3284,38309,38310,38312],{},[898,38311,1701],{},[1762,38313,1764],{},[1693,38315,1715],{},[3284,38317,38318,38320],{},[898,38319,1701],{},[1762,38321,2398],{},[898,38323,5957],{},[1693,38325,1892],{},[3284,38327,38328,38330],{},[898,38329,1701],{},[1762,38331,2398],{},[1693,38333,1715],{},[3284,38335,38336,38338],{},[898,38337,1701],{},[1762,38339,1764],{},[898,38341,5957],{},[1693,38343,1695],{},[1762,38345,2398],{},[3284,38347,38348,38350],{},[898,38349,1701],{},[1762,38351,1764],{},[3284,38353,38354,38356],{},[898,38355,1701],{},[1762,38357,2398],{},[898,38359,5957],{},[902,38361,38362],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,38365,38367],{"className":38366},[886],[888,38368,38369],{"xmlns":890,"display":34854},[892,38370,38371,38414],{},[3626,38372,38373],{"width":34859},[3632,38374,38375,38377,38407,38409],{},[3635,38376],{"width":34864},[3635,38378,38379],{},[895,38380,38381,38383,38385,38405],{},[898,38382,5957],{},[1693,38384,1695],{},[2132,38386,38387,38389],{},[898,38388,4618],{},[895,38390,38391,38393,38399],{},[1762,38392,2398],{},[3284,38394,38395,38397],{},[898,38396,1701],{},[1762,38398,1764],{},[3284,38400,38401,38403],{},[898,38402,1701],{},[1762,38404,2398],{},[898,38406,1789],{"mathvariant":1704},[3635,38408],{"width":34864},[3635,38410,38411],{},[1915,38412,38413],{},"(6.20)",[902,38415,38416],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,38418,38419],{},"Zpětně:",[883,38421,38423],{"className":38422},[886],[888,38424,38425],{"xmlns":890,"display":34854},[892,38426,38427,38504],{},[3626,38428,38429],{"width":34859},[3632,38430,38431,38433,38497,38499],{},[3635,38432],{"width":34864},[3635,38434,38435],{},[19664,38436,38437],{"notation":19666},[3638,38438,38439],{"scriptlevel":1911,"displaystyle":1708},[3638,38440,38441],{"scriptlevel":1911,"displaystyle":1708},[3638,38442,38443],{"scriptlevel":1911,"displaystyle":1898},[895,38444,38445,38447,38453,38455,38469,38471,38473,38479,38481,38495],{},[1915,38446,1917],{},[3284,38448,38449,38451],{},[898,38450,1712],{},[1762,38452,1764],{},[1693,38454,1695],{},[2132,38456,38457,38459],{},[898,38458,4618],{},[895,38460,38461,38463],{},[1762,38462,2398],{},[3284,38464,38465,38467],{},[898,38466,1701],{},[1762,38468,1764],{},[1693,38470,1899],{"separator":1898},[1901,38472],{"width":3630},[3284,38474,38475,38477],{},[898,38476,1712],{},[1762,38478,2398],{},[1693,38480,1695],{},[2132,38482,38483,38485],{},[898,38484,4618],{},[895,38486,38487,38489],{},[1762,38488,2398],{},[3284,38490,38491,38493],{},[898,38492,1701],{},[1762,38494,2398],{},[1915,38496,1917],{},[3635,38498],{"width":34864},[3635,38500,38501],{},[1915,38502,38503],{},"(6.21)",[902,38505,38506],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,38508,38510],{"id":38509},"engelova-funkce","Engelova funkce",[724,38512,16518,38513,38516,38517,38520,38521,26676,38538,1343,38568,38598,38599,38633,38634,1343,38660,38686],{},[38,38514,38515],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,38518,38519],{},"Engelovou funkcí",": pro ",[883,38522,38524],{"className":38523},[886],[888,38525,38526],{"xmlns":890},[892,38527,38528,38536],{},[895,38529,38530,38532,38534],{},[898,38531,4618],{},[1693,38533,1695],{},[1762,38535,9987],{},[902,38537,27126],{"encoding":904},[883,38539,38541],{"className":38540},[886],[888,38542,38543],{"xmlns":890},[892,38544,38545,38565],{},[895,38546,38547,38553,38555,38557,38559],{},[3284,38548,38549,38551],{},[898,38550,1712],{},[1762,38552,1764],{},[1693,38554,1695],{},[1762,38556,10017],{},[898,38558,1705],{"mathvariant":1704},[3284,38560,38561,38563],{},[898,38562,1701],{},[1762,38564,1764],{},[902,38566,38567],{"encoding":904},"Q_1 = 50\u002FP_1",[883,38569,38571],{"className":38570},[886],[888,38572,38573],{"xmlns":890},[892,38574,38575,38595],{},[895,38576,38577,38583,38585,38587,38589],{},[3284,38578,38579,38581],{},[898,38580,1712],{},[1762,38582,2398],{},[1693,38584,1695],{},[1762,38586,10017],{},[898,38588,1705],{"mathvariant":1704},[3284,38590,38591,38593],{},[898,38592,1701],{},[1762,38594,2398],{},[902,38596,38597],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,38600,38602],{"className":38601},[886],[888,38603,38604],{"xmlns":890},[892,38605,38606,38630],{},[895,38607,38608,38614,38616,38618,38620,38626,38628],{},[3284,38609,38610,38612],{},[898,38611,1701],{},[1762,38613,1764],{},[1693,38615,1695],{},[1762,38617,9763],{},[1693,38619,1899],{"separator":1898},[3284,38621,38622,38624],{},[898,38623,1701],{},[1762,38625,2398],{},[1693,38627,1695],{},[1762,38629,15892],{},[902,38631,38632],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,38635,38637],{"className":38636},[886],[888,38638,38639],{"xmlns":890},[892,38640,38641,38657],{},[895,38642,38643,38649,38651,38653,38655],{},[3284,38644,38645,38647],{},[898,38646,1712],{},[1762,38648,1764],{},[1693,38650,1695],{},[898,38652,4618],{},[898,38654,1705],{"mathvariant":1704},[1762,38656,15892],{},[902,38658,38659],{"encoding":904},"Q_1 = Y\u002F20",[883,38661,38663],{"className":38662},[886],[888,38664,38665],{"xmlns":890},[892,38666,38667,38683],{},[895,38668,38669,38675,38677,38679,38681],{},[3284,38670,38671,38673],{},[898,38672,1712],{},[1762,38674,2398],{},[1693,38676,1695],{},[898,38678,4618],{},[898,38680,1705],{"mathvariant":1704},[1762,38682,12079],{},[902,38684,38685],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,38688,38690],{"id":38689},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,38692,38693],{},"Výdaje spotřebitele jsou",[883,38695,38697],{"className":38696},[886],[888,38698,38699],{"xmlns":890,"display":34854},[892,38700,38701,38776],{},[3626,38702,38703],{"width":34859},[3632,38704,38705,38707,38769,38771],{},[3635,38706],{"width":34864},[3635,38708,38709],{},[895,38710,38711,38713,38715,38717,38719,38725,38727,38733,38735,38737,38745,38751,38753,38761,38767],{},[898,38712,1691],{},[1693,38714,1695],{},[898,38716,1691],{},[1693,38718,1709],{"stretchy":1708},[3284,38720,38721,38723],{},[898,38722,1712],{},[1762,38724,1764],{},[1693,38726,1899],{"separator":1898},[3284,38728,38729,38731],{},[898,38730,1712],{},[1762,38732,2398],{},[1693,38734,1731],{"stretchy":1708},[1693,38736,1695],{},[5688,38738,38739,38741,38743],{},[898,38740,1701],{},[1762,38742,1764],{},[1693,38744,3672],{},[3284,38746,38747,38749],{},[898,38748,1712],{},[1762,38750,1764],{},[1693,38752,1892],{},[5688,38754,38755,38757,38759],{},[898,38756,1701],{},[1762,38758,2398],{},[1693,38760,3672],{},[3284,38762,38763,38765],{},[898,38764,1712],{},[1762,38766,2398],{},[1693,38768,1899],{"separator":1898},[3635,38770],{"width":34864},[3635,38772,38773],{},[1915,38774,38775],{},"(6.22)",[902,38777,38778],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,38780,38781],{},"a je pevně zadána hladina užitečnosti",[883,38783,38785],{"className":38784},[886],[888,38786,38787],{"xmlns":890,"display":34854},[892,38788,38789,38836],{},[3626,38790,38791],{"width":34859},[3632,38792,38793,38795,38829,38831],{},[3635,38794],{"width":34864},[3635,38796,38797],{},[895,38798,38799,38805,38807,38809,38811,38817,38819,38825,38827],{},[1717,38800,38801,38803],{},[898,38802,900],{},[1693,38804,3672],{},[1693,38806,1695],{},[898,38808,900],{},[1693,38810,1709],{"stretchy":1708},[3284,38812,38813,38815],{},[898,38814,1712],{},[1762,38816,1764],{},[1693,38818,1899],{"separator":1898},[3284,38820,38821,38823],{},[898,38822,1712],{},[1762,38824,2398],{},[1693,38826,1731],{"stretchy":1708},[898,38828,1789],{"mathvariant":1704},[3635,38830],{"width":34864},[3635,38832,38833],{},[1915,38834,38835],{},"(6.23)",[902,38837,38838],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,38840,38841,38844,38845,38877,38878,1789],{},[38,38842,38843],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,38846,38848],{"className":38847},[886],[888,38849,38850],{"xmlns":890},[892,38851,38852,38874],{},[895,38853,38854,38856,38858,38864,38866,38872],{},[898,38855,1691],{},[1693,38857,1709],{"stretchy":1708},[3284,38859,38860,38862],{},[898,38861,1712],{},[1762,38863,1764],{},[1693,38865,1899],{"separator":1898},[3284,38867,38868,38870],{},[898,38869,1712],{},[1762,38871,2398],{},[1693,38873,1731],{"stretchy":1708},[902,38875,38876],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,38879,38881],{"className":38880},[886],[888,38882,38883],{"xmlns":890},[892,38884,38885,38941],{},[895,38886,38887,38889,38891,38897,38899,38905,38907,38909,38915,38917,38919,38921,38927,38929,38935,38937,38939],{},[898,38888,17887],{},[1693,38890,1709],{"stretchy":1708},[3284,38892,38893,38895],{},[898,38894,1712],{},[1762,38896,1764],{},[1693,38898,1899],{"separator":1898},[3284,38900,38901,38903],{},[898,38902,1712],{},[1762,38904,2398],{},[1693,38906,1731],{"stretchy":1708},[1693,38908,1695],{},[1717,38910,38911,38913],{},[898,38912,900],{},[1693,38914,3672],{},[1693,38916,1698],{},[898,38918,900],{},[1693,38920,1709],{"stretchy":1708},[3284,38922,38923,38925],{},[898,38924,1712],{},[1762,38926,1764],{},[1693,38928,1899],{"separator":1898},[3284,38930,38931,38933],{},[898,38932,1712],{},[1762,38934,2398],{},[1693,38936,1731],{"stretchy":1708},[1693,38938,1695],{},[1762,38940,1911],{},[902,38942,38943],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,38945,38947],{"id":38946},"lagrangeova-funkce","Lagrangeova funkce",[883,38949,38951],{"className":38950},[886],[888,38952,38953],{"xmlns":890,"display":34854},[892,38954,38955,39066],{},[3626,38956,38957],{"width":34859},[3632,38958,38959,38961,39059,39061],{},[3635,38960],{"width":34864},[3635,38962,38963],{},[895,38964,38965,38967,38969,38975,38977,38983,38985,38987,38989,38991,38999,39005,39007,39015,39021,39023,39025,39027,39033,39035,39037,39039,39045,39047,39053,39055,39057],{},[898,38966,4840],{"mathvariant":5936},[1693,38968,1709],{"stretchy":1708},[3284,38970,38971,38973],{},[898,38972,1712],{},[1762,38974,1764],{},[1693,38976,1899],{"separator":1898},[3284,38978,38979,38981],{},[898,38980,1712],{},[1762,38982,2398],{},[1693,38984,1899],{"separator":1898},[898,38986,5957],{},[1693,38988,1731],{"stretchy":1708},[1693,38990,1695],{},[5688,38992,38993,38995,38997],{},[898,38994,1701],{},[1762,38996,1764],{},[1693,38998,3672],{},[3284,39000,39001,39003],{},[898,39002,1712],{},[1762,39004,1764],{},[1693,39006,1892],{},[5688,39008,39009,39011,39013],{},[898,39010,1701],{},[1762,39012,2398],{},[1693,39014,3672],{},[3284,39016,39017,39019],{},[898,39018,1712],{},[1762,39020,2398],{},[1693,39022,1892],{},[898,39024,5957],{},[1693,39026,1709],{"stretchy":1708},[1717,39028,39029,39031],{},[898,39030,900],{},[1693,39032,3672],{},[1693,39034,1698],{},[898,39036,900],{},[1693,39038,1709],{"stretchy":1708},[3284,39040,39041,39043],{},[898,39042,1712],{},[1762,39044,1764],{},[1693,39046,1899],{"separator":1898},[3284,39048,39049,39051],{},[898,39050,1712],{},[1762,39052,2398],{},[1693,39054,1731],{"stretchy":1708},[1693,39056,1731],{"stretchy":1708},[898,39058,1789],{"mathvariant":1704},[3635,39060],{"width":34864},[3635,39062,39063],{},[1915,39064,39065],{},"(6.24)",[902,39067,39068],{"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}",[724,39070,39071],{},"Soustava podmínek prvního řádu:",[883,39073,39075],{"className":39074},[886],[888,39076,39077],{"xmlns":890,"display":34854},[892,39078,39079,39252],{},[3626,39080,39081],{"width":34859},[3632,39082,39083,39085,39245,39247],{},[3635,39084],{"width":34864},[3635,39086,39087],{},[3626,39088,39089,39139,39189],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,39090,39091,39103],{},[3635,39092,39093],{},[3638,39094,39095],{"scriptlevel":1911,"displaystyle":1898},[5688,39096,39097,39099,39101],{},[898,39098,4840],{"mathvariant":5936},[1762,39100,1764],{},[1693,39102,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,39104,39105],{},[3638,39106,39107],{"scriptlevel":1911,"displaystyle":1898},[895,39108,39109,39111,39113,39121,39123,39125,39133,39135,39137],{},[895,39110],{},[1693,39112,1695],{},[5688,39114,39115,39117,39119],{},[898,39116,1701],{},[1762,39118,1764],{},[1693,39120,3672],{},[1693,39122,1698],{},[898,39124,5957],{},[5688,39126,39127,39129,39131],{},[898,39128,900],{},[1762,39130,1764],{},[1693,39132,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,39134,1695],{},[1762,39136,1911],{},[1693,39138,1899],{"separator":1898},[3632,39140,39141,39153],{},[3635,39142,39143],{},[3638,39144,39145],{"scriptlevel":1911,"displaystyle":1898},[5688,39146,39147,39149,39151],{},[898,39148,4840],{"mathvariant":5936},[1762,39150,2398],{},[1693,39152,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,39154,39155],{},[3638,39156,39157],{"scriptlevel":1911,"displaystyle":1898},[895,39158,39159,39161,39163,39171,39173,39175,39183,39185,39187],{},[895,39160],{},[1693,39162,1695],{},[5688,39164,39165,39167,39169],{},[898,39166,1701],{},[1762,39168,2398],{},[1693,39170,3672],{},[1693,39172,1698],{},[898,39174,5957],{},[5688,39176,39177,39179,39181],{},[898,39178,900],{},[1762,39180,2398],{},[1693,39182,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,39184,1695],{},[1762,39186,1911],{},[1693,39188,1899],{"separator":1898},[3632,39190,39191,39203],{},[3635,39192,39193],{},[3638,39194,39195],{"scriptlevel":1911,"displaystyle":1898},[5688,39196,39197,39199,39201],{},[898,39198,4840],{"mathvariant":5936},[898,39200,5957],{},[1693,39202,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,39204,39205],{},[3638,39206,39207],{"scriptlevel":1911,"displaystyle":1898},[895,39208,39209,39211,39213,39219,39221,39223,39225,39231,39233,39239,39241,39243],{},[895,39210],{},[1693,39212,1695],{},[1717,39214,39215,39217],{},[898,39216,900],{},[1693,39218,3672],{},[1693,39220,1698],{},[898,39222,900],{},[1693,39224,1709],{"stretchy":1708},[3284,39226,39227,39229],{},[898,39228,1712],{},[1762,39230,1764],{},[1693,39232,1899],{"separator":1898},[3284,39234,39235,39237],{},[898,39236,1712],{},[1762,39238,2398],{},[1693,39240,1731],{"stretchy":1708},[1693,39242,1695],{},[1762,39244,19295],{},[3635,39246],{"width":34864},[3635,39248,39249],{},[1915,39250,39251],{},"(6.25)",[902,39253,39254],{"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}",[724,39256,39257],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,39259,39261],{"className":39260},[886],[888,39262,39263],{"xmlns":890,"display":34854},[892,39264,39265,39363],{},[3626,39266,39267],{"width":34859},[3632,39268,39269,39271,39356,39358],{},[3635,39270],{"width":34864},[3635,39272,39273],{},[895,39274,39275,39277,39279,39285,39287,39293,39295,39297,39299,39301,39303,39305,39354],{},[898,39276,2738],{},[1693,39278,1709],{"stretchy":1708},[3284,39280,39281,39283],{},[898,39282,1712],{},[1762,39284,1764],{},[1693,39286,1899],{"separator":1898},[3284,39288,39289,39291],{},[898,39290,1712],{},[1762,39292,2398],{},[1693,39294,1899],{"separator":1898},[898,39296,5957],{},[1693,39298,1731],{"stretchy":1708},[1693,39300,1695],{},[1693,39302,1698],{},[898,39304,5957],{},[895,39306,39307,39309,39321,39323,39336,39338,39340,39352],{},[1693,39308,1709],{"fence":1898},[5688,39310,39311,39313,39315],{},[898,39312,900],{},[1762,39314,9803],{},[895,39316,39317,39319],{},[1693,39318,1724],{"mathvariant":1704},[1693,39320,1724],{"mathvariant":1704},[1693,39322,1892],{},[5688,39324,39325,39327,39330],{},[898,39326,900],{},[1762,39328,39329],{},"22",[895,39331,39332,39334],{},[1693,39333,1724],{"mathvariant":1704},[1693,39335,1724],{"mathvariant":1704},[1693,39337,1892],{},[1762,39339,2398],{},[5688,39341,39342,39344,39346],{},[898,39343,900],{},[1762,39345,10402],{},[895,39347,39348,39350],{},[1693,39349,1724],{"mathvariant":1704},[1693,39351,1724],{"mathvariant":1704},[1693,39353,1731],{"fence":1898},[898,39355,1789],{"mathvariant":1704},[3635,39357],{"width":34864},[3635,39359,39360],{},[1915,39361,39362],{},"(6.26)",[902,39364,39365],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,39367,39368,39371,39372,39411,39412,39451,39452,39502,39503,39529,39530,39547,39548,39574],{},[38,39369,39370],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,39373,39375],{"className":39374},[886],[888,39376,39377],{"xmlns":890},[892,39378,39379,39409],{},[895,39380,39381,39387,39389,39397,39399,39407],{},[1717,39382,39383,39385],{},[898,39384,1712],{},[1693,39386,3672],{},[1693,39388,9392],{"stretchy":1708},[5688,39390,39391,39393,39395],{},[898,39392,1712],{},[1762,39394,1764],{},[1693,39396,3672],{},[1693,39398,1899],{"separator":1898},[5688,39400,39401,39403,39405],{},[898,39402,1712],{},[1762,39404,2398],{},[1693,39406,3672],{},[1693,39408,9407],{"stretchy":1708},[902,39410,35115],{"encoding":904}," dotyku křivky užitečnosti ",[883,39413,39415],{"className":39414},[886],[888,39416,39417],{"xmlns":890},[892,39418,39419,39449],{},[895,39420,39421,39427,39429,39431,39433,39439,39441,39447],{},[1717,39422,39423,39425],{},[898,39424,900],{},[1693,39426,3672],{},[1693,39428,1695],{},[898,39430,900],{},[1693,39432,1709],{"stretchy":1708},[3284,39434,39435,39437],{},[898,39436,1712],{},[1762,39438,1764],{},[1693,39440,1899],{"separator":1898},[3284,39442,39443,39445],{},[898,39444,1712],{},[1762,39446,2398],{},[1693,39448,1731],{"stretchy":1708},[902,39450,24484],{"encoding":904}," s přímkou výdajů ",[883,39453,39455],{"className":39454},[886],[888,39456,39457],{"xmlns":890},[892,39458,39459,39499],{},[895,39460,39461,39467,39469,39477,39483,39485,39493],{},[1717,39462,39463,39465],{},[898,39464,1691],{},[1693,39466,3672],{},[1693,39468,1695],{},[5688,39470,39471,39473,39475],{},[898,39472,1701],{},[1762,39474,1764],{},[1693,39476,3672],{},[3284,39478,39479,39481],{},[898,39480,1712],{},[1762,39482,1764],{},[1693,39484,1892],{},[5688,39486,39487,39489,39491],{},[898,39488,1701],{},[1762,39490,2398],{},[1693,39492,3672],{},[3284,39494,39495,39497],{},[898,39496,1712],{},[1762,39498,2398],{},[902,39500,39501],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,39504,39506],{"className":39505},[886],[888,39507,39508],{"xmlns":890},[892,39509,39510,39526],{},[895,39511,39512,39518,39520],{},[3284,39513,39514,39516],{},[898,39515,1691],{},[1762,39517,1911],{},[1693,39519,1908],{},[1717,39521,39522,39524],{},[898,39523,1691],{},[1693,39525,3672],{},[902,39527,39528],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,39531,39533],{"className":39532},[886],[888,39534,39535],{"xmlns":890},[892,39536,39537,39545],{},[895,39538,39539],{},[1717,39540,39541,39543],{},[898,39542,900],{},[1693,39544,3672],{},[902,39546,34750],{"encoding":904},", hladina ",[883,39549,39551],{"className":39550},[886],[888,39552,39553],{"xmlns":890},[892,39554,39555,39571],{},[895,39556,39557,39563,39565],{},[3284,39558,39559,39561],{},[898,39560,1691],{},[1762,39562,1764],{},[1693,39564,1922],{},[1717,39566,39567,39569],{},[898,39568,1691],{},[1693,39570,3672],{},[902,39572,39573],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1636,39576,39577,39582],{},[724,39578,39579,39581],{},[883,39580,8620],{}," Postup — duální úloha (minimalizace výdajů)",[152,39583,39584,39634,39720,39760,39835],{},[123,39585,39586,1863,39589,39633],{},[38,39587,39588],{},"Zapiš vazbu",[883,39590,39592],{"className":39591},[886],[888,39593,39594],{"xmlns":890},[892,39595,39596,39630],{},[895,39597,39598,39604,39606,39608,39610,39616,39618,39624,39626,39628],{},[1717,39599,39600,39602],{},[898,39601,900],{},[1693,39603,3672],{},[1693,39605,1698],{},[898,39607,900],{},[1693,39609,1709],{"stretchy":1708},[3284,39611,39612,39614],{},[898,39613,1712],{},[1762,39615,1764],{},[1693,39617,1899],{"separator":1898},[3284,39619,39620,39622],{},[898,39621,1712],{},[1762,39623,2398],{},[1693,39625,1731],{"stretchy":1708},[1693,39627,1695],{},[1762,39629,1911],{},[902,39631,39632],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,39635,39636,1863,39638,1789],{},[38,39637,36044],{},[883,39639,39641],{"className":39640},[886],[888,39642,39643],{"xmlns":890},[892,39644,39645,39717],{},[895,39646,39647,39649,39651,39659,39665,39667,39675,39681,39683,39685,39687,39693,39695,39697,39699,39705,39707,39713,39715],{},[898,39648,4840],{"mathvariant":5936},[1693,39650,1695],{},[5688,39652,39653,39655,39657],{},[898,39654,1701],{},[1762,39656,1764],{},[1693,39658,3672],{},[3284,39660,39661,39663],{},[898,39662,1712],{},[1762,39664,1764],{},[1693,39666,1892],{},[5688,39668,39669,39671,39673],{},[898,39670,1701],{},[1762,39672,2398],{},[1693,39674,3672],{},[3284,39676,39677,39679],{},[898,39678,1712],{},[1762,39680,2398],{},[1693,39682,1892],{},[898,39684,5957],{},[1693,39686,1709],{"stretchy":1708},[1717,39688,39689,39691],{},[898,39690,900],{},[1693,39692,3672],{},[1693,39694,1698],{},[898,39696,900],{},[1693,39698,1709],{"stretchy":1708},[3284,39700,39701,39703],{},[898,39702,1712],{},[1762,39704,1764],{},[1693,39706,1899],{"separator":1898},[3284,39708,39709,39711],{},[898,39710,1712],{},[1762,39712,2398],{},[1693,39714,1731],{"stretchy":1708},[1693,39716,1731],{"stretchy":1708},[902,39718,39719],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,39721,39722,39725,39726,39759],{},[38,39723,39724],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,39727,39729],{"className":39728},[886],[888,39730,39731],{"xmlns":890},[892,39732,39733,39757],{},[895,39734,39735,39737,39739,39747,39749],{},[1915,39736,5315],{},[1693,39738,1695],{},[5688,39740,39741,39743,39745],{},[898,39742,1701],{},[1762,39744,1764],{},[1693,39746,3672],{},[898,39748,1705],{"mathvariant":1704},[5688,39750,39751,39753,39755],{},[898,39752,1701],{},[1762,39754,2398],{},[1693,39756,3672],{},[902,39758,35766],{"encoding":904}," (stejná jako u maximalizace!).",[123,39761,39762,1863,39765,39805,39806,1789],{},[38,39763,39764],{},"Dosaď do vazby",[883,39766,39768],{"className":39767},[886],[888,39769,39770],{"xmlns":890},[892,39771,39772,39802],{},[895,39773,39774,39776,39778,39784,39786,39792,39794,39796],{},[898,39775,900],{},[1693,39777,1709],{"stretchy":1708},[3284,39779,39780,39782],{},[898,39781,1712],{},[1762,39783,1764],{},[1693,39785,1899],{"separator":1898},[3284,39787,39788,39790],{},[898,39789,1712],{},[1762,39791,2398],{},[1693,39793,1731],{"stretchy":1708},[1693,39795,1695],{},[1717,39797,39798,39800],{},[898,39799,900],{},[1693,39801,3672],{},[902,39803,39804],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,39807,39809],{"className":39808},[886],[888,39810,39811],{"xmlns":890},[892,39812,39813,39833],{},[895,39814,39815,39823,39825],{},[5688,39816,39817,39819,39821],{},[898,39818,1712],{},[1762,39820,1764],{},[1693,39822,3672],{},[1693,39824,1899],{"separator":1898},[5688,39826,39827,39829,39831],{},[898,39828,1712],{},[1762,39830,2398],{},[1693,39832,3672],{},[902,39834,36285],{"encoding":904},[123,39836,39837,1863,39840,39894],{},[38,39838,39839],{},"Vypočítej minimální výdaje",[883,39841,39843],{"className":39842},[886],[888,39844,39845],{"xmlns":890},[892,39846,39847,39891],{},[895,39848,39849,39855,39857,39865,39873,39875,39883],{},[1717,39850,39851,39853],{},[898,39852,1691],{},[1693,39854,3672],{},[1693,39856,1695],{},[5688,39858,39859,39861,39863],{},[898,39860,1701],{},[1762,39862,1764],{},[1693,39864,3672],{},[5688,39866,39867,39869,39871],{},[898,39868,1712],{},[1762,39870,1764],{},[1693,39872,3672],{},[1693,39874,1892],{},[5688,39876,39877,39879,39881],{},[898,39878,1701],{},[1762,39880,2398],{},[1693,39882,3672],{},[5688,39884,39885,39887,39889],{},[898,39886,1712],{},[1762,39888,2398],{},[1693,39890,3672],{},[902,39892,39893],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,39896,39898,39899],{"id":39897},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,39900,39902],{"className":39901},[886],[888,39903,39904],{"xmlns":890},[892,39905,39906,39940],{},[895,39907,39908,39910,39912,39926],{},[898,39909,900],{},[1693,39911,1695],{},[5688,39913,39914,39916,39918],{},[898,39915,1712],{},[1762,39917,1764],{},[895,39919,39920,39922,39924],{},[1762,39921,1764],{},[898,39923,1705],{"mathvariant":1704},[1762,39925,2398],{},[5688,39927,39928,39930,39932],{},[898,39929,1712],{},[1762,39931,2398],{},[895,39933,39934,39936,39938],{},[1762,39935,1764],{},[898,39937,1705],{"mathvariant":1704},[1762,39939,2398],{},[902,39941,39942],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,39944,39945,39946,1343,39968,1343,39992,37129],{},"Dáno ",[883,39947,39949],{"className":39948},[886],[888,39950,39951],{"xmlns":890},[892,39952,39953,39965],{},[895,39954,39955,39961,39963],{},[1717,39956,39957,39959],{},[898,39958,900],{},[1693,39960,3672],{},[1693,39962,1695],{},[1762,39964,2398],{},[902,39966,39967],{"encoding":904},"U^* = 2",[883,39969,39971],{"className":39970},[886],[888,39972,39973],{"xmlns":890},[892,39974,39975,39989],{},[895,39976,39977,39985,39987],{},[5688,39978,39979,39981,39983],{},[898,39980,1701],{},[1762,39982,1764],{},[1693,39984,3672],{},[1693,39986,1695],{},[1762,39988,30588],{},[902,39990,39991],{"encoding":904},"P_1^* = 0{,}25",[883,39993,39995],{"className":39994},[886],[888,39996,39997],{"xmlns":890},[892,39998,39999,40013],{},[895,40000,40001,40009,40011],{},[5688,40002,40003,40005,40007],{},[898,40004,1701],{},[1762,40006,2398],{},[1693,40008,3672],{},[1693,40010,1695],{},[1762,40012,1764],{},[902,40014,40015],{"encoding":904},"P_2^* = 1",[883,40017,40019],{"className":40018},[886],[888,40020,40021],{"xmlns":890,"display":34854},[892,40022,40023,40087],{},[895,40024,40025,40027,40029,40031,40037,40039,40045,40047,40049,40051,40053,40055,40069,40083,40085],{},[898,40026,4840],{"mathvariant":5936},[1693,40028,1695],{},[1762,40030,30588],{},[3284,40032,40033,40035],{},[898,40034,1712],{},[1762,40036,1764],{},[1693,40038,1892],{},[3284,40040,40041,40043],{},[898,40042,1712],{},[1762,40044,2398],{},[1693,40046,1892],{},[898,40048,5957],{},[1693,40050,1709],{"stretchy":1708},[1762,40052,2398],{},[1693,40054,1698],{},[5688,40056,40057,40059,40061],{},[898,40058,1712],{},[1762,40060,1764],{},[895,40062,40063,40065,40067],{},[1762,40064,1764],{},[898,40066,1705],{"mathvariant":1704},[1762,40068,2398],{},[5688,40070,40071,40073,40075],{},[898,40072,1712],{},[1762,40074,2398],{},[895,40076,40077,40079,40081],{},[1762,40078,1764],{},[898,40080,1705],{"mathvariant":1704},[1762,40082,2398],{},[1693,40084,1731],{"stretchy":1708},[898,40086,1789],{"mathvariant":1704},[902,40088,40089],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,40091,37214],{},[883,40093,40095],{"className":40094},[886],[888,40096,40097],{"xmlns":890,"display":34854},[892,40098,40099,40313],{},[3626,40100,40101,40177,40253],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,40102,40103,40115],{},[3635,40104,40105],{},[3638,40106,40107],{"scriptlevel":1911,"displaystyle":1898},[5688,40108,40109,40111,40113],{},[898,40110,4840],{"mathvariant":5936},[1762,40112,1764],{},[1693,40114,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,40116,40117],{},[3638,40118,40119],{"scriptlevel":1911,"displaystyle":1898},[895,40120,40121,40123,40125,40127,40129,40131,40133,40141,40157,40171,40173,40175],{},[895,40122],{},[1693,40124,1695],{},[1762,40126,30588],{},[1693,40128,1698],{},[898,40130,5957],{},[1693,40132,1715],{},[3638,40134,40135],{"scriptlevel":1911,"displaystyle":1708},[2132,40136,40137,40139],{},[1762,40138,1764],{},[1762,40140,2398],{},[5688,40142,40143,40145,40147],{},[898,40144,1712],{},[1762,40146,1764],{},[895,40148,40149,40151,40153,40155],{},[1693,40150,1698],{},[1762,40152,1764],{},[898,40154,1705],{"mathvariant":1704},[1762,40156,2398],{},[5688,40158,40159,40161,40163],{},[898,40160,1712],{},[1762,40162,2398],{},[895,40164,40165,40167,40169],{},[1762,40166,1764],{},[898,40168,1705],{"mathvariant":1704},[1762,40170,2398],{},[1693,40172,1695],{},[1762,40174,1911],{},[1693,40176,1899],{"separator":1898},[3632,40178,40179,40191],{},[3635,40180,40181],{},[3638,40182,40183],{"scriptlevel":1911,"displaystyle":1898},[5688,40184,40185,40187,40189],{},[898,40186,4840],{"mathvariant":5936},[1762,40188,2398],{},[1693,40190,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,40192,40193],{},[3638,40194,40195],{"scriptlevel":1911,"displaystyle":1898},[895,40196,40197,40199,40201,40203,40205,40207,40209,40217,40231,40247,40249,40251],{},[895,40198],{},[1693,40200,1695],{},[1762,40202,1764],{},[1693,40204,1698],{},[898,40206,5957],{},[1693,40208,1715],{},[3638,40210,40211],{"scriptlevel":1911,"displaystyle":1708},[2132,40212,40213,40215],{},[1762,40214,1764],{},[1762,40216,2398],{},[5688,40218,40219,40221,40223],{},[898,40220,1712],{},[1762,40222,1764],{},[895,40224,40225,40227,40229],{},[1762,40226,1764],{},[898,40228,1705],{"mathvariant":1704},[1762,40230,2398],{},[5688,40232,40233,40235,40237],{},[898,40234,1712],{},[1762,40236,2398],{},[895,40238,40239,40241,40243,40245],{},[1693,40240,1698],{},[1762,40242,1764],{},[898,40244,1705],{"mathvariant":1704},[1762,40246,2398],{},[1693,40248,1695],{},[1762,40250,1911],{},[1693,40252,1899],{"separator":1898},[3632,40254,40255,40267],{},[3635,40256,40257],{},[3638,40258,40259],{"scriptlevel":1911,"displaystyle":1898},[5688,40260,40261,40263,40265],{},[898,40262,4840],{"mathvariant":5936},[898,40264,5957],{},[1693,40266,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,40268,40269],{},[3638,40270,40271],{"scriptlevel":1911,"displaystyle":1898},[895,40272,40273,40275,40277,40279,40281,40295,40309,40311],{},[895,40274],{},[1693,40276,1695],{},[1762,40278,2398],{},[1693,40280,1698],{},[5688,40282,40283,40285,40287],{},[898,40284,1712],{},[1762,40286,1764],{},[895,40288,40289,40291,40293],{},[1762,40290,1764],{},[898,40292,1705],{"mathvariant":1704},[1762,40294,2398],{},[5688,40296,40297,40299,40301],{},[898,40298,1712],{},[1762,40300,2398],{},[895,40302,40303,40305,40307],{},[1762,40304,1764],{},[898,40306,1705],{"mathvariant":1704},[1762,40308,2398],{},[1693,40310,1695],{},[1762,40312,19295],{},[902,40314,40315],{"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}",[724,40317,40318,40319,24395,40349,40377,40378,12457,40440,1343,40490,40512,40513,1789],{},"Podílem prvních dvou rovnic: ",[883,40320,40322],{"className":40321},[886],[888,40323,40324],{"xmlns":890},[892,40325,40326,40346],{},[895,40327,40328,40330,40332,40338,40340],{},[1762,40329,30588],{},[1693,40331,1695],{},[3284,40333,40334,40336],{},[898,40335,1712],{},[1762,40337,2398],{},[898,40339,1705],{"mathvariant":1704},[3284,40341,40342,40344],{},[898,40343,1712],{},[1762,40345,1764],{},[902,40347,40348],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,40350,40352],{"className":40351},[886],[888,40353,40354],{"xmlns":890},[892,40355,40356,40374],{},[895,40357,40358,40364,40366,40368],{},[3284,40359,40360,40362],{},[898,40361,1712],{},[1762,40363,2398],{},[1693,40365,1695],{},[1762,40367,30588],{},[3284,40369,40370,40372],{},[898,40371,1712],{},[1762,40373,1764],{},[902,40375,40376],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,40379,40381],{"className":40380},[886],[888,40382,40383],{"xmlns":890},[892,40384,40385,40437],{},[895,40386,40387,40401,40403,40405,40411,40423,40425,40427,40433,40435],{},[5688,40388,40389,40391,40393],{},[898,40390,1712],{},[1762,40392,1764],{},[895,40394,40395,40397,40399],{},[1762,40396,1764],{},[898,40398,1705],{"mathvariant":1704},[1762,40400,2398],{},[1693,40402,1709],{"stretchy":1708},[1762,40404,30588],{},[3284,40406,40407,40409],{},[898,40408,1712],{},[1762,40410,1764],{},[1717,40412,40413,40415],{},[1693,40414,1731],{"stretchy":1708},[895,40416,40417,40419,40421],{},[1762,40418,1764],{},[898,40420,1705],{"mathvariant":1704},[1762,40422,2398],{},[1693,40424,1695],{},[1762,40426,11877],{},[3284,40428,40429,40431],{},[898,40430,1712],{},[1762,40432,1764],{},[1693,40434,1695],{},[1762,40436,2398],{},[902,40438,40439],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,40441,40442,1343,40466],{},[883,40443,40445],{"className":40444},[886],[888,40446,40447],{"xmlns":890},[892,40448,40449,40463],{},[895,40450,40451,40459,40461],{},[5688,40452,40453,40455,40457],{},[898,40454,1712],{},[1762,40456,1764],{},[1693,40458,3672],{},[1693,40460,1695],{},[1762,40462,9262],{},[902,40464,40465],{"encoding":904},"Q_1^* = 4",[883,40467,40469],{"className":40468},[886],[888,40470,40471],{"xmlns":890},[892,40472,40473,40487],{},[895,40474,40475,40483,40485],{},[5688,40476,40477,40479,40481],{},[898,40478,1712],{},[1762,40480,2398],{},[1693,40482,3672],{},[1693,40484,1695],{},[1762,40486,1764],{},[902,40488,40489],{"encoding":904},"Q_2^* = 1",[883,40491,40493],{"className":40492},[886],[888,40494,40495],{"xmlns":890},[892,40496,40497,40509],{},[895,40498,40499,40505,40507],{},[1717,40500,40501,40503],{},[898,40502,5957],{},[1693,40504,3672],{},[1693,40506,1695],{},[1762,40508,1764],{},[902,40510,40511],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,40514,40516],{"className":40515},[886],[888,40517,40518],{"xmlns":890},[892,40519,40520,40548],{},[895,40521,40522,40528,40530,40532,40534,40536,40538,40540,40542,40544,40546],{},[1717,40523,40524,40526],{},[898,40525,1691],{},[1693,40527,3672],{},[1693,40529,1695],{},[1762,40531,30588],{},[1693,40533,1715],{},[1762,40535,9262],{},[1693,40537,1892],{},[1762,40539,1764],{},[1693,40541,1715],{},[1762,40543,1764],{},[1693,40545,1695],{},[1762,40547,2398],{},[902,40549,40550],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,40552,40553,40556,40557,1343,40623,1343,40689,40755,40756,40793,40794,40816,40817,1789],{},[614,40554,40555],{},"Ověření postačující podmínky"," (6.26): ",[883,40558,40560],{"className":40559},[886],[888,40561,40562],{"xmlns":890},[892,40563,40564,40620],{},[895,40565,40566,40578,40580,40582,40590,40606],{},[5688,40567,40568,40570,40572],{},[898,40569,900],{},[1762,40571,9803],{},[895,40573,40574,40576],{},[1693,40575,1724],{"mathvariant":1704},[1693,40577,1724],{"mathvariant":1704},[1693,40579,1695],{},[1693,40581,1698],{},[3638,40583,40584],{"scriptlevel":1911,"displaystyle":1708},[2132,40585,40586,40588],{},[1762,40587,1764],{},[1762,40589,9262],{},[5688,40591,40592,40594,40596],{},[898,40593,1712],{},[1762,40595,1764],{},[895,40597,40598,40600,40602,40604],{},[1693,40599,1698],{},[1762,40601,8357],{},[898,40603,1705],{"mathvariant":1704},[1762,40605,2398],{},[5688,40607,40608,40610,40612],{},[898,40609,1712],{},[1762,40611,2398],{},[895,40613,40614,40616,40618],{},[1762,40615,1764],{},[898,40617,1705],{"mathvariant":1704},[1762,40619,2398],{},[902,40621,40622],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,40624,40626],{"className":40625},[886],[888,40627,40628],{"xmlns":890},[892,40629,40630,40686],{},[895,40631,40632,40644,40646,40648,40656,40670],{},[5688,40633,40634,40636,40638],{},[898,40635,900],{},[1762,40637,39329],{},[895,40639,40640,40642],{},[1693,40641,1724],{"mathvariant":1704},[1693,40643,1724],{"mathvariant":1704},[1693,40645,1695],{},[1693,40647,1698],{},[3638,40649,40650],{"scriptlevel":1911,"displaystyle":1708},[2132,40651,40652,40654],{},[1762,40653,1764],{},[1762,40655,9262],{},[5688,40657,40658,40660,40662],{},[898,40659,1712],{},[1762,40661,1764],{},[895,40663,40664,40666,40668],{},[1762,40665,1764],{},[898,40667,1705],{"mathvariant":1704},[1762,40669,2398],{},[5688,40671,40672,40674,40676],{},[898,40673,1712],{},[1762,40675,2398],{},[895,40677,40678,40680,40682,40684],{},[1693,40679,1698],{},[1762,40681,8357],{},[898,40683,1705],{"mathvariant":1704},[1762,40685,2398],{},[902,40687,40688],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,40690,40692],{"className":40691},[886],[888,40693,40694],{"xmlns":890},[892,40695,40696,40752],{},[895,40697,40698,40710,40712,40720,40736],{},[5688,40699,40700,40702,40704],{},[898,40701,900],{},[1762,40703,10402],{},[895,40705,40706,40708],{},[1693,40707,1724],{"mathvariant":1704},[1693,40709,1724],{"mathvariant":1704},[1693,40711,1695],{},[3638,40713,40714],{"scriptlevel":1911,"displaystyle":1708},[2132,40715,40716,40718],{},[1762,40717,1764],{},[1762,40719,9262],{},[5688,40721,40722,40724,40726],{},[898,40723,1712],{},[1762,40725,1764],{},[895,40727,40728,40730,40732,40734],{},[1693,40729,1698],{},[1762,40731,1764],{},[898,40733,1705],{"mathvariant":1704},[1762,40735,2398],{},[5688,40737,40738,40740,40742],{},[898,40739,1712],{},[1762,40741,2398],{},[895,40743,40744,40746,40748,40750],{},[1693,40745,1698],{},[1762,40747,1764],{},[898,40749,1705],{"mathvariant":1704},[1762,40751,2398],{},[902,40753,40754],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,40757,40759],{"className":40758},[886],[888,40760,40761],{"xmlns":890},[892,40762,40763,40790],{},[895,40764,40765,40767,40769,40771,40773,40775,40777,40779,40781,40783,40786,40788],{},[898,40766,2738],{},[1693,40768,1709],{"stretchy":1708},[1762,40770,9262],{},[1693,40772,1899],{"separator":1898},[1762,40774,1764],{},[1693,40776,1899],{"separator":1898},[1762,40778,1764],{},[1693,40780,1731],{"stretchy":1708},[1693,40782,1695],{},[1762,40784,40785],{},"0,28125",[1693,40787,1922],{},[1762,40789,1911],{},[902,40791,40792],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,40795,40797],{"className":40796},[886],[888,40798,40799],{"xmlns":890},[892,40800,40801,40813],{},[895,40802,40803,40805,40807,40809,40811],{},[1693,40804,9392],{"stretchy":1708},[1762,40806,9262],{},[1693,40808,1899],{"separator":1898},[1762,40810,1764],{},[1693,40812,9407],{"stretchy":1708},[902,40814,40815],{"encoding":904},"[4, 1]"," je vázané ",[38,40818,10667],{},[115,40820,40822],{"id":40821},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,40824,40825],{},"Obecně:",[883,40827,40829],{"className":40828},[886],[888,40830,40831],{"xmlns":890,"display":34854},[892,40832,40833,40928],{},[3626,40834,40835],{"width":34859},[3632,40836,40837,40839,40921,40923],{},[3635,40838],{"width":34864},[3635,40840,40841],{},[895,40842,40843,40849,40851,40857,40859,40865,40867,40873,40875,40877,40879,40881,40883,40889,40891,40897,40899,40905,40907,40913,40915,40917,40919],{},[3284,40844,40845,40847],{},[898,40846,1712],{},[1762,40848,1764],{},[1693,40850,1695],{},[3284,40852,40853,40855],{},[898,40854,2738],{},[1762,40856,1764],{},[1693,40858,1709],{"stretchy":1708},[3284,40860,40861,40863],{},[898,40862,1701],{},[1762,40864,1764],{},[1693,40866,1899],{"separator":1898},[3284,40868,40869,40871],{},[898,40870,1701],{},[1762,40872,2398],{},[1693,40874,1899],{"separator":1898},[898,40876,900],{},[1693,40878,1731],{"stretchy":1708},[1693,40880,1899],{"separator":1898},[1901,40882],{"width":3630},[3284,40884,40885,40887],{},[898,40886,1712],{},[1762,40888,2398],{},[1693,40890,1695],{},[3284,40892,40893,40895],{},[898,40894,2738],{},[1762,40896,2398],{},[1693,40898,1709],{"stretchy":1708},[3284,40900,40901,40903],{},[898,40902,1701],{},[1762,40904,1764],{},[1693,40906,1899],{"separator":1898},[3284,40908,40909,40911],{},[898,40910,1701],{},[1762,40912,2398],{},[1693,40914,1899],{"separator":1898},[898,40916,900],{},[1693,40918,1731],{"stretchy":1708},[1693,40920,1899],{"separator":1898},[3635,40922],{"width":34864},[3635,40924,40925],{},[1915,40926,40927],{},"(6.27)",[902,40929,40930],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,40932,40934],{"className":40933},[886],[888,40935,40936],{"xmlns":890,"display":34854},[892,40937,40938,40985],{},[3626,40939,40940],{"width":34859},[3632,40941,40942,40944,40978,40980],{},[3635,40943],{"width":34864},[3635,40945,40946],{},[895,40947,40948,40950,40952,40954,40956,40962,40964,40970,40972,40974,40976],{},[898,40949,5957],{},[1693,40951,1695],{},[898,40953,5957],{},[1693,40955,1709],{"stretchy":1708},[3284,40957,40958,40960],{},[898,40959,1701],{},[1762,40961,1764],{},[1693,40963,1899],{"separator":1898},[3284,40965,40966,40968],{},[898,40967,1701],{},[1762,40969,2398],{},[1693,40971,1899],{"separator":1898},[898,40973,900],{},[1693,40975,1731],{"stretchy":1708},[898,40977,1789],{"mathvariant":1704},[3635,40979],{"width":34864},[3635,40981,40982],{},[1915,40983,40984],{},"(6.28)",[902,40986,40987],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,40989,40990,40991,1863,40994,41007,41008,41021],{},"Hicksova poptávka závisí na ",[38,40992,40993],{},"hladině užitečnosti",[883,40995,40997],{"className":40996},[886],[888,40998,40999],{"xmlns":890},[892,41000,41001,41005],{},[895,41002,41003],{},[898,41004,900],{},[902,41006,900],{"encoding":904}," (nikoli na důchodu ",[883,41009,41011],{"className":41010},[886],[888,41012,41013],{"xmlns":890},[892,41014,41015,41019],{},[895,41016,41017],{},[898,41018,4618],{},[902,41020,4618],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,41023,41025,41026],{"id":41024},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,41027,41029],{"className":41028},[886],[888,41030,41031],{"xmlns":890},[892,41032,41033,41067],{},[895,41034,41035,41037,41039,41053],{},[898,41036,900],{},[1693,41038,1695],{},[5688,41040,41041,41043,41045],{},[898,41042,1712],{},[1762,41044,1764],{},[895,41046,41047,41049,41051],{},[1762,41048,1764],{},[898,41050,1705],{"mathvariant":1704},[1762,41052,2398],{},[5688,41054,41055,41057,41059],{},[898,41056,1712],{},[1762,41058,2398],{},[895,41060,41061,41063,41065],{},[1762,41062,1764],{},[898,41064,1705],{"mathvariant":1704},[1762,41066,2398],{},[902,41068,39942],{"encoding":904},[724,41070,41071,41101],{},[883,41072,41074],{"className":41073},[886],[888,41075,41076],{"xmlns":890},[892,41077,41078,41098],{},[895,41079,41080,41086,41088,41094,41096],{},[3284,41081,41082,41084],{},[898,41083,1701],{},[1762,41085,1764],{},[1693,41087,1899],{"separator":1898},[3284,41089,41090,41092],{},[898,41091,1701],{},[1762,41093,2398],{},[1693,41095,1899],{"separator":1898},[898,41097,900],{},[902,41099,41100],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,41103,41105],{"className":41104},[886],[888,41106,41107],{"xmlns":890,"display":34854},[892,41108,41109,41183],{},[895,41110,41111,41113,41115,41121,41127,41129,41135,41141,41143,41145,41147,41149,41151,41165,41179,41181],{},[898,41112,4840],{"mathvariant":5936},[1693,41114,1695],{},[3284,41116,41117,41119],{},[898,41118,1701],{},[1762,41120,1764],{},[3284,41122,41123,41125],{},[898,41124,1712],{},[1762,41126,1764],{},[1693,41128,1892],{},[3284,41130,41131,41133],{},[898,41132,1701],{},[1762,41134,2398],{},[3284,41136,41137,41139],{},[898,41138,1712],{},[1762,41140,2398],{},[1693,41142,1892],{},[898,41144,5957],{},[1693,41146,1709],{"stretchy":1708},[898,41148,900],{},[1693,41150,1698],{},[5688,41152,41153,41155,41157],{},[898,41154,1712],{},[1762,41156,1764],{},[895,41158,41159,41161,41163],{},[1762,41160,1764],{},[898,41162,1705],{"mathvariant":1704},[1762,41164,2398],{},[5688,41166,41167,41169,41171],{},[898,41168,1712],{},[1762,41170,2398],{},[895,41172,41173,41175,41177],{},[1762,41174,1764],{},[898,41176,1705],{"mathvariant":1704},[1762,41178,2398],{},[1693,41180,1731],{"stretchy":1708},[898,41182,1789],{"mathvariant":1704},[902,41184,41185],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,41187,37214],{},[883,41189,41191],{"className":41190},[886],[888,41192,41193],{"xmlns":890,"display":34854},[892,41194,41195,41417],{},[3626,41196,41197,41277,41357],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,41198,41199,41211],{},[3635,41200,41201],{},[3638,41202,41203],{"scriptlevel":1911,"displaystyle":1898},[5688,41204,41205,41207,41209],{},[898,41206,4840],{"mathvariant":5936},[1762,41208,1764],{},[1693,41210,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,41212,41213],{},[3638,41214,41215],{"scriptlevel":1911,"displaystyle":1898},[895,41216,41217,41219,41221,41227,41229,41231,41233,41241,41257,41271,41273,41275],{},[895,41218],{},[1693,41220,1695],{},[3284,41222,41223,41225],{},[898,41224,1701],{},[1762,41226,1764],{},[1693,41228,1698],{},[898,41230,5957],{},[1693,41232,1715],{},[3638,41234,41235],{"scriptlevel":1911,"displaystyle":1708},[2132,41236,41237,41239],{},[1762,41238,1764],{},[1762,41240,2398],{},[5688,41242,41243,41245,41247],{},[898,41244,1712],{},[1762,41246,1764],{},[895,41248,41249,41251,41253,41255],{},[1693,41250,1698],{},[1762,41252,1764],{},[898,41254,1705],{"mathvariant":1704},[1762,41256,2398],{},[5688,41258,41259,41261,41263],{},[898,41260,1712],{},[1762,41262,2398],{},[895,41264,41265,41267,41269],{},[1762,41266,1764],{},[898,41268,1705],{"mathvariant":1704},[1762,41270,2398],{},[1693,41272,1695],{},[1762,41274,1911],{},[1693,41276,1899],{"separator":1898},[3632,41278,41279,41291],{},[3635,41280,41281],{},[3638,41282,41283],{"scriptlevel":1911,"displaystyle":1898},[5688,41284,41285,41287,41289],{},[898,41286,4840],{"mathvariant":5936},[1762,41288,2398],{},[1693,41290,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,41292,41293],{},[3638,41294,41295],{"scriptlevel":1911,"displaystyle":1898},[895,41296,41297,41299,41301,41307,41309,41311,41313,41321,41335,41351,41353,41355],{},[895,41298],{},[1693,41300,1695],{},[3284,41302,41303,41305],{},[898,41304,1701],{},[1762,41306,2398],{},[1693,41308,1698],{},[898,41310,5957],{},[1693,41312,1715],{},[3638,41314,41315],{"scriptlevel":1911,"displaystyle":1708},[2132,41316,41317,41319],{},[1762,41318,1764],{},[1762,41320,2398],{},[5688,41322,41323,41325,41327],{},[898,41324,1712],{},[1762,41326,1764],{},[895,41328,41329,41331,41333],{},[1762,41330,1764],{},[898,41332,1705],{"mathvariant":1704},[1762,41334,2398],{},[5688,41336,41337,41339,41341],{},[898,41338,1712],{},[1762,41340,2398],{},[895,41342,41343,41345,41347,41349],{},[1693,41344,1698],{},[1762,41346,1764],{},[898,41348,1705],{"mathvariant":1704},[1762,41350,2398],{},[1693,41352,1695],{},[1762,41354,1911],{},[1693,41356,1899],{"separator":1898},[3632,41358,41359,41371],{},[3635,41360,41361],{},[3638,41362,41363],{"scriptlevel":1911,"displaystyle":1898},[5688,41364,41365,41367,41369],{},[898,41366,4840],{"mathvariant":5936},[898,41368,5957],{},[1693,41370,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[3635,41372,41373],{},[3638,41374,41375],{"scriptlevel":1911,"displaystyle":1898},[895,41376,41377,41379,41381,41383,41385,41399,41413,41415],{},[895,41378],{},[1693,41380,1695],{},[898,41382,900],{},[1693,41384,1698],{},[5688,41386,41387,41389,41391],{},[898,41388,1712],{},[1762,41390,1764],{},[895,41392,41393,41395,41397],{},[1762,41394,1764],{},[898,41396,1705],{"mathvariant":1704},[1762,41398,2398],{},[5688,41400,41401,41403,41405],{},[898,41402,1712],{},[1762,41404,2398],{},[895,41406,41407,41409,41411],{},[1762,41408,1764],{},[898,41410,1705],{"mathvariant":1704},[1762,41412,2398],{},[1693,41414,1695],{},[1762,41416,19295],{},[902,41418,41419],{"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}",[724,41421,41422,41423,41493,41494,41552],{},"Podílem rovnic: ",[883,41424,41426],{"className":41425},[886],[888,41427,41428],{"xmlns":890},[892,41429,41430,41490],{},[895,41431,41432,41438,41440,41446,41448,41454,41456,41462,41464,41470,41476,41478,41484],{},[3284,41433,41434,41436],{},[898,41435,1701],{},[1762,41437,1764],{},[898,41439,1705],{"mathvariant":1704},[3284,41441,41442,41444],{},[898,41443,1701],{},[1762,41445,2398],{},[1693,41447,1695],{},[3284,41449,41450,41452],{},[898,41451,1712],{},[1762,41453,2398],{},[898,41455,1705],{"mathvariant":1704},[3284,41457,41458,41460],{},[898,41459,1712],{},[1762,41461,1764],{},[1693,41463,10870],{},[3284,41465,41466,41468],{},[898,41467,1701],{},[1762,41469,1764],{},[3284,41471,41472,41474],{},[898,41473,1712],{},[1762,41475,1764],{},[1693,41477,1695],{},[3284,41479,41480,41482],{},[898,41481,1701],{},[1762,41483,2398],{},[3284,41485,41486,41488],{},[898,41487,1712],{},[1762,41489,2398],{},[902,41491,41492],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,41495,41497],{"className":41496},[886],[888,41498,41499],{"xmlns":890},[892,41500,41501,41549],{},[895,41502,41503,41505,41507,41513,41519,41521,41527,41533,41535,41537,41543],{},[898,41504,1691],{},[1693,41506,1695],{},[3284,41508,41509,41511],{},[898,41510,1701],{},[1762,41512,1764],{},[3284,41514,41515,41517],{},[898,41516,1712],{},[1762,41518,1764],{},[1693,41520,1892],{},[3284,41522,41523,41525],{},[898,41524,1701],{},[1762,41526,2398],{},[3284,41528,41529,41531],{},[898,41530,1712],{},[1762,41532,2398],{},[1693,41534,1695],{},[1762,41536,2398],{},[3284,41538,41539,41541],{},[898,41540,1701],{},[1762,41542,1764],{},[3284,41544,41545,41547],{},[898,41546,1712],{},[1762,41548,1764],{},[902,41550,41551],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,41554,41556],{"className":41555},[886],[888,41557,41558],{"xmlns":890,"display":34854},[892,41559,41560,41627],{},[3626,41561,41562],{"width":34859},[3632,41563,41564,41566,41620,41622],{},[3635,41565],{"width":34864},[3635,41567,41568],{},[895,41569,41570,41576,41578,41592,41594,41596,41602,41604,41618],{},[3284,41571,41572,41574],{},[898,41573,1712],{},[1762,41575,1764],{},[1693,41577,1695],{},[2132,41579,41580,41582],{},[898,41581,1691],{},[895,41583,41584,41586],{},[1762,41585,2398],{},[3284,41587,41588,41590],{},[898,41589,1701],{},[1762,41591,1764],{},[1693,41593,1899],{"separator":1898},[1901,41595],{"width":3630},[3284,41597,41598,41600],{},[898,41599,1712],{},[1762,41601,2398],{},[1693,41603,1695],{},[2132,41605,41606,41608],{},[898,41607,1691],{},[895,41609,41610,41612],{},[1762,41611,2398],{},[3284,41613,41614,41616],{},[898,41615,1701],{},[1762,41617,2398],{},[898,41619,1789],{"mathvariant":1704},[3635,41621],{"width":34864},[3635,41623,41624],{},[1915,41625,41626],{},"(6.29)",[902,41628,41629],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,41631,41632,41633,24395,41715,41751],{},"Ze třetí rovnice ",[883,41634,41636],{"className":41635},[886],[888,41637,41638],{"xmlns":890},[892,41639,41640,41712],{},[895,41641,41642,41644,41646,41684,41686],{},[898,41643,900],{},[1693,41645,1695],{},[14976,41647,41648],{},[895,41649,41650,41666,41668],{},[3638,41651,41652],{"scriptlevel":1911,"displaystyle":1708},[2132,41653,41654,41656],{},[898,41655,1691],{},[895,41657,41658,41660],{},[1762,41659,2398],{},[3284,41661,41662,41664],{},[898,41663,1701],{},[1762,41665,1764],{},[1693,41667,1715],{},[3638,41669,41670],{"scriptlevel":1911,"displaystyle":1708},[2132,41671,41672,41674],{},[898,41673,1691],{},[895,41675,41676,41678],{},[1762,41677,2398],{},[3284,41679,41680,41682],{},[898,41681,1701],{},[1762,41683,2398],{},[1693,41685,1695],{},[3638,41687,41688],{"scriptlevel":1911,"displaystyle":1708},[2132,41689,41690,41692],{},[898,41691,1691],{},[895,41693,41694,41696],{},[1762,41695,2398],{},[14976,41697,41698],{},[895,41699,41700,41706],{},[3284,41701,41702,41704],{},[898,41703,1701],{},[1762,41705,1764],{},[3284,41707,41708,41710],{},[898,41709,1701],{},[1762,41711,2398],{},[902,41713,41714],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,41716,41718],{"className":41717},[886],[888,41719,41720],{"xmlns":890},[892,41721,41722,41748],{},[895,41723,41724,41726,41728,41730,41732],{},[898,41725,1691],{},[1693,41727,1695],{},[1762,41729,2398],{},[898,41731,900],{},[14976,41733,41734],{},[895,41735,41736,41742],{},[3284,41737,41738,41740],{},[898,41739,1701],{},[1762,41741,1764],{},[3284,41743,41744,41746],{},[898,41745,1701],{},[1762,41747,2398],{},[902,41749,41750],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,41753,41755],{"className":41754},[886],[888,41756,41757],{"xmlns":890,"display":34854},[892,41758,41759,41904],{},[3626,41760,41761],{"width":34859},[3632,41762,41763,41765,41897,41899],{},[3635,41764],{"width":34864},[3635,41766,41767],{},[19664,41768,41769],{"notation":19666},[3638,41770,41771],{"scriptlevel":1911,"displaystyle":1708},[3638,41772,41773],{"scriptlevel":1911,"displaystyle":1708},[3638,41774,41775],{"scriptlevel":1911,"displaystyle":1898},[895,41776,41777,41779,41785,41787,41789,41805,41807,41813,41815,41821,41823,41829,41831,41833,41835,41837,41839,41845,41847,41849,41865,41867,41873,41875,41881,41883,41889,41891,41893,41895],{},[1915,41778,1917],{},[3284,41780,41781,41783],{},[898,41782,1712],{},[1762,41784,1764],{},[1693,41786,1695],{},[898,41788,900],{},[14976,41790,41791],{},[2132,41792,41793,41799],{},[3284,41794,41795,41797],{},[898,41796,1701],{},[1762,41798,2398],{},[3284,41800,41801,41803],{},[898,41802,1701],{},[1762,41804,1764],{},[1693,41806,1695],{},[3284,41808,41809,41811],{},[898,41810,2738],{},[1762,41812,1764],{},[1693,41814,1709],{"stretchy":1708},[3284,41816,41817,41819],{},[898,41818,1701],{},[1762,41820,1764],{},[1693,41822,1899],{"separator":1898},[3284,41824,41825,41827],{},[898,41826,1701],{},[1762,41828,2398],{},[1693,41830,1899],{"separator":1898},[898,41832,900],{},[1693,41834,1731],{"stretchy":1708},[1693,41836,1899],{"separator":1898},[1901,41838],{"width":3630},[3284,41840,41841,41843],{},[898,41842,1712],{},[1762,41844,2398],{},[1693,41846,1695],{},[898,41848,900],{},[14976,41850,41851],{},[2132,41852,41853,41859],{},[3284,41854,41855,41857],{},[898,41856,1701],{},[1762,41858,1764],{},[3284,41860,41861,41863],{},[898,41862,1701],{},[1762,41864,2398],{},[1693,41866,1695],{},[3284,41868,41869,41871],{},[898,41870,2738],{},[1762,41872,2398],{},[1693,41874,1709],{"stretchy":1708},[3284,41876,41877,41879],{},[898,41878,1701],{},[1762,41880,1764],{},[1693,41882,1899],{"separator":1898},[3284,41884,41885,41887],{},[898,41886,1701],{},[1762,41888,2398],{},[1693,41890,1899],{"separator":1898},[898,41892,900],{},[1693,41894,1731],{"stretchy":1708},[1915,41896,1917],{},[3635,41898],{"width":34864},[3635,41900,41901],{},[1915,41902,41903],{},"(6.30)",[902,41905,41906],{"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}",[115,41908,41910],{"id":41909},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,41912,41913,41914,41927,41928,41945,41946,41959,41960,41977,41978,41981,41982,42021,42022,42051],{},"Primární (max ",[883,41915,41917],{"className":41916},[886],[888,41918,41919],{"xmlns":890},[892,41920,41921,41925],{},[895,41922,41923],{},[898,41924,900],{},[902,41926,900],{"encoding":904}," při rozpočtu ",[883,41929,41931],{"className":41930},[886],[888,41932,41933],{"xmlns":890},[892,41934,41935,41943],{},[895,41936,41937],{},[1717,41938,41939,41941],{},[898,41940,4618],{},[1693,41942,3672],{},[902,41944,34816],{"encoding":904},") a duální (min ",[883,41947,41949],{"className":41948},[886],[888,41950,41951],{"xmlns":890},[892,41952,41953,41957],{},[895,41954,41955],{},[898,41956,1691],{},[902,41958,1691],{"encoding":904}," při užitečnosti ",[883,41961,41963],{"className":41962},[886],[888,41964,41965],{"xmlns":890},[892,41966,41967,41975],{},[895,41968,41969],{},[1717,41970,41971,41973],{},[898,41972,900],{},[1693,41974,3672],{},[902,41976,34750],{"encoding":904},") úloha jsou ",[38,41979,41980],{},"ekvivalentní",": mají tentýž bod optima ",[883,41983,41985],{"className":41984},[886],[888,41986,41987],{"xmlns":890},[892,41988,41989,42019],{},[895,41990,41991,41997,41999,42007,42009,42017],{},[1717,41992,41993,41995],{},[898,41994,1712],{},[1693,41996,3672],{},[1693,41998,9392],{"stretchy":1708},[5688,42000,42001,42003,42005],{},[898,42002,1712],{},[1762,42004,1764],{},[1693,42006,3672],{},[1693,42008,1899],{"separator":1898},[5688,42010,42011,42013,42015],{},[898,42012,1712],{},[1762,42014,2398],{},[1693,42016,3672],{},[1693,42018,9407],{"stretchy":1708},[902,42020,35115],{"encoding":904}," a v obou platí ",[883,42023,42025],{"className":42024},[886],[888,42026,42027],{"xmlns":890},[892,42028,42029,42049],{},[895,42030,42031,42033,42035,42041,42043],{},[1915,42032,5315],{},[1693,42034,1695],{},[3284,42036,42037,42039],{},[898,42038,1701],{},[1762,42040,1764],{},[898,42042,1705],{"mathvariant":1704},[3284,42044,42045,42047],{},[898,42046,1701],{},[1762,42048,2398],{},[902,42050,34786],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,42053,42054],{},[9465,42055],{"alt":42056,"className":42057,"src":42058},"imek-primarni-vs-dualni",[210,9469],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,42060,42061,42172],{},[123,42062,42063,42066,42067,42080,42081,42121,42122,1789],{},[38,42064,42065],{},"Primární"," (Marshall): zadáno ",[883,42068,42070],{"className":42069},[886],[888,42071,42072],{"xmlns":890},[892,42073,42074,42078],{},[895,42075,42076],{},[898,42077,4618],{},[902,42079,4618],{"encoding":904},", hledáme maximální ",[883,42082,42084],{"className":42083},[886],[888,42085,42086],{"xmlns":890},[892,42087,42088,42118],{},[895,42089,42090,42096,42098,42104,42106,42112,42114,42116],{},[1717,42091,42092,42094],{},[898,42093,900],{},[1693,42095,3672],{},[1693,42097,1709],{"stretchy":1708},[3284,42099,42100,42102],{},[898,42101,1701],{},[1762,42103,1764],{},[1693,42105,1899],{"separator":1898},[3284,42107,42108,42110],{},[898,42109,1701],{},[1762,42111,2398],{},[1693,42113,1899],{"separator":1898},[898,42115,4618],{},[1693,42117,1731],{"stretchy":1708},[902,42119,42120],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,42123,42125],{"className":42124},[886],[888,42126,42127],{"xmlns":890},[892,42128,42129,42169],{},[895,42130,42131,42137,42139,42147,42149,42155,42157,42163,42165,42167],{},[3284,42132,42133,42135],{},[898,42134,1712],{},[898,42136,5696],{},[1693,42138,1695],{},[5688,42140,42141,42143,42145],{},[898,42142,2738],{},[898,42144,5696],{},[898,42146,2839],{},[1693,42148,1709],{"stretchy":1708},[3284,42150,42151,42153],{},[898,42152,1701],{},[1762,42154,1764],{},[1693,42156,1899],{"separator":1898},[3284,42158,42159,42161],{},[898,42160,1701],{},[1762,42162,2398],{},[1693,42164,1899],{"separator":1898},[898,42166,4618],{},[1693,42168,1731],{"stretchy":1708},[902,42170,42171],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,42173,42174,42177,42178,42191,42192,42121,42232,1789],{},[38,42175,42176],{},"Duální"," (Hicks): zadáno ",[883,42179,42181],{"className":42180},[886],[888,42182,42183],{"xmlns":890},[892,42184,42185,42189],{},[895,42186,42187],{},[898,42188,900],{},[902,42190,900],{"encoding":904},", hledáme minimální ",[883,42193,42195],{"className":42194},[886],[888,42196,42197],{"xmlns":890},[892,42198,42199,42229],{},[895,42200,42201,42207,42209,42215,42217,42223,42225,42227],{},[1717,42202,42203,42205],{},[898,42204,1691],{},[1693,42206,3672],{},[1693,42208,1709],{"stretchy":1708},[3284,42210,42211,42213],{},[898,42212,1701],{},[1762,42214,1764],{},[1693,42216,1899],{"separator":1898},[3284,42218,42219,42221],{},[898,42220,1701],{},[1762,42222,2398],{},[1693,42224,1899],{"separator":1898},[898,42226,900],{},[1693,42228,1731],{"stretchy":1708},[902,42230,42231],{"encoding":904},"E^*(P_1, P_2, U)",[883,42233,42235],{"className":42234},[886],[888,42236,42237],{"xmlns":890},[892,42238,42239,42280],{},[895,42240,42241,42247,42249,42258,42260,42266,42268,42274,42276,42278],{},[3284,42242,42243,42245],{},[898,42244,1712],{},[898,42246,5696],{},[1693,42248,1695],{},[5688,42250,42251,42253,42255],{},[898,42252,2738],{},[898,42254,5696],{},[898,42256,42257],{},"H",[1693,42259,1709],{"stretchy":1708},[3284,42261,42262,42264],{},[898,42263,1701],{},[1762,42265,1764],{},[1693,42267,1899],{"separator":1898},[3284,42269,42270,42272],{},[898,42271,1701],{},[1762,42273,2398],{},[1693,42275,1899],{"separator":1898},[898,42277,900],{},[1693,42279,1731],{"stretchy":1708},[902,42281,42282],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,42284,42285,42286,42289,42290,42293],{},"Proč se studují obě? Marshallova poptávka je ",[38,42287,42288],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,42291,42292],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,42295,42297],{"id":42296},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,42299,42301],{"id":42300},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,42303,42304,42307,42308,42340,42341,42379,42380,42406],{},[38,42305,42306],{},"6.8"," Jsou dány užitečnost ",[883,42309,42311],{"className":42310},[886],[888,42312,42313],{"xmlns":890},[892,42314,42315,42337],{},[895,42316,42317,42319,42321,42329],{},[898,42318,900],{},[1693,42320,1695],{},[5688,42322,42323,42325,42327],{},[898,42324,1712],{},[1762,42326,1764],{},[1762,42328,11877],{},[5688,42330,42331,42333,42335],{},[898,42332,1712],{},[1762,42334,2398],{},[1762,42336,11877],{},[902,42338,42339],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,42342,42344],{"className":42343},[886],[888,42345,42346],{"xmlns":890},[892,42347,42348,42376],{},[895,42349,42350,42358,42360,42362,42364,42372,42374],{},[5688,42351,42352,42354,42356],{},[898,42353,1701],{},[1762,42355,1764],{},[1693,42357,3672],{},[1693,42359,1695],{},[1762,42361,9262],{},[1693,42363,1899],{"separator":1898},[5688,42365,42366,42368,42370],{},[898,42367,1701],{},[1762,42369,2398],{},[1693,42371,3672],{},[1693,42373,1695],{},[1762,42375,9763],{},[902,42377,42378],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,42381,42383],{"className":42382},[886],[888,42384,42385],{"xmlns":890},[892,42386,42387,42403],{},[895,42388,42389,42395,42397],{},[3284,42390,42391,42393],{},[898,42392,1712],{},[1762,42394,1764],{},[1693,42396,1899],{"separator":1898},[3284,42398,42399,42401],{},[898,42400,1712],{},[1762,42402,2398],{},[902,42404,42405],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,42408,42409,42412,42413,42454,42455,42486,42487,42509,42510,1789],{},[38,42410,42411],{},"6.9"," Jsou dány rozpočtové omezení ",[883,42414,42416],{"className":42415},[886],[888,42417,42418],{"xmlns":890},[892,42419,42420,42452],{},[895,42421,42422,42424,42426,42432,42438,42440,42446],{},[898,42423,4618],{},[1693,42425,1695],{},[3284,42427,42428,42430],{},[898,42429,1701],{},[1762,42431,1764],{},[3284,42433,42434,42436],{},[898,42435,1712],{},[1762,42437,1764],{},[1693,42439,1892],{},[3284,42441,42442,42444],{},[898,42443,1701],{},[1762,42445,2398],{},[3284,42447,42448,42450],{},[898,42449,1712],{},[1762,42451,2398],{},[902,42453,5877],{"encoding":904}," a užitečnost ",[883,42456,42458],{"className":42457},[886],[888,42459,42460],{"xmlns":890},[892,42461,42462,42484],{},[895,42463,42464,42466,42468,42476],{},[898,42465,900],{},[1693,42467,1695],{},[5688,42469,42470,42472,42474],{},[898,42471,1712],{},[1762,42473,1764],{},[1762,42475,11877],{},[5688,42477,42478,42480,42482],{},[898,42479,1712],{},[1762,42481,2398],{},[1762,42483,11877],{},[902,42485,42339],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,42488,42490],{"className":42489},[886],[888,42491,42492],{"xmlns":890},[892,42493,42494,42506],{},[895,42495,42496,42502,42504],{},[1717,42497,42498,42500],{},[898,42499,4618],{},[1693,42501,3672],{},[1693,42503,1695],{},[1762,42505,21936],{},[902,42507,42508],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,42511,42513],{"className":42512},[886],[888,42514,42515],{"xmlns":890},[892,42516,42517,42545],{},[895,42518,42519,42527,42529,42531,42533,42541,42543],{},[5688,42520,42521,42523,42525],{},[898,42522,1701],{},[1762,42524,1764],{},[1693,42526,3672],{},[1693,42528,1695],{},[1762,42530,9147],{},[1693,42532,1899],{"separator":1898},[5688,42534,42535,42537,42539],{},[898,42536,1701],{},[1762,42538,2398],{},[1693,42540,3672],{},[1693,42542,1695],{},[1762,42544,9763],{},[902,42546,42547],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,42549,42550,42553,42554,28397,42586,42616,42617,1789],{},[38,42551,42552],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,42555,42557],{"className":42556},[886],[888,42558,42559],{"xmlns":890},[892,42560,42561,42583],{},[895,42562,42563,42565,42567,42575],{},[898,42564,900],{},[1693,42566,1695],{},[5688,42568,42569,42571,42573],{},[898,42570,1712],{},[1762,42572,1764],{},[898,42574,207],{},[5688,42576,42577,42579,42581],{},[898,42578,1712],{},[1762,42580,2398],{},[898,42582,1895],{},[902,42584,42585],{"encoding":904},"U = Q_1^a Q_2^b",[883,42587,42589],{"className":42588},[886],[888,42590,42591],{"xmlns":890},[892,42592,42593,42613],{},[895,42594,42595,42597,42599,42601,42603,42605,42607,42609,42611],{},[898,42596,207],{},[1693,42598,1899],{"separator":1898},[898,42600,1895],{},[1693,42602,13370],{},[1693,42604,12192],{"stretchy":1708},[1762,42606,1911],{},[1693,42608,1899],{"separator":1898},[1762,42610,1764],{},[1693,42612,12209],{"stretchy":1708},[902,42614,42615],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,42618,42620],{"className":42619},[886],[888,42621,42622],{"xmlns":890},[892,42623,42624,42656],{},[895,42625,42626,42628,42630,42636,42642,42644,42650],{},[898,42627,4618],{},[1693,42629,1695],{},[3284,42631,42632,42634],{},[898,42633,1701],{},[1762,42635,1764],{},[3284,42637,42638,42640],{},[898,42639,1712],{},[1762,42641,1764],{},[1693,42643,1892],{},[3284,42645,42646,42648],{},[898,42647,1701],{},[1762,42649,2398],{},[3284,42651,42652,42654],{},[898,42653,1712],{},[1762,42655,2398],{},[902,42657,5877],{"encoding":904},[724,42659,42660,42663,42664,28397,42698,42616,42716,1789],{},[38,42661,42662],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,42665,42667],{"className":42666},[886],[888,42668,42669],{"xmlns":890},[892,42670,42671,42695],{},[895,42672,42673,42675,42677,42685,42687],{},[898,42674,900],{},[1693,42676,1695],{},[5688,42678,42679,42681,42683],{},[898,42680,1712],{},[1762,42682,1764],{},[898,42684,207],{},[1693,42686,1892],{},[5688,42688,42689,42691,42693],{},[898,42690,1712],{},[1762,42692,2398],{},[898,42694,207],{},[902,42696,42697],{"encoding":904},"U = Q_1^a + Q_2^a",[883,42699,42701],{"className":42700},[886],[888,42702,42703],{"xmlns":890},[892,42704,42705,42713],{},[895,42706,42707,42709,42711],{},[898,42708,207],{},[1693,42710,10266],{"mathvariant":1704},[1762,42712,1911],{},[902,42714,42715],{"encoding":904},"a \\neq 0",[883,42717,42719],{"className":42718},[886],[888,42720,42721],{"xmlns":890},[892,42722,42723,42755],{},[895,42724,42725,42727,42729,42735,42741,42743,42749],{},[898,42726,4618],{},[1693,42728,1695],{},[3284,42730,42731,42733],{},[898,42732,1701],{},[1762,42734,1764],{},[3284,42736,42737,42739],{},[898,42738,1712],{},[1762,42740,1764],{},[1693,42742,1892],{},[3284,42744,42745,42747],{},[898,42746,1701],{},[1762,42748,2398],{},[3284,42750,42751,42753],{},[898,42752,1712],{},[1762,42754,2398],{},[902,42756,5877],{"encoding":904},[198,42758,42760],{"id":42759},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,42762,42763,42307,42766,1343,42793,42815,42816,1343,42839,42863,42864,42889,42890,1789],{},[38,42764,42765],{},"6.12",[883,42767,42769],{"className":42768},[886],[888,42770,42771],{"xmlns":890},[892,42772,42773,42791],{},[895,42774,42775,42777,42779,42785],{},[898,42776,900],{},[1693,42778,1695],{},[3284,42780,42781,42783],{},[898,42782,1712],{},[1762,42784,1764],{},[3284,42786,42787,42789],{},[898,42788,1712],{},[1762,42790,2398],{},[902,42792,37009],{"encoding":904},[883,42794,42796],{"className":42795},[886],[888,42797,42798],{"xmlns":890},[892,42799,42800,42812],{},[895,42801,42802,42808,42810],{},[1717,42803,42804,42806],{},[898,42805,900],{},[1693,42807,3672],{},[1693,42809,1695],{},[1762,42811,9763],{},[902,42813,42814],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,42817,42819],{"className":42818},[886],[888,42820,42821],{"xmlns":890},[892,42822,42823,42837],{},[895,42824,42825,42833,42835],{},[5688,42826,42827,42829,42831],{},[898,42828,1701],{},[1762,42830,1764],{},[1693,42832,3672],{},[1693,42834,1695],{},[1762,42836,2398],{},[902,42838,37082],{"encoding":904},[883,42840,42842],{"className":42841},[886],[888,42843,42844],{"xmlns":890},[892,42845,42846,42860],{},[895,42847,42848,42856,42858],{},[5688,42849,42850,42852,42854],{},[898,42851,1701],{},[1762,42853,2398],{},[1693,42855,3672],{},[1693,42857,1695],{},[1762,42859,9262],{},[902,42861,42862],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,42865,42867],{"className":42866},[886],[888,42868,42869],{"xmlns":890},[892,42870,42871,42887],{},[895,42872,42873,42879,42881],{},[3284,42874,42875,42877],{},[898,42876,1712],{},[1762,42878,1764],{},[1693,42880,1899],{"separator":1898},[3284,42882,42883,42885],{},[898,42884,1712],{},[1762,42886,2398],{},[902,42888,42405],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,42891,42893],{"className":42892},[886],[888,42894,42895],{"xmlns":890},[892,42896,42897,42917],{},[895,42898,42899,42901,42903,42909,42911],{},[898,42900,900],{},[1693,42902,1695],{},[3284,42904,42905,42907],{},[898,42906,1712],{},[1762,42908,1764],{},[1693,42910,1715],{},[3284,42912,42913,42915],{},[898,42914,1712],{},[1762,42916,2398],{},[902,42918,42919],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,42921,42922,42925,42926,42967,42968,42990,42991,1789],{},[38,42923,42924],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,42927,42929],{"className":42928},[886],[888,42930,42931],{"xmlns":890},[892,42932,42933,42965],{},[895,42934,42935,42937,42939,42945,42951,42953,42959],{},[898,42936,1691],{},[1693,42938,1695],{},[3284,42940,42941,42943],{},[898,42942,1701],{},[1762,42944,1764],{},[3284,42946,42947,42949],{},[898,42948,1712],{},[1762,42950,1764],{},[1693,42952,1892],{},[3284,42954,42955,42957],{},[898,42956,1701],{},[1762,42958,2398],{},[3284,42960,42961,42963],{},[898,42962,1712],{},[1762,42964,2398],{},[902,42966,34731],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,42969,42971],{"className":42970},[886],[888,42972,42973],{"xmlns":890},[892,42974,42975,42987],{},[895,42976,42977,42983,42985],{},[1717,42978,42979,42981],{},[898,42980,900],{},[1693,42982,3672],{},[1693,42984,1695],{},[1762,42986,11872],{},[902,42988,42989],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,42992,42994],{"className":42993},[886],[888,42995,42996],{"xmlns":890},[892,42997,42998,43027],{},[895,42999,43000,43008,43010,43012,43014,43022,43024],{},[5688,43001,43002,43004,43006],{},[898,43003,1701],{},[1762,43005,1764],{},[1693,43007,3672],{},[1693,43009,1695],{},[1762,43011,15892],{},[1693,43013,1899],{"separator":1898},[5688,43015,43016,43018,43020],{},[898,43017,1701],{},[1762,43019,2398],{},[1693,43021,3672],{},[1693,43023,1695],{},[1762,43025,43026],{},"15",[902,43028,43029],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,43031,22545],{"id":22544},[120,43033,43034,43091,43130,43150,43185,43239,43244,43250,43346,43391],{},[123,43035,43036,1863,43039,43088,43089,1789],{},[38,43037,43038],{},"Rozpočtové omezení (budget constraint)",[883,43040,43042],{"className":43041},[886],[888,43043,43044],{"xmlns":890},[892,43045,43046,43086],{},[895,43047,43048,43054,43056,43064,43070,43072,43080],{},[1717,43049,43050,43052],{},[898,43051,4618],{},[1693,43053,3672],{},[1693,43055,1695],{},[5688,43057,43058,43060,43062],{},[898,43059,1701],{},[1762,43061,1764],{},[1693,43063,3672],{},[3284,43065,43066,43068],{},[898,43067,1712],{},[1762,43069,1764],{},[1693,43071,1892],{},[5688,43073,43074,43076,43078],{},[898,43075,1701],{},[1762,43077,2398],{},[1693,43079,3672],{},[3284,43081,43082,43084],{},[898,43083,1712],{},[1762,43085,2398],{},[902,43087,24117],{"encoding":904}," — (6.12); ",[38,43090,34924],{},[123,43092,43093,43096,43097,1789],{},[38,43094,43095],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,43098,43100],{"className":43099},[886],[888,43101,43102],{"xmlns":890},[892,43103,43104,43128],{},[895,43105,43106,43108,43110,43118,43120],{},[1915,43107,5315],{},[1693,43109,1695],{},[5688,43111,43112,43114,43116],{},[898,43113,1701],{},[1762,43115,1764],{},[1693,43117,3672],{},[898,43119,1705],{"mathvariant":1704},[5688,43121,43122,43124,43126],{},[898,43123,1701],{},[1762,43125,2398],{},[1693,43127,3672],{},[902,43129,35766],{"encoding":904},[123,43131,43132,43147,43148,1789],{},[38,43133,35908,43134],{},[883,43135,43137],{"className":43136},[886],[888,43138,43139],{"xmlns":890},[892,43140,43141,43145],{},[895,43142,43143],{},[898,43144,5957],{},[902,43146,6054],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,43149,35930],{},[123,43151,43152,43155,43156,1789],{},[38,43153,43154],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,43157,43159],{"className":43158},[886],[888,43160,43161],{"xmlns":890},[892,43162,43163,43183],{},[895,43164,43165,43167,43169,43175,43177],{},[1915,43166,5315],{},[1693,43168,1695],{},[3284,43170,43171,43173],{},[898,43172,1701],{},[1762,43174,1764],{},[898,43176,1705],{"mathvariant":1704},[3284,43178,43179,43181],{},[898,43180,1701],{},[1762,43182,2398],{},[902,43184,34786],{"encoding":904},[123,43186,43187,13877,43190,43238],{},[38,43188,43189],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,43191,43193],{"className":43192},[886],[888,43194,43195],{"xmlns":890},[892,43196,43197,43235],{},[895,43198,43199,43205,43207,43213,43215,43221,43223,43229,43231,43233],{},[3284,43200,43201,43203],{},[898,43202,1712],{},[898,43204,5696],{},[1693,43206,1695],{},[3284,43208,43209,43211],{},[898,43210,2738],{},[898,43212,5696],{},[1693,43214,1709],{"stretchy":1708},[3284,43216,43217,43219],{},[898,43218,1701],{},[1762,43220,1764],{},[1693,43222,1899],{"separator":1898},[3284,43224,43225,43227],{},[898,43226,1701],{},[1762,43228,2398],{},[1693,43230,1899],{"separator":1898},[898,43232,4618],{},[1693,43234,1731],{"stretchy":1708},[902,43236,43237],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,43240,43241,43243],{},[38,43242,38510],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,43245,43246,43249],{},[38,43247,43248],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,43251,43252,13877,43254,43301,43302,43345],{},[38,43253,40822],{},[883,43255,43257],{"className":43256},[886],[888,43258,43259],{"xmlns":890},[892,43260,43261,43299],{},[895,43262,43263,43269,43271,43277,43279,43285,43287,43293,43295,43297],{},[3284,43264,43265,43267],{},[898,43266,1712],{},[898,43268,5696],{},[1693,43270,1695],{},[3284,43272,43273,43275],{},[898,43274,2738],{},[898,43276,5696],{},[1693,43278,1709],{"stretchy":1708},[3284,43280,43281,43283],{},[898,43282,1701],{},[1762,43284,1764],{},[1693,43286,1899],{"separator":1898},[3284,43288,43289,43291],{},[898,43290,1701],{},[1762,43292,2398],{},[1693,43294,1899],{"separator":1898},[898,43296,900],{},[1693,43298,1731],{"stretchy":1708},[902,43300,24641],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,43303,43305],{"className":43304},[886],[888,43306,43307],{"xmlns":890},[892,43308,43309,43343],{},[895,43310,43311,43313,43315,43329],{},[898,43312,900],{},[1693,43314,1695],{},[5688,43316,43317,43319,43321],{},[898,43318,1712],{},[1762,43320,1764],{},[895,43322,43323,43325,43327],{},[1762,43324,1764],{},[898,43326,1705],{"mathvariant":1704},[1762,43328,2398],{},[5688,43330,43331,43333,43335],{},[898,43332,1712],{},[1762,43334,2398],{},[895,43336,43337,43339,43341],{},[1762,43338,1764],{},[898,43340,1705],{"mathvariant":1704},[1762,43342,2398],{},[902,43344,39942],{"encoding":904},": (6.30).",[123,43347,43348,43390],{},[38,43349,43350,43351],{},"Bod dotyku ",[883,43352,43354],{"className":43353},[886],[888,43355,43356],{"xmlns":890},[892,43357,43358,43388],{},[895,43359,43360,43366,43368,43376,43378,43386],{},[1717,43361,43362,43364],{},[898,43363,1712],{},[1693,43365,3672],{},[1693,43367,9392],{"stretchy":1708},[5688,43369,43370,43372,43374],{},[898,43371,1712],{},[1762,43373,1764],{},[1693,43375,3672],{},[1693,43377,1899],{"separator":1898},[5688,43379,43380,43382,43384],{},[898,43381,1712],{},[1762,43383,2398],{},[1693,43385,3672],{},[1693,43387,9407],{"stretchy":1708},[902,43389,35115],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,43392,43393,43396,43397,43410,43411,43424],{},[38,43394,43395],{},"Dualita"," — ekvivalence max ",[883,43398,43400],{"className":43399},[886],[888,43401,43402],{"xmlns":890},[892,43403,43404,43408],{},[895,43405,43406],{},[898,43407,900],{},[902,43409,900],{"encoding":904}," a min ",[883,43412,43414],{"className":43413},[886],[888,43415,43416],{"xmlns":890},[892,43417,43418,43422],{},[895,43419,43420],{},[898,43421,1691],{},[902,43423,1691],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,43426,8685],{"id":8684},[120,43428,43429,43452,43467,43480,43491],{},[123,43430,43431,1863,43434,43437,43438,43451],{},[38,43432,43433],{},"Teorie před optimalizací:",[207,43435,880],{"className":43436,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,43439,43441],{"className":43440},[886],[888,43442,43443],{"xmlns":890},[892,43444,43445,43449],{},[895,43446,43447],{},[898,43448,900],{},[902,43450,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,43453,43454,1863,43456,43459,43460,43463,43464,1789],{},[38,43455,8722],{},[207,43457,793],{"className":43458,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,43461,784],{"className":43462,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,43465,8726],{"className":43466,"dataFsResolvedFilePath":764,"href":765},[210],[123,43468,43469,1863,43472,43475,43476,43479],{},[38,43470,43471],{},"Paralely:",[207,43473,8763],{"className":43474,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,43477,2181],{"className":43478,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,43481,43482,1863,43485,1343,43488],{},[38,43483,43484],{},"Přednášky:",[207,43486,1094],{"className":43487,"dataFsResolvedFilePath":838,"href":839},[210],[207,43489,1101],{"className":43490,"dataFsResolvedFilePath":868,"href":869},[210],[123,43492,43493,1863,43495],{},[38,43494,8692],{},[207,43496,1653],{"className":43497,"dataFsResolvedFilePath":1651,"href":1652},[210],{"title":641,"searchDepth":642,"depth":642,"links":43499},[43500,43501,43502,43507,43508,43509,43511,43514,43517,43519,43520,43522,43523,43527,43528],{"id":18850,"depth":642,"text":18851},{"id":34794,"depth":642,"text":34795},{"id":35192,"depth":642,"text":35193,"children":43503},[43504,43505],{"id":35312,"depth":649,"text":35313},{"id":35890,"depth":649,"text":43506},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":36351,"depth":642,"text":36352},{"id":36661,"depth":642,"text":36662},{"id":36980,"depth":642,"text":43510},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":37753,"depth":642,"text":37754,"children":43512},[43513],{"id":38509,"depth":649,"text":38510},{"id":38689,"depth":642,"text":38690,"children":43515},[43516],{"id":38946,"depth":649,"text":38947},{"id":39897,"depth":642,"text":43518},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":40821,"depth":642,"text":40822},{"id":41024,"depth":642,"text":43521},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":41909,"depth":642,"text":41910},{"id":42296,"depth":642,"text":42297,"children":43524},[43525,43526],{"id":42300,"depth":649,"text":42301},{"id":42759,"depth":649,"text":42760},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":5829,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,43535,1144,16628,43536,43537,43538],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":43541,"title":802,"body":43542,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":57574,"navigation":664,"path":57575,"seo":57576,"sources":57577,"stem":57578,"tags":57579,"type":10745,"updated":677,"__hash__":57585},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":43543,"toc":57530},[43544,43547,43573,43577,43584,43733,43747,43749,43751,43838,43842,43878,43951,43972,44097,44107,44120,44124,44129,44159,44221,44230,44234,44296,44303,44324,44442,44519,44523,44526,44585,44700,44705,44737,44799,44847,44902,44906,44927,44951,44999,45003,45015,45019,45128,45132,45148,45189,45200,45359,45369,45374,45378,45499,45509,45516,45520,45598,45609,45689,45695,45702,45841,45848,45851,45908,45912,45990,46036,46080,46086,46199,46203,46206,46401,46405,46642,46645,46799,46952,46954,46956,47035,47038,47142,47211,47220,47224,47227,47288,47297,47301,47334,47412,47451,47455,47504,47558,47562,47591,47620,47672,47679,47733,47811,47815,47858,47924,47968,48072,48091,48093,48097,48205,48209,48277,48326,48333,48418,48422,48494,48499,48547,48736,48740,48745,48921,48926,48985,49090,49094,49121,49125,49132,49295,49382,49387,49389,49392,49490,49640,49712,49786,49788,49792,49806,49810,49942,49997,50108,50185,50189,50246,50349,50408,50569,50573,50648,50720,50818,50876,50970,51023,51044,51098,51103,51181,51229,51316,51354,51442,51595,51631,51685,51688,51690,51692,51740,51747,51755,51842,51850,51937,51944,51946,51950,52175,52177,52181,52185,52254,52305,52508,52514,52525,52593,52599,53021,53025,53089,53113,53309,53315,53329,53397,53400,53440,53664,53732,54034,54443,54520,54686,54692,54695,54770,55223,55274,55680,55785,56448,56451,56528,56536,56610,56641,56643,56646,56690,56692,56694,56698,56927,56931,57021,57026,57120,57124,57297,57301,57419,57424,57473,57475,57477],[12,43545,802],{"id":43546},"poptávka-nabídka-a-tržní-rovnováha",[1636,43548,43549],{},[724,43550,43551,43553,43554,43557,43558,43561,43562,43565,43566,43568,43569,43572],{},[883,43552,11036],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,43555,43556],{},"poptávka",") a výrobce (",[38,43559,43560],{},"nabídka","), jejich interakci v ",[38,43563,43564],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,43567,24795],{},"). Uzavírá ji pojem ",[38,43570,43571],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,43574,43576],{"id":43575},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,43578,43579,43580,43583],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,43581,43582],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,43585,43586,43603,43644,43660],{},[123,43587,43588,43589,43602],{},"cena ",[883,43590,43592],{"className":43591},[886],[888,43593,43594],{"xmlns":890},[892,43595,43596,43600],{},[895,43597,43598],{},[898,43599,1701],{},[902,43601,1701],{"encoding":904}," zkoumaného zboží,",[123,43604,43605,43606,1899],{},"ceny alternativních zboží ",[883,43607,43609],{"className":43608},[886],[888,43610,43611],{"xmlns":890},[892,43612,43613,43641],{},[895,43614,43615,43621,43623,43629,43631,43633,43635],{},[3284,43616,43617,43619],{},[898,43618,1701],{},[1762,43620,1764],{},[1693,43622,1899],{"separator":1898},[3284,43624,43625,43627],{},[898,43626,1701],{},[1762,43628,2398],{},[1693,43630,1899],{"separator":1898},[1693,43632,16501],{},[1693,43634,1899],{"separator":1898},[3284,43636,43637,43639],{},[898,43638,1701],{},[898,43640,5362],{},[902,43642,43643],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,43645,43646,43647,1899],{},"důchod ",[883,43648,43650],{"className":43649},[886],[888,43651,43652],{"xmlns":890},[892,43653,43654,43658],{},[895,43655,43656],{},[898,43657,4618],{},[902,43659,4618],{"encoding":904},[123,43661,43662,43663,5473,43676,43689,43690,43703,43704,43718,43719,43732],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,43664,43666],{"className":43665},[886],[888,43667,43668],{"xmlns":890},[892,43669,43670,43674],{},[895,43671,43672],{},[898,43673,4840],{},[902,43675,4840],{"encoding":904},[883,43677,43679],{"className":43678},[886],[888,43680,43681],{"xmlns":890},[892,43682,43683,43687],{},[895,43684,43685],{},[898,43686,4845],{},[902,43688,4845],{"encoding":904},", půda ",[883,43691,43693],{"className":43692},[886],[888,43694,43695],{"xmlns":890},[892,43696,43697,43701],{},[895,43698,43699],{},[898,43700,1691],{},[902,43702,1691],{"encoding":904},"), technologie, počet výrobců ",[883,43705,43707],{"className":43706},[886],[888,43708,43709],{"xmlns":890},[892,43710,43711,43716],{},[895,43712,43713],{},[898,43714,43715],{},"O",[902,43717,43715],{"encoding":904},", počasí ",[883,43720,43722],{"className":43721},[886],[888,43723,43724],{"xmlns":890},[892,43725,43726,43730],{},[895,43727,43728],{},[898,43729,6450],{},[902,43731,6450],{"encoding":904}," atd.",[724,43734,43735,43736,43739,43740,43743,43744,1789],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,43737,43738],{},"ceteris paribus","), hovoříme o ",[38,43741,43742],{},"jednofaktorovém modelu","; jinak jde o model ",[38,43745,43746],{},"vícefaktorový",[1852,43748],{},[115,43750,19993],{"id":43556},[1636,43752,43753],{},[724,43754,43755,43757,43758,43771,43772,43785,43786,43789,43790,43813,43814,1789],{},[883,43756,11036],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,43759,43761],{"className":43760},[886],[888,43762,43763],{"xmlns":890},[892,43764,43765,43769],{},[895,43766,43767],{},[898,43768,1712],{},[902,43770,1712],{"encoding":904}," na ceně ",[883,43773,43775],{"className":43774},[886],[888,43776,43777],{"xmlns":890},[892,43778,43779,43783],{},[895,43780,43781],{},[898,43782,1701],{},[902,43784,1701],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,43787,43788],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,43791,43793],{"className":43792},[886],[888,43794,43795],{"xmlns":890},[892,43796,43797,43811],{},[895,43798,43799,43801,43803,43805,43807,43809],{},[898,43800,1712],{},[1693,43802,1695],{},[898,43804,2738],{},[1693,43806,1709],{"stretchy":1708},[898,43808,1701],{},[1693,43810,1731],{"stretchy":1708},[902,43812,11072],{"encoding":904}," a jeho lineární verzí ",[883,43815,43817],{"className":43816},[886],[888,43818,43819],{"xmlns":890},[892,43820,43821,43835],{},[895,43822,43823,43825,43827,43829,43831,43833],{},[898,43824,1701],{},[1693,43826,1695],{},[898,43828,207],{},[898,43830,1712],{},[1693,43832,1892],{},[898,43834,1895],{},[902,43836,43837],{"encoding":904},"P = aQ + b",[198,43839,43841],{"id":43840},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,43843,43844,43845,43858,43859,43872,43873,16877,43875,10048],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,43846,43848],{"className":43847},[886],[888,43849,43850],{"xmlns":890},[892,43851,43852,43856],{},[895,43853,43854],{},[898,43855,1712],{},[902,43857,1712],{"encoding":904}," závisí na ceně ",[883,43860,43862],{"className":43861},[886],[888,43863,43864],{"xmlns":890},[892,43865,43866,43870],{},[895,43867,43868],{},[898,43869,1701],{},[902,43871,1701],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,43874,34790],{},[614,43876,43877],{},"demand function",[883,43879,43881],{"className":43880},[886],[888,43882,43883],{"xmlns":890,"display":34854},[892,43884,43885,43948],{},[3626,43886,43887],{"width":34859},[3632,43888,43889,43891,43941,43943],{},[3635,43890],{"width":34864},[3635,43892,43893],{},[895,43894,43895,43897,43899,43901,43903,43905,43907,43913,43915,43921,43923,43925,43927,43933,43935,43937,43939],{},[898,43896,1712],{},[1693,43898,1695],{},[898,43900,2738],{},[1693,43902,1709],{"stretchy":1708},[898,43904,1701],{},[1693,43906,1899],{"separator":1898},[3284,43908,43909,43911],{},[898,43910,1701],{},[1762,43912,1764],{},[1693,43914,1899],{"separator":1898},[3284,43916,43917,43919],{},[898,43918,1701],{},[1762,43920,2398],{},[1693,43922,1899],{"separator":1898},[1693,43924,16501],{},[1693,43926,1899],{"separator":1898},[3284,43928,43929,43931],{},[898,43930,1701],{},[898,43932,5362],{},[1693,43934,1899],{"separator":1898},[898,43936,4618],{},[1693,43938,1731],{"stretchy":1708},[898,43940,1789],{"mathvariant":1704},[3635,43942],{"width":34864},[3635,43944,43945],{},[1915,43946,43947],{},"(2.1)",[902,43949,43950],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,43952,43953,43954,43957,43958,43971],{},"Důležitou vlastností je ",[38,43955,43956],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,43959,43961],{"className":43960},[886],[888,43962,43963],{"xmlns":890},[892,43964,43965,43969],{},[895,43966,43967],{},[898,43968,6629],{},[902,43970,6629],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,43973,43975],{"className":43974},[886],[888,43976,43977],{"xmlns":890,"display":34854},[892,43978,43979,44094],{},[3626,43980,43981],{"width":34859},[3632,43982,43983,43985,44087,44089],{},[3635,43984],{"width":34864},[3635,43986,43987],{},[895,43988,43989,43991,43993,43995,43997,43999,44001,44003,44005,44011,44013,44015,44021,44023,44025,44027,44029,44035,44037,44039,44041,44043,44045,44047,44049,44051,44053,44059,44061,44067,44069,44071,44073,44079,44081,44083,44085],{},[898,43990,1712],{},[1693,43992,1695],{},[898,43994,2738],{},[1693,43996,1709],{"stretchy":1708},[898,43998,6629],{},[898,44000,1701],{},[1693,44002,1899],{"separator":1898},[898,44004,6629],{},[3284,44006,44007,44009],{},[898,44008,1701],{},[1762,44010,1764],{},[1693,44012,1899],{"separator":1898},[898,44014,6629],{},[3284,44016,44017,44019],{},[898,44018,1701],{},[1762,44020,2398],{},[1693,44022,1899],{"separator":1898},[1693,44024,16501],{},[1693,44026,1899],{"separator":1898},[898,44028,6629],{},[3284,44030,44031,44033],{},[898,44032,1701],{},[898,44034,5362],{},[1693,44036,1899],{"separator":1898},[898,44038,6629],{},[898,44040,4618],{},[1693,44042,1731],{"stretchy":1708},[1693,44044,1695],{},[898,44046,2738],{},[1693,44048,1709],{"stretchy":1708},[898,44050,1701],{},[1693,44052,1899],{"separator":1898},[3284,44054,44055,44057],{},[898,44056,1701],{},[1762,44058,1764],{},[1693,44060,1899],{"separator":1898},[3284,44062,44063,44065],{},[898,44064,1701],{},[1762,44066,2398],{},[1693,44068,1899],{"separator":1898},[1693,44070,16501],{},[1693,44072,1899],{"separator":1898},[3284,44074,44075,44077],{},[898,44076,1701],{},[898,44078,5362],{},[1693,44080,1899],{"separator":1898},[898,44082,4618],{},[1693,44084,1731],{"stretchy":1708},[898,44086,1789],{"mathvariant":1704},[3635,44088],{"width":34864},[3635,44090,44091],{},[1915,44092,44093],{},"(2.2)",[902,44095,44096],{"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}",[1636,44098,44099],{},[724,44100,44101,44103,44104,1789],{},[883,44102,8654],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,44105,44106],{},"v jednofaktorových modelech neplatí",[724,44108,44109,44110,1343,44113,4286,44116,44119],{},"Rozlišuje se poptávka ",[38,44111,44112],{},"individuální",[38,44114,44115],{},"tržní",[38,44117,44118],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,44121,44123],{"id":44122},"jednofaktorové-modely","Jednofaktorové modely",[44125,44126,44128],"h4",{"id":44127},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,44130,44131,44132,44145,44146,4300],{},"Poptávané množství ",[883,44133,44135],{"className":44134},[886],[888,44136,44137],{"xmlns":890},[892,44138,44139,44143],{},[895,44140,44141],{},[898,44142,1712],{},[902,44144,1712],{"encoding":904}," závisí pouze na ceně ",[883,44147,44149],{"className":44148},[886],[888,44150,44151],{"xmlns":890},[892,44152,44153,44157],{},[895,44154,44155],{},[898,44156,1701],{},[902,44158,1701],{"encoding":904},[883,44160,44162],{"className":44161},[886],[888,44163,44164],{"xmlns":890,"display":34854},[892,44165,44166,44218],{},[3626,44167,44168],{"width":34859},[3632,44169,44170,44172,44211,44213],{},[3635,44171],{"width":34864},[3635,44173,44174],{},[895,44175,44176,44178,44180,44182,44184,44186,44188,44190,44192,44195,44197,44199,44201,44203,44205,44207,44209],{},[898,44177,1712],{},[1693,44179,1695],{},[898,44181,2738],{},[1693,44183,1709],{"stretchy":1708},[898,44185,1701],{},[1693,44187,1731],{"stretchy":1708},[1693,44189,1899],{"separator":1898},[1901,44191],{"width":1903},[1915,44193,44194],{},"resp.",[1901,44196],{"width":1903},[898,44198,1701],{},[1693,44200,1695],{},[898,44202,2738],{},[1693,44204,1709],{"stretchy":1708},[898,44206,1712],{},[1693,44208,1731],{"stretchy":1708},[898,44210,1789],{"mathvariant":1704},[3635,44212],{"width":34864},[3635,44214,44215],{},[1915,44216,44217],{},"(2.3)",[902,44219,44220],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,44222,44223,44224,16877,44227,3042],{},"Graf této funkce se nazývá ",[38,44225,44226],{},"křivka poptávky",[614,44228,44229],{},"demand curve",[44125,44231,44233],{"id":44232},"zákon-klesající-poptávky","Zákon klesající poptávky",[1636,44235,44236],{},[724,44237,44238],{},[38,44239,44240,44241,44254,44255,44268,44269,44254,44282,44295],{},"Roste-li cena ",[883,44242,44244],{"className":44243},[886],[888,44245,44246],{"xmlns":890},[892,44247,44248,44252],{},[895,44249,44250],{},[898,44251,1701],{},[902,44253,1701],{"encoding":904},", pak množství ",[883,44256,44258],{"className":44257},[886],[888,44259,44260],{"xmlns":890},[892,44261,44262,44266],{},[895,44263,44264],{},[898,44265,1712],{},[902,44267,1712],{"encoding":904}," klesá; klesá-li cena ",[883,44270,44272],{"className":44271},[886],[888,44273,44274],{"xmlns":890},[892,44275,44276,44280],{},[895,44277,44278],{},[898,44279,1701],{},[902,44281,1701],{"encoding":904},[883,44283,44285],{"className":44284},[886],[888,44286,44287],{"xmlns":890},[892,44288,44289,44293],{},[895,44290,44291],{},[898,44292,1712],{},[902,44294,1712],{"encoding":904}," roste.",[724,44297,44298,44299,44302],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,44300,44301],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1636,44304,44305,44310],{},[724,44306,44307,44309],{},[883,44308,11036],{}," Intuice — proč zákon platí",[120,44311,44312,44318],{},[123,44313,44314,44317],{},[38,44315,44316],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,44319,44320,44323],{},[38,44321,44322],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,44325,44326,44327,44340,44341,44354,44355,44381,44382,44408,44409,6055,44435,44438,44439,1789],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,44328,44330],{"className":44329},[886],[888,44331,44332],{"xmlns":890},[892,44333,44334,44338],{},[895,44335,44336],{},[898,44337,1701],{},[902,44339,1701],{"encoding":904}," se vynáší na svislou osu, množství ",[883,44342,44344],{"className":44343},[886],[888,44345,44346],{"xmlns":890},[892,44347,44348,44352],{},[895,44349,44350],{},[898,44351,1712],{},[902,44353,1712],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,44356,44358],{"className":44357},[886],[888,44359,44360],{"xmlns":890},[892,44361,44362,44378],{},[895,44363,44364,44366,44368,44370,44376],{},[1693,44365,9392],{"stretchy":1708},[1762,44367,1911],{},[1693,44369,1899],{"separator":1898},[3284,44371,44372,44374],{},[898,44373,1701],{},[1762,44375,1911],{},[1693,44377,9407],{"stretchy":1708},[902,44379,44380],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,44383,44385],{"className":44384},[886],[888,44386,44387],{"xmlns":890},[892,44388,44389,44405],{},[895,44390,44391,44393,44399,44401,44403],{},[1693,44392,9392],{"stretchy":1708},[3284,44394,44395,44397],{},[898,44396,1712],{},[1762,44398,1911],{},[1693,44400,1899],{"separator":1898},[1762,44402,1911],{},[1693,44404,9407],{"stretchy":1708},[902,44406,44407],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,44410,44412],{"className":44411},[886],[888,44413,44414],{"xmlns":890},[892,44415,44416,44432],{},[895,44417,44418,44420,44422,44424,44430],{},[1693,44419,1709],{"stretchy":1708},[1762,44421,1911],{},[1693,44423,1899],{"separator":1898},[3284,44425,44426,44428],{},[898,44427,1701],{},[1762,44429,1911],{},[1693,44431,1731],{"stretchy":1708},[902,44433,44434],{"encoding":904},"(0, P_0)",[38,44436,44437],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,44440,44441],{},"konvexní",[724,44443,44444],{},[614,44445,44446,44447,44468,44469,4286,44494,1789],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,44448,44450],{"className":44449},[886],[888,44451,44452],{"xmlns":890},[892,44453,44454,44466],{},[895,44455,44456,44458,44460,44462,44464],{},[1693,44457,1709],{"stretchy":1708},[898,44459,1712],{},[1693,44461,1899],{"separator":1898},[898,44463,1701],{},[1693,44465,1731],{"stretchy":1708},[902,44467,1978],{"encoding":904}," — klesající, konvexní, procházející body ",[883,44470,44472],{"className":44471},[886],[888,44473,44474],{"xmlns":890},[892,44475,44476,44492],{},[895,44477,44478,44480,44482,44484,44490],{},[1693,44479,9392],{"stretchy":1708},[1762,44481,1911],{},[1693,44483,1899],{"separator":1898},[3284,44485,44486,44488],{},[898,44487,1701],{},[1762,44489,1911],{},[1693,44491,9407],{"stretchy":1708},[902,44493,44380],{"encoding":904},[883,44495,44497],{"className":44496},[886],[888,44498,44499],{"xmlns":890},[892,44500,44501,44517],{},[895,44502,44503,44505,44511,44513,44515],{},[1693,44504,9392],{"stretchy":1708},[3284,44506,44507,44509],{},[898,44508,1712],{},[1762,44510,1911],{},[1693,44512,1899],{"separator":1898},[1762,44514,1911],{},[1693,44516,9407],{"stretchy":1708},[902,44518,44407],{"encoding":904},[44125,44520,44522],{"id":44521},"lineární-model-poptávky","Lineární model poptávky",[724,44524,44525],{},"Nejjednodušší závislostí je",[883,44527,44529],{"className":44528},[886],[888,44530,44531],{"xmlns":890,"display":34854},[892,44532,44533,44582],{},[3626,44534,44535],{"width":34859},[3632,44536,44537,44539,44575,44577],{},[3635,44538],{"width":34864},[3635,44540,44541],{},[895,44542,44543,44545,44547,44549,44551,44553,44555,44557,44559,44561,44563,44565,44567,44569,44571,44573],{},[898,44544,1701],{},[1693,44546,1695],{},[898,44548,207],{},[898,44550,1712],{},[1693,44552,1892],{},[898,44554,1895],{},[1693,44556,1899],{"separator":1898},[1901,44558],{"width":1903},[898,44560,207],{},[1693,44562,1908],{},[1762,44564,1911],{},[1693,44566,1899],{"separator":1898},[1915,44568,9204],{},[898,44570,1895],{},[1693,44572,1922],{},[1762,44574,19295],{},[3635,44576],{"width":34864},[3635,44578,44579],{},[1915,44580,44581],{},"(2.4)",[902,44583,44584],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,44586,44587,44588,28397,44624,4286,44648,14897,44674,44696,44697,1789],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,44589,44591],{"className":44590},[886],[888,44592,44593],{"xmlns":890},[892,44594,44595,44621],{},[895,44596,44597,44599,44601,44609,44611,44613],{},[898,44598,1712],{},[1693,44600,1695],{},[3638,44602,44603],{"scriptlevel":1911,"displaystyle":1708},[2132,44604,44605,44607],{},[1762,44606,1764],{},[898,44608,207],{},[898,44610,1701],{},[1693,44612,1698],{},[3638,44614,44615],{"scriptlevel":1911,"displaystyle":1708},[2132,44616,44617,44619],{},[898,44618,1895],{},[898,44620,207],{},[902,44622,44623],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,44625,44627],{"className":44626},[886],[888,44628,44629],{"xmlns":890},[892,44630,44631,44645],{},[895,44632,44633,44641,44643],{},[3638,44634,44635],{"scriptlevel":1911,"displaystyle":1708},[2132,44636,44637,44639],{},[1762,44638,1764],{},[898,44640,207],{},[1693,44642,1908],{},[1762,44644,1911],{},[902,44646,44647],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,44649,44651],{"className":44650},[886],[888,44652,44653],{"xmlns":890},[892,44654,44655,44671],{},[895,44656,44657,44659,44667,44669],{},[1693,44658,1698],{},[3638,44660,44661],{"scriptlevel":1911,"displaystyle":1708},[2132,44662,44663,44665],{},[898,44664,1895],{},[898,44666,207],{},[1693,44668,1922],{},[1762,44670,1911],{},[902,44672,44673],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,44675,44677],{"className":44676},[886],[888,44678,44679],{"xmlns":890},[892,44680,44681,44693],{},[895,44682,44683,44685,44687,44689,44691],{},[1693,44684,1709],{"stretchy":1708},[1762,44686,1911],{},[1693,44688,1899],{"separator":1898},[898,44690,1895],{},[1693,44692,1731],{"stretchy":1708},[902,44694,44695],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,44698,44699],{},"nedokonalé konkurenci",[44701,44702,44704],"h5",{"id":44703},"příklad-21","Příklad 2.1",[724,44706,44707,44710,44711,1789],{},[38,44708,44709],{},"Zadání:"," Lineární poptávka ",[883,44712,44714],{"className":44713},[886],[888,44715,44716],{"xmlns":890},[892,44717,44718,44734],{},[895,44719,44720,44722,44724,44726,44728,44730,44732],{},[898,44721,1701],{},[1693,44723,1695],{},[1693,44725,1698],{},[1762,44727,2398],{},[898,44729,1712],{},[1693,44731,1892],{},[1762,44733,10023],{},[902,44735,44736],{"encoding":904},"P = -2Q + 60",[724,44738,44739,44742,44743,44765,44766,1789],{},[38,44740,44741],{},"Řešení:"," Reálné cenové rozpětí je ",[883,44744,44746],{"className":44745},[886],[888,44747,44748],{"xmlns":890},[892,44749,44750,44762],{},[895,44751,44752,44754,44756,44758,44760],{},[1693,44753,1709],{"stretchy":1708},[1762,44755,1911],{},[1693,44757,1899],{"separator":1898},[1762,44759,10023],{},[1693,44761,1731],{"stretchy":1708},[902,44763,44764],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,44767,44769],{"className":44768},[886],[888,44770,44771],{"xmlns":890},[892,44772,44773,44796],{},[895,44774,44775,44777,44779,44781,44789,44791,44793],{},[898,44776,1712],{},[1693,44778,1695],{},[1693,44780,1698],{},[3638,44782,44783],{"scriptlevel":1911,"displaystyle":1708},[2132,44784,44785,44787],{},[1762,44786,1764],{},[1762,44788,2398],{},[898,44790,1701],{},[1693,44792,1892],{},[1762,44794,44795],{},"30",[902,44797,44798],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,44800,44801,44824],{},[19,44802,44803],{},[22,44804,44805,44820,44822],{},[25,44806,44807],{},[883,44808,44810],{"className":44809},[886],[888,44811,44812],{"xmlns":890},[892,44813,44814,44818],{},[895,44815,44816],{},[898,44817,1701],{},[902,44819,1701],{"encoding":904},[25,44821,12079],{},[25,44823,15892],{},[30,44825,44826],{},[22,44827,44828,44843,44845],{},[35,44829,44830],{},[883,44831,44833],{"className":44832},[886],[888,44834,44835],{"xmlns":890},[892,44836,44837,44841],{},[895,44838,44839],{},[898,44840,1712],{},[902,44842,1712],{"encoding":904},[35,44844,9763],{},[35,44846,15892],{},[724,44848,44849],{},[614,44850,44851,44852,4286,44874,1789],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,44853,44855],{"className":44854},[886],[888,44856,44857],{"xmlns":890},[892,44858,44859,44871],{},[895,44860,44861,44863,44865,44867,44869],{},[1693,44862,9392],{"stretchy":1708},[1762,44864,1911],{},[1693,44866,1899],{"separator":1898},[898,44868,1895],{},[1693,44870,9407],{"stretchy":1708},[902,44872,44873],{"encoding":904},"[0, b]",[883,44875,44877],{"className":44876},[886],[888,44878,44879],{"xmlns":890},[892,44880,44881,44899],{},[895,44882,44883,44885,44887,44889,44891,44893,44895,44897],{},[1693,44884,9392],{"stretchy":1708},[1693,44886,1698],{},[898,44888,1895],{},[898,44890,1705],{"mathvariant":1704},[898,44892,207],{},[1693,44894,1899],{"separator":1898},[1762,44896,1911],{},[1693,44898,9407],{"stretchy":1708},[902,44900,44901],{"encoding":904},"[-b\u002Fa, 0]",[44125,44903,44905],{"id":44904},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,44907,44908,44909,44926],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,44910,44912],{"className":44911},[886],[888,44913,44914],{"xmlns":890},[892,44915,44916,44924],{},[895,44917,44918],{},[1717,44919,44920,44922],{},[898,44921,1701],{},[1693,44923,3672],{},[902,44925,11280],{"encoding":904},", je funkce poptávky konstantní:",[883,44928,44930],{"className":44929},[886],[888,44931,44932],{"xmlns":890,"display":34854},[892,44933,44934,44948],{},[895,44935,44936,44938,44940,44946],{},[898,44937,1701],{},[1693,44939,1695],{},[1717,44941,44942,44944],{},[898,44943,1701],{},[1693,44945,3672],{},[898,44947,1789],{"mathvariant":1704},[902,44949,44950],{"encoding":904},"P = P^*.",[724,44952,44953],{},[614,44954,44955,44956,44977,44978,1789],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,44957,44959],{"className":44958},[886],[888,44960,44961],{"xmlns":890},[892,44962,44963,44975],{},[895,44964,44965,44967,44969,44971,44973],{},[1693,44966,1709],{"stretchy":1708},[898,44968,1712],{},[1693,44970,1899],{"separator":1898},[898,44972,1701],{},[1693,44974,1731],{"stretchy":1708},[902,44976,1978],{"encoding":904}," na úrovni ",[883,44979,44981],{"className":44980},[886],[888,44982,44983],{"xmlns":890},[892,44984,44985,44997],{},[895,44986,44987,44989,44991],{},[898,44988,1701],{},[1693,44990,1695],{},[1717,44992,44993,44995],{},[898,44994,1701],{},[1693,44996,3672],{},[902,44998,11234],{"encoding":904},[44125,45000,45002],{"id":45001},"giffenův-statek","Giffenův statek",[724,45004,45005,45006,45008,45009,45011,45012,1789],{},"Existují zboží, u nichž je křivka poptávky ",[38,45007,20488],{}," — tzv. ",[38,45010,45002],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,45013,45014],{},"podřadnému zboží",[44701,45016,45018],{"id":45017},"příklad-22","Příklad 2.2",[724,45020,45021,45024,45025,45043,45044,45066,45067,45084,45085,45103,45104,45127],{},[38,45022,45023],{},"Zadání a popis:"," Křivka ",[883,45026,45028],{"className":45027},[886],[888,45029,45030],{"xmlns":890},[892,45031,45032,45040],{},[895,45033,45034],{},[3284,45035,45036,45038],{},[898,45037,2738],{},[1762,45039,1764],{},[902,45041,45042],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,45045,45047],{"className":45046},[886],[888,45048,45049],{"xmlns":890},[892,45050,45051,45063],{},[895,45052,45053,45055,45057,45059,45061],{},[1693,45054,1709],{"stretchy":1708},[1762,45056,1911],{},[1693,45058,1899],{"separator":1898},[1762,45060,43026],{},[1693,45062,1731],{"stretchy":1708},[902,45064,45065],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,45068,45070],{"className":45069},[886],[888,45071,45072],{"xmlns":890},[892,45073,45074,45082],{},[895,45075,45076],{},[3284,45077,45078,45080],{},[898,45079,1712],{},[1762,45081,1911],{},[902,45083,6293],{"encoding":904}," konkávní, se saturací kolem 17 liber. Křivka ",[883,45086,45088],{"className":45087},[886],[888,45089,45090],{"xmlns":890},[892,45091,45092,45100],{},[895,45093,45094],{},[3284,45095,45096,45098],{},[898,45097,2738],{},[1762,45099,2398],{},[902,45101,45102],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,45105,45107],{"className":45106},[886],[888,45108,45109],{"xmlns":890},[892,45110,45111,45124],{},[895,45112,45113,45115,45117,45119,45122],{},[1693,45114,9392],{"stretchy":1708},[1762,45116,1911],{},[1693,45118,1899],{"separator":1898},[1762,45120,45121],{},"21",[1693,45123,9407],{"stretchy":1708},[902,45125,45126],{"encoding":904},"[0, 21]"," centů.",[198,45129,45131],{"id":45130},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,45133,45134,45135,4300],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,45136,45138],{"className":45137},[886],[888,45139,45140],{"xmlns":890},[892,45141,45142,45146],{},[895,45143,45144],{},[898,45145,4618],{},[902,45147,4618],{"encoding":904},[883,45149,45151],{"className":45150},[886],[888,45152,45153],{"xmlns":890,"display":34854},[892,45154,45155,45186],{},[3626,45156,45157],{"width":34859},[3632,45158,45159,45161,45179,45181],{},[3635,45160],{"width":34864},[3635,45162,45163],{},[895,45164,45165,45167,45169,45171,45173,45175,45177],{},[898,45166,1712],{},[1693,45168,1695],{},[898,45170,1691],{},[1693,45172,1709],{"stretchy":1708},[898,45174,4618],{},[1693,45176,1731],{"stretchy":1708},[898,45178,1789],{"mathvariant":1704},[3635,45180],{"width":34864},[3635,45182,45183],{},[1915,45184,45185],{},"(2.5)",[902,45187,45188],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,45190,45191,45192,45195,45196,45199],{},"Funkce se nazývá ",[38,45193,45194],{},"Engelova",", její graf ",[38,45197,45198],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,45201,45202,45334],{},[123,45203,45204,13877,45207,45220,45221,45234,45235,45252,45253],{},[38,45205,45206],{},"Normální (superior) zboží",[883,45208,45210],{"className":45209},[886],[888,45211,45212],{"xmlns":890},[892,45213,45214,45218],{},[895,45215,45216],{},[898,45217,1712],{},[902,45219,1712],{"encoding":904}," roste s ",[883,45222,45224],{"className":45223},[886],[888,45225,45226],{"xmlns":890},[892,45227,45228,45232],{},[895,45229,45230],{},[898,45231,4618],{},[902,45233,4618],{"encoding":904},", nepřesáhne hodnotu ",[883,45236,45238],{"className":45237},[886],[888,45239,45240],{"xmlns":890},[892,45241,45242,45250],{},[895,45243,45244],{},[3284,45245,45246,45248],{},[898,45247,1712],{},[1762,45249,1911],{},[902,45251,6293],{"encoding":904},":\n",[120,45254,45255,45287],{},[123,45256,45257,45260,45261,45264,45265,1789],{},[38,45258,45259],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,45262,45263],{},"konkávní"," křivka, autonomní spotřeba ",[883,45266,45268],{"className":45267},[886],[888,45269,45270],{"xmlns":890},[892,45271,45272,45284],{},[895,45273,45274,45280,45282],{},[3284,45275,45276,45278],{},[898,45277,1712],{},[1762,45279,1764],{},[1693,45281,1922],{},[1762,45283,1911],{},[902,45285,45286],{"encoding":904},"Q_1 > 0",[123,45288,45289,45292,45293,45311,45312,45314,45315,1863,45332,1789],{},[38,45290,45291],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,45294,45296],{"className":45295},[886],[888,45297,45298],{"xmlns":890},[892,45299,45300,45308],{},[895,45301,45302],{},[3284,45303,45304,45306],{},[898,45305,4618],{},[1762,45307,1764],{},[902,45309,45310],{"encoding":904},"Y_1",", křivka je nejprve ",[38,45313,44441],{}," a od ",[883,45316,45318],{"className":45317},[886],[888,45319,45320],{"xmlns":890},[892,45321,45322,45330],{},[895,45323,45324],{},[3284,45325,45326,45328],{},[898,45327,4618],{},[1762,45329,1764],{},[902,45331,45310],{"encoding":904},[38,45333,45263],{},[123,45335,45336,45339,45340,45358],{},[38,45337,45338],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,45341,45343],{"className":45342},[886],[888,45344,45345],{"xmlns":890},[892,45346,45347,45355],{},[895,45348,45349],{},[3284,45350,45351,45353],{},[898,45352,4618],{},[1762,45354,1911],{},[902,45356,45357],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,45360,45361,45362,45365,45366,3042],{},"Mírou citlivosti je ",[614,45363,45364],{},"důchodová elasticita"," (viz ",[207,45367,10783],{"className":45368,"dataFsResolvedFilePath":848,"href":849},[210],[724,45370,45371],{},[614,45372,45373],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[44125,45375,45377],{"id":45376},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1636,45379,45380,45451,45493],{},[724,45381,45382,45384,45385,1863,45388,1863,45401,12537,45403,45416,45417,45420,45421,1789],{},[883,45383,8654],{}," Pozor — nezbytné ≠ podřadné\n",[38,45386,45387],{},"Nezbytné zboží:",[883,45389,45391],{"className":45390},[886],[888,45392,45393],{"xmlns":890},[892,45394,45395,45399],{},[895,45396,45397],{},[898,45398,1712],{},[902,45400,1712],{"encoding":904},[38,45402,14182],{},[883,45404,45406],{"className":45405},[886],[888,45407,45408],{"xmlns":890},[892,45409,45410,45414],{},[895,45411,45412],{},[898,45413,4618],{},[902,45415,4618],{"encoding":904},", ale ",[38,45418,45419],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,45422,45424],{"className":45423},[886],[888,45425,45426],{"xmlns":890},[892,45427,45428,45448],{},[895,45429,45430,45436,45438,45440,45442,45444,45446],{},[3284,45431,45432,45434],{},[898,45433,1691],{},[898,45435,4618],{},[1693,45437,13370],{},[1693,45439,1709],{"stretchy":1708},[1762,45441,1911],{},[1693,45443,1899],{"separator":1898},[1762,45445,1764],{},[1693,45447,1731],{"stretchy":1708},[902,45449,45450],{"encoding":904},"E_Y \\in (0, 1)",[724,45452,45453,1863,45456,1863,45469,45471,45472,1789],{},[38,45454,45455],{},"Podřadné zboží:",[883,45457,45459],{"className":45458},[886],[888,45460,45461],{"xmlns":890},[892,45462,45463,45467],{},[895,45464,45465],{},[898,45466,1712],{},[902,45468,1712],{"encoding":904},[38,45470,14202],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,45473,45475],{"className":45474},[886],[888,45476,45477],{"xmlns":890},[892,45478,45479,45491],{},[895,45480,45481,45487,45489],{},[3284,45482,45483,45485],{},[898,45484,1691],{},[898,45486,4618],{},[1693,45488,1908],{},[1762,45490,1911],{},[902,45492,4800],{"encoding":904},[724,45494,45495,45496,1789],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,45497,45498],{},"méně kusů, ne jen proporčně méně",[724,45500,45501,45504,45505,45508],{},[38,45502,45503],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,45506,45507],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,45510,45511],{},[9465,45512],{"alt":45513,"className":45514,"src":45515},"imek-engelovy-krivky-3typy",[210,9469],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[44701,45517,45519],{"id":45518},"české-příklady","České příklady",[16,45521,45522,45532],{},[19,45523,45524],{},[22,45525,45526,45529],{},[25,45527,45528],{},"Podřadné",[25,45530,45531],{},"Nahradí se za",[30,45533,45534,45542,45550,45558,45566,45574,45582,45590],{},[22,45535,45536,45539],{},[35,45537,45538],{},"Instantní polévky, ramen",[35,45540,45541],{},"Čerstvé jídlo, restaurace",[22,45543,45544,45547],{},[35,45545,45546],{},"MHD (autobus, tramvaj)",[35,45548,45549],{},"Vlastní auto, Uber, taxi",[22,45551,45552,45555],{},[35,45553,45554],{},"Mražené polotovary, pizza z mrazáku",[35,45556,45557],{},"Čerstvé suroviny, hotovky",[22,45559,45560,45563],{},[35,45561,45562],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,45564,45565],{},"Značkové produkty",[22,45567,45568,45571],{},[35,45569,45570],{},"Paštika Májka, obyčejný měkký salám",[35,45572,45573],{},"Kvalitní uzeniny, šunka od kosti",[22,45575,45576,45579],{},[35,45577,45578],{},"Second hand oblečení",[35,45580,45581],{},"Nové oblečení, značky",[22,45583,45584,45587],{},[35,45585,45586],{},"Krabicové víno, nejlevnější pivo",[35,45588,45589],{},"Lahvové víno, řemeslná piva",[22,45591,45592,45595],{},[35,45593,45594],{},"Ojetá auta nižších tříd",[35,45596,45597],{},"Nová auta, prémiové značky",[1636,45599,45600],{},[724,45601,45602,45604,45605,45608],{},[883,45603,8620],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,45606,45607],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,45610,45611,45614,45615,16877,45618,45640,45641,16877,45644,45665,45666,45684,45685,45688],{},[38,45612,45613],{},"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 ",[38,45616,45617],{},"luxus",[883,45619,45621],{"className":45620},[886],[888,45622,45623],{"xmlns":890},[892,45624,45625,45637],{},[895,45626,45627,45633,45635],{},[3284,45628,45629,45631],{},[898,45630,1691],{},[898,45632,4618],{},[1693,45634,1922],{},[1762,45636,1764],{},[902,45638,45639],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,45642,45643],{},"podřadné",[883,45645,45647],{"className":45646},[886],[888,45648,45649],{"xmlns":890},[892,45650,45651,45663],{},[895,45652,45653,45659,45661],{},[3284,45654,45655,45657],{},[898,45656,1691],{},[898,45658,4618],{},[1693,45660,1908],{},[1762,45662,1911],{},[902,45664,4800],{"encoding":904},"). Proto je ",[883,45667,45669],{"className":45668},[886],[888,45670,45671],{"xmlns":890},[892,45672,45673,45681],{},[895,45674,45675],{},[3284,45676,45677,45679],{},[898,45678,1691],{},[898,45680,4618],{},[902,45682,45683],{"encoding":904},"E_Y"," vždy ",[38,45686,45687],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,45690,45691,45692,45694],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,45693,45002],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,45696,45698,45699,1731],{"id":45697},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,45700,45701],{},"shift of demand",[724,45703,45704,45705,45723,45724,45741,45742,45755,45756,9591,45769,45791,45792,45809,45810,45836,45837,45840],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,45706,45708],{"className":45707},[886],[888,45709,45710],{"xmlns":890},[892,45711,45712,45720],{},[895,45713,45714],{},[3284,45715,45716,45718],{},[898,45717,1701],{},[1762,45719,1911],{},[902,45721,45722],{"encoding":904},"P_0"," odpovídá množství ",[883,45725,45727],{"className":45726},[886],[888,45728,45729],{"xmlns":890},[892,45730,45731,45739],{},[895,45732,45733],{},[3284,45734,45735,45737],{},[898,45736,1712],{},[1762,45738,1911],{},[902,45740,6293],{"encoding":904}," na křivce ",[883,45743,45745],{"className":45744},[886],[888,45746,45747],{"xmlns":890},[892,45748,45749,45753],{},[895,45750,45751],{},[898,45752,2738],{},[902,45754,2738],{"encoding":904},"; vzroste-li důchod z ",[883,45757,45759],{"className":45758},[886],[888,45760,45761],{"xmlns":890},[892,45762,45763,45767],{},[895,45764,45765],{},[898,45766,4618],{},[902,45768,4618],{"encoding":904},[883,45770,45772],{"className":45771},[886],[888,45773,45774],{"xmlns":890},[892,45775,45776,45788],{},[895,45777,45778,45784,45786],{},[3284,45779,45780,45782],{},[898,45781,4618],{},[1762,45783,1764],{},[1693,45785,1922],{},[898,45787,4618],{},[902,45789,45790],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,45793,45795],{"className":45794},[886],[888,45796,45797],{"xmlns":890},[892,45798,45799,45807],{},[895,45800,45801],{},[3284,45802,45803,45805],{},[898,45804,1701],{},[1762,45806,1911],{},[902,45808,45722],{"encoding":904}," odpovídá vyšší ",[883,45811,45813],{"className":45812},[886],[888,45814,45815],{"xmlns":890},[892,45816,45817,45833],{},[895,45818,45819,45825,45827],{},[3284,45820,45821,45823],{},[898,45822,1712],{},[1762,45824,1764],{},[1693,45826,1922],{},[3284,45828,45829,45831],{},[898,45830,1712],{},[1762,45832,1911],{},[902,45834,45835],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,45838,45839],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,45842,45843],{},[9465,45844],{"alt":45845,"className":45846,"src":45847},"imek-posun-vs-pohyb-po-krivce",[210,9469],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,45849,45850],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,45852,45853],{},[614,45854,45855,45856,20840,45886,45907],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,45857,45859],{"className":45858},[886],[888,45860,45861],{"xmlns":890},[892,45862,45863,45883],{},[895,45864,45865,45871,45873,45875,45877],{},[3284,45866,45867,45869],{},[898,45868,2738],{},[1762,45870,2398],{},[1693,45872,1899],{"separator":1898},[898,45874,2738],{},[1693,45876,1899],{"separator":1898},[3284,45878,45879,45881],{},[898,45880,2738],{},[1762,45882,1764],{},[902,45884,45885],{"encoding":904},"D_2, D, D_1",[883,45887,45889],{"className":45888},[886],[888,45890,45891],{"xmlns":890},[892,45892,45893,45905],{},[895,45894,45895,45897,45899,45901,45903],{},[1693,45896,1709],{"stretchy":1708},[898,45898,1712],{},[1693,45900,1899],{"separator":1898},[898,45902,1701],{},[1693,45904,1731],{"stretchy":1708},[902,45906,1978],{"encoding":904},", šipky naznačují posuny.",[44701,45909,45911],{"id":45910},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,45913,45914,45916,45917,45940,45941,45958,45959,45976,45977,1789],{},[38,45915,44709],{}," Poptávce ",[883,45918,45920],{"className":45919},[886],[888,45921,45922],{"xmlns":890},[892,45923,45924,45938],{},[895,45925,45926,45928,45930,45932,45934,45936],{},[898,45927,1701],{},[1693,45929,1695],{},[898,45931,2738],{},[1693,45933,1709],{"stretchy":1708},[898,45935,1712],{},[1693,45937,1731],{"stretchy":1708},[902,45939,3980],{"encoding":904}," odpovídá ceně ",[883,45942,45944],{"className":45943},[886],[888,45945,45946],{"xmlns":890},[892,45947,45948,45956],{},[895,45949,45950],{},[3284,45951,45952,45954],{},[898,45953,1701],{},[1762,45955,1911],{},[902,45957,45722],{"encoding":904}," množství ",[883,45960,45962],{"className":45961},[886],[888,45963,45964],{"xmlns":890},[892,45965,45966,45974],{},[895,45967,45968],{},[3284,45969,45970,45972],{},[898,45971,1712],{},[1762,45973,1911],{},[902,45975,6293],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,45978,45980],{"className":45979},[886],[888,45981,45982],{"xmlns":890},[892,45983,45984,45988],{},[895,45985,45986],{},[898,45987,2663],{},[902,45989,2663],{"encoding":904},[724,45991,45992,45994,45995,46012,46013,46035],{},[38,45993,44741],{}," Kupující nakupuje množství ",[883,45996,45998],{"className":45997},[886],[888,45999,46000],{"xmlns":890},[892,46001,46002,46010],{},[895,46003,46004],{},[3284,46005,46006,46008],{},[898,46007,1712],{},[1762,46009,1764],{},[902,46011,5809],{"encoding":904},", které odpovídá ceně ",[883,46014,46016],{"className":46015},[886],[888,46017,46018],{"xmlns":890},[892,46019,46020,46032],{},[895,46021,46022,46028,46030],{},[3284,46023,46024,46026],{},[898,46025,1701],{},[1762,46027,1911],{},[1693,46029,1892],{},[898,46031,2663],{},[902,46033,46034],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,46037,46039],{"className":46038},[886],[888,46040,46041],{"xmlns":890,"display":34854},[892,46042,46043,46077],{},[895,46044,46045,46047,46049,46055,46057,46059,46061,46063,46065,46067,46069,46071,46073,46075],{},[898,46046,1701],{},[1693,46048,1695],{},[3284,46050,46051,46053],{},[898,46052,2738],{},[1762,46054,1764],{},[1693,46056,1709],{"stretchy":1708},[898,46058,1712],{},[1693,46060,1731],{"stretchy":1708},[1693,46062,1695],{},[898,46064,2738],{},[1693,46066,1709],{"stretchy":1708},[898,46068,1712],{},[1693,46070,1731],{"stretchy":1708},[1693,46072,1698],{},[898,46074,2663],{},[1693,46076,1899],{"separator":1898},[902,46078,46079],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,46081,46082,46083,1789],{},"tj. dojde k ",[38,46084,46085],{},"posunu poptávky doleva",[724,46087,46088],{},[614,46089,46090,46091,46112,46113,1343,46130,1343,46143,46164,46165,4286,46182,1789],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,46092,46094],{"className":46093},[886],[888,46095,46096],{"xmlns":890},[892,46097,46098,46110],{},[895,46099,46100,46102,46104,46106,46108],{},[1693,46101,1709],{"stretchy":1708},[898,46103,1712],{},[1693,46105,1899],{"separator":1898},[898,46107,1701],{},[1693,46109,1731],{"stretchy":1708},[902,46111,1978],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,46114,46116],{"className":46115},[886],[888,46117,46118],{"xmlns":890},[892,46119,46120,46128],{},[895,46121,46122],{},[3284,46123,46124,46126],{},[898,46125,1701],{},[1762,46127,1911],{},[902,46129,45722],{"encoding":904},[883,46131,46133],{"className":46132},[886],[888,46134,46135],{"xmlns":890},[892,46136,46137,46141],{},[895,46138,46139],{},[898,46140,2663],{},[902,46142,2663],{"encoding":904},[883,46144,46146],{"className":46145},[886],[888,46147,46148],{"xmlns":890},[892,46149,46150,46162],{},[895,46151,46152,46158,46160],{},[3284,46153,46154,46156],{},[898,46155,1701],{},[1762,46157,1911],{},[1693,46159,1892],{},[898,46161,2663],{},[902,46163,46034],{"encoding":904},"; na vodorovné ",[883,46166,46168],{"className":46167},[886],[888,46169,46170],{"xmlns":890},[892,46171,46172,46180],{},[895,46173,46174],{},[3284,46175,46176,46178],{},[898,46177,1712],{},[1762,46179,1764],{},[902,46181,5809],{"encoding":904},[883,46183,46185],{"className":46184},[886],[888,46186,46187],{"xmlns":890},[892,46188,46189,46197],{},[895,46190,46191],{},[3284,46192,46193,46195],{},[898,46194,1712],{},[1762,46196,1911],{},[902,46198,6293],{"encoding":904},[198,46200,46202],{"id":46201},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,46204,46205],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,46207,46209],{"className":46208},[886],[888,46210,46211],{"xmlns":890,"display":34854},[892,46212,46213,46398],{},[3626,46214,46215],{"width":34859},[3632,46216,46217,46219,46391,46393],{},[3635,46218],{"width":34864},[3635,46220,46221],{},[3626,46222,46223,46307],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,46224,46225,46235],{},[3635,46226,46227],{},[3638,46228,46229],{"scriptlevel":1911,"displaystyle":1898},[3284,46230,46231,46233],{},[898,46232,1712],{},[1762,46234,1764],{},[3635,46236,46237],{},[3638,46238,46239],{"scriptlevel":1911,"displaystyle":1898},[895,46240,46241,46243,46245,46251,46253,46259,46261,46267,46269,46271,46277,46279,46285,46291,46293,46299,46305],{},[895,46242],{},[1693,46244,1695],{},[3284,46246,46247,46249],{},[898,46248,2738],{},[1762,46250,1764],{},[1693,46252,1709],{"stretchy":1708},[3284,46254,46255,46257],{},[898,46256,1701],{},[1762,46258,1764],{},[1693,46260,1899],{"separator":1898},[3284,46262,46263,46265],{},[898,46264,1701],{},[1762,46266,2398],{},[1693,46268,1731],{"stretchy":1708},[1693,46270,1695],{},[3284,46272,46273,46275],{},[898,46274,207],{},[1762,46276,1764],{},[1693,46278,1892],{},[3284,46280,46281,46283],{},[898,46282,1895],{},[1762,46284,1764],{},[3284,46286,46287,46289],{},[898,46288,1701],{},[1762,46290,1764],{},[1693,46292,1892],{},[3284,46294,46295,46297],{},[898,46296,2000],{},[1762,46298,1764],{},[3284,46300,46301,46303],{},[898,46302,1701],{},[1762,46304,2398],{},[1693,46306,1899],{"separator":1898},[3632,46308,46309,46319],{},[3635,46310,46311],{},[3638,46312,46313],{"scriptlevel":1911,"displaystyle":1898},[3284,46314,46315,46317],{},[898,46316,1712],{},[1762,46318,2398],{},[3635,46320,46321],{},[3638,46322,46323],{"scriptlevel":1911,"displaystyle":1898},[895,46324,46325,46327,46329,46335,46337,46343,46345,46351,46353,46355,46361,46363,46369,46375,46377,46383,46389],{},[895,46326],{},[1693,46328,1695],{},[3284,46330,46331,46333],{},[898,46332,2738],{},[1762,46334,2398],{},[1693,46336,1709],{"stretchy":1708},[3284,46338,46339,46341],{},[898,46340,1701],{},[1762,46342,1764],{},[1693,46344,1899],{"separator":1898},[3284,46346,46347,46349],{},[898,46348,1701],{},[1762,46350,2398],{},[1693,46352,1731],{"stretchy":1708},[1693,46354,1695],{},[3284,46356,46357,46359],{},[898,46358,207],{},[1762,46360,2398],{},[1693,46362,1892],{},[3284,46364,46365,46367],{},[898,46366,1895],{},[1762,46368,2398],{},[3284,46370,46371,46373],{},[898,46372,1701],{},[1762,46374,1764],{},[1693,46376,1892],{},[3284,46378,46379,46381],{},[898,46380,2000],{},[1762,46382,2398],{},[3284,46384,46385,46387],{},[898,46386,1701],{},[1762,46388,2398],{},[898,46390,1789],{"mathvariant":1704},[3635,46392],{"width":34864},[3635,46394,46395],{},[1915,46396,46397],{},"(2.6)",[902,46399,46400],{"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}",[44125,46402,46404],{"id":46403},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,46406,46407,46454,46501],{},[123,46408,46409,1343,46431,46453],{},[883,46410,46412],{"className":46411},[886],[888,46413,46414],{"xmlns":890},[892,46415,46416,46428],{},[895,46417,46418,46424,46426],{},[3284,46419,46420,46422],{},[898,46421,207],{},[1762,46423,1764],{},[1693,46425,1922],{},[1762,46427,1911],{},[902,46429,46430],{"encoding":904},"a_1 > 0",[883,46432,46434],{"className":46433},[886],[888,46435,46436],{"xmlns":890},[892,46437,46438,46450],{},[895,46439,46440,46446,46448],{},[3284,46441,46442,46444],{},[898,46443,207],{},[1762,46445,2398],{},[1693,46447,1922],{},[1762,46449,1911],{},[902,46451,46452],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,46455,46456,1343,46478,46500],{},[883,46457,46459],{"className":46458},[886],[888,46460,46461],{"xmlns":890},[892,46462,46463,46475],{},[895,46464,46465,46471,46473],{},[3284,46466,46467,46469],{},[898,46468,1895],{},[1762,46470,1764],{},[1693,46472,1908],{},[1762,46474,1911],{},[902,46476,46477],{"encoding":904},"b_1 \u003C 0",[883,46479,46481],{"className":46480},[886],[888,46482,46483],{"xmlns":890},[892,46484,46485,46497],{},[895,46486,46487,46493,46495],{},[3284,46488,46489,46491],{},[898,46490,2000],{},[1762,46492,2398],{},[1693,46494,1908],{},[1762,46496,1911],{},[902,46498,46499],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,46502,46503,46504,1343,46521,46539,46540],{},"zkřížené koeficienty ",[883,46505,46507],{"className":46506},[886],[888,46508,46509],{"xmlns":890},[892,46510,46511,46519],{},[895,46512,46513],{},[3284,46514,46515,46517],{},[898,46516,2000],{},[1762,46518,1764],{},[902,46520,36583],{"encoding":904},[883,46522,46524],{"className":46523},[886],[888,46525,46526],{"xmlns":890},[892,46527,46528,46536],{},[895,46529,46530],{},[3284,46531,46532,46534],{},[898,46533,1895],{},[1762,46535,2398],{},[902,46537,46538],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,46541,46542,46592],{},[123,46543,46544,46547,46548,1343,46570,1899],{},[38,46545,46546],{},"substituty"," (máslo vs. margarín): ",[883,46549,46551],{"className":46550},[886],[888,46552,46553],{"xmlns":890},[892,46554,46555,46567],{},[895,46556,46557,46563,46565],{},[3284,46558,46559,46561],{},[898,46560,2000],{},[1762,46562,1764],{},[1693,46564,1922],{},[1762,46566,1911],{},[902,46568,46569],{"encoding":904},"c_1 > 0",[883,46571,46573],{"className":46572},[886],[888,46574,46575],{"xmlns":890},[892,46576,46577,46589],{},[895,46578,46579,46585,46587],{},[3284,46580,46581,46583],{},[898,46582,1895],{},[1762,46584,2398],{},[1693,46586,1922],{},[1762,46588,1911],{},[902,46590,46591],{"encoding":904},"b_2 > 0",[123,46593,46594,46597,46598,1343,46620,1789],{},[38,46595,46596],{},"komplementy"," (auto vs. benzín): ",[883,46599,46601],{"className":46600},[886],[888,46602,46603],{"xmlns":890},[892,46604,46605,46617],{},[895,46606,46607,46613,46615],{},[3284,46608,46609,46611],{},[898,46610,2000],{},[1762,46612,1764],{},[1693,46614,1908],{},[1762,46616,1911],{},[902,46618,46619],{"encoding":904},"c_1 \u003C 0",[883,46621,46623],{"className":46622},[886],[888,46624,46625],{"xmlns":890},[892,46626,46627,46639],{},[895,46628,46629,46635,46637],{},[3284,46630,46631,46633],{},[898,46632,1895],{},[1762,46634,2398],{},[1693,46636,1908],{},[1762,46638,1911],{},[902,46640,46641],{"encoding":904},"b_2 \u003C 0",[724,46643,46644],{},"Schematicky:",[724,46646,46647,46650],{},[38,46648,46649],{},"Substituty",[883,46651,46653],{"className":46652},[886],[888,46654,46655],{"xmlns":890},[892,46656,46657,46796],{},[895,46658,46659,46665,46667,46682,46684,46704,46706,46726,46728,46730,46736,46738,46752,46754,46774,46776],{},[3284,46660,46661,46663],{},[898,46662,1712],{},[1762,46664,1764],{},[1693,46666,1695],{},[898,46668,46669],{},[46670,46671,46672,46680],"munder",{},[1693,46673,46674],{},[3284,46675,46676,46678],{},[898,46677,207],{},[1762,46679,1764],{},[1693,46681,1892],{"lspace":1723,"rspace":1723},[1693,46683,1892],{},[898,46685,46686],{},[46670,46687,46688,46702],{},[1693,46689,46690,46696],{},[3284,46691,46692,46694],{},[898,46693,1895],{},[1762,46695,1764],{},[3284,46697,46698,46700],{},[898,46699,1701],{},[1762,46701,1764],{},[1693,46703,1698],{"lspace":1723,"rspace":1723},[1693,46705,1892],{},[898,46707,46708],{},[46670,46709,46710,46724],{},[1693,46711,46712,46718],{},[3284,46713,46714,46716],{},[898,46715,2000],{},[1762,46717,1764],{},[3284,46719,46720,46722],{},[898,46721,1701],{},[1762,46723,2398],{},[1693,46725,1892],{"lspace":1723,"rspace":1723},[1693,46727,1899],{"separator":1898},[1901,46729],{"width":1903},[3284,46731,46732,46734],{},[898,46733,1712],{},[1762,46735,2398],{},[1693,46737,1695],{},[898,46739,46740],{},[46670,46741,46742,46750],{},[1693,46743,46744],{},[3284,46745,46746,46748],{},[898,46747,207],{},[1762,46749,2398],{},[1693,46751,1892],{"lspace":1723,"rspace":1723},[1693,46753,1892],{},[898,46755,46756],{},[46670,46757,46758,46772],{},[1693,46759,46760,46766],{},[3284,46761,46762,46764],{},[898,46763,1895],{},[1762,46765,2398],{},[3284,46767,46768,46770],{},[898,46769,1701],{},[1762,46771,1764],{},[1693,46773,1892],{"lspace":1723,"rspace":1723},[1693,46775,1892],{},[898,46777,46778],{},[46670,46779,46780,46794],{},[1693,46781,46782,46788],{},[3284,46783,46784,46786],{},[898,46785,2000],{},[1762,46787,2398],{},[3284,46789,46790,46792],{},[898,46791,1701],{},[1762,46793,2398],{},[1693,46795,1698],{"lspace":1723,"rspace":1723},[902,46797,46798],{"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}",[724,46800,46801,46804],{},[38,46802,46803],{},"Komplementy",[883,46805,46807],{"className":46806},[886],[888,46808,46809],{"xmlns":890},[892,46810,46811,46949],{},[895,46812,46813,46819,46821,46835,46837,46857,46859,46879,46881,46883,46889,46891,46905,46907,46927,46929],{},[3284,46814,46815,46817],{},[898,46816,1712],{},[1762,46818,1764],{},[1693,46820,1695],{},[898,46822,46823],{},[46670,46824,46825,46833],{},[1693,46826,46827],{},[3284,46828,46829,46831],{},[898,46830,207],{},[1762,46832,1764],{},[1693,46834,1892],{"lspace":1723,"rspace":1723},[1693,46836,1892],{},[898,46838,46839],{},[46670,46840,46841,46855],{},[1693,46842,46843,46849],{},[3284,46844,46845,46847],{},[898,46846,1895],{},[1762,46848,1764],{},[3284,46850,46851,46853],{},[898,46852,1701],{},[1762,46854,1764],{},[1693,46856,1698],{"lspace":1723,"rspace":1723},[1693,46858,1892],{},[898,46860,46861],{},[46670,46862,46863,46877],{},[1693,46864,46865,46871],{},[3284,46866,46867,46869],{},[898,46868,2000],{},[1762,46870,1764],{},[3284,46872,46873,46875],{},[898,46874,1701],{},[1762,46876,2398],{},[1693,46878,1698],{"lspace":1723,"rspace":1723},[1693,46880,1899],{"separator":1898},[1901,46882],{"width":1903},[3284,46884,46885,46887],{},[898,46886,1712],{},[1762,46888,2398],{},[1693,46890,1695],{},[898,46892,46893],{},[46670,46894,46895,46903],{},[1693,46896,46897],{},[3284,46898,46899,46901],{},[898,46900,207],{},[1762,46902,2398],{},[1693,46904,1892],{"lspace":1723,"rspace":1723},[1693,46906,1892],{},[898,46908,46909],{},[46670,46910,46911,46925],{},[1693,46912,46913,46919],{},[3284,46914,46915,46917],{},[898,46916,1895],{},[1762,46918,2398],{},[3284,46920,46921,46923],{},[898,46922,1701],{},[1762,46924,1764],{},[1693,46926,1698],{"lspace":1723,"rspace":1723},[1693,46928,1892],{},[898,46930,46931],{},[46670,46932,46933,46947],{},[1693,46934,46935,46941],{},[3284,46936,46937,46939],{},[898,46938,2000],{},[1762,46940,2398],{},[3284,46942,46943,46945],{},[898,46944,1701],{},[1762,46946,2398],{},[1693,46948,1698],{"lspace":1723,"rspace":1723},[902,46950,46951],{"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}",[1852,46953],{},[115,46955,19957],{"id":43560},[1636,46957,46958],{},[724,46959,46960,46962,46963,43771,46976,43785,46989,46991,46992,12537,47016,47034],{},[883,46961,11036],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,46964,46966],{"className":46965},[886],[888,46967,46968],{"xmlns":890},[892,46969,46970,46974],{},[895,46971,46972],{},[898,46973,1712],{},[902,46975,1712],{"encoding":904},[883,46977,46979],{"className":46978},[886],[888,46980,46981],{"xmlns":890},[892,46982,46983,46987],{},[895,46984,46985],{},[898,46986,1701],{},[902,46988,1701],{"encoding":904},[38,46990,2036],{},": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,46993,46995],{"className":46994},[886],[888,46996,46997],{"xmlns":890},[892,46998,46999,47013],{},[895,47000,47001,47003,47005,47007,47009,47011],{},[898,47002,1701],{},[1693,47004,1695],{},[898,47006,2000],{},[898,47008,1712],{},[1693,47010,1892],{},[898,47012,1771],{},[902,47014,47015],{"encoding":904},"P = cQ + d",[883,47017,47019],{"className":47018},[886],[888,47020,47021],{"xmlns":890},[892,47022,47023,47031],{},[895,47024,47025,47027,47029],{},[898,47026,2000],{},[1693,47028,1922],{},[1762,47030,1911],{},[902,47032,47033],{"encoding":904},"c > 0"," je standardní aproximací.",[198,47036,43841],{"id":47037},"obecný-vícefaktorový-model-1",[724,47039,47040,16877,47043,47046,47047,47060,47061,5473,47074,43689,47087,47100,47101,47114,47115,43718,47128,47141],{},[38,47041,47042],{},"Nabízené množství",[614,47044,47045],{},"quantity supplied",") závisí na ceně ",[883,47048,47050],{"className":47049},[886],[888,47051,47052],{"xmlns":890},[892,47053,47054,47058],{},[895,47055,47056],{},[898,47057,1701],{},[902,47059,1701],{"encoding":904},", cenách výrobních faktorů (práce ",[883,47062,47064],{"className":47063},[886],[888,47065,47066],{"xmlns":890},[892,47067,47068,47072],{},[895,47069,47070],{},[898,47071,4840],{},[902,47073,4840],{"encoding":904},[883,47075,47077],{"className":47076},[886],[888,47078,47079],{"xmlns":890},[892,47080,47081,47085],{},[895,47082,47083],{},[898,47084,4845],{},[902,47086,4845],{"encoding":904},[883,47088,47090],{"className":47089},[886],[888,47091,47092],{"xmlns":890},[892,47093,47094,47098],{},[895,47095,47096],{},[898,47097,1691],{},[902,47099,1691],{"encoding":904},"), očekávání ",[883,47102,47104],{"className":47103},[886],[888,47105,47106],{"xmlns":890},[892,47107,47108,47112],{},[895,47109,47110],{},[898,47111,2985],{},[902,47113,2985],{"encoding":904},", počtu výrobců ",[883,47116,47118],{"className":47117},[886],[888,47119,47120],{"xmlns":890},[892,47121,47122,47126],{},[895,47123,47124],{},[898,47125,43715],{},[902,47127,43715],{"encoding":904},[883,47129,47131],{"className":47130},[886],[888,47132,47133],{"xmlns":890},[892,47134,47135,47139],{},[895,47136,47137],{},[898,47138,6450],{},[902,47140,6450],{"encoding":904}," a dalších:",[883,47143,47145],{"className":47144},[886],[888,47146,47147],{"xmlns":890,"display":34854},[892,47148,47149,47208],{},[3626,47150,47151],{"width":34859},[3632,47152,47153,47155,47201,47203],{},[3635,47154],{"width":34864},[3635,47156,47157],{},[895,47158,47159,47161,47163,47165,47167,47169,47171,47173,47175,47177,47179,47181,47183,47185,47187,47189,47191,47193,47195,47197,47199],{},[898,47160,1712],{},[1693,47162,1695],{},[898,47164,3611],{},[1693,47166,1709],{"stretchy":1708},[898,47168,1701],{},[1693,47170,1899],{"separator":1898},[898,47172,4840],{},[1693,47174,1899],{"separator":1898},[898,47176,4845],{},[1693,47178,1899],{"separator":1898},[898,47180,1691],{},[1693,47182,1899],{"separator":1898},[898,47184,2985],{},[1693,47186,1899],{"separator":1898},[898,47188,43715],{},[1693,47190,1899],{"separator":1898},[898,47192,6450],{},[1693,47194,1899],{"separator":1898},[1693,47196,16501],{},[1693,47198,1731],{"stretchy":1708},[898,47200,1789],{"mathvariant":1704},[3635,47202],{"width":34864},[3635,47204,47205],{},[1915,47206,47207],{},"(2.7)",[902,47209,47210],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,47212,45191,47213,16877,47216,47219],{},[38,47214,47215],{},"funkce nabídky",[614,47217,47218],{},"supply function",") v širším slova smyslu.",[198,47221,47223],{"id":47222},"jednofaktorový-model","Jednofaktorový model",[724,47225,47226],{},"V nejpřirozenějším jednofaktorovém modelu",[883,47228,47230],{"className":47229},[886],[888,47231,47232],{"xmlns":890,"display":34854},[892,47233,47234,47285],{},[3626,47235,47236],{"width":34859},[3632,47237,47238,47240,47278,47280],{},[3635,47239],{"width":34864},[3635,47241,47242],{},[895,47243,47244,47246,47248,47250,47252,47254,47256,47258,47260,47262,47264,47266,47268,47270,47272,47274,47276],{},[898,47245,1712],{},[1693,47247,1695],{},[898,47249,3611],{},[1693,47251,1709],{"stretchy":1708},[898,47253,1701],{},[1693,47255,1731],{"stretchy":1708},[1693,47257,1899],{"separator":1898},[1901,47259],{"width":1903},[1915,47261,44194],{},[1901,47263],{"width":1903},[898,47265,1701],{},[1693,47267,1695],{},[898,47269,3611],{},[1693,47271,1709],{"stretchy":1708},[898,47273,1712],{},[1693,47275,1731],{"stretchy":1708},[898,47277,1789],{"mathvariant":1704},[3635,47279],{"width":34864},[3635,47281,47282],{},[1915,47283,47284],{},"(2.8)",[902,47286,47287],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,47289,47290,47291,16877,47294,3042],{},"Graf je ",[38,47292,47293],{},"křivka nabídky",[614,47295,47296],{},"supply curve",[44125,47298,47300],{"id":47299},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1636,47302,47303],{},[724,47304,47305],{},[38,47306,44240,47307,47320,47321,44295],{},[883,47308,47310],{"className":47309},[886],[888,47311,47312],{"xmlns":890},[892,47313,47314,47318],{},[895,47315,47316],{},[898,47317,1701],{},[902,47319,1701],{"encoding":904},", pak nabízené množství ",[883,47322,47324],{"className":47323},[886],[888,47325,47326],{"xmlns":890},[892,47327,47328,47332],{},[895,47329,47330],{},[898,47331,1712],{},[902,47333,1712],{"encoding":904},[724,47335,47336,47337,47362,47363,47393,47394,47411],{},"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 ",[883,47338,47340],{"className":47339},[886],[888,47341,47342],{"xmlns":890},[892,47343,47344,47360],{},[895,47345,47346,47348,47350,47352,47358],{},[1693,47347,9392],{"stretchy":1708},[1762,47349,1911],{},[1693,47351,1899],{"separator":1898},[3284,47353,47354,47356],{},[898,47355,1701],{},[1762,47357,1911],{},[1693,47359,9407],{"stretchy":1708},[902,47361,44380],{"encoding":904}," na svislé ose (případně z ",[883,47364,47366],{"className":47365},[886],[888,47367,47368],{"xmlns":890},[892,47369,47370,47390],{},[895,47371,47372,47374,47380,47382,47388],{},[1693,47373,9392],{"stretchy":1708},[3284,47375,47376,47378],{},[898,47377,1712],{},[1762,47379,1764],{},[1693,47381,1899],{"separator":1898},[3284,47383,47384,47386],{},[898,47385,1701],{},[1762,47387,1764],{},[1693,47389,9407],{"stretchy":1708},[902,47391,47392],{"encoding":904},"[Q_1, P_1]","), kde ",[883,47395,47397],{"className":47396},[886],[888,47398,47399],{"xmlns":890},[892,47400,47401,47409],{},[895,47402,47403],{},[3284,47404,47405,47407],{},[898,47406,1701],{},[1762,47408,1911],{},[902,47410,45722],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,47413,47414],{},[614,47415,47416,47417,1654,47430,1789],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,47418,47420],{"className":47419},[886],[888,47421,47422],{"xmlns":890},[892,47423,47424,47428],{},[895,47425,47426],{},[898,47427,3611],{},[902,47429,3611],{"encoding":904},[883,47431,47433],{"className":47432},[886],[888,47434,47435],{"xmlns":890},[892,47436,47437,47449],{},[895,47438,47439,47441,47443,47445,47447],{},[1693,47440,1709],{"stretchy":1708},[898,47442,1712],{},[1693,47444,1899],{"separator":1898},[898,47446,1701],{},[1693,47448,1731],{"stretchy":1708},[902,47450,1978],{"encoding":904},[44125,47452,47454],{"id":47453},"lineární-model-nabídky","Lineární model nabídky",[883,47456,47458],{"className":47457},[886],[888,47459,47460],{"xmlns":890,"display":34854},[892,47461,47462,47501],{},[3626,47463,47464],{"width":34859},[3632,47465,47466,47468,47494,47496],{},[3635,47467],{"width":34864},[3635,47469,47470],{},[895,47471,47472,47474,47476,47478,47480,47482,47484,47486,47488,47490,47492],{},[898,47473,1701],{},[1693,47475,1695],{},[898,47477,2000],{},[898,47479,1712],{},[1693,47481,1892],{},[898,47483,1771],{},[1693,47485,1899],{"separator":1898},[1901,47487],{"width":1903},[898,47489,2000],{},[1693,47491,1922],{},[1762,47493,19295],{},[3635,47495],{"width":34864},[3635,47497,47498],{},[1915,47499,47500],{},"(2.9)",[902,47502,47503],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,47505,47506,47507,47543,47544,47557],{},"Alternativně ",[883,47508,47510],{"className":47509},[886],[888,47511,47512],{"xmlns":890},[892,47513,47514,47540],{},[895,47515,47516,47518,47520,47528,47530,47532],{},[898,47517,1712],{},[1693,47519,1695],{},[3638,47521,47522],{"scriptlevel":1911,"displaystyle":1708},[2132,47523,47524,47526],{},[1762,47525,1764],{},[898,47527,2000],{},[898,47529,1701],{},[1693,47531,1698],{},[3638,47533,47534],{"scriptlevel":1911,"displaystyle":1708},[2132,47535,47536,47538],{},[898,47537,1771],{},[898,47539,2000],{},[902,47541,47542],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,47545,47547],{"className":47546},[886],[888,47548,47549],{"xmlns":890},[892,47550,47551,47555],{},[895,47552,47553],{},[898,47554,1701],{},[902,47556,1701],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[44701,47559,47561],{"id":47560},"příklad-25","Příklad 2.5",[724,47563,47564,47566,47567,1789],{},[38,47565,44709],{}," Lineární nabídka ",[883,47568,47570],{"className":47569},[886],[888,47571,47572],{"xmlns":890},[892,47573,47574,47588],{},[895,47575,47576,47578,47580,47582,47584,47586],{},[898,47577,1701],{},[1693,47579,1695],{},[1762,47581,11877],{},[898,47583,1712],{},[1693,47585,1892],{},[1762,47587,11872],{},[902,47589,47590],{"encoding":904},"P = 0{,}5Q + 25",[724,47592,47593,47595,47596,1789],{},[38,47594,44741],{}," Alternativní tvar ",[883,47597,47599],{"className":47598},[886],[888,47600,47601],{"xmlns":890},[892,47602,47603,47617],{},[895,47604,47605,47607,47609,47611,47613,47615],{},[898,47606,1712],{},[1693,47608,1695],{},[1762,47610,2398],{},[898,47612,1701],{},[1693,47614,1698],{},[1762,47616,10017],{},[902,47618,47619],{"encoding":904},"Q = 2P - 50",[16,47621,47622,47647],{},[19,47623,47624],{},[22,47625,47626,47641,47643,47645],{},[25,47627,47628],{},[883,47629,47631],{"className":47630},[886],[888,47632,47633],{"xmlns":890},[892,47634,47635,47639],{},[895,47636,47637],{},[898,47638,1701],{},[902,47640,1701],{"encoding":904},[25,47642,44795],{},[25,47644,21864],{},[25,47646,12079],{},[30,47648,47649],{},[22,47650,47651,47666,47668,47670],{},[35,47652,47653],{},[883,47654,47656],{"className":47655},[886],[888,47657,47658],{"xmlns":890},[892,47659,47660,47664],{},[895,47661,47662],{},[898,47663,1712],{},[902,47665,1712],{"encoding":904},[35,47667,9763],{},[35,47669,15892],{},[35,47671,44795],{},[198,47673,47675,47676,1731],{"id":47674},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,47677,47678],{},"shift of supply",[724,47680,47681,47682,47685,47686,47703,47704,47729,47730,1789],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,47683,47684],{},"doprava",": při stejné ceně ",[883,47687,47689],{"className":47688},[886],[888,47690,47691],{"xmlns":890},[892,47692,47693,47701],{},[895,47694,47695],{},[3284,47696,47697,47699],{},[898,47698,1701],{},[1762,47700,1911],{},[902,47702,45722],{"encoding":904}," vyrobí výrobce větší ",[883,47705,47707],{"className":47706},[886],[888,47708,47709],{"xmlns":890},[892,47710,47711,47727],{},[895,47712,47713,47719,47721],{},[3284,47714,47715,47717],{},[898,47716,1712],{},[1762,47718,1764],{},[1693,47720,1922],{},[3284,47722,47723,47725],{},[898,47724,1712],{},[1762,47726,1911],{},[902,47728,45835],{"encoding":904},"); zdražení vstupů posune křivku ",[38,47731,47732],{},"doleva",[724,47734,47735],{},[614,47736,47737,47738,47751,47752,47770,47771,47789,47790,1789],{},"Obrázek 2.11: Původní ",[883,47739,47741],{"className":47740},[886],[888,47742,47743],{"xmlns":890},[892,47744,47745,47749],{},[895,47746,47747],{},[898,47748,3611],{},[902,47750,3611],{"encoding":904},", posunuté ",[883,47753,47755],{"className":47754},[886],[888,47756,47757],{"xmlns":890},[892,47758,47759,47767],{},[895,47760,47761],{},[3284,47762,47763,47765],{},[898,47764,3611],{},[1762,47766,1764],{},[902,47768,47769],{"encoding":904},"S_1"," (doprava) a ",[883,47772,47774],{"className":47773},[886],[888,47775,47776],{"xmlns":890},[892,47777,47778,47786],{},[895,47779,47780],{},[3284,47781,47782,47784],{},[898,47783,3611],{},[1762,47785,2398],{},[902,47787,47788],{"encoding":904},"S_2"," (doleva) v ",[883,47791,47793],{"className":47792},[886],[888,47794,47795],{"xmlns":890},[892,47796,47797,47809],{},[895,47798,47799,47801,47803,47805,47807],{},[1693,47800,1709],{"stretchy":1708},[898,47802,1712],{},[1693,47804,1899],{"separator":1898},[898,47806,1701],{},[1693,47808,1731],{"stretchy":1708},[902,47810,1978],{"encoding":904},[44701,47812,47814],{"id":47813},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,47816,47817,47819,47820,47844,47845,1789],{},[38,47818,44709],{}," Nabídka ",[883,47821,47823],{"className":47822},[886],[888,47824,47825],{"xmlns":890},[892,47826,47827,47841],{},[895,47828,47829,47831,47833,47835,47837,47839],{},[898,47830,1701],{},[1693,47832,1695],{},[898,47834,3611],{},[1693,47836,1709],{"stretchy":1708},[898,47838,1712],{},[1693,47840,1731],{"stretchy":1708},[902,47842,47843],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,47846,47848],{"className":47847},[886],[888,47849,47850],{"xmlns":890},[892,47851,47852,47856],{},[895,47853,47854],{},[898,47855,2663],{},[902,47857,2663],{"encoding":904},[724,47859,47860,47862,47863,47876,47877,47895,47896,47923],{},[38,47861,44741],{}," Spotřebitel zaplatí ",[883,47864,47866],{"className":47865},[886],[888,47867,47868],{"xmlns":890},[892,47869,47870,47874],{},[895,47871,47872],{},[898,47873,1701],{},[902,47875,1701],{"encoding":904},", výrobce obdrží ",[883,47878,47880],{"className":47879},[886],[888,47881,47882],{"xmlns":890},[892,47883,47884,47892],{},[895,47885,47886,47888,47890],{},[898,47887,1701],{},[1693,47889,1698],{},[898,47891,2663],{},[902,47893,47894],{"encoding":904},"P - T",". Z podmínky ",[883,47897,47899],{"className":47898},[886],[888,47900,47901],{"xmlns":890},[892,47902,47903,47921],{},[895,47904,47905,47907,47909,47911,47913,47915,47917,47919],{},[898,47906,1701],{},[1693,47908,1698],{},[898,47910,2663],{},[1693,47912,1695],{},[898,47914,3611],{},[1693,47916,1709],{"stretchy":1708},[898,47918,1712],{},[1693,47920,1731],{"stretchy":1708},[902,47922,6670],{"encoding":904}," plyne",[883,47925,47927],{"className":47926},[886],[888,47928,47929],{"xmlns":890,"display":34854},[892,47930,47931,47965],{},[895,47932,47933,47935,47937,47943,47945,47947,47949,47951,47953,47955,47957,47959,47961,47963],{},[898,47934,1701],{},[1693,47936,1695],{},[3284,47938,47939,47941],{},[898,47940,3611],{},[1762,47942,1764],{},[1693,47944,1709],{"stretchy":1708},[898,47946,1712],{},[1693,47948,1731],{"stretchy":1708},[1693,47950,1695],{},[898,47952,3611],{},[1693,47954,1709],{"stretchy":1708},[898,47956,1712],{},[1693,47958,1731],{"stretchy":1708},[1693,47960,1892],{},[898,47962,2663],{},[898,47964,1789],{"mathvariant":1704},[902,47966,47967],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,47969,47970,47971,47984,47985,1863,47998,48001,48002,4286,48022,6055,48040,1789],{},"Křivka ",[883,47972,47974],{"className":47973},[886],[888,47975,47976],{"xmlns":890},[892,47977,47978,47982],{},[895,47979,47980],{},[898,47981,3611],{},[902,47983,3611],{"encoding":904}," se tedy posune o ",[883,47986,47988],{"className":47987},[886],[888,47989,47990],{"xmlns":890},[892,47991,47992,47996],{},[895,47993,47994],{},[898,47995,2663],{},[902,47997,2663],{"encoding":904},[38,47999,48000],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,48003,48005],{"className":48004},[886],[888,48006,48007],{"xmlns":890},[892,48008,48009,48019],{},[895,48010,48011,48013,48015,48017],{},[898,48012,1701],{},[1693,48014,1695],{},[1762,48016,2398],{},[898,48018,1712],{},[902,48020,48021],{"encoding":904},"P = 2Q",[883,48023,48025],{"className":48024},[886],[888,48026,48027],{"xmlns":890},[892,48028,48029,48037],{},[895,48030,48031,48033,48035],{},[898,48032,2663],{},[1693,48034,1695],{},[1762,48036,9154],{},[902,48038,48039],{"encoding":904},"T = 6",[883,48041,48043],{"className":48042},[886],[888,48044,48045],{"xmlns":890},[892,48046,48047,48069],{},[895,48048,48049,48055,48057,48059,48061,48063,48065,48067],{},[3284,48050,48051,48053],{},[898,48052,3611],{},[1762,48054,1764],{},[1693,48056,4300],{},[898,48058,1701],{},[1693,48060,1695],{},[1762,48062,2398],{},[898,48064,1712],{},[1693,48066,1892],{},[1762,48068,9154],{},[902,48070,48071],{"encoding":904},"S_1: P = 2Q + 6",[724,48073,48074],{},[614,48075,48076,48077,48090],{},"Obrázek 2.12: Posun nabídky o ",[883,48078,48080],{"className":48079},[886],[888,48081,48082],{"xmlns":890},[892,48083,48084,48088],{},[895,48085,48086],{},[898,48087,2663],{},[902,48089,2663],{"encoding":904}," svisle nahoru.",[1852,48092],{},[115,48094,48096],{"id":48095},"tržní-rovnováha","Tržní rovnováha",[1636,48098,48099],{},[724,48100,48101,48103,48104,1863,48107,48139,48140,1343,48163,48186,48187,48190,48191,48204],{},[883,48102,11036],{}," TL;DR\nV ",[38,48105,48106],{},"rovnovážném bodě",[883,48108,48110],{"className":48109},[886],[888,48111,48112],{"xmlns":890},[892,48113,48114,48136],{},[895,48115,48116,48118,48120,48126,48128,48134],{},[898,48117,1691],{},[1693,48119,9392],{"stretchy":1708},[1717,48121,48122,48124],{},[898,48123,1712],{},[898,48125,1691],{},[1693,48127,1899],{"separator":1898},[1717,48129,48130,48132],{},[898,48131,1701],{},[898,48133,1691],{},[1693,48135,9407],{"stretchy":1708},[902,48137,48138],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,48141,48143],{"className":48142},[886],[888,48144,48145],{"xmlns":890},[892,48146,48147,48161],{},[895,48148,48149,48151,48153,48155,48157,48159],{},[898,48150,1701],{},[1693,48152,1695],{},[898,48154,2738],{},[1693,48156,1709],{"stretchy":1708},[898,48158,1712],{},[1693,48160,1731],{"stretchy":1708},[902,48162,3980],{"encoding":904},[883,48164,48166],{"className":48165},[886],[888,48167,48168],{"xmlns":890},[892,48169,48170,48184],{},[895,48171,48172,48174,48176,48178,48180,48182],{},[898,48173,1701],{},[1693,48175,1695],{},[898,48177,3611],{},[1693,48179,1709],{"stretchy":1708},[898,48181,1712],{},[1693,48183,1731],{"stretchy":1708},[902,48185,47843],{"encoding":904},". Čtyři ",[38,48188,48189],{},"pravidla komparativní statiky"," popisují, jak se ",[883,48192,48194],{"className":48193},[886],[888,48195,48196],{"xmlns":890},[892,48197,48198,48202],{},[895,48199,48200],{},[898,48201,1691],{},[902,48203,1691],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,48206,48208],{"id":48207},"definice","Definice",[724,48210,48211,16877,48213,48216,48217,1863,48220,48238,48239,48270,48271,16877,48274,3042],{},[38,48212,48096],{},[614,48214,48215],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,48218,48219],{},"rovnovážné ceně",[883,48221,48223],{"className":48222},[886],[888,48224,48225],{"xmlns":890},[892,48226,48227,48235],{},[895,48228,48229],{},[1717,48230,48231,48233],{},[898,48232,1701],{},[898,48234,1691],{},[902,48236,48237],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,48240,48242],{"className":48241},[886],[888,48243,48244],{"xmlns":890},[892,48245,48246,48268],{},[895,48247,48248,48250,48252,48258,48260,48266],{},[898,48249,1691],{},[1693,48251,9392],{"stretchy":1708},[1717,48253,48254,48256],{},[898,48255,1712],{},[898,48257,1691],{},[1693,48259,1899],{"separator":1898},[1717,48261,48262,48264],{},[898,48263,1701],{},[898,48265,1691],{},[1693,48267,9407],{"stretchy":1708},[902,48269,48138],{"encoding":904}," se nazývá ",[38,48272,48273],{},"rovnovážný bod",[614,48275,48276],{},"equilibrium point",[724,48278,48279,48280,1343,48303,1789],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,48281,48283],{"className":48282},[886],[888,48284,48285],{"xmlns":890},[892,48286,48287,48301],{},[895,48288,48289,48291,48293,48295,48297,48299],{},[898,48290,1701],{},[1693,48292,1695],{},[898,48294,2738],{},[1693,48296,1709],{"stretchy":1708},[898,48298,1712],{},[1693,48300,1731],{"stretchy":1708},[902,48302,3980],{"encoding":904},[883,48304,48306],{"className":48305},[886],[888,48307,48308],{"xmlns":890},[892,48309,48310,48324],{},[895,48311,48312,48314,48316,48318,48320,48322],{},[898,48313,1701],{},[1693,48315,1695],{},[898,48317,3611],{},[1693,48319,1709],{"stretchy":1708},[898,48321,1712],{},[1693,48323,1731],{"stretchy":1708},[902,48325,47843],{"encoding":904},[724,48327,48328],{},[9465,48329],{"alt":48330,"className":48331,"src":48332},"imek-poptavka-nabidka-rovnovaha",[210,9469],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,48334,48335],{},[614,48336,48337,48338,48351,48352,20840,48365,48386,48387,1789],{},"Obrázek 2.13: Klesající ",[883,48339,48341],{"className":48340},[886],[888,48342,48343],{"xmlns":890},[892,48344,48345,48349],{},[895,48346,48347],{},[898,48348,2738],{},[902,48350,2738],{"encoding":904}," a rostoucí ",[883,48353,48355],{"className":48354},[886],[888,48356,48357],{"xmlns":890},[892,48358,48359,48363],{},[895,48360,48361],{},[898,48362,3611],{},[902,48364,3611],{"encoding":904},[883,48366,48368],{"className":48367},[886],[888,48369,48370],{"xmlns":890},[892,48371,48372,48384],{},[895,48373,48374,48376,48378,48380,48382],{},[1693,48375,1709],{"stretchy":1708},[898,48377,1712],{},[1693,48379,1899],{"separator":1898},[898,48381,1701],{},[1693,48383,1731],{"stretchy":1708},[902,48385,1978],{"encoding":904}," protínající se v ",[883,48388,48390],{"className":48389},[886],[888,48391,48392],{"xmlns":890},[892,48393,48394,48416],{},[895,48395,48396,48398,48400,48406,48408,48414],{},[898,48397,1691],{},[1693,48399,9392],{"stretchy":1708},[1717,48401,48402,48404],{},[898,48403,1712],{},[898,48405,1691],{},[1693,48407,1899],{"separator":1898},[1717,48409,48410,48412],{},[898,48411,1701],{},[898,48413,1691],{},[1693,48415,9407],{"stretchy":1708},[902,48417,48138],{"encoding":904},[198,48419,48421],{"id":48420},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,48423,48424,48426,48427,48461,48462,1789],{},[38,48425,44709],{}," Poptávka ",[883,48428,48430],{"className":48429},[886],[888,48431,48432],{"xmlns":890},[892,48433,48434,48458],{},[895,48435,48436,48438,48440,48442,48448,48450,48452,48454,48456],{},[898,48437,1701],{},[1693,48439,1695],{},[1693,48441,1698],{},[1717,48443,48444,48446],{},[898,48445,1712],{},[1762,48447,2398],{},[1693,48449,1698],{},[1762,48451,9763],{},[898,48453,1712],{},[1693,48455,1892],{},[1762,48457,15660],{},[902,48459,48460],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,48463,48465],{"className":48464},[886],[888,48466,48467],{"xmlns":890},[892,48468,48469,48491],{},[895,48470,48471,48473,48475,48481,48483,48485,48487,48489],{},[898,48472,1701],{},[1693,48474,1695],{},[1717,48476,48477,48479],{},[898,48478,1712],{},[1762,48480,2398],{},[1693,48482,1892],{},[1762,48484,29746],{},[898,48486,1712],{},[1693,48488,1892],{},[1762,48490,39329],{},[902,48492,48493],{"encoding":904},"P = Q^2 + 14Q + 22",[724,48495,48496,48498],{},[38,48497,44741],{}," Z rovnosti",[883,48500,48502],{"className":48501},[886],[888,48503,48504],{"xmlns":890,"display":34854},[892,48505,48506,48544],{},[895,48507,48508,48510,48516,48518,48520,48522,48524,48526,48528,48534,48536,48538,48540,48542],{},[1693,48509,1698],{},[1717,48511,48512,48514],{},[898,48513,1712],{},[1762,48515,2398],{},[1693,48517,1698],{},[1762,48519,9763],{},[898,48521,1712],{},[1693,48523,1892],{},[1762,48525,15660],{},[1693,48527,1695],{},[1717,48529,48530,48532],{},[898,48531,1712],{},[1762,48533,2398],{},[1693,48535,1892],{},[1762,48537,29746],{},[898,48539,1712],{},[1693,48541,1892],{},[1762,48543,39329],{},[902,48545,48546],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,48548,48549,48550,48585,48586,48619,48620,48637,48638,48651,48652,1343,48674,48711,48712,1789],{},"dostaneme ",[883,48551,48553],{"className":48552},[886],[888,48554,48555],{"xmlns":890},[892,48556,48557,48582],{},[895,48558,48559,48561,48567,48569,48572,48574,48576,48578,48580],{},[1762,48560,2398],{},[1717,48562,48563,48565],{},[898,48564,1712],{},[1762,48566,2398],{},[1693,48568,1892],{},[1762,48570,48571],{},"24",[898,48573,1712],{},[1693,48575,1698],{},[1762,48577,12485],{},[1693,48579,1695],{},[1762,48581,1911],{},[902,48583,48584],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,48587,48589],{"className":48588},[886],[888,48590,48591],{"xmlns":890},[892,48592,48593,48616],{},[895,48594,48595,48601,48603,48605,48607,48609,48612,48614],{},[1717,48596,48597,48599],{},[898,48598,1712],{},[1762,48600,2398],{},[1693,48602,1892],{},[1762,48604,10402],{},[898,48606,1712],{},[1693,48608,1698],{},[1762,48610,48611],{},"64",[1693,48613,1695],{},[1762,48615,1911],{},[902,48617,48618],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,48621,48623],{"className":48622},[886],[888,48624,48625],{"xmlns":890},[892,48626,48627,48634],{},[895,48628,48629,48631],{},[1693,48630,1698],{},[1762,48632,48633],{},"16",[902,48635,48636],{"encoding":904},"-16"," (nevyhovuje) a ",[883,48639,48641],{"className":48640},[886],[888,48642,48643],{"xmlns":890},[892,48644,48645,48649],{},[895,48646,48647],{},[1762,48648,9262],{},[902,48650,9262],{"encoding":904},". Tedy ",[883,48653,48655],{"className":48654},[886],[888,48656,48657],{"xmlns":890},[892,48658,48659,48671],{},[895,48660,48661,48667,48669],{},[1717,48662,48663,48665],{},[898,48664,1712],{},[898,48666,1691],{},[1693,48668,1695],{},[1762,48670,9262],{},[902,48672,48673],{"encoding":904},"Q^E = 4",[883,48675,48677],{"className":48676},[886],[888,48678,48679],{"xmlns":890},[892,48680,48681,48708],{},[895,48682,48683,48689,48691,48693,48695,48697,48699,48701,48703,48705],{},[1717,48684,48685,48687],{},[898,48686,1701],{},[898,48688,1691],{},[1693,48690,1695],{},[1693,48692,1698],{},[1762,48694,48633],{},[1693,48696,1698],{},[1762,48698,12079],{},[1693,48700,1892],{},[1762,48702,15660],{},[1693,48704,1695],{},[1762,48706,48707],{},"94",[902,48709,48710],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,48713,48715],{"className":48714},[886],[888,48716,48717],{"xmlns":890},[892,48718,48719,48733],{},[895,48720,48721,48723,48725,48727,48729,48731],{},[898,48722,1691],{},[1693,48724,9392],{"stretchy":1708},[1762,48726,9262],{},[1693,48728,1899],{"separator":1898},[1762,48730,48707],{},[1693,48732,9407],{"stretchy":1708},[902,48734,48735],{"encoding":904},"E[4, 94]",[198,48737,48739],{"id":48738},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,48741,48742,48744],{},[38,48743,44709],{}," Poptávky a nabídky dvou zboží",[883,48746,48748],{"className":48747},[886],[888,48749,48750],{"xmlns":890,"display":34854},[892,48751,48752,48918],{},[3626,48753,48756,48844],{"rowspacing":27562,"columnalign":48754,"columnspacing":48755},"right left right left","0em 1em 0em",[3632,48757,48758,48768,48800,48810],{},[3635,48759,48760],{},[3638,48761,48762],{"scriptlevel":1911,"displaystyle":1898},[3284,48763,48764,48766],{},[898,48765,1712],{},[1762,48767,1764],{},[3635,48769,48770],{},[3638,48771,48772],{"scriptlevel":1911,"displaystyle":1898},[895,48773,48774,48776,48778,48780,48782,48784,48790,48792,48798],{},[895,48775],{},[1693,48777,1695],{},[1762,48779,12079],{},[1693,48781,1698],{},[1762,48783,9147],{},[3284,48785,48786,48788],{},[898,48787,1701],{},[1762,48789,1764],{},[1693,48791,1698],{},[3284,48793,48794,48796],{},[898,48795,1701],{},[1762,48797,2398],{},[1693,48799,1899],{"separator":1898},[3635,48801,48802],{},[3638,48803,48804],{"scriptlevel":1911,"displaystyle":1898},[3284,48805,48806,48808],{},[898,48807,1712],{},[1762,48809,2398],{},[3635,48811,48812],{},[3638,48813,48814],{"scriptlevel":1911,"displaystyle":1898},[895,48815,48816,48818,48820,48822,48824,48826,48832,48834,48836,48842],{},[895,48817],{},[1693,48819,1695],{},[1762,48821,10017],{},[1693,48823,1698],{},[1762,48825,2398],{},[3284,48827,48828,48830],{},[898,48829,1701],{},[1762,48831,1764],{},[1693,48833,1698],{},[1762,48835,9262],{},[3284,48837,48838,48840],{},[898,48839,1701],{},[1762,48841,2398],{},[1693,48843,1899],{"separator":1898},[3632,48845,48846,48856,48882,48892],{},[3635,48847,48848],{},[3638,48849,48850],{"scriptlevel":1911,"displaystyle":1898},[3284,48851,48852,48854],{},[898,48853,1712],{},[1762,48855,1764],{},[3635,48857,48858],{},[3638,48859,48860],{"scriptlevel":1911,"displaystyle":1898},[895,48861,48862,48864,48866,48868,48870,48872,48874,48880],{},[895,48863],{},[1693,48865,1695],{},[1693,48867,1698],{},[1762,48869,8357],{},[1693,48871,1892],{},[1762,48873,9262],{},[3284,48875,48876,48878],{},[898,48877,1701],{},[1762,48879,1764],{},[1693,48881,1899],{"separator":1898},[3635,48883,48884],{},[3638,48885,48886],{"scriptlevel":1911,"displaystyle":1898},[3284,48887,48888,48890],{},[898,48889,1712],{},[1762,48891,2398],{},[3635,48893,48894],{},[3638,48895,48896],{"scriptlevel":1911,"displaystyle":1898},[895,48897,48898,48900,48902,48904,48906,48908,48910,48916],{},[895,48899],{},[1693,48901,1695],{},[1693,48903,1698],{},[1762,48905,31000],{},[1693,48907,1892],{},[1762,48909,8357],{},[3284,48911,48912,48914],{},[898,48913,1701],{},[1762,48915,2398],{},[898,48917,1789],{"mathvariant":1704},[902,48919,48920],{"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}",[724,48922,48923,48925],{},[38,48924,44741],{}," Z rovností poptávek a nabídek dostaneme",[883,48927,48929],{"className":48928},[886],[888,48930,48931],{"xmlns":890,"display":34854},[892,48932,48933,48982],{},[895,48934,48935,48937,48943,48945,48951,48953,48955,48957,48959,48961,48967,48969,48971,48977,48979],{},[1762,48936,10881],{},[3284,48938,48939,48941],{},[898,48940,1701],{},[1762,48942,1764],{},[1693,48944,1892],{},[3284,48946,48947,48949],{},[898,48948,1701],{},[1762,48950,2398],{},[1693,48952,1695],{},[1762,48954,28006],{},[1693,48956,1899],{"separator":1898},[1901,48958],{"width":1903},[1762,48960,2398],{},[3284,48962,48963,48965],{},[898,48964,1701],{},[1762,48966,1764],{},[1693,48968,1892],{},[1762,48970,31000],{},[3284,48972,48973,48975],{},[898,48974,1701],{},[1762,48976,2398],{},[1693,48978,1695],{},[1762,48980,48981],{},"57.",[902,48983,48984],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,48986,48987,48988,1343,49012,49036,49037,1343,49062,49086,49087,49089],{},"Řešením je ",[883,48989,48991],{"className":48990},[886],[888,48992,48993],{"xmlns":890},[892,48994,48995,49009],{},[895,48996,48997,49005,49007],{},[5688,48998,48999,49001,49003],{},[898,49000,1701],{},[1762,49002,1764],{},[898,49004,1691],{},[1693,49006,1695],{},[1762,49008,9262],{},[902,49010,49011],{"encoding":904},"P_1^E = 4",[883,49013,49015],{"className":49014},[886],[888,49016,49017],{"xmlns":890},[892,49018,49019,49033],{},[895,49020,49021,49029,49031],{},[5688,49022,49023,49025,49027],{},[898,49024,1701],{},[1762,49026,2398],{},[898,49028,1691],{},[1693,49030,1695],{},[1762,49032,31000],{},[902,49034,49035],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,49038,49040],{"className":49039},[886],[888,49041,49042],{"xmlns":890},[892,49043,49044,49059],{},[895,49045,49046,49054,49056],{},[5688,49047,49048,49050,49052],{},[898,49049,1712],{},[1762,49051,1764],{},[898,49053,1691],{},[1693,49055,1695],{},[1762,49057,49058],{},"13",[902,49060,49061],{"encoding":904},"Q_1^E = 13",[883,49063,49065],{"className":49064},[886],[888,49066,49067],{"xmlns":890},[892,49068,49069,49083],{},[895,49070,49071,49079,49081],{},[5688,49072,49073,49075,49077],{},[898,49074,1712],{},[1762,49076,2398],{},[898,49078,1691],{},[1693,49080,1695],{},[1762,49082,29746],{},[902,49084,49085],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,49088,46596],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,49091,49093],{"id":49092},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,49095,49096,49097,49114,49115,16877,49118,3042],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,49098,49100],{"className":49099},[886],[888,49101,49102],{"xmlns":890},[892,49103,49104,49112],{},[895,49105,49106],{},[1717,49107,49108,49110],{},[898,49109,1701],{},[898,49111,1691],{},[902,49113,48237],{"encoding":904},"; mechanismus popisuje ",[38,49116,49117],{},"teorém pavučiny",[614,49119,49120],{},"cobweb model",[198,49122,49124],{"id":49123},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,49126,49127],{},[9465,49128],{"alt":49129,"className":49130,"src":49131},"imek-komparativni-statika-4pripady",[210,9469],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1636,49133,49134,49174,49214,49254],{},[724,49135,49136,49139,49140,13055,49157,1789],{},[38,49137,49138],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,49141,49143],{"className":49142},[886],[888,49144,49145],{"xmlns":890},[892,49146,49147,49155],{},[895,49148,49149],{},[1717,49150,49151,49153],{},[898,49152,1701],{},[898,49154,1691],{},[902,49156,48237],{"encoding":904},[883,49158,49160],{"className":49159},[886],[888,49161,49162],{"xmlns":890},[892,49163,49164,49172],{},[895,49165,49166],{},[1717,49167,49168,49170],{},[898,49169,1712],{},[898,49171,1691],{},[902,49173,2204],{"encoding":904},[724,49175,49176,49179,49180,13055,49197,1789],{},[38,49177,49178],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,49181,49183],{"className":49182},[886],[888,49184,49185],{"xmlns":890},[892,49186,49187,49195],{},[895,49188,49189],{},[1717,49190,49191,49193],{},[898,49192,1701],{},[898,49194,1691],{},[902,49196,48237],{"encoding":904},[883,49198,49200],{"className":49199},[886],[888,49201,49202],{"xmlns":890},[892,49203,49204,49212],{},[895,49205,49206],{},[1717,49207,49208,49210],{},[898,49209,1712],{},[898,49211,1691],{},[902,49213,2204],{"encoding":904},[724,49215,49216,49219,49220,16210,49237,1789],{},[38,49217,49218],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,49221,49223],{"className":49222},[886],[888,49224,49225],{"xmlns":890},[892,49226,49227,49235],{},[895,49228,49229],{},[1717,49230,49231,49233],{},[898,49232,1701],{},[898,49234,1691],{},[902,49236,48237],{"encoding":904},[883,49238,49240],{"className":49239},[886],[888,49241,49242],{"xmlns":890},[892,49243,49244,49252],{},[895,49245,49246],{},[1717,49247,49248,49250],{},[898,49249,1712],{},[898,49251,1691],{},[902,49253,2204],{"encoding":904},[724,49255,49256,49259,49260,49277,49278,1789],{},[38,49257,49258],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,49261,49263],{"className":49262},[886],[888,49264,49265],{"xmlns":890},[892,49266,49267,49275],{},[895,49268,49269],{},[1717,49270,49271,49273],{},[898,49272,1701],{},[898,49274,1691],{},[902,49276,48237],{"encoding":904},", pokles ",[883,49279,49281],{"className":49280},[886],[888,49282,49283],{"xmlns":890},[892,49284,49285,49293],{},[895,49286,49287],{},[1717,49288,49289,49291],{},[898,49290,1712],{},[898,49292,1691],{},[902,49294,2204],{"encoding":904},[16,49296,49297,49342],{},[19,49298,49299],{},[22,49300,49301,49304,49323],{},[25,49302,49303],{},"Změna",[25,49305,49306],{},[883,49307,49309],{"className":49308},[886],[888,49310,49311],{"xmlns":890},[892,49312,49313,49321],{},[895,49314,49315],{},[1717,49316,49317,49319],{},[898,49318,1701],{},[898,49320,1691],{},[902,49322,48237],{"encoding":904},[25,49324,49325],{},[883,49326,49328],{"className":49327},[886],[888,49329,49330],{"xmlns":890},[892,49331,49332,49340],{},[895,49333,49334],{},[1717,49335,49336,49338],{},[898,49337,1712],{},[898,49339,1691],{},[902,49341,2204],{"encoding":904},[30,49343,49344,49354,49364,49373],{},[22,49345,49346,49349,49352],{},[35,49347,49348],{},"Růst poptávky",[35,49350,49351],{},"↑",[35,49353,49351],{},[22,49355,49356,49359,49362],{},[35,49357,49358],{},"Pokles poptávky",[35,49360,49361],{},"↓",[35,49363,49361],{},[22,49365,49366,49369,49371],{},[35,49367,49368],{},"Růst nabídky",[35,49370,49361],{},[35,49372,49351],{},[22,49374,49375,49378,49380],{},[35,49376,49377],{},"Pokles nabídky",[35,49379,49351],{},[35,49381,49361],{},[724,49383,49384],{},[614,49385,49386],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[1852,49388],{},[115,49390,811],{"id":49391},"zdanění-trhu",[1636,49393,49394,49481],{},[724,49395,49396,49398,49399,49412,49413,7617,49426,49429,49430,43557,49452,49476,49477,49480],{},[883,49397,11036],{}," TL;DR\nJednotková daň ",[883,49400,49402],{"className":49401},[886],[888,49403,49404],{"xmlns":890},[892,49405,49406,49410],{},[895,49407,49408],{},[898,49409,2663],{},[902,49411,2663],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,49414,49416],{"className":49415},[886],[888,49417,49418],{"xmlns":890},[892,49419,49420,49424],{},[895,49421,49422],{},[898,49423,2663],{},[902,49425,2663],{"encoding":904},[38,49427,49428],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,49431,49433],{"className":49432},[886],[888,49434,49435],{"xmlns":890},[892,49436,49437,49449],{},[895,49438,49439],{},[3284,49440,49441,49443],{},[898,49442,2663],{},[895,49444,49445,49447],{},[898,49446,6746],{},[898,49448,724],{},[902,49450,49451],{"encoding":904},"T_{sp}",[883,49453,49455],{"className":49454},[886],[888,49456,49457],{"xmlns":890},[892,49458,49459,49473],{},[895,49460,49461],{},[3284,49462,49463,49465],{},[898,49464,2663],{},[895,49466,49467,49469,49471],{},[898,49468,6759],{},[898,49470,6560],{},[898,49472,6629],{},[902,49474,49475],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,49478,49479],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,49482,49483],{},[614,49484,49485,49486,1789],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,49487,49489],{"className":49488,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,49491,49492,49493,49496,49497,49523,49524,49527,49528,49554,49555,49572,49573,49613,49614,4286,49627,1789],{},"Existují dvě formy zdanění — daň uložená ",[38,49494,49495],{},"výrobci"," (posun nabídky ",[883,49498,49500],{"className":49499},[886],[888,49501,49502],{"xmlns":890},[892,49503,49504,49520],{},[895,49505,49506,49512,49514,49516,49518],{},[3284,49507,49508,49510],{},[898,49509,3611],{},[1762,49511,1764],{},[1693,49513,1695],{},[898,49515,3611],{},[1693,49517,1892],{},[898,49519,2663],{},[902,49521,49522],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,49525,49526],{},"spotřebiteli"," (posun poptávky ",[883,49529,49531],{"className":49530},[886],[888,49532,49533],{"xmlns":890},[892,49534,49535,49551],{},[895,49536,49537,49543,49545,49547,49549],{},[3284,49538,49539,49541],{},[898,49540,2738],{},[1762,49542,2398],{},[1693,49544,1695],{},[898,49546,2738],{},[1693,49548,1698],{},[898,49550,2663],{},[902,49552,49553],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,49556,49558],{"className":49557},[886],[888,49559,49560],{"xmlns":890},[892,49561,49562,49570],{},[895,49563,49564],{},[1717,49565,49566,49568],{},[898,49567,1712],{},[898,49569,1691],{},[902,49571,2204],{"encoding":904}," klesá a vzniká rozklad daně ",[883,49574,49576],{"className":49575},[886],[888,49577,49578],{"xmlns":890},[892,49579,49580,49610],{},[895,49581,49582,49584,49586,49596,49598],{},[898,49583,2663],{},[1693,49585,1695],{},[3284,49587,49588,49590],{},[898,49589,2663],{},[895,49591,49592,49594],{},[898,49593,6746],{},[898,49595,724],{},[1693,49597,1892],{},[3284,49599,49600,49602],{},[898,49601,2663],{},[895,49603,49604,49606,49608],{},[898,49605,6759],{},[898,49607,6560],{},[898,49609,6629],{},[902,49611,49612],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,49615,49617],{"className":49616},[886],[888,49618,49619],{"xmlns":890},[892,49620,49621,49625],{},[895,49622,49623],{},[898,49624,2738],{},[902,49626,2738],{"encoding":904},[883,49628,49630],{"className":49629},[886],[888,49631,49632],{"xmlns":890},[892,49633,49634,49638],{},[895,49635,49636],{},[898,49637,3611],{},[902,49639,3611],{"encoding":904},[724,49641,49642,49643,49646,49647,4286,49677,49711],{},"Zásadním výsledkem kapitoly je ",[38,49644,49645],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,49648,49650],{"className":49649},[886],[888,49651,49652],{"xmlns":890},[892,49653,49654,49674],{},[895,49655,49656,49664,49666],{},[5688,49657,49658,49660,49662],{},[898,49659,1712],{},[1762,49661,1764],{},[898,49663,1691],{},[1693,49665,1695],{},[5688,49667,49668,49670,49672],{},[898,49669,1712],{},[1762,49671,2398],{},[898,49673,1691],{},[902,49675,49676],{"encoding":904},"Q_1^E = Q_2^E",[883,49678,49680],{"className":49679},[886],[888,49681,49682],{"xmlns":890},[892,49683,49684,49708],{},[895,49685,49686,49694,49696,49698,49700],{},[5688,49687,49688,49690,49692],{},[898,49689,1701],{},[1762,49691,1764],{},[898,49693,1691],{},[1693,49695,1698],{},[898,49697,2663],{},[1693,49699,1695],{},[5688,49701,49702,49704,49706],{},[898,49703,1701],{},[1762,49705,2398],{},[898,49707,1691],{},[902,49709,49710],{"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.",[724,49713,49714,49715,49718,49719,49745,49746,49774,49775,49778,49779,49782,49783,1789],{},"Podrobný výklad, Příklady ",[38,49716,49717],{},"2.9"," (daň výrobci, ",[883,49720,49722],{"className":49721},[886],[888,49723,49724],{"xmlns":890},[892,49725,49726,49742],{},[895,49727,49728,49738,49740],{},[3284,49729,49730,49732],{},[898,49731,2663],{},[895,49733,49734,49736],{},[898,49735,6746],{},[898,49737,724],{},[1693,49739,1695],{},[1762,49741,2398],{},[902,49743,49744],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,49747,49749],{"className":49748},[886],[888,49750,49751],{"xmlns":890},[892,49752,49753,49771],{},[895,49754,49755,49767,49769],{},[3284,49756,49757,49759],{},[898,49758,2663],{},[895,49760,49761,49763,49765],{},[898,49762,6759],{},[898,49764,6560],{},[898,49766,6629],{},[1693,49768,1695],{},[1762,49770,9262],{},[902,49772,49773],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,49776,49777],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,49780,49781],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,49784,49489],{"className":49785,"dataFsResolvedFilePath":809,"href":810},[210],[1852,49787],{},[115,49789,49791],{"id":49790},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1636,49793,49794],{},[724,49795,49796,49798,49799,49802,49803,49805],{},[883,49797,11036],{}," TL;DR\nMultiplikátory jsou ",[38,49800,49801],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,49804,43738],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,49807,49809],{"id":49808},"redukovaný-tvar","Redukovaný tvar",[724,49811,49812,49813,16877,49836,1343,49854,8586,49871,16877,49894,49911,49912,49941],{},"Pro lineární model ",[883,49814,49816],{"className":49815},[886],[888,49817,49818],{"xmlns":890},[892,49819,49820,49834],{},[895,49821,49822,49824,49826,49828,49830,49832],{},[898,49823,1701],{},[1693,49825,1695],{},[898,49827,207],{},[898,49829,1712],{},[1693,49831,1892],{},[898,49833,1895],{},[902,49835,43837],{"encoding":904},[883,49837,49839],{"className":49838},[886],[888,49840,49841],{"xmlns":890},[892,49842,49843,49851],{},[895,49844,49845,49847,49849],{},[898,49846,207],{},[1693,49848,1908],{},[1762,49850,1911],{},[902,49852,49853],{"encoding":904},"a \u003C 0",[883,49855,49857],{"className":49856},[886],[888,49858,49859],{"xmlns":890},[892,49860,49861,49869],{},[895,49862,49863,49865,49867],{},[898,49864,1895],{},[1693,49866,1922],{},[1762,49868,1911],{},[902,49870,7157],{"encoding":904},[883,49872,49874],{"className":49873},[886],[888,49875,49876],{"xmlns":890},[892,49877,49878,49892],{},[895,49879,49880,49882,49884,49886,49888,49890],{},[898,49881,1701],{},[1693,49883,1695],{},[898,49885,2000],{},[898,49887,1712],{},[1693,49889,1892],{},[898,49891,1771],{},[902,49893,47015],{"encoding":904},[883,49895,49897],{"className":49896},[886],[888,49898,49899],{"xmlns":890},[892,49900,49901,49909],{},[895,49902,49903,49905,49907],{},[898,49904,2000],{},[1693,49906,1922],{},[1762,49908,1911],{},[902,49910,47033],{"encoding":904},") dává podmínka rovnováhy ",[883,49913,49915],{"className":49914},[886],[888,49916,49917],{"xmlns":890},[892,49918,49919,49939],{},[895,49920,49921,49923,49925,49927,49929,49931,49933,49935,49937],{},[898,49922,207],{},[898,49924,1712],{},[1693,49926,1892],{},[898,49928,1895],{},[1693,49930,1695],{},[898,49932,2000],{},[898,49934,1712],{},[1693,49936,1892],{},[898,49938,1771],{},[902,49940,2097],{"encoding":904},", odkud",[883,49943,49945],{"className":49944},[886],[888,49946,49947],{"xmlns":890,"display":34854},[892,49948,49949,49994],{},[3626,49950,49951],{"width":34859},[3632,49952,49953,49955,49987,49989],{},[3635,49954],{"width":34864},[3635,49956,49957],{},[895,49958,49959,49965,49967,49985],{},[1717,49960,49961,49963],{},[898,49962,1712],{},[898,49964,1691],{},[1693,49966,1695],{},[2132,49968,49969,49977],{},[895,49970,49971,49973,49975],{},[898,49972,1895],{},[1693,49974,1698],{},[898,49976,1771],{},[895,49978,49979,49981,49983],{},[898,49980,2000],{},[1693,49982,1698],{},[898,49984,207],{},[898,49986,1789],{"mathvariant":1704},[3635,49988],{"width":34864},[3635,49990,49991],{},[1915,49992,49993],{},"(2.10)",[902,49995,49996],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,49998,49999,50000,16877,50002,50005,50006,50023,50024,1863,50027,50053,50054,50067,50068,50085,50086,3042],{},"Vztah (2.10) je ",[38,50001,27757],{},[614,50003,50004],{},"reduced form",") pro ",[883,50007,50009],{"className":50008},[886],[888,50010,50011],{"xmlns":890},[892,50012,50013,50021],{},[895,50014,50015],{},[1717,50016,50017,50019],{},[898,50018,1712],{},[898,50020,1691],{},[902,50022,2204],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,50025,50026],{},"parametrů",[883,50028,50030],{"className":50029},[886],[888,50031,50032],{"xmlns":890},[892,50033,50034,50050],{},[895,50035,50036,50038,50040,50042,50044,50046,50048],{},[898,50037,207],{},[1693,50039,1899],{"separator":1898},[898,50041,1895],{},[1693,50043,1899],{"separator":1898},[898,50045,2000],{},[1693,50047,1899],{"separator":1898},[898,50049,1771],{},[902,50051,50052],{"encoding":904},"a, b, c, d",". Aby ",[883,50055,50057],{"className":50056},[886],[888,50058,50059],{"xmlns":890},[892,50060,50061,50065],{},[895,50062,50063],{},[898,50064,1691],{},[902,50066,1691],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,50069,50071],{"className":50070},[886],[888,50072,50073],{"xmlns":890},[892,50074,50075,50083],{},[895,50076,50077,50079,50081],{},[898,50078,1895],{},[1693,50080,1922],{},[898,50082,1771],{},[902,50084,2055],{"encoding":904}," (neboť ",[883,50087,50089],{"className":50088},[886],[888,50090,50091],{"xmlns":890},[892,50092,50093,50105],{},[895,50094,50095,50097,50099,50101,50103],{},[898,50096,2000],{},[1693,50098,1698],{},[898,50100,207],{},[1693,50102,1922],{},[1762,50104,1911],{},[902,50106,50107],{"encoding":904},"c - a > 0",[724,50109,50110],{},[614,50111,50112,50113,50126,50127,50140,50141,25461,50154,48711,50171,50184],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,50114,50116],{"className":50115},[886],[888,50117,50118],{"xmlns":890},[892,50119,50120,50124],{},[895,50121,50122],{},[898,50123,1895],{},[902,50125,1895],{"encoding":904}," na ose ",[883,50128,50130],{"className":50129},[886],[888,50131,50132],{"xmlns":890},[892,50133,50134,50138],{},[895,50135,50136],{},[898,50137,1701],{},[902,50139,1701],{"encoding":904},") a nabídka (úsek ",[883,50142,50144],{"className":50143},[886],[888,50145,50146],{"xmlns":890},[892,50147,50148,50152],{},[895,50149,50150],{},[898,50151,1771],{},[902,50153,1771],{"encoding":904},[883,50155,50157],{"className":50156},[886],[888,50158,50159],{"xmlns":890},[892,50160,50161,50169],{},[895,50162,50163,50165,50167],{},[898,50164,1895],{},[1693,50166,1922],{},[898,50168,1771],{},[902,50170,2055],{"encoding":904},[883,50172,50174],{"className":50173},[886],[888,50175,50176],{"xmlns":890},[892,50177,50178,50182],{},[895,50179,50180],{},[898,50181,1691],{},[902,50183,1691],{"encoding":904}," v 1. kvadrantu.",[198,50186,50188],{"id":50187},"definice-multiplikátorů","Definice multiplikátorů",[724,50190,50191,50192,50217,50218,50231,50232,50245],{},"V komparativní statice jsou ",[883,50193,50195],{"className":50194},[886],[888,50196,50197],{"xmlns":890},[892,50198,50199,50215],{},[895,50200,50201,50203,50205,50207,50209,50211,50213],{},[898,50202,207],{},[1693,50204,1899],{"separator":1898},[898,50206,1895],{},[1693,50208,1899],{"separator":1898},[898,50210,2000],{},[1693,50212,1899],{"separator":1898},[898,50214,1771],{},[902,50216,50052],{"encoding":904}," exogenní proměnné a ",[883,50219,50221],{"className":50220},[886],[888,50222,50223],{"xmlns":890},[892,50224,50225,50229],{},[895,50226,50227],{},[898,50228,1712],{},[902,50230,1712],{"encoding":904}," endogenní. Přibližná změna ",[883,50233,50235],{"className":50234},[886],[888,50236,50237],{"xmlns":890},[892,50238,50239,50243],{},[895,50240,50241],{},[898,50242,1712],{},[902,50244,1712],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,50247,50249],{"className":50248},[886],[888,50250,50251],{"xmlns":890,"display":34854},[892,50252,50253,50346],{},[3626,50254,50255],{"width":34859},[3632,50256,50257,50259,50339,50341],{},[3635,50258],{"width":34864},[3635,50260,50261],{},[895,50262,50263,50265,50267,50269,50271,50273,50275,50283,50285,50287,50289,50291,50299,50301,50303,50305,50307,50315,50317,50319,50321,50323,50331,50333,50335,50337],{},[898,50264,3890],{"mathvariant":1704},[898,50266,1712],{},[1693,50268,4110],{},[898,50270,1771],{},[898,50272,1712],{},[1693,50274,1695],{},[5688,50276,50277,50279,50281],{},[898,50278,1712],{},[898,50280,207],{},[1693,50282,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,50284,2239],{},[898,50286,1771],{},[898,50288,207],{},[1693,50290,1892],{},[5688,50292,50293,50295,50297],{},[898,50294,1712],{},[898,50296,1895],{},[1693,50298,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,50300,2239],{},[898,50302,1771],{},[898,50304,1895],{},[1693,50306,1892],{},[5688,50308,50309,50311,50313],{},[898,50310,1712],{},[898,50312,2000],{},[1693,50314,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,50316,2239],{},[898,50318,1771],{},[898,50320,2000],{},[1693,50322,1892],{},[5688,50324,50325,50327,50329],{},[898,50326,1712],{},[898,50328,1771],{},[1693,50330,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,50332,2239],{},[898,50334,1771],{},[898,50336,1771],{},[898,50338,1789],{"mathvariant":1704},[3635,50340],{"width":34864},[3635,50342,50343],{},[1915,50344,50345],{},"(2.11)",[902,50347,50348],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,50350,50351,50352,50402,50403,16877,50405,10048],{},"Parciální derivace ",[883,50353,50355],{"className":50354},[886],[888,50356,50357],{"xmlns":890},[892,50358,50359,50399],{},[895,50360,50361,50369,50371,50379,50381,50389,50391],{},[5688,50362,50363,50365,50367],{},[898,50364,1712],{},[898,50366,207],{},[1693,50368,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50370,1899],{"separator":1898},[5688,50372,50373,50375,50377],{},[898,50374,1712],{},[898,50376,1895],{},[1693,50378,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50380,1899],{"separator":1898},[5688,50382,50383,50385,50387],{},[898,50384,1712],{},[898,50386,2000],{},[1693,50388,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50390,1899],{"separator":1898},[5688,50392,50393,50395,50397],{},[898,50394,1712],{},[898,50396,1771],{},[1693,50398,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,50400,50401],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,50404,24795],{},[614,50406,50407],{},"multipliers",[883,50409,50411],{"className":50410},[886],[888,50412,50413],{"xmlns":890,"display":34854},[892,50414,50415,50566],{},[3626,50416,50417],{"width":34859},[3632,50418,50419,50421,50559,50561],{},[3635,50420],{"width":34864},[3635,50422,50423],{},[895,50424,50425,50433,50435,50461,50463,50465,50473,50475,50487,50489,50491,50499,50501,50503,50529,50531,50533,50541,50543,50545,50557],{},[5688,50426,50427,50429,50431],{},[898,50428,1712],{},[898,50430,207],{},[1693,50432,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50434,1695],{},[2132,50436,50437,50445],{},[895,50438,50439,50441,50443],{},[898,50440,1895],{},[1693,50442,1698],{},[898,50444,1771],{},[895,50446,50447,50449,50451,50453,50455],{},[1693,50448,1709],{"stretchy":1708},[898,50450,2000],{},[1693,50452,1698],{},[898,50454,207],{},[1717,50456,50457,50459],{},[1693,50458,1731],{"stretchy":1708},[1762,50460,2398],{},[1693,50462,1899],{"separator":1898},[1901,50464],{"width":3630},[5688,50466,50467,50469,50471],{},[898,50468,1712],{},[898,50470,1895],{},[1693,50472,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50474,1695],{},[2132,50476,50477,50479],{},[1762,50478,1764],{},[895,50480,50481,50483,50485],{},[898,50482,2000],{},[1693,50484,1698],{},[898,50486,207],{},[1693,50488,1899],{"separator":1898},[1901,50490],{"width":3630},[5688,50492,50493,50495,50497],{},[898,50494,1712],{},[898,50496,2000],{},[1693,50498,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50500,1695],{},[1693,50502,1698],{},[2132,50504,50505,50513],{},[895,50506,50507,50509,50511],{},[898,50508,1895],{},[1693,50510,1698],{},[898,50512,1771],{},[895,50514,50515,50517,50519,50521,50523],{},[1693,50516,1709],{"stretchy":1708},[898,50518,2000],{},[1693,50520,1698],{},[898,50522,207],{},[1717,50524,50525,50527],{},[1693,50526,1731],{"stretchy":1708},[1762,50528,2398],{},[1693,50530,1899],{"separator":1898},[1901,50532],{"width":3630},[5688,50534,50535,50537,50539],{},[898,50536,1712],{},[898,50538,1771],{},[1693,50540,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50542,1695],{},[1693,50544,1698],{},[2132,50546,50547,50549],{},[1762,50548,1764],{},[895,50550,50551,50553,50555],{},[898,50552,2000],{},[1693,50554,1698],{},[898,50556,207],{},[898,50558,1789],{"mathvariant":1704},[3635,50560],{"width":34864},[3635,50562,50563],{},[1915,50564,50565],{},"(2.12)",[902,50567,50568],{"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}",[198,50570,50572],{"id":50571},"znaménka-a-interpretace","Znaménka a interpretace",[724,50574,50575,50576,1343,50593,1343,50610,1343,50627,50644,50645,10048],{},"Za podmínek ",[883,50577,50579],{"className":50578},[886],[888,50580,50581],{"xmlns":890},[892,50582,50583,50591],{},[895,50584,50585,50587,50589],{},[898,50586,207],{},[1693,50588,1908],{},[1762,50590,1911],{},[902,50592,49853],{"encoding":904},[883,50594,50596],{"className":50595},[886],[888,50597,50598],{"xmlns":890},[892,50599,50600,50608],{},[895,50601,50602,50604,50606],{},[898,50603,1895],{},[1693,50605,1922],{},[1762,50607,1911],{},[902,50609,7157],{"encoding":904},[883,50611,50613],{"className":50612},[886],[888,50614,50615],{"xmlns":890},[892,50616,50617,50625],{},[895,50618,50619,50621,50623],{},[898,50620,2000],{},[1693,50622,1922],{},[1762,50624,1911],{},[902,50626,47033],{"encoding":904},[883,50628,50630],{"className":50629},[886],[888,50631,50632],{"xmlns":890},[892,50633,50634,50642],{},[895,50635,50636,50638,50640],{},[898,50637,1895],{},[1693,50639,1922],{},[898,50641,1771],{},[902,50643,2055],{"encoding":904}," platí (znaménka se ",[38,50646,50647],{},"nemění",[883,50649,50651],{"className":50650},[886],[888,50652,50653],{"xmlns":890,"display":34854},[892,50654,50655,50717],{},[895,50656,50657,50665,50667,50669,50671,50673,50681,50683,50685,50687,50689,50697,50699,50701,50703,50705,50713,50715],{},[5688,50658,50659,50661,50663],{},[898,50660,1712],{},[898,50662,207],{},[1693,50664,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50666,1922],{},[1762,50668,1911],{},[1693,50670,1899],{"separator":1898},[1901,50672],{"width":1903},[5688,50674,50675,50677,50679],{},[898,50676,1712],{},[898,50678,1895],{},[1693,50680,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50682,1922],{},[1762,50684,1911],{},[1693,50686,1899],{"separator":1898},[1901,50688],{"width":1903},[5688,50690,50691,50693,50695],{},[898,50692,1712],{},[898,50694,2000],{},[1693,50696,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50698,1908],{},[1762,50700,1911],{},[1693,50702,1899],{"separator":1898},[1901,50704],{"width":1903},[5688,50706,50707,50709,50711],{},[898,50708,1712],{},[898,50710,1771],{},[1693,50712,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50714,1908],{},[1762,50716,19295],{},[902,50718,50719],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,50721,50722,50781],{},[123,50723,50724,1863,50727,50747,50748,50765,50766,1343,50779,1789],{},[38,50725,50726],{},"Kvantitativní smysl:",[883,50728,50730],{"className":50729},[886],[888,50731,50732],{"xmlns":890},[892,50733,50734,50744],{},[895,50735,50736],{},[5688,50737,50738,50740,50742],{},[898,50739,1712],{},[898,50741,2590],{},[1693,50743,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,50745,50746],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,50749,50751],{"className":50750},[886],[888,50752,50753],{"xmlns":890},[892,50754,50755,50763],{},[895,50756,50757],{},[1717,50758,50759,50761],{},[898,50760,1712],{},[898,50762,1691],{},[902,50764,2204],{"encoding":904}," při jednotkové změně parametru ",[883,50767,50769],{"className":50768},[886],[888,50770,50771],{"xmlns":890},[892,50772,50773,50777],{},[895,50774,50775],{},[898,50776,2590],{},[902,50778,2590],{"encoding":904},[614,50780,43738],{},[123,50782,50783,50786,50787,50804,50805,1789],{},[38,50784,50785],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,50788,50790],{"className":50789},[886],[888,50791,50792],{"xmlns":890},[892,50793,50794,50802],{},[895,50795,50796],{},[1717,50797,50798,50800],{},[898,50799,1712],{},[898,50801,1691],{},[902,50803,2204],{"encoding":904}," na růst ",[883,50806,50808],{"className":50807},[886],[888,50809,50810],{"xmlns":890},[892,50811,50812,50816],{},[895,50813,50814],{},[898,50815,2590],{},[902,50817,2590],{"encoding":904},[724,50819,50820,50821,50834,50835,50085,50852,3042],{},"Např. růst ",[883,50822,50824],{"className":50823},[886],[888,50825,50826],{"xmlns":890},[892,50827,50828,50832],{},[895,50829,50830],{},[898,50831,2000],{},[902,50833,2000],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,50836,50838],{"className":50837},[886],[888,50839,50840],{"xmlns":890},[892,50841,50842,50850],{},[895,50843,50844],{},[1717,50845,50846,50848],{},[898,50847,1712],{},[898,50849,1691],{},[902,50851,2204],{"encoding":904},[883,50853,50855],{"className":50854},[886],[888,50856,50857],{"xmlns":890},[892,50858,50859,50873],{},[895,50860,50861,50869,50871],{},[5688,50862,50863,50865,50867],{},[898,50864,1712],{},[898,50866,2000],{},[1693,50868,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,50870,1908],{},[1762,50872,1911],{},[902,50874,50875],{"encoding":904},"Q'_c \u003C 0",[724,50877,50878],{},[614,50879,50880,50881,50901,50902,50926,50927,50949,50950,1789],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,50882,50884],{"className":50883},[886],[888,50885,50886],{"xmlns":890},[892,50887,50888,50898],{},[895,50889,50890,50892,50894,50896],{},[898,50891,2000],{},[898,50893,1712],{},[1693,50895,1892],{},[898,50897,1771],{},[902,50899,50900],{"encoding":904},"cQ + d"," na strmější ",[883,50903,50905],{"className":50904},[886],[888,50906,50907],{"xmlns":890},[892,50908,50909,50923],{},[895,50910,50911,50917,50919,50921],{},[3284,50912,50913,50915],{},[898,50914,2000],{},[1762,50916,1764],{},[898,50918,1712],{},[1693,50920,1892],{},[898,50922,1771],{},[902,50924,50925],{"encoding":904},"c_1 Q + d"," (při ",[883,50928,50930],{"className":50929},[886],[888,50931,50932],{"xmlns":890},[892,50933,50934,50946],{},[895,50935,50936,50942,50944],{},[3284,50937,50938,50940],{},[898,50939,2000],{},[1762,50941,1764],{},[1693,50943,1922],{},[898,50945,2000],{},[902,50947,50948],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,50951,50953],{"className":50952},[886],[888,50954,50955],{"xmlns":890},[892,50956,50957,50967],{},[895,50958,50959,50965],{},[1717,50960,50961,50963],{},[898,50962,1712],{},[898,50964,1691],{},[1693,50966,49361],{},[902,50968,50969],{"encoding":904},"Q^E \\downarrow",[724,50971,50972,50973,51005,51006,1789],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,50974,50976],{"className":50975},[886],[888,50977,50978],{"xmlns":890},[892,50979,50980,51002],{},[895,50981,50982,50984,50986,50988,50996,50998,51000],{},[898,50983,3890],{"mathvariant":1704},[898,50985,1712],{},[1693,50987,4110],{},[5688,50989,50990,50992,50994],{},[898,50991,1712],{},[898,50993,1895],{},[1693,50995,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,50997,2239],{},[898,50999,1771],{},[898,51001,1895],{},[902,51003,51004],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,51007,51009],{"className":51008},[886],[888,51010,51011],{"xmlns":890},[892,51012,51013,51021],{},[895,51014,51015],{},[1717,51016,51017,51019],{},[898,51018,1701],{},[898,51020,1691],{},[902,51022,48237],{"encoding":904},[198,51024,51026,51027],{"id":51025},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,51028,51030],{"className":51029},[886],[888,51031,51032],{"xmlns":890},[892,51033,51034,51042],{},[895,51035,51036],{},[1717,51037,51038,51040],{},[898,51039,1712],{},[898,51041,1691],{},[902,51043,2204],{"encoding":904},[724,51045,51046,48426,51048,48461,51074,1789],{},[38,51047,44709],{},[883,51049,51051],{"className":51050},[886],[888,51052,51053],{"xmlns":890},[892,51054,51055,51071],{},[895,51056,51057,51059,51061,51063,51065,51067,51069],{},[898,51058,1701],{},[1693,51060,1695],{},[1693,51062,1698],{},[1762,51064,8357],{},[898,51066,1712],{},[1693,51068,1892],{},[1762,51070,12079],{},[902,51072,51073],{"encoding":904},"P = -3Q + 40",[883,51075,51077],{"className":51076},[886],[888,51078,51079],{"xmlns":890},[892,51080,51081,51095],{},[895,51082,51083,51085,51087,51089,51091,51093],{},[898,51084,1701],{},[1693,51086,1695],{},[1762,51088,11877],{},[898,51090,1712],{},[1693,51092,1892],{},[1762,51094,9763],{},[902,51096,51097],{"encoding":904},"P = 0{,}5Q + 10",[724,51099,51100,51102],{},[38,51101,44741],{}," Rovnovážné množství",[883,51104,51106],{"className":51105},[886],[888,51107,51108],{"xmlns":890,"display":34854},[892,51109,51110,51178],{},[895,51111,51112,51118,51120,51138,51140,51164,51166,51173,51175],{},[1717,51113,51114,51116],{},[898,51115,1712],{},[898,51117,1691],{},[1693,51119,1695],{},[2132,51121,51122,51130],{},[895,51123,51124,51126,51128],{},[898,51125,1895],{},[1693,51127,1698],{},[898,51129,1771],{},[895,51131,51132,51134,51136],{},[898,51133,2000],{},[1693,51135,1698],{},[898,51137,207],{},[1693,51139,1695],{},[2132,51141,51142,51150],{},[895,51143,51144,51146,51148],{},[1762,51145,12079],{},[1693,51147,1698],{},[1762,51149,9763],{},[895,51151,51152,51154,51156,51158,51160,51162],{},[1762,51153,11877],{},[1693,51155,1698],{},[1693,51157,1709],{"stretchy":1708},[1693,51159,1698],{},[1762,51161,8357],{},[1693,51163,1731],{"stretchy":1708},[1693,51165,1695],{},[2132,51167,51168,51170],{},[1762,51169,44795],{},[1762,51171,51172],{},"3,5",[1693,51174,4110],{},[1762,51176,51177],{},"8,571.",[902,51179,51180],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,51182,51183,51228],{},[38,51184,51185,51186,9577,51199,9591,51213,51227],{},"(a) Změna ",[883,51187,51189],{"className":51188},[886],[888,51190,51191],{"xmlns":890},[892,51192,51193,51197],{},[895,51194,51195],{},[898,51196,2000],{},[902,51198,2000],{"encoding":904},[883,51200,51202],{"className":51201},[886],[888,51203,51204],{"xmlns":890},[892,51205,51206,51210],{},[895,51207,51208],{},[1762,51209,11877],{},[902,51211,51212],{"encoding":904},"0{,}5",[883,51214,51216],{"className":51215},[886],[888,51217,51218],{"xmlns":890},[892,51219,51220,51224],{},[895,51221,51222],{},[1762,51223,26132],{},[902,51225,51226],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,51230,51232],{"className":51231},[886],[888,51233,51234],{"xmlns":890,"display":34854},[892,51235,51236,51313],{},[895,51237,51238,51246,51248,51250,51252,51254,51256,51282,51284,51286,51288,51290,51292,51302,51304,51306,51308,51310],{},[5688,51239,51240,51242,51244],{},[898,51241,1712],{},[898,51243,2000],{},[1693,51245,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,51247,2239],{},[898,51249,1771],{},[898,51251,2000],{},[1693,51253,1695],{},[1693,51255,1698],{},[2132,51257,51258,51266],{},[895,51259,51260,51262,51264],{},[898,51261,1895],{},[1693,51263,1698],{},[898,51265,1771],{},[895,51267,51268,51270,51272,51274,51276],{},[1693,51269,1709],{"stretchy":1708},[898,51271,2000],{},[1693,51273,1698],{},[898,51275,207],{},[1717,51277,51278,51280],{},[1693,51279,1731],{"stretchy":1708},[1762,51281,2398],{},[1915,51283,2239],{},[898,51285,1771],{},[898,51287,2000],{},[1693,51289,1695],{},[1693,51291,1698],{},[2132,51293,51294,51296],{},[1762,51295,44795],{},[1717,51297,51298,51300],{},[1762,51299,51172],{},[1762,51301,2398],{},[1693,51303,1715],{},[1762,51305,9695],{},[1693,51307,4110],{},[1693,51309,1698],{},[1762,51311,51312],{},"0,245.",[902,51314,51315],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,51317,51318,51319,1789],{},"Nové rovnovážné množství ",[883,51320,51322],{"className":51321},[886],[888,51323,51324],{"xmlns":890},[892,51325,51326,51351],{},[895,51327,51328,51336,51338,51341,51343,51346,51348],{},[5688,51329,51330,51332,51334],{},[898,51331,1712],{},[1762,51333,1764],{},[898,51335,1691],{},[1693,51337,4110],{},[1762,51339,51340],{},"8,571",[1693,51342,1698],{},[1762,51344,51345],{},"0,245",[1693,51347,1695],{},[1762,51349,51350],{},"8,326",[902,51352,51353],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,51355,51356,51441],{},[38,51357,51358,51359,1343,51379,1343,51401,1343,51421,1789],{},"(b) Současné změny ",[883,51360,51362],{"className":51361},[886],[888,51363,51364],{"xmlns":890},[892,51365,51366,51376],{},[895,51367,51368,51370,51372,51374],{},[898,51369,1771],{},[898,51371,207],{},[1693,51373,1695],{},[1762,51375,11877],{},[902,51377,51378],{"encoding":904},"da = 0{,}5",[883,51380,51382],{"className":51381},[886],[888,51383,51384],{"xmlns":890},[892,51385,51386,51398],{},[895,51387,51388,51390,51392,51394,51396],{},[898,51389,1771],{},[898,51391,1895],{},[1693,51393,1695],{},[1693,51395,1698],{},[1762,51397,9147],{},[902,51399,51400],{"encoding":904},"db = -5",[883,51402,51404],{"className":51403},[886],[888,51405,51406],{"xmlns":890},[892,51407,51408,51418],{},[895,51409,51410,51412,51414,51416],{},[898,51411,1771],{},[898,51413,2000],{},[1693,51415,1695],{},[1762,51417,9695],{},[902,51419,51420],{"encoding":904},"dc = 0{,}1",[883,51422,51424],{"className":51423},[886],[888,51425,51426],{"xmlns":890},[892,51427,51428,51438],{},[895,51429,51430,51432,51434,51436],{},[898,51431,1771],{},[898,51433,1771],{},[1693,51435,1695],{},[1762,51437,1764],{},[902,51439,51440],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,51443,51445],{"className":51444},[886],[888,51446,51447],{"xmlns":890,"display":34854},[892,51448,51449,51592],{},[3626,51450,51451,51533,51569],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,51452,51453,51463],{},[3635,51454,51455],{},[3638,51456,51457],{"scriptlevel":1911,"displaystyle":1898},[895,51458,51459,51461],{},[898,51460,3890],{"mathvariant":1704},[898,51462,1712],{},[3635,51464,51465],{},[3638,51466,51467],{"scriptlevel":1911,"displaystyle":1898},[895,51468,51469,51471,51473,51483,51485,51487,51489,51495,51497,51499,51501,51503,51505,51507,51517,51519,51521,51523,51529,51531],{},[895,51470],{},[1693,51472,4110],{},[2132,51474,51475,51477],{},[1762,51476,44795],{},[1717,51478,51479,51481],{},[1762,51480,51172],{},[1762,51482,2398],{},[1693,51484,1715],{},[1762,51486,11877],{},[1693,51488,1892],{},[2132,51490,51491,51493],{},[1762,51492,1764],{},[1762,51494,51172],{},[1693,51496,1715],{},[1693,51498,1709],{"stretchy":1708},[1693,51500,1698],{},[1762,51502,9147],{},[1693,51504,1731],{"stretchy":1708},[1693,51506,1698],{},[2132,51508,51509,51511],{},[1762,51510,44795],{},[1717,51512,51513,51515],{},[1762,51514,51172],{},[1762,51516,2398],{},[1693,51518,1715],{},[1762,51520,9695],{},[1693,51522,1698],{},[2132,51524,51525,51527],{},[1762,51526,1764],{},[1762,51528,51172],{},[1693,51530,1715],{},[1762,51532,1764],{},[3632,51534,51535,51541],{},[3635,51536,51537],{},[3638,51538,51539],{"scriptlevel":1911,"displaystyle":1898},[895,51540],{},[3635,51542,51543],{},[3638,51544,51545],{"scriptlevel":1911,"displaystyle":1898},[895,51546,51547,51549,51551,51554,51556,51559,51561,51564,51566],{},[895,51548],{},[1693,51550,1695],{},[1762,51552,51553],{},"1,2245",[1693,51555,1698],{},[1762,51557,51558],{},"1,4286",[1693,51560,1698],{},[1762,51562,51563],{},"0,2449",[1693,51565,1698],{},[1762,51567,51568],{},"0,2857",[3632,51570,51571,51577],{},[3635,51572,51573],{},[3638,51574,51575],{"scriptlevel":1911,"displaystyle":1898},[895,51576],{},[3635,51578,51579],{},[3638,51580,51581],{"scriptlevel":1911,"displaystyle":1898},[895,51582,51583,51585,51587,51589],{},[895,51584],{},[1693,51586,4110],{},[1693,51588,1698],{},[1762,51590,51591],{},"0,735.",[902,51593,51594],{"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}",[724,51596,36848,51597,1789],{},[883,51598,51600],{"className":51599},[886],[888,51601,51602],{"xmlns":890},[892,51603,51604,51628],{},[895,51605,51606,51614,51616,51618,51620,51623,51625],{},[5688,51607,51608,51610,51612],{},[898,51609,1712],{},[1762,51611,1764],{},[898,51613,1691],{},[1693,51615,4110],{},[1762,51617,51340],{},[1693,51619,1698],{},[1762,51621,51622],{},"0,735",[1693,51624,1695],{},[1762,51626,51627],{},"7,836",[902,51629,51630],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1636,51632,51633],{},[724,51634,51635,51637,51638,51661,51662,51684],{},[883,51636,8654],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,51639,51641],{"className":51640},[886],[888,51642,51643],{"xmlns":890},[892,51644,51645,51658],{},[895,51646,51647,51649,51651,51653,51655],{},[898,51648,3890],{"mathvariant":1704},[898,51650,1712],{},[1693,51652,4110],{},[1693,51654,1698],{},[1762,51656,51657],{},"2,69",[902,51659,51660],{"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 ",[883,51663,51665],{"className":51664},[886],[888,51666,51667],{"xmlns":890},[892,51668,51669,51681],{},[895,51670,51671,51673,51675,51677,51679],{},[898,51672,3890],{"mathvariant":1704},[898,51674,1712],{},[1693,51676,4110],{},[1693,51678,1698],{},[1762,51680,51622],{},[902,51682,51683],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,51686,51687],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[1852,51689],{},[115,51691,820],{"id":18629},[1636,51693,51694],{},[724,51695,51696,10760,51698,16877,51700,8586,51716,16877,51719,51735,51736,1789],{},[883,51697,11036],{},[38,51699,6189],{},[883,51701,51703],{"className":51702},[886],[888,51704,51705],{"xmlns":890},[892,51706,51707,51713],{},[895,51708,51709,51711],{},[898,51710,2971],{},[898,51712,3611],{},[902,51714,51715],{"encoding":904},"CS",[38,51717,51718],{},"přebytek výrobce",[883,51720,51722],{"className":51721},[886],[888,51723,51724],{"xmlns":890},[892,51725,51726,51732],{},[895,51727,51728,51730],{},[898,51729,1701],{},[898,51731,3611],{},[902,51733,51734],{"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 ",[207,51737,51739],{"className":51738,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,51741,51742],{},[9465,51743],{"alt":51744,"className":51745,"src":51746},"imek-prebytky-cs-ps",[210,9469],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,51748,51749,16877,51751,51754],{},[38,51750,6189],{},[614,51752,51753],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,51756,51758],{"className":51757},[886],[888,51759,51760],{"xmlns":890,"display":34854},[892,51761,51762,51839],{},[3626,51763,51764],{"width":34859},[3632,51765,51766,51768,51832,51834],{},[3635,51767],{"width":34864},[3635,51769,51770],{},[895,51771,51772,51774,51776,51778,51784,51786,51788,51800,51802,51804,51806,51808,51810,51812,51814,51816,51822,51824,51830],{},[898,51773,2971],{},[898,51775,3611],{},[1693,51777,1709],{"stretchy":1708},[3284,51779,51780,51782],{},[898,51781,1712],{},[1762,51783,1911],{},[1693,51785,1731],{"stretchy":1708},[1693,51787,1695],{},[5688,51789,51790,51792,51794],{},[1693,51791,6221],{},[1762,51793,1911],{},[3284,51795,51796,51798],{},[898,51797,1712],{},[1762,51799,1911],{},[898,51801,2738],{},[1693,51803,1709],{"stretchy":1708},[898,51805,1712],{},[1693,51807,1731],{"stretchy":1708},[1915,51809,2239],{},[898,51811,1771],{},[898,51813,1712],{},[1693,51815,1698],{},[3284,51817,51818,51820],{},[898,51819,1701],{},[1762,51821,1911],{},[1915,51823,2239],{},[3284,51825,51826,51828],{},[898,51827,1712],{},[1762,51829,1911],{},[898,51831,1789],{"mathvariant":1704},[3635,51833],{"width":34864},[3635,51835,51836],{},[1915,51837,51838],{},"(2.14)",[902,51840,51841],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,51843,51844,16877,51846,51849],{},[38,51845,6329],{},[614,51847,51848],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,51851,51853],{"className":51852},[886],[888,51854,51855],{"xmlns":890,"display":34854},[892,51856,51857,51934],{},[3626,51858,51859],{"width":34859},[3632,51860,51861,51863,51927,51929],{},[3635,51862],{"width":34864},[3635,51864,51865],{},[895,51866,51867,51869,51871,51873,51879,51881,51883,51889,51891,51897,51899,51911,51913,51915,51917,51919,51921,51923,51925],{},[898,51868,1701],{},[898,51870,3611],{},[1693,51872,1709],{"stretchy":1708},[3284,51874,51875,51877],{},[898,51876,1712],{},[1762,51878,1911],{},[1693,51880,1731],{"stretchy":1708},[1693,51882,1695],{},[3284,51884,51885,51887],{},[898,51886,1701],{},[1762,51888,1911],{},[1915,51890,2239],{},[3284,51892,51893,51895],{},[898,51894,1712],{},[1762,51896,1911],{},[1693,51898,1698],{},[5688,51900,51901,51903,51905],{},[1693,51902,6221],{},[1762,51904,1911],{},[3284,51906,51907,51909],{},[898,51908,1712],{},[1762,51910,1911],{},[898,51912,3611],{},[1693,51914,1709],{"stretchy":1708},[898,51916,1712],{},[1693,51918,1731],{"stretchy":1708},[1915,51920,2239],{},[898,51922,1771],{},[898,51924,1712],{},[898,51926,1789],{"mathvariant":1704},[3635,51928],{"width":34864},[3635,51930,51931],{},[1915,51932,51933],{},"(2.15)",[902,51935,51936],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,51938,51939,51940,1789],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,51941,51943],{"className":51942,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[1852,51945],{},[115,51947,51949],{"id":51948},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,51951,51952,51983,51988,51994,52022,52028,52057,52063,52143,52169],{},[123,51953,51954,51956,51957,51982],{},[38,51955,44704],{}," — lineární poptávka ",[883,51958,51960],{"className":51959},[886],[888,51961,51962],{"xmlns":890},[892,51963,51964,51980],{},[895,51965,51966,51968,51970,51972,51974,51976,51978],{},[898,51967,1701],{},[1693,51969,1695],{},[1693,51971,1698],{},[1762,51973,2398],{},[898,51975,1712],{},[1693,51977,1892],{},[1762,51979,10023],{},[902,51981,44736],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,51984,51985,51987],{},[38,51986,45018],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,51989,51990,51993],{},[38,51991,51992],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,51995,51996,51998,51999,1789],{},[38,51997,47561],{}," — lineární nabídka ",[883,52000,52002],{"className":52001},[886],[888,52003,52004],{"xmlns":890},[892,52005,52006,52020],{},[895,52007,52008,52010,52012,52014,52016,52018],{},[898,52009,1701],{},[1693,52011,1695],{},[1762,52013,11877],{},[898,52015,1712],{},[1693,52017,1892],{},[1762,52019,11872],{},[902,52021,47590],{"encoding":904},[123,52023,52024,52027],{},[38,52025,52026],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,52029,52030,52033,52034,1789],{},[38,52031,52032],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,52035,52037],{"className":52036},[886],[888,52038,52039],{"xmlns":890},[892,52040,52041,52055],{},[895,52042,52043,52045,52047,52049,52051,52053],{},[898,52044,1691],{},[1693,52046,9392],{"stretchy":1708},[1762,52048,9262],{},[1693,52050,1899],{"separator":1898},[1762,52052,48707],{},[1693,52054,9407],{"stretchy":1708},[902,52056,48735],{"encoding":904},[123,52058,52059,52062],{},[38,52060,52061],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,52064,52065,52068,52069,52086,52087,1343,52112,52139,52140,9849],{},[38,52066,52067],{},"Příklad 2.9"," — daň ",[883,52070,52072],{"className":52071},[886],[888,52073,52074],{"xmlns":890},[892,52075,52076,52084],{},[895,52077,52078,52080,52082],{},[898,52079,2663],{},[1693,52081,1695],{},[1762,52083,9154],{},[902,52085,48039],{"encoding":904}," na výrobce; rozklad ",[883,52088,52090],{"className":52089},[886],[888,52091,52092],{"xmlns":890},[892,52093,52094,52110],{},[895,52095,52096,52106,52108],{},[3284,52097,52098,52100],{},[898,52099,2663],{},[895,52101,52102,52104],{},[898,52103,6746],{},[898,52105,724],{},[1693,52107,1695],{},[1762,52109,2398],{},[902,52111,49744],{"encoding":904},[883,52113,52115],{"className":52114},[886],[888,52116,52117],{"xmlns":890},[892,52118,52119,52137],{},[895,52120,52121,52133,52135],{},[3284,52122,52123,52125],{},[898,52124,2663],{},[895,52126,52127,52129,52131],{},[898,52128,6759],{},[898,52130,6560],{},[898,52132,6629],{},[1693,52134,1695],{},[1762,52136,9262],{},[902,52138,49773],{"encoding":904},". (Viz ",[207,52141,49489],{"className":52142,"dataFsResolvedFilePath":809,"href":810},[210],[123,52144,52145,52068,52148,52165,52166,9849],{},[38,52146,52147],{},"Příklad 2.10",[883,52149,52151],{"className":52150},[886],[888,52152,52153],{"xmlns":890},[892,52154,52155,52163],{},[895,52156,52157,52159,52161],{},[898,52158,2663],{},[1693,52160,1695],{},[1762,52162,9154],{},[902,52164,48039],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,52167,49489],{"className":52168,"dataFsResolvedFilePath":809,"href":810},[210],[123,52170,52171,52174],{},[38,52172,52173],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[1852,52176],{},[115,52178,52180],{"id":52179},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,52182,52184],{"id":52183},"základní-analýza-poptávky","Základní analýza poptávky",[724,52186,52187,52190,52191,52226,52227,52253],{},[38,52188,52189],{},"2.1"," Je dána poptávka ",[883,52192,52194],{"className":52193},[886],[888,52195,52196],{"xmlns":890},[892,52197,52198,52223],{},[895,52199,52200,52202,52204,52206,52208,52210,52212,52214,52217,52219,52221],{},[898,52201,1712],{},[1693,52203,1695],{},[898,52205,2738],{},[1693,52207,1709],{"stretchy":1708},[898,52209,1701],{},[1693,52211,1731],{"stretchy":1708},[1693,52213,1695],{},[1762,52215,52216],{},"75",[1693,52218,1698],{},[1762,52220,9147],{},[898,52222,1701],{},[902,52224,52225],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,52228,52230],{"className":52229},[886],[888,52231,52232],{"xmlns":890},[892,52233,52234,52250],{},[895,52235,52236,52238,52240,52242,52244,52246,52248],{},[1762,52237,1911],{},[1693,52239,1899],{"separator":1898},[1762,52241,9147],{},[1693,52243,1899],{"separator":1898},[1762,52245,9763],{},[1693,52247,1899],{"separator":1898},[1762,52249,43026],{},[902,52251,52252],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,52255,52256,52259,52260,52278,52279,10048],{},[38,52257,52258],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,52261,52263],{"className":52262},[886],[888,52264,52265],{"xmlns":890},[892,52266,52267,52275],{},[895,52268,52269,52271,52273],{},[898,52270,1701],{},[1693,52272,1899],{"separator":1898},[898,52274,1712],{},[902,52276,52277],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,52280,52282],{"className":52281},[886],[888,52283,52284],{"xmlns":890},[892,52285,52286,52302],{},[895,52287,52288,52290,52292,52294,52296,52298,52300],{},[898,52289,207],{},[1693,52291,1899],{"separator":1898},[898,52293,1895],{},[1693,52295,1899],{"separator":1898},[898,52297,2000],{},[1693,52299,1922],{},[1762,52301,1911],{},[902,52303,52304],{"encoding":904},"a, b, c > 0",[120,52306,52307,52340,52371,52406,52437,52472],{},[123,52308,52309,52310],{},"(a) ",[883,52311,52313],{"className":52312},[886],[888,52314,52315],{"xmlns":890},[892,52316,52317,52337],{},[895,52318,52319,52321,52323],{},[898,52320,1712],{},[1693,52322,1695],{},[3638,52324,52325],{"scriptlevel":1911,"displaystyle":1898},[2132,52326,52327,52329],{},[898,52328,207],{},[895,52330,52331,52333,52335],{},[898,52332,1701],{},[1693,52334,1892],{},[898,52336,2000],{},[902,52338,52339],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,52341,52342,52343],{},"(b) ",[883,52344,52346],{"className":52345},[886],[888,52347,52348],{"xmlns":890},[892,52349,52350,52368],{},[895,52351,52352,52354,52356],{},[898,52353,1712],{},[1693,52355,1695],{},[14976,52357,52358],{},[895,52359,52360,52362,52364,52366],{},[898,52361,207],{},[1693,52363,1698],{},[898,52365,1895],{},[898,52367,1712],{},[902,52369,52370],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,52372,52373,52374],{},"(c) ",[883,52375,52377],{"className":52376},[886],[888,52378,52379],{"xmlns":890},[892,52380,52381,52403],{},[895,52382,52383,52385,52387],{},[898,52384,1712],{},[1693,52386,1695],{},[3638,52388,52389],{"scriptlevel":1911,"displaystyle":1898},[2132,52390,52391,52401],{},[895,52392,52393,52395,52397],{},[898,52394,207],{},[1693,52396,1698],{},[14976,52398,52399],{},[898,52400,1701],{},[898,52402,1895],{},[902,52404,52405],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,52407,52408,52409],{},"(d) ",[883,52410,52412],{"className":52411},[886],[888,52413,52414],{"xmlns":890},[892,52415,52416,52434],{},[895,52417,52418,52420,52422,52424,52426,52428],{},[898,52419,1701],{},[1693,52421,1695],{},[898,52423,207],{},[1693,52425,1698],{},[898,52427,1895],{},[1717,52429,52430,52432],{},[898,52431,1712],{},[1762,52433,2398],{},[902,52435,52436],{"encoding":904},"P = a - bQ^2",[123,52438,52439,52440],{},"(e) ",[883,52441,52443],{"className":52442},[886],[888,52444,52445],{"xmlns":890},[892,52446,52447,52469],{},[895,52448,52449,52451,52453,52455,52465,52467],{},[898,52450,1712],{},[1693,52452,1695],{},[898,52454,1895],{},[1717,52456,52457,52459],{},[898,52458,1701],{},[895,52460,52461,52463],{},[1693,52462,1698],{},[898,52464,207],{},[1693,52466,1892],{},[898,52468,2000],{},[902,52470,52471],{"encoding":904},"Q = bP^{-a} + c",[123,52473,52474,52475],{},"(f) ",[883,52476,52478],{"className":52477},[886],[888,52479,52480],{"xmlns":890},[892,52481,52482,52505],{},[895,52483,52484,52486,52488,52490,52492],{},[898,52485,1712],{},[1693,52487,1695],{},[898,52489,207],{},[1693,52491,1715],{},[1717,52493,52494,52497],{},[898,52495,52496],{},"e",[895,52498,52499,52501,52503],{},[1693,52500,1698],{},[898,52502,1895],{},[898,52504,1701],{},[902,52506,52507],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,52509,52510,52513],{},[38,52511,52512],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,52515,52516,52519,52522],{},[123,52517,52518],{},"(a) Cena substitutu.",[123,52520,52521],{},"(b) Cena komplementu.",[123,52523,52524],{},"(c) Výdaje na reklamu.",[724,52526,52527,52190,52529,52563,52564,52592],{},[38,52528,31441],{},[883,52530,52532],{"className":52531},[886],[888,52533,52534],{"xmlns":890},[892,52535,52536,52560],{},[895,52537,52538,52540,52542,52544,52546,52548,52550,52552,52554,52556,52558],{},[898,52539,1701],{},[1693,52541,1695],{},[898,52543,2738],{},[1693,52545,1709],{"stretchy":1708},[898,52547,1712],{},[1693,52549,1731],{"stretchy":1708},[1693,52551,1695],{},[1762,52553,10402],{},[1693,52555,1698],{},[1762,52557,2398],{},[898,52559,1712],{},[902,52561,52562],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,52565,52567],{"className":52566},[886],[888,52568,52569],{"xmlns":890},[892,52570,52571,52589],{},[895,52572,52573,52575,52577,52583,52585,52587],{},[898,52574,1701],{},[1693,52576,1695],{},[1717,52578,52579,52581],{},[898,52580,2738],{},[1693,52582,3672],{},[1693,52584,1709],{"stretchy":1708},[898,52586,1712],{},[1693,52588,1731],{"stretchy":1708},[902,52590,52591],{"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.",[724,52594,52595,52598],{},[38,52596,52597],{},"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:",[120,52600,52601,52685,52761,52847,52935],{},[123,52602,52309,52603,1343,52643,1789],{},[883,52604,52606],{"className":52605},[886],[888,52607,52608],{"xmlns":890},[892,52609,52610,52640],{},[895,52611,52612,52618,52620,52622,52624,52626,52632,52634],{},[3284,52613,52614,52616],{},[898,52615,7520],{},[1762,52617,1764],{},[1693,52619,1695],{},[1762,52621,15892],{},[1693,52623,1698],{},[1762,52625,9262],{},[3284,52627,52628,52630],{},[898,52629,2719],{},[1762,52631,1764],{},[1693,52633,1892],{},[3284,52635,52636,52638],{},[898,52637,2719],{},[1762,52639,2398],{},[902,52641,52642],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,52644,52646],{"className":52645},[886],[888,52647,52648],{"xmlns":890},[892,52649,52650,52682],{},[895,52651,52652,52658,52660,52662,52664,52666,52672,52674,52676],{},[3284,52653,52654,52656],{},[898,52655,7520],{},[1762,52657,2398],{},[1693,52659,1695],{},[1762,52661,9763],{},[1693,52663,1892],{},[1762,52665,2398],{},[3284,52667,52668,52670],{},[898,52669,2719],{},[1762,52671,1764],{},[1693,52673,1698],{},[1762,52675,9262],{},[3284,52677,52678,52680],{},[898,52679,2719],{},[1762,52681,2398],{},[902,52683,52684],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,52686,52342,52687,1343,52729,1789],{},[883,52688,52690],{"className":52689},[886],[888,52691,52692],{"xmlns":890},[892,52693,52694,52726],{},[895,52695,52696,52702,52704,52706,52708,52710,52716,52718,52720],{},[3284,52697,52698,52700],{},[898,52699,7520],{},[1762,52701,1764],{},[1693,52703,1695],{},[1762,52705,10017],{},[1693,52707,1698],{},[1762,52709,9763],{},[3284,52711,52712,52714],{},[898,52713,2719],{},[1762,52715,1764],{},[1693,52717,1698],{},[1762,52719,9154],{},[3284,52721,52722,52724],{},[898,52723,2719],{},[1762,52725,2398],{},[902,52727,52728],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,52730,52732],{"className":52731},[886],[888,52733,52734],{"xmlns":890},[892,52735,52736,52758],{},[895,52737,52738,52744,52746,52748,52750,52752],{},[3284,52739,52740,52742],{},[898,52741,7520],{},[1762,52743,2398],{},[1693,52745,1695],{},[1762,52747,43026],{},[1693,52749,1698],{},[1762,52751,9763],{},[3284,52753,52754,52756],{},[898,52755,2719],{},[1762,52757,2398],{},[902,52759,52760],{"encoding":904},"B_2 = 15 - 10A_2",[123,52762,52373,52763,1343,52805,1789],{},[883,52764,52766],{"className":52765},[886],[888,52767,52768],{"xmlns":890},[892,52769,52770,52802],{},[895,52771,52772,52778,52780,52782,52784,52786,52792,52794,52796],{},[3284,52773,52774,52776],{},[898,52775,7520],{},[1762,52777,1764],{},[1693,52779,1695],{},[1762,52781,44795],{},[1693,52783,1698],{},[1762,52785,2398],{},[3284,52787,52788,52790],{},[898,52789,2719],{},[1762,52791,1764],{},[1693,52793,1698],{},[1762,52795,9262],{},[3284,52797,52798,52800],{},[898,52799,2719],{},[1762,52801,2398],{},[902,52803,52804],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,52806,52808],{"className":52807},[886],[888,52809,52810],{"xmlns":890},[892,52811,52812,52844],{},[895,52813,52814,52820,52822,52824,52826,52828,52834,52836,52838],{},[3284,52815,52816,52818],{},[898,52817,7520],{},[1762,52819,2398],{},[1693,52821,1695],{},[1762,52823,43026],{},[1693,52825,1892],{},[1762,52827,2398],{},[3284,52829,52830,52832],{},[898,52831,2719],{},[1762,52833,1764],{},[1693,52835,1698],{},[1762,52837,2398],{},[3284,52839,52840,52842],{},[898,52841,2719],{},[1762,52843,2398],{},[902,52845,52846],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,52848,52408,52849,1343,52893,1789],{},[883,52850,52852],{"className":52851},[886],[888,52853,52854],{"xmlns":890},[892,52855,52856,52890],{},[895,52857,52858,52864,52866,52868,52870,52872,52874,52880,52882,52884],{},[3284,52859,52860,52862],{},[898,52861,7520],{},[1762,52863,1764],{},[1693,52865,1695],{},[1693,52867,1698],{},[1762,52869,15892],{},[1693,52871,1698],{},[1762,52873,2398],{},[3284,52875,52876,52878],{},[898,52877,2719],{},[1762,52879,1764],{},[1693,52881,1892],{},[1762,52883,8357],{},[3284,52885,52886,52888],{},[898,52887,2719],{},[1762,52889,2398],{},[902,52891,52892],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,52894,52896],{"className":52895},[886],[888,52897,52898],{"xmlns":890},[892,52899,52900,52932],{},[895,52901,52902,52908,52910,52912,52914,52916,52922,52924,52926],{},[3284,52903,52904,52906],{},[898,52905,7520],{},[1762,52907,2398],{},[1693,52909,1695],{},[1762,52911,9763],{},[1693,52913,1892],{},[1762,52915,2398],{},[3284,52917,52918,52920],{},[898,52919,2719],{},[1762,52921,1764],{},[1693,52923,1698],{},[1762,52925,2398],{},[3284,52927,52928,52930],{},[898,52929,2719],{},[1762,52931,2398],{},[902,52933,52934],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,52936,52439,52937,1343,52979,1789],{},[883,52938,52940],{"className":52939},[886],[888,52941,52942],{"xmlns":890},[892,52943,52944,52976],{},[895,52945,52946,52952,52954,52956,52958,52960,52966,52968,52970],{},[3284,52947,52948,52950],{},[898,52949,7520],{},[1762,52951,1764],{},[1693,52953,1695],{},[1762,52955,15892],{},[1693,52957,1892],{},[1762,52959,2398],{},[3284,52961,52962,52964],{},[898,52963,2719],{},[1762,52965,1764],{},[1693,52967,1892],{},[1762,52969,9262],{},[3284,52971,52972,52974],{},[898,52973,2719],{},[1762,52975,2398],{},[902,52977,52978],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,52980,52982],{"className":52981},[886],[888,52983,52984],{"xmlns":890},[892,52985,52986,53018],{},[895,52987,52988,52994,52996,52998,53000,53002,53008,53010,53012],{},[3284,52989,52990,52992],{},[898,52991,7520],{},[1762,52993,2398],{},[1693,52995,1695],{},[1762,52997,12079],{},[1693,52999,1698],{},[1762,53001,8357],{},[3284,53003,53004,53006],{},[898,53005,2719],{},[1762,53007,1764],{},[1693,53009,1892],{},[1762,53011,9147],{},[3284,53013,53014,53016],{},[898,53015,2719],{},[1762,53017,2398],{},[902,53019,53020],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,53022,53024],{"id":53023},"základní-analýza-nabídky","Základní analýza nabídky",[724,53026,53027,53030,53031,53065,53066,53088],{},[38,53028,53029],{},"2.6"," Je dána nabídka ",[883,53032,53034],{"className":53033},[886],[888,53035,53036],{"xmlns":890},[892,53037,53038,53062],{},[895,53039,53040,53042,53044,53046,53048,53050,53052,53054,53056,53058,53060],{},[898,53041,1701],{},[1693,53043,1695],{},[898,53045,3611],{},[1693,53047,1709],{"stretchy":1708},[898,53049,1712],{},[1693,53051,1731],{"stretchy":1708},[1693,53053,1695],{},[1762,53055,15892],{},[1693,53057,1892],{},[1762,53059,9739],{},[898,53061,1712],{},[902,53063,53064],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,53067,53069],{"className":53068},[886],[888,53070,53071],{"xmlns":890},[892,53072,53073,53085],{},[895,53074,53075,53077,53079,53081,53083],{},[1762,53076,11872],{},[1693,53078,1899],{"separator":1898},[1762,53080,44795],{},[1693,53082,1899],{"separator":1898},[1762,53084,21864],{},[902,53086,53087],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,53090,53091,53094,53095,53112],{},[38,53092,53093],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,53096,53098],{"className":53097},[886],[888,53099,53100],{"xmlns":890},[892,53101,53102,53110],{},[895,53103,53104,53106,53108],{},[898,53105,1701],{},[1693,53107,1899],{"separator":1898},[898,53109,1712],{},[902,53111,52277],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,53114,53115,53141,53169,53202,53236,53272],{},[123,53116,52309,53117],{},[883,53118,53120],{"className":53119},[886],[888,53121,53122],{"xmlns":890},[892,53123,53124,53138],{},[895,53125,53126,53128,53130,53132,53134,53136],{},[898,53127,1701],{},[1693,53129,1695],{},[1762,53131,44795],{},[1693,53133,1892],{},[1762,53135,2398],{},[898,53137,1712],{},[902,53139,53140],{"encoding":904},"P = 30 + 2Q",[123,53142,52342,53143],{},[883,53144,53146],{"className":53145},[886],[888,53147,53148],{"xmlns":890},[892,53149,53150,53166],{},[895,53151,53152,53154,53156,53158,53160,53162,53164],{},[898,53153,1712],{},[1693,53155,1695],{},[1693,53157,1698],{},[1762,53159,8357],{},[1693,53161,1892],{},[1762,53163,10402],{},[898,53165,1701],{},[902,53167,53168],{"encoding":904},"Q = -3 + 12P",[123,53170,52373,53171],{},[883,53172,53174],{"className":53173},[886],[888,53175,53176],{"xmlns":890},[892,53177,53178,53200],{},[895,53179,53180,53182,53184,53190,53192,53194,53196,53198],{},[898,53181,1701],{},[1693,53183,1695],{},[1717,53185,53186,53188],{},[898,53187,1712],{},[1762,53189,2398],{},[1693,53191,1892],{},[1762,53193,29746],{},[898,53195,1712],{},[1693,53197,1892],{},[1762,53199,39329],{},[902,53201,48493],{"encoding":904},[123,53203,52408,53204],{},[883,53205,53207],{"className":53206},[886],[888,53208,53209],{"xmlns":890},[892,53210,53211,53233],{},[895,53212,53213,53215,53217,53223,53225,53227,53229,53231],{},[898,53214,1701],{},[1693,53216,1695],{},[1717,53218,53219,53221],{},[898,53220,1712],{},[1762,53222,2398],{},[1693,53224,1892],{},[1762,53226,2398],{},[898,53228,1712],{},[1693,53230,1892],{},[1762,53232,10402],{},[902,53234,53235],{"encoding":904},"P = Q^2 + 2Q + 12",[123,53237,52439,53238],{},[883,53239,53241],{"className":53240},[886],[888,53242,53243],{"xmlns":890},[892,53244,53245,53269],{},[895,53246,53247,53249,53251,53253,53255,53257,53259,53261,53263],{},[898,53248,1712],{},[1693,53250,1695],{},[1762,53252,15660],{},[1693,53254,1892],{},[1762,53256,9147],{},[898,53258,1701],{},[1693,53260,1892],{},[1762,53262,9695],{},[1717,53264,53265,53267],{},[898,53266,1701],{},[1762,53268,2398],{},[902,53270,53271],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,53273,52474,53274],{},[883,53275,53277],{"className":53276},[886],[888,53278,53279],{"xmlns":890},[892,53280,53281,53306],{},[895,53282,53283,53285,53287,53289,53291,53293,53295,53297,53300],{},[898,53284,1712],{},[1693,53286,1695],{},[1762,53288,31000],{},[1693,53290,1892],{},[1762,53292,9695],{},[898,53294,1701],{},[1693,53296,1892],{},[1762,53298,53299],{},"0,004",[1717,53301,53302,53304],{},[898,53303,1701],{},[1762,53305,2398],{},[902,53307,53308],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,53310,53311,53314],{},[38,53312,53313],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,53316,53317,53320,53323,53326],{},[123,53318,53319],{},"(a) Sníží ceny surovin — vstupů.",[123,53321,53322],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,53324,53325],{},"(c) Zvýší ceny všech energií.",[123,53327,53328],{},"(d) Sníží daňové odvody státu.",[724,53330,53331,53030,53333,53367,53368,53396],{},[38,53332,49717],{},[883,53334,53336],{"className":53335},[886],[888,53337,53338],{"xmlns":890},[892,53339,53340,53364],{},[895,53341,53342,53344,53346,53348,53350,53352,53354,53356,53358,53360,53362],{},[898,53343,1701],{},[1693,53345,1695],{},[898,53347,3611],{},[1693,53349,1709],{"stretchy":1708},[898,53351,1712],{},[1693,53353,1731],{"stretchy":1708},[1693,53355,1695],{},[1762,53357,11877],{},[898,53359,1712],{},[1693,53361,1892],{},[1762,53363,43026],{},[902,53365,53366],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,53369,53371],{"className":53370},[886],[888,53372,53373],{"xmlns":890},[892,53374,53375,53393],{},[895,53376,53377,53379,53381,53387,53389,53391],{},[898,53378,1701],{},[1693,53380,1695],{},[1717,53382,53383,53385],{},[898,53384,3611],{},[1693,53386,3672],{},[1693,53388,1709],{"stretchy":1708},[898,53390,1712],{},[1693,53392,1731],{"stretchy":1708},[902,53394,53395],{"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.",[198,53398,48096],{"id":53399},"tržní-rovnováha-1",[724,53401,53402,53404,53405,53422,53423,4300],{},[38,53403,49777],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,53406,53408],{"className":53407},[886],[888,53409,53410],{"xmlns":890},[892,53411,53412,53420],{},[895,53413,53414],{},[1717,53415,53416,53418],{},[898,53417,1712],{},[898,53419,1691],{},[902,53421,2204],{"encoding":904}," a rovnovážnou cenu ",[883,53424,53426],{"className":53425},[886],[888,53427,53428],{"xmlns":890},[892,53429,53430,53438],{},[895,53431,53432],{},[1717,53433,53434,53436],{},[898,53435,1701],{},[898,53437,1691],{},[902,53439,48237],{"encoding":904},[120,53441,53442,53495,53546,53605],{},[123,53443,52309,53444,1343,53471,1789],{},[883,53445,53447],{"className":53446},[886],[888,53448,53449],{"xmlns":890},[892,53450,53451,53468],{},[895,53452,53453,53455,53457,53459,53461,53463,53465],{},[898,53454,1701],{},[1693,53456,1695],{},[1693,53458,1698],{},[1762,53460,9147],{},[898,53462,1712],{},[1693,53464,1892],{},[1762,53466,53467],{},"80",[902,53469,53470],{"encoding":904},"P = -5Q + 80",[883,53472,53474],{"className":53473},[886],[888,53475,53476],{"xmlns":890},[892,53477,53478,53492],{},[895,53479,53480,53482,53484,53486,53488,53490],{},[898,53481,1701],{},[1693,53483,1695],{},[1762,53485,2398],{},[898,53487,1712],{},[1693,53489,1892],{},[1762,53491,9763],{},[902,53493,53494],{"encoding":904},"P = 2Q + 10",[123,53496,52342,53497,1343,53523,1789],{},[883,53498,53500],{"className":53499},[886],[888,53501,53502],{"xmlns":890},[892,53503,53504,53520],{},[895,53505,53506,53508,53510,53512,53514,53516,53518],{},[898,53507,1712],{},[1693,53509,1695],{},[1693,53511,1698],{},[1762,53513,11877],{},[898,53515,1701],{},[1693,53517,1892],{},[1762,53519,11872],{},[902,53521,53522],{"encoding":904},"Q = -0{,}5P + 25",[883,53524,53526],{"className":53525},[886],[888,53527,53528],{"xmlns":890},[892,53529,53530,53544],{},[895,53531,53532,53534,53536,53538,53540,53542],{},[898,53533,1712],{},[1693,53535,1695],{},[1762,53537,2398],{},[898,53539,1701],{},[1693,53541,1698],{},[1762,53543,10017],{},[902,53545,47619],{"encoding":904},[123,53547,52373,53548,1343,53574,1789],{},[883,53549,53551],{"className":53550},[886],[888,53552,53553],{"xmlns":890},[892,53554,53555,53571],{},[895,53556,53557,53559,53561,53563,53565,53567,53569],{},[898,53558,1701],{},[1693,53560,1695],{},[1693,53562,1698],{},[1762,53564,9262],{},[898,53566,1712],{},[1693,53568,1892],{},[1762,53570,10928],{},[902,53572,53573],{"encoding":904},"P = -4Q + 120",[883,53575,53577],{"className":53576},[886],[888,53578,53579],{"xmlns":890},[892,53580,53581,53602],{},[895,53582,53583,53585,53587,53595,53597,53599],{},[898,53584,1701],{},[1693,53586,1695],{},[3638,53588,53589],{"scriptlevel":1911,"displaystyle":1708},[2132,53590,53591,53593],{},[1762,53592,1764],{},[1762,53594,8357],{},[898,53596,1712],{},[1693,53598,1892],{},[1762,53600,53601],{},"29",[902,53603,53604],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,53606,52408,53607,1343,53636,1789],{},[883,53608,53610],{"className":53609},[886],[888,53611,53612],{"xmlns":890},[892,53613,53614,53633],{},[895,53615,53616,53618,53620,53622,53628,53630],{},[898,53617,1701],{},[1693,53619,1695],{},[1693,53621,1698],{},[1717,53623,53624,53626],{},[898,53625,1712],{},[1762,53627,2398],{},[1693,53629,1892],{},[1762,53631,53632],{},"52",[902,53634,53635],{"encoding":904},"P = -Q^2 + 52",[883,53637,53639],{"className":53638},[886],[888,53640,53641],{"xmlns":890},[892,53642,53643,53661],{},[895,53644,53645,53647,53649,53651,53657,53659],{},[898,53646,1701],{},[1693,53648,1695],{},[1762,53650,2398],{},[1717,53652,53653,53655],{},[898,53654,1712],{},[1762,53656,2398],{},[1693,53658,1892],{},[1762,53660,9763],{},[902,53662,53663],{"encoding":904},"P = 2Q^2 + 10",[724,53665,53666,53669,53670,53700,53701,53731],{},[38,53667,53668],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,53671,53673],{"className":53672},[886],[888,53674,53675],{"xmlns":890},[892,53676,53677,53697],{},[895,53678,53679,53687,53689],{},[5688,53680,53681,53683,53685],{},[898,53682,1712],{},[1762,53684,1764],{},[898,53686,1691],{},[1693,53688,1899],{"separator":1898},[5688,53690,53691,53693,53695],{},[898,53692,1712],{},[1762,53694,2398],{},[898,53696,1691],{},[902,53698,53699],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,53702,53704],{"className":53703},[886],[888,53705,53706],{"xmlns":890},[892,53707,53708,53728],{},[895,53709,53710,53718,53720],{},[5688,53711,53712,53714,53716],{},[898,53713,1701],{},[1762,53715,1764],{},[898,53717,1691],{},[1693,53719,1899],{"separator":1898},[5688,53721,53722,53724,53726],{},[898,53723,1701],{},[1762,53725,2398],{},[898,53727,1691],{},[902,53729,53730],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,53733,53734,53886],{},[123,53735,52309,53736,1343,53776,1343,53818,1343,53852,1789],{},[883,53737,53739],{"className":53738},[886],[888,53740,53741],{"xmlns":890},[892,53742,53743,53773],{},[895,53744,53745,53751,53753,53755,53757,53759,53765,53767],{},[3284,53746,53747,53749],{},[898,53748,1712],{},[1762,53750,1764],{},[1693,53752,1695],{},[1762,53754,9763],{},[1693,53756,1698],{},[1762,53758,2398],{},[3284,53760,53761,53763],{},[898,53762,1701],{},[1762,53764,1764],{},[1693,53766,1892],{},[3284,53768,53769,53771],{},[898,53770,1701],{},[1762,53772,2398],{},[902,53774,53775],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,53777,53779],{"className":53778},[886],[888,53780,53781],{"xmlns":890},[892,53782,53783,53815],{},[895,53784,53785,53791,53793,53795,53797,53799,53805,53807,53809],{},[3284,53786,53787,53789],{},[898,53788,1712],{},[1762,53790,2398],{},[1693,53792,1695],{},[1762,53794,9147],{},[1693,53796,1892],{},[1762,53798,2398],{},[3284,53800,53801,53803],{},[898,53802,1701],{},[1762,53804,1764],{},[1693,53806,1698],{},[1762,53808,2398],{},[3284,53810,53811,53813],{},[898,53812,1701],{},[1762,53814,2398],{},[902,53816,53817],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,53819,53821],{"className":53820},[886],[888,53822,53823],{"xmlns":890},[892,53824,53825,53849],{},[895,53826,53827,53833,53835,53837,53839,53841,53843],{},[3284,53828,53829,53831],{},[898,53830,1712],{},[1762,53832,1764],{},[1693,53834,1695],{},[1693,53836,1698],{},[1762,53838,8357],{},[1693,53840,1892],{},[1762,53842,2398],{},[3284,53844,53845,53847],{},[898,53846,1701],{},[1762,53848,1764],{},[902,53850,53851],{"encoding":904},"Q_1 = -3 + 2P_1",[883,53853,53855],{"className":53854},[886],[888,53856,53857],{"xmlns":890},[892,53858,53859,53883],{},[895,53860,53861,53867,53869,53871,53873,53875,53877],{},[3284,53862,53863,53865],{},[898,53864,1712],{},[1762,53866,2398],{},[1693,53868,1695],{},[1693,53870,1698],{},[1762,53872,2398],{},[1693,53874,1892],{},[1762,53876,8357],{},[3284,53878,53879,53881],{},[898,53880,1701],{},[1762,53882,2398],{},[902,53884,53885],{"encoding":904},"Q_2 = -2 + 3P_2",[123,53887,52342,53888,1343,53928,1343,53970,1343,54002,1789],{},[883,53889,53891],{"className":53890},[886],[888,53892,53893],{"xmlns":890},[892,53894,53895,53925],{},[895,53896,53897,53903,53905,53907,53909,53911,53917,53919],{},[3284,53898,53899,53901],{},[898,53900,1712],{},[1762,53902,1764],{},[1693,53904,1695],{},[1762,53906,9987],{},[1693,53908,1698],{},[1762,53910,2398],{},[3284,53912,53913,53915],{},[898,53914,1701],{},[1762,53916,1764],{},[1693,53918,1892],{},[3284,53920,53921,53923],{},[898,53922,1701],{},[1762,53924,2398],{},[902,53926,53927],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,53929,53931],{"className":53930},[886],[888,53932,53933],{"xmlns":890},[892,53934,53935,53967],{},[895,53936,53937,53943,53945,53947,53949,53951,53957,53959,53961],{},[3284,53938,53939,53941],{},[898,53940,1712],{},[1762,53942,2398],{},[1693,53944,1695],{},[1762,53946,9147],{},[1693,53948,1892],{},[1762,53950,2398],{},[3284,53952,53953,53955],{},[898,53954,1701],{},[1762,53956,1764],{},[1693,53958,1698],{},[1762,53960,8357],{},[3284,53962,53963,53965],{},[898,53964,1701],{},[1762,53966,2398],{},[902,53968,53969],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,53971,53973],{"className":53972},[886],[888,53974,53975],{"xmlns":890},[892,53976,53977,53999],{},[895,53978,53979,53985,53987,53989,53991,53993],{},[3284,53980,53981,53983],{},[898,53982,1712],{},[1762,53984,1764],{},[1693,53986,1695],{},[1693,53988,1698],{},[1762,53990,9763],{},[1693,53992,1892],{},[3284,53994,53995,53997],{},[898,53996,1701],{},[1762,53998,1764],{},[902,54000,54001],{"encoding":904},"Q_1 = -10 + P_1",[883,54003,54005],{"className":54004},[886],[888,54006,54007],{"xmlns":890},[892,54008,54009,54031],{},[895,54010,54011,54017,54019,54021,54023,54025],{},[3284,54012,54013,54015],{},[898,54014,1712],{},[1762,54016,2398],{},[1693,54018,1695],{},[1762,54020,9147],{},[1693,54022,1892],{},[1762,54024,9154],{},[3284,54026,54027,54029],{},[898,54028,1701],{},[1762,54030,2398],{},[902,54032,54033],{"encoding":904},"Q_2 = 5 + 6P_2",[724,54035,54036,54039,54040,1343,54088,1343,54134,54184,54185,1343,54217,1343,54251,28397,54285,4286,54303,54321,54322,54335,54336,54362,54363,53700,54403,1789],{},[38,54037,54038],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,54041,54043],{"className":54042},[886],[888,54044,54045],{"xmlns":890},[892,54046,54047,54085],{},[895,54048,54049,54055,54057,54059,54061,54067,54069,54071,54077,54079],{},[3284,54050,54051,54053],{},[898,54052,1712],{},[1762,54054,1764],{},[1693,54056,1695],{},[1762,54058,43026],{},[1693,54060,1698],{},[3284,54062,54063,54065],{},[898,54064,1701],{},[1762,54066,1764],{},[1693,54068,1892],{},[1762,54070,2398],{},[3284,54072,54073,54075],{},[898,54074,1701],{},[1762,54076,2398],{},[1693,54078,1892],{},[3284,54080,54081,54083],{},[898,54082,1701],{},[1762,54084,8357],{},[902,54086,54087],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,54089,54091],{"className":54090},[886],[888,54092,54093],{"xmlns":890},[892,54094,54095,54131],{},[895,54096,54097,54103,54105,54107,54109,54115,54117,54123,54125],{},[3284,54098,54099,54101],{},[898,54100,1712],{},[1762,54102,2398],{},[1693,54104,1695],{},[1762,54106,10881],{},[1693,54108,1892],{},[3284,54110,54111,54113],{},[898,54112,1701],{},[1762,54114,1764],{},[1693,54116,1698],{},[3284,54118,54119,54121],{},[898,54120,1701],{},[1762,54122,2398],{},[1693,54124,1698],{},[3284,54126,54127,54129],{},[898,54128,1701],{},[1762,54130,8357],{},[902,54132,54133],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,54135,54137],{"className":54136},[886],[888,54138,54139],{"xmlns":890},[892,54140,54141,54181],{},[895,54142,54143,54149,54151,54153,54155,54157,54163,54165,54171,54173,54175],{},[3284,54144,54145,54147],{},[898,54146,1712],{},[1762,54148,8357],{},[1693,54150,1695],{},[1762,54152,12453],{},[1693,54154,1892],{},[1762,54156,2398],{},[3284,54158,54159,54161],{},[898,54160,1701],{},[1762,54162,1764],{},[1693,54164,1698],{},[3284,54166,54167,54169],{},[898,54168,1701],{},[1762,54170,2398],{},[1693,54172,1698],{},[1762,54174,9262],{},[3284,54176,54177,54179],{},[898,54178,1701],{},[1762,54180,8357],{},[902,54182,54183],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,54186,54188],{"className":54187},[886],[888,54189,54190],{"xmlns":890},[892,54191,54192,54214],{},[895,54193,54194,54200,54202,54204,54206,54208],{},[3284,54195,54196,54198],{},[898,54197,1712],{},[1762,54199,1764],{},[1693,54201,1695],{},[1693,54203,1698],{},[1762,54205,31000],{},[1693,54207,1892],{},[3284,54209,54210,54212],{},[898,54211,1701],{},[1762,54213,1764],{},[902,54215,54216],{"encoding":904},"Q_1 = -7 + P_1",[883,54218,54220],{"className":54219},[886],[888,54221,54222],{"xmlns":890},[892,54223,54224,54248],{},[895,54225,54226,54232,54234,54236,54238,54240,54242],{},[3284,54227,54228,54230],{},[898,54229,1712],{},[1762,54231,2398],{},[1693,54233,1695],{},[1693,54235,1698],{},[1762,54237,9262],{},[1693,54239,1892],{},[1762,54241,9262],{},[3284,54243,54244,54246],{},[898,54245,1701],{},[1762,54247,2398],{},[902,54249,54250],{"encoding":904},"Q_2 = -4 + 4P_2",[883,54252,54254],{"className":54253},[886],[888,54255,54256],{"xmlns":890},[892,54257,54258,54282],{},[895,54259,54260,54266,54268,54270,54272,54274,54276],{},[3284,54261,54262,54264],{},[898,54263,1712],{},[1762,54265,8357],{},[1693,54267,1695],{},[1693,54269,1698],{},[1762,54271,9147],{},[1693,54273,1892],{},[1762,54275,2398],{},[3284,54277,54278,54280],{},[898,54279,1701],{},[1762,54281,8357],{},[902,54283,54284],{"encoding":904},"Q_3 = -5 + 2P_3",[883,54286,54288],{"className":54287},[886],[888,54289,54290],{"xmlns":890},[892,54291,54292,54300],{},[895,54293,54294],{},[3284,54295,54296,54298],{},[898,54297,1712],{},[898,54299,5696],{},[902,54301,54302],{"encoding":904},"Q_i",[883,54304,54306],{"className":54305},[886],[888,54307,54308],{"xmlns":890},[892,54309,54310,54318],{},[895,54311,54312],{},[3284,54313,54314,54316],{},[898,54315,1701],{},[898,54317,5696],{},[902,54319,54320],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,54323,54325],{"className":54324},[886],[888,54326,54327],{"xmlns":890},[892,54328,54329,54333],{},[895,54330,54331],{},[898,54332,5696],{},[902,54334,5696],{"encoding":904},"-tého zboží, ",[883,54337,54339],{"className":54338},[886],[888,54340,54341],{"xmlns":890},[892,54342,54343,54359],{},[895,54344,54345,54347,54349,54351,54353,54355,54357],{},[898,54346,5696],{},[1693,54348,1695],{},[1762,54350,1764],{},[1693,54352,1899],{"separator":1898},[1762,54354,2398],{},[1693,54356,1899],{"separator":1898},[1762,54358,8357],{},[902,54360,54361],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,54364,54366],{"className":54365},[886],[888,54367,54368],{"xmlns":890},[892,54369,54370,54400],{},[895,54371,54372,54380,54382,54390,54392],{},[5688,54373,54374,54376,54378],{},[898,54375,1712],{},[1762,54377,1764],{},[898,54379,1691],{},[1693,54381,1899],{"separator":1898},[5688,54383,54384,54386,54388],{},[898,54385,1712],{},[1762,54387,2398],{},[898,54389,1691],{},[1693,54391,1899],{"separator":1898},[5688,54393,54394,54396,54398],{},[898,54395,1712],{},[1762,54397,8357],{},[898,54399,1691],{},[902,54401,54402],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,54404,54406],{"className":54405},[886],[888,54407,54408],{"xmlns":890},[892,54409,54410,54440],{},[895,54411,54412,54420,54422,54430,54432],{},[5688,54413,54414,54416,54418],{},[898,54415,1701],{},[1762,54417,1764],{},[898,54419,1691],{},[1693,54421,1899],{"separator":1898},[5688,54423,54424,54426,54428],{},[898,54425,1701],{},[1762,54427,2398],{},[898,54429,1691],{},[1693,54431,1899],{"separator":1898},[5688,54433,54434,54436,54438],{},[898,54435,1701],{},[1762,54437,8357],{},[898,54439,1691],{},[902,54441,54442],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,54444,54445,54448,54449,54485,54486,1789],{},[38,54446,54447],{},"2.13"," Jsou dány poptávka ",[883,54450,54452],{"className":54451},[886],[888,54453,54454],{"xmlns":890},[892,54455,54456,54482],{},[895,54457,54458,54460,54462,54464,54466,54468,54470,54472,54474,54476,54478,54480],{},[898,54459,1701],{},[1693,54461,1695],{},[898,54463,2738],{},[1693,54465,1709],{"stretchy":1708},[898,54467,1712],{},[1693,54469,1731],{"stretchy":1708},[1693,54471,1695],{},[1693,54473,1698],{},[1762,54475,9262],{},[898,54477,1712],{},[1693,54479,1892],{},[1762,54481,53467],{},[902,54483,54484],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,54487,54489],{"className":54488},[886],[888,54490,54491],{"xmlns":890},[892,54492,54493,54517],{},[895,54494,54495,54497,54499,54501,54503,54505,54507,54509,54511,54513,54515],{},[898,54496,1701],{},[1693,54498,1695],{},[898,54500,3611],{},[1693,54502,1709],{"stretchy":1708},[898,54504,1712],{},[1693,54506,1731],{"stretchy":1708},[1693,54508,1695],{},[1762,54510,8357],{},[898,54512,1712],{},[1693,54514,1892],{},[1762,54516,9763],{},[902,54518,54519],{"encoding":904},"P = S(Q) = 3Q + 10",[120,54521,54522,54559,54623,54683],{},[123,54523,54524,54525,53422,54542,1789],{},"(a) Určete rovnovážné množství ",[883,54526,54528],{"className":54527},[886],[888,54529,54530],{"xmlns":890},[892,54531,54532,54540],{},[895,54533,54534],{},[1717,54535,54536,54538],{},[898,54537,1712],{},[898,54539,1691],{},[902,54541,2204],{"encoding":904},[883,54543,54545],{"className":54544},[886],[888,54546,54547],{"xmlns":890},[892,54548,54549,54557],{},[895,54550,54551],{},[1717,54552,54553,54555],{},[898,54554,1701],{},[898,54556,1691],{},[902,54558,48237],{"encoding":904},[123,54560,54561,54562,54580,54581,54601,54602,54622],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,54563,54565],{"className":54564},[886],[888,54566,54567],{"xmlns":890},[892,54568,54569,54577],{},[895,54570,54571,54573,54575],{},[898,54572,2663],{},[1693,54574,1695],{},[1762,54576,31000],{},[902,54578,54579],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,54582,54584],{"className":54583},[886],[888,54585,54586],{"xmlns":890},[892,54587,54588,54598],{},[895,54589,54590],{},[5688,54591,54592,54594,54596],{},[898,54593,1712],{},[1762,54595,1764],{},[898,54597,1691],{},[902,54599,54600],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,54603,54605],{"className":54604},[886],[888,54606,54607],{"xmlns":890},[892,54608,54609,54619],{},[895,54610,54611],{},[5688,54612,54613,54615,54617],{},[898,54614,1701],{},[1762,54616,1764],{},[898,54618,1691],{},[902,54620,54621],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,54624,54625,54626,54580,54643,54601,54663,54622],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,54627,54629],{"className":54628},[886],[888,54630,54631],{"xmlns":890},[892,54632,54633,54641],{},[895,54634,54635,54637,54639],{},[898,54636,2663],{},[1693,54638,1695],{},[1762,54640,31000],{},[902,54642,54579],{"encoding":904},[883,54644,54646],{"className":54645},[886],[888,54647,54648],{"xmlns":890},[892,54649,54650,54660],{},[895,54651,54652],{},[5688,54653,54654,54656,54658],{},[898,54655,1712],{},[1762,54657,2398],{},[898,54659,1691],{},[902,54661,54662],{"encoding":904},"Q_2^E",[883,54664,54666],{"className":54665},[886],[888,54667,54668],{"xmlns":890},[892,54669,54670,54680],{},[895,54671,54672],{},[5688,54673,54674,54676,54678],{},[898,54675,1701],{},[1762,54677,2398],{},[898,54679,1691],{},[902,54681,54682],{"encoding":904},"P_2^E",[123,54684,54685],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,54687,54688,54689,1789],{},"Viz též ",[207,54690,49489],{"className":54691,"dataFsResolvedFilePath":809,"href":810},[210],[198,54693,49791],{"id":54694},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,54696,54697,54448,54700,54485,54736,1789],{},[38,54698,54699],{},"2.14",[883,54701,54703],{"className":54702},[886],[888,54704,54705],{"xmlns":890},[892,54706,54707,54733],{},[895,54708,54709,54711,54713,54715,54717,54719,54721,54723,54725,54727,54729,54731],{},[898,54710,1701],{},[1693,54712,1695],{},[898,54714,207],{},[898,54716,1712],{},[1693,54718,1892],{},[898,54720,1895],{},[1693,54722,1695],{},[1693,54724,1698],{},[1762,54726,2398],{},[898,54728,1712],{},[1693,54730,1892],{},[1762,54732,10017],{},[902,54734,54735],{"encoding":904},"P = aQ + b = -2Q + 50",[883,54737,54739],{"className":54738},[886],[888,54740,54741],{"xmlns":890},[892,54742,54743,54767],{},[895,54744,54745,54747,54749,54751,54753,54755,54757,54759,54761,54763,54765],{},[898,54746,1701],{},[1693,54748,1695],{},[898,54750,2000],{},[898,54752,1712],{},[1693,54754,1892],{},[898,54756,1771],{},[1693,54758,1695],{},[1762,54760,26132],{},[898,54762,1712],{},[1693,54764,1892],{},[1762,54766,15892],{},[902,54768,54769],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,54771,54772,54808,54811,54897,54950,55030,55084],{},[123,54773,54524,54774,53422,54791,1789],{},[883,54775,54777],{"className":54776},[886],[888,54778,54779],{"xmlns":890},[892,54780,54781,54789],{},[895,54782,54783],{},[1717,54784,54785,54787],{},[898,54786,1712],{},[898,54788,1691],{},[902,54790,2204],{"encoding":904},[883,54792,54794],{"className":54793},[886],[888,54795,54796],{"xmlns":890},[892,54797,54798,54806],{},[895,54799,54800],{},[1717,54801,54802,54804],{},[898,54803,1701],{},[898,54805,1691],{},[902,54807,48237],{"encoding":904},[123,54809,54810],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,54812,54813,54814,54831,54832,9577,54845,9591,54861,54877,54878,1789],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,54815,54817],{"className":54816},[886],[888,54818,54819],{"xmlns":890},[892,54820,54821,54829],{},[895,54822,54823],{},[1717,54824,54825,54827],{},[898,54826,1712],{},[898,54828,1691],{},[902,54830,2204],{"encoding":904}," odpovídající změně ",[883,54833,54835],{"className":54834},[886],[888,54836,54837],{"xmlns":890},[892,54838,54839,54843],{},[895,54840,54841],{},[898,54842,207],{},[902,54844,207],{"encoding":904},[883,54846,54848],{"className":54847},[886],[888,54849,54850],{"xmlns":890},[892,54851,54852,54858],{},[895,54853,54854,54856],{},[1693,54855,1698],{},[1762,54857,2398],{},[902,54859,54860],{"encoding":904},"-2",[883,54862,54864],{"className":54863},[886],[888,54865,54866],{"xmlns":890},[892,54867,54868,54874],{},[895,54869,54870,54872],{},[1693,54871,1698],{},[1762,54873,8357],{},[902,54875,54876],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,54879,54881],{"className":54880},[886],[888,54882,54883],{"xmlns":890},[892,54884,54885,54895],{},[895,54886,54887],{},[5688,54888,54889,54891,54893],{},[898,54890,1712],{},[1762,54892,1764],{},[898,54894,1691],{},[902,54896,54600],{"encoding":904},[123,54898,54899,54900,54831,54917,54930,54931,1789],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,54901,54903],{"className":54902},[886],[888,54904,54905],{"xmlns":890},[892,54906,54907,54915],{},[895,54908,54909],{},[1717,54910,54911,54913],{},[898,54912,1712],{},[898,54914,1691],{},[902,54916,2204],{"encoding":904},[883,54918,54920],{"className":54919},[886],[888,54921,54922],{"xmlns":890},[892,54923,54924,54928],{},[895,54925,54926],{},[898,54927,1895],{},[902,54929,1895],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,54932,54934],{"className":54933},[886],[888,54935,54936],{"xmlns":890},[892,54937,54938,54948],{},[895,54939,54940],{},[5688,54941,54942,54944,54946],{},[898,54943,1712],{},[1762,54945,2398],{},[898,54947,1691],{},[902,54949,54662],{"encoding":904},[123,54951,54952,54953,54831,54970,9577,54983,9591,54996,54877,55010,1789],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,54954,54956],{"className":54955},[886],[888,54957,54958],{"xmlns":890},[892,54959,54960,54968],{},[895,54961,54962],{},[1717,54963,54964,54966],{},[898,54965,1712],{},[898,54967,1691],{},[902,54969,2204],{"encoding":904},[883,54971,54973],{"className":54972},[886],[888,54974,54975],{"xmlns":890},[892,54976,54977,54981],{},[895,54978,54979],{},[898,54980,2000],{},[902,54982,2000],{"encoding":904},[883,54984,54986],{"className":54985},[886],[888,54987,54988],{"xmlns":890},[892,54989,54990,54994],{},[895,54991,54992],{},[1762,54993,26132],{},[902,54995,51226],{"encoding":904},[883,54997,54999],{"className":54998},[886],[888,55000,55001],{"xmlns":890},[892,55002,55003,55007],{},[895,55004,55005],{},[1762,55006,21416],{},[902,55008,55009],{"encoding":904},"0{,}8",[883,55011,55013],{"className":55012},[886],[888,55014,55015],{"xmlns":890},[892,55016,55017,55027],{},[895,55018,55019],{},[5688,55020,55021,55023,55025],{},[898,55022,1712],{},[1762,55024,8357],{},[898,55026,1691],{},[902,55028,55029],{"encoding":904},"Q_3^E",[123,55031,55032,55033,54831,55050,55063,55064,1789],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,55034,55036],{"className":55035},[886],[888,55037,55038],{"xmlns":890},[892,55039,55040,55048],{},[895,55041,55042],{},[1717,55043,55044,55046],{},[898,55045,1712],{},[898,55047,1691],{},[902,55049,2204],{"encoding":904},[883,55051,55053],{"className":55052},[886],[888,55054,55055],{"xmlns":890},[892,55056,55057,55061],{},[895,55058,55059],{},[898,55060,1771],{},[902,55062,1771],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,55065,55067],{"className":55066},[886],[888,55068,55069],{"xmlns":890},[892,55070,55071,55081],{},[895,55072,55073],{},[5688,55074,55075,55077,55079],{},[898,55076,1712],{},[1762,55078,9262],{},[898,55080,1691],{},[902,55082,55083],{"encoding":904},"Q_4^E",[123,55085,55086,55087,55104,55105,55118,55119,28223,55132,1343,55147,28223,55160,4286,55174,28223,55187,55202,55203,1789],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,55088,55090],{"className":55089},[886],[888,55091,55092],{"xmlns":890},[892,55093,55094,55102],{},[895,55095,55096],{},[1717,55097,55098,55100],{},[898,55099,1712],{},[898,55101,1691],{},[902,55103,2204],{"encoding":904}," odpovídající změnám ",[883,55106,55108],{"className":55107},[886],[888,55109,55110],{"xmlns":890},[892,55111,55112,55116],{},[895,55113,55114],{},[898,55115,207],{},[902,55117,207],{"encoding":904}," o 1, ",[883,55120,55122],{"className":55121},[886],[888,55123,55124],{"xmlns":890},[892,55125,55126,55130],{},[895,55127,55128],{},[898,55129,1895],{},[902,55131,1895],{"encoding":904},[883,55133,55135],{"className":55134},[886],[888,55136,55137],{"xmlns":890},[892,55138,55139,55145],{},[895,55140,55141,55143],{},[1693,55142,1698],{},[1762,55144,9763],{},[902,55146,26266],{"encoding":904},[883,55148,55150],{"className":55149},[886],[888,55151,55152],{"xmlns":890},[892,55153,55154,55158],{},[895,55155,55156],{},[898,55157,2000],{},[902,55159,2000],{"encoding":904},[883,55161,55163],{"className":55162},[886],[888,55164,55165],{"xmlns":890},[892,55166,55167,55171],{},[895,55168,55169],{},[1762,55170,9695],{},[902,55172,55173],{"encoding":904},"0{,}1",[883,55175,55177],{"className":55176},[886],[888,55178,55179],{"xmlns":890},[892,55180,55181,55185],{},[895,55182,55183],{},[898,55184,1771],{},[902,55186,1771],{"encoding":904},[883,55188,55190],{"className":55189},[886],[888,55191,55192],{"xmlns":890},[892,55193,55194,55200],{},[895,55195,55196,55198],{},[1693,55197,1698],{},[1762,55199,9763],{},[902,55201,26266],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,55204,55206],{"className":55205},[886],[888,55207,55208],{"xmlns":890},[892,55209,55210,55220],{},[895,55211,55212],{},[5688,55213,55214,55216,55218],{},[898,55215,1712],{},[1762,55217,9147],{},[898,55219,1691],{},[902,55221,55222],{"encoding":904},"Q_5^E",[724,55224,55225,54448,55228,54485,55251,1789],{},[38,55226,55227],{},"2.15",[883,55229,55231],{"className":55230},[886],[888,55232,55233],{"xmlns":890},[892,55234,55235,55249],{},[895,55236,55237,55239,55241,55243,55245,55247],{},[898,55238,1701],{},[1693,55240,1695],{},[898,55242,207],{},[898,55244,1712],{},[1693,55246,1892],{},[898,55248,1895],{},[902,55250,43837],{"encoding":904},[883,55252,55254],{"className":55253},[886],[888,55255,55256],{"xmlns":890},[892,55257,55258,55272],{},[895,55259,55260,55262,55264,55266,55268,55270],{},[898,55261,1701],{},[1693,55263,1695],{},[898,55265,2000],{},[898,55267,1712],{},[1693,55269,1892],{},[898,55271,1771],{},[902,55273,47015],{"encoding":904},[120,55275,55276,55351,55368,55477,55530,55584],{},[123,55277,55278,55279,55292,55293,55318,55319,55350],{},"(a) Odvoďte redukovaný tvar pro ",[883,55280,55282],{"className":55281},[886],[888,55283,55284],{"xmlns":890},[892,55285,55286,55290],{},[895,55287,55288],{},[898,55289,1701],{},[902,55291,1701],{"encoding":904},". Stanovte podmínky pro ",[883,55294,55296],{"className":55295},[886],[888,55297,55298],{"xmlns":890},[892,55299,55300,55316],{},[895,55301,55302,55304,55306,55308,55310,55312,55314],{},[898,55303,207],{},[1693,55305,1899],{"separator":1898},[898,55307,1895],{},[1693,55309,1899],{"separator":1898},[898,55311,2000],{},[1693,55313,1899],{"separator":1898},[898,55315,1771],{},[902,55317,50052],{"encoding":904}," tak, aby rovnovážný bod ",[883,55320,55322],{"className":55321},[886],[888,55323,55324],{"xmlns":890},[892,55325,55326,55348],{},[895,55327,55328,55330,55332,55338,55340,55346],{},[898,55329,1691],{},[1693,55331,9392],{"stretchy":1708},[1717,55333,55334,55336],{},[898,55335,1712],{},[898,55337,1691],{},[1693,55339,1899],{"separator":1898},[1717,55341,55342,55344],{},[898,55343,1701],{},[898,55345,1691],{},[1693,55347,9407],{"stretchy":1708},[902,55349,48138],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,55352,55353,55354,55367],{},"(b) Vypočtěte multiplikátory pro ",[883,55355,55357],{"className":55356},[886],[888,55358,55359],{"xmlns":890},[892,55360,55361,55365],{},[895,55362,55363],{},[898,55364,1701],{},[902,55366,1701],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,55369,55370,55371,1343,55391,1343,55409,1343,55427,55445,55446,55463,55464,1789],{},"(c) Pro hodnoty parametrů ",[883,55372,55374],{"className":55373},[886],[888,55375,55376],{"xmlns":890},[892,55377,55378,55388],{},[895,55379,55380,55382,55384,55386],{},[898,55381,207],{},[1693,55383,1695],{},[1693,55385,1698],{},[1762,55387,2398],{},[902,55389,55390],{"encoding":904},"a = -2",[883,55392,55394],{"className":55393},[886],[888,55395,55396],{"xmlns":890},[892,55397,55398,55406],{},[895,55399,55400,55402,55404],{},[898,55401,1895],{},[1693,55403,1695],{},[1762,55405,12079],{},[902,55407,55408],{"encoding":904},"b = 40",[883,55410,55412],{"className":55411},[886],[888,55413,55414],{"xmlns":890},[892,55415,55416,55424],{},[895,55417,55418,55420,55422],{},[898,55419,2000],{},[1693,55421,1695],{},[1762,55423,11877],{},[902,55425,55426],{"encoding":904},"c = 0{,}5",[883,55428,55430],{"className":55429},[886],[888,55431,55432],{"xmlns":890},[892,55433,55434,55442],{},[895,55435,55436,55438,55440],{},[898,55437,1771],{},[1693,55439,1695],{},[1762,55441,9763],{},[902,55443,55444],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,55447,55449],{"className":55448},[886],[888,55450,55451],{"xmlns":890},[892,55452,55453,55461],{},[895,55454,55455],{},[1717,55456,55457,55459],{},[898,55458,1701],{},[898,55460,1691],{},[902,55462,48237],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,55465,55467],{"className":55466},[886],[888,55468,55469],{"xmlns":890},[892,55470,55471,55475],{},[895,55472,55473],{},[898,55474,1701],{},[902,55476,1701],{"encoding":904},[123,55478,55479,55480,54831,55497,55510,55511,1789],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,55481,55483],{"className":55482},[886],[888,55484,55485],{"xmlns":890},[892,55486,55487,55495],{},[895,55488,55489],{},[1717,55490,55491,55493],{},[898,55492,1701],{},[898,55494,1691],{},[902,55496,48237],{"encoding":904},[883,55498,55500],{"className":55499},[886],[888,55501,55502],{"xmlns":890},[892,55503,55504,55508],{},[895,55505,55506],{},[898,55507,207],{},[902,55509,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,55512,55514],{"className":55513},[886],[888,55515,55516],{"xmlns":890},[892,55517,55518,55528],{},[895,55519,55520],{},[5688,55521,55522,55524,55526],{},[898,55523,1701],{},[1762,55525,1764],{},[898,55527,1691],{},[902,55529,54621],{"encoding":904},[123,55531,55532,55533,55550,55551,55564,55565,1789],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,55534,55536],{"className":55535},[886],[888,55537,55538],{"xmlns":890},[892,55539,55540,55548],{},[895,55541,55542],{},[1717,55543,55544,55546],{},[898,55545,1701],{},[898,55547,1691],{},[902,55549,48237],{"encoding":904}," odpovídající poklesu ",[883,55552,55554],{"className":55553},[886],[888,55555,55556],{"xmlns":890},[892,55557,55558,55562],{},[895,55559,55560],{},[898,55561,207],{},[902,55563,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,55566,55568],{"className":55567},[886],[888,55569,55570],{"xmlns":890},[892,55571,55572,55582],{},[895,55573,55574],{},[5688,55575,55576,55578,55580],{},[898,55577,1701],{},[1762,55579,2398],{},[898,55581,1691],{},[902,55583,54682],{"encoding":904},[123,55585,55586,55587,55104,55604,55617,55618,9591,55631,4286,55646,55659,55660,1789],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,55588,55590],{"className":55589},[886],[888,55591,55592],{"xmlns":890},[892,55593,55594,55602],{},[895,55595,55596],{},[1717,55597,55598,55600],{},[898,55599,1701],{},[898,55601,1691],{},[902,55603,48237],{"encoding":904},[883,55605,55607],{"className":55606},[886],[888,55608,55609],{"xmlns":890},[892,55610,55611,55615],{},[895,55612,55613],{},[898,55614,207],{},[902,55616,207],{"encoding":904}," na 35, ",[883,55619,55621],{"className":55620},[886],[888,55622,55623],{"xmlns":890},[892,55624,55625,55629],{},[895,55626,55627],{},[898,55628,2000],{},[902,55630,2000],{"encoding":904},[883,55632,55634],{"className":55633},[886],[888,55635,55636],{"xmlns":890},[892,55637,55638,55643],{},[895,55639,55640],{},[1762,55641,55642],{},"0,7",[902,55644,55645],{"encoding":904},"0{,}7",[883,55647,55649],{"className":55648},[886],[888,55650,55651],{"xmlns":890},[892,55652,55653,55657],{},[895,55654,55655],{},[898,55656,1771],{},[902,55658,1771],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,55661,55663],{"className":55662},[886],[888,55664,55665],{"xmlns":890},[892,55666,55667,55677],{},[895,55668,55669],{},[5688,55670,55671,55673,55675],{},[898,55672,1701],{},[1762,55674,8357],{},[898,55676,1691],{},[902,55678,55679],{"encoding":904},"P_3^E",[724,55681,55682,54448,55685,54485,55713,28397,55741,4286,55767,1789],{},[38,55683,55684],{},"2.16",[883,55686,55688],{"className":55687},[886],[888,55689,55690],{"xmlns":890},[892,55691,55692,55710],{},[895,55693,55694,55696,55698,55700,55702,55704],{},[898,55695,1701],{},[1693,55697,1695],{},[898,55699,207],{},[1693,55701,1892],{},[898,55703,1895],{},[1717,55705,55706,55708],{},[898,55707,1712],{},[1762,55709,2398],{},[902,55711,55712],{"encoding":904},"P = a + bQ^2",[883,55714,55716],{"className":55715},[886],[888,55717,55718],{"xmlns":890},[892,55719,55720,55738],{},[895,55721,55722,55724,55726,55728,55730,55732],{},[898,55723,1701],{},[1693,55725,1695],{},[898,55727,2000],{},[1693,55729,1892],{},[898,55731,1771],{},[1717,55733,55734,55736],{},[898,55735,1712],{},[1762,55737,2398],{},[902,55739,55740],{"encoding":904},"P = c + dQ^2",[883,55742,55744],{"className":55743},[886],[888,55745,55746],{"xmlns":890},[892,55747,55748,55764],{},[895,55749,55750,55752,55754,55756,55758,55760,55762],{},[898,55751,207],{},[1693,55753,1899],{"separator":1898},[898,55755,2000],{},[1693,55757,1899],{"separator":1898},[898,55759,1771],{},[1693,55761,1922],{},[1762,55763,1911],{},[902,55765,55766],{"encoding":904},"a, c, d > 0",[883,55768,55770],{"className":55769},[886],[888,55771,55772],{"xmlns":890},[892,55773,55774,55782],{},[895,55775,55776,55778,55780],{},[898,55777,1895],{},[1693,55779,1908],{},[1762,55781,1911],{},[902,55783,55784],{"encoding":904},"b \u003C 0",[120,55786,55787,55835,55851,55958,56010,56062,56171,56187,56286,56339],{},[123,55788,55278,55789,55802,55803,55834],{},[883,55790,55792],{"className":55791},[886],[888,55793,55794],{"xmlns":890},[892,55795,55796,55800],{},[895,55797,55798],{},[898,55799,1712],{},[902,55801,1712],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,55804,55806],{"className":55805},[886],[888,55807,55808],{"xmlns":890},[892,55809,55810,55832],{},[895,55811,55812,55814,55816,55822,55824,55830],{},[898,55813,1691],{},[1693,55815,9392],{"stretchy":1708},[1717,55817,55818,55820],{},[898,55819,1712],{},[898,55821,1691],{},[1693,55823,1899],{"separator":1898},[1717,55825,55826,55828],{},[898,55827,1701],{},[898,55829,1691],{},[1693,55831,9407],{"stretchy":1708},[902,55833,48138],{"encoding":904}," patřil do 1. kvadrantu.",[123,55836,55353,55837,55850],{},[883,55838,55840],{"className":55839},[886],[888,55841,55842],{"xmlns":890},[892,55843,55844,55848],{},[895,55845,55846],{},[898,55847,1712],{},[902,55849,1712],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,55852,55370,55853,1343,55871,1343,55891,1343,55909,55927,55928,55463,55945,1789],{},[883,55854,55856],{"className":55855},[886],[888,55857,55858],{"xmlns":890},[892,55859,55860,55868],{},[895,55861,55862,55864,55866],{},[898,55863,207],{},[1693,55865,1695],{},[1762,55867,9987],{},[902,55869,55870],{"encoding":904},"a = 100",[883,55872,55874],{"className":55873},[886],[888,55875,55876],{"xmlns":890},[892,55877,55878,55888],{},[895,55879,55880,55882,55884,55886],{},[898,55881,1895],{},[1693,55883,1695],{},[1693,55885,1698],{},[1762,55887,1764],{},[902,55889,55890],{"encoding":904},"b = -1",[883,55892,55894],{"className":55893},[886],[888,55895,55896],{"xmlns":890},[892,55897,55898,55906],{},[895,55899,55900,55902,55904],{},[898,55901,2000],{},[1693,55903,1695],{},[1762,55905,15892],{},[902,55907,55908],{"encoding":904},"c = 20",[883,55910,55912],{"className":55911},[886],[888,55913,55914],{"xmlns":890},[892,55915,55916,55924],{},[895,55917,55918,55920,55922],{},[898,55919,1771],{},[1693,55921,1695],{},[1762,55923,1764],{},[902,55925,55926],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,55929,55931],{"className":55930},[886],[888,55932,55933],{"xmlns":890},[892,55934,55935,55943],{},[895,55936,55937],{},[1717,55938,55939,55941],{},[898,55940,1712],{},[898,55942,1691],{},[902,55944,2204],{"encoding":904},[883,55946,55948],{"className":55947},[886],[888,55949,55950],{"xmlns":890},[892,55951,55952,55956],{},[895,55953,55954],{},[898,55955,1712],{},[902,55957,1712],{"encoding":904},[123,55959,54899,55960,54831,55977,55990,55991,1789],{},[883,55961,55963],{"className":55962},[886],[888,55964,55965],{"xmlns":890},[892,55966,55967,55975],{},[895,55968,55969],{},[1717,55970,55971,55973],{},[898,55972,1712],{},[898,55974,1691],{},[902,55976,2204],{"encoding":904},[883,55978,55980],{"className":55979},[886],[888,55981,55982],{"xmlns":890},[892,55983,55984,55988],{},[895,55985,55986],{},[898,55987,207],{},[902,55989,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,55992,55994],{"className":55993},[886],[888,55995,55996],{"xmlns":890},[892,55997,55998,56008],{},[895,55999,56000],{},[5688,56001,56002,56004,56006],{},[898,56003,1712],{},[1762,56005,1764],{},[898,56007,1691],{},[902,56009,54600],{"encoding":904},[123,56011,54952,56012,54831,56029,56042,56043,1789],{},[883,56013,56015],{"className":56014},[886],[888,56016,56017],{"xmlns":890},[892,56018,56019,56027],{},[895,56020,56021],{},[1717,56022,56023,56025],{},[898,56024,1712],{},[898,56026,1691],{},[902,56028,2204],{"encoding":904},[883,56030,56032],{"className":56031},[886],[888,56033,56034],{"xmlns":890},[892,56035,56036,56040],{},[895,56037,56038],{},[898,56039,2000],{},[902,56041,2000],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,56044,56046],{"className":56045},[886],[888,56047,56048],{"xmlns":890},[892,56049,56050,56060],{},[895,56051,56052],{},[5688,56053,56054,56056,56058],{},[898,56055,1712],{},[1762,56057,2398],{},[898,56059,1691],{},[902,56061,54662],{"encoding":904},[123,56063,55032,56064,55104,56081,56094,56095,9591,56108,56123,56124,56137,56138,56151,56152,1789],{},[883,56065,56067],{"className":56066},[886],[888,56068,56069],{"xmlns":890},[892,56070,56071,56079],{},[895,56072,56073],{},[1717,56074,56075,56077],{},[898,56076,1712],{},[898,56078,1691],{},[902,56080,2204],{"encoding":904},[883,56082,56084],{"className":56083},[886],[888,56085,56086],{"xmlns":890},[892,56087,56088,56092],{},[895,56089,56090],{},[898,56091,207],{},[902,56093,207],{"encoding":904}," na 110, poklesu ",[883,56096,56098],{"className":56097},[886],[888,56099,56100],{"xmlns":890},[892,56101,56102,56106],{},[895,56103,56104],{},[898,56105,1895],{},[902,56107,1895],{"encoding":904},[883,56109,56111],{"className":56110},[886],[888,56112,56113],{"xmlns":890},[892,56114,56115,56121],{},[895,56116,56117,56119],{},[1693,56118,1698],{},[1762,56120,2398],{},[902,56122,54860],{"encoding":904},", růstu ",[883,56125,56127],{"className":56126},[886],[888,56128,56129],{"xmlns":890},[892,56130,56131,56135],{},[895,56132,56133],{},[898,56134,2000],{},[902,56136,2000],{"encoding":904}," na 25 a růstu ",[883,56139,56141],{"className":56140},[886],[888,56142,56143],{"xmlns":890},[892,56144,56145,56149],{},[895,56146,56147],{},[898,56148,1771],{},[902,56150,1771],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,56153,56155],{"className":56154},[886],[888,56156,56157],{"xmlns":890},[892,56158,56159,56169],{},[895,56160,56161],{},[5688,56162,56163,56165,56167],{},[898,56164,1712],{},[1762,56166,8357],{},[898,56168,1691],{},[902,56170,55029],{"encoding":904},[123,56172,56173,56174,55850],{},"(i) Vypočtěte multiplikátory pro ",[883,56175,56177],{"className":56176},[886],[888,56178,56179],{"xmlns":890},[892,56180,56181,56185],{},[895,56182,56183],{},[898,56184,1701],{},[902,56186,1701],{"encoding":904},[123,56188,56189,56190,55463,56207,56220,56221,54831,56238,9591,56251,56266,56267,1789],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,56191,56193],{"className":56192},[886],[888,56194,56195],{"xmlns":890},[892,56196,56197,56205],{},[895,56198,56199],{},[1717,56200,56201,56203],{},[898,56202,1701],{},[898,56204,1691],{},[902,56206,48237],{"encoding":904},[883,56208,56210],{"className":56209},[886],[888,56211,56212],{"xmlns":890},[892,56213,56214,56218],{},[895,56215,56216],{},[898,56217,1701],{},[902,56219,1701],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,56222,56224],{"className":56223},[886],[888,56225,56226],{"xmlns":890},[892,56227,56228,56236],{},[895,56229,56230],{},[1717,56231,56232,56234],{},[898,56233,1701],{},[898,56235,1691],{},[902,56237,48237],{"encoding":904},[883,56239,56241],{"className":56240},[886],[888,56242,56243],{"xmlns":890},[892,56244,56245,56249],{},[895,56246,56247],{},[898,56248,207],{},[902,56250,207],{"encoding":904},[883,56252,56254],{"className":56253},[886],[888,56255,56256],{"xmlns":890},[892,56257,56258,56264],{},[895,56259,56260,56262],{},[1693,56261,1698],{},[1762,56263,8357],{},[902,56265,54876],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,56268,56270],{"className":56269},[886],[888,56271,56272],{"xmlns":890},[892,56273,56274,56284],{},[895,56275,56276],{},[5688,56277,56278,56280,56282],{},[898,56279,1701],{},[1762,56281,1764],{},[898,56283,1691],{},[902,56285,54621],{"encoding":904},[123,56287,56288,56289,54831,56306,56319,56320,1789],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,56290,56292],{"className":56291},[886],[888,56293,56294],{"xmlns":890},[892,56295,56296,56304],{},[895,56297,56298],{},[1717,56299,56300,56302],{},[898,56301,1701],{},[898,56303,1691],{},[902,56305,48237],{"encoding":904},[883,56307,56309],{"className":56308},[886],[888,56310,56311],{"xmlns":890},[892,56312,56313,56317],{},[895,56314,56315],{},[898,56316,207],{},[902,56318,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,56321,56323],{"className":56322},[886],[888,56324,56325],{"xmlns":890},[892,56326,56327,56337],{},[895,56328,56329],{},[5688,56330,56331,56333,56335],{},[898,56332,1701],{},[1762,56334,2398],{},[898,56336,1691],{},[902,56338,54682],{"encoding":904},[123,56340,56341,56342,55550,56359,56372,56373,9591,56386,56123,56401,56414,56415,56428,56429,1789],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,56343,56345],{"className":56344},[886],[888,56346,56347],{"xmlns":890},[892,56348,56349,56357],{},[895,56350,56351],{},[1717,56352,56353,56355],{},[898,56354,1701],{},[898,56356,1691],{},[902,56358,48237],{"encoding":904},[883,56360,56362],{"className":56361},[886],[888,56363,56364],{"xmlns":890},[892,56365,56366,56370],{},[895,56367,56368],{},[898,56369,207],{},[902,56371,207],{"encoding":904}," na 90, poklesu ",[883,56374,56376],{"className":56375},[886],[888,56377,56378],{"xmlns":890},[892,56379,56380,56384],{},[895,56381,56382],{},[898,56383,1895],{},[902,56385,1895],{"encoding":904},[883,56387,56389],{"className":56388},[886],[888,56390,56391],{"xmlns":890},[892,56392,56393,56399],{},[895,56394,56395,56397],{},[1693,56396,1698],{},[1762,56398,8357],{},[902,56400,54876],{"encoding":904},[883,56402,56404],{"className":56403},[886],[888,56405,56406],{"xmlns":890},[892,56407,56408,56412],{},[895,56409,56410],{},[898,56411,2000],{},[902,56413,2000],{"encoding":904}," na 30 a růstu ",[883,56416,56418],{"className":56417},[886],[888,56419,56420],{"xmlns":890},[892,56421,56422,56426],{},[895,56423,56424],{},[898,56425,1771],{},[902,56427,1771],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,56430,56432],{"className":56431},[886],[888,56433,56434],{"xmlns":890},[892,56435,56436,56446],{},[895,56437,56438],{},[5688,56439,56440,56442,56444],{},[898,56441,1701],{},[1762,56443,8357],{},[898,56445,1691],{},[902,56447,55679],{"encoding":904},[198,56449,820],{"id":56450},"přebytek-spotřebitele-a-výrobce-1",[724,56452,56453,54448,56456,54485,56492,1789],{},[38,56454,56455],{},"2.17",[883,56457,56459],{"className":56458},[886],[888,56460,56461],{"xmlns":890},[892,56462,56463,56489],{},[895,56464,56465,56467,56469,56471,56473,56475,56477,56479,56481,56483],{},[898,56466,1701],{},[1693,56468,1695],{},[898,56470,2738],{},[1693,56472,1709],{"stretchy":1708},[898,56474,1712],{},[1693,56476,1731],{"stretchy":1708},[1693,56478,1695],{},[1762,56480,21864],{},[1693,56482,1698],{},[1717,56484,56485,56487],{},[898,56486,1712],{},[1762,56488,2398],{},[902,56490,56491],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,56493,56495],{"className":56494},[886],[888,56496,56497],{"xmlns":890},[892,56498,56499,56525],{},[895,56500,56501,56503,56505,56507,56509,56511,56513,56515,56517,56519],{},[898,56502,1701],{},[1693,56504,1695],{},[898,56506,3611],{},[1693,56508,1709],{"stretchy":1708},[898,56510,1712],{},[1693,56512,1731],{"stretchy":1708},[1693,56514,1695],{},[1762,56516,8357],{},[1693,56518,1892],{},[1717,56520,56521,56523],{},[898,56522,1712],{},[1762,56524,2398],{},[902,56526,56527],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,56529,56530,56533],{},[123,56531,56532],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,56534,56535],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,56537,56538,54448,56541,54485,56575,1789],{},[38,56539,56540],{},"2.18",[883,56542,56544],{"className":56543},[886],[888,56545,56546],{"xmlns":890},[892,56547,56548,56572],{},[895,56549,56550,56552,56554,56556,56558,56560,56562,56564,56566,56568,56570],{},[898,56551,1701],{},[1693,56553,1695],{},[898,56555,2738],{},[1693,56557,1709],{"stretchy":1708},[898,56559,1712],{},[1693,56561,1731],{"stretchy":1708},[1693,56563,1695],{},[1762,56565,10600],{},[1693,56567,1698],{},[1762,56569,2398],{},[898,56571,1712],{},[902,56573,56574],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,56576,56578],{"className":56577},[886],[888,56579,56580],{"xmlns":890},[892,56581,56582,56608],{},[895,56583,56584,56586,56588,56590,56592,56594,56596,56598,56600,56602],{},[898,56585,1701],{},[1693,56587,1695],{},[898,56589,3611],{},[1693,56591,1709],{"stretchy":1708},[898,56593,1712],{},[1693,56595,1731],{"stretchy":1708},[1693,56597,1695],{},[1762,56599,8357],{},[1693,56601,1892],{},[1717,56603,56604,56606],{},[898,56605,1712],{},[1762,56607,2398],{},[902,56609,56527],{"encoding":904},[120,56611,56612,56632,56635,56638],{},[123,56613,56614,56615,1789],{},"(a) Vypočtěte rovnovážné množství ",[883,56616,56618],{"className":56617},[886],[888,56619,56620],{"xmlns":890},[892,56621,56622,56630],{},[895,56623,56624],{},[1717,56625,56626,56628],{},[898,56627,1712],{},[898,56629,1691],{},[902,56631,2204],{"encoding":904},[123,56633,56634],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,56636,56637],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,56639,56640],{},"(c) Graficky interpretujte.",[1852,56642],{},[115,56644,8674],{"id":56645},"otázky-k-sebehodnocení",[152,56647,56648,56651,56654,56657,56660,56663,56666,56669,56672,56675,56678,56681,56684,56687],{},[123,56649,56650],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,56652,56653],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,56655,56656],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,56658,56659],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,56661,56662],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,56664,56665],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,56667,56668],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,56670,56671],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,56673,56674],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,56676,56677],{},"K čemu slouží multiplikátory?",[123,56679,56680],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,56682,56683],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,56685,56686],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,56688,56689],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[1852,56691],{},[115,56693,22545],{"id":22544},[724,56695,56696],{},[38,56697,19993],{},[120,56699,56700,56735,56740,56770,56775,56837,56863,56868,56898,56907,56914,56920],{},[123,56701,56702,16877,56705,25461,56708,1863,56710,1343,56733],{},[38,56703,56704],{},"Poptávané množství",[614,56706,56707],{},"quantity demanded",[38,56709,34790],{},[883,56711,56713],{"className":56712},[886],[888,56714,56715],{"xmlns":890},[892,56716,56717,56731],{},[895,56718,56719,56721,56723,56725,56727,56729],{},[898,56720,1712],{},[1693,56722,1695],{},[898,56724,2738],{},[1693,56726,1709],{"stretchy":1708},[898,56728,1701],{},[1693,56730,1731],{"stretchy":1708},[902,56732,11072],{"encoding":904},[38,56734,44226],{},[123,56736,56737,56739],{},[38,56738,44233],{}," — substituční + důchodový efekt",[123,56741,56742,1863,56745],{},[38,56743,56744],{},"Reálné cenové rozpětí",[883,56746,56748],{"className":56747},[886],[888,56749,56750],{"xmlns":890},[892,56751,56752,56768],{},[895,56753,56754,56756,56758,56760,56766],{},[1693,56755,1709],{"stretchy":1708},[1762,56757,1911],{},[1693,56759,1899],{"separator":1898},[3284,56761,56762,56764],{},[898,56763,1701],{},[1762,56765,1911],{},[1693,56767,1731],{"stretchy":1708},[902,56769,44434],{"encoding":904},[123,56771,56772,17942],{},[38,56773,56774],{},"Homogenita poptávky",[123,56776,56777,1863,56779,1343,56802,1343,56819,56836],{},[38,56778,1870],{},[883,56780,56782],{"className":56781},[886],[888,56783,56784],{"xmlns":890},[892,56785,56786,56800],{},[895,56787,56788,56790,56792,56794,56796,56798],{},[898,56789,1701],{},[1693,56791,1695],{},[898,56793,207],{},[898,56795,1712],{},[1693,56797,1892],{},[898,56799,1895],{},[902,56801,43837],{"encoding":904},[883,56803,56805],{"className":56804},[886],[888,56806,56807],{"xmlns":890},[892,56808,56809,56817],{},[895,56810,56811,56813,56815],{},[898,56812,207],{},[1693,56814,1908],{},[1762,56816,1911],{},[902,56818,49853],{"encoding":904},[883,56820,56822],{"className":56821},[886],[888,56823,56824],{"xmlns":890},[892,56825,56826,56834],{},[895,56827,56828,56830,56832],{},[898,56829,1895],{},[1693,56831,1922],{},[1762,56833,1911],{},[902,56835,7157],{"encoding":904}," — nedokonalá konkurence",[123,56838,56839,13877,56842],{},[38,56840,56841],{},"Dokonalá konkurence",[883,56843,56845],{"className":56844},[886],[888,56846,56847],{"xmlns":890},[892,56848,56849,56861],{},[895,56850,56851,56853,56855],{},[898,56852,1701],{},[1693,56854,1695],{},[1717,56856,56857,56859],{},[898,56858,1701],{},[1693,56860,3672],{},[902,56862,11234],{"encoding":904},[123,56864,56865,56867],{},[38,56866,45002],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,56869,56870,1863,56872,1343,56896],{},[38,56871,38510],{},[883,56873,56875],{"className":56874},[886],[888,56876,56877],{"xmlns":890},[892,56878,56879,56893],{},[895,56880,56881,56883,56885,56887,56889,56891],{},[898,56882,1712],{},[1693,56884,1695],{},[898,56886,1691],{},[1693,56888,1709],{"stretchy":1708},[898,56890,4618],{},[1693,56892,1731],{"stretchy":1708},[902,56894,56895],{"encoding":904},"Q = E(Y)",[38,56897,45198],{},[123,56899,56900,56903,56904,56906],{},[38,56901,56902],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,56905,45643],{}," zboží",[123,56908,56909,4286,56911,56913],{},[38,56910,46649],{},[38,56912,46596],{}," — znaménka zkřížených koeficientů",[123,56915,56916,56919],{},[38,56917,56918],{},"Dvoukomoditní trh"," (2.6)",[123,56921,56922,16877,56925,1731],{},[38,56923,56924],{},"Posun poptávky",[614,56926,45701],{},[724,56928,56929],{},[38,56930,19957],{},[120,56932,56933,56966,56970,57014],{},[123,56934,56935,16877,56937,25461,56939,1863,56941,1343,56964],{},[38,56936,47042],{},[614,56938,47045],{},[38,56940,47215],{},[883,56942,56944],{"className":56943},[886],[888,56945,56946],{"xmlns":890},[892,56947,56948,56962],{},[895,56949,56950,56952,56954,56956,56958,56960],{},[898,56951,1712],{},[1693,56953,1695],{},[898,56955,3611],{},[1693,56957,1709],{"stretchy":1708},[898,56959,1701],{},[1693,56961,1731],{"stretchy":1708},[902,56963,15539],{"encoding":904},[38,56965,47293],{},[123,56967,56968],{},[38,56969,47300],{},[123,56971,56972,1863,56974,1343,56997],{},[38,56973,1982],{},[883,56975,56977],{"className":56976},[886],[888,56978,56979],{"xmlns":890},[892,56980,56981,56995],{},[895,56982,56983,56985,56987,56989,56991,56993],{},[898,56984,1701],{},[1693,56986,1695],{},[898,56988,2000],{},[898,56990,1712],{},[1693,56992,1892],{},[898,56994,1771],{},[902,56996,47015],{"encoding":904},[883,56998,57000],{"className":56999},[886],[888,57001,57002],{"xmlns":890},[892,57003,57004,57012],{},[895,57005,57006,57008,57010],{},[898,57007,2000],{},[1693,57009,1922],{},[1762,57011,1911],{},[902,57013,47033],{"encoding":904},[123,57015,57016,16877,57019,1731],{},[38,57017,57018],{},"Posun nabídky",[614,57020,47678],{},[724,57022,57023],{},[38,57024,57025],{},"Rovnováha a komparativní statika",[120,57027,57028,57107,57113],{},[123,57029,57030,16877,57032,25461,57034,1863,57037,1343,57054,1863,57057,1343,57074,1863,57076],{},[38,57031,48096],{},[614,57033,48215],{},[38,57035,57036],{},"rovnovážná cena",[883,57038,57040],{"className":57039},[886],[888,57041,57042],{"xmlns":890},[892,57043,57044,57052],{},[895,57045,57046],{},[1717,57047,57048,57050],{},[898,57049,1701],{},[898,57051,1691],{},[902,57053,48237],{"encoding":904},[38,57055,57056],{},"rovnovážné množství",[883,57058,57060],{"className":57059},[886],[888,57061,57062],{"xmlns":890},[892,57063,57064,57072],{},[895,57065,57066],{},[1717,57067,57068,57070],{},[898,57069,1712],{},[898,57071,1691],{},[902,57073,2204],{"encoding":904},[38,57075,48273],{},[883,57077,57079],{"className":57078},[886],[888,57080,57081],{"xmlns":890},[892,57082,57083,57105],{},[895,57084,57085,57087,57089,57095,57097,57103],{},[898,57086,1691],{},[1693,57088,9392],{"stretchy":1708},[1717,57090,57091,57093],{},[898,57092,1712],{},[898,57094,1691],{},[1693,57096,1899],{"separator":1898},[1717,57098,57099,57101],{},[898,57100,1701],{},[898,57102,1691],{},[1693,57104,9407],{"stretchy":1708},[902,57106,48138],{"encoding":904},[123,57108,57109,57112],{},[38,57110,57111],{},"Pravidla 1–4"," komparativní statiky",[123,57114,57115,16877,57118,1731],{},[38,57116,57117],{},"Teorém pavučiny",[614,57119,49120],{},[724,57121,57122],{},[38,57123,8747],{},[120,57125,57126,57182,57230],{},[123,57127,57128,57130,57131,57156,57157,1731],{},[38,57129,8747],{}," — daň výrobci (",[883,57132,57134],{"className":57133},[886],[888,57135,57136],{"xmlns":890},[892,57137,57138,57154],{},[895,57139,57140,57146,57148,57150,57152],{},[3284,57141,57142,57144],{},[898,57143,3611],{},[1762,57145,1764],{},[1693,57147,1695],{},[898,57149,3611],{},[1693,57151,1892],{},[898,57153,2663],{},[902,57155,49522],{"encoding":904},") vs. daň spotřebiteli (",[883,57158,57160],{"className":57159},[886],[888,57161,57162],{"xmlns":890},[892,57163,57164,57180],{},[895,57165,57166,57172,57174,57176,57178],{},[3284,57167,57168,57170],{},[898,57169,2738],{},[1762,57171,2398],{},[1693,57173,1695],{},[898,57175,2738],{},[1693,57177,1698],{},[898,57179,2663],{},[902,57181,49553],{"encoding":904},[123,57183,57184,1863,57186,1343,57207],{},[38,57185,49428],{},[883,57187,57189],{"className":57188},[886],[888,57190,57191],{"xmlns":890},[892,57192,57193,57205],{},[895,57194,57195],{},[3284,57196,57197,57199],{},[898,57198,2663],{},[895,57200,57201,57203],{},[898,57202,6746],{},[898,57204,724],{},[902,57206,49451],{"encoding":904},[883,57208,57210],{"className":57209},[886],[888,57211,57212],{"xmlns":890},[892,57213,57214,57228],{},[895,57215,57216],{},[3284,57217,57218,57220],{},[898,57219,2663],{},[895,57221,57222,57224,57226],{},[898,57223,6759],{},[898,57225,6560],{},[898,57227,6629],{},[902,57229,49475],{"encoding":904},[123,57231,57232,1863,57235,1343,57264],{},[38,57233,57234],{},"Ekvivalence zdanění",[883,57236,57238],{"className":57237},[886],[888,57239,57240],{"xmlns":890},[892,57241,57242,57262],{},[895,57243,57244,57252,57254],{},[5688,57245,57246,57248,57250],{},[898,57247,1712],{},[1762,57249,1764],{},[898,57251,1691],{},[1693,57253,1695],{},[5688,57255,57256,57258,57260],{},[898,57257,1712],{},[1762,57259,2398],{},[898,57261,1691],{},[902,57263,49676],{"encoding":904},[883,57265,57267],{"className":57266},[886],[888,57268,57269],{"xmlns":890},[892,57270,57271,57295],{},[895,57272,57273,57281,57283,57285,57287],{},[5688,57274,57275,57277,57279],{},[898,57276,1701],{},[1762,57278,1764],{},[898,57280,1691],{},[1693,57282,1698],{},[898,57284,2663],{},[1693,57286,1695],{},[5688,57288,57289,57291,57293],{},[898,57290,1701],{},[1762,57292,2398],{},[898,57294,1691],{},[902,57296,49710],{"encoding":904},[724,57298,57299],{},[38,57300,33198],{},[120,57302,57303,57349,57380,57385,57391,57398],{},[123,57304,57305,1863,57307],{},[38,57306,49809],{},[883,57308,57310],{"className":57309},[886],[888,57311,57312],{"xmlns":890},[892,57313,57314,57346],{},[895,57315,57316,57322,57324,57326,57328,57330,57332,57334,57336,57338,57340,57342,57344],{},[1717,57317,57318,57320],{},[898,57319,1712],{},[898,57321,1691],{},[1693,57323,1695],{},[1693,57325,1709],{"stretchy":1708},[898,57327,1895],{},[1693,57329,1698],{},[898,57331,1771],{},[1693,57333,1731],{"stretchy":1708},[898,57335,1705],{"mathvariant":1704},[1693,57337,1709],{"stretchy":1708},[898,57339,2000],{},[1693,57341,1698],{},[898,57343,207],{},[1693,57345,1731],{"stretchy":1708},[902,57347,57348],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,57350,57351,1863,57354,57379],{},[38,57352,57353],{},"Parametry",[883,57355,57357],{"className":57356},[886],[888,57358,57359],{"xmlns":890},[892,57360,57361,57377],{},[895,57362,57363,57365,57367,57369,57371,57373,57375],{},[898,57364,207],{},[1693,57366,1899],{"separator":1898},[898,57368,1895],{},[1693,57370,1899],{"separator":1898},[898,57372,2000],{},[1693,57374,1899],{"separator":1898},[898,57376,1771],{},[902,57378,50052],{"encoding":904}," — exogenní proměnné",[123,57381,57382],{},[38,57383,57384],{},"Endogenní \u002F exogenní proměnná",[123,57386,57387,57390],{},[38,57388,57389],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,57392,57393,1343,57396],{},[38,57394,57395],{},"Komparativní statika",[38,57397,43738],{},[123,57399,57400,1863,57402,57418],{},[38,57401,9853],{},[883,57403,57405],{"className":57404},[886],[888,57406,57407],{"xmlns":890},[892,57408,57409,57415],{},[895,57410,57411,57413],{},[898,57412,1771],{},[898,57414,1712],{},[902,57416,57417],{"encoding":904},"dQ"," (2.11)",[724,57420,57421],{},[38,57422,57423],{},"Přebytky a ostatní",[120,57425,57426,57464],{},[123,57427,57428,1863,57430,57445,57446,1863,57448,57463],{},[38,57429,6189],{},[883,57431,57433],{"className":57432},[886],[888,57434,57435],{"xmlns":890},[892,57436,57437,57443],{},[895,57438,57439,57441],{},[898,57440,2971],{},[898,57442,3611],{},[902,57444,51715],{"encoding":904}," (2.14), ",[38,57447,51718],{},[883,57449,57451],{"className":57450},[886],[888,57452,57453],{"xmlns":890},[892,57454,57455,57461],{},[895,57456,57457,57459],{},[898,57458,1701],{},[898,57460,3611],{},[902,57462,51734],{"encoding":904}," (2.15)",[123,57465,57466,1343,57469,57472],{},[38,57467,57468],{},"Homo economicus",[38,57470,57471],{},"Marshallova formulace"," (1890)",[1852,57474],{},[115,57476,8685],{"id":8684},[120,57478,57479,57514,57523],{},[123,57480,57481,1863,57484,57487,57488,1343,57491,57494,57495,57498,57499,57502,57503,57506,57507,57510,57511],{},[38,57482,57483],{},"Související témata:",[207,57485,811],{"className":57486,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,57489,820],{"className":57490,"dataFsResolvedFilePath":818,"href":819},[210],[207,57492,8726],{"className":57493,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,57496,775],{"className":57497,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,57500,784],{"className":57501,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,57504,793],{"className":57505,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,57508,8759],{"className":57509,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,57512,3261],{"className":57513,"dataFsResolvedFilePath":827,"href":828},[210],[123,57515,57516,1863,57519],{},[38,57517,57518],{},"Shrnutí přednášek:",[207,57520,57522],{"className":57521,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,57524,57525,1863,57527],{},[38,57526,8692],{},[207,57528,1653],{"className":57529,"dataFsResolvedFilePath":1651,"href":1652},[210],{"title":641,"searchDepth":642,"depth":642,"links":57531},[57532,57533,57541,57547,57554,57555,57562,57563,57564,57571,57572,57573],{"id":43575,"depth":642,"text":43576},{"id":43556,"depth":642,"text":19993,"children":57534},[57535,57536,57537,57538,57540],{"id":43840,"depth":649,"text":43841},{"id":44122,"depth":649,"text":44123},{"id":45130,"depth":649,"text":45131},{"id":45697,"depth":649,"text":57539},"Posun poptávky (shift of demand)",{"id":46201,"depth":649,"text":46202},{"id":43560,"depth":642,"text":19957,"children":57542},[57543,57544,57545],{"id":47037,"depth":649,"text":43841},{"id":47222,"depth":649,"text":47223},{"id":47674,"depth":649,"text":57546},"Posun nabídky (shift of supply)",{"id":48095,"depth":642,"text":48096,"children":57548},[57549,57550,57551,57552,57553],{"id":48207,"depth":649,"text":48208},{"id":48420,"depth":649,"text":48421},{"id":48738,"depth":649,"text":48739},{"id":49092,"depth":649,"text":49093},{"id":49123,"depth":649,"text":49124},{"id":49391,"depth":642,"text":811},{"id":49790,"depth":642,"text":49791,"children":57556},[57557,57558,57559,57560],{"id":49808,"depth":649,"text":49809},{"id":50187,"depth":649,"text":50188},{"id":50571,"depth":649,"text":50572},{"id":51025,"depth":649,"text":57561},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":18629,"depth":642,"text":820},{"id":51948,"depth":642,"text":51949},{"id":52179,"depth":642,"text":52180,"children":57565},[57566,57567,57568,57569,57570],{"id":52183,"depth":649,"text":52184},{"id":53023,"depth":649,"text":53024},{"id":53399,"depth":649,"text":48096},{"id":54694,"depth":649,"text":49791},{"id":56450,"depth":649,"text":820},{"id":56645,"depth":642,"text":8674},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,57580,57581,57582,24701,57583,57584],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":57587,"title":820,"body":57588,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":61863,"navigation":664,"path":61864,"seo":61865,"sources":61866,"stem":61867,"tags":61868,"type":10745,"updated":677,"__hash__":61873},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":57589,"toc":61841},[57590,57592,57660,57710,57712,57715,57973,58049,58054,58056,58075,58079,58155,58240,58242,58556,58649,58651,58670,58674,58748,58833,58836,59012,59017,59019,59437,59439,59443,59447,59683,59727,59827,59893,59896,59929,60105,60166,60296,60374,60485,60519,60717,60736,60755,60820,60824,60827,60872,60875,60993,61039,61041,61045,61392,61394,61396,61674,61676,61680,61715,61722,61795,61797,61799],[12,57591,820],{"id":18629},[1636,57593,57594],{},[724,57595,57596,10760,57598,16877,57600,57615,57616,16877,57618,57633,57634,57656,57657,1789],{},[883,57597,1642],{},[38,57599,6189],{},[883,57601,57603],{"className":57602},[886],[888,57604,57605],{"xmlns":890},[892,57606,57607,57613],{},[895,57608,57609,57611],{},[898,57610,2971],{},[898,57612,3611],{},[902,57614,51715],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,57617,6329],{},[883,57619,57621],{"className":57620},[886],[888,57622,57623],{"xmlns":890},[892,57624,57625,57631],{},[895,57626,57627,57629],{},[898,57628,1701],{},[898,57630,3611],{},[902,57632,51734],{"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 ",[883,57635,57637],{"className":57636},[886],[888,57638,57639],{"xmlns":890},[892,57640,57641,57653],{},[895,57642,57643,57645,57647,57649,57651],{},[898,57644,2971],{},[898,57646,3611],{},[1693,57648,1892],{},[898,57650,1701],{},[898,57652,3611],{},[902,57654,57655],{"encoding":904},"CS + PS"," měří ",[38,57658,57659],{},"celkový blahobyt trhu",[724,57661,57662,16877,57664,1343,57666,8586,57681,16877,57683,1343,57685,57700,57701,57705,57706,1789],{},[38,57663,6189],{},[614,57665,51753],{},[883,57667,57669],{"className":57668},[886],[888,57670,57671],{"xmlns":890},[892,57672,57673,57679],{},[895,57674,57675,57677],{},[898,57676,2971],{},[898,57678,3611],{},[902,57680,51715],{"encoding":904},[38,57682,51718],{},[614,57684,51848],{},[883,57686,57688],{"className":57687},[886],[888,57689,57690],{"xmlns":890},[892,57691,57692,57698],{},[895,57693,57694,57696],{},[898,57695,1701],{},[898,57697,3611],{},[902,57699,51734],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,57702,57704],{"className":57703,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,57707,57709],{"className":57708,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[1852,57711],{},[115,57713,1241],{"id":57714},"úvod",[724,57716,57717,57718,57741,57742,57765,57766,57783,57784,10796,57816,57848,57849,57875,57876,57879,57880,57883,57884,20840,57918,28397,57939,1789],{},"Je dána funkce poptávky ",[883,57719,57721],{"className":57720},[886],[888,57722,57723],{"xmlns":890},[892,57724,57725,57739],{},[895,57726,57727,57729,57731,57733,57735,57737],{},[898,57728,1701],{},[1693,57730,1695],{},[898,57732,2738],{},[1693,57734,1709],{"stretchy":1708},[898,57736,1712],{},[1693,57738,1731],{"stretchy":1708},[902,57740,3980],{"encoding":904},", resp. funkce nabídky ",[883,57743,57745],{"className":57744},[886],[888,57746,57747],{"xmlns":890},[892,57748,57749,57763],{},[895,57750,57751,57753,57755,57757,57759,57761],{},[898,57752,1701],{},[1693,57754,1695],{},[898,57756,3611],{},[1693,57758,1709],{"stretchy":1708},[898,57760,1712],{},[1693,57762,1731],{"stretchy":1708},[902,57764,47843],{"encoding":904},". Pro pevně zadané množství ",[883,57767,57769],{"className":57768},[886],[888,57770,57771],{"xmlns":890},[892,57772,57773,57781],{},[895,57774,57775],{},[3284,57776,57777,57779],{},[898,57778,1712],{},[1762,57780,1911],{},[902,57782,6293],{"encoding":904}," je odpovídající cena ",[883,57785,57787],{"className":57786},[886],[888,57788,57789],{"xmlns":890},[892,57790,57791,57813],{},[895,57792,57793,57799,57801,57803,57805,57811],{},[3284,57794,57795,57797],{},[898,57796,1701],{},[1762,57798,1911],{},[1693,57800,1695],{},[898,57802,2738],{},[1693,57804,1709],{"stretchy":1708},[3284,57806,57807,57809],{},[898,57808,1712],{},[1762,57810,1911],{},[1693,57812,1731],{"stretchy":1708},[902,57814,57815],{"encoding":904},"P_0 = D(Q_0)",[883,57817,57819],{"className":57818},[886],[888,57820,57821],{"xmlns":890},[892,57822,57823,57845],{},[895,57824,57825,57831,57833,57835,57837,57843],{},[3284,57826,57827,57829],{},[898,57828,1701],{},[1762,57830,1911],{},[1693,57832,1695],{},[898,57834,3611],{},[1693,57836,1709],{"stretchy":1708},[3284,57838,57839,57841],{},[898,57840,1712],{},[1762,57842,1911],{},[1693,57844,1731],{"stretchy":1708},[902,57846,57847],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,57850,57852],{"className":57851},[886],[888,57853,57854],{"xmlns":890},[892,57855,57856,57872],{},[895,57857,57858,57864,57866],{},[3284,57859,57860,57862],{},[898,57861,1701],{},[1762,57863,1911],{},[1915,57865,2239],{},[3284,57867,57868,57870],{},[898,57869,1712],{},[1762,57871,1911],{},[902,57873,57874],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,57877,57878],{},"výdaje spotřebitele",", nebo ",[38,57881,57882],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,57885,57887],{"className":57886},[886],[888,57888,57889],{"xmlns":890},[892,57890,57891,57915],{},[895,57892,57893,57895,57897,57903,57905,57907,57909],{},[1762,57894,1911],{},[1915,57896,2239],{},[3284,57898,57899,57901],{},[898,57900,1712],{},[1762,57902,1911],{},[1915,57904,2239],{},[898,57906,2719],{},[1915,57908,2239],{},[3284,57910,57911,57913],{},[898,57912,1701],{},[1762,57914,1911],{},[902,57916,57917],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,57919,57921],{"className":57920},[886],[888,57922,57923],{"xmlns":890},[892,57924,57925,57937],{},[895,57926,57927,57929,57931,57933,57935],{},[1693,57928,1709],{"stretchy":1708},[898,57930,1712],{},[1693,57932,1899],{"separator":1898},[898,57934,1701],{},[1693,57936,1731],{"stretchy":1708},[902,57938,1978],{"encoding":904},[883,57940,57942],{"className":57941},[886],[888,57943,57944],{"xmlns":890},[892,57945,57946,57970],{},[895,57947,57948,57950,57952,57954,57960,57962,57968],{},[898,57949,2719],{},[1693,57951,1695],{},[1693,57953,9392],{"stretchy":1708},[3284,57955,57956,57958],{},[898,57957,1712],{},[1762,57959,1911],{},[1693,57961,1899],{"separator":1898},[3284,57963,57964,57966],{},[898,57965,1701],{},[1762,57967,1911],{},[1693,57969,9407],{"stretchy":1708},[902,57971,57972],{"encoding":904},"A = [Q_0, P_0]",[1636,57974,57975,57980,58038],{},[724,57976,57977,57979],{},[883,57978,11036],{}," Intuice",[120,57981,57982,58010],{},[123,57983,57984,57985,57988,57989,57991,57992,58009],{},"Za jednotky zboží nakoupené ",[38,57986,57987],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,57990,32063],{}," než ",[883,57993,57995],{"className":57994},[886],[888,57996,57997],{"xmlns":890},[892,57998,57999,58007],{},[895,58000,58001],{},[3284,58002,58003,58005],{},[898,58004,1701],{},[1762,58006,1911],{},[902,58008,45722],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,58011,58012,58013,58015,58016,58019,58020,58037],{},"Za jednotky zboží prodané ",[38,58014,57987],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,58017,58018],{},"nižší"," cenu než ",[883,58021,58023],{"className":58022},[886],[888,58024,58025],{"xmlns":890},[892,58026,58027,58035],{},[895,58028,58029],{},[3284,58030,58031,58033],{},[898,58032,1701],{},[1762,58034,1911],{},[902,58036,45722],{"encoding":904}," — rozdíl je jeho přebytek.",[724,58039,58040,58041,58044,58045,58048],{},"Přebytek je tedy rozdíl mezi ",[614,58042,58043],{},"ochotou"," (platit \u002F prodávat) a ",[614,58046,58047],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,58050,58051],{},[9465,58052],{"alt":51744,"className":58053,"src":51746},[210,9469],[1852,58055],{},[115,58057,58059,58060,1731],{"id":58058},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,58061,58063],{"className":58062},[886],[888,58064,58065],{"xmlns":890},[892,58066,58067,58073],{},[895,58068,58069,58071],{},[898,58070,2971],{},[898,58072,3611],{},[902,58074,51715],{"encoding":904},[198,58076,58078],{"id":58077},"definice-vzorec-214","Definice (vzorec 2.14)",[724,58080,58081,58082,58105,58106,58123,58124,4300],{},"Pro poptávku ",[883,58083,58085],{"className":58084},[886],[888,58086,58087],{"xmlns":890},[892,58088,58089,58103],{},[895,58090,58091,58093,58095,58097,58099,58101],{},[898,58092,1701],{},[1693,58094,1695],{},[898,58096,2738],{},[1693,58098,1709],{"stretchy":1708},[898,58100,1712],{},[1693,58102,1731],{"stretchy":1708},[902,58104,3980],{"encoding":904}," a pevně zadané ",[883,58107,58109],{"className":58108},[886],[888,58110,58111],{"xmlns":890},[892,58112,58113,58121],{},[895,58114,58115],{},[3284,58116,58117,58119],{},[898,58118,1712],{},[1762,58120,1911],{},[902,58122,6293],{"encoding":904}," s cenou ",[883,58125,58127],{"className":58126},[886],[888,58128,58129],{"xmlns":890},[892,58130,58131,58153],{},[895,58132,58133,58139,58141,58143,58145,58151],{},[3284,58134,58135,58137],{},[898,58136,1701],{},[1762,58138,1911],{},[1693,58140,1695],{},[898,58142,2738],{},[1693,58144,1709],{"stretchy":1708},[3284,58146,58147,58149],{},[898,58148,1712],{},[1762,58150,1911],{},[1693,58152,1731],{"stretchy":1708},[902,58154,57815],{"encoding":904},[883,58156,58158],{"className":58157},[886],[888,58159,58160],{"xmlns":890,"display":34854},[892,58161,58162,58238],{},[3626,58163,58164],{"width":34859},[3632,58165,58166,58168,58232,58234],{},[3635,58167],{"width":34864},[3635,58169,58170],{},[895,58171,58172,58174,58176,58178,58184,58186,58188,58200,58202,58204,58206,58208,58210,58212,58214,58216,58222,58224,58230],{},[898,58173,2971],{},[898,58175,3611],{},[1693,58177,1709],{"stretchy":1708},[3284,58179,58180,58182],{},[898,58181,1712],{},[1762,58183,1911],{},[1693,58185,1731],{"stretchy":1708},[1693,58187,1695],{},[5688,58189,58190,58192,58194],{},[1693,58191,6221],{},[1762,58193,1911],{},[3284,58195,58196,58198],{},[898,58197,1712],{},[1762,58199,1911],{},[898,58201,2738],{},[1693,58203,1709],{"stretchy":1708},[898,58205,1712],{},[1693,58207,1731],{"stretchy":1708},[1915,58209,2239],{},[898,58211,1771],{},[898,58213,1712],{},[1693,58215,1698],{},[3284,58217,58218,58220],{},[898,58219,1701],{},[1762,58221,1911],{},[1915,58223,2239],{},[3284,58225,58226,58228],{},[898,58227,1712],{},[1762,58229,1911],{},[898,58231,1789],{"mathvariant":1704},[3635,58233],{"width":34864},[3635,58235,58236],{},[1915,58237,51838],{},[902,58239,51841],{"encoding":904},[198,58241,9351],{"id":9350},[120,58243,58244,58336,58398],{},[123,58245,58246,58286,58287,58313,58314,58317,58318,58335],{},[883,58247,58249],{"className":58248},[886],[888,58250,58251],{"xmlns":890},[892,58252,58253,58283],{},[895,58254,58255],{},[3638,58256,58257,58269,58271,58273,58275,58277,58279,58281],{"scriptlevel":1911,"displaystyle":1898},[5688,58258,58259,58261,58263],{},[1693,58260,6221],{},[1762,58262,1911],{},[3284,58264,58265,58267],{},[898,58266,1712],{},[1762,58268,1911],{},[898,58270,2738],{},[1693,58272,1709],{"stretchy":1708},[898,58274,1712],{},[1693,58276,1731],{"stretchy":1708},[1915,58278,2239],{},[898,58280,1771],{},[898,58282,1712],{},[902,58284,58285],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,58288,58290],{"className":58289},[886],[888,58291,58292],{"xmlns":890},[892,58293,58294,58310],{},[895,58295,58296,58298,58300,58302,58308],{},[1693,58297,9392],{"stretchy":1708},[1762,58299,1911],{},[1693,58301,1899],{"separator":1898},[3284,58303,58304,58306],{},[898,58305,1712],{},[1762,58307,1911],{},[1693,58309,9407],{"stretchy":1708},[902,58311,58312],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,58315,58316],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,58319,58321],{"className":58320},[886],[888,58322,58323],{"xmlns":890},[892,58324,58325,58333],{},[895,58326,58327],{},[3284,58328,58329,58331],{},[898,58330,1712],{},[1762,58332,1911],{},[902,58334,6293],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,58337,58338,58364,58365,3042],{},[883,58339,58341],{"className":58340},[886],[888,58342,58343],{"xmlns":890},[892,58344,58345,58361],{},[895,58346,58347,58353,58355],{},[3284,58348,58349,58351],{},[898,58350,1701],{},[1762,58352,1911],{},[1915,58354,2239],{},[3284,58356,58357,58359],{},[898,58358,1712],{},[1762,58360,1911],{},[902,58362,58363],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,58366,58368],{"className":58367},[886],[888,58369,58370],{"xmlns":890},[892,58371,58372,58396],{},[895,58373,58374,58376,58378,58384,58386,58388,58390],{},[1762,58375,1911],{},[1915,58377,2239],{},[3284,58379,58380,58382],{},[898,58381,1712],{},[1762,58383,1911],{},[1915,58385,2239],{},[898,58387,2719],{},[1915,58389,2239],{},[3284,58391,58392,58394],{},[898,58393,1701],{},[1762,58395,1911],{},[902,58397,57917],{"encoding":904},[123,58399,58400,58415,58416,58438,58439,58464,58465,28397,58491,4286,58523,1789],{},[883,58401,58403],{"className":58402},[886],[888,58404,58405],{"xmlns":890},[892,58406,58407,58413],{},[895,58408,58409,58411],{},[898,58410,2971],{},[898,58412,3611],{},[902,58414,51715],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,58417,58419],{"className":58418},[886],[888,58420,58421],{"xmlns":890},[892,58422,58423,58435],{},[895,58424,58425,58427,58429],{},[898,58426,1701],{},[1693,58428,1695],{},[3284,58430,58431,58433],{},[898,58432,1701],{},[1762,58434,1911],{},[902,58436,58437],{"encoding":904},"P = P_0"," v pásu ",[883,58440,58442],{"className":58441},[886],[888,58443,58444],{"xmlns":890},[892,58445,58446,58462],{},[895,58447,58448,58450,58452,58454,58460],{},[1693,58449,9392],{"stretchy":1708},[1762,58451,1911],{},[1693,58453,1899],{"separator":1898},[3284,58455,58456,58458],{},[898,58457,1712],{},[1762,58459,1911],{},[1693,58461,9407],{"stretchy":1708},[902,58463,58312],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,58466,58468],{"className":58467},[886],[888,58469,58470],{"xmlns":890},[892,58471,58472,58488],{},[895,58473,58474,58480,58482,58484,58486],{},[3284,58475,58476,58478],{},[898,58477,1701],{},[1762,58479,1911],{},[1915,58481,2239],{},[898,58483,7520],{},[1915,58485,2239],{},[898,58487,2719],{},[902,58489,58490],{"encoding":904},"P_0\\,B\\,A",[883,58492,58494],{"className":58493},[886],[888,58495,58496],{"xmlns":890},[892,58497,58498,58520],{},[895,58499,58500,58502,58504,58506,58508,58510,58512,58514,58516,58518],{},[898,58501,7520],{},[1693,58503,1695],{},[1693,58505,9392],{"stretchy":1708},[1762,58507,1911],{},[1693,58509,1899],{"separator":1898},[898,58511,2738],{},[1693,58513,1709],{"stretchy":1708},[1762,58515,1911],{},[1693,58517,1731],{"stretchy":1708},[1693,58519,9407],{"stretchy":1708},[902,58521,58522],{"encoding":904},"B = [0, D(0)]",[883,58524,58526],{"className":58525},[886],[888,58527,58528],{"xmlns":890},[892,58529,58530,58554],{},[895,58531,58532,58534,58536,58538,58544,58546,58552],{},[898,58533,2719],{},[1693,58535,1695],{},[1693,58537,9392],{"stretchy":1708},[3284,58539,58540,58542],{},[898,58541,1712],{},[1762,58543,1911],{},[1693,58545,1899],{"separator":1898},[3284,58547,58548,58550],{},[898,58549,1701],{},[1762,58551,1911],{},[1693,58553,9407],{"stretchy":1708},[902,58555,57972],{"encoding":904},[724,58557,58558],{},[614,58559,58560,58561,58574,58575,58608,58609,35927,58634,1789],{},"Obrázek 2.24: Křivka poptávky ",[883,58562,58564],{"className":58563},[886],[888,58565,58566],{"xmlns":890},[892,58567,58568,58572],{},[895,58569,58570],{},[898,58571,2738],{},[902,58573,2738],{"encoding":904},", bod ",[883,58576,58578],{"className":58577},[886],[888,58579,58580],{"xmlns":890},[892,58581,58582,58606],{},[895,58583,58584,58586,58588,58590,58596,58598,58604],{},[898,58585,2719],{},[1693,58587,1695],{},[1693,58589,9392],{"stretchy":1708},[3284,58591,58592,58594],{},[898,58593,1712],{},[1762,58595,1911],{},[1693,58597,1899],{"separator":1898},[3284,58599,58600,58602],{},[898,58601,1701],{},[1762,58603,1911],{},[1693,58605,9407],{"stretchy":1708},[902,58607,57972],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,58610,58612],{"className":58611},[886],[888,58613,58614],{"xmlns":890},[892,58615,58616,58632],{},[895,58617,58618,58624,58626,58628,58630],{},[3284,58619,58620,58622],{},[898,58621,1701],{},[1762,58623,1911],{},[1915,58625,2239],{},[898,58627,7520],{},[1915,58629,2239],{},[898,58631,2719],{},[902,58633,58490],{"encoding":904},[883,58635,58637],{"className":58636},[886],[888,58638,58639],{"xmlns":890},[892,58640,58641,58647],{},[895,58642,58643,58645],{},[898,58644,2971],{},[898,58646,3611],{},[902,58648,51715],{"encoding":904},[1852,58650],{},[115,58652,58654,58655,1731],{"id":58653},"přebytek-výrobce-psps","Přebytek výrobce (",[883,58656,58658],{"className":58657},[886],[888,58659,58660],{"xmlns":890},[892,58661,58662,58668],{},[895,58663,58664,58666],{},[898,58665,1701],{},[898,58667,3611],{},[902,58669,51734],{"encoding":904},[198,58671,58673],{"id":58672},"definice-vzorec-215","Definice (vzorec 2.15)",[724,58675,58676,58677,58105,58700,58123,58717,4300],{},"Analogicky — pro nabídku ",[883,58678,58680],{"className":58679},[886],[888,58681,58682],{"xmlns":890},[892,58683,58684,58698],{},[895,58685,58686,58688,58690,58692,58694,58696],{},[898,58687,1701],{},[1693,58689,1695],{},[898,58691,3611],{},[1693,58693,1709],{"stretchy":1708},[898,58695,1712],{},[1693,58697,1731],{"stretchy":1708},[902,58699,47843],{"encoding":904},[883,58701,58703],{"className":58702},[886],[888,58704,58705],{"xmlns":890},[892,58706,58707,58715],{},[895,58708,58709],{},[3284,58710,58711,58713],{},[898,58712,1712],{},[1762,58714,1911],{},[902,58716,6293],{"encoding":904},[883,58718,58720],{"className":58719},[886],[888,58721,58722],{"xmlns":890},[892,58723,58724,58746],{},[895,58725,58726,58732,58734,58736,58738,58744],{},[3284,58727,58728,58730],{},[898,58729,1701],{},[1762,58731,1911],{},[1693,58733,1695],{},[898,58735,3611],{},[1693,58737,1709],{"stretchy":1708},[3284,58739,58740,58742],{},[898,58741,1712],{},[1762,58743,1911],{},[1693,58745,1731],{"stretchy":1708},[902,58747,57847],{"encoding":904},[883,58749,58751],{"className":58750},[886],[888,58752,58753],{"xmlns":890,"display":34854},[892,58754,58755,58831],{},[3626,58756,58757],{"width":34859},[3632,58758,58759,58761,58825,58827],{},[3635,58760],{"width":34864},[3635,58762,58763],{},[895,58764,58765,58767,58769,58771,58777,58779,58781,58787,58789,58795,58797,58809,58811,58813,58815,58817,58819,58821,58823],{},[898,58766,1701],{},[898,58768,3611],{},[1693,58770,1709],{"stretchy":1708},[3284,58772,58773,58775],{},[898,58774,1712],{},[1762,58776,1911],{},[1693,58778,1731],{"stretchy":1708},[1693,58780,1695],{},[3284,58782,58783,58785],{},[898,58784,1701],{},[1762,58786,1911],{},[1915,58788,2239],{},[3284,58790,58791,58793],{},[898,58792,1712],{},[1762,58794,1911],{},[1693,58796,1698],{},[5688,58798,58799,58801,58803],{},[1693,58800,6221],{},[1762,58802,1911],{},[3284,58804,58805,58807],{},[898,58806,1712],{},[1762,58808,1911],{},[898,58810,3611],{},[1693,58812,1709],{"stretchy":1708},[898,58814,1712],{},[1693,58816,1731],{"stretchy":1708},[1915,58818,2239],{},[898,58820,1771],{},[898,58822,1712],{},[898,58824,1789],{"mathvariant":1704},[3635,58826],{"width":34864},[3635,58828,58829],{},[1915,58830,51933],{},[902,58832,51936],{"encoding":904},[198,58834,9351],{"id":58835},"geometrická-interpretace-1",[120,58837,58838,58886,58947],{},[123,58839,58840,13877,58865,58868,58869,1789],{},[883,58841,58843],{"className":58842},[886],[888,58844,58845],{"xmlns":890},[892,58846,58847,58863],{},[895,58848,58849,58855,58857],{},[3284,58850,58851,58853],{},[898,58852,1701],{},[1762,58854,1911],{},[1915,58856,2239],{},[3284,58858,58859,58861],{},[898,58860,1712],{},[1762,58862,1911],{},[902,58864,58363],{"encoding":904},[38,58866,58867],{},"tržba"," výrobce za prodané množství ",[883,58870,58872],{"className":58871},[886],[888,58873,58874],{"xmlns":890},[892,58875,58876,58884],{},[895,58877,58878],{},[3284,58879,58880,58882],{},[898,58881,1712],{},[1762,58883,1911],{},[902,58885,6293],{"encoding":904},[123,58887,58888,58928,58929,58946],{},[883,58889,58891],{"className":58890},[886],[888,58892,58893],{"xmlns":890},[892,58894,58895,58925],{},[895,58896,58897],{},[3638,58898,58899,58911,58913,58915,58917,58919,58921,58923],{"scriptlevel":1911,"displaystyle":1898},[5688,58900,58901,58903,58905],{},[1693,58902,6221],{},[1762,58904,1911],{},[3284,58906,58907,58909],{},[898,58908,1712],{},[1762,58910,1911],{},[898,58912,3611],{},[1693,58914,1709],{"stretchy":1708},[898,58916,1712],{},[1693,58918,1731],{"stretchy":1708},[1915,58920,2239],{},[898,58922,1771],{},[898,58924,1712],{},[902,58926,58927],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,58930,58932],{"className":58931},[886],[888,58933,58934],{"xmlns":890},[892,58935,58936,58944],{},[895,58937,58938],{},[3284,58939,58940,58942],{},[898,58941,1712],{},[1762,58943,1911],{},[902,58945,6293],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,58948,58949,58964,58965,58986,58987,1789],{},[883,58950,58952],{"className":58951},[886],[888,58953,58954],{"xmlns":890},[892,58955,58956,58962],{},[895,58957,58958,58960],{},[898,58959,1701],{},[898,58961,3611],{},[902,58963,51734],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,58966,58968],{"className":58967},[886],[888,58969,58970],{"xmlns":890},[892,58971,58972,58984],{},[895,58973,58974,58976,58978],{},[898,58975,1701],{},[1693,58977,1695],{},[3284,58979,58980,58982],{},[898,58981,1701],{},[1762,58983,1911],{},[902,58985,58437],{"encoding":904}," a křivkou nabídky v pásu ",[883,58988,58990],{"className":58989},[886],[888,58991,58992],{"xmlns":890},[892,58993,58994,59010],{},[895,58995,58996,58998,59000,59002,59008],{},[1693,58997,9392],{"stretchy":1708},[1762,58999,1911],{},[1693,59001,1899],{"separator":1898},[3284,59003,59004,59006],{},[898,59005,1712],{},[1762,59007,1911],{},[1693,59009,9407],{"stretchy":1708},[902,59011,58312],{"encoding":904},[724,59013,59014],{},[614,59015,59016],{},"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.",[1852,59018],{},[1636,59020,59021,59026],{},[724,59022,59023,59025],{},[883,59024,8620],{}," Postup výpočtu CS a PS",[152,59027,59028,59158,59268,59296,59430],{},[123,59029,59030,59031,59048,59049,6671,59080,59111,59112,1789],{},"Zjisti (nebo si zvol) množství ",[883,59032,59034],{"className":59033},[886],[888,59035,59036],{"xmlns":890},[892,59037,59038,59046],{},[895,59039,59040],{},[3284,59041,59042,59044],{},[898,59043,1712],{},[1762,59045,1911],{},[902,59047,6293],{"encoding":904}," a odpovídající cenu ",[883,59050,59052],{"className":59051},[886],[888,59053,59054],{"xmlns":890},[892,59055,59056,59078],{},[895,59057,59058,59064,59066,59068,59070,59076],{},[3284,59059,59060,59062],{},[898,59061,1701],{},[1762,59063,1911],{},[1693,59065,1695],{},[898,59067,2738],{},[1693,59069,1709],{"stretchy":1708},[3284,59071,59072,59074],{},[898,59073,1712],{},[1762,59075,1911],{},[1693,59077,1731],{"stretchy":1708},[902,59079,57815],{"encoding":904},[883,59081,59083],{"className":59082},[886],[888,59084,59085],{"xmlns":890},[892,59086,59087,59109],{},[895,59088,59089,59095,59097,59099,59101,59107],{},[3284,59090,59091,59093],{},[898,59092,1701],{},[1762,59094,1911],{},[1693,59096,1695],{},[898,59098,3611],{},[1693,59100,1709],{"stretchy":1708},[3284,59102,59103,59105],{},[898,59104,1712],{},[1762,59106,1911],{},[1693,59108,1731],{"stretchy":1708},[902,59110,57847],{"encoding":904},". V rovnováze platí ",[883,59113,59115],{"className":59114},[886],[888,59116,59117],{"xmlns":890},[892,59118,59119,59155],{},[895,59120,59121,59123,59125,59131,59133,59135,59137,59139,59145,59147,59149],{},[898,59122,2738],{},[1693,59124,1709],{"stretchy":1708},[1717,59126,59127,59129],{},[898,59128,1712],{},[898,59130,1691],{},[1693,59132,1731],{"stretchy":1708},[1693,59134,1695],{},[898,59136,3611],{},[1693,59138,1709],{"stretchy":1708},[1717,59140,59141,59143],{},[898,59142,1712],{},[898,59144,1691],{},[1693,59146,1731],{"stretchy":1708},[1693,59148,1695],{},[1717,59150,59151,59153],{},[898,59152,1701],{},[898,59154,1691],{},[902,59156,59157],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,59159,59160,59161,26933,59199,59214,59215,26933,59253,3042],{},"Spočti určitý integrál ",[883,59162,59164],{"className":59163},[886],[888,59165,59166],{"xmlns":890},[892,59167,59168,59196],{},[895,59169,59170,59182,59184,59186,59188,59190,59192,59194],{},[5688,59171,59172,59174,59176],{},[1693,59173,6221],{},[1762,59175,1911],{},[3284,59177,59178,59180],{},[898,59179,1712],{},[1762,59181,1911],{},[898,59183,2738],{},[1693,59185,1709],{"stretchy":1708},[898,59187,1712],{},[1693,59189,1731],{"stretchy":1708},[1915,59191,2239],{},[898,59193,1771],{},[898,59195,1712],{},[902,59197,59198],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,59200,59202],{"className":59201},[886],[888,59203,59204],{"xmlns":890},[892,59205,59206,59212],{},[895,59207,59208,59210],{},[898,59209,2971],{},[898,59211,3611],{},[902,59213,51715],{"encoding":904},") nebo ",[883,59216,59218],{"className":59217},[886],[888,59219,59220],{"xmlns":890},[892,59221,59222,59250],{},[895,59223,59224,59236,59238,59240,59242,59244,59246,59248],{},[5688,59225,59226,59228,59230],{},[1693,59227,6221],{},[1762,59229,1911],{},[3284,59231,59232,59234],{},[898,59233,1712],{},[1762,59235,1911],{},[898,59237,3611],{},[1693,59239,1709],{"stretchy":1708},[898,59241,1712],{},[1693,59243,1731],{"stretchy":1708},[1915,59245,2239],{},[898,59247,1771],{},[898,59249,1712],{},[902,59251,59252],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,59254,59256],{"className":59255},[886],[888,59257,59258],{"xmlns":890},[892,59259,59260,59266],{},[895,59261,59262,59264],{},[898,59263,1701],{},[898,59265,3611],{},[902,59267,51734],{"encoding":904},[123,59269,59270,59271,1789],{},"Sestav obdélník ",[883,59272,59274],{"className":59273},[886],[888,59275,59276],{"xmlns":890},[892,59277,59278,59294],{},[895,59279,59280,59286,59288],{},[3284,59281,59282,59284],{},[898,59283,1701],{},[1762,59285,1911],{},[1693,59287,1715],{},[3284,59289,59290,59292],{},[898,59291,1712],{},[1762,59293,1911],{},[902,59295,6323],{"encoding":904},[123,59297,59298,59299],{},"Dosaď:\n",[120,59300,59301,59366],{},[123,59302,59303,59361,59362,59365],{},[883,59304,59306],{"className":59305},[886],[888,59307,59308],{"xmlns":890},[892,59309,59310,59358],{},[895,59311,59312,59314,59316,59318,59330,59332,59334,59336,59338,59340,59342,59344,59346,59352],{},[898,59313,2971],{},[898,59315,3611],{},[1693,59317,1695],{},[5688,59319,59320,59322,59324],{},[1693,59321,6221],{},[1762,59323,1911],{},[3284,59325,59326,59328],{},[898,59327,1712],{},[1762,59329,1911],{},[898,59331,2738],{},[1693,59333,1709],{"stretchy":1708},[898,59335,1712],{},[1693,59337,1731],{"stretchy":1708},[1915,59339,2239],{},[898,59341,1771],{},[898,59343,1712],{},[1693,59345,1698],{},[3284,59347,59348,59350],{},[898,59349,1701],{},[1762,59351,1911],{},[3284,59353,59354,59356],{},[898,59355,1712],{},[1762,59357,1911],{},[902,59359,59360],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,59363,59364],{},"mínus"," obdélník)",[123,59367,59368,59426,59427,59429],{},[883,59369,59371],{"className":59370},[886],[888,59372,59373],{"xmlns":890},[892,59374,59375,59423],{},[895,59376,59377,59379,59381,59383,59389,59395,59397,59409,59411,59413,59415,59417,59419,59421],{},[898,59378,1701],{},[898,59380,3611],{},[1693,59382,1695],{},[3284,59384,59385,59387],{},[898,59386,1701],{},[1762,59388,1911],{},[3284,59390,59391,59393],{},[898,59392,1712],{},[1762,59394,1911],{},[1693,59396,1698],{},[5688,59398,59399,59401,59403],{},[1693,59400,6221],{},[1762,59402,1911],{},[3284,59404,59405,59407],{},[898,59406,1712],{},[1762,59408,1911],{},[898,59410,3611],{},[1693,59412,1709],{"stretchy":1708},[898,59414,1712],{},[1693,59416,1731],{"stretchy":1708},[1915,59418,2239],{},[898,59420,1771],{},[898,59422,1712],{},[902,59424,59425],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,59428,59364],{}," integrál)",[123,59431,59432,59433,59436],{},"Kontrola znaménka: obě hodnoty musí být ",[38,59434,59435],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[1852,59438],{},[115,59440,59442],{"id":59441},"příklady","Příklady",[198,59444,59446],{"id":59445},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1636,59448,59449],{},[724,59450,59451,59454,59455,54485,59478,59501,59502,1343,59522,1343,59539,1343,59556,59573,59574,59650,59651,59668,59669,59682],{},[883,59452,59453],{},"!example"," Zadání\nJsou dány poptávka ",[883,59456,59458],{"className":59457},[886],[888,59459,59460],{"xmlns":890},[892,59461,59462,59476],{},[895,59463,59464,59466,59468,59470,59472,59474],{},[898,59465,1701],{},[1693,59467,1695],{},[898,59469,207],{},[898,59471,1712],{},[1693,59473,1892],{},[898,59475,1895],{},[902,59477,43837],{"encoding":904},[883,59479,59481],{"className":59480},[886],[888,59482,59483],{"xmlns":890},[892,59484,59485,59499],{},[895,59486,59487,59489,59491,59493,59495,59497],{},[898,59488,1701],{},[1693,59490,1695],{},[898,59492,2000],{},[898,59494,1712],{},[1693,59496,1892],{},[898,59498,1771],{},[902,59500,47015],{"encoding":904}," s hodnotami ",[883,59503,59505],{"className":59504},[886],[888,59506,59507],{"xmlns":890},[892,59508,59509,59519],{},[895,59510,59511,59513,59515,59517],{},[898,59512,207],{},[1693,59514,1695],{},[1693,59516,1698],{},[1762,59518,8357],{},[902,59520,59521],{"encoding":904},"a = -3",[883,59523,59525],{"className":59524},[886],[888,59526,59527],{"xmlns":890},[892,59528,59529,59537],{},[895,59530,59531,59533,59535],{},[898,59532,1895],{},[1693,59534,1695],{},[1762,59536,12079],{},[902,59538,55408],{"encoding":904},[883,59540,59542],{"className":59541},[886],[888,59543,59544],{"xmlns":890},[892,59545,59546,59554],{},[895,59547,59548,59550,59552],{},[898,59549,2000],{},[1693,59551,1695],{},[1762,59553,11877],{},[902,59555,55426],{"encoding":904},[883,59557,59559],{"className":59558},[886],[888,59560,59561],{"xmlns":890},[892,59562,59563,59571],{},[895,59564,59565,59567,59569],{},[898,59566,1771],{},[1693,59568,1695],{},[1762,59570,9763],{},[902,59572,55444],{"encoding":904},".\nRovnovážné množství:\n",[883,59575,59577],{"className":59576},[886],[888,59578,59579],{"xmlns":890},[892,59580,59581,59647],{},[895,59582,59583,59589,59591,59609,59611,59635,59637,59643,59645],{},[1717,59584,59585,59587],{},[898,59586,1712],{},[898,59588,1691],{},[1693,59590,1695],{},[2132,59592,59593,59601],{},[895,59594,59595,59597,59599],{},[898,59596,1895],{},[1693,59598,1698],{},[898,59600,1771],{},[895,59602,59603,59605,59607],{},[898,59604,2000],{},[1693,59606,1698],{},[898,59608,207],{},[1693,59610,1695],{},[2132,59612,59613,59621],{},[895,59614,59615,59617,59619],{},[1762,59616,12079],{},[1693,59618,1698],{},[1762,59620,9763],{},[895,59622,59623,59625,59627,59629,59631,59633],{},[1762,59624,11877],{},[1693,59626,1698],{},[1693,59628,1709],{"stretchy":1708},[1693,59630,1698],{},[1762,59632,8357],{},[1693,59634,1731],{"stretchy":1708},[1693,59636,1695],{},[2132,59638,59639,59641],{},[1762,59640,44795],{},[1762,59642,51172],{},[1693,59644,12766],{},[1762,59646,51177],{},[902,59648,59649],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,59652,59654],{"className":59653},[886],[888,59655,59656],{"xmlns":890},[892,59657,59658,59666],{},[895,59659,59660],{},[1717,59661,59662,59664],{},[898,59663,1712],{},[898,59665,1691],{},[902,59667,2204],{"encoding":904}," (a) při změně samotného parametru ",[883,59670,59672],{"className":59671},[886],[888,59673,59674],{"xmlns":890},[892,59675,59676,59680],{},[895,59677,59678],{},[898,59679,2000],{},[902,59681,2000],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,59684,59685],{},[38,59686,59687,59688,9577,59701,9591,59714,16150],{},"Řešení (a) — změna ",[883,59689,59691],{"className":59690},[886],[888,59692,59693],{"xmlns":890},[892,59694,59695,59699],{},[895,59696,59697],{},[898,59698,2000],{},[902,59700,2000],{"encoding":904},[883,59702,59704],{"className":59703},[886],[888,59705,59706],{"xmlns":890},[892,59707,59708,59712],{},[895,59709,59710],{},[1762,59711,11877],{},[902,59713,51212],{"encoding":904},[883,59715,59717],{"className":59716},[886],[888,59718,59719],{"xmlns":890},[892,59720,59721,59725],{},[895,59722,59723],{},[1762,59724,26132],{},[902,59726,51226],{"encoding":904},[724,59728,59729,59730,59794,59795,4300],{},"Pomocí vzorce (2.13) pro ",[883,59731,59733],{"className":59732},[886],[888,59734,59735],{"xmlns":890},[892,59736,59737,59791],{},[895,59738,59739,59759,59761,59763],{},[3638,59740,59741],{"scriptlevel":1911,"displaystyle":1898},[2132,59742,59743,59753],{},[895,59744,59745,59747],{},[898,59746,2228],{"mathvariant":1704},[1717,59748,59749,59751],{},[898,59750,1712],{},[898,59752,1691],{},[895,59754,59755,59757],{},[898,59756,2228],{"mathvariant":1704},[898,59758,2000],{},[1693,59760,1695],{},[1693,59762,1698],{},[3638,59764,59765],{"scriptlevel":1911,"displaystyle":1898},[2132,59766,59767,59775],{},[895,59768,59769,59771,59773],{},[898,59770,1895],{},[1693,59772,1698],{},[898,59774,1771],{},[895,59776,59777,59779,59781,59783,59785],{},[1693,59778,1709],{"stretchy":1708},[898,59780,2000],{},[1693,59782,1698],{},[898,59784,207],{},[1717,59786,59787,59789],{},[1693,59788,1731],{"stretchy":1708},[1762,59790,2398],{},[902,59792,59793],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,59796,59798],{"className":59797},[886],[888,59799,59800],{"xmlns":890},[892,59801,59802,59824],{},[895,59803,59804,59806],{},[1693,59805,1698],{},[3638,59807,59808],{"scriptlevel":1911,"displaystyle":1898},[2132,59809,59810,59816],{},[1717,59811,59812,59814],{},[898,59813,1712],{},[898,59815,1691],{},[895,59817,59818,59820,59822],{},[898,59819,2000],{},[1693,59821,1698],{},[898,59823,207],{},[902,59825,59826],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,59828,59830],{"className":59829},[886],[888,59831,59832],{"xmlns":890,"display":34854},[892,59833,59834,59890],{},[895,59835,59836,59838,59844,59846,59848,59864,59866,59868,59870,59872,59874,59880,59882,59884,59886,59888],{},[898,59837,1771],{},[1717,59839,59840,59842],{},[898,59841,1712],{},[898,59843,1691],{},[1693,59845,1695],{},[1693,59847,1698],{},[2132,59849,59850,59856],{},[1717,59851,59852,59854],{},[898,59853,1712],{},[898,59855,1691],{},[895,59857,59858,59860,59862],{},[898,59859,2000],{},[1693,59861,1698],{},[898,59863,207],{},[1915,59865,2239],{},[898,59867,1771],{},[898,59869,2000],{},[1693,59871,1695],{},[1693,59873,1698],{},[2132,59875,59876,59878],{},[1762,59877,51340],{},[1762,59879,51172],{},[1693,59881,1715],{},[1762,59883,9695],{},[1693,59885,12766],{},[1693,59887,1698],{},[1762,59889,51312],{},[902,59891,59892],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,59894,59895],{},"Nové rovnovážné množství:",[883,59897,59899],{"className":59898},[886],[888,59900,59901],{"xmlns":890,"display":34854},[892,59902,59903,59926],{},[895,59904,59905,59913,59915,59917,59919,59921,59923],{},[5688,59906,59907,59909,59911],{},[898,59908,1712],{},[1762,59910,1764],{},[898,59912,1691],{},[1693,59914,4110],{},[1762,59916,51340],{},[1693,59918,1698],{},[1762,59920,51345],{},[1693,59922,1695],{},[1762,59924,59925],{},"8,326.",[902,59927,59928],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,59930,59931,1863,59934,1343,59961,1343,59983,1343,60005,12457,60027,1343,60046,1343,60067,1343,60086,1789],{},[38,59932,59933],{},"Řešení (b) — současná změna všech parametrů:",[883,59935,59937],{"className":59936},[886],[888,59938,59939],{"xmlns":890},[892,59940,59941,59958],{},[895,59942,59943,59945,59947,59949,59951,59953,59955],{},[898,59944,207],{},[1693,59946,4300],{},[1693,59948,1698],{},[1762,59950,8357],{},[1693,59952,10020],{},[1693,59954,1698],{},[1762,59956,59957],{},"2,5",[902,59959,59960],{"encoding":904},"a: -3 \\to -2{,}5",[883,59962,59964],{"className":59963},[886],[888,59965,59966],{"xmlns":890},[892,59967,59968,59980],{},[895,59969,59970,59972,59974,59976,59978],{},[898,59971,1895],{},[1693,59973,4300],{},[1762,59975,12079],{},[1693,59977,10020],{},[1762,59979,21864],{},[902,59981,59982],{"encoding":904},"b: 40 \\to 35",[883,59984,59986],{"className":59985},[886],[888,59987,59988],{"xmlns":890},[892,59989,59990,60002],{},[895,59991,59992,59994,59996,59998,60000],{},[898,59993,2000],{},[1693,59995,4300],{},[1762,59997,11877],{},[1693,59999,10020],{},[1762,60001,26132],{},[902,60003,60004],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,60006,60008],{"className":60007},[886],[888,60009,60010],{"xmlns":890},[892,60011,60012,60024],{},[895,60013,60014,60016,60018,60020,60022],{},[898,60015,1771],{},[1693,60017,4300],{},[1762,60019,9763],{},[1693,60021,10020],{},[1762,60023,9803],{},[902,60025,60026],{"encoding":904},"d: 10 \\to 11",[883,60028,60030],{"className":60029},[886],[888,60031,60032],{"xmlns":890},[892,60033,60034,60044],{},[895,60035,60036,60038,60040,60042],{},[898,60037,1771],{},[898,60039,207],{},[1693,60041,1695],{},[1762,60043,11877],{},[902,60045,51378],{"encoding":904},[883,60047,60049],{"className":60048},[886],[888,60050,60051],{"xmlns":890},[892,60052,60053,60065],{},[895,60054,60055,60057,60059,60061,60063],{},[898,60056,1771],{},[898,60058,1895],{},[1693,60060,1695],{},[1693,60062,1698],{},[1762,60064,9147],{},[902,60066,51400],{"encoding":904},[883,60068,60070],{"className":60069},[886],[888,60071,60072],{"xmlns":890},[892,60073,60074,60084],{},[895,60075,60076,60078,60080,60082],{},[898,60077,1771],{},[898,60079,2000],{},[1693,60081,1695],{},[1762,60083,9695],{},[902,60085,51420],{"encoding":904},[883,60087,60089],{"className":60088},[886],[888,60090,60091],{"xmlns":890},[892,60092,60093,60103],{},[895,60094,60095,60097,60099,60101],{},[898,60096,1771],{},[898,60098,1771],{},[1693,60100,1695],{},[1762,60102,1764],{},[902,60104,51440],{"encoding":904},[724,60106,2186,60107,60165],{},[883,60108,60110],{"className":60109},[886],[888,60111,60112],{"xmlns":890},[892,60113,60114,60162],{},[895,60115,60116,60122,60124,60126,60128,60130,60132,60134,60136,60138,60140,60142],{},[1717,60117,60118,60120],{},[898,60119,1712],{},[898,60121,1691],{},[1693,60123,1709],{"stretchy":1708},[898,60125,207],{},[1693,60127,1899],{"separator":1898},[898,60129,1895],{},[1693,60131,1899],{"separator":1898},[898,60133,2000],{},[1693,60135,1899],{"separator":1898},[898,60137,1771],{},[1693,60139,1731],{"stretchy":1708},[1693,60141,1695],{},[3638,60143,60144],{"scriptlevel":1911,"displaystyle":1898},[2132,60145,60146,60154],{},[895,60147,60148,60150,60152],{},[898,60149,1895],{},[1693,60151,1698],{},[898,60153,1771],{},[895,60155,60156,60158,60160],{},[898,60157,2000],{},[1693,60159,1698],{},[898,60161,207],{},[902,60163,60164],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,60167,60169],{"className":60168},[886],[888,60170,60171],{"xmlns":890,"display":34854},[892,60172,60173,60293],{},[895,60174,60175,60177,60183,60185,60211,60213,60215,60217,60219,60231,60233,60235,60237,60239,60265,60267,60269,60271,60273,60285,60287,60289,60291],{},[898,60176,1771],{},[1717,60178,60179,60181],{},[898,60180,1712],{},[898,60182,1691],{},[1693,60184,1695],{},[2132,60186,60187,60195],{},[895,60188,60189,60191,60193],{},[898,60190,1895],{},[1693,60192,1698],{},[898,60194,1771],{},[895,60196,60197,60199,60201,60203,60205],{},[1693,60198,1709],{"stretchy":1708},[898,60200,2000],{},[1693,60202,1698],{},[898,60204,207],{},[1717,60206,60207,60209],{},[1693,60208,1731],{"stretchy":1708},[1762,60210,2398],{},[1915,60212,2239],{},[898,60214,1771],{},[898,60216,207],{},[1693,60218,1892],{},[2132,60220,60221,60223],{},[1762,60222,1764],{},[895,60224,60225,60227,60229],{},[898,60226,2000],{},[1693,60228,1698],{},[898,60230,207],{},[1915,60232,2239],{},[898,60234,1771],{},[898,60236,1895],{},[1693,60238,1698],{},[2132,60240,60241,60249],{},[895,60242,60243,60245,60247],{},[898,60244,1895],{},[1693,60246,1698],{},[898,60248,1771],{},[895,60250,60251,60253,60255,60257,60259],{},[1693,60252,1709],{"stretchy":1708},[898,60254,2000],{},[1693,60256,1698],{},[898,60258,207],{},[1717,60260,60261,60263],{},[1693,60262,1731],{"stretchy":1708},[1762,60264,2398],{},[1915,60266,2239],{},[898,60268,1771],{},[898,60270,2000],{},[1693,60272,1698],{},[2132,60274,60275,60277],{},[1762,60276,1764],{},[895,60278,60279,60281,60283],{},[898,60280,2000],{},[1693,60282,1698],{},[898,60284,207],{},[1915,60286,2239],{},[898,60288,1771],{},[898,60290,1771],{},[898,60292,1789],{"mathvariant":1704},[902,60294,60295],{"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.",[724,60297,60298,60299,1343,60321,1343,60352,10048],{},"Dosazením číselných hodnot (",[883,60300,60302],{"className":60301},[886],[888,60303,60304],{"xmlns":890},[892,60305,60306,60318],{},[895,60307,60308,60310,60312,60314,60316],{},[898,60309,2000],{},[1693,60311,1698],{},[898,60313,207],{},[1693,60315,1695],{},[1762,60317,51172],{},[902,60319,60320],{"encoding":904},"c - a = 3{,}5",[883,60322,60324],{"className":60323},[886],[888,60325,60326],{"xmlns":890},[892,60327,60328,60349],{},[895,60329,60330,60332,60334,60336,60338,60344,60346],{},[1693,60331,1709],{"stretchy":1708},[898,60333,2000],{},[1693,60335,1698],{},[898,60337,207],{},[1717,60339,60340,60342],{},[1693,60341,1731],{"stretchy":1708},[1762,60343,2398],{},[1693,60345,1695],{},[1762,60347,60348],{},"12,25",[902,60350,60351],{"encoding":904},"(c-a)^2 = 12{,}25",[883,60353,60355],{"className":60354},[886],[888,60356,60357],{"xmlns":890},[892,60358,60359,60371],{},[895,60360,60361,60363,60365,60367,60369],{},[898,60362,1895],{},[1693,60364,1698],{},[898,60366,1771],{},[1693,60368,1695],{},[1762,60370,44795],{},[902,60372,60373],{"encoding":904},"b - d = 30",[883,60375,60377],{"className":60376},[886],[888,60378,60379],{"xmlns":890,"display":34854},[892,60380,60381,60482],{},[895,60382,60383,60385,60391,60393,60401,60403,60405,60407,60409,60417,60419,60421,60423,60425,60427,60435,60437,60439,60441,60443,60451,60453,60455,60457,60459,60462,60464,60467,60469,60471,60473,60476,60478,60480],{},[898,60384,1771],{},[1717,60386,60387,60389],{},[898,60388,1712],{},[898,60390,1691],{},[1693,60392,4110],{},[3638,60394,60395],{"scriptlevel":1911,"displaystyle":1708},[2132,60396,60397,60399],{},[1762,60398,44795],{},[1762,60400,60348],{},[1693,60402,1709],{"stretchy":1708},[1762,60404,11877],{},[1693,60406,1731],{"stretchy":1708},[1693,60408,1892],{},[3638,60410,60411],{"scriptlevel":1911,"displaystyle":1708},[2132,60412,60413,60415],{},[1762,60414,1764],{},[1762,60416,51172],{},[1693,60418,1709],{"stretchy":1708},[1693,60420,1698],{},[1762,60422,9147],{},[1693,60424,1731],{"stretchy":1708},[1693,60426,1698],{},[3638,60428,60429],{"scriptlevel":1911,"displaystyle":1708},[2132,60430,60431,60433],{},[1762,60432,44795],{},[1762,60434,60348],{},[1693,60436,1709],{"stretchy":1708},[1762,60438,9695],{},[1693,60440,1731],{"stretchy":1708},[1693,60442,1698],{},[3638,60444,60445],{"scriptlevel":1911,"displaystyle":1708},[2132,60446,60447,60449],{},[1762,60448,1764],{},[1762,60450,51172],{},[1693,60452,1709],{"stretchy":1708},[1762,60454,1764],{},[1693,60456,1731],{"stretchy":1708},[1693,60458,12766],{},[1762,60460,60461],{},"1,224",[1693,60463,1698],{},[1762,60465,60466],{},"1,429",[1693,60468,1698],{},[1762,60470,51345],{},[1693,60472,1698],{},[1762,60474,60475],{},"0,286",[1693,60477,12766],{},[1693,60479,1698],{},[1762,60481,51591],{},[902,60483,60484],{"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.",[724,60486,36848,60487,1789],{},[883,60488,60490],{"className":60489},[886],[888,60491,60492],{"xmlns":890},[892,60493,60494,60516],{},[895,60495,60496,60504,60506,60508,60510,60512,60514],{},[5688,60497,60498,60500,60502],{},[898,60499,1712],{},[1762,60501,1764],{},[898,60503,1691],{},[1693,60505,4110],{},[1762,60507,51340],{},[1693,60509,1698],{},[1762,60511,51622],{},[1693,60513,12766],{},[1762,60515,51627],{},[902,60517,60518],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1636,60520,60521],{},[724,60522,60523,60525,60526,60547,60548,60574,60575,60578,60579,60675,60676,60699,60700,60716],{},[883,60524,8654],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,60527,60529],{"className":60528},[886],[888,60530,60531],{"xmlns":890},[892,60532,60533,60545],{},[895,60534,60535,60537,60539,60541,60543],{},[898,60536,3890],{"mathvariant":1704},[898,60538,1712],{},[1693,60540,4110],{},[1693,60542,1698],{},[1762,60544,51657],{},[902,60546,51660],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,60549,60551],{"className":60550},[886],[888,60552,60553],{"xmlns":890},[892,60554,60555,60571],{},[895,60556,60557,60559,60565,60567,60569],{},[898,60558,1771],{},[1717,60560,60561,60563],{},[898,60562,1712],{},[898,60564,1691],{},[1693,60566,12766],{},[1693,60568,1698],{},[1762,60570,51622],{},[902,60572,60573],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,60576,60577],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,60580,60582],{"className":60581},[886],[888,60583,60584],{"xmlns":890},[892,60585,60586,60672],{},[895,60587,60588,60596,60598,60632,60634,60658,60660,60667,60669],{},[5688,60589,60590,60592,60594],{},[898,60591,1712],{},[1762,60593,1764],{},[898,60595,1691],{},[1693,60597,1695],{},[2132,60599,60600,60616],{},[895,60601,60602,60608,60610],{},[1717,60603,60604,60606],{},[898,60605,1895],{},[1693,60607,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,60609,1698],{},[1717,60611,60612,60614],{},[898,60613,1771],{},[1693,60615,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[895,60617,60618,60624,60626],{},[1717,60619,60620,60622],{},[898,60621,2000],{},[1693,60623,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,60625,1698],{},[1717,60627,60628,60630],{},[898,60629,207],{},[1693,60631,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,60633,1695],{},[2132,60635,60636,60644],{},[895,60637,60638,60640,60642],{},[1762,60639,21864],{},[1693,60641,1698],{},[1762,60643,9803],{},[895,60645,60646,60648,60650,60652,60654,60656],{},[1762,60647,26132],{},[1693,60649,1698],{},[1693,60651,1709],{"stretchy":1708},[1693,60653,1698],{},[1762,60655,59957],{},[1693,60657,1731],{"stretchy":1708},[1693,60659,1695],{},[2132,60661,60662,60664],{},[1762,60663,48571],{},[1762,60665,60666],{},"3,1",[1693,60668,12766],{},[1762,60670,60671],{},"7,742",[902,60673,60674],{"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 ",[883,60677,60679],{"className":60678},[886],[888,60680,60681],{"xmlns":890},[892,60682,60683,60696],{},[895,60684,60685,60687,60689,60691,60693],{},[898,60686,3890],{"mathvariant":1704},[898,60688,1712],{},[1693,60690,12766],{},[1693,60692,1698],{},[1762,60694,60695],{},"0,829",[902,60697,60698],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,60701,60703],{"className":60702},[886],[888,60704,60705],{"xmlns":890},[892,60706,60707,60713],{},[895,60708,60709,60711],{},[1693,60710,1698],{},[1762,60712,51657],{},[902,60714,60715],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,60718,60719],{},[614,60720,60721,60722,60735],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,60723,60725],{"className":60724},[886],[888,60726,60727],{"xmlns":890},[892,60728,60729,60733],{},[895,60730,60731],{},[898,60732,1712],{},[902,60734,1712],{"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.",[198,60737,60739,60740],{"id":60738},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,60741,60743],{"className":60742},[886],[888,60744,60745],{"xmlns":890},[892,60746,60747,60753],{},[895,60748,60749,60751],{},[898,60750,1701],{},[898,60752,3611],{},[902,60754,51734],{"encoding":904},[1636,60756,60757],{},[724,60758,60759,60761,60762,60796,60797,60819],{},[883,60760,59453],{}," Zadání\nPro nabídku ",[883,60763,60765],{"className":60764},[886],[888,60766,60767],{"xmlns":890},[892,60768,60769,60793],{},[895,60770,60771,60773,60775,60777,60779,60781,60783,60785,60787,60789,60791],{},[898,60772,1701],{},[1693,60774,1695],{},[898,60776,3611],{},[1693,60778,1709],{"stretchy":1708},[898,60780,1712],{},[1693,60782,1731],{"stretchy":1708},[1693,60784,1695],{},[1762,60786,9763],{},[1693,60788,1892],{},[1762,60790,2398],{},[898,60792,1712],{},[902,60794,60795],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,60798,60800],{"className":60799},[886],[888,60801,60802],{"xmlns":890},[892,60803,60804,60816],{},[895,60805,60806,60812,60814],{},[3284,60807,60808,60810],{},[898,60809,1712],{},[1762,60811,1911],{},[1693,60813,1695],{},[1762,60815,9763],{},[902,60817,60818],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,60821,60822],{},[38,60823,29570],{},[724,60825,60826],{},"Odpovídající cena:",[883,60828,60830],{"className":60829},[886],[888,60831,60832],{"xmlns":890,"display":34854},[892,60833,60834,60869],{},[895,60835,60836,60842,60844,60846,60848,60850,60852,60854,60856,60858,60860,60862,60864,60866],{},[3284,60837,60838,60840],{},[898,60839,1701],{},[1762,60841,1911],{},[1693,60843,1695],{},[898,60845,3611],{},[1693,60847,1709],{"stretchy":1708},[1762,60849,9763],{},[1693,60851,1731],{"stretchy":1708},[1693,60853,1695],{},[1762,60855,9763],{},[1693,60857,1892],{},[1762,60859,2398],{},[1693,60861,1715],{},[1762,60863,9763],{},[1693,60865,1695],{},[1762,60867,60868],{},"30.",[902,60870,60871],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,60873,60874],{},"Dle vzorce (2.15):",[883,60876,60878],{"className":60877},[886],[888,60879,60880],{"xmlns":890,"display":34854},[892,60881,60882,60990],{},[895,60883,60884,60886,60888,60890,60892,60894,60896,60902,60908,60910,60918,60920,60922,60924,60926,60928,60930,60932,60934,60936,60938,60940,60942,60944,60946,60949,60951,60953,60955,60961,60969,60971,60973,60975,60977,60979,60981,60983,60985,60987],{},[898,60885,1701],{},[898,60887,3611],{},[1693,60889,1709],{"stretchy":1708},[1762,60891,9763],{},[1693,60893,1731],{"stretchy":1708},[1693,60895,1695],{},[3284,60897,60898,60900],{},[898,60899,1701],{},[1762,60901,1911],{},[3284,60903,60904,60906],{},[898,60905,1712],{},[1762,60907,1911],{},[1693,60909,1698],{},[5688,60911,60912,60914,60916],{},[1693,60913,6221],{},[1762,60915,1911],{},[1762,60917,9763],{},[1693,60919,1709],{"stretchy":1708},[1762,60921,9763],{},[1693,60923,1892],{},[1762,60925,2398],{},[898,60927,1712],{},[1693,60929,1731],{"stretchy":1708},[1915,60931,2239],{},[898,60933,1771],{},[898,60935,1712],{},[1693,60937,1695],{},[1762,60939,9763],{},[1693,60941,1715],{},[1762,60943,44795],{},[1693,60945,1698],{},[1693,60947,9392],{"fence":1708,"stretchy":1898,"minsize":60948,"maxsize":60948},"1.8em",[1762,60950,9763],{},[898,60952,1712],{},[1693,60954,1892],{},[1717,60956,60957,60959],{},[898,60958,1712],{},[1762,60960,2398],{},[5688,60962,60963,60965,60967],{},[1693,60964,9407],{"fence":1708,"stretchy":1898,"minsize":60948,"maxsize":60948},[1762,60966,1911],{},[1762,60968,9763],{},[1693,60970,1695],{},[1762,60972,36864],{},[1693,60974,1698],{},[1693,60976,1709],{"stretchy":1708},[1762,60978,9987],{},[1693,60980,1892],{},[1762,60982,9987],{},[1693,60984,1731],{"stretchy":1708},[1693,60986,1695],{},[1762,60988,60989],{},"100.",[902,60991,60992],{"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.",[724,60994,60995,60996,61017,61018,61038],{},"Přebytek výrobce při množství ",[883,60997,60999],{"className":60998},[886],[888,61000,61001],{"xmlns":890},[892,61002,61003,61015],{},[895,61004,61005,61011,61013],{},[3284,61006,61007,61009],{},[898,61008,1712],{},[1762,61010,1911],{},[1693,61012,1695],{},[1762,61014,9763],{},[902,61016,60818],{"encoding":904}," je tedy ",[883,61019,61021],{"className":61020},[886],[888,61022,61023],{"xmlns":890},[892,61024,61025,61035],{},[895,61026,61027,61029,61031,61033],{},[898,61028,1701],{},[898,61030,3611],{},[1693,61032,1695],{},[1762,61034,9987],{},[902,61036,61037],{"encoding":904},"PS = 100"," (peněžních jednotek).",[1852,61040],{},[115,61042,61044],{"id":61043},"cheat-sheet","Cheat sheet",[16,61046,61047,61060],{},[19,61048,61049],{},[22,61050,61051,61054,61057],{},[25,61052,61053],{},"Veličina",[25,61055,61056],{},"Vzorec",[25,61058,61059],{},"Geometrie",[30,61061,61062,61180,61294,61361],{},[22,61063,61064,61092,61148],{},[35,61065,61066],{},[883,61067,61069],{"className":61068},[886],[888,61070,61071],{"xmlns":890},[892,61072,61073,61089],{},[895,61074,61075,61077,61079,61081,61087],{},[898,61076,2971],{},[898,61078,3611],{},[1693,61080,1709],{"stretchy":1708},[3284,61082,61083,61085],{},[898,61084,1712],{},[1762,61086,1911],{},[1693,61088,1731],{"stretchy":1708},[902,61090,61091],{"encoding":904},"CS(Q_0)",[35,61093,61094],{},[883,61095,61097],{"className":61096},[886],[888,61098,61099],{"xmlns":890},[892,61100,61101,61145],{},[895,61102,61103],{},[3638,61104,61105,61117,61119,61121,61123,61125,61127,61129,61131,61133,61139],{"scriptlevel":1911,"displaystyle":1898},[5688,61106,61107,61109,61111],{},[1693,61108,6221],{},[1762,61110,1911],{},[3284,61112,61113,61115],{},[898,61114,1712],{},[1762,61116,1911],{},[898,61118,2738],{},[1693,61120,1709],{"stretchy":1708},[898,61122,1712],{},[1693,61124,1731],{"stretchy":1708},[1915,61126,2239],{},[898,61128,1771],{},[898,61130,1712],{},[1693,61132,1698],{},[3284,61134,61135,61137],{},[898,61136,1701],{},[1762,61138,1911],{},[3284,61140,61141,61143],{},[898,61142,1712],{},[1762,61144,1911],{},[902,61146,61147],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,61149,61150,61151,61154,61155,61158,61159],{},"plocha ",[38,61152,61153],{},"pod"," křivkou poptávky, ",[38,61156,61157],{},"nad"," čárou ",[883,61160,61162],{"className":61161},[886],[888,61163,61164],{"xmlns":890},[892,61165,61166,61178],{},[895,61167,61168,61170,61172],{},[898,61169,1701],{},[1693,61171,1695],{},[3284,61173,61174,61176],{},[898,61175,1701],{},[1762,61177,1911],{},[902,61179,58437],{"encoding":904},[22,61181,61182,61210,61266],{},[35,61183,61184],{},[883,61185,61187],{"className":61186},[886],[888,61188,61189],{"xmlns":890},[892,61190,61191,61207],{},[895,61192,61193,61195,61197,61199,61205],{},[898,61194,1701],{},[898,61196,3611],{},[1693,61198,1709],{"stretchy":1708},[3284,61200,61201,61203],{},[898,61202,1712],{},[1762,61204,1911],{},[1693,61206,1731],{"stretchy":1708},[902,61208,61209],{"encoding":904},"PS(Q_0)",[35,61211,61212],{},[883,61213,61215],{"className":61214},[886],[888,61216,61217],{"xmlns":890},[892,61218,61219,61263],{},[895,61220,61221],{},[3638,61222,61223,61229,61235,61237,61249,61251,61253,61255,61257,61259,61261],{"scriptlevel":1911,"displaystyle":1898},[3284,61224,61225,61227],{},[898,61226,1701],{},[1762,61228,1911],{},[3284,61230,61231,61233],{},[898,61232,1712],{},[1762,61234,1911],{},[1693,61236,1698],{},[5688,61238,61239,61241,61243],{},[1693,61240,6221],{},[1762,61242,1911],{},[3284,61244,61245,61247],{},[898,61246,1712],{},[1762,61248,1911],{},[898,61250,3611],{},[1693,61252,1709],{"stretchy":1708},[898,61254,1712],{},[1693,61256,1731],{"stretchy":1708},[1915,61258,2239],{},[898,61260,1771],{},[898,61262,1712],{},[902,61264,61265],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,61267,61150,61268,61270,61271,61158,61273],{},[38,61269,61157],{}," křivkou nabídky, ",[38,61272,61153],{},[883,61274,61276],{"className":61275},[886],[888,61277,61278],{"xmlns":890},[892,61279,61280,61292],{},[895,61281,61282,61284,61286],{},[898,61283,1701],{},[1693,61285,1695],{},[3284,61287,61288,61290],{},[898,61289,1701],{},[1762,61291,1911],{},[902,61293,58437],{"encoding":904},[22,61295,61296,61299,61326],{},[35,61297,61298],{},"Výdaje \u002F tržby",[35,61300,61301],{},[883,61302,61304],{"className":61303},[886],[888,61305,61306],{"xmlns":890},[892,61307,61308,61324],{},[895,61309,61310,61316,61318],{},[3284,61311,61312,61314],{},[898,61313,1701],{},[1762,61315,1911],{},[1693,61317,1715],{},[3284,61319,61320,61322],{},[898,61321,1712],{},[1762,61323,1911],{},[902,61325,6323],{"encoding":904},[35,61327,6297,61328],{},[883,61329,61331],{"className":61330},[886],[888,61332,61333],{"xmlns":890},[892,61334,61335,61359],{},[895,61336,61337,61339,61341,61347,61349,61351,61353],{},[1762,61338,1911],{},[1915,61340,2239],{},[3284,61342,61343,61345],{},[898,61344,1712],{},[1762,61346,1911],{},[1915,61348,2239],{},[898,61350,2719],{},[1915,61352,2239],{},[3284,61354,61355,61357],{},[898,61356,1701],{},[1762,61358,1911],{},[902,61360,57917],{"encoding":904},[22,61362,61363,61366,61389],{},[35,61364,61365],{},"Celkový přebytek",[35,61367,61368],{},[883,61369,61371],{"className":61370},[886],[888,61372,61373],{"xmlns":890},[892,61374,61375,61387],{},[895,61376,61377,61379,61381,61383,61385],{},[898,61378,2971],{},[898,61380,3611],{},[1693,61382,1892],{},[898,61384,1701],{},[898,61386,3611],{},[902,61388,57655],{"encoding":904},[35,61390,61391],{},"součet obou ploch v rovnováze",[1852,61393],{},[115,61395,22545],{"id":22544},[120,61397,61398,61420,61442,61486,61530,61593,61621],{},[123,61399,61400,16877,61402,1343,61417,61419],{},[38,61401,6189],{},[883,61403,61405],{"className":61404},[886],[888,61406,61407],{"xmlns":890},[892,61408,61409,61415],{},[895,61410,61411,61413],{},[898,61412,2971],{},[898,61414,3611],{},[902,61416,51715],{"encoding":904},[614,61418,51753],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,61421,61422,16877,61424,1343,61439,61441],{},[38,61423,6329],{},[883,61425,61427],{"className":61426},[886],[888,61428,61429],{"xmlns":890},[892,61430,61431,61437],{},[895,61432,61433,61435],{},[898,61434,1701],{},[898,61436,3611],{},[902,61438,51734],{"encoding":904},[614,61440,51848],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,61443,61444,13877,61447,1789],{},[38,61445,61446],{},"Ochota platit",[883,61448,61450],{"className":61449},[886],[888,61451,61452],{"xmlns":890},[892,61453,61454,61484],{},[895,61455,61456],{},[3638,61457,61458,61470,61472,61474,61476,61478,61480,61482],{"scriptlevel":1911,"displaystyle":1898},[5688,61459,61460,61462,61464],{},[1693,61461,6221],{},[1762,61463,1911],{},[3284,61465,61466,61468],{},[898,61467,1712],{},[1762,61469,1911],{},[898,61471,2738],{},[1693,61473,1709],{"stretchy":1708},[898,61475,1712],{},[1693,61477,1731],{"stretchy":1708},[1915,61479,2239],{},[898,61481,1771],{},[898,61483,1712],{},[902,61485,58285],{"encoding":904},[123,61487,61488,13877,61491,1789],{},[38,61489,61490],{},"Minimální cena výrobce",[883,61492,61494],{"className":61493},[886],[888,61495,61496],{"xmlns":890},[892,61497,61498,61528],{},[895,61499,61500],{},[3638,61501,61502,61514,61516,61518,61520,61522,61524,61526],{"scriptlevel":1911,"displaystyle":1898},[5688,61503,61504,61506,61508],{},[1693,61505,6221],{},[1762,61507,1911],{},[3284,61509,61510,61512],{},[898,61511,1712],{},[1762,61513,1911],{},[898,61515,3611],{},[1693,61517,1709],{"stretchy":1708},[898,61519,1712],{},[1693,61521,1731],{"stretchy":1708},[1915,61523,2239],{},[898,61525,1771],{},[898,61527,1712],{},[902,61529,58927],{"encoding":904},[123,61531,61532,13877,61535,59426,61560,3042],{},[38,61533,61534],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,61536,61538],{"className":61537},[886],[888,61539,61540],{"xmlns":890},[892,61541,61542,61558],{},[895,61543,61544,61550,61552],{},[3284,61545,61546,61548],{},[898,61547,1701],{},[1762,61549,1911],{},[1915,61551,2239],{},[3284,61553,61554,61556],{},[898,61555,1712],{},[1762,61557,1911],{},[902,61559,58363],{"encoding":904},[883,61561,61563],{"className":61562},[886],[888,61564,61565],{"xmlns":890},[892,61566,61567,61591],{},[895,61568,61569,61571,61573,61579,61581,61583,61585],{},[1762,61570,1911],{},[1915,61572,2239],{},[3284,61574,61575,61577],{},[898,61576,1712],{},[1762,61578,1911],{},[1915,61580,2239],{},[898,61582,2719],{},[1915,61584,2239],{},[3284,61586,61587,61589],{},[898,61588,1701],{},[1762,61590,1911],{},[902,61592,57917],{"encoding":904},[123,61594,61595,61598,61599,61620],{},[38,61596,61597],{},"Celkový přebytek trhu"," — součet ",[883,61600,61602],{"className":61601},[886],[888,61603,61604],{"xmlns":890},[892,61605,61606,61618],{},[895,61607,61608,61610,61612,61614,61616],{},[898,61609,2971],{},[898,61611,3611],{},[1693,61613,1892],{},[898,61615,1701],{},[898,61617,3611],{},[902,61619,57655],{"encoding":904}," v rovnovážném bodě.",[123,61622,61623,61625,61626,1343,61639,61652,61653,1789],{},[38,61624,9351],{}," — plochy ohraničené křivkami ",[883,61627,61629],{"className":61628},[886],[888,61630,61631],{"xmlns":890},[892,61632,61633,61637],{},[895,61634,61635],{},[898,61636,2738],{},[902,61638,2738],{"encoding":904},[883,61640,61642],{"className":61641},[886],[888,61643,61644],{"xmlns":890},[892,61645,61646,61650],{},[895,61647,61648],{},[898,61649,3611],{},[902,61651,3611],{"encoding":904}," a přímkou ",[883,61654,61656],{"className":61655},[886],[888,61657,61658],{"xmlns":890},[892,61659,61660,61672],{},[895,61661,61662,61664,61666],{},[898,61663,1701],{},[1693,61665,1695],{},[3284,61667,61668,61670],{},[898,61669,1701],{},[1762,61671,1911],{},[902,61673,58437],{"encoding":904},[1852,61675],{},[115,61677,61679],{"id":61678},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,61681,61682,61683,61696,61697,61714],{},"Uvalení jednotkové daně ",[883,61684,61686],{"className":61685},[886],[888,61687,61688],{"xmlns":890},[892,61689,61690,61694],{},[895,61691,61692],{},[898,61693,2663],{},[902,61695,2663],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,61698,61700],{"className":61699},[886],[888,61701,61702],{"xmlns":890},[892,61703,61704,61712],{},[895,61705,61706],{},[1717,61707,61708,61710],{},[898,61709,1712],{},[898,61711,1691],{},[902,61713,2204],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,61716,61717],{},[9465,61718],{"alt":61719,"className":61720,"src":61721},"imek-prebytky-s-dani-deadweight",[210,9469],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,61723,61724,61725,61740,61741,61756,61757,59426,61760,61784,61785,16877,61788,61791,61792,1789],{},"Přebytek spotřebitele ",[883,61726,61728],{"className":61727},[886],[888,61729,61730],{"xmlns":890},[892,61731,61732,61738],{},[895,61733,61734,61736],{},[898,61735,2971],{},[898,61737,3611],{},[902,61739,51715],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,61742,61744],{"className":61743},[886],[888,61745,61746],{"xmlns":890},[892,61747,61748,61754],{},[895,61749,61750,61752],{},[898,61751,1701],{},[898,61753,3611],{},[902,61755,51734],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,61758,61759],{},"daňový příjem",[883,61761,61763],{"className":61762},[886],[888,61764,61765],{"xmlns":890},[892,61766,61767,61781],{},[895,61768,61769,61771,61773],{},[898,61770,2663],{},[1693,61772,1715],{},[5688,61774,61775,61777,61779],{},[898,61776,1712],{},[1762,61778,1764],{},[898,61780,1691],{},[902,61782,61783],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,61786,61787],{},"mrtvá ztráta",[614,61789,61790],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,61793,811],{"className":61794,"dataFsResolvedFilePath":809,"href":810},[210],[1852,61796],{},[115,61798,8685],{"id":8684},[120,61800,61801,61808,61820,61827,61834],{},[123,61802,61803,1863,61805],{},[38,61804,23042],{},[207,61806,802],{"className":61807,"dataFsResolvedFilePath":800,"href":801},[210],[123,61809,61810,1863,61812,61815,61816,61819],{},[38,61811,8722],{},[207,61813,775],{"className":61814,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,61817,8726],{"className":61818,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,61821,61822,1863,61824],{},[38,61823,23052],{},[207,61825,3261],{"className":61826,"dataFsResolvedFilePath":827,"href":828},[210],[123,61828,61829,1863,61831],{},[38,61830,57518],{},[207,61832,57522],{"className":61833,"dataFsResolvedFilePath":745,"href":746},[210],[123,61835,61836,1863,61838],{},[38,61837,8692],{},[207,61839,1653],{"className":61840,"dataFsResolvedFilePath":1651,"href":1652},[210],{"title":641,"searchDepth":642,"depth":642,"links":61842},[61843,61844,61849,61854,61859,61860,61861,61862],{"id":57714,"depth":642,"text":1241},{"id":58058,"depth":642,"text":61845,"children":61846},"Přebytek spotřebitele (CSCS)",[61847,61848],{"id":58077,"depth":649,"text":58078},{"id":9350,"depth":649,"text":9351},{"id":58653,"depth":642,"text":61850,"children":61851},"Přebytek výrobce (PSPS)",[61852,61853],{"id":58672,"depth":649,"text":58673},{"id":58835,"depth":649,"text":9351},{"id":59441,"depth":642,"text":59442,"children":61855},[61856,61857],{"id":59445,"depth":649,"text":59446},{"id":60738,"depth":649,"text":61858},"Příklad 2.13 — numerický výpočet PSPS",{"id":61043,"depth":642,"text":61044},{"id":22544,"depth":642,"text":22545},{"id":61678,"depth":642,"text":61679},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,57584,61869,61870,18833,23060,61871,61872],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":61875,"title":2645,"body":61876,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":81163,"navigation":664,"path":81164,"seo":81165,"sources":81166,"stem":81167,"tags":81168,"type":10745,"updated":677,"__hash__":81174},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md",{"type":9,"value":61877,"toc":81127},[61878,61881,62063,62065,62156,62161,62482,62486,62493,62495,62540,62607,62638,62688,62723,62727,62786,62791,62857,62974,63076,63078,63101,63179,63222,63224,63253,63320,63326,63440,63444,63524,63561,63613,63811,63875,63962,63966,63969,64048,64051,64169,64188,64253,64257,64349,64417,64458,64512,64580,64617,64621,64679,64709,64920,64992,65044,65210,65303,65338,65342,65344,65381,65446,65501,65503,65526,65615,65719,65788,65792,65889,66002,66058,66111,66169,66230,66233,66269,66334,66364,66593,66651,66685,66687,66714,66793,66907,66928,67007,67009,67117,67121,67259,67581,67585,67588,67592,67641,67645,67899,68051,68058,68131,68315,68320,68663,68665,68688,68690,68711,68770,68780,68829,68971,69045,69139,69254,69351,69469,69473,69542,69547,69659,69804,69855,69967,70009,70011,70031,70092,70119,70181,70185,70207,70276,70556,70563,70593,70600,70793,70797,70875,70880,70956,70959,71047,71123,71190,71239,71342,71415,71536,71887,72000,72102,72104,72107,72114,72117,72153,72212,72221,72369,72593,72597,72660,72839,72931,72986,72990,73046,73116,73168,73189,73270,73273,73348,73392,73396,73436,73479,73505,73509,73580,73676,73738,73790,73893,73971,73994,74023,74027,74193,74306,74376,74691,74851,74855,74906,74967,75002,75032,75132,75174,75343,75348,75444,75482,75486,75605,75905,75907,75942,75946,75950,76078,76210,76532,76720,76798,76802,77107,77220,77366,77551,77657,77889,78004,78086,78205,78303,78344,78348,78403,78547,78701,78861,78954,79148,79460,79591,79720,79724,79796,79838,79889,79891,81085,81087],[12,61879,2645],{"id":61880},"příjem-náklady-zisk-a-nabídka-firmy",[1636,61882,61883],{},[724,61884,61885,10760,61887,1863,61890,61905,61906,1863,61909,61924,61925,1863,61928,61955,61956,61977,61978,62002,62003,62025,62026,62029,62030,62045,62046,1789],{},[883,61886,1642],{},[38,61888,61889],{},"Příjem",[883,61891,61893],{"className":61892},[886],[888,61894,61895],{"xmlns":890},[892,61896,61897,61903],{},[895,61898,61899,61901],{},[898,61900,2663],{},[898,61902,2666],{},[902,61904,2883],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,61907,61908],{},"náklady",[883,61910,61912],{"className":61911},[886],[888,61913,61914],{"xmlns":890},[892,61915,61916,61922],{},[895,61917,61918,61920],{},[898,61919,2663],{},[898,61921,2971],{},[902,61923,3225],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,61926,61927],{},"zisk",[883,61929,61931],{"className":61930},[886],[888,61932,61933],{"xmlns":890},[892,61934,61935,61953],{},[895,61936,61937,61939,61941,61943,61945,61947,61949,61951],{},[898,61938,1701],{},[898,61940,2666],{},[1693,61942,1695],{},[898,61944,2663],{},[898,61946,2666],{},[1693,61948,1698],{},[898,61950,2663],{},[898,61952,2971],{},[902,61954,3537],{"encoding":904}," 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: ",[883,61957,61959],{"className":61958},[886],[888,61960,61961],{"xmlns":890},[892,61962,61963,61975],{},[895,61964,61965,61967,61969,61971,61973],{},[898,61966,2719],{},[898,61968,2971],{},[1693,61970,1695],{},[898,61972,2839],{},[898,61974,2971],{},[902,61976,5062],{"encoding":904}," v minimu průměrných nákladů, ",[883,61979,61981],{"className":61980},[886],[888,61982,61983],{"xmlns":890},[892,61984,61985,61999],{},[895,61986,61987,61989,61991,61993,61995,61997],{},[898,61988,2719],{},[898,61990,2985],{},[898,61992,2971],{},[1693,61994,1695],{},[898,61996,2839],{},[898,61998,2971],{},[902,62000,62001],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,62004,62006],{"className":62005},[886],[888,62007,62008],{"xmlns":890},[892,62009,62010,62022],{},[895,62011,62012,62014,62016,62018,62020],{},[898,62013,2839],{},[898,62015,2666],{},[1693,62017,1695],{},[898,62019,2839],{},[898,62021,2971],{},[902,62023,62024],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,62027,62028],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,62031,62033],{"className":62032},[886],[888,62034,62035],{"xmlns":890},[892,62036,62037,62043],{},[895,62038,62039,62041],{},[898,62040,2839],{},[898,62042,2971],{},[902,62044,3810],{"encoding":904}," nad bodem minima ",[883,62047,62049],{"className":62048},[886],[888,62050,62051],{"xmlns":890},[892,62052,62053,62061],{},[895,62054,62055,62057,62059],{},[898,62056,2719],{},[898,62058,2985],{},[898,62060,2971],{},[902,62062,3789],{"encoding":904},[115,62064,1241],{"id":57714},[724,62066,62067,62068,62071,62072,62074,62075,1343,62078,1343,62081,62083,62084,62087,62088,62091,62092,62095,62096,9577,62111,1348,62126,9577,62141,3042],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,62069,62070],{},"příjmem"," (revenue) a ",[38,62073,61908],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,62076,62077],{},"zisku",[38,62079,62080],{},"bodů zvratu",[38,62082,8907],{}," a konstrukcí ",[38,62085,62086],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,62089,1145],{"className":62090,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,62093,17976],{"className":62094,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,62097,62099],{"className":62098},[886],[888,62100,62101],{"xmlns":890},[892,62102,62103,62109],{},[895,62104,62105,62107],{},[898,62106,2663],{},[898,62108,2666],{},[902,62110,2883],{"encoding":904},[883,62112,62114],{"className":62113},[886],[888,62115,62116],{"xmlns":890},[892,62117,62118,62124],{},[895,62119,62120,62122],{},[898,62121,2839],{},[898,62123,2666],{},[902,62125,2919],{"encoding":904},[883,62127,62129],{"className":62128},[886],[888,62130,62131],{"xmlns":890},[892,62132,62133,62139],{},[895,62134,62135,62137],{},[898,62136,2663],{},[898,62138,2971],{},[902,62140,3225],{"encoding":904},[883,62142,62144],{"className":62143},[886],[888,62145,62146],{"xmlns":890},[892,62147,62148,62154],{},[895,62149,62150,62152],{},[898,62151,2839],{},[898,62153,2971],{},[902,62155,3810],{"encoding":904},[724,62157,62158],{},[38,62159,62160],{},"Cílové znalosti:",[120,62162,62163,62322,62325,62328,62421,62468,62475],{},[123,62164,62165,62166,1343,62181,1343,62196,4286,62211,1343,62226,1343,62241,1343,62258,1343,62275,1343,62292,1343,62307,15283],{},"odvodit a interpretovat funkce ",[883,62167,62169],{"className":62168},[886],[888,62170,62171],{"xmlns":890},[892,62172,62173,62179],{},[895,62174,62175,62177],{},[898,62176,2663],{},[898,62178,2666],{},[902,62180,2883],{"encoding":904},[883,62182,62184],{"className":62183},[886],[888,62185,62186],{"xmlns":890},[892,62187,62188,62194],{},[895,62189,62190,62192],{},[898,62191,2719],{},[898,62193,2666],{},[902,62195,2820],{"encoding":904},[883,62197,62199],{"className":62198},[886],[888,62200,62201],{"xmlns":890},[892,62202,62203,62209],{},[895,62204,62205,62207],{},[898,62206,2839],{},[898,62208,2666],{},[902,62210,2919],{"encoding":904},[883,62212,62214],{"className":62213},[886],[888,62215,62216],{"xmlns":890},[892,62217,62218,62224],{},[895,62219,62220,62222],{},[898,62221,2663],{},[898,62223,2971],{},[902,62225,3225],{"encoding":904},[883,62227,62229],{"className":62228},[886],[888,62230,62231],{"xmlns":890},[892,62232,62233,62239],{},[895,62234,62235,62237],{},[898,62236,2976],{},[898,62238,2971],{},[902,62240,3022],{"encoding":904},[883,62242,62244],{"className":62243},[886],[888,62245,62246],{"xmlns":890},[892,62247,62248,62256],{},[895,62249,62250,62252,62254],{},[898,62251,2663],{},[898,62253,2985],{},[898,62255,2971],{},[902,62257,3041],{"encoding":904},[883,62259,62261],{"className":62260},[886],[888,62262,62263],{"xmlns":890},[892,62264,62265,62273],{},[895,62266,62267,62269,62271],{},[898,62268,2719],{},[898,62270,2976],{},[898,62272,2971],{},[902,62274,3150],{"encoding":904},[883,62276,62278],{"className":62277},[886],[888,62279,62280],{"xmlns":890},[892,62281,62282,62290],{},[895,62283,62284,62286,62288],{},[898,62285,2719],{},[898,62287,2985],{},[898,62289,2971],{},[902,62291,3789],{"encoding":904},[883,62293,62295],{"className":62294},[886],[888,62296,62297],{"xmlns":890},[892,62298,62299,62305],{},[895,62300,62301,62303],{},[898,62302,2719],{},[898,62304,2971],{},[902,62306,3331],{"encoding":904},[883,62308,62310],{"className":62309},[886],[888,62311,62312],{"xmlns":890},[892,62313,62314,62320],{},[895,62315,62316,62318],{},[898,62317,2839],{},[898,62319,2971],{},[902,62321,3810],{"encoding":904},[123,62323,62324],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,62326,62327],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,62329,62330,62331,62334,62335,48585,62377,15283],{},"osvojit si ",[38,62332,62333],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,62336,62338],{"className":62337},[886],[888,62339,62340],{"xmlns":890},[892,62341,62342,62374],{},[895,62343,62344,62346,62348,62350,62356,62358,62360,62362,62364,62366,62372],{},[898,62345,2719],{},[898,62347,2971],{},[1693,62349,1709],{"stretchy":1708},[3284,62351,62352,62354],{},[898,62353,1712],{},[1762,62355,1911],{},[1693,62357,1731],{"stretchy":1708},[1693,62359,1695],{},[898,62361,2839],{},[898,62363,2971],{},[1693,62365,1709],{"stretchy":1708},[3284,62367,62368,62370],{},[898,62369,1712],{},[1762,62371,1911],{},[1693,62373,1731],{"stretchy":1708},[902,62375,62376],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,62378,62380],{"className":62379},[886],[888,62381,62382],{"xmlns":890},[892,62383,62384,62418],{},[895,62385,62386,62388,62390,62392,62394,62400,62402,62404,62406,62408,62410,62416],{},[898,62387,2719],{},[898,62389,2985],{},[898,62391,2971],{},[1693,62393,1709],{"stretchy":1708},[3284,62395,62396,62398],{},[898,62397,1712],{},[1762,62399,1911],{},[1693,62401,1731],{"stretchy":1708},[1693,62403,1695],{},[898,62405,2839],{},[898,62407,2971],{},[1693,62409,1709],{"stretchy":1708},[3284,62411,62412,62414],{},[898,62413,1712],{},[1762,62415,1911],{},[1693,62417,1731],{"stretchy":1708},[902,62419,62420],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,62422,62330,62423,62334,62426,15283],{},[38,62424,62425],{},"princip maximalizace zisku",[883,62427,62429],{"className":62428},[886],[888,62430,62431],{"xmlns":890},[892,62432,62433,62465],{},[895,62434,62435,62437,62439,62441,62447,62449,62451,62453,62455,62457,62463],{},[898,62436,2839],{},[898,62438,2666],{},[1693,62440,1709],{"stretchy":1708},[3284,62442,62443,62445],{},[898,62444,1712],{},[1762,62446,1911],{},[1693,62448,1731],{"stretchy":1708},[1693,62450,1695],{},[898,62452,2839],{},[898,62454,2971],{},[1693,62456,1709],{"stretchy":1708},[3284,62458,62459,62461],{},[898,62460,1712],{},[1762,62462,1911],{},[1693,62464,1731],{"stretchy":1708},[902,62466,62467],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,62469,62470,62471,62474],{},"stanovit ",[38,62472,62473],{},"body zvratu"," a interval zisku;",[123,62476,62477,62478,62481],{},"zkonstruovat ",[38,62479,62480],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,62483,62485],{"id":62484},"příjem-firmy","Příjem firmy",[724,62487,62488],{},[9465,62489],{"alt":62490,"className":62491,"src":62492},"imek-ar-mr-dvojnasobny-sklon",[210,9469],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,62494,2649],{"id":2648},[724,62496,62497,62498,16877,62513,62516,62517,36727],{},"Celkový příjem ",[883,62499,62501],{"className":62500},[886],[888,62502,62503],{"xmlns":890},[892,62504,62505,62511],{},[895,62506,62507,62509],{},[898,62508,2663],{},[898,62510,2666],{},[902,62512,2883],{"encoding":904},[38,62514,62515],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,62518,62520],{"className":62519},[886],[888,62521,62522],{"xmlns":890},[892,62523,62524,62538],{},[895,62525,62526,62528,62530,62532,62534,62536],{},[898,62527,1701],{},[1693,62529,1695],{},[898,62531,2738],{},[1693,62533,1709],{"stretchy":1708},[898,62535,1712],{},[1693,62537,1731],{"stretchy":1708},[902,62539,3980],{"encoding":904},[883,62541,62543],{"className":62542},[886],[888,62544,62545],{"xmlns":890,"display":34854},[892,62546,62547,62604],{},[3626,62548,62549],{"width":34859},[3632,62550,62551,62553,62597,62599],{},[3635,62552],{"width":34864},[3635,62554,62555],{},[895,62556,62557,62559,62561,62563,62565,62567,62569,62571,62573,62575,62577,62579,62581,62583,62585,62587,62589,62591,62593,62595],{},[898,62558,2663],{},[898,62560,2666],{},[1693,62562,1695],{},[898,62564,2663],{},[898,62566,2666],{},[1693,62568,1709],{"stretchy":1708},[898,62570,1712],{},[1693,62572,1731],{"stretchy":1708},[1693,62574,1695],{},[898,62576,1701],{},[1693,62578,1715],{},[898,62580,1712],{},[1693,62582,1695],{},[898,62584,2738],{},[1693,62586,1709],{"stretchy":1708},[898,62588,1712],{},[1693,62590,1731],{"stretchy":1708},[1693,62592,1715],{},[898,62594,1712],{},[898,62596,1789],{"mathvariant":1704},[3635,62598],{"width":34864},[3635,62600,62601],{},[1915,62602,62603],{},"(3.1)",[902,62605,62606],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,62608,62609,62610,62613,62614,62637],{},"Graf funkce se nazývá ",[38,62611,62612],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,62615,62617],{"className":62616},[886],[888,62618,62619],{"xmlns":890},[892,62620,62621,62635],{},[895,62622,62623,62625,62627,62629,62631,62633],{},[898,62624,1701],{},[1693,62626,1695],{},[898,62628,207],{},[898,62630,1712],{},[1693,62632,1892],{},[898,62634,1895],{},[902,62636,43837],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,62639,62641],{"className":62640},[886],[888,62642,62643],{"xmlns":890,"display":34854},[892,62644,62645,62685],{},[895,62646,62647,62649,62651,62653,62655,62657,62659,62661,62663,62665,62667,62669,62671,62677,62679,62681,62683],{},[898,62648,2663],{},[898,62650,2666],{},[1693,62652,1695],{},[898,62654,1712],{},[1693,62656,1709],{"stretchy":1708},[898,62658,207],{},[898,62660,1712],{},[1693,62662,1892],{},[898,62664,1895],{},[1693,62666,1731],{"stretchy":1708},[1693,62668,1695],{},[898,62670,207],{},[1717,62672,62673,62675],{},[898,62674,1712],{},[1762,62676,2398],{},[1693,62678,1892],{},[898,62680,1895],{},[898,62682,1712],{},[1693,62684,1899],{"separator":1898},[902,62686,62687],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,62689,62690,62691,62704,62705,62722],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,62692,62694],{"className":62693},[886],[888,62695,62696],{"xmlns":890},[892,62697,62698,62702],{},[895,62699,62700],{},[898,62701,900],{},[902,62703,900],{"encoding":904}," (jelikož ",[883,62706,62708],{"className":62707},[886],[888,62709,62710],{"xmlns":890},[892,62711,62712,62720],{},[895,62713,62714,62716,62718],{},[898,62715,207],{},[1693,62717,1908],{},[1762,62719,1911],{},[902,62721,49853],{"encoding":904},") procházející počátkem.",[44125,62724,62726],{"id":62725},"příklad-31","Příklad 3.1",[724,62728,62729,62732,62733,62769,62770,62785],{},[38,62730,62731],{},"Zadání."," Pro poptávku ",[883,62734,62736],{"className":62735},[886],[888,62737,62738],{"xmlns":890},[892,62739,62740,62766],{},[895,62741,62742,62744,62746,62748,62750,62752,62754,62756,62758,62760,62762,62764],{},[898,62743,1701],{},[1693,62745,1695],{},[898,62747,2738],{},[1693,62749,1709],{"stretchy":1708},[898,62751,1712],{},[1693,62753,1731],{"stretchy":1708},[1693,62755,1695],{},[1693,62757,1698],{},[1762,62759,2398],{},[898,62761,1712],{},[1693,62763,1892],{},[1762,62765,9987],{},[902,62767,62768],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,62771,62773],{"className":62772},[886],[888,62774,62775],{"xmlns":890},[892,62776,62777,62783],{},[895,62778,62779,62781],{},[898,62780,2663],{},[898,62782,2666],{},[902,62784,2883],{"encoding":904}," a charakterizujte jeho křivku.",[724,62787,62788,62790],{},[38,62789,29570],{}," Celkový příjem je",[883,62792,62794],{"className":62793},[886],[888,62795,62796],{"xmlns":890,"display":34854},[892,62797,62798,62854],{},[895,62799,62800,62802,62804,62806,62808,62810,62812,62814,62816,62818,62820,62822,62824,62826,62828,62830,62832,62834,62836,62838,62840,62846,62848,62850,62852],{},[898,62801,2663],{},[898,62803,2666],{},[1693,62805,1695],{},[898,62807,2663],{},[898,62809,2666],{},[1693,62811,1709],{"stretchy":1708},[898,62813,1712],{},[1693,62815,1731],{"stretchy":1708},[1693,62817,1695],{},[898,62819,1712],{},[1693,62821,1709],{"stretchy":1708},[1693,62823,1698],{},[1762,62825,2398],{},[898,62827,1712],{},[1693,62829,1892],{},[1762,62831,9987],{},[1693,62833,1731],{"stretchy":1708},[1693,62835,1695],{},[1693,62837,1698],{},[1762,62839,2398],{},[1717,62841,62842,62844],{},[898,62843,1712],{},[1762,62845,2398],{},[1693,62847,1892],{},[1762,62849,9987],{},[898,62851,1712],{},[898,62853,1789],{"mathvariant":1704},[902,62855,62856],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,62858,62859,62860,4286,62882,62904,62905,62923,62924,1789],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,62861,62863],{"className":62862},[886],[888,62864,62865],{"xmlns":890},[892,62866,62867,62879],{},[895,62868,62869,62875,62877],{},[3284,62870,62871,62873],{},[898,62872,1712],{},[1762,62874,1764],{},[1693,62876,1695],{},[1762,62878,1911],{},[902,62880,62881],{"encoding":904},"Q_1 = 0",[883,62883,62885],{"className":62884},[886],[888,62886,62887],{"xmlns":890},[892,62888,62889,62901],{},[895,62890,62891,62897,62899],{},[3284,62892,62893,62895],{},[898,62894,1712],{},[1762,62896,2398],{},[1693,62898,1695],{},[1762,62900,10017],{},[902,62902,62903],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,62906,62908],{"className":62907},[886],[888,62909,62910],{"xmlns":890},[892,62911,62912,62920],{},[895,62913,62914,62916,62918],{},[898,62915,1712],{},[1693,62917,1695],{},[1762,62919,11872],{},[902,62921,62922],{"encoding":904},"Q = 25"," ve výši ",[883,62925,62927],{"className":62926},[886],[888,62928,62929],{"xmlns":890},[892,62930,62931,62971],{},[895,62932,62933,62935,62944,62946,62948,62950,62952,62955,62957,62959,62961,62963,62965,62967,62969],{},[898,62934,2663],{},[3284,62936,62937,62939,62942],{},[898,62938,2666],{},[898,62940,62941],{},"max",[1693,62943,3742],{},[1693,62945,1695],{},[1693,62947,1698],{},[1762,62949,2398],{},[1693,62951,1715],{},[1762,62953,62954],{},"625",[1693,62956,1892],{},[1762,62958,9987],{},[1693,62960,1715],{},[1762,62962,11872],{},[1693,62964,1695],{},[1762,62966,1764],{},[1915,62968,2239],{},[1762,62970,37526],{},[902,62972,62973],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,62975,62976],{},[614,62977,62978,62979,63013,63014,4286,63027,63040,63041,9530,63059,1789],{},"Obrázek 3.1: Parabola ",[883,62980,62982],{"className":62981},[886],[888,62983,62984],{"xmlns":890},[892,62985,62986,63010],{},[895,62987,62988,62990,62992,62994,62996,62998,63004,63006,63008],{},[898,62989,2663],{},[898,62991,2666],{},[1693,62993,1695],{},[1693,62995,1698],{},[1762,62997,2398],{},[1717,62999,63000,63002],{},[898,63001,1712],{},[1762,63003,2398],{},[1693,63005,1892],{},[1762,63007,9987],{},[898,63009,1712],{},[902,63011,63012],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,63015,63017],{"className":63016},[886],[888,63018,63019],{"xmlns":890},[892,63020,63021,63025],{},[895,63022,63023],{},[1762,63024,1911],{},[902,63026,1911],{"encoding":904},[883,63028,63030],{"className":63029},[886],[888,63031,63032],{"xmlns":890},[892,63033,63034,63038],{},[895,63035,63036],{},[1762,63037,10017],{},[902,63039,10017],{"encoding":904}," a maximem ",[883,63042,63044],{"className":63043},[886],[888,63045,63046],{"xmlns":890},[892,63047,63048,63056],{},[895,63049,63050,63052,63054],{},[1762,63051,1764],{},[1915,63053,2239],{},[1762,63055,37526],{},[902,63057,63058],{"encoding":904},"1\\,250",[883,63060,63062],{"className":63061},[886],[888,63063,63064],{"xmlns":890},[892,63065,63066,63074],{},[895,63067,63068,63070,63072],{},[898,63069,1712],{},[1693,63071,1695],{},[1762,63073,11872],{},[902,63075,62922],{"encoding":904},[198,63077,2705],{"id":2704},[724,63079,63080,1863,63082,16877,63097,63100],{},[38,63081,2705],{},[883,63083,63085],{"className":63084},[886],[888,63086,63087],{"xmlns":890},[892,63088,63089,63095],{},[895,63090,63091,63093],{},[898,63092,2719],{},[898,63094,2666],{},[902,63096,2820],{"encoding":904},[38,63098,63099],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,63102,63104],{"className":63103},[886],[888,63105,63106],{"xmlns":890,"display":34854},[892,63107,63108,63176],{},[895,63109,63110,63112,63114,63116,63118,63120,63122,63124,63126,63128,63144,63146,63164,63166,63168,63170,63172,63174],{},[898,63111,2719],{},[898,63113,2666],{},[1693,63115,1695],{},[898,63117,2719],{},[898,63119,2666],{},[1693,63121,1709],{"stretchy":1708},[898,63123,1712],{},[1693,63125,1731],{"stretchy":1708},[1693,63127,1695],{},[2132,63129,63130,63142],{},[895,63131,63132,63134,63136,63138,63140],{},[898,63133,2663],{},[898,63135,2666],{},[1693,63137,1709],{"stretchy":1708},[898,63139,1712],{},[1693,63141,1731],{"stretchy":1708},[898,63143,1712],{},[1693,63145,1695],{},[2132,63147,63148,63162],{},[895,63149,63150,63152,63154,63156,63158,63160],{},[898,63151,1712],{},[1915,63153,2239],{},[898,63155,2738],{},[1693,63157,1709],{"stretchy":1708},[898,63159,1712],{},[1693,63161,1731],{"stretchy":1708},[898,63163,1712],{},[1693,63165,1695],{},[898,63167,2738],{},[1693,63169,1709],{"stretchy":1708},[898,63171,1712],{},[1693,63173,1731],{"stretchy":1708},[898,63175,1789],{"mathvariant":1704},[902,63177,63178],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1636,63180,63181],{},[724,63182,63183,63186,63187,1343,63190,1789],{},[883,63184,63185],{},"!note"," Klíčové pozorování\n",[38,63188,63189],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,63191,63193],{"className":63192},[886],[888,63194,63195],{"xmlns":890},[892,63196,63197,63219],{},[895,63198,63199,63201,63203,63205,63207,63209,63211,63213,63215,63217],{},[898,63200,2719],{},[898,63202,2666],{},[1693,63204,1709],{"stretchy":1708},[898,63206,1712],{},[1693,63208,1731],{"stretchy":1708},[1693,63210,1695],{},[898,63212,2738],{},[1693,63214,1709],{"stretchy":1708},[898,63216,1712],{},[1693,63218,1731],{"stretchy":1708},[902,63220,63221],{"encoding":904},"AR(Q) = D(Q)",[198,63223,2825],{"id":2824},[724,63225,63226,63227,1863,63230,16877,63245,63248,63249,63252],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,63228,63229],{},"mezní příjem",[883,63231,63233],{"className":63232},[886],[888,63234,63235],{"xmlns":890},[892,63236,63237,63243],{},[895,63238,63239,63241],{},[898,63240,2839],{},[898,63242,2666],{},[902,63244,2919],{"encoding":904},[38,63246,63247],{},"marginal revenue","), definovaný jako ",[207,63250,1145],{"className":63251,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,63254,63256],{"className":63255},[886],[888,63257,63258],{"xmlns":890,"display":34854},[892,63259,63260,63317],{},[3626,63261,63262],{"width":34859},[3632,63263,63264,63266,63310,63312],{},[3635,63265],{"width":34864},[3635,63267,63268],{},[895,63269,63270,63272,63274,63276,63292,63294,63296,63302,63304,63306,63308],{},[898,63271,2839],{},[898,63273,2666],{},[1693,63275,1695],{},[2132,63277,63278,63286],{},[895,63279,63280,63282,63284],{},[898,63281,1771],{"mathvariant":1704},[898,63283,2663],{},[898,63285,2666],{},[895,63287,63288,63290],{},[898,63289,1771],{"mathvariant":1704},[898,63291,1712],{},[1693,63293,1695],{},[898,63295,2663],{},[1717,63297,63298,63300],{},[898,63299,2666],{},[1693,63301,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,63303,1709],{"stretchy":1708},[898,63305,1712],{},[1693,63307,1731],{"stretchy":1708},[898,63309,1789],{"mathvariant":1704},[3635,63311],{"width":34864},[3635,63313,63314],{},[1915,63315,63316],{},"(3.2)",[902,63318,63319],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,63321,63322,63323,63325],{},"Mezní příjem udává ",[38,63324,9502],{}," celkového příjmu vzhledem k množství.",[1636,63327,63328],{},[724,63329,63330,63332,63333,63359,63360,63377,63378,1789],{},[883,63331,11036],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,63334,63336],{"className":63335},[886],[888,63337,63338],{"xmlns":890},[892,63339,63340,63356],{},[895,63341,63342,63344,63346,63348,63354],{},[898,63343,2839],{},[898,63345,2666],{},[1693,63347,1709],{"stretchy":1708},[1717,63349,63350,63352],{},[898,63351,1712],{},[1693,63353,3672],{},[1693,63355,1731],{"stretchy":1708},[902,63357,63358],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,63361,63363],{"className":63362},[886],[888,63364,63365],{"xmlns":890},[892,63366,63367,63375],{},[895,63368,63369],{},[1717,63370,63371,63373],{},[898,63372,1712],{},[1693,63374,3672],{},[902,63376,3770],{"encoding":904},". Jinak řečeno: ",[883,63379,63381],{"className":63380},[886],[888,63382,63383],{"xmlns":890},[892,63384,63385,63437],{},[895,63386,63387,63389,63391,63393,63399,63401,63403,63405,63407,63409,63415,63417,63419,63421,63423,63425,63427,63429,63435],{},[898,63388,2839],{},[898,63390,2666],{},[1693,63392,1709],{"stretchy":1708},[1717,63394,63395,63397],{},[898,63396,1712],{},[1693,63398,3672],{},[1693,63400,1731],{"stretchy":1708},[1693,63402,4110],{},[898,63404,2663],{},[898,63406,2666],{},[1693,63408,1709],{"stretchy":1708},[1717,63410,63411,63413],{},[898,63412,1712],{},[1693,63414,3672],{},[1693,63416,1892],{},[1762,63418,1764],{},[1693,63420,1731],{"stretchy":1708},[1693,63422,1698],{},[898,63424,2663],{},[898,63426,2666],{},[1693,63428,1709],{"stretchy":1708},[1717,63430,63431,63433],{},[898,63432,1712],{},[1693,63434,3672],{},[1693,63436,1731],{"stretchy":1708},[902,63438,63439],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[44125,63441,63443],{"id":63442},"příklad-32","Příklad 3.2",[724,63445,63446,62732,63448,62769,63482,63497,63498,1789],{},[38,63447,62731],{},[883,63449,63451],{"className":63450},[886],[888,63452,63453],{"xmlns":890},[892,63454,63455,63479],{},[895,63456,63457,63459,63461,63463,63465,63467,63469,63471,63473,63475,63477],{},[898,63458,1701],{},[1693,63460,1695],{},[898,63462,2738],{},[1693,63464,1709],{"stretchy":1708},[898,63466,1712],{},[1693,63468,1731],{"stretchy":1708},[1693,63470,1695],{},[1762,63472,9987],{},[1693,63474,1698],{},[1762,63476,2398],{},[898,63478,1712],{},[902,63480,63481],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,63483,63485],{"className":63484},[886],[888,63486,63487],{"xmlns":890},[892,63488,63489,63495],{},[895,63490,63491,63493],{},[898,63492,2839],{},[898,63494,2666],{},[902,63496,2919],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,63499,63501],{"className":63500},[886],[888,63502,63503],{"xmlns":890},[892,63504,63505,63521],{},[895,63506,63507,63509,63511,63513,63515,63517,63519],{},[898,63508,1712],{},[1693,63510,1695],{},[1762,63512,43026],{},[1693,63514,1899],{"separator":1898},[1762,63516,48633],{},[1693,63518,1899],{"separator":1898},[1762,63520,15892],{},[902,63522,63523],{"encoding":904},"Q = 15, 16, 20",[724,63525,63526,1863,63528,63560],{},[38,63527,29570],{},[883,63529,63531],{"className":63530},[886],[888,63532,63533],{"xmlns":890},[892,63534,63535,63557],{},[895,63536,63537,63539,63541,63543,63545,63547,63549,63551],{},[898,63538,2663],{},[898,63540,2666],{},[1693,63542,1695],{},[1762,63544,9987],{},[898,63546,1712],{},[1693,63548,1698],{},[1762,63550,2398],{},[1717,63552,63553,63555],{},[898,63554,1712],{},[1762,63556,2398],{},[902,63558,63559],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,63562,63564],{"className":63563},[886],[888,63565,63566],{"xmlns":890,"display":34854},[892,63567,63568,63610],{},[895,63569,63570,63572,63574,63576,63578,63580,63582,63584,63586,63592,63598,63600,63602,63604,63606,63608],{},[898,63571,2839],{},[898,63573,2666],{},[1693,63575,1695],{},[1693,63577,1709],{"stretchy":1708},[1762,63579,9987],{},[898,63581,1712],{},[1693,63583,1698],{},[1762,63585,2398],{},[1717,63587,63588,63590],{},[898,63589,1712],{},[1762,63591,2398],{},[1717,63593,63594,63596],{},[1693,63595,1731],{"stretchy":1708},[1693,63597,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,63599,1695],{},[1762,63601,9987],{},[1693,63603,1698],{},[1762,63605,9262],{},[898,63607,1712],{},[898,63609,1789],{"mathvariant":1704},[902,63611,63612],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,63614,16518,63615,6055,63633,63659,63660,2783,63673,63688,63689,63702,63703,28223,63716,2783,63729,63744,63745,63758,63759,63790,63791,63810],{},[883,63616,63618],{"className":63617},[886],[888,63619,63620],{"xmlns":890},[892,63621,63622,63630],{},[895,63623,63624,63626,63628],{},[898,63625,1712],{},[1693,63627,1695],{},[1762,63629,43026],{},[902,63631,63632],{"encoding":904},"Q = 15",[883,63634,63636],{"className":63635},[886],[888,63637,63638],{"xmlns":890},[892,63639,63640,63656],{},[895,63641,63642,63644,63646,63648,63650,63652,63654],{},[898,63643,2839],{},[898,63645,2666],{},[1693,63647,1709],{"stretchy":1708},[1762,63649,43026],{},[1693,63651,1731],{"stretchy":1708},[1693,63653,1695],{},[1762,63655,12079],{},[902,63657,63658],{"encoding":904},"MR(15) = 40",": při množství ",[883,63661,63663],{"className":63662},[886],[888,63664,63665],{"xmlns":890},[892,63666,63667,63671],{},[895,63668,63669],{},[1762,63670,43026],{},[902,63672,43026],{"encoding":904},[883,63674,63676],{"className":63675},[886],[888,63677,63678],{"xmlns":890},[892,63679,63680,63686],{},[895,63681,63682,63684],{},[898,63683,2663],{},[898,63685,2666],{},[902,63687,2883],{"encoding":904}," mění asi ",[883,63690,63692],{"className":63691},[886],[888,63693,63694],{"xmlns":890},[892,63695,63696,63700],{},[895,63697,63698],{},[1762,63699,12079],{},[902,63701,12079],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,63704,63706],{"className":63705},[886],[888,63707,63708],{"xmlns":890},[892,63709,63710,63714],{},[895,63711,63712],{},[898,63713,1712],{},[902,63715,1712],{"encoding":904},[883,63717,63719],{"className":63718},[886],[888,63720,63721],{"xmlns":890},[892,63722,63723,63727],{},[895,63724,63725],{},[1762,63726,1764],{},[902,63728,1764],{"encoding":904},[883,63730,63732],{"className":63731},[886],[888,63733,63734],{"xmlns":890},[892,63735,63736,63742],{},[895,63737,63738,63740],{},[898,63739,2663],{},[898,63741,2666],{},[902,63743,2883],{"encoding":904}," zvýší přibližně o ",[883,63746,63748],{"className":63747},[886],[888,63749,63750],{"xmlns":890},[892,63751,63752,63756],{},[895,63753,63754],{},[1762,63755,12079],{},[902,63757,12079],{"encoding":904},", tj. ze skutečné hodnoty ",[883,63760,63762],{"className":63761},[886],[888,63763,63764],{"xmlns":890},[892,63765,63766,63787],{},[895,63767,63768,63770,63772,63774,63776,63778,63780,63782,63784],{},[898,63769,2663],{},[898,63771,2666],{},[1693,63773,1709],{"stretchy":1708},[1762,63775,43026],{},[1693,63777,1731],{"stretchy":1708},[1693,63779,1695],{},[1762,63781,1764],{},[1915,63783,2239],{},[1762,63785,63786],{},"050",[902,63788,63789],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,63792,63794],{"className":63793},[886],[888,63795,63796],{"xmlns":890},[892,63797,63798,63807],{},[895,63799,63800,63802,63804],{},[1762,63801,1764],{},[1915,63803,2239],{},[1762,63805,63806],{},"090",[902,63808,63809],{"encoding":904},"1\\,090",". Skutečná změna je",[883,63812,63814],{"className":63813},[886],[888,63815,63816],{"xmlns":890,"display":34854},[892,63817,63818,63872],{},[895,63819,63820,63822,63824,63826,63828,63830,63832,63834,63836,63838,63840,63842,63844,63846,63848,63850,63852,63854,63856,63859,63861,63863,63865,63867,63869],{},[898,63821,3890],{"mathvariant":1704},[898,63823,2663],{},[898,63825,2666],{},[1693,63827,1695],{},[898,63829,2663],{},[898,63831,2666],{},[1693,63833,1709],{"stretchy":1708},[1762,63835,48633],{},[1693,63837,1731],{"stretchy":1708},[1693,63839,1698],{},[898,63841,2663],{},[898,63843,2666],{},[1693,63845,1709],{"stretchy":1708},[1762,63847,43026],{},[1693,63849,1731],{"stretchy":1708},[1693,63851,1695],{},[1762,63853,1764],{},[1915,63855,2239],{},[1762,63857,63858],{},"088",[1693,63860,1698],{},[1762,63862,1764],{},[1915,63864,2239],{},[1762,63866,63786],{},[1693,63868,1695],{},[1762,63870,63871],{},"38.",[902,63873,63874],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,63876,63877,63878,1343,63904,7617,63930,63945,63946,63961],{},"Podobně ",[883,63879,63881],{"className":63880},[886],[888,63882,63883],{"xmlns":890},[892,63884,63885,63901],{},[895,63886,63887,63889,63891,63893,63895,63897,63899],{},[898,63888,2839],{},[898,63890,2666],{},[1693,63892,1709],{"stretchy":1708},[1762,63894,48633],{},[1693,63896,1731],{"stretchy":1708},[1693,63898,1695],{},[1762,63900,12433],{},[902,63902,63903],{"encoding":904},"MR(16) = 36",[883,63905,63907],{"className":63906},[886],[888,63908,63909],{"xmlns":890},[892,63910,63911,63927],{},[895,63912,63913,63915,63917,63919,63921,63923,63925],{},[898,63914,2839],{},[898,63916,2666],{},[1693,63918,1709],{"stretchy":1708},[1762,63920,15892],{},[1693,63922,1731],{"stretchy":1708},[1693,63924,1695],{},[1762,63926,15892],{},[902,63928,63929],{"encoding":904},"MR(20) = 20",[883,63931,63933],{"className":63932},[886],[888,63934,63935],{"xmlns":890},[892,63936,63937,63943],{},[895,63938,63939,63941],{},[898,63940,2839],{},[898,63942,2666],{},[902,63944,2919],{"encoding":904}," je klesající funkce — rychlost změny ",[883,63947,63949],{"className":63948},[886],[888,63950,63951],{"xmlns":890},[892,63952,63953,63959],{},[895,63954,63955,63957],{},[898,63956,2663],{},[898,63958,2666],{},[902,63960,2883],{"encoding":904}," s růstem množství klesá.",[198,63963,63965],{"id":63964},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,63967,63968],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,63970,63972],{"className":63971},[886],[888,63973,63974],{"xmlns":890,"display":34854},[892,63975,63976,64045],{},[3626,63977,63978],{"width":34859},[3632,63979,63980,63982,64038,64040],{},[3635,63981],{"width":34864},[3635,63983,63984],{},[895,63985,63986,63988,63990,63992,63994,63996,63998,64000,64002,64004,64006,64008,64010,64012,64018,64020,64022,64024,64026,64028,64030,64032,64034,64036],{},[898,63987,3890],{"mathvariant":1704},[898,63989,2663],{},[898,63991,2666],{},[1915,63993,1917],{},[1693,63995,4110],{},[1915,63997,1917],{},[898,63999,1771],{"mathvariant":1704},[898,64001,2663],{},[898,64003,2666],{},[1693,64005,1695],{},[1693,64007,1709],{"stretchy":1708},[898,64009,2663],{},[898,64011,2666],{},[1717,64013,64014,64016],{},[1693,64015,1731],{"stretchy":1708},[1693,64017,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,64019,2239],{},[898,64021,1771],{"mathvariant":1704},[898,64023,1712],{},[1693,64025,1695],{},[898,64027,2839],{},[898,64029,2666],{},[1915,64031,2239],{},[898,64033,1771],{"mathvariant":1704},[898,64035,1712],{},[1693,64037,1899],{"separator":1898},[3635,64039],{"width":34864},[3635,64041,64042],{},[1915,64043,64044],{},"(3.3)",[902,64046,64047],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,64049,64050],{},"schematicky:",[883,64052,64054],{"className":64053},[886],[888,64055,64056],{"xmlns":890,"display":34854},[892,64057,64058,64166],{},[895,64059,64060,64098,64100,64102,64104,64133,64136,64164],{},[895,64061,64062,64065,64071,64074,64080,64083,64089,64095],{},[1915,64063,64064],{},"zm",[4467,64066,64067,64069],{"accent":1898},[1915,64068,52496],{},[1693,64070,6552],{},[1915,64072,64073],{},"na celkov",[4467,64075,64076,64078],{"accent":1898},[1915,64077,52496],{},[1693,64079,4474],{},[1915,64081,64082],{},"ho p",[4467,64084,64085,64087],{"accent":1898},[1915,64086,6629],{},[1693,64088,6552],{},[4467,64090,64091,64093],{"accent":1898},[1915,64092,4471],{},[1693,64094,4474],{},[1915,64096,64097],{},"jmu",[1915,64099,1917],{},[1693,64101,4110],{},[1915,64103,1917],{},[895,64105,64106,64109,64115,64118,64124,64130],{},[1915,64107,64108],{},"mezn",[4467,64110,64111,64113],{"accent":1898},[1915,64112,4471],{},[1693,64114,4474],{},[1915,64116,64117],{}," p",[4467,64119,64120,64122],{"accent":1898},[1915,64121,6629],{},[1693,64123,6552],{},[4467,64125,64126,64128],{"accent":1898},[1915,64127,4471],{},[1693,64129,4474],{},[1915,64131,64132],{},"jem",[1693,64134,64135],{},"×",[895,64137,64138,64140,64146,64149,64155,64158],{},[1915,64139,64064],{},[4467,64141,64142,64144],{"accent":1898},[1915,64143,52496],{},[1693,64145,6552],{},[1915,64147,64148],{},"na mno",[4467,64150,64151,64153],{"accent":1898},[1915,64152,16449],{},[1693,64154,6552],{},[1915,64156,64157],{},"stv",[4467,64159,64160,64162],{"accent":1898},[1915,64161,4471],{},[1693,64163,4474],{},[898,64165,1789],{"mathvariant":1704},[902,64167,64168],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,64170,64171,64172,64187],{},"Pro porovnání skutečná změna ",[883,64173,64175],{"className":64174},[886],[888,64176,64177],{"xmlns":890},[892,64178,64179,64185],{},[895,64180,64181,64183],{},[898,64182,2663],{},[898,64184,2666],{},[902,64186,2883],{"encoding":904}," je",[883,64189,64191],{"className":64190},[886],[888,64192,64193],{"xmlns":890,"display":34854},[892,64194,64195,64250],{},[3626,64196,64197],{"width":34859},[3632,64198,64199,64201,64243,64245],{},[3635,64200],{"width":34864},[3635,64202,64203],{},[895,64204,64205,64207,64209,64211,64213,64215,64217,64219,64221,64223,64225,64227,64229,64231,64233,64235,64237,64239,64241],{},[898,64206,3890],{"mathvariant":1704},[898,64208,2663],{},[898,64210,2666],{},[1693,64212,1695],{},[898,64214,2663],{},[898,64216,2666],{},[1693,64218,1709],{"stretchy":1708},[898,64220,1712],{},[1693,64222,1892],{},[898,64224,1771],{"mathvariant":1704},[898,64226,1712],{},[1693,64228,1731],{"stretchy":1708},[1693,64230,1698],{},[898,64232,2663],{},[898,64234,2666],{},[1693,64236,1709],{"stretchy":1708},[898,64238,1712],{},[1693,64240,1731],{"stretchy":1708},[898,64242,1789],{"mathvariant":1704},[3635,64244],{"width":34864},[3635,64246,64247],{},[1915,64248,64249],{},"(3.4)",[902,64251,64252],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[44125,64254,64256],{"id":64255},"příklad-33","Příklad 3.3",[724,64258,64259,64261,64262,64292,64293,9563,64308,9577,64321,9591,64334,64348],{},[38,64260,62731],{}," Pro ",[883,64263,64265],{"className":64264},[886],[888,64266,64267],{"xmlns":890},[892,64268,64269,64289],{},[895,64270,64271,64273,64275,64277,64279,64281,64283],{},[898,64272,2663],{},[898,64274,2666],{},[1693,64276,1695],{},[1762,64278,9987],{},[898,64280,1712],{},[1693,64282,1698],{},[1717,64284,64285,64287],{},[898,64286,1712],{},[1762,64288,2398],{},[902,64290,64291],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,64294,64296],{"className":64295},[886],[888,64297,64298],{"xmlns":890},[892,64299,64300,64306],{},[895,64301,64302,64304],{},[898,64303,2663],{},[898,64305,2666],{},[902,64307,2883],{"encoding":904},[883,64309,64311],{"className":64310},[886],[888,64312,64313],{"xmlns":890},[892,64314,64315,64319],{},[895,64316,64317],{},[898,64318,1712],{},[902,64320,1712],{"encoding":904},[883,64322,64324],{"className":64323},[886],[888,64325,64326],{"xmlns":890},[892,64327,64328,64332],{},[895,64329,64330],{},[1762,64331,10023],{},[902,64333,10023],{"encoding":904},[883,64335,64337],{"className":64336},[886],[888,64338,64339],{"xmlns":890},[892,64340,64341,64346],{},[895,64342,64343],{},[1762,64344,64345],{},"63",[902,64347,64345],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,64350,64351,1863,64353,64378,64379,1343,64397,4300],{},[38,64352,29570],{},[883,64354,64356],{"className":64355},[886],[888,64357,64358],{"xmlns":890},[892,64359,64360,64376],{},[895,64361,64362,64364,64366,64368,64370,64372,64374],{},[898,64363,2839],{},[898,64365,2666],{},[1693,64367,1695],{},[1762,64369,9987],{},[1693,64371,1698],{},[1762,64373,2398],{},[898,64375,1712],{},[902,64377,18281],{"encoding":904},", tedy při ",[883,64380,64382],{"className":64381},[886],[888,64383,64384],{"xmlns":890},[892,64385,64386,64394],{},[895,64387,64388,64390,64392],{},[898,64389,1712],{},[1693,64391,1695],{},[1762,64393,10023],{},[902,64395,64396],{"encoding":904},"Q = 60",[883,64398,64400],{"className":64399},[886],[888,64401,64402],{"xmlns":890},[892,64403,64404,64414],{},[895,64405,64406,64408,64410,64412],{},[898,64407,1771],{"mathvariant":1704},[898,64409,1712],{},[1693,64411,1695],{},[1762,64413,8357],{},[902,64415,64416],{"encoding":904},"\\mathrm{d}Q = 3",[883,64418,64420],{"className":64419},[886],[888,64421,64422],{"xmlns":890,"display":34854},[892,64423,64424,64455],{},[895,64425,64426,64428,64430,64432,64434,64436,64438,64440,64442,64444,64446,64448,64450,64452],{},[898,64427,1771],{"mathvariant":1704},[898,64429,2663],{},[898,64431,2666],{},[1693,64433,1695],{},[1693,64435,1709],{"stretchy":1708},[1762,64437,9987],{},[1693,64439,1698],{},[1762,64441,10928],{},[1693,64443,1731],{"stretchy":1708},[1693,64445,1715],{},[1762,64447,8357],{},[1693,64449,1695],{},[1693,64451,1698],{},[1762,64453,64454],{},"60.",[902,64456,64457],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,64459,64460,64461,64491,64492,64511],{},"Celkový příjem klesne z ",[883,64462,64464],{"className":64463},[886],[888,64465,64466],{"xmlns":890},[892,64467,64468,64488],{},[895,64469,64470,64472,64474,64476,64478,64480,64482,64484,64486],{},[898,64471,2663],{},[898,64473,2666],{},[1693,64475,1709],{"stretchy":1708},[1762,64477,10023],{},[1693,64479,1731],{"stretchy":1708},[1693,64481,1695],{},[1762,64483,2398],{},[1915,64485,2239],{},[1762,64487,26949],{},[902,64489,64490],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,64493,64495],{"className":64494},[886],[888,64496,64497],{"xmlns":890},[892,64498,64499,64508],{},[895,64500,64501,64503,64505],{},[1762,64502,2398],{},[1915,64504,2239],{},[1762,64506,64507],{},"340",[902,64509,64510],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,64513,64515],{"className":64514},[886],[888,64516,64517],{"xmlns":890,"display":34854},[892,64518,64519,64577],{},[895,64520,64521,64523,64525,64527,64529,64531,64533,64535,64537,64539,64541,64543,64545,64547,64549,64551,64553,64555,64557,64560,64562,64564,64566,64568,64570,64572,64575],{},[898,64522,3890],{"mathvariant":1704},[898,64524,2663],{},[898,64526,2666],{},[1693,64528,1695],{},[898,64530,2663],{},[898,64532,2666],{},[1693,64534,1709],{"stretchy":1708},[1762,64536,64345],{},[1693,64538,1731],{"stretchy":1708},[1693,64540,1698],{},[898,64542,2663],{},[898,64544,2666],{},[1693,64546,1709],{"stretchy":1708},[1762,64548,10023],{},[1693,64550,1731],{"stretchy":1708},[1693,64552,1695],{},[1762,64554,2398],{},[1915,64556,2239],{},[1762,64558,64559],{},"331",[1693,64561,1698],{},[1762,64563,2398],{},[1915,64565,2239],{},[1762,64567,26949],{},[1693,64569,1695],{},[1693,64571,1698],{},[1762,64573,64574],{},"69",[1693,64576,1899],{"separator":1898},[902,64578,64579],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,64581,64582,64583,64598,64599,1789],{},"tj. ",[883,64584,64586],{"className":64585},[886],[888,64587,64588],{"xmlns":890},[892,64589,64590,64596],{},[895,64591,64592,64594],{},[898,64593,2663],{},[898,64595,2666],{},[902,64597,2883],{"encoding":904}," klesne na ",[883,64600,64602],{"className":64601},[886],[888,64603,64604],{"xmlns":890},[892,64605,64606,64614],{},[895,64607,64608,64610,64612],{},[1762,64609,2398],{},[1915,64611,2239],{},[1762,64613,64559],{},[902,64615,64616],{"encoding":904},"2\\,331",[198,64618,64620],{"id":64619},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,64622,64623,64624,17244,64647,38363],{},"Obecně pro lineární poptávku ",[883,64625,64627],{"className":64626},[886],[888,64628,64629],{"xmlns":890},[892,64630,64631,64645],{},[895,64632,64633,64635,64637,64639,64641,64643],{},[898,64634,1701],{},[1693,64636,1695],{},[898,64638,207],{},[898,64640,1712],{},[1693,64642,1892],{},[898,64644,1895],{},[902,64646,43837],{"encoding":904},[883,64648,64650],{"className":64649},[886],[888,64651,64652],{"xmlns":890},[892,64653,64654,64676],{},[895,64655,64656,64658,64660,64662,64664,64670,64672,64674],{},[898,64657,2663],{},[898,64659,2666],{},[1693,64661,1695],{},[898,64663,207],{},[1717,64665,64666,64668],{},[898,64667,1712],{},[1762,64669,2398],{},[1693,64671,1892],{},[898,64673,1895],{},[898,64675,1712],{},[902,64677,64678],{"encoding":904},"TR = aQ^2 + bQ",[883,64680,64682],{"className":64681},[886],[888,64683,64684],{"xmlns":890,"display":34854},[892,64685,64686,64706],{},[895,64687,64688,64690,64692,64694,64696,64698,64700,64702,64704],{},[898,64689,2839],{},[898,64691,2666],{},[1693,64693,1695],{},[1762,64695,2398],{},[898,64697,207],{},[898,64699,1712],{},[1693,64701,1892],{},[898,64703,1895],{},[898,64705,1789],{"mathvariant":1704},[902,64707,64708],{"encoding":904},"MR = 2aQ + b.",[724,64710,64711,64712,64727,64728,64743,64744,64757,64758,16877,64761,64777,64778,64791,64792,64807,64808,64823,64824,64839,64840,9530,64853,64883,64884,64903,64904,64919],{},"Křivky ",[883,64713,64715],{"className":64714},[886],[888,64716,64717],{"xmlns":890},[892,64718,64719,64725],{},[895,64720,64721,64723],{},[898,64722,2839],{},[898,64724,2666],{},[902,64726,2919],{"encoding":904}," a poptávky (resp. ",[883,64729,64731],{"className":64730},[886],[888,64732,64733],{"xmlns":890},[892,64734,64735,64741],{},[895,64736,64737,64739],{},[898,64738,2719],{},[898,64740,2666],{},[902,64742,2820],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,64745,64747],{"className":64746},[886],[888,64748,64749],{"xmlns":890},[892,64750,64751,64755],{},[895,64752,64753],{},[898,64754,1895],{},[902,64756,1895],{"encoding":904},", přičemž ",[38,64759,64760],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,64762,64764],{"className":64763},[886],[888,64765,64766],{"xmlns":890},[892,64767,64768,64774],{},[895,64769,64770,64772],{},[1762,64771,2398],{},[898,64773,207],{},[902,64775,64776],{"encoding":904},"2a"," vs. ",[883,64779,64781],{"className":64780},[886],[888,64782,64783],{"xmlns":890},[892,64784,64785,64789],{},[895,64786,64787],{},[898,64788,207],{},[902,64790,207],{"encoding":904},", obrázek 3.2). ",[883,64793,64795],{"className":64794},[886],[888,64796,64797],{"xmlns":890},[892,64798,64799,64805],{},[895,64800,64801,64803],{},[898,64802,2839],{},[898,64804,2666],{},[902,64806,2919],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,64809,64811],{"className":64810},[886],[888,64812,64813],{"xmlns":890},[892,64814,64815,64821],{},[895,64816,64817,64819],{},[898,64818,2663],{},[898,64820,2666],{},[902,64822,2883],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,64825,64827],{"className":64826},[886],[888,64828,64829],{"xmlns":890},[892,64830,64831,64837],{},[895,64832,64833,64835],{},[898,64834,2839],{},[898,64836,2666],{},[902,64838,2919],{"encoding":904}," osu ",[883,64841,64843],{"className":64842},[886],[888,64844,64845],{"xmlns":890},[892,64846,64847,64851],{},[895,64848,64849],{},[898,64850,1712],{},[902,64852,1712],{"encoding":904},[883,64854,64856],{"className":64855},[886],[888,64857,64858],{"xmlns":890},[892,64859,64860,64880],{},[895,64861,64862,64864,64866,64868],{},[898,64863,1712],{},[1693,64865,1695],{},[1693,64867,1698],{},[3638,64869,64870],{"scriptlevel":1911,"displaystyle":1708},[2132,64871,64872,64874],{},[898,64873,1895],{},[895,64875,64876,64878],{},[1762,64877,2398],{},[898,64879,207],{},[902,64881,64882],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,64885,64887],{"className":64886},[886],[888,64888,64889],{"xmlns":890},[892,64890,64891,64901],{},[895,64892,64893,64895,64897,64899],{},[898,64894,2839],{},[898,64896,2666],{},[1693,64898,1695],{},[1762,64900,1911],{},[902,64902,4425],{"encoding":904},", a dále ",[883,64905,64907],{"className":64906},[886],[888,64908,64909],{"xmlns":890},[892,64910,64911,64917],{},[895,64912,64913,64915],{},[898,64914,2663],{},[898,64916,2666],{},[902,64918,2883],{"encoding":904}," klesá.",[724,64921,64922,64923,64929,64930,64962,64963,64991],{},"V případě ",[38,64924,64925],{},[207,64926,64928],{"className":64927,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,64931,64933],{"className":64932},[886],[888,64934,64935],{"xmlns":890},[892,64936,64937,64959],{},[895,64938,64939,64941,64943,64945,64947,64949,64951,64953],{},[898,64940,1701],{},[1693,64942,1695],{},[898,64944,2738],{},[1693,64946,1709],{"stretchy":1708},[898,64948,1712],{},[1693,64950,1731],{"stretchy":1708},[1693,64952,1695],{},[1717,64954,64955,64957],{},[898,64956,1701],{},[1693,64958,3672],{},[902,64960,64961],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,64964,64966],{"className":64965},[886],[888,64967,64968],{"xmlns":890},[892,64969,64970,64988],{},[895,64971,64972,64974,64976,64978,64980,64982],{},[898,64973,2663],{},[898,64975,2666],{},[1693,64977,1695],{},[898,64979,1712],{},[1693,64981,1715],{},[1717,64983,64984,64986],{},[898,64985,1701],{},[1693,64987,3672],{},[902,64989,64990],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,64993,64995],{"className":64994},[886],[888,64996,64997],{"xmlns":890,"display":34854},[892,64998,64999,65041],{},[895,65000,65001,65003,65005,65007,65009,65011,65013,65019,65021,65023,65037,65039],{},[898,65002,2839],{},[898,65004,2666],{},[1693,65006,1695],{},[898,65008,2719],{},[898,65010,2666],{},[1693,65012,1695],{},[1717,65014,65015,65017],{},[898,65016,1701],{},[1693,65018,3672],{},[1901,65020],{"width":3630},[1693,65022,1709],{"stretchy":1708},[895,65024,65025,65028,65034],{},[1915,65026,65027],{},"obr",[4467,65029,65030,65032],{"accent":1898},[1915,65031,207],{},[1693,65033,4474],{},[1915,65035,65036],{},"zek 3.4",[1693,65038,1731],{"stretchy":1708},[898,65040,1789],{"mathvariant":1704},[902,65042,65043],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,65045,65046],{},[614,65047,65048,65049,4286,65075,65103,65104,65117,65118,65133,65134,1654,65147,1343,65173,1654,65188,1789],{},"Obrázek 3.2: Přímky ",[883,65050,65052],{"className":65051},[886],[888,65053,65054],{"xmlns":890},[892,65055,65056,65072],{},[895,65057,65058,65060,65062,65064,65066,65068,65070],{},[898,65059,2719],{},[898,65061,2666],{},[1693,65063,1695],{},[898,65065,207],{},[898,65067,1712],{},[1693,65069,1892],{},[898,65071,1895],{},[902,65073,65074],{"encoding":904},"AR = aQ + b",[883,65076,65078],{"className":65077},[886],[888,65079,65080],{"xmlns":890},[892,65081,65082,65100],{},[895,65083,65084,65086,65088,65090,65092,65094,65096,65098],{},[898,65085,2839],{},[898,65087,2666],{},[1693,65089,1695],{},[1762,65091,2398],{},[898,65093,207],{},[898,65095,1712],{},[1693,65097,1892],{},[898,65099,1895],{},[902,65101,65102],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,65105,65107],{"className":65106},[886],[888,65108,65109],{"xmlns":890},[892,65110,65111,65115],{},[895,65112,65113],{},[898,65114,1895],{},[902,65116,1895],{"encoding":904}," se svislou osou, ",[883,65119,65121],{"className":65120},[886],[888,65122,65123],{"xmlns":890},[892,65124,65125,65131],{},[895,65126,65127,65129],{},[898,65128,2839],{},[898,65130,2666],{},[902,65132,2919],{"encoding":904}," protíná osu ",[883,65135,65137],{"className":65136},[886],[888,65138,65139],{"xmlns":890},[892,65140,65141,65145],{},[895,65142,65143],{},[898,65144,1712],{},[902,65146,1712],{"encoding":904},[883,65148,65150],{"className":65149},[886],[888,65151,65152],{"xmlns":890},[892,65153,65154,65170],{},[895,65155,65156,65158],{},[1693,65157,1698],{},[3638,65159,65160],{"scriptlevel":1911,"displaystyle":1708},[2132,65161,65162,65164],{},[898,65163,1895],{},[895,65165,65166,65168],{},[1762,65167,2398],{},[898,65169,207],{},[902,65171,65172],{"encoding":904},"-\\tfrac{b}{2a}",[883,65174,65176],{"className":65175},[886],[888,65177,65178],{"xmlns":890},[892,65179,65180,65186],{},[895,65181,65182,65184],{},[898,65183,2719],{},[898,65185,2666],{},[902,65187,2820],{"encoding":904},[883,65189,65191],{"className":65190},[886],[888,65192,65193],{"xmlns":890},[892,65194,65195,65207],{},[895,65196,65197,65199],{},[1693,65198,1698],{},[3638,65200,65201],{"scriptlevel":1911,"displaystyle":1708},[2132,65202,65203,65205],{},[898,65204,1895],{},[898,65206,207],{},[902,65208,65209],{"encoding":904},"-\\tfrac{b}{a}",[724,65211,65212],{},[614,65213,65214,65215,65246,65247,65276,65277,1789],{},"Obrázek 3.3: Parabola ",[883,65216,65218],{"className":65217},[886],[888,65219,65220],{"xmlns":890},[892,65221,65222,65244],{},[895,65223,65224,65226,65228,65230,65232,65238,65240,65242],{},[898,65225,2663],{},[898,65227,2666],{},[1693,65229,1695],{},[898,65231,207],{},[1717,65233,65234,65236],{},[898,65235,1712],{},[1762,65237,2398],{},[1693,65239,1892],{},[898,65241,1895],{},[898,65243,1712],{},[902,65245,64678],{"encoding":904}," s maximem v ",[883,65248,65250],{"className":65249},[886],[888,65251,65252],{"xmlns":890},[892,65253,65254,65274],{},[895,65255,65256,65258,65260,65262],{},[898,65257,1712],{},[1693,65259,1695],{},[1693,65261,1698],{},[3638,65263,65264],{"scriptlevel":1911,"displaystyle":1708},[2132,65265,65266,65268],{},[898,65267,1895],{},[895,65269,65270,65272],{},[1762,65271,2398],{},[898,65273,207],{},[902,65275,64882],{"encoding":904}," a nulou v ",[883,65278,65280],{"className":65279},[886],[888,65281,65282],{"xmlns":890},[892,65283,65284,65300],{},[895,65285,65286,65288,65290,65292],{},[898,65287,1712],{},[1693,65289,1695],{},[1693,65291,1698],{},[3638,65293,65294],{"scriptlevel":1911,"displaystyle":1708},[2132,65295,65296,65298],{},[898,65297,1895],{},[898,65299,207],{},[902,65301,65302],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,65304,65305],{},[614,65306,65307,65308,1789],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,65309,65311],{"className":65310},[886],[888,65312,65313],{"xmlns":890},[892,65314,65315,65335],{},[895,65316,65317,65319,65321,65323,65325,65327,65329],{},[898,65318,2719],{},[898,65320,2666],{},[1693,65322,1695],{},[898,65324,2839],{},[898,65326,2666],{},[1693,65328,1695],{},[1717,65330,65331,65333],{},[898,65332,1701],{},[1693,65334,3672],{},[902,65336,65337],{"encoding":904},"AR = MR = P^*",[115,65339,65341],{"id":65340},"náklady-firmy","Náklady firmy",[198,65343,2955],{"id":2954},[724,65345,65346,1863,65348,16877,65363,65366,65367,65380],{},[38,65347,2955],{},[883,65349,65351],{"className":65350},[886],[888,65352,65353],{"xmlns":890},[892,65354,65355,65361],{},[895,65356,65357,65359],{},[898,65358,2663],{},[898,65360,2971],{},[902,65362,3225],{"encoding":904},[38,65364,65365],{},"total cost",") jsou veškeré náklady na realizaci ",[883,65368,65370],{"className":65369},[886],[888,65371,65372],{"xmlns":890},[892,65373,65374,65378],{},[895,65375,65376],{},[898,65377,1712],{},[902,65379,1712],{"encoding":904}," jednotek produkce:",[883,65382,65384],{"className":65383},[886],[888,65385,65386],{"xmlns":890,"display":34854},[892,65387,65388,65443],{},[3626,65389,65390],{"width":34859},[3632,65391,65392,65394,65436,65438],{},[3635,65393],{"width":34864},[3635,65395,65396],{},[895,65397,65398,65400,65402,65404,65406,65408,65410,65412,65414,65416,65418,65420,65422,65424,65426,65428,65430,65432,65434],{},[898,65399,2663],{},[898,65401,2971],{},[1693,65403,1695],{},[898,65405,2663],{},[898,65407,2971],{},[1693,65409,1709],{"stretchy":1708},[898,65411,1712],{},[1693,65413,1731],{"stretchy":1708},[1693,65415,1695],{},[898,65417,2976],{},[898,65419,2971],{},[1693,65421,1892],{},[898,65423,2663],{},[898,65425,2985],{},[898,65427,2971],{},[1693,65429,1709],{"stretchy":1708},[898,65431,1712],{},[1693,65433,1731],{"stretchy":1708},[1693,65435,1899],{"separator":1898},[3635,65437],{"width":34864},[3635,65439,65440],{},[1915,65441,65442],{},"(3.5)",[902,65444,65445],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,65447,11188,65448,65463,65464,16877,65467,8586,65470,65463,65494,16877,65497,65500],{},[883,65449,65451],{"className":65450},[886],[888,65452,65453],{"xmlns":890},[892,65454,65455,65461],{},[895,65456,65457,65459],{},[898,65458,2976],{},[898,65460,2971],{},[902,65462,3022],{"encoding":904}," jsou ",[38,65465,65466],{},"fixní náklady",[38,65468,65469],{},"fixed cost",[883,65471,65473],{"className":65472},[886],[888,65474,65475],{"xmlns":890},[892,65476,65477,65491],{},[895,65478,65479,65481,65483,65485,65487,65489],{},[898,65480,2663],{},[898,65482,2985],{},[898,65484,2971],{},[1693,65486,1709],{"stretchy":1708},[898,65488,1712],{},[1693,65490,1731],{"stretchy":1708},[902,65492,65493],{"encoding":904},"TVC(Q)",[38,65495,65496],{},"celkové variabilní náklady",[38,65498,65499],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,65502,3046],{"id":3045},[724,65504,65505,1863,65507,16877,65522,65525],{},[38,65506,3046],{},[883,65508,65510],{"className":65509},[886],[888,65511,65512],{"xmlns":890},[892,65513,65514,65520],{},[895,65515,65516,65518],{},[898,65517,2719],{},[898,65519,2971],{},[902,65521,3331],{"encoding":904},[38,65523,65524],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,65527,65529],{"className":65528},[886],[888,65530,65531],{"xmlns":890,"display":34854},[892,65532,65533,65612],{},[3626,65534,65535],{"width":34859},[3632,65536,65537,65539,65605,65607],{},[3635,65538],{"width":34864},[3635,65540,65541],{},[895,65542,65543,65545,65547,65549,65551,65553,65555,65557,65559,65561,65571,65573,65583,65585,65603],{},[898,65544,2719],{},[898,65546,2971],{},[1693,65548,1695],{},[898,65550,2719],{},[898,65552,2971],{},[1693,65554,1709],{"stretchy":1708},[898,65556,1712],{},[1693,65558,1731],{"stretchy":1708},[1693,65560,1695],{},[2132,65562,65563,65569],{},[895,65564,65565,65567],{},[898,65566,2663],{},[898,65568,2971],{},[898,65570,1712],{},[1693,65572,1695],{},[2132,65574,65575,65581],{},[895,65576,65577,65579],{},[898,65578,2976],{},[898,65580,2971],{},[898,65582,1712],{},[1693,65584,1892],{},[2132,65586,65587,65601],{},[895,65588,65589,65591,65593,65595,65597,65599],{},[898,65590,2663],{},[898,65592,2985],{},[898,65594,2971],{},[1693,65596,1709],{"stretchy":1708},[898,65598,1712],{},[1693,65600,1731],{"stretchy":1708},[898,65602,1712],{},[1693,65604,1899],{"separator":1898},[3635,65606],{"width":34864},[3635,65608,65609],{},[1915,65610,65611],{},"(3.6)",[902,65613,65614],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,65616,11188,65617,65463,65641,1863,65644,16877,65661,8586,65664,65463,65696,1863,65699,16877,65716,10048],{},[883,65618,65620],{"className":65619},[886],[888,65621,65622],{"xmlns":890},[892,65623,65624,65638],{},[895,65625,65626],{},[3638,65627,65628],{"scriptlevel":1911,"displaystyle":1708},[2132,65629,65630,65636],{},[895,65631,65632,65634],{},[898,65633,2976],{},[898,65635,2971],{},[898,65637,1712],{},[902,65639,65640],{"encoding":904},"\\tfrac{FC}{Q}",[38,65642,65643],{},"průměrné fixní náklady",[883,65645,65647],{"className":65646},[886],[888,65648,65649],{"xmlns":890},[892,65650,65651,65659],{},[895,65652,65653,65655,65657],{},[898,65654,2719],{},[898,65656,2976],{},[898,65658,2971],{},[902,65660,3150],{"encoding":904},[38,65662,65663],{},"average fixed cost",[883,65665,65667],{"className":65666},[886],[888,65668,65669],{"xmlns":890},[892,65670,65671,65693],{},[895,65672,65673],{},[3638,65674,65675],{"scriptlevel":1911,"displaystyle":1708},[2132,65676,65677,65691],{},[895,65678,65679,65681,65683,65685,65687,65689],{},[898,65680,2663],{},[898,65682,2985],{},[898,65684,2971],{},[1693,65686,1709],{"stretchy":1708},[898,65688,1712],{},[1693,65690,1731],{"stretchy":1708},[898,65692,1712],{},[902,65694,65695],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,65697,65698],{},"průměrné variabilní náklady",[883,65700,65702],{"className":65701},[886],[888,65703,65704],{"xmlns":890},[892,65705,65706,65714],{},[895,65707,65708,65710,65712],{},[898,65709,2719],{},[898,65711,2985],{},[898,65713,2971],{},[902,65715,3789],{"encoding":904},[38,65717,65718],{},"average variable cost",[883,65720,65722],{"className":65721},[886],[888,65723,65724],{"xmlns":890,"display":34854},[892,65725,65726,65785],{},[3626,65727,65728],{"width":34859},[3632,65729,65730,65732,65778,65780],{},[3635,65731],{"width":34864},[3635,65733,65734],{},[895,65735,65736,65738,65740,65742,65744,65746,65748,65750,65752,65754,65756,65758,65776],{},[898,65737,2719],{},[898,65739,2985],{},[898,65741,2971],{},[1693,65743,1695],{},[898,65745,2719],{},[898,65747,2985],{},[898,65749,2971],{},[1693,65751,1709],{"stretchy":1708},[898,65753,1712],{},[1693,65755,1731],{"stretchy":1708},[1693,65757,1695],{},[2132,65759,65760,65774],{},[895,65761,65762,65764,65766,65768,65770,65772],{},[898,65763,2663],{},[898,65765,2985],{},[898,65767,2971],{},[1693,65769,1709],{"stretchy":1708},[898,65771,1712],{},[1693,65773,1731],{"stretchy":1708},[898,65775,1712],{},[898,65777,1789],{"mathvariant":1704},[3635,65779],{"width":34864},[3635,65781,65782],{},[1915,65783,65784],{},"(3.7)",[902,65786,65787],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[44125,65789,65791],{"id":65790},"příklad-34","Příklad 3.4",[724,65793,65794,64261,65796,4286,65821,62769,65845,4286,65860,65875,65876,1789],{},[38,65795,62731],{},[883,65797,65799],{"className":65798},[886],[888,65800,65801],{"xmlns":890},[892,65802,65803,65818],{},[895,65804,65805,65807,65809,65811,65813,65815],{},[898,65806,2976],{},[898,65808,2971],{},[1693,65810,1695],{},[1762,65812,1764],{},[1915,65814,2239],{},[1762,65816,65817],{},"000",[902,65819,65820],{"encoding":904},"FC = 1\\,000",[883,65822,65824],{"className":65823},[886],[888,65825,65826],{"xmlns":890},[892,65827,65828,65842],{},[895,65829,65830,65832,65834,65836,65838,65840],{},[898,65831,2663],{},[898,65833,2985],{},[898,65835,2971],{},[1693,65837,1695],{},[1762,65839,9262],{},[898,65841,1712],{},[902,65843,65844],{"encoding":904},"TVC = 4Q",[883,65846,65848],{"className":65847},[886],[888,65849,65850],{"xmlns":890},[892,65851,65852,65858],{},[895,65853,65854,65856],{},[898,65855,2663],{},[898,65857,2971],{},[902,65859,3225],{"encoding":904},[883,65861,65863],{"className":65862},[886],[888,65864,65865],{"xmlns":890},[892,65866,65867,65873],{},[895,65868,65869,65871],{},[898,65870,2719],{},[898,65872,2971],{},[902,65874,3331],{"encoding":904}," a jejich chování s rostoucím ",[883,65877,65879],{"className":65878},[886],[888,65880,65881],{"xmlns":890},[892,65882,65883,65887],{},[895,65884,65885],{},[898,65886,1712],{},[902,65888,1712],{"encoding":904},[724,65890,65891,1863,65893,4286,65923,65959,65960,2783,65973,65988,65989,4300],{},[38,65892,29570],{},[883,65894,65896],{"className":65895},[886],[888,65897,65898],{"xmlns":890},[892,65899,65900,65920],{},[895,65901,65902,65904,65906,65908,65910,65912,65914,65916,65918],{},[898,65903,2663],{},[898,65905,2971],{},[1693,65907,1695],{},[1762,65909,1764],{},[1915,65911,2239],{},[1762,65913,65817],{},[1693,65915,1892],{},[1762,65917,9262],{},[898,65919,1712],{},[902,65921,65922],{"encoding":904},"TC = 1\\,000 + 4Q",[883,65924,65926],{"className":65925},[886],[888,65927,65928],{"xmlns":890},[892,65929,65930,65956],{},[895,65931,65932,65934,65936,65938,65952,65954],{},[898,65933,2719],{},[898,65935,2971],{},[1693,65937,1695],{},[3638,65939,65940],{"scriptlevel":1911,"displaystyle":1708},[2132,65941,65942,65950],{},[895,65943,65944,65946,65948],{},[1762,65945,1764],{},[1915,65947,2239],{},[1762,65949,65817],{},[898,65951,1712],{},[1693,65953,1892],{},[1762,65955,9262],{},[902,65957,65958],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,65961,65963],{"className":65962},[886],[888,65964,65965],{"xmlns":890},[892,65966,65967,65971],{},[895,65968,65969],{},[898,65970,1712],{},[902,65972,1712],{"encoding":904},[883,65974,65976],{"className":65975},[886],[888,65977,65978],{"xmlns":890},[892,65979,65980,65986],{},[895,65981,65982,65984],{},[898,65983,2719],{},[898,65985,2971],{},[902,65987,3331],{"encoding":904}," blíží ",[883,65990,65992],{"className":65991},[886],[888,65993,65994],{"xmlns":890},[892,65995,65996,66000],{},[895,65997,65998],{},[1762,65999,9262],{},[902,66001,9262],{"encoding":904},[883,66003,66005],{"className":66004},[886],[888,66006,66007],{"xmlns":890,"display":34854},[892,66008,66009,66055],{},[895,66010,66011,66028,66050,66052],{},[46670,66012,66013,66020],{},[895,66014,66015,66018],{},[898,66016,66017],{},"lim",[1693,66019,3742],{},[895,66021,66022,66024,66026],{},[898,66023,1712],{},[1693,66025,10020],{},[898,66027,13162],{"mathvariant":1704},[895,66029,66030,66032,66044,66046,66048],{},[1693,66031,1709],{"fence":1898},[2132,66033,66034,66042],{},[895,66035,66036,66038,66040],{},[1762,66037,1764],{},[1915,66039,2239],{},[1762,66041,65817],{},[898,66043,1712],{},[1693,66045,1892],{},[1762,66047,9262],{},[1693,66049,1731],{"fence":1898},[1693,66051,1695],{},[1762,66053,66054],{},"4.",[902,66056,66057],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,66059,66060,3151,66098,1789],{},[883,66061,66063],{"className":66062},[886],[888,66064,66065],{"xmlns":890},[892,66066,66067,66095],{},[895,66068,66069,66071,66073,66075,66077,66091,66093],{},[898,66070,2719],{},[898,66072,2976],{},[898,66074,2971],{},[1693,66076,1695],{},[3638,66078,66079],{"scriptlevel":1911,"displaystyle":1708},[2132,66080,66081,66089],{},[895,66082,66083,66085,66087],{},[1762,66084,1764],{},[1915,66086,2239],{},[1762,66088,65817],{},[898,66090,1712],{},[1693,66092,10020],{},[1762,66094,1911],{},[902,66096,66097],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0",[883,66099,66101],{"className":66100},[886],[888,66102,66103],{"xmlns":890},[892,66104,66105,66109],{},[895,66106,66107],{},[898,66108,1712],{},[902,66110,1712],{"encoding":904},[724,66112,66113],{},[614,66114,66115,66116,66145,66146,1789],{},"Obrázek 3.5: Přímka ",[883,66117,66119],{"className":66118},[886],[888,66120,66121],{"xmlns":890},[892,66122,66123,66143],{},[895,66124,66125,66127,66129,66131,66133,66135,66137,66139,66141],{},[898,66126,2663],{},[898,66128,2971],{},[1693,66130,1695],{},[1762,66132,1764],{},[1915,66134,2239],{},[1762,66136,65817],{},[1693,66138,1892],{},[1762,66140,9262],{},[898,66142,1712],{},[902,66144,65922],{"encoding":904}," protínající svislou osu ve výši ",[883,66147,66149],{"className":66148},[886],[888,66150,66151],{"xmlns":890},[892,66152,66153,66167],{},[895,66154,66155,66157,66159,66161,66163,66165],{},[898,66156,2976],{},[898,66158,2971],{},[1693,66160,1695],{},[1762,66162,1764],{},[1915,66164,2239],{},[1762,66166,65817],{},[902,66168,65820],{"encoding":904},[724,66170,66171],{},[614,66172,66173,66174,66209,66210,1789],{},"Obrázek 3.6: Hyperbola ",[883,66175,66177],{"className":66176},[886],[888,66178,66179],{"xmlns":890},[892,66180,66181,66207],{},[895,66182,66183,66185,66187,66189,66203,66205],{},[898,66184,2719],{},[898,66186,2971],{},[1693,66188,1695],{},[3638,66190,66191],{"scriptlevel":1911,"displaystyle":1708},[2132,66192,66193,66201],{},[895,66194,66195,66197,66199],{},[1762,66196,1764],{},[1915,66198,2239],{},[1762,66200,65817],{},[898,66202,1712],{},[1693,66204,1892],{},[1762,66206,9262],{},[902,66208,65958],{"encoding":904}," s vodorovnou asymptotou ",[883,66211,66213],{"className":66212},[886],[888,66214,66215],{"xmlns":890},[892,66216,66217,66227],{},[895,66218,66219,66221,66223,66225],{},[898,66220,2719],{},[898,66222,2971],{},[1693,66224,1695],{},[1762,66226,9262],{},[902,66228,66229],{"encoding":904},"AC = 4",[724,66231,66232],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,66234,66236],{"className":66235},[886],[888,66237,66238],{"xmlns":890,"display":34854},[892,66239,66240,66266],{},[895,66241,66242,66244,66246,66248,66250,66252,66254,66256,66258,66260,66262,66264],{},[898,66243,2663],{},[898,66245,2985],{},[898,66247,2971],{},[1693,66249,1695],{},[898,66251,1712],{},[1693,66253,1715],{},[898,66255,2985],{},[898,66257,2971],{},[1693,66259,1709],{"stretchy":1708},[898,66261,1712],{},[1693,66263,1731],{"stretchy":1708},[1693,66265,1899],{"separator":1898},[902,66267,66268],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,66270,11188,66271,65463,66299,66302,66303,66333],{},[883,66272,66274],{"className":66273},[886],[888,66275,66276],{"xmlns":890},[892,66277,66278,66296],{},[895,66279,66280,66282,66284,66286,66288,66290,66292,66294],{},[898,66281,2985],{},[898,66283,2971],{},[1693,66285,1695],{},[898,66287,2985],{},[898,66289,2971],{},[1693,66291,1709],{"stretchy":1708},[898,66293,1712],{},[1693,66295,1731],{"stretchy":1708},[902,66297,66298],{"encoding":904},"VC = VC(Q)",[38,66300,66301],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,66304,66306],{"className":66305},[886],[888,66307,66308],{"xmlns":890},[892,66309,66310,66330],{},[895,66311,66312,66314,66316,66318,66320,66322,66324,66326,66328],{},[898,66313,2663],{},[898,66315,2985],{},[898,66317,2971],{},[1693,66319,1709],{"stretchy":1708},[898,66321,1712],{},[1693,66323,1731],{"stretchy":1708},[1693,66325,1695],{},[898,66327,207],{},[898,66329,1712],{},[902,66331,66332],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,66335,66337],{"className":66336},[886],[888,66338,66339],{"xmlns":890,"display":34854},[892,66340,66341,66361],{},[895,66342,66343,66345,66347,66349,66351,66353,66355,66357,66359],{},[898,66344,2663],{},[898,66346,2971],{},[1693,66348,1695],{},[898,66350,2976],{},[898,66352,2971],{},[1693,66354,1892],{},[898,66356,207],{},[898,66358,1712],{},[898,66360,1789],{"mathvariant":1704},[902,66362,66363],{"encoding":904},"TC = FC + aQ.",[724,66365,66366,66367,66382,66383,66398,66399,66422,66423,66457,66458,66209,66471,66484,66485,4286,66533,66577,66578,1789],{},"Křivkou ",[883,66368,66370],{"className":66369},[886],[888,66371,66372],{"xmlns":890},[892,66373,66374,66380],{},[895,66375,66376,66378],{},[898,66377,2663],{},[898,66379,2971],{},[902,66381,3225],{"encoding":904}," je přímka se svislým průsečíkem ",[883,66384,66386],{"className":66385},[886],[888,66387,66388],{"xmlns":890},[892,66389,66390,66396],{},[895,66391,66392,66394],{},[898,66393,2976],{},[898,66395,2971],{},[902,66397,3022],{"encoding":904}," a sklonem ",[883,66400,66402],{"className":66401},[886],[888,66403,66404],{"xmlns":890},[892,66405,66406,66419],{},[895,66407,66408,66411,66413,66415,66417],{},[898,66409,66410],{},"tan",[1693,66412,3742],{},[898,66414,25673],{},[1693,66416,1695],{},[898,66418,207],{},[902,66420,66421],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,66424,66426],{"className":66425},[886],[888,66427,66428],{"xmlns":890},[892,66429,66430,66454],{},[895,66431,66432,66434,66436,66438,66450,66452],{},[898,66433,2719],{},[898,66435,2971],{},[1693,66437,1695],{},[3638,66439,66440],{"scriptlevel":1911,"displaystyle":1708},[2132,66441,66442,66448],{},[895,66443,66444,66446],{},[898,66445,2976],{},[898,66447,2971],{},[898,66449,1712],{},[1693,66451,1892],{},[898,66453,207],{},[902,66455,66456],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,66459,66461],{"className":66460},[886],[888,66462,66463],{"xmlns":890},[892,66464,66465,66469],{},[895,66466,66467],{},[898,66468,4840],{},[902,66470,4840],{"encoding":904},[883,66472,66474],{"className":66473},[886],[888,66475,66476],{"xmlns":890},[892,66477,66478,66482],{},[895,66479,66480],{},[898,66481,207],{},[902,66483,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,66486,66488],{"className":66487},[886],[888,66489,66490],{"xmlns":890},[892,66491,66492,66530],{},[895,66493,66494,66514,66526,66528],{},[3284,66495,66496,66502],{},[895,66497,66498,66500],{},[898,66499,66017],{},[1693,66501,3742],{},[895,66503,66504,66506,66508],{},[898,66505,1712],{},[1693,66507,10020],{},[1717,66509,66510,66512],{},[1762,66511,1911],{},[1693,66513,1892],{},[3638,66515,66516],{"scriptlevel":1911,"displaystyle":1708},[2132,66517,66518,66524],{},[895,66519,66520,66522],{},[898,66521,2976],{},[898,66523,2971],{},[898,66525,1712],{},[1693,66527,1695],{},[898,66529,13162],{"mathvariant":1704},[902,66531,66532],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,66534,66536],{"className":66535},[886],[888,66537,66538],{"xmlns":890},[892,66539,66540,66574],{},[895,66541,66542,66558,66570,66572],{},[3284,66543,66544,66550],{},[895,66545,66546,66548],{},[898,66547,66017],{},[1693,66549,3742],{},[895,66551,66552,66554,66556],{},[898,66553,1712],{},[1693,66555,10020],{},[898,66557,13162],{"mathvariant":1704},[3638,66559,66560],{"scriptlevel":1911,"displaystyle":1708},[2132,66561,66562,66568],{},[895,66563,66564,66566],{},[898,66565,2976],{},[898,66567,2971],{},[898,66569,1712],{},[1693,66571,1695],{},[1762,66573,1911],{},[902,66575,66576],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,66579,66581],{"className":66580},[886],[888,66582,66583],{"xmlns":890},[892,66584,66585,66591],{},[895,66586,66587,66589],{},[898,66588,2719],{},[898,66590,2971],{},[902,66592,3331],{"encoding":904},[724,66594,66595],{},[614,66596,66597,66598,66613,66614,66629,66630,1789],{},"Obrázek 3.7: Přímka ",[883,66599,66601],{"className":66600},[886],[888,66602,66603],{"xmlns":890},[892,66604,66605,66611],{},[895,66606,66607,66609],{},[898,66608,2663],{},[898,66610,2971],{},[902,66612,3225],{"encoding":904}," s osovým průsečíkem ve výši ",[883,66615,66617],{"className":66616},[886],[888,66618,66619],{"xmlns":890},[892,66620,66621,66627],{},[895,66622,66623,66625],{},[898,66624,2976],{},[898,66626,2971],{},[902,66628,3022],{"encoding":904}," a se sklonem ",[883,66631,66633],{"className":66632},[886],[888,66634,66635],{"xmlns":890},[892,66636,66637,66649],{},[895,66638,66639,66641,66643,66645,66647],{},[898,66640,66410],{},[1693,66642,3742],{},[898,66644,25673],{},[1693,66646,1695],{},[898,66648,207],{},[902,66650,66421],{"encoding":904},[724,66652,66653],{},[614,66654,66655,66656,66671,66672,1789],{},"Obrázek 3.8: Klesající hyperbola ",[883,66657,66659],{"className":66658},[886],[888,66660,66661],{"xmlns":890},[892,66662,66663,66669],{},[895,66664,66665,66667],{},[898,66666,2719],{},[898,66668,2971],{},[902,66670,3331],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,66673,66675],{"className":66674},[886],[888,66676,66677],{"xmlns":890},[892,66678,66679,66683],{},[895,66680,66681],{},[898,66682,207],{},[902,66684,207],{"encoding":904},[198,66686,3169],{"id":3168},[724,66688,66689,1863,66691,16877,66706,66709,66710,66713],{},[38,66690,3169],{},[883,66692,66694],{"className":66693},[886],[888,66695,66696],{"xmlns":890},[892,66697,66698,66704],{},[895,66699,66700,66702],{},[898,66701,2839],{},[898,66703,2971],{},[902,66705,3810],{"encoding":904},[38,66707,66708],{},"marginal cost",") jsou ",[207,66711,1145],{"className":66712,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,66715,66717],{"className":66716},[886],[888,66718,66719],{"xmlns":890,"display":34854},[892,66720,66721,66790],{},[3626,66722,66723],{"width":34859},[3632,66724,66725,66727,66783,66785],{},[3635,66726],{"width":34864},[3635,66728,66729],{},[895,66730,66731,66733,66735,66737,66739,66741,66743,66745,66747,66749,66765,66767,66769,66775,66777,66779,66781],{},[898,66732,2839],{},[898,66734,2971],{},[1693,66736,1695],{},[898,66738,2839],{},[898,66740,2971],{},[1693,66742,1709],{"stretchy":1708},[898,66744,1712],{},[1693,66746,1731],{"stretchy":1708},[1693,66748,1695],{},[2132,66750,66751,66759],{},[895,66752,66753,66755,66757],{},[898,66754,1771],{"mathvariant":1704},[898,66756,2663],{},[898,66758,2971],{},[895,66760,66761,66763],{},[898,66762,1771],{"mathvariant":1704},[898,66764,1712],{},[1693,66766,1695],{},[898,66768,2663],{},[1717,66770,66771,66773],{},[898,66772,2971],{},[1693,66774,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,66776,1709],{"stretchy":1708},[898,66778,1712],{},[1693,66780,1731],{"stretchy":1708},[898,66782,1789],{"mathvariant":1704},[3635,66784],{"width":34864},[3635,66786,66787],{},[1915,66788,66789],{},"(3.8)",[902,66791,66792],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1636,66794,66795],{},[724,66796,66797,66799,66800,66826,66827,66844,66845,1789],{},[883,66798,11036],{}," Intuice — „kolik stojí další kus\"\n",[883,66801,66803],{"className":66802},[886],[888,66804,66805],{"xmlns":890},[892,66806,66807,66823],{},[895,66808,66809,66811,66813,66815,66821],{},[898,66810,2839],{},[898,66812,2971],{},[1693,66814,1709],{"stretchy":1708},[1717,66816,66817,66819],{},[898,66818,1712],{},[1693,66820,3672],{},[1693,66822,1731],{"stretchy":1708},[902,66824,66825],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,66828,66830],{"className":66829},[886],[888,66831,66832],{"xmlns":890},[892,66833,66834,66842],{},[895,66835,66836],{},[1717,66837,66838,66840],{},[898,66839,1712],{},[1693,66841,3672],{},[902,66843,3770],{"encoding":904},". Formálně ",[883,66846,66848],{"className":66847},[886],[888,66849,66850],{"xmlns":890},[892,66851,66852,66904],{},[895,66853,66854,66856,66858,66860,66866,66868,66870,66872,66874,66876,66882,66884,66886,66888,66890,66892,66894,66896,66902],{},[898,66855,2839],{},[898,66857,2971],{},[1693,66859,1709],{"stretchy":1708},[1717,66861,66862,66864],{},[898,66863,1712],{},[1693,66865,3672],{},[1693,66867,1731],{"stretchy":1708},[1693,66869,4110],{},[898,66871,2663],{},[898,66873,2971],{},[1693,66875,1709],{"stretchy":1708},[1717,66877,66878,66880],{},[898,66879,1712],{},[1693,66881,3672],{},[1693,66883,1892],{},[1762,66885,1764],{},[1693,66887,1731],{"stretchy":1708},[1693,66889,1698],{},[898,66891,2663],{},[898,66893,2971],{},[1693,66895,1709],{"stretchy":1708},[1717,66897,66898,66900],{},[898,66899,1712],{},[1693,66901,3672],{},[1693,66903,1731],{"stretchy":1708},[902,66905,66906],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,66908,66909,66910,4300],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,66911,66913],{"className":66912},[886],[888,66914,66915],{"xmlns":890},[892,66916,66917,66925],{},[895,66918,66919,66921,66923],{},[898,66920,3890],{"mathvariant":1704},[898,66922,2663],{},[898,66924,2971],{},[902,66926,66927],{"encoding":904},"\\Delta TC",[883,66929,66931],{"className":66930},[886],[888,66932,66933],{"xmlns":890,"display":34854},[892,66934,66935,67004],{},[3626,66936,66937],{"width":34859},[3632,66938,66939,66941,66997,66999],{},[3635,66940],{"width":34864},[3635,66942,66943],{},[895,66944,66945,66947,66949,66951,66953,66955,66957,66959,66961,66963,66965,66967,66969,66971,66977,66979,66981,66983,66985,66987,66989,66991,66993,66995],{},[898,66946,3890],{"mathvariant":1704},[898,66948,2663],{},[898,66950,2971],{},[1915,66952,1917],{},[1693,66954,4110],{},[1915,66956,1917],{},[898,66958,1771],{"mathvariant":1704},[898,66960,2663],{},[898,66962,2971],{},[1693,66964,1695],{},[1693,66966,1709],{"stretchy":1708},[898,66968,2663],{},[898,66970,2971],{},[1717,66972,66973,66975],{},[1693,66974,1731],{"stretchy":1708},[1693,66976,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,66978,2239],{},[898,66980,1771],{"mathvariant":1704},[898,66982,1712],{},[1693,66984,1695],{},[898,66986,2839],{},[898,66988,2971],{},[1915,66990,2239],{},[898,66992,1771],{"mathvariant":1704},[898,66994,1712],{},[1693,66996,1899],{"separator":1898},[3635,66998],{"width":34864},[3635,67000,67001],{},[1915,67002,67003],{},"(3.9)",[902,67005,67006],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,67008,64050],{},[883,67010,67012],{"className":67011},[886],[888,67013,67014],{"xmlns":890,"display":34854},[892,67015,67016,67114],{},[895,67017,67018,67056,67058,67060,67062,67084,67086,67112],{},[895,67019,67020,67022,67028,67030,67036,67039,67045,67048],{},[1915,67021,64064],{},[4467,67023,67024,67026],{"accent":1898},[1915,67025,52496],{},[1693,67027,6552],{},[1915,67029,64073],{},[4467,67031,67032,67034],{"accent":1898},[1915,67033,6560],{},[1693,67035,4474],{},[1915,67037,67038],{},"ch n",[4467,67040,67041,67043],{"accent":1898},[1915,67042,207],{},[1693,67044,4474],{},[1915,67046,67047],{},"klad",[4467,67049,67050,67053],{"accent":1898},[1915,67051,67052],{},"u",[1693,67054,67055],{},"˚",[1915,67057,1917],{},[1693,67059,4110],{},[1915,67061,1917],{},[895,67063,67064,67066,67072,67075,67081],{},[1915,67065,64108],{},[4467,67067,67068,67070],{"accent":1898},[1915,67069,4471],{},[1693,67071,4474],{},[1915,67073,67074],{}," n",[4467,67076,67077,67079],{"accent":1898},[1915,67078,207],{},[1693,67080,4474],{},[1915,67082,67083],{},"klady",[1693,67085,64135],{},[895,67087,67088,67090,67096,67098,67104,67106],{},[1915,67089,64064],{},[4467,67091,67092,67094],{"accent":1898},[1915,67093,52496],{},[1693,67095,6552],{},[1915,67097,64148],{},[4467,67099,67100,67102],{"accent":1898},[1915,67101,16449],{},[1693,67103,6552],{},[1915,67105,64157],{},[4467,67107,67108,67110],{"accent":1898},[1915,67109,4471],{},[1693,67111,4474],{},[898,67113,1789],{"mathvariant":1704},[902,67115,67116],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[44125,67118,67120],{"id":67119},"příklad-35","Příklad 3.5",[724,67122,67123,64261,67125,62769,67161,67176,67177,67192,67193,9577,67206,9591,67219,67232,67233,9591,67246,1789],{},[38,67124,62731],{},[883,67126,67128],{"className":67127},[886],[888,67129,67130],{"xmlns":890},[892,67131,67132,67158],{},[895,67133,67134,67136,67138,67140,67142,67144,67146,67148,67150,67152],{},[898,67135,2663],{},[898,67137,2971],{},[1693,67139,1695],{},[1762,67141,15236],{},[1693,67143,1892],{},[1762,67145,9154],{},[898,67147,1712],{},[1693,67149,1892],{},[1762,67151,2398],{},[1717,67153,67154,67156],{},[898,67155,1712],{},[1762,67157,2398],{},[902,67159,67160],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,67162,67164],{"className":67163},[886],[888,67165,67166],{"xmlns":890},[892,67167,67168,67174],{},[895,67169,67170,67172],{},[898,67171,2839],{},[898,67173,2971],{},[902,67175,3810],{"encoding":904}," a odhadněte změny ",[883,67178,67180],{"className":67179},[886],[888,67181,67182],{"xmlns":890},[892,67183,67184,67190],{},[895,67185,67186,67188],{},[898,67187,2663],{},[898,67189,2971],{},[902,67191,3225],{"encoding":904}," při změnách ",[883,67194,67196],{"className":67195},[886],[888,67197,67198],{"xmlns":890},[892,67199,67200,67204],{},[895,67201,67202],{},[898,67203,1712],{},[902,67205,1712],{"encoding":904},[883,67207,67209],{"className":67208},[886],[888,67210,67211],{"xmlns":890},[892,67212,67213,67217],{},[895,67214,67215],{},[1762,67216,43026],{},[902,67218,43026],{"encoding":904},[883,67220,67222],{"className":67221},[886],[888,67223,67224],{"xmlns":890},[892,67225,67226,67230],{},[895,67227,67228],{},[1762,67229,48633],{},[902,67231,48633],{"encoding":904}," a z ",[883,67234,67236],{"className":67235},[886],[888,67237,67238],{"xmlns":890},[892,67239,67240,67244],{},[895,67241,67242],{},[1762,67243,43026],{},[902,67245,43026],{"encoding":904},[883,67247,67249],{"className":67248},[886],[888,67250,67251],{"xmlns":890},[892,67252,67253,67257],{},[895,67254,67255],{},[1762,67256,10402],{},[902,67258,10402],{"encoding":904},[724,67260,67261,1863,67263,7617,67289,1343,67316,67343,67344,67359,67360,67375,67376,67403,67404,67424,67425,27338,67446,67502,67503,9577,67516,9591,67529,6055,67542,1789],{},[38,67262,29570],{},[883,67264,67266],{"className":67265},[886],[888,67267,67268],{"xmlns":890},[892,67269,67270,67286],{},[895,67271,67272,67274,67276,67278,67280,67282,67284],{},[898,67273,2839],{},[898,67275,2971],{},[1693,67277,1695],{},[1762,67279,9154],{},[1693,67281,1892],{},[1762,67283,9262],{},[898,67285,1712],{},[902,67287,67288],{"encoding":904},"MC = 6 + 4Q",[883,67290,67292],{"className":67291},[886],[888,67293,67294],{"xmlns":890},[892,67295,67296,67313],{},[895,67297,67298,67300,67302,67304,67306,67308,67310],{},[898,67299,2839],{},[898,67301,2971],{},[1693,67303,1709],{"stretchy":1708},[1762,67305,43026],{},[1693,67307,1731],{"stretchy":1708},[1693,67309,1695],{},[1762,67311,67312],{},"66",[902,67314,67315],{"encoding":904},"MC(15) = 66",[883,67317,67319],{"className":67318},[886],[888,67320,67321],{"xmlns":890},[892,67322,67323,67340],{},[895,67324,67325,67327,67329,67331,67333,67335,67337],{},[898,67326,2839],{},[898,67328,2971],{},[1693,67330,1709],{"stretchy":1708},[1762,67332,15892],{},[1693,67334,1731],{"stretchy":1708},[1693,67336,1695],{},[1762,67338,67339],{},"86",[902,67341,67342],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,67345,67347],{"className":67346},[886],[888,67348,67349],{"xmlns":890},[892,67350,67351,67357],{},[895,67352,67353,67355],{},[898,67354,2663],{},[898,67356,2971],{},[902,67358,3225],{"encoding":904}," zvyšuje (",[883,67361,67363],{"className":67362},[886],[888,67364,67365],{"xmlns":890},[892,67366,67367,67373],{},[895,67368,67369,67371],{},[898,67370,2839],{},[898,67372,2971],{},[902,67374,3810],{"encoding":904}," je rostoucí). Z ",[883,67377,67379],{"className":67378},[886],[888,67380,67381],{"xmlns":890},[892,67382,67383,67400],{},[895,67384,67385,67387,67389,67391,67393,67395,67397],{},[898,67386,2663],{},[898,67388,2971],{},[1693,67390,1709],{"stretchy":1708},[1762,67392,43026],{},[1693,67394,1731],{"stretchy":1708},[1693,67396,1695],{},[1762,67398,67399],{},"740",[902,67401,67402],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,67405,67407],{"className":67406},[886],[888,67408,67409],{"xmlns":890},[892,67410,67411,67421],{},[895,67412,67413,67415,67417,67419],{},[898,67414,1771],{"mathvariant":1704},[898,67416,1712],{},[1693,67418,1695],{},[1762,67420,1764],{},[902,67422,67423],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,67426,67428],{"className":67427},[886],[888,67429,67430],{"xmlns":890},[892,67431,67432,67443],{},[895,67433,67434,67436,67438,67440],{},[898,67435,2663],{},[898,67437,2971],{},[1693,67439,4110],{},[1762,67441,67442],{},"806",[902,67444,67445],{"encoding":904},"TC \\approx 806",[883,67447,67449],{"className":67448},[886],[888,67450,67451],{"xmlns":890},[892,67452,67453,67499],{},[895,67454,67455,67457,67459,67461,67463,67465,67467,67469,67471,67473,67475,67477,67479,67481,67483,67485,67487,67490,67492,67494,67496],{},[898,67456,3890],{"mathvariant":1704},[898,67458,2663],{},[898,67460,2971],{},[1693,67462,1695],{},[898,67464,2663],{},[898,67466,2971],{},[1693,67468,1709],{"stretchy":1708},[1762,67470,48633],{},[1693,67472,1731],{"stretchy":1708},[1693,67474,1698],{},[898,67476,2663],{},[898,67478,2971],{},[1693,67480,1709],{"stretchy":1708},[1762,67482,43026],{},[1693,67484,1731],{"stretchy":1708},[1693,67486,1695],{},[1762,67488,67489],{},"808",[1693,67491,1698],{},[1762,67493,67399],{},[1693,67495,1695],{},[1762,67497,67498],{},"68",[902,67500,67501],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,67504,67506],{"className":67505},[886],[888,67507,67508],{"xmlns":890},[892,67509,67510,67514],{},[895,67511,67512],{},[898,67513,1712],{},[902,67515,1712],{"encoding":904},[883,67517,67519],{"className":67518},[886],[888,67520,67521],{"xmlns":890},[892,67522,67523,67527],{},[895,67524,67525],{},[1762,67526,43026],{},[902,67528,43026],{"encoding":904},[883,67530,67532],{"className":67531},[886],[888,67533,67534],{"xmlns":890},[892,67535,67536,67540],{},[895,67537,67538],{},[1762,67539,10402],{},[902,67541,10402],{"encoding":904},[883,67543,67545],{"className":67544},[886],[888,67546,67547],{"xmlns":890},[892,67548,67549,67578],{},[895,67550,67551,67553,67555,67557,67559,67561,67563,67565,67567,67569,67571,67573,67575],{},[898,67552,3890],{"mathvariant":1704},[898,67554,2663],{},[898,67556,2971],{},[1693,67558,4110],{},[1762,67560,67312],{},[1693,67562,1715],{},[1693,67564,1709],{"stretchy":1708},[1693,67566,1698],{},[1762,67568,8357],{},[1693,67570,1731],{"stretchy":1708},[1693,67572,1695],{},[1693,67574,1698],{},[1762,67576,67577],{},"198",[902,67579,67580],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,67582,67584],{"id":67583},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,67586,67587],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[44125,67589,67591],{"id":67590},"příklad-36","Příklad 3.6",[724,67593,67594,64261,67596,67640],{},[38,67595,62731],{},[883,67597,67599],{"className":67598},[886],[888,67600,67601],{"xmlns":890},[892,67602,67603,67637],{},[895,67604,67605,67607,67609,67611,67613,67615,67617,67619,67621,67623,67629,67631],{},[898,67606,2663],{},[898,67608,2971],{},[1693,67610,1695],{},[1762,67612,9987],{},[1693,67614,1892],{},[1762,67616,11872],{},[898,67618,1712],{},[1693,67620,1698],{},[1762,67622,9147],{},[1717,67624,67625,67627],{},[898,67626,1712],{},[1762,67628,2398],{},[1693,67630,1892],{},[1717,67632,67633,67635],{},[898,67634,1712],{},[1762,67636,8357],{},[902,67638,67639],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,67642,67643],{},[38,67644,29570],{},[883,67646,67648],{"className":67647},[886],[888,67649,67650],{"xmlns":890,"display":34854},[892,67651,67652,67896],{},[3626,67653,67654,67680,67728,67762,67804,67854],{"rowspacing":27562,"columnalign":27563,"columnspacing":1723},[3632,67655,67656,67666],{},[3635,67657,67658],{},[3638,67659,67660],{"scriptlevel":1911,"displaystyle":1898},[895,67661,67662,67664],{},[898,67663,2976],{},[898,67665,2971],{},[3635,67667,67668],{},[3638,67669,67670],{"scriptlevel":1911,"displaystyle":1898},[895,67671,67672,67674,67676,67678],{},[895,67673],{},[1693,67675,1695],{},[1762,67677,9987],{},[1693,67679,1899],{"separator":1898},[3632,67681,67682,67694],{},[3635,67683,67684],{},[3638,67685,67686],{"scriptlevel":1911,"displaystyle":1898},[895,67687,67688,67690,67692],{},[898,67689,2663],{},[898,67691,2985],{},[898,67693,2971],{},[3635,67695,67696],{},[3638,67697,67698],{"scriptlevel":1911,"displaystyle":1898},[895,67699,67700,67702,67704,67706,67708,67710,67712,67718,67720,67726],{},[895,67701],{},[1693,67703,1695],{},[1762,67705,11872],{},[898,67707,1712],{},[1693,67709,1698],{},[1762,67711,9147],{},[1717,67713,67714,67716],{},[898,67715,1712],{},[1762,67717,2398],{},[1693,67719,1892],{},[1717,67721,67722,67724],{},[898,67723,1712],{},[1762,67725,8357],{},[1693,67727,1899],{"separator":1898},[3632,67729,67730,67742],{},[3635,67731,67732],{},[3638,67733,67734],{"scriptlevel":1911,"displaystyle":1898},[895,67735,67736,67738,67740],{},[898,67737,2719],{},[898,67739,2976],{},[898,67741,2971],{},[3635,67743,67744],{},[3638,67745,67746],{"scriptlevel":1911,"displaystyle":1898},[895,67747,67748,67750,67752,67760],{},[895,67749],{},[1693,67751,1695],{},[3638,67753,67754],{"scriptlevel":1911,"displaystyle":1708},[2132,67755,67756,67758],{},[1762,67757,9987],{},[898,67759,1712],{},[1693,67761,1899],{"separator":1898},[3632,67763,67764,67776],{},[3635,67765,67766],{},[3638,67767,67768],{"scriptlevel":1911,"displaystyle":1898},[895,67769,67770,67772,67774],{},[898,67771,2719],{},[898,67773,2985],{},[898,67775,2971],{},[3635,67777,67778],{},[3638,67779,67780],{"scriptlevel":1911,"displaystyle":1898},[895,67781,67782,67784,67786,67788,67790,67792,67794,67796,67802],{},[895,67783],{},[1693,67785,1695],{},[1762,67787,11872],{},[1693,67789,1698],{},[1762,67791,9147],{},[898,67793,1712],{},[1693,67795,1892],{},[1717,67797,67798,67800],{},[898,67799,1712],{},[1762,67801,2398],{},[1693,67803,1899],{"separator":1898},[3632,67805,67806,67816],{},[3635,67807,67808],{},[3638,67809,67810],{"scriptlevel":1911,"displaystyle":1898},[895,67811,67812,67814],{},[898,67813,2719],{},[898,67815,2971],{},[3635,67817,67818],{},[3638,67819,67820],{"scriptlevel":1911,"displaystyle":1898},[895,67821,67822,67824,67826,67834,67836,67838,67840,67842,67844,67846,67852],{},[895,67823],{},[1693,67825,1695],{},[3638,67827,67828],{"scriptlevel":1911,"displaystyle":1708},[2132,67829,67830,67832],{},[1762,67831,9987],{},[898,67833,1712],{},[1693,67835,1892],{},[1762,67837,11872],{},[1693,67839,1698],{},[1762,67841,9147],{},[898,67843,1712],{},[1693,67845,1892],{},[1717,67847,67848,67850],{},[898,67849,1712],{},[1762,67851,2398],{},[1693,67853,1899],{"separator":1898},[3632,67855,67856,67866],{},[3635,67857,67858],{},[3638,67859,67860],{"scriptlevel":1911,"displaystyle":1898},[895,67861,67862,67864],{},[898,67863,2839],{},[898,67865,2971],{},[3635,67867,67868],{},[3638,67869,67870],{"scriptlevel":1911,"displaystyle":1898},[895,67871,67872,67874,67876,67878,67880,67882,67884,67886,67888,67894],{},[895,67873],{},[1693,67875,1695],{},[1762,67877,11872],{},[1693,67879,1698],{},[1762,67881,9763],{},[898,67883,1712],{},[1693,67885,1892],{},[1762,67887,8357],{},[1717,67889,67890,67892],{},[898,67891,1712],{},[1762,67893,2398],{},[898,67895,1789],{"mathvariant":1704},[902,67897,67898],{"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}",[724,67900,67901,67902,22617,67917,22617,67932,67947,67948,67963,67964,1343,67982,67963,67999,1343,68017,67963,68032,68050],{},"Význačné body ",[883,67903,67905],{"className":67904},[886],[888,67906,67907],{"xmlns":890},[892,67908,67909,67914],{},[895,67910,67911],{},[1762,67912,67913],{},"1,67",[902,67915,67916],{"encoding":904},"1{,}67",[883,67918,67920],{"className":67919},[886],[888,67921,67922],{"xmlns":890},[892,67923,67924,67929],{},[895,67925,67926],{},[1762,67927,67928],{},"2,50",[902,67930,67931],{"encoding":904},"2{,}50",[883,67933,67935],{"className":67934},[886],[888,67936,67937],{"xmlns":890},[892,67938,67939,67944],{},[895,67940,67941],{},[1762,67942,67943],{},"4,73",[902,67945,67946],{"encoding":904},"4{,}73"," odpovídají: ",[883,67949,67951],{"className":67950},[886],[888,67952,67953],{"xmlns":890},[892,67954,67955,67961],{},[895,67956,67957,67959],{},[898,67958,2839],{},[898,67960,2971],{},[902,67962,3810],{"encoding":904}," minimum v ",[883,67965,67967],{"className":67966},[886],[888,67968,67969],{"xmlns":890},[892,67970,67971,67979],{},[895,67972,67973,67975,67977],{},[898,67974,1712],{},[1693,67976,12766],{},[1762,67978,67913],{},[902,67980,67981],{"encoding":904},"Q \\doteq 1{,}67",[883,67983,67985],{"className":67984},[886],[888,67986,67987],{"xmlns":890},[892,67988,67989,67997],{},[895,67990,67991,67993,67995],{},[898,67992,2719],{},[898,67994,2985],{},[898,67996,2971],{},[902,67998,3789],{"encoding":904},[883,68000,68002],{"className":68001},[886],[888,68003,68004],{"xmlns":890},[892,68005,68006,68014],{},[895,68007,68008,68010,68012],{},[898,68009,1712],{},[1693,68011,1695],{},[1762,68013,67928],{},[902,68015,68016],{"encoding":904},"Q = 2{,}50",[883,68018,68020],{"className":68019},[886],[888,68021,68022],{"xmlns":890},[892,68023,68024,68030],{},[895,68025,68026,68028],{},[898,68027,2719],{},[898,68029,2971],{},[902,68031,3331],{"encoding":904},[883,68033,68035],{"className":68034},[886],[888,68036,68037],{"xmlns":890},[892,68038,68039,68047],{},[895,68040,68041,68043,68045],{},[898,68042,1712],{},[1693,68044,12766],{},[1762,68046,67943],{},[902,68048,68049],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,68052,68053],{},[9465,68054],{"alt":68055,"className":68056,"src":68057},"imek-ac-avc-mc",[210,9469],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,68059,68060],{},[614,68061,68062,68063,4286,68078,68095,68096,22617,68115,68130],{},"Obrázek 3.9: Kubické křivky ",[883,68064,68066],{"className":68065},[886],[888,68067,68068],{"xmlns":890},[892,68069,68070,68076],{},[895,68071,68072,68074],{},[898,68073,2663],{},[898,68075,2971],{},[902,68077,3225],{"encoding":904},[883,68079,68081],{"className":68080},[886],[888,68082,68083],{"xmlns":890},[892,68084,68085,68093],{},[895,68086,68087,68089,68091],{},[898,68088,2663],{},[898,68090,2985],{},[898,68092,2971],{},[902,68094,3041],{"encoding":904}," rostoucí od bodu ",[883,68097,68099],{"className":68098},[886],[888,68100,68101],{"xmlns":890},[892,68102,68103,68113],{},[895,68104,68105,68107,68109,68111],{},[898,68106,2976],{},[898,68108,2971],{},[1693,68110,1695],{},[1762,68112,9987],{},[902,68114,18478],{"encoding":904},[883,68116,68118],{"className":68117},[886],[888,68119,68120],{"xmlns":890},[892,68121,68122,68128],{},[895,68123,68124,68126],{},[898,68125,2976],{},[898,68127,2971],{},[902,68129,3022],{"encoding":904}," je vodorovná přímka.",[724,68132,68133],{},[614,68134,68135,68136,1343,68151,1343,68168,35985,68183,68196,68197,7617,68214,68229,68230,13055,68247,68262,68263,32979,68276,1343,68289,1343,68302,1789],{},"Obrázek 3.10: Křivky ",[883,68137,68139],{"className":68138},[886],[888,68140,68141],{"xmlns":890},[892,68142,68143,68149],{},[895,68144,68145,68147],{},[898,68146,2719],{},[898,68148,2971],{},[902,68150,3331],{"encoding":904},[883,68152,68154],{"className":68153},[886],[888,68155,68156],{"xmlns":890},[892,68157,68158,68166],{},[895,68159,68160,68162,68164],{},[898,68161,2719],{},[898,68163,2985],{},[898,68165,2971],{},[902,68167,3789],{"encoding":904},[883,68169,68171],{"className":68170},[886],[888,68172,68173],{"xmlns":890},[892,68174,68175,68181],{},[895,68176,68177,68179],{},[898,68178,2839],{},[898,68180,2971],{},[902,68182,3810],{"encoding":904},[883,68184,68186],{"className":68185},[886],[888,68187,68188],{"xmlns":890},[892,68189,68190,68194],{},[895,68191,68192],{},[898,68193,900],{},[902,68195,900],{"encoding":904}," a klesající hyperbola ",[883,68198,68200],{"className":68199},[886],[888,68201,68202],{"xmlns":890},[892,68203,68204,68212],{},[895,68205,68206,68208,68210],{},[898,68207,2719],{},[898,68209,2976],{},[898,68211,2971],{},[902,68213,3150],{"encoding":904},[883,68215,68217],{"className":68216},[886],[888,68218,68219],{"xmlns":890},[892,68220,68221,68227],{},[895,68222,68223,68225],{},[898,68224,2839],{},[898,68226,2971],{},[902,68228,3810],{"encoding":904}," protíná ",[883,68231,68233],{"className":68232},[886],[888,68234,68235],{"xmlns":890},[892,68236,68237,68245],{},[895,68238,68239,68241,68243],{},[898,68240,2719],{},[898,68242,2985],{},[898,68244,2971],{},[902,68246,3789],{"encoding":904},[883,68248,68250],{"className":68249},[886],[888,68251,68252],{"xmlns":890},[892,68253,68254,68260],{},[895,68255,68256,68258],{},[898,68257,2719],{},[898,68259,2971],{},[902,68261,3331],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,68264,68266],{"className":68265},[886],[888,68267,68268],{"xmlns":890},[892,68269,68270,68274],{},[895,68271,68272],{},[898,68273,1712],{},[902,68275,1712],{"encoding":904},[883,68277,68279],{"className":68278},[886],[888,68280,68281],{"xmlns":890},[892,68282,68283,68287],{},[895,68284,68285],{},[1762,68286,67913],{},[902,68288,67916],{"encoding":904},[883,68290,68292],{"className":68291},[886],[888,68293,68294],{"xmlns":890},[892,68295,68296,68300],{},[895,68297,68298],{},[1762,68299,67928],{},[902,68301,67931],{"encoding":904},[883,68303,68305],{"className":68304},[886],[888,68306,68307],{"xmlns":890},[892,68308,68309,68313],{},[895,68310,68311],{},[1762,68312,67943],{},[902,68314,67946],{"encoding":904},[724,68316,68317],{},[38,68318,68319],{},"Standardní vlastnosti:",[120,68321,68322,68357,68421,68489,68539,68559],{},[123,68323,68324,4286,68339,68356],{},[883,68325,68327],{"className":68326},[886],[888,68328,68329],{"xmlns":890},[892,68330,68331,68337],{},[895,68332,68333,68335],{},[898,68334,2663],{},[898,68336,2971],{},[902,68338,3225],{"encoding":904},[883,68340,68342],{"className":68341},[886],[888,68343,68344],{"xmlns":890},[892,68345,68346,68354],{},[895,68347,68348,68350,68352],{},[898,68349,2663],{},[898,68351,2985],{},[898,68353,2971],{},[902,68355,3041],{"encoding":904}," jsou kubické funkce;",[123,68358,68359,1343,68374,1343,68391,68406,68407,68420],{},[883,68360,68362],{"className":68361},[886],[888,68363,68364],{"xmlns":890},[892,68365,68366,68372],{},[895,68367,68368,68370],{},[898,68369,2719],{},[898,68371,2971],{},[902,68373,3331],{"encoding":904},[883,68375,68377],{"className":68376},[886],[888,68378,68379],{"xmlns":890},[892,68380,68381,68389],{},[895,68382,68383,68385,68387],{},[898,68384,2719],{},[898,68386,2985],{},[898,68388,2971],{},[902,68390,3789],{"encoding":904},[883,68392,68394],{"className":68393},[886],[888,68395,68396],{"xmlns":890},[892,68397,68398,68404],{},[895,68399,68400,68402],{},[898,68401,2839],{},[898,68403,2971],{},[902,68405,3810],{"encoding":904}," jsou křivky tvaru ",[883,68408,68410],{"className":68409},[886],[888,68411,68412],{"xmlns":890},[892,68413,68414,68418],{},[895,68415,68416],{},[898,68417,900],{},[902,68419,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,68422,68423,68438,68439,1343,68456,68473,68474,15283],{},[883,68424,68426],{"className":68425},[886],[888,68427,68428],{"xmlns":890},[892,68429,68430,68436],{},[895,68431,68432,68434],{},[898,68433,2839],{},[898,68435,2971],{},[902,68437,3810],{"encoding":904}," nabývá minima před ",[883,68440,68442],{"className":68441},[886],[888,68443,68444],{"xmlns":890},[892,68445,68446,68454],{},[895,68447,68448,68450,68452],{},[898,68449,2719],{},[898,68451,2985],{},[898,68453,2971],{},[902,68455,3789],{"encoding":904},[883,68457,68459],{"className":68458},[886],[888,68460,68461],{"xmlns":890},[892,68462,68463,68471],{},[895,68464,68465,68467,68469],{},[898,68466,2719],{},[898,68468,2985],{},[898,68470,2971],{},[902,68472,3789],{"encoding":904}," před ",[883,68475,68477],{"className":68476},[886],[888,68478,68479],{"xmlns":890},[892,68480,68481,68487],{},[895,68482,68483,68485],{},[898,68484,2719],{},[898,68486,2971],{},[902,68488,3331],{"encoding":904},[123,68490,68491,68229,68506,4286,68521,68538],{},[883,68492,68494],{"className":68493},[886],[888,68495,68496],{"xmlns":890},[892,68497,68498,68504],{},[895,68499,68500,68502],{},[898,68501,2839],{},[898,68503,2971],{},[902,68505,3810],{"encoding":904},[883,68507,68509],{"className":68508},[886],[888,68510,68511],{"xmlns":890},[892,68512,68513,68519],{},[895,68514,68515,68517],{},[898,68516,2719],{},[898,68518,2971],{},[902,68520,3331],{"encoding":904},[883,68522,68524],{"className":68523},[886],[888,68525,68526],{"xmlns":890},[892,68527,68528,68536],{},[895,68529,68530,68532,68534],{},[898,68531,2719],{},[898,68533,2985],{},[898,68535,2971],{},[902,68537,3789],{"encoding":904}," zdola právě v jejich minimech;",[123,68540,68541,68558],{},[883,68542,68544],{"className":68543},[886],[888,68545,68546],{"xmlns":890},[892,68547,68548,68556],{},[895,68549,68550,68552,68554],{},[898,68551,2719],{},[898,68553,2976],{},[898,68555,2971],{},[902,68557,3150],{"encoding":904}," je hyperbola, stále klesající;",[123,68560,68561,68593,68594,4286,68609,68626,68627,68640,68641,3042],{},[883,68562,68564],{"className":68563},[886],[888,68565,68566],{"xmlns":890},[892,68567,68568,68590],{},[895,68569,68570,68572,68574,68576,68578,68580,68582,68584,68586,68588],{},[898,68571,2719],{},[898,68573,2971],{},[1693,68575,1695],{},[898,68577,2719],{},[898,68579,2976],{},[898,68581,2971],{},[1693,68583,1892],{},[898,68585,2719],{},[898,68587,2985],{},[898,68589,2971],{},[902,68591,68592],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,68595,68597],{"className":68596},[886],[888,68598,68599],{"xmlns":890},[892,68600,68601,68607],{},[895,68602,68603,68605],{},[898,68604,2719],{},[898,68606,2971],{},[902,68608,3331],{"encoding":904},[883,68610,68612],{"className":68611},[886],[888,68613,68614],{"xmlns":890},[892,68615,68616,68624],{},[895,68617,68618,68620,68622],{},[898,68619,2719],{},[898,68621,2985],{},[898,68623,2971],{},[902,68625,3789],{"encoding":904}," klesá s rostoucím ",[883,68628,68630],{"className":68629},[886],[888,68631,68632],{"xmlns":890},[892,68633,68634,68638],{},[895,68635,68636],{},[898,68637,1712],{},[902,68639,1712],{"encoding":904}," (protože ",[883,68642,68644],{"className":68643},[886],[888,68645,68646],{"xmlns":890},[892,68647,68648,68660],{},[895,68649,68650,68652,68654,68656,68658],{},[898,68651,2719],{},[898,68653,2976],{},[898,68655,2971],{},[1693,68657,10020],{},[1762,68659,1911],{},[902,68661,68662],{"encoding":904},"AFC \\to 0",[115,68664,3265],{"id":3264},[724,68666,68667,68668,68671,68672,68687],{},"Častou optimalizační úlohou je ",[38,68669,68670],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,68673,68675],{"className":68674},[886],[888,68676,68677],{"xmlns":890},[892,68678,68679,68685],{},[895,68680,68681,68683],{},[898,68682,2719],{},[898,68684,2971],{},[902,68686,3331],{"encoding":904}," minimální.",[198,68689,23233],{"id":23232},[724,68691,68692,68693,68710],{},"Mají-li průměrné náklady minimum v bodě ",[883,68694,68696],{"className":68695},[886],[888,68697,68698],{"xmlns":890},[892,68699,68700,68708],{},[895,68701,68702],{},[3284,68703,68704,68706],{},[898,68705,1712],{},[1762,68707,1911],{},[902,68709,6293],{"encoding":904},", pak platí",[883,68712,68714],{"className":68713},[886],[888,68715,68716],{"xmlns":890,"display":34854},[892,68717,68718,68767],{},[3626,68719,68720],{"width":34859},[3632,68721,68722,68724,68760,68762],{},[3635,68723],{"width":34864},[3635,68725,68726],{},[895,68727,68728,68730,68732,68734,68740,68742,68744,68746,68748,68750,68756,68758],{},[898,68729,2719],{},[898,68731,2971],{},[1693,68733,1709],{"stretchy":1708},[3284,68735,68736,68738],{},[898,68737,1712],{},[1762,68739,1911],{},[1693,68741,1731],{"stretchy":1708},[1693,68743,1695],{},[898,68745,2839],{},[898,68747,2971],{},[1693,68749,1709],{"stretchy":1708},[3284,68751,68752,68754],{},[898,68753,1712],{},[1762,68755,1911],{},[1693,68757,1731],{"stretchy":1708},[898,68759,1789],{"mathvariant":1704},[3635,68761],{"width":34864},[3635,68763,68764],{},[1915,68765,68766],{},"(3.10)",[902,68768,68769],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1636,68771,68772],{},[724,68773,68774,68776,68777],{},[883,68775,63185],{}," Princip\n",[38,68778,68779],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,68781,68782,68785,68786,68828],{},[38,68783,68784],{},"Odvození."," Z ",[883,68787,68789],{"className":68788},[886],[888,68790,68791],{"xmlns":890},[892,68792,68793,68825],{},[895,68794,68795,68797,68799,68801,68803,68805,68807],{},[898,68796,2719],{},[898,68798,2971],{},[1693,68800,1709],{"stretchy":1708},[898,68802,1712],{},[1693,68804,1731],{"stretchy":1708},[1693,68806,1695],{},[3638,68808,68809],{"scriptlevel":1911,"displaystyle":1708},[2132,68810,68811,68823],{},[895,68812,68813,68815,68817,68819,68821],{},[898,68814,2663],{},[898,68816,2971],{},[1693,68818,1709],{"stretchy":1708},[898,68820,1712],{},[1693,68822,1731],{"stretchy":1708},[898,68824,1712],{},[902,68826,68827],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,68830,68832],{"className":68831},[886],[888,68833,68834],{"xmlns":890,"display":34854},[892,68835,68836,68968],{},[895,68837,68838,68840,68846,68848,68850,68852,68854,68894,68896,68936,68938,68966],{},[898,68839,2719],{},[1717,68841,68842,68844],{},[898,68843,2971],{},[1693,68845,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,68847,1709],{"stretchy":1708},[898,68849,1712],{},[1693,68851,1731],{"stretchy":1708},[1693,68853,1695],{},[2132,68855,68856,68888],{},[895,68857,68858,68860,68866,68868,68870,68872,68874,68876,68878,68880,68882,68884,68886],{},[898,68859,2663],{},[1717,68861,68862,68864],{},[898,68863,2971],{},[1693,68865,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,68867,1709],{"stretchy":1708},[898,68869,1712],{},[1693,68871,1731],{"stretchy":1708},[1693,68873,1715],{},[898,68875,1712],{},[1693,68877,1698],{},[898,68879,2663],{},[898,68881,2971],{},[1693,68883,1709],{"stretchy":1708},[898,68885,1712],{},[1693,68887,1731],{"stretchy":1708},[1717,68889,68890,68892],{},[898,68891,1712],{},[1762,68893,2398],{},[1693,68895,1695],{},[2132,68897,68898,68930],{},[895,68899,68900,68902,68904,68906,68908,68910,68912,68914,68916,68918,68920,68922,68924,68926,68928],{},[898,68901,2839],{},[898,68903,2971],{},[1693,68905,1709],{"stretchy":1708},[898,68907,1712],{},[1693,68909,1731],{"stretchy":1708},[1693,68911,1715],{},[898,68913,1712],{},[1693,68915,1698],{},[898,68917,2719],{},[898,68919,2971],{},[1693,68921,1709],{"stretchy":1708},[898,68923,1712],{},[1693,68925,1731],{"stretchy":1708},[1693,68927,1715],{},[898,68929,1712],{},[1717,68931,68932,68934],{},[898,68933,1712],{},[1762,68935,2398],{},[1693,68937,1695],{},[2132,68939,68940,68964],{},[895,68941,68942,68944,68946,68948,68950,68952,68954,68956,68958,68960,68962],{},[898,68943,2839],{},[898,68945,2971],{},[1693,68947,1709],{"stretchy":1708},[898,68949,1712],{},[1693,68951,1731],{"stretchy":1708},[1693,68953,1698],{},[898,68955,2719],{},[898,68957,2971],{},[1693,68959,1709],{"stretchy":1708},[898,68961,1712],{},[1693,68963,1731],{"stretchy":1708},[898,68965,1712],{},[898,68967,1789],{"mathvariant":1704},[902,68969,68970],{"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}.",[724,68972,68973,68974,9530,68989,6055,69011,63560],{},"Nutnou podmínkou minima ",[883,68975,68977],{"className":68976},[886],[888,68978,68979],{"xmlns":890},[892,68980,68981,68987],{},[895,68982,68983,68985],{},[898,68984,2719],{},[898,68986,2971],{},[902,68988,3331],{"encoding":904},[883,68990,68992],{"className":68991},[886],[888,68993,68994],{"xmlns":890},[892,68995,68996,69008],{},[895,68997,68998,69004,69006],{},[3284,68999,69000,69002],{},[898,69001,1712],{},[1762,69003,1911],{},[1693,69005,1922],{},[1762,69007,1911],{},[902,69009,69010],{"encoding":904},"Q_0 > 0",[883,69012,69014],{"className":69013},[886],[888,69015,69016],{"xmlns":890},[892,69017,69018,69042],{},[895,69019,69020,69022,69028,69030,69036,69038,69040],{},[898,69021,2719],{},[1717,69023,69024,69026],{},[898,69025,2971],{},[1693,69027,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,69029,1709],{"stretchy":1708},[3284,69031,69032,69034],{},[898,69033,1712],{},[1762,69035,1911],{},[1693,69037,1731],{"stretchy":1708},[1693,69039,1695],{},[1762,69041,1911],{},[902,69043,69044],{"encoding":904},"AC'(Q_0) = 0",[883,69046,69048],{"className":69047},[886],[888,69049,69050],{"xmlns":890,"display":34854},[892,69051,69052,69136],{},[895,69053,69054,69094,69096,69098,69100,69102,69104,69106,69108,69110,69116,69118,69120,69122,69124,69126,69132,69134],{},[2132,69055,69056,69088],{},[895,69057,69058,69060,69062,69064,69070,69072,69074,69076,69078,69080,69086],{},[898,69059,2839],{},[898,69061,2971],{},[1693,69063,1709],{"stretchy":1708},[3284,69065,69066,69068],{},[898,69067,1712],{},[1762,69069,1911],{},[1693,69071,1731],{"stretchy":1708},[1693,69073,1698],{},[898,69075,2719],{},[898,69077,2971],{},[1693,69079,1709],{"stretchy":1708},[3284,69081,69082,69084],{},[898,69083,1712],{},[1762,69085,1911],{},[1693,69087,1731],{"stretchy":1708},[3284,69089,69090,69092],{},[898,69091,1712],{},[1762,69093,1911],{},[1693,69095,1695],{},[1762,69097,1911],{},[1901,69099],{"width":3630},[1693,69101,6117],{},[1901,69103],{"width":3630},[898,69105,2839],{},[898,69107,2971],{},[1693,69109,1709],{"stretchy":1708},[3284,69111,69112,69114],{},[898,69113,1712],{},[1762,69115,1911],{},[1693,69117,1731],{"stretchy":1708},[1693,69119,1695],{},[898,69121,2719],{},[898,69123,2971],{},[1693,69125,1709],{"stretchy":1708},[3284,69127,69128,69130],{},[898,69129,1712],{},[1762,69131,1911],{},[1693,69133,1731],{"stretchy":1708},[898,69135,1789],{"mathvariant":1704},[902,69137,69138],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,69140,69141,1863,69144,68229,69159,69174,69175,69190,69191,6055,69208,69230,69231,69253],{},[38,69142,69143],{},"Geometrická interpretace.",[883,69145,69147],{"className":69146},[886],[888,69148,69149],{"xmlns":890},[892,69150,69151,69157],{},[895,69152,69153,69155],{},[898,69154,2839],{},[898,69156,2971],{},[902,69158,3810],{"encoding":904},[883,69160,69162],{"className":69161},[886],[888,69163,69164],{"xmlns":890},[892,69165,69166,69172],{},[895,69167,69168,69170],{},[898,69169,2719],{},[898,69171,2971],{},[902,69173,3331],{"encoding":904}," právě v bodě minima ",[883,69176,69178],{"className":69177},[886],[888,69179,69180],{"xmlns":890},[892,69181,69182,69188],{},[895,69183,69184,69186],{},[898,69185,2719],{},[898,69187,2971],{},[902,69189,3331],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,69192,69194],{"className":69193},[886],[888,69195,69196],{"xmlns":890},[892,69197,69198,69206],{},[895,69199,69200],{},[3284,69201,69202,69204],{},[898,69203,1712],{},[1762,69205,1911],{},[902,69207,6293],{"encoding":904},[883,69209,69211],{"className":69210},[886],[888,69212,69213],{"xmlns":890},[892,69214,69215,69227],{},[895,69216,69217,69219,69221,69223,69225],{},[898,69218,2839],{},[898,69220,2971],{},[1693,69222,1908],{},[898,69224,2719],{},[898,69226,2971],{},[902,69228,69229],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,69232,69234],{"className":69233},[886],[888,69235,69236],{"xmlns":890},[892,69237,69238,69250],{},[895,69239,69240,69242,69244,69246,69248],{},[898,69241,2839],{},[898,69243,2971],{},[1693,69245,1922],{},[898,69247,2719],{},[898,69249,2971],{},[902,69251,69252],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,69255,69256,69257,69298,69299,69316,69317,1789],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,69258,69260],{"className":69259},[886],[888,69261,69262],{"xmlns":890},[892,69263,69264,69296],{},[895,69265,69266,69268,69270,69272,69278,69280,69282,69284,69286,69288,69294],{},[898,69267,2719],{},[898,69269,2971],{},[1693,69271,1709],{"stretchy":1708},[3284,69273,69274,69276],{},[898,69275,1712],{},[1762,69277,1911],{},[1693,69279,1731],{"stretchy":1708},[1693,69281,1695],{},[898,69283,2839],{},[898,69285,2971],{},[1693,69287,1709],{"stretchy":1708},[3284,69289,69290,69292],{},[898,69291,1712],{},[1762,69293,1911],{},[1693,69295,1731],{"stretchy":1708},[902,69297,3310],{"encoding":904},", pak ",[883,69300,69302],{"className":69301},[886],[888,69303,69304],{"xmlns":890},[892,69305,69306,69314],{},[895,69307,69308],{},[3284,69309,69310,69312],{},[898,69311,1712],{},[1762,69313,1911],{},[902,69315,6293],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,69318,69320],{"className":69319},[886],[888,69321,69322],{"xmlns":890},[892,69323,69324,69348],{},[895,69325,69326,69328,69330,69332,69334,69336,69338,69340,69342,69344,69346],{},[898,69327,2719],{},[898,69329,2971],{},[1693,69331,1709],{"stretchy":1708},[898,69333,1712],{},[1693,69335,1731],{"stretchy":1708},[1693,69337,1695],{},[898,69339,2839],{},[898,69341,2971],{},[1693,69343,1709],{"stretchy":1708},[898,69345,1712],{},[1693,69347,1731],{"stretchy":1708},[902,69349,69350],{"encoding":904},"AC(Q) = MC(Q)",[1636,69352,69353],{},[724,69354,69355,69357,69358,17244,69376,69397,69398,17244,69401,69422,69423,69438,69439,64777,69454,3042],{},[883,69356,8654],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,69359,69360,69361],{},"minimum ",[883,69362,69364],{"className":69363},[886],[888,69365,69366],{"xmlns":890},[892,69367,69368,69374],{},[895,69369,69370,69372],{},[898,69371,2719],{},[898,69373,2971],{},[902,69375,3331],{"encoding":904},[883,69377,69379],{"className":69378},[886],[888,69380,69381],{"xmlns":890},[892,69382,69383,69395],{},[895,69384,69385,69387,69389,69391,69393],{},[898,69386,2719],{},[898,69388,2971],{},[1693,69390,1695],{},[898,69392,2839],{},[898,69394,2971],{},[902,69396,5062],{"encoding":904},", pro ",[38,69399,69400],{},"maximum zisku",[883,69402,69404],{"className":69403},[886],[888,69405,69406],{"xmlns":890},[892,69407,69408,69420],{},[895,69409,69410,69412,69414,69416,69418],{},[898,69411,2839],{},[898,69413,2666],{},[1693,69415,1695],{},[898,69417,2839],{},[898,69419,2971],{},[902,69421,62024],{"encoding":904},". Obě podmínky využívají ",[883,69424,69426],{"className":69425},[886],[888,69427,69428],{"xmlns":890},[892,69429,69430,69436],{},[895,69431,69432,69434],{},[898,69433,2839],{},[898,69435,2971],{},[902,69437,3810],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,69440,69442],{"className":69441},[886],[888,69443,69444],{"xmlns":890},[892,69445,69446,69452],{},[895,69447,69448,69450],{},[898,69449,2719],{},[898,69451,2971],{},[902,69453,3331],{"encoding":904},[883,69455,69457],{"className":69456},[886],[888,69458,69459],{"xmlns":890},[892,69460,69461,69467],{},[895,69462,69463,69465],{},[898,69464,2839],{},[898,69466,2666],{},[902,69468,2919],{"encoding":904},[44125,69470,69472],{"id":69471},"příklad-37","Příklad 3.7",[724,69474,69475,64261,69477,69511,69512,69525,69526,69541],{},[38,69476,62731],{},[883,69478,69480],{"className":69479},[886],[888,69481,69482],{"xmlns":890},[892,69483,69484,69508],{},[895,69485,69486,69488,69490,69492,69498,69500,69502,69504,69506],{},[898,69487,2663],{},[898,69489,2971],{},[1693,69491,1695],{},[1717,69493,69494,69496],{},[898,69495,1712],{},[1762,69497,2398],{},[1693,69499,1892],{},[1762,69501,8357],{},[898,69503,1712],{},[1693,69505,1892],{},[1762,69507,12433],{},[902,69509,69510],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,69513,69515],{"className":69514},[886],[888,69516,69517],{"xmlns":890},[892,69518,69519,69523],{},[895,69520,69521],{},[898,69522,1712],{},[902,69524,1712],{"encoding":904}," minimalizující ",[883,69527,69529],{"className":69528},[886],[888,69530,69531],{"xmlns":890},[892,69532,69533,69539],{},[895,69534,69535,69537],{},[898,69536,2719],{},[898,69538,2971],{},[902,69540,3331],{"encoding":904}," a ověřte princip (3.10).",[724,69543,69544,69546],{},[38,69545,29570],{}," Přímý výpočet:",[883,69548,69550],{"className":69549},[886],[888,69551,69552],{"xmlns":890,"display":34854},[892,69553,69554,69656],{},[895,69555,69556,69558,69560,69562,69584,69586,69588,69590,69592,69594,69600,69602,69604,69606,69608,69610,69616,69618,69620,69622,69632,69634,69654],{},[898,69557,2719],{},[898,69559,2971],{},[1693,69561,1695],{},[2132,69563,69564,69582],{},[895,69565,69566,69572,69574,69576,69578,69580],{},[1717,69567,69568,69570],{},[898,69569,1712],{},[1762,69571,2398],{},[1693,69573,1892],{},[1762,69575,8357],{},[898,69577,1712],{},[1693,69579,1892],{},[1762,69581,12433],{},[898,69583,1712],{},[1693,69585,1695],{},[898,69587,1712],{},[1693,69589,1892],{},[1762,69591,8357],{},[1693,69593,1892],{},[2132,69595,69596,69598],{},[1762,69597,12433],{},[898,69599,1712],{},[1693,69601,1899],{"separator":1898},[1901,69603],{"width":1903},[1693,69605,1709],{"stretchy":1708},[898,69607,2719],{},[898,69609,2971],{},[1717,69611,69612,69614],{},[1693,69613,1731],{"stretchy":1708},[1693,69615,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,69617,1695],{},[1762,69619,1764],{},[1693,69621,1698],{},[2132,69623,69624,69626],{},[1762,69625,12433],{},[1717,69627,69628,69630],{},[898,69629,1712],{},[1762,69631,2398],{},[1693,69633,1695],{},[2132,69635,69636,69648],{},[895,69637,69638,69644,69646],{},[1717,69639,69640,69642],{},[898,69641,1712],{},[1762,69643,2398],{},[1693,69645,1698],{},[1762,69647,12433],{},[1717,69649,69650,69652],{},[898,69651,1712],{},[1762,69653,2398],{},[898,69655,1789],{"mathvariant":1704},[902,69657,69658],{"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}.",[724,69660,69661,69701,69702,69726,69727,69777,69778,1789],{},[883,69662,69664],{"className":69663},[886],[888,69665,69666],{"xmlns":890},[892,69667,69668,69698],{},[895,69669,69670,69672,69674,69676,69682,69684,69686,69688,69694,69696],{},[1693,69671,1709],{"stretchy":1708},[898,69673,2719],{},[898,69675,2971],{},[1717,69677,69678,69680],{},[1693,69679,1731],{"stretchy":1708},[1693,69681,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,69683,1695],{},[1762,69685,1911],{},[1693,69687,10870],{},[3284,69689,69690,69692],{},[898,69691,1712],{},[1762,69693,1764],{},[1693,69695,1695],{},[1762,69697,9154],{},[902,69699,69700],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,69703,69705],{"className":69704},[886],[888,69706,69707],{"xmlns":890},[892,69708,69709,69723],{},[895,69710,69711,69717,69719,69721],{},[3284,69712,69713,69715],{},[898,69714,1712],{},[1762,69716,2398],{},[1693,69718,1695],{},[1693,69720,1698],{},[1762,69722,9154],{},[902,69724,69725],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,69728,69730],{"className":69729},[886],[888,69731,69732],{"xmlns":890},[892,69733,69734,69774],{},[895,69735,69736,69738,69740,69742,69752,69754,69756,69758,69760,69768,69770,69772],{},[1693,69737,1709],{"stretchy":1708},[898,69739,2719],{},[898,69741,2971],{},[1717,69743,69744,69746],{},[1693,69745,1731],{"stretchy":1708},[895,69747,69748,69750],{},[1693,69749,1724],{"mathvariant":1704},[1693,69751,1724],{"mathvariant":1704},[1693,69753,1709],{"stretchy":1708},[1762,69755,9154],{},[1693,69757,1731],{"stretchy":1708},[1693,69759,1695],{},[3638,69761,69762],{"scriptlevel":1911,"displaystyle":1708},[2132,69763,69764,69766],{},[1762,69765,1764],{},[1762,69767,8357],{},[1693,69769,1922],{},[1762,69771,1911],{},[1693,69773,10870],{},[902,69775,69776],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,69779,69781],{"className":69780},[886],[888,69782,69783],{"xmlns":890},[892,69784,69785,69801],{},[895,69786,69787,69789,69791,69793,69795,69797,69799],{},[898,69788,2719],{},[898,69790,2971],{},[1693,69792,1709],{"stretchy":1708},[1762,69794,9154],{},[1693,69796,1731],{"stretchy":1708},[1693,69798,1695],{},[1762,69800,43026],{},[902,69802,69803],{"encoding":904},"AC(6) = 15",[724,69805,69806,69807,69833,69834,4300],{},"Pomocí principu: ",[883,69808,69810],{"className":69809},[886],[888,69811,69812],{"xmlns":890},[892,69813,69814,69830],{},[895,69815,69816,69818,69820,69822,69824,69826,69828],{},[898,69817,2839],{},[898,69819,2971],{},[1693,69821,1695],{},[1762,69823,2398],{},[898,69825,1712],{},[1693,69827,1892],{},[1762,69829,8357],{},[902,69831,69832],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,69835,69837],{"className":69836},[886],[888,69838,69839],{"xmlns":890},[892,69840,69841,69853],{},[895,69842,69843,69845,69847,69849,69851],{},[898,69844,2719],{},[898,69846,2971],{},[1693,69848,1695],{},[898,69850,2839],{},[898,69852,2971],{},[902,69854,5062],{"encoding":904},[883,69856,69858],{"className":69857},[886],[888,69859,69860],{"xmlns":890,"display":34854},[892,69861,69862,69964],{},[895,69863,69864,69886,69888,69890,69892,69894,69896,69898,69900,69902,69908,69910,69912,69914,69916,69918,69920,69922,69928,69930,69932,69934,69936,69938,69940,69946,69948,69950,69952,69954,69956,69958,69960,69962],{},[2132,69865,69866,69884],{},[895,69867,69868,69874,69876,69878,69880,69882],{},[1717,69869,69870,69872],{},[898,69871,1712],{},[1762,69873,2398],{},[1693,69875,1892],{},[1762,69877,8357],{},[898,69879,1712],{},[1693,69881,1892],{},[1762,69883,12433],{},[898,69885,1712],{},[1693,69887,1695],{},[1762,69889,2398],{},[898,69891,1712],{},[1693,69893,1892],{},[1762,69895,8357],{},[1915,69897,1917],{},[1693,69899,10870],{},[1915,69901,1917],{},[1717,69903,69904,69906],{},[898,69905,1712],{},[1762,69907,2398],{},[1693,69909,1892],{},[1762,69911,8357],{},[898,69913,1712],{},[1693,69915,1892],{},[1762,69917,12433],{},[1693,69919,1695],{},[1762,69921,2398],{},[1717,69923,69924,69926],{},[898,69925,1712],{},[1762,69927,2398],{},[1693,69929,1892],{},[1762,69931,8357],{},[898,69933,1712],{},[1915,69935,1917],{},[1693,69937,10870],{},[1915,69939,1917],{},[1717,69941,69942,69944],{},[898,69943,1712],{},[1762,69945,2398],{},[1693,69947,1695],{},[1762,69949,12433],{},[1915,69951,1917],{},[1693,69953,10870],{},[1915,69955,1917],{},[898,69957,1712],{},[1693,69959,1695],{},[1762,69961,9154],{},[1693,69963,1899],{"separator":1898},[902,69965,69966],{"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,",[724,69968,69969,69970,70008],{},"a ",[883,69971,69973],{"className":69972},[886],[888,69974,69975],{"xmlns":890},[892,69976,69977,70005],{},[895,69978,69979,69981,69983,69985,69987,69989,69991,69993,69995,69997,69999,70001,70003],{},[898,69980,2719],{},[898,69982,2971],{},[1693,69984,1709],{"stretchy":1708},[1762,69986,9154],{},[1693,69988,1731],{"stretchy":1708},[1693,69990,1695],{},[898,69992,2839],{},[898,69994,2971],{},[1693,69996,1709],{"stretchy":1708},[1762,69998,9154],{},[1693,70000,1731],{"stretchy":1708},[1693,70002,1695],{},[1762,70004,43026],{},[902,70006,70007],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,70010,3362],{"id":3361},[724,70012,70013,70014,4300],{},"Analogicky pro ",[883,70015,70017],{"className":70016},[886],[888,70018,70019],{"xmlns":890},[892,70020,70021,70029],{},[895,70022,70023,70025,70027],{},[898,70024,2719],{},[898,70026,2985],{},[898,70028,2971],{},[902,70030,3789],{"encoding":904},[883,70032,70034],{"className":70033},[886],[888,70035,70036],{"xmlns":890,"display":34854},[892,70037,70038,70089],{},[3626,70039,70040],{"width":34859},[3632,70041,70042,70044,70082,70084],{},[3635,70043],{"width":34864},[3635,70045,70046],{},[895,70047,70048,70050,70052,70054,70056,70062,70064,70066,70068,70070,70072,70078,70080],{},[898,70049,2719],{},[898,70051,2985],{},[898,70053,2971],{},[1693,70055,1709],{"stretchy":1708},[3284,70057,70058,70060],{},[898,70059,1712],{},[1762,70061,1911],{},[1693,70063,1731],{"stretchy":1708},[1693,70065,1695],{},[898,70067,2839],{},[898,70069,2971],{},[1693,70071,1709],{"stretchy":1708},[3284,70073,70074,70076],{},[898,70075,1712],{},[1762,70077,1911],{},[1693,70079,1731],{"stretchy":1708},[898,70081,1789],{"mathvariant":1704},[3635,70083],{"width":34864},[3635,70085,70086],{},[1915,70087,70088],{},"(3.11)",[902,70090,70091],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1636,70093,70094],{},[724,70095,70096,68776,70098],{},[883,70097,63185],{},[38,70099,70100,70101,70118],{},"V bodě minima průměrných variabilních nákladů se ",[883,70102,70104],{"className":70103},[886],[888,70105,70106],{"xmlns":890},[892,70107,70108,70116],{},[895,70109,70110,70112,70114],{},[898,70111,2719],{},[898,70113,2985],{},[898,70115,2971],{},[902,70117,3789],{"encoding":904}," rovnají mezním nákladům.",[724,70120,70121,70122,70144,70145,1789],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,70123,70125],{"className":70124},[886],[888,70126,70127],{"xmlns":890},[892,70128,70129,70141],{},[895,70130,70131,70137,70139],{},[3284,70132,70133,70135],{},[898,70134,1712],{},[1762,70136,1911],{},[1693,70138,1695],{},[1762,70140,59957],{},[902,70142,70143],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,70146,70148],{"className":70147},[886],[888,70149,70150],{"xmlns":890},[892,70151,70152,70178],{},[895,70153,70154,70156,70158,70160,70162,70164,70166,70168,70170,70172,70174,70176],{},[898,70155,2719],{},[898,70157,2985],{},[898,70159,2971],{},[1693,70161,1709],{"stretchy":1708},[898,70163,1712],{},[1693,70165,1731],{"stretchy":1708},[1693,70167,1695],{},[898,70169,2839],{},[898,70171,2971],{},[1693,70173,1709],{"stretchy":1708},[898,70175,1712],{},[1693,70177,1731],{"stretchy":1708},[902,70179,70180],{"encoding":904},"AVC(Q) = MC(Q)",[115,70182,70184],{"id":70183},"zisk-a-body-zvratu","Zisk a body zvratu",[724,70186,70187,1863,70190,70206],{},[38,70188,70189],{},"Zisk",[883,70191,70193],{"className":70192},[886],[888,70194,70195],{"xmlns":890},[892,70196,70197,70203],{},[895,70198,70199,70201],{},[898,70200,1701],{},[898,70202,2666],{},[902,70204,70205],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,70208,70210],{"className":70209},[886],[888,70211,70212],{"xmlns":890,"display":34854},[892,70213,70214,70273],{},[3626,70215,70216],{"width":34859},[3632,70217,70218,70220,70266,70268],{},[3635,70219],{"width":34864},[3635,70221,70222],{},[895,70223,70224,70226,70228,70230,70232,70234,70236,70238,70240,70242,70244,70246,70248,70250,70252,70254,70256,70258,70260,70262,70264],{},[898,70225,1701],{},[898,70227,2666],{},[1693,70229,1695],{},[898,70231,1701],{},[898,70233,2666],{},[1693,70235,1709],{"stretchy":1708},[898,70237,1712],{},[1693,70239,1731],{"stretchy":1708},[1693,70241,1695],{},[898,70243,2663],{},[898,70245,2666],{},[1693,70247,1709],{"stretchy":1708},[898,70249,1712],{},[1693,70251,1731],{"stretchy":1708},[1693,70253,1698],{},[898,70255,2663],{},[898,70257,2971],{},[1693,70259,1709],{"stretchy":1708},[898,70261,1712],{},[1693,70263,1731],{"stretchy":1708},[898,70265,1789],{"mathvariant":1704},[3635,70267],{"width":34864},[3635,70269,70270],{},[1915,70271,70272],{},"(3.12)",[902,70274,70275],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,70277,70278,70279,4286,70294,50402,70309,70311,70312,70315,70316,70332,70333,70348,70349,70364,70365,1343,70378,70391,70392,1343,70410,70428,70429,16877,70432,70435,70436,1348,70458,6055,70480,70502,70503,6055,70533,70555],{},"Body rovnosti ",[883,70280,70282],{"className":70281},[886],[888,70283,70284],{"xmlns":890},[892,70285,70286,70292],{},[895,70287,70288,70290],{},[898,70289,2663],{},[898,70291,2666],{},[902,70293,2883],{"encoding":904},[883,70295,70297],{"className":70296},[886],[888,70298,70299],{"xmlns":890},[892,70300,70301,70307],{},[895,70302,70303,70305],{},[898,70304,2663],{},[898,70306,2971],{},[902,70308,3225],{"encoding":904},[38,70310,62473],{}," (též vyrovnání, ",[614,70313,70314],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,70317,70319],{"className":70318},[886],[888,70320,70321],{"xmlns":890},[892,70322,70323,70329],{},[895,70324,70325,70327],{},[898,70326,2985],{},[898,70328,2971],{},[902,70330,70331],{"encoding":904},"VC",") je ",[883,70334,70336],{"className":70335},[886],[888,70337,70338],{"xmlns":890},[892,70339,70340,70346],{},[895,70341,70342,70344],{},[898,70343,2663],{},[898,70345,2666],{},[902,70347,2883],{"encoding":904}," kvadratická a ",[883,70350,70352],{"className":70351},[886],[888,70353,70354],{"xmlns":890},[892,70355,70356,70362],{},[895,70357,70358,70360],{},[898,70359,2663],{},[898,70361,2971],{},[902,70363,3225],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,70366,70368],{"className":70367},[886],[888,70369,70370],{"xmlns":890},[892,70371,70372,70376],{},[895,70373,70374],{},[898,70375,2719],{},[902,70377,2719],{"encoding":904},[883,70379,70381],{"className":70380},[886],[888,70382,70383],{"xmlns":890},[892,70384,70385,70389],{},[895,70386,70387],{},[898,70388,7520],{},[902,70390,7520],{"encoding":904}," odpovídajících množstvím ",[883,70393,70395],{"className":70394},[886],[888,70396,70397],{"xmlns":890},[892,70398,70399,70407],{},[895,70400,70401],{},[3284,70402,70403,70405],{},[898,70404,1712],{},[898,70406,2719],{},[902,70408,70409],{"encoding":904},"Q_A",[883,70411,70413],{"className":70412},[886],[888,70414,70415],{"xmlns":890},[892,70416,70417,70425],{},[895,70418,70419],{},[3284,70420,70421,70423],{},[898,70422,1712],{},[898,70424,7520],{},[902,70426,70427],{"encoding":904},"Q_B"," — firma je na ",[38,70430,70431],{},"prahu rentability",[614,70433,70434],{},"break even","). Pro ",[883,70437,70439],{"className":70438},[886],[888,70440,70441],{"xmlns":890},[892,70442,70443,70455],{},[895,70444,70445,70447,70449],{},[898,70446,1712],{},[1693,70448,1908],{},[3284,70450,70451,70453],{},[898,70452,1712],{},[898,70454,2719],{},[902,70456,70457],{"encoding":904},"Q \u003C Q_A",[883,70459,70461],{"className":70460},[886],[888,70462,70463],{"xmlns":890},[892,70464,70465,70477],{},[895,70466,70467,70469,70471],{},[898,70468,1712],{},[1693,70470,1922],{},[3284,70472,70473,70475],{},[898,70474,1712],{},[898,70476,7520],{},[902,70478,70479],{"encoding":904},"Q > Q_B",[883,70481,70483],{"className":70482},[886],[888,70484,70485],{"xmlns":890},[892,70486,70487,70499],{},[895,70488,70489,70491,70493,70495,70497],{},[898,70490,2663],{},[898,70492,2971],{},[1693,70494,1922],{},[898,70496,2663],{},[898,70498,2666],{},[902,70500,70501],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,70504,70506],{"className":70505},[886],[888,70507,70508],{"xmlns":890},[892,70509,70510,70530],{},[895,70511,70512,70518,70520,70522,70524],{},[3284,70513,70514,70516],{},[898,70515,1712],{},[898,70517,2719],{},[1693,70519,1908],{},[898,70521,1712],{},[1693,70523,1908],{},[3284,70525,70526,70528],{},[898,70527,1712],{},[898,70529,7520],{},[902,70531,70532],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,70534,70536],{"className":70535},[886],[888,70537,70538],{"xmlns":890},[892,70539,70540,70552],{},[895,70541,70542,70544,70546,70548,70550],{},[898,70543,2663],{},[898,70545,2666],{},[1693,70547,1922],{},[898,70549,2663],{},[898,70551,2971],{},[902,70553,70554],{"encoding":904},"TR > TC"," (zisk).",[1636,70557,70558],{},[724,70559,70560,70562],{},[883,70561,11036],{}," 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.",[724,70564,70565,70566,70592],{},"Body zvratu jsou řešení rovnice ",[883,70567,70569],{"className":70568},[886],[888,70570,70571],{"xmlns":890},[892,70572,70573,70589],{},[895,70574,70575,70577,70579,70581,70583,70585,70587],{},[898,70576,1701],{},[898,70578,2666],{},[1693,70580,1709],{"stretchy":1708},[898,70582,1712],{},[1693,70584,1731],{"stretchy":1708},[1693,70586,1695],{},[1762,70588,1911],{},[902,70590,70591],{"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.",[724,70594,70595],{},[9465,70596],{"alt":70597,"className":70598,"src":70599},"imek-tr-tc-body-zvratu",[210,9469],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,70601,70602],{},[614,70603,70604,70605,70620,70621,70636,70637,4286,70650,50126,70663,70676,70677,4286,70694,70711,70712,70732,70733,4286,70748,7721,70763,70792],{},"Obrázek 3.11: Body zvratu — křivky ",[883,70606,70608],{"className":70607},[886],[888,70609,70610],{"xmlns":890},[892,70611,70612,70618],{},[895,70613,70614,70616],{},[898,70615,2663],{},[898,70617,2666],{},[902,70619,2883],{"encoding":904}," (obrácená parabola) a ",[883,70622,70624],{"className":70623},[886],[888,70625,70626],{"xmlns":890},[892,70627,70628,70634],{},[895,70629,70630,70632],{},[898,70631,2663],{},[898,70633,2971],{},[902,70635,3225],{"encoding":904}," (přímka) se protínají v bodech ",[883,70638,70640],{"className":70639},[886],[888,70641,70642],{"xmlns":890},[892,70643,70644,70648],{},[895,70645,70646],{},[898,70647,2719],{},[902,70649,2719],{"encoding":904},[883,70651,70653],{"className":70652},[886],[888,70654,70655],{"xmlns":890},[892,70656,70657,70661],{},[895,70658,70659],{},[898,70660,7520],{},[902,70662,7520],{"encoding":904},[883,70664,70666],{"className":70665},[886],[888,70667,70668],{"xmlns":890},[892,70669,70670,70674],{},[895,70671,70672],{},[898,70673,1712],{},[902,70675,1712],{"encoding":904}," v hodnotách ",[883,70678,70680],{"className":70679},[886],[888,70681,70682],{"xmlns":890},[892,70683,70684,70692],{},[895,70685,70686],{},[3284,70687,70688,70690],{},[898,70689,1712],{},[898,70691,2719],{},[902,70693,70409],{"encoding":904},[883,70695,70697],{"className":70696},[886],[888,70698,70699],{"xmlns":890},[892,70700,70701,70709],{},[895,70702,70703],{},[3284,70704,70705,70707],{},[898,70706,1712],{},[898,70708,7520],{},[902,70710,70427],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,70713,70715],{"className":70714},[886],[888,70716,70717],{"xmlns":890},[892,70718,70719,70729],{},[895,70720,70721],{},[3284,70722,70723,70725,70727],{},[898,70724,1712],{},[898,70726,62941],{},[1693,70728,3742],{},[902,70730,70731],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,70734,70736],{"className":70735},[886],[888,70737,70738],{"xmlns":890},[892,70739,70740,70746],{},[895,70741,70742,70744],{},[898,70743,2663],{},[898,70745,2666],{},[902,70747,2883],{"encoding":904},[883,70749,70751],{"className":70750},[886],[888,70752,70753],{"xmlns":890},[892,70754,70755,70761],{},[895,70756,70757,70759],{},[898,70758,2663],{},[898,70760,2971],{},[902,70762,3225],{"encoding":904},[883,70764,70766],{"className":70765},[886],[888,70767,70768],{"xmlns":890},[892,70769,70770,70790],{},[895,70771,70772,70778,70780,70782,70784],{},[3284,70773,70774,70776],{},[898,70775,1712],{},[898,70777,2719],{},[1693,70779,1908],{},[898,70781,1712],{},[1693,70783,1908],{},[3284,70785,70786,70788],{},[898,70787,1712],{},[898,70789,7520],{},[902,70791,70532],{"encoding":904}," vyznačuje zisk.",[44125,70794,70796],{"id":70795},"příklad-38","Příklad 3.8",[724,70798,70799,70801,70802,1343,70822,1343,70848,70874],{},[38,70800,62731],{}," Dáno ",[883,70803,70805],{"className":70804},[886],[888,70806,70807],{"xmlns":890},[892,70808,70809,70819],{},[895,70810,70811,70813,70815,70817],{},[898,70812,2976],{},[898,70814,2971],{},[1693,70816,1695],{},[1762,70818,9262],{},[902,70820,70821],{"encoding":904},"FC = 4",[883,70823,70825],{"className":70824},[886],[888,70826,70827],{"xmlns":890},[892,70828,70829,70845],{},[895,70830,70831,70833,70835,70837,70839],{},[898,70832,2663],{},[898,70834,2985],{},[898,70836,2971],{},[1693,70838,1695],{},[1717,70840,70841,70843],{},[898,70842,1712],{},[1762,70844,2398],{},[902,70846,70847],{"encoding":904},"TVC = Q^2",[883,70849,70851],{"className":70850},[886],[888,70852,70853],{"xmlns":890},[892,70854,70855,70871],{},[895,70856,70857,70859,70861,70863,70865,70867,70869],{},[898,70858,1701],{},[1693,70860,1695],{},[1693,70862,1698],{},[1762,70864,2398],{},[898,70866,1712],{},[1693,70868,1892],{},[1762,70870,10881],{},[902,70872,70873],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,70876,70877,70879],{},[38,70878,29570],{}," Celkové náklady a příjem:",[883,70881,70883],{"className":70882},[886],[888,70884,70885],{"xmlns":890,"display":34854},[892,70886,70887,70953],{},[895,70888,70889,70891,70893,70895,70897,70899,70905,70907,70909,70911,70913,70915,70917,70919,70921,70923,70925,70927,70929,70931,70933,70935,70937,70939,70945,70947,70949,70951],{},[898,70890,2663],{},[898,70892,2971],{},[1693,70894,1695],{},[1762,70896,9262],{},[1693,70898,1892],{},[1717,70900,70901,70903],{},[898,70902,1712],{},[1762,70904,2398],{},[1693,70906,1899],{"separator":1898},[1901,70908],{"width":1903},[898,70910,2663],{},[898,70912,2666],{},[1693,70914,1695],{},[898,70916,1712],{},[1693,70918,1715],{},[1693,70920,1709],{"stretchy":1708},[1693,70922,1698],{},[1762,70924,2398],{},[898,70926,1712],{},[1693,70928,1892],{},[1762,70930,10881],{},[1693,70932,1731],{"stretchy":1708},[1693,70934,1695],{},[1693,70936,1698],{},[1762,70938,2398],{},[1717,70940,70941,70943],{},[898,70942,1712],{},[1762,70944,2398],{},[1693,70946,1892],{},[1762,70948,10881],{},[898,70950,1712],{},[898,70952,1789],{"mathvariant":1704},[902,70954,70955],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,70957,70958],{},"Zisk dle (3.12):",[883,70960,70962],{"className":70961},[886],[888,70963,70964],{"xmlns":890,"display":34854},[892,70965,70966,71044],{},[895,70967,70968,70970,70972,70974,70976,70978,70980,70982,70984,70986,70988,70990,70992,70998,71000,71002,71004,71006,71008,71010,71012,71014,71020,71022,71024,71026,71028,71034,71036,71038,71040,71042],{},[898,70969,1701],{},[898,70971,2666],{},[1693,70973,1695],{},[898,70975,2663],{},[898,70977,2666],{},[1693,70979,1698],{},[898,70981,2663],{},[898,70983,2971],{},[1693,70985,1695],{},[1693,70987,1709],{"stretchy":1708},[1693,70989,1698],{},[1762,70991,2398],{},[1717,70993,70994,70996],{},[898,70995,1712],{},[1762,70997,2398],{},[1693,70999,1892],{},[1762,71001,10881],{},[898,71003,1712],{},[1693,71005,1731],{"stretchy":1708},[1693,71007,1698],{},[1693,71009,1709],{"stretchy":1708},[1762,71011,9262],{},[1693,71013,1892],{},[1717,71015,71016,71018],{},[898,71017,1712],{},[1762,71019,2398],{},[1693,71021,1731],{"stretchy":1708},[1693,71023,1695],{},[1693,71025,1698],{},[1762,71027,8357],{},[1717,71029,71030,71032],{},[898,71031,1712],{},[1762,71033,2398],{},[1693,71035,1892],{},[1762,71037,10881],{},[898,71039,1712],{},[1693,71041,1698],{},[1762,71043,66054],{},[902,71045,71046],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,71048,71049,71052,71053,24395,71089,4300],{},[38,71050,71051],{},"Body zvratu"," jsou kořeny rovnice ",[883,71054,71056],{"className":71055},[886],[888,71057,71058],{"xmlns":890},[892,71059,71060,71086],{},[895,71061,71062,71064,71066,71072,71074,71076,71078,71080,71082,71084],{},[1693,71063,1698],{},[1762,71065,8357],{},[1717,71067,71068,71070],{},[898,71069,1712],{},[1762,71071,2398],{},[1693,71073,1892],{},[1762,71075,10881],{},[898,71077,1712],{},[1693,71079,1698],{},[1762,71081,9262],{},[1693,71083,1695],{},[1762,71085,1911],{},[902,71087,71088],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,71090,71092],{"className":71091},[886],[888,71093,71094],{"xmlns":890},[892,71095,71096,71120],{},[895,71097,71098,71100,71106,71108,71110,71112,71114,71116,71118],{},[1762,71099,8357],{},[1717,71101,71102,71104],{},[898,71103,1712],{},[1762,71105,2398],{},[1693,71107,1698],{},[1762,71109,10881],{},[898,71111,1712],{},[1693,71113,1892],{},[1762,71115,9262],{},[1693,71117,1695],{},[1762,71119,1911],{},[902,71121,71122],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,71124,71126],{"className":71125},[886],[888,71127,71128],{"xmlns":890,"display":34854},[892,71129,71130,71187],{},[895,71131,71132,71144,71146,71169,71171,71185],{},[3284,71133,71134,71136],{},[898,71135,1712],{},[895,71137,71138,71140,71142],{},[1762,71139,1764],{},[1693,71141,1899],{"separator":1898},[1762,71143,2398],{},[1693,71145,1695],{},[2132,71147,71148,71167],{},[895,71149,71150,71152,71155],{},[1762,71151,10881],{},[1693,71153,71154],{},"±",[14976,71156,71157],{},[895,71158,71159,71162,71164],{},[1762,71160,71161],{},"81",[1693,71163,1698],{},[1762,71165,71166],{},"48",[1762,71168,9154],{},[1693,71170,1695],{},[2132,71172,71173,71183],{},[895,71174,71175,71177,71179],{},[1762,71176,10881],{},[1693,71178,71154],{},[14976,71180,71181],{},[1762,71182,15808],{},[1762,71184,9154],{},[1693,71186,1899],{"separator":1898},[902,71188,71189],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,71191,71192,71193,4286,71216,1789],{},"numericky ",[883,71194,71196],{"className":71195},[886],[888,71197,71198],{"xmlns":890},[892,71199,71200,71213],{},[895,71201,71202,71208,71210],{},[3284,71203,71204,71206],{},[898,71205,1712],{},[1762,71207,1764],{},[1693,71209,12766],{},[1762,71211,71212],{},"0,543",[902,71214,71215],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,71217,71219],{"className":71218},[886],[888,71220,71221],{"xmlns":890},[892,71222,71223,71236],{},[895,71224,71225,71231,71233],{},[3284,71226,71227,71229],{},[898,71228,1712],{},[1762,71230,2398],{},[1693,71232,12766],{},[1762,71234,71235],{},"2,457",[902,71237,71238],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,71240,71241,1863,71244,14412,71289,24395,71323,71341],{},[38,71242,71243],{},"Maximum zisku.",[883,71245,71247],{"className":71246},[886],[888,71248,71249],{"xmlns":890},[892,71250,71251,71286],{},[895,71252,71253,71255,71261,71263,71265,71267,71269,71271,71273,71275,71277,71279,71281,71283],{},[898,71254,1701],{},[1717,71256,71257,71259],{},[898,71258,2666],{},[1693,71260,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,71262,1695],{},[1693,71264,1698],{},[1762,71266,9154],{},[898,71268,1712],{},[1693,71270,1892],{},[1762,71272,10881],{},[1693,71274,1695],{},[1762,71276,1911],{},[1693,71278,10870],{},[898,71280,1712],{},[1693,71282,1695],{},[1762,71284,71285],{},"1,5",[902,71287,71288],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,71290,71292],{"className":71291},[886],[888,71293,71294],{"xmlns":890},[892,71295,71296,71320],{},[895,71297,71298,71300,71310,71312,71314,71316,71318],{},[898,71299,1701],{},[1717,71301,71302,71304],{},[898,71303,2666],{},[895,71305,71306,71308],{},[1693,71307,1724],{"mathvariant":1704},[1693,71309,1724],{"mathvariant":1704},[1693,71311,1695],{},[1693,71313,1698],{},[1762,71315,9154],{},[1693,71317,1908],{},[1762,71319,1911],{},[902,71321,71322],{"encoding":904},"PR'' = -6 \u003C 0",[883,71324,71326],{"className":71325},[886],[888,71327,71328],{"xmlns":890},[892,71329,71330,71338],{},[895,71331,71332,71334,71336],{},[898,71333,1712],{},[1693,71335,1695],{},[1762,71337,71285],{},[902,71339,71340],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,71343,71345],{"className":71344},[886],[888,71346,71347],{"xmlns":890,"display":34854},[892,71348,71349,71412],{},[895,71350,71351,71353,71355,71357,71359,71361,71363,71365,71367,71369,71371,71373,71379,71381,71383,71385,71387,71389,71391,71393,71395,71398,71400,71403,71405,71407,71409],{},[898,71352,1701],{},[898,71354,2666],{},[1693,71356,1709],{"stretchy":1708},[1762,71358,71285],{},[1693,71360,1731],{"stretchy":1708},[1693,71362,1695],{},[1693,71364,1698],{},[1762,71366,8357],{},[1693,71368,1715],{},[1693,71370,1709],{"stretchy":1708},[1762,71372,71285],{},[1717,71374,71375,71377],{},[1693,71376,1731],{"stretchy":1708},[1762,71378,2398],{},[1693,71380,1892],{},[1762,71382,10881],{},[1693,71384,1715],{},[1762,71386,71285],{},[1693,71388,1698],{},[1762,71390,9262],{},[1693,71392,1695],{},[1693,71394,1698],{},[1762,71396,71397],{},"6,75",[1693,71399,1892],{},[1762,71401,71402],{},"13,5",[1693,71404,1698],{},[1762,71406,9262],{},[1693,71408,1695],{},[1762,71410,71411],{},"2,75.",[902,71413,71414],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,71416,71417,71418,1343,71463,71516,71517,71535],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,71419,71421],{"className":71420},[886],[888,71422,71423],{"xmlns":890},[892,71424,71425,71460],{},[895,71426,71427,71429,71435,71437,71439,71441,71443,71445,71447,71449,71451,71453,71455,71457],{},[898,71428,2663],{},[1717,71430,71431,71433],{},[898,71432,2666],{},[1693,71434,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,71436,1695],{},[1693,71438,1698],{},[1762,71440,9262],{},[898,71442,1712],{},[1693,71444,1892],{},[1762,71446,10881],{},[1693,71448,1695],{},[1762,71450,1911],{},[1693,71452,10870],{},[898,71454,1712],{},[1693,71456,1695],{},[1762,71458,71459],{},"2,25",[902,71461,71462],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,71464,71466],{"className":71465},[886],[888,71467,71468],{"xmlns":890},[892,71469,71470,71513],{},[895,71471,71472,71474,71482,71484,71486,71488,71490,71492,71494,71500,71502,71504,71506,71508,71510],{},[898,71473,2663],{},[3284,71475,71476,71478,71480],{},[898,71477,2666],{},[898,71479,62941],{},[1693,71481,3742],{},[1693,71483,1695],{},[1693,71485,1698],{},[1762,71487,2398],{},[1693,71489,1715],{},[1693,71491,1709],{"stretchy":1708},[1762,71493,71459],{},[1717,71495,71496,71498],{},[1693,71497,1731],{"stretchy":1708},[1762,71499,2398],{},[1693,71501,1892],{},[1762,71503,10881],{},[1693,71505,1715],{},[1762,71507,71459],{},[1693,71509,1695],{},[1762,71511,71512],{},"10,125",[902,71514,71515],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,71518,71520],{"className":71519},[886],[888,71521,71522],{"xmlns":890},[892,71523,71524,71532],{},[895,71525,71526,71528,71530],{},[898,71527,1712],{},[1693,71529,1695],{},[1762,71531,71459],{},[902,71533,71534],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1636,71537,71538],{},[724,71539,71540,71542,71543,1343,71565,71587,71588,1343,71605,71626,71627,71659,71660,71698,71699,9577,71717,71734,71735,4286,71763,71797,71798,14545,71836,4286,71860,1789],{},[883,71541,8654],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,71544,71546],{"className":71545},[886],[888,71547,71548],{"xmlns":890},[892,71549,71550,71562],{},[895,71551,71552,71558,71560],{},[3284,71553,71554,71556],{},[898,71555,1712],{},[1762,71557,1764],{},[1693,71559,1695],{},[1762,71561,11877],{},[902,71563,71564],{"encoding":904},"Q_1 = 0{,}5",[883,71566,71568],{"className":71567},[886],[888,71569,71570],{"xmlns":890},[892,71571,71572,71584],{},[895,71573,71574,71580,71582],{},[3284,71575,71576,71578],{},[898,71577,1712],{},[1762,71579,2398],{},[1693,71581,1695],{},[1762,71583,9262],{},[902,71585,71586],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,71589,71591],{"className":71590},[886],[888,71592,71593],{"xmlns":890},[892,71594,71595,71603],{},[895,71596,71597,71599,71601],{},[898,71598,1712],{},[1693,71600,1695],{},[1762,71602,71459],{},[902,71604,71534],{"encoding":904},[883,71606,71608],{"className":71607},[886],[888,71609,71610],{"xmlns":890},[892,71611,71612,71623],{},[895,71613,71614,71616,71618,71620],{},[898,71615,1701],{},[898,71617,2666],{},[1693,71619,1695],{},[1762,71621,71622],{},"6,125",[902,71624,71625],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,71628,71630],{"className":71629},[886],[888,71631,71632],{"xmlns":890},[892,71633,71634,71656],{},[895,71635,71636,71638,71644,71646,71648,71650,71652,71654],{},[898,71637,1701],{},[1717,71639,71640,71642],{},[898,71641,2666],{},[1693,71643,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,71645,1695],{},[1693,71647,1698],{},[1762,71649,9262],{},[898,71651,1712],{},[1693,71653,1892],{},[1762,71655,10881],{},[902,71657,71658],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,71661,71663],{"className":71662},[886],[888,71664,71665],{"xmlns":890},[892,71666,71667,71695],{},[895,71668,71669,71671,71673,71675,71677,71679,71685,71687,71689,71691,71693],{},[898,71670,1701],{},[898,71672,2666],{},[1693,71674,1695],{},[1693,71676,1698],{},[1762,71678,2398],{},[1717,71680,71681,71683],{},[898,71682,1712],{},[1762,71684,2398],{},[1693,71686,1892],{},[1762,71688,10881],{},[898,71690,1712],{},[1693,71692,1698],{},[1762,71694,9262],{},[902,71696,71697],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,71700,71702],{"className":71701},[886],[888,71703,71704],{"xmlns":890},[892,71705,71706,71714],{},[895,71707,71708],{},[1717,71709,71710,71712],{},[898,71711,1712],{},[1762,71713,2398],{},[902,71715,71716],{"encoding":904},"Q^2",[883,71718,71720],{"className":71719},[886],[888,71721,71722],{"xmlns":890},[892,71723,71724,71732],{},[895,71725,71726,71728,71730],{},[898,71727,2663],{},[898,71729,2985],{},[898,71731,2971],{},[902,71733,3041],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,71736,71738],{"className":71737},[886],[888,71739,71740],{"xmlns":890},[892,71741,71742,71760],{},[895,71743,71744,71746,71748,71750,71752,71754],{},[898,71745,2663],{},[898,71747,2971],{},[1693,71749,1695],{},[1762,71751,9262],{},[1693,71753,1892],{},[1717,71755,71756,71758],{},[898,71757,1712],{},[1762,71759,2398],{},[902,71761,71762],{"encoding":904},"TC = 4 + Q^2",[883,71764,71766],{"className":71765},[886],[888,71767,71768],{"xmlns":890},[892,71769,71770,71794],{},[895,71771,71772,71774,71776,71778,71780,71782,71788,71790,71792],{},[898,71773,2663],{},[898,71775,2666],{},[1693,71777,1695],{},[1693,71779,1698],{},[1762,71781,2398],{},[1717,71783,71784,71786],{},[898,71785,1712],{},[1762,71787,2398],{},[1693,71789,1892],{},[1762,71791,10881],{},[898,71793,1712],{},[902,71795,71796],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,71799,71801],{"className":71800},[886],[888,71802,71803],{"xmlns":890},[892,71804,71805,71833],{},[895,71806,71807,71809,71811,71813,71815,71817,71823,71825,71827,71829,71831],{},[898,71808,1701],{},[898,71810,2666],{},[1693,71812,1695],{},[1693,71814,1698],{},[1762,71816,8357],{},[1717,71818,71819,71821],{},[898,71820,1712],{},[1762,71822,2398],{},[1693,71824,1892],{},[1762,71826,10881],{},[898,71828,1712],{},[1693,71830,1698],{},[1762,71832,9262],{},[902,71834,71835],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,71837,71839],{"className":71838},[886],[888,71840,71841],{"xmlns":890},[892,71842,71843,71857],{},[895,71844,71845,71853,71855],{},[3284,71846,71847,71849,71851],{},[898,71848,1712],{},[898,71850,62941],{},[1693,71852,3742],{},[1693,71854,1695],{},[1762,71856,71285],{},[902,71858,71859],{"encoding":904},"Q_{\\max} = 1{,}5",[883,71861,71863],{"className":71862},[886],[888,71864,71865],{"xmlns":890},[892,71866,71867,71884],{},[895,71868,71869,71871,71879,71881],{},[898,71870,1701],{},[3284,71872,71873,71875,71877],{},[898,71874,2666],{},[898,71876,62941],{},[1693,71878,3742],{},[1693,71880,1695],{},[1762,71882,71883],{},"2,75",[902,71885,71886],{"encoding":904},"PR_{\\max} = 2{,}75",[724,71888,71889],{},[614,71890,71891,71892,71919,71920,71953,71954,1343,71977,1789],{},"Obrázek 3.12: Graf ",[883,71893,71895],{"className":71894},[886],[888,71896,71897],{"xmlns":890},[892,71898,71899,71917],{},[895,71900,71901,71903,71905,71907,71909,71911],{},[898,71902,2663],{},[898,71904,2971],{},[1693,71906,1695],{},[1762,71908,9262],{},[1693,71910,1892],{},[1717,71912,71913,71915],{},[898,71914,1712],{},[1762,71916,2398],{},[902,71918,71762],{"encoding":904}," (parabola) a ",[883,71921,71923],{"className":71922},[886],[888,71924,71925],{"xmlns":890},[892,71926,71927,71951],{},[895,71928,71929,71931,71933,71935,71937,71939,71945,71947,71949],{},[898,71930,2663],{},[898,71932,2666],{},[1693,71934,1695],{},[1693,71936,1698],{},[1762,71938,2398],{},[1717,71940,71941,71943],{},[898,71942,1712],{},[1762,71944,2398],{},[1693,71946,1892],{},[1762,71948,10881],{},[898,71950,1712],{},[902,71952,71796],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,71955,71957],{"className":71956},[886],[888,71958,71959],{"xmlns":890},[892,71960,71961,71974],{},[895,71962,71963,71969,71971],{},[3284,71964,71965,71967],{},[898,71966,1712],{},[1762,71968,1764],{},[1693,71970,12766],{},[1762,71972,71973],{},"0,54",[902,71975,71976],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,71978,71980],{"className":71979},[886],[888,71981,71982],{"xmlns":890},[892,71983,71984,71997],{},[895,71985,71986,71992,71994],{},[3284,71987,71988,71990],{},[898,71989,1712],{},[1762,71991,2398],{},[1693,71993,12766],{},[1762,71995,71996],{},"2,46",[902,71998,71999],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,72001,72002],{},[614,72003,72004,72005,65246,72042,72059,72060,1343,72081,1789],{},"Obrázek 3.13: Graf zisku ",[883,72006,72008],{"className":72007},[886],[888,72009,72010],{"xmlns":890},[892,72011,72012,72040],{},[895,72013,72014,72016,72018,72020,72022,72024,72030,72032,72034,72036,72038],{},[898,72015,1701],{},[898,72017,2666],{},[1693,72019,1695],{},[1693,72021,1698],{},[1762,72023,8357],{},[1717,72025,72026,72028],{},[898,72027,1712],{},[1762,72029,2398],{},[1693,72031,1892],{},[1762,72033,10881],{},[898,72035,1712],{},[1693,72037,1698],{},[1762,72039,9262],{},[902,72041,71835],{"encoding":904},[883,72043,72045],{"className":72044},[886],[888,72046,72047],{"xmlns":890},[892,72048,72049,72057],{},[895,72050,72051,72053,72055],{},[898,72052,1712],{},[1693,72054,1695],{},[1762,72056,71285],{},[902,72058,71340],{"encoding":904}," a nulami ",[883,72061,72063],{"className":72062},[886],[888,72064,72065],{"xmlns":890},[892,72066,72067,72079],{},[895,72068,72069,72075,72077],{},[3284,72070,72071,72073],{},[898,72072,1712],{},[1762,72074,1764],{},[1693,72076,12766],{},[1762,72078,71973],{},[902,72080,71976],{"encoding":904},[883,72082,72084],{"className":72083},[886],[888,72085,72086],{"xmlns":890},[892,72087,72088,72100],{},[895,72089,72090,72096,72098],{},[3284,72091,72092,72094],{},[898,72093,1712],{},[1762,72095,2398],{},[1693,72097,12766],{},[1762,72099,71996],{},[902,72101,71999],{"encoding":904},[115,72103,3460],{"id":3459},[724,72105,72106],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,72108,72109],{},[9465,72110],{"alt":72111,"className":72112,"src":72113},"imek-max-zisku-dva-pohledy",[210,9469],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,72115,23233],{"id":72116},"princip-1",[724,72118,72119,72120,9530,72135,72152],{},"Má-li zisk ",[883,72121,72123],{"className":72122},[886],[888,72124,72125],{"xmlns":890},[892,72126,72127,72133],{},[895,72128,72129,72131],{},[898,72130,1701],{},[898,72132,2666],{},[902,72134,70205],{"encoding":904},[883,72136,72138],{"className":72137},[886],[888,72139,72140],{"xmlns":890},[892,72141,72142,72150],{},[895,72143,72144],{},[3284,72145,72146,72148],{},[898,72147,1712],{},[1762,72149,1911],{},[902,72151,6293],{"encoding":904}," maximum, pak platí",[883,72154,72156],{"className":72155},[886],[888,72157,72158],{"xmlns":890,"display":34854},[892,72159,72160,72209],{},[3626,72161,72162],{"width":34859},[3632,72163,72164,72166,72202,72204],{},[3635,72165],{"width":34864},[3635,72167,72168],{},[895,72169,72170,72172,72174,72176,72182,72184,72186,72188,72190,72192,72198,72200],{},[898,72171,2839],{},[898,72173,2666],{},[1693,72175,1709],{"stretchy":1708},[3284,72177,72178,72180],{},[898,72179,1712],{},[1762,72181,1911],{},[1693,72183,1731],{"stretchy":1708},[1693,72185,1695],{},[898,72187,2839],{},[898,72189,2971],{},[1693,72191,1709],{"stretchy":1708},[3284,72193,72194,72196],{},[898,72195,1712],{},[1762,72197,1911],{},[1693,72199,1731],{"stretchy":1708},[898,72201,1789],{"mathvariant":1704},[3635,72203],{"width":34864},[3635,72205,72206],{},[1915,72207,72208],{},"(3.13)",[902,72210,72211],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1636,72213,72214],{},[724,72215,72216,68776,72218],{},[883,72217,63185],{},[38,72219,72220],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,72222,72223,72226,72227,6055,72254,24395,72328,1789],{},[38,72224,72225],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,72228,72230],{"className":72229},[886],[888,72231,72232],{"xmlns":890},[892,72233,72234,72252],{},[895,72235,72236,72238,72240,72242,72244,72246,72248,72250],{},[898,72237,1701],{},[898,72239,2666],{},[1693,72241,1695],{},[898,72243,2663],{},[898,72245,2666],{},[1693,72247,1698],{},[898,72249,2663],{},[898,72251,2971],{},[902,72253,3537],{"encoding":904},[883,72255,72257],{"className":72256},[886],[888,72258,72259],{"xmlns":890},[892,72260,72261,72325],{},[895,72262,72263,72265,72271,72273,72279,72281,72283,72285,72291,72293,72299,72301,72303,72305,72311,72313,72319,72321,72323],{},[898,72264,1701],{},[1717,72266,72267,72269],{},[898,72268,2666],{},[1693,72270,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,72272,1709],{"stretchy":1708},[3284,72274,72275,72277],{},[898,72276,1712],{},[1762,72278,1911],{},[1693,72280,1731],{"stretchy":1708},[1693,72282,1695],{},[898,72284,2663],{},[1717,72286,72287,72289],{},[898,72288,2666],{},[1693,72290,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,72292,1709],{"stretchy":1708},[3284,72294,72295,72297],{},[898,72296,1712],{},[1762,72298,1911],{},[1693,72300,1731],{"stretchy":1708},[1693,72302,1698],{},[898,72304,2663],{},[1717,72306,72307,72309],{},[898,72308,2971],{},[1693,72310,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,72312,1709],{"stretchy":1708},[3284,72314,72315,72317],{},[898,72316,1712],{},[1762,72318,1911],{},[1693,72320,1731],{"stretchy":1708},[1693,72322,1695],{},[1762,72324,1911],{},[902,72326,72327],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,72329,72331],{"className":72330},[886],[888,72332,72333],{"xmlns":890},[892,72334,72335,72367],{},[895,72336,72337,72339,72341,72343,72349,72351,72353,72355,72357,72359,72365],{},[898,72338,2839],{},[898,72340,2666],{},[1693,72342,1709],{"stretchy":1708},[3284,72344,72345,72347],{},[898,72346,1712],{},[1762,72348,1911],{},[1693,72350,1731],{"stretchy":1708},[1693,72352,1695],{},[898,72354,2839],{},[898,72356,2971],{},[1693,72358,1709],{"stretchy":1708},[3284,72360,72361,72363],{},[898,72362,1712],{},[1762,72364,1911],{},[1693,72366,1731],{"stretchy":1708},[902,72368,3504],{"encoding":904},[1636,72370,72371,72376],{},[724,72372,72373,72375],{},[883,72374,8620],{}," Postup — jak najít maximum zisku",[152,72377,72378,72442,72497,72534,72562],{},[123,72379,72380,72381,4286,72396,72411,72412,3042],{},"Sestavte ",[883,72382,72384],{"className":72383},[886],[888,72385,72386],{"xmlns":890},[892,72387,72388,72394],{},[895,72389,72390,72392],{},[898,72391,2663],{},[898,72393,2666],{},[902,72395,2883],{"encoding":904},[883,72397,72399],{"className":72398},[886],[888,72400,72401],{"xmlns":890},[892,72402,72403,72409],{},[895,72404,72405,72407],{},[898,72406,2663],{},[898,72408,2971],{},[902,72410,3225],{"encoding":904}," ze zadání (typicky ",[883,72413,72415],{"className":72414},[886],[888,72416,72417],{"xmlns":890},[892,72418,72419,72439],{},[895,72420,72421,72423,72425,72427,72429,72431,72433,72435,72437],{},[898,72422,2663],{},[898,72424,2666],{},[1693,72426,1695],{},[898,72428,1701],{},[1693,72430,1709],{"stretchy":1708},[898,72432,1712],{},[1693,72434,1731],{"stretchy":1708},[1693,72436,1715],{},[898,72438,1712],{},[902,72440,72441],{"encoding":904},"TR = P(Q) \\cdot Q",[123,72443,72444,72445,4286,72471,1789],{},"Vypočtěte ",[883,72446,72448],{"className":72447},[886],[888,72449,72450],{"xmlns":890},[892,72451,72452,72468],{},[895,72453,72454,72456,72458,72460,72462],{},[898,72455,2839],{},[898,72457,2666],{},[1693,72459,1695],{},[898,72461,2663],{},[1717,72463,72464,72466],{},[898,72465,2666],{},[1693,72467,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,72469,72470],{"encoding":904},"MR = TR'",[883,72472,72474],{"className":72473},[886],[888,72475,72476],{"xmlns":890},[892,72477,72478,72494],{},[895,72479,72480,72482,72484,72486,72488],{},[898,72481,2839],{},[898,72483,2971],{},[1693,72485,1695],{},[898,72487,2663],{},[1717,72489,72490,72492],{},[898,72491,2971],{},[1693,72493,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,72495,72496],{"encoding":904},"MC = TC'",[123,72498,72499,72500,1789],{},"Řešte rovnici ",[883,72501,72503],{"className":72502},[886],[888,72504,72505],{"xmlns":890},[892,72506,72507,72531],{},[895,72508,72509,72511,72513,72515,72517,72519,72521,72523,72525,72527,72529],{},[898,72510,2839],{},[898,72512,2666],{},[1693,72514,1709],{"stretchy":1708},[898,72516,1712],{},[1693,72518,1731],{"stretchy":1708},[1693,72520,1695],{},[898,72522,2839],{},[898,72524,2971],{},[1693,72526,1709],{"stretchy":1708},[898,72528,1712],{},[1693,72530,1731],{"stretchy":1708},[902,72532,72533],{"encoding":904},"MR(Q) = MC(Q)",[123,72535,72536,72537,72561],{},"Ověřte druhou derivaci ",[883,72538,72540],{"className":72539},[886],[888,72541,72542],{"xmlns":890},[892,72543,72544,72558],{},[895,72545,72546,72548],{},[898,72547,1701],{},[1717,72549,72550,72552],{},[898,72551,2666],{},[895,72553,72554,72556],{},[1693,72555,1724],{"mathvariant":1704},[1693,72557,1724],{"mathvariant":1704},[902,72559,72560],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,72563,72564,72565,72592],{},"Dosaďte do ",[883,72566,72568],{"className":72567},[886],[888,72569,72570],{"xmlns":890},[892,72571,72572,72590],{},[895,72573,72574,72576,72578,72580,72582,72584,72586,72588],{},[898,72575,1701],{},[898,72577,2666],{},[1693,72579,1695],{},[898,72581,2663],{},[898,72583,2666],{},[1693,72585,1698],{},[898,72587,2663],{},[898,72589,2971],{},[902,72591,3537],{"encoding":904}," pro hodnotu maxima.",[44125,72594,72596],{"id":72595},"příklad-39","Příklad 3.9",[724,72598,72599,62732,72601,4286,72623,72659],{},[38,72600,62731],{},[883,72602,72604],{"className":72603},[886],[888,72605,72606],{"xmlns":890},[892,72607,72608,72620],{},[895,72609,72610,72612,72614,72616,72618],{},[898,72611,1701],{},[1693,72613,1695],{},[1762,72615,44795],{},[1693,72617,1698],{},[898,72619,1712],{},[902,72621,72622],{"encoding":904},"P = 30 - Q",[883,72624,72626],{"className":72625},[886],[888,72627,72628],{"xmlns":890},[892,72629,72630,72656],{},[895,72631,72632,72634,72636,72638,72640,72646,72648,72650,72652,72654],{},[898,72633,2663],{},[898,72635,2971],{},[1693,72637,1695],{},[1762,72639,11877],{},[1717,72641,72642,72644],{},[898,72643,1712],{},[1762,72645,2398],{},[1693,72647,1892],{},[1762,72649,9154],{},[898,72651,1712],{},[1693,72653,1892],{},[1762,72655,31000],{},[902,72657,72658],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,72661,72662,1863,72664,1343,72694,72732,72733,22617,72777,72811,72812,1789],{},[38,72663,29570],{},[883,72665,72667],{"className":72666},[886],[888,72668,72669],{"xmlns":890},[892,72670,72671,72691],{},[895,72672,72673,72675,72677,72679,72681,72683,72685],{},[898,72674,2663],{},[898,72676,2666],{},[1693,72678,1695],{},[1762,72680,44795],{},[898,72682,1712],{},[1693,72684,1698],{},[1717,72686,72687,72689],{},[898,72688,1712],{},[1762,72690,2398],{},[902,72692,72693],{"encoding":904},"TR = 30Q - Q^2",[883,72695,72697],{"className":72696},[886],[888,72698,72699],{"xmlns":890},[892,72700,72701,72729],{},[895,72702,72703,72705,72707,72709,72711,72713,72719,72721,72723,72725,72727],{},[898,72704,1701],{},[898,72706,2666],{},[1693,72708,1695],{},[1693,72710,1698],{},[1762,72712,71285],{},[1717,72714,72715,72717],{},[898,72716,1712],{},[1762,72718,2398],{},[1693,72720,1892],{},[1762,72722,48571],{},[898,72724,1712],{},[1693,72726,1698],{},[1762,72728,31000],{},[902,72730,72731],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,72734,72736],{"className":72735},[886],[888,72737,72738],{"xmlns":890},[892,72739,72740,72774],{},[895,72741,72742,72744,72750,72752,72754,72756,72758,72760,72762,72764,72766,72768,72770,72772],{},[898,72743,1701],{},[1717,72745,72746,72748],{},[898,72747,2666],{},[1693,72749,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,72751,1695],{},[1693,72753,1698],{},[1762,72755,8357],{},[898,72757,1712],{},[1693,72759,1892],{},[1762,72761,48571],{},[1693,72763,1695],{},[1762,72765,1911],{},[1693,72767,10870],{},[898,72769,1712],{},[1693,72771,1695],{},[1762,72773,12453],{},[902,72775,72776],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,72778,72780],{"className":72779},[886],[888,72781,72782],{"xmlns":890},[892,72783,72784,72808],{},[895,72785,72786,72788,72798,72800,72802,72804,72806],{},[898,72787,1701],{},[1717,72789,72790,72792],{},[898,72791,2666],{},[895,72793,72794,72796],{},[1693,72795,1724],{"mathvariant":1704},[1693,72797,1724],{"mathvariant":1704},[1693,72799,1695],{},[1693,72801,1698],{},[1762,72803,8357],{},[1693,72805,1908],{},[1762,72807,1911],{},[902,72809,72810],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,72813,72815],{"className":72814},[886],[888,72816,72817],{"xmlns":890},[892,72818,72819,72836],{},[895,72820,72821,72823,72825,72827,72829,72831,72833],{},[898,72822,1701],{},[898,72824,2666],{},[1693,72826,1709],{"stretchy":1708},[1762,72828,12453],{},[1693,72830,1731],{"stretchy":1708},[1693,72832,1695],{},[1762,72834,72835],{},"89",[902,72837,72838],{"encoding":904},"PR(8) = 89",[724,72840,72841,72842,1343,72868,22617,72892,72930],{},"Ověření principu: ",[883,72843,72845],{"className":72844},[886],[888,72846,72847],{"xmlns":890},[892,72848,72849,72865],{},[895,72850,72851,72853,72855,72857,72859,72861,72863],{},[898,72852,2839],{},[898,72854,2666],{},[1693,72856,1695],{},[1762,72858,44795],{},[1693,72860,1698],{},[1762,72862,2398],{},[898,72864,1712],{},[902,72866,72867],{"encoding":904},"MR = 30 - 2Q",[883,72869,72871],{"className":72870},[886],[888,72872,72873],{"xmlns":890},[892,72874,72875,72889],{},[895,72876,72877,72879,72881,72883,72885,72887],{},[898,72878,2839],{},[898,72880,2971],{},[1693,72882,1695],{},[898,72884,1712],{},[1693,72886,1892],{},[1762,72888,9154],{},[902,72890,72891],{"encoding":904},"MC = Q + 6",[883,72893,72895],{"className":72894},[886],[888,72896,72897],{"xmlns":890},[892,72898,72899,72927],{},[895,72900,72901,72903,72905,72907,72909,72911,72913,72915,72917,72919,72921,72923,72925],{},[898,72902,2839],{},[898,72904,2666],{},[1693,72906,1709],{"stretchy":1708},[1762,72908,12453],{},[1693,72910,1731],{"stretchy":1708},[1693,72912,1695],{},[1762,72914,29746],{},[1693,72916,1695],{},[898,72918,2839],{},[898,72920,2971],{},[1693,72922,1709],{"stretchy":1708},[1762,72924,12453],{},[1693,72926,1731],{"stretchy":1708},[902,72928,72929],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,72932,72933,72934,72967,72968,72985],{},"V řadě případů — má-li rovnice ",[883,72935,72937],{"className":72936},[886],[888,72938,72939],{"xmlns":890},[892,72940,72941,72965],{},[895,72942,72943,72945,72947,72949,72951,72953,72955,72957,72959,72961,72963],{},[898,72944,2839],{},[898,72946,2666],{},[1693,72948,1709],{"stretchy":1708},[898,72950,1712],{},[1693,72952,1731],{"stretchy":1708},[1693,72954,1695],{},[898,72956,2839],{},[898,72958,2971],{},[1693,72960,1709],{"stretchy":1708},[898,72962,1712],{},[1693,72964,1731],{"stretchy":1708},[902,72966,72533],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,72969,72971],{"className":72970},[886],[888,72972,72973],{"xmlns":890},[892,72974,72975,72983],{},[895,72976,72977],{},[3284,72978,72979,72981],{},[898,72980,1712],{},[1762,72982,1911],{},[902,72984,6293],{"encoding":904}," — není třeba provádět test druhé derivace.",[44125,72987,72989],{"id":72988},"příklad-310","Příklad 3.10",[724,72991,72992,72994,72995,72999,73000,73013,73014,73045],{},[38,72993,62731],{}," Firma vyrábí minipočítače v ",[207,72996,72998],{"className":72997,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,73001,73003],{"className":73002},[886],[888,73004,73005],{"xmlns":890},[892,73006,73007,73011],{},[895,73008,73009],{},[1762,73010,22017],{},[902,73012,22017],{"encoding":904}," EUR\u002Fks. ",[883,73015,73017],{"className":73016},[886],[888,73018,73019],{"xmlns":890},[892,73020,73021,73042],{},[895,73022,73023,73025,73027,73029,73031,73033,73036],{},[898,73024,2663],{},[898,73026,2971],{},[1693,73028,1695],{},[1762,73030,10017],{},[1693,73032,1892],{},[1762,73034,73035],{},"28",[1717,73037,73038,73040],{},[898,73039,1712],{},[1762,73041,2398],{},[902,73043,73044],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,73047,73048,1863,73050,1343,73072,1343,73092,73115],{},[38,73049,29570],{},[883,73051,73053],{"className":73052},[886],[888,73054,73055],{"xmlns":890},[892,73056,73057,73069],{},[895,73058,73059,73061,73063,73065,73067],{},[898,73060,2663],{},[898,73062,2666],{},[1693,73064,1695],{},[1762,73066,22017],{},[898,73068,1712],{},[902,73070,73071],{"encoding":904},"TR = 900Q",[883,73073,73075],{"className":73074},[886],[888,73076,73077],{"xmlns":890},[892,73078,73079,73089],{},[895,73080,73081,73083,73085,73087],{},[898,73082,2839],{},[898,73084,2666],{},[1693,73086,1695],{},[1762,73088,22017],{},[902,73090,73091],{"encoding":904},"MR = 900",[883,73093,73095],{"className":73094},[886],[888,73096,73097],{"xmlns":890},[892,73098,73099,73112],{},[895,73100,73101,73103,73105,73107,73110],{},[898,73102,2839],{},[898,73104,2971],{},[1693,73106,1695],{},[1762,73108,73109],{},"56",[898,73111,1712],{},[902,73113,73114],{"encoding":904},"MC = 56Q",". Z principu:",[883,73117,73119],{"className":73118},[886],[888,73120,73121],{"xmlns":890,"display":34854},[892,73122,73123,73165],{},[895,73124,73125,73127,73129,73131,73133,73135,73137,73139,73141,73143,73151,73153,73156,73158,73160,73162],{},[1762,73126,22017],{},[1693,73128,1695],{},[1762,73130,73109],{},[898,73132,1712],{},[1915,73134,1917],{},[1693,73136,10870],{},[1915,73138,1917],{},[898,73140,1712],{},[1693,73142,1695],{},[3638,73144,73145],{"scriptlevel":1911,"displaystyle":1708},[2132,73146,73147,73149],{},[1762,73148,22017],{},[1762,73150,73109],{},[1693,73152,12766],{},[1762,73154,73155],{},"16,07",[1915,73157,1917],{},[1693,73159,4110],{},[1915,73161,1917],{},[1762,73163,73164],{},"16.",[902,73166,73167],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,73169,73170,73171,4300],{},"Zisk při ",[883,73172,73174],{"className":73173},[886],[888,73175,73176],{"xmlns":890},[892,73177,73178,73186],{},[895,73179,73180,73182,73184],{},[898,73181,1712],{},[1693,73183,1695],{},[1762,73185,48633],{},[902,73187,73188],{"encoding":904},"Q = 16",[883,73190,73192],{"className":73191},[886],[888,73193,73194],{"xmlns":890,"display":34854},[892,73195,73196,73267],{},[895,73197,73198,73200,73202,73204,73206,73208,73210,73212,73214,73216,73218,73220,73222,73224,73226,73228,73234,73236,73238,73240,73242,73244,73246,73248,73250,73253,73255,73257,73259,73262,73265],{},[898,73199,1701],{},[898,73201,2666],{},[1693,73203,1709],{"stretchy":1708},[1762,73205,48633],{},[1693,73207,1731],{"stretchy":1708},[1693,73209,1695],{},[1762,73211,22017],{},[1693,73213,1715],{},[1762,73215,48633],{},[1693,73217,1698],{},[1693,73219,1709],{"stretchy":1708},[1762,73221,10017],{},[1693,73223,1892],{},[1762,73225,73035],{},[1693,73227,1715],{},[1717,73229,73230,73232],{},[1762,73231,48633],{},[1762,73233,2398],{},[1693,73235,1731],{"stretchy":1708},[1693,73237,1695],{},[1762,73239,29746],{},[1915,73241,2239],{},[1762,73243,26949],{},[1693,73245,1698],{},[1762,73247,31000],{},[1915,73249,2239],{},[1762,73251,73252],{},"218",[1693,73254,1695],{},[1762,73256,31000],{},[1915,73258,2239],{},[1762,73260,73261],{},"182",[1915,73263,73264],{}," EUR",[898,73266,1789],{"mathvariant":1704},[902,73268,73269],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,73271,73272],{},"Pro srovnání při původních 30 ks:",[883,73274,73276],{"className":73275},[886],[888,73277,73278],{"xmlns":890,"display":34854},[892,73279,73280,73345],{},[895,73281,73282,73284,73286,73288,73290,73292,73294,73296,73298,73300,73302,73304,73306,73308,73310,73312,73314,73316,73318,73321,73323,73325,73327,73329,73331,73333,73335,73337,73339,73341,73343],{},[898,73283,1701],{},[898,73285,2666],{},[1693,73287,1709],{"stretchy":1708},[1762,73289,44795],{},[1693,73291,1731],{"stretchy":1708},[1693,73293,1695],{},[1762,73295,22017],{},[1693,73297,1715],{},[1762,73299,44795],{},[1693,73301,1698],{},[1693,73303,1709],{"stretchy":1708},[1762,73305,10017],{},[1693,73307,1892],{},[1762,73309,73035],{},[1693,73311,1715],{},[1762,73313,22017],{},[1693,73315,1731],{"stretchy":1708},[1693,73317,1695],{},[1762,73319,73320],{},"27",[1915,73322,2239],{},[1762,73324,65817],{},[1693,73326,1698],{},[1762,73328,11872],{},[1915,73330,2239],{},[1762,73332,37526],{},[1693,73334,1695],{},[1762,73336,1764],{},[1915,73338,2239],{},[1762,73340,30542],{},[1915,73342,73264],{},[898,73344,1789],{"mathvariant":1704},[902,73346,73347],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,73349,73350,73353,73354,73372,73373,73391],{},[38,73351,73352],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,73355,73357],{"className":73356},[886],[888,73358,73359],{"xmlns":890},[892,73360,73361,73369],{},[895,73362,73363,73365,73367],{},[1762,73364,31000],{},[1915,73366,2239],{},[1762,73368,73261],{},[902,73370,73371],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,73374,73376],{"className":73375},[886],[888,73377,73378],{"xmlns":890},[892,73379,73380,73388],{},[895,73381,73382,73384,73386],{},[1762,73383,1764],{},[1915,73385,2239],{},[1762,73387,30542],{},[902,73389,73390],{"encoding":904},"1\\,750"," EUR.",[198,73393,73395],{"id":73394},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,73397,73398,73399,69298,73412,73435],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,73400,73402],{"className":73401},[886],[888,73403,73404],{"xmlns":890},[892,73405,73406,73410],{},[895,73407,73408],{},[898,73409,1701],{},[902,73411,1701],{"encoding":904},[883,73413,73415],{"className":73414},[886],[888,73416,73417],{"xmlns":890},[892,73418,73419,73433],{},[895,73420,73421,73423,73425,73427,73429,73431],{},[898,73422,2663],{},[898,73424,2666],{},[1693,73426,1695],{},[898,73428,1701],{},[1693,73430,1715],{},[898,73432,1712],{},[902,73434,2677],{"encoding":904}," a z (3.13) speciálně:",[883,73437,73439],{"className":73438},[886],[888,73440,73441],{"xmlns":890,"display":34854},[892,73442,73443,73476],{},[3626,73444,73445],{"width":34859},[3632,73446,73447,73449,73469,73471],{},[3635,73448],{"width":34864},[3635,73450,73451],{},[895,73452,73453,73455,73457,73459,73461,73463,73465,73467],{},[898,73454,1701],{},[1693,73456,1695],{},[898,73458,2839],{},[898,73460,2971],{},[1693,73462,1709],{"stretchy":1708},[898,73464,1712],{},[1693,73466,1731],{"stretchy":1708},[898,73468,1789],{"mathvariant":1704},[3635,73470],{"width":34864},[3635,73472,73473],{},[1915,73474,73475],{},"(3.14)",[902,73477,73478],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,73480,73481,73482,1789],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,73483,73485],{"className":73484},[886],[888,73486,73487],{"xmlns":890},[892,73488,73489,73503],{},[895,73490,73491,73493],{},[898,73492,1701],{},[1717,73494,73495,73497],{},[898,73496,2666],{},[895,73498,73499,73501],{},[1693,73500,1724],{"mathvariant":1704},[1693,73502,1724],{"mathvariant":1704},[902,73504,72560],{"encoding":904},[44125,73506,73508],{"id":73507},"příklad-311","Příklad 3.11",[724,73510,73511,64261,73513,73560,73561,73579],{},[38,73512,62731],{},[883,73514,73516],{"className":73515},[886],[888,73517,73518],{"xmlns":890},[892,73519,73520,73557],{},[895,73521,73522,73524,73526,73528,73531,73537,73539,73541,73547,73549,73551,73553,73555],{},[898,73523,2663],{},[898,73525,2971],{},[1693,73527,1695],{},[1762,73529,73530],{},"0,04",[1717,73532,73533,73535],{},[898,73534,1712],{},[1762,73536,8357],{},[1693,73538,1698],{},[1762,73540,29345],{},[1717,73542,73543,73545],{},[898,73544,1712],{},[1762,73546,2398],{},[1693,73548,1892],{},[1762,73550,9763],{},[898,73552,1712],{},[1693,73554,1892],{},[1762,73556,9147],{},[902,73558,73559],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,73562,73564],{"className":73563},[886],[888,73565,73566],{"xmlns":890},[892,73567,73568,73576],{},[895,73569,73570,73572,73574],{},[898,73571,1701],{},[1693,73573,1695],{},[1762,73575,9262],{},[902,73577,73578],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,73581,73582,73584,73585,24395,73627,73661,73662,4300],{},[38,73583,29570],{}," Z (3.14): ",[883,73586,73588],{"className":73587},[886],[888,73589,73590],{"xmlns":890},[892,73591,73592,73624],{},[895,73593,73594,73596,73598,73600,73603,73609,73611,73614,73616,73618,73620,73622],{},[898,73595,2839],{},[898,73597,2971],{},[1693,73599,1695],{},[1762,73601,73602],{},"0,12",[1717,73604,73605,73607],{},[898,73606,1712],{},[1762,73608,2398],{},[1693,73610,1698],{},[1762,73612,73613],{},"1,8",[898,73615,1712],{},[1693,73617,1892],{},[1762,73619,9763],{},[1693,73621,1695],{},[1762,73623,9262],{},[902,73625,73626],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,73628,73630],{"className":73629},[886],[888,73631,73632],{"xmlns":890},[892,73633,73634,73658],{},[895,73635,73636,73638,73644,73646,73648,73650,73652,73654,73656],{},[1762,73637,73602],{},[1717,73639,73640,73642],{},[898,73641,1712],{},[1762,73643,2398],{},[1693,73645,1698],{},[1762,73647,73613],{},[898,73649,1712],{},[1693,73651,1892],{},[1762,73653,9154],{},[1693,73655,1695],{},[1762,73657,1911],{},[902,73659,73660],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,73663,73665],{"className":73664},[886],[888,73666,73667],{"xmlns":890},[892,73668,73669,73673],{},[895,73670,73671],{},[1762,73672,73602],{},[902,73674,73675],{"encoding":904},"0{,}12",[883,73677,73679],{"className":73678},[886],[888,73680,73681],{"xmlns":890,"display":34854},[892,73682,73683,73735],{},[895,73684,73685,73691,73693,73695,73697,73699,73701,73703,73705,73707,73709,73711,73717,73719,73721,73723,73725,73731,73733],{},[1717,73686,73687,73689],{},[898,73688,1712],{},[1762,73690,2398],{},[1693,73692,1698],{},[1762,73694,43026],{},[898,73696,1712],{},[1693,73698,1892],{},[1762,73700,10017],{},[1693,73702,1695],{},[1762,73704,1911],{},[1915,73706,1917],{},[1693,73708,10870],{},[1915,73710,1917],{},[3284,73712,73713,73715],{},[898,73714,1712],{},[1762,73716,1764],{},[1693,73718,1695],{},[1762,73720,9147],{},[1693,73722,1899],{"separator":1898},[1915,73724,1917],{},[3284,73726,73727,73729],{},[898,73728,1712],{},[1762,73730,2398],{},[1693,73732,1695],{},[1762,73734,26139],{},[902,73736,73737],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,73739,73740,73741,4300],{},"Dále ",[883,73742,73744],{"className":73743},[886],[888,73745,73746],{"xmlns":890},[892,73747,73748,73787],{},[895,73749,73750,73752,73762,73764,73766,73768,73774,73776,73778,73781,73783,73785],{},[898,73751,1701],{},[1717,73753,73754,73756],{},[898,73755,2666],{},[895,73757,73758,73760],{},[1693,73759,1724],{"mathvariant":1704},[1693,73761,1724],{"mathvariant":1704},[1693,73763,1695],{},[1693,73765,1698],{},[898,73767,2839],{},[1717,73769,73770,73772],{},[898,73771,2971],{},[1693,73773,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,73775,1695],{},[1693,73777,1698],{},[1762,73779,73780],{},"0,24",[898,73782,1712],{},[1693,73784,1892],{},[1762,73786,73613],{},[902,73788,73789],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,73791,73792,73842],{},[123,73793,73794,73838,73839,73841],{},[883,73795,73797],{"className":73796},[886],[888,73798,73799],{"xmlns":890},[892,73800,73801,73835],{},[895,73802,73803,73805,73815,73817,73819,73821,73823,73825,73827,73829,73831,73833],{},[898,73804,1701],{},[1717,73806,73807,73809],{},[898,73808,2666],{},[895,73810,73811,73813],{},[1693,73812,1724],{"mathvariant":1704},[1693,73814,1724],{"mathvariant":1704},[1693,73816,1709],{"stretchy":1708},[1762,73818,9147],{},[1693,73820,1731],{"stretchy":1708},[1693,73822,1695],{},[1762,73824,26132],{},[1693,73826,1922],{},[1762,73828,1911],{},[1915,73830,1917],{},[1693,73832,10870],{},[1915,73834,1917],{},[902,73836,73837],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,73840,10667],{}," zisku (minimalizace ztráty);",[123,73843,73844,73838,73890,73892],{},[883,73845,73847],{"className":73846},[886],[888,73848,73849],{"xmlns":890},[892,73850,73851,73887],{},[895,73852,73853,73855,73865,73867,73869,73871,73873,73875,73877,73879,73881,73883,73885],{},[898,73854,1701],{},[1717,73856,73857,73859],{},[898,73858,2666],{},[895,73860,73861,73863],{},[1693,73862,1724],{"mathvariant":1704},[1693,73864,1724],{"mathvariant":1704},[1693,73866,1709],{"stretchy":1708},[1762,73868,9763],{},[1693,73870,1731],{"stretchy":1708},[1693,73872,1695],{},[1693,73874,1698],{},[1762,73876,26132],{},[1693,73878,1908],{},[1762,73880,1911],{},[1915,73882,1917],{},[1693,73884,10870],{},[1915,73886,1917],{},[902,73888,73889],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,73891,10610],{}," zisku, avšak",[883,73894,73896],{"className":73895},[886],[888,73897,73898],{"xmlns":890,"display":34854},[892,73899,73900,73968],{},[895,73901,73902,73904,73906,73908,73910,73912,73914,73916,73918,73920,73922,73924,73926,73928,73930,73932,73934,73936,73938,73940,73942,73944,73946,73948,73950,73952,73954,73956,73958,73960,73962,73964,73966],{},[898,73903,1701],{},[898,73905,2666],{},[1693,73907,1709],{"stretchy":1708},[1762,73909,9763],{},[1693,73911,1731],{"stretchy":1708},[1693,73913,1695],{},[1762,73915,9262],{},[1693,73917,1715],{},[1762,73919,9763],{},[1693,73921,1698],{},[1693,73923,1709],{"stretchy":1708},[1762,73925,73530],{},[1693,73927,1715],{},[1762,73929,1764],{},[1915,73931,2239],{},[1762,73933,65817],{},[1693,73935,1698],{},[1762,73937,29345],{},[1693,73939,1715],{},[1762,73941,9987],{},[1693,73943,1892],{},[1762,73945,9987],{},[1693,73947,1892],{},[1762,73949,9147],{},[1693,73951,1731],{"stretchy":1708},[1693,73953,1695],{},[1762,73955,12079],{},[1693,73957,1698],{},[1762,73959,27983],{},[1693,73961,1695],{},[1693,73963,1698],{},[1762,73965,43026],{},[1693,73967,1899],{"separator":1898},[902,73969,73970],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,73972,73973,73974,1789],{},"tj. ztráta větší než ",[883,73975,73977],{"className":73976},[886],[888,73978,73979],{"xmlns":890},[892,73980,73981,73991],{},[895,73982,73983,73985,73987,73989],{},[898,73984,2976],{},[898,73986,2971],{},[1693,73988,1695],{},[1762,73990,9147],{},[902,73992,73993],{"encoding":904},"FC = 5",[724,73995,73996,73999,74000,74003,74004,1789],{},[38,73997,73998],{},"Závěr:"," firma by měla ",[38,74001,74002],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,74005,74007],{"className":74006},[886],[888,74008,74009],{"xmlns":890},[892,74010,74011,74021],{},[895,74012,74013,74015,74017,74019],{},[898,74014,2976],{},[898,74016,2971],{},[1693,74018,1695],{},[1762,74020,9147],{},[902,74022,73993],{"encoding":904},[115,74024,74026],{"id":74025},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,74028,74029,74030,74032,74033,74048,74049,74062,74063,74089,74090,74103,74104,74121,74122,9530,74139,74142,74143,74163,74164,74179,74180,4300],{},"Důležitým završením analýzy je konstrukce ",[38,74031,62028],{},". S nabízeným množstvím rostou mezní náklady ",[883,74034,74036],{"className":74035},[886],[888,74037,74038],{"xmlns":890},[892,74039,74040,74046],{},[895,74041,74042,74044],{},[898,74043,2839],{},[898,74045,2971],{},[902,74047,3810],{"encoding":904}," a tyto určují cenu ",[883,74050,74052],{"className":74051},[886],[888,74053,74054],{"xmlns":890},[892,74055,74056,74060],{},[895,74057,74058],{},[898,74059,1701],{},[902,74061,1701],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,74064,74066],{"className":74065},[886],[888,74067,74068],{"xmlns":890},[892,74069,74070,74086],{},[895,74071,74072,74074,74076,74078,74080,74082,74084],{},[898,74073,1701],{},[1693,74075,1695],{},[898,74077,2839],{},[898,74079,2971],{},[1693,74081,1709],{"stretchy":1708},[898,74083,1712],{},[1693,74085,1731],{"stretchy":1708},[902,74087,74088],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,74091,74093],{"className":74092},[886],[888,74094,74095],{"xmlns":890},[892,74096,74097,74101],{},[895,74098,74099],{},[898,74100,1701],{},[902,74102,1701],{"encoding":904}," však nemůže být nižší než ",[883,74105,74107],{"className":74106},[886],[888,74108,74109],{"xmlns":890},[892,74110,74111,74119],{},[895,74112,74113],{},[1717,74114,74115,74117],{},[898,74116,1701],{},[1693,74118,3672],{},[902,74120,11280],{"encoding":904}," odpovídající množství ",[883,74123,74125],{"className":74124},[886],[888,74126,74127],{"xmlns":890},[892,74128,74129,74137],{},[895,74130,74131],{},[1717,74132,74133,74135],{},[898,74134,1712],{},[1693,74136,3672],{},[902,74138,3770],{"encoding":904},[38,74140,74141],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,74144,74146],{"className":74145},[886],[888,74147,74148],{"xmlns":890},[892,74149,74150,74160],{},[895,74151,74152,74154],{},[1762,74153,1911],{},[1717,74155,74156,74158],{},[898,74157,1712],{},[1693,74159,3672],{},[902,74161,74162],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,74165,74167],{"className":74166},[886],[888,74168,74169],{"xmlns":890},[892,74170,74171,74177],{},[895,74172,74173,74175],{},[898,74174,2839],{},[898,74176,2971],{},[902,74178,3810],{"encoding":904}," nad bodem ",[883,74181,74183],{"className":74182},[886],[888,74184,74185],{"xmlns":890},[892,74186,74187,74191],{},[895,74188,74189],{},[898,74190,2719],{},[902,74192,2719],{"encoding":904},[883,74194,74196],{"className":74195},[886],[888,74197,74198],{"xmlns":890,"display":34854},[892,74199,74200,74303],{},[3626,74201,74202],{"width":34859},[3632,74203,74204,74206,74296,74298],{},[3635,74205],{"width":34864},[3635,74207,74208],{},[895,74209,74210,74212,74214,74216,74218,74220,74222,74224],{},[898,74211,1701],{},[1693,74213,1695],{},[898,74215,3611],{},[1693,74217,1709],{"stretchy":1708},[898,74219,1712],{},[1693,74221,1731],{"stretchy":1708},[1693,74223,1695],{},[895,74225,74226,74228],{},[1693,74227,3624],{"fence":1898},[3626,74229,74230,74268],{"rowspacing":3628,"columnalign":3629,"columnspacing":3630},[3632,74231,74232,74248],{},[3635,74233,74234],{},[3638,74235,74236],{"scriptlevel":1911,"displaystyle":1708},[895,74237,74238,74240,74242,74244,74246],{},[898,74239,2839],{},[898,74241,2971],{},[1693,74243,1709],{"stretchy":1708},[898,74245,1712],{},[1693,74247,1731],{"stretchy":1708},[3635,74249,74250],{},[3638,74251,74252],{"scriptlevel":1911,"displaystyle":1708},[895,74253,74254,74256,74258,74260,74266],{},[1915,74255,3660],{},[898,74257,1712],{},[1693,74259,3665],{},[1717,74261,74262,74264],{},[898,74263,1712],{},[1693,74265,3672],{},[1693,74267,1899],{"separator":1898},[3632,74269,74270,74276],{},[3635,74271,74272],{},[3638,74273,74274],{"scriptlevel":1911,"displaystyle":1708},[1762,74275,1911],{},[3635,74277,74278],{},[3638,74279,74280],{"scriptlevel":1911,"displaystyle":1708},[895,74281,74282,74284,74286,74288,74294],{},[1915,74283,3660],{},[898,74285,1712],{},[1693,74287,1908],{},[1717,74289,74290,74292],{},[898,74291,1712],{},[1693,74293,3672],{},[1693,74295,1899],{"separator":1898},[3635,74297],{"width":34864},[3635,74299,74300],{},[1915,74301,74302],{},"(3.15)",[902,74304,74305],{"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}",[724,74307,11188,74308,3771,74325,74342,74343,48270,74373,74375],{},[883,74309,74311],{"className":74310},[886],[888,74312,74313],{"xmlns":890},[892,74314,74315,74323],{},[895,74316,74317],{},[1717,74318,74319,74321],{},[898,74320,1712],{},[1693,74322,3672],{},[902,74324,3770],{"encoding":904},[883,74326,74328],{"className":74327},[886],[888,74329,74330],{"xmlns":890},[892,74331,74332,74340],{},[895,74333,74334,74336,74338],{},[898,74335,2719],{},[898,74337,2985],{},[898,74339,2971],{},[902,74341,3789],{"encoding":904},". Bod ",[883,74344,74346],{"className":74345},[886],[888,74347,74348],{"xmlns":890},[892,74349,74350,74370],{},[895,74351,74352,74354,74360,74362,74368],{},[1693,74353,1709],{"stretchy":1708},[1717,74355,74356,74358],{},[898,74357,1712],{},[1693,74359,3672],{},[1693,74361,1899],{"separator":1898},[1717,74363,74364,74366],{},[898,74365,1701],{},[1693,74367,3672],{},[1693,74369,1731],{"stretchy":1708},[902,74371,74372],{"encoding":904},"(Q^*, P^*)",[38,74374,3455],{}," — pod ním se firmě nevyplatí produkovat.",[1636,74377,74378,74383],{},[724,74379,74380,74382],{},[883,74381,8620],{}," Postup — jak odvodit nabídku firmy",[152,74384,74385,74434,74529,74584,74655],{},[123,74386,74387,74388,4286,74410,1789],{},"Ze zadaných nákladů určete ",[883,74389,74391],{"className":74390},[886],[888,74392,74393],{"xmlns":890},[892,74394,74395,74407],{},[895,74396,74397,74399,74401,74403,74405],{},[898,74398,2839],{},[898,74400,2971],{},[1693,74402,1709],{"stretchy":1708},[898,74404,1712],{},[1693,74406,1731],{"stretchy":1708},[902,74408,74409],{"encoding":904},"MC(Q)",[883,74411,74413],{"className":74412},[886],[888,74414,74415],{"xmlns":890},[892,74416,74417,74431],{},[895,74418,74419,74421,74423,74425,74427,74429],{},[898,74420,2719],{},[898,74422,2985],{},[898,74424,2971],{},[1693,74426,1709],{"stretchy":1708},[898,74428,1712],{},[1693,74430,1731],{"stretchy":1708},[902,74432,74433],{"encoding":904},"AVC(Q)",[123,74435,74436,74437,74454,74455,74472,74473,74505,74506,3042],{},"Najděte ",[883,74438,74440],{"className":74439},[886],[888,74441,74442],{"xmlns":890},[892,74443,74444,74452],{},[895,74445,74446],{},[1717,74447,74448,74450],{},[898,74449,1712],{},[1693,74451,3672],{},[902,74453,3770],{"encoding":904}," jako bod minima ",[883,74456,74458],{"className":74457},[886],[888,74459,74460],{"xmlns":890},[892,74461,74462,74470],{},[895,74463,74464,74466,74468],{},[898,74465,2719],{},[898,74467,2985],{},[898,74469,2971],{},[902,74471,3789],{"encoding":904}," (řešením ",[883,74474,74476],{"className":74475},[886],[888,74477,74478],{"xmlns":890},[892,74479,74480,74502],{},[895,74481,74482,74484,74486,74492,74494,74496,74498,74500],{},[898,74483,2719],{},[898,74485,2985],{},[1717,74487,74488,74490],{},[898,74489,2971],{},[1693,74491,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,74493,1709],{"stretchy":1708},[898,74495,1712],{},[1693,74497,1731],{"stretchy":1708},[1693,74499,1695],{},[1762,74501,1911],{},[902,74503,74504],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,74507,74509],{"className":74508},[886],[888,74510,74511],{"xmlns":890},[892,74512,74513,74527],{},[895,74514,74515,74517,74519,74521,74523,74525],{},[898,74516,2719],{},[898,74518,2985],{},[898,74520,2971],{},[1693,74522,1695],{},[898,74524,2839],{},[898,74526,2971],{},[902,74528,62001],{"encoding":904},[123,74530,72444,74531,74583],{},[883,74532,74534],{"className":74533},[886],[888,74535,74536],{"xmlns":890},[892,74537,74538,74580],{},[895,74539,74540,74546,74548,74550,74552,74554,74560,74562,74564,74566,74568,74570,74572,74578],{},[1717,74541,74542,74544],{},[898,74543,1701],{},[1693,74545,3672],{},[1693,74547,1695],{},[898,74549,2839],{},[898,74551,2971],{},[1693,74553,1709],{"stretchy":1708},[1717,74555,74556,74558],{},[898,74557,1712],{},[1693,74559,3672],{},[1693,74561,1731],{"stretchy":1708},[1693,74563,1695],{},[898,74565,2719],{},[898,74567,2985],{},[898,74569,2971],{},[1693,74571,1709],{"stretchy":1708},[1717,74573,74574,74576],{},[898,74575,1712],{},[1693,74577,3672],{},[1693,74579,1731],{"stretchy":1708},[902,74581,74582],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,74585,74586,74587,7721,74619,74641,74642,1789],{},"Zapište nabídku: ",[883,74588,74590],{"className":74589},[886],[888,74591,74592],{"xmlns":890},[892,74593,74594,74616],{},[895,74595,74596,74598,74600,74602,74604,74606,74608,74610,74612,74614],{},[898,74597,3611],{},[1693,74599,1709],{"stretchy":1708},[898,74601,1712],{},[1693,74603,1731],{"stretchy":1708},[1693,74605,1695],{},[898,74607,2839],{},[898,74609,2971],{},[1693,74611,1709],{"stretchy":1708},[898,74613,1712],{},[1693,74615,1731],{"stretchy":1708},[902,74617,74618],{"encoding":904},"S(Q) = MC(Q)",[883,74620,74622],{"className":74621},[886],[888,74623,74624],{"xmlns":890},[892,74625,74626,74638],{},[895,74627,74628,74630,74632],{},[898,74629,1712],{},[1693,74631,3665],{},[1717,74633,74634,74636],{},[898,74635,1712],{},[1693,74637,3672],{},[902,74639,74640],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,74643,74645],{"className":74644},[886],[888,74646,74647],{"xmlns":890},[892,74648,74649,74653],{},[895,74650,74651],{},[1762,74652,1911],{},[902,74654,1911],{"encoding":904},[123,74656,74657,74658,74690],{},"V případě potřeby vyjádřete inverzi ",[883,74659,74661],{"className":74660},[886],[888,74662,74663],{"xmlns":890},[892,74664,74665,74687],{},[895,74666,74667,74669,74671,74681,74683,74685],{},[898,74668,1712],{},[1693,74670,1695],{},[1717,74672,74673,74675],{},[898,74674,3611],{},[895,74676,74677,74679],{},[1693,74678,1698],{},[1762,74680,1764],{},[1693,74682,1709],{"stretchy":1708},[898,74684,1701],{},[1693,74686,1731],{"stretchy":1708},[902,74688,74689],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,74692,74693],{},[614,74694,74695,74696,1343,74711,4286,74728,35985,74743,74756,74757,74782,74783,74796,74797,74814,74815,74832,74833,74850],{},"Obrázek 3.14: Křivky ",[883,74697,74699],{"className":74698},[886],[888,74700,74701],{"xmlns":890},[892,74702,74703,74709],{},[895,74704,74705,74707],{},[898,74706,2719],{},[898,74708,2971],{},[902,74710,3331],{"encoding":904},[883,74712,74714],{"className":74713},[886],[888,74715,74716],{"xmlns":890},[892,74717,74718,74726],{},[895,74719,74720,74722,74724],{},[898,74721,2719],{},[898,74723,2985],{},[898,74725,2971],{},[902,74727,3789],{"encoding":904},[883,74729,74731],{"className":74730},[886],[888,74732,74733],{"xmlns":890},[892,74734,74735,74741],{},[895,74736,74737,74739],{},[898,74738,2839],{},[898,74740,2971],{},[902,74742,3810],{"encoding":904},[883,74744,74746],{"className":74745},[886],[888,74747,74748],{"xmlns":890},[892,74749,74750,74754],{},[895,74751,74752],{},[898,74753,900],{},[902,74755,900],{"encoding":904},"; křivka nabídky ",[883,74758,74760],{"className":74759},[886],[888,74761,74762],{"xmlns":890},[892,74763,74764,74780],{},[895,74765,74766,74768,74770,74772,74774,74776,74778],{},[898,74767,1701],{},[1693,74769,1695],{},[898,74771,2839],{},[898,74773,2971],{},[1693,74775,1709],{"stretchy":1708},[898,74777,1712],{},[1693,74779,1731],{"stretchy":1708},[902,74781,74088],{"encoding":904}," začíná v bodě ",[883,74784,74786],{"className":74785},[886],[888,74787,74788],{"xmlns":890},[892,74789,74790,74794],{},[895,74791,74792],{},[898,74793,2719],{},[902,74795,2719],{"encoding":904}," odpovídajícím minimu ",[883,74798,74800],{"className":74799},[886],[888,74801,74802],{"xmlns":890},[892,74803,74804,74812],{},[895,74805,74806,74808,74810],{},[898,74807,2719],{},[898,74809,2985],{},[898,74811,2971],{},[902,74813,3789],{"encoding":904}," při ceně ",[883,74816,74818],{"className":74817},[886],[888,74819,74820],{"xmlns":890},[892,74821,74822,74830],{},[895,74823,74824],{},[1717,74825,74826,74828],{},[898,74827,1701],{},[1693,74829,3672],{},[902,74831,11280],{"encoding":904}," (minimální cena nabídky); pod ",[883,74834,74836],{"className":74835},[886],[888,74837,74838],{"xmlns":890},[892,74839,74840,74848],{},[895,74841,74842],{},[1717,74843,74844,74846],{},[898,74845,1712],{},[1693,74847,3672],{},[902,74849,3770],{"encoding":904}," je nabídka nulová.",[44125,74852,74854],{"id":74853},"příklad-312","Příklad 3.12",[724,74856,74857,64261,74859,74905],{},[38,74858,62731],{},[883,74860,74862],{"className":74861},[886],[888,74863,74864],{"xmlns":890},[892,74865,74866,74902],{},[895,74867,74868,74870,74872,74874,74876,74882,74884,74886,74892,74894,74896,74898,74900],{},[898,74869,2663],{},[898,74871,2971],{},[1693,74873,1695],{},[1762,74875,9695],{},[1717,74877,74878,74880],{},[898,74879,1712],{},[1762,74881,8357],{},[1693,74883,1698],{},[1762,74885,2398],{},[1717,74887,74888,74890],{},[898,74889,1712],{},[1762,74891,2398],{},[1693,74893,1892],{},[1762,74895,43026],{},[898,74897,1712],{},[1693,74899,1892],{},[1762,74901,9763],{},[902,74903,74904],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,74907,74908,1863,74910,74947,74948,4300],{},[38,74909,29570],{},[883,74911,74913],{"className":74912},[886],[888,74914,74915],{"xmlns":890},[892,74916,74917,74944],{},[895,74918,74919,74921,74923,74925,74928,74934,74936,74938,74940,74942],{},[898,74920,2839],{},[898,74922,2971],{},[1693,74924,1695],{},[1762,74926,74927],{},"0,3",[1717,74929,74930,74932],{},[898,74931,1712],{},[1762,74933,2398],{},[1693,74935,1698],{},[1762,74937,9262],{},[898,74939,1712],{},[1693,74941,1892],{},[1762,74943,43026],{},[902,74945,74946],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,74949,74951],{"className":74950},[886],[888,74952,74953],{"xmlns":890},[892,74954,74955,74965],{},[895,74956,74957,74959,74961,74963],{},[898,74958,1701],{},[1693,74960,1695],{},[898,74962,2839],{},[898,74964,2971],{},[902,74966,3726],{"encoding":904},[883,74968,74970],{"className":74969},[886],[888,74971,74972],{"xmlns":890,"display":34854},[892,74973,74974,74999],{},[895,74975,74976,74978,74980,74982,74988,74990,74992,74994,74996],{},[898,74977,1701],{},[1693,74979,1695],{},[1762,74981,74927],{},[1717,74983,74984,74986],{},[898,74985,1712],{},[1762,74987,2398],{},[1693,74989,1698],{},[1762,74991,9262],{},[898,74993,1712],{},[1693,74995,1892],{},[1762,74997,74998],{},"15.",[902,75000,75001],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,75003,75004,75005,12250,75018,75031],{},"Vyjádření ",[883,75006,75008],{"className":75007},[886],[888,75009,75010],{"xmlns":890},[892,75011,75012,75016],{},[895,75013,75014],{},[898,75015,1712],{},[902,75017,1712],{"encoding":904},[883,75019,75021],{"className":75020},[886],[888,75022,75023],{"xmlns":890},[892,75024,75025,75029],{},[895,75026,75027],{},[898,75028,1701],{},[902,75030,1701],{"encoding":904}," doplněním na čtverec:",[883,75033,75035],{"className":75034},[886],[888,75036,75037],{"xmlns":890,"display":34854},[892,75038,75039,75129],{},[895,75040,75041,75043,75045,75047,75085,75087,75089,75111,75113,75127],{},[898,75042,1701],{},[1693,75044,1695],{},[1762,75046,74927],{},[895,75048,75049,75051,75073,75075,75083],{},[1693,75050,1709],{"fence":1898},[1717,75052,75053,75071],{},[895,75054,75055,75057,75059,75061,75069],{},[1693,75056,1709],{"fence":1898},[898,75058,1712],{},[1693,75060,1698],{},[3638,75062,75063],{"scriptlevel":1911,"displaystyle":1708},[2132,75064,75065,75067],{},[1762,75066,15892],{},[1762,75068,8357],{},[1693,75070,1731],{"fence":1898},[1762,75072,2398],{},[1693,75074,1892],{},[3638,75076,75077],{"scriptlevel":1911,"displaystyle":1708},[2132,75078,75079,75081],{},[1762,75080,10017],{},[1762,75082,10881],{},[1693,75084,1731],{"fence":1898},[1693,75086,1899],{"separator":1898},[1901,75088],{"width":1903},[1717,75090,75091,75109],{},[895,75092,75093,75095,75097,75099,75107],{},[1693,75094,1709],{"fence":1898},[898,75096,1712],{},[1693,75098,1698],{},[3638,75100,75101],{"scriptlevel":1911,"displaystyle":1708},[2132,75102,75103,75105],{},[1762,75104,15892],{},[1762,75106,8357],{},[1693,75108,1731],{"fence":1898},[1762,75110,2398],{},[1693,75112,1695],{},[2132,75114,75115,75125],{},[895,75116,75117,75119,75121,75123],{},[1762,75118,44795],{},[898,75120,1701],{},[1693,75122,1698],{},[1762,75124,10017],{},[1762,75126,10881],{},[1693,75128,1899],{"separator":1898},[902,75130,75131],{"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},",[883,75133,75135],{"className":75134},[886],[888,75136,75137],{"xmlns":890,"display":34854},[892,75138,75139,75171],{},[895,75140,75141,75143,75145,75151,75153,75169],{},[898,75142,1712],{},[1693,75144,1695],{},[2132,75146,75147,75149],{},[1762,75148,15892],{},[1762,75150,8357],{},[1693,75152,1892],{},[2132,75154,75155,75167],{},[14976,75156,75157],{},[895,75158,75159,75161,75163,75165],{},[1762,75160,44795],{},[898,75162,1701],{},[1693,75164,1698],{},[1762,75166,10017],{},[1762,75168,8357],{},[898,75170,1789],{"mathvariant":1704},[902,75172,75173],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,75175,73740,75176,1343,75214,1343,75262,75296,75297,1789],{},[883,75177,75179],{"className":75178},[886],[888,75180,75181],{"xmlns":890},[892,75182,75183,75211],{},[895,75184,75185,75187,75189,75191,75193,75195,75201,75203,75205,75207,75209],{},[898,75186,2719],{},[898,75188,2985],{},[898,75190,2971],{},[1693,75192,1695],{},[1762,75194,9695],{},[1717,75196,75197,75199],{},[898,75198,1712],{},[1762,75200,2398],{},[1693,75202,1698],{},[1762,75204,2398],{},[898,75206,1712],{},[1693,75208,1892],{},[1762,75210,43026],{},[902,75212,75213],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,75215,75217],{"className":75216},[886],[888,75218,75219],{"xmlns":890},[892,75220,75221,75259],{},[895,75222,75223,75225,75227,75233,75235,75237,75239,75241,75243,75245,75247,75249,75255,75257],{},[898,75224,2719],{},[898,75226,2985],{},[1717,75228,75229,75231],{},[898,75230,2971],{},[1693,75232,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,75234,1695],{},[1762,75236,9739],{},[898,75238,1712],{},[1693,75240,1698],{},[1762,75242,2398],{},[1693,75244,1695],{},[1762,75246,1911],{},[1693,75248,10870],{},[1717,75250,75251,75253],{},[898,75252,1712],{},[1693,75254,3672],{},[1693,75256,1695],{},[1762,75258,9763],{},[902,75260,75261],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,75263,75265],{"className":75264},[886],[888,75266,75267],{"xmlns":890},[892,75268,75269,75293],{},[895,75270,75271,75273,75275,75285,75287,75289,75291],{},[898,75272,2719],{},[898,75274,2985],{},[1717,75276,75277,75279],{},[898,75278,2971],{},[895,75280,75281,75283],{},[1693,75282,1724],{"mathvariant":1704},[1693,75284,1724],{"mathvariant":1704},[1693,75286,1695],{},[1762,75288,9739],{},[1693,75290,1922],{},[1762,75292,1911],{},[902,75294,75295],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,75298,75300],{"className":75299},[886],[888,75301,75302],{"xmlns":890},[892,75303,75304,75340],{},[895,75305,75306,75312,75314,75316,75318,75320,75322,75324,75326,75328,75330,75332,75334,75336,75338],{},[1717,75307,75308,75310],{},[898,75309,1701],{},[1693,75311,3672],{},[1693,75313,1695],{},[898,75315,2839],{},[898,75317,2971],{},[1693,75319,1709],{"stretchy":1708},[1762,75321,9763],{},[1693,75323,1731],{"stretchy":1708},[1693,75325,1695],{},[1762,75327,44795],{},[1693,75329,1698],{},[1762,75331,12079],{},[1693,75333,1892],{},[1762,75335,43026],{},[1693,75337,1695],{},[1762,75339,9147],{},[902,75341,75342],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,75344,75345],{},[38,75346,75347],{},"Závěr.",[883,75349,75351],{"className":75350},[886],[888,75352,75353],{"xmlns":890,"display":34854},[892,75354,75355,75441],{},[895,75356,75357,75359,75361,75363,75365,75367,75369,75371],{},[898,75358,1701],{},[1693,75360,1695],{},[898,75362,3611],{},[1693,75364,1709],{"stretchy":1708},[898,75366,1712],{},[1693,75368,1731],{"stretchy":1708},[1693,75370,1695],{},[895,75372,75373,75375],{},[1693,75374,3624],{"fence":1898},[3626,75376,75377,75419],{"rowspacing":3628,"columnalign":3629,"columnspacing":3630},[3632,75378,75379,75403],{},[3635,75380,75381],{},[3638,75382,75383],{"scriptlevel":1911,"displaystyle":1708},[895,75384,75385,75387,75393,75395,75397,75399,75401],{},[1762,75386,74927],{},[1717,75388,75389,75391],{},[898,75390,1712],{},[1762,75392,2398],{},[1693,75394,1698],{},[1762,75396,9262],{},[898,75398,1712],{},[1693,75400,1892],{},[1762,75402,43026],{},[3635,75404,75405],{},[3638,75406,75407],{"scriptlevel":1911,"displaystyle":1708},[895,75408,75409,75411,75413,75415,75417],{},[1915,75410,3660],{},[898,75412,1712],{},[1693,75414,3665],{},[1762,75416,9763],{},[1693,75418,1899],{"separator":1898},[3632,75420,75421,75427],{},[3635,75422,75423],{},[3638,75424,75425],{"scriptlevel":1911,"displaystyle":1708},[1762,75426,1911],{},[3635,75428,75429],{},[3638,75430,75431],{"scriptlevel":1911,"displaystyle":1708},[895,75432,75433,75435,75437,75439],{},[1915,75434,3660],{},[898,75436,1712],{},[1693,75438,1908],{},[1762,75440,26139],{},[902,75442,75443],{"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}",[724,75445,75446],{},[614,75447,75448,75449,75464,75465,1789],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,75450,75452],{"className":75451},[886],[888,75453,75454],{"xmlns":890},[892,75455,75456,75462],{},[895,75457,75458,75460],{},[898,75459,2839],{},[898,75461,2971],{},[902,75463,3810],{"encoding":904}," ležící nad minimem ",[883,75466,75468],{"className":75467},[886],[888,75469,75470],{"xmlns":890},[892,75471,75472,75480],{},[895,75473,75474,75476,75478],{},[898,75475,2719],{},[898,75477,2985],{},[898,75479,2971],{},[902,75481,3789],{"encoding":904},[115,75483,75485],{"id":75484},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,75487,75488,75489,75493,75494,75509,75510,75530,75531,4286,75534,75537,75538,75540,75541,26752,75563,75565,75566,4286,75568,65463,75571,1863,75574,48585,75589,75604],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,75490,75492],{"className":75491,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,75495,75497],{"className":75496},[886],[888,75498,75499],{"xmlns":890},[892,75500,75501,75507],{},[895,75502,75503,75505],{},[898,75504,2663],{},[898,75506,2666],{},[902,75508,2883],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,75511,75513],{"className":75512},[886],[888,75514,75515],{"xmlns":890},[892,75516,75517,75527],{},[895,75518,75519,75521,75523,75525],{},[898,75520,2663],{},[898,75522,2666],{},[898,75524,1705],{"mathvariant":1704},[898,75526,1712],{},[902,75528,75529],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,75532,75533],{},"fixních",[38,75535,75536],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,75539,71051],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,75542,75544],{"className":75543},[886],[888,75545,75546],{"xmlns":890},[892,75547,75548,75560],{},[895,75549,75550,75552,75554,75556,75558],{},[898,75551,2663],{},[898,75553,2666],{},[1693,75555,1698],{},[898,75557,2663],{},[898,75559,2971],{},[902,75561,75562],{"encoding":904},"TR - TC",[38,75564,61927],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,75567,2825],{},[38,75569,75570],{},"mezní náklady",[207,75572,1145],{"className":75573,"dataFsResolvedFilePath":764,"href":765},[210],[883,75575,75577],{"className":75576},[886],[888,75578,75579],{"xmlns":890},[892,75580,75581,75587],{},[895,75582,75583,75585],{},[898,75584,2663],{},[898,75586,2666],{},[902,75588,2883],{"encoding":904},[883,75590,75592],{"className":75591},[886],[888,75593,75594],{"xmlns":890},[892,75595,75596,75602],{},[895,75597,75598,75600],{},[898,75599,2663],{},[898,75601,2971],{},[902,75603,3225],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,75606,75607,75669,75734,75796],{},[123,75608,75609,75612,75613,17244,75628,1789],{},[38,75610,75611],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,75614,75616],{"className":75615},[886],[888,75617,75618],{"xmlns":890},[892,75619,75620,75626],{},[895,75621,75622,75624],{},[898,75623,2719],{},[898,75625,2971],{},[902,75627,3331],{"encoding":904},[883,75629,75631],{"className":75630},[886],[888,75632,75633],{"xmlns":890},[892,75634,75635,75667],{},[895,75636,75637,75639,75641,75643,75649,75651,75653,75655,75657,75659,75665],{},[898,75638,2719],{},[898,75640,2971],{},[1693,75642,1709],{"stretchy":1708},[3284,75644,75645,75647],{},[898,75646,1712],{},[1762,75648,1911],{},[1693,75650,1731],{"stretchy":1708},[1693,75652,1695],{},[898,75654,2839],{},[898,75656,2971],{},[1693,75658,1709],{"stretchy":1708},[3284,75660,75661,75663],{},[898,75662,1712],{},[1762,75664,1911],{},[1693,75666,1731],{"stretchy":1708},[902,75668,3310],{"encoding":904},[123,75670,75671,75612,75674,17244,75691,1789],{},[38,75672,75673],{},"Princip minimalizace průměrných variabilních nákladů:",[883,75675,75677],{"className":75676},[886],[888,75678,75679],{"xmlns":890},[892,75680,75681,75689],{},[895,75682,75683,75685,75687],{},[898,75684,2719],{},[898,75686,2985],{},[898,75688,2971],{},[902,75690,3789],{"encoding":904},[883,75692,75694],{"className":75693},[886],[888,75695,75696],{"xmlns":890},[892,75697,75698,75732],{},[895,75699,75700,75702,75704,75706,75708,75714,75716,75718,75720,75722,75724,75730],{},[898,75701,2719],{},[898,75703,2985],{},[898,75705,2971],{},[1693,75707,1709],{"stretchy":1708},[3284,75709,75710,75712],{},[898,75711,1712],{},[1762,75713,1911],{},[1693,75715,1731],{"stretchy":1708},[1693,75717,1695],{},[898,75719,2839],{},[898,75721,2971],{},[1693,75723,1709],{"stretchy":1708},[3284,75725,75726,75728],{},[898,75727,1712],{},[1762,75729,1911],{},[1693,75731,1731],{"stretchy":1708},[902,75733,3408],{"encoding":904},[123,75735,75736,75739,75740,17244,75755,1789],{},[38,75737,75738],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,75741,75743],{"className":75742},[886],[888,75744,75745],{"xmlns":890},[892,75746,75747,75753],{},[895,75748,75749,75751],{},[898,75750,1701],{},[898,75752,2666],{},[902,75754,70205],{"encoding":904},[883,75756,75758],{"className":75757},[886],[888,75759,75760],{"xmlns":890},[892,75761,75762,75794],{},[895,75763,75764,75766,75768,75770,75776,75778,75780,75782,75784,75786,75792],{},[898,75765,2839],{},[898,75767,2666],{},[1693,75769,1709],{"stretchy":1708},[3284,75771,75772,75774],{},[898,75773,1712],{},[1762,75775,1911],{},[1693,75777,1731],{"stretchy":1708},[1693,75779,1695],{},[898,75781,2839],{},[898,75783,2971],{},[1693,75785,1709],{"stretchy":1708},[3284,75787,75788,75790],{},[898,75789,1712],{},[1762,75791,1911],{},[1693,75793,1731],{"stretchy":1708},[902,75795,3504],{"encoding":904},[123,75797,75798,1863,75801,7721,75837,74641,75858,28397,75871,3771,75888,1789],{},[38,75799,75800],{},"Funkce nabídky firmy:",[883,75802,75804],{"className":75803},[886],[888,75805,75806],{"xmlns":890},[892,75807,75808,75834],{},[895,75809,75810,75812,75814,75816,75818,75820,75822,75824,75826,75828,75830,75832],{},[898,75811,1701],{},[1693,75813,1695],{},[898,75815,3611],{},[1693,75817,1709],{"stretchy":1708},[898,75819,1712],{},[1693,75821,1731],{"stretchy":1708},[1693,75823,1695],{},[898,75825,2839],{},[898,75827,2971],{},[1693,75829,1709],{"stretchy":1708},[898,75831,1712],{},[1693,75833,1731],{"stretchy":1708},[902,75835,75836],{"encoding":904},"P = S(Q) = MC(Q)",[883,75838,75840],{"className":75839},[886],[888,75841,75842],{"xmlns":890},[892,75843,75844,75856],{},[895,75845,75846,75848,75850],{},[898,75847,1712],{},[1693,75849,3665],{},[1717,75851,75852,75854],{},[898,75853,1712],{},[1693,75855,3672],{},[902,75857,74640],{"encoding":904},[883,75859,75861],{"className":75860},[886],[888,75862,75863],{"xmlns":890},[892,75864,75865,75869],{},[895,75866,75867],{},[1762,75868,1911],{},[902,75870,1911],{"encoding":904},[883,75872,75874],{"className":75873},[886],[888,75875,75876],{"xmlns":890},[892,75877,75878,75886],{},[895,75879,75880],{},[1717,75881,75882,75884],{},[898,75883,1712],{},[1693,75885,3672],{},[902,75887,3770],{"encoding":904},[883,75889,75891],{"className":75890},[886],[888,75892,75893],{"xmlns":890},[892,75894,75895,75903],{},[895,75896,75897,75899,75901],{},[898,75898,2719],{},[898,75900,2985],{},[898,75902,2971],{},[902,75904,3789],{"encoding":904},[115,75906,8674],{"id":56645},[152,75908,75909,75912,75915,75918,75921,75924,75927,75930,75933,75936,75939],{},[123,75910,75911],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,75913,75914],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,75916,75917],{},"Jak se vypočte mezní příjem a co udává?",[123,75919,75920],{},"Z jakých složek se skládají celkové náklady?",[123,75922,75923],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,75925,75926],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,75928,75929],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,75931,75932],{},"Jak se vypočte zisk?",[123,75934,75935],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,75937,75938],{},"Co jsou body zvratu? Jak se najdou?",[123,75940,75941],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,75943,75945],{"id":75944},"úlohy-31328","Úlohy 3.1–3.28",[198,75947,75949],{"id":75948},"příjem-3135","Příjem (3.1–3.5)",[724,75951,75952,52190,75955,75983,75984,75999,76000,76015,76016,76031,76032,1343,76047,1343,76062,76077],{},[38,75953,75954],{},"3.1",[883,75956,75958],{"className":75957},[886],[888,75959,75960],{"xmlns":890},[892,75961,75962,75980],{},[895,75963,75964,75966,75968,75970,75972,75974,75976,75978],{},[898,75965,1701],{},[1693,75967,1695],{},[898,75969,2738],{},[1693,75971,1709],{"stretchy":1708},[898,75973,1712],{},[1693,75975,1731],{"stretchy":1708},[1693,75977,1695],{},[1762,75979,9987],{},[902,75981,75982],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,75985,75987],{"className":75986},[886],[888,75988,75989],{"xmlns":890},[892,75990,75991,75997],{},[895,75992,75993,75995],{},[898,75994,2663],{},[898,75996,2666],{},[902,75998,2883],{"encoding":904},", průměrný příjem ",[883,76001,76003],{"className":76002},[886],[888,76004,76005],{"xmlns":890},[892,76006,76007,76013],{},[895,76008,76009,76011],{},[898,76010,2719],{},[898,76012,2666],{},[902,76014,2820],{"encoding":904}," a mezní příjem ",[883,76017,76019],{"className":76018},[886],[888,76020,76021],{"xmlns":890},[892,76022,76023,76029],{},[895,76024,76025,76027],{},[898,76026,2839],{},[898,76028,2666],{},[902,76030,2919],{"encoding":904},". (c) Vypočtěte ",[883,76033,76035],{"className":76034},[886],[888,76036,76037],{"xmlns":890},[892,76038,76039,76045],{},[895,76040,76041,76043],{},[898,76042,2663],{},[898,76044,2666],{},[902,76046,2883],{"encoding":904},[883,76048,76050],{"className":76049},[886],[888,76051,76052],{"xmlns":890},[892,76053,76054,76060],{},[895,76055,76056,76058],{},[898,76057,2719],{},[898,76059,2666],{},[902,76061,2820],{"encoding":904},[883,76063,76065],{"className":76064},[886],[888,76066,76067],{"xmlns":890},[892,76068,76069,76075],{},[895,76070,76071,76073],{},[898,76072,2839],{},[898,76074,2666],{},[902,76076,2919],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,76079,76080,52190,76083,75983,76119,75999,76134,76015,76149,76031,76164,1343,76179,1343,76194,76209],{},[38,76081,76082],{},"3.2",[883,76084,76086],{"className":76085},[886],[888,76087,76088],{"xmlns":890},[892,76089,76090,76116],{},[895,76091,76092,76094,76096,76098,76100,76102,76104,76106,76108,76110,76112,76114],{},[898,76093,1701],{},[1693,76095,1695],{},[898,76097,2738],{},[1693,76099,1709],{"stretchy":1708},[898,76101,1712],{},[1693,76103,1731],{"stretchy":1708},[1693,76105,1695],{},[1693,76107,1698],{},[1762,76109,11877],{},[898,76111,1712],{},[1693,76113,1892],{},[1762,76115,15892],{},[902,76117,76118],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,76120,76122],{"className":76121},[886],[888,76123,76124],{"xmlns":890},[892,76125,76126,76132],{},[895,76127,76128,76130],{},[898,76129,2663],{},[898,76131,2666],{},[902,76133,2883],{"encoding":904},[883,76135,76137],{"className":76136},[886],[888,76138,76139],{"xmlns":890},[892,76140,76141,76147],{},[895,76142,76143,76145],{},[898,76144,2719],{},[898,76146,2666],{},[902,76148,2820],{"encoding":904},[883,76150,76152],{"className":76151},[886],[888,76153,76154],{"xmlns":890},[892,76155,76156,76162],{},[895,76157,76158,76160],{},[898,76159,2839],{},[898,76161,2666],{},[902,76163,2919],{"encoding":904},[883,76165,76167],{"className":76166},[886],[888,76168,76169],{"xmlns":890},[892,76170,76171,76177],{},[895,76172,76173,76175],{},[898,76174,2663],{},[898,76176,2666],{},[902,76178,2883],{"encoding":904},[883,76180,76182],{"className":76181},[886],[888,76183,76184],{"xmlns":890},[892,76185,76186,76192],{},[895,76187,76188,76190],{},[898,76189,2719],{},[898,76191,2666],{},[902,76193,2820],{"encoding":904},[883,76195,76197],{"className":76196},[886],[888,76198,76199],{"xmlns":890},[892,76200,76201,76207],{},[895,76202,76203,76205],{},[898,76204,2839],{},[898,76206,2666],{},[902,76208,2919],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,76211,76212,52190,76215,76252,76253,75999,76268,76015,76283,76298,76299,7721,76314,76340,76341,76356,76357,1343,76372,7721,76387,76340,76412,76427,76428,76441,76442,76457,76458,76473,76474,1343,76487,1343,76502,1343,76517,1789],{},[38,76213,76214],{},"3.3",[883,76216,76218],{"className":76217},[886],[888,76219,76220],{"xmlns":890},[892,76221,76222,76249],{},[895,76223,76224,76226,76228,76230,76232,76234,76236,76238,76241,76243],{},[898,76225,1701],{},[1693,76227,1695],{},[898,76229,2738],{},[1693,76231,1709],{"stretchy":1708},[898,76233,1712],{},[1693,76235,1731],{"stretchy":1708},[1693,76237,1695],{},[1762,76239,76240],{},"1200",[1693,76242,1698],{},[1717,76244,76245,76247],{},[898,76246,1712],{},[1762,76248,2398],{},[902,76250,76251],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,76254,76256],{"className":76255},[886],[888,76257,76258],{"xmlns":890},[892,76259,76260,76266],{},[895,76261,76262,76264],{},[898,76263,2663],{},[898,76265,2666],{},[902,76267,2883],{"encoding":904},[883,76269,76271],{"className":76270},[886],[888,76272,76273],{"xmlns":890},[892,76274,76275,76281],{},[895,76276,76277,76279],{},[898,76278,2719],{},[898,76280,2666],{},[902,76282,2820],{"encoding":904},[883,76284,76286],{"className":76285},[886],[888,76287,76288],{"xmlns":890},[892,76289,76290,76296],{},[895,76291,76292,76294],{},[898,76293,2839],{},[898,76295,2666],{},[902,76297,2919],{"encoding":904},". (b) Vypočtěte ",[883,76300,76302],{"className":76301},[886],[888,76303,76304],{"xmlns":890},[892,76305,76306,76312],{},[895,76307,76308,76310],{},[898,76309,2663],{},[898,76311,2666],{},[902,76313,2883],{"encoding":904},[883,76315,76317],{"className":76316},[886],[888,76318,76319],{"xmlns":890},[892,76320,76321,76337],{},[895,76322,76323,76325,76327,76329,76331,76333,76335],{},[898,76324,1712],{},[1693,76326,1695],{},[1762,76328,9763],{},[1693,76330,1899],{"separator":1898},[1762,76332,15892],{},[1693,76334,1899],{"separator":1898},[1762,76336,44795],{},[902,76338,76339],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,76342,76344],{"className":76343},[886],[888,76345,76346],{"xmlns":890},[892,76347,76348,76354],{},[895,76349,76350,76352],{},[898,76351,2663],{},[898,76353,2666],{},[902,76355,2883],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,76358,76360],{"className":76359},[886],[888,76361,76362],{"xmlns":890},[892,76363,76364,76370],{},[895,76365,76366,76368],{},[898,76367,2719],{},[898,76369,2666],{},[902,76371,2820],{"encoding":904},[883,76373,76375],{"className":76374},[886],[888,76376,76377],{"xmlns":890},[892,76378,76379,76385],{},[895,76380,76381,76383],{},[898,76382,2839],{},[898,76384,2666],{},[902,76386,2919],{"encoding":904},[883,76388,76390],{"className":76389},[886],[888,76391,76392],{"xmlns":890},[892,76393,76394,76410],{},[895,76395,76396,76398,76400,76402,76404,76406,76408],{},[898,76397,1712],{},[1693,76399,1695],{},[1762,76401,9763],{},[1693,76403,1899],{"separator":1898},[1762,76405,15892],{},[1693,76407,1899],{"separator":1898},[1762,76409,44795],{},[902,76411,76339],{"encoding":904},[883,76413,76415],{"className":76414},[886],[888,76416,76417],{"xmlns":890},[892,76418,76419,76425],{},[895,76420,76421,76423],{},[898,76422,2839],{},[898,76424,2666],{},[902,76426,2919],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,76429,76431],{"className":76430},[886],[888,76432,76433],{"xmlns":890},[892,76434,76435,76439],{},[895,76436,76437],{},[898,76438,1712],{},[902,76440,1712],{"encoding":904},", které maximalizuje ",[883,76443,76445],{"className":76444},[886],[888,76446,76447],{"xmlns":890},[892,76448,76449,76455],{},[895,76450,76451,76453],{},[898,76452,2663],{},[898,76454,2666],{},[902,76456,2883],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,76459,76461],{"className":76460},[886],[888,76462,76463],{"xmlns":890},[892,76464,76465,76471],{},[895,76466,76467,76469],{},[898,76468,2663],{},[898,76470,2666],{},[902,76472,2883],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,76475,76477],{"className":76476},[886],[888,76478,76479],{"xmlns":890},[892,76480,76481,76485],{},[895,76482,76483],{},[898,76484,2738],{},[902,76486,2738],{"encoding":904},[883,76488,76490],{"className":76489},[886],[888,76491,76492],{"xmlns":890},[892,76493,76494,76500],{},[895,76495,76496,76498],{},[898,76497,2663],{},[898,76499,2666],{},[902,76501,2883],{"encoding":904},[883,76503,76505],{"className":76504},[886],[888,76506,76507],{"xmlns":890},[892,76508,76509,76515],{},[895,76510,76511,76513],{},[898,76512,2719],{},[898,76514,2666],{},[902,76516,2820],{"encoding":904},[883,76518,76520],{"className":76519},[886],[888,76521,76522],{"xmlns":890},[892,76523,76524,76530],{},[895,76525,76526,76528],{},[898,76527,2839],{},[898,76529,2666],{},[902,76531,2919],{"encoding":904},[724,76533,76534,76537,76538,76568,76569,76584,76585,4148,76598,1343,76616,1343,76633,76651,76652,76674,76675,76690,76691,76704,76705,1789],{},[38,76535,76536],{},"3.4"," Je dán celkový příjem ",[883,76539,76541],{"className":76540},[886],[888,76542,76543],{"xmlns":890},[892,76544,76545,76565],{},[895,76546,76547,76549,76551,76553,76555,76557,76559],{},[898,76548,2663],{},[898,76550,2666],{},[1693,76552,1695],{},[1762,76554,76240],{},[898,76556,1712],{},[1693,76558,1698],{},[1717,76560,76561,76563],{},[898,76562,1712],{},[1762,76564,8357],{},[902,76566,76567],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,76570,76572],{"className":76571},[886],[888,76573,76574],{"xmlns":890},[892,76575,76576,76582],{},[895,76577,76578,76580],{},[898,76579,2663],{},[898,76581,2666],{},[902,76583,2883],{"encoding":904}," vzhledem ke ",[883,76586,76588],{"className":76587},[886],[888,76589,76590],{"xmlns":890},[892,76591,76592,76596],{},[895,76593,76594],{},[898,76595,1712],{},[902,76597,1712],{"encoding":904},[883,76599,76601],{"className":76600},[886],[888,76602,76603],{"xmlns":890},[892,76604,76605,76613],{},[895,76606,76607,76609,76611],{},[898,76608,1712],{},[1693,76610,1695],{},[1762,76612,9147],{},[902,76614,76615],{"encoding":904},"Q = 5",[883,76617,76619],{"className":76618},[886],[888,76620,76621],{"xmlns":890},[892,76622,76623,76631],{},[895,76624,76625,76627,76629],{},[898,76626,1712],{},[1693,76628,1695],{},[1762,76630,12453],{},[902,76632,12456],{"encoding":904},[883,76634,76636],{"className":76635},[886],[888,76637,76638],{"xmlns":890},[892,76639,76640,76648],{},[895,76641,76642,76644,76646],{},[898,76643,1712],{},[1693,76645,1695],{},[1762,76647,10402],{},[902,76649,76650],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,76653,76655],{"className":76654},[886],[888,76656,76657],{"xmlns":890},[892,76658,76659,76671],{},[895,76660,76661,76663,76665,76667,76669],{},[898,76662,2839],{},[898,76664,2666],{},[1693,76666,1709],{"stretchy":1708},[1762,76668,9763],{},[1693,76670,1731],{"stretchy":1708},[902,76672,76673],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,76676,76678],{"className":76677},[886],[888,76679,76680],{"xmlns":890},[892,76681,76682,76688],{},[895,76683,76684,76686],{},[898,76685,2663],{},[898,76687,2666],{},[902,76689,2883],{"encoding":904},", jestliže se ",[883,76692,76694],{"className":76693},[886],[888,76695,76696],{"xmlns":890},[892,76697,76698,76702],{},[895,76699,76700],{},[898,76701,1712],{},[902,76703,1712],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,76706,76708],{"className":76707},[886],[888,76709,76710],{"xmlns":890},[892,76711,76712,76718],{},[895,76713,76714,76716],{},[898,76715,2663],{},[898,76717,2666],{},[902,76719,2883],{"encoding":904},[724,76721,76722,76725,76726,76752,76753,76768,76769,76690,76784,76797],{},[38,76723,76724],{},"3.5"," Je dán mezní příjem ",[883,76727,76729],{"className":76728},[886],[888,76730,76731],{"xmlns":890},[892,76732,76733,76749],{},[895,76734,76735,76737,76739,76741,76743,76745,76747],{},[898,76736,2839],{},[898,76738,2666],{},[1693,76740,1695],{},[1693,76742,1698],{},[898,76744,1712],{},[1693,76746,1892],{},[1762,76748,15892],{},[902,76750,76751],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,76754,76756],{"className":76755},[886],[888,76757,76758],{"xmlns":890},[892,76759,76760,76766],{},[895,76761,76762,76764],{},[898,76763,2663],{},[898,76765,2666],{},[902,76767,2883],{"encoding":904},". (b) Vypočtěte změnu ",[883,76770,76772],{"className":76771},[886],[888,76773,76774],{"xmlns":890},[892,76775,76776,76782],{},[895,76777,76778,76780],{},[898,76779,2663],{},[898,76781,2666],{},[902,76783,2883],{"encoding":904},[883,76785,76787],{"className":76786},[886],[888,76788,76789],{"xmlns":890},[892,76790,76791,76795],{},[895,76792,76793],{},[898,76794,1712],{},[902,76796,1712],{"encoding":904}," změní z 8 na 12.",[198,76799,76801],{"id":76800},"náklady-36316","Náklady (3.6–3.16)",[724,76803,76804,76807,76808,76848,76849,76864,76865,76882,76883,76900,76901,76916,76917,76932,76933,76298,76948,1343,76963,1343,76980,1343,76997,1343,77012,1343,77027,7721,77042,77060,77061,1343,77076,1343,77091,77106],{},[38,76805,76806],{},"3.6"," Jsou dány celkové náklady ",[883,76809,76811],{"className":76810},[886],[888,76812,76813],{"xmlns":890},[892,76814,76815,76845],{},[895,76816,76817,76819,76821,76823,76825,76827,76829,76831,76833],{},[898,76818,2663],{},[898,76820,2971],{},[1693,76822,1695],{},[1762,76824,9987],{},[1693,76826,1892],{},[1762,76828,2398],{},[898,76830,1712],{},[1693,76832,1892],{},[3638,76834,76835],{"scriptlevel":1911,"displaystyle":1708},[2132,76836,76837,76843],{},[1717,76838,76839,76841],{},[898,76840,1712],{},[1762,76842,2398],{},[1762,76844,9763],{},[902,76846,76847],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,76850,76852],{"className":76851},[886],[888,76853,76854],{"xmlns":890},[892,76855,76856,76862],{},[895,76857,76858,76860],{},[898,76859,2976],{},[898,76861,2971],{},[902,76863,3022],{"encoding":904},", celkové variabilní náklady ",[883,76866,76868],{"className":76867},[886],[888,76869,76870],{"xmlns":890},[892,76871,76872,76880],{},[895,76873,76874,76876,76878],{},[898,76875,2663],{},[898,76877,2985],{},[898,76879,2971],{},[902,76881,3041],{"encoding":904},", průměrné variabilní náklady ",[883,76884,76886],{"className":76885},[886],[888,76887,76888],{"xmlns":890},[892,76889,76890,76898],{},[895,76891,76892,76894,76896],{},[898,76893,2719],{},[898,76895,2985],{},[898,76897,2971],{},[902,76899,3789],{"encoding":904},", variabilní náklady na jednotku ",[883,76902,76904],{"className":76903},[886],[888,76905,76906],{"xmlns":890},[892,76907,76908,76914],{},[895,76909,76910,76912],{},[898,76911,2985],{},[898,76913,2971],{},[902,76915,70331],{"encoding":904},", průměrné náklady ",[883,76918,76920],{"className":76919},[886],[888,76921,76922],{"xmlns":890},[892,76923,76924,76930],{},[895,76925,76926,76928],{},[898,76927,2719],{},[898,76929,2971],{},[902,76931,3331],{"encoding":904}," a mezní náklady ",[883,76934,76936],{"className":76935},[886],[888,76937,76938],{"xmlns":890},[892,76939,76940,76946],{},[895,76941,76942,76944],{},[898,76943,2839],{},[898,76945,2971],{},[902,76947,3810],{"encoding":904},[883,76949,76951],{"className":76950},[886],[888,76952,76953],{"xmlns":890},[892,76954,76955,76961],{},[895,76956,76957,76959],{},[898,76958,2663],{},[898,76960,2971],{},[902,76962,3225],{"encoding":904},[883,76964,76966],{"className":76965},[886],[888,76967,76968],{"xmlns":890},[892,76969,76970,76978],{},[895,76971,76972,76974,76976],{},[898,76973,2663],{},[898,76975,2985],{},[898,76977,2971],{},[902,76979,3041],{"encoding":904},[883,76981,76983],{"className":76982},[886],[888,76984,76985],{"xmlns":890},[892,76986,76987,76995],{},[895,76988,76989,76991,76993],{},[898,76990,2719],{},[898,76992,2985],{},[898,76994,2971],{},[902,76996,3789],{"encoding":904},[883,76998,77000],{"className":76999},[886],[888,77001,77002],{"xmlns":890},[892,77003,77004,77010],{},[895,77005,77006,77008],{},[898,77007,2985],{},[898,77009,2971],{},[902,77011,70331],{"encoding":904},[883,77013,77015],{"className":77014},[886],[888,77016,77017],{"xmlns":890},[892,77018,77019,77025],{},[895,77020,77021,77023],{},[898,77022,2719],{},[898,77024,2971],{},[902,77026,3331],{"encoding":904},[883,77028,77030],{"className":77029},[886],[888,77031,77032],{"xmlns":890},[892,77033,77034,77040],{},[895,77035,77036,77038],{},[898,77037,2839],{},[898,77039,2971],{},[902,77041,3810],{"encoding":904},[883,77043,77045],{"className":77044},[886],[888,77046,77047],{"xmlns":890},[892,77048,77049,77057],{},[895,77050,77051,77053,77055],{},[898,77052,1712],{},[1693,77054,1695],{},[1762,77056,10017],{},[902,77058,77059],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,77062,77064],{"className":77063},[886],[888,77065,77066],{"xmlns":890},[892,77067,77068,77074],{},[895,77069,77070,77072],{},[898,77071,2663],{},[898,77073,2971],{},[902,77075,3225],{"encoding":904},[883,77077,77079],{"className":77078},[886],[888,77080,77081],{"xmlns":890},[892,77082,77083,77089],{},[895,77084,77085,77087],{},[898,77086,2719],{},[898,77088,2971],{},[902,77090,3331],{"encoding":904},[883,77092,77094],{"className":77093},[886],[888,77095,77096],{"xmlns":890},[892,77097,77098,77104],{},[895,77099,77100,77102],{},[898,77101,2839],{},[898,77103,2971],{},[902,77105,3810],{"encoding":904}," rostou, resp. klesají.",[724,77108,77109,77112,77113,76932,77143,77158,77159,77174,77175,1343,77190,1343,77205,1789],{},[38,77110,77111],{},"3.7"," Jsou dány průměrné náklady ",[883,77114,77116],{"className":77115},[886],[888,77117,77118],{"xmlns":890},[892,77119,77120,77140],{},[895,77121,77122,77124,77126,77128,77136,77138],{},[898,77123,2719],{},[898,77125,2971],{},[1693,77127,1695],{},[3638,77129,77130],{"scriptlevel":1911,"displaystyle":1708},[2132,77131,77132,77134],{},[1762,77133,9987],{},[898,77135,1712],{},[1693,77137,1892],{},[1762,77139,15892],{},[902,77141,77142],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,77144,77146],{"className":77145},[886],[888,77147,77148],{"xmlns":890},[892,77149,77150,77156],{},[895,77151,77152,77154],{},[898,77153,2839],{},[898,77155,2971],{},[902,77157,3810],{"encoding":904},". (a) Určete celkové náklady ",[883,77160,77162],{"className":77161},[886],[888,77163,77164],{"xmlns":890},[892,77165,77166,77172],{},[895,77167,77168,77170],{},[898,77169,2663],{},[898,77171,2971],{},[902,77173,3225],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,77176,77178],{"className":77177},[886],[888,77179,77180],{"xmlns":890},[892,77181,77182,77188],{},[895,77183,77184,77186],{},[898,77185,2719],{},[898,77187,2971],{},[902,77189,3331],{"encoding":904},[883,77191,77193],{"className":77192},[886],[888,77194,77195],{"xmlns":890},[892,77196,77197,77203],{},[895,77198,77199,77201],{},[898,77200,2663],{},[898,77202,2971],{},[902,77204,3225],{"encoding":904},[883,77206,77208],{"className":77207},[886],[888,77209,77210],{"xmlns":890},[892,77211,77212,77218],{},[895,77213,77214,77216],{},[898,77215,2839],{},[898,77217,2971],{},[902,77219,3810],{"encoding":904},[724,77221,77222,76807,77225,77269,77270,1343,77287,1343,77302,1343,77319,1343,77334,1343,77351,1789],{},[38,77223,77224],{},"3.8",[883,77226,77228],{"className":77227},[886],[888,77229,77230],{"xmlns":890},[892,77231,77232,77266],{},[895,77233,77234,77236,77238,77240,77242,77244,77246,77248,77250,77252,77258,77260],{},[898,77235,2663],{},[898,77237,2971],{},[1693,77239,1695],{},[1762,77241,53467],{},[1693,77243,1892],{},[1762,77245,44795],{},[898,77247,1712],{},[1693,77249,1698],{},[1762,77251,9154],{},[1717,77253,77254,77256],{},[898,77255,1712],{},[1762,77257,2398],{},[1693,77259,1892],{},[1717,77261,77262,77264],{},[898,77263,1712],{},[1762,77265,8357],{},[902,77267,77268],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,77271,77273],{"className":77272},[886],[888,77274,77275],{"xmlns":890},[892,77276,77277,77285],{},[895,77278,77279,77281,77283],{},[898,77280,2663],{},[898,77282,2985],{},[898,77284,2971],{},[902,77286,3041],{"encoding":904},[883,77288,77290],{"className":77289},[886],[888,77291,77292],{"xmlns":890},[892,77293,77294,77300],{},[895,77295,77296,77298],{},[898,77297,2976],{},[898,77299,2971],{},[902,77301,3022],{"encoding":904},[883,77303,77305],{"className":77304},[886],[888,77306,77307],{"xmlns":890},[892,77308,77309,77317],{},[895,77310,77311,77313,77315],{},[898,77312,2719],{},[898,77314,2985],{},[898,77316,2971],{},[902,77318,3789],{"encoding":904},[883,77320,77322],{"className":77321},[886],[888,77323,77324],{"xmlns":890},[892,77325,77326,77332],{},[895,77327,77328,77330],{},[898,77329,2719],{},[898,77331,2971],{},[902,77333,3331],{"encoding":904},[883,77335,77337],{"className":77336},[886],[888,77338,77339],{"xmlns":890},[892,77340,77341,77349],{},[895,77342,77343,77345,77347],{},[898,77344,2719],{},[898,77346,2976],{},[898,77348,2971],{},[902,77350,3150],{"encoding":904},[883,77352,77354],{"className":77353},[886],[888,77355,77356],{"xmlns":890},[892,77357,77358,77364],{},[895,77359,77360,77362],{},[898,77361,2839],{},[898,77363,2971],{},[902,77365,3810],{"encoding":904},[724,77367,77368,76807,77371,77401,77402,76584,77417,7721,77430,1343,77448,1343,77466,76651,77484,76674,77506,77521,77522,77535,77536,1789],{},[38,77369,77370],{},"3.9",[883,77372,77374],{"className":77373},[886],[888,77375,77376],{"xmlns":890},[892,77377,77378,77398],{},[895,77379,77380,77382,77384,77386,77388,77390,77392],{},[898,77381,2663],{},[898,77383,2971],{},[1693,77385,1695],{},[1762,77387,21936],{},[1693,77389,1892],{},[1762,77391,26132],{},[1717,77393,77394,77396],{},[898,77395,1712],{},[1762,77397,2398],{},[902,77399,77400],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,77403,77405],{"className":77404},[886],[888,77406,77407],{"xmlns":890},[892,77408,77409,77415],{},[895,77410,77411,77413],{},[898,77412,2663],{},[898,77414,2971],{},[902,77416,3225],{"encoding":904},[883,77418,77420],{"className":77419},[886],[888,77421,77422],{"xmlns":890},[892,77423,77424,77428],{},[895,77425,77426],{},[898,77427,1712],{},[902,77429,1712],{"encoding":904},[883,77431,77433],{"className":77432},[886],[888,77434,77435],{"xmlns":890},[892,77436,77437,77445],{},[895,77438,77439,77441,77443],{},[898,77440,1712],{},[1693,77442,1695],{},[1762,77444,9763],{},[902,77446,77447],{"encoding":904},"Q = 10",[883,77449,77451],{"className":77450},[886],[888,77452,77453],{"xmlns":890},[892,77454,77455,77463],{},[895,77456,77457,77459,77461],{},[898,77458,1712],{},[1693,77460,1695],{},[1762,77462,15892],{},[902,77464,77465],{"encoding":904},"Q = 20",[883,77467,77469],{"className":77468},[886],[888,77470,77471],{"xmlns":890},[892,77472,77473,77481],{},[895,77474,77475,77477,77479],{},[898,77476,1712],{},[1693,77478,1695],{},[1762,77480,44795],{},[902,77482,77483],{"encoding":904},"Q = 30",[883,77485,77487],{"className":77486},[886],[888,77488,77489],{"xmlns":890},[892,77490,77491,77503],{},[895,77492,77493,77495,77497,77499,77501],{},[898,77494,2839],{},[898,77496,2971],{},[1693,77498,1709],{"stretchy":1708},[1762,77500,43026],{},[1693,77502,1731],{"stretchy":1708},[902,77504,77505],{"encoding":904},"MC(15)",[883,77507,77509],{"className":77508},[886],[888,77510,77511],{"xmlns":890},[892,77512,77513,77519],{},[895,77514,77515,77517],{},[898,77516,2663],{},[898,77518,2971],{},[902,77520,3225],{"encoding":904}," v důsledku změny ",[883,77523,77525],{"className":77524},[886],[888,77526,77527],{"xmlns":890},[892,77528,77529,77533],{},[895,77530,77531],{},[898,77532,1712],{},[902,77534,1712],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,77537,77539],{"className":77538},[886],[888,77540,77541],{"xmlns":890},[892,77542,77543,77549],{},[895,77544,77545,77547],{},[898,77546,2663],{},[898,77548,2971],{},[902,77550,3225],{"encoding":904},[724,77552,77553,77556,77557,77158,77593,77608,77609,76768,77628,77521,77643,77656],{},[38,77554,77555],{},"3.10"," Jsou dány mezní náklady ",[883,77558,77560],{"className":77559},[886],[888,77561,77562],{"xmlns":890},[892,77563,77564,77590],{},[895,77565,77566,77568,77570,77572,77574,77576,77578,77580,77582,77584],{},[898,77567,2839],{},[898,77569,2971],{},[1693,77571,1695],{},[1762,77573,10023],{},[1693,77575,1698],{},[1762,77577,48633],{},[898,77579,1712],{},[1693,77581,1892],{},[1762,77583,71285],{},[1717,77585,77586,77588],{},[898,77587,1712],{},[1762,77589,2398],{},[902,77591,77592],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,77594,77596],{"className":77595},[886],[888,77597,77598],{"xmlns":890},[892,77599,77600,77606],{},[895,77601,77602,77604],{},[898,77603,2663],{},[898,77605,2971],{},[902,77607,3225],{"encoding":904},", jestliže fixní náklady ",[883,77610,77612],{"className":77611},[886],[888,77613,77614],{"xmlns":890},[892,77615,77616,77626],{},[895,77617,77618,77620,77622,77624],{},[898,77619,2976],{},[898,77621,2971],{},[1693,77623,1695],{},[1762,77625,9987],{},[902,77627,18478],{"encoding":904},[883,77629,77631],{"className":77630},[886],[888,77632,77633],{"xmlns":890},[892,77634,77635,77641],{},[895,77636,77637,77639],{},[898,77638,2663],{},[898,77640,2971],{},[902,77642,3225],{"encoding":904},[883,77644,77646],{"className":77645},[886],[888,77647,77648],{"xmlns":890},[892,77649,77650,77654],{},[895,77651,77652],{},[898,77653,1712],{},[902,77655,1712],{"encoding":904}," z 15 na 20.",[724,77658,77659,76807,77662,77705,77706,77719,77720,77735,77736,77751,77752,77719,77765,77735,77782,77799,77800,77719,77813,77735,77828,77843,77844,77864,77865,77888],{},[38,77660,77661],{},"3.11",[883,77663,77665],{"className":77664},[886],[888,77666,77667],{"xmlns":890},[892,77668,77669,77703],{},[895,77670,77671,77673,77675,77677,77679,77681,77683,77685,77687,77689,77695,77697],{},[898,77672,2663],{},[898,77674,2971],{},[1693,77676,1695],{},[1762,77678,9987],{},[1693,77680,1892],{},[1762,77682,11872],{},[898,77684,1712],{},[1693,77686,1698],{},[1762,77688,9147],{},[1717,77690,77691,77693],{},[898,77692,1712],{},[1762,77694,2398],{},[1693,77696,1892],{},[1717,77698,77699,77701],{},[898,77700,1712],{},[1762,77702,8357],{},[902,77704,67639],{"encoding":904},". (a) Určete ",[883,77707,77709],{"className":77708},[886],[888,77710,77711],{"xmlns":890},[892,77712,77713,77717],{},[895,77714,77715],{},[898,77716,1712],{},[902,77718,1712],{"encoding":904},", které minimalizuje ",[883,77721,77723],{"className":77722},[886],[888,77724,77725],{"xmlns":890},[892,77726,77727,77733],{},[895,77728,77729,77731],{},[898,77730,2839],{},[898,77732,2971],{},[902,77734,3810],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,77737,77739],{"className":77738},[886],[888,77740,77741],{"xmlns":890},[892,77742,77743,77749],{},[895,77744,77745,77747],{},[898,77746,2839],{},[898,77748,2971],{},[902,77750,3810],{"encoding":904},". (b) Určete ",[883,77753,77755],{"className":77754},[886],[888,77756,77757],{"xmlns":890},[892,77758,77759,77763],{},[895,77760,77761],{},[898,77762,1712],{},[902,77764,1712],{"encoding":904},[883,77766,77768],{"className":77767},[886],[888,77769,77770],{"xmlns":890},[892,77771,77772,77780],{},[895,77773,77774,77776,77778],{},[898,77775,2719],{},[898,77777,2985],{},[898,77779,2971],{},[902,77781,3789],{"encoding":904},[883,77783,77785],{"className":77784},[886],[888,77786,77787],{"xmlns":890},[892,77788,77789,77797],{},[895,77790,77791,77793,77795],{},[898,77792,2719],{},[898,77794,2985],{},[898,77796,2971],{},[902,77798,3789],{"encoding":904},". (c) Určete ",[883,77801,77803],{"className":77802},[886],[888,77804,77805],{"xmlns":890},[892,77806,77807,77811],{},[895,77808,77809],{},[898,77810,1712],{},[902,77812,1712],{"encoding":904},[883,77814,77816],{"className":77815},[886],[888,77817,77818],{"xmlns":890},[892,77819,77820,77826],{},[895,77821,77822,77824],{},[898,77823,2719],{},[898,77825,2971],{},[902,77827,3331],{"encoding":904},[883,77829,77831],{"className":77830},[886],[888,77832,77833],{"xmlns":890},[892,77834,77835,77841],{},[895,77836,77837,77839],{},[898,77838,2719],{},[898,77840,2971],{},[902,77842,3331],{"encoding":904}," (rada: hledaný kořen ",[883,77845,77847],{"className":77846},[886],[888,77848,77849],{"xmlns":890},[892,77850,77851,77861],{},[895,77852,77853,77855],{},[898,77854,2719],{},[1717,77856,77857,77859],{},[898,77858,2971],{},[1693,77860,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,77862,77863],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,77866,77868],{"className":77867},[886],[888,77869,77870],{"xmlns":890},[892,77871,77872,77885],{},[895,77873,77874,77876,77879,77881,77883],{},[1693,77875,1709],{"stretchy":1708},[1762,77877,77878],{},"4,7",[1693,77880,15283],{"separator":1898},[1762,77882,12147],{},[1693,77884,1731],{"stretchy":1708},[902,77886,77887],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,77890,77891,77894,77895,9530,77923,77940,77941,28397,77982,78003],{},[38,77892,77893],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,77896,77898],{"className":77897},[886],[888,77899,77900],{"xmlns":890},[892,77901,77902,77920],{},[895,77903,77904,77906,77908,77910,77912,77914,77916,77918],{},[898,77905,2719],{},[898,77907,2971],{},[1693,77909,1695],{},[898,77911,2719],{},[898,77913,2971],{},[1693,77915,1709],{"stretchy":1708},[898,77917,1712],{},[1693,77919,1731],{"stretchy":1708},[902,77921,77922],{"encoding":904},"AC = AC(Q)",[883,77924,77926],{"className":77925},[886],[888,77927,77928],{"xmlns":890},[892,77929,77930,77938],{},[895,77931,77932],{},[3284,77933,77934,77936],{},[898,77935,1712],{},[1762,77937,1911],{},[902,77939,6293],{"encoding":904}," minimum, pak platí ",[883,77942,77944],{"className":77943},[886],[888,77945,77946],{"xmlns":890},[892,77947,77948,77980],{},[895,77949,77950,77952,77954,77956,77962,77964,77966,77968,77970,77972,77978],{},[898,77951,2719],{},[898,77953,2971],{},[1693,77955,1709],{"stretchy":1708},[3284,77957,77958,77960],{},[898,77959,1712],{},[1762,77961,1911],{},[1693,77963,1731],{"stretchy":1708},[1693,77965,1695],{},[898,77967,2839],{},[898,77969,2971],{},[1693,77971,1709],{"stretchy":1708},[3284,77973,77974,77976],{},[898,77975,1712],{},[1762,77977,1911],{},[1693,77979,1731],{"stretchy":1708},[902,77981,3310],{"encoding":904},[883,77983,77985],{"className":77984},[886],[888,77986,77987],{"xmlns":890},[892,77988,77989,78001],{},[895,77990,77991,77993,77995,77997,77999],{},[898,77992,2839],{},[898,77994,2971],{},[1693,77996,1709],{"stretchy":1708},[898,77998,1712],{},[1693,78000,1731],{"stretchy":1708},[902,78002,74409],{"encoding":904}," jsou mezní náklady.",[724,78005,78006,76807,78009,77269,78043,77719,78056,77735,78071,1789],{},[38,78007,78008],{},"3.13",[883,78010,78012],{"className":78011},[886],[888,78013,78014],{"xmlns":890},[892,78015,78016,78040],{},[895,78017,78018,78020,78022,78024,78030,78032,78034,78036,78038],{},[898,78019,2663],{},[898,78021,2971],{},[1693,78023,1695],{},[1717,78025,78026,78028],{},[898,78027,1712],{},[1762,78029,2398],{},[1693,78031,1892],{},[1762,78033,2398],{},[898,78035,1712],{},[1693,78037,1892],{},[1762,78039,11872],{},[902,78041,78042],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,78044,78046],{"className":78045},[886],[888,78047,78048],{"xmlns":890},[892,78049,78050,78054],{},[895,78051,78052],{},[898,78053,1712],{},[902,78055,1712],{"encoding":904},[883,78057,78059],{"className":78058},[886],[888,78060,78061],{"xmlns":890},[892,78062,78063,78069],{},[895,78064,78065,78067],{},[898,78066,2719],{},[898,78068,2971],{},[902,78070,3331],{"encoding":904},[883,78072,78074],{"className":78073},[886],[888,78075,78076],{"xmlns":890},[892,78077,78078,78084],{},[895,78079,78080,78082],{},[898,78081,2719],{},[898,78083,2971],{},[902,78085,3331],{"encoding":904},[724,78087,78088,78091,78092,9530,78124,77940,78141,28397,78184,78003],{},[38,78089,78090],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,78093,78095],{"className":78094},[886],[888,78096,78097],{"xmlns":890},[892,78098,78099,78121],{},[895,78100,78101,78103,78105,78107,78109,78111,78113,78115,78117,78119],{},[898,78102,2719],{},[898,78104,2985],{},[898,78106,2971],{},[1693,78108,1695],{},[898,78110,2719],{},[898,78112,2985],{},[898,78114,2971],{},[1693,78116,1709],{"stretchy":1708},[898,78118,1712],{},[1693,78120,1731],{"stretchy":1708},[902,78122,78123],{"encoding":904},"AVC = AVC(Q)",[883,78125,78127],{"className":78126},[886],[888,78128,78129],{"xmlns":890},[892,78130,78131,78139],{},[895,78132,78133],{},[3284,78134,78135,78137],{},[898,78136,1712],{},[1762,78138,1911],{},[902,78140,6293],{"encoding":904},[883,78142,78144],{"className":78143},[886],[888,78145,78146],{"xmlns":890},[892,78147,78148,78182],{},[895,78149,78150,78152,78154,78156,78158,78164,78166,78168,78170,78172,78174,78180],{},[898,78151,2719],{},[898,78153,2985],{},[898,78155,2971],{},[1693,78157,1709],{"stretchy":1708},[3284,78159,78160,78162],{},[898,78161,1712],{},[1762,78163,1911],{},[1693,78165,1731],{"stretchy":1708},[1693,78167,1695],{},[898,78169,2839],{},[898,78171,2971],{},[1693,78173,1709],{"stretchy":1708},[3284,78175,78176,78178],{},[898,78177,1712],{},[1762,78179,1911],{},[1693,78181,1731],{"stretchy":1708},[902,78183,3408],{"encoding":904},[883,78185,78187],{"className":78186},[886],[888,78188,78189],{"xmlns":890},[892,78190,78191,78203],{},[895,78192,78193,78195,78197,78199,78201],{},[898,78194,2839],{},[898,78196,2971],{},[1693,78198,1709],{"stretchy":1708},[898,78200,1712],{},[1693,78202,1731],{"stretchy":1708},[902,78204,74409],{"encoding":904},[724,78206,78207,76807,78210,77269,78256,77719,78269,77735,78286,1789],{},[38,78208,78209],{},"3.15",[883,78211,78213],{"className":78212},[886],[888,78214,78215],{"xmlns":890},[892,78216,78217,78253],{},[895,78218,78219,78221,78223,78225,78227,78229,78231,78233,78235,78237,78243,78245,78247],{},[898,78220,2663],{},[898,78222,2971],{},[1693,78224,1695],{},[1762,78226,10017],{},[1693,78228,1892],{},[1762,78230,43026],{},[898,78232,1712],{},[1693,78234,1698],{},[1762,78236,2398],{},[1717,78238,78239,78241],{},[898,78240,1712],{},[1762,78242,2398],{},[1693,78244,1892],{},[1762,78246,9739],{},[1717,78248,78249,78251],{},[898,78250,1712],{},[1762,78252,8357],{},[902,78254,78255],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,78257,78259],{"className":78258},[886],[888,78260,78261],{"xmlns":890},[892,78262,78263,78267],{},[895,78264,78265],{},[898,78266,1712],{},[902,78268,1712],{"encoding":904},[883,78270,78272],{"className":78271},[886],[888,78273,78274],{"xmlns":890},[892,78275,78276,78284],{},[895,78277,78278,78280,78282],{},[898,78279,2719],{},[898,78281,2985],{},[898,78283,2971],{},[902,78285,3789],{"encoding":904},[883,78287,78289],{"className":78288},[886],[888,78290,78291],{"xmlns":890},[892,78292,78293,78301],{},[895,78294,78295,78297,78299],{},[898,78296,2719],{},[898,78298,2985],{},[898,78300,2971],{},[902,78302,3789],{"encoding":904},[724,78304,78305,78308,78309,78322,78323,78343],{},[38,78306,78307],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,78310,78312],{"className":78311},[886],[888,78313,78314],{"xmlns":890},[892,78315,78316,78320],{},[895,78317,78318],{},[898,78319,2590],{},[902,78321,2590],{"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 ",[883,78324,78326],{"className":78325},[886],[888,78327,78328],{"xmlns":890},[892,78329,78330,78340],{},[895,78331,78332,78334,78336,78338],{},[1762,78333,9763],{},[1915,78335,2239],{},[1762,78337,65817],{},[898,78339,2590],{},[902,78341,78342],{"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.",[198,78345,78347],{"id":78346},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,78349,78350,78353,78354,4286,78376,78402],{},[38,78351,78352],{},"3.17"," Jsou dány ",[883,78355,78357],{"className":78356},[886],[888,78358,78359],{"xmlns":890},[892,78360,78361,78373],{},[895,78362,78363,78365,78367,78369,78371],{},[898,78364,2663],{},[898,78366,2666],{},[1693,78368,1695],{},[1762,78370,9763],{},[898,78372,1712],{},[902,78374,78375],{"encoding":904},"TR = 10Q",[883,78377,78379],{"className":78378},[886],[888,78380,78381],{"xmlns":890},[892,78382,78383,78399],{},[895,78384,78385,78387,78389,78391,78393,78395,78397],{},[898,78386,2663],{},[898,78388,2971],{},[1693,78390,1695],{},[1762,78392,9987],{},[1693,78394,1892],{},[1762,78396,9147],{},[898,78398,1712],{},[902,78400,78401],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,78404,78405,78408,78409,13055,78424,78439,78440,1343,78462,28397,78489,78511,78512,78546],{},[38,78406,78407],{},"3.18"," Odvoďte, že jestliže ",[883,78410,78412],{"className":78411},[886],[888,78413,78414],{"xmlns":890},[892,78415,78416,78422],{},[895,78417,78418,78420],{},[898,78419,2663],{},[898,78421,2666],{},[902,78423,2883],{"encoding":904},[883,78425,78427],{"className":78426},[886],[888,78428,78429],{"xmlns":890},[892,78430,78431,78437],{},[895,78432,78433,78435],{},[898,78434,2663],{},[898,78436,2971],{},[902,78438,3225],{"encoding":904}," jsou lineární tvaru ",[883,78441,78443],{"className":78442},[886],[888,78444,78445],{"xmlns":890},[892,78446,78447,78459],{},[895,78448,78449,78451,78453,78455,78457],{},[898,78450,2663],{},[898,78452,2666],{},[1693,78454,1695],{},[898,78456,724],{},[898,78458,1712],{},[902,78460,78461],{"encoding":904},"TR = pQ",[883,78463,78465],{"className":78464},[886],[888,78466,78467],{"xmlns":890},[892,78468,78469,78486],{},[895,78470,78471,78473,78475,78477,78480,78482,78484],{},[898,78472,2663],{},[898,78474,2971],{},[1693,78476,1695],{},[898,78478,78479],{},"m",[1693,78481,1892],{},[898,78483,5362],{},[898,78485,1712],{},[902,78487,78488],{"encoding":904},"TC = m + nQ",[883,78490,78492],{"className":78491},[886],[888,78493,78494],{"xmlns":890},[892,78495,78496,78508],{},[895,78497,78498,78500,78502,78504,78506],{},[898,78499,78479],{},[1693,78501,1899],{"separator":1898},[898,78503,5362],{},[1693,78505,1899],{"separator":1898},[898,78507,724],{},[902,78509,78510],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,78513,78515],{"className":78514},[886],[888,78516,78517],{"xmlns":890},[892,78518,78519,78543],{},[895,78520,78521,78527,78529],{},[1717,78522,78523,78525],{},[898,78524,1712],{},[1693,78526,3672],{},[1693,78528,1695],{},[3638,78530,78531],{"scriptlevel":1911,"displaystyle":1708},[2132,78532,78533,78535],{},[898,78534,78479],{},[895,78536,78537,78539,78541],{},[898,78538,724],{},[1693,78540,1698],{},[898,78542,5362],{},[902,78544,78545],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,78548,78549,78353,78552,4286,78586,77705,78612,78625,78626,76457,78641,78656,78657,76441,78670,76457,78685,78700],{},[38,78550,78551],{},"3.19",[883,78553,78555],{"className":78554},[886],[888,78556,78557],{"xmlns":890},[892,78558,78559,78583],{},[895,78560,78561,78563,78565,78567,78569,78571,78577,78579,78581],{},[898,78562,2663],{},[898,78564,2666],{},[1693,78566,1695],{},[1693,78568,1698],{},[1762,78570,2398],{},[1717,78572,78573,78575],{},[898,78574,1712],{},[1762,78576,2398],{},[1693,78578,1892],{},[1762,78580,29746],{},[898,78582,1712],{},[902,78584,78585],{"encoding":904},"TR = -2Q^2 + 14Q",[883,78587,78589],{"className":78588},[886],[888,78590,78591],{"xmlns":890},[892,78592,78593,78609],{},[895,78594,78595,78597,78599,78601,78603,78605,78607],{},[898,78596,2663],{},[898,78598,2971],{},[1693,78600,1695],{},[1762,78602,2398],{},[898,78604,1712],{},[1693,78606,1892],{},[1762,78608,9763],{},[902,78610,78611],{"encoding":904},"TC = 2Q + 10",[883,78613,78615],{"className":78614},[886],[888,78616,78617],{"xmlns":890},[892,78618,78619,78623],{},[895,78620,78621],{},[898,78622,1712],{},[902,78624,1712],{"encoding":904},", které maximalizuje zisk ",[883,78627,78629],{"className":78628},[886],[888,78630,78631],{"xmlns":890},[892,78632,78633,78639],{},[895,78634,78635,78637],{},[898,78636,1701],{},[898,78638,2666],{},[902,78640,70205],{"encoding":904},[883,78642,78644],{"className":78643},[886],[888,78645,78646],{"xmlns":890},[892,78647,78648,78654],{},[895,78649,78650,78652],{},[898,78651,1701],{},[898,78653,2666],{},[902,78655,70205],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,78658,78660],{"className":78659},[886],[888,78661,78662],{"xmlns":890},[892,78663,78664,78668],{},[895,78665,78666],{},[898,78667,1712],{},[902,78669,1712],{"encoding":904},[883,78671,78673],{"className":78672},[886],[888,78674,78675],{"xmlns":890},[892,78676,78677,78683],{},[895,78678,78679,78681],{},[898,78680,2663],{},[898,78682,2666],{},[902,78684,2883],{"encoding":904},[883,78686,78688],{"className":78687},[886],[888,78689,78690],{"xmlns":890},[892,78691,78692,78698],{},[895,78693,78694,78696],{},[898,78695,2663],{},[898,78697,2666],{},[902,78699,2883],{"encoding":904},". (d) Graficky interpretujte.",[724,78702,78703,54448,78706,1343,78732,1343,78751,77705,78771,78625,78784,76457,78799,78814,78815,78837,78838,77888],{},[38,78704,78705],{},"3.20",[883,78707,78709],{"className":78708},[886],[888,78710,78711],{"xmlns":890},[892,78712,78713,78729],{},[895,78714,78715,78717,78719,78721,78723],{},[898,78716,1701],{},[1693,78718,1695],{},[1762,78720,26949],{},[1693,78722,1698],{},[1717,78724,78725,78727],{},[898,78726,1712],{},[1762,78728,2398],{},[902,78730,78731],{"encoding":904},"P = 400 - Q^2",[883,78733,78735],{"className":78734},[886],[888,78736,78737],{"xmlns":890},[892,78738,78739,78749],{},[895,78740,78741,78743,78745,78747],{},[898,78742,2976],{},[898,78744,2971],{},[1693,78746,1695],{},[1762,78748,9987],{},[902,78750,18478],{"encoding":904},[883,78752,78754],{"className":78753},[886],[888,78755,78756],{"xmlns":890},[892,78757,78758,78768],{},[895,78759,78760,78762,78764,78766],{},[898,78761,2839],{},[898,78763,2971],{},[1693,78765,1695],{},[1762,78767,15892],{},[902,78769,78770],{"encoding":904},"MC = 20",[883,78772,78774],{"className":78773},[886],[888,78775,78776],{"xmlns":890},[892,78777,78778,78782],{},[895,78779,78780],{},[898,78781,1712],{},[902,78783,1712],{"encoding":904},[883,78785,78787],{"className":78786},[886],[888,78788,78789],{"xmlns":890},[892,78790,78791,78797],{},[895,78792,78793,78795],{},[898,78794,1701],{},[898,78796,2666],{},[902,78798,70205],{"encoding":904},[883,78800,78802],{"className":78801},[886],[888,78803,78804],{"xmlns":890},[892,78805,78806,78812],{},[895,78807,78808,78810],{},[898,78809,1701],{},[898,78811,2666],{},[902,78813,70205],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,78816,78818],{"className":78817},[886],[888,78819,78820],{"xmlns":890},[892,78821,78822,78834],{},[895,78823,78824,78826,78828,78830,78832],{},[1693,78825,1709],{"stretchy":1708},[1762,78827,1911],{},[1693,78829,1899],{"separator":1898},[1762,78831,1764],{},[1693,78833,1731],{"stretchy":1708},[902,78835,78836],{"encoding":904},"(0, 1)",", druhý do ",[883,78839,78841],{"className":78840},[886],[888,78842,78843],{"xmlns":890},[892,78844,78845,78858],{},[895,78846,78847,78849,78852,78854,78856],{},[1693,78848,1709],{"stretchy":1708},[1762,78850,78851],{},"19",[1693,78853,1899],{"separator":1898},[1762,78855,15892],{},[1693,78857,1731],{"stretchy":1708},[902,78859,78860],{"encoding":904},"(19, 20)",[724,78862,78863,78866,78867,9530,78895,78912,78913,1789],{},[38,78864,78865],{},"3.21"," Dokažte, že má-li zisk ",[883,78868,78870],{"className":78869},[886],[888,78871,78872],{"xmlns":890},[892,78873,78874,78892],{},[895,78875,78876,78878,78880,78882,78884,78886,78888,78890],{},[898,78877,1701],{},[898,78879,2666],{},[1693,78881,1695],{},[898,78883,1701],{},[898,78885,2666],{},[1693,78887,1709],{"stretchy":1708},[898,78889,1712],{},[1693,78891,1731],{"stretchy":1708},[902,78893,78894],{"encoding":904},"PR = PR(Q)",[883,78896,78898],{"className":78897},[886],[888,78899,78900],{"xmlns":890},[892,78901,78902,78910],{},[895,78903,78904],{},[3284,78905,78906,78908],{},[898,78907,1712],{},[1762,78909,1911],{},[902,78911,6293],{"encoding":904}," maximum, pak platí ",[883,78914,78916],{"className":78915},[886],[888,78917,78918],{"xmlns":890},[892,78919,78920,78952],{},[895,78921,78922,78924,78926,78928,78934,78936,78938,78940,78942,78944,78950],{},[898,78923,2839],{},[898,78925,2666],{},[1693,78927,1709],{"stretchy":1708},[3284,78929,78930,78932],{},[898,78931,1712],{},[1762,78933,1911],{},[1693,78935,1731],{"stretchy":1708},[1693,78937,1695],{},[898,78939,2839],{},[898,78941,2971],{},[1693,78943,1709],{"stretchy":1708},[3284,78945,78946,78948],{},[898,78947,1712],{},[1762,78949,1911],{},[1693,78951,1731],{"stretchy":1708},[902,78953,3504],{"encoding":904},[724,78955,78956,78959,78960,4286,78975,62769,78990,78625,79003,79018,79019,1343,79046,79083,79084,1343,79111,1789],{},[38,78957,78958],{},"3.22"," Pro zadané ",[883,78961,78963],{"className":78962},[886],[888,78964,78965],{"xmlns":890},[892,78966,78967,78973],{},[895,78968,78969,78971],{},[898,78970,2839],{},[898,78972,2666],{},[902,78974,2919],{"encoding":904},[883,78976,78978],{"className":78977},[886],[888,78979,78980],{"xmlns":890},[892,78981,78982,78988],{},[895,78983,78984,78986],{},[898,78985,2839],{},[898,78987,2971],{},[902,78989,3810],{"encoding":904},[883,78991,78993],{"className":78992},[886],[888,78994,78995],{"xmlns":890},[892,78996,78997,79001],{},[895,78998,78999],{},[898,79000,1712],{},[902,79002,1712],{"encoding":904},[883,79004,79006],{"className":79005},[886],[888,79007,79008],{"xmlns":890},[892,79009,79010,79016],{},[895,79011,79012,79014],{},[898,79013,1701],{},[898,79015,2666],{},[902,79017,70205],{"encoding":904},". (a) ",[883,79020,79022],{"className":79021},[886],[888,79023,79024],{"xmlns":890},[892,79025,79026,79043],{},[895,79027,79028,79030,79032,79034,79037,79039,79041],{},[898,79029,2839],{},[898,79031,2666],{},[1693,79033,1695],{},[1762,79035,79036],{},"236",[1693,79038,1698],{},[1762,79040,48633],{},[898,79042,1712],{},[902,79044,79045],{"encoding":904},"MR = 236 - 16Q",[883,79047,79049],{"className":79048},[886],[888,79050,79051],{"xmlns":890},[892,79052,79053,79080],{},[895,79054,79055,79057,79059,79061,79063,79069,79071,79074,79076,79078],{},[898,79056,2839],{},[898,79058,2971],{},[1693,79060,1695],{},[1762,79062,8357],{},[1717,79064,79065,79067],{},[898,79066,1712],{},[1762,79068,2398],{},[1693,79070,1698],{},[1762,79072,79073],{},"32",[898,79075,1712],{},[1693,79077,1892],{},[1762,79079,12612],{},[902,79081,79082],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,79085,79087],{"className":79086},[886],[888,79088,79089],{"xmlns":890},[892,79090,79091,79108],{},[895,79092,79093,79095,79097,79099,79102,79104,79106],{},[898,79094,2839],{},[898,79096,2666],{},[1693,79098,1695],{},[1762,79100,79101],{},"280",[1693,79103,1698],{},[1762,79105,15892],{},[898,79107,1712],{},[902,79109,79110],{"encoding":904},"MR = 280 - 20Q",[883,79112,79114],{"className":79113},[886],[888,79115,79116],{"xmlns":890},[892,79117,79118,79145],{},[895,79119,79120,79122,79124,79126,79129,79135,79137,79139,79141,79143],{},[898,79121,2839],{},[898,79123,2971],{},[1693,79125,1695],{},[1762,79127,79128],{},"1,6",[1717,79130,79131,79133],{},[898,79132,1712],{},[1762,79134,2398],{},[1693,79136,1698],{},[1762,79138,43026],{},[898,79140,1712],{},[1693,79142,1892],{},[1762,79144,10023],{},[902,79146,79147],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,79149,79150,78959,79153,4286,79168,62769,79183,76441,79196,76457,79211,79018,79226,1343,79257,79083,79293,1343,79325,79369,79370,1343,79402,1789],{},[38,79151,79152],{},"3.23",[883,79154,79156],{"className":79155},[886],[888,79157,79158],{"xmlns":890},[892,79159,79160,79166],{},[895,79161,79162,79164],{},[898,79163,2663],{},[898,79165,2666],{},[902,79167,2883],{"encoding":904},[883,79169,79171],{"className":79170},[886],[888,79172,79173],{"xmlns":890},[892,79174,79175,79181],{},[895,79176,79177,79179],{},[898,79178,2663],{},[898,79180,2971],{},[902,79182,3225],{"encoding":904},[883,79184,79186],{"className":79185},[886],[888,79187,79188],{"xmlns":890},[892,79189,79190,79194],{},[895,79191,79192],{},[898,79193,1712],{},[902,79195,1712],{"encoding":904},[883,79197,79199],{"className":79198},[886],[888,79200,79201],{"xmlns":890},[892,79202,79203,79209],{},[895,79204,79205,79207],{},[898,79206,1701],{},[898,79208,2666],{},[902,79210,70205],{"encoding":904},[883,79212,79214],{"className":79213},[886],[888,79215,79216],{"xmlns":890},[892,79217,79218,79224],{},[895,79219,79220,79222],{},[898,79221,1701],{},[898,79223,2666],{},[902,79225,70205],{"encoding":904},[883,79227,79229],{"className":79228},[886],[888,79230,79231],{"xmlns":890},[892,79232,79233,79254],{},[895,79234,79235,79237,79239,79241,79244,79246,79248],{},[898,79236,2663],{},[898,79238,2666],{},[1693,79240,1695],{},[1762,79242,79243],{},"125",[898,79245,1712],{},[1693,79247,1698],{},[1717,79249,79250,79252],{},[898,79251,1712],{},[1762,79253,2398],{},[902,79255,79256],{"encoding":904},"TR = 125Q - Q^2",[883,79258,79260],{"className":79259},[886],[888,79261,79262],{"xmlns":890},[892,79263,79264,79290],{},[895,79265,79266,79268,79270,79272,79274,79276,79278,79280,79282,79284],{},[898,79267,2663],{},[898,79269,2971],{},[1693,79271,1695],{},[1762,79273,21936],{},[1693,79275,1892],{},[1762,79277,9147],{},[898,79279,1712],{},[1693,79281,1892],{},[1762,79283,11877],{},[1717,79285,79286,79288],{},[898,79287,1712],{},[1762,79289,2398],{},[902,79291,79292],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,79294,79296],{"className":79295},[886],[888,79297,79298],{"xmlns":890},[892,79299,79300,79322],{},[895,79301,79302,79304,79306,79308,79310,79312,79314,79316],{},[898,79303,2663],{},[898,79305,2666],{},[1693,79307,1695],{},[1762,79309,15892],{},[898,79311,1712],{},[1693,79313,1698],{},[1762,79315,2398],{},[1717,79317,79318,79320],{},[898,79319,1712],{},[1762,79321,2398],{},[902,79323,79324],{"encoding":904},"TR = 20Q - 2Q^2",[883,79326,79328],{"className":79327},[886],[888,79329,79330],{"xmlns":890},[892,79331,79332,79366],{},[895,79333,79334,79336,79338,79340,79342,79344,79346,79348,79350,79352,79358,79360],{},[898,79335,2663],{},[898,79337,2971],{},[1693,79339,1695],{},[1762,79341,2398],{},[1693,79343,1892],{},[1762,79345,15892],{},[898,79347,1712],{},[1693,79349,1698],{},[1762,79351,12453],{},[1717,79353,79354,79356],{},[898,79355,1712],{},[1762,79357,2398],{},[1693,79359,1892],{},[1717,79361,79362,79364],{},[898,79363,1712],{},[1762,79365,8357],{},[902,79367,79368],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,79371,79373],{"className":79372},[886],[888,79374,79375],{"xmlns":890},[892,79376,79377,79399],{},[895,79378,79379,79381,79383,79385,79387,79389,79391,79393],{},[898,79380,2663],{},[898,79382,2666],{},[1693,79384,1695],{},[1762,79386,9262],{},[898,79388,1712],{},[1693,79390,1698],{},[1762,79392,30588],{},[1717,79394,79395,79397],{},[898,79396,1712],{},[1762,79398,2398],{},[902,79400,79401],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,79403,79405],{"className":79404},[886],[888,79406,79407],{"xmlns":890},[892,79408,79409,79457],{},[895,79410,79411,79413,79415,79417,79419,79421,79423,79425,79427,79443,79445],{},[898,79412,2663],{},[898,79414,2971],{},[1693,79416,1695],{},[1762,79418,9262],{},[1693,79420,1892],{},[1762,79422,2398],{},[898,79424,1712],{},[1693,79426,1698],{},[3638,79428,79429],{"scriptlevel":1911,"displaystyle":1708},[2132,79430,79431,79441],{},[895,79432,79433,79435],{},[1762,79434,8357],{},[1717,79436,79437,79439],{},[898,79438,1712],{},[1762,79440,2398],{},[1762,79442,9763],{},[1693,79444,1892],{},[3638,79446,79447],{"scriptlevel":1911,"displaystyle":1708},[2132,79448,79449,79455],{},[1717,79450,79451,79453],{},[898,79452,1712],{},[1762,79454,8357],{},[1762,79456,15892],{},[902,79458,79459],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,79461,79462,79465,79466,79496,79497,79529,79530,28397,79560,79590],{},[38,79463,79464],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,79467,79469],{"className":79468},[886],[888,79470,79471],{"xmlns":890},[892,79472,79473,79493],{},[895,79474,79475,79481,79483,79485,79487],{},[3284,79476,79477,79479],{},[898,79478,1701],{},[1762,79480,1764],{},[1693,79482,1695],{},[1762,79484,21936],{},[1693,79486,1698],{},[3284,79488,79489,79491],{},[898,79490,1712],{},[1762,79492,1764],{},[902,79494,79495],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,79498,79500],{"className":79499},[886],[888,79501,79502],{"xmlns":890},[892,79503,79504,79526],{},[895,79505,79506,79512,79514,79516,79518,79520],{},[3284,79507,79508,79510],{},[898,79509,1701],{},[1762,79511,2398],{},[1693,79513,1695],{},[1762,79515,36864],{},[1693,79517,1698],{},[1762,79519,71285],{},[3284,79521,79522,79524],{},[898,79523,1712],{},[1762,79525,2398],{},[902,79527,79528],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,79531,79533],{"className":79532},[886],[888,79534,79535],{"xmlns":890},[892,79536,79537,79557],{},[895,79538,79539,79541,79543,79545,79547,79549,79551,79553,79555],{},[898,79540,2663],{},[898,79542,2971],{},[1693,79544,1695],{},[1762,79546,10017],{},[1915,79548,2239],{},[1762,79550,65817],{},[1693,79552,1892],{},[1762,79554,15892],{},[898,79556,1712],{},[902,79558,79559],{"encoding":904},"TC = 50\\,000 + 20Q",[883,79561,79563],{"className":79562},[886],[888,79564,79565],{"xmlns":890},[892,79566,79567,79587],{},[895,79568,79569,79571,79573,79579,79581],{},[898,79570,1712],{},[1693,79572,1695],{},[3284,79574,79575,79577],{},[898,79576,1712],{},[1762,79578,1764],{},[1693,79580,1892],{},[3284,79582,79583,79585],{},[898,79584,1712],{},[1762,79586,2398],{},[902,79588,79589],{"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.",[724,79592,79593,79596,79597,79627,79628,79529,79660,28397,79690,79719],{},[38,79594,79595],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,79598,79600],{"className":79599},[886],[888,79601,79602],{"xmlns":890},[892,79603,79604,79624],{},[895,79605,79606,79612,79614,79616,79618],{},[3284,79607,79608,79610],{},[898,79609,1701],{},[1762,79611,1764],{},[1693,79613,1695],{},[1762,79615,36864],{},[1693,79617,1698],{},[3284,79619,79620,79622],{},[898,79621,1712],{},[1762,79623,1764],{},[902,79625,79626],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,79629,79631],{"className":79630},[886],[888,79632,79633],{"xmlns":890},[892,79634,79635,79657],{},[895,79636,79637,79643,79645,79647,79649,79651],{},[3284,79638,79639,79641],{},[898,79640,1701],{},[1762,79642,2398],{},[1693,79644,1695],{},[1762,79646,15236],{},[1693,79648,1698],{},[1762,79650,11877],{},[3284,79652,79653,79655],{},[898,79654,1712],{},[1762,79656,2398],{},[902,79658,79659],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,79661,79663],{"className":79662},[886],[888,79664,79665],{"xmlns":890},[892,79666,79667,79687],{},[895,79668,79669,79671,79673,79675,79677,79679,79681,79683,79685],{},[898,79670,2663],{},[898,79672,2971],{},[1693,79674,1695],{},[1762,79676,9147],{},[1915,79678,2239],{},[1762,79680,65817],{},[1693,79682,1892],{},[1762,79684,9987],{},[898,79686,1712],{},[902,79688,79689],{"encoding":904},"TC = 5\\,000 + 100Q",[883,79691,79693],{"className":79692},[886],[888,79694,79695],{"xmlns":890},[892,79696,79697,79717],{},[895,79698,79699,79701,79703,79709,79711],{},[898,79700,1712],{},[1693,79702,1695],{},[3284,79704,79705,79707],{},[898,79706,1712],{},[1762,79708,1764],{},[1693,79710,1892],{},[3284,79712,79713,79715],{},[898,79714,1712],{},[1762,79716,2398],{},[902,79718,79589],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,79721,79723],{"id":79722},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,79725,79726,79729,79730,79777,79778,79795],{},[38,79727,79728],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,79731,79733],{"className":79732},[886],[888,79734,79735],{"xmlns":890},[892,79736,79737,79774],{},[895,79738,79739,79741,79743,79745,79747,79750,79756,79758,79761,79767,79769,79772],{},[898,79740,2663],{},[898,79742,2985],{},[898,79744,2971],{},[1693,79746,1695],{},[1762,79748,79749],{},"0,85",[1717,79751,79752,79754],{},[898,79753,1712],{},[1762,79755,8357],{},[1693,79757,1698],{},[1762,79759,79760],{},"11,9",[1717,79762,79763,79765],{},[898,79764,1712],{},[1762,79766,2398],{},[1693,79768,1892],{},[1762,79770,79771],{},"102",[898,79773,1712],{},[902,79775,79776],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,79779,79781],{"className":79780},[886],[888,79782,79783],{"xmlns":890},[892,79784,79785,79793],{},[895,79786,79787],{},[1717,79788,79789,79791],{},[898,79790,1701],{},[1693,79792,3672],{},[902,79794,11280],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,79797,79798,77556,79801,79837],{},[38,79799,79800],{},"3.27",[883,79802,79804],{"className":79803},[886],[888,79805,79806],{"xmlns":890},[892,79807,79808,79834],{},[895,79809,79810,79812,79814,79816,79818,79824,79826,79828,79830,79832],{},[898,79811,2839],{},[898,79813,2971],{},[1693,79815,1695],{},[1762,79817,9822],{},[1717,79819,79820,79822],{},[898,79821,1712],{},[1762,79823,2398],{},[1693,79825,1698],{},[1762,79827,71166],{},[898,79829,1712],{},[1693,79831,1892],{},[1762,79833,37526],{},[902,79835,79836],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,79839,79840,76807,79843,79837],{},[38,79841,79842],{},"3.28",[883,79844,79846],{"className":79845},[886],[888,79847,79848],{"xmlns":890},[892,79849,79850,79886],{},[895,79851,79852,79854,79856,79858,79860,79866,79868,79870,79876,79878,79880,79882,79884],{},[898,79853,2663],{},[898,79855,2971],{},[1693,79857,1695],{},[1762,79859,11877],{},[1717,79861,79862,79864],{},[898,79863,1712],{},[1762,79865,8357],{},[1693,79867,1698],{},[1762,79869,31000],{},[1717,79871,79872,79874],{},[898,79873,1712],{},[1762,79875,2398],{},[1693,79877,1892],{},[1762,79879,10023],{},[898,79881,1712],{},[1693,79883,1892],{},[1762,79885,21936],{},[902,79887,79888],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,79890,22545],{"id":22544},[120,79892,79893,79921,79966,80038,80103,80142,80234,80340,80380,80494,80587,80651,80683,80743,80749,80813,80862,80916,81024,81079],{},[123,79894,79895,1863,79897,79920],{},[38,79896,2649],{},[883,79898,79900],{"className":79899},[886],[888,79901,79902],{"xmlns":890},[892,79903,79904,79918],{},[895,79905,79906,79908,79910,79912,79914,79916],{},[898,79907,2663],{},[898,79909,2666],{},[1693,79911,1695],{},[898,79913,1701],{},[1693,79915,1715],{},[898,79917,1712],{},[902,79919,2677],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,79922,79923,1863,79925,79965],{},[38,79924,2705],{},[883,79926,79928],{"className":79927},[886],[888,79929,79930],{"xmlns":890},[892,79931,79932,79962],{},[895,79933,79934,79936,79938,79940,79952,79954,79956,79958,79960],{},[898,79935,2719],{},[898,79937,2666],{},[1693,79939,1695],{},[3638,79941,79942],{"scriptlevel":1911,"displaystyle":1708},[2132,79943,79944,79950],{},[895,79945,79946,79948],{},[898,79947,2663],{},[898,79949,2666],{},[898,79951,1712],{},[1693,79953,1695],{},[898,79955,2738],{},[1693,79957,1709],{"stretchy":1708},[898,79959,1712],{},[1693,79961,1731],{"stretchy":1708},[902,79963,79964],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,79967,79968,1863,79970,80006,80007,80022,80023,1789],{},[38,79969,2825],{},[883,79971,79973],{"className":79972},[886],[888,79974,79975],{"xmlns":890},[892,79976,79977,80003],{},[895,79978,79979,79981,79983,79985],{},[898,79980,2839],{},[898,79982,2666],{},[1693,79984,1695],{},[3638,79986,79987],{"scriptlevel":1911,"displaystyle":1708},[2132,79988,79989,79997],{},[895,79990,79991,79993,79995],{},[898,79992,1771],{"mathvariant":1704},[898,79994,2663],{},[898,79996,2666],{},[895,79998,79999,80001],{},[898,80000,1771],{"mathvariant":1704},[898,80002,1712],{},[902,80004,80005],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,80008,80010],{"className":80009},[886],[888,80011,80012],{"xmlns":890},[892,80013,80014,80020],{},[895,80015,80016,80018],{},[898,80017,2663],{},[898,80019,2666],{},[902,80021,2883],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,80024,80026],{"className":80025},[886],[888,80027,80028],{"xmlns":890},[892,80029,80030,80036],{},[895,80031,80032,80034],{},[898,80033,2719],{},[898,80035,2666],{},[902,80037,2820],{"encoding":904},[123,80039,80040,1863,80043,1343,80073,1789],{},[38,80041,80042],{},"Diferenciál příjmu\u002Fnákladů",[883,80044,80046],{"className":80045},[886],[888,80047,80048],{"xmlns":890},[892,80049,80050,80070],{},[895,80051,80052,80054,80056,80058,80060,80062,80064,80066,80068],{},[898,80053,3890],{"mathvariant":1704},[898,80055,2663],{},[898,80057,2666],{},[1693,80059,4110],{},[898,80061,2839],{},[898,80063,2666],{},[1915,80065,2239],{},[898,80067,1771],{"mathvariant":1704},[898,80069,1712],{},[902,80071,80072],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,80074,80076],{"className":80075},[886],[888,80077,80078],{"xmlns":890},[892,80079,80080,80100],{},[895,80081,80082,80084,80086,80088,80090,80092,80094,80096,80098],{},[898,80083,3890],{"mathvariant":1704},[898,80085,2663],{},[898,80087,2971],{},[1693,80089,4110],{},[898,80091,2839],{},[898,80093,2971],{},[1915,80095,2239],{},[898,80097,1771],{"mathvariant":1704},[898,80099,1712],{},[902,80101,80102],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,80104,80105,1863,80107,1789],{},[38,80106,2955],{},[883,80108,80110],{"className":80109},[886],[888,80111,80112],{"xmlns":890},[892,80113,80114,80140],{},[895,80115,80116,80118,80120,80122,80124,80126,80128,80130,80132,80134,80136,80138],{},[898,80117,2663],{},[898,80119,2971],{},[1693,80121,1695],{},[898,80123,2976],{},[898,80125,2971],{},[1693,80127,1892],{},[898,80129,2663],{},[898,80131,2985],{},[898,80133,2971],{},[1693,80135,1709],{"stretchy":1708},[898,80137,1712],{},[1693,80139,1731],{"stretchy":1708},[902,80141,2996],{"encoding":904},[123,80143,80144,1863,80147,1343,80162,1863,80164,1343,80187,1863,80190,1789],{},[38,80145,80146],{},"Fixní náklady",[883,80148,80150],{"className":80149},[886],[888,80151,80152],{"xmlns":890},[892,80153,80154,80160],{},[895,80155,80156,80158],{},[898,80157,2976],{},[898,80159,2971],{},[902,80161,3022],{"encoding":904},[38,80163,65496],{},[883,80165,80167],{"className":80166},[886],[888,80168,80169],{"xmlns":890},[892,80170,80171,80185],{},[895,80172,80173,80175,80177,80179,80181,80183],{},[898,80174,2663],{},[898,80176,2985],{},[898,80178,2971],{},[1693,80180,1709],{"stretchy":1708},[898,80182,1712],{},[1693,80184,1731],{"stretchy":1708},[902,80186,65493],{"encoding":904},[38,80188,80189],{},"variabilní náklady na jednotku",[883,80191,80193],{"className":80192},[886],[888,80194,80195],{"xmlns":890},[892,80196,80197,80231],{},[895,80198,80199,80201,80203,80205,80207,80209,80211],{},[898,80200,2985],{},[898,80202,2971],{},[1693,80204,1709],{"stretchy":1708},[898,80206,1712],{},[1693,80208,1731],{"stretchy":1708},[1693,80210,1695],{},[3638,80212,80213],{"scriptlevel":1911,"displaystyle":1708},[2132,80214,80215,80229],{},[895,80216,80217,80219,80221,80223,80225,80227],{},[898,80218,2663],{},[898,80220,2985],{},[898,80222,2971],{},[1693,80224,1709],{"stretchy":1708},[898,80226,1712],{},[1693,80228,1731],{"stretchy":1708},[898,80230,1712],{},[902,80232,80233],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,80235,80236,1863,80238,1343,80268,1863,80271,1343,80303,1863,80306,1789],{},[38,80237,3046],{},[883,80239,80241],{"className":80240},[886],[888,80242,80243],{"xmlns":890},[892,80244,80245,80265],{},[895,80246,80247,80249,80251,80253],{},[898,80248,2719],{},[898,80250,2971],{},[1693,80252,1695],{},[3638,80254,80255],{"scriptlevel":1911,"displaystyle":1708},[2132,80256,80257,80263],{},[895,80258,80259,80261],{},[898,80260,2663],{},[898,80262,2971],{},[898,80264,1712],{},[902,80266,80267],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,80269,80270],{},"průměrné fixní",[883,80272,80274],{"className":80273},[886],[888,80275,80276],{"xmlns":890},[892,80277,80278,80300],{},[895,80279,80280,80282,80284,80286,80288],{},[898,80281,2719],{},[898,80283,2976],{},[898,80285,2971],{},[1693,80287,1695],{},[3638,80289,80290],{"scriptlevel":1911,"displaystyle":1708},[2132,80291,80292,80298],{},[895,80293,80294,80296],{},[898,80295,2976],{},[898,80297,2971],{},[898,80299,1712],{},[902,80301,80302],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,80304,80305],{},"průměrné variabilní",[883,80307,80309],{"className":80308},[886],[888,80310,80311],{"xmlns":890},[892,80312,80313,80337],{},[895,80314,80315,80317,80319,80321,80323],{},[898,80316,2719],{},[898,80318,2985],{},[898,80320,2971],{},[1693,80322,1695],{},[3638,80324,80325],{"scriptlevel":1911,"displaystyle":1708},[2132,80326,80327,80335],{},[895,80328,80329,80331,80333],{},[898,80330,2663],{},[898,80332,2985],{},[898,80334,2971],{},[898,80336,1712],{},[902,80338,80339],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,80341,80342,1863,80344,1789],{},[38,80343,3169],{},[883,80345,80347],{"className":80346},[886],[888,80348,80349],{"xmlns":890},[892,80350,80351,80377],{},[895,80352,80353,80355,80357,80359],{},[898,80354,2839],{},[898,80356,2971],{},[1693,80358,1695],{},[3638,80360,80361],{"scriptlevel":1911,"displaystyle":1708},[2132,80362,80363,80371],{},[895,80364,80365,80367,80369],{},[898,80366,1771],{"mathvariant":1704},[898,80368,2663],{},[898,80370,2971],{},[895,80372,80373,80375],{},[898,80374,1771],{"mathvariant":1704},[898,80376,1712],{},[902,80378,80379],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,80381,80382,1863,80384,80432,80433,80446,80447,1343,80462,1343,80479,1789],{},[38,80383,67584],{},[883,80385,80387],{"className":80386},[886],[888,80388,80389],{"xmlns":890},[892,80390,80391,80429],{},[895,80392,80393,80395,80397,80399,80401,80403,80405,80407,80409,80411,80413,80419,80421,80423],{},[898,80394,2663],{},[898,80396,2971],{},[1693,80398,1695],{},[898,80400,2976],{},[898,80402,2971],{},[1693,80404,1892],{},[898,80406,207],{},[898,80408,1712],{},[1693,80410,1892],{},[898,80412,1895],{},[1717,80414,80415,80417],{},[898,80416,1712],{},[1762,80418,2398],{},[1693,80420,1892],{},[898,80422,2000],{},[1717,80424,80425,80427],{},[898,80426,1712],{},[1762,80428,8357],{},[902,80430,80431],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,80434,80436],{"className":80435},[886],[888,80437,80438],{"xmlns":890},[892,80439,80440,80444],{},[895,80441,80442],{},[898,80443,900],{},[902,80445,900],{"encoding":904},"-průběhem ",[883,80448,80450],{"className":80449},[886],[888,80451,80452],{"xmlns":890},[892,80453,80454,80460],{},[895,80455,80456,80458],{},[898,80457,2719],{},[898,80459,2971],{},[902,80461,3331],{"encoding":904},[883,80463,80465],{"className":80464},[886],[888,80466,80467],{"xmlns":890},[892,80468,80469,80477],{},[895,80470,80471,80473,80475],{},[898,80472,2719],{},[898,80474,2985],{},[898,80476,2971],{},[902,80478,3789],{"encoding":904},[883,80480,80482],{"className":80481},[886],[888,80483,80484],{"xmlns":890},[892,80485,80486,80492],{},[895,80487,80488,80490],{},[898,80489,2839],{},[898,80491,2971],{},[902,80493,3810],{"encoding":904},[123,80495,80496,80498,80499,17244,80514,80555,80556,68229,80571,80586],{},[38,80497,3265],{},": v bodě minima ",[883,80500,80502],{"className":80501},[886],[888,80503,80504],{"xmlns":890},[892,80505,80506,80512],{},[895,80507,80508,80510],{},[898,80509,2719],{},[898,80511,2971],{},[902,80513,3331],{"encoding":904},[883,80515,80517],{"className":80516},[886],[888,80518,80519],{"xmlns":890},[892,80520,80521,80553],{},[895,80522,80523,80525,80527,80529,80535,80537,80539,80541,80543,80545,80551],{},[898,80524,2719],{},[898,80526,2971],{},[1693,80528,1709],{"stretchy":1708},[3284,80530,80531,80533],{},[898,80532,1712],{},[1762,80534,1911],{},[1693,80536,1731],{"stretchy":1708},[1693,80538,1695],{},[898,80540,2839],{},[898,80542,2971],{},[1693,80544,1709],{"stretchy":1708},[3284,80546,80547,80549],{},[898,80548,1712],{},[1762,80550,1911],{},[1693,80552,1731],{"stretchy":1708},[902,80554,3310],{"encoding":904},"; geometricky ",[883,80557,80559],{"className":80558},[886],[888,80560,80561],{"xmlns":890},[892,80562,80563,80569],{},[895,80564,80565,80567],{},[898,80566,2839],{},[898,80568,2971],{},[902,80570,3810],{"encoding":904},[883,80572,80574],{"className":80573},[886],[888,80575,80576],{"xmlns":890},[892,80577,80578,80584],{},[895,80579,80580,80582],{},[898,80581,2719],{},[898,80583,2971],{},[902,80585,3331],{"encoding":904}," v jejím minimu.",[123,80588,80589,80498,80591,17244,80608,1789],{},[38,80590,3362],{},[883,80592,80594],{"className":80593},[886],[888,80595,80596],{"xmlns":890},[892,80597,80598,80606],{},[895,80599,80600,80602,80604],{},[898,80601,2719],{},[898,80603,2985],{},[898,80605,2971],{},[902,80607,3789],{"encoding":904},[883,80609,80611],{"className":80610},[886],[888,80612,80613],{"xmlns":890},[892,80614,80615,80649],{},[895,80616,80617,80619,80621,80623,80625,80631,80633,80635,80637,80639,80641,80647],{},[898,80618,2719],{},[898,80620,2985],{},[898,80622,2971],{},[1693,80624,1709],{"stretchy":1708},[3284,80626,80627,80629],{},[898,80628,1712],{},[1762,80630,1911],{},[1693,80632,1731],{"stretchy":1708},[1693,80634,1695],{},[898,80636,2839],{},[898,80638,2971],{},[1693,80640,1709],{"stretchy":1708},[3284,80642,80643,80645],{},[898,80644,1712],{},[1762,80646,1911],{},[1693,80648,1731],{"stretchy":1708},[902,80650,3408],{"encoding":904},[123,80652,80653,1863,80655,80682],{},[38,80654,70189],{},[883,80656,80658],{"className":80657},[886],[888,80659,80660],{"xmlns":890},[892,80661,80662,80680],{},[895,80663,80664,80666,80668,80670,80672,80674,80676,80678],{},[898,80665,1701],{},[898,80667,2666],{},[1693,80669,1695],{},[898,80671,2663],{},[898,80673,2666],{},[1693,80675,1698],{},[898,80677,2663],{},[898,80679,2971],{},[902,80681,3537],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,80684,80685,16877,80687,80689,80690,80716,80717,80742],{},[38,80686,71051],{},[614,80688,70314],{},") — hodnoty ",[883,80691,80693],{"className":80692},[886],[888,80694,80695],{"xmlns":890},[892,80696,80697,80713],{},[895,80698,80699,80705,80707],{},[3284,80700,80701,80703],{},[898,80702,1712],{},[898,80704,2719],{},[1693,80706,1899],{"separator":1898},[3284,80708,80709,80711],{},[898,80710,1712],{},[898,80712,7520],{},[902,80714,80715],{"encoding":904},"Q_A, Q_B"," splňující ",[883,80718,80720],{"className":80719},[886],[888,80721,80722],{"xmlns":890},[892,80723,80724,80740],{},[895,80725,80726,80728,80730,80732,80734,80736,80738],{},[898,80727,1701],{},[898,80729,2666],{},[1693,80731,1709],{"stretchy":1708},[898,80733,1712],{},[1693,80735,1731],{"stretchy":1708},[1693,80737,1695],{},[1762,80739,1911],{},[902,80741,70591],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,80744,80745,80748],{},[38,80746,80747],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,80750,80751,80753,80754,17244,80771,80812],{},[38,80752,3460],{}," — v bodě maxima zisku ",[883,80755,80757],{"className":80756},[886],[888,80758,80759],{"xmlns":890},[892,80760,80761,80769],{},[895,80762,80763],{},[3284,80764,80765,80767],{},[898,80766,1712],{},[1762,80768,1911],{},[902,80770,6293],{"encoding":904},[883,80772,80774],{"className":80773},[886],[888,80775,80776],{"xmlns":890},[892,80777,80778,80810],{},[895,80779,80780,80782,80784,80786,80792,80794,80796,80798,80800,80802,80808],{},[898,80781,2839],{},[898,80783,2666],{},[1693,80785,1709],{"stretchy":1708},[3284,80787,80788,80790],{},[898,80789,1712],{},[1762,80791,1911],{},[1693,80793,1731],{"stretchy":1708},[1693,80795,1695],{},[898,80797,2839],{},[898,80799,2971],{},[1693,80801,1709],{"stretchy":1708},[3284,80803,80804,80806],{},[898,80805,1712],{},[1762,80807,1911],{},[1693,80809,1731],{"stretchy":1708},[902,80811,3504],{"encoding":904}," (3.13).",[123,80814,80815,27108,80817,17244,80836,80861],{},[38,80816,73395],{},[883,80818,80820],{"className":80819},[886],[888,80821,80822],{"xmlns":890},[892,80823,80824,80833],{},[895,80825,80826,80828,80830],{},[898,80827,1701],{},[1693,80829,1695],{},[1915,80831,80832],{},"konst",[902,80834,80835],{"encoding":904},"P = \\text{konst}",[883,80837,80839],{"className":80838},[886],[888,80840,80841],{"xmlns":890},[892,80842,80843,80859],{},[895,80844,80845,80847,80849,80851,80853,80855,80857],{},[898,80846,1701],{},[1693,80848,1695],{},[898,80850,2839],{},[898,80852,2971],{},[1693,80854,1709],{"stretchy":1708},[898,80856,1712],{},[1693,80858,1731],{"stretchy":1708},[902,80860,74088],{"encoding":904}," (3.14).",[123,80863,80864,80867,80868,80897,80898,80915],{},[38,80865,80866],{},"Shutdown point"," — bod ",[883,80869,80871],{"className":80870},[886],[888,80872,80873],{"xmlns":890},[892,80874,80875,80895],{},[895,80876,80877,80879,80885,80887,80893],{},[1693,80878,1709],{"stretchy":1708},[1717,80880,80881,80883],{},[898,80882,1712],{},[1693,80884,3672],{},[1693,80886,1899],{"separator":1898},[1717,80888,80889,80891],{},[898,80890,1701],{},[1693,80892,3672],{},[1693,80894,1731],{"stretchy":1708},[902,80896,74372],{"encoding":904}," v minimu ",[883,80899,80901],{"className":80900},[886],[888,80902,80903],{"xmlns":890},[892,80904,80905,80913],{},[895,80906,80907,80909,80911],{},[898,80908,2719],{},[898,80910,2985],{},[898,80912,2971],{},[902,80914,3789],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,80917,80918,1863,80921,7721,80956,74641,80977,80990,80991,81006,81007,1789],{},[38,80919,80920],{},"Funkce nabídky firmy",[883,80922,80924],{"className":80923},[886],[888,80925,80926],{"xmlns":890},[892,80927,80928,80954],{},[895,80929,80930,80932,80934,80936,80938,80940,80942,80944,80946,80948,80950,80952],{},[898,80931,1701],{},[1693,80933,1695],{},[898,80935,3611],{},[1693,80937,1709],{"stretchy":1708},[898,80939,1712],{},[1693,80941,1731],{"stretchy":1708},[1693,80943,1695],{},[898,80945,2839],{},[898,80947,2971],{},[1693,80949,1709],{"stretchy":1708},[898,80951,1712],{},[1693,80953,1731],{"stretchy":1708},[902,80955,75836],{"encoding":904},[883,80957,80959],{"className":80958},[886],[888,80960,80961],{"xmlns":890},[892,80962,80963,80975],{},[895,80964,80965,80967,80969],{},[898,80966,1712],{},[1693,80968,3665],{},[1717,80970,80971,80973],{},[898,80972,1712],{},[1693,80974,3672],{},[902,80976,74640],{"encoding":904},[883,80978,80980],{"className":80979},[886],[888,80981,80982],{"xmlns":890},[892,80983,80984,80988],{},[895,80985,80986],{},[1762,80987,1911],{},[902,80989,1911],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,80992,80994],{"className":80993},[886],[888,80995,80996],{"xmlns":890},[892,80997,80998,81004],{},[895,80999,81000,81002],{},[898,81001,2839],{},[898,81003,2971],{},[902,81005,3810],{"encoding":904}," nad minimem ",[883,81008,81010],{"className":81009},[886],[888,81011,81012],{"xmlns":890},[892,81013,81014,81022],{},[895,81015,81016,81018,81020],{},[898,81017,2719],{},[898,81019,2985],{},[898,81021,2971],{},[902,81023,3789],{"encoding":904},[123,81025,81026,13877,81028,81049,81050,1789],{},[38,81027,56841],{},[883,81029,81031],{"className":81030},[886],[888,81032,81033],{"xmlns":890},[892,81034,81035,81047],{},[895,81036,81037,81039,81041],{},[898,81038,1701],{},[1693,81040,1695],{},[1717,81042,81043,81045],{},[898,81044,1701],{},[1693,81046,3672],{},[902,81048,11234],{"encoding":904}," konstantní ⇒ ",[883,81051,81053],{"className":81052},[886],[888,81054,81055],{"xmlns":890},[892,81056,81057,81077],{},[895,81058,81059,81061,81063,81065,81067,81069,81071],{},[898,81060,2719],{},[898,81062,2666],{},[1693,81064,1695],{},[898,81066,2839],{},[898,81068,2666],{},[1693,81070,1695],{},[1717,81072,81073,81075],{},[898,81074,1701],{},[1693,81076,3672],{},[902,81078,65337],{"encoding":904},[123,81080,81081,81084],{},[38,81082,81083],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,81086,8685],{"id":8684},[120,81088,81089,81108,81120],{},[123,81090,81091,1863,81093,1343,81096,1343,81099,1343,81102,1343,81105],{},[38,81092,57483],{},[207,81094,2181],{"className":81095,"dataFsResolvedFilePath":800,"href":801},[210],[207,81097,8759],{"className":81098,"dataFsResolvedFilePath":848,"href":849},[210],[207,81100,8726],{"className":81101,"dataFsResolvedFilePath":764,"href":765},[210],[207,81103,775],{"className":81104,"dataFsResolvedFilePath":773,"href":774},[210],[207,81106,859],{"className":81107,"dataFsResolvedFilePath":857,"href":858},[210],[123,81109,81110,1863,81112,1343,81116],{},[38,81111,43484],{},[207,81113,81115],{"className":81114,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,81117,81119],{"className":81118,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,81121,81122,1863,81124],{},[38,81123,8692],{},[207,81125,1653],{"className":81126,"dataFsResolvedFilePath":1651,"href":1652},[210],{"title":641,"searchDepth":642,"depth":642,"links":81128},[81129,81130,81137,81143,81147,81148,81152,81153,81154,81155,81161,81162],{"id":57714,"depth":642,"text":1241},{"id":62484,"depth":642,"text":62485,"children":81131},[81132,81133,81134,81135,81136],{"id":2648,"depth":649,"text":2649},{"id":2704,"depth":649,"text":2705},{"id":2824,"depth":649,"text":2825},{"id":63964,"depth":649,"text":63965},{"id":64619,"depth":649,"text":64620},{"id":65340,"depth":642,"text":65341,"children":81138},[81139,81140,81141,81142],{"id":2954,"depth":649,"text":2955},{"id":3045,"depth":649,"text":3046},{"id":3168,"depth":649,"text":3169},{"id":67583,"depth":649,"text":67584},{"id":3264,"depth":642,"text":3265,"children":81144},[81145,81146],{"id":23232,"depth":649,"text":23233},{"id":3361,"depth":649,"text":3362},{"id":70183,"depth":642,"text":70184},{"id":3459,"depth":642,"text":3460,"children":81149},[81150,81151],{"id":72116,"depth":649,"text":23233},{"id":73394,"depth":649,"text":73395},{"id":74025,"depth":642,"text":74026},{"id":75484,"depth":642,"text":75485},{"id":56645,"depth":642,"text":8674},{"id":75944,"depth":642,"text":75945,"children":81156},[81157,81158,81159,81160],{"id":75948,"depth":649,"text":75949},{"id":76800,"depth":649,"text":76801},{"id":78346,"depth":649,"text":78347},{"id":79722,"depth":649,"text":79723},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":2645,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,81169,81170,61927,81171,81172,81173],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":81176,"title":4815,"body":81177,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":93264,"navigation":664,"path":93265,"seo":93266,"sources":93267,"stem":93268,"tags":93269,"type":10745,"updated":677,"__hash__":93275},"topics\u002Ftopics\u002Fprodukce.md",{"type":9,"value":81178,"toc":93221},[81179,81182,81537,81541,81544,81612,81664,81674,81678,81712,81753,81777,81800,81829,81896,82003,82046,82103,82178,82223,82227,82235,82243,82246,82511,82562,82642,82712,82735,82762,82807,82829,82833,82840,82889,82915,83066,83069,83106,83269,83377,83381,83418,83493,83562,83681,83803,83884,83890,83931,84004,84097,84101,84137,84225,84339,84444,84529,84669,84673,84721,84766,84772,84774,84777,84828,84878,84885,84951,85084,85129,85133,85154,85533,85628,85645,85699,85703,85785,85869,86039,86042,86085,86152,86226,86230,86235,86304,86312,86321,86399,86465,86470,86564,86607,86612,86660,86665,86713,86831,86914,86952,87055,87114,87255,87257,87300,87373,87396,87450,87457,87459,87504,87549,87560,87565,87601,87663,87686,87694,87795,87862,87935,87942,88033,88095,88131,88188,88247,88432,88528,88532,88536,88615,88620,88744,88830,88836,88946,88983,89074,89172,89175,89179,89245,89282,89404,89456,89460,89488,89540,89614,89719,89743,89802,89806,89824,89967,90115,90117,90152,90156,90158,90248,90378,90504,90596,90671,90675,90791,90895,91085,91121,91215,91221,91334,91637,91643,91761,91860,91936,91938,93099,93101],[12,81180,4815],{"id":81181},"produkce-produkční-funkce-cobb-douglas-mrts",[1636,81183,81184],{},[724,81185,81186,10760,81188,81190,81191,5473,81204,81217,81218,23197,81231,16877,81233,81257,81258,1863,81260,4286,81294,1863,81297,81325,81326,17244,81346,81375,81376,16877,81379,81407,81408,81411,81412,81442,81443,81473,81474,1863,81477,81517,81518,81536],{},[883,81187,1642],{},[38,81189,859],{}," popisuje vztah mezi vstupy (práce ",[883,81192,81194],{"className":81193},[886],[888,81195,81196],{"xmlns":890},[892,81197,81198,81202],{},[895,81199,81200],{},[898,81201,4840],{},[902,81203,4840],{"encoding":904},[883,81205,81207],{"className":81206},[886],[888,81208,81209],{"xmlns":890},[892,81210,81211,81215],{},[895,81212,81213],{},[898,81214,4845],{},[902,81216,4845],{"encoding":904},") a výstupem ",[883,81219,81221],{"className":81220},[886],[888,81222,81223],{"xmlns":890},[892,81224,81225,81229],{},[895,81226,81227],{},[898,81228,1712],{},[902,81230,1712],{"encoding":904},[38,81232,43742],{},[883,81234,81236],{"className":81235},[886],[888,81237,81238],{"xmlns":890},[892,81239,81240,81254],{},[895,81241,81242,81244,81246,81248,81250,81252],{},[898,81243,1712],{},[1693,81245,1695],{},[898,81247,1712],{},[1693,81249,1709],{"stretchy":1708},[898,81251,4840],{},[1693,81253,1731],{"stretchy":1708},[902,81255,81256],{"encoding":904},"Q = Q(L)",") studujeme ",[614,81259,16876],{},[883,81261,81263],{"className":81262},[886],[888,81264,81265],{"xmlns":890},[892,81266,81267,81291],{},[895,81268,81269,81271,81277,81279,81285,81287,81289],{},[898,81270,2839],{},[3284,81272,81273,81275],{},[898,81274,1701],{},[898,81276,4840],{},[1693,81278,1695],{},[1717,81280,81281,81283],{},[898,81282,1712],{},[1693,81284,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,81286,1709],{"stretchy":1708},[898,81288,4840],{},[1693,81290,1731],{"stretchy":1708},[902,81292,81293],{"encoding":904},"MP_L = Q'(L)",[614,81295,81296],{},"průměrný produkt",[883,81298,81300],{"className":81299},[886],[888,81301,81302],{"xmlns":890},[892,81303,81304,81322],{},[895,81305,81306,81308,81314,81316,81318,81320],{},[898,81307,2719],{},[3284,81309,81310,81312],{},[898,81311,1701],{},[898,81313,4840],{},[1693,81315,1695],{},[898,81317,1712],{},[898,81319,1705],{"mathvariant":1704},[898,81321,4840],{},[902,81323,81324],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,81327,81329],{"className":81328},[886],[888,81330,81331],{"xmlns":890},[892,81332,81333,81343],{},[895,81334,81335,81337],{},[898,81336,2719],{},[3284,81338,81339,81341],{},[898,81340,1701],{},[898,81342,4840],{},[902,81344,81345],{"encoding":904},"AP_L",[883,81347,81349],{"className":81348},[886],[888,81350,81351],{"xmlns":890},[892,81352,81353,81373],{},[895,81354,81355,81357,81363,81365,81367],{},[898,81356,2839],{},[3284,81358,81359,81361],{},[898,81360,1701],{},[898,81362,4840],{},[1693,81364,1695],{},[898,81366,2719],{},[3284,81368,81369,81371],{},[898,81370,1701],{},[898,81372,4840],{},[902,81374,5039],{"encoding":904},". Ve ",[38,81377,81378],{},"dvoufaktorovém modelu",[883,81380,81382],{"className":81381},[886],[888,81383,81384],{"xmlns":890},[892,81385,81386,81404],{},[895,81387,81388,81390,81392,81394,81396,81398,81400,81402],{},[898,81389,1712],{},[1693,81391,1695],{},[898,81393,1712],{},[1693,81395,1709],{"stretchy":1708},[898,81397,4840],{},[1693,81399,1899],{"separator":1898},[898,81401,4845],{},[1693,81403,1731],{"stretchy":1708},[902,81405,81406],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,81409,81410],{},"Cobb-Douglasovy"," funkce ",[883,81413,81415],{"className":81414},[886],[888,81416,81417],{"xmlns":890},[892,81418,81419,81439],{},[895,81420,81421,81423,81425,81427,81433],{},[898,81422,1712],{},[1693,81424,1695],{},[898,81426,2719],{},[1717,81428,81429,81431],{},[898,81430,4840],{},[898,81432,207],{},[1717,81434,81435,81437],{},[898,81436,4845],{},[898,81438,1895],{},[902,81440,81441],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,81444,81446],{"className":81445},[886],[888,81447,81448],{"xmlns":890},[892,81449,81450,81470],{},[895,81451,81452,81454,81460,81462,81464],{},[898,81453,2839],{},[3284,81455,81456,81458],{},[898,81457,1701],{},[898,81459,4840],{},[1693,81461,1899],{"separator":1898},[898,81463,2839],{},[3284,81465,81466,81468],{},[898,81467,1701],{},[898,81469,4845],{},[902,81471,81472],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,81475,81476],{},"mezní míru technické substituce",[883,81478,81480],{"className":81479},[886],[888,81481,81482],{"xmlns":890},[892,81483,81484,81514],{},[895,81485,81486,81488,81490,81492,81494,81496,81498,81504,81506,81508],{},[898,81487,2839],{},[898,81489,2666],{},[898,81491,2663],{},[898,81493,3611],{},[1693,81495,1695],{},[898,81497,2839],{},[3284,81499,81500,81502],{},[898,81501,1701],{},[898,81503,4840],{},[898,81505,1705],{"mathvariant":1704},[898,81507,2839],{},[3284,81509,81510,81512],{},[898,81511,1701],{},[898,81513,4845],{},[902,81515,81516],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,81519,81521],{"className":81520},[886],[888,81522,81523],{"xmlns":890},[892,81524,81525,81533],{},[895,81526,81527,81529,81531],{},[898,81528,207],{},[1693,81530,1892],{},[898,81532,1895],{},[902,81534,81535],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,81538,81540],{"id":81539},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,81542,81543],{},"Po prostudování kapitoly 5 student umí:",[120,81545,81546,81552,81562,81568,81574,81579,81585,81595,81600,81606],{},[123,81547,81548,81549,1899],{},"popsat ",[38,81550,81551],{},"jednofaktorový model produkce",[123,81553,81554,81555,4286,81558,81561],{},"vypočítat ",[38,81556,81557],{},"mezní",[38,81559,81560],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,81563,81564,81565,1899],{},"charakterizovat průběh ",[38,81566,81567],{},"křivky produkce",[123,81569,81570,81571,1899],{},"formulovat ",[38,81572,81573],{},"princip maximalizace průměrného produktu práce",[123,81575,81548,81576,1899],{},[38,81577,81578],{},"dvoufaktorový model produkce",[123,81580,81581,81582,1899],{},"uvést tvar ",[38,81583,81584],{},"Cobb–Douglasových produkčních funkcí",[123,81586,81587,81588,1343,81590,1343,81592,1899],{},"vyložit, co jsou ",[38,81589,31412],{},[38,81591,20488],{},[38,81593,81594],{},"klesající výnosy z rozsahu",[123,81596,81554,81597,81561],{},[38,81598,81599],{},"mezní produkty práce a kapitálu",[123,81601,81602,81603,1899],{},"najít ",[38,81604,81605],{},"izokvanty",[123,81607,81554,81608,81611],{},[38,81609,81610],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,81613,81614,81615,81618,81619,81622,81623,1863,81626,1343,81639,1863,81642,4286,81655,81658,81659,81661,81662,1789],{},"Každý proces produkce je určován ",[38,81616,81617],{},"faktory"," (též ",[38,81620,81621],{},"vstupy",") produkce. K hlavním patří ",[38,81624,81625],{},"práce",[883,81627,81629],{"className":81628},[886],[888,81630,81631],{"xmlns":890},[892,81632,81633,81637],{},[895,81634,81635],{},[898,81636,4840],{},[902,81638,4840],{"encoding":904},[38,81640,81641],{},"kapitál",[883,81643,81645],{"className":81644},[886],[888,81646,81647],{"xmlns":890},[892,81648,81649,81653],{},[895,81650,81651],{},[898,81652,4845],{},[902,81654,4845],{"encoding":904},[38,81656,81657],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,81660,43742],{}," (produkce závisí jen na práci); v opačném případě o ",[38,81663,81378],{},[724,81665,81666,81667,1343,81670,81673],{},"Související matematický aparát: ",[207,81668,8726],{"className":81669,"dataFsResolvedFilePath":764,"href":765},[210],[207,81671,784],{"className":81672,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,81675,81677],{"id":81676},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,81679,81680,81681,81694,81695,81708,81709],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,81682,81684],{"className":81683},[886],[888,81685,81686],{"xmlns":890},[892,81687,81688,81692],{},[895,81689,81690],{},[898,81691,1712],{},[902,81693,1712],{"encoding":904}," na práci ",[883,81696,81698],{"className":81697},[886],[888,81699,81700],{"xmlns":890},[892,81701,81702,81706],{},[895,81703,81704],{},[898,81705,4840],{},[902,81707,4840],{"encoding":904}," vyjadřuje ",[38,81710,81711],{},"produkční funkce",[883,81713,81715],{"className":81714},[886],[888,81716,81717],{"xmlns":890,"display":34854},[892,81718,81719,81750],{},[3626,81720,81721],{"width":34859},[3632,81722,81723,81725,81743,81745],{},[3635,81724],{"width":34864},[3635,81726,81727],{},[895,81728,81729,81731,81733,81735,81737,81739,81741],{},[898,81730,1712],{},[1693,81732,1695],{},[898,81734,1712],{},[1693,81736,1709],{"stretchy":1708},[898,81738,4840],{},[1693,81740,1731],{"stretchy":1708},[1693,81742,1899],{"separator":1898},[3635,81744],{"width":34864},[3635,81746,81747],{},[1915,81748,81749],{},"(5.1)",[902,81751,81752],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,81754,81755,81756,16877,81759,81762,81763,81776],{},"jejíž graf se nazývá ",[38,81757,81758],{},"křivka produkce",[614,81760,81761],{},"production curve","). Práce ",[883,81764,81766],{"className":81765},[886],[888,81767,81768],{"xmlns":890},[892,81769,81770,81774],{},[895,81771,81772],{},[898,81773,4840],{},[902,81775,4840],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,81778,81780,81781,1731],{"id":81779},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,81782,81784],{"className":81783},[886],[888,81785,81786],{"xmlns":890},[892,81787,81788,81798],{},[895,81789,81790,81792],{},[898,81791,2839],{},[3284,81793,81794,81796],{},[898,81795,1701],{},[898,81797,4840],{},[902,81799,4964],{"encoding":904},[724,81801,81802,16877,81805,81808,81809,81828],{},[38,81803,81804],{},"Mezní produkt práce",[614,81806,81807],{},"marginal product of labour",") ",[883,81810,81812],{"className":81811},[886],[888,81813,81814],{"xmlns":890},[892,81815,81816,81826],{},[895,81817,81818,81820],{},[898,81819,2839],{},[3284,81821,81822,81824],{},[898,81823,1701],{},[898,81825,4840],{},[902,81827,4964],{"encoding":904}," je derivace produkce podle práce:",[883,81830,81832],{"className":81831},[886],[888,81833,81834],{"xmlns":890,"display":34854},[892,81835,81836,81893],{},[3626,81837,81838],{"width":34859},[3632,81839,81840,81842,81886,81888],{},[3635,81841],{"width":34864},[3635,81843,81844],{},[895,81845,81846,81848,81854,81856,81870,81872,81878,81880,81882,81884],{},[898,81847,2839],{},[3284,81849,81850,81852],{},[898,81851,1701],{},[898,81853,4840],{},[1693,81855,1695],{},[2132,81857,81858,81864],{},[895,81859,81860,81862],{},[898,81861,1771],{},[898,81863,1712],{},[895,81865,81866,81868],{},[898,81867,1771],{},[898,81869,4840],{},[1693,81871,1695],{},[1717,81873,81874,81876],{},[898,81875,1712],{},[1693,81877,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,81879,1709],{"stretchy":1708},[898,81881,4840],{},[1693,81883,1731],{"stretchy":1708},[898,81885,1789],{"mathvariant":1704},[3635,81887],{"width":34864},[3635,81889,81890],{},[1915,81891,81892],{},"(5.2)",[902,81894,81895],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,81897,81898,81899,26752,81917,81945,81946,81963,81964,9591,81981,3042],{},"Pro pevnou hodnotu ",[883,81900,81902],{"className":81901},[886],[888,81903,81904],{"xmlns":890},[892,81905,81906,81914],{},[895,81907,81908],{},[1717,81909,81910,81912],{},[898,81911,4840],{},[1693,81913,3672],{},[902,81915,81916],{"encoding":904},"L^*",[883,81918,81920],{"className":81919},[886],[888,81921,81922],{"xmlns":890},[892,81923,81924,81942],{},[895,81925,81926,81932,81934,81940],{},[1717,81927,81928,81930],{},[898,81929,1712],{},[1693,81931,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,81933,1709],{"stretchy":1708},[1717,81935,81936,81938],{},[898,81937,4840],{},[1693,81939,3672],{},[1693,81941,1731],{"stretchy":1708},[902,81943,81944],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,81947,81949],{"className":81948},[886],[888,81950,81951],{"xmlns":890},[892,81952,81953,81961],{},[895,81954,81955],{},[1717,81956,81957,81959],{},[898,81958,4840],{},[1693,81960,3672],{},[902,81962,81916],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,81965,81967],{"className":81966},[886],[888,81968,81969],{"xmlns":890},[892,81970,81971,81979],{},[895,81972,81973],{},[1717,81974,81975,81977],{},[898,81976,4840],{},[1693,81978,3672],{},[902,81980,81916],{"encoding":904},[883,81982,81984],{"className":81983},[886],[888,81985,81986],{"xmlns":890},[892,81987,81988,82000],{},[895,81989,81990,81996,81998],{},[1717,81991,81992,81994],{},[898,81993,4840],{},[1693,81995,3672],{},[1693,81997,1892],{},[1762,81999,1764],{},[902,82001,82002],{"encoding":904},"L^*+1",[1636,82004,82005],{},[724,82006,82007,24841,82009,82028,82029,82032,82033,1789],{},[883,82008,11036],{},[883,82010,82012],{"className":82011},[886],[888,82013,82014],{"xmlns":890},[892,82015,82016,82026],{},[895,82017,82018,82020],{},[898,82019,2839],{},[3284,82021,82022,82024],{},[898,82023,1701],{},[898,82025,4840],{},[902,82027,4964],{"encoding":904}," odpovídá na otázku „",[38,82030,82031],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,82034,82036],{"className":82035},[886],[888,82037,82038],{"xmlns":890},[892,82039,82040,82044],{},[895,82041,82042],{},[898,82043,4840],{},[902,82045,4840],{"encoding":904},[724,82047,82048,82051,82052,82068,82069,9591,82082,82102],{},[38,82049,82050],{},"Přibližná změna produkce"," pro změnu práce o ",[883,82053,82055],{"className":82054},[886],[888,82056,82057],{"xmlns":890},[892,82058,82059,82065],{},[895,82060,82061,82063],{},[898,82062,1771],{},[898,82064,4840],{},[902,82066,82067],{"encoding":904},"dL"," (z ",[883,82070,82072],{"className":82071},[886],[888,82073,82074],{"xmlns":890},[892,82075,82076,82080],{},[895,82077,82078],{},[898,82079,4840],{},[902,82081,4840],{"encoding":904},[883,82083,82085],{"className":82084},[886],[888,82086,82087],{"xmlns":890},[892,82088,82089,82099],{},[895,82090,82091,82093,82095,82097],{},[898,82092,4840],{},[1693,82094,1892],{},[898,82096,1771],{},[898,82098,4840],{},[902,82100,82101],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,82104,82106],{"className":82105},[886],[888,82107,82108],{"xmlns":890,"display":34854},[892,82109,82110,82175],{},[3626,82111,82112],{"width":34859},[3632,82113,82114,82116,82168,82170],{},[3635,82115],{"width":34864},[3635,82117,82118],{},[895,82119,82120,82122,82124,82126,82128,82130,82132,82138,82140,82142,82144,82146,82148,82150,82152,82154,82160,82162,82164,82166],{},[898,82121,3890],{"mathvariant":1704},[898,82123,1712],{},[1693,82125,4110],{},[898,82127,1771],{},[898,82129,1712],{},[1693,82131,1695],{},[1717,82133,82134,82136],{},[898,82135,1712],{},[1693,82137,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,82139,1709],{"stretchy":1708},[898,82141,4840],{},[1693,82143,1731],{"stretchy":1708},[1915,82145,2239],{},[898,82147,1771],{},[898,82149,4840],{},[1693,82151,1695],{},[898,82153,2839],{},[3284,82155,82156,82158],{},[898,82157,1701],{},[898,82159,4840],{},[1915,82161,2239],{},[898,82163,1771],{},[898,82165,4840],{},[898,82167,1789],{"mathvariant":1704},[3635,82169],{"width":34864},[3635,82171,82172],{},[1915,82173,82174],{},"(5.3)",[902,82176,82177],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,82179,82180,82181,1789],{},"Skutečná změna je ",[883,82182,82184],{"className":82183},[886],[888,82185,82186],{"xmlns":890},[892,82187,82188,82220],{},[895,82189,82190,82192,82194,82196,82198,82200,82202,82204,82206,82208,82210,82212,82214,82216,82218],{},[898,82191,3890],{"mathvariant":1704},[898,82193,1712],{},[1693,82195,1695],{},[898,82197,1712],{},[1693,82199,1709],{"stretchy":1708},[898,82201,4840],{},[1693,82203,1892],{},[898,82205,1771],{},[898,82207,4840],{},[1693,82209,1731],{"stretchy":1708},[1693,82211,1698],{},[898,82213,1712],{},[1693,82215,1709],{"stretchy":1708},[898,82217,4840],{},[1693,82219,1731],{"stretchy":1708},[902,82221,82222],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,82224,82226],{"id":82225},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,82228,82229,16877,82232,10048],{},[38,82230,82231],{},"Zákon klesajících výnosů",[614,82233,82234],{},"law of diminishing marginal productivity",[1636,82236,82237],{},[724,82238,82239,82240,82242],{},"Roste-li postupně některý ze vstupů (",[614,82241,43738],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,82244,82245],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,82247,82248,82249,1863,82270,82289,82290,82340,82341,82343,82344,1863,82364,82383,82384,82340,82416,7617,82418,82437,82438,28397,82455,82489,82490,6055,82507,82510],{},"1° ",[38,82250,82251,82252,4300],{},"Do bodu ",[883,82253,82255],{"className":82254},[886],[888,82256,82257],{"xmlns":890},[892,82258,82259,82267],{},[895,82260,82261],{},[3284,82262,82263,82265],{},[898,82264,4840],{},[1762,82266,1911],{},[902,82268,82269],{"encoding":904},"L_0",[883,82271,82273],{"className":82272},[886],[888,82274,82275],{"xmlns":890},[892,82276,82277,82287],{},[895,82278,82279,82281],{},[898,82280,2839],{},[3284,82282,82283,82285],{},[898,82284,1701],{},[898,82286,4840],{},[902,82288,4964],{"encoding":904}," roste, tj. ",[883,82291,82293],{"className":82292},[886],[888,82294,82295],{"xmlns":890},[892,82296,82297,82337],{},[895,82298,82299,82301,82303,82309,82315,82317,82327,82329,82331,82333,82335],{},[1693,82300,1709],{"stretchy":1708},[898,82302,2839],{},[3284,82304,82305,82307],{},[898,82306,1701],{},[898,82308,4840],{},[1717,82310,82311,82313],{},[1693,82312,1731],{"stretchy":1708},[1693,82314,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,82316,1695],{},[1717,82318,82319,82321],{},[898,82320,1712],{},[895,82322,82323,82325],{},[1693,82324,1724],{"mathvariant":1704},[1693,82326,1724],{"mathvariant":1704},[1693,82328,1709],{"stretchy":1708},[898,82330,4840],{},[1693,82332,1731],{"stretchy":1708},[1693,82334,1922],{},[1762,82336,1911],{},[902,82338,82339],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,82342,44441],{},".\n2° ",[38,82345,82346,82347,4300],{},"Od bodu ",[883,82348,82350],{"className":82349},[886],[888,82351,82352],{"xmlns":890},[892,82353,82354,82362],{},[895,82355,82356],{},[3284,82357,82358,82360],{},[898,82359,4840],{},[1762,82361,1911],{},[902,82363,82269],{"encoding":904},[883,82365,82367],{"className":82366},[886],[888,82368,82369],{"xmlns":890},[892,82370,82371,82381],{},[895,82372,82373,82375],{},[898,82374,2839],{},[3284,82376,82377,82379],{},[898,82378,1701],{},[898,82380,4840],{},[902,82382,4964],{"encoding":904}," klesá, ",[883,82385,82387],{"className":82386},[886],[888,82388,82389],{"xmlns":890},[892,82390,82391,82413],{},[895,82392,82393,82403,82405,82407,82409,82411],{},[1717,82394,82395,82397],{},[898,82396,1712],{},[895,82398,82399,82401],{},[1693,82400,1724],{"mathvariant":1704},[1693,82402,1724],{"mathvariant":1704},[1693,82404,1709],{"stretchy":1708},[898,82406,4840],{},[1693,82408,1731],{"stretchy":1708},[1693,82410,1908],{},[1762,82412,1911],{},[902,82414,82415],{"encoding":904},"Q''(L) \u003C 0",[38,82417,45263],{},[883,82419,82421],{"className":82420},[886],[888,82422,82423],{"xmlns":890},[892,82424,82425,82435],{},[895,82426,82427,82429],{},[898,82428,2839],{},[3284,82430,82431,82433],{},[898,82432,1701],{},[898,82434,4840],{},[902,82436,4964],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,82439,82441],{"className":82440},[886],[888,82442,82443],{"xmlns":890},[892,82444,82445,82453],{},[895,82446,82447],{},[3284,82448,82449,82451],{},[898,82450,4840],{},[1762,82452,1764],{},[902,82454,20044],{"encoding":904},[883,82456,82458],{"className":82457},[886],[888,82459,82460],{"xmlns":890},[892,82461,82462,82486],{},[895,82463,82464,82466,82472,82474,82480,82482,82484],{},[898,82465,2839],{},[3284,82467,82468,82470],{},[898,82469,1701],{},[898,82471,4840],{},[1693,82473,1709],{"stretchy":1708},[3284,82475,82476,82478],{},[898,82477,4840],{},[1762,82479,1764],{},[1693,82481,1731],{"stretchy":1708},[1693,82483,1695],{},[1762,82485,1911],{},[902,82487,82488],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,82491,82493],{"className":82492},[886],[888,82494,82495],{"xmlns":890},[892,82496,82497,82505],{},[895,82498,82499],{},[3284,82500,82501,82503],{},[898,82502,4840],{},[1762,82504,1911],{},[902,82506,82269],{"encoding":904},[38,82508,82509],{},"inflexním bodem"," produkční funkce.",[724,82512,82513,82514,17244,82531,1789],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,82515,82517],{"className":82516},[886],[888,82518,82519],{"xmlns":890},[892,82520,82521,82529],{},[895,82522,82523],{},[3284,82524,82525,82527],{},[898,82526,4840],{},[1762,82528,1911],{},[902,82530,82269],{"encoding":904},[883,82532,82534],{"className":82533},[886],[888,82535,82536],{"xmlns":890},[892,82537,82538,82560],{},[895,82539,82540,82550,82552,82554,82556,82558],{},[1717,82541,82542,82544],{},[898,82543,1712],{},[895,82545,82546,82548],{},[1693,82547,1724],{"mathvariant":1704},[1693,82549,1724],{"mathvariant":1704},[1693,82551,1709],{"stretchy":1708},[898,82553,4840],{},[1693,82555,1731],{"stretchy":1708},[1693,82557,1908],{},[1762,82559,1911],{},[902,82561,82415],{"encoding":904},[724,82563,82564,1863,82567,12537,82607,1343,82624,82641],{},[38,82565,82566],{},"Typický polynom třetího stupně:",[883,82568,82570],{"className":82569},[886],[888,82571,82572],{"xmlns":890},[892,82573,82574,82604],{},[895,82575,82576,82578,82580,82582,82584,82586,82588,82594,82596,82598],{},[898,82577,1712],{},[1693,82579,1709],{"stretchy":1708},[898,82581,4840],{},[1693,82583,1731],{"stretchy":1708},[1693,82585,1695],{},[898,82587,207],{},[1717,82589,82590,82592],{},[898,82591,4840],{},[1762,82593,8357],{},[1693,82595,1892],{},[898,82597,1895],{},[1717,82599,82600,82602],{},[898,82601,4840],{},[1762,82603,2398],{},[902,82605,82606],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,82608,82610],{"className":82609},[886],[888,82611,82612],{"xmlns":890},[892,82613,82614,82622],{},[895,82615,82616,82618,82620],{},[898,82617,207],{},[1693,82619,1908],{},[1762,82621,1911],{},[902,82623,49853],{"encoding":904},[883,82625,82627],{"className":82626},[886],[888,82628,82629],{"xmlns":890},[892,82630,82631,82639],{},[895,82632,82633,82635,82637],{},[898,82634,1895],{},[1693,82636,1922],{},[1762,82638,1911],{},[902,82640,7157],{"encoding":904},". Pak",[883,82643,82645],{"className":82644},[886],[888,82646,82647],{"xmlns":890,"display":34854},[892,82648,82649,82709],{},[895,82650,82651,82657,82659,82661,82669,82677,82679,82681,82687,82689,82691,82699,82707],{},[3284,82652,82653,82655],{},[898,82654,4840],{},[1762,82656,1911],{},[1693,82658,1695],{},[1693,82660,1698],{},[3638,82662,82663],{"scriptlevel":1911,"displaystyle":1708},[2132,82664,82665,82667],{},[1762,82666,1764],{},[1762,82668,8357],{},[3638,82670,82671],{"scriptlevel":1911,"displaystyle":1708},[2132,82672,82673,82675],{},[898,82674,1895],{},[898,82676,207],{},[1693,82678,1899],{"separator":1898},[1901,82680],{"width":1903},[3284,82682,82683,82685],{},[898,82684,4840],{},[1762,82686,1764],{},[1693,82688,1695],{},[1693,82690,1698],{},[3638,82692,82693],{"scriptlevel":1911,"displaystyle":1708},[2132,82694,82695,82697],{},[1762,82696,2398],{},[1762,82698,8357],{},[3638,82700,82701],{"scriptlevel":1911,"displaystyle":1708},[2132,82702,82703,82705],{},[898,82704,1895],{},[898,82706,207],{},[898,82708,1789],{"mathvariant":1704},[902,82710,82711],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,82713,82715,82716,1731],{"id":82714},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,82717,82719],{"className":82718},[886],[888,82720,82721],{"xmlns":890},[892,82722,82723,82733],{},[895,82724,82725,82727],{},[898,82726,2719],{},[3284,82728,82729,82731],{},[898,82730,1701],{},[898,82732,4840],{},[902,82734,81345],{"encoding":904},[724,82736,82737,16877,82739,81808,82742,82761],{},[38,82738,4969],{},[614,82740,82741],{},"average product of labour",[883,82743,82745],{"className":82744},[886],[888,82746,82747],{"xmlns":890},[892,82748,82749,82759],{},[895,82750,82751,82753],{},[898,82752,2719],{},[3284,82754,82755,82757],{},[898,82756,1701],{},[898,82758,4840],{},[902,82760,81345],{"encoding":904}," je podíl produkce a práce:",[883,82763,82765],{"className":82764},[886],[888,82766,82767],{"xmlns":890,"display":34854},[892,82768,82769,82804],{},[3626,82770,82771],{"width":34859},[3632,82772,82773,82775,82797,82799],{},[3635,82774],{"width":34864},[3635,82776,82777],{},[895,82778,82779,82781,82787,82789,82795],{},[898,82780,2719],{},[3284,82782,82783,82785],{},[898,82784,1701],{},[898,82786,4840],{},[1693,82788,1695],{},[2132,82790,82791,82793],{},[898,82792,1712],{},[898,82794,4840],{},[898,82796,1789],{"mathvariant":1704},[3635,82798],{"width":34864},[3635,82800,82801],{},[1915,82802,82803],{},"(5.4)",[902,82805,82806],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,82808,82809,82810,1789],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,82811,82813],{"className":82812},[886],[888,82814,82815],{"xmlns":890},[892,82816,82817,82827],{},[895,82818,82819,82821],{},[898,82820,2719],{},[3284,82822,82823,82825],{},[898,82824,1701],{},[898,82826,4840],{},[902,82828,81345],{"encoding":904},[115,82830,82832],{"id":82831},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,82834,82835],{},[9465,82836],{"alt":82837,"className":82838,"src":82839},"imek-q-mpl-apl-tripanel",[210,9469],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1636,82841,82842],{},[724,82843,82844,82847,82848,9530,82867,82884,82885],{},[38,82845,82846],{},"Princip:"," Má-li ",[883,82849,82851],{"className":82850},[886],[888,82852,82853],{"xmlns":890},[892,82854,82855,82865],{},[895,82856,82857,82859],{},[898,82858,2719],{},[3284,82860,82861,82863],{},[898,82862,1701],{},[898,82864,4840],{},[902,82866,81345],{"encoding":904},[883,82868,82870],{"className":82869},[886],[888,82871,82872],{"xmlns":890},[892,82873,82874,82882],{},[895,82875,82876],{},[3284,82877,82878,82880],{},[898,82879,4840],{},[1762,82881,1911],{},[902,82883,82269],{"encoding":904}," maximum, pak platí\n",[883,82886,82888],{"className":82887,"title":11080,"style":11081},[11079],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,82890,82891,82892,82895,82896,1863,82900,1789],{},"Slovně: ",[38,82893,82894],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,82897,82899],{"className":82898,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,82901,82903],{"className":82902},[886],[888,82904,82905],{"xmlns":890},[892,82906,82907,82913],{},[895,82908,82909,82911],{},[898,82910,2719],{},[898,82912,2971],{},[902,82914,3331],{"encoding":904},[1636,82916,82917,82941],{},[724,82918,82919,82921,82922],{},[883,82920,8620],{}," Postup — jak najít max ",[883,82923,82925],{"className":82924},[886],[888,82926,82927],{"xmlns":890},[892,82928,82929,82939],{},[895,82930,82931,82933],{},[898,82932,2719],{},[3284,82934,82935,82937],{},[898,82936,1701],{},[898,82938,4840],{},[902,82940,81345],{"encoding":904},[152,82942,82943,82981,83063],{},[123,82944,82945,82946,82980],{},"Napište ",[883,82947,82949],{"className":82948},[886],[888,82950,82951],{"xmlns":890},[892,82952,82953,82977],{},[895,82954,82955,82957,82963,82965,82967,82969,82971,82973,82975],{},[898,82956,2719],{},[3284,82958,82959,82961],{},[898,82960,1701],{},[898,82962,4840],{},[1693,82964,1695],{},[898,82966,1712],{},[1693,82968,1709],{"stretchy":1708},[898,82970,4840],{},[1693,82972,1731],{"stretchy":1708},[898,82974,1705],{"mathvariant":1704},[898,82976,4840],{},[902,82978,82979],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,82982,82983,82984,83016,83017,83020,83021,1789],{},"Položte ",[883,82985,82987],{"className":82986},[886],[888,82988,82989],{"xmlns":890},[892,82990,82991,83013],{},[895,82992,82993,82995,82997,83003,83009,83011],{},[1693,82994,1709],{"stretchy":1708},[898,82996,2719],{},[3284,82998,82999,83001],{},[898,83000,1701],{},[898,83002,4840],{},[1717,83004,83005,83007],{},[1693,83006,1731],{"stretchy":1708},[1693,83008,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,83010,1695],{},[1762,83012,1911],{},[902,83014,83015],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,83018,83019],{},"Zkratka:"," můžete rovnou řešit ",[883,83022,83024],{"className":83023},[886],[888,83025,83026],{"xmlns":890},[892,83027,83028,83060],{},[895,83029,83030,83032,83038,83040,83042,83044,83046,83048,83054,83056,83058],{},[898,83031,2839],{},[3284,83033,83034,83036],{},[898,83035,1701],{},[898,83037,4840],{},[1693,83039,1709],{"stretchy":1708},[898,83041,4840],{},[1693,83043,1731],{"stretchy":1708},[1693,83045,1695],{},[898,83047,2719],{},[3284,83049,83050,83052],{},[898,83051,1701],{},[898,83053,4840],{},[1693,83055,1709],{"stretchy":1708},[898,83057,4840],{},[1693,83059,1731],{"stretchy":1708},[902,83061,83062],{"encoding":904},"MP_L(L) = AP_L(L)",[123,83064,83065],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,83067,72225],{"id":83068},"odvození",[724,83070,83071,83072,83105],{},"Z ",[883,83073,83075],{"className":83074},[886],[888,83076,83077],{"xmlns":890},[892,83078,83079,83103],{},[895,83080,83081,83083,83089,83091,83093,83095,83097,83099,83101],{},[898,83082,2719],{},[3284,83084,83085,83087],{},[898,83086,1701],{},[898,83088,4840],{},[1693,83090,1695],{},[898,83092,1712],{},[1693,83094,1709],{"stretchy":1708},[898,83096,4840],{},[1693,83098,1731],{"stretchy":1708},[898,83100,1705],{"mathvariant":1704},[898,83102,4840],{},[902,83104,82979],{"encoding":904}," a derivace podílu:",[883,83107,83109],{"className":83108},[886],[888,83110,83111],{"xmlns":890,"display":34854},[892,83112,83113,83266],{},[895,83114,83115,83117,83119,83125,83131,83133,83135,83137,83139,83179,83181,83187,83221,83223,83229,83232,83234,83240,83242,83244,83246,83248,83250,83256,83258,83260,83262,83264],{},[1693,83116,1709],{"stretchy":1708},[898,83118,2719],{},[3284,83120,83121,83123],{},[898,83122,1701],{},[898,83124,4840],{},[1717,83126,83127,83129],{},[1693,83128,1731],{"stretchy":1708},[1693,83130,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,83132,1709],{"stretchy":1708},[898,83134,4840],{},[1693,83136,1731],{"stretchy":1708},[1693,83138,1695],{},[2132,83140,83141,83173],{},[895,83142,83143,83149,83151,83153,83155,83157,83159,83161,83163,83165,83167,83169,83171],{},[1717,83144,83145,83147],{},[898,83146,1712],{},[1693,83148,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,83150,1709],{"stretchy":1708},[898,83152,4840],{},[1693,83154,1731],{"stretchy":1708},[1693,83156,1715],{},[898,83158,4840],{},[1693,83160,1698],{},[898,83162,1712],{},[1693,83164,1709],{"stretchy":1708},[898,83166,4840],{},[1693,83168,1731],{"stretchy":1708},[1693,83170,1715],{},[1762,83172,1764],{},[1717,83174,83175,83177],{},[898,83176,4840],{},[1762,83178,2398],{},[1693,83180,1695],{},[2132,83182,83183,83185],{},[1762,83184,1764],{},[898,83186,4840],{},[895,83188,83189,83191,83197,83199,83201,83203,83205,83219],{},[1693,83190,1709],{"fence":1898},[1717,83192,83193,83195],{},[898,83194,1712],{},[1693,83196,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,83198,1709],{"stretchy":1708},[898,83200,4840],{},[1693,83202,1731],{"stretchy":1708},[1693,83204,1698],{},[2132,83206,83207,83217],{},[895,83208,83209,83211,83213,83215],{},[898,83210,1712],{},[1693,83212,1709],{"stretchy":1708},[898,83214,4840],{},[1693,83216,1731],{"stretchy":1708},[898,83218,4840],{},[1693,83220,1731],{"fence":1898},[1693,83222,1695],{},[2132,83224,83225,83227],{},[1762,83226,1764],{},[898,83228,4840],{},[1693,83230,1709],{"fence":1898,"stretchy":1898,"minsize":83231,"maxsize":83231},"1.2em",[898,83233,2839],{},[3284,83235,83236,83238],{},[898,83237,1701],{},[898,83239,4840],{},[1693,83241,1709],{"stretchy":1708},[898,83243,4840],{},[1693,83245,1731],{"stretchy":1708},[1693,83247,1698],{},[898,83249,2719],{},[3284,83251,83252,83254],{},[898,83253,1701],{},[898,83255,4840],{},[1693,83257,1709],{"stretchy":1708},[898,83259,4840],{},[1693,83261,1731],{"stretchy":1708},[1693,83263,1731],{"fence":1898,"stretchy":1898,"minsize":83231,"maxsize":83231},[898,83265,1789],{"mathvariant":1704},[902,83267,83268],{"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).",[724,83270,16518,83271,6055,83293,83376],{},[883,83272,83274],{"className":83273},[886],[888,83275,83276],{"xmlns":890},[892,83277,83278,83290],{},[895,83279,83280,83286,83288],{},[3284,83281,83282,83284],{},[898,83283,4840],{},[1762,83285,1911],{},[1693,83287,1922],{},[1762,83289,1911],{},[902,83291,83292],{"encoding":904},"L_0 > 0",[883,83294,83296],{"className":83295},[886],[888,83297,83298],{"xmlns":890},[892,83299,83300,83373],{},[895,83301,83302,83304,83306,83312,83318,83320,83326,83328,83330,83332,83335,83337,83343,83345,83351,83353,83355,83357,83363,83365,83371],{},[1693,83303,1709],{"stretchy":1708},[898,83305,2719],{},[3284,83307,83308,83310],{},[898,83309,1701],{},[898,83311,4840],{},[1717,83313,83314,83316],{},[1693,83315,1731],{"stretchy":1708},[1693,83317,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,83319,1709],{"stretchy":1708},[3284,83321,83322,83324],{},[898,83323,4840],{},[1762,83325,1911],{},[1693,83327,1731],{"stretchy":1708},[1693,83329,1695],{},[1762,83331,1911],{},[1693,83333,83334],{},"⇔",[898,83336,2839],{},[3284,83338,83339,83341],{},[898,83340,1701],{},[898,83342,4840],{},[1693,83344,1709],{"stretchy":1708},[3284,83346,83347,83349],{},[898,83348,4840],{},[1762,83350,1911],{},[1693,83352,1731],{"stretchy":1708},[1693,83354,1695],{},[898,83356,2719],{},[3284,83358,83359,83361],{},[898,83360,1701],{},[898,83362,4840],{},[1693,83364,1709],{"stretchy":1708},[3284,83366,83367,83369],{},[898,83368,4840],{},[1762,83370,1911],{},[1693,83372,1731],{"stretchy":1708},[902,83374,83375],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,83378,83380],{"id":83379},"příklad-51","Příklad 5.1",[724,83382,83383,83384,1789],{},"Je dána produkce ",[883,83385,83387],{"className":83386},[886],[888,83388,83389],{"xmlns":890},[892,83390,83391,83415],{},[895,83392,83393,83395,83397,83399,83405,83407,83409],{},[898,83394,1712],{},[1693,83396,1695],{},[1762,83398,9154],{},[1717,83400,83401,83403],{},[898,83402,4840],{},[1762,83404,2398],{},[1693,83406,1698],{},[1762,83408,9739],{},[1717,83410,83411,83413],{},[898,83412,4840],{},[1762,83414,8357],{},[902,83416,83417],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,83419,83420,64261,83423,83473,83474,1789],{},[38,83421,83422],{},"(a)",[883,83424,83426],{"className":83425},[886],[888,83427,83428],{"xmlns":890},[892,83429,83430,83470],{},[895,83431,83432,83434,83436,83438,83440,83442,83444,83446,83448,83450,83452,83454,83456,83458,83460,83462,83464,83466,83468],{},[898,83433,4840],{},[1693,83435,1695],{},[1762,83437,2398],{},[1693,83439,1899],{"separator":1898},[1762,83441,9147],{},[1693,83443,1899],{"separator":1898},[1762,83445,12453],{},[1693,83447,1899],{"separator":1898},[1762,83449,9763],{},[1693,83451,1899],{"separator":1898},[1762,83453,29746],{},[1693,83455,1899],{"separator":1898},[1762,83457,10600],{},[1693,83459,1899],{"separator":1898},[1762,83461,15892],{},[1693,83463,1899],{"separator":1898},[1762,83465,45121],{},[1693,83467,1899],{"separator":1898},[1762,83469,11872],{},[902,83471,83472],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,83475,83477],{"className":83476},[886],[888,83478,83479],{"xmlns":890},[892,83480,83481,83491],{},[895,83482,83483,83485],{},[898,83484,2839],{},[3284,83486,83487,83489],{},[898,83488,1701],{},[898,83490,4840],{},[902,83492,4964],{"encoding":904},[724,83494,83495,83496,41751],{},"Podle (5.2): ",[883,83497,83499],{"className":83498},[886],[888,83500,83501],{"xmlns":890},[892,83502,83503,83559],{},[895,83504,83505,83507,83513,83515,83521,83523,83525,83527,83529,83531,83533,83535,83537,83543,83545,83547,83549,83551,83553,83555,83557],{},[898,83506,2839],{},[3284,83508,83509,83511],{},[898,83510,1701],{},[898,83512,4840],{},[1693,83514,1695],{},[1717,83516,83517,83519],{},[898,83518,1712],{},[1693,83520,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,83522,1709],{"stretchy":1708},[898,83524,4840],{},[1693,83526,1731],{"stretchy":1708},[1693,83528,1695],{},[1762,83530,10402],{},[898,83532,4840],{},[1693,83534,1698],{},[1762,83536,26132],{},[1717,83538,83539,83541],{},[898,83540,4840],{},[1762,83542,2398],{},[1693,83544,1695],{},[898,83546,4840],{},[1693,83548,1709],{"stretchy":1708},[1762,83550,10402],{},[1693,83552,1698],{},[1762,83554,26132],{},[898,83556,4840],{},[1693,83558,1731],{"stretchy":1708},[902,83560,83561],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,83563,83564,83601],{},[19,83565,83566],{},[22,83567,83568,83583,83585,83587,83589,83591,83593,83595,83597,83599],{},[25,83569,83570],{},[883,83571,83573],{"className":83572},[886],[888,83574,83575],{"xmlns":890},[892,83576,83577,83581],{},[895,83578,83579],{},[898,83580,4840],{},[902,83582,4840],{"encoding":904},[25,83584,2398],{},[25,83586,9147],{},[25,83588,12453],{},[25,83590,9763],{},[25,83592,29746],{},[25,83594,10600],{},[25,83596,15892],{},[25,83598,45121],{},[25,83600,11872],{},[30,83602,83603],{},[22,83604,83605,83626,83629,83632,83635,83637,83640,83642,83644,83663],{},[35,83606,83607],{},[883,83608,83610],{"className":83609},[886],[888,83611,83612],{"xmlns":890},[892,83613,83614,83624],{},[895,83615,83616,83618],{},[898,83617,2839],{},[3284,83619,83620,83622],{},[898,83621,1701],{},[898,83623,4840],{},[902,83625,4964],{"encoding":904},[35,83627,83628],{},"21,6",[35,83630,83631],{},"45",[35,83633,83634],{},"57,6",[35,83636,10023],{},[35,83638,83639],{},"50,4",[35,83641,83628],{},[35,83643,1911],{},[35,83645,83646],{},[883,83647,83649],{"className":83648},[886],[888,83650,83651],{"xmlns":890},[892,83652,83653,83660],{},[895,83654,83655,83657],{},[1693,83656,1698],{},[1762,83658,83659],{},"12,6",[902,83661,83662],{"encoding":904},"-12{,}6",[35,83664,83665],{},[883,83666,83668],{"className":83667},[886],[888,83669,83670],{"xmlns":890},[892,83671,83672,83678],{},[895,83673,83674,83676],{},[1693,83675,1698],{},[1762,83677,52216],{},[902,83679,83680],{"encoding":904},"-75",[724,83682,83683,83702,83703,83721,83722,83739,83740,83758,83759,83783,83784,83802],{},[883,83684,83686],{"className":83685},[886],[888,83687,83688],{"xmlns":890},[892,83689,83690,83700],{},[895,83691,83692,83694],{},[898,83693,2839],{},[3284,83695,83696,83698],{},[898,83697,1701],{},[898,83699,4840],{},[902,83701,4964],{"encoding":904}," nabývá maxima pro ",[883,83704,83706],{"className":83705},[886],[888,83707,83708],{"xmlns":890},[892,83709,83710,83718],{},[895,83711,83712,83714,83716],{},[898,83713,4840],{},[1693,83715,1695],{},[1762,83717,9763],{},[902,83719,83720],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,83723,83725],{"className":83724},[886],[888,83726,83727],{"xmlns":890},[892,83728,83729,83737],{},[895,83730,83731,83733,83735],{},[898,83732,4840],{},[1693,83734,1695],{},[1762,83736,9763],{},[902,83738,83720],{"encoding":904}," přírůstky klesají, v ",[883,83741,83743],{"className":83742},[886],[888,83744,83745],{"xmlns":890},[892,83746,83747,83755],{},[895,83748,83749,83751,83753],{},[898,83750,4840],{},[1693,83752,1695],{},[1762,83754,15892],{},[902,83756,83757],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,83760,83762],{"className":83761},[886],[888,83763,83764],{"xmlns":890},[892,83765,83766,83780],{},[895,83767,83768,83770,83772,83774,83776,83778],{},[898,83769,1712],{},[1693,83771,1709],{"stretchy":1708},[1762,83773,15892],{},[1693,83775,1731],{"stretchy":1708},[1693,83777,1695],{},[1762,83779,30657],{},[902,83781,83782],{"encoding":904},"Q(20) = 800","), od ",[883,83785,83787],{"className":83786},[886],[888,83788,83789],{"xmlns":890},[892,83790,83791,83799],{},[895,83792,83793,83795,83797],{},[898,83794,4840],{},[1693,83796,1922],{},[1762,83798,15892],{},[902,83800,83801],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,83804,83805],{},[614,83806,83807,83808,83848,83849,9530,83867,1789],{},"Obrázek 5.1 — graf produkce ",[883,83809,83811],{"className":83810},[886],[888,83812,83813],{"xmlns":890},[892,83814,83815,83845],{},[895,83816,83817,83819,83821,83823,83825,83827,83829,83835,83837,83839],{},[898,83818,1712],{},[1693,83820,1709],{"stretchy":1708},[898,83822,4840],{},[1693,83824,1731],{"stretchy":1708},[1693,83826,1695],{},[1762,83828,9154],{},[1717,83830,83831,83833],{},[898,83832,4840],{},[1762,83834,2398],{},[1693,83836,1698],{},[1762,83838,9739],{},[1717,83840,83841,83843],{},[898,83842,4840],{},[1762,83844,8357],{},[902,83846,83847],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,83850,83852],{"className":83851},[886],[888,83853,83854],{"xmlns":890},[892,83855,83856,83864],{},[895,83857,83858,83860,83862],{},[898,83859,1712],{},[1693,83861,1695],{},[1762,83863,30657],{},[902,83865,83866],{"encoding":904},"Q = 800",[883,83868,83870],{"className":83869},[886],[888,83871,83872],{"xmlns":890},[892,83873,83874,83882],{},[895,83875,83876,83878,83880],{},[898,83877,4840],{},[1693,83879,1695],{},[1762,83881,15892],{},[902,83883,83757],{"encoding":904},[724,83885,83886,83889],{},[38,83887,83888],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,83891,83892,83893,1343,83911,4300],{},"Podle (5.3) s ",[883,83894,83896],{"className":83895},[886],[888,83897,83898],{"xmlns":890},[892,83899,83900,83908],{},[895,83901,83902,83904,83906],{},[898,83903,4840],{},[1693,83905,1695],{},[1762,83907,9154],{},[902,83909,83910],{"encoding":904},"L = 6",[883,83912,83914],{"className":83913},[886],[888,83915,83916],{"xmlns":890},[892,83917,83918,83928],{},[895,83919,83920,83922,83924,83926],{},[898,83921,1771],{},[898,83923,4840],{},[1693,83925,1695],{},[1762,83927,8357],{},[902,83929,83930],{"encoding":904},"dL = 3",[883,83932,83934],{"className":83933},[886],[888,83935,83936],{"xmlns":890,"display":34854},[892,83937,83938,84001],{},[895,83939,83940,83942,83944,83946,83948,83954,83956,83958,83960,83962,83964,83966,83968,83970,83972,83974,83976,83978,83980,83982,83984,83986,83988,83990,83992,83994,83996,83998],{},[898,83941,1771],{},[898,83943,1712],{},[1693,83945,1695],{},[898,83947,2839],{},[3284,83949,83950,83952],{},[898,83951,1701],{},[898,83953,4840],{},[1693,83955,1709],{"stretchy":1708},[1762,83957,9154],{},[1693,83959,1731],{"stretchy":1708},[1693,83961,1715],{},[1762,83963,8357],{},[1693,83965,1695],{},[1693,83967,1709],{"stretchy":1708},[1762,83969,10402],{},[1693,83971,1715],{},[1762,83973,9154],{},[1693,83975,1698],{},[1762,83977,26132],{},[1693,83979,1715],{},[1762,83981,12433],{},[1693,83983,1731],{"stretchy":1708},[1693,83985,1715],{},[1762,83987,8357],{},[1693,83989,1695],{},[1762,83991,83639],{},[1693,83993,1715],{},[1762,83995,8357],{},[1693,83997,1695],{},[1762,83999,84000],{},"151,2.",[902,84002,84003],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,84005,84006,84007,64491,84032,84046,84047,1789],{},"Produkce vzroste z ",[883,84008,84010],{"className":84009},[886],[888,84011,84012],{"xmlns":890},[892,84013,84014,84029],{},[895,84015,84016,84018,84020,84022,84024,84026],{},[898,84017,1712],{},[1693,84019,1709],{"stretchy":1708},[1762,84021,9154],{},[1693,84023,1731],{"stretchy":1708},[1693,84025,1695],{},[1762,84027,84028],{},"172,8",[902,84030,84031],{"encoding":904},"Q(6) = 172{,}8",[883,84033,84035],{"className":84034},[886],[888,84036,84037],{"xmlns":890},[892,84038,84039,84044],{},[895,84040,84041],{},[1762,84042,84043],{},"324",[902,84045,84043],{"encoding":904},". Skutečná hodnota: ",[883,84048,84050],{"className":84049},[886],[888,84051,84052],{"xmlns":890},[892,84053,84054,84094],{},[895,84055,84056,84058,84060,84062,84064,84066,84068,84070,84072,84074,84076,84078,84080,84082,84085,84087,84089,84091],{},[898,84057,3890],{"mathvariant":1704},[898,84059,1712],{},[1693,84061,1695],{},[898,84063,1712],{},[1693,84065,1709],{"stretchy":1708},[1762,84067,10881],{},[1693,84069,1731],{"stretchy":1708},[1693,84071,1698],{},[898,84073,1712],{},[1693,84075,1709],{"stretchy":1708},[1762,84077,9154],{},[1693,84079,1731],{"stretchy":1708},[1693,84081,1695],{},[1762,84083,84084],{},"340,2",[1693,84086,1698],{},[1762,84088,84028],{},[1693,84090,1695],{},[1762,84092,84093],{},"167,4",[902,84095,84096],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,84098,84100],{"id":84099},"příklad-52","Příklad 5.2",[724,84102,84103,84104,1789],{},"Ověříme princip (5.5) pro ",[883,84105,84107],{"className":84106},[886],[888,84108,84109],{"xmlns":890},[892,84110,84111,84135],{},[895,84112,84113,84115,84117,84119,84125,84127,84129],{},[898,84114,1712],{},[1693,84116,1695],{},[1762,84118,9154],{},[1717,84120,84121,84123],{},[898,84122,4840],{},[1762,84124,2398],{},[1693,84126,1698],{},[1762,84128,9739],{},[1717,84130,84131,84133],{},[898,84132,4840],{},[1762,84134,8357],{},[902,84136,83417],{"encoding":904},[883,84138,84140],{"className":84139},[886],[888,84141,84142],{"xmlns":890,"display":34854},[892,84143,84144,84222],{},[895,84145,84146,84148,84154,84156,84162,84164,84166,84168,84170,84172,84178,84180,84182,84184,84192,84194,84196,84198,84200,84202,84204,84206,84208,84210,84212,84218,84220],{},[898,84147,2719],{},[3284,84149,84150,84152],{},[898,84151,1701],{},[898,84153,4840],{},[1693,84155,1695],{},[2132,84157,84158,84160],{},[898,84159,1712],{},[898,84161,4840],{},[1693,84163,1695],{},[1762,84165,9154],{},[898,84167,4840],{},[1693,84169,1698],{},[1762,84171,9739],{},[1717,84173,84174,84176],{},[898,84175,4840],{},[1762,84177,2398],{},[1693,84179,1899],{"separator":1898},[1901,84181],{"width":3630},[898,84183,2719],{},[5688,84185,84186,84188,84190],{},[898,84187,1701],{},[898,84189,4840],{},[1693,84191,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,84193,1695],{},[1762,84195,9154],{},[1693,84197,1698],{},[1762,84199,26082],{},[898,84201,4840],{},[1693,84203,1695],{},[1762,84205,1911],{},[1915,84207,1917],{},[1693,84209,10870],{},[1915,84211,1917],{},[3284,84213,84214,84216],{},[898,84215,4840],{},[1762,84217,1911],{},[1693,84219,1695],{},[1762,84221,74998],{},[902,84223,84224],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,84226,84227,84263,84264,84282,84283,1789],{},[883,84228,84230],{"className":84229},[886],[888,84231,84232],{"xmlns":890},[892,84233,84234,84260],{},[895,84235,84236,84238,84250,84252,84254,84256,84258],{},[898,84237,2719],{},[5688,84239,84240,84242,84244],{},[898,84241,1701],{},[898,84243,4840],{},[895,84245,84246,84248],{},[1693,84247,1724],{"mathvariant":1704},[1693,84249,1724],{"mathvariant":1704},[1693,84251,1695],{},[1693,84253,1698],{},[1762,84255,26082],{},[1693,84257,1908],{},[1762,84259,1911],{},[902,84261,84262],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,84265,84267],{"className":84266},[886],[888,84268,84269],{"xmlns":890},[892,84270,84271,84279],{},[895,84272,84273,84275,84277],{},[898,84274,4840],{},[1693,84276,1695],{},[1762,84278,43026],{},[902,84280,84281],{"encoding":904},"L = 15"," je maximum, ",[883,84284,84286],{"className":84285},[886],[888,84287,84288],{"xmlns":890},[892,84289,84290,84336],{},[895,84291,84292,84294,84300,84302,84304,84306,84308,84310,84312,84314,84316,84318,84320,84323,84325,84328,84330,84332,84334],{},[898,84293,2719],{},[3284,84295,84296,84298],{},[898,84297,1701],{},[898,84299,4840],{},[1693,84301,1709],{"stretchy":1708},[1762,84303,43026],{},[1693,84305,1731],{"stretchy":1708},[1693,84307,1695],{},[1762,84309,9154],{},[1693,84311,1715],{},[1762,84313,43026],{},[1693,84315,1698],{},[1762,84317,9739],{},[1693,84319,1715],{},[1762,84321,84322],{},"225",[1693,84324,1695],{},[1762,84326,84327],{},"90",[1693,84329,1698],{},[1762,84331,83631],{},[1693,84333,1695],{},[1762,84335,83631],{},[902,84337,84338],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,84340,84341,48651,84397,84443],{},[883,84342,84344],{"className":84343},[886],[888,84345,84346],{"xmlns":890},[892,84347,84348,84394],{},[895,84349,84350,84352,84358,84360,84362,84364,84366,84368,84370,84372,84374,84376,84378,84380,84382,84385,84387,84390,84392],{},[898,84351,2839],{},[3284,84353,84354,84356],{},[898,84355,1701],{},[898,84357,4840],{},[1693,84359,1709],{"stretchy":1708},[1762,84361,43026],{},[1693,84363,1731],{"stretchy":1708},[1693,84365,1695],{},[1762,84367,10402],{},[1693,84369,1715],{},[1762,84371,43026],{},[1693,84373,1698],{},[1762,84375,26132],{},[1693,84377,1715],{},[1762,84379,84322],{},[1693,84381,1695],{},[1762,84383,84384],{},"180",[1693,84386,1698],{},[1762,84388,84389],{},"135",[1693,84391,1695],{},[1762,84393,83631],{},[902,84395,84396],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,84398,84400],{"className":84399},[886],[888,84401,84402],{"xmlns":890},[892,84403,84404,84440],{},[895,84405,84406,84408,84414,84416,84418,84420,84422,84424,84430,84432,84434,84436,84438],{},[898,84407,2839],{},[3284,84409,84410,84412],{},[898,84411,1701],{},[898,84413,4840],{},[1693,84415,1709],{"stretchy":1708},[1762,84417,43026],{},[1693,84419,1731],{"stretchy":1708},[1693,84421,1695],{},[898,84423,2719],{},[3284,84425,84426,84428],{},[898,84427,1701],{},[898,84429,4840],{},[1693,84431,1709],{"stretchy":1708},[1762,84433,43026],{},[1693,84435,1731],{"stretchy":1708},[1693,84437,1695],{},[1762,84439,83631],{},[902,84441,84442],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,84445,84446,84449,84450,24395,84479,1789],{},[38,84447,84448],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,84451,84453],{"className":84452},[886],[888,84454,84455],{"xmlns":890},[892,84456,84457,84477],{},[895,84458,84459,84461,84467,84469,84471],{},[898,84460,2839],{},[3284,84462,84463,84465],{},[898,84464,1701],{},[898,84466,4840],{},[1693,84468,1695],{},[898,84470,2719],{},[3284,84472,84473,84475],{},[898,84474,1701],{},[898,84476,4840],{},[902,84478,5039],{"encoding":904},[883,84480,84482],{"className":84481},[886],[888,84483,84484],{"xmlns":890},[892,84485,84486,84526],{},[895,84487,84488,84490,84492,84494,84496,84502,84504,84506,84508,84510,84512,84518,84520,84522,84524],{},[1762,84489,10402],{},[898,84491,4840],{},[1693,84493,1698],{},[1762,84495,26132],{},[1717,84497,84498,84500],{},[898,84499,4840],{},[1762,84501,2398],{},[1693,84503,1695],{},[1762,84505,9154],{},[898,84507,4840],{},[1693,84509,1698],{},[1762,84511,9739],{},[1717,84513,84514,84516],{},[898,84515,4840],{},[1762,84517,2398],{},[1693,84519,10870],{},[898,84521,4840],{},[1693,84523,1695],{},[1762,84525,43026],{},[902,84527,84528],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,84530,84531],{},[614,84532,84533,84534,84553,84554,8586,84572,84591,84592,84610,84611,84628,84629,84648,84649,84668],{},"Obrázek 5.3 — křivky ",[883,84535,84537],{"className":84536},[886],[888,84538,84539],{"xmlns":890},[892,84540,84541,84551],{},[895,84542,84543,84545],{},[898,84544,2839],{},[3284,84546,84547,84549],{},[898,84548,1701],{},[898,84550,4840],{},[902,84552,4964],{"encoding":904}," (max 60 při ",[883,84555,84557],{"className":84556},[886],[888,84558,84559],{"xmlns":890},[892,84560,84561,84569],{},[895,84562,84563,84565,84567],{},[898,84564,4840],{},[1693,84566,1695],{},[1762,84568,9763],{},[902,84570,84571],{"encoding":904},"L=10",[883,84573,84575],{"className":84574},[886],[888,84576,84577],{"xmlns":890},[892,84578,84579,84589],{},[895,84580,84581,84583],{},[898,84582,2719],{},[3284,84584,84585,84587],{},[898,84586,1701],{},[898,84588,4840],{},[902,84590,81345],{"encoding":904}," (max 45 při ",[883,84593,84595],{"className":84594},[886],[888,84596,84597],{"xmlns":890},[892,84598,84599,84607],{},[895,84600,84601,84603,84605],{},[898,84602,4840],{},[1693,84604,1695],{},[1762,84606,43026],{},[902,84608,84609],{"encoding":904},"L=15","), průsečík v ",[883,84612,84614],{"className":84613},[886],[888,84615,84616],{"xmlns":890},[892,84617,84618,84626],{},[895,84619,84620,84622,84624],{},[898,84621,4840],{},[1693,84623,1695],{},[1762,84625,43026],{},[902,84627,84281],{"encoding":904},". Nalevo od 15 leží ",[883,84630,84632],{"className":84631},[886],[888,84633,84634],{"xmlns":890},[892,84635,84636,84646],{},[895,84637,84638,84640],{},[898,84639,2839],{},[3284,84641,84642,84644],{},[898,84643,1701],{},[898,84645,4840],{},[902,84647,4964],{"encoding":904}," nad ",[883,84650,84652],{"className":84651},[886],[888,84653,84654],{"xmlns":890},[892,84655,84656,84666],{},[895,84657,84658,84660],{},[898,84659,2719],{},[3284,84661,84662,84664],{},[898,84663,1701],{},[898,84665,4840],{},[902,84667,81345],{"encoding":904},", napravo pod ní.",[115,84670,84672],{"id":84671},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,84674,84675,84676,9591,84689,1863,84692,13055,84705,1863,84708,4300],{},"V dvoufaktorovém modelu závisí produkce ",[883,84677,84679],{"className":84678},[886],[888,84680,84681],{"xmlns":890},[892,84682,84683,84687],{},[895,84684,84685],{},[898,84686,1712],{},[902,84688,1712],{"encoding":904},[38,84690,84691],{},"práci",[883,84693,84695],{"className":84694},[886],[888,84696,84697],{"xmlns":890},[892,84698,84699,84703],{},[895,84700,84701],{},[898,84702,4840],{},[902,84704,4840],{"encoding":904},[38,84706,84707],{},"kapitálu",[883,84709,84711],{"className":84710},[886],[888,84712,84713],{"xmlns":890},[892,84714,84715,84719],{},[895,84716,84717],{},[898,84718,4845],{},[902,84720,4845],{"encoding":904},[883,84722,84724],{"className":84723},[886],[888,84725,84726],{"xmlns":890,"display":34854},[892,84727,84728,84763],{},[3626,84729,84730],{"width":34859},[3632,84731,84732,84734,84756,84758],{},[3635,84733],{"width":34864},[3635,84735,84736],{},[895,84737,84738,84740,84742,84744,84746,84748,84750,84752,84754],{},[898,84739,1712],{},[1693,84741,1695],{},[898,84743,1712],{},[1693,84745,1709],{"stretchy":1708},[898,84747,4840],{},[1693,84749,1899],{"separator":1898},[898,84751,4845],{},[1693,84753,1731],{"stretchy":1708},[898,84755,1789],{"mathvariant":1704},[3635,84757],{"width":34864},[3635,84759,84760],{},[1915,84761,84762],{},"(5.6)",[902,84764,84765],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,84767,84768,84769,84771],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,84770,81711],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,84773,5066],{"id":5065},[724,84775,84776],{},"Široce používané produkční funkce mají tvar",[883,84778,84780],{"className":84779},[886],[888,84781,84782],{"xmlns":890,"display":34854},[892,84783,84784,84825],{},[3626,84785,84786],{"width":34859},[3632,84787,84788,84790,84818,84820],{},[3635,84789],{"width":34864},[3635,84791,84792],{},[895,84793,84794,84796,84798,84800,84802,84808,84810,84816],{},[898,84795,1712],{},[1693,84797,1695],{},[898,84799,2719],{},[1915,84801,2239],{},[1717,84803,84804,84806],{},[898,84805,4840],{},[898,84807,207],{},[1915,84809,2239],{},[1717,84811,84812,84814],{},[898,84813,4845],{},[898,84815,1895],{},[1693,84817,1899],{"separator":1898},[3635,84819],{"width":34864},[3635,84821,84822],{},[1915,84823,84824],{},"(5.7)",[902,84826,84827],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,84829,11188,84830,84852,84853,84855,84856,1789],{},[883,84831,84833],{"className":84832},[886],[888,84834,84835],{"xmlns":890},[892,84836,84837,84849],{},[895,84838,84839,84841,84843,84845,84847],{},[898,84840,2719],{},[1693,84842,1899],{"separator":1898},[898,84844,207],{},[1693,84846,1899],{"separator":1898},[898,84848,1895],{},[902,84850,84851],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,84854,81410],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,84857,84859],{"className":84858},[886],[888,84860,84861],{"xmlns":890},[892,84862,84863,84875],{},[895,84864,84865,84867,84869,84871,84873],{},[898,84866,207],{},[1693,84868,1899],{"separator":1898},[898,84870,1895],{},[1693,84872,1908],{},[1762,84874,1764],{},[902,84876,84877],{"encoding":904},"a, b \u003C 1",[724,84879,84880],{},[9465,84881],{"alt":84882,"className":84883,"src":84884},"imek-vynosy-z-rozsahu-3typy",[210,9469],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,84886,84887,84888,84891,84892,9591,84905,84921,84922,9591,84935,4300],{},"Reflektují ekonomickou zákonitost, že ",[38,84889,84890],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,84893,84895],{"className":84894},[886],[888,84896,84897],{"xmlns":890},[892,84898,84899,84903],{},[895,84900,84901],{},[898,84902,4840],{},[902,84904,4840],{"encoding":904},[883,84906,84908],{"className":84907},[886],[888,84909,84910],{"xmlns":890},[892,84911,84912,84918],{},[895,84913,84914,84916],{},[898,84915,6629],{},[898,84917,4840],{},[902,84919,84920],{"encoding":904},"rL"," a kapitál z ",[883,84923,84925],{"className":84924},[886],[888,84926,84927],{"xmlns":890},[892,84928,84929,84933],{},[895,84930,84931],{},[898,84932,4845],{},[902,84934,4845],{"encoding":904},[883,84936,84938],{"className":84937},[886],[888,84939,84940],{"xmlns":890},[892,84941,84942,84948],{},[895,84943,84944,84946],{},[898,84945,6629],{},[898,84947,4845],{},[902,84949,84950],{"encoding":904},"rK",[883,84952,84954],{"className":84953},[886],[888,84955,84956],{"xmlns":890,"display":34854},[892,84957,84958,85081],{},[3626,84959,84960],{"width":34859},[3632,84961,84962,84964,85074,85076],{},[3635,84963],{"width":34864},[3635,84965,84966],{},[895,84967,84968,84970,84972,84974,84976,84978,84980,84982,84984,84986,84988,84990,84992,84994,85000,85002,85004,85006,85012,85014,85016,85018,85030,85032,85038,85044,85046,85058,85060,85062,85064,85066,85068,85070,85072],{},[898,84969,1712],{},[1693,84971,1709],{"stretchy":1708},[898,84973,6629],{},[898,84975,4840],{},[1693,84977,1899],{"separator":1898},[898,84979,6629],{},[898,84981,4845],{},[1693,84983,1731],{"stretchy":1708},[1693,84985,1695],{},[898,84987,2719],{},[1693,84989,1709],{"stretchy":1708},[898,84991,6629],{},[898,84993,4840],{},[1717,84995,84996,84998],{},[1693,84997,1731],{"stretchy":1708},[898,84999,207],{},[1693,85001,1709],{"stretchy":1708},[898,85003,6629],{},[898,85005,4845],{},[1717,85007,85008,85010],{},[1693,85009,1731],{"stretchy":1708},[898,85011,1895],{},[1693,85013,1695],{},[898,85015,2719],{},[1915,85017,2239],{},[1717,85019,85020,85022],{},[898,85021,6629],{},[895,85023,85024,85026,85028],{},[898,85025,207],{},[1693,85027,1892],{},[898,85029,1895],{},[1915,85031,2239],{},[1717,85033,85034,85036],{},[898,85035,4840],{},[898,85037,207],{},[1717,85039,85040,85042],{},[898,85041,4845],{},[898,85043,1895],{},[1693,85045,1695],{},[1717,85047,85048,85050],{},[898,85049,6629],{},[895,85051,85052,85054,85056],{},[898,85053,207],{},[1693,85055,1892],{},[898,85057,1895],{},[1915,85059,2239],{},[898,85061,1712],{},[1693,85063,1709],{"stretchy":1708},[898,85065,4840],{},[1693,85067,1899],{"separator":1898},[898,85069,4845],{},[1693,85071,1731],{"stretchy":1708},[898,85073,1789],{"mathvariant":1704},[3635,85075],{"width":34864},[3635,85077,85078],{},[1915,85079,85080],{},"(5.8)",[902,85082,85083],{"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}",[724,85085,85086,85087],{},"Volně: ",[38,85088,85089,85090,85103,85104,85128],{},"změní-li se vstupy ",[883,85091,85093],{"className":85092},[886],[888,85094,85095],{"xmlns":890},[892,85096,85097,85101],{},[895,85098,85099],{},[898,85100,6629],{},[902,85102,6629],{"encoding":904},"-krát, změní se výstup ",[883,85105,85107],{"className":85106},[886],[888,85108,85109],{"xmlns":890},[892,85110,85111,85125],{},[895,85112,85113],{},[1717,85114,85115,85117],{},[898,85116,6629],{},[895,85118,85119,85121,85123],{},[898,85120,207],{},[1693,85122,1892],{},[898,85124,1895],{},[902,85126,85127],{"encoding":904},"r^{a+b}","-krát.",[198,85130,85132],{"id":85131},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,85134,85135,85136,85153],{},"Součet exponentů ",[883,85137,85139],{"className":85138},[886],[888,85140,85141],{"xmlns":890},[892,85142,85143,85151],{},[895,85144,85145,85147,85149],{},[898,85146,207],{},[1693,85148,1892],{},[898,85150,1895],{},[902,85152,81535],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,85155,85156,85185],{},[19,85157,85158],{},[22,85159,85160,85163,85166,85183],{},[25,85161,85162],{},"Typ",[25,85164,85165],{},"Podmínka",[25,85167,85168,85169,85182],{},"Chování produkce při ",[883,85170,85172],{"className":85171},[886],[888,85173,85174],{"xmlns":890},[892,85175,85176,85180],{},[895,85177,85178],{},[898,85179,6629],{},[902,85181,6629],{"encoding":904},"-násobném zvýšení vstupů",[25,85184,9967],{},[30,85186,85187,85298,85413],{},[22,85188,85189,85197,85221,85254],{},[35,85190,82248,85191,16877,85194,1731],{},[38,85192,85193],{},"Konstantní",[614,85195,85196],{},"constant returns",[35,85198,85199],{},[883,85200,85202],{"className":85201},[886],[888,85203,85204],{"xmlns":890},[892,85205,85206,85218],{},[895,85207,85208,85210,85212,85214,85216],{},[898,85209,207],{},[1693,85211,1892],{},[898,85213,1895],{},[1693,85215,1695],{},[1762,85217,1764],{},[902,85219,85220],{"encoding":904},"a+b = 1",[35,85222,85223,85236,85237,1863,85240,85253],{},[883,85224,85226],{"className":85225},[886],[888,85227,85228],{"xmlns":890},[892,85229,85230,85234],{},[895,85231,85232],{},[898,85233,1712],{},[902,85235,1712],{"encoding":904}," vzroste ",[38,85238,85239],{},"přesně",[883,85241,85243],{"className":85242},[886],[888,85244,85245],{"xmlns":890},[892,85246,85247,85251],{},[895,85248,85249],{},[898,85250,6629],{},[902,85252,6629],{"encoding":904},"-krát",[35,85255,85256],{},[883,85257,85259],{"className":85258},[886],[888,85260,85261],{"xmlns":890},[892,85262,85263,85295],{},[895,85264,85265,85267,85269,85271,85283],{},[898,85266,1712],{},[1693,85268,1695],{},[1762,85270,2398],{},[1717,85272,85273,85275],{},[898,85274,4840],{},[895,85276,85277,85279,85281],{},[1762,85278,1764],{},[898,85280,1705],{"mathvariant":1704},[1762,85282,9262],{},[1717,85284,85285,85287],{},[898,85286,4845],{},[895,85288,85289,85291,85293],{},[1762,85290,8357],{},[898,85292,1705],{"mathvariant":1704},[1762,85294,9262],{},[902,85296,85297],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,85299,85300,85309,85333,85363],{},[35,85301,85302,85303,16877,85306,1731],{},"2° ",[38,85304,85305],{},"Rostoucí",[614,85307,85308],{},"increasing returns",[35,85310,85311],{},[883,85312,85314],{"className":85313},[886],[888,85315,85316],{"xmlns":890},[892,85317,85318,85330],{},[895,85319,85320,85322,85324,85326,85328],{},[898,85321,207],{},[1693,85323,1892],{},[898,85325,1895],{},[1693,85327,1922],{},[1762,85329,1764],{},[902,85331,85332],{"encoding":904},"a+b > 1",[35,85334,85335,85236,85348,57991,85350,85253],{},[883,85336,85338],{"className":85337},[886],[888,85339,85340],{"xmlns":890},[892,85341,85342,85346],{},[895,85343,85344],{},[898,85345,1712],{},[902,85347,1712],{"encoding":904},[38,85349,32063],{},[883,85351,85353],{"className":85352},[886],[888,85354,85355],{"xmlns":890},[892,85356,85357,85361],{},[895,85358,85359],{},[898,85360,6629],{},[902,85362,6629],{"encoding":904},[35,85364,85365,16877,85391,1731],{},[883,85366,85368],{"className":85367},[886],[888,85369,85370],{"xmlns":890},[892,85371,85372,85388],{},[895,85373,85374,85376,85378,85380,85382],{},[898,85375,1712],{},[1693,85377,1695],{},[1762,85379,31000],{},[898,85381,4840],{},[1717,85383,85384,85386],{},[898,85385,4845],{},[1762,85387,2398],{},[902,85389,85390],{"encoding":904},"Q = 7LK^2",[883,85392,85394],{"className":85393},[886],[888,85395,85396],{"xmlns":890},[892,85397,85398,85410],{},[895,85399,85400,85402,85404,85406,85408],{},[898,85401,207],{},[1693,85403,1892],{},[898,85405,1895],{},[1693,85407,1695],{},[1762,85409,8357],{},[902,85411,85412],{"encoding":904},"a+b = 3",[22,85414,85415,85424,85448,85479],{},[35,85416,85417,85418,16877,85421,1731],{},"3° ",[38,85419,85420],{},"Klesající",[614,85422,85423],{},"decreasing returns",[35,85425,85426],{},[883,85427,85429],{"className":85428},[886],[888,85430,85431],{"xmlns":890},[892,85432,85433,85445],{},[895,85434,85435,85437,85439,85441,85443],{},[898,85436,207],{},[1693,85438,1892],{},[898,85440,1895],{},[1693,85442,1908],{},[1762,85444,1764],{},[902,85446,85447],{"encoding":904},"a+b \u003C 1",[35,85449,85450,85236,85463,57991,85466,85253],{},[883,85451,85453],{"className":85452},[886],[888,85454,85455],{"xmlns":890},[892,85456,85457,85461],{},[895,85458,85459],{},[898,85460,1712],{},[902,85462,1712],{"encoding":904},[38,85464,85465],{},"méně",[883,85467,85469],{"className":85468},[886],[888,85470,85471],{"xmlns":890},[892,85472,85473,85477],{},[895,85474,85475],{},[898,85476,6629],{},[902,85478,6629],{"encoding":904},[35,85480,85481,16877,85511,1731],{},[883,85482,85484],{"className":85483},[886],[888,85485,85486],{"xmlns":890},[892,85487,85488,85508],{},[895,85489,85490,85492,85494,85496,85502],{},[898,85491,1712],{},[1693,85493,1695],{},[1762,85495,9763],{},[1717,85497,85498,85500],{},[898,85499,4840],{},[1762,85501,74927],{},[1717,85503,85504,85506],{},[898,85505,4845],{},[1762,85507,11877],{},[902,85509,85510],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,85512,85514],{"className":85513},[886],[888,85515,85516],{"xmlns":890},[892,85517,85518,85530],{},[895,85519,85520,85522,85524,85526,85528],{},[898,85521,207],{},[1693,85523,1892],{},[898,85525,1895],{},[1693,85527,1695],{},[1762,85529,21416],{},[902,85531,85532],{"encoding":904},"a+b = 0{,}8",[1636,85534,85535],{},[724,85536,85537,85539,85540,85557,85558,85561,85562,1863,85565,85601,85602,85624,85625,1789],{},[883,85538,8654],{}," Pozor\nSoučet ",[883,85541,85543],{"className":85542},[886],[888,85544,85545],{"xmlns":890},[892,85546,85547,85555],{},[895,85548,85549,85551,85553],{},[898,85550,207],{},[1693,85552,1892],{},[898,85554,1895],{},[902,85556,81535],{"encoding":904}," neudává velikost produkce, ale ",[38,85559,85560],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,85563,85564],{},"ryzí Cobb-Douglas",[883,85566,85568],{"className":85567},[886],[888,85569,85570],{"xmlns":890},[892,85571,85572,85598],{},[895,85573,85574,85576,85578,85580,85586],{},[898,85575,1712],{},[1693,85577,1695],{},[898,85579,2719],{},[1717,85581,85582,85584],{},[898,85583,4840],{},[898,85585,207],{},[1717,85587,85588,85590],{},[898,85589,4845],{},[895,85591,85592,85594,85596],{},[1762,85593,1764],{},[1693,85595,1698],{},[898,85597,207],{},[902,85599,85600],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,85603,85605],{"className":85604},[886],[888,85606,85607],{"xmlns":890},[892,85608,85609,85621],{},[895,85610,85611,85613,85615,85617,85619],{},[898,85612,1895],{},[1693,85614,1695],{},[1762,85616,1764],{},[1693,85618,1698],{},[898,85620,207],{},[902,85622,85623],{"encoding":904},"b = 1-a",", tedy vždy ",[38,85626,85627],{},"konstantní výnosy z rozsahu",[198,85629,85631,85632],{"id":85630},"parametr-efektivity-aa","Parametr efektivity ",[883,85633,85635],{"className":85634},[886],[888,85636,85637],{"xmlns":890},[892,85638,85639,85643],{},[895,85640,85641],{},[898,85642,2719],{},[902,85644,2719],{"encoding":904},[724,85646,85647,85648,85661,85662,85675,85676,85694,85695,85698],{},"Konstanta ",[883,85649,85651],{"className":85650},[886],[888,85652,85653],{"xmlns":890},[892,85654,85655,85659],{},[895,85656,85657],{},[898,85658,2719],{},[902,85660,2719],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,85663,85665],{"className":85664},[886],[888,85666,85667],{"xmlns":890},[892,85668,85669,85673],{},[895,85670,85671],{},[898,85672,1712],{},[902,85674,1712],{"encoding":904}," při pevně zadaných ",[883,85677,85679],{"className":85678},[886],[888,85680,85681],{"xmlns":890},[892,85682,85683,85691],{},[895,85684,85685,85687,85689],{},[898,85686,4840],{},[1693,85688,1899],{"separator":1898},[898,85690,4845],{},[902,85692,85693],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,85696,85697],{},"parametr efektivity"," — indikátor stavu technologie.",[198,85700,85702],{"id":85701},"příklad-53","Příklad 5.3",[724,85704,85705,85706,85601,85748,85750,85751,1789],{},"Produkční funkce ",[883,85707,85709],{"className":85708},[886],[888,85710,85711],{"xmlns":890},[892,85712,85713,85745],{},[895,85714,85715,85717,85719,85721,85733],{},[898,85716,1712],{},[1693,85718,1695],{},[1762,85720,2398],{},[1717,85722,85723,85725],{},[898,85724,4840],{},[895,85726,85727,85729,85731],{},[1762,85728,1764],{},[898,85730,1705],{"mathvariant":1704},[1762,85732,9262],{},[1717,85734,85735,85737],{},[898,85736,4845],{},[895,85738,85739,85741,85743],{},[1762,85740,8357],{},[898,85742,1705],{"mathvariant":1704},[1762,85744,9262],{},[902,85746,85747],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,85749,31412],{}," výnosy z rozsahu, neboť ",[883,85752,85754],{"className":85753},[886],[888,85755,85756],{"xmlns":890},[892,85757,85758,85782],{},[895,85759,85760,85768,85770,85778,85780],{},[3638,85761,85762],{"scriptlevel":1911,"displaystyle":1708},[2132,85763,85764,85766],{},[1762,85765,1764],{},[1762,85767,9262],{},[1693,85769,1892],{},[3638,85771,85772],{"scriptlevel":1911,"displaystyle":1708},[2132,85773,85774,85776],{},[1762,85775,8357],{},[1762,85777,9262],{},[1693,85779,1695],{},[1762,85781,1764],{},[902,85783,85784],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,85786,85787,85788,13055,85801,85814,85815,1863,85828,85868],{},"Změní-li se ",[883,85789,85791],{"className":85790},[886],[888,85792,85793],{"xmlns":890},[892,85794,85795,85799],{},[895,85796,85797],{},[898,85798,4840],{},[902,85800,4840],{"encoding":904},[883,85802,85804],{"className":85803},[886],[888,85805,85806],{"xmlns":890},[892,85807,85808,85812],{},[895,85809,85810],{},[898,85811,4845],{},[902,85813,4845],{"encoding":904}," čtyřnásobně, změní se ",[883,85816,85818],{"className":85817},[886],[888,85819,85820],{"xmlns":890},[892,85821,85822,85826],{},[895,85823,85824],{},[898,85825,1712],{},[902,85827,1712],{"encoding":904},[883,85829,85831],{"className":85830},[886],[888,85832,85833],{"xmlns":890},[892,85834,85835,85865],{},[895,85836,85837,85857,85859],{},[1717,85838,85839,85841],{},[1762,85840,9262],{},[895,85842,85843,85845,85847,85849,85851,85853,85855],{},[1762,85844,1764],{},[898,85846,1705],{"mathvariant":1704},[1762,85848,9262],{},[1693,85850,1892],{},[1762,85852,8357],{},[898,85854,1705],{"mathvariant":1704},[1762,85856,9262],{},[1693,85858,1695],{},[1717,85860,85861,85863],{},[1762,85862,9262],{},[1762,85864,1764],{},[902,85866,85867],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,85870,85872],{"className":85871},[886],[888,85873,85874],{"xmlns":890,"display":34854},[892,85875,85876,86036],{},[895,85877,85878,85880,85882,85884,85886,85888,85890,85892,85894,85896,85898,85900,85902,85904,85916,85918,85920,85922,85934,85936,85938,85940,85960,85972,85984,85986,85988,85990,85992,86004,86016,86018,86020,86022,86024,86026,86028,86030,86032,86034],{},[898,85879,1712],{},[1693,85881,1709],{"stretchy":1708},[1762,85883,9262],{},[898,85885,4840],{},[1693,85887,1899],{"separator":1898},[1762,85889,9262],{},[898,85891,4845],{},[1693,85893,1731],{"stretchy":1708},[1693,85895,1695],{},[1762,85897,2398],{},[1693,85899,1709],{"stretchy":1708},[1762,85901,9262],{},[898,85903,4840],{},[1717,85905,85906,85908],{},[1693,85907,1731],{"stretchy":1708},[895,85909,85910,85912,85914],{},[1762,85911,1764],{},[898,85913,1705],{"mathvariant":1704},[1762,85915,9262],{},[1693,85917,1709],{"stretchy":1708},[1762,85919,9262],{},[898,85921,4845],{},[1717,85923,85924,85926],{},[1693,85925,1731],{"stretchy":1708},[895,85927,85928,85930,85932],{},[1762,85929,8357],{},[898,85931,1705],{"mathvariant":1704},[1762,85933,9262],{},[1693,85935,1695],{},[1762,85937,2398],{},[1693,85939,1715],{},[1717,85941,85942,85944],{},[1762,85943,9262],{},[895,85945,85946,85948,85950,85952,85954,85956,85958],{},[1762,85947,1764],{},[898,85949,1705],{"mathvariant":1704},[1762,85951,9262],{},[1693,85953,1892],{},[1762,85955,8357],{},[898,85957,1705],{"mathvariant":1704},[1762,85959,9262],{},[1717,85961,85962,85964],{},[898,85963,4840],{},[895,85965,85966,85968,85970],{},[1762,85967,1764],{},[898,85969,1705],{"mathvariant":1704},[1762,85971,9262],{},[1717,85973,85974,85976],{},[898,85975,4845],{},[895,85977,85978,85980,85982],{},[1762,85979,8357],{},[898,85981,1705],{"mathvariant":1704},[1762,85983,9262],{},[1693,85985,1695],{},[1762,85987,9262],{},[1693,85989,1715],{},[1762,85991,2398],{},[1717,85993,85994,85996],{},[898,85995,4840],{},[895,85997,85998,86000,86002],{},[1762,85999,1764],{},[898,86001,1705],{"mathvariant":1704},[1762,86003,9262],{},[1717,86005,86006,86008],{},[898,86007,4845],{},[895,86009,86010,86012,86014],{},[1762,86011,8357],{},[898,86013,1705],{"mathvariant":1704},[1762,86015,9262],{},[1693,86017,1695],{},[1762,86019,9262],{},[1915,86021,2239],{},[898,86023,1712],{},[1693,86025,1709],{"stretchy":1708},[898,86027,4840],{},[1693,86029,1899],{"separator":1898},[898,86031,4845],{},[1693,86033,1731],{"stretchy":1708},[898,86035,1789],{"mathvariant":1704},[902,86037,86038],{"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).",[198,86040,86041],{"id":43956},"Homogenita",[724,86043,86044,86045,6055,86068,86084],{},"Funkce ",[883,86046,86048],{"className":86047},[886],[888,86049,86050],{"xmlns":890},[892,86051,86052,86066],{},[895,86053,86054,86056,86058,86060,86062,86064],{},[898,86055,1712],{},[1693,86057,1709],{"stretchy":1708},[898,86059,4840],{},[1693,86061,1899],{"separator":1898},[898,86063,4845],{},[1693,86065,1731],{"stretchy":1708},[902,86067,16849],{"encoding":904},[38,86069,86070,86071],{},"homogenní stupně ",[883,86072,86074],{"className":86073},[886],[888,86075,86076],{"xmlns":890},[892,86077,86078,86082],{},[895,86079,86080],{},[898,86081,5362],{},[902,86083,5362],{"encoding":904},", jestliže",[883,86086,86088],{"className":86087},[886],[888,86089,86090],{"xmlns":890,"display":34854},[892,86091,86092,86149],{},[3626,86093,86094],{"width":34859},[3632,86095,86096,86098,86142,86144],{},[3635,86097],{"width":34864},[3635,86099,86100],{},[895,86101,86102,86104,86106,86108,86110,86112,86114,86116,86118,86120,86126,86128,86130,86132,86134,86136,86138,86140],{},[898,86103,1712],{},[1693,86105,1709],{"stretchy":1708},[898,86107,6629],{},[898,86109,4840],{},[1693,86111,1899],{"separator":1898},[898,86113,6629],{},[898,86115,4845],{},[1693,86117,1731],{"stretchy":1708},[1693,86119,1695],{},[1717,86121,86122,86124],{},[898,86123,6629],{},[898,86125,5362],{},[1915,86127,2239],{},[898,86129,1712],{},[1693,86131,1709],{"stretchy":1708},[898,86133,4840],{},[1693,86135,1899],{"separator":1898},[898,86137,4845],{},[1693,86139,1731],{"stretchy":1708},[1693,86141,1899],{"separator":1898},[3635,86143],{"width":34864},[3635,86145,86146],{},[1915,86147,86148],{},"(5.10)",[902,86150,86151],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,86153,11188,86154,86172,86173,86191,86192,50402,86205,86208,86209,1789],{},[883,86155,86157],{"className":86156},[886],[888,86158,86159],{"xmlns":890},[892,86160,86161,86169],{},[895,86162,86163,86165,86167],{},[898,86164,5362],{},[1693,86166,3665],{},[1762,86168,1911],{},[902,86170,86171],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,86174,86176],{"className":86175},[886],[888,86177,86178],{"xmlns":890},[892,86179,86180,86188],{},[895,86181,86182,86184,86186],{},[898,86183,6629],{},[1693,86185,1922],{},[1762,86187,1911],{},[902,86189,86190],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,86193,86195],{"className":86194},[886],[888,86196,86197],{"xmlns":890},[892,86198,86199,86203],{},[895,86200,86201],{},[1762,86202,1764],{},[902,86204,1764],{"encoding":904},[38,86206,86207],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,86210,86212],{"className":86211},[886],[888,86213,86214],{"xmlns":890},[892,86215,86216,86224],{},[895,86217,86218,86220,86222],{},[898,86219,207],{},[1693,86221,1892],{},[898,86223,1895],{},[902,86225,81535],{"encoding":904},[115,86227,86229],{"id":86228},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,86231,86232],{},[38,86233,86234],{},"Ryzí Cobb-Douglasovy funkce:",[883,86236,86238],{"className":86237},[886],[888,86239,86240],{"xmlns":890,"display":34854},[892,86241,86242,86301],{},[3626,86243,86244],{"width":34859},[3632,86245,86246,86248,86294,86296],{},[3635,86247],{"width":34864},[3635,86249,86250],{},[895,86251,86252,86254,86256,86258,86260,86266,86268,86280,86282,86284,86286,86288,86290,86292],{},[898,86253,1712],{},[1693,86255,1695],{},[898,86257,2719],{},[1915,86259,2239],{},[1717,86261,86262,86264],{},[898,86263,4840],{},[898,86265,207],{},[1915,86267,2239],{},[1717,86269,86270,86272],{},[898,86271,4845],{},[895,86273,86274,86276,86278],{},[1762,86275,1764],{},[1693,86277,1698],{},[898,86279,207],{},[1693,86281,1899],{"separator":1898},[1901,86283],{"width":3630},[1762,86285,1911],{},[1693,86287,1908],{},[898,86289,207],{},[1693,86291,1908],{},[1762,86293,20091],{},[3635,86295],{"width":34864},[3635,86297,86298],{},[1915,86299,86300],{},"(5.9)",[902,86302,86303],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,86305,86306,86307,86309,86310,1789],{},"Mají vždy ",[38,86308,85627],{}," a jsou ",[38,86311,86207],{},[724,86313,86314,16877,86317,86320],{},[38,86315,86316],{},"CES produkční funkce",[614,86318,86319],{},"Constant Elasticity of Substitution",", 1961):",[883,86322,86324],{"className":86323},[886],[888,86325,86326],{"xmlns":890,"display":34854},[892,86327,86328,86396],{},[895,86329,86330,86332,86334,86336,86394],{},[898,86331,1712],{},[1693,86333,1695],{},[898,86335,2719],{},[1717,86337,86338,86382],{},[895,86339,86340,86342,86344,86346,86348,86350,86352,86354,86364,86366,86368,86370,86380],{},[1693,86341,9392],{"fence":1898},[1693,86343,1709],{"stretchy":1708},[1762,86345,1764],{},[1693,86347,1698],{},[898,86349,207],{},[1693,86351,1731],{"stretchy":1708},[1915,86353,2239],{},[1717,86355,86356,86358],{},[898,86357,4840],{},[895,86359,86360,86362],{},[1693,86361,1698],{},[898,86363,1895],{},[1693,86365,1892],{},[898,86367,207],{},[1915,86369,2239],{},[1717,86371,86372,86374],{},[898,86373,4845],{},[895,86375,86376,86378],{},[1693,86377,1698],{},[898,86379,1895],{},[1693,86381,9407],{"fence":1898},[895,86383,86384,86386],{},[1693,86385,1698],{},[3638,86387,86388],{"scriptlevel":1911,"displaystyle":1708},[2132,86389,86390,86392],{},[1762,86391,1764],{},[898,86393,1895],{},[1693,86395,1899],{"separator":1898},[902,86397,86398],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,86400,11188,86401,1343,86419,1343,86440,86464],{},[883,86402,86404],{"className":86403},[886],[888,86405,86406],{"xmlns":890},[892,86407,86408,86416],{},[895,86409,86410,86412,86414],{},[898,86411,2719],{},[1693,86413,1922],{},[1762,86415,1911],{},[902,86417,86418],{"encoding":904},"A > 0",[883,86420,86422],{"className":86421},[886],[888,86423,86424],{"xmlns":890},[892,86425,86426,86438],{},[895,86427,86428,86430,86432,86434,86436],{},[1762,86429,1911],{},[1693,86431,1908],{},[898,86433,207],{},[1693,86435,1908],{},[1762,86437,1764],{},[902,86439,7139],{"encoding":904},[883,86441,86443],{"className":86442},[886],[888,86444,86445],{"xmlns":890},[892,86446,86447,86461],{},[895,86448,86449,86451,86453,86455,86457,86459],{},[1693,86450,1698],{},[1762,86452,1764],{},[1693,86454,1908],{},[898,86456,1895],{},[1693,86458,10266],{"mathvariant":1704},[1762,86460,1911],{},[902,86462,86463],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,86466,86467],{},[38,86468,86469],{},"Další typy:",[120,86471,86472,86514],{},[123,86473,86474,1863,86477,86513],{},[38,86475,86476],{},"Lineární:",[883,86478,86480],{"className":86479},[886],[888,86481,86482],{"xmlns":890},[892,86483,86484,86510],{},[895,86485,86486,86488,86490,86492,86494,86496,86498,86500,86502,86504,86506,86508],{},[898,86487,1712],{},[1693,86489,1709],{"stretchy":1708},[898,86491,4840],{},[1693,86493,1899],{"separator":1898},[898,86495,4845],{},[1693,86497,1731],{"stretchy":1708},[1693,86499,1695],{},[898,86501,207],{},[898,86503,4840],{},[1693,86505,1892],{},[898,86507,1895],{},[898,86509,4845],{},[902,86511,86512],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,86515,86516,1863,86519,86563],{},[38,86517,86518],{},"Leontiefova:",[883,86520,86522],{"className":86521},[886],[888,86523,86524],{"xmlns":890},[892,86525,86526,86560],{},[895,86527,86528,86530,86532,86534,86536,86538,86540,86542,86544,86546,86548,86550,86552,86554,86556,86558],{},[898,86529,1712],{},[1693,86531,1709],{"stretchy":1708},[898,86533,4840],{},[1693,86535,1899],{"separator":1898},[898,86537,4845],{},[1693,86539,1731],{"stretchy":1708},[1693,86541,1695],{},[898,86543,3739],{},[1693,86545,3742],{},[1693,86547,1709],{"stretchy":1708},[898,86549,207],{},[898,86551,4840],{},[1693,86553,1899],{"separator":1898},[898,86555,1895],{},[898,86557,4845],{},[1693,86559,1731],{"stretchy":1708},[902,86561,86562],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,86565,86567,86568,1343,86587,86606],{"id":86566},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,86569,86571],{"className":86570},[886],[888,86572,86573],{"xmlns":890},[892,86574,86575,86585],{},[895,86576,86577,86579],{},[898,86578,2839],{},[3284,86580,86581,86583],{},[898,86582,1701],{},[898,86584,4840],{},[902,86586,4964],{"encoding":904},[883,86588,86590],{"className":86589},[886],[888,86591,86592],{"xmlns":890},[892,86593,86594,86604],{},[895,86595,86596,86598],{},[898,86597,2839],{},[3284,86599,86600,86602],{},[898,86601,1701],{},[898,86603,4845],{},[902,86605,16941],{"encoding":904}," a totální diferenciál",[724,86608,86609],{},[38,86610,86611],{},"Mezní produkt práce:",[883,86613,86615],{"className":86614},[886],[888,86616,86617],{"xmlns":890,"display":34854},[892,86618,86619,86657],{},[895,86620,86621,86623,86629,86631,86639,86641,86655],{},[898,86622,2839],{},[3284,86624,86625,86627],{},[898,86626,1701],{},[898,86628,4840],{},[1693,86630,1695],{},[5688,86632,86633,86635,86637],{},[898,86634,1712],{},[898,86636,4840],{},[1693,86638,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,86640,1695],{},[2132,86642,86643,86649],{},[895,86644,86645,86647],{},[898,86646,2228],{"mathvariant":1704},[898,86648,1712],{},[895,86650,86651,86653],{},[898,86652,2228],{"mathvariant":1704},[898,86654,4840],{},[898,86656,1789],{"mathvariant":1704},[902,86658,86659],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,86661,86662],{},[38,86663,86664],{},"Mezní produkt kapitálu:",[883,86666,86668],{"className":86667},[886],[888,86669,86670],{"xmlns":890,"display":34854},[892,86671,86672,86710],{},[895,86673,86674,86676,86682,86684,86692,86694,86708],{},[898,86675,2839],{},[3284,86677,86678,86680],{},[898,86679,1701],{},[898,86681,4845],{},[1693,86683,1695],{},[5688,86685,86686,86688,86690],{},[898,86687,1712],{},[898,86689,4845],{},[1693,86691,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,86693,1695],{},[2132,86695,86696,86702],{},[895,86697,86698,86700],{},[898,86699,2228],{"mathvariant":1704},[898,86701,1712],{},[895,86703,86704,86706],{},[898,86705,2228],{"mathvariant":1704},[898,86707,4845],{},[898,86709,1789],{"mathvariant":1704},[902,86711,86712],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,86714,86715,86745,86746,86767,86768,86786,86787,86800,86801,1789],{},[883,86716,86718],{"className":86717},[886],[888,86719,86720],{"xmlns":890},[892,86721,86722,86742],{},[895,86723,86724,86726,86732,86734,86736,86738,86740],{},[898,86725,2839],{},[3284,86727,86728,86730],{},[898,86729,1701],{},[898,86731,4840],{},[1693,86733,1709],{"stretchy":1708},[898,86735,207],{},[1693,86737,1899],{"separator":1898},[898,86739,1895],{},[1693,86741,1731],{"stretchy":1708},[902,86743,86744],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,86747,86749],{"className":86748},[886],[888,86750,86751],{"xmlns":890},[892,86752,86753,86765],{},[895,86754,86755,86757,86759,86761,86763],{},[1693,86756,9392],{"stretchy":1708},[898,86758,207],{},[1693,86760,1899],{"separator":1898},[898,86762,1895],{},[1693,86764,9407],{"stretchy":1708},[902,86766,17670],{"encoding":904}," (na hladině ",[883,86769,86771],{"className":86770},[886],[888,86772,86773],{"xmlns":890},[892,86774,86775,86783],{},[895,86776,86777,86779,86781],{},[898,86778,4845],{},[1693,86780,1695],{},[898,86782,1895],{},[902,86784,86785],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,86788,86790],{"className":86789},[886],[888,86791,86792],{"xmlns":890},[892,86793,86794,86798],{},[895,86795,86796],{},[898,86797,4840],{},[902,86799,4840],{"encoding":904},". Analogicky ",[883,86802,86804],{"className":86803},[886],[888,86805,86806],{"xmlns":890},[892,86807,86808,86828],{},[895,86809,86810,86812,86818,86820,86822,86824,86826],{},[898,86811,2839],{},[3284,86813,86814,86816],{},[898,86815,1701],{},[898,86817,4845],{},[1693,86819,1709],{"stretchy":1708},[898,86821,207],{},[1693,86823,1899],{"separator":1898},[898,86825,1895],{},[1693,86827,1731],{"stretchy":1708},[902,86829,86830],{"encoding":904},"MP_K(a, b)",[1636,86832,86833,86837],{},[724,86834,86835,57979],{},[883,86836,11036],{},[120,86838,86839,86877],{},[123,86840,86841,32979,86860],{},[883,86842,86844],{"className":86843},[886],[888,86845,86846],{"xmlns":890},[892,86847,86848,86858],{},[895,86849,86850,86852],{},[898,86851,2839],{},[3284,86853,86854,86856],{},[898,86855,1701],{},[898,86857,4840],{},[902,86859,4964],{"encoding":904},[614,86861,86862,86863,86876],{},"„o kolik vzroste ",[883,86864,86866],{"className":86865},[886],[888,86867,86868],{"xmlns":890},[892,86869,86870,86874],{},[895,86871,86872],{},[898,86873,1712],{},[902,86875,1712],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,86878,86879,32979,86898],{},[883,86880,86882],{"className":86881},[886],[888,86883,86884],{"xmlns":890},[892,86885,86886,86896],{},[895,86887,86888,86890],{},[898,86889,2839],{},[3284,86891,86892,86894],{},[898,86893,1701],{},[898,86895,4845],{},[902,86897,16941],{"encoding":904},[614,86899,86862,86900,86913],{},[883,86901,86903],{"className":86902},[886],[888,86904,86905],{"xmlns":890},[892,86906,86907,86911],{},[895,86908,86909],{},[898,86910,1712],{},[902,86912,1712],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,86915,86916,86919,86920,86935,86936,4300],{},[38,86917,86918],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,86921,86923],{"className":86922},[886],[888,86924,86925],{"xmlns":890},[892,86926,86927,86933],{},[895,86928,86929,86931],{},[898,86930,1771],{},[898,86932,4840],{},[902,86934,82067],{"encoding":904}," a kapitálu o ",[883,86937,86939],{"className":86938},[886],[888,86940,86941],{"xmlns":890},[892,86942,86943,86949],{},[895,86944,86945,86947],{},[898,86946,1771],{},[898,86948,4845],{},[902,86950,86951],{"encoding":904},"dK",[883,86953,86955],{"className":86954},[886],[888,86956,86957],{"xmlns":890,"display":34854},[892,86958,86959,87052],{},[3626,86960,86961],{"width":34859},[3632,86962,86963,86965,87045,87047],{},[3635,86964],{"width":34864},[3635,86966,86967],{},[895,86968,86969,86971,86973,86975,86977,86979,86981,86989,86991,86993,86995,86997,87005,87007,87009,87011,87013,87015,87021,87023,87025,87027,87029,87031,87037,87039,87041,87043],{},[898,86970,3890],{"mathvariant":1704},[898,86972,1712],{},[1693,86974,4110],{},[898,86976,1771],{},[898,86978,1712],{},[1693,86980,1695],{},[5688,86982,86983,86985,86987],{},[898,86984,1712],{},[898,86986,4840],{},[1693,86988,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,86990,2239],{},[898,86992,1771],{},[898,86994,4840],{},[1693,86996,1892],{},[5688,86998,86999,87001,87003],{},[898,87000,1712],{},[898,87002,4845],{},[1693,87004,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1915,87006,2239],{},[898,87008,1771],{},[898,87010,4845],{},[1693,87012,1695],{},[898,87014,2839],{},[3284,87016,87017,87019],{},[898,87018,1701],{},[898,87020,4840],{},[1915,87022,2239],{},[898,87024,1771],{},[898,87026,4840],{},[1693,87028,1892],{},[898,87030,2839],{},[3284,87032,87033,87035],{},[898,87034,1701],{},[898,87036,4845],{},[1915,87038,2239],{},[898,87040,1771],{},[898,87042,4845],{},[898,87044,1789],{"mathvariant":1704},[3635,87046],{"width":34864},[3635,87048,87049],{},[1915,87050,87051],{},"(5.11)",[902,87053,87054],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,87056,87057,87058,1789],{},"Skutečná změna: ",[883,87059,87061],{"className":87060},[886],[888,87062,87063],{"xmlns":890},[892,87064,87065,87111],{},[895,87066,87067,87069,87071,87073,87075,87077,87079,87081,87083,87085,87087,87089,87091,87093,87095,87097,87099,87101,87103,87105,87107,87109],{},[898,87068,3890],{"mathvariant":1704},[898,87070,1712],{},[1693,87072,1695],{},[898,87074,1712],{},[1693,87076,1709],{"stretchy":1708},[898,87078,4840],{},[1693,87080,1892],{},[898,87082,1771],{},[898,87084,4840],{},[1693,87086,1899],{"separator":1898},[898,87088,4845],{},[1693,87090,1892],{},[898,87092,1771],{},[898,87094,4845],{},[1693,87096,1731],{"stretchy":1708},[1693,87098,1698],{},[898,87100,1712],{},[1693,87102,1709],{"stretchy":1708},[898,87104,4840],{},[1693,87106,1899],{"separator":1898},[898,87108,4845],{},[1693,87110,1731],{"stretchy":1708},[902,87112,87113],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,87115,87116,87118,87119,87137,87138,87151,87152,87171,87172,87204,87205,87237,87238,1789],{},[38,87117,82231],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,87120,87122],{"className":87121},[886],[888,87123,87124],{"xmlns":890},[892,87125,87126,87134],{},[895,87127,87128],{},[3284,87129,87130,87132],{},[898,87131,4845],{},[1762,87133,1911],{},[902,87135,87136],{"encoding":904},"K_0"," se od jistého ",[883,87139,87141],{"className":87140},[886],[888,87142,87143],{"xmlns":890},[892,87144,87145,87149],{},[895,87146,87147],{},[898,87148,4840],{},[902,87150,4840],{"encoding":904}," stane ",[883,87153,87155],{"className":87154},[886],[888,87156,87157],{"xmlns":890},[892,87158,87159,87169],{},[895,87160,87161,87163],{},[898,87162,2839],{},[3284,87164,87165,87167],{},[898,87166,1701],{},[898,87168,4840],{},[902,87170,4964],{"encoding":904}," klesající (",[883,87173,87175],{"className":87174},[886],[888,87176,87177],{"xmlns":890},[892,87178,87179,87201],{},[895,87180,87181,87197,87199],{},[5688,87182,87183,87185,87191],{},[898,87184,1712],{},[895,87186,87187,87189],{},[898,87188,4840],{},[898,87190,4840],{},[895,87192,87193,87195],{},[1693,87194,1724],{"mathvariant":1704},[1693,87196,1724],{"mathvariant":1704},[1693,87198,1908],{},[1762,87200,1911],{},[902,87202,87203],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,87206,87208],{"className":87207},[886],[888,87209,87210],{"xmlns":890},[892,87211,87212,87234],{},[895,87213,87214,87230,87232],{},[5688,87215,87216,87218,87224],{},[898,87217,1712],{},[895,87219,87220,87222],{},[898,87221,4845],{},[898,87223,4845],{},[895,87225,87226,87228],{},[1693,87227,1724],{"mathvariant":1704},[1693,87229,1724],{"mathvariant":1704},[1693,87231,1908],{},[1762,87233,1911],{},[902,87235,87236],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,87239,87241],{"className":87240},[886],[888,87242,87243],{"xmlns":890},[892,87244,87245,87253],{},[895,87246,87247],{},[3284,87248,87249,87251],{},[898,87250,4840],{},[1762,87252,1911],{},[902,87254,82269],{"encoding":904},[115,87256,5320],{"id":5319},[724,87258,87259,87262,87263,87286,87287,36727],{},[38,87260,87261],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,87264,87266],{"className":87265},[886],[888,87267,87268],{"xmlns":890},[892,87269,87270,87284],{},[895,87271,87272,87274,87276,87278,87280,87282],{},[898,87273,1712],{},[1693,87275,1709],{"stretchy":1708},[898,87277,4840],{},[1693,87279,1899],{"separator":1898},[898,87281,4845],{},[1693,87283,1731],{"stretchy":1708},[902,87285,16849],{"encoding":904}," stupně ",[883,87288,87290],{"className":87289},[886],[888,87291,87292],{"xmlns":890},[892,87293,87294,87298],{},[895,87295,87296],{},[898,87297,5362],{},[902,87299,5362],{"encoding":904},[883,87301,87303],{"className":87302},[886],[888,87304,87305],{"xmlns":890,"display":34854},[892,87306,87307,87370],{},[3626,87308,87309],{"width":34859},[3632,87310,87311,87313,87363,87365],{},[3635,87312],{"width":34864},[3635,87314,87315],{},[895,87316,87317,87319,87321,87329,87331,87333,87335,87343,87345,87347,87349,87351,87353,87355,87357,87359,87361],{},[898,87318,4840],{},[1915,87320,2239],{},[5688,87322,87323,87325,87327],{},[898,87324,1712],{},[898,87326,4840],{},[1693,87328,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,87330,1892],{},[898,87332,4845],{},[1915,87334,2239],{},[5688,87336,87337,87339,87341],{},[898,87338,1712],{},[898,87340,4845],{},[1693,87342,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,87344,1695],{},[898,87346,5362],{},[1915,87348,2239],{},[898,87350,1712],{},[1693,87352,1709],{"stretchy":1708},[898,87354,4840],{},[1693,87356,1899],{"separator":1898},[898,87358,4845],{},[1693,87360,1731],{"stretchy":1708},[898,87362,1789],{"mathvariant":1704},[3635,87364],{"width":34864},[3635,87366,87367],{},[1915,87368,87369],{},"(5.12)",[902,87371,87372],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,87374,87375,87395],{},[38,87376,87377,87378],{},"Speciální případ ",[883,87379,87381],{"className":87380},[886],[888,87382,87383],{"xmlns":890},[892,87384,87385,87393],{},[895,87386,87387,87389,87391],{},[898,87388,5362],{},[1693,87390,1695],{},[1762,87392,1764],{},[902,87394,5443],{"encoding":904}," (konstantní výnosy z rozsahu):",[883,87397,87399],{"className":87398},[886],[888,87400,87401],{"xmlns":890,"display":34854},[892,87402,87403,87447],{},[895,87404,87405,87407,87409,87411,87417,87419,87421,87423,87425,87431,87433,87435,87437,87439,87441,87443,87445],{},[898,87406,4840],{},[1693,87408,1715],{},[898,87410,2839],{},[3284,87412,87413,87415],{},[898,87414,1701],{},[898,87416,4840],{},[1693,87418,1892],{},[898,87420,4845],{},[1693,87422,1715],{},[898,87424,2839],{},[3284,87426,87427,87429],{},[898,87428,1701],{},[898,87430,4845],{},[1693,87432,1695],{},[898,87434,1712],{},[1693,87436,1709],{"stretchy":1708},[898,87438,4840],{},[1693,87440,1899],{"separator":1898},[898,87442,4845],{},[1693,87444,1731],{"stretchy":1708},[898,87446,1789],{"mathvariant":1704},[902,87448,87449],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,87451,87452,87453,87456],{},"Slovně — ",[38,87454,87455],{},"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).",[115,87458,16633],{"id":81605},[724,87460,87461,16877,87463,87466,87467,87489,87490,4300],{},[38,87462,16633],{},[614,87464,87465],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,87468,87470],{"className":87469},[886],[888,87471,87472],{"xmlns":890},[892,87473,87474,87486],{},[895,87475,87476,87478,87480,87482,87484],{},[1693,87477,9392],{"stretchy":1708},[898,87479,4840],{},[1693,87481,1899],{"separator":1898},[898,87483,4845],{},[1693,87485,9407],{"stretchy":1708},[902,87487,87488],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,87491,87493],{"className":87492},[886],[888,87494,87495],{"xmlns":890},[892,87496,87497,87502],{},[895,87498,87499],{},[898,87500,87501],{},"q",[902,87503,87501],{"encoding":904},[883,87505,87507],{"className":87506},[886],[888,87508,87509],{"xmlns":890,"display":34854},[892,87510,87511,87546],{},[3626,87512,87513],{"width":34859},[3632,87514,87515,87517,87539,87541],{},[3635,87516],{"width":34864},[3635,87518,87519],{},[895,87520,87521,87523,87525,87527,87529,87531,87533,87535,87537],{},[898,87522,1712],{},[1693,87524,1709],{"stretchy":1708},[898,87526,4840],{},[1693,87528,1899],{"separator":1898},[898,87530,4845],{},[1693,87532,1731],{"stretchy":1708},[1693,87534,1695],{},[898,87536,87501],{},[898,87538,1789],{"mathvariant":1704},[3635,87540],{"width":34864},[3635,87542,87543],{},[1915,87544,87545],{},"(5.13)",[902,87547,87548],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,87550,87551,87552,87555,87556,3042],{},"Jsou to ",[38,87553,87554],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,87557,87559],{"className":87558,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,87561,87562],{},[38,87563,87564],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,87566,87567,87572,87577,87582],{},[123,87568,87569,87571],{},[38,87570,5676],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,87573,87574,87576],{},[38,87575,44441],{}," (úloha 5.14);",[123,87578,87579,15283],{},[38,87580,87581],{},"neprotínají se",[123,87583,87584,87585,2783,87598,1789],{},"s rostoucím ",[883,87586,87588],{"className":87587},[886],[888,87589,87590],{"xmlns":890},[892,87591,87592,87596],{},[895,87593,87594],{},[898,87595,87501],{},[902,87597,87501],{"encoding":904},[38,87599,87600],{},"vzdalují od počátku",[724,87602,87603],{},[614,87604,87605,87606,87628,87629,1789],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,87607,87609],{"className":87608},[886],[888,87610,87611],{"xmlns":890},[892,87612,87613,87625],{},[895,87614,87615,87617,87619,87621,87623],{},[1693,87616,1709],{"stretchy":1708},[898,87618,4840],{},[1693,87620,1899],{"separator":1898},[898,87622,4845],{},[1693,87624,1731],{"stretchy":1708},[902,87626,87627],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,87630,87632],{"className":87631},[886],[888,87633,87634],{"xmlns":890},[892,87635,87636,87660],{},[895,87637,87638,87644,87646,87652,87654],{},[3284,87639,87640,87642],{},[898,87641,87501],{},[1762,87643,1764],{},[1693,87645,1908],{},[3284,87647,87648,87650],{},[898,87649,87501],{},[1762,87651,1911],{},[1693,87653,1908],{},[3284,87655,87656,87658],{},[898,87657,87501],{},[1762,87659,2398],{},[902,87661,87662],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,87664,87666,87667,1731],{"id":87665},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,87668,87670],{"className":87669},[886],[888,87671,87672],{"xmlns":890},[892,87673,87674,87684],{},[895,87675,87676,87678,87680,87682],{},[898,87677,2839],{},[898,87679,2666],{},[898,87681,2663],{},[898,87683,3611],{},[902,87685,5814],{"encoding":904},[724,87687,87688,16877,87690,87693],{},[38,87689,5255],{},[614,87691,87692],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,87695,87697],{"className":87696},[886],[888,87698,87699],{"xmlns":890,"display":34854},[892,87700,87701,87792],{},[3626,87702,87703],{"width":34859},[3632,87704,87705,87707,87785,87787],{},[3635,87706],{"width":34864},[3635,87708,87709],{},[895,87710,87711,87713,87715,87717,87719,87721,87723,87725,87727,87729,87731,87733,87735,87737,87739,87741,87763,87765,87783],{},[898,87712,2839],{},[898,87714,2666],{},[898,87716,2663],{},[898,87718,3611],{},[1693,87720,1695],{},[898,87722,2839],{},[898,87724,2666],{},[898,87726,2663],{},[898,87728,3611],{},[1693,87730,1709],{"stretchy":1708},[898,87732,4840],{},[1693,87734,1899],{"separator":1898},[898,87736,4845],{},[1693,87738,1731],{"stretchy":1708},[1693,87740,1695],{},[2132,87742,87743,87753],{},[895,87744,87745,87747],{},[898,87746,2839],{},[3284,87748,87749,87751],{},[898,87750,1701],{},[898,87752,4840],{},[895,87754,87755,87757],{},[898,87756,2839],{},[3284,87758,87759,87761],{},[898,87760,1701],{},[898,87762,4845],{},[1693,87764,1695],{},[2132,87766,87767,87775],{},[5688,87768,87769,87771,87773],{},[898,87770,1712],{},[898,87772,4840],{},[1693,87774,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,87776,87777,87779,87781],{},[898,87778,1712],{},[898,87780,4845],{},[1693,87782,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[898,87784,1789],{"mathvariant":1704},[3635,87786],{"width":34864},[3635,87788,87789],{},[1915,87790,87791],{},"(5.14)",[902,87793,87794],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,87796,87797,1863,87799,87829,87830,87861],{},[38,87798,16071],{},[883,87800,87802],{"className":87801},[886],[888,87803,87804],{"xmlns":890},[892,87805,87806,87826],{},[895,87807,87808,87810,87812,87814,87816,87818,87820,87822,87824],{},[898,87809,2839],{},[898,87811,2666],{},[898,87813,2663],{},[898,87815,3611],{},[1693,87817,1709],{"stretchy":1708},[898,87819,4840],{},[1693,87821,1899],{"separator":1898},[898,87823,4845],{},[1693,87825,1731],{"stretchy":1708},[902,87827,87828],{"encoding":904},"MRTS(L, K)"," udává, ",[38,87831,87832,87833,87846,87847,87860],{},"o kolik se musí přibližně změnit kapitál ",[883,87834,87836],{"className":87835},[886],[888,87837,87838],{"xmlns":890},[892,87839,87840,87844],{},[895,87841,87842],{},[898,87843,4845],{},[902,87845,4845],{"encoding":904},", jestliže se práce ",[883,87848,87850],{"className":87849},[886],[888,87851,87852],{"xmlns":890},[892,87853,87854,87858],{},[895,87855,87856],{},[898,87857,4840],{},[902,87859,4840],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1636,87863,87864],{},[724,87865,87866,24841,87868,87887,87888,87925,87926,87929,87930,87934],{},[883,87867,11036],{},[883,87869,87871],{"className":87870},[886],[888,87872,87873],{"xmlns":890},[892,87874,87875,87885],{},[895,87876,87877,87879,87881,87883],{},[898,87878,2839],{},[898,87880,2666],{},[898,87882,2663],{},[898,87884,3611],{},[902,87886,5814],{"encoding":904}," říká: ",[614,87889,87890,87891,87910,87911,87924],{},"„jednu jednotku práce musím nahradit přibližně ",[883,87892,87894],{"className":87893},[886],[888,87895,87896],{"xmlns":890},[892,87897,87898,87908],{},[895,87899,87900,87902,87904,87906],{},[898,87901,2839],{},[898,87903,2666],{},[898,87905,2663],{},[898,87907,3611],{},[902,87909,5814],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,87912,87914],{"className":87913},[886],[888,87915,87916],{"xmlns":890},[892,87917,87918,87922],{},[895,87919,87920],{},[898,87921,1712],{},[902,87923,1712],{"encoding":904}," zůstala stejná.\""," Je to ",[38,87927,87928],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,87931,87933],{"className":87932,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,87936,87937],{},[9465,87938],{"alt":87939,"className":87940,"src":87941},"imek-izokvanty-mrts",[210,9469],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,87943,87944,87947,87948,6055,87978,88000,88001,10048],{},[38,87945,87946],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,87949,87951],{"className":87950},[886],[888,87952,87953],{"xmlns":890},[892,87954,87955,87975],{},[895,87956,87957,87959,87965,87967,87973],{},[1693,87958,9392],{"stretchy":1708},[3284,87960,87961,87963],{},[898,87962,4840],{},[1762,87964,1911],{},[1693,87966,1899],{"separator":1898},[3284,87968,87969,87971],{},[898,87970,4845],{},[1762,87972,1911],{},[1693,87974,9407],{"stretchy":1708},[902,87976,87977],{"encoding":904},"[L_0, K_0]",[883,87979,87981],{"className":87980},[886],[888,87982,87983],{"xmlns":890},[892,87984,87985,87997],{},[895,87986,87987,87989,87991,87993,87995],{},[1693,87988,1698],{},[898,87990,2839],{},[898,87992,2666],{},[898,87994,2663],{},[898,87996,3611],{},[902,87998,87999],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,88002,88004],{"className":88003},[886],[888,88005,88006],{"xmlns":890},[892,88007,88008,88030],{},[895,88009,88010,88012,88014,88016,88018,88020,88022,88024],{},[898,88011,1712],{},[1693,88013,1709],{"stretchy":1708},[898,88015,4840],{},[1693,88017,1899],{"separator":1898},[898,88019,4845],{},[1693,88021,1731],{"stretchy":1708},[1693,88023,1695],{},[3284,88025,88026,88028],{},[898,88027,87501],{},[1762,88029,1911],{},[902,88031,88032],{"encoding":904},"Q(L,K) = q_0",[883,88034,88036],{"className":88035},[886],[888,88037,88038],{"xmlns":890,"display":34854},[892,88039,88040,88092],{},[895,88041,88042,88056,88058,88060,88078,88080,88082,88084,88086,88088,88090],{},[2132,88043,88044,88050],{},[895,88045,88046,88048],{},[898,88047,1771],{},[898,88049,4845],{},[895,88051,88052,88054],{},[898,88053,1771],{},[898,88055,4840],{},[1693,88057,1695],{},[1693,88059,1698],{},[2132,88061,88062,88070],{},[5688,88063,88064,88066,88068],{},[898,88065,1712],{},[898,88067,4840],{},[1693,88069,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,88071,88072,88074,88076],{},[898,88073,1712],{},[898,88075,4845],{},[1693,88077,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,88079,1695],{},[1693,88081,1698],{},[898,88083,2839],{},[898,88085,2666],{},[898,88087,2663],{},[898,88089,3611],{},[898,88091,1789],{"mathvariant":1704},[902,88093,88094],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,88096,88097,88098,88113,88114,88130],{},"Změní-li se práce o ",[883,88099,88101],{"className":88100},[886],[888,88102,88103],{"xmlns":890},[892,88104,88105,88111],{},[895,88106,88107,88109],{},[898,88108,1771],{},[898,88110,4840],{},[902,88112,82067],{"encoding":904},", lze pro odhad změny kapitálu ",[883,88115,88117],{"className":88116},[886],[888,88118,88119],{"xmlns":890},[892,88120,88121,88127],{},[895,88122,88123,88125],{},[898,88124,3890],{"mathvariant":1704},[898,88126,4845],{},[902,88128,88129],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,88132,88134],{"className":88133},[886],[888,88135,88136],{"xmlns":890,"display":34854},[892,88137,88138,88185],{},[3626,88139,88140],{"width":34859},[3632,88141,88142,88144,88178,88180],{},[3635,88143],{"width":34864},[3635,88145,88146],{},[895,88147,88148,88150,88152,88154,88156,88158,88160,88162,88164,88166,88168,88170,88172,88174,88176],{},[898,88149,3890],{"mathvariant":1704},[898,88151,4845],{},[1693,88153,4110],{},[898,88155,1771],{},[898,88157,4845],{},[1693,88159,1695],{},[1693,88161,1698],{},[898,88163,2839],{},[898,88165,2666],{},[898,88167,2663],{},[898,88169,3611],{},[1915,88171,2239],{},[898,88173,1771],{},[898,88175,4840],{},[1693,88177,1899],{"separator":1898},[3635,88179],{"width":34864},[3635,88181,88182],{},[1915,88183,88184],{},"(5.15)",[902,88186,88187],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,88189,88191],{"className":88190},[886],[888,88192,88193],{"xmlns":890,"display":34854},[892,88194,88195,88244],{},[3626,88196,88197],{"width":34859},[3632,88198,88199,88201,88237,88239],{},[3635,88200],{"width":34864},[3635,88202,88203],{},[895,88204,88205,88207,88209,88211,88229,88231,88233,88235],{},[898,88206,1771],{},[898,88208,4840],{},[1693,88210,1695],{},[2132,88212,88213,88219],{},[895,88214,88215,88217],{},[1693,88216,1698],{},[1762,88218,1764],{},[895,88220,88221,88223,88225,88227],{},[898,88222,2839],{},[898,88224,2666],{},[898,88226,2663],{},[898,88228,3611],{},[1915,88230,2239],{},[898,88232,1771],{},[898,88234,4845],{},[898,88236,1789],{"mathvariant":1704},[3635,88238],{"width":34864},[3635,88240,88241],{},[1915,88242,88243],{},"(5.16)",[902,88245,88246],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1636,88248,88249,88273],{},[724,88250,88251,88253,88254],{},[883,88252,8620],{}," Postup — jak spočítat ",[883,88255,88257],{"className":88256},[886],[888,88258,88259],{"xmlns":890},[892,88260,88261,88271],{},[895,88262,88263,88265,88267,88269],{},[898,88264,2839],{},[898,88266,2666],{},[898,88268,2663],{},[898,88270,3611],{},[902,88272,5814],{"encoding":904},[152,88274,88275,88316,88359,88391],{},[123,88276,88277,88278,4286,88297,1789],{},"Vypočtěte parciální derivace ",[883,88279,88281],{"className":88280},[886],[888,88282,88283],{"xmlns":890},[892,88284,88285,88295],{},[895,88286,88287],{},[5688,88288,88289,88291,88293],{},[898,88290,1712],{},[898,88292,4840],{},[1693,88294,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,88296,16873],{"encoding":904},[883,88298,88300],{"className":88299},[886],[888,88301,88302],{"xmlns":890},[892,88303,88304,88314],{},[895,88305,88306],{},[5688,88307,88308,88310,88312],{},[898,88309,1712],{},[898,88311,4845],{},[1693,88313,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,88315,16918],{"encoding":904},[123,88317,72564,88318,88358],{},[883,88319,88321],{"className":88320},[886],[888,88322,88323],{"xmlns":890},[892,88324,88325,88355],{},[895,88326,88327,88329,88331,88333,88335,88337,88345,88347],{},[898,88328,2839],{},[898,88330,2666],{},[898,88332,2663],{},[898,88334,3611],{},[1693,88336,1695],{},[5688,88338,88339,88341,88343],{},[898,88340,1712],{},[898,88342,4840],{},[1693,88344,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[898,88346,1705],{"mathvariant":1704},[5688,88348,88349,88351,88353],{},[898,88350,1712],{},[898,88352,4845],{},[1693,88354,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,88356,88357],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,88360,88361,88362,1789],{},"Případně dosaďte konkrétní ",[883,88363,88365],{"className":88364},[886],[888,88366,88367],{"xmlns":890},[892,88368,88369,88389],{},[895,88370,88371,88373,88379,88381,88387],{},[1693,88372,9392],{"stretchy":1708},[3284,88374,88375,88377],{},[898,88376,4840],{},[1762,88378,1911],{},[1693,88380,1899],{"separator":1898},[3284,88382,88383,88385],{},[898,88384,4845],{},[1762,88386,1911],{},[1693,88388,9407],{"stretchy":1708},[902,88390,87977],{"encoding":904},[123,88392,88393,88394,88428,88429,88431],{},"Pro odhad substituce použijte ",[883,88395,88397],{"className":88396},[886],[888,88398,88399],{"xmlns":890},[892,88400,88401,88425],{},[895,88402,88403,88405,88407,88409,88411,88413,88415,88417,88419,88421,88423],{},[898,88404,3890],{"mathvariant":1704},[898,88406,4845],{},[1693,88408,4110],{},[1693,88410,1698],{},[898,88412,2839],{},[898,88414,2666],{},[898,88416,2663],{},[898,88418,3611],{},[1693,88420,1715],{},[898,88422,3890],{"mathvariant":1704},[898,88424,4840],{},[902,88426,88427],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,88430,59364],{}," — substituce, ne doplnění).",[724,88433,88434],{},[614,88435,88436,88437,88469,88470,9530,88483,22617,88512,88527],{},"Obrázek 5.7 — izokvanta ",[883,88438,88440],{"className":88439},[886],[888,88441,88442],{"xmlns":890},[892,88443,88444,88466],{},[895,88445,88446,88452,88454,88456,88458,88460,88462,88464],{},[3284,88447,88448,88450],{},[898,88449,87501],{},[1762,88451,1911],{},[1693,88453,1695],{},[898,88455,1712],{},[1693,88457,1709],{"stretchy":1708},[898,88459,4840],{},[1693,88461,1899],{"separator":1898},[898,88463,4845],{},[1693,88465,1731],{"stretchy":1708},[902,88467,88468],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,88471,88473],{"className":88472},[886],[888,88474,88475],{"xmlns":890},[892,88476,88477,88481],{},[895,88478,88479],{},[898,88480,25666],{},[902,88482,25666],{"encoding":904},[883,88484,88486],{"className":88485},[886],[888,88487,88488],{"xmlns":890},[892,88489,88490,88510],{},[895,88491,88492,88494,88500,88502,88508],{},[1693,88493,9392],{"stretchy":1708},[3284,88495,88496,88498],{},[898,88497,4840],{},[1762,88499,1911],{},[1693,88501,1899],{"separator":1898},[3284,88503,88504,88506],{},[898,88505,4845],{},[1762,88507,1911],{},[1693,88509,9407],{"stretchy":1708},[902,88511,87977],{"encoding":904},[883,88513,88515],{"className":88514},[886],[888,88516,88517],{"xmlns":890},[892,88518,88519,88525],{},[895,88520,88521,88523],{},[898,88522,3890],{"mathvariant":1704},[898,88524,4845],{},[902,88526,88129],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,88529,88531],{"id":88530},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,88533,88535],{"id":88534},"příklad-54","Příklad 5.4",[724,88537,83383,88538,1343,88580,1343,88597,1789],{},[883,88539,88541],{"className":88540},[886],[888,88542,88543],{"xmlns":890},[892,88544,88545,88577],{},[895,88546,88547,88549,88551,88553,88565],{},[898,88548,1712],{},[1693,88550,1695],{},[1762,88552,43026],{},[1717,88554,88555,88557],{},[898,88556,4840],{},[895,88558,88559,88561,88563],{},[1762,88560,1764],{},[898,88562,1705],{"mathvariant":1704},[1762,88564,2398],{},[1717,88566,88567,88569],{},[898,88568,4845],{},[895,88570,88571,88573,88575],{},[1762,88572,1764],{},[898,88574,1705],{"mathvariant":1704},[1762,88576,8357],{},[902,88578,88579],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,88581,88583],{"className":88582},[886],[888,88584,88585],{"xmlns":890},[892,88586,88587,88595],{},[895,88588,88589,88591,88593],{},[898,88590,4840],{},[1693,88592,1695],{},[1762,88594,15892],{},[902,88596,83757],{"encoding":904},[883,88598,88600],{"className":88599},[886],[888,88601,88602],{"xmlns":890},[892,88603,88604,88612],{},[895,88605,88606,88608,88610],{},[898,88607,4845],{},[1693,88609,1695],{},[1762,88611,9987],{},[902,88613,88614],{"encoding":904},"K = 100",[724,88616,88617],{},[38,88618,88619],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,88621,88623],{"className":88622},[886],[888,88624,88625],{"xmlns":890,"display":34854},[892,88626,88627,88741],{},[895,88628,88629,88631,88637,88639,88647,88649,88657,88671,88683,88685,88687,88689,88695,88697,88699,88701,88703,88705,88707,88715,88717,88727,88729,88736,88738],{},[898,88630,2839],{},[3284,88632,88633,88635],{},[898,88634,1701],{},[898,88636,4840],{},[1693,88638,1695],{},[5688,88640,88641,88643,88645],{},[898,88642,1712],{},[898,88644,4840],{},[1693,88646,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,88648,1695],{},[3638,88650,88651],{"scriptlevel":1911,"displaystyle":1708},[2132,88652,88653,88655],{},[1762,88654,43026],{},[1762,88656,2398],{},[1717,88658,88659,88661],{},[898,88660,4840],{},[895,88662,88663,88665,88667,88669],{},[1693,88664,1698],{},[1762,88666,1764],{},[898,88668,1705],{"mathvariant":1704},[1762,88670,2398],{},[1717,88672,88673,88675],{},[898,88674,4845],{},[895,88676,88677,88679,88681],{},[1762,88678,1764],{},[898,88680,1705],{"mathvariant":1704},[1762,88682,8357],{},[1693,88684,1899],{"separator":1898},[1901,88686],{"width":3630},[898,88688,2839],{},[3284,88690,88691,88693],{},[898,88692,1701],{},[898,88694,4840],{},[1693,88696,1709],{"stretchy":1708},[1762,88698,15892],{},[1693,88700,1899],{"separator":1898},[1762,88702,9987],{},[1693,88704,1731],{"stretchy":1708},[1693,88706,1695],{},[3638,88708,88709],{"scriptlevel":1911,"displaystyle":1708},[2132,88710,88711,88713],{},[1762,88712,43026],{},[1762,88714,2398],{},[1693,88716,1715],{},[3638,88718,88719],{"scriptlevel":1911,"displaystyle":1708},[2132,88720,88721,88723],{},[1762,88722,1764],{},[14976,88724,88725],{},[1762,88726,15892],{},[1693,88728,1715],{},[88730,88731,88732,88734],"mroot",{},[1762,88733,9987],{},[1762,88735,8357],{},[1693,88737,4110],{},[1762,88739,88740],{},"7,153.",[902,88742,88743],{"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.",[724,88745,88746,88747,50926,88769,17083,88786,88807,88808,88829],{},"Přibližná změna při ",[883,88748,88750],{"className":88749},[886],[888,88751,88752],{"xmlns":890},[892,88753,88754,88766],{},[895,88755,88756,88758,88760,88762,88764],{},[898,88757,4840],{},[1693,88759,4300],{},[1762,88761,15892],{},[1693,88763,10020],{},[1762,88765,45121],{},[902,88767,88768],{"encoding":904},"L: 20 \\to 21",[883,88770,88772],{"className":88771},[886],[888,88773,88774],{"xmlns":890},[892,88775,88776,88784],{},[895,88777,88778,88780,88782],{},[898,88779,4845],{},[1693,88781,1695],{},[1762,88783,9987],{},[902,88785,88614],{"encoding":904},[883,88787,88789],{"className":88788},[886],[888,88790,88791],{"xmlns":890},[892,88792,88793,88804],{},[895,88794,88795,88797,88799,88801],{},[898,88796,3890],{"mathvariant":1704},[898,88798,1712],{},[1693,88800,4110],{},[1762,88802,88803],{},"7,153",[902,88805,88806],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,88809,88811],{"className":88810},[886],[888,88812,88813],{"xmlns":890},[892,88814,88815,88826],{},[895,88816,88817,88819,88821,88823],{},[898,88818,3890],{"mathvariant":1704},[898,88820,1712],{},[1693,88822,4110],{},[1762,88824,88825],{},"26,888",[902,88827,88828],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,88831,88832,88835],{},[38,88833,88834],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,88837,88839],{"className":88838},[886],[888,88840,88841],{"xmlns":890,"display":34854},[892,88842,88843,88943],{},[895,88844,88845,88847,88853,88855,88863,88865,88867,88879,88893,88895,88897,88899,88905,88907,88909,88911,88913,88915,88917,88919,88923,88925,88938,88940],{},[898,88846,2839],{},[3284,88848,88849,88851],{},[898,88850,1701],{},[898,88852,4845],{},[1693,88854,1695],{},[5688,88856,88857,88859,88861],{},[898,88858,1712],{},[898,88860,4845],{},[1693,88862,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,88864,1695],{},[1762,88866,9147],{},[1717,88868,88869,88871],{},[898,88870,4840],{},[895,88872,88873,88875,88877],{},[1762,88874,1764],{},[898,88876,1705],{"mathvariant":1704},[1762,88878,2398],{},[1717,88880,88881,88883],{},[898,88882,4845],{},[895,88884,88885,88887,88889,88891],{},[1693,88886,1698],{},[1762,88888,2398],{},[898,88890,1705],{"mathvariant":1704},[1762,88892,8357],{},[1693,88894,1899],{"separator":1898},[1901,88896],{"width":3630},[898,88898,2839],{},[3284,88900,88901,88903],{},[898,88902,1701],{},[898,88904,4845],{},[1693,88906,1709],{"stretchy":1708},[1762,88908,15892],{},[1693,88910,1899],{"separator":1898},[1762,88912,9987],{},[1693,88914,1731],{"stretchy":1708},[1693,88916,1695],{},[1762,88918,9147],{},[14976,88920,88921],{},[1762,88922,15892],{},[1693,88924,1715],{},[3638,88926,88927],{"scriptlevel":1911,"displaystyle":1708},[2132,88928,88929,88931],{},[1762,88930,1764],{},[88730,88932,88933,88936],{},[1762,88934,88935],{},"10000",[1762,88937,8357],{},[1693,88939,4110],{},[1762,88941,88942],{},"4,525.",[902,88944,88945],{"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.",[724,88947,88948,88949,9591,88966,3042],{},"Produkce poklesne přibližně o 4,525 (z ",[883,88950,88952],{"className":88951},[886],[888,88953,88954],{"xmlns":890},[892,88955,88956,88963],{},[895,88957,88958,88960],{},[1693,88959,4110],{},[1762,88961,88962],{},"905,126",[902,88964,88965],{"encoding":904},"\\approx 905{,}126",[883,88967,88969],{"className":88968},[886],[888,88970,88971],{"xmlns":890},[892,88972,88973,88980],{},[895,88974,88975,88977],{},[1693,88976,4110],{},[1762,88978,88979],{},"900,601",[902,88981,88982],{"encoding":904},"\\approx 900{,}601",[724,88984,88985,10027,89032,1343,89054,3042],{},[38,88986,88987,88988,4286,89010],{},"(c) Změna ",[883,88989,88991],{"className":88990},[886],[888,88992,88993],{"xmlns":890},[892,88994,88995,89007],{},[895,88996,88997,88999,89001,89003,89005],{},[898,88998,4840],{},[1693,89000,4300],{},[1762,89002,15892],{},[1693,89004,10020],{},[1762,89006,43026],{},[902,89008,89009],{"encoding":904},"L: 20 \\to 15",[883,89011,89013],{"className":89012},[886],[888,89014,89015],{"xmlns":890},[892,89016,89017,89029],{},[895,89018,89019,89021,89023,89025,89027],{},[898,89020,4845],{},[1693,89022,4300],{},[1762,89024,9987],{},[1693,89026,10020],{},[1762,89028,15660],{},[902,89030,89031],{"encoding":904},"K: 100 \\to 150",[883,89033,89035],{"className":89034},[886],[888,89036,89037],{"xmlns":890},[892,89038,89039,89051],{},[895,89040,89041,89043,89045,89047,89049],{},[898,89042,1771],{},[898,89044,4840],{},[1693,89046,1695],{},[1693,89048,1698],{},[1762,89050,9147],{},[902,89052,89053],{"encoding":904},"dL = -5",[883,89055,89057],{"className":89056},[886],[888,89058,89059],{"xmlns":890},[892,89060,89061,89071],{},[895,89062,89063,89065,89067,89069],{},[898,89064,1771],{},[898,89066,4845],{},[1693,89068,1695],{},[1762,89070,10017],{},[902,89072,89073],{"encoding":904},"dK = 50",[883,89075,89077],{"className":89076},[886],[888,89078,89079],{"xmlns":890,"display":34854},[892,89080,89081,89169],{},[895,89082,89083,89085,89087,89089,89091,89097,89099,89101,89103,89105,89107,89109,89111,89113,89115,89117,89119,89121,89127,89129,89131,89133,89135,89137,89139,89141,89143,89145,89147,89149,89151,89153,89155,89157,89160,89162,89164,89166],{},[898,89084,1771],{},[898,89086,1712],{},[1693,89088,1695],{},[898,89090,2839],{},[3284,89092,89093,89095],{},[898,89094,1701],{},[898,89096,4840],{},[1693,89098,1709],{"stretchy":1708},[1762,89100,15892],{},[1693,89102,1899],{"separator":1898},[1762,89104,9987],{},[1693,89106,1731],{"stretchy":1708},[1693,89108,1715],{},[1693,89110,1709],{"stretchy":1708},[1693,89112,1698],{},[1762,89114,9147],{},[1693,89116,1731],{"stretchy":1708},[1693,89118,1892],{},[898,89120,2839],{},[3284,89122,89123,89125],{},[898,89124,1701],{},[898,89126,4845],{},[1693,89128,1709],{"stretchy":1708},[1762,89130,15892],{},[1693,89132,1899],{"separator":1898},[1762,89134,9987],{},[1693,89136,1731],{"stretchy":1708},[1693,89138,1715],{},[1762,89140,10017],{},[1693,89142,1695],{},[1762,89144,88803],{},[1693,89146,1715],{},[1693,89148,1709],{"stretchy":1708},[1693,89150,1698],{},[1762,89152,9147],{},[1693,89154,1731],{"stretchy":1708},[1693,89156,1892],{},[1762,89158,89159],{},"4,525",[1693,89161,1715],{},[1762,89163,10017],{},[1693,89165,4110],{},[1762,89167,89168],{},"190,485.",[902,89170,89171],{"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.",[724,89173,89174],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,89176,89178],{"id":89177},"příklad-55","Příklad 5.5",[724,89180,89181,89182,89218,89219,1789],{},"Pro produkci ",[883,89183,89185],{"className":89184},[886],[888,89186,89187],{"xmlns":890},[892,89188,89189,89215],{},[895,89190,89191,89193,89195,89197,89199,89201,89203,89205,89211],{},[898,89192,1712],{},[1693,89194,1709],{"stretchy":1708},[898,89196,4840],{},[1693,89198,1899],{"separator":1898},[898,89200,4845],{},[1693,89202,1731],{"stretchy":1708},[1693,89204,1695],{},[88730,89206,89207,89209],{},[898,89208,4840],{},[1762,89210,8357],{},[14976,89212,89213],{},[898,89214,4845],{},[902,89216,89217],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,89220,89222],{"className":89221},[886],[888,89223,89224],{"xmlns":890},[892,89225,89226,89242],{},[895,89227,89228,89234,89238,89240],{},[88730,89229,89230,89232],{},[898,89231,4840],{},[1762,89233,8357],{},[14976,89235,89236],{},[898,89237,4845],{},[1693,89239,1695],{},[898,89241,87501],{},[902,89243,89244],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,89246,89247,89248,1789],{},"Umocněním na druhou: ",[883,89249,89251],{"className":89250},[886],[888,89252,89253],{"xmlns":890},[892,89254,89255,89279],{},[895,89256,89257,89259,89261,89267,89269],{},[898,89258,4845],{},[1693,89260,1695],{},[1717,89262,89263,89265],{},[898,89264,87501],{},[1762,89266,2398],{},[898,89268,1705],{"mathvariant":1704},[88730,89270,89271,89277],{},[1717,89272,89273,89275],{},[898,89274,4840],{},[1762,89276,2398],{},[1762,89278,8357],{},[902,89280,89281],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,89283,89284,89324,89364],{},[123,89285,89286],{},[883,89287,89289],{"className":89288},[886],[888,89290,89291],{"xmlns":890},[892,89292,89293,89321],{},[895,89294,89295,89297,89299,89301,89303,89305,89307,89309,89311],{},[898,89296,87501],{},[1693,89298,1695],{},[1762,89300,1764],{},[1693,89302,10870],{},[898,89304,4845],{},[1693,89306,1695],{},[1762,89308,1764],{},[898,89310,1705],{"mathvariant":1704},[88730,89312,89313,89319],{},[1717,89314,89315,89317],{},[898,89316,4840],{},[1762,89318,2398],{},[1762,89320,8357],{},[902,89322,89323],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,89325,89326],{},[883,89327,89329],{"className":89328},[886],[888,89330,89331],{"xmlns":890},[892,89332,89333,89361],{},[895,89334,89335,89337,89339,89341,89343,89345,89347,89349,89351],{},[898,89336,87501],{},[1693,89338,1695],{},[1762,89340,2398],{},[1693,89342,10870],{},[898,89344,4845],{},[1693,89346,1695],{},[1762,89348,9262],{},[898,89350,1705],{"mathvariant":1704},[88730,89352,89353,89359],{},[1717,89354,89355,89357],{},[898,89356,4840],{},[1762,89358,2398],{},[1762,89360,8357],{},[902,89362,89363],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,89365,89366],{},[883,89367,89369],{"className":89368},[886],[888,89370,89371],{"xmlns":890},[892,89372,89373,89401],{},[895,89374,89375,89377,89379,89381,89383,89385,89387,89389,89391],{},[898,89376,87501],{},[1693,89378,1695],{},[1762,89380,8357],{},[1693,89382,10870],{},[898,89384,4845],{},[1693,89386,1695],{},[1762,89388,10881],{},[898,89390,1705],{"mathvariant":1704},[88730,89392,89393,89399],{},[1717,89394,89395,89397],{},[898,89396,4840],{},[1762,89398,2398],{},[1762,89400,8357],{},[902,89402,89403],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,89405,89406],{},[614,89407,89408,89409,7721,89430,1789],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,89410,89412],{"className":89411},[886],[888,89413,89414],{"xmlns":890},[892,89415,89416,89428],{},[895,89417,89418,89420,89422,89424,89426],{},[1693,89419,1709],{"stretchy":1708},[898,89421,4840],{},[1693,89423,1899],{"separator":1898},[898,89425,4845],{},[1693,89427,1731],{"stretchy":1708},[902,89429,87627],{"encoding":904},[883,89431,89433],{"className":89432},[886],[888,89434,89435],{"xmlns":890},[892,89436,89437,89453],{},[895,89438,89439,89441,89443,89445,89447,89449,89451],{},[898,89440,87501],{},[1693,89442,1695],{},[1762,89444,1764],{},[1693,89446,1899],{"separator":1898},[1762,89448,2398],{},[1693,89450,1899],{"separator":1898},[1762,89452,8357],{},[902,89454,89455],{"encoding":904},"q = 1, 2, 3",[198,89457,89459],{"id":89458},"příklad-56","Příklad 5.6",[724,89461,83383,89462,1789],{},[883,89463,89465],{"className":89464},[886],[888,89466,89467],{"xmlns":890},[892,89468,89469,89485],{},[895,89470,89471,89473,89475,89477,89479,89481],{},[898,89472,1712],{},[1693,89474,1695],{},[1762,89476,2398],{},[898,89478,4840],{},[1693,89480,1892],{},[14976,89482,89483],{},[898,89484,4845],{},[902,89486,89487],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,89489,89491],{"className":89490},[886],[888,89492,89493],{"xmlns":890,"display":34854},[892,89494,89495,89537],{},[895,89496,89497,89499,89505,89507,89509,89511,89513,89515,89521,89523,89535],{},[898,89498,2839],{},[3284,89500,89501,89503],{},[898,89502,1701],{},[898,89504,4840],{},[1693,89506,1695],{},[1762,89508,2398],{},[1693,89510,1899],{"separator":1898},[1901,89512],{"width":1903},[898,89514,2839],{},[3284,89516,89517,89519],{},[898,89518,1701],{},[898,89520,4845],{},[1693,89522,1695],{},[2132,89524,89525,89527],{},[1762,89526,1764],{},[895,89528,89529,89531],{},[1762,89530,2398],{},[14976,89532,89533],{},[898,89534,4845],{},[898,89536,1789],{"mathvariant":1704},[902,89538,89539],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,89541,89543],{"className":89542},[886],[888,89544,89545],{"xmlns":890,"display":34854},[892,89546,89547,89611],{},[895,89548,89549,89551,89553,89555,89557,89559,89581,89583,89601,89603,89605,89609],{},[898,89550,2839],{},[898,89552,2666],{},[898,89554,2663],{},[898,89556,3611],{},[1693,89558,1695],{},[2132,89560,89561,89571],{},[895,89562,89563,89565],{},[898,89564,2839],{},[3284,89566,89567,89569],{},[898,89568,1701],{},[898,89570,4840],{},[895,89572,89573,89575],{},[898,89574,2839],{},[3284,89576,89577,89579],{},[898,89578,1701],{},[898,89580,4845],{},[1693,89582,1695],{},[2132,89584,89585,89587],{},[1762,89586,2398],{},[3638,89588,89589],{"scriptlevel":1911,"displaystyle":1708},[2132,89590,89591,89593],{},[1762,89592,1764],{},[895,89594,89595,89597],{},[1762,89596,2398],{},[14976,89598,89599],{},[898,89600,4845],{},[1693,89602,1695],{},[1762,89604,9262],{},[14976,89606,89607],{},[898,89608,4845],{},[898,89610,1789],{"mathvariant":1704},[902,89612,89613],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,89615,89616,89617,89660,89661,89700,89701,1789],{},"Například ",[883,89618,89620],{"className":89619},[886],[888,89621,89622],{"xmlns":890},[892,89623,89624,89657],{},[895,89625,89626,89628,89630,89632,89634,89636,89638,89640,89642,89644,89646,89648,89652,89654],{},[898,89627,2839],{},[898,89629,2666],{},[898,89631,2663],{},[898,89633,3611],{},[1693,89635,1709],{"stretchy":1708},[1762,89637,9262],{},[1693,89639,1899],{"separator":1898},[1762,89641,31000],{},[1693,89643,1731],{"stretchy":1708},[1693,89645,1695],{},[1762,89647,9262],{},[14976,89649,89650],{},[1762,89651,31000],{},[1693,89653,4110],{},[1762,89655,89656],{},"10,58",[902,89658,89659],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,89662,89664],{"className":89663},[886],[888,89665,89666],{"xmlns":890},[892,89667,89668,89697],{},[895,89669,89670,89672,89674,89676,89678,89680,89682,89684,89686,89688,89692,89694],{},[898,89671,1712],{},[1693,89673,1709],{"stretchy":1708},[1762,89675,9262],{},[1693,89677,1899],{"separator":1898},[1762,89679,31000],{},[1693,89681,1731],{"stretchy":1708},[1693,89683,1695],{},[1762,89685,12453],{},[1693,89687,1892],{},[14976,89689,89690],{},[1762,89691,31000],{},[1693,89693,4110],{},[1762,89695,89696],{},"10,646",[902,89698,89699],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,89702,89704],{"className":89703},[886],[888,89705,89706],{"xmlns":890},[892,89707,89708,89716],{},[895,89709,89710,89712],{},[1762,89711,9262],{},[14976,89713,89714],{},[1762,89715,31000],{},[902,89717,89718],{"encoding":904},"4\\sqrt{7}",[724,89720,89721,89722,89742],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,89723,89725],{"className":89724},[886],[888,89726,89727],{"xmlns":890},[892,89728,89729,89739],{},[895,89730,89731,89733,89735,89737],{},[898,89732,1771],{},[898,89734,4840],{},[1693,89736,1695],{},[1762,89738,2398],{},[902,89740,89741],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,89744,89746],{"className":89745},[886],[888,89747,89748],{"xmlns":890,"display":34854},[892,89749,89750,89799],{},[895,89751,89752,89754,89756,89758,89760,89762,89764,89766,89768,89770,89772,89774,89776,89778,89780,89782,89784,89786,89788,89792,89794,89796],{},[898,89753,1771],{},[898,89755,4845],{},[1693,89757,1695],{},[1693,89759,1698],{},[898,89761,2839],{},[898,89763,2666],{},[898,89765,2663],{},[898,89767,3611],{},[1693,89769,1709],{"stretchy":1708},[1762,89771,9262],{},[1693,89773,1899],{"separator":1898},[1762,89775,31000],{},[1693,89777,1731],{"stretchy":1708},[1693,89779,1715],{},[1762,89781,2398],{},[1693,89783,1695],{},[1693,89785,1698],{},[1762,89787,12453],{},[14976,89789,89790],{},[1762,89791,31000],{},[1693,89793,4110],{},[1693,89795,1698],{},[1762,89797,89798],{},"21,17.",[902,89800,89801],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,89803,89805],{"id":89804},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,89807,89808,89809,1343,89811,4286,89813,89815,89816,89819,89820,89823],{},"Hlavními faktory produkce jsou ",[38,89810,81625],{},[38,89812,81641],{},[38,89814,81657],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,89817,89818],{},"jednofaktorový"," (pouze práce) a ",[38,89821,89822],{},"dvoufaktorový"," (práce + kapitál) model.",[724,89825,89826,89827,89830,89831,89833,89834,89836,89837,32979,89840,89859,89860,89877,89878,89895,89896,89918,89919,2783,89938,1789],{},"V ",[38,89828,89829],{},"1F modelu"," se definuje ",[38,89832,16876],{}," (derivace produkce podle práce) a ",[38,89835,81560],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,89838,89839],{},"zákonu klesajících výnosů",[883,89841,89843],{"className":89842},[886],[888,89844,89845],{"xmlns":890},[892,89846,89847,89857],{},[895,89848,89849,89851],{},[898,89850,2839],{},[3284,89852,89853,89855],{},[898,89854,1701],{},[898,89856,4840],{},[902,89858,4964],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,89861,89863],{"className":89862},[886],[888,89864,89865],{"xmlns":890},[892,89866,89867,89875],{},[895,89868,89869],{},[3284,89870,89871,89873],{},[898,89872,4840],{},[1762,89874,1911],{},[902,89876,82269],{"encoding":904}," klesá a v bodě ",[883,89879,89881],{"className":89880},[886],[888,89882,89883],{"xmlns":890},[892,89884,89885,89893],{},[895,89886,89887],{},[3284,89888,89889,89891],{},[898,89890,4840],{},[1762,89892,1764],{},[902,89894,20044],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,89897,89898,89899],{},"princip maximalizace ",[883,89900,89902],{"className":89901},[886],[888,89903,89904],{"xmlns":890},[892,89905,89906,89916],{},[895,89907,89908,89910],{},[898,89909,2719],{},[3284,89911,89912,89914],{},[898,89913,1701],{},[898,89915,4840],{},[902,89917,81345],{"encoding":904},": v bodě maxima ",[883,89920,89922],{"className":89921},[886],[888,89923,89924],{"xmlns":890},[892,89925,89926,89936],{},[895,89927,89928,89930],{},[898,89929,2719],{},[3284,89931,89932,89934],{},[898,89933,1701],{},[898,89935,4840],{},[902,89937,81345],{"encoding":904},[883,89939,89941],{"className":89940},[886],[888,89942,89943],{"xmlns":890},[892,89944,89945,89965],{},[895,89946,89947,89949,89955,89957,89959],{},[898,89948,2839],{},[3284,89950,89951,89953],{},[898,89952,1701],{},[898,89954,4840],{},[1693,89956,1695],{},[898,89958,2719],{},[3284,89960,89961,89963],{},[898,89962,1701],{},[898,89964,4840],{},[902,89966,5039],{"encoding":904},[724,89968,89969,89970,89973,89974,1863,89977,90006,90007,90024,90025,90028,90029,90058,90059,90061,90062,6055,90092,90114],{},"Ve ",[38,89971,89972],{},"2F modelu"," se obvykle používají ",[38,89975,89976],{},"Cobb-Douglasovy funkce",[883,89978,89980],{"className":89979},[886],[888,89981,89982],{"xmlns":890},[892,89983,89984,90004],{},[895,89985,89986,89988,89990,89992,89998],{},[898,89987,1712],{},[1693,89989,1695],{},[898,89991,2719],{},[1717,89993,89994,89996],{},[898,89995,4840],{},[898,89997,207],{},[1717,89999,90000,90002],{},[898,90001,4845],{},[898,90003,1895],{},[902,90005,81441],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,90008,90010],{"className":90009},[886],[888,90011,90012],{"xmlns":890},[892,90013,90014,90022],{},[895,90015,90016,90018,90020],{},[898,90017,207],{},[1693,90019,1892],{},[898,90021,1895],{},[902,90023,81535],{"encoding":904}," rozlišujeme ",[38,90026,90027],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,90030,90032],{"className":90031},[886],[888,90033,90034],{"xmlns":890},[892,90035,90036,90056],{},[895,90037,90038,90040,90046,90048,90050],{},[898,90039,2839],{},[3284,90041,90042,90044],{},[898,90043,1701],{},[898,90045,4840],{},[1693,90047,1899],{"separator":1898},[898,90049,2839],{},[3284,90051,90052,90054],{},[898,90053,1701],{},[898,90055,4845],{},[902,90057,81472],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,90060,16633],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,90063,90065],{"className":90064},[886],[888,90066,90067],{"xmlns":890},[892,90068,90069,90089],{},[895,90070,90071,90073,90079,90081,90083],{},[898,90072,2839],{},[3284,90074,90075,90077],{},[898,90076,1701],{},[898,90078,4840],{},[898,90080,1705],{"mathvariant":1704},[898,90082,2839],{},[3284,90084,90085,90087],{},[898,90086,1701],{},[898,90088,4845],{},[902,90090,90091],{"encoding":904},"MP_L\u002FMP_K",[38,90093,90094,90095,1731],{},"mezní míra technické substituce (",[883,90096,90098],{"className":90097},[886],[888,90099,90100],{"xmlns":890},[892,90101,90102,90112],{},[895,90103,90104,90106,90108,90110],{},[898,90105,2839],{},[898,90107,2666],{},[898,90109,2663],{},[898,90111,3611],{},[902,90113,5814],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,90116,8674],{"id":56645},[152,90118,90119,90122,90125,90128,90131,90134,90137,90140,90143,90146,90149],{},[123,90120,90121],{},"Jaké jsou faktory produkce?",[123,90123,90124],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,90126,90127],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,90129,90130],{},"Co udává mezní produkt práce?",[123,90132,90133],{},"Co musí respektovat průběh křivky produkce?",[123,90135,90136],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,90138,90139],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,90141,90142],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,90144,90145],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,90147,90148],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,90150,90151],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,90153,90155],{"id":90154},"úlohy-51517","Úlohy 5.1–5.17",[198,90157,47223],{"id":47222},[724,90159,90160,90163,90164,90186,90187,1343,90207,1343,90227,90247],{},[38,90161,90162],{},"5.1"," Je dána produkce ",[883,90165,90167],{"className":90166},[886],[888,90168,90169],{"xmlns":890},[892,90170,90171,90183],{},[895,90172,90173,90175,90177,90179],{},[898,90174,1712],{},[1693,90176,1695],{},[1762,90178,9763],{},[14976,90180,90181],{},[898,90182,4840],{},[902,90184,90185],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,90188,90190],{"className":90189},[886],[888,90191,90192],{"xmlns":890},[892,90193,90194,90204],{},[895,90195,90196,90198,90200,90202],{},[898,90197,1712],{},[1693,90199,1709],{"stretchy":1708},[1762,90201,1764],{},[1693,90203,1731],{"stretchy":1708},[902,90205,90206],{"encoding":904},"Q(1)",[883,90208,90210],{"className":90209},[886],[888,90211,90212],{"xmlns":890},[892,90213,90214,90224],{},[895,90215,90216,90218,90220,90222],{},[898,90217,1712],{},[1693,90219,1709],{"stretchy":1708},[1762,90221,9262],{},[1693,90223,1731],{"stretchy":1708},[902,90225,90226],{"encoding":904},"Q(4)",[883,90228,90230],{"className":90229},[886],[888,90231,90232],{"xmlns":890},[892,90233,90234,90244],{},[895,90235,90236,90238,90240,90242],{},[898,90237,1712],{},[1693,90239,1709],{"stretchy":1708},[1762,90241,10881],{},[1693,90243,1731],{"stretchy":1708},[902,90245,90246],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,90249,90250,90163,90253,90289,90290,90303,90304,90323,90324,90350,90351,9591,90364,90377],{},[38,90251,90252],{},"5.2",[883,90254,90256],{"className":90255},[886],[888,90257,90258],{"xmlns":890},[892,90259,90260,90286],{},[895,90261,90262,90264,90266,90268,90270,90276,90278,90280],{},[898,90263,1712],{},[1693,90265,1695],{},[1693,90267,1698],{},[1762,90269,9695],{},[1717,90271,90272,90274],{},[898,90273,4840],{},[1762,90275,8357],{},[1693,90277,1892],{},[1762,90279,10881],{},[1717,90281,90282,90284],{},[898,90283,4840],{},[1762,90285,2398],{},[902,90287,90288],{"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 ",[883,90291,90293],{"className":90292},[886],[888,90294,90295],{"xmlns":890},[892,90296,90297,90301],{},[895,90298,90299],{},[898,90300,4840],{},[902,90302,4840],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,90305,90307],{"className":90306},[886],[888,90308,90309],{"xmlns":890},[892,90310,90311,90321],{},[895,90312,90313,90315],{},[898,90314,2839],{},[3284,90316,90317,90319],{},[898,90318,1701],{},[898,90320,4840],{},[902,90322,4964],{"encoding":904},". (f) Vypočtěte ",[883,90325,90327],{"className":90326},[886],[888,90328,90329],{"xmlns":890},[892,90330,90331,90347],{},[895,90332,90333,90335,90341,90343,90345],{},[898,90334,2839],{},[3284,90336,90337,90339],{},[898,90338,1701],{},[898,90340,4840],{},[1693,90342,1709],{"stretchy":1708},[1762,90344,9763],{},[1693,90346,1731],{"stretchy":1708},[902,90348,90349],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,90352,90354],{"className":90353},[886],[888,90355,90356],{"xmlns":890},[892,90357,90358,90362],{},[895,90359,90360],{},[1762,90361,9763],{},[902,90363,9763],{"encoding":904},[883,90365,90367],{"className":90366},[886],[888,90368,90369],{"xmlns":890},[892,90370,90371,90375],{},[895,90372,90373],{},[1762,90374,49058],{},[902,90376,49058],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,90379,90380,90383,90384,90406,90407,90435,90436,90467,90468,1789],{},[38,90381,90382],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,90385,90387],{"className":90386},[886],[888,90388,90389],{"xmlns":890},[892,90390,90391,90403],{},[895,90392,90393,90395,90397,90399],{},[898,90394,1712],{},[1693,90396,1695],{},[1762,90398,21936],{},[14976,90400,90401],{},[898,90402,4840],{},[902,90404,90405],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,90408,90410],{"className":90409},[886],[888,90411,90412],{"xmlns":890},[892,90413,90414,90432],{},[895,90415,90416,90418,90420,90422,90426,90428,90430],{},[898,90417,1712],{},[1693,90419,1695],{},[1762,90421,36864],{},[14976,90423,90424],{},[898,90425,4840],{},[1693,90427,1698],{},[1762,90429,9262],{},[898,90431,4840],{},[902,90433,90434],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,90437,90439],{"className":90438},[886],[888,90440,90441],{"xmlns":890},[892,90442,90443,90464],{},[895,90444,90445,90447,90449,90451,90453,90455,90458],{},[898,90446,1712],{},[1693,90448,1695],{},[1762,90450,10017],{},[898,90452,4840],{},[1693,90454,1698],{},[1762,90456,90457],{},"0,01",[1717,90459,90460,90462],{},[898,90461,4840],{},[1762,90463,2398],{},[902,90465,90466],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,90469,90471],{"className":90470},[886],[888,90472,90473],{"xmlns":890},[892,90474,90475,90501],{},[895,90476,90477,90479,90481,90483,90485,90491,90493,90495],{},[898,90478,1712],{},[1693,90480,1695],{},[1693,90482,1698],{},[1762,90484,74927],{},[1717,90486,90487,90489],{},[898,90488,4840],{},[1762,90490,8357],{},[1693,90492,1892],{},[1762,90494,10881],{},[1717,90496,90497,90499],{},[898,90498,4840],{},[1762,90500,2398],{},[902,90502,90503],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,90505,90506,90509,90510,9530,90529,78912,90546,1789],{},[38,90507,90508],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,90511,90513],{"className":90512},[886],[888,90514,90515],{"xmlns":890},[892,90516,90517,90527],{},[895,90518,90519,90521],{},[898,90520,2719],{},[3284,90522,90523,90525],{},[898,90524,1701],{},[898,90526,4840],{},[902,90528,81345],{"encoding":904},[883,90530,90532],{"className":90531},[886],[888,90533,90534],{"xmlns":890},[892,90535,90536,90544],{},[895,90537,90538],{},[3284,90539,90540,90542],{},[898,90541,4840],{},[1762,90543,1911],{},[902,90545,82269],{"encoding":904},[883,90547,90549],{"className":90548},[886],[888,90550,90551],{"xmlns":890},[892,90552,90553,90593],{},[895,90554,90555,90557,90563,90565,90571,90573,90575,90577,90583,90585,90591],{},[898,90556,2719],{},[3284,90558,90559,90561],{},[898,90560,1701],{},[898,90562,4840],{},[1693,90564,1709],{"stretchy":1708},[3284,90566,90567,90569],{},[898,90568,4840],{},[1762,90570,1911],{},[1693,90572,1731],{"stretchy":1708},[1693,90574,1695],{},[898,90576,2839],{},[3284,90578,90579,90581],{},[898,90580,1701],{},[898,90582,4840],{},[1693,90584,1709],{"stretchy":1708},[3284,90586,90587,90589],{},[898,90588,4840],{},[1762,90590,1911],{},[1693,90592,1731],{"stretchy":1708},[902,90594,90595],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,90597,90598,90163,90601,28397,90637,90650,90651,90670],{},[38,90599,90600],{},"5.5",[883,90602,90604],{"className":90603},[886],[888,90605,90606],{"xmlns":890},[892,90607,90608,90634],{},[895,90609,90610,90612,90614,90616,90618,90624,90626,90628],{},[898,90611,1712],{},[1693,90613,1695],{},[1693,90615,1698],{},[1762,90617,9739],{},[1717,90619,90620,90622],{},[898,90621,4840],{},[1762,90623,8357],{},[1693,90625,1892],{},[1762,90627,10402],{},[1717,90629,90630,90632],{},[898,90631,4840],{},[1762,90633,2398],{},[902,90635,90636],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,90638,90640],{"className":90639},[886],[888,90641,90642],{"xmlns":890},[892,90643,90644,90648],{},[895,90645,90646],{},[898,90647,4840],{},[902,90649,4840],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,90652,90654],{"className":90653},[886],[888,90655,90656],{"xmlns":890},[892,90657,90658,90668],{},[895,90659,90660,90662],{},[898,90661,2719],{},[3284,90663,90664,90666],{},[898,90665,1701],{},[898,90667,4840],{},[902,90669,81345],{"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.",[198,90672,90674],{"id":90673},"dvoufaktorový-model","Dvoufaktorový model",[724,90676,90677,90680,90681,90406,90707,90435,90749,1789],{},[38,90678,90679],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,90682,90684],{"className":90683},[886],[888,90685,90686],{"xmlns":890},[892,90687,90688,90704],{},[895,90689,90690,90692,90694,90696,90698],{},[898,90691,1712],{},[1693,90693,1695],{},[1762,90695,31000],{},[898,90697,4840],{},[1717,90699,90700,90702],{},[898,90701,4845],{},[1762,90703,2398],{},[902,90705,90706],{"encoding":904},"Q = 7 L K^{2}",[883,90708,90710],{"className":90709},[886],[888,90711,90712],{"xmlns":890},[892,90713,90714,90746],{},[895,90715,90716,90718,90720,90722,90734],{},[898,90717,1712],{},[1693,90719,1695],{},[1762,90721,10017],{},[1717,90723,90724,90726],{},[898,90725,4840],{},[895,90727,90728,90730,90732],{},[1762,90729,2398],{},[898,90731,1705],{"mathvariant":1704},[1762,90733,8357],{},[1717,90735,90736,90738],{},[898,90737,4845],{},[895,90739,90740,90742,90744],{},[1762,90741,1764],{},[898,90743,1705],{"mathvariant":1704},[1762,90745,8357],{},[902,90747,90748],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,90750,90752],{"className":90751},[886],[888,90753,90754],{"xmlns":890},[892,90755,90756,90788],{},[895,90757,90758,90760,90762,90764,90776],{},[898,90759,1712],{},[1693,90761,1695],{},[1762,90763,10600],{},[1717,90765,90766,90768],{},[898,90767,4840],{},[895,90769,90770,90772,90774],{},[1762,90771,8357],{},[898,90773,1705],{"mathvariant":1704},[1762,90775,9147],{},[1717,90777,90778,90780],{},[898,90779,4845],{},[895,90781,90782,90784,90786],{},[1762,90783,2398],{},[898,90785,1705],{"mathvariant":1704},[1762,90787,9147],{},[902,90789,90790],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,90792,90793,90163,90796,90838,90839,1343,90857,90876,90877,90894],{},[38,90794,90795],{},"5.7",[883,90797,90799],{"className":90798},[886],[888,90800,90801],{"xmlns":890},[892,90802,90803,90835],{},[895,90804,90805,90807,90809,90811,90823],{},[898,90806,1712],{},[1693,90808,1695],{},[1762,90810,9763],{},[1717,90812,90813,90815],{},[898,90814,4840],{},[895,90816,90817,90819,90821],{},[1762,90818,1764],{},[898,90820,1705],{"mathvariant":1704},[1762,90822,2398],{},[1717,90824,90825,90827],{},[898,90826,4845],{},[895,90828,90829,90831,90833],{},[1762,90830,1764],{},[898,90832,1705],{"mathvariant":1704},[1762,90834,2398],{},[902,90836,90837],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,90840,90842],{"className":90841},[886],[888,90843,90844],{"xmlns":890},[892,90845,90846,90854],{},[895,90847,90848,90850,90852],{},[898,90849,4840],{},[1693,90851,1695],{},[1762,90853,26949],{},[902,90855,90856],{"encoding":904},"L = 400",[883,90858,90860],{"className":90859},[886],[888,90861,90862],{"xmlns":890},[892,90863,90864,90873],{},[895,90865,90866,90868,90870],{},[898,90867,4845],{},[1693,90869,1695],{},[1762,90871,90872],{},"17576",[902,90874,90875],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,90878,90880],{"className":90879},[886],[888,90881,90882],{"xmlns":890},[892,90883,90884,90892],{},[895,90885,90886,90888,90890],{},[898,90887,4840],{},[1693,90889,1899],{"separator":1898},[898,90891,4845],{},[902,90893,85693],{"encoding":904}," zdvojnásobí.",[724,90896,90897,90900,90901,90838,90932,1343,90950,76298,90968,90998,90999,91029,91030,9591,91043,91057,91058,9591,91071,91084],{},[38,90898,90899],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,90902,90904],{"className":90903},[886],[888,90905,90906],{"xmlns":890},[892,90907,90908,90929],{},[895,90909,90910,90912,90914,90917,90923],{},[898,90911,1712],{},[1693,90913,1695],{},[1762,90915,90916],{},"1,01",[1717,90918,90919,90921],{},[898,90920,4840],{},[1762,90922,30529],{},[1717,90924,90925,90927],{},[898,90926,4845],{},[1762,90928,30588],{},[902,90930,90931],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,90933,90935],{"className":90934},[886],[888,90936,90937],{"xmlns":890},[892,90938,90939,90947],{},[895,90940,90941,90943,90945],{},[898,90942,4840],{},[1693,90944,1695],{},[1762,90946,37526],{},[902,90948,90949],{"encoding":904},"L = 250",[883,90951,90953],{"className":90952},[886],[888,90954,90955],{"xmlns":890},[892,90956,90957,90965],{},[895,90958,90959,90961,90963],{},[898,90960,4845],{},[1693,90962,1695],{},[1762,90964,9684],{},[902,90966,90967],{"encoding":904},"K = 1000",[883,90969,90971],{"className":90970},[886],[888,90972,90973],{"xmlns":890},[892,90974,90975,90995],{},[895,90976,90977,90979,90985,90987,90989,90991,90993],{},[898,90978,2839],{},[3284,90980,90981,90983],{},[898,90982,1701],{},[898,90984,4840],{},[1693,90986,1709],{"stretchy":1708},[1762,90988,37526],{},[1693,90990,1899],{"separator":1898},[1762,90992,9684],{},[1693,90994,1731],{"stretchy":1708},[902,90996,90997],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,91000,91002],{"className":91001},[886],[888,91003,91004],{"xmlns":890},[892,91005,91006,91026],{},[895,91007,91008,91010,91016,91018,91020,91022,91024],{},[898,91009,2839],{},[3284,91011,91012,91014],{},[898,91013,1701],{},[898,91015,4845],{},[1693,91017,1709],{"stretchy":1708},[1762,91019,37526],{},[1693,91021,1899],{"separator":1898},[1762,91023,9684],{},[1693,91025,1731],{"stretchy":1708},[902,91027,91028],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,91031,91033],{"className":91032},[886],[888,91034,91035],{"xmlns":890},[892,91036,91037,91041],{},[895,91038,91039],{},[898,91040,4840],{},[902,91042,4840],{"encoding":904},[883,91044,91046],{"className":91045},[886],[888,91047,91048],{"xmlns":890},[892,91049,91050,91055],{},[895,91051,91052],{},[1762,91053,91054],{},"260",[902,91056,91054],{"encoding":904}," a současném poklesu ",[883,91059,91061],{"className":91060},[886],[888,91062,91063],{"xmlns":890},[892,91064,91065,91069],{},[895,91066,91067],{},[898,91068,4845],{},[902,91070,4845],{"encoding":904},[883,91072,91074],{"className":91073},[886],[888,91075,91076],{"xmlns":890},[892,91077,91078,91082],{},[895,91079,91080],{},[1762,91081,22017],{},[902,91083,22017],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,91086,91087,91090,91091,1789],{},[38,91088,91089],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,91092,91094],{"className":91093},[886],[888,91095,91096],{"xmlns":890},[892,91097,91098,91118],{},[895,91099,91100,91102,91104,91106,91112],{},[898,91101,1712],{},[1693,91103,1695],{},[1762,91105,9763],{},[1717,91107,91108,91110],{},[898,91109,4840],{},[1762,91111,74927],{},[1717,91113,91114,91116],{},[898,91115,4845],{},[1762,91117,11877],{},[902,91119,91120],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,91122,91123,91126,91127,87286,91150,17244,91163,16877,91213,3042],{},[38,91124,91125],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,91128,91130],{"className":91129},[886],[888,91131,91132],{"xmlns":890},[892,91133,91134,91148],{},[895,91135,91136,91138,91140,91142,91144,91146],{},[898,91137,1712],{},[1693,91139,1709],{"stretchy":1708},[898,91141,4840],{},[1693,91143,1899],{"separator":1898},[898,91145,4845],{},[1693,91147,1731],{"stretchy":1708},[902,91149,16849],{"encoding":904},[883,91151,91153],{"className":91152},[886],[888,91154,91155],{"xmlns":890},[892,91156,91157,91161],{},[895,91158,91159],{},[898,91160,5362],{},[902,91162,5362],{"encoding":904},[883,91164,91166],{"className":91165},[886],[888,91167,91168],{"xmlns":890},[892,91169,91170,91210],{},[895,91171,91172,91174,91182,91184,91186,91194,91196,91198,91200,91202,91204,91206,91208],{},[898,91173,4840],{},[5688,91175,91176,91178,91180],{},[898,91177,1712],{},[898,91179,4840],{},[1693,91181,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,91183,1892],{},[898,91185,4845],{},[5688,91187,91188,91190,91192],{},[898,91189,1712],{},[898,91191,4845],{},[1693,91193,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,91195,1695],{},[898,91197,5362],{},[898,91199,1712],{},[1693,91201,1709],{"stretchy":1708},[898,91203,4840],{},[1693,91205,1899],{"separator":1898},[898,91207,4845],{},[1693,91209,1731],{"stretchy":1708},[902,91211,91212],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,91214,87261],{},[724,91216,91217,91220],{},[38,91218,91219],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,91222,91223,90163,91226,91266,91267,1343,91289,1343,91311,91333],{},[38,91224,91225],{},"5.12",[883,91227,91229],{"className":91228},[886],[888,91230,91231],{"xmlns":890},[892,91232,91233,91263],{},[895,91234,91235,91237,91239,91251],{},[898,91236,1712],{},[1693,91238,1695],{},[1717,91240,91241,91243],{},[898,91242,4840],{},[895,91244,91245,91247,91249],{},[1762,91246,1764],{},[898,91248,1705],{"mathvariant":1704},[1762,91250,8357],{},[1717,91252,91253,91255],{},[898,91254,4845],{},[895,91256,91257,91259,91261],{},[1762,91258,1764],{},[898,91260,1705],{"mathvariant":1704},[1762,91262,9262],{},[902,91264,91265],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,91268,91270],{"className":91269},[886],[888,91271,91272],{"xmlns":890},[892,91273,91274,91286],{},[895,91275,91276,91282,91284],{},[3284,91277,91278,91280],{},[898,91279,87501],{},[1762,91281,1911],{},[1693,91283,1695],{},[1762,91285,1764],{},[902,91287,91288],{"encoding":904},"q_0 = 1",[883,91290,91292],{"className":91291},[886],[888,91293,91294],{"xmlns":890},[892,91295,91296,91308],{},[895,91297,91298,91304,91306],{},[3284,91299,91300,91302],{},[898,91301,87501],{},[1762,91303,1764],{},[1693,91305,1695],{},[1762,91307,2398],{},[902,91309,91310],{"encoding":904},"q_1 = 2",[883,91312,91314],{"className":91313},[886],[888,91315,91316],{"xmlns":890},[892,91317,91318,91330],{},[895,91319,91320,91326,91328],{},[3284,91321,91322,91324],{},[898,91323,87501],{},[1762,91325,2398],{},[1693,91327,1695],{},[1762,91329,8357],{},[902,91331,91332],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,91335,91336,90163,91339,91379,91380,1343,91408,1343,91436,1343,91464,1343,91493,1343,91522,1343,91551,1343,91580,1343,91609,1789],{},[38,91337,91338],{},"5.13",[883,91340,91342],{"className":91341},[886],[888,91343,91344],{"xmlns":890},[892,91345,91346,91376],{},[895,91347,91348,91350,91352,91364],{},[898,91349,1712],{},[1693,91351,1695],{},[1717,91353,91354,91356],{},[898,91355,4840],{},[895,91357,91358,91360,91362],{},[1762,91359,1764],{},[898,91361,1705],{"mathvariant":1704},[1762,91363,8357],{},[1717,91365,91366,91368],{},[898,91367,4845],{},[895,91369,91370,91372,91374],{},[1762,91371,1764],{},[898,91373,1705],{"mathvariant":1704},[1762,91375,2398],{},[902,91377,91378],{"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): ",[883,91381,91383],{"className":91382},[886],[888,91384,91385],{"xmlns":890},[892,91386,91387,91405],{},[895,91388,91389,91395,91397,91399,91401,91403],{},[3284,91390,91391,91393],{},[898,91392,2719],{},[1762,91394,1764],{},[1693,91396,9392],{"stretchy":1708},[1762,91398,1764],{},[1693,91400,15283],{"separator":1898},[1762,91402,1764],{},[1693,91404,9407],{"stretchy":1708},[902,91406,91407],{"encoding":904},"A_1[1; 1]",[883,91409,91411],{"className":91410},[886],[888,91412,91413],{"xmlns":890},[892,91414,91415,91433],{},[895,91416,91417,91423,91425,91427,91429,91431],{},[3284,91418,91419,91421],{},[898,91420,2719],{},[1762,91422,2398],{},[1693,91424,9392],{"stretchy":1708},[1762,91426,1764],{},[1693,91428,15283],{"separator":1898},[1762,91430,12453],{},[1693,91432,9407],{"stretchy":1708},[902,91434,91435],{"encoding":904},"A_2[1; 8]",[883,91437,91439],{"className":91438},[886],[888,91440,91441],{"xmlns":890},[892,91442,91443,91461],{},[895,91444,91445,91451,91453,91455,91457,91459],{},[3284,91446,91447,91449],{},[898,91448,2719],{},[1762,91450,8357],{},[1693,91452,9392],{"stretchy":1708},[1762,91454,1764],{},[1693,91456,15283],{"separator":1898},[1762,91458,73320],{},[1693,91460,9407],{"stretchy":1708},[902,91462,91463],{"encoding":904},"A_3[1; 27]",[883,91465,91467],{"className":91466},[886],[888,91468,91469],{"xmlns":890},[892,91470,91471,91490],{},[895,91472,91473,91479,91481,91483,91485,91488],{},[3284,91474,91475,91477],{},[898,91476,2719],{},[1762,91478,9262],{},[1693,91480,9392],{"stretchy":1708},[1762,91482,2398],{},[1693,91484,15283],{"separator":1898},[1762,91486,91487],{},"0,353",[1693,91489,9407],{"stretchy":1708},[902,91491,91492],{"encoding":904},"A_4[2; 0{,}353]",[883,91494,91496],{"className":91495},[886],[888,91497,91498],{"xmlns":890},[892,91499,91500,91519],{},[895,91501,91502,91508,91510,91512,91514,91517],{},[3284,91503,91504,91506],{},[898,91505,2719],{},[1762,91507,9147],{},[1693,91509,9392],{"stretchy":1708},[1762,91511,2398],{},[1693,91513,15283],{"separator":1898},[1762,91515,91516],{},"2,828",[1693,91518,9407],{"stretchy":1708},[902,91520,91521],{"encoding":904},"A_5[2; 2{,}828]",[883,91523,91525],{"className":91524},[886],[888,91526,91527],{"xmlns":890},[892,91528,91529,91548],{},[895,91530,91531,91537,91539,91541,91543,91546],{},[3284,91532,91533,91535],{},[898,91534,2719],{},[1762,91536,9154],{},[1693,91538,9392],{"stretchy":1708},[1762,91540,2398],{},[1693,91542,15283],{"separator":1898},[1762,91544,91545],{},"9,545",[1693,91547,9407],{"stretchy":1708},[902,91549,91550],{"encoding":904},"A_6[2; 9{,}545]",[883,91552,91554],{"className":91553},[886],[888,91555,91556],{"xmlns":890},[892,91557,91558,91577],{},[895,91559,91560,91566,91568,91570,91572,91575],{},[3284,91561,91562,91564],{},[898,91563,2719],{},[1762,91565,31000],{},[1693,91567,9392],{"stretchy":1708},[1762,91569,71285],{},[1693,91571,15283],{"separator":1898},[1762,91573,91574],{},"0,544",[1693,91576,9407],{"stretchy":1708},[902,91578,91579],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,91581,91583],{"className":91582},[886],[888,91584,91585],{"xmlns":890},[892,91586,91587,91606],{},[895,91588,91589,91595,91597,91599,91601,91604],{},[3284,91590,91591,91593],{},[898,91592,2719],{},[1762,91594,12453],{},[1693,91596,9392],{"stretchy":1708},[1762,91598,71285],{},[1693,91600,15283],{"separator":1898},[1762,91602,91603],{},"14,696",[1693,91605,9407],{"stretchy":1708},[902,91607,91608],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,91610,91612],{"className":91611},[886],[888,91613,91614],{"xmlns":890},[892,91615,91616,91634],{},[895,91617,91618,91624,91626,91628,91630,91632],{},[3284,91619,91620,91622],{},[898,91621,2719],{},[1762,91623,10881],{},[1693,91625,9392],{"stretchy":1708},[1762,91627,2398],{},[1693,91629,15283],{"separator":1898},[1762,91631,9147],{},[1693,91633,9407],{"stretchy":1708},[902,91635,91636],{"encoding":904},"A_9[2; 5]",[724,91638,91639,91642],{},[38,91640,91641],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,91644,91645,91648,91649,91679,91680,91693,91694,91707,91708,76031,91727,91746,91747,1789],{},[38,91646,91647],{},"5.15"," Produkce firmy je dána vztahem ",[883,91650,91652],{"className":91651},[886],[888,91653,91654],{"xmlns":890},[892,91655,91656,91676],{},[895,91657,91658,91660,91662,91664,91670],{},[898,91659,1712],{},[1693,91661,1695],{},[1762,91663,2398],{},[1717,91665,91666,91668],{},[898,91667,4840],{},[1762,91669,11877],{},[1717,91671,91672,91674],{},[898,91673,4845],{},[1762,91675,30588],{},[902,91677,91678],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,91681,91683],{"className":91682},[886],[888,91684,91685],{"xmlns":890},[892,91686,91687,91691],{},[895,91688,91689],{},[1762,91690,9987],{},[902,91692,9987],{"encoding":904}," pracovníků a disponuje-li ",[883,91695,91697],{"className":91696},[886],[888,91698,91699],{"xmlns":890},[892,91700,91701,91705],{},[895,91702,91703],{},[1762,91704,71161],{},[902,91706,71161],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,91709,91711],{"className":91710},[886],[888,91712,91713],{"xmlns":890},[892,91714,91715,91725],{},[895,91716,91717,91719,91721,91723],{},[898,91718,2839],{},[898,91720,2666],{},[898,91722,2663],{},[898,91724,3611],{},[902,91726,5814],{"encoding":904},[883,91728,91730],{"className":91729},[886],[888,91731,91732],{"xmlns":890},[892,91733,91734,91744],{},[895,91735,91736,91738,91740,91742],{},[898,91737,2839],{},[898,91739,2666],{},[898,91741,2663],{},[898,91743,3611],{},[902,91745,5814],{"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 ",[883,91748,91750],{"className":91749},[886],[888,91751,91752],{"xmlns":890},[892,91753,91754,91759],{},[895,91755,91756],{},[1762,91757,91758],{},"95",[902,91760,91758],{"encoding":904},[724,91762,91763,90163,91766,77705,91798,91817,91818,91831,91832,91845,91846,91859],{},[38,91764,91765],{},"5.16",[883,91767,91769],{"className":91768},[886],[888,91770,91771],{"xmlns":890},[892,91772,91773,91795],{},[895,91774,91775,91777,91779,91785,91787,91789],{},[898,91776,1712],{},[1693,91778,1695],{},[1717,91780,91781,91783],{},[898,91782,4845],{},[1762,91784,2398],{},[1693,91786,1892],{},[1762,91788,2398],{},[1717,91790,91791,91793],{},[898,91792,4840],{},[1762,91794,2398],{},[902,91796,91797],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,91799,91801],{"className":91800},[886],[888,91802,91803],{"xmlns":890},[892,91804,91805,91815],{},[895,91806,91807,91809,91811,91813],{},[898,91808,2839],{},[898,91810,2666],{},[898,91812,2663],{},[898,91814,3611],{},[902,91816,5814],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,91819,91821],{"className":91820},[886],[888,91822,91823],{"xmlns":890},[892,91824,91825,91829],{},[895,91826,91827],{},[1762,91828,10017],{},[902,91830,10017],{"encoding":904}," pracovníky a ",[883,91833,91835],{"className":91834},[886],[888,91836,91837],{"xmlns":890},[892,91838,91839,91843],{},[895,91840,91841],{},[1762,91842,84327],{},[902,91844,84327],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,91847,91849],{"className":91848},[886],[888,91850,91851],{"xmlns":890},[892,91852,91853,91857],{},[895,91854,91855],{},[1762,91856,53467],{},[902,91858,53467],{"encoding":904}," jednotek.",[724,91861,91862,91865,91866,17244,91896,1789],{},[38,91863,91864],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,91867,91869],{"className":91868},[886],[888,91870,91871],{"xmlns":890},[892,91872,91873,91893],{},[895,91874,91875,91877,91879,91881,91887],{},[898,91876,1712],{},[1693,91878,1695],{},[898,91880,2719],{},[1717,91882,91883,91885],{},[898,91884,4840],{},[898,91886,207],{},[1717,91888,91889,91891],{},[898,91890,4845],{},[898,91892,1895],{},[902,91894,91895],{"encoding":904},"Q = A L^{a} K^{b}",[883,91897,91899],{"className":91898},[886],[888,91900,91901],{"xmlns":890},[892,91902,91903,91933],{},[895,91904,91905,91907,91909,91911,91913,91915,91923,91925],{},[898,91906,2839],{},[898,91908,2666],{},[898,91910,2663],{},[898,91912,3611],{},[1693,91914,1695],{},[3638,91916,91917],{"scriptlevel":1911,"displaystyle":1708},[2132,91918,91919,91921],{},[898,91920,207],{},[898,91922,1895],{},[1693,91924,1715],{},[3638,91926,91927],{"scriptlevel":1911,"displaystyle":1708},[2132,91928,91929,91931],{},[898,91930,4845],{},[898,91932,4840],{},[902,91934,91935],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,91937,22545],{"id":22544},[120,91939,91940,91973,92000,92009,92059,92090,92143,92166,92221,92294,92372,92415,92446,92479,92520,92592,92653,92719,92736,92809,92875,92927,92983,93017,93060],{},[123,91941,91942,91945,91946,5473,91959,91972],{},[38,91943,91944],{},"Faktory (vstupy) produkce:"," práce ",[883,91947,91949],{"className":91948},[886],[888,91950,91951],{"xmlns":890},[892,91952,91953,91957],{},[895,91954,91955],{},[898,91956,4840],{},[902,91958,4840],{"encoding":904},[883,91960,91962],{"className":91961},[886],[888,91963,91964],{"xmlns":890},[892,91965,91966,91970],{},[895,91967,91968],{},[898,91969,4845],{},[902,91971,4845],{"encoding":904},", půda.",[123,91974,91975,13877,91977,1789],{},[38,91976,47223],{},[883,91978,91980],{"className":91979},[886],[888,91981,91982],{"xmlns":890},[892,91983,91984,91998],{},[895,91985,91986,91988,91990,91992,91994,91996],{},[898,91987,1712],{},[1693,91989,1695],{},[898,91991,1712],{},[1693,91993,1709],{"stretchy":1708},[898,91995,4840],{},[1693,91997,1731],{"stretchy":1708},[902,91999,81256],{"encoding":904},[123,92001,92002,16877,92004,8586,92007,1789],{},[38,92003,859],{},[614,92005,92006],{},"production function",[38,92008,81758],{},[123,92010,92011,1863,92013,1789],{},[38,92012,81804],{},[883,92014,92016],{"className":92015},[886],[888,92017,92018],{"xmlns":890},[892,92019,92020,92056],{},[895,92021,92022,92024,92030,92032,92034,92036,92038,92040,92042,92044,92050,92052,92054],{},[898,92023,2839],{},[3284,92025,92026,92028],{},[898,92027,1701],{},[898,92029,4840],{},[1693,92031,1695],{},[898,92033,1771],{},[898,92035,1712],{},[898,92037,1705],{"mathvariant":1704},[898,92039,1771],{},[898,92041,4840],{},[1693,92043,1695],{},[1717,92045,92046,92048],{},[898,92047,1712],{},[1693,92049,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,92051,1709],{"stretchy":1708},[898,92053,4840],{},[1693,92055,1731],{"stretchy":1708},[902,92057,92058],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,92060,92061,1863,92063,1789],{},[38,92062,4969],{},[883,92064,92066],{"className":92065},[886],[888,92067,92068],{"xmlns":890},[892,92069,92070,92088],{},[895,92071,92072,92074,92080,92082,92084,92086],{},[898,92073,2719],{},[3284,92075,92076,92078],{},[898,92077,1701],{},[898,92079,4840],{},[1693,92081,1695],{},[898,92083,1712],{},[898,92085,1705],{"mathvariant":1704},[898,92087,4840],{},[902,92089,81324],{"encoding":904},[123,92091,92092,92094,92095,17244,92112,1789],{},[38,92093,82226],{}," — od určitého ",[883,92096,92098],{"className":92097},[886],[888,92099,92100],{"xmlns":890},[892,92101,92102,92110],{},[895,92103,92104],{},[3284,92105,92106,92108],{},[898,92107,4840],{},[1762,92109,1911],{},[902,92111,82269],{"encoding":904},[883,92113,92115],{"className":92114},[886],[888,92116,92117],{"xmlns":890},[892,92118,92119,92141],{},[895,92120,92121,92131,92133,92135,92137,92139],{},[1717,92122,92123,92125],{},[898,92124,1712],{},[895,92126,92127,92129],{},[1693,92128,1724],{"mathvariant":1704},[1693,92130,1724],{"mathvariant":1704},[1693,92132,1709],{"stretchy":1708},[898,92134,4840],{},[1693,92136,1731],{"stretchy":1708},[1693,92138,1908],{},[1762,92140,1911],{},[902,92142,82415],{"encoding":904},[123,92144,92145,1863,92148,92165],{},[38,92146,92147],{},"Inflexní bod",[883,92149,92151],{"className":92150},[886],[888,92152,92153],{"xmlns":890},[892,92154,92155,92163],{},[895,92156,92157],{},[3284,92158,92159,92161],{},[898,92160,4840],{},[1762,92162,1911],{},[902,92164,82269],{"encoding":904}," — přechod z konvexity do konkavity.",[123,92167,92168,1863,92171,13877,92188,1789],{},[38,92169,92170],{},"Bod maxima produkce",[883,92172,92174],{"className":92173},[886],[888,92175,92176],{"xmlns":890},[892,92177,92178,92186],{},[895,92179,92180],{},[3284,92181,92182,92184],{},[898,92183,4840],{},[1762,92185,1764],{},[902,92187,20044],{"encoding":904},[883,92189,92191],{"className":92190},[886],[888,92192,92193],{"xmlns":890},[892,92194,92195,92219],{},[895,92196,92197,92199,92205,92207,92213,92215,92217],{},[898,92198,2839],{},[3284,92200,92201,92203],{},[898,92202,1701],{},[898,92204,4840],{},[1693,92206,1709],{"stretchy":1708},[3284,92208,92209,92211],{},[898,92210,4840],{},[1762,92212,1764],{},[1693,92214,1731],{"stretchy":1708},[1693,92216,1695],{},[1762,92218,1911],{},[902,92220,82488],{"encoding":904},[123,92222,92223,92245,92246,17244,92265,1789],{},[38,92224,92225,92226],{},"Princip maximalizace ",[883,92227,92229],{"className":92228},[886],[888,92230,92231],{"xmlns":890},[892,92232,92233,92243],{},[895,92234,92235,92237],{},[898,92236,2719],{},[3284,92238,92239,92241],{},[898,92240,1701],{},[898,92242,4840],{},[902,92244,81345],{"encoding":904}," — v bodě maxima ",[883,92247,92249],{"className":92248},[886],[888,92250,92251],{"xmlns":890},[892,92252,92253,92263],{},[895,92254,92255,92257],{},[898,92256,2719],{},[3284,92258,92259,92261],{},[898,92260,1701],{},[898,92262,4840],{},[902,92264,81345],{"encoding":904},[883,92266,92268],{"className":92267},[886],[888,92269,92270],{"xmlns":890},[892,92271,92272,92292],{},[895,92273,92274,92276,92282,92284,92286],{},[898,92275,2839],{},[3284,92277,92278,92280],{},[898,92279,1701],{},[898,92281,4840],{},[1693,92283,1695],{},[898,92285,2719],{},[3284,92287,92288,92290],{},[898,92289,1701],{},[898,92291,4840],{},[902,92293,5039],{"encoding":904},[123,92295,92296,1863,92299,1343,92338,1343,92355,1789],{},[38,92297,92298],{},"Polynomiální produkční funkce",[883,92300,92302],{"className":92301},[886],[888,92303,92304],{"xmlns":890},[892,92305,92306,92336],{},[895,92307,92308,92310,92312,92314,92316,92318,92320,92326,92328,92330],{},[898,92309,1712],{},[1693,92311,1709],{"stretchy":1708},[898,92313,4840],{},[1693,92315,1731],{"stretchy":1708},[1693,92317,1695],{},[898,92319,207],{},[1717,92321,92322,92324],{},[898,92323,4840],{},[1762,92325,8357],{},[1693,92327,1892],{},[898,92329,1895],{},[1717,92331,92332,92334],{},[898,92333,4840],{},[1762,92335,2398],{},[902,92337,82606],{"encoding":904},[883,92339,92341],{"className":92340},[886],[888,92342,92343],{"xmlns":890},[892,92344,92345,92353],{},[895,92346,92347,92349,92351],{},[898,92348,207],{},[1693,92350,1908],{},[1762,92352,1911],{},[902,92354,49853],{"encoding":904},[883,92356,92358],{"className":92357},[886],[888,92359,92360],{"xmlns":890},[892,92361,92362,92370],{},[895,92363,92364,92366,92368],{},[898,92365,1895],{},[1693,92367,1922],{},[1762,92369,1911],{},[902,92371,7157],{"encoding":904},[123,92373,92374,1863,92377,1789],{},[38,92375,92376],{},"Diferenciál produkce",[883,92378,92380],{"className":92379},[886],[888,92381,92382],{"xmlns":890},[892,92383,92384,92412],{},[895,92385,92386,92388,92390,92392,92394,92396,92398,92400,92406,92408,92410],{},[898,92387,3890],{"mathvariant":1704},[898,92389,1712],{},[1693,92391,4110],{},[898,92393,1771],{},[898,92395,1712],{},[1693,92397,1695],{},[898,92399,2839],{},[3284,92401,92402,92404],{},[898,92403,1701],{},[898,92405,4840],{},[1915,92407,2239],{},[898,92409,1771],{},[898,92411,4840],{},[902,92413,92414],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,92416,92417,13877,92419,1789],{},[38,92418,90674],{},[883,92420,92422],{"className":92421},[886],[888,92423,92424],{"xmlns":890},[892,92425,92426,92444],{},[895,92427,92428,92430,92432,92434,92436,92438,92440,92442],{},[898,92429,1712],{},[1693,92431,1695],{},[898,92433,1712],{},[1693,92435,1709],{"stretchy":1708},[898,92437,4840],{},[1693,92439,1899],{"separator":1898},[898,92441,4845],{},[1693,92443,1731],{"stretchy":1708},[902,92445,4850],{"encoding":904},[123,92447,92448,13877,92450,1789],{},[38,92449,5066],{},[883,92451,92453],{"className":92452},[886],[888,92454,92455],{"xmlns":890},[892,92456,92457,92477],{},[895,92458,92459,92461,92463,92465,92471],{},[898,92460,1712],{},[1693,92462,1695],{},[898,92464,2719],{},[1717,92466,92467,92469],{},[898,92468,4840],{},[898,92470,207],{},[1717,92472,92473,92475],{},[898,92474,4845],{},[898,92476,1895],{},[902,92478,81441],{"encoding":904},[123,92480,92481,13877,92484,92519],{},[38,92482,92483],{},"Ryzí Cobb-Douglas",[883,92485,92487],{"className":92486},[886],[888,92488,92489],{"xmlns":890},[892,92490,92491,92517],{},[895,92492,92493,92495,92497,92499,92505],{},[898,92494,1712],{},[1693,92496,1695],{},[898,92498,2719],{},[1717,92500,92501,92503],{},[898,92502,4840],{},[898,92504,207],{},[1717,92506,92507,92509],{},[898,92508,4845],{},[895,92510,92511,92513,92515],{},[1762,92512,1764],{},[1693,92514,1698],{},[898,92516,207],{},[902,92518,85600],{"encoding":904}," (konstantní výnosy).",[123,92521,92522,13877,92524,1789],{},[38,92523,86316],{},[883,92525,92527],{"className":92526},[886],[888,92528,92529],{"xmlns":890},[892,92530,92531,92589],{},[895,92532,92533,92535,92537,92539,92541,92543,92545,92547,92549,92551,92561,92563,92565,92575],{},[898,92534,1712],{},[1693,92536,1695],{},[898,92538,2719],{},[1693,92540,9392],{"stretchy":1708},[1693,92542,1709],{"stretchy":1708},[1762,92544,1764],{},[1693,92546,1698],{},[898,92548,207],{},[1693,92550,1731],{"stretchy":1708},[1717,92552,92553,92555],{},[898,92554,4840],{},[895,92556,92557,92559],{},[1693,92558,1698],{},[898,92560,1895],{},[1693,92562,1892],{},[898,92564,207],{},[1717,92566,92567,92569],{},[898,92568,4845],{},[895,92570,92571,92573],{},[1693,92572,1698],{},[898,92574,1895],{},[1717,92576,92577,92579],{},[1693,92578,9407],{"stretchy":1708},[895,92580,92581,92583,92585,92587],{},[1693,92582,1698],{},[1762,92584,1764],{},[898,92586,1705],{"mathvariant":1704},[898,92588,1895],{},[902,92590,92591],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,92593,92594,16877,92597,8586,92619,16877,92622,92652],{},[38,92595,92596],{},"Lineární",[883,92598,92600],{"className":92599},[886],[888,92601,92602],{"xmlns":890},[892,92603,92604,92616],{},[895,92605,92606,92608,92610,92612,92614],{},[898,92607,207],{},[898,92609,4840],{},[1693,92611,1892],{},[898,92613,1895],{},[898,92615,4845],{},[902,92617,92618],{"encoding":904},"aL + bK",[38,92620,92621],{},"Leontiefova",[883,92623,92625],{"className":92624},[886],[888,92626,92627],{"xmlns":890},[892,92628,92629,92649],{},[895,92630,92631,92633,92635,92637,92639,92641,92643,92645,92647],{},[898,92632,3739],{},[1693,92634,3742],{},[1693,92636,1709],{"stretchy":1708},[898,92638,207],{},[898,92640,4840],{},[1693,92642,1899],{"separator":1898},[898,92644,1895],{},[898,92646,4845],{},[1693,92648,1731],{"stretchy":1708},[902,92650,92651],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,92654,92655,13877,92671,1789],{},[38,92656,92657,92658],{},"Homogenita stupně ",[883,92659,92661],{"className":92660},[886],[888,92662,92663],{"xmlns":890},[892,92664,92665,92669],{},[895,92666,92667],{},[898,92668,5362],{},[902,92670,5362],{"encoding":904},[883,92672,92674],{"className":92673},[886],[888,92675,92676],{"xmlns":890},[892,92677,92678,92716],{},[895,92679,92680,92682,92684,92686,92688,92690,92692,92694,92696,92698,92704,92706,92708,92710,92712,92714],{},[898,92681,1712],{},[1693,92683,1709],{"stretchy":1708},[898,92685,6629],{},[898,92687,4840],{},[1693,92689,1899],{"separator":1898},[898,92691,6629],{},[898,92693,4845],{},[1693,92695,1731],{"stretchy":1708},[1693,92697,1695],{},[1717,92699,92700,92702],{},[898,92701,6629],{},[898,92703,5362],{},[898,92705,1712],{},[1693,92707,1709],{"stretchy":1708},[898,92709,4840],{},[1693,92711,1899],{"separator":1898},[898,92713,4845],{},[1693,92715,1731],{"stretchy":1708},[902,92717,92718],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,92720,92721,85698],{},[38,92722,85631,92723],{},[883,92724,92726],{"className":92725},[886],[888,92727,92728],{"xmlns":890},[892,92729,92730,92734],{},[895,92731,92732],{},[898,92733,2719],{},[902,92735,2719],{"encoding":904},[123,92737,92738,92740,92741,92763,92764,92786,92787,3042],{},[38,92739,85132],{}," — konstantní (",[883,92742,92744],{"className":92743},[886],[888,92745,92746],{"xmlns":890},[892,92747,92748,92760],{},[895,92749,92750,92752,92754,92756,92758],{},[898,92751,207],{},[1693,92753,1892],{},[898,92755,1895],{},[1693,92757,1695],{},[1762,92759,1764],{},[902,92761,92762],{"encoding":904},"a+b=1","), rostoucí (",[883,92765,92767],{"className":92766},[886],[888,92768,92769],{"xmlns":890},[892,92770,92771,92783],{},[895,92772,92773,92775,92777,92779,92781],{},[898,92774,207],{},[1693,92776,1892],{},[898,92778,1895],{},[1693,92780,1922],{},[1762,92782,1764],{},[902,92784,92785],{"encoding":904},"a+b>1","), klesající (",[883,92788,92790],{"className":92789},[886],[888,92791,92792],{"xmlns":890},[892,92793,92794,92806],{},[895,92795,92796,92798,92800,92802,92804],{},[898,92797,207],{},[1693,92799,1892],{},[898,92801,1895],{},[1693,92803,1908],{},[1762,92805,1764],{},[902,92807,92808],{"encoding":904},"a+b\u003C1",[123,92810,92811,1863,92813,1343,92843,1863,92845,1789],{},[38,92812,81804],{},[883,92814,92816],{"className":92815},[886],[888,92817,92818],{"xmlns":890},[892,92819,92820,92840],{},[895,92821,92822,92824,92830,92832],{},[898,92823,2839],{},[3284,92825,92826,92828],{},[898,92827,1701],{},[898,92829,4840],{},[1693,92831,1695],{},[5688,92833,92834,92836,92838],{},[898,92835,1712],{},[898,92837,4840],{},[1693,92839,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,92841,92842],{"encoding":904},"MP_L = Q'_L",[38,92844,84707],{},[883,92846,92848],{"className":92847},[886],[888,92849,92850],{"xmlns":890},[892,92851,92852,92872],{},[895,92853,92854,92856,92862,92864],{},[898,92855,2839],{},[3284,92857,92858,92860],{},[898,92859,1701],{},[898,92861,4845],{},[1693,92863,1695],{},[5688,92865,92866,92868,92870],{},[898,92867,1712],{},[898,92869,4845],{},[1693,92871,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,92873,92874],{"encoding":904},"MP_K = Q'_K",[123,92876,92877,1863,92879,1789],{},[38,92878,86918],{},[883,92880,92882],{"className":92881},[886],[888,92883,92884],{"xmlns":890},[892,92885,92886,92924],{},[895,92887,92888,92890,92892,92894,92896,92902,92904,92906,92908,92910,92912,92918,92920,92922],{},[898,92889,1771],{},[898,92891,1712],{},[1693,92893,1695],{},[898,92895,2839],{},[3284,92897,92898,92900],{},[898,92899,1701],{},[898,92901,4840],{},[1915,92903,2239],{},[898,92905,1771],{},[898,92907,4840],{},[1693,92909,1892],{},[898,92911,2839],{},[3284,92913,92914,92916],{},[898,92915,1701],{},[898,92917,4845],{},[1915,92919,2239],{},[898,92921,1771],{},[898,92923,4845],{},[902,92925,92926],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,92928,92929,13877,92931,1789],{},[38,92930,87261],{},[883,92932,92934],{"className":92933},[886],[888,92935,92936],{"xmlns":890},[892,92937,92938,92980],{},[895,92939,92940,92942,92950,92952,92954,92962,92964,92966,92968,92970,92972,92974,92976,92978],{},[898,92941,4840],{},[5688,92943,92944,92946,92948],{},[898,92945,1712],{},[898,92947,4840],{},[1693,92949,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,92951,1892],{},[898,92953,4845],{},[5688,92955,92956,92958,92960],{},[898,92957,1712],{},[898,92959,4845],{},[1693,92961,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,92963,1695],{},[898,92965,5362],{},[1915,92967,2239],{},[898,92969,1712],{},[1693,92971,1709],{"stretchy":1708},[898,92973,4840],{},[1693,92975,1899],{"separator":1898},[898,92977,4845],{},[1693,92979,1731],{"stretchy":1708},[902,92981,92982],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,92984,92985,92988,92989,1789],{},[38,92986,92987],{},"Izokvanta"," — křivka ",[883,92990,92992],{"className":92991},[886],[888,92993,92994],{"xmlns":890},[892,92995,92996,93014],{},[895,92997,92998,93000,93002,93004,93006,93008,93010,93012],{},[898,92999,1712],{},[1693,93001,1709],{"stretchy":1708},[898,93003,4840],{},[1693,93005,1899],{"separator":1898},[898,93007,4845],{},[1693,93009,1731],{"stretchy":1708},[1693,93011,1695],{},[898,93013,87501],{},[902,93015,93016],{"encoding":904},"Q(L, K) = q",[123,93018,93019,1863,93021,1789],{},[38,93020,5255],{},[883,93022,93024],{"className":93023},[886],[888,93025,93026],{"xmlns":890},[892,93027,93028,93058],{},[895,93029,93030,93032,93034,93036,93038,93040,93042,93048,93050,93052],{},[898,93031,2839],{},[898,93033,2666],{},[898,93035,2663],{},[898,93037,3611],{},[1693,93039,1695],{},[898,93041,2839],{},[3284,93043,93044,93046],{},[898,93045,1701],{},[898,93047,4840],{},[898,93049,1705],{"mathvariant":1704},[898,93051,2839],{},[3284,93053,93054,93056],{},[898,93055,1701],{},[898,93057,4845],{},[902,93059,81516],{"encoding":904},[123,93061,93062,1863,93065,1789],{},[38,93063,93064],{},"Substituční vztah",[883,93066,93068],{"className":93067},[886],[888,93069,93070],{"xmlns":890},[892,93071,93072,93096],{},[895,93073,93074,93076,93078,93080,93082,93084,93086,93088,93090,93092,93094],{},[898,93075,3890],{"mathvariant":1704},[898,93077,4845],{},[1693,93079,4110],{},[1693,93081,1698],{},[898,93083,2839],{},[898,93085,2666],{},[898,93087,2663],{},[898,93089,3611],{},[1915,93091,2239],{},[898,93093,1771],{},[898,93095,4840],{},[902,93097,93098],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,93100,8685],{"id":8684},[120,93102,93103,93200,93207,93214],{},[123,93104,93105,1863,93107,93110,93111,1343,93114,93117,93118,93121,93122,93141,93142,25461,93161,93164,93165,93184,93185,3042],{},[38,93106,57483],{},[207,93108,784],{"className":93109,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,93112,8726],{"className":93113,"dataFsResolvedFilePath":764,"href":765},[210],[207,93115,793],{"className":93116,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,93119,880],{"className":93120,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,93123,93125],{"className":93124},[886],[888,93126,93127],{"xmlns":890},[892,93128,93129,93139],{},[895,93130,93131,93133,93135,93137],{},[898,93132,2839],{},[898,93134,2666],{},[898,93136,2663],{},[898,93138,3611],{},[902,93140,5814],{"encoding":904}," ↔ ",[883,93143,93145],{"className":93144},[886],[888,93146,93147],{"xmlns":890},[892,93148,93149,93159],{},[895,93150,93151,93153,93155,93157],{},[898,93152,2839],{},[898,93154,2666],{},[898,93156,2971],{},[898,93158,3611],{},[902,93160,5315],{"encoding":904},[207,93162,3261],{"className":93163,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,93166,93168],{"className":93167},[886],[888,93169,93170],{"xmlns":890},[892,93171,93172,93182],{},[895,93173,93174,93176],{},[898,93175,2719],{},[3284,93177,93178,93180],{},[898,93179,1701],{},[898,93181,4840],{},[902,93183,81345],{"encoding":904}," ↔ min ",[883,93186,93188],{"className":93187},[886],[888,93189,93190],{"xmlns":890},[892,93191,93192,93198],{},[895,93193,93194,93196],{},[898,93195,2719],{},[898,93197,2971],{},[902,93199,3331],{"encoding":904},[123,93201,93202,1863,93204,1789],{},[38,93203,10689],{},[207,93205,8759],{"className":93206,"dataFsResolvedFilePath":848,"href":849},[210],[123,93208,93209,1863,93211,1789],{},[38,93210,23033],{},[207,93212,1094],{"className":93213,"dataFsResolvedFilePath":838,"href":839},[210],[123,93215,93216,1863,93218,1789],{},[38,93217,8692],{},[207,93219,1653],{"className":93220,"dataFsResolvedFilePath":1651,"href":1652},[210],{"title":641,"searchDepth":642,"depth":642,"links":93222},[93223,93224,93225,93229,93231,93236,93237,93244,93245,93247,93248,93249,93251,93256,93257,93258,93262,93263],{"id":81539,"depth":642,"text":81540},{"id":81676,"depth":642,"text":81677},{"id":81779,"depth":642,"text":93226,"children":93227},"Mezní produkt práce (MPLMP_L)",[93228],{"id":82225,"depth":649,"text":82226},{"id":82714,"depth":642,"text":93230},"Průměrný produkt práce (APLAP_L)",{"id":82831,"depth":642,"text":82832,"children":93232},[93233,93234,93235],{"id":83068,"depth":649,"text":72225},{"id":83379,"depth":649,"text":83380},{"id":84099,"depth":649,"text":84100},{"id":84671,"depth":642,"text":84672},{"id":5065,"depth":642,"text":5066,"children":93238},[93239,93240,93242,93243],{"id":85131,"depth":649,"text":85132},{"id":85630,"depth":649,"text":93241},"Parametr efektivity AA",{"id":85701,"depth":649,"text":85702},{"id":43956,"depth":649,"text":86041},{"id":86228,"depth":642,"text":86229},{"id":86566,"depth":642,"text":93246},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":5319,"depth":642,"text":5320},{"id":81605,"depth":642,"text":16633},{"id":87665,"depth":642,"text":93250},"Mezní míra technické substituce (MRTSMRTS)",{"id":88530,"depth":642,"text":88531,"children":93252},[93253,93254,93255],{"id":88534,"depth":649,"text":88535},{"id":89177,"depth":649,"text":89178},{"id":89458,"depth":649,"text":89459},{"id":89804,"depth":642,"text":89805},{"id":56645,"depth":642,"text":8674},{"id":90154,"depth":642,"text":90155,"children":93259},[93260,93261],{"id":47222,"depth":649,"text":47223},{"id":90673,"depth":649,"text":90674},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fprodukce",{"title":4815,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,16666,93270,93271,93272,81605,93273,93274],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":93277,"title":93278,"body":93279,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":102219,"navigation":664,"path":102220,"seo":102221,"sources":102222,"stem":102223,"tags":102224,"type":10745,"updated":677,"__hash__":102227},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":93280,"toc":102193},[93281,93284,93286,93482,93491,93495,93498,93551,93555,93567,93571,93574,93591,93714,93720,93864,93874,93878,93913,93951,93999,94056,94116,94157,94733,94737,94820,94929,95022,95280,95283,95336,95447,95529,95533,95544,95777,95832,95838,95878,95941,95952,96143,96249,96401,96449,96454,96568,96606,96732,96778,96805,96882,96957,97037,97167,97228,97316,97320,97323,97392,97474,97481,97541,97851,97855,97861,97914,97930,97981,98119,98195,98308,98625,98629,98636,98796,98855,98859,98880,98977,99098,99212,99235,99298,99355,99607,99615,99619,99626,99880,99930,99986,99989,100153,100157,100255,100257,100289,100293,100426,100668,100852,101020,101327,101460,101647,101659,101661,102094,102096],[12,93282,93278],{"id":93283},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,93285,18851],{"id":18850},[724,93287,93288,1863,93290,93321,93322,93324,93325,93355,93356,93374,93375,93415,93416,93419,93420,93433,93434,35041,93437,93450,93451,93464,93465,93478,93479,1789],{},[38,93289,880],{},[883,93291,93293],{"className":93292},[886],[888,93294,93295],{"xmlns":890},[892,93296,93297,93319],{},[895,93298,93299,93301,93303,93309,93311,93317],{},[898,93300,900],{},[1693,93302,1709],{"stretchy":1708},[3284,93304,93305,93307],{},[898,93306,1712],{},[1762,93308,1764],{},[1693,93310,1899],{"separator":1898},[3284,93312,93313,93315],{},[898,93314,1712],{},[1762,93316,2398],{},[1693,93318,1731],{"stretchy":1708},[902,93320,23164],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,93323,5580],{}," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,93326,93328],{"className":93327},[886],[888,93329,93330],{"xmlns":890},[892,93331,93332,93352],{},[895,93333,93334,93336,93342,93344],{},[898,93335,2839],{},[3284,93337,93338,93340],{},[898,93339,900],{},[898,93341,5696],{},[1693,93343,1695],{},[5688,93345,93346,93348,93350],{},[898,93347,900],{},[898,93349,5696],{},[1693,93351,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,93353,93354],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,93357,93359],{"className":93358},[886],[888,93360,93361],{"xmlns":890},[892,93362,93363,93371],{},[895,93364,93365,93367,93369],{},[898,93366,900],{},[1693,93368,1695],{},[898,93370,2000],{},[902,93372,93373],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,93376,93378],{"className":93377},[886],[888,93379,93380],{"xmlns":890},[892,93381,93382,93412],{},[895,93383,93384,93386,93388,93390,93392,93394,93396,93402,93404,93406],{},[898,93385,2839],{},[898,93387,2666],{},[898,93389,2971],{},[898,93391,3611],{},[1693,93393,1695],{},[898,93395,2839],{},[3284,93397,93398,93400],{},[898,93399,900],{},[1762,93401,1764],{},[898,93403,1705],{"mathvariant":1704},[898,93405,2839],{},[3284,93407,93408,93410],{},[898,93409,900],{},[1762,93411,2398],{},[902,93413,93414],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,93417,93418],{},"teorii užitečnosti"," — funkce ",[883,93421,93423],{"className":93422},[886],[888,93424,93425],{"xmlns":890},[892,93426,93427,93431],{},[895,93428,93429],{},[898,93430,900],{},[902,93432,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,93435,93436],{},"Optimalizaci spotřebitele",[883,93438,93440],{"className":93439},[886],[888,93441,93442],{"xmlns":890},[892,93443,93444,93448],{},[895,93445,93446],{},[898,93447,900],{},[902,93449,900],{"encoding":904}," při rozpočtu, min ",[883,93452,93454],{"className":93453},[886],[888,93455,93456],{"xmlns":890},[892,93457,93458,93462],{},[895,93459,93460],{},[898,93461,1691],{},[902,93463,1691],{"encoding":904}," při dané ",[883,93466,93468],{"className":93467},[886],[888,93469,93470],{"xmlns":890},[892,93471,93472,93476],{},[895,93473,93474],{},[898,93475,900],{},[902,93477,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,93480,913],{"className":93481,"dataFsResolvedFilePath":911,"href":912},[210],[724,93483,93484,93485,93487,93488,1789],{},"Kapitola 6 knihy ",[614,93486,1653],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,93489,43535],{"className":93490,"dataFsResolvedFilePath":911,"href":912},[210],[115,93492,93494],{"id":93493},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,93496,93497],{},"Po prostudování této kapitoly byste měli umět:",[120,93499,93500,93506,93515,93520,93523,93529,93535,93538,93544],{},[123,93501,93502,93503,1899],{},"vyložit, co se rozumí termínem ",[38,93504,93505],{},"užitečnost",[123,93507,93508,93509,4286,93512,1899],{},"definovat pojmy ",[38,93510,93511],{},"svazek zboží",[38,93513,93514],{},"funkce užitečnosti",[123,93516,81554,93517,81561],{},[38,93518,93519],{},"mezní užitečnosti",[123,93521,93522],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,93524,81581,93525,93528],{},[38,93526,93527],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,93530,81602,93531,93534],{},[38,93532,93533],{},"křivky užitečnosti"," (indiferenční křivky),",[123,93536,93537],{},"vyjmenovat jejich základní vlastnosti,",[123,93539,81554,93540,93543],{},[38,93541,93542],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,93545,93546,93547,93550],{},"řešit ",[38,93548,93549],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,93552,93554],{"id":93553},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,93556,93557,93558,93562,93563,93566],{},"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 ",[207,93559,93561],{"className":93560,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,93564,93565],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,93568,93570],{"id":93569},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,93572,93573],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,93575,93576,93582],{},[123,93577,93578,93581],{},[38,93579,93580],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,93583,93584,93587,93588,93590],{},[38,93585,93586],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,93589,5580],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1636,93592,93593],{},[724,93594,93595,93597,93598,93601,93602,1863,93615,93618,93619,4286,93632,93651,93652,1343,93678,93705,93706,93709,93710,93713],{},[883,93596,8654],{}," Pozor — ordinalisté užitečnost ",[38,93599,93600],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,93603,93605],{"className":93604},[886],[888,93606,93607],{"xmlns":890},[892,93608,93609,93613],{},[895,93610,93611],{},[898,93612,900],{},[902,93614,900],{"encoding":904},[38,93616,93617],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,93620,93622],{"className":93621},[886],[888,93623,93624],{"xmlns":890},[892,93625,93626,93630],{},[895,93627,93628],{},[898,93629,900],{},[902,93631,900],{"encoding":904},[883,93633,93635],{"className":93634},[886],[888,93636,93637],{"xmlns":890},[892,93638,93639,93648],{},[895,93640,93641],{},[4467,93642,93643,93645],{"accent":1898},[898,93644,900],{},[1693,93646,93647],{},"~",[902,93649,93650],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,93653,93655],{"className":93654},[886],[888,93656,93657],{"xmlns":890},[892,93658,93659,93675],{},[895,93660,93661,93667,93669],{},[4467,93662,93663,93665],{"accent":1898},[898,93664,900],{},[1693,93666,93647],{},[1693,93668,1695],{},[1717,93670,93671,93673],{},[898,93672,900],{},[1762,93674,2398],{},[902,93676,93677],{"encoding":904},"\\tilde U = U^2",[883,93679,93681],{"className":93680},[886],[888,93682,93683],{"xmlns":890},[892,93684,93685,93702],{},[895,93686,93687,93693,93695,93698,93700],{},[4467,93688,93689,93691],{"accent":1898},[898,93690,900],{},[1693,93692,93647],{},[1693,93694,1695],{},[898,93696,93697],{},"ln",[1693,93699,3742],{},[898,93701,900],{},[902,93703,93704],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,93707,93708],{},"porovnání"," mezi svazky a ",[38,93711,93712],{},"poměry"," mezních veličin.",[724,93715,93716,93717,4300],{},"Ordinalistický přístup vychází z ",[38,93718,93719],{},"pěti hlavních předpokladů",[152,93721,93722,93728,93734,93852,93858],{},[123,93723,93724,93727],{},[38,93725,93726],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,93729,93730,93733],{},[38,93731,93732],{},"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.",[123,93735,93736,93739,93740,68473,93753,93766,93767,68473,93780,7617,93793,93796,93797,4286,93816,69298,93834,1789],{},[38,93737,93738],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,93741,93743],{"className":93742},[886],[888,93744,93745],{"xmlns":890},[892,93746,93747,93751],{},[895,93748,93749],{},[898,93750,2719],{},[902,93752,2719],{"encoding":904},[883,93754,93756],{"className":93755},[886],[888,93757,93758],{"xmlns":890},[892,93759,93760,93764],{},[895,93761,93762],{},[898,93763,7520],{},[902,93765,7520],{"encoding":904},", nebude jindy preferovat ",[883,93768,93770],{"className":93769},[886],[888,93771,93772],{"xmlns":890},[892,93773,93774,93778],{},[895,93775,93776],{},[898,93777,7520],{},[902,93779,7520],{"encoding":904},[883,93781,93783],{"className":93782},[886],[888,93784,93785],{"xmlns":890},[892,93786,93787,93791],{},[895,93788,93789],{},[898,93790,2719],{},[902,93792,2719],{"encoding":904},[38,93794,93795],{},"Tranzitivita",": pokud ",[883,93798,93800],{"className":93799},[886],[888,93801,93802],{"xmlns":890},[892,93803,93804,93813],{},[895,93805,93806,93808,93811],{},[898,93807,2719],{},[1693,93809,93810],{},"≻",[898,93812,7520],{},[902,93814,93815],{"encoding":904},"A \\succ B",[883,93817,93819],{"className":93818},[886],[888,93820,93821],{"xmlns":890},[892,93822,93823,93831],{},[895,93824,93825,93827,93829],{},[898,93826,7520],{},[1693,93828,93810],{},[898,93830,2971],{},[902,93832,93833],{"encoding":904},"B \\succ C",[883,93835,93837],{"className":93836},[886],[888,93838,93839],{"xmlns":890},[892,93840,93841,93849],{},[895,93842,93843,93845,93847],{},[898,93844,2719],{},[1693,93846,93810],{},[898,93848,2971],{},[902,93850,93851],{"encoding":904},"A \\succ C",[123,93853,93854,93857],{},[38,93855,93856],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,93859,93860,93863],{},[38,93861,93862],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,93865,93866,93867,93870,93871,1789],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,93868,93869],{},"preference"," a na příbuzné ",[614,93872,93873],{},"funkci užitečnosti",[115,93875,93877],{"id":93876},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,93879,93880,93881,93894,93895,93898,93899,93912],{},"Uvažujme ",[883,93882,93884],{"className":93883},[886],[888,93885,93886],{"xmlns":890},[892,93887,93888,93892],{},[895,93889,93890],{},[898,93891,5362],{},[902,93893,5362],{"encoding":904}," různých zboží. ",[38,93896,93897],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,93900,93902],{"className":93901},[886],[888,93903,93904],{"xmlns":890},[892,93905,93906,93910],{},[895,93907,93908],{},[898,93909,5362],{},[902,93911,5362],{"encoding":904},"-tice",[724,93914,93915],{},[883,93916,93918],{"className":93917},[886],[888,93919,93920],{"xmlns":890},[892,93921,93922,93948],{},[895,93923,93924,93926,93932,93934,93936,93938,93944,93946],{},[1693,93925,1709],{"stretchy":1708},[3284,93927,93928,93930],{},[898,93929,1712],{},[1762,93931,1764],{},[1693,93933,1899],{"separator":1898},[1693,93935,16501],{},[1693,93937,1899],{"separator":1898},[3284,93939,93940,93942],{},[898,93941,1712],{},[898,93943,5362],{},[1693,93945,1731],{"stretchy":1708},[1693,93947,1899],{"separator":1898},[902,93949,93950],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,93952,11188,93953,93970,93971,93984,93985,93988,93989,93992,93993,93996,93997,4300],{},[883,93954,93956],{"className":93955},[886],[888,93957,93958],{"xmlns":890},[892,93959,93960,93968],{},[895,93961,93962],{},[3284,93963,93964,93966],{},[898,93965,1712],{},[898,93967,5696],{},[902,93969,54302],{"encoding":904}," značí množství ",[883,93972,93974],{"className":93973},[886],[888,93975,93976],{"xmlns":890},[892,93977,93978,93982],{},[895,93979,93980],{},[898,93981,5696],{},[902,93983,5696],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,93986,93987],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,93990,93991],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,93994,93995],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,93998,93873],{},[883,94000,94002],{"className":94001},[886],[888,94003,94004],{"xmlns":890,"display":34854},[892,94005,94006,94053],{},[3626,94007,94008],{"width":34859},[3632,94009,94010,94012,94046,94048],{},[3635,94011],{"width":34864},[3635,94013,94014],{},[895,94015,94016,94018,94020,94022,94024,94030,94032,94034,94036,94042,94044],{},[898,94017,900],{},[1693,94019,1695],{},[898,94021,900],{},[1693,94023,1709],{"stretchy":1708},[3284,94025,94026,94028],{},[898,94027,1712],{},[1762,94029,1764],{},[1693,94031,1899],{"separator":1898},[1693,94033,16501],{},[1693,94035,1899],{"separator":1898},[3284,94037,94038,94040],{},[898,94039,1712],{},[898,94041,5362],{},[1693,94043,1731],{"stretchy":1708},[1693,94045,1899],{"separator":1898},[3635,94047],{"width":34864},[3635,94049,94050],{},[1915,94051,94052],{},"(6.1)",[902,94054,94055],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,94057,11188,94058,94088,94089,94111,94112,94115],{},[883,94059,94061],{"className":94060},[886],[888,94062,94063],{"xmlns":890},[892,94064,94065,94085],{},[895,94066,94067,94073,94075,94077,94079],{},[3284,94068,94069,94071],{},[898,94070,1712],{},[1762,94072,1764],{},[1693,94074,1899],{"separator":1898},[1693,94076,16501],{},[1693,94078,1899],{"separator":1898},[3284,94080,94081,94083],{},[898,94082,1712],{},[898,94084,5362],{},[902,94086,94087],{"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 ",[883,94090,94092],{"className":94091},[886],[888,94093,94094],{"xmlns":890},[892,94095,94096,94108],{},[895,94097,94098,94100,94102],{},[898,94099,900],{},[1693,94101,1899],{"separator":1898},[4467,94103,94104,94106],{"accent":1898},[898,94105,900],{},[1693,94107,93647],{},[902,94109,94110],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,94113,94114],{},"monotónní transformace"," zachovávající pořadí.",[724,94117,94118,94119,13877,94122,1789],{},"Dále se omezíme na funkce pro ",[38,94120,94121],{},"dvě zboží",[883,94123,94125],{"className":94124},[886],[888,94126,94127],{"xmlns":890},[892,94128,94129,94155],{},[895,94130,94131,94133,94135,94137,94139,94145,94147,94153],{},[898,94132,900],{},[1693,94134,1695],{},[898,94136,900],{},[1693,94138,1709],{"stretchy":1708},[3284,94140,94141,94143],{},[898,94142,1712],{},[1762,94144,1764],{},[1693,94146,1899],{"separator":1898},[3284,94148,94149,94151],{},[898,94150,1712],{},[1762,94152,2398],{},[1693,94154,1731],{"stretchy":1708},[902,94156,5567],{"encoding":904},[1636,94158,94159,94234],{},[724,94160,94161,94163,94164,4300],{},[883,94162,59453],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,94165,94167],{"className":94166},[886],[888,94168,94169],{"xmlns":890},[892,94170,94171,94231],{},[895,94172,94173,94175,94177,94179,94181,94187,94189,94195,94197,94203,94205,94207,94209],{},[898,94174,900],{},[1693,94176,1695],{},[898,94178,900],{},[1693,94180,1709],{"stretchy":1708},[3284,94182,94183,94185],{},[898,94184,1712],{},[1762,94186,1764],{},[1693,94188,1899],{"separator":1898},[3284,94190,94191,94193],{},[898,94192,1712],{},[1762,94194,2398],{},[1693,94196,1899],{"separator":1898},[3284,94198,94199,94201],{},[898,94200,1712],{},[1762,94202,8357],{},[1693,94204,1731],{"stretchy":1708},[1693,94206,1695],{},[1762,94208,2398],{},[14976,94210,94211],{},[895,94212,94213,94219,94225],{},[3284,94214,94215,94217],{},[898,94216,1712],{},[1762,94218,1764],{},[3284,94220,94221,94223],{},[898,94222,1712],{},[1762,94224,2398],{},[3284,94226,94227,94229],{},[898,94228,1712],{},[1762,94230,8357],{},[902,94232,94233],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,94235,94236,94429],{},[123,94237,94238,94239,94265,94266,19770,94292,4286,94351,12457,94411,15283],{},"svazek ",[883,94240,94242],{"className":94241},[886],[888,94243,94244],{"xmlns":890},[892,94245,94246,94262],{},[895,94247,94248,94250,94252,94254,94256,94258,94260],{},[1693,94249,1709],{"stretchy":1708},[1762,94251,48633],{},[1693,94253,1899],{"separator":1898},[1762,94255,9262],{},[1693,94257,1899],{"separator":1898},[1762,94259,48611],{},[1693,94261,1731],{"stretchy":1708},[902,94263,94264],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,94267,94269],{"className":94268},[886],[888,94270,94271],{"xmlns":890},[892,94272,94273,94289],{},[895,94274,94275,94277,94279,94281,94283,94285,94287],{},[1693,94276,1709],{"stretchy":1708},[1762,94278,10881],{},[1693,94280,1899],{"separator":1898},[1762,94282,10881],{},[1693,94284,1899],{"separator":1898},[1762,94286,73320],{},[1693,94288,1731],{"stretchy":1708},[902,94290,94291],{"encoding":904},"(9, 9, 27)",[883,94293,94295],{"className":94294},[886],[888,94296,94297],{"xmlns":890},[892,94298,94299,94348],{},[895,94300,94301,94303,94305,94307,94309,94311,94313,94315,94317,94319,94321,94335,94337,94339,94344,94346],{},[898,94302,900],{},[1693,94304,1709],{"stretchy":1708},[1762,94306,48633],{},[1693,94308,1899],{"separator":1898},[1762,94310,9262],{},[1693,94312,1899],{"separator":1898},[1762,94314,48611],{},[1693,94316,1731],{"stretchy":1708},[1693,94318,1695],{},[1762,94320,2398],{},[14976,94322,94323],{},[895,94324,94325,94327,94329,94331,94333],{},[1762,94326,48633],{},[1693,94328,1715],{},[1762,94330,9262],{},[1693,94332,1715],{},[1762,94334,48611],{},[1693,94336,1695],{},[1762,94338,2398],{},[14976,94340,94341],{},[1762,94342,94343],{},"4096",[1693,94345,1695],{},[1762,94347,12485],{},[902,94349,94350],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,94352,94354],{"className":94353},[886],[888,94355,94356],{"xmlns":890},[892,94357,94358,94408],{},[895,94359,94360,94362,94364,94366,94368,94370,94372,94374,94376,94378,94380,94394,94396,94398,94403,94405],{},[898,94361,900],{},[1693,94363,1709],{"stretchy":1708},[1762,94365,10881],{},[1693,94367,1899],{"separator":1898},[1762,94369,10881],{},[1693,94371,1899],{"separator":1898},[1762,94373,73320],{},[1693,94375,1731],{"stretchy":1708},[1693,94377,1695],{},[1762,94379,2398],{},[14976,94381,94382],{},[895,94383,94384,94386,94388,94390,94392],{},[1762,94385,10881],{},[1693,94387,1715],{},[1762,94389,10881],{},[1693,94391,1715],{},[1762,94393,73320],{},[1693,94395,1695],{},[1762,94397,2398],{},[14976,94399,94400],{},[1762,94401,94402],{},"2187",[1693,94404,12766],{},[1762,94406,94407],{},"93,53",[902,94409,94410],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,94412,94414],{"className":94413},[886],[888,94415,94416],{"xmlns":890},[892,94417,94418,94426],{},[895,94419,94420,94422,94424],{},[1762,94421,12485],{},[1693,94423,1922],{},[1762,94425,94407],{},[902,94427,94428],{"encoding":904},"128 > 93{,}53",[123,94430,94431,94432,4286,94458,94484,94485,4286,94525,94566,94567,94613,94614,4286,94640,9745,94666,4286,94684,94702,94703,1789],{},"svazky ",[883,94433,94435],{"className":94434},[886],[888,94436,94437],{"xmlns":890},[892,94438,94439,94455],{},[895,94440,94441,94443,94445,94447,94449,94451,94453],{},[1693,94442,1709],{"stretchy":1708},[1762,94444,9262],{},[1693,94446,1899],{"separator":1898},[1762,94448,12453],{},[1693,94450,1899],{"separator":1898},[1762,94452,2398],{},[1693,94454,1731],{"stretchy":1708},[902,94456,94457],{"encoding":904},"(4, 8, 2)",[883,94459,94461],{"className":94460},[886],[888,94462,94463],{"xmlns":890},[892,94464,94465,94481],{},[895,94466,94467,94469,94471,94473,94475,94477,94479],{},[1693,94468,1709],{"stretchy":1708},[1762,94470,48611],{},[1693,94472,1899],{"separator":1898},[1762,94474,1764],{},[1693,94476,1899],{"separator":1898},[1762,94478,9262],{},[1693,94480,1731],{"stretchy":1708},[902,94482,94483],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,94486,94488],{"className":94487},[886],[888,94489,94490],{"xmlns":890},[892,94491,94492,94522],{},[895,94493,94494,94496,94498,94500,94502,94504,94506,94508,94510,94512,94514,94518,94520],{},[898,94495,900],{},[1693,94497,1709],{"stretchy":1708},[1762,94499,9262],{},[1693,94501,1899],{"separator":1898},[1762,94503,12453],{},[1693,94505,1899],{"separator":1898},[1762,94507,2398],{},[1693,94509,1731],{"stretchy":1708},[1693,94511,1695],{},[1762,94513,2398],{},[14976,94515,94516],{},[1762,94517,48611],{},[1693,94519,1695],{},[1762,94521,48633],{},[902,94523,94524],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,94526,94528],{"className":94527},[886],[888,94529,94530],{"xmlns":890},[892,94531,94532,94563],{},[895,94533,94534,94536,94538,94540,94542,94544,94546,94548,94550,94552,94554,94559,94561],{},[898,94535,900],{},[1693,94537,1709],{"stretchy":1708},[1762,94539,48611],{},[1693,94541,1899],{"separator":1898},[1762,94543,1764],{},[1693,94545,1899],{"separator":1898},[1762,94547,9262],{},[1693,94549,1731],{"stretchy":1708},[1693,94551,1695],{},[1762,94553,2398],{},[14976,94555,94556],{},[1762,94557,94558],{},"256",[1693,94560,1695],{},[1762,94562,79073],{},[902,94564,94565],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,94568,94570],{"className":94569},[886],[888,94571,94572],{"xmlns":890},[892,94573,94574,94610],{},[895,94575,94576,94578,94580,94582,94584,94586,94588,94590,94592,94594,94596,94598,94600,94602,94604,94606,94608],{},[898,94577,900],{},[1693,94579,1709],{"stretchy":1708},[1762,94581,9262],{},[1693,94583,1899],{"separator":1898},[1762,94585,12453],{},[1693,94587,1899],{"separator":1898},[1762,94589,2398],{},[1693,94591,1731],{"stretchy":1708},[1693,94593,1695],{},[898,94595,900],{},[1693,94597,1709],{"stretchy":1708},[1762,94599,48611],{},[1693,94601,1899],{"separator":1898},[1762,94603,1764],{},[1693,94605,1899],{"separator":1898},[1762,94607,9262],{},[1693,94609,1731],{"stretchy":1708},[902,94611,94612],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,94615,94617],{"className":94616},[886],[888,94618,94619],{"xmlns":890},[892,94620,94621,94637],{},[895,94622,94623,94625,94627,94629,94631,94633,94635],{},[1762,94624,9262],{},[1693,94626,1715],{},[1762,94628,12453],{},[1693,94630,1715],{},[1762,94632,2398],{},[1693,94634,1695],{},[1762,94636,48611],{},[902,94638,94639],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,94641,94643],{"className":94642},[886],[888,94644,94645],{"xmlns":890},[892,94646,94647,94663],{},[895,94648,94649,94651,94653,94655,94657,94659,94661],{},[1762,94650,48611],{},[1693,94652,1715],{},[1762,94654,1764],{},[1693,94656,1715],{},[1762,94658,9262],{},[1693,94660,1695],{},[1762,94662,94558],{},[902,94664,94665],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,94667,94669],{"className":94668},[886],[888,94670,94671],{"xmlns":890},[892,94672,94673,94681],{},[895,94674,94675,94677,94679],{},[898,94676,900],{},[1693,94678,1695],{},[1762,94680,48633],{},[902,94682,94683],{"encoding":904},"U = 16",[883,94685,94687],{"className":94686},[886],[888,94688,94689],{"xmlns":890},[892,94690,94691,94699],{},[895,94692,94693,94695,94697],{},[898,94694,900],{},[1693,94696,1695],{},[1762,94698,79073],{},[902,94700,94701],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,94704,94706],{"className":94705},[886],[888,94707,94708],{"xmlns":890},[892,94709,94710,94730],{},[895,94711,94712,94718,94724],{},[3284,94713,94714,94716],{},[898,94715,1712],{},[1762,94717,1764],{},[3284,94719,94720,94722],{},[898,94721,1712],{},[1762,94723,2398],{},[3284,94725,94726,94728],{},[898,94727,1712],{},[1762,94729,8357],{},[902,94731,94732],{"encoding":904},"Q_1 Q_2 Q_3",[115,94734,94736],{"id":94735},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,94738,94739,94740,6055,94775,1863,94778,48585,94795,16877,94812,94815,94816,94819],{},"Pro funkci užitečnosti ",[883,94741,94743],{"className":94742},[886],[888,94744,94745],{"xmlns":890},[892,94746,94747,94773],{},[895,94748,94749,94751,94753,94755,94757,94763,94765,94771],{},[898,94750,900],{},[1693,94752,1695],{},[898,94754,900],{},[1693,94756,1709],{"stretchy":1708},[3284,94758,94759,94761],{},[898,94760,1712],{},[1762,94762,1764],{},[1693,94764,1899],{"separator":1898},[3284,94766,94767,94769],{},[898,94768,1712],{},[1762,94770,2398],{},[1693,94772,1731],{"stretchy":1708},[902,94774,5567],{"encoding":904},[38,94776,94777],{},"mezní užitečnost",[883,94779,94781],{"className":94780},[886],[888,94782,94783],{"xmlns":890},[892,94784,94785,94793],{},[895,94786,94787],{},[3284,94788,94789,94791],{},[898,94790,1712],{},[1762,94792,1764],{},[902,94794,5809],{"encoding":904},[883,94796,94798],{"className":94797},[886],[888,94799,94800],{"xmlns":890},[892,94801,94802,94810],{},[895,94803,94804],{},[3284,94805,94806,94808],{},[898,94807,1712],{},[1762,94809,2398],{},[902,94811,5790],{"encoding":904},[38,94813,94814],{},"marginal utility",") parciální ",[207,94817,1145],{"className":94818,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,94821,94823],{"className":94822},[886],[888,94824,94825],{"xmlns":890,"display":34854},[892,94826,94827,94926],{},[3626,94828,94829],{"width":34859},[3632,94830,94831,94833,94919,94921],{},[3635,94832],{"width":34864},[3635,94834,94835],{},[895,94836,94837,94839,94845,94847,94855,94857,94875,94877,94879,94881,94887,94889,94897,94899,94917],{},[898,94838,2839],{},[3284,94840,94841,94843],{},[898,94842,900],{},[1762,94844,1764],{},[1693,94846,1695],{},[5688,94848,94849,94851,94853],{},[898,94850,900],{},[1762,94852,1764],{},[1693,94854,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,94856,1695],{},[2132,94858,94859,94865],{},[895,94860,94861,94863],{},[898,94862,2228],{"mathvariant":1704},[898,94864,900],{},[895,94866,94867,94869],{},[898,94868,2228],{"mathvariant":1704},[3284,94870,94871,94873],{},[898,94872,1712],{},[1762,94874,1764],{},[1693,94876,1899],{"separator":1898},[1901,94878],{"width":3630},[898,94880,2839],{},[3284,94882,94883,94885],{},[898,94884,900],{},[1762,94886,2398],{},[1693,94888,1695],{},[5688,94890,94891,94893,94895],{},[898,94892,900],{},[1762,94894,2398],{},[1693,94896,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,94898,1695],{},[2132,94900,94901,94907],{},[895,94902,94903,94905],{},[898,94904,2228],{"mathvariant":1704},[898,94906,900],{},[895,94908,94909,94911],{},[898,94910,2228],{"mathvariant":1704},[3284,94912,94913,94915],{},[898,94914,1712],{},[1762,94916,2398],{},[898,94918,1789],{"mathvariant":1704},[3635,94920],{"width":34864},[3635,94922,94923],{},[1915,94924,94925],{},"(6.2)",[902,94927,94928],{"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}",[724,94930,94931,94932,94966,94967,94997,94998,1863,95001,1789],{},"Pro pevné ",[883,94933,94935],{"className":94934},[886],[888,94936,94937],{"xmlns":890},[892,94938,94939,94963],{},[895,94940,94941,94947,94949,94951,94953,94959,94961],{},[3284,94942,94943,94945],{},[898,94944,1712],{},[1762,94946,1764],{},[1693,94948,1695],{},[898,94950,207],{},[1693,94952,1899],{"separator":1898},[3284,94954,94955,94957],{},[898,94956,1712],{},[1762,94958,2398],{},[1693,94960,1695],{},[898,94962,1895],{},[902,94964,94965],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,94968,94970],{"className":94969},[886],[888,94971,94972],{"xmlns":890},[892,94973,94974,94994],{},[895,94975,94976,94978,94984,94986,94988,94990,94992],{},[898,94977,2839],{},[3284,94979,94980,94982],{},[898,94981,900],{},[1762,94983,1764],{},[1693,94985,1709],{"stretchy":1708},[898,94987,207],{},[1693,94989,1899],{"separator":1898},[898,94991,1895],{},[1693,94993,1731],{"stretchy":1708},[902,94995,94996],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,94999,95000],{},"v bodě (na hladině)",[883,95002,95004],{"className":95003},[886],[888,95005,95006],{"xmlns":890},[892,95007,95008,95020],{},[895,95009,95010,95012,95014,95016,95018],{},[1693,95011,9392],{"stretchy":1708},[898,95013,207],{},[1693,95015,1899],{"separator":1898},[898,95017,1895],{},[1693,95019,9407],{"stretchy":1708},[902,95021,17670],{"encoding":904},[1636,95023,95024],{},[724,95025,95026,95028,95029,95059,95088,95089,9516,95102,9530,95119,95140,95141,9577,95158,9591,95171,95188,95189,95211,95212,95241,95242,7721,95262,95279],{},[883,95027,11036],{}," Intuice — co říká ",[883,95030,95032],{"className":95031},[886],[888,95033,95034],{"xmlns":890},[892,95035,95036,95056],{},[895,95037,95038,95040,95046,95048,95050,95052,95054],{},[898,95039,2839],{},[3284,95041,95042,95044],{},[898,95043,900],{},[1762,95045,1764],{},[1693,95047,1709],{"stretchy":1708},[898,95049,207],{},[1693,95051,1899],{"separator":1898},[898,95053,1895],{},[1693,95055,1731],{"stretchy":1708},[902,95057,95058],{"encoding":904},"MU_1(a,b)",[883,95060,95062],{"className":95061},[886],[888,95063,95064],{"xmlns":890},[892,95065,95066,95086],{},[895,95067,95068,95070,95076,95078,95080,95082,95084],{},[898,95069,2839],{},[3284,95071,95072,95074],{},[898,95073,900],{},[1762,95075,1764],{},[1693,95077,1709],{"stretchy":1708},[898,95079,207],{},[1693,95081,1899],{"separator":1898},[898,95083,1895],{},[1693,95085,1731],{"stretchy":1708},[902,95087,94996],{"encoding":904}," je rychlost změny ",[883,95090,95092],{"className":95091},[886],[888,95093,95094],{"xmlns":890},[892,95095,95096,95100],{},[895,95097,95098],{},[898,95099,900],{},[902,95101,900],{"encoding":904},[883,95103,95105],{"className":95104},[886],[888,95106,95107],{"xmlns":890},[892,95108,95109,95117],{},[895,95110,95111],{},[3284,95112,95113,95115],{},[898,95114,1712],{},[1762,95116,1764],{},[902,95118,5809],{"encoding":904},[883,95120,95122],{"className":95121},[886],[888,95123,95124],{"xmlns":890},[892,95125,95126,95138],{},[895,95127,95128,95130,95132,95134,95136],{},[1693,95129,9392],{"stretchy":1708},[898,95131,207],{},[1693,95133,1899],{"separator":1898},[898,95135,1895],{},[1693,95137,9407],{"stretchy":1708},[902,95139,17670],{"encoding":904},". Přibližně: změní-li se ",[883,95142,95144],{"className":95143},[886],[888,95145,95146],{"xmlns":890},[892,95147,95148,95156],{},[895,95149,95150],{},[3284,95151,95152,95154],{},[898,95153,1712],{},[1762,95155,1764],{},[902,95157,5809],{"encoding":904},[883,95159,95161],{"className":95160},[886],[888,95162,95163],{"xmlns":890},[892,95164,95165,95169],{},[895,95166,95167],{},[898,95168,207],{},[902,95170,207],{"encoding":904},[883,95172,95174],{"className":95173},[886],[888,95175,95176],{"xmlns":890},[892,95177,95178,95186],{},[895,95179,95180,95182,95184],{},[898,95181,207],{},[1693,95183,1892],{},[1762,95185,1764],{},[902,95187,9609],{"encoding":904}," při pevném ",[883,95190,95192],{"className":95191},[886],[888,95193,95194],{"xmlns":890},[892,95195,95196,95208],{},[895,95197,95198,95204,95206],{},[3284,95199,95200,95202],{},[898,95201,1712],{},[1762,95203,2398],{},[1693,95205,1695],{},[898,95207,1895],{},[902,95209,95210],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,95213,95215],{"className":95214},[886],[888,95216,95217],{"xmlns":890},[892,95218,95219,95239],{},[895,95220,95221,95223,95229,95231,95233,95235,95237],{},[898,95222,2839],{},[3284,95224,95225,95227],{},[898,95226,900],{},[1762,95228,1764],{},[1693,95230,1709],{"stretchy":1708},[898,95232,207],{},[1693,95234,1899],{"separator":1898},[898,95236,1895],{},[1693,95238,1731],{"stretchy":1708},[902,95240,94996],{"encoding":904},". Stejně tak ",[883,95243,95245],{"className":95244},[886],[888,95246,95247],{"xmlns":890},[892,95248,95249,95259],{},[895,95250,95251,95253],{},[898,95252,2839],{},[3284,95254,95255,95257],{},[898,95256,900],{},[1762,95258,2398],{},[902,95260,95261],{"encoding":904},"MU_2",[883,95263,95265],{"className":95264},[886],[888,95266,95267],{"xmlns":890},[892,95268,95269,95277],{},[895,95270,95271],{},[3284,95272,95273,95275],{},[898,95274,1712],{},[1762,95276,2398],{},[902,95278,5790],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,95281,86918],{"id":95282},"totální-diferenciál",[724,95284,95285,95286,55104,95302,95332,95333,4300],{},"Přibližnou změnu užitečnosti ",[883,95287,95289],{"className":95288},[886],[888,95290,95291],{"xmlns":890},[892,95292,95293,95299],{},[895,95294,95295,95297],{},[898,95296,3890],{"mathvariant":1704},[898,95298,900],{},[902,95300,95301],{"encoding":904},"\\Delta U",[883,95303,95305],{"className":95304},[886],[888,95306,95307],{"xmlns":890},[892,95308,95309,95329],{},[895,95310,95311,95313,95319,95321,95323],{},[898,95312,1771],{"mathvariant":1704},[3284,95314,95315,95317],{},[898,95316,1712],{},[1762,95318,1764],{},[1693,95320,1899],{"separator":1898},[898,95322,1771],{"mathvariant":1704},[3284,95324,95325,95327],{},[898,95326,1712],{},[1762,95328,2398],{},[902,95330,95331],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,95334,95335],{},"totálního diferenciálu",[883,95337,95339],{"className":95338},[886],[888,95340,95341],{"xmlns":890,"display":34854},[892,95342,95343,95444],{},[3626,95344,95345],{"width":34859},[3632,95346,95347,95349,95437,95439],{},[3635,95348],{"width":34864},[3635,95350,95351],{},[895,95352,95353,95355,95357,95359,95361,95363,95365,95373,95375,95381,95383,95391,95393,95399,95401,95403,95409,95411,95417,95419,95421,95427,95429,95435],{},[898,95354,3890],{"mathvariant":1704},[898,95356,900],{},[1693,95358,4110],{},[898,95360,1771],{"mathvariant":1704},[898,95362,900],{},[1693,95364,1695],{},[5688,95366,95367,95369,95371],{},[898,95368,900],{},[1762,95370,1764],{},[1693,95372,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[898,95374,1771],{"mathvariant":1704},[3284,95376,95377,95379],{},[898,95378,1712],{},[1762,95380,1764],{},[1693,95382,1892],{},[5688,95384,95385,95387,95389],{},[898,95386,900],{},[1762,95388,2398],{},[1693,95390,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[898,95392,1771],{"mathvariant":1704},[3284,95394,95395,95397],{},[898,95396,1712],{},[1762,95398,2398],{},[1693,95400,1695],{},[898,95402,2839],{},[3284,95404,95405,95407],{},[898,95406,900],{},[1762,95408,1764],{},[898,95410,1771],{"mathvariant":1704},[3284,95412,95413,95415],{},[898,95414,1712],{},[1762,95416,1764],{},[1693,95418,1892],{},[898,95420,2839],{},[3284,95422,95423,95425],{},[898,95424,900],{},[1762,95426,2398],{},[898,95428,1771],{"mathvariant":1704},[3284,95430,95431,95433],{},[898,95432,1712],{},[1762,95434,2398],{},[898,95436,1789],{"mathvariant":1704},[3635,95438],{"width":34864},[3635,95440,95441],{},[1915,95442,95443],{},"(6.3)",[902,95445,95446],{"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}",[724,95448,82180,95449,1789],{},[883,95450,95452],{"className":95451},[886],[888,95453,95454],{"xmlns":890},[892,95455,95456,95526],{},[895,95457,95458,95460,95462,95464,95466,95468,95474,95476,95478,95484,95486,95492,95494,95496,95502,95504,95506,95508,95510,95516,95518,95524],{},[898,95459,3890],{"mathvariant":1704},[898,95461,900],{},[1693,95463,1695],{},[898,95465,900],{},[1693,95467,1709],{"stretchy":1708},[3284,95469,95470,95472],{},[898,95471,1712],{},[1762,95473,1764],{},[1693,95475,1892],{},[898,95477,1771],{"mathvariant":1704},[3284,95479,95480,95482],{},[898,95481,1712],{},[1762,95483,1764],{},[1693,95485,1899],{"separator":1898},[3284,95487,95488,95490],{},[898,95489,1712],{},[1762,95491,2398],{},[1693,95493,1892],{},[898,95495,1771],{"mathvariant":1704},[3284,95497,95498,95500],{},[898,95499,1712],{},[1762,95501,2398],{},[1693,95503,1731],{"stretchy":1708},[1693,95505,1698],{},[898,95507,900],{},[1693,95509,1709],{"stretchy":1708},[3284,95511,95512,95514],{},[898,95513,1712],{},[1762,95515,1764],{},[1693,95517,1899],{"separator":1898},[3284,95519,95520,95522],{},[898,95521,1712],{},[1762,95523,2398],{},[1693,95525,1731],{"stretchy":1708},[902,95527,95528],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,95530,95532],{"id":95531},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,95534,95535,95536,95539,95540,95543],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,95537,95538],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,95541,95542],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,95545,95546,95549,95550,48585,95576,95602,95603,1343,95635,95667,95668,4286,95722,95776],{},[38,95547,95548],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,95551,95553],{"className":95552},[886],[888,95554,95555],{"xmlns":890},[892,95556,95557,95573],{},[895,95558,95559,95565,95567],{},[3284,95560,95561,95563],{},[898,95562,1712],{},[1762,95564,2398],{},[1693,95566,1695],{},[3284,95568,95569,95571],{},[898,95570,207],{},[1762,95572,1911],{},[902,95574,95575],{"encoding":904},"Q_2 = a_0",[883,95577,95579],{"className":95578},[886],[888,95580,95581],{"xmlns":890},[892,95582,95583,95599],{},[895,95584,95585,95591,95593],{},[3284,95586,95587,95589],{},[898,95588,1712],{},[1762,95590,1764],{},[1693,95592,1695],{},[3284,95594,95595,95597],{},[898,95596,1895],{},[1762,95598,1911],{},[902,95600,95601],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,95604,95606],{"className":95605},[886],[888,95607,95608],{"xmlns":890},[892,95609,95610,95632],{},[895,95611,95612,95614,95616,95622,95624,95630],{},[898,95613,900],{},[1693,95615,1709],{"stretchy":1708},[3284,95617,95618,95620],{},[898,95619,1712],{},[1762,95621,1764],{},[1693,95623,1899],{"separator":1898},[3284,95625,95626,95628],{},[898,95627,207],{},[1762,95629,1911],{},[1693,95631,1731],{"stretchy":1708},[902,95633,95634],{"encoding":904},"U(Q_1, a_0)",[883,95636,95638],{"className":95637},[886],[888,95639,95640],{"xmlns":890},[892,95641,95642,95664],{},[895,95643,95644,95646,95648,95654,95656,95662],{},[898,95645,900],{},[1693,95647,1709],{"stretchy":1708},[3284,95649,95650,95652],{},[898,95651,1895],{},[1762,95653,1911],{},[1693,95655,1899],{"separator":1898},[3284,95657,95658,95660],{},[898,95659,1712],{},[1762,95661,2398],{},[1693,95663,1731],{"stretchy":1708},[902,95665,95666],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,95669,95671],{"className":95670},[886],[888,95672,95673],{"xmlns":890},[892,95674,95675,95719],{},[895,95676,95677,95715,95717],{},[3638,95678,95679],{"scriptlevel":1911,"displaystyle":1898},[2132,95680,95681,95705],{},[895,95682,95683,95685,95687,95689,95695,95697,95703],{},[898,95684,1771],{"mathvariant":1704},[898,95686,900],{},[1693,95688,1709],{"stretchy":1708},[3284,95690,95691,95693],{},[898,95692,1712],{},[1762,95694,1764],{},[1693,95696,1899],{"separator":1898},[3284,95698,95699,95701],{},[898,95700,207],{},[1762,95702,1911],{},[1693,95704,1731],{"stretchy":1708},[895,95706,95707,95709],{},[898,95708,1771],{"mathvariant":1704},[3284,95710,95711,95713],{},[898,95712,1712],{},[1762,95714,1764],{},[1693,95716,1922],{},[1762,95718,1911],{},[902,95720,95721],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,95723,95725],{"className":95724},[886],[888,95726,95727],{"xmlns":890},[892,95728,95729,95773],{},[895,95730,95731,95769,95771],{},[3638,95732,95733],{"scriptlevel":1911,"displaystyle":1898},[2132,95734,95735,95759],{},[895,95736,95737,95739,95741,95743,95749,95751,95757],{},[898,95738,1771],{"mathvariant":1704},[898,95740,900],{},[1693,95742,1709],{"stretchy":1708},[3284,95744,95745,95747],{},[898,95746,1895],{},[1762,95748,1911],{},[1693,95750,1899],{"separator":1898},[3284,95752,95753,95755],{},[898,95754,1712],{},[1762,95756,2398],{},[1693,95758,1731],{"stretchy":1708},[895,95760,95761,95763],{},[898,95762,1771],{"mathvariant":1704},[3284,95764,95765,95767],{},[898,95766,1712],{},[1762,95768,2398],{},[1693,95770,1922],{},[1762,95772,1911],{},[902,95774,95775],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,95778,95780],{"className":95779},[886],[888,95781,95782],{"xmlns":890,"display":34854},[892,95783,95784,95829],{},[3626,95785,95786],{"width":34859},[3632,95787,95788,95790,95822,95824],{},[3635,95789],{"width":34864},[3635,95791,95792],{},[895,95793,95794,95802,95804,95806,95808,95810,95818,95820],{},[5688,95795,95796,95798,95800],{},[898,95797,900],{},[1762,95799,1764],{},[1693,95801,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,95803,1922],{},[1762,95805,1911],{},[1693,95807,1899],{"separator":1898},[1901,95809],{"width":3630},[5688,95811,95812,95814,95816],{},[898,95813,900],{},[1762,95815,2398],{},[1693,95817,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,95819,1922],{},[1762,95821,19295],{},[3635,95823],{"width":34864},[3635,95825,95826],{},[1915,95827,95828],{},"(6.4)",[902,95830,95831],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,95833,95834,95835,95837],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,95836,59435],{}," — užitečnost roste s množstvím každého zboží.",[724,95839,95840,95843,95844,95874,95875,4300],{},[38,95841,95842],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,95845,95847],{"className":95846},[886],[888,95848,95849],{"xmlns":890},[892,95850,95851,95871],{},[895,95852,95853,95861,95863],{},[5688,95854,95855,95857,95859],{},[898,95856,900],{},[1762,95858,1764],{},[1693,95860,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,95862,1899],{"separator":1898},[5688,95864,95865,95867,95869],{},[898,95866,900],{},[1762,95868,2398],{},[1693,95870,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,95872,95873],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,95876,95877],{},"záporné",[883,95879,95881],{"className":95880},[886],[888,95882,95883],{"xmlns":890,"display":34854},[892,95884,95885,95938],{},[3626,95886,95887],{"width":34859},[3632,95888,95889,95891,95931,95933],{},[3635,95890],{"width":34864},[3635,95892,95893],{},[895,95894,95895,95907,95909,95911,95913,95915,95927,95929],{},[5688,95896,95897,95899,95901],{},[898,95898,900],{},[1762,95900,9803],{},[895,95902,95903,95905],{},[1693,95904,1724],{"mathvariant":1704},[1693,95906,1724],{"mathvariant":1704},[1693,95908,1908],{},[1762,95910,1911],{},[1693,95912,1899],{"separator":1898},[1901,95914],{"width":3630},[5688,95916,95917,95919,95921],{},[898,95918,900],{},[1762,95920,39329],{},[895,95922,95923,95925],{},[1693,95924,1724],{"mathvariant":1704},[1693,95926,1724],{"mathvariant":1704},[1693,95928,1908],{},[1762,95930,19295],{},[3635,95932],{"width":34864},[3635,95934,95935],{},[1915,95936,95937],{},"(6.5)",[902,95939,95940],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,95942,95943,95944,95947,95948,1789],{},"Podmínka (6.5) je známa jako ",[38,95945,95946],{},"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 ",[207,95949,95951],{"className":95950,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,95953,95954,95955,4286,95987,96019,96020,4286,96046,96072,96073,96101,96102,4286,96104,96106,96107,96142],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,95956,95958],{"className":95957},[886],[888,95959,95960],{"xmlns":890},[892,95961,95962,95984],{},[895,95963,95964,95966,95968,95974,95976,95982],{},[898,95965,900],{},[1693,95967,1709],{"stretchy":1708},[3284,95969,95970,95972],{},[898,95971,1712],{},[1762,95973,1764],{},[1693,95975,1899],{"separator":1898},[3284,95977,95978,95980],{},[898,95979,1895],{},[1762,95981,1911],{},[1693,95983,1731],{"stretchy":1708},[902,95985,95986],{"encoding":904},"U(Q_1, b_0)",[883,95988,95990],{"className":95989},[886],[888,95991,95992],{"xmlns":890},[892,95993,95994,96016],{},[895,95995,95996,95998,96000,96006,96008,96014],{},[898,95997,900],{},[1693,95999,1709],{"stretchy":1708},[3284,96001,96002,96004],{},[898,96003,207],{},[1762,96005,1911],{},[1693,96007,1899],{"separator":1898},[3284,96009,96010,96012],{},[898,96011,1712],{},[1762,96013,2398],{},[1693,96015,1731],{"stretchy":1708},[902,96017,96018],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,96021,96023],{"className":96022},[886],[888,96024,96025],{"xmlns":890},[892,96026,96027,96043],{},[895,96028,96029,96031,96033,96035,96041],{},[1693,96030,1709],{"stretchy":1708},[898,96032,900],{},[1693,96034,1899],{"separator":1898},[3284,96036,96037,96039],{},[898,96038,1712],{},[1762,96040,1764],{},[1693,96042,1731],{"stretchy":1708},[902,96044,96045],{"encoding":904},"(U, Q_1)",[883,96047,96049],{"className":96048},[886],[888,96050,96051],{"xmlns":890},[892,96052,96053,96069],{},[895,96054,96055,96057,96059,96061,96067],{},[1693,96056,1709],{"stretchy":1708},[898,96058,900],{},[1693,96060,1899],{"separator":1898},[3284,96062,96063,96065],{},[898,96064,1712],{},[1762,96066,2398],{},[1693,96068,1731],{"stretchy":1708},[902,96070,96071],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,96074,96076],{"className":96075},[886],[888,96077,96078],{"xmlns":890},[892,96079,96080,96098],{},[895,96081,96082,96084,96086,96088,96090,96092,96094,96096],{},[898,96083,900],{},[1693,96085,1709],{"stretchy":1708},[1762,96087,1911],{},[1693,96089,1899],{"separator":1898},[1762,96091,1911],{},[1693,96093,1731],{"stretchy":1708},[1693,96095,1695],{},[1762,96097,1911],{},[902,96099,96100],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,96103,20488],{},[38,96105,45263],{},". Typický tvar grafu ",[883,96108,96110],{"className":96109},[886],[888,96111,96112],{"xmlns":890},[892,96113,96114,96140],{},[895,96115,96116,96118,96120,96122,96124,96130,96132,96138],{},[898,96117,900],{},[1693,96119,1695],{},[898,96121,900],{},[1693,96123,1709],{"stretchy":1708},[3284,96125,96126,96128],{},[898,96127,1712],{},[1762,96129,1764],{},[1693,96131,1899],{"separator":1898},[3284,96133,96134,96136],{},[898,96135,1712],{},[1762,96137,2398],{},[1693,96139,1731],{"stretchy":1708},[902,96141,5567],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,96144,96145],{},[614,96146,96147,96148,95188,96176,96197,96198,95188,96226,96248],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,96149,96151],{"className":96150},[886],[888,96152,96153],{"xmlns":890},[892,96154,96155,96173],{},[895,96156,96157,96159,96161,96167,96169,96171],{},[898,96158,900],{},[1693,96160,1709],{"stretchy":1708},[3284,96162,96163,96165],{},[898,96164,1712],{},[1762,96166,1764],{},[1693,96168,1899],{"separator":1898},[898,96170,1895],{},[1693,96172,1731],{"stretchy":1708},[902,96174,96175],{"encoding":904},"U(Q_1, b)",[883,96177,96179],{"className":96178},[886],[888,96180,96181],{"xmlns":890},[892,96182,96183,96195],{},[895,96184,96185,96191,96193],{},[3284,96186,96187,96189],{},[898,96188,1712],{},[1762,96190,2398],{},[1693,96192,1695],{},[898,96194,1895],{},[902,96196,95210],{"encoding":904}," (vlevo) a ",[883,96199,96201],{"className":96200},[886],[888,96202,96203],{"xmlns":890},[892,96204,96205,96223],{},[895,96206,96207,96209,96211,96213,96215,96221],{},[898,96208,900],{},[1693,96210,1709],{"stretchy":1708},[898,96212,207],{},[1693,96214,1899],{"separator":1898},[3284,96216,96217,96219],{},[898,96218,1712],{},[1762,96220,2398],{},[1693,96222,1731],{"stretchy":1708},[902,96224,96225],{"encoding":904},"U(a, Q_2)",[883,96227,96229],{"className":96228},[886],[888,96230,96231],{"xmlns":890},[892,96232,96233,96245],{},[895,96234,96235,96241,96243],{},[3284,96236,96237,96239],{},[898,96238,1712],{},[1762,96240,1764],{},[1693,96242,1695],{},[898,96244,207],{},[902,96246,96247],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,96250,96251],{},[614,96252,96253,96254,96289,96290,96319,96320,4286,96343,96365,96366,1789],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,96255,96257],{"className":96256},[886],[888,96258,96259],{"xmlns":890},[892,96260,96261,96287],{},[895,96262,96263,96265,96267,96269,96271,96277,96279,96285],{},[898,96264,900],{},[1693,96266,1695],{},[898,96268,900],{},[1693,96270,1709],{"stretchy":1708},[3284,96272,96273,96275],{},[898,96274,1712],{},[1762,96276,1764],{},[1693,96278,1899],{"separator":1898},[3284,96280,96281,96283],{},[898,96282,1712],{},[1762,96284,2398],{},[1693,96286,1731],{"stretchy":1708},[902,96288,5567],{"encoding":904}," nad rovinou ",[883,96291,96293],{"className":96292},[886],[888,96294,96295],{"xmlns":890},[892,96296,96297,96317],{},[895,96298,96299,96301,96307,96309,96315],{},[1693,96300,1709],{"stretchy":1708},[3284,96302,96303,96305],{},[898,96304,1712],{},[1762,96306,1764],{},[1693,96308,1899],{"separator":1898},[3284,96310,96311,96313],{},[898,96312,1712],{},[1762,96314,2398],{},[1693,96316,1731],{"stretchy":1708},[902,96318,5917],{"encoding":904}," s řezy rovinami ",[883,96321,96323],{"className":96322},[886],[888,96324,96325],{"xmlns":890},[892,96326,96327,96340],{},[895,96328,96329,96335,96337],{},[3284,96330,96331,96333],{},[898,96332,1712],{},[1762,96334,1764],{},[1693,96336,1695],{},[1915,96338,96339],{},"const",[902,96341,96342],{"encoding":904},"Q_1 = \\text{const}",[883,96344,96346],{"className":96345},[886],[888,96347,96348],{"xmlns":890},[892,96349,96350,96362],{},[895,96351,96352,96358,96360],{},[3284,96353,96354,96356],{},[898,96355,1712],{},[1762,96357,2398],{},[1693,96359,1695],{},[1915,96361,96339],{},[902,96363,96364],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,96367,96369],{"className":96368},[886],[888,96370,96371],{"xmlns":890},[892,96372,96373,96399],{},[895,96374,96375,96377,96379,96385,96387,96393,96395,96397],{},[898,96376,900],{},[1693,96378,1709],{"stretchy":1708},[3284,96380,96381,96383],{},[898,96382,1712],{},[1762,96384,1764],{},[1693,96386,1899],{"separator":1898},[3284,96388,96389,96391],{},[898,96390,1712],{},[1762,96392,2398],{},[1693,96394,1731],{"stretchy":1708},[1693,96396,1695],{},[898,96398,2000],{},[902,96400,16623],{"encoding":904},[198,96402,96404,96405],{"id":96403},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,96406,96408],{"className":96407},[886],[888,96409,96410],{"xmlns":890},[892,96411,96412,96446],{},[895,96413,96414,96416,96418,96432],{},[898,96415,900],{},[1693,96417,1695],{},[5688,96419,96420,96422,96424],{},[898,96421,1712],{},[1762,96423,1764],{},[895,96425,96426,96428,96430],{},[1762,96427,1764],{},[898,96429,1705],{"mathvariant":1704},[1762,96431,2398],{},[5688,96433,96434,96436,96438],{},[898,96435,1712],{},[1762,96437,2398],{},[895,96439,96440,96442,96444],{},[1762,96441,1764],{},[898,96443,1705],{"mathvariant":1704},[1762,96445,8357],{},[902,96447,96448],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,96450,96451],{},[38,96452,96453],{},"Ověření (6.4) a (6.5).",[883,96455,96457],{"className":96456},[886],[888,96458,96459],{"xmlns":890,"display":34854},[892,96460,96461,96565],{},[895,96462,96463,96471,96473,96481,96497,96511,96513,96515,96523,96525,96533,96547,96563],{},[5688,96464,96465,96467,96469],{},[898,96466,900],{},[1762,96468,1764],{},[1693,96470,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,96472,1695],{},[3638,96474,96475],{"scriptlevel":1911,"displaystyle":1708},[2132,96476,96477,96479],{},[1762,96478,1764],{},[1762,96480,2398],{},[5688,96482,96483,96485,96487],{},[898,96484,1712],{},[1762,96486,1764],{},[895,96488,96489,96491,96493,96495],{},[1693,96490,1698],{},[1762,96492,1764],{},[898,96494,1705],{"mathvariant":1704},[1762,96496,2398],{},[5688,96498,96499,96501,96503],{},[898,96500,1712],{},[1762,96502,2398],{},[895,96504,96505,96507,96509],{},[1762,96506,1764],{},[898,96508,1705],{"mathvariant":1704},[1762,96510,8357],{},[1693,96512,1899],{"separator":1898},[1901,96514],{"width":3630},[5688,96516,96517,96519,96521],{},[898,96518,900],{},[1762,96520,2398],{},[1693,96522,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,96524,1695],{},[3638,96526,96527],{"scriptlevel":1911,"displaystyle":1708},[2132,96528,96529,96531],{},[1762,96530,1764],{},[1762,96532,8357],{},[5688,96534,96535,96537,96539],{},[898,96536,1712],{},[1762,96538,1764],{},[895,96540,96541,96543,96545],{},[1762,96542,1764],{},[898,96544,1705],{"mathvariant":1704},[1762,96546,2398],{},[5688,96548,96549,96551,96553],{},[898,96550,1712],{},[1762,96552,2398],{},[895,96554,96555,96557,96559,96561],{},[1693,96556,1698],{},[1762,96558,2398],{},[898,96560,1705],{"mathvariant":1704},[1762,96562,8357],{},[1693,96564,1899],{"separator":1898},[902,96566,96567],{"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},",[724,96569,96570,96571,96605],{},"zřejmě ",[883,96572,96574],{"className":96573},[886],[888,96575,96576],{"xmlns":890},[892,96577,96578,96602],{},[895,96579,96580,96588,96590,96598,96600],{},[5688,96581,96582,96584,96586],{},[898,96583,900],{},[1762,96585,1764],{},[1693,96587,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,96589,1899],{"separator":1898},[5688,96591,96592,96594,96596],{},[898,96593,900],{},[1762,96595,2398],{},[1693,96597,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,96599,1922],{},[1762,96601,1911],{},[902,96603,96604],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,96607,96609],{"className":96608},[886],[888,96610,96611],{"xmlns":890,"display":34854},[892,96612,96613,96729],{},[895,96614,96615,96627,96629,96631,96639,96655,96669,96671,96673,96685,96687,96689,96697,96711,96727],{},[5688,96616,96617,96619,96621],{},[898,96618,900],{},[1762,96620,9803],{},[895,96622,96623,96625],{},[1693,96624,1724],{"mathvariant":1704},[1693,96626,1724],{"mathvariant":1704},[1693,96628,1695],{},[1693,96630,1698],{},[3638,96632,96633],{"scriptlevel":1911,"displaystyle":1708},[2132,96634,96635,96637],{},[1762,96636,1764],{},[1762,96638,9262],{},[5688,96640,96641,96643,96645],{},[898,96642,1712],{},[1762,96644,1764],{},[895,96646,96647,96649,96651,96653],{},[1693,96648,1698],{},[1762,96650,8357],{},[898,96652,1705],{"mathvariant":1704},[1762,96654,2398],{},[5688,96656,96657,96659,96661],{},[898,96658,1712],{},[1762,96660,2398],{},[895,96662,96663,96665,96667],{},[1762,96664,1764],{},[898,96666,1705],{"mathvariant":1704},[1762,96668,8357],{},[1693,96670,1899],{"separator":1898},[1901,96672],{"width":3630},[5688,96674,96675,96677,96679],{},[898,96676,900],{},[1762,96678,39329],{},[895,96680,96681,96683],{},[1693,96682,1724],{"mathvariant":1704},[1693,96684,1724],{"mathvariant":1704},[1693,96686,1695],{},[1693,96688,1698],{},[3638,96690,96691],{"scriptlevel":1911,"displaystyle":1708},[2132,96692,96693,96695],{},[1762,96694,2398],{},[1762,96696,10881],{},[5688,96698,96699,96701,96703],{},[898,96700,1712],{},[1762,96702,1764],{},[895,96704,96705,96707,96709],{},[1762,96706,1764],{},[898,96708,1705],{"mathvariant":1704},[1762,96710,2398],{},[5688,96712,96713,96715,96717],{},[898,96714,1712],{},[1762,96716,2398],{},[895,96718,96719,96721,96723,96725],{},[1693,96720,1698],{},[1762,96722,9147],{},[898,96724,1705],{"mathvariant":1704},[1762,96726,8357],{},[1693,96728,1899],{"separator":1898},[902,96730,96731],{"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},",[724,96733,96734,96735,96777],{},"opět ",[883,96736,96738],{"className":96737},[886],[888,96739,96740],{"xmlns":890},[892,96741,96742,96774],{},[895,96743,96744,96756,96758,96770,96772],{},[5688,96745,96746,96748,96750],{},[898,96747,900],{},[1762,96749,9803],{},[895,96751,96752,96754],{},[1693,96753,1724],{"mathvariant":1704},[1693,96755,1724],{"mathvariant":1704},[1693,96757,1899],{"separator":1898},[5688,96759,96760,96762,96764],{},[898,96761,900],{},[1762,96763,39329],{},[895,96765,96766,96768],{},[1693,96767,1724],{"mathvariant":1704},[1693,96769,1724],{"mathvariant":1704},[1693,96771,1908],{},[1762,96773,1911],{},[902,96775,96776],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,96779,96780],{},[38,96781,96782,96783,1789],{},"(a) Mezní užitečnosti v bodě ",[883,96784,96786],{"className":96785},[886],[888,96787,96788],{"xmlns":890},[892,96789,96790,96802],{},[895,96791,96792,96794,96796,96798,96800],{},[1693,96793,9392],{"stretchy":1708},[1762,96795,9987],{},[1693,96797,1899],{"separator":1898},[1762,96799,15236],{},[1693,96801,9407],{"stretchy":1708},[902,96803,96804],{"encoding":904},"[100, 200]",[883,96806,96808],{"className":96807},[886],[888,96809,96810],{"xmlns":890,"display":34854},[892,96811,96812,96879],{},[895,96813,96814,96816,96822,96824,96826,96828,96830,96832,96834,96842,96844,96858,96860,96872,96874,96877],{},[898,96815,2839],{},[3284,96817,96818,96820],{},[898,96819,900],{},[1762,96821,1764],{},[1693,96823,1709],{"stretchy":1708},[1762,96825,9987],{},[1693,96827,1899],{"separator":1898},[1762,96829,15236],{},[1693,96831,1731],{"stretchy":1708},[1693,96833,1695],{},[3638,96835,96836],{"scriptlevel":1911,"displaystyle":1708},[2132,96837,96838,96840],{},[1762,96839,1764],{},[1762,96841,2398],{},[1693,96843,1715],{},[1717,96845,96846,96848],{},[1762,96847,9987],{},[895,96849,96850,96852,96854,96856],{},[1693,96851,1698],{},[1762,96853,1764],{},[898,96855,1705],{"mathvariant":1704},[1762,96857,2398],{},[1693,96859,1715],{},[1717,96861,96862,96864],{},[1762,96863,15236],{},[895,96865,96866,96868,96870],{},[1762,96867,1764],{},[898,96869,1705],{"mathvariant":1704},[1762,96871,8357],{},[1693,96873,12766],{},[1762,96875,96876],{},"0,4204",[1693,96878,1899],{"separator":1898},[902,96880,96881],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,96883,96885],{"className":96884},[886],[888,96886,96887],{"xmlns":890,"display":34854},[892,96888,96889,96954],{},[895,96890,96891,96893,96899,96901,96903,96905,96907,96909,96911,96919,96921,96933,96935,96949,96951],{},[898,96892,2839],{},[3284,96894,96895,96897],{},[898,96896,900],{},[1762,96898,2398],{},[1693,96900,1709],{"stretchy":1708},[1762,96902,9987],{},[1693,96904,1899],{"separator":1898},[1762,96906,15236],{},[1693,96908,1731],{"stretchy":1708},[1693,96910,1695],{},[3638,96912,96913],{"scriptlevel":1911,"displaystyle":1708},[2132,96914,96915,96917],{},[1762,96916,1764],{},[1762,96918,8357],{},[1693,96920,1715],{},[1717,96922,96923,96925],{},[1762,96924,9987],{},[895,96926,96927,96929,96931],{},[1762,96928,1764],{},[898,96930,1705],{"mathvariant":1704},[1762,96932,2398],{},[1693,96934,1715],{},[1717,96936,96937,96939],{},[1762,96938,15236],{},[895,96940,96941,96943,96945,96947],{},[1693,96942,1698],{},[1762,96944,2398],{},[898,96946,1705],{"mathvariant":1704},[1762,96948,8357],{},[1693,96950,12766],{},[1762,96952,96953],{},"0,63067.",[902,96955,96956],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,96958,96959,1863,96961,96996,96997,97018,97019,97036],{},[614,96960,16071],{},[883,96962,96964],{"className":96963},[886],[888,96965,96966],{"xmlns":890},[892,96967,96968,96993],{},[895,96969,96970,96972,96978,96980,96982,96984,96986,96988,96990],{},[898,96971,2839],{},[3284,96973,96974,96976],{},[898,96975,900],{},[1762,96977,2398],{},[1693,96979,1709],{"stretchy":1708},[1762,96981,9987],{},[1693,96983,1899],{"separator":1898},[1762,96985,15236],{},[1693,96987,1731],{"stretchy":1708},[1693,96989,12766],{},[1762,96991,96992],{},"0,63067",[902,96994,96995],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,96998,97000],{"className":96999},[886],[888,97001,97002],{"xmlns":890},[892,97003,97004,97016],{},[895,97005,97006,97008,97010,97012,97014],{},[1693,97007,9392],{"stretchy":1708},[1762,97009,9987],{},[1693,97011,1899],{"separator":1898},[1762,97013,15236],{},[1693,97015,9407],{"stretchy":1708},[902,97017,96804],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,97020,97022],{"className":97021},[886],[888,97023,97024],{"xmlns":890},[892,97025,97026,97034],{},[895,97027,97028],{},[3284,97029,97030,97032],{},[898,97031,1712],{},[1762,97033,2398],{},[902,97035,5790],{"encoding":904}," přibližně o 0,63067.",[724,97038,97039,97058,97059,45958,97080,97097,97098,97124,97125,97142,97143,10048],{},[38,97040,97041,97042,97057],{},"(b) Odhad změny ",[883,97043,97045],{"className":97044},[886],[888,97046,97047],{"xmlns":890},[892,97048,97049,97055],{},[895,97050,97051,97053],{},[898,97052,3890],{"mathvariant":1704},[898,97054,900],{},[902,97056,95301],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,97060,97062],{"className":97061},[886],[888,97063,97064],{"xmlns":890},[892,97065,97066,97078],{},[895,97067,97068,97070,97072,97074,97076],{},[1693,97069,9392],{"stretchy":1708},[1762,97071,9987],{},[1693,97073,1899],{"separator":1898},[1762,97075,15236],{},[1693,97077,9407],{"stretchy":1708},[902,97079,96804],{"encoding":904},[883,97081,97083],{"className":97082},[886],[888,97084,97085],{"xmlns":890},[892,97086,97087,97095],{},[895,97088,97089],{},[3284,97090,97091,97093],{},[898,97092,1712],{},[1762,97094,1764],{},[902,97096,5809],{"encoding":904}," na 98 (tj. ",[883,97099,97101],{"className":97100},[886],[888,97102,97103],{"xmlns":890},[892,97104,97105,97121],{},[895,97106,97107,97109,97115,97117,97119],{},[898,97108,1771],{"mathvariant":1704},[3284,97110,97111,97113],{},[898,97112,1712],{},[1762,97114,1764],{},[1693,97116,1695],{},[1693,97118,1698],{},[1762,97120,2398],{},[902,97122,97123],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,97126,97128],{"className":97127},[886],[888,97129,97130],{"xmlns":890},[892,97131,97132,97140],{},[895,97133,97134],{},[3284,97135,97136,97138],{},[898,97137,1712],{},[1762,97139,2398],{},[902,97141,5790],{"encoding":904}," o 3 (tj. ",[883,97144,97146],{"className":97145},[886],[888,97147,97148],{"xmlns":890},[892,97149,97150,97164],{},[895,97151,97152,97154,97160,97162],{},[898,97153,1771],{"mathvariant":1704},[3284,97155,97156,97158],{},[898,97157,1712],{},[1762,97159,2398],{},[1693,97161,1695],{},[1762,97163,8357],{},[902,97165,97166],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,97168,97170],{"className":97169},[886],[888,97171,97172],{"xmlns":890,"display":34854},[892,97173,97174,97225],{},[895,97175,97176,97178,97180,97182,97184,97186,97188,97190,97192,97194,97196,97198,97200,97202,97204,97206,97208,97210,97212,97215,97217,97220,97222],{},[898,97177,3890],{"mathvariant":1704},[898,97179,900],{},[1693,97181,4110],{},[898,97183,1771],{"mathvariant":1704},[898,97185,900],{},[1693,97187,1695],{},[1762,97189,96876],{},[1693,97191,1715],{},[1693,97193,1709],{"stretchy":1708},[1693,97195,1698],{},[1762,97197,2398],{},[1693,97199,1731],{"stretchy":1708},[1693,97201,1892],{},[1762,97203,96992],{},[1693,97205,1715],{},[1762,97207,8357],{},[1693,97209,1695],{},[1693,97211,1698],{},[1762,97213,97214],{},"0,8408",[1693,97216,1892],{},[1762,97218,97219],{},"1,89201",[1693,97221,12766],{},[1762,97223,97224],{},"1,05.",[902,97226,97227],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,97229,97230,97231,97234,97235,97286,97287,1789],{},"Užitečnost se tedy zvýší přibližně o ",[38,97232,97233],{},"1,05",". Skutečná změna je ",[883,97236,97238],{"className":97237},[886],[888,97239,97240],{"xmlns":890},[892,97241,97242,97283],{},[895,97243,97244,97246,97248,97250,97252,97254,97257,97259,97262,97264,97266,97268,97270,97272,97274,97276,97278,97280],{},[898,97245,3890],{"mathvariant":1704},[898,97247,900],{},[1693,97249,1695],{},[898,97251,900],{},[1693,97253,1709],{"stretchy":1708},[1762,97255,97256],{},"98",[1693,97258,1899],{"separator":1898},[1762,97260,97261],{},"203",[1693,97263,1731],{"stretchy":1708},[1693,97265,1698],{},[898,97267,900],{},[1693,97269,1709],{"stretchy":1708},[1762,97271,9987],{},[1693,97273,1899],{"separator":1898},[1762,97275,15236],{},[1693,97277,1731],{"stretchy":1708},[1693,97279,12766],{},[1762,97281,97282],{},"1,031",[902,97284,97285],{"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 ",[883,97288,97290],{"className":97289},[886],[888,97291,97292],{"xmlns":890},[892,97293,97294,97314],{},[895,97295,97296,97298,97304,97306,97308],{},[898,97297,1771],{"mathvariant":1704},[3284,97299,97300,97302],{},[898,97301,1712],{},[1762,97303,1764],{},[1693,97305,1899],{"separator":1898},[898,97307,1771],{"mathvariant":1704},[3284,97309,97310,97312],{},[898,97311,1712],{},[1762,97313,2398],{},[902,97315,95331],{"encoding":904},[115,97317,97319],{"id":97318},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,97321,97322],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,97324,97326],{"className":97325},[886],[888,97327,97328],{"xmlns":890,"display":34854},[892,97329,97330,97389],{},[3626,97331,97332],{"width":34859},[3632,97333,97334,97336,97382,97384],{},[3635,97335],{"width":34864},[3635,97337,97338],{},[895,97339,97340,97342,97344,97350,97352,97358,97360,97362,97370,97372,97380],{},[898,97341,900],{},[1693,97343,1709],{"stretchy":1708},[3284,97345,97346,97348],{},[898,97347,1712],{},[1762,97349,1764],{},[1693,97351,1899],{"separator":1898},[3284,97353,97354,97356],{},[898,97355,1712],{},[1762,97357,2398],{},[1693,97359,1731],{"stretchy":1708},[1693,97361,1695],{},[5688,97363,97364,97366,97368],{},[898,97365,1712],{},[1762,97367,1764],{},[898,97369,207],{},[1693,97371,1715],{},[5688,97373,97374,97376,97378],{},[898,97375,1712],{},[1762,97377,2398],{},[898,97379,1895],{},[1693,97381,1899],{"separator":1898},[3635,97383],{"width":34864},[3635,97385,97386],{},[1915,97387,97388],{},"(6.6)",[902,97390,97391],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,97393,11188,97394,97411,97412,97414,97415,97419,97420,97450,97451,97473],{},[883,97395,97397],{"className":97396},[886],[888,97398,97399],{"xmlns":890},[892,97400,97401,97409],{},[895,97402,97403,97405,97407],{},[898,97404,207],{},[1693,97406,1899],{"separator":1898},[898,97408,1895],{},[902,97410,2611],{"encoding":904}," jsou kladná čísla; nazývají se ",[38,97413,81410],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,97416,97418],{"className":97417,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,97421,97423],{"className":97422},[886],[888,97424,97425],{"xmlns":890},[892,97426,97427,97447],{},[895,97428,97429,97431,97433,97435,97437,97439,97441,97443,97445],{},[898,97430,207],{},[1693,97432,1899],{"separator":1898},[898,97434,1895],{},[1693,97436,13370],{},[1693,97438,1709],{"stretchy":1708},[1762,97440,1911],{},[1693,97442,1899],{"separator":1898},[1762,97444,1764],{},[1693,97446,1731],{"stretchy":1708},[902,97448,97449],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,97452,97454],{"className":97453},[886],[888,97455,97456],{"xmlns":890},[892,97457,97458,97470],{},[895,97459,97460,97462,97464,97466,97468],{},[898,97461,1895],{},[1693,97463,1695],{},[1762,97465,1764],{},[1693,97467,1698],{},[898,97469,207],{},[902,97471,97472],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,97475,97476],{},[9465,97477],{"alt":97478,"className":97479,"src":97480},"imek-cobb-douglas-3d-plus-ic",[210,9469],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,97482,97484],{"className":97483},[886],[888,97485,97486],{"xmlns":890,"display":34854},[892,97487,97488,97538],{},[895,97489,97490,97492,97494,97500,97502,97508,97510,97512,97520,97522,97536],{},[898,97491,900],{},[1693,97493,1709],{"stretchy":1708},[3284,97495,97496,97498],{},[898,97497,1712],{},[1762,97499,1764],{},[1693,97501,1899],{"separator":1898},[3284,97503,97504,97506],{},[898,97505,1712],{},[1762,97507,2398],{},[1693,97509,1731],{"stretchy":1708},[1693,97511,1695],{},[5688,97513,97514,97516,97518],{},[898,97515,1712],{},[1762,97517,1764],{},[898,97519,207],{},[1693,97521,1715],{},[5688,97523,97524,97526,97528],{},[898,97525,1712],{},[1762,97527,2398],{},[895,97529,97530,97532,97534],{},[1762,97531,1764],{},[1693,97533,1698],{},[898,97535,207],{},[898,97537,1789],{"mathvariant":1704},[902,97539,97540],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1636,97542,97543,97592,97714,97848],{},[724,97544,97545,97547,97548],{},[883,97546,59453],{}," Příklad 6.3 — ověření vlastností pro ",[883,97549,97551],{"className":97550},[886],[888,97552,97553],{"xmlns":890},[892,97554,97555,97589],{},[895,97556,97557,97559,97561,97575],{},[898,97558,900],{},[1693,97560,1695],{},[5688,97562,97563,97565,97567],{},[898,97564,1712],{},[1762,97566,1764],{},[895,97568,97569,97571,97573],{},[1762,97570,1764],{},[898,97572,1705],{"mathvariant":1704},[1762,97574,9262],{},[5688,97576,97577,97579,97581],{},[898,97578,1712],{},[1762,97580,2398],{},[895,97582,97583,97585,97587],{},[1762,97584,8357],{},[898,97586,1705],{"mathvariant":1704},[1762,97588,9262],{},[902,97590,97591],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,97593,97595],{"className":97594},[886],[888,97596,97597],{"xmlns":890,"display":34854},[892,97598,97599,97711],{},[895,97600,97601,97609,97611,97619,97635,97649,97651,97653,97655,97657,97665,97667,97675,97689,97705,97707,97709],{},[5688,97602,97603,97605,97607],{},[898,97604,900],{},[1762,97606,1764],{},[1693,97608,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,97610,1695],{},[3638,97612,97613],{"scriptlevel":1911,"displaystyle":1708},[2132,97614,97615,97617],{},[1762,97616,1764],{},[1762,97618,9262],{},[5688,97620,97621,97623,97625],{},[898,97622,1712],{},[1762,97624,1764],{},[895,97626,97627,97629,97631,97633],{},[1693,97628,1698],{},[1762,97630,8357],{},[898,97632,1705],{"mathvariant":1704},[1762,97634,9262],{},[5688,97636,97637,97639,97641],{},[898,97638,1712],{},[1762,97640,2398],{},[895,97642,97643,97645,97647],{},[1762,97644,8357],{},[898,97646,1705],{"mathvariant":1704},[1762,97648,9262],{},[1693,97650,1922],{},[1762,97652,1911],{},[1693,97654,1899],{"separator":1898},[1901,97656],{"width":3630},[5688,97658,97659,97661,97663],{},[898,97660,900],{},[1762,97662,2398],{},[1693,97664,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,97666,1695],{},[3638,97668,97669],{"scriptlevel":1911,"displaystyle":1708},[2132,97670,97671,97673],{},[1762,97672,8357],{},[1762,97674,9262],{},[5688,97676,97677,97679,97681],{},[898,97678,1712],{},[1762,97680,1764],{},[895,97682,97683,97685,97687],{},[1762,97684,1764],{},[898,97686,1705],{"mathvariant":1704},[1762,97688,9262],{},[5688,97690,97691,97693,97695],{},[898,97692,1712],{},[1762,97694,2398],{},[895,97696,97697,97699,97701,97703],{},[1693,97698,1698],{},[1762,97700,1764],{},[898,97702,1705],{"mathvariant":1704},[1762,97704,9262],{},[1693,97706,1922],{},[1762,97708,1911],{},[1693,97710,1899],{"separator":1898},[902,97712,97713],{"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,",[883,97715,97717],{"className":97716},[886],[888,97718,97719],{"xmlns":890,"display":34854},[892,97720,97721,97845],{},[895,97722,97723,97735,97737,97739,97747,97763,97777,97779,97781,97783,97785,97797,97799,97801,97809,97823,97839,97841,97843],{},[5688,97724,97725,97727,97729],{},[898,97726,900],{},[1762,97728,9803],{},[895,97730,97731,97733],{},[1693,97732,1724],{"mathvariant":1704},[1693,97734,1724],{"mathvariant":1704},[1693,97736,1695],{},[1693,97738,1698],{},[3638,97740,97741],{"scriptlevel":1911,"displaystyle":1708},[2132,97742,97743,97745],{},[1762,97744,8357],{},[1762,97746,48633],{},[5688,97748,97749,97751,97753],{},[898,97750,1712],{},[1762,97752,1764],{},[895,97754,97755,97757,97759,97761],{},[1693,97756,1698],{},[1762,97758,31000],{},[898,97760,1705],{"mathvariant":1704},[1762,97762,9262],{},[5688,97764,97765,97767,97769],{},[898,97766,1712],{},[1762,97768,2398],{},[895,97770,97771,97773,97775],{},[1762,97772,8357],{},[898,97774,1705],{"mathvariant":1704},[1762,97776,9262],{},[1693,97778,1908],{},[1762,97780,1911],{},[1693,97782,1899],{"separator":1898},[1901,97784],{"width":3630},[5688,97786,97787,97789,97791],{},[898,97788,900],{},[1762,97790,39329],{},[895,97792,97793,97795],{},[1693,97794,1724],{"mathvariant":1704},[1693,97796,1724],{"mathvariant":1704},[1693,97798,1695],{},[1693,97800,1698],{},[3638,97802,97803],{"scriptlevel":1911,"displaystyle":1708},[2132,97804,97805,97807],{},[1762,97806,8357],{},[1762,97808,48633],{},[5688,97810,97811,97813,97815],{},[898,97812,1712],{},[1762,97814,1764],{},[895,97816,97817,97819,97821],{},[1762,97818,1764],{},[898,97820,1705],{"mathvariant":1704},[1762,97822,9262],{},[5688,97824,97825,97827,97829],{},[898,97826,1712],{},[1762,97828,2398],{},[895,97830,97831,97833,97835,97837],{},[1693,97832,1698],{},[1762,97834,9147],{},[898,97836,1705],{"mathvariant":1704},[1762,97838,9262],{},[1693,97840,1908],{},[1762,97842,1911],{},[1693,97844,1899],{"separator":1898},[902,97846,97847],{"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,",[724,97849,97850],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,97852,97854],{"id":97853},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,97856,97857,97860],{},[38,97858,97859],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,97862,97864],{"className":97863},[886],[888,97865,97866],{"xmlns":890,"display":34854},[892,97867,97868,97911],{},[3626,97869,97870],{"width":34859},[3632,97871,97872,97874,97904,97906],{},[3635,97873],{"width":34864},[3635,97875,97876],{},[895,97877,97878,97880,97882,97888,97890,97896,97898,97900,97902],{},[898,97879,900],{},[1693,97881,1709],{"stretchy":1708},[3284,97883,97884,97886],{},[898,97885,1712],{},[1762,97887,1764],{},[1693,97889,1899],{"separator":1898},[3284,97891,97892,97894],{},[898,97893,1712],{},[1762,97895,2398],{},[1693,97897,1731],{"stretchy":1708},[1693,97899,1695],{},[898,97901,2000],{},[1693,97903,1899],{"separator":1898},[3635,97905],{"width":34864},[3635,97907,97908],{},[1915,97909,97910],{},"(6.7)",[902,97912,97913],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,97915,11188,97916,97929],{},[883,97917,97919],{"className":97918},[886],[888,97920,97921],{"xmlns":890},[892,97922,97923,97927],{},[895,97924,97925],{},[898,97926,2000],{},[902,97928,2000],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,97931,97933],{"className":97932},[886],[888,97934,97935],{"xmlns":890,"display":34854},[892,97936,97937,97978],{},[3626,97938,97939],{"width":34859},[3632,97940,97941,97943,97971,97973],{},[3635,97942],{"width":34864},[3635,97944,97945],{},[895,97946,97947,97955,97957,97965,97967,97969],{},[5688,97948,97949,97951,97953],{},[898,97950,1712],{},[1762,97952,1764],{},[898,97954,207],{},[1693,97956,1715],{},[5688,97958,97959,97961,97963],{},[898,97960,1712],{},[1762,97962,2398],{},[898,97964,1895],{},[1693,97966,1695],{},[898,97968,2000],{},[898,97970,1789],{"mathvariant":1704},[3635,97972],{"width":34864},[3635,97974,97975],{},[1915,97976,97977],{},"(6.8)",[902,97979,97980],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,97982,97983,97984,2783,98014,1863,98017,98030,98031,98066,98067,98084,98085,98114,98115,98118],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,97985,97987],{"className":97986},[886],[888,97988,97989],{"xmlns":890},[892,97990,97991,98011],{},[895,97992,97993,97995,98001,98003,98009],{},[1693,97994,9392],{"stretchy":1708},[3284,97996,97997,97999],{},[898,97998,1712],{},[1762,98000,1764],{},[1693,98002,1899],{"separator":1898},[3284,98004,98005,98007],{},[898,98006,1712],{},[1762,98008,2398],{},[1693,98010,9407],{"stretchy":1708},[902,98012,98013],{"encoding":904},"[Q_1, Q_2]",[38,98015,98016],{},"stejnou úrovní uspokojení",[883,98018,98020],{"className":98019},[886],[888,98021,98022],{"xmlns":890},[892,98023,98024,98028],{},[895,98025,98026],{},[898,98027,2000],{},[902,98029,2000],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,98032,98034],{"className":98033},[886],[888,98035,98036],{"xmlns":890},[892,98037,98038,98064],{},[895,98039,98040,98042,98044,98046,98048,98054,98056,98062],{},[898,98041,900],{},[1693,98043,1695],{},[898,98045,900],{},[1693,98047,1709],{"stretchy":1708},[3284,98049,98050,98052],{},[898,98051,1712],{},[1762,98053,1764],{},[1693,98055,1899],{"separator":1898},[3284,98057,98058,98060],{},[898,98059,1712],{},[1762,98061,2398],{},[1693,98063,1731],{"stretchy":1708},[902,98065,5567],{"encoding":904}," s rovinami ",[883,98068,98070],{"className":98069},[886],[888,98071,98072],{"xmlns":890},[892,98073,98074,98082],{},[895,98075,98076,98078,98080],{},[898,98077,900],{},[1693,98079,1695],{},[898,98081,2000],{},[902,98083,93373],{"encoding":904}," rovnoběžnými s rovinou ",[883,98086,98088],{"className":98087},[886],[888,98089,98090],{"xmlns":890},[892,98091,98092,98112],{},[895,98093,98094,98096,98102,98104,98110],{},[1693,98095,1709],{"stretchy":1708},[3284,98097,98098,98100],{},[898,98099,1712],{},[1762,98101,1764],{},[1693,98103,1899],{"separator":1898},[3284,98105,98106,98108],{},[898,98107,1712],{},[1762,98109,2398],{},[1693,98111,1731],{"stretchy":1708},[902,98113,5917],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,98116,98117],{},"izokvantami"," produkčních funkcí.",[724,98120,98121],{},[614,98122,98123,98124,96197,98142,98160,98161,1789],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,98125,98127],{"className":98126},[886],[888,98128,98129],{"xmlns":890},[892,98130,98131,98139],{},[895,98132,98133,98135,98137],{},[898,98134,207],{},[1693,98136,1908],{},[898,98138,1895],{},[902,98140,98141],{"encoding":904},"a \u003C b",[883,98143,98145],{"className":98144},[886],[888,98146,98147],{"xmlns":890},[892,98148,98149,98157],{},[895,98150,98151,98153,98155],{},[898,98152,207],{},[1693,98154,1922],{},[898,98156,1895],{},[902,98158,98159],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,98162,98164],{"className":98163},[886],[888,98165,98166],{"xmlns":890},[892,98167,98168,98192],{},[895,98169,98170,98176,98178,98184,98186],{},[3284,98171,98172,98174],{},[898,98173,2000],{},[1762,98175,1911],{},[1693,98177,1908],{},[3284,98179,98180,98182],{},[898,98181,2000],{},[1762,98183,1764],{},[1693,98185,1908],{},[3284,98187,98188,98190],{},[898,98189,2000],{},[1762,98191,2398],{},[902,98193,98194],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,98196,98197],{},[614,98198,98199,98200,98229,98230,98288,98289,98307],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,98201,98203],{"className":98202},[886],[888,98204,98205],{"xmlns":890},[892,98206,98207,98227],{},[895,98208,98209,98211,98217,98219,98225],{},[1693,98210,1709],{"stretchy":1708},[3284,98212,98213,98215],{},[898,98214,1712],{},[1762,98216,1764],{},[1693,98218,1899],{"separator":1898},[3284,98220,98221,98223],{},[898,98222,1712],{},[1762,98224,2398],{},[1693,98226,1731],{"stretchy":1708},[902,98228,5917],{"encoding":904},"; body ",[883,98231,98233],{"className":98232},[886],[888,98234,98235],{"xmlns":890},[892,98236,98237,98285],{},[895,98238,98239,98241,98243,98245,98251,98253,98259,98261,98263,98265,98267,98269,98275,98277,98283],{},[898,98240,2719],{},[1693,98242,1695],{},[1693,98244,9392],{"stretchy":1708},[3284,98246,98247,98249],{},[898,98248,207],{},[1762,98250,1764],{},[1693,98252,1899],{"separator":1898},[3284,98254,98255,98257],{},[898,98256,207],{},[1762,98258,2398],{},[1693,98260,9407],{"stretchy":1708},[1693,98262,1899],{"separator":1898},[898,98264,7520],{},[1693,98266,1695],{},[1693,98268,9392],{"stretchy":1708},[3284,98270,98271,98273],{},[898,98272,1895],{},[1762,98274,1764],{},[1693,98276,1899],{"separator":1898},[3284,98278,98279,98281],{},[898,98280,1895],{},[1762,98282,2398],{},[1693,98284,9407],{"stretchy":1708},[902,98286,98287],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,98290,98292],{"className":98291},[886],[888,98293,98294],{"xmlns":890},[892,98295,98296,98304],{},[895,98297,98298,98300,98302],{},[898,98299,2971],{},[1693,98301,1899],{"separator":1898},[898,98303,2738],{},[902,98305,98306],{"encoding":904},"C, D"," na vyšší hladině.",[1636,98309,98310],{},[724,98311,98312,98314,98315,98377,98378,98422,98423,98457,98458,32979,98476,98457,98530,32979,98548,98624],{},[883,98313,59453],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,98316,98318],{"className":98317},[886],[888,98319,98320],{"xmlns":890},[892,98321,98322,98374],{},[895,98323,98324,98326,98328,98334,98336,98342,98344,98346,98360],{},[898,98325,900],{},[1693,98327,1709],{"stretchy":1708},[3284,98329,98330,98332],{},[898,98331,1712],{},[1762,98333,1764],{},[1693,98335,1899],{"separator":1898},[3284,98337,98338,98340],{},[898,98339,1712],{},[1762,98341,2398],{},[1693,98343,1731],{"stretchy":1708},[1693,98345,1695],{},[5688,98347,98348,98350,98352],{},[898,98349,1712],{},[1762,98351,1764],{},[895,98353,98354,98356,98358],{},[1762,98355,1764],{},[898,98357,1705],{"mathvariant":1704},[1762,98359,9262],{},[5688,98361,98362,98364,98366],{},[898,98363,1712],{},[1762,98365,2398],{},[895,98367,98368,98370,98372],{},[1762,98369,8357],{},[898,98371,1705],{"mathvariant":1704},[1762,98373,9262],{},[902,98375,98376],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,98379,98381],{"className":98380},[886],[888,98382,98383],{"xmlns":890},[892,98384,98385,98419],{},[895,98386,98387,98401,98415,98417],{},[5688,98388,98389,98391,98393],{},[898,98390,1712],{},[1762,98392,1764],{},[895,98394,98395,98397,98399],{},[1762,98396,1764],{},[898,98398,1705],{"mathvariant":1704},[1762,98400,9262],{},[5688,98402,98403,98405,98407],{},[898,98404,1712],{},[1762,98406,2398],{},[895,98408,98409,98411,98413],{},[1762,98410,8357],{},[898,98412,1705],{"mathvariant":1704},[1762,98414,9262],{},[1693,98416,1695],{},[898,98418,2000],{},[902,98420,98421],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,98424,98426],{"className":98425},[886],[888,98427,98428],{"xmlns":890},[892,98429,98430,98454],{},[895,98431,98432,98438,98446,98448],{},[3284,98433,98434,98436],{},[898,98435,1712],{},[1762,98437,1764],{},[5688,98439,98440,98442,98444],{},[898,98441,1712],{},[1762,98443,2398],{},[1762,98445,8357],{},[1693,98447,1695],{},[1717,98449,98450,98452],{},[898,98451,2000],{},[1762,98453,9262],{},[902,98455,98456],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,98459,98461],{"className":98460},[886],[888,98462,98463],{"xmlns":890},[892,98464,98465,98473],{},[895,98466,98467,98469,98471],{},[898,98468,2000],{},[1693,98470,1695],{},[1762,98472,1764],{},[902,98474,98475],{"encoding":904},"c = 1",[883,98477,98479],{"className":98478},[886],[888,98480,98481],{"xmlns":890},[892,98482,98483,98527],{},[895,98484,98485,98491,98493,98509,98511],{},[3284,98486,98487,98489],{},[898,98488,1712],{},[1762,98490,2398],{},[1693,98492,1695],{},[5688,98494,98495,98497,98499],{},[898,98496,1712],{},[1762,98498,1764],{},[895,98500,98501,98503,98505,98507],{},[1693,98502,1698],{},[1762,98504,1764],{},[898,98506,1705],{"mathvariant":1704},[1762,98508,8357],{},[1693,98510,1695],{},[3638,98512,98513],{"scriptlevel":1911,"displaystyle":1898},[2132,98514,98515,98517],{},[1762,98516,1764],{},[88730,98518,98519,98525],{},[3284,98520,98521,98523],{},[898,98522,1712],{},[1762,98524,1764],{},[1762,98526,8357],{},[902,98528,98529],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,98531,98533],{"className":98532},[886],[888,98534,98535],{"xmlns":890},[892,98536,98537,98545],{},[895,98538,98539,98541,98543],{},[898,98540,2000],{},[1693,98542,1695],{},[1762,98544,2398],{},[902,98546,98547],{"encoding":904},"c = 2",[883,98549,98551],{"className":98550},[886],[888,98552,98553],{"xmlns":890},[892,98554,98555,98621],{},[895,98556,98557,98563,98565,98577,98579,98595,98597],{},[3284,98558,98559,98561],{},[898,98560,1712],{},[1762,98562,2398],{},[1693,98564,1695],{},[1717,98566,98567,98569],{},[1762,98568,2398],{},[895,98570,98571,98573,98575],{},[1762,98572,9262],{},[898,98574,1705],{"mathvariant":1704},[1762,98576,8357],{},[1693,98578,1715],{},[5688,98580,98581,98583,98585],{},[898,98582,1712],{},[1762,98584,1764],{},[895,98586,98587,98589,98591,98593],{},[1693,98588,1698],{},[1762,98590,1764],{},[898,98592,1705],{"mathvariant":1704},[1762,98594,8357],{},[1693,98596,1695],{},[3638,98598,98599],{"scriptlevel":1911,"displaystyle":1898},[2132,98600,98601,98611],{},[895,98602,98603,98605],{},[1762,98604,2398],{},[88730,98606,98607,98609],{},[1762,98608,2398],{},[1762,98610,8357],{},[88730,98612,98613,98619],{},[3284,98614,98615,98617],{},[898,98616,1712],{},[1762,98618,1764],{},[1762,98620,8357],{},[902,98622,98623],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,98626,98628],{"id":98627},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,98630,98631],{},[9465,98632],{"alt":98633,"className":98634,"src":98635},"imek-ic-4vlastnosti-anotovane",[210,9469],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1636,98637,98638,98647,98694,98738,98744,98750],{},[724,98639,98640,98642,98643,98646],{},[883,98641,8654],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,98644,98645],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,98648,98649],{},[883,98650,98652],{"className":98651},[886],[888,98653,98654],{"xmlns":890},[892,98655,98656,98691],{},[895,98657,98658,98661,98663,98665,98667,98669,98687,98689],{},[898,98659,98660],{"mathvariant":1704},"tg",[1693,98662,3742],{},[898,98664,25673],{},[1693,98666,1695],{},[1693,98668,1698],{},[2132,98670,98671,98679],{},[5688,98672,98673,98675,98677],{},[898,98674,900],{},[1762,98676,1764],{},[1693,98678,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,98680,98681,98683,98685],{},[898,98682,900],{},[1762,98684,2398],{},[1693,98686,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,98688,1908],{},[1762,98690,1911],{},[902,98692,98693],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,98695,98696,98697,98737],{},"(derivace implicitně zadané funkce ",[883,98698,98700],{"className":98699},[886],[888,98701,98702],{"xmlns":890},[892,98703,98704,98734],{},[895,98705,98706,98708,98710,98716,98718,98724,98726,98728,98730,98732],{},[898,98707,900],{},[1693,98709,1709],{"stretchy":1708},[3284,98711,98712,98714],{},[898,98713,1712],{},[1762,98715,1764],{},[1693,98717,1899],{"separator":1898},[3284,98719,98720,98722],{},[898,98721,1712],{},[1762,98723,2398],{},[1693,98725,1731],{"stretchy":1708},[1693,98727,1698],{},[898,98729,2000],{},[1693,98731,1695],{},[1762,98733,1911],{},[902,98735,98736],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,98739,98740,98743],{},[38,98741,98742],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,98745,98746,98749],{},[38,98747,98748],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,98751,98752,98755,98756,98774,98775,98791,98792,98795],{},[38,98753,98754],{},"4° Konvexní."," Pro každé dva body ",[883,98757,98759],{"className":98758},[886],[888,98760,98761],{"xmlns":890},[892,98762,98763,98771],{},[895,98764,98765,98767,98769],{},[898,98766,2719],{},[1693,98768,1899],{"separator":1898},[898,98770,7520],{},[902,98772,98773],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,98776,98778],{"className":98777},[886],[888,98779,98780],{"xmlns":890},[892,98781,98782,98788],{},[895,98783,98784,98786],{},[898,98785,2719],{},[898,98787,7520],{},[902,98789,98790],{"encoding":904},"AB"," ve ",[38,98793,98794],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,98797,98798],{},[614,98799,98800,98801,98836,98837,1789],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,98802,98804],{"className":98803},[886],[888,98805,98806],{"xmlns":890},[892,98807,98808,98834],{},[895,98809,98810,98812,98814,98820,98822,98828,98830,98832],{},[898,98811,900],{},[1693,98813,1709],{"stretchy":1708},[3284,98815,98816,98818],{},[898,98817,1712],{},[1762,98819,1764],{},[1693,98821,1899],{"separator":1898},[3284,98823,98824,98826],{},[898,98825,1712],{},[1762,98827,2398],{},[1693,98829,1731],{"stretchy":1708},[1693,98831,1695],{},[898,98833,2000],{},[902,98835,16623],{"encoding":904}," s tečnou se sklonem ",[883,98838,98840],{"className":98839},[886],[888,98841,98842],{"xmlns":890},[892,98843,98844,98852],{},[895,98845,98846,98848,98850],{},[898,98847,98660],{"mathvariant":1704},[1693,98849,3742],{},[898,98851,25673],{},[902,98853,98854],{"encoding":904},"\\operatorname{tg}\\alpha",[115,98856,98858],{"id":98857},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,98860,98861,1863,98863,16877,98876,98879],{},[38,98862,5716],{},[883,98864,98866],{"className":98865},[886],[888,98867,98868],{"xmlns":890},[892,98869,98870,98874],{},[895,98871,98872],{},[1915,98873,5315],{},[902,98875,35026],{"encoding":904},[38,98877,98878],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,98881,98883],{"className":98882},[886],[888,98884,98885],{"xmlns":890,"display":34854},[892,98886,98887,98974],{},[3626,98888,98889],{"width":34859},[3632,98890,98891,98893,98967,98969],{},[3635,98892],{"width":34864},[3635,98894,98895],{},[895,98896,98897,98899,98901,98903,98905,98911,98913,98919,98921,98923,98945,98947,98965],{},[1915,98898,5315],{},[1693,98900,1695],{},[1915,98902,5315],{},[1693,98904,1709],{"stretchy":1708},[3284,98906,98907,98909],{},[898,98908,1712],{},[1762,98910,1764],{},[1693,98912,1899],{"separator":1898},[3284,98914,98915,98917],{},[898,98916,1712],{},[1762,98918,2398],{},[1693,98920,1731],{"stretchy":1708},[1693,98922,1695],{},[2132,98924,98925,98935],{},[895,98926,98927,98929],{},[898,98928,2839],{},[3284,98930,98931,98933],{},[898,98932,900],{},[1762,98934,1764],{},[895,98936,98937,98939],{},[898,98938,2839],{},[3284,98940,98941,98943],{},[898,98942,900],{},[1762,98944,2398],{},[1693,98946,1695],{},[2132,98948,98949,98957],{},[5688,98950,98951,98953,98955],{},[898,98952,900],{},[1762,98954,1764],{},[1693,98956,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,98958,98959,98961,98963],{},[898,98960,900],{},[1762,98962,2398],{},[1693,98964,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[898,98966,1789],{"mathvariant":1704},[3635,98968],{"width":34864},[3635,98970,98971],{},[1915,98972,98973],{},"(6.9)",[902,98975,98976],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,98978,98979,98980,99014,99015,99047,99048,99083,99084,99097],{},"Geometricky: ",[883,98981,98983],{"className":98982},[886],[888,98984,98985],{"xmlns":890},[892,98986,98987,99011],{},[895,98988,98989,98991],{},[1693,98990,1698],{},[3638,98992,98993],{"scriptlevel":1911,"displaystyle":1708},[2132,98994,98995,99003],{},[5688,98996,98997,98999,99001],{},[898,98998,900],{},[1762,99000,1764],{},[1693,99002,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,99004,99005,99007,99009],{},[898,99006,900],{},[1762,99008,2398],{},[1693,99010,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,99012,99013],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,99016,99018],{"className":99017},[886],[888,99019,99020],{"xmlns":890},[892,99021,99022,99044],{},[895,99023,99024,99030,99032,99034,99036,99042],{},[3284,99025,99026,99028],{},[898,99027,1712],{},[1762,99029,2398],{},[1693,99031,1695],{},[898,99033,8934],{},[1693,99035,1709],{"stretchy":1708},[3284,99037,99038,99040],{},[898,99039,1712],{},[1762,99041,1764],{},[1693,99043,1731],{"stretchy":1708},[902,99045,99046],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,99049,99051],{"className":99050},[886],[888,99052,99053],{"xmlns":890},[892,99054,99055,99081],{},[895,99056,99057,99059,99061,99067,99069,99075,99077,99079],{},[898,99058,900],{},[1693,99060,1709],{"stretchy":1708},[3284,99062,99063,99065],{},[898,99064,1712],{},[1762,99066,1764],{},[1693,99068,1899],{"separator":1898},[3284,99070,99071,99073],{},[898,99072,1712],{},[1762,99074,2398],{},[1693,99076,1731],{"stretchy":1708},[1693,99078,1695],{},[898,99080,2000],{},[902,99082,16623],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,99085,99087],{"className":99086},[886],[888,99088,99089],{"xmlns":890},[892,99090,99091,99095],{},[895,99092,99093],{},[1915,99094,5315],{},[902,99096,35026],{"encoding":904}," chápeme jako velikost kompenzace.",[1636,99099,99100],{},[724,99101,99102,99104,99105,6055,99137,99175,99176,99193,99194,99211],{},[883,99103,11036],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,99106,99108],{"className":99107},[886],[888,99109,99110],{"xmlns":890},[892,99111,99112,99134],{},[895,99113,99114,99116,99118,99124,99126,99132],{},[1915,99115,5315],{},[1693,99117,1709],{"stretchy":1708},[3284,99119,99120,99122],{},[898,99121,1712],{},[1762,99123,1764],{},[1693,99125,1899],{"separator":1898},[3284,99127,99128,99130],{},[898,99129,1712],{},[1762,99131,2398],{},[1693,99133,1731],{"stretchy":1708},[902,99135,99136],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,99138,99139,99140,35789,99157,99174],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,99141,99143],{"className":99142},[886],[888,99144,99145],{"xmlns":890},[892,99146,99147,99155],{},[895,99148,99149],{},[3284,99150,99151,99153],{},[898,99152,1712],{},[1762,99154,1764],{},[902,99156,5809],{"encoding":904},[883,99158,99160],{"className":99159},[886],[888,99161,99162],{"xmlns":890},[892,99163,99164,99172],{},[895,99165,99166],{},[3284,99167,99168,99170],{},[898,99169,1712],{},[1762,99171,2398],{},[902,99173,5790],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,99177,99179],{"className":99178},[886],[888,99180,99181],{"xmlns":890},[892,99182,99183,99191],{},[895,99184,99185],{},[3284,99186,99187,99189],{},[898,99188,1712],{},[1762,99190,2398],{},[902,99192,5790],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,99195,99197],{"className":99196},[886],[888,99198,99199],{"xmlns":890},[892,99200,99201,99209],{},[895,99202,99203],{},[3284,99204,99205,99207],{},[898,99206,1712],{},[1762,99208,1764],{},[902,99210,5809],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,99213,99214,99215,36727],{},"Pro obecnou změnu ",[883,99216,99218],{"className":99217},[886],[888,99219,99220],{"xmlns":890},[892,99221,99222,99232],{},[895,99223,99224,99226],{},[898,99225,1771],{"mathvariant":1704},[3284,99227,99228,99230],{},[898,99229,1712],{},[1762,99231,1764],{},[902,99233,99234],{"encoding":904},"\\mathrm{d} Q_1",[883,99236,99238],{"className":99237},[886],[888,99239,99240],{"xmlns":890,"display":34854},[892,99241,99242,99295],{},[3626,99243,99244],{"width":34859},[3632,99245,99246,99248,99288,99290],{},[3635,99247],{"width":34864},[3635,99249,99250],{},[895,99251,99252,99254,99260,99262,99264,99270,99272,99274,99276,99278,99280,99286],{},[898,99253,3890],{"mathvariant":1704},[3284,99255,99256,99258],{},[898,99257,1712],{},[1762,99259,2398],{},[1693,99261,4110],{},[898,99263,1771],{"mathvariant":1704},[3284,99265,99266,99268],{},[898,99267,1712],{},[1762,99269,2398],{},[1693,99271,1695],{},[1693,99273,1698],{},[1915,99275,5315],{},[1693,99277,1715],{},[898,99279,1771],{"mathvariant":1704},[3284,99281,99282,99284],{},[898,99283,1712],{},[1762,99285,1764],{},[1693,99287,1899],{"separator":1898},[3635,99289],{"width":34864},[3635,99291,99292],{},[1915,99293,99294],{},"(6.10)",[902,99296,99297],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,99299,99301],{"className":99300},[886],[888,99302,99303],{"xmlns":890,"display":34854},[892,99304,99305,99352],{},[3626,99306,99307],{"width":34859},[3632,99308,99309,99311,99345,99347],{},[3635,99310],{"width":34864},[3635,99312,99313],{},[895,99314,99315,99317,99323,99325,99327,99333,99335,99337,99343],{},[898,99316,1771],{"mathvariant":1704},[3284,99318,99319,99321],{},[898,99320,1712],{},[1762,99322,1764],{},[1693,99324,1695],{},[1693,99326,1698],{},[2132,99328,99329,99331],{},[1762,99330,1764],{},[1915,99332,5315],{},[1915,99334,2239],{},[898,99336,1771],{"mathvariant":1704},[3284,99338,99339,99341],{},[898,99340,1712],{},[1762,99342,2398],{},[898,99344,1789],{"mathvariant":1704},[3635,99346],{"width":34864},[3635,99348,99349],{},[1915,99350,99351],{},"(6.11)",[902,99353,99354],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1636,99356,99357,99423,99540],{},[724,99358,99359,99361,99362,36727],{},[883,99360,59453],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,99363,99365],{"className":99364},[886],[888,99366,99367],{"xmlns":890},[892,99368,99369,99421],{},[895,99370,99371,99373,99375,99381,99383,99389,99391,99393,99407],{},[898,99372,900],{},[1693,99374,1709],{"stretchy":1708},[3284,99376,99377,99379],{},[898,99378,1712],{},[1762,99380,1764],{},[1693,99382,1899],{"separator":1898},[3284,99384,99385,99387],{},[898,99386,1712],{},[1762,99388,2398],{},[1693,99390,1731],{"stretchy":1708},[1693,99392,1695],{},[5688,99394,99395,99397,99399],{},[898,99396,1712],{},[1762,99398,1764],{},[895,99400,99401,99403,99405],{},[1762,99402,1764],{},[898,99404,1705],{"mathvariant":1704},[1762,99406,2398],{},[5688,99408,99409,99411,99413],{},[898,99410,1712],{},[1762,99412,2398],{},[895,99414,99415,99417,99419],{},[1762,99416,1764],{},[898,99418,1705],{"mathvariant":1704},[1762,99420,2398],{},[902,99422,36726],{"encoding":904},[724,99424,99425],{},[883,99426,99428],{"className":99427},[886],[888,99429,99430],{"xmlns":890},[892,99431,99432,99538],{},[895,99433,99434,99436,99438,99520,99522,99536],{},[1915,99435,5315],{},[1693,99437,1695],{},[2132,99439,99440,99480],{},[895,99441,99442,99450,99466],{},[3638,99443,99444],{"scriptlevel":1911,"displaystyle":1708},[2132,99445,99446,99448],{},[1762,99447,1764],{},[1762,99449,2398],{},[5688,99451,99452,99454,99456],{},[898,99453,1712],{},[1762,99455,1764],{},[895,99457,99458,99460,99462,99464],{},[1693,99459,1698],{},[1762,99461,1764],{},[898,99463,1705],{"mathvariant":1704},[1762,99465,2398],{},[5688,99467,99468,99470,99472],{},[898,99469,1712],{},[1762,99471,2398],{},[895,99473,99474,99476,99478],{},[1762,99475,1764],{},[898,99477,1705],{"mathvariant":1704},[1762,99479,2398],{},[895,99481,99482,99490,99504],{},[3638,99483,99484],{"scriptlevel":1911,"displaystyle":1708},[2132,99485,99486,99488],{},[1762,99487,1764],{},[1762,99489,2398],{},[5688,99491,99492,99494,99496],{},[898,99493,1712],{},[1762,99495,1764],{},[895,99497,99498,99500,99502],{},[1762,99499,1764],{},[898,99501,1705],{"mathvariant":1704},[1762,99503,2398],{},[5688,99505,99506,99508,99510],{},[898,99507,1712],{},[1762,99509,2398],{},[895,99511,99512,99514,99516,99518],{},[1693,99513,1698],{},[1762,99515,1764],{},[898,99517,1705],{"mathvariant":1704},[1762,99519,2398],{},[1693,99521,1695],{},[2132,99523,99524,99530],{},[3284,99525,99526,99528],{},[898,99527,1712],{},[1762,99529,2398],{},[3284,99531,99532,99534],{},[898,99533,1712],{},[1762,99535,1764],{},[898,99537,1789],{"mathvariant":1704},[902,99539,36845],{"encoding":904},[724,99541,36848,99542,7617,99585,36896,99587,99606],{},[883,99543,99545],{"className":99544},[886],[888,99546,99547],{"xmlns":890},[892,99548,99549,99583],{},[895,99550,99551,99553,99555,99557,99559,99561,99563,99565,99573,99575],{},[1915,99552,5315],{},[1693,99554,1709],{"stretchy":1708},[1762,99556,36864],{},[1693,99558,1899],{"separator":1898},[1762,99560,21936],{},[1693,99562,1731],{"stretchy":1708},[1693,99564,1695],{},[3638,99566,99567],{"scriptlevel":1911,"displaystyle":1708},[2132,99568,99569,99571],{},[1762,99570,21936],{},[1762,99572,36864],{},[1693,99574,1695],{},[3638,99576,99577],{"scriptlevel":1911,"displaystyle":1708},[2132,99578,99579,99581],{},[1762,99580,9147],{},[1762,99582,8357],{},[902,99584,36893],{"encoding":904},[614,99586,16071],{},[883,99588,99590],{"className":99589},[886],[888,99591,99592],{"xmlns":890},[892,99593,99594,99604],{},[895,99595,99596],{},[3638,99597,99598],{"scriptlevel":1911,"displaystyle":1708},[2132,99599,99600,99602],{},[1762,99601,9147],{},[1762,99603,8357],{},[902,99605,36916],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,99608,99609,99610,99614],{},"(Paralelou je ",[207,99611,99613],{"className":99612,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,99616,99618],{"id":99617},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,99620,99621,99622,99625],{},"Rámcově se v kapitole 6 studují ",[38,99623,99624],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,99627,99628,99764],{},[123,99629,99630,99632,99633,4148,99664,1863,99667,99716,99717,1789],{},[38,99631,35040],{}," — maximalizace ",[883,99634,99636],{"className":99635},[886],[888,99637,99638],{"xmlns":890},[892,99639,99640,99662],{},[895,99641,99642,99644,99646,99652,99654,99660],{},[898,99643,900],{},[1693,99645,1709],{"stretchy":1708},[3284,99647,99648,99650],{},[898,99649,1712],{},[1762,99651,1764],{},[1693,99653,1899],{"separator":1898},[3284,99655,99656,99658],{},[898,99657,1712],{},[1762,99659,2398],{},[1693,99661,1731],{"stretchy":1708},[902,99663,23164],{"encoding":904},[38,99665,99666],{},"rozpočtovém omezení",[883,99668,99670],{"className":99669},[886],[888,99671,99672],{"xmlns":890},[892,99673,99674,99714],{},[895,99675,99676,99682,99684,99692,99698,99700,99708],{},[1717,99677,99678,99680],{},[898,99679,4618],{},[1693,99681,3672],{},[1693,99683,1695],{},[5688,99685,99686,99688,99690],{},[898,99687,1701],{},[1762,99689,1764],{},[1693,99691,3672],{},[3284,99693,99694,99696],{},[898,99695,1712],{},[1762,99697,1764],{},[1693,99699,1892],{},[5688,99701,99702,99704,99706],{},[898,99703,1701],{},[1762,99705,2398],{},[1693,99707,3672],{},[3284,99709,99710,99712],{},[898,99711,1712],{},[1762,99713,2398],{},[902,99715,24117],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,99718,99720],{"className":99719},[886],[888,99721,99722],{"xmlns":890},[892,99723,99724,99762],{},[895,99725,99726,99732,99734,99740,99742,99748,99750,99756,99758,99760],{},[3284,99727,99728,99730],{},[898,99729,1712],{},[898,99731,5696],{},[1693,99733,1695],{},[3284,99735,99736,99738],{},[898,99737,2738],{},[898,99739,5696],{},[1693,99741,1709],{"stretchy":1708},[3284,99743,99744,99746],{},[898,99745,1701],{},[1762,99747,1764],{},[1693,99749,1899],{"separator":1898},[3284,99751,99752,99754],{},[898,99753,1701],{},[1762,99755,2398],{},[1693,99757,1899],{"separator":1898},[898,99759,4618],{},[1693,99761,1731],{"stretchy":1708},[902,99763,43237],{"encoding":904},[123,99765,99766,34689,99769,34732,99815,99832,99833,1789],{},[38,99767,99768],{},"Duální úloha",[883,99770,99772],{"className":99771},[886],[888,99773,99774],{"xmlns":890},[892,99775,99776,99812],{},[895,99777,99778,99780,99782,99790,99796,99798,99806],{},[898,99779,1691],{},[1693,99781,1695],{},[5688,99783,99784,99786,99788],{},[898,99785,1701],{},[1762,99787,1764],{},[1693,99789,3672],{},[3284,99791,99792,99794],{},[898,99793,1712],{},[1762,99795,1764],{},[1693,99797,1892],{},[5688,99799,99800,99802,99804],{},[898,99801,1701],{},[1762,99803,2398],{},[1693,99805,3672],{},[3284,99807,99808,99810],{},[898,99809,1712],{},[1762,99811,2398],{},[902,99813,99814],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,99816,99818],{"className":99817},[886],[888,99819,99820],{"xmlns":890},[892,99821,99822,99830],{},[895,99823,99824],{},[1717,99825,99826,99828],{},[898,99827,900],{},[1693,99829,3672],{},[902,99831,34750],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,99834,99836],{"className":99835},[886],[888,99837,99838],{"xmlns":890},[892,99839,99840,99878],{},[895,99841,99842,99848,99850,99856,99858,99864,99866,99872,99874,99876],{},[3284,99843,99844,99846],{},[898,99845,1712],{},[898,99847,5696],{},[1693,99849,1695],{},[3284,99851,99852,99854],{},[898,99853,2738],{},[898,99855,5696],{},[1693,99857,1709],{"stretchy":1708},[3284,99859,99860,99862],{},[898,99861,1701],{},[1762,99863,1764],{},[1693,99865,1899],{"separator":1898},[3284,99867,99868,99870],{},[898,99869,1701],{},[1762,99871,2398],{},[1693,99873,1899],{"separator":1898},[898,99875,900],{},[1693,99877,1731],{"stretchy":1708},[902,99879,24641],{"encoding":904},[724,99881,99882,99883,99886,99887,1863,99890,99929],{},"Obě úlohy se řeší ",[207,99884,34755],{"className":99885,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,99888,99889],{},"tentýž bod dotyku",[883,99891,99893],{"className":99892},[886],[888,99894,99895],{"xmlns":890},[892,99896,99897,99927],{},[895,99898,99899,99905,99907,99915,99917,99925],{},[1717,99900,99901,99903],{},[898,99902,1712],{},[1693,99904,3672],{},[1693,99906,9392],{"stretchy":1708},[5688,99908,99909,99911,99913],{},[898,99910,1712],{},[1762,99912,1764],{},[1693,99914,3672],{},[1693,99916,1899],{"separator":1898},[5688,99918,99919,99921,99923],{},[898,99920,1712],{},[1762,99922,2398],{},[1693,99924,3672],{},[1693,99926,9407],{"stretchy":1708},[902,99928,35115],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,99931,99933],{"className":99932},[886],[888,99934,99935],{"xmlns":890,"display":34854},[892,99936,99937,99983],{},[895,99938,99939,99941,99943,99961,99963,99981],{},[1915,99940,5315],{},[1693,99942,1695],{},[2132,99944,99945,99953],{},[5688,99946,99947,99949,99951],{},[898,99948,900],{},[1762,99950,1764],{},[1693,99952,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[5688,99954,99955,99957,99959],{},[898,99956,900],{},[1762,99958,2398],{},[1693,99960,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,99962,1695],{},[2132,99964,99965,99973],{},[5688,99966,99967,99969,99971],{},[898,99968,1701],{},[1762,99970,1764],{},[1693,99972,3672],{},[5688,99974,99975,99977,99979],{},[898,99976,1701],{},[1762,99978,2398],{},[1693,99980,3672],{},[898,99982,1789],{"mathvariant":1704},[902,99984,99985],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,99987,99988],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1636,99990,99991],{},[724,99992,99993,99995,99996,99999,100000,100003,100004,100031,100032,100066,100067,100101,100102,100145,100146,100149,100150,1789],{},[883,99994,11036],{}," Pro detailní postup viz ",[207,99997,43535],{"className":99998,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,100001,100002],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,100005,100007],{"className":100006},[886],[888,100008,100009],{"xmlns":890},[892,100010,100011,100029],{},[895,100012,100013,100015,100017,100023],{},[898,100014,900],{},[1693,100016,1695],{},[3284,100018,100019,100021],{},[898,100020,1712],{},[1762,100022,1764],{},[3284,100024,100025,100027],{},[898,100026,1712],{},[1762,100028,2398],{},[902,100030,37009],{"encoding":904}," s výsledkem ",[883,100033,100035],{"className":100034},[886],[888,100036,100037],{"xmlns":890},[892,100038,100039,100063],{},[895,100040,100041,100047,100049,100051,100053,100059,100061],{},[3284,100042,100043,100045],{},[898,100044,1712],{},[1762,100046,1764],{},[1693,100048,1695],{},[1762,100050,11872],{},[1693,100052,1899],{"separator":1898},[3284,100054,100055,100057],{},[898,100056,1712],{},[1762,100058,2398],{},[1693,100060,1695],{},[1762,100062,9763],{},[902,100064,100065],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,100068,100070],{"className":100069},[886],[888,100071,100072],{"xmlns":890},[892,100073,100074,100098],{},[895,100075,100076,100082,100084,100086,100088,100094,100096],{},[3284,100077,100078,100080],{},[898,100079,1712],{},[1762,100081,1764],{},[1693,100083,1695],{},[1762,100085,9262],{},[1693,100087,1899],{"separator":1898},[3284,100089,100090,100092],{},[898,100091,1712],{},[1762,100093,2398],{},[1693,100095,1695],{},[1762,100097,1764],{},[902,100099,100100],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,100103,100105],{"className":100104},[886],[888,100106,100107],{"xmlns":890},[892,100108,100109,100143],{},[895,100110,100111,100113,100115,100129],{},[898,100112,900],{},[1693,100114,1695],{},[5688,100116,100117,100119,100121],{},[898,100118,1712],{},[1762,100120,1764],{},[895,100122,100123,100125,100127],{},[1762,100124,1764],{},[898,100126,1705],{"mathvariant":1704},[1762,100128,2398],{},[5688,100130,100131,100133,100135],{},[898,100132,1712],{},[1762,100134,2398],{},[895,100136,100137,100139,100141],{},[1762,100138,1764],{},[898,100140,1705],{"mathvariant":1704},[1762,100142,2398],{},[902,100144,39942],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,100147,100148],{},"6.8–6.13"," jsou na stránce ",[207,100151,5829],{"className":100152,"dataFsResolvedFilePath":911,"href":912},[210],[115,100154,100156],{"id":100155},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,100158,100159,100160,100173,100174,100176,100177,100179,100180,100182,100183,100185,100186,100188,100189,100191,100192,1863,100194,100229,100230,100243,100244,100247,100248,100251,100252,1789],{},"Každá ",[883,100161,100163],{"className":100162},[886],[888,100164,100165],{"xmlns":890},[892,100166,100167,100171],{},[895,100168,100169],{},[898,100170,5362],{},[902,100172,5362],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,100175,93511],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,100178,93995],{}," a současně ",[38,100181,93514],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,100184,93519],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,100187,59435],{}," (6.4) a druhé parciální derivace ",[38,100190,95877],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,100193,16586],{},[883,100195,100197],{"className":100196},[886],[888,100198,100199],{"xmlns":890},[892,100200,100201,100227],{},[895,100202,100203,100205,100207,100213,100215,100221,100223,100225],{},[898,100204,900],{},[1693,100206,1709],{"stretchy":1708},[3284,100208,100209,100211],{},[898,100210,1712],{},[1762,100212,1764],{},[1693,100214,1899],{"separator":1898},[3284,100216,100217,100219],{},[898,100218,1712],{},[1762,100220,2398],{},[1693,100222,1731],{"stretchy":1708},[1693,100224,1695],{},[898,100226,2000],{},[902,100228,16623],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,100231,100233],{"className":100232},[886],[888,100234,100235],{"xmlns":890},[892,100236,100237,100241],{},[895,100238,100239],{},[1915,100240,5315],{},[902,100242,35026],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,100245,100246],{},"maximalizace užitečnosti"," a duální ",[38,100249,100250],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,100253,43535],{"className":100254,"dataFsResolvedFilePath":911,"href":912},[210],[115,100256,8674],{"id":56645},[152,100258,100259,100262,100265,100268,100271,100274,100277,100280,100283,100286],{},[123,100260,100261],{},"Co se zahrnuje pod termín užitečnost?",[123,100263,100264],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,100266,100267],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,100269,100270],{},"Jak se vypočítá mezní užitečnost?",[123,100272,100273],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,100275,100276],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,100278,100279],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,100281,100282],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,100284,100285],{},"Proč mají křivky užitečnosti záporný sklon?",[123,100287,100288],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,100290,100292],{"id":100291},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,100294,100295,100298,100299,90186,100341,1343,100369,1343,100397,100425],{},[38,100296,100297],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,100300,100302],{"className":100301},[886],[888,100303,100304],{"xmlns":890},[892,100305,100306,100338],{},[895,100307,100308,100310,100312,100318,100320,100322,100328,100330,100332],{},[898,100309,900],{},[1693,100311,1695],{},[3284,100313,100314,100316],{},[898,100315,1712],{},[1762,100317,1764],{},[1693,100319,1892],{},[1762,100321,71285],{},[3284,100323,100324,100326],{},[898,100325,1712],{},[1762,100327,2398],{},[1693,100329,1892],{},[1762,100331,2398],{},[3284,100333,100334,100336],{},[898,100335,1712],{},[1762,100337,8357],{},[902,100339,100340],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,100342,100344],{"className":100343},[886],[888,100345,100346],{"xmlns":890},[892,100347,100348,100366],{},[895,100349,100350,100352,100354,100356,100358,100360,100362,100364],{},[898,100351,900],{},[1693,100353,1709],{"stretchy":1708},[1762,100355,9262],{},[1693,100357,1899],{"separator":1898},[1762,100359,2398],{},[1693,100361,1899],{"separator":1898},[1762,100363,2398],{},[1693,100365,1731],{"stretchy":1708},[902,100367,100368],{"encoding":904},"U(4, 2, 2)",[883,100370,100372],{"className":100371},[886],[888,100373,100374],{"xmlns":890},[892,100375,100376,100394],{},[895,100377,100378,100380,100382,100384,100386,100388,100390,100392],{},[898,100379,900],{},[1693,100381,1709],{"stretchy":1708},[1762,100383,1764],{},[1693,100385,1899],{"separator":1898},[1762,100387,9262],{},[1693,100389,1899],{"separator":1898},[1762,100391,2398],{},[1693,100393,1731],{"stretchy":1708},[902,100395,100396],{"encoding":904},"U(1, 4, 2)",[883,100398,100400],{"className":100399},[886],[888,100401,100402],{"xmlns":890},[892,100403,100404,100422],{},[895,100405,100406,100408,100410,100412,100414,100416,100418,100420],{},[898,100407,900],{},[1693,100409,1709],{"stretchy":1708},[1762,100411,2398],{},[1693,100413,1899],{"separator":1898},[1762,100415,8357],{},[1693,100417,1899],{"separator":1898},[1762,100419,1764],{},[1693,100421,1731],{"stretchy":1708},[902,100423,100424],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,100427,100428,100431,100432,100484,100485,1343,100511,1343,100537,1343,100563,1343,100589,1343,100615,1343,100641,100667],{},[38,100429,100430],{},"6.2"," Je dána užitečnost ",[883,100433,100435],{"className":100434},[886],[888,100436,100437],{"xmlns":890},[892,100438,100439,100481],{},[895,100440,100441,100443,100445,100447,100461,100475],{},[898,100442,900],{},[1693,100444,1695],{},[1762,100446,2398],{},[5688,100448,100449,100451,100453],{},[898,100450,1712],{},[1762,100452,1764],{},[895,100454,100455,100457,100459],{},[1762,100456,1764],{},[898,100458,1705],{"mathvariant":1704},[1762,100460,8357],{},[5688,100462,100463,100465,100467],{},[898,100464,1712],{},[1762,100466,2398],{},[895,100468,100469,100471,100473],{},[1762,100470,1764],{},[898,100472,1705],{"mathvariant":1704},[1762,100474,2398],{},[3284,100476,100477,100479],{},[898,100478,1712],{},[1762,100480,8357],{},[902,100482,100483],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,100486,100488],{"className":100487},[886],[888,100489,100490],{"xmlns":890},[892,100491,100492,100508],{},[895,100493,100494,100496,100498,100500,100502,100504,100506],{},[1693,100495,1709],{"stretchy":1708},[1762,100497,12433],{},[1693,100499,1899],{"separator":1898},[1762,100501,73320],{},[1693,100503,1899],{"separator":1898},[1762,100505,9763],{},[1693,100507,1731],{"stretchy":1708},[902,100509,100510],{"encoding":904},"(36, 27, 10)",[883,100512,100514],{"className":100513},[886],[888,100515,100516],{"xmlns":890},[892,100517,100518,100534],{},[895,100519,100520,100522,100524,100526,100528,100530,100532],{},[1693,100521,1709],{"stretchy":1708},[1762,100523,48611],{},[1693,100525,1899],{"separator":1898},[1762,100527,12453],{},[1693,100529,1899],{"separator":1898},[1762,100531,15892],{},[1693,100533,1731],{"stretchy":1708},[902,100535,100536],{"encoding":904},"(64, 8, 20)",[883,100538,100540],{"className":100539},[886],[888,100541,100542],{"xmlns":890},[892,100543,100544,100560],{},[895,100545,100546,100548,100550,100552,100554,100556,100558],{},[1693,100547,1709],{"stretchy":1708},[1762,100549,11872],{},[1693,100551,1899],{"separator":1898},[1762,100553,48611],{},[1693,100555,1899],{"separator":1898},[1762,100557,12453],{},[1693,100559,1731],{"stretchy":1708},[902,100561,100562],{"encoding":904},"(25, 64, 8)",[883,100564,100566],{"className":100565},[886],[888,100567,100568],{"xmlns":890},[892,100569,100570,100586],{},[895,100571,100572,100574,100576,100578,100580,100582,100584],{},[1693,100573,1709],{"stretchy":1708},[1762,100575,9262],{},[1693,100577,1899],{"separator":1898},[1762,100579,79243],{},[1693,100581,1899],{"separator":1898},[1762,100583,9154],{},[1693,100585,1731],{"stretchy":1708},[902,100587,100588],{"encoding":904},"(4, 125, 6)",[883,100590,100592],{"className":100591},[886],[888,100593,100594],{"xmlns":890},[892,100595,100596,100612],{},[895,100597,100598,100600,100602,100604,100606,100608,100610],{},[1693,100599,1709],{"stretchy":1708},[1762,100601,10881],{},[1693,100603,1899],{"separator":1898},[1762,100605,12079],{},[1693,100607,1899],{"separator":1898},[1762,100609,10402],{},[1693,100611,1731],{"stretchy":1708},[902,100613,100614],{"encoding":904},"(9, 40, 12)",[883,100616,100618],{"className":100617},[886],[888,100619,100620],{"xmlns":890},[892,100621,100622,100638],{},[895,100623,100624,100626,100628,100630,100632,100634,100636],{},[1693,100625,1709],{"stretchy":1708},[1762,100627,10881],{},[1693,100629,1899],{"separator":1898},[1762,100631,48611],{},[1693,100633,1899],{"separator":1898},[1762,100635,9147],{},[1693,100637,1731],{"stretchy":1708},[902,100639,100640],{"encoding":904},"(9, 64, 5)",[883,100642,100644],{"className":100643},[886],[888,100645,100646],{"xmlns":890},[892,100647,100648,100664],{},[895,100649,100650,100652,100654,100656,100658,100660,100662],{},[1693,100651,1709],{"stretchy":1708},[1762,100653,48611],{},[1693,100655,1899],{"separator":1898},[1762,100657,12453],{},[1693,100659,1899],{"separator":1898},[1762,100661,9763],{},[1693,100663,1731],{"stretchy":1708},[902,100665,100666],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,100669,100670,100431,100673,100716,100717,100751,100752,7721,100782,100815,100816,100833,100834,100851],{},[38,100671,100672],{},"6.3",[883,100674,100676],{"className":100675},[886],[888,100677,100678],{"xmlns":890},[892,100679,100680,100714],{},[895,100681,100682,100684,100686,100700],{},[898,100683,900],{},[1693,100685,1695],{},[5688,100687,100688,100690,100692],{},[898,100689,1712],{},[1762,100691,1764],{},[895,100693,100694,100696,100698],{},[1762,100695,1764],{},[898,100697,1705],{"mathvariant":1704},[1762,100699,2398],{},[5688,100701,100702,100704,100706],{},[898,100703,1712],{},[1762,100705,2398],{},[895,100707,100708,100710,100712],{},[1762,100709,1764],{},[898,100711,1705],{"mathvariant":1704},[1762,100713,2398],{},[902,100715,39942],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,100718,100720],{"className":100719},[886],[888,100721,100722],{"xmlns":890},[892,100723,100724,100748],{},[895,100725,100726,100732,100734,100736,100738,100744,100746],{},[3284,100727,100728,100730],{},[898,100729,1712],{},[1762,100731,1764],{},[1693,100733,1695],{},[1762,100735,10017],{},[1693,100737,1899],{"separator":1898},[3284,100739,100740,100742],{},[898,100741,1712],{},[1762,100743,2398],{},[1693,100745,1695],{},[1762,100747,53467],{},[902,100749,100750],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,100753,100755],{"className":100754},[886],[888,100756,100757],{"xmlns":890},[892,100758,100759,100779],{},[895,100760,100761,100763,100769,100771,100773],{},[898,100762,2839],{},[3284,100764,100765,100767],{},[898,100766,900],{},[1762,100768,1764],{},[1693,100770,1899],{"separator":1898},[898,100772,2839],{},[3284,100774,100775,100777],{},[898,100776,900],{},[1762,100778,2398],{},[902,100780,100781],{"encoding":904},"MU_1, MU_2",[883,100783,100785],{"className":100784},[886],[888,100786,100787],{"xmlns":890},[892,100788,100789,100813],{},[895,100790,100791,100797,100799,100801,100803,100809,100811],{},[3284,100792,100793,100795],{},[898,100794,1712],{},[1762,100796,1764],{},[1693,100798,1695],{},[1762,100800,10017],{},[1693,100802,1899],{"separator":1898},[3284,100804,100805,100807],{},[898,100806,1712],{},[1762,100808,2398],{},[1693,100810,1695],{},[1762,100812,53467],{},[902,100814,100750],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,100817,100819],{"className":100818},[886],[888,100820,100821],{"xmlns":890},[892,100822,100823,100831],{},[895,100824,100825],{},[3284,100826,100827,100829],{},[898,100828,1712],{},[1762,100830,1764],{},[902,100832,5809],{"encoding":904}," na 60 a poklesu ",[883,100835,100837],{"className":100836},[886],[888,100838,100839],{"xmlns":890},[892,100840,100841,100849],{},[895,100842,100843],{},[3284,100844,100845,100847],{},[898,100846,1712],{},[1762,100848,2398],{},[902,100850,5790],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,100853,100854,100857,100858,100919,100920,1789],{},[38,100855,100856],{},"6.4"," Je dána funkce ",[883,100859,100861],{"className":100860},[886],[888,100862,100863],{"xmlns":890},[892,100864,100865,100917],{},[895,100866,100867,100869,100871,100877,100879,100885,100887,100889,100903],{},[898,100868,900],{},[1693,100870,1709],{"stretchy":1708},[3284,100872,100873,100875],{},[898,100874,1712],{},[1762,100876,1764],{},[1693,100878,1899],{"separator":1898},[3284,100880,100881,100883],{},[898,100882,1712],{},[1762,100884,2398],{},[1693,100886,1731],{"stretchy":1708},[1693,100888,1695],{},[5688,100890,100891,100893,100895],{},[898,100892,1712],{},[1762,100894,1764],{},[895,100896,100897,100899,100901],{},[1762,100898,1764],{},[898,100900,1705],{"mathvariant":1704},[1762,100902,2398],{},[5688,100904,100905,100907,100909],{},[898,100906,1712],{},[1762,100908,2398],{},[895,100910,100911,100913,100915],{},[1762,100912,1764],{},[898,100914,1705],{"mathvariant":1704},[1762,100916,2398],{},[902,100918,36726],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,100921,100923],{"className":100922},[886],[888,100924,100925],{"xmlns":890},[892,100926,100927,101017],{},[895,100928,100929,100931,100933,100939,100941,100943,100945,100947,100949,100951,100957,100959,100961,100963,100965,100967,100969,100971,100973,100979,100981,100983,100985,100987,100989,100991,100997,100999,101001,101003,101005,101007,101009,101015],{},[898,100930,900],{},[1693,100932,1709],{"stretchy":1708},[3284,100934,100935,100937],{},[898,100936,1712],{},[1762,100938,1764],{},[1693,100940,1899],{"separator":1898},[1762,100942,1764],{},[1693,100944,1731],{"stretchy":1708},[1693,100946,1899],{"separator":1898},[898,100948,900],{},[1693,100950,1709],{"stretchy":1708},[3284,100952,100953,100955],{},[898,100954,1712],{},[1762,100956,1764],{},[1693,100958,1899],{"separator":1898},[1762,100960,2398],{},[1693,100962,1731],{"stretchy":1708},[1693,100964,1899],{"separator":1898},[898,100966,900],{},[1693,100968,1709],{"stretchy":1708},[1762,100970,1764],{},[1693,100972,1899],{"separator":1898},[3284,100974,100975,100977],{},[898,100976,1712],{},[1762,100978,2398],{},[1693,100980,1731],{"stretchy":1708},[1693,100982,1899],{"separator":1898},[898,100984,900],{},[1693,100986,1709],{"stretchy":1708},[1762,100988,2398],{},[1693,100990,1899],{"separator":1898},[3284,100992,100993,100995],{},[898,100994,1712],{},[1762,100996,2398],{},[1693,100998,1731],{"stretchy":1708},[1693,101000,1899],{"separator":1898},[898,101002,900],{},[1693,101004,1709],{"stretchy":1708},[1762,101006,8357],{},[1693,101008,1899],{"separator":1898},[3284,101010,101011,101013],{},[898,101012,1712],{},[1762,101014,2398],{},[1693,101016,1731],{"stretchy":1708},[902,101018,101019],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,101021,101022,100431,101025,101069,101070,101178,101179,1343,101204,1343,101229,101271,101272,1343,101301,101326],{},[38,101023,101024],{},"6.5",[883,101026,101028],{"className":101027},[886],[888,101029,101030],{"xmlns":890},[892,101031,101032,101066],{},[895,101033,101034,101036,101038,101052],{},[898,101035,900],{},[1693,101037,1695],{},[5688,101039,101040,101042,101044],{},[898,101041,1712],{},[1762,101043,1764],{},[895,101045,101046,101048,101050],{},[1762,101047,2398],{},[898,101049,1705],{"mathvariant":1704},[1762,101051,8357],{},[5688,101053,101054,101056,101058],{},[898,101055,1712],{},[1762,101057,2398],{},[895,101059,101060,101062,101064],{},[1762,101061,1764],{},[898,101063,1705],{"mathvariant":1704},[1762,101065,8357],{},[902,101067,101068],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,101071,101073],{"className":101072},[886],[888,101074,101075],{"xmlns":890},[892,101076,101077,101175],{},[895,101078,101079,101081,101083,101089,101091,101097,101099,101101,101103,101105,101107,101109,101115,101117,101119,101121,101123,101125,101127,101133,101135,101137,101139,101141,101143,101145,101147,101149,101155,101157,101159,101161,101163,101165,101167,101173],{},[898,101080,900],{},[1693,101082,1709],{"stretchy":1708},[3284,101084,101085,101087],{},[898,101086,1712],{},[1762,101088,1764],{},[1693,101090,1899],{"separator":1898},[3284,101092,101093,101095],{},[898,101094,1712],{},[1762,101096,2398],{},[1693,101098,1731],{"stretchy":1708},[1693,101100,1695],{},[1762,101102,2398],{},[1693,101104,1899],{"separator":1898},[898,101106,900],{},[1693,101108,1709],{"stretchy":1708},[3284,101110,101111,101113],{},[898,101112,1712],{},[1762,101114,1764],{},[1693,101116,1899],{"separator":1898},[1762,101118,8357],{},[1693,101120,1731],{"stretchy":1708},[1693,101122,1899],{"separator":1898},[898,101124,900],{},[1693,101126,1709],{"stretchy":1708},[3284,101128,101129,101131],{},[898,101130,1712],{},[1762,101132,1764],{},[1693,101134,1899],{"separator":1898},[1762,101136,2398],{},[1693,101138,1731],{"stretchy":1708},[1693,101140,1899],{"separator":1898},[898,101142,900],{},[1693,101144,1709],{"stretchy":1708},[1762,101146,2398],{},[1693,101148,1899],{"separator":1898},[3284,101150,101151,101153],{},[898,101152,1712],{},[1762,101154,2398],{},[1693,101156,1731],{"stretchy":1708},[1693,101158,1899],{"separator":1898},[898,101160,900],{},[1693,101162,1709],{"stretchy":1708},[1762,101164,8357],{},[1693,101166,1899],{"separator":1898},[3284,101168,101169,101171],{},[898,101170,1712],{},[1762,101172,2398],{},[1693,101174,1731],{"stretchy":1708},[902,101176,101177],{"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 ",[883,101180,101182],{"className":101181},[886],[888,101183,101184],{"xmlns":890},[892,101185,101186,101201],{},[895,101187,101188,101190,101192,101194,101196,101199],{},[898,101189,2719],{},[1693,101191,9392],{"stretchy":1708},[1762,101193,71285],{},[1693,101195,15283],{"separator":1898},[1762,101197,101198],{},"3,555",[1693,101200,9407],{"stretchy":1708},[902,101202,101203],{"encoding":904},"A[1{,}5; 3{,}555]",[883,101205,101207],{"className":101206},[886],[888,101208,101209],{"xmlns":890},[892,101210,101211,101226],{},[895,101212,101213,101215,101217,101219,101221,101224],{},[898,101214,7520],{},[1693,101216,9392],{"stretchy":1708},[1762,101218,59957],{},[1693,101220,15283],{"separator":1898},[1762,101222,101223],{},"1,28",[1693,101225,9407],{"stretchy":1708},[902,101227,101228],{"encoding":904},"B[2{,}5; 1{,}28]",[883,101230,101232],{"className":101231},[886],[888,101233,101234],{"xmlns":890},[892,101235,101236,101268],{},[895,101237,101238,101240,101242,101244,101246,101248,101250,101256,101258,101260,101262,101264,101266],{},[898,101239,2971],{},[1693,101241,9392],{"stretchy":1708},[1762,101243,2398],{},[1693,101245,15283],{"separator":1898},[898,101247,900],{},[1693,101249,1709],{"stretchy":1708},[3284,101251,101252,101254],{},[898,101253,1712],{},[1762,101255,1764],{},[1693,101257,1899],{"separator":1898},[1762,101259,8357],{},[1693,101261,1731],{"stretchy":1708},[1693,101263,1695],{},[1762,101265,8357],{},[1693,101267,9407],{"stretchy":1708},[902,101269,101270],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,101273,101275],{"className":101274},[886],[888,101276,101277],{"xmlns":890},[892,101278,101279,101298],{},[895,101280,101281,101283,101285,101287,101289,101291,101293,101296],{},[898,101282,2738],{},[1693,101284,9392],{"stretchy":1708},[1762,101286,8357],{},[1693,101288,15283],{"separator":1898},[1762,101290,1764],{},[1693,101292,15283],{"separator":1898},[1762,101294,101295],{},"0,832",[1693,101297,9407],{"stretchy":1708},[902,101299,101300],{"encoding":904},"D[3; 1; 0{,}832]",[883,101302,101304],{"className":101303},[886],[888,101305,101306],{"xmlns":890},[892,101307,101308,101323],{},[895,101309,101310,101312,101314,101316,101318,101321],{},[898,101311,1691],{},[1693,101313,9392],{"stretchy":1708},[1762,101315,59957],{},[1693,101317,15283],{"separator":1898},[1762,101319,101320],{},"4,32",[1693,101322,9407],{"stretchy":1708},[902,101324,101325],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,101328,101329,100431,101332,101375,101376,7721,101389,101423,101424,101441,101442,101459],{},[38,101330,101331],{},"6.6",[883,101333,101335],{"className":101334},[886],[888,101336,101337],{"xmlns":890},[892,101338,101339,101373],{},[895,101340,101341,101343,101345,101359],{},[898,101342,900],{},[1693,101344,1695],{},[5688,101346,101347,101349,101351],{},[898,101348,1712],{},[1762,101350,1764],{},[895,101352,101353,101355,101357],{},[1762,101354,2398],{},[898,101356,1705],{"mathvariant":1704},[1762,101358,8357],{},[5688,101360,101361,101363,101365],{},[898,101362,1712],{},[1762,101364,2398],{},[895,101366,101367,101369,101371],{},[1762,101368,1764],{},[898,101370,1705],{"mathvariant":1704},[1762,101372,8357],{},[902,101374,101068],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,101377,101379],{"className":101378},[886],[888,101380,101381],{"xmlns":890},[892,101382,101383,101387],{},[895,101384,101385],{},[1915,101386,5315],{},[902,101388,35026],{"encoding":904},[883,101390,101392],{"className":101391},[886],[888,101393,101394],{"xmlns":890},[892,101395,101396,101420],{},[895,101397,101398,101404,101406,101408,101410,101416,101418],{},[3284,101399,101400,101402],{},[898,101401,1712],{},[1762,101403,1764],{},[1693,101405,1695],{},[1762,101407,9987],{},[1693,101409,1899],{"separator":1898},[3284,101411,101412,101414],{},[898,101413,1712],{},[1762,101415,2398],{},[1693,101417,1695],{},[1762,101419,15236],{},[902,101421,101422],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,101425,101427],{"className":101426},[886],[888,101428,101429],{"xmlns":890},[892,101430,101431,101439],{},[895,101432,101433],{},[3284,101434,101435,101437],{},[898,101436,1712],{},[1762,101438,1764],{},[902,101440,5809],{"encoding":904},", poklesne-li ",[883,101443,101445],{"className":101444},[886],[888,101446,101447],{"xmlns":890},[892,101448,101449,101457],{},[895,101450,101451],{},[3284,101452,101453,101455],{},[898,101454,1712],{},[1762,101456,2398],{},[902,101458,5790],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,101461,101462,101465,101466,101483,101484,101501,101502,101534,101535,101560,101561,101574,101575,1343,101599,1343,101623,1789],{},[38,101463,101464],{},"6.7"," Míra uspokojení z nákupu množství ",[883,101467,101469],{"className":101468},[886],[888,101470,101471],{"xmlns":890},[892,101472,101473,101481],{},[895,101474,101475],{},[3284,101476,101477,101479],{},[898,101478,1712],{},[1762,101480,1764],{},[902,101482,5809],{"encoding":904}," nealko nápojů a množství ",[883,101485,101487],{"className":101486},[886],[888,101488,101489],{"xmlns":890},[892,101490,101491,101499],{},[895,101492,101493],{},[3284,101494,101495,101497],{},[898,101496,1712],{},[1762,101498,2398],{},[902,101500,5790],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,101503,101505],{"className":101504},[886],[888,101506,101507],{"xmlns":890},[892,101508,101509,101531],{},[895,101510,101511,101513,101515],{},[898,101512,900],{},[1693,101514,1695],{},[14976,101516,101517],{},[895,101518,101519,101525],{},[3284,101520,101521,101523],{},[898,101522,1712],{},[1762,101524,1764],{},[3284,101526,101527,101529],{},[898,101528,1712],{},[1762,101530,2398],{},[902,101532,101533],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,101536,101538],{"className":101537},[886],[888,101539,101540],{"xmlns":890},[892,101541,101542,101558],{},[895,101543,101544,101550,101552],{},[3284,101545,101546,101548],{},[898,101547,1712],{},[1762,101549,1764],{},[1693,101551,1899],{"separator":1898},[3284,101553,101554,101556],{},[898,101555,1712],{},[1762,101557,2398],{},[902,101559,42405],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,101562,101564],{"className":101563},[886],[888,101565,101566],{"xmlns":890},[892,101567,101568,101572],{},[895,101569,101570],{},[1915,101571,5315],{},[902,101573,35026],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,101576,101578],{"className":101577},[886],[888,101579,101580],{"xmlns":890},[892,101581,101582,101596],{},[895,101583,101584,101586,101588,101590,101592,101594],{},[1915,101585,5315],{},[1693,101587,1709],{"stretchy":1708},[1762,101589,9147],{},[1693,101591,1899],{"separator":1898},[1762,101593,15892],{},[1693,101595,1731],{"stretchy":1708},[902,101597,101598],{"encoding":904},"\\text{MRCS}(5, 20)",[883,101600,101602],{"className":101601},[886],[888,101603,101604],{"xmlns":890},[892,101605,101606,101620],{},[895,101607,101608,101610,101612,101614,101616,101618],{},[1915,101609,5315],{},[1693,101611,1709],{"stretchy":1708},[1762,101613,15892],{},[1693,101615,1899],{"separator":1898},[1762,101617,9147],{},[1693,101619,1731],{"stretchy":1708},[902,101621,101622],{"encoding":904},"\\text{MRCS}(20, 5)",[883,101624,101626],{"className":101625},[886],[888,101627,101628],{"xmlns":890},[892,101629,101630,101644],{},[895,101631,101632,101634,101636,101638,101640,101642],{},[1915,101633,5315],{},[1693,101635,1709],{"stretchy":1708},[1762,101637,2398],{},[1693,101639,1899],{"separator":1898},[1762,101641,10017],{},[1693,101643,1731],{"stretchy":1708},[902,101645,101646],{"encoding":904},"\\text{MRCS}(2, 50)",[1636,101648,101649],{},[724,101650,101651,101653,101654,1789],{},[883,101652,8620],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,101655,101658],{"className":101656,"dataFsResolvedFilePath":911,"href":101657},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,101660,22545],{"id":22544},[120,101662,101663,101669,101674,101680,101733,101743,101788,101843,101905,101962,102017,102056],{},[123,101664,101665,101668],{},[38,101666,101667],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,101670,101671,101673],{},[38,101672,93570],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,101675,101676,101679],{},[38,101677,101678],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,101681,101682,101684,101685,101698,101699,1789],{},[38,101683,93897],{}," — uspořádaná ",[883,101686,101688],{"className":101687},[886],[888,101689,101690],{"xmlns":890},[892,101691,101692,101696],{},[895,101693,101694],{},[898,101695,5362],{},[902,101697,5362],{"encoding":904},"-tice ",[883,101700,101702],{"className":101701},[886],[888,101703,101704],{"xmlns":890},[892,101705,101706,101730],{},[895,101707,101708,101710,101716,101718,101720,101722,101728],{},[1693,101709,1709],{"stretchy":1708},[3284,101711,101712,101714],{},[898,101713,1712],{},[1762,101715,1764],{},[1693,101717,1899],{"separator":1898},[1693,101719,16501],{},[1693,101721,1899],{"separator":1898},[3284,101723,101724,101726],{},[898,101725,1712],{},[898,101727,5362],{},[1693,101729,1731],{"stretchy":1708},[902,101731,101732],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,101734,101735,101738,101739,101742],{},[38,101736,101737],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,101740,101741],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,101744,101745,1863,101747,101787],{},[38,101746,5529],{},[883,101748,101750],{"className":101749},[886],[888,101751,101752],{"xmlns":890},[892,101753,101754,101784],{},[895,101755,101756,101758,101760,101762,101764,101770,101772,101774,101776,101782],{},[898,101757,900],{},[1693,101759,1695],{},[898,101761,900],{},[1693,101763,1709],{"stretchy":1708},[3284,101765,101766,101768],{},[898,101767,1712],{},[1762,101769,1764],{},[1693,101771,1899],{"separator":1898},[1693,101773,16501],{},[1693,101775,1899],{"separator":1898},[3284,101777,101778,101780],{},[898,101779,1712],{},[898,101781,5362],{},[1693,101783,1731],{"stretchy":1708},[902,101785,101786],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,101789,101790,1863,101793,101822,101823,1863,101826,101842],{},[38,101791,101792],{},"Mezní užitečnost",[883,101794,101796],{"className":101795},[886],[888,101797,101798],{"xmlns":890},[892,101799,101800,101820],{},[895,101801,101802,101804,101810,101812],{},[898,101803,2839],{},[3284,101805,101806,101808],{},[898,101807,900],{},[898,101809,5696],{},[1693,101811,1695],{},[5688,101813,101814,101816,101818],{},[898,101815,900],{},[898,101817,5696],{},[1693,101819,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[902,101821,93354],{"encoding":904}," — vzorec (6.2); ",[38,101824,101825],{},"totální diferenciál",[883,101827,101829],{"className":101828},[886],[888,101830,101831],{"xmlns":890},[892,101832,101833,101839],{},[895,101834,101835,101837],{},[898,101836,1771],{"mathvariant":1704},[898,101838,900],{},[902,101840,101841],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,101844,101845,101847,101848,101872,101873,101904],{},[38,101846,95532],{}," — (6.4) ",[883,101849,101851],{"className":101850},[886],[888,101852,101853],{"xmlns":890},[892,101854,101855,101869],{},[895,101856,101857,101865,101867],{},[5688,101858,101859,101861,101863],{},[898,101860,900],{},[898,101862,5696],{},[1693,101864,1724],{"mathvariant":1704,"lspace":1723,"rspace":1723},[1693,101866,1922],{},[1762,101868,1911],{},[902,101870,101871],{"encoding":904},"U'_i > 0",", (6.5) ",[883,101874,101876],{"className":101875},[886],[888,101877,101878],{"xmlns":890},[892,101879,101880,101902],{},[895,101881,101882,101898,101900],{},[5688,101883,101884,101886,101892],{},[898,101885,900],{},[895,101887,101888,101890],{},[898,101889,5696],{},[898,101891,5696],{},[895,101893,101894,101896],{},[1693,101895,1724],{"mathvariant":1704},[1693,101897,1724],{"mathvariant":1704},[1693,101899,1908],{},[1762,101901,1911],{},[902,101903,5711],{"encoding":904}," (zákon klesající mezní užitečnosti).",[123,101906,101907,1863,101909,101940,101941,1789],{},[38,101908,97319],{},[883,101910,101912],{"className":101911},[886],[888,101913,101914],{"xmlns":890},[892,101915,101916,101938],{},[895,101917,101918,101920,101922,101930],{},[898,101919,900],{},[1693,101921,1695],{},[5688,101923,101924,101926,101928],{},[898,101925,1712],{},[1762,101927,1764],{},[898,101929,207],{},[5688,101931,101932,101934,101936],{},[898,101933,1712],{},[1762,101935,2398],{},[898,101937,1895],{},[902,101939,42585],{"encoding":904}," — (6.6), speciálně ",[883,101942,101944],{"className":101943},[886],[888,101945,101946],{"xmlns":890},[892,101947,101948,101960],{},[895,101949,101950,101952,101954,101956,101958],{},[898,101951,1895],{},[1693,101953,1695],{},[1762,101955,1764],{},[1693,101957,1698],{},[898,101959,207],{},[902,101961,97472],{"encoding":904},[123,101963,101964,1863,101967,102002,102003,102016],{},[38,101965,101966],{},"Křivky užitečnosti (indiferenční)",[883,101968,101970],{"className":101969},[886],[888,101971,101972],{"xmlns":890},[892,101973,101974,102000],{},[895,101975,101976,101978,101980,101986,101988,101994,101996,101998],{},[898,101977,900],{},[1693,101979,1709],{"stretchy":1708},[3284,101981,101982,101984],{},[898,101983,1712],{},[1762,101985,1764],{},[1693,101987,1899],{"separator":1898},[3284,101989,101990,101992],{},[898,101991,1712],{},[1762,101993,2398],{},[1693,101995,1731],{"stretchy":1708},[1693,101997,1695],{},[898,101999,2000],{},[902,102001,16623],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,102004,102006],{"className":102005},[886],[888,102007,102008],{"xmlns":890},[892,102009,102010,102014],{},[895,102011,102012],{},[898,102013,900],{},[902,102015,900],{"encoding":904},", konvexní.",[123,102018,102019,1863,102021,102055],{},[38,102020,5716],{},[883,102022,102024],{"className":102023},[886],[888,102025,102026],{"xmlns":890},[892,102027,102028,102052],{},[895,102029,102030,102032,102034,102036,102042,102044,102046],{},[1915,102031,5315],{},[1693,102033,1695],{},[898,102035,2839],{},[3284,102037,102038,102040],{},[898,102039,900],{},[1762,102041,1764],{},[898,102043,1705],{"mathvariant":1704},[898,102045,2839],{},[3284,102047,102048,102050],{},[898,102049,900],{},[1762,102051,2398],{},[902,102053,102054],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,102057,102058,1863,102061,16624,102090,102093],{},[38,102059,102060],{},"Podmínka optimality",[883,102062,102064],{"className":102063},[886],[888,102065,102066],{"xmlns":890},[892,102067,102068,102088],{},[895,102069,102070,102072,102074,102080,102082],{},[1915,102071,5315],{},[1693,102073,1695],{},[3284,102075,102076,102078],{},[898,102077,1701],{},[1762,102079,1764],{},[898,102081,1705],{"mathvariant":1704},[3284,102083,102084,102086],{},[898,102085,1701],{},[1762,102087,2398],{},[902,102089,34786],{"encoding":904},[207,102091,43535],{"className":102092,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,102095,8685],{"id":8684},[120,102097,102098,102135,102176,102186],{},[123,102099,102100,1863,102103,102106,102107,102120,102121,102134],{},[38,102101,102102],{},"Navazující téma:",[207,102104,913],{"className":102105,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,102108,102110],{"className":102109},[886],[888,102111,102112],{"xmlns":890},[892,102113,102114,102118],{},[895,102115,102116],{},[898,102117,900],{},[902,102119,900],{"encoding":904},", min ",[883,102122,102124],{"className":102123},[886],[888,102125,102126],{"xmlns":890},[892,102127,102128,102132],{},[895,102129,102130],{},[898,102131,1691],{},[902,102133,1691],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,102136,102137,1863,102140,17938,102143,93110,102146,102149,102150,102153,102154,25461,102172,102175],{},[38,102138,102139],{},"Související pojmy:",[207,102141,784],{"className":102142,"dataFsResolvedFilePath":782,"href":783},[210],[207,102144,8726],{"className":102145,"dataFsResolvedFilePath":764,"href":765},[210],[207,102147,8763],{"className":102148,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,102151,2181],{"className":102152,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,102155,102157],{"className":102156},[886],[888,102158,102159],{"xmlns":890},[892,102160,102161,102169],{},[895,102162,102163],{},[3284,102164,102165,102167],{},[898,102166,2738],{},[898,102168,5696],{},[902,102170,102171],{"encoding":904},"D_i",[207,102173,793],{"className":102174,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,102177,102178,1863,102180,1343,102183],{},[38,102179,43484],{},[207,102181,1094],{"className":102182,"dataFsResolvedFilePath":838,"href":839},[210],[207,102184,1101],{"className":102185,"dataFsResolvedFilePath":868,"href":869},[210],[123,102187,102188,1863,102190],{},[38,102189,8692],{},[207,102191,1653],{"className":102192,"dataFsResolvedFilePath":1651,"href":1652},[210],{"title":641,"searchDepth":642,"depth":642,"links":102194},[102195,102196,102197,102200,102201,102204,102208,102209,102212,102213,102214,102215,102216,102217,102218],{"id":18850,"depth":642,"text":18851},{"id":93493,"depth":642,"text":93494},{"id":93553,"depth":642,"text":93554,"children":102198},[102199],{"id":93569,"depth":649,"text":93570},{"id":93876,"depth":642,"text":93877},{"id":94735,"depth":642,"text":94736,"children":102202},[102203],{"id":95282,"depth":649,"text":86918},{"id":95531,"depth":642,"text":95532,"children":102205},[102206],{"id":96403,"depth":649,"text":102207},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":97318,"depth":642,"text":97319},{"id":97853,"depth":642,"text":97854,"children":102210},[102211],{"id":98627,"depth":649,"text":98628},{"id":98857,"depth":642,"text":98858},{"id":99617,"depth":642,"text":99618},{"id":100155,"depth":642,"text":100156},{"id":56645,"depth":642,"text":8674},{"id":100291,"depth":642,"text":100292},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fuzitecnost",{"title":93278,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,16628,102225,93272,17968,102226],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":102229,"title":757,"body":102230,"course":1128,"courses":659,"created":1129,"description":102502,"extension":661,"meta":102503,"navigation":664,"path":102504,"seo":102505,"sources":102506,"stem":102507,"tags":102508,"type":10745,"updated":677,"__hash__":102514},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":102231,"toc":102494},[102232,102235,102242,102249,102253,102263,102265,102299,102303,102346,102349,102407,102411,102441,102445,102465,102467],[12,102233,757],{"id":102234},"základy-matematické-ekonomie",[724,102236,102237,102238,102241],{},"Úvodní pojmy a princip modelování v ",[207,102239,23201],{"className":102240,"dataFsResolvedFilePath":1651,"href":1652},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,102243,102244],{},[9465,102245],{"alt":102246,"className":102247,"src":102248},"imek-model-promenne",[210,9469],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,102250,102252],{"id":102251},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,102254,102255,102258,102259,102262],{},[38,102256,102257],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,102260,102261],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,102264,22545],{"id":22544},[120,102266,102267,102273,102279,102285,102294],{},[123,102268,102269,102272],{},[38,102270,102271],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,102274,102275,102278],{},[38,102276,102277],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,102280,102281,102284],{},[38,102282,102283],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,102286,102287,13877,102290,102293],{},[38,102288,102289],{},"Ceteris paribus",[614,102291,102292],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,102295,102296,102298],{},[38,102297,57395],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,102300,102302],{"id":102301},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,102304,102305,102345],{},[883,102306,102308],{"className":102307},[886],[888,102309,102310],{"xmlns":890},[892,102311,102312,102342],{},[895,102313,102314,102316,102318,102320,102322,102324,102326,102328,102330,102332,102334,102336,102338,102340],{},[898,102315,1712],{},[1693,102317,1695],{},[898,102319,2738],{},[1693,102321,1709],{"stretchy":1708},[898,102323,1701],{},[1693,102325,1899],{"separator":1898},[898,102327,4618],{},[1693,102329,1899],{"separator":1898},[898,102331,6987],{},[1693,102333,1899],{"separator":1898},[898,102335,900],{},[1693,102337,1899],{"separator":1898},[1693,102339,16501],{},[1693,102341,1731],{"stretchy":1708},[902,102343,102344],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,102347,102348],{},"Zjednodušení:",[120,102350,102351,102379],{},[123,102352,102353,1863,102356],{},[38,102354,102355],{},"Jednofaktorový model:",[883,102357,102359],{"className":102358},[886],[888,102360,102361],{"xmlns":890},[892,102362,102363,102377],{},[895,102364,102365,102367,102369,102371,102373,102375],{},[898,102366,1712],{},[1693,102368,1695],{},[898,102370,2738],{},[1693,102372,1709],{"stretchy":1708},[898,102374,1701],{},[1693,102376,1731],{"stretchy":1708},[902,102378,11072],{"encoding":904},[123,102380,102381,1863,102384],{},[38,102382,102383],{},"Inverzní zápis:",[883,102385,102387],{"className":102386},[886],[888,102388,102389],{"xmlns":890},[892,102390,102391,102405],{},[895,102392,102393,102395,102397,102399,102401,102403],{},[898,102394,1701],{},[1693,102396,1695],{},[898,102398,2738],{},[1693,102400,1709],{"stretchy":1708},[898,102402,1712],{},[1693,102404,1731],{"stretchy":1708},[902,102406,3980],{"encoding":904},[115,102408,102410],{"id":102409},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,102412,102413,102422],{},[123,102414,102415,102418,102419,3042],{},[38,102416,102417],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,102420,23060],{"className":102421,"dataFsResolvedFilePath":800,"href":801},[210],[123,102423,102424,102427,102428,102431,102432,102435,102436,102440],{},[38,102425,102426],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,102429,1145],{"className":102430,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,102433,23073],{"className":102434,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,102437,102439],{"className":102438,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,102442,102444],{"id":102443},"konvence-z-přednášek","Konvence z přednášek",[120,102446,102447,102453,102459],{},[123,102448,102449,102450,102452],{},"Symbol ",[2164,102451,4110],{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,102454,102455,102456,1789],{},"Numerické výsledky ",[38,102457,102458],{},"na 3 desetinná místa",[123,102460,10780,102461,102464],{},[614,102462,102463],{},"jednotková změna"," má standardní význam (změna o 1).",[115,102466,8685],{"id":8684},[120,102468,102469,102474,102482],{},[123,102470,102471,102473],{},[38,102472,10689],{}," —",[123,102475,102476,1863,102478],{},[38,102477,10697],{},[207,102479,102481],{"className":102480,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,102483,102484,1863,102486,1343,102490],{},[38,102485,10705],{},[207,102487,102489],{"className":102488,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,102491,102493],{"className":102492,"dataFsResolvedFilePath":1651,"href":1652},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":102495},[102496,102497,102498,102499,102500,102501],{"id":102251,"depth":642,"text":102252},{"id":22544,"depth":642,"text":22545},{"id":102301,"depth":642,"text":102302},{"id":102409,"depth":642,"text":102410},{"id":102443,"depth":642,"text":102444},{"id":8684,"depth":642,"text":8685},"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":102502},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,102509,102510,102511,102512,102513],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":102516,"title":6493,"body":102517,"course":1128,"courses":659,"created":16411,"description":641,"extension":661,"meta":106786,"navigation":664,"path":106787,"seo":106788,"sources":106789,"stem":106790,"tags":106791,"type":10745,"updated":677,"__hash__":106795},"topics\u002Ftopics\u002Fzdaneni-trhu.md",{"type":9,"value":102518,"toc":106769},[102519,102522,102616,102620,102642,102656,102708,102710,102714,102777,102820,102839,103002,103101,103104,103171,103175,103304,103343,103373,103485,103530,103596,103649,103725,103781,103783,103787,103850,103894,103914,104075,104078,104162,104259,104262,104328,104332,104381,104407,104512,104576,104581,104677,104724,104726,104729,104751,104793,104800,104833,104835,104906,104960,105069,105073,105162,105236,105500,105538,105540,105544,105547,105554,105865,105868,105926,106106,106135,106137,106141,106147,106285,106294,106296,106298,106723,106725,106727],[12,102520,6493],{"id":102521},"zdanění-trhu-dopady-daně-na-rovnováhu",[1636,102523,102524],{},[724,102525,102526,49398,102528,102541,102542,102545,102546,102548,102549,102552,102553,102574,102575,102598,102599,102602,102603,1789],{},[883,102527,11036],{},[883,102529,102531],{"className":102530},[886],[888,102532,102533],{"xmlns":890},[892,102534,102535,102539],{},[895,102536,102537],{},[898,102538,2663],{},[902,102540,2663],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,102543,102544],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,102547,93561],{}," (je-li uložena spotřebiteli). Výsledné ",[38,102550,102551],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,102554,102556],{"className":102555},[886],[888,102557,102558],{"xmlns":890},[892,102559,102560,102572],{},[895,102561,102562],{},[3284,102563,102564,102566],{},[898,102565,2663],{},[895,102567,102568,102570],{},[898,102569,6746],{},[898,102571,724],{},[902,102573,49451],{"encoding":904}," (spotřebitel) a ",[883,102576,102578],{"className":102577},[886],[888,102579,102580],{"xmlns":890},[892,102581,102582,102596],{},[895,102583,102584],{},[3284,102585,102586,102588],{},[898,102587,2663],{},[895,102589,102590,102592,102594],{},[898,102591,6759],{},[898,102593,6560],{},[898,102595,6629],{},[902,102597,49475],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,102600,102601],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,102604,102606],{"className":102605},[886],[888,102607,102608],{"xmlns":890},[892,102609,102610,102614],{},[895,102611,102612],{},[898,102613,2663],{},[902,102615,2663],{"encoding":904},[115,102617,102619],{"id":102618},"dvě-formy-zdanění","Dvě formy zdanění",[724,102621,102622,102623,102641],{},"Uvažujme jednotkovou daň ",[883,102624,102626],{"className":102625},[886],[888,102627,102628],{"xmlns":890},[892,102629,102630,102638],{},[895,102631,102632,102634,102636],{},[898,102633,2663],{},[1693,102635,1922],{},[1762,102637,1911],{},[902,102639,102640],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,102643,102644,102650],{},[123,102645,102646,102649],{},[38,102647,102648],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,102651,102652,102655],{},[38,102653,102654],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,102657,102658,102659,102672,102673,102676,102677,1789],{},"V obou případech dochází k posunu jedné z křivek o ",[883,102660,102662],{"className":102661},[886],[888,102663,102664],{"xmlns":890},[892,102665,102666,102670],{},[895,102667,102668],{},[898,102669,2663],{},[902,102671,2663],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,102674,102675],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,102678,102680],{"className":102679},[886],[888,102681,102682],{"xmlns":890},[892,102683,102684,102706],{},[895,102685,102686,102688,102690,102696,102698,102704],{},[898,102687,1691],{},[1693,102689,9392],{"stretchy":1708},[1717,102691,102692,102694],{},[898,102693,1712],{},[898,102695,1691],{},[1693,102697,1899],{"separator":1898},[1717,102699,102700,102702],{},[898,102701,1701],{},[898,102703,1691],{},[1693,102705,9407],{"stretchy":1708},[902,102707,48138],{"encoding":904},[1852,102709],{},[115,102711,102713],{"id":102712},"daň-uložená-výrobci","Daň uložená výrobci",[724,102715,102716,102717,102730,102731,102748,102749,102776],{},"Je-li daň ",[883,102718,102720],{"className":102719},[886],[888,102721,102722],{"xmlns":890},[892,102723,102724,102728],{},[895,102725,102726],{},[898,102727,2663],{},[902,102729,2663],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,102732,102734],{"className":102733},[886],[888,102735,102736],{"xmlns":890},[892,102737,102738,102746],{},[895,102739,102740,102742,102744],{},[898,102741,1701],{},[1693,102743,1698],{},[898,102745,2663],{},[902,102747,47894],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,102750,102752],{"className":102751},[886],[888,102753,102754],{"xmlns":890},[892,102755,102756,102774],{},[895,102757,102758,102760,102762,102764,102766,102768,102770,102772],{},[898,102759,1701],{},[1693,102761,1698],{},[898,102763,2663],{},[1693,102765,1695],{},[898,102767,3611],{},[1693,102769,1709],{"stretchy":1708},[898,102771,1712],{},[1693,102773,1731],{"stretchy":1708},[902,102775,6670],{"encoding":904}," nová funkce nabídky:",[883,102778,102780],{"className":102779},[886],[888,102781,102782],{"xmlns":890,"display":34854},[892,102783,102784,102818],{},[895,102785,102786,102788,102790,102796,102798,102800,102802,102804,102806,102808,102810,102812,102814,102816],{},[898,102787,1701],{},[1693,102789,1695],{},[3284,102791,102792,102794],{},[898,102793,3611],{},[1762,102795,1764],{},[1693,102797,1709],{"stretchy":1708},[898,102799,1712],{},[1693,102801,1731],{"stretchy":1708},[1693,102803,1695],{},[898,102805,3611],{},[1693,102807,1709],{"stretchy":1708},[898,102809,1712],{},[1693,102811,1731],{"stretchy":1708},[1693,102813,1892],{},[898,102815,2663],{},[898,102817,1789],{"mathvariant":1704},[902,102819,47967],{"encoding":904},[724,102821,102822,102823,1863,102836,102838],{},"Nabídka se tedy posouvá o ",[883,102824,102826],{"className":102825},[886],[888,102827,102828],{"xmlns":890},[892,102829,102830,102834],{},[895,102831,102832],{},[898,102833,2663],{},[902,102835,2663],{"encoding":904},[38,102837,48000],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,102840,102841,102842,102882,102883,4286,102911,102939,102940,102959,102960,102984,102985,3042],{},"Nový rovnovážný bod ",[883,102843,102845],{"className":102844},[886],[888,102846,102847],{"xmlns":890},[892,102848,102849,102879],{},[895,102850,102851,102857,102859,102867,102869,102877],{},[3284,102852,102853,102855],{},[898,102854,1691],{},[1762,102856,1764],{},[1693,102858,9392],{"stretchy":1708},[5688,102860,102861,102863,102865],{},[898,102862,1712],{},[1762,102864,1764],{},[898,102866,1691],{},[1693,102868,1899],{"separator":1898},[5688,102870,102871,102873,102875],{},[898,102872,1701],{},[1762,102874,1764],{},[898,102876,1691],{},[1693,102878,9407],{"stretchy":1708},[902,102880,102881],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,102884,102886],{"className":102885},[886],[888,102887,102888],{"xmlns":890},[892,102889,102890,102908],{},[895,102891,102892,102900,102902],{},[5688,102893,102894,102896,102898],{},[898,102895,1712],{},[1762,102897,1764],{},[898,102899,1691],{},[1693,102901,1908],{},[1717,102903,102904,102906],{},[898,102905,1712],{},[898,102907,1691],{},[902,102909,102910],{"encoding":904},"Q_1^E \u003C Q^E",[883,102912,102914],{"className":102913},[886],[888,102915,102916],{"xmlns":890},[892,102917,102918,102936],{},[895,102919,102920,102928,102930],{},[5688,102921,102922,102924,102926],{},[898,102923,1701],{},[1762,102925,1764],{},[898,102927,1691],{},[1693,102929,1922],{},[1717,102931,102932,102934],{},[898,102933,1701],{},[898,102935,1691],{},[902,102937,102938],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,102941,102943],{"className":102942},[886],[888,102944,102945],{"xmlns":890},[892,102946,102947,102957],{},[895,102948,102949],{},[5688,102950,102951,102953,102955],{},[898,102952,1701],{},[1762,102954,1764],{},[898,102956,1691],{},[902,102958,54621],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,102961,102963],{"className":102962},[886],[888,102964,102965],{"xmlns":890},[892,102966,102967,102981],{},[895,102968,102969,102977,102979],{},[5688,102970,102971,102973,102975],{},[898,102972,1701],{},[1762,102974,1764],{},[898,102976,1691],{},[1693,102978,1698],{},[898,102980,2663],{},[902,102982,102983],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,102986,102988],{"className":102987},[886],[888,102989,102990],{"xmlns":890},[892,102991,102992,103000],{},[895,102993,102994],{},[1717,102995,102996,102998],{},[898,102997,1701],{},[898,102999,1691],{},[902,103001,48237],{"encoding":904},[724,103003,103004],{},[614,103005,103006,103007,103037,103038,103051,103052,12537,103069,103082,103083,1789],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,103008,103010],{"className":103009},[886],[888,103011,103012],{"xmlns":890},[892,103013,103014,103034],{},[895,103015,103016,103018,103020,103026,103028,103030,103032],{},[898,103017,3611],{},[1693,103019,10020],{},[3284,103021,103022,103024],{},[898,103023,3611],{},[1762,103025,1764],{},[1693,103027,1695],{},[898,103029,3611],{},[1693,103031,1892],{},[898,103033,2663],{},[902,103035,103036],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,103039,103041],{"className":103040},[886],[888,103042,103043],{"xmlns":890},[892,103044,103045,103049],{},[895,103046,103047],{},[898,103048,2663],{},[902,103050,2663],{"encoding":904},". Průsečík ",[883,103053,103055],{"className":103054},[886],[888,103056,103057],{"xmlns":890},[892,103058,103059,103067],{},[895,103060,103061],{},[3284,103062,103063,103065],{},[898,103064,3611],{},[1762,103066,1764],{},[902,103068,47769],{"encoding":904},[883,103070,103072],{"className":103071},[886],[888,103073,103074],{"xmlns":890},[892,103075,103076,103080],{},[895,103077,103078],{},[898,103079,2738],{},[902,103081,2738],{"encoding":904}," je nový rovnovážný bod ",[883,103084,103086],{"className":103085},[886],[888,103087,103088],{"xmlns":890},[892,103089,103090,103098],{},[895,103091,103092],{},[3284,103093,103094,103096],{},[898,103095,1691],{},[1762,103097,1764],{},[902,103099,103100],{"encoding":904},"E_1",[198,103102,52067],{"id":103103},"příklad-29",[724,103105,103106,48426,103108,48461,103132,103152,103153,103170],{},[38,103107,44709],{},[883,103109,103111],{"className":103110},[886],[888,103112,103113],{"xmlns":890},[892,103114,103115,103129],{},[895,103116,103117,103119,103121,103123,103125,103127],{},[898,103118,1701],{},[1693,103120,1695],{},[1762,103122,10402],{},[1693,103124,1698],{},[1762,103126,2398],{},[898,103128,1712],{},[902,103130,103131],{"encoding":904},"P = 12 - 2Q",[883,103133,103135],{"className":103134},[886],[888,103136,103137],{"xmlns":890},[892,103138,103139,103149],{},[895,103140,103141,103143,103145,103147],{},[898,103142,1701],{},[1693,103144,1695],{},[1762,103146,9262],{},[898,103148,1712],{},[902,103150,103151],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,103154,103156],{"className":103155},[886],[888,103157,103158],{"xmlns":890},[892,103159,103160,103168],{},[895,103161,103162,103164,103166],{},[898,103163,2663],{},[1693,103165,1695],{},[1762,103167,9154],{},[902,103169,48039],{"encoding":904}," Kč.",[724,103172,103173],{},[38,103174,44741],{},[724,103176,103177,103180,103181,12437,103207,12457,103227,1343,103249,103279,103280,1789],{},[614,103178,103179],{},"Bez daně."," Z rovnosti ",[883,103182,103184],{"className":103183},[886],[888,103185,103186],{"xmlns":890},[892,103187,103188,103204],{},[895,103189,103190,103192,103194,103196,103198,103200,103202],{},[1762,103191,10402],{},[1693,103193,1698],{},[1762,103195,2398],{},[898,103197,1712],{},[1693,103199,1695],{},[1762,103201,9262],{},[898,103203,1712],{},[902,103205,103206],{"encoding":904},"12 - 2Q = 4Q",[883,103208,103210],{"className":103209},[886],[888,103211,103212],{"xmlns":890},[892,103213,103214,103224],{},[895,103215,103216,103218,103220,103222],{},[1762,103217,9154],{},[898,103219,1712],{},[1693,103221,1695],{},[1762,103223,10402],{},[902,103225,103226],{"encoding":904},"6Q = 12",[883,103228,103230],{"className":103229},[886],[888,103231,103232],{"xmlns":890},[892,103233,103234,103246],{},[895,103235,103236,103242,103244],{},[1717,103237,103238,103240],{},[898,103239,1712],{},[898,103241,1691],{},[1693,103243,1695],{},[1762,103245,2398],{},[902,103247,103248],{"encoding":904},"Q^E = 2",[883,103250,103252],{"className":103251},[886],[888,103253,103254],{"xmlns":890},[892,103255,103256,103276],{},[895,103257,103258,103264,103266,103268,103270,103272,103274],{},[1717,103259,103260,103262],{},[898,103261,1701],{},[898,103263,1691],{},[1693,103265,1695],{},[1762,103267,9262],{},[1693,103269,1715],{},[1762,103271,2398],{},[1693,103273,1695],{},[1762,103275,12453],{},[902,103277,103278],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,103281,103283],{"className":103282},[886],[888,103284,103285],{"xmlns":890},[892,103286,103287,103301],{},[895,103288,103289,103291,103293,103295,103297,103299],{},[898,103290,1691],{},[1693,103292,9392],{"stretchy":1708},[1762,103294,2398],{},[1693,103296,1899],{"separator":1898},[1762,103298,12453],{},[1693,103300,9407],{"stretchy":1708},[902,103302,103303],{"encoding":904},"E[2, 8]",[724,103305,103306,103309,103310,103342],{},[614,103307,103308],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,103311,103313],{"className":103312},[886],[888,103314,103315],{"xmlns":890},[892,103316,103317,103339],{},[895,103318,103319,103325,103327,103329,103331,103333,103335,103337],{},[3284,103320,103321,103323],{},[898,103322,3611],{},[1762,103324,1764],{},[1693,103326,4300],{},[898,103328,1701],{},[1693,103330,1695],{},[1762,103332,9262],{},[898,103334,1712],{},[1693,103336,1892],{},[1762,103338,9154],{},[902,103340,103341],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,103344,103346],{"className":103345},[886],[888,103347,103348],{"xmlns":890,"display":34854},[892,103349,103350,103370],{},[895,103351,103352,103354,103356,103358,103360,103362,103364,103366,103368],{},[1762,103353,10402],{},[1693,103355,1698],{},[1762,103357,2398],{},[898,103359,1712],{},[1693,103361,1695],{},[1762,103363,9262],{},[898,103365,1712],{},[1693,103367,1892],{},[1762,103369,9154],{},[902,103371,103372],{"encoding":904},"12 - 2Q = 4Q + 6",[724,103374,103375,103376,12457,103396,1343,103420,103456,103457,1789],{},"plyne ",[883,103377,103379],{"className":103378},[886],[888,103380,103381],{"xmlns":890},[892,103382,103383,103393],{},[895,103384,103385,103387,103389,103391],{},[1762,103386,9154],{},[898,103388,1712],{},[1693,103390,1695],{},[1762,103392,9154],{},[902,103394,103395],{"encoding":904},"6Q = 6",[883,103397,103399],{"className":103398},[886],[888,103400,103401],{"xmlns":890},[892,103402,103403,103417],{},[895,103404,103405,103413,103415],{},[5688,103406,103407,103409,103411],{},[898,103408,1712],{},[1762,103410,1764],{},[898,103412,1691],{},[1693,103414,1695],{},[1762,103416,1764],{},[902,103418,103419],{"encoding":904},"Q_1^E = 1",[883,103421,103423],{"className":103422},[886],[888,103424,103425],{"xmlns":890},[892,103426,103427,103453],{},[895,103428,103429,103437,103439,103441,103443,103445,103447,103449,103451],{},[5688,103430,103431,103433,103435],{},[898,103432,1701],{},[1762,103434,1764],{},[898,103436,1691],{},[1693,103438,1695],{},[1762,103440,9262],{},[1693,103442,1715],{},[1762,103444,1764],{},[1693,103446,1892],{},[1762,103448,9154],{},[1693,103450,1695],{},[1762,103452,9763],{},[902,103454,103455],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,103458,103460],{"className":103459},[886],[888,103461,103462],{"xmlns":890},[892,103463,103464,103482],{},[895,103465,103466,103472,103474,103476,103478,103480],{},[3284,103467,103468,103470],{},[898,103469,1691],{},[1762,103471,1764],{},[1693,103473,9392],{"stretchy":1708},[1762,103475,1764],{},[1693,103477,1899],{"separator":1898},[1762,103479,9763],{},[1693,103481,9407],{"stretchy":1708},[902,103483,103484],{"encoding":904},"E_1[1, 10]",[724,103486,103487,103490,103491,103515,103516,103529],{},[614,103488,103489],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,103492,103494],{"className":103493},[886],[888,103495,103496],{"xmlns":890},[892,103497,103498,103512],{},[895,103499,103500,103508,103510],{},[5688,103501,103502,103504,103506],{},[898,103503,1701],{},[1762,103505,1764],{},[898,103507,1691],{},[1693,103509,1695],{},[1762,103511,9763],{},[902,103513,103514],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,103517,103519],{"className":103518},[886],[888,103520,103521],{"xmlns":890},[892,103522,103523,103527],{},[895,103524,103525],{},[1762,103526,12453],{},[902,103528,12453],{"encoding":904},", navýšení je",[883,103531,103533],{"className":103532},[886],[888,103534,103535],{"xmlns":890,"display":34854},[892,103536,103537,103593],{},[895,103538,103539,103549,103551,103559,103561,103567,103569,103571,103573,103575,103577,103579,103581,103591],{},[3284,103540,103541,103543],{},[898,103542,2663],{},[895,103544,103545,103547],{},[898,103546,6746],{},[898,103548,724],{},[1693,103550,1695],{},[5688,103552,103553,103555,103557],{},[898,103554,1701],{},[1762,103556,1764],{},[898,103558,1691],{},[1693,103560,1698],{},[1717,103562,103563,103565],{},[898,103564,1701],{},[898,103566,1691],{},[1693,103568,1695],{},[1762,103570,9763],{},[1693,103572,1698],{},[1762,103574,12453],{},[1693,103576,1695],{},[1762,103578,2398],{},[1915,103580,9204],{},[895,103582,103583,103585],{},[1915,103584,4845],{},[4467,103586,103587,103589],{"accent":1898},[1915,103588,2000],{},[1693,103590,6552],{},[898,103592,1789],{"mathvariant":1704},[902,103594,103595],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,103597,103598,103599,103515,103635,103648],{},"Výrobci zůstává čistá cena ",[883,103600,103602],{"className":103601},[886],[888,103603,103604],{"xmlns":890},[892,103605,103606,103632],{},[895,103607,103608,103616,103618,103620,103622,103624,103626,103628,103630],{},[5688,103609,103610,103612,103614],{},[898,103611,1701],{},[1762,103613,1764],{},[898,103615,1691],{},[1693,103617,1698],{},[898,103619,2663],{},[1693,103621,1695],{},[1762,103623,9763],{},[1693,103625,1698],{},[1762,103627,9154],{},[1693,103629,1695],{},[1762,103631,9262],{},[902,103633,103634],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,103636,103638],{"className":103637},[886],[888,103639,103640],{"xmlns":890},[892,103641,103642,103646],{},[895,103643,103644],{},[1762,103645,12453],{},[902,103647,12453],{"encoding":904},", pokles je",[883,103650,103652],{"className":103651},[886],[888,103653,103654],{"xmlns":890,"display":34854},[892,103655,103656,103722],{},[895,103657,103658,103670,103672,103678,103680,103682,103690,103692,103694,103696,103698,103700,103702,103704,103706,103708,103710,103720],{},[3284,103659,103660,103662],{},[898,103661,2663],{},[895,103663,103664,103666,103668],{},[898,103665,6759],{},[898,103667,6560],{},[898,103669,6629],{},[1693,103671,1695],{},[1717,103673,103674,103676],{},[898,103675,1701],{},[898,103677,1691],{},[1693,103679,1698],{},[1693,103681,1709],{"stretchy":1708},[5688,103683,103684,103686,103688],{},[898,103685,1701],{},[1762,103687,1764],{},[898,103689,1691],{},[1693,103691,1698],{},[898,103693,2663],{},[1693,103695,1731],{"stretchy":1708},[1693,103697,1695],{},[1762,103699,12453],{},[1693,103701,1698],{},[1762,103703,9262],{},[1693,103705,1695],{},[1762,103707,9262],{},[1915,103709,9204],{},[895,103711,103712,103714],{},[1915,103713,4845],{},[4467,103715,103716,103718],{"accent":1898},[1915,103717,2000],{},[1693,103719,6552],{},[898,103721,1789],{"mathvariant":1704},[902,103723,103724],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,103726,103727,103728,103780],{},"Kontrola: ",[883,103729,103731],{"className":103730},[886],[888,103732,103733],{"xmlns":890},[892,103734,103735,103777],{},[895,103736,103737,103747,103749,103761,103763,103765,103767,103769,103771,103773,103775],{},[3284,103738,103739,103741],{},[898,103740,2663],{},[895,103742,103743,103745],{},[898,103744,6746],{},[898,103746,724],{},[1693,103748,1892],{},[3284,103750,103751,103753],{},[898,103752,2663],{},[895,103754,103755,103757,103759],{},[898,103756,6759],{},[898,103758,6560],{},[898,103760,6629],{},[1693,103762,1695],{},[1762,103764,2398],{},[1693,103766,1892],{},[1762,103768,9262],{},[1693,103770,1695],{},[1762,103772,9154],{},[1693,103774,1695],{},[898,103776,2663],{},[902,103778,103779],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[1852,103782],{},[115,103784,103786],{"id":103785},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,103788,102716,103789,103802,103803,103821,103822,103849],{},[883,103790,103792],{"className":103791},[886],[888,103793,103794],{"xmlns":890},[892,103795,103796,103800],{},[895,103797,103798],{},[898,103799,2663],{},[902,103801,2663],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,103804,103806],{"className":103805},[886],[888,103807,103808],{"xmlns":890},[892,103809,103810,103818],{},[895,103811,103812,103814,103816],{},[898,103813,1701],{},[1693,103815,1892],{},[898,103817,2663],{},[902,103819,103820],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,103823,103825],{"className":103824},[886],[888,103826,103827],{"xmlns":890},[892,103828,103829,103847],{},[895,103830,103831,103833,103835,103837,103839,103841,103843,103845],{},[898,103832,1701],{},[1693,103834,1892],{},[898,103836,2663],{},[1693,103838,1695],{},[898,103840,2738],{},[1693,103842,1709],{"stretchy":1708},[898,103844,1712],{},[1693,103846,1731],{"stretchy":1708},[902,103848,6699],{"encoding":904}," plyne nová funkce poptávky:",[883,103851,103853],{"className":103852},[886],[888,103854,103855],{"xmlns":890,"display":34854},[892,103856,103857,103891],{},[895,103858,103859,103861,103863,103869,103871,103873,103875,103877,103879,103881,103883,103885,103887,103889],{},[898,103860,1701],{},[1693,103862,1695],{},[3284,103864,103865,103867],{},[898,103866,2738],{},[1762,103868,2398],{},[1693,103870,1709],{"stretchy":1708},[898,103872,1712],{},[1693,103874,1731],{"stretchy":1708},[1693,103876,1695],{},[898,103878,2738],{},[1693,103880,1709],{"stretchy":1708},[898,103882,1712],{},[1693,103884,1731],{"stretchy":1708},[1693,103886,1698],{},[898,103888,2663],{},[898,103890,1789],{"mathvariant":1704},[902,103892,103893],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,103895,103896,103897,1863,103910,103913],{},"Poptávka se tedy posouvá o ",[883,103898,103900],{"className":103899},[886],[888,103901,103902],{"xmlns":890},[892,103903,103904,103908],{},[895,103905,103906],{},[898,103907,2663],{},[902,103909,2663],{"encoding":904},[38,103911,103912],{},"svisle dolů",". Nabídka se nemění.",[724,103915,102841,103916,102882,103956,4286,103984,104012,104013,104032,104033,104057,104058,3042],{},[883,103917,103919],{"className":103918},[886],[888,103920,103921],{"xmlns":890},[892,103922,103923,103953],{},[895,103924,103925,103931,103933,103941,103943,103951],{},[3284,103926,103927,103929],{},[898,103928,1691],{},[1762,103930,2398],{},[1693,103932,9392],{"stretchy":1708},[5688,103934,103935,103937,103939],{},[898,103936,1712],{},[1762,103938,2398],{},[898,103940,1691],{},[1693,103942,1899],{"separator":1898},[5688,103944,103945,103947,103949],{},[898,103946,1701],{},[1762,103948,2398],{},[898,103950,1691],{},[1693,103952,9407],{"stretchy":1708},[902,103954,103955],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,103957,103959],{"className":103958},[886],[888,103960,103961],{"xmlns":890},[892,103962,103963,103981],{},[895,103964,103965,103973,103975],{},[5688,103966,103967,103969,103971],{},[898,103968,1712],{},[1762,103970,2398],{},[898,103972,1691],{},[1693,103974,1908],{},[1717,103976,103977,103979],{},[898,103978,1712],{},[898,103980,1691],{},[902,103982,103983],{"encoding":904},"Q_2^E \u003C Q^E",[883,103985,103987],{"className":103986},[886],[888,103988,103989],{"xmlns":890},[892,103990,103991,104009],{},[895,103992,103993,104001,104003],{},[5688,103994,103995,103997,103999],{},[898,103996,1701],{},[1762,103998,2398],{},[898,104000,1691],{},[1693,104002,1908],{},[1717,104004,104005,104007],{},[898,104006,1701],{},[898,104008,1691],{},[902,104010,104011],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,104014,104016],{"className":104015},[886],[888,104017,104018],{"xmlns":890},[892,104019,104020,104030],{},[895,104021,104022],{},[5688,104023,104024,104026,104028],{},[898,104025,1701],{},[1762,104027,2398],{},[898,104029,1691],{},[902,104031,54682],{"encoding":904},", spotřebitel platí celkem ",[883,104034,104036],{"className":104035},[886],[888,104037,104038],{"xmlns":890},[892,104039,104040,104054],{},[895,104041,104042,104050,104052],{},[5688,104043,104044,104046,104048],{},[898,104045,1701],{},[1762,104047,2398],{},[898,104049,1691],{},[1693,104051,1892],{},[898,104053,2663],{},[902,104055,104056],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,104059,104061],{"className":104060},[886],[888,104062,104063],{"xmlns":890},[892,104064,104065,104073],{},[895,104066,104067],{},[1717,104068,104069,104071],{},[898,104070,1701],{},[898,104072,1691],{},[902,104074,48237],{"encoding":904},[724,104076,104077],{},"Daňové břemeno:",[883,104079,104081],{"className":104080},[886],[888,104082,104083],{"xmlns":890,"display":34854},[892,104084,104085,104159],{},[895,104086,104087,104097,104099,104101,104109,104111,104113,104115,104117,104123,104125,104127,104139,104141,104147,104149,104157],{},[3284,104088,104089,104091],{},[898,104090,2663],{},[895,104092,104093,104095],{},[898,104094,6746],{},[898,104096,724],{},[1693,104098,1695],{},[1693,104100,1709],{"stretchy":1708},[5688,104102,104103,104105,104107],{},[898,104104,1701],{},[1762,104106,2398],{},[898,104108,1691],{},[1693,104110,1892],{},[898,104112,2663],{},[1693,104114,1731],{"stretchy":1708},[1693,104116,1698],{},[1717,104118,104119,104121],{},[898,104120,1701],{},[898,104122,1691],{},[1693,104124,1899],{"separator":1898},[1901,104126],{"width":1903},[3284,104128,104129,104131],{},[898,104130,2663],{},[895,104132,104133,104135,104137],{},[898,104134,6759],{},[898,104136,6560],{},[898,104138,6629],{},[1693,104140,1695],{},[1717,104142,104143,104145],{},[898,104144,1701],{},[898,104146,1691],{},[1693,104148,1698],{},[5688,104150,104151,104153,104155],{},[898,104152,1701],{},[1762,104154,2398],{},[898,104156,1691],{},[898,104158,1789],{"mathvariant":1704},[902,104160,104161],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,104163,104164],{},[614,104165,104166,104167,104197,104198,103051,104211,12537,104228,103082,104241,1789],{},"Obrázek 2.19: Posun ",[883,104168,104170],{"className":104169},[886],[888,104171,104172],{"xmlns":890},[892,104173,104174,104194],{},[895,104175,104176,104178,104180,104186,104188,104190,104192],{},[898,104177,2738],{},[1693,104179,10020],{},[3284,104181,104182,104184],{},[898,104183,2738],{},[1762,104185,2398],{},[1693,104187,1695],{},[898,104189,2738],{},[1693,104191,1698],{},[898,104193,2663],{},[902,104195,104196],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,104199,104201],{"className":104200},[886],[888,104202,104203],{"xmlns":890},[892,104204,104205,104209],{},[895,104206,104207],{},[898,104208,2663],{},[902,104210,2663],{"encoding":904},[883,104212,104214],{"className":104213},[886],[888,104215,104216],{"xmlns":890},[892,104217,104218,104226],{},[895,104219,104220],{},[3284,104221,104222,104224],{},[898,104223,2738],{},[1762,104225,2398],{},[902,104227,45102],{"encoding":904},[883,104229,104231],{"className":104230},[886],[888,104232,104233],{"xmlns":890},[892,104234,104235,104239],{},[895,104236,104237],{},[898,104238,3611],{},[902,104240,3611],{"encoding":904},[883,104242,104244],{"className":104243},[886],[888,104245,104246],{"xmlns":890},[892,104247,104248,104256],{},[895,104249,104250],{},[3284,104251,104252,104254],{},[898,104253,1691],{},[1762,104255,2398],{},[902,104257,104258],{"encoding":904},"E_2",[198,104260,52147],{"id":104261},"příklad-210",[724,104263,104264,104266,104267,48461,104290,104309,104310,104327],{},[38,104265,44709],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,104268,104270],{"className":104269},[886],[888,104271,104272],{"xmlns":890},[892,104273,104274,104288],{},[895,104275,104276,104278,104280,104282,104284,104286],{},[898,104277,1701],{},[1693,104279,1695],{},[1762,104281,10402],{},[1693,104283,1698],{},[1762,104285,2398],{},[898,104287,1712],{},[902,104289,103131],{"encoding":904},[883,104291,104293],{"className":104292},[886],[888,104294,104295],{"xmlns":890},[892,104296,104297,104307],{},[895,104298,104299,104301,104303,104305],{},[898,104300,1701],{},[1693,104302,1695],{},[1762,104304,9262],{},[898,104306,1712],{},[902,104308,103151],{"encoding":904},". Daň ",[883,104311,104313],{"className":104312},[886],[888,104314,104315],{"xmlns":890},[892,104316,104317,104325],{},[895,104318,104319,104321,104323],{},[898,104320,2663],{},[1693,104322,1695],{},[1762,104324,9154],{},[902,104326,48039],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,104329,104330],{},[38,104331,44741],{},[724,104333,104334,104335,103342],{},"Nová poptávka je ",[883,104336,104338],{"className":104337},[886],[888,104339,104340],{"xmlns":890},[892,104341,104342,104378],{},[895,104343,104344,104350,104352,104354,104356,104358,104360,104362,104364,104366,104368,104370,104372,104374,104376],{},[3284,104345,104346,104348],{},[898,104347,2738],{},[1762,104349,2398],{},[1693,104351,4300],{},[898,104353,1701],{},[1693,104355,1695],{},[1762,104357,10402],{},[1693,104359,1698],{},[1762,104361,2398],{},[898,104363,1712],{},[1693,104365,1698],{},[1762,104367,9154],{},[1693,104369,1695],{},[1762,104371,9154],{},[1693,104373,1698],{},[1762,104375,2398],{},[898,104377,1712],{},[902,104379,104380],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,104382,104384],{"className":104383},[886],[888,104385,104386],{"xmlns":890,"display":34854},[892,104387,104388,104404],{},[895,104389,104390,104392,104394,104396,104398,104400,104402],{},[1762,104391,9154],{},[1693,104393,1698],{},[1762,104395,2398],{},[898,104397,1712],{},[1693,104399,1695],{},[1762,104401,9262],{},[898,104403,1712],{},[902,104405,104406],{"encoding":904},"6 - 2Q = 4Q",[724,104408,103375,104409,12457,104428,1343,104452,103456,104484,1789],{},[883,104410,104412],{"className":104411},[886],[888,104413,104414],{"xmlns":890},[892,104415,104416,104426],{},[895,104417,104418,104420,104422,104424],{},[1762,104419,9154],{},[898,104421,1712],{},[1693,104423,1695],{},[1762,104425,9154],{},[902,104427,103395],{"encoding":904},[883,104429,104431],{"className":104430},[886],[888,104432,104433],{"xmlns":890},[892,104434,104435,104449],{},[895,104436,104437,104445,104447],{},[5688,104438,104439,104441,104443],{},[898,104440,1712],{},[1762,104442,2398],{},[898,104444,1691],{},[1693,104446,1695],{},[1762,104448,1764],{},[902,104450,104451],{"encoding":904},"Q_2^E = 1",[883,104453,104455],{"className":104454},[886],[888,104456,104457],{"xmlns":890},[892,104458,104459,104481],{},[895,104460,104461,104469,104471,104473,104475,104477,104479],{},[5688,104462,104463,104465,104467],{},[898,104464,1701],{},[1762,104466,2398],{},[898,104468,1691],{},[1693,104470,1695],{},[1762,104472,9262],{},[1693,104474,1715],{},[1762,104476,1764],{},[1693,104478,1695],{},[1762,104480,9262],{},[902,104482,104483],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,104485,104487],{"className":104486},[886],[888,104488,104489],{"xmlns":890},[892,104490,104491,104509],{},[895,104492,104493,104499,104501,104503,104505,104507],{},[3284,104494,104495,104497],{},[898,104496,1691],{},[1762,104498,2398],{},[1693,104500,9392],{"stretchy":1708},[1762,104502,1764],{},[1693,104504,1899],{"separator":1898},[1762,104506,9262],{},[1693,104508,9407],{"stretchy":1708},[902,104510,104511],{"encoding":904},"E_2[1, 4]",[724,104513,104514,104515,104551,104552,103170],{},"Spotřebitel platí celkem ",[883,104516,104518],{"className":104517},[886],[888,104519,104520],{"xmlns":890},[892,104521,104522,104548],{},[895,104523,104524,104532,104534,104536,104538,104540,104542,104544,104546],{},[5688,104525,104526,104528,104530],{},[898,104527,1701],{},[1762,104529,2398],{},[898,104531,1691],{},[1693,104533,1892],{},[898,104535,2663],{},[1693,104537,1695],{},[1762,104539,9262],{},[1693,104541,1892],{},[1762,104543,9154],{},[1693,104545,1695],{},[1762,104547,9763],{},[902,104549,104550],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,104553,104555],{"className":104554},[886],[888,104556,104557],{"xmlns":890},[892,104558,104559,104573],{},[895,104560,104561,104569,104571],{},[5688,104562,104563,104565,104567],{},[898,104564,1701],{},[1762,104566,2398],{},[898,104568,1691],{},[1693,104570,1695],{},[1762,104572,9262],{},[902,104574,104575],{"encoding":904},"P_2^E = 4",[724,104577,104578],{},[614,104579,104580],{},"Rozklad daňového břemene:",[883,104582,104584],{"className":104583},[886],[888,104585,104586],{"xmlns":890,"display":34854},[892,104587,104588,104674],{},[895,104589,104590,104600,104602,104604,104606,104608,104610,104612,104614,104616,104618,104620,104622,104632,104634,104636,104648,104650,104652,104654,104656,104658,104660,104662,104672],{},[3284,104591,104592,104594],{},[898,104593,2663],{},[895,104595,104596,104598],{},[898,104597,6746],{},[898,104599,724],{},[1693,104601,1695],{},[1693,104603,1709],{"stretchy":1708},[1762,104605,9262],{},[1693,104607,1892],{},[1762,104609,9154],{},[1693,104611,1731],{"stretchy":1708},[1693,104613,1698],{},[1762,104615,12453],{},[1693,104617,1695],{},[1762,104619,2398],{},[1915,104621,9204],{},[895,104623,104624,104626],{},[1915,104625,4845],{},[4467,104627,104628,104630],{"accent":1898},[1915,104629,2000],{},[1693,104631,6552],{},[1693,104633,1899],{"separator":1898},[1901,104635],{"width":1903},[3284,104637,104638,104640],{},[898,104639,2663],{},[895,104641,104642,104644,104646],{},[898,104643,6759],{},[898,104645,6560],{},[898,104647,6629],{},[1693,104649,1695],{},[1762,104651,12453],{},[1693,104653,1698],{},[1762,104655,9262],{},[1693,104657,1695],{},[1762,104659,9262],{},[1915,104661,9204],{},[895,104663,104664,104666],{},[1915,104665,4845],{},[4467,104667,104668,104670],{"accent":1898},[1915,104669,2000],{},[1693,104671,6552],{},[898,104673,1789],{"mathvariant":1704},[902,104675,104676],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,104678,104679,104680,1789],{},"Opět ",[883,104681,104683],{"className":104682},[886],[888,104684,104685],{"xmlns":890},[892,104686,104687,104721],{},[895,104688,104689,104699,104701,104713,104715,104717,104719],{},[3284,104690,104691,104693],{},[898,104692,2663],{},[895,104694,104695,104697],{},[898,104696,6746],{},[898,104698,724],{},[1693,104700,1892],{},[3284,104702,104703,104705],{},[898,104704,2663],{},[895,104706,104707,104709,104711],{},[898,104708,6759],{},[898,104710,6560],{},[898,104712,6629],{},[1693,104714,1695],{},[1762,104716,9154],{},[1693,104718,1695],{},[898,104720,2663],{},[902,104722,104723],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[1852,104725],{},[115,104727,49428],{"id":104728},"daňové-břemeno",[724,104730,104731,16877,104733,104736,104737,104750],{},[38,104732,49428],{},[614,104734,104735],{},"tax burden",") je rozdělení zaplacené daně ",[883,104738,104740],{"className":104739},[886],[888,104741,104742],{"xmlns":890},[892,104743,104744,104748],{},[895,104745,104746],{},[898,104747,2663],{},[902,104749,2663],{"encoding":904}," mezi spotřebitele a výrobce:",[883,104752,104754],{"className":104753},[886],[888,104755,104756],{"xmlns":890,"display":34854},[892,104757,104758,104790],{},[895,104759,104760,104762,104764,104774,104776,104788],{},[898,104761,2663],{},[1693,104763,1695],{},[3284,104765,104766,104768],{},[898,104767,2663],{},[895,104769,104770,104772],{},[898,104771,6746],{},[898,104773,724],{},[1693,104775,1892],{},[3284,104777,104778,104780],{},[898,104779,2663],{},[895,104781,104782,104784,104786],{},[898,104783,6759],{},[898,104785,6560],{},[898,104787,6629],{},[898,104789,1789],{"mathvariant":1704},[902,104791,104792],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,104794,104795],{},[9465,104796],{"alt":104797,"className":104798,"src":104799},"imek-dan-rozklad-bremene-sklony",[210,9469],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1636,104801,104802],{},[724,104803,104804,104806,104807,4286,104820,1789],{},[883,104805,11036],{}," 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 ",[883,104808,104810],{"className":104809},[886],[888,104811,104812],{"xmlns":890},[892,104813,104814,104818],{},[895,104815,104816],{},[898,104817,2738],{},[902,104819,2738],{"encoding":904},[883,104821,104823],{"className":104822},[886],[888,104824,104825],{"xmlns":890},[892,104826,104827,104831],{},[895,104828,104829],{},[898,104830,3611],{},[902,104832,3611],{"encoding":904},[198,104834,9351],{"id":9350},[724,104836,104837,104838,104859,104860,104873,104874,104891,104892,104905],{},"V grafu ",[883,104839,104841],{"className":104840},[886],[888,104842,104843],{"xmlns":890},[892,104844,104845,104857],{},[895,104846,104847,104849,104851,104853,104855],{},[1693,104848,1709],{"stretchy":1708},[898,104850,1712],{},[1693,104852,1899],{"separator":1898},[898,104854,1701],{},[1693,104856,1731],{"stretchy":1708},[902,104858,1978],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,104861,104863],{"className":104862},[886],[888,104864,104865],{"xmlns":890},[892,104866,104867,104871],{},[895,104868,104869],{},[898,104870,2663],{},[902,104872,2663],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,104875,104877],{"className":104876},[886],[888,104878,104879],{"xmlns":890},[892,104880,104881,104889],{},[895,104882,104883],{},[1717,104884,104885,104887],{},[898,104886,1701],{},[898,104888,1691],{},[902,104890,48237],{"encoding":904},", rozdělí se úsečka ",[883,104893,104895],{"className":104894},[886],[888,104896,104897],{"xmlns":890},[892,104898,104899,104903],{},[895,104900,104901],{},[898,104902,2663],{},[902,104904,2663],{"encoding":904}," na dvě části:",[120,104907,104908,104933],{},[123,104909,104910,104911,104932],{},"horní část odpovídá ",[883,104912,104914],{"className":104913},[886],[888,104915,104916],{"xmlns":890},[892,104917,104918,104930],{},[895,104919,104920],{},[3284,104921,104922,104924],{},[898,104923,2663],{},[895,104925,104926,104928],{},[898,104927,6746],{},[898,104929,724],{},[902,104931,49451],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,104934,104935,104936,104959],{},"dolní část odpovídá ",[883,104937,104939],{"className":104938},[886],[888,104940,104941],{"xmlns":890},[892,104942,104943,104957],{},[895,104944,104945],{},[3284,104946,104947,104949],{},[898,104948,2663],{},[895,104950,104951,104953,104955],{},[898,104952,6759],{},[898,104954,6560],{},[898,104956,6629],{},[902,104958,49475],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,104961,104962],{},[614,104963,104964,104965,9591,104978,104999,105000,105023,105024,4286,105045,105068],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,104966,104968],{"className":104967},[886],[888,104969,104970],{"xmlns":890},[892,104971,104972,104976],{},[895,104973,104974],{},[898,104975,2663],{},[902,104977,2663],{"encoding":904},[883,104979,104981],{"className":104980},[886],[888,104982,104983],{"xmlns":890},[892,104984,104985,104997],{},[895,104986,104987],{},[3284,104988,104989,104991],{},[898,104990,2663],{},[895,104992,104993,104995],{},[898,104994,6746],{},[898,104996,724],{},[902,104998,49451],{"encoding":904}," (nahoře) a ",[883,105001,105003],{"className":105002},[886],[888,105004,105005],{"xmlns":890},[892,105006,105007,105021],{},[895,105008,105009],{},[3284,105010,105011,105013],{},[898,105012,2663],{},[895,105014,105015,105017,105019],{},[898,105016,6759],{},[898,105018,6560],{},[898,105020,6629],{},[902,105022,49475],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,105025,105027],{"className":105026},[886],[888,105028,105029],{"xmlns":890},[892,105030,105031,105043],{},[895,105032,105033],{},[3284,105034,105035,105037],{},[898,105036,2663],{},[895,105038,105039,105041],{},[898,105040,6746],{},[898,105042,724],{},[902,105044,49451],{"encoding":904},[883,105046,105048],{"className":105047},[886],[888,105049,105050],{"xmlns":890},[892,105051,105052,105066],{},[895,105053,105054],{},[3284,105055,105056,105058],{},[898,105057,2663],{},[895,105059,105060,105062,105064],{},[898,105061,6759],{},[898,105063,6560],{},[898,105065,6629],{},[902,105067,49475],{"encoding":904}," je v obou případech stejná.",[198,105070,105072],{"id":105071},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,105074,105075,105076,105079,105080,16877,105103,105120,105121,16877,105144,105161],{},"Platí obecně: ",[38,105077,105078],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,105081,105083],{"className":105082},[886],[888,105084,105085],{"xmlns":890},[892,105086,105087,105101],{},[895,105088,105089,105091,105093,105095,105097,105099],{},[898,105090,1701],{},[1693,105092,1695],{},[898,105094,207],{},[898,105096,1712],{},[1693,105098,1892],{},[898,105100,1895],{},[902,105102,43837],{"encoding":904},[883,105104,105106],{"className":105105},[886],[888,105107,105108],{"xmlns":890},[892,105109,105110,105118],{},[895,105111,105112,105114,105116],{},[898,105113,207],{},[1693,105115,1908],{},[1762,105117,1911],{},[902,105119,49853],{"encoding":904},") a lineární nabídku ",[883,105122,105124],{"className":105123},[886],[888,105125,105126],{"xmlns":890},[892,105127,105128,105142],{},[895,105129,105130,105132,105134,105136,105138,105140],{},[898,105131,1701],{},[1693,105133,1695],{},[898,105135,2000],{},[898,105137,1712],{},[1693,105139,1892],{},[898,105141,1771],{},[902,105143,47015],{"encoding":904},[883,105145,105147],{"className":105146},[886],[888,105148,105149],{"xmlns":890},[892,105150,105151,105159],{},[895,105152,105153,105155,105157],{},[898,105154,2000],{},[1693,105156,1922],{},[1762,105158,1911],{},[902,105160,47033],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,105163,105165],{"className":105164},[886],[888,105166,105167],{"xmlns":890,"display":34854},[892,105168,105169,105233],{},[895,105170,105171,105195,105197,105207,105209,105231],{},[2132,105172,105173,105183],{},[3284,105174,105175,105177],{},[898,105176,2663],{},[895,105178,105179,105181],{},[898,105180,6746],{},[898,105182,724],{},[3284,105184,105185,105187],{},[898,105186,2663],{},[895,105188,105189,105191,105193],{},[898,105190,6759],{},[898,105192,6560],{},[898,105194,6629],{},[1693,105196,1695],{},[2132,105198,105199,105201],{},[898,105200,2000],{},[895,105202,105203,105205],{},[1693,105204,1698],{},[898,105206,207],{},[1693,105208,1695],{},[2132,105210,105211,105221],{},[895,105212,105213,105215,105217,105219],{},[898,105214,6844],{"mathvariant":1704},[1915,105216,6847],{},[898,105218,3611],{},[898,105220,6844],{"mathvariant":1704},[895,105222,105223,105225,105227,105229],{},[898,105224,6844],{"mathvariant":1704},[1915,105226,6847],{},[898,105228,2738],{},[898,105230,6844],{"mathvariant":1704},[898,105232,1789],{"mathvariant":1704},[902,105234,105235],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1636,105237,105238,105243],{},[724,105239,105240,105242],{},[883,105241,8620],{}," Postup výpočtu rozkladu",[152,105244,105245,105280,105333,105412],{},[123,105246,105247,105248,105279],{},"Spočti rovnovážný bod ",[883,105249,105251],{"className":105250},[886],[888,105252,105253],{"xmlns":890},[892,105254,105255,105277],{},[895,105256,105257,105259,105261,105267,105269,105275],{},[898,105258,1691],{},[1693,105260,9392],{"stretchy":1708},[1717,105262,105263,105265],{},[898,105264,1712],{},[898,105266,1691],{},[1693,105268,1899],{"separator":1898},[1717,105270,105271,105273],{},[898,105272,1701],{},[898,105274,1691],{},[1693,105276,9407],{"stretchy":1708},[902,105278,48138],{"encoding":904}," bez daně.",[123,105281,105282,105283,1348,105308,3042],{},"Urči posunutou křivku (",[883,105284,105286],{"className":105285},[886],[888,105287,105288],{"xmlns":890},[892,105289,105290,105306],{},[895,105291,105292,105298,105300,105302,105304],{},[3284,105293,105294,105296],{},[898,105295,3611],{},[1762,105297,1764],{},[1693,105299,1695],{},[898,105301,3611],{},[1693,105303,1892],{},[898,105305,2663],{},[902,105307,49522],{"encoding":904},[883,105309,105311],{"className":105310},[886],[888,105312,105313],{"xmlns":890},[892,105314,105315,105331],{},[895,105316,105317,105323,105325,105327,105329],{},[3284,105318,105319,105321],{},[898,105320,2738],{},[1762,105322,2398],{},[1693,105324,1695],{},[898,105326,2738],{},[1693,105328,1698],{},[898,105330,2663],{},[902,105332,49553],{"encoding":904},[123,105334,105335,105336,10796,105355,8586,105374,10796,105393,3042],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,105337,105339],{"className":105338},[886],[888,105340,105341],{"xmlns":890},[892,105342,105343,105353],{},[895,105344,105345],{},[5688,105346,105347,105349,105351],{},[898,105348,1712],{},[1762,105350,1764],{},[898,105352,1691],{},[902,105354,54600],{"encoding":904},[883,105356,105358],{"className":105357},[886],[888,105359,105360],{"xmlns":890},[892,105361,105362,105372],{},[895,105363,105364],{},[5688,105365,105366,105368,105370],{},[898,105367,1712],{},[1762,105369,2398],{},[898,105371,1691],{},[902,105373,54662],{"encoding":904},[883,105375,105377],{"className":105376},[886],[888,105378,105379],{"xmlns":890},[892,105380,105381,105391],{},[895,105382,105383],{},[5688,105384,105385,105387,105389],{},[898,105386,1701],{},[1762,105388,1764],{},[898,105390,1691],{},[902,105392,54621],{"encoding":904},[883,105394,105396],{"className":105395},[886],[888,105397,105398],{"xmlns":890},[892,105399,105400,105410],{},[895,105401,105402],{},[5688,105403,105404,105406,105408],{},[898,105405,1701],{},[1762,105407,2398],{},[898,105409,1691],{},[902,105411,54682],{"encoding":904},[123,105413,105414,105415,4286,105436,105459,105460,1789],{},"Dopočítej ",[883,105416,105418],{"className":105417},[886],[888,105419,105420],{"xmlns":890},[892,105421,105422,105434],{},[895,105423,105424],{},[3284,105425,105426,105428],{},[898,105427,2663],{},[895,105429,105430,105432],{},[898,105431,6746],{},[898,105433,724],{},[902,105435,49451],{"encoding":904},[883,105437,105439],{"className":105438},[886],[888,105440,105441],{"xmlns":890},[892,105442,105443,105457],{},[895,105444,105445],{},[3284,105446,105447,105449],{},[898,105448,2663],{},[895,105450,105451,105453,105455],{},[898,105452,6759],{},[898,105454,6560],{},[898,105456,6629],{},[902,105458,49475],{"encoding":904}," z definice, vždy ověř ",[883,105461,105463],{"className":105462},[886],[888,105464,105465],{"xmlns":890},[892,105466,105467,105497],{},[895,105468,105469,105479,105481,105493,105495],{},[3284,105470,105471,105473],{},[898,105472,2663],{},[895,105474,105475,105477],{},[898,105476,6746],{},[898,105478,724],{},[1693,105480,1892],{},[3284,105482,105483,105485],{},[898,105484,2663],{},[895,105486,105487,105489,105491],{},[898,105488,6759],{},[898,105490,6560],{},[898,105492,6629],{},[1693,105494,1695],{},[898,105496,2663],{},[902,105498,105499],{"encoding":904},"T_{sp} + T_{vyr} = T",[1636,105501,105502],{},[724,105503,105504,105506,105507,105510,105511,4286,105524,105537],{},[883,105505,8654],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,105508,105509],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,105512,105514],{"className":105513},[886],[888,105515,105516],{"xmlns":890},[892,105517,105518,105522],{},[895,105519,105520],{},[898,105521,2738],{},[902,105523,2738],{"encoding":904},[883,105525,105527],{"className":105526},[886],[888,105528,105529],{"xmlns":890},[892,105530,105531,105535],{},[895,105532,105533],{},[898,105534,3611],{},[902,105536,3611],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[1852,105539],{},[115,105541,105543],{"id":105542},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,105545,105546],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,105548,105549],{},[9465,105550],{"alt":105551,"className":105552,"src":105553},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,9469],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,105555,105556,105568],{},[19,105557,105558],{},[22,105559,105560,105562,105565],{},[25,105561,61053],{},[25,105563,105564],{},"(a) daň výrobci",[25,105566,105567],{},"(b) daň spotřebiteli",[30,105569,105570,105625,105692,105752],{},[22,105571,105572,105575,105600],{},[35,105573,105574],{},"Rovnovážné množství",[35,105576,105577],{},[883,105578,105580],{"className":105579},[886],[888,105581,105582],{"xmlns":890},[892,105583,105584,105598],{},[895,105585,105586,105594,105596],{},[5688,105587,105588,105590,105592],{},[898,105589,1712],{},[1762,105591,1764],{},[898,105593,1691],{},[1693,105595,1695],{},[1762,105597,1764],{},[902,105599,103419],{"encoding":904},[35,105601,105602],{},[883,105603,105605],{"className":105604},[886],[888,105606,105607],{"xmlns":890},[892,105608,105609,105623],{},[895,105610,105611,105619,105621],{},[5688,105612,105613,105615,105617],{},[898,105614,1712],{},[1762,105616,2398],{},[898,105618,1691],{},[1693,105620,1695],{},[1762,105622,1764],{},[902,105624,104451],{"encoding":904},[22,105626,105627,105630,105655],{},[35,105628,105629],{},"Cena placená spotřebitelem",[35,105631,105632],{},[883,105633,105635],{"className":105634},[886],[888,105636,105637],{"xmlns":890},[892,105638,105639,105653],{},[895,105640,105641,105649,105651],{},[5688,105642,105643,105645,105647],{},[898,105644,1701],{},[1762,105646,1764],{},[898,105648,1691],{},[1693,105650,1695],{},[1762,105652,9763],{},[902,105654,103514],{"encoding":904},[35,105656,105657],{},[883,105658,105660],{"className":105659},[886],[888,105661,105662],{"xmlns":890},[892,105663,105664,105690],{},[895,105665,105666,105674,105676,105678,105680,105682,105684,105686,105688],{},[5688,105667,105668,105670,105672],{},[898,105669,1701],{},[1762,105671,2398],{},[898,105673,1691],{},[1693,105675,1892],{},[898,105677,2663],{},[1693,105679,1695],{},[1762,105681,9262],{},[1693,105683,1892],{},[1762,105685,9154],{},[1693,105687,1695],{},[1762,105689,9763],{},[902,105691,104550],{"encoding":904},[22,105693,105694,105697,105727],{},[35,105695,105696],{},"Cena přijímaná výrobcem",[35,105698,105699],{},[883,105700,105702],{"className":105701},[886],[888,105703,105704],{"xmlns":890},[892,105705,105706,105724],{},[895,105707,105708,105716,105718,105720,105722],{},[5688,105709,105710,105712,105714],{},[898,105711,1701],{},[1762,105713,1764],{},[898,105715,1691],{},[1693,105717,1698],{},[898,105719,2663],{},[1693,105721,1695],{},[1762,105723,9262],{},[902,105725,105726],{"encoding":904},"P_1^E - T = 4",[35,105728,105729],{},[883,105730,105732],{"className":105731},[886],[888,105733,105734],{"xmlns":890},[892,105735,105736,105750],{},[895,105737,105738,105746,105748],{},[5688,105739,105740,105742,105744],{},[898,105741,1701],{},[1762,105743,2398],{},[898,105745,1691],{},[1693,105747,1695],{},[1762,105749,9262],{},[902,105751,104575],{"encoding":904},[22,105753,105754,105757,105811],{},[35,105755,105756],{},"Rozklad břemene",[35,105758,105759,1343,105784],{},[883,105760,105762],{"className":105761},[886],[888,105763,105764],{"xmlns":890},[892,105765,105766,105782],{},[895,105767,105768,105778,105780],{},[3284,105769,105770,105772],{},[898,105771,2663],{},[895,105773,105774,105776],{},[898,105775,6746],{},[898,105777,724],{},[1693,105779,1695],{},[1762,105781,2398],{},[902,105783,49744],{"encoding":904},[883,105785,105787],{"className":105786},[886],[888,105788,105789],{"xmlns":890},[892,105790,105791,105809],{},[895,105792,105793,105805,105807],{},[3284,105794,105795,105797],{},[898,105796,2663],{},[895,105798,105799,105801,105803],{},[898,105800,6759],{},[898,105802,6560],{},[898,105804,6629],{},[1693,105806,1695],{},[1762,105808,9262],{},[902,105810,49773],{"encoding":904},[35,105812,105813,1343,105838],{},[883,105814,105816],{"className":105815},[886],[888,105817,105818],{"xmlns":890},[892,105819,105820,105836],{},[895,105821,105822,105832,105834],{},[3284,105823,105824,105826],{},[898,105825,2663],{},[895,105827,105828,105830],{},[898,105829,6746],{},[898,105831,724],{},[1693,105833,1695],{},[1762,105835,2398],{},[902,105837,49744],{"encoding":904},[883,105839,105841],{"className":105840},[886],[888,105842,105843],{"xmlns":890},[892,105844,105845,105863],{},[895,105846,105847,105859,105861],{},[3284,105848,105849,105851],{},[898,105850,2663],{},[895,105852,105853,105855,105857],{},[898,105854,6759],{},[898,105856,6560],{},[898,105858,6629],{},[1693,105860,1695],{},[1762,105862,9262],{},[902,105864,49773],{"encoding":904},[724,105866,105867],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,105869,105871],{"className":105870},[886],[888,105872,105873],{"xmlns":890,"display":34854},[892,105874,105875,105923],{},[895,105876,105877,105885,105887,105895,105897,105899,105907,105909,105911,105913,105921],{},[5688,105878,105879,105881,105883],{},[898,105880,1712],{},[1762,105882,1764],{},[898,105884,1691],{},[1693,105886,1695],{},[5688,105888,105889,105891,105893],{},[898,105890,1712],{},[1762,105892,2398],{},[898,105894,1691],{},[1693,105896,1899],{"separator":1898},[1901,105898],{"width":1903},[5688,105900,105901,105903,105905],{},[898,105902,1701],{},[1762,105904,1764],{},[898,105906,1691],{},[1693,105908,1698],{},[898,105910,2663],{},[1693,105912,1695],{},[5688,105914,105915,105917,105919],{},[898,105916,1701],{},[1762,105918,2398],{},[898,105920,1691],{},[898,105922,1789],{"mathvariant":1704},[902,105924,105925],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1636,105927,105928,105947,106101],{},[724,105929,105930,105932,105933,105946],{},[883,105931,8620],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,105934,105936],{"className":105935},[886],[888,105937,105938],{"xmlns":890},[892,105939,105940,105944],{},[895,105941,105942],{},[898,105943,2663],{},[902,105945,2663],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,105948,105949,105981,106017,106054],{},[123,105950,105951,105952,1899],{},"rovnovážná množství obou režimů, ",[883,105953,105955],{"className":105954},[886],[888,105956,105957],{"xmlns":890},[892,105958,105959,105979],{},[895,105960,105961,105969,105971],{},[5688,105962,105963,105965,105967],{},[898,105964,1712],{},[1762,105966,1764],{},[898,105968,1691],{},[1693,105970,1695],{},[5688,105972,105973,105975,105977],{},[898,105974,1712],{},[1762,105976,2398],{},[898,105978,1691],{},[902,105980,49676],{"encoding":904},[123,105982,105983,105984,1899],{},"čistá cena přijímaná výrobcem, ",[883,105985,105987],{"className":105986},[886],[888,105988,105989],{"xmlns":890},[892,105990,105991,106015],{},[895,105992,105993,106001,106003,106005,106007],{},[5688,105994,105995,105997,105999],{},[898,105996,1701],{},[1762,105998,1764],{},[898,106000,1691],{},[1693,106002,1698],{},[898,106004,2663],{},[1693,106006,1695],{},[5688,106008,106009,106011,106013],{},[898,106010,1701],{},[1762,106012,2398],{},[898,106014,1691],{},[902,106016,49710],{"encoding":904},[123,106018,106019,106020,1899],{},"celková cena placená spotřebitelem, ",[883,106021,106023],{"className":106022},[886],[888,106024,106025],{"xmlns":890},[892,106026,106027,106051],{},[895,106028,106029,106037,106039,106047,106049],{},[5688,106030,106031,106033,106035],{},[898,106032,1701],{},[1762,106034,1764],{},[898,106036,1691],{},[1693,106038,1695],{},[5688,106040,106041,106043,106045],{},[898,106042,1701],{},[1762,106044,2398],{},[898,106046,1691],{},[1693,106048,1892],{},[898,106050,2663],{},[902,106052,106053],{"encoding":904},"P_1^E = P_2^E + T",[123,106055,106056,106057,4286,106078,1789],{},"rozklad daňového břemene ",[883,106058,106060],{"className":106059},[886],[888,106061,106062],{"xmlns":890},[892,106063,106064,106076],{},[895,106065,106066],{},[3284,106067,106068,106070],{},[898,106069,2663],{},[895,106071,106072,106074],{},[898,106073,6746],{},[898,106075,724],{},[902,106077,49451],{"encoding":904},[883,106079,106081],{"className":106080},[886],[888,106082,106083],{"xmlns":890},[892,106084,106085,106099],{},[895,106086,106087],{},[3284,106088,106089,106091],{},[898,106090,2663],{},[895,106092,106093,106095,106097],{},[898,106094,6759],{},[898,106096,6560],{},[898,106098,6629],{},[902,106100,49475],{"encoding":904},[724,106102,106103,106104,1789],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,106105,41980],{},[724,106107,106108,106109,4286,106122,3042],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,106110,106112],{"className":106111},[886],[888,106113,106114],{"xmlns":890},[892,106115,106116,106120],{},[895,106117,106118],{},[898,106119,2738],{},[902,106121,2738],{"encoding":904},[883,106123,106125],{"className":106124},[886],[888,106126,106127],{"xmlns":890},[892,106128,106129,106133],{},[895,106130,106131],{},[898,106132,3611],{},[902,106134,3611],{"encoding":904},[1852,106136],{},[115,106138,106140],{"id":106139},"úlohy","Úlohy",[724,106142,106143,106144,10048],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,106145,23060],{"className":106146,"dataFsResolvedFilePath":800,"href":801},[210],[120,106148,106149,106179,106210],{},[123,106150,106151,106154,106155,106178],{},[38,106152,106153],{},"Úloha 2.4"," — Poptávka ",[883,106156,106158],{"className":106157},[886],[888,106159,106160],{"xmlns":890},[892,106161,106162,106176],{},[895,106163,106164,106166,106168,106170,106172,106174],{},[898,106165,1701],{},[1693,106167,1695],{},[1762,106169,10402],{},[1693,106171,1698],{},[1762,106173,2398],{},[898,106175,1712],{},[902,106177,103131],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,106180,106181,106184,106185,106209],{},[38,106182,106183],{},"Úloha 2.9"," — Nabídka ",[883,106186,106188],{"className":106187},[886],[888,106189,106190],{"xmlns":890},[892,106191,106192,106206],{},[895,106193,106194,106196,106198,106200,106202,106204],{},[898,106195,1701],{},[1693,106197,1695],{},[1762,106199,11877],{},[898,106201,1712],{},[1693,106203,1892],{},[1762,106205,43026],{},[902,106207,106208],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,106211,106212,106215,106216,4286,106242,106266,106267,106284],{},[38,106213,106214],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,106217,106219],{"className":106218},[886],[888,106220,106221],{"xmlns":890},[892,106222,106223,106239],{},[895,106224,106225,106227,106229,106231,106233,106235,106237],{},[898,106226,1701],{},[1693,106228,1695],{},[1693,106230,1698],{},[1762,106232,9262],{},[898,106234,1712],{},[1693,106236,1892],{},[1762,106238,53467],{},[902,106240,106241],{"encoding":904},"P = -4Q + 80",[883,106243,106245],{"className":106244},[886],[888,106246,106247],{"xmlns":890},[892,106248,106249,106263],{},[895,106250,106251,106253,106255,106257,106259,106261],{},[898,106252,1701],{},[1693,106254,1695],{},[1762,106256,8357],{},[898,106258,1712],{},[1693,106260,1892],{},[1762,106262,9763],{},[902,106264,106265],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,106268,106270],{"className":106269},[886],[888,106271,106272],{"xmlns":890},[892,106273,106274,106282],{},[895,106275,106276,106278,106280],{},[898,106277,2663],{},[1693,106279,1695],{},[1762,106281,31000],{},[902,106283,54579],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,106286,106287,106288,106290,106291,106293],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,106289,51992],{}," (posun poptávky při zdanění kupujícího) a ",[38,106292,52026],{}," (posun nabídky při zdanění výrobce).",[1852,106295],{},[115,106297,22545],{"id":22544},[120,106299,106300,106319,106377,106434,106517,106563,106606,106651,106717],{},[123,106301,106302,1863,106305,106318],{},[38,106303,106304],{},"Jednotková daň",[883,106306,106308],{"className":106307},[886],[888,106309,106310],{"xmlns":890},[892,106311,106312,106316],{},[895,106313,106314],{},[898,106315,2663],{},[902,106317,2663],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,106320,106321,106323,106324,106362,106363,106376],{},[38,106322,102713],{}," — posun nabídky ",[883,106325,106327],{"className":106326},[886],[888,106328,106329],{"xmlns":890},[892,106330,106331,106359],{},[895,106332,106333,106339,106341,106343,106345,106347,106349,106351,106353,106355,106357],{},[3284,106334,106335,106337],{},[898,106336,3611],{},[1762,106338,1764],{},[1693,106340,1709],{"stretchy":1708},[898,106342,1712],{},[1693,106344,1731],{"stretchy":1708},[1693,106346,1695],{},[898,106348,3611],{},[1693,106350,1709],{"stretchy":1708},[898,106352,1712],{},[1693,106354,1731],{"stretchy":1708},[1693,106356,1892],{},[898,106358,2663],{},[902,106360,106361],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,106364,106366],{"className":106365},[886],[888,106367,106368],{"xmlns":890},[892,106369,106370,106374],{},[895,106371,106372],{},[898,106373,2663],{},[902,106375,2663],{"encoding":904}," svisle nahoru)",[123,106378,106379,106381,106382,106362,106420,106433],{},[38,106380,103786],{}," — posun poptávky ",[883,106383,106385],{"className":106384},[886],[888,106386,106387],{"xmlns":890},[892,106388,106389,106417],{},[895,106390,106391,106397,106399,106401,106403,106405,106407,106409,106411,106413,106415],{},[3284,106392,106393,106395],{},[898,106394,2738],{},[1762,106396,2398],{},[1693,106398,1709],{"stretchy":1708},[898,106400,1712],{},[1693,106402,1731],{"stretchy":1708},[1693,106404,1695],{},[898,106406,2738],{},[1693,106408,1709],{"stretchy":1708},[898,106410,1712],{},[1693,106412,1731],{"stretchy":1708},[1693,106414,1698],{},[898,106416,2663],{},[902,106418,106419],{"encoding":904},"D_2(Q) = D(Q) - T",[883,106421,106423],{"className":106422},[886],[888,106424,106425],{"xmlns":890},[892,106426,106427,106431],{},[895,106428,106429],{},[898,106430,2663],{},[902,106432,2663],{"encoding":904}," svisle dolů)",[123,106435,106436,13877,106439,48585,106478],{},[38,106437,106438],{},"Rovnovážný bod s daní",[883,106440,106442],{"className":106441},[886],[888,106443,106444],{"xmlns":890},[892,106445,106446,106476],{},[895,106447,106448,106454,106456,106464,106466,106474],{},[3284,106449,106450,106452],{},[898,106451,1691],{},[1762,106453,1764],{},[1693,106455,9392],{"stretchy":1708},[5688,106457,106458,106460,106462],{},[898,106459,1712],{},[1762,106461,1764],{},[898,106463,1691],{},[1693,106465,1899],{"separator":1898},[5688,106467,106468,106470,106472],{},[898,106469,1701],{},[1762,106471,1764],{},[898,106473,1691],{},[1693,106475,9407],{"stretchy":1708},[902,106477,102881],{"encoding":904},[883,106479,106481],{"className":106480},[886],[888,106482,106483],{"xmlns":890},[892,106484,106485,106515],{},[895,106486,106487,106493,106495,106503,106505,106513],{},[3284,106488,106489,106491],{},[898,106490,1691],{},[1762,106492,2398],{},[1693,106494,9392],{"stretchy":1708},[5688,106496,106497,106499,106501],{},[898,106498,1712],{},[1762,106500,2398],{},[898,106502,1691],{},[1693,106504,1899],{"separator":1898},[5688,106506,106507,106509,106511],{},[898,106508,1701],{},[1762,106510,2398],{},[898,106512,1691],{},[1693,106514,9407],{"stretchy":1708},[902,106516,103955],{"encoding":904},[123,106518,106519,16877,106521,106523,106524],{},[38,106520,49428],{},[614,106522,104735],{},") — rozklad ",[883,106525,106527],{"className":106526},[886],[888,106528,106529],{"xmlns":890},[892,106530,106531,106561],{},[895,106532,106533,106535,106537,106547,106549],{},[898,106534,2663],{},[1693,106536,1695],{},[3284,106538,106539,106541],{},[898,106540,2663],{},[895,106542,106543,106545],{},[898,106544,6746],{},[898,106546,724],{},[1693,106548,1892],{},[3284,106550,106551,106553],{},[898,106552,2663],{},[895,106554,106555,106557,106559],{},[898,106556,6759],{},[898,106558,6560],{},[898,106560,6629],{},[902,106562,49612],{"encoding":904},[123,106564,106565,106588,106589,1731],{},[38,106566,106567],{},[883,106568,106570],{"className":106569},[886],[888,106571,106572],{"xmlns":890},[892,106573,106574,106586],{},[895,106575,106576],{},[3284,106577,106578,106580],{},[898,106579,2663],{},[895,106581,106582,106584],{},[898,106583,6746],{},[898,106585,724],{},[902,106587,49451],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,106590,106592],{"className":106591},[886],[888,106593,106594],{"xmlns":890},[892,106595,106596,106604],{},[895,106597,106598],{},[1717,106599,106600,106602],{},[898,106601,1701],{},[898,106603,1691],{},[902,106605,48237],{"encoding":904},[123,106607,106608,106633,106634,1731],{},[38,106609,106610],{},[883,106611,106613],{"className":106612},[886],[888,106614,106615],{"xmlns":890},[892,106616,106617,106631],{},[895,106618,106619],{},[3284,106620,106621,106623],{},[898,106622,2663],{},[895,106624,106625,106627,106629],{},[898,106626,6759],{},[898,106628,6560],{},[898,106630,6629],{},[902,106632,49475],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,106635,106637],{"className":106636},[886],[888,106638,106639],{"xmlns":890},[892,106640,106641,106649],{},[895,106642,106643],{},[1717,106644,106645,106647],{},[898,106646,1701],{},[898,106648,1691],{},[902,106650,48237],{"encoding":904},[123,106652,106653,13877,106655,1343,106684],{},[38,106654,57234],{},[883,106656,106658],{"className":106657},[886],[888,106659,106660],{"xmlns":890},[892,106661,106662,106682],{},[895,106663,106664,106672,106674],{},[5688,106665,106666,106668,106670],{},[898,106667,1712],{},[1762,106669,1764],{},[898,106671,1691],{},[1693,106673,1695],{},[5688,106675,106676,106678,106680],{},[898,106677,1712],{},[1762,106679,2398],{},[898,106681,1691],{},[902,106683,49676],{"encoding":904},[883,106685,106687],{"className":106686},[886],[888,106688,106689],{"xmlns":890},[892,106690,106691,106715],{},[895,106692,106693,106701,106703,106705,106707],{},[5688,106694,106695,106697,106699],{},[898,106696,1701],{},[1762,106698,1764],{},[898,106700,1691],{},[1693,106702,1698],{},[898,106704,2663],{},[1693,106706,1695],{},[5688,106708,106709,106711,106713],{},[898,106710,1701],{},[1762,106712,2398],{},[898,106714,1691],{},[902,106716,49710],{"encoding":904},[123,106718,106719,106722],{},[38,106720,106721],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[1852,106724],{},[115,106726,8685],{"id":8684},[120,106728,106729,106737,106755,106762],{},[123,106730,106731,1863,106734],{},[38,106732,106733],{},"Kontext (hub):",[207,106735,802],{"className":106736,"dataFsResolvedFilePath":800,"href":801},[210],[123,106738,106739,1863,106741,106744,106745,25461,106747,106750,106751,106754],{},[38,106740,57483],{},[207,106742,820],{"className":106743,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,106746,61790],{},[207,106748,8726],{"className":106749,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,106752,8759],{"className":106753,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,106756,106757,1863,106759],{},[38,106758,57518],{},[207,106760,57522],{"className":106761,"dataFsResolvedFilePath":745,"href":746},[210],[123,106763,106764,1863,106766],{},[38,106765,8692],{},[207,106767,1653],{"className":106768,"dataFsResolvedFilePath":1651,"href":1652},[210],{"title":641,"searchDepth":642,"depth":642,"links":106770},[106771,106772,106775,106778,106782,106783,106784,106785],{"id":102618,"depth":642,"text":102619},{"id":102712,"depth":642,"text":102713,"children":106773},[106774],{"id":103103,"depth":649,"text":52067},{"id":103785,"depth":642,"text":103786,"children":106776},[106777],{"id":104261,"depth":649,"text":52147},{"id":104728,"depth":642,"text":49428,"children":106779},[106780,106781],{"id":9350,"depth":649,"text":9351},{"id":105071,"depth":649,"text":105072},{"id":105542,"depth":642,"text":105543},{"id":106139,"depth":642,"text":106140},{"id":22544,"depth":642,"text":22545},{"id":8684,"depth":642,"text":8685},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":6493,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,57583,106792,106793,106794,23060],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[106797],{"slug":1128,"path":1652,"title":681,"snippet":106798},"… nní rovnováha trhu zboží a peněz, fiskální\u002Fmonetární politika ## Reference a přehledy - \u003C\u003Cimek-vzorce-prehled>> — všechny klíčové vzorce kurzu v definičním tvaru, se zdrojem a intuicí. Referenční list …",[106800,106803,106804,106807],{"slug":106801,"title":106802,"path":1109,"sharedTags":649},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*",{"slug":23093,"title":18842,"path":944,"sharedTags":642},{"slug":106805,"title":106806,"path":746,"sharedTags":642},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie",{"slug":23046,"title":936,"path":935,"sharedTags":642},1777154981678]